HANDBOOK OF MULTIPHASE FLOW
ASSURANCE
HANDBOOK OF
MULTIPHASE
FLOW
ASSURANCE
Taras Y. Makogon
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Dedication
To my teachers Prof. Yuri F. Makogon, Yakov F. Lerner, Prof. E. Dendy Sloan, and Prof.
M. Sami Selim.
v
Preface
This handbook is a compilation of reference materials and experiences related to
flow assurance collected over the years. This
handbook may help the production operator
identify and solve issues faster and also help
a project development engineer design the
most critical flow assurance issues out of the
system more cost-effectively. The intent of
this book is to deliver safe, reliable and economic design and operation of multiphase
production systems with flow assurance
threats. Flow assurance is used in onshore,
offshore and subsurface flow of petroleum
fluids. This diversity of application of flow
assurance control methods motivated the development of this handbook.
xi
C H A P T E R
1
Introduction
O U T L I N E
Threats to product value or process safety
(asset integrity)
24
Multiphase production problems: Blockages
and restrictions
2
Savings from using flow assurance
3
Examples of flow assurance problems
5
How flow assurance and production
chemistry work together
10
When is flow assurance applied
14
Knowledge required in flow assurance
15
Why flow assurance failures happen
15
Flow assurance background
17
Flow assurance requirements
Basis of design
Units for fluid characterization
21
21
22
Hardware cost
24
Cost of subsea hardware related to flow
assurance
24
Introduction to flow assurance risk
analysis
22
Threats to flow are normally attributed to
flow assurance
24
Monitoring and data mining
28
Flow assurance in operations
Onshore production
Offshore production
Deepwater production
28
28
28
29
Systematic approach to solving flow
assurance problems
29
Process safety
30
System of measures for flow assurance
30
Outlook for flow assurance
30
References
31
Flow assurance aims to make sure oil and gas keep flowing. To achieve that goal, flow
assurance relies on the analysis of multiphase flow and on the selection and use of production chemicals. Flow assurance engineers commonly analyze the flow of oil and gas in wells,
production flowlines, process facilities and export pipelines. Complex networks of gathering
lines feeding into trunk flowlines exist in onshore and offshore fields, and the analysis to optimize flow routing through such networks is equally complex.
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00001-4
1
© 2019 Elsevier Inc. All rights reserved.
2
1. Introduction
Definitions of flow assurance are numerous, including this one: Flow Assurance is the
analysis of thermal, hydraulic and fluid-related threats to flow and product quality and their
mitigation using equipment, chemicals and procedure.
Multiphase production problems: Blockages and restrictions
Oil and gas are currently produced through wells and pipelines. The lack of flow in wells
and pipelines may be due to low reservoir pressure or productivity, due to complete blockages or due to partial restrictions.
Flow restrictions may happen in a reservoir, in a well production tubing or a tree, in a
jumper between a well and a flowline, in a flowline, in a riser or in an export pipeline. In
some cases, restrictions may happen in several locations simultaneously. The largest number
I have seen is five blockages in the same production flowline at the same time. Restrictions
may also occur in water and gas injection systems as in wells, flowlines or reservoirs.
Restrictions may be hydraulic, such as liquid accumulation also known as a holdup in
flowlines and risers, liquid loading in wells, or mechanical such as a partly closed valve or
a scraper. Restrictions or blockages may also be solid, including organic (e.g., paraffin wax),
inorganic (scale) or particulate (sand). The hydraulic, mechanical or solid restrictions may be
stationary such as the liquid holdup or moving such as the slugging. A flow assurance practitioner should be able to recognize the signs of and potential for any type of restriction and
either economically design it out of a new system or mitigate it in an existing system.
In some cases, restrictions may lead to other restrictions. There is an early 2000s example
from West Africa offshore production where a wax deposit in a flowline got scraped by a
formed hydrate plug into a solid paraffin wax blockage. Similarly, combined hydrate-paraffin
restrictions have also formed in the North Sea in the early 1990s and asphaltene-hydrate in
the Gulf of Mexico in the 2010s. Paraffin-asphaltene-sand restrictions have been common in
Siberian pipelines through the decades.
Modeling of multiphase flow can be done to find optimal conditions for a stable production of gas and hydrocarbon liquids with water. When the gas flow rate is not high enough
to sweep the liquid hydrocarbons and liquid water from a well or a pipeline, these liquids
accumulate in low spots because of gravity.
The liquids can accumulate either downhole in a vertical well or at a heel or a toe, whichever is lower, in a horizontal well which is known as liquid loading. Both deepwater and
shale horizontal wells are susceptible to liquid loading.
Severe slugging is one of the issues in multiphase flow also related to gravity. Liquids can
accumulate at a subsea riser base and then get periodically produced to a topsides separator
after a sufficient gas pressure has built up behind the accumulated liquids as a large sudden
gush of liquid preceded by a period of no or limited flow, which is known as severe slugging.
Wells keep producing during severe slugging at a steady rate, but backpressure on wells may
change noticeably between slug accumulation and displacement. Severe slugs keep repeating, and slug size and momentum are substantial as to cause vibration at pipe bends in flow
geometry, overfill the process vessel or both.
Liquids also can accumulate in the low spots of a near-horizontal pipeline and get periodically displaced by a steady flow of gas, which leads to terrain slugging. Terrain slugs keep
repeating and are usually smaller in size and don't overfill the process vessel but may cause
Savings from using flow assurance
3
vibration at pipe bends. Hydrodynamic slugging occurs as liquids holdup is displaced by an
increasing flow of gas from a flowline in form of a liquid surge. If the surge volume is significant, the hydrodynamic slugs can be as detrimental as severe slugs. Hydrodynamic slugs
occur once per a change in production rate and don't repeat.
In all three cases of liquid loading, severe slugging and terrain slugging gravity plays the
key role in overcoming the energy emerging from the expanding gas or a single phase or supercritical fluid (also known as the dense phase) or an aquifer which is less than sufficient to
lift the liquids to the separator or a slugcatcher.
Analysis of multiphase fluid flow is in part based on information from reservoir modeling
prediction of flow rates and on thermodynamic PVT characterization of produced fluids.
Software which tracks and balances masses and velocities of produced fluids is available to
help predict and analyze the flow velocities and the quantities of accumulation (also known as
holdups) of liquid and other phases in the production system. An accurate prediction allows
the design engineer to select proper sizes for the well production tubing and for gathering
flow lines, and also to identify which technologies would be necessary and most economically suited to produce gas and oil from a reservoir.
Savings from using flow assurance
Flow, which may be single phase (natural gas, oil, water, CO2) or multiphase (two or more
single phases) is the key metric of the main product of petroleum companies. Those companies
which have more barrels of flowing product per employee generally do well, and vice versa.
Flow assurance is becoming a critical path discipline when other disciplines such as pipeline engineering, subsea layout, artificial lift equipment, and, in some projects, reservoir
engineering, wait for flow assurance to compare and validate the viability of an overall architecture for a concept of field development before proceeding with the design. The accuracy
in flow assurance makes a project more, less or not at all profitable. This handbook helps
organize and streamline the work in flow assurance, in order to make it more accurate.
The use of flow assurance technology saved billions of dollars for oil companies. There
are several examples of how multiphase flow tools have resulted in savings for Statoil, Shell,
BP, ENI:
• Multiphase technology & OLGA—Norske Shell—Troll—30 Billion NOK
The flow assurance savings for the Norske Shell—Troll field from multiphase technology and
the use of an early version of the OLGA software were 30B NOK which is billions of dollars.
“Direct electric heating has saved us billions of kroner on the Norwegian shelf,” said Atle
Harald Børnes, who is a specialist at Statoil's Technology and New Energy Business Area.
This system has been installed during the laying of pipelines linked to the Åsgard, Huldra,
Kristin, Urd, Tyrihans, Alve and Morvin fields. A version of this heating system has also been
prepared as a contingency measure for installation on the pipeline leading from the Ormen
Lange field to Aukra.
The heating system was also installed at the BP-operated Skarv field, which has been put
on stream after 2011.
The Italian company ENI has also opted to utilize the same system for its Goliat field development offshore Finnmark (Nilsson et al., 2010).
• Hydrates and electrical heating—Statoil, BP—N.Sea—Billions of NOK
4
1. Introduction
Construction initiative of the multiphase flow loop at Tiller near Trondheim, Norway was
pioneered by Esso Norge looking to evaluate the stability of multiphase oil and gas production
from offshore reservoirs, and supported by this and other companies. The cost to construct this
flow loop was over 26 million in 1980 US dollars. The choice of location was economically justified because the Norwegian sector of the North Sea showed promising acreage and because the
Norwegian law allowed some research cost to be deducted from taxable revenue. Numerous sets
of data were collected from this test facility which, to this day, are used to validate multiphase
software (Caspersen et al., 2011).
The Tiller multiphase flow loop shown in Fig. 1.1 is perhaps the one most important facility used for development of data sets for validation of several multiphase flow models.
Fig. 1.1 Tiller flow loop and tower for multiphase flow research.
Examples of flow assurance problems
5
Flow assurance technology development also has its roots in PROCAP 1000, a technology
program executed by Petrobras from 1986 to 1991, comprised 109 multidisciplinary projects.
The cost of the program was 68 million USD. The projects developed under PROCAP 1000
gave rise to a significant part of the 251 patents obtained by Petrobras between 1987 and 1992.
It also allowed access to subsea oil fields in water deeper than 300 m which could not be accessed through diving, and the development of deepwater assets to a water depth of 1000 m,
which led to capital investment in fields such as Marlim and Albacora and multi-billion profits from Petrobras' deepwater projects (Morais, 2013).
Examples of flow assurance problems
Solids such as hydrates shown in Fig. 1.2–1.4, wax or scale can form blockages and restrict
production. These solids can also affect mechanical integrity of a production system in multiple ways, such as erosion, rupture or collapse of pipelines. For example, hydrates can move
as projectiles. In a few instances offshore, a partly dissociated hydrate plug got launched from
a platform scraper receiver by gas pressurized behind the hydrate.
Ice blockages also can present a problem. In an onshore operation in Alaska, an ice blockage formed in the smaller of the two flowlines operating in parallel due to differences in flow
distribution. Freezing caused a 24-in. long rupture as shown in Fig. 1.5 at the bottom of a
three-phase common line carrying a mixture of crude oil, produced water, and natural gas.
Corrosion caused a similar event in 2007 with imagery available at Alaska (2008). A 6-in.
long crack (about 1/8 in. wide at the center) formed in the flow line due to external corrosion.
Hydrates can also crush or collapse steel tubing such as a well production tubing as shown
in Fig. 1.6 in locations where water and gas accumulate at hydrate conditions in the same way
ice can crack an engine block if water is used as a coolant instead of an antifreeze.
A paraffin wax deposit can form when heavy hydrocarbon molecules with straight
chains of carbon atoms, also known as normal paraffins, precipitate on cold surfaces and
Fig. 1.2 Hydrate slush in a flowline after hydrate blockage was dissociated by depressurization in
an onshore Teapot Dome oil field.
6
1. Introduction
Fig. 1.3 Hydrate slush accumulated and compacted in service platform scraper receiver during
flowline depressurization offshore Brazil, ca 1992.
Fig. 1.4 Hydrate extracted from service platform scraper receiver after subsea line depressurization.
The compacted hydrate remained solid and did not break upon falling from the scraper receiver.
accumulate, which restricts normal production. In some cases, condensates produced with
free gas from deposits may contain heavier hydrocarbon molecules so wax can deposit from
condensate during gas production as well as during oil production. In subsea practice, one
solid may lead to another.
In the analysis of wax deposition, one should distinguish such fluid characteristics as
wax appearance temperature (WAT) when the first visible or detectable solid wax crystal
precipitate, and wax dissolution temperature (WDT) when the precipitated wax crystals
completely redissolve in the volume of oil from which they crystallized. There is also another term which is important for wax management design: the “wax deposit melting
Examples of flow assurance problems
Fig. 1.5 Thermal image of Alaska hydrocarbon loss of containment caused by ice blockage
(Alaska, 2010).
Fig. 1.6 Well tubing collapsed by hydrate formation in a shut-in well annulus between tubing and
casing. Onshore Siberia, 1965. T = 8°C, P collapse >800 atm, Tubing wall thickness 6 mm, inside
diameter 63 mm. Photo by Yuri F. Makogon.
7
8
1. Introduction
t­emperature” (WDMT). The WDMT occurs at a temperature when a wax deposit accumulated over time in a field flowline melts without added oil or solvent. WDT is typically
10–20 °C higher than WAT, whereas WDMT can be 30–40 °C higher than WAT, depending
on how long the wax had to age in the field flowline and how much of the heavy fractions
it had concentrated.
Crystals of normal paraffin wax, as well as many other crystals, can rotate the plane of
light linear polarization and shine. This phenomenon is used in cross-polarized microscopy (CPM) to determine WAT. Networks of waxy crystals called gels, which also shine
in a cross-polarized microscope, are therefore composed of wax crystals, not of amorphous non-crystalline material. The term gel is used in relation to wax to signify that the
whole bulk of oil converts to a non-flowing material when its temperature drops below
pour point and a waxy gel is formed. However, the waxy gel material is not uniform and
contains both solid wax and liquid oil trapped between solids. One should recognize
when discussing incipient, or initial, wax deposition on a pipe wall that it is wax crystals
made up of concentrated normal paraffins or isomerized saturated alkanes that deposit,
not a gel which has the same composition as base oil.
A combined hydrate and wax blockage formed in the North Sea in the past in the Staffa
field led to costly remediation by depressurization to melt the hydrate. After the first blockage got removed, the second blockage formed, which led to an abandonment of the subsea
flowline.
In another case offshore West Africa, an incompletely dissociated hydrate plug started to
move in a pipeline and acted as a scraper, compacting the existing paraffin wax deposit into
a solid blockage, which could no longer be melted simply by depressurization, and led to a
lengthy process of solvent injection past the low-permeability paraffin plug which eventually
got removed.
Scale can form as shown in Figs. 1.7 and 1.8 when reservoir water, which may exist near
the oil or gas deposit, has some minerals dissolved in it. At reservoir conditions, the formation water is usually partly saturated with salt, or in some cases may be near the equilibrium
Fig. 1.7
Scale buildup inside a heat exchanger tube (Lebedev, 2010).
Examples of flow assurance problems
9
Fig. 1.8 Solid salt scale plug in an Orenburg gas-condensate well, 100 mm diameter. Photo by Yuri F.
Makogon, Originally published by PennWell Corporation in Hydrates of Hydrocarbons, 1997 and reprinted with permission.
saturation. As water flows from the reservoir with the produced gas or oil, its pressure and
temperature change, which affects the solubility of dissolved ions in water. Saturation limit
for some ions may also be reached because water composition changes if the water table rises
to the produced zone from another zone. Similarly, waters saturated with different ions from
different zones mix, some ions combine and solid scale may form and restrict the pores in
reservoir rock or in well tubing, thus limiting the productivity.
Saturation limit for salt ions in water may also be reached because water molecules get
consumed to form a hydrate leading to a concentrated brine, or because of the change of
pressure or temperature.
Hydrate formation can also lead to precipitation of solid salt scale in small-volume closed
systems (Hu et al. 2017a,b, 2018)
Petroleum industry access to ultra deep reservoirs often has to deal with high-pressure
and high-salinity fluids. Reservoirs with fluid pressure over 180 MPa are in appraisal and
development. Fluids in the reservoir may also be nearly saturated with salt in pre-salt
deposits located under salt domes and diapirs. This combination of high pressure and
high salinity of such fluids presents a unique set of challenges for wellwork and production engineers because in order to complete a well or to produce such fluids, formation of
solid phases must be avoided. Solid phases may include gas hydrates or scales such as halite. During well completion, heavy brines are used to offset by their hydrostatic pressure
the high pressure of reservoir fluids in order to avoid a well blowout. At the same time,
10
1. Introduction
completion brines must remain hydrate-free at mudline (seabed) conditions in case light
hydrocarbon gases migrate from the bottom of the well up the wellbore to the location
where well completion fluid is exposed to cold (approx. 277K) seawater if a well is drilled
in offshore environment. Thus, accurate prediction of hydrate equilibria in high salinity
brines is important. Similarly, during production of reservoir fluids through a completed
well, hydrates must still be avoided, lest the well gets plugged with solids. If a chemical,
such as pure methanol or a low dosage hydrate inhibitor formulated in methanol, is used
to control hydrate formation, this may cause a salting out effect as scale forms due to colligative properties of water and inability to dissolve both salt and methanol simultaneously
beyond the solubility limit. This has led to past incidents such as blockage of a North Sea
production line with halite scale [ca.2009]. The ability to account for high salinity brines
with respect to high pressure hydrate equilibria and scale formation is also important
during production.
Usually, stability of brines decreases with decreasing temperature. This may lead to precipitation and deposition of solid scale such as halite or barium sulfate. In case of carbonate
scales, brine stability decreases with increasing temperature, leading, for example to a calcium carbonate scale in hot systems.
How flow assurance and production chemistry work together
Multiphase flow assurance is complemented by production chemistry whose aim is to
prevent the reduction of product value and process safety such as water in oil, oil in water,
salt in oil, oxygen in water, mercury in fluids, H2S in gas, corrosivity, and/or bacteria. Sour
crude is less valuable than sweet, so souring of crude oil in reservoirs may be prevented by
using chemistry. Similarly, it is the goal of production chemistry to maintain specified quality
of product oil and produced water so they are fit for export to refinery, reinjection into a well
or discharge overboard. The chemicals are selected and deployed by chemists in multiple locations including reservoir, wellbore, flowlines, process facilities and export pipelines to help
produce oil and gas most economically.
The flow assurance and production chemistry work side by side to achieve related goals,
and sometimes that work may be performed by the same person if that person has sufficient
experience in both disciplines.
The combined scope of some of the flow assurance and production chemistry items is
shown below in Table 1.1:
Many of the items from the above table get summarized in a Basis of Design document for
flow assurance work.
The allocation between flow assurance and production chemistry is only suggested depending on whether the issue is more flow-transformation or fluid-transformation related,
and may vary from project to project. For example, foaming may be caused either by a fluid
containing high amounts of natural surfactant or by high shear of flow through a choke or
orifice. Foaming may be prevented by the use of production chemistry to improve separation
of oil and gas or it may be sought by flow assurance to help lift fluids from a well with multiphase flow. Both flow assurance and production chemistry specialists should be experienced
in all of the above items.
11
How flow assurance and production chemistry work together
TABLE 1.1 Combined scope of flow assurance (FA) and production chemistry (PC)
FA
Asphaltenes precipitation, deposition and remediation
Artificial lift or boosting method selection and optimization
PC
X
X
Bacterial analysis, modeling and control in flowlines and wells
X
Bacterial biomass accumulation in process equipment
X
Basis of design for flow assurance analysis
X
Chemical selection, dosages and compatibility screening
Chemical injection locations, rates and chemical tubing or umbilical sizing
X
X
Corrosion analysis, monitoring and treatment
X
Corrosion products accumulation in pipes and in process equipment
X
Cross-flow between wells or multiple zones in a well
X
Diamondoids precipitation from produced fluid (typically gas)
X
Drilling and wellwork fluids formulation for hydrate and scale control
X
Electrical heating analysis for flow lines
X
Emulsion separation in separators, flowlines and wells
X
Emulsified fluids viscosity and flow
X
Erosional velocity analysis
X
Flexible line inflation during filling with fluid
X
Flow metering strategy and locations
X
Fluid sampling plan, PVT analysis and EoS tuning during appraisal
X
Fluid sampling and laboratory planning for process facility in operation
X
Foaming of produced fluids
X
Gelled oil blockage and waxy gel break pressure
X
Glycol or methanol regeneration
X
Hydrate formation prediction, inhibition and remediation planning
X
Ice blockage
X
Joule-Thompson cooling or J-T heating of produced fluids
X
Liquids holdup in produced fluid transport lines
X
Liquids loading of wells during multiphase flow of gas, oil and water
X
Mercury accumulation in flow lines, equipment and product streams
X
Monitoring of flow and blockage detection with online system
X
Multiphase flow and pulsation in wells, flowlines, process equipment
X
Continued
12
1. Introduction
TABLE 1.1 Combined scope of flow assurance (FA) and production chemistry (PC)—Cont’d
FA
PC
Naphthenate scale analysis and remediation
X
Oil quality non-compliance due to water content
X
Paraffin wax analysis, deposition and remediation
X
Scraping of flowlines and pipelines
X
Pressure drop analysis in single phase and multiphase flow
X
Produced fluids export, discharge or reinjection plan
X
Relief and flare lines flow capacity and blockage potential analysis
X
Sand transport flow velocity analysis
X
Scale precipitation and deposition analysis and remediation plan
X
Souring of reservoir fluids: analysis, modeling and mitigation
X
Sulfur (elemental and organomercury)
X
Sizing of flowlines for control of multiphase flow slugging and erosion
X
Steam condensation and evaporation in distribution lines
X
Stuck scraper during pipeline commissioning or during flow line maintenance
X
Transient surge volume analysis for production separator or slugcatcher
X
Under-deposit corrosion
X
Value loss from hydrocarbon contaminant metals, methanol or water
X
Vibration induced by phase transition in process equipment
X
Viscous oil or viscous emulsion flow
X
Water or gas injection for pressure maintenance
X
Water quality, filtration and treatment with clarifier, oxygen scavenger
Water hammer, HIPPS flow analysis
X
X
Distribution of items varies by operator company.
An operator company which neglects or misses to check and quantify any one of these
items at the project design stage carries a risk of increased cost or abandonment during
operation.
Some companies maintain internal boundaries between flow assurance and production
chemistry disciplines, while others combine the two along with materials and corrosion issues, depending on the company size and the depth of available engineering resources.
The American Petroleum Institute have clearly listed nine flow assurance issues as follows:
– hydrate formation,
– wax formation,
– asphaltene formation,
13
How flow assurance and production chemistry work together
–
–
–
–
–
–
emulsions,
foaming,
scale formation,
sand production,
slugging,
materials-related issues.
The API 17 TR4 list above captures most of the scope and is fairly comprehensive for a
typical oil or gas field development.
Flow assurance prevention methods are usually thermal (insulation or a cooling spool) or
chemical (inhibitors) whereas mitigation can be mechanical (pumps), chemical (solvents) or
thermal (active heating).
Production chemistry prevention is usually chemical (surfactants or inhibitors) or mechanical (segregation of incompatible fluid streams). Mitigation is chemical (chelants, dispersants,
dissolvers) or mechanical (milling). Chemical injection dosages are, on average, 100 ppm with
typical range of 50–250 ppm, and can be much higher for hydrate inhibitors ranging from 10,000
to 500,000 ppm or much lower at 5–10 ppm for emulsion breakers and corrosion inhibitors.
In some sub-cases such as under-treated severe bacterial accumulation or foaming, flow
also gets affected.
Main focus of production chemistry is on product value including: oil quality (water content), water quality (organics content and total dissolved solids, oxygen content, souring and
corrosion potential).
Chemicals may be deployed in a variety of locations. Typical ranges of chemical dosages
are needed to design a chemical delivery system. Such ranges are shown below in Table 1.2.
TABLE 1.2 Initial estimates of chemical dosages and typical locations of chemical injection
Chemical
Dosage, ppm mass basis
Place of injection usually
Emulsion breaker
5–10
Downhole, tree, topsides
Reverse demulsifier (water clarifier)
15–50
Topsides
Corrosion inhibitor (liquid and multiphase)
30–200
Tree
Corrosion inhibitor (gas export)
5–10
Topsides, process plant
Wax inhibitors
50–800
Downhole, tree
Wax dispersant
50–1000
Downhole, tree
Asphaltene inhibitor/dispersant
50–800
Downhole
Drag (friction) reducers: oil
100–1000
Process plant
Drag (friction) reducers: water
20–100
Tree, topsides, process plant
Pour point depressant (PPD)
25–1000
Downhole, tree
Scale inhibitors
5–100
Donwhole, tree
Scale dissolvers
Batch
Downhole, topsides
Continued
14
1. Introduction
TABLE 1.2 Initial estimates of chemical dosages and typical locations of chemical injection­—Cont’d
Chemical
Dosage, ppm mass basis
Place of injection usually
Foamers
5000–10,000
Downhole
Defoamers
100–150
Tree
LDHI: kinetic hydrate inhibitors
10,000–50,000
Tree
LDHI: AA hydrate inhibitors
5000–30,000
Tree
H2S scavenger
5000–10,000
Downhole, topsides
O2 scavenger
5–500
Topsides
Biocides
50–1500 (batch)
Topsides
Methanol or glycol—hydrate inhibition
5000–500,000
Downhole, tree
When is flow assurance applied
Flow assurance is commonly applied in project design and/or in operations support. At
the project design stage, the engineering talent evaluate several ways of combining different
technologies which would allow to extract oil and gas from the reservoir both reliably and
economically.
Examples of such technologies range from simple methods, such as passive insulation to
keep produced fluids as close to the reservoir temperature as possible, to the complex ones,
such as subsea processing equipment to separate and pump fluids to their destinations.
Flow assurance is also applied in operations to optimize the economics of production
by tuning the performance of artificial lift, optimizing the routing of the produced fluids
through the flowline network, and by solving the problems of restrictions and blockages or
surges in reservoirs, wells, flowlines, processing equipment and in export pipelines using a
variety of methods.
The tasks for flow assurance and production chemistry in project development design are
listed earlier in “How flow assurance and production chemistry work together.”
Tasks for flow assurance support in operations:
•
•
•
•
•
•
•
•
•
•
•
•
Production system monitoring for flow assurance model tuning with system data
System flow assurance condition surveillance for blockages.
Maintenance implementation.
Well Start-up temperature insulation performance measurement.
Chemical Injection residuals' and performance monitoring.
Shut-in cooldown temperature insulation performance measurement.
Operator training program implementation and updates.
Operating procedures updates and verification.
Verification of chemicals performance.
Chemicals incompatibility with materials management.
Chemicals substitution and field trials.
Verification of chemical vendor performance.
Why flow assurance failures happen
15
Knowledge required in flow assurance
It is not sufficient to just analyze the flow of fluids, but one must also recognize and
predict the temperature and phase transitions as vapor, liquid and solid phases appear at
different temperatures and pressures. Therefore, a flow assurance engineer must first be
prepared in measuring and calculating fluid properties and phase equilibria, which is commonly taught in chemical engineering, heat transfer, which is taught in mechanical engineering, or chemical engineering, and oilfield process equipment operation which is taught
in petroleum engineering, as well as a range of other disciplines such as materials science,
biochemistry, chemistry.
It is not possible to get trained in all these specialties at once, so a flow assurance knowledge is acquired over time. Flow assurance is a relatively young discipline and only a few
universities recently started to teach flow assurance.
It is not enough to be skillful in setting up a multiphase flow model, but it is important
to understand what can happen to the fluids as they flow from the reservoir to the refinery.
Equally, it is not sufficient to know how to set up a scale or asphaltene precipitation model,
but necessary to understand the underlying lab work and what eventualities may lead to a
change in the steady operating conditions and to design chemical injection program with
such eventualities taken into account.
Why flow assurance failures happen
Two main reasons which explain the majority of flow assurance related incidents are: incomplete understanding of fluid properties and exceeding the safe operating limits. The first
usually happens from lack of training or experience. The second may happen either due to
an operator error or from operator's inability to explain to the management how exceeding
the designed operating conditions will lead to a failure. Management may be motivated by a
short-term incentive to reach a certain production target and request production operations
to exceed the pre-determined limits; such operational deviations done without proper laboratory evaluations and technical plan seldom result in sustained improvement but can often
lead to production interruptions followed by downtime, costly remediation and/or loss of
confidence.
A typical subsea blockage related to flow assurance may cause several months downtime
plus cost upwards of $15 million, as of the writing of this book, to hire a technology for clearing it if remediation program is successfully implemented, or lead to an even costlier well
workover, flowline replacement or well abandonment if remediation is unsuccessful. In extreme cases, flow assurance failure may lead to contractual sanctions stemming from inability
to deliver produced oil or gas, which cost may escalate into hundreds of millions of dollars,
or to a complete loss of license to operate in a given country. Usually gas hydrate or paraffin
wax blockages may lead to such extreme cases.
In the most extreme cases, blockages may lead to casualties. In an onshore field, a hydrate
blockage driven by pressure differential moved inside a pipeline, ruptured the pipe bend
and hit an operator. In the Piper Alpha offshore platform, a hydrate blockage in a condensate
16
1. Introduction
line was considered among the four likely root causes for the condensate leak and fire which
sank the platform (Cullen, 1989), with 167 fatalities.
In other situations, the disaster caused by solid blockages leading to a pipe rupture and a
release of hydrocarbons may be narrowly averted. In one FPSO in West African waters, an ice
blockage formed in a flare relief line when a cold gas stream and a warm gas stream carrying
water moisture combined, which led to a rupture and formation of an explosive gas cloud,
but the wind on that day was blowing away from the furnaces.
In another example from US deepwater, nature may intervene to help remove a blockage,
such as when a hurricane cleared a hydrate blockage. A deepwater chemical injection system methanol line connected to a scraping crossover valve got plugged as produced fluids
hydrocarbon and water back-flowed past a checkvalve into the methanol line and formed
a hydrate. The methanol line remained plugged until a hurricane led to an evacuation of
the platform. This, in turn, triggered an automated opening of the scraping crossover valve.
Warm water, accumulated behind the crossover valve in a dead leg of an actively heated
flowline, flowed through the crossover valve and past the methanol line plugged with hydrate. The warm water flow initiated in the automated response to the hurricane heated
and cleared the methanol line of hydrate, which was understood upon the restart of the
field. This example teaches us to seek sources of energy available and accessible to overcome a blockage.
In a yet another example, an onshore oil field in Siberia experienced multiple hydrate
blockages in early summer within months of being put on production because the initial water cut was low (under 5%), and methanol was not being injected. Additional resources were
provided to supply methanol to treat the produced fluids. However, this was costly as methanol had to be airlifted by a helicopter during the summer months because the roads were
impassable. A storage facility was then constructed to provide methanol supply through the
year, but a longer-term ingenious solution was implemented, which came from a local technologist, who suggested to convert one of the several producer wells to a water-producer
by re-perforating the well in the aquifer zone. Heat carried by water from one well was sufficient to keep produced fluids from all the wells warm and outside of the hydrate stability
region. This was possible because all wells were equipped with ESPs for artificial lift. This
example not only induces us to seek the nearby energy sources which can be used for flow
assurance but also shows that operators of the field have a better understanding of the field's
capability and should be consulted with during concept evaluation.
Blockages in onshore wells and flowlines are more routine and are much less costly to
deal with. In one onshore field in North America, partial hydrate blockages occurred in
wells nearly daily during the cold season, and were cleared promptly by methanol injection
from a pump truck.
Engineers and chemists perform various analyses of properties for reservoir fluids,
including hydrocarbons, water and gas. In some cases, the fluids are not sampled adequately, and some properties, such as the presence of H2S or mercury, may be not noticed
until after the startup. Retrofitting a facility to take care of such problems, if they are not
known at first and discovered later, is both costly and time consuming. Proper sampling
is the foundation on which the good flow assurance design and production chemistry
selection are based.
17
Flow assurance background
Flow assurance background
Prior to petroleum production there was water, and water was produced through wells.
There are reports of scale encrustation of water wells in ancient Egypt water production
system.
Initial small-scale use of petroleum began in Persia and China. Early oil came from natural
seeps, and wells were dug by hand or pierced with a spring pole. One of the uses of petroleum was Early petroleum production in Northern Persia, now Azerbaijan was indicated by
Marco Polo and other travelers. By the early 1800s production in the region averaged 80–90
barrels per day.
Large scale production of petroleum did not start until half a century later driven by
increasing demand for petroleum. Around 1853, a modern version of the kerosene lamp
was invented by a Polish inventor in Lviv, then part of the Russian empire and Poland,
and now located in Ukraine. The reliable kerosene lamp created a steady demand for kerosene and for petroleum. Today, kerosene makes up just over 1% of refined oil products
whereas 5% goes to jet fuel and 50% to gasoline (DOE, 2017, 2019). Kerosene lamps still
consume as much fuel worldwide as all US jet planes combined. Besides the light, heating and transportation, petroleum also helped to reduce the hunting of whales and the
dismantling of forests for fuel.
The global production of petroleum kept increasing through the years. The upward
inflections as shown in Fig. 1.9 in the cumulative global oil produced observed around
1860, 1910, 1960 represent technology shifts which came in response to the production
demand. Below in Figs. 1.10–1.14 are few examples of how the use of technology transformed the industry to make it more efficient.
In 1859, the first application of drilling technology and creation of the E&P industry took
place.
10,000
1000
100
10
1
1800
0.1
1850
1900
1950
2000
0.01
0.001
Fig. 1.9 World oil produced, Billions of barrels (Azerbaijan, 2017; Geohelp, 2017; Oil150, 2017;
TSP, 2017; US EIA, 2017).
Fig. 1.10
Drilling a well with a spring pole.
Fig. 1.11 Well drilled for oil using an engine.
Fig. 1.12
Geophysical survey of a well.
Fig. 1.13
Offshore drilling rig, 1947.
Fig. 1.14
Offshore rig, vessels, and barge in the Gulf of Mexico (BOEM, 1956).
20
1. Introduction
The 1910s saw science and engineering first applied to exploration & reservoir
management.
In the 1940s and 1950s, after the leftover military equipment and barges became available at low cost, E&P industry moved offshore; first well was drilled beyond the sight
of land.
The need for dealing with blockages emerged with petroleum production and became
more pronounced as the production moved offshore.
The paraffin deposition was observed during the early oil production in the United
States and in the Russian Empire in Baku. Petroleum was first commercially produced by
digging wells with a person inside an oil well bailing out the oil (Said, 1937). Early commercial production through drilled wells started in United States and Baku. Oil in Baku
is waxy, but wax blockages were not reported because the oil was transported by barrels
and in rail cars and was at ambient temperature, while wax deposition requires cooling.
The oil was transported by wooden barrels, and later by a pipeline. The wax deposits
formed on barrels and then on pump rods. Oilfield workers noticed that that clear wax helped
heal scratches. Wax was then marketed as Petroleum Jelly or as Vaseline.
Ludvig Nobel expanded production of petroleum to provide light and energy (it was his
younger brother who invented dynamite). He also established laboratories in St. Petersburg
and in Baku for research on kerosene and transport of oil in 1880 (Economides and
Oligney, 2000).
This energy, mainly through availability of hot water and hygiene, increased the living
standards and lifespan during the 20th century. The same energy led to cheap transportation,
globalization of labor sources and a decline of many developed economies and the rise of the
developing countries.
Natural gas production has encountered formation of hydrate blockages as early as 1930s
in United States (Hammerschmidt, 1934) and 1950s USSR (Makogon, 1965). In the 1930s, natural gas production was increasing in the United States and initial blockages were reported
in gas pipelines.
By the 1950s, the petroleum industry also developed in Russia, and hydrate blockages also
took place.
It was not until the 1960s when the gas hydrates in nature were encountered. This event
led to a laboratory work in Russia, and proof of the discovery of gas hydrates in nature was
made by Prof. Yuri Makogon.
The discipline of flow assurance started to coalesce during the 1980s as offshore production encountered phenomena such as severe slugging. Offshore production did not have the
technical ability to separate gas from oil at the well site as in onshore production. The reservoir fluids, including oil, gas and water, had to flow together to an offshore platform where
the multiple phases could be separated. Severe slugging occurred as liquids accumulated at
the riser base when the riser pipe diameter was too large and gas only periodically lifted the
liquids to the top of the platform. Engineers realized the need for predicting pressure drop
in multiphase flow to select the most economic pipe size for subsea production which also
allowed a stable multiphase flow.
The formulas for multiphase flow then existed only in the nuclear industry which were
used to calculate the flow of water and steam. Those correlations were adopted to calculate
the flow of oil and gas, and with more experience and lab tests, new correlations were devel-
Flow assurance requirements
21
oped for petroleum multiphase flow as Beggs and Brill, etc. Vertical flow correlations were
developed and updated by Coleman, Turner, which allowed to estimate the gas flow rate at
which liquids accumulate at well bottom in a production tubing pipe if gas velocity is insufficient to lift the liquids from a well.
Production and process engineers realized that individual aspects of multiphase flow assurance worked together as flow through pipes submerged in cold subsea water and gas
expansion in wells and riser caused cooling of fluids which led to the formation of wax, hydrates, and sulfate scale.
The term “Flow Assurance” is a literal translation of Portuguese phrase “Garantia de
Escoamento.” The term "flow assurance" was coined in 1994, at the Deepstar-PROCAP
Technology Exchange Workshop held at Petrobras and focused mainly on paraffins and hydrates, by the lady from Colombia by the name Magali Cotrim, who was the technology program manager for Petrobras (Minami, 2017). The term translated easily and meaningfully into
English and took root. Since then, the petroleum industry saw a lot of change. Several companies recently started to use internally a new term Production Assurance. The term “Flow
assurance” also exists around the globe. In Hindi, this would translate as “Pravaah Sunishchit
Karya” प्रवाह सुनिश्चित करना (flow assurance work), in Russian, it would be “Obespechenie
Potoka” Обеспечение Потока (assurance of flow), and in Mandarin it would be “Liu Dong
Bao Zhang” 流动保障 (flow security). Prior to the English translation, the term "Garantia de
Escoamento" existed as part of the Petrobras PROCAP 1000 program in Brazil (Neto, 2006).
The PROCAP program which stands for Programa de Capacitação Tecnológica em Sistemas
de Produção para Águas Profundas also promoted the standardization of subsea trees.
Flow assurance requirements
With that brief introduction we can discuss what the flow assurance comprises and what
information is necessary to perform a reliable analysis of a petroleum system to assure uninterrupted oil and gas production.
Basis of design
A document listing all parameters necessary to allow planning of an approach to solving
flow assurance challenges usually is known as a basis of design.
Key knowledge requirements for flow assurance analysis of a system include:
1. depth profile of a wellbore and an onshore flow line elevation profile or bathymetry of a
subsea flow line, a riser and an export pipeline
2. expected flow rate of produced fluids
3. environment properties
4. fluid characterization
These four basic categories include multiple sub-elements. Basis of design should have as
detailed information as possible about bathymetry, fluids, production profile and environment properties. Often exact information is not readily available or is too costly to obtain.
In such cases, field analogs from the region may provide approximate indication of typical
22
1. Introduction
TABLE 1.3 Examples of reference conditions
Temperature
Pressure
Standard cubic foot of gas United
States
60 °F = 15.555 °C
14.73 psia = 1.002 atm = 101.560 kPa
Normal cubic meter of gas Europe
15 °C = 59 °F
1 atm = 101.325 kPa = 14.696 psia
Stock tank barrel
60 °F = 15.555 °C
1 atm = 14.696 psia = 0.101325 MPa
Stock tank conditions for oil in United States: 14.696 psia = 1 atm, and 60 °F = 15.555 °C.
Standard conditions for gas in Russia: 101.325 kPa = 1 atm and 20 °C = 68 °F.
Normal conditions for gas: 760 mm mercury = 1 atm and 0 °C.
US standard conditions: 1 bar = 100 kPa = 0.1 MPa and 15 °C = 59 °F.
Standard conditions NIST, United States, 101.325 kPa = 1 atm and 20 °C.
Standard conditions GOST, Russia: 760 mm mercury = 101.325 kPa and 25 °C.
bathymetry, fluid behavior and environment parameters. However, analogs may differ significantly from the target reservoir.
Units for fluid characterization
Reference conditions for measurement of hydrocarbon properties vary regionally. It is important to define which system of units will be used in a project. Standard conditions even
vary for defining the linked units such as quantities of gas and oil used in the gas oil ratio
(GOR). Gas is measured in standard cubic feet, standard cubic meters or in normal cubic
meters. However, gas is sold by its heating value because different compositions provide
different amounts of heat when combusted
Oil can be measured and is sold by stock tank barrels, cubic meters or metric tons, with
various quality oils getting different market price. The “standard” conditions at which fluid
quantities are defined vary for liquid and for gas. Measurement of liquids by mass usually
yields the least error compared to measurement by volume. Several examples are shown below in Table 1.3.
An engineer has to verify in any PVT-related fluid analysis work that the units used to
describe fluid properties match those used in the project. The reference conditions should be
defined in the Basis of Design. Mass definition of a metric ton does not vary with temperature
or pressure. The variability of the volume metrics leads to sale contracts for natural gas using
caloric or heating value of the gas obtained upon its combustion.
Introduction to flow assurance risk analysis
A flow assurance specialist's objective is to make sure that a project is designed for safe and
reliable operation in relation to flow assurance issues and that all “boxes are checked.” For
that, we first must define what those boxes are because if we can measure, we can improve.
Flow assurance becomes an analysis of thermal, hydraulic and fluid-related threats to flow
and fluid quality and mitigation of these threats with equipment, chemistry and procedure.
This analysis lends itself well to a “bowtie” risk analysis (Fig. 1.15).
23
Introduction to flow assurance risk analysis
Fluid flow
Thermal
hydraulic
fluid-related
Fig. 1.15
Threats to
Fluid quality
Pipe integrity
Equipment
Mitigation with
chemistry
procedure
Graphic of a bow-tie risk analysis for flow assurance.
The bowtie risk analysis is well suited to look at how well the protective barriers against
flow assurance threats are placed, and how well the remediation efforts can prevent the undesirable consequences.
Thermal threat may seem redundant as viscosity (hydraulic) and solids (fluid-related)
effects emerge as fluids cool down, but one should remember about the high temperature
aspects of HPHT. We can't flow if we can't effectively use corrosion inhibition at high temperatures. Flow assurance helps with HPHT as well. An example is the 143 km long Snohvit line
in the N.Sea. Typical corrosion inhibitor chemicals may lose efficiency above 250 °F. Snohvit
field uses a cooling spool section of flowline long enough to cool the hot produced fluid with
seawater to 250 °F before switching to a carbon steel flowline. Regular corrosion-resistant
alloys (CRA), which may be used to transport corrosive fluids, also may have temperature
limitation of 85 °C.
The seven steps to flow assurance risk management include:
(1) Define data source
(2) Define objects to view
(3) Define the factors and threats
(4) Describer the mitigations and inspections
(5) Create an integrity model
(6) Calculate relative risk from threats
(7) Assign mitigations and inspections to each threat
After the mitigations and inspections are identified, the operations cycle may go into the
usual continuous improvement loop of Plan-Do-Check-Adjust to eventually achieve steady
quality. Risk analysis aims to quantify threats in order to achieve an economic balance between prevention and cure. Every field is different, and in very remote areas without developed infrastructure, the access to remediation technology for a formed blockage may take a
very long time which will significantly affect production and revenue, so less risk may lead
to a better project profitability. Conversely, in a region with abundant services, the time to
call in blockage removal specialists may be minimal so more risk may be taken and some upfront capital and operating cost may be saved without significant additional impact to the net
value of the project.
Before one starts to analyze flow assurance risk in order to save cost and optimize budgets,
one should develop a list of relevant parameters to allow planning of our approach to solving
flow assurance challenges. As said above, the relevant parameters will be region-specific.
24
1. Introduction
Threats to flow are normally attributed to flow assurance
Flow assurance aims to achieve an economic balance between prevention and mitigation
of mechanical or hydraulic restriction threats to flow such as hydrate plugs, scale plugs, severe slugs, liquids holdup, wax plugs, asphaltene plugs, without reaching the costly remediation stage. The detailed risk analysis of each threat compares the probability or frequency
of it happening during the life of field and the cost of the consequence against the cost limit
acceptable to each specific operator. Some operators may have a company policy that no
risk of blockage is acceptable because the contractual cost of a disruption to production can
be very high while others rely on their own experience and laboratory verification to accept
some amount of risk. However, risk analysis performed by specialists, who may soon retire,
should be viewed with additional independent verification.
A detailed understanding of the flow system and fluid properties are required in order to
develop a coherent design for field development.
Threats to product value or process safety (asset integrity)
Asset integrity or product value also get affected in some cases, such as severe slugging
in an un-braced flowline or jumper, a hydrate projectile movement during depressurization,
erosion by sand or treatment with methanol.
Production chemistry deals with prevention and mitigation of fluid composition threats to
product value or process safety (asset integrity) such as water in oil, oil in water, salt in oil,
oxygen in water, mercury in fluids, H2S in gas, corrosivity, and/or bacteria.
Hardware cost
The cost of hardware keeps continually increasing. The cost of subsea tiebacks has been
getting more expensive in the past two decades well outpacing the inflation.
Cost of subsea hardware related to flow assurance
It is prohibitively expensive to place a floating host facility with separation and processing
of produced fluids over each drill center. Such platforms, like Pompano, do exist in deepwater and use dry trees to produce fluids. It is more economic to use subsea tiebacks to produce
hydrocarbons from several drill centers or several neighboring fields to the same host facility.
Infrastructure-led exploration (ILX), or looking for more hydrocarbons near the existing facility, is key to deepwater profitability. Not only this allows to tie in new fields to the existing
facility, but it also allows export of separated hydrocarbons via existing export lines, which
improves project economics.
The highest net present value (NPV) deepwater project to-date is Na-Kika (Riazi, 2016) designed by Shell and operated by BP in the US Gulf of Mexico with multiple subsea tie-backs.
Na Kika translates as octopus (Encyclopedia Mythica). ILX means that several commercially
producible average sized fields must exist within a 10–20 km radius which can be tied back to
the common host facility. Production of petroleum from these fields may then be scheduled
in phases, allowing less risk in capital investment.
25
Hardware cost
An asset similar to the Na-Kika semi-submersible platform with several gas and gas condensate fields producing to the common host Independence is operated by Anadarko.
However, an oil company venturing into deepwater must first be able to find the oil before
flow assurance analysis gets done. As a recent example, the largest US exploration and production operator had to exit its deepwater exploration business in 2015 as the costs of several
dry hole wells which didn't strike commercial oil quantities and the subsequent contractual
costs of the drilling rig termination amounted to near one billion dollars (Conoco, 2016a,b).
The deepwater assets also range in quality and range from top-tier assess such as Na-Kika or
Atlantis, to technology-intensive and risky Paleogene assets which often carry the whole range
of flow assurance fluid problems such as high oil density, asphaltenes, wax, scale and hydrates.
ILX is key, but we also need to be smart about how we produce and process multiple fluids because fluids may be incompatible and create flow assurance problems when mixed or
comingled.
Flow assurance analysis of multiphase flow stability and flowline sizing analysis, together
with reservoir model, define production rates and the project NPV. Flow assurance has the
tools to optimize the project and to deliver production reliably from nearly any distance.
However, average installed cost for longer subsea tiebacks has been getting progressively
more expensive in the past. This is not a recent but a sustained trend.
A similar trend in pipeline costs as shown in Fig.1.16 is present both offshore and onshore,
with offshore costs being roughly double the onshore cost due to the higher cost of installation and insulation. Recent growth in shale production saw the use of less costly fiberglass
gathering pipelines in response to the need to rapidly and inexpensively establish a gathering
infrastructure. The fiber lines serve well but are not resilient to freezing weather when pipes
sometimes fail due to soil heaving. Fiber lines are well suited for service as single phase flow
for water or stock tank crude, but their use as gathering flowlines carrying multiphase flow
needs to be decided with care and flow assurance analysis because tee fittings at pipe merge
points sometimes fail due to the repeated impacts of slugging flow on the tee connections.
8
R² = 0.9948
4
2
1
1990
1995
2000
2005
2010
2015
Fig. 1.16 Cost-per-installed-mile of offshore tiebacks doubles every 8 years (in USD million). 1996
average cost-per-mile for offshore construction was $1.61M. 2001 average cost-per-mile for offshore
construction was $2.58M. 2008 average cost-per-mile for offshore construction was $5.37M. 2013
average cost-per-mile for offshore pipeline construction was $7.6M (USAID, 2008; Smith, 2012, 2013).
26
1. Introduction
As of 2017, offshore shelf production is among the most economic sources of petroleum.
While it costs US$54 to produce one barrel on average in the world, both offshore shelf and
deepwater are below the average as shown in Fig. 1.17.
To become profitable, the wells have to produce roughly three times their cost. Average
onshore well may cost $3–4 million. Average shale well may cost $6–7 million including drilling, completion and fracturing. A deepwater wells cost significantly more, with a range of
$75–175 million depending on depth and time it takes to drill. This means that an average
deepwater well must produce, on average, 7 million barrels of oil to bring profit. Deepwater
reservoirs are usually prolific, with annual decline rate of around 10%, and last for at least 20,
sometimes 30+ years, with typical host facility design life of 25–40 years. If a deepwater well
produces for 10 years, it has to flow at least 2000 barrels per day to bring profit. Such rates are
on the low side for deepwater, with most wells flowing 10–20 thousand barrels per day (Riazi,
2016, p. 636). Payback time for the best producing wells in deepwater is less than a year.
Conversely, shale wells decline rapidly, with first year decline rate of around 60% as shown
in Fig. 1.18 and Table 1.4 (meaning production in year 2 is just 40% of production in year 1).
However, there is a large resource to tap with shale production, in both oil and gas.
If a shale well produces for 10 years, it has to flow at least 628 barrels every day in the first
year to bring profit. Such rates do exist in shale production as shown in Table 1.5, but are on
the high side, with average new Bakken well producing 476 bo/d in 2016, Wolfcamp in Texas
producing 463 bo/d and US-average new 2016 shale well flowing 241 barrels of oil per day in
the first year (Shaleprofile, 2017).
While comparatively more productive, fields in deepwater present more risk due to its
remoteness and cold, deep environment, and require a more thorough engineering design.
Flow assurance is applicable both to shale onshore and to deepwater, but the much higher
cost of fixing a problem makes flow assurance analysis mandatory if not central in the development of deepwater projects. Of course, flow assurance analysis can only be performed after
the oil is found, which leaves the seismic data processing as the most important technology
for the deepwater petroleum industry.
Average cost to produce 1 barrel of oil, USD
80
70
60
50
40
30
20
10
0
Middle
East
Fig. 1.17
Shelf
offshore
Russia
Other
Deepwater Shale
Oil sands
Arctic
Cost of oil production, based on Rystad Energy, Morgan Stanley Commodities Research.
27
Hardware cost
Fig. 1.18
U.S. Shale oil production (Shaleprofile, 2017).
TABLE 1.4 Unconventional shale production and decline rates
Year of start
2010
2011
2012
2013
2014
2015
2016
Wells
5285
8938
11,390
13,140
15,050
11,052
6363
1st year bo/d
335,850
819,919
1,346,022
1,832,589
2,526,619
2,001,761
1,532,171
2nd year
bo/d
154,364
346,053
565,828
737,020
1,006,962
789,541
Decline
54%
58%
58%
60%
60%
61%
1st year
bopd/well
64
92
118
139
168
181
(Shaleprofile, 2017).
TABLE 1.5 Production rates from prominent shale plays in 2016
Bakken
Wolfcamp
United States
bo/d
235,341
326,847
1,532,171
Wells
494
706
6363
bopd/well
476
463
241
233
28
1. Introduction
Monitoring and data mining
A consistent set of metrics allows for lasting risk mitigation, and for the ability to extract
value from technology. If we can measure, we can improve.
Integrated analysis based on monitoring and modeling would allow near-term forecasting of flow assurance issues with automated response. Realtime monitoring of production
allows operator to know downhole parameters, plan the deployment of chemicals and to
perform integrated analysis of production & near-term issues forecasting. All fields are
equipped with some instrumentation for measurements and automation. Many fields analyze these collected data to forecast the production. Some fields rely on automation to monitor and analyze the data in real time to alert the operator to changes in flow. Few fields
actually can automatically predict and alert of an imminent flow assurance restriction or
plug so the operator could deploy the mitigation measures such as chemical injection or
heating.
With time the integrated analysis based on flow monitoring and modeling would allow
near-term forecasting of flow assurance issues with automated response in more fields.
Flow assurance in operations
Onshore production
Common problems encountered in onshore operations are: reservoir souring, liquids
loading and slugging in wells, hydrate, scale and paraffin blockages in wells and gathering flowlines, slugging in in-field gathering lines, hydrate blockages in process plant lines
and equipment. Asphaltenes can occur in undersaturated reservoirs without gas cap and in
wells.
Gas fields can experience deposition of diamondoids and elemental sulfur in well tubing.
Sour fluids have elevated content of CO2 or H2S or both. Mercury is not uncommon in gas
fields near continental rifts such as Asia-Pacific region.
Overpressured reservoirs contain fluids at pressure higher than hydrostatic. This is rare
but can happen in consolidated reservoirs, fractured reservoirs and in weakly consolidated
reservoirs both onshore and offshore. High pressure high temperature reservoirs bring additional constraints on material selection.
Offshore production
Shallow water production encounters the same problems as onshore with addition of severe slugging caused by a significant elevation difference between a subsea flowline and
the platform topsides. Similar to liquid loading in an onshore well, liquids accumulate at
the riser base and get periodically produced by gas backpressure to the topsides separator.
Severe slugging affects stability of production in two ways: periodic movement of liquid
slugs causes regular impacts at flow path elbows and fatigue of both flexible and rigid risers,
and also surge of liquid can overfill the separator volume if the transfer pumps or the separator size or both are undersized.
Systematic approach to solving flow assurance problems
29
Deepwater production
Deepwater reservoirs tend to be at pressure higher than bubble point thus undersaturated
and can be pre-salt or subsalt. In addition to the above problems, this adds the problems of
asphaltene deposition in flowlines and deepwater wells. High salt content in produced water
may also affect the potential for scale deposition and limit the types of chemicals which may be
brought in contact with produced water without forcing salt to precipitate out of the water as
scale.
Both onshore and subsea production of oil and gas experience flow assurance issues. The
key distinction between the two is the remoteness of subsea equipment. The remoteness of
deepwater fields makes fixing any issues much more complex subsea, requiring the development and use of new technologies and significantly more planning in the project development stage not unlike a space station. Attempts to design one piece of equipment and to build
many have mostly been uneconomic because the reservoirs and fluids vary from well to well
and from zone to zone. However, subsea tree pressure ratings have become standardized in
5000 psi increments.
Flow assurance as a discipline started with the needs of subsea production. With the advent of subsea and then deepwater production hydraulic restrictions to flow such as liquid
holdup began to affect production causing flow instabilities. Currently the horizontal wells
experience similar flow instability and may benefit from the experience accumulated in subsea production.
Systematic approach to solving flow assurance problems
The knowledge of all possible flow assurance issues and their interdependence may help
correctly identify and treat a problem.
Many other aspects of flow assurance exist that are not listed above among threats such
as flow performance of various artificial lift methods, performance of various restriction prevention and blockage remediation technologies, multiphase boosting, controlling high fluid
temperature and these will be discussed further.
Some of the flow assurance threats may appear in any location of the production system:
from reservoir pores and production well perforations to topsides or surface process equipment to export or water injection pipelines and injection well perforations.
These threats are known to happen onshore or offshore, in surface or topsides lines, in
fluid separation process equipment or LNG liquefaction process, flares or any other location
where conditions allow any of these threats to appear.
Temperature, pressure and fluid composition dictate where one or more of these threats
will appear. Therefore it is common to overlay curves showing where each threat may appear
(known as phase boundaries) on the Pressure-Temperature chart showing where vapor and
liquid coexist (known as a phase diagram or a phase map).
The phase diagram may be regarded by a practicing engineer as a map. The more detailed
and accurate is the knowledge about fluid and environment properties, the better flow assurance strategy may be developed using that map. Flow assurance analysis may rely on very little knowledge, utilizing rules of thumb or common perceptions about flow assurance threats
30
1. Introduction
for systems where blockages are easily remediated and leaks easily addressed. However, for
remote systems in deep and ultra-deep water the amount and the level of detail of required
knowledge about the reservoir fluids and the environment is substantial.
Process safety
One of the more notable yet sad examples of the interaction of flow assurance and process
safety is the 1989 Piper Alpha disaster. The Lord Cullen investigation report named gas hydrates as one of the four potential causes for the condensate leak which was the root cause of
the explosion.
Loss of primary containment (also known as leaks) are known to have been caused by
hydrate or ice blockages formation because both expand upon freezing or by their sudden
dislodging and movement, mainly onshore or on topsides. Subsea water may act as a buffer
partially absorbing movement of the pipe with blockage moving inside it, thus subsea leaks
caused by flow assurance blockages are less known.
A field operation example and learning of process safety during depressurization of hydrate blockages has been described by Makogon (ICGH9, 2017).
System of measures for flow assurance
Three characteristics named above (safety, reliability and economics) are related to the socalled iron triangle of flow assurance project management which measures are: quality, time
and cost. Safety includes both process safety and personal safety. Safety and reliability fall
under the quality category; a higher quality system will have fewer incidents and will be
safer to operate. Reliability is measured as time and economics is measured as cost; a lower
cost system may have more failures, and project economics will be affected. Reliability translates into the expected frequency of failures. Safety and economics also have the time metric;
non-­productive downtime and the number of recordable incidents and reportable process excursions are reported per unit time. Thus every component of flow assurance project management is related to time, the only measure not subject to inflation. A flow assurance engineer
engaged in a design of a new project has to keep all three metrics in mind, otherwise designs
will be too costly and not get sanctioned for implementation.
A proper design addresses all personal and process safety threats presented by produced
fluids, strikes a price-performance balance between complete prevention and partial control
of flow assurance threats for the duration of the life of field, and allows the operator to reliably produce reservoir fluids.
Outlook for flow assurance
Easy flow assurance challenges in onshore and deepwater have been solved with multiple
technologies developed and deployed over the past two decades. As energy operators may
be moving to new ultra-deep basins or to more complex fluids, flow assurance will be faced
with new challenges and with their combinations, where one change in fluid composition
References
31
or property may trigger one or more other changes. There will also be an increasing need
for the development of more cost-effective solutions for unconventional onshore and then
unconventional offshore production. Use of multiphase flow tools to optimize well geometry
would extend the time of natural depletion production and generate CapEx savings because
fewer wells would be needed. The use of realtime monitoring and multiphase flow modeling
for production and chemical deployment optimization would also optimize OpEx. This represents a total net value approach to flow assurance.
Similar to the total net value analysis, there is an integrated system or a holistic analysis.
As industrial and academic research jointly developed low dosage hydrate inhibitor (LDHI)
chemistries, so there is happening a conceptual change where keeping multiphase flow analysis and chemistry selection apart is no longer an affordable approach because project design
solutions depend on both multiphase flow and chemistry simultaneously.
One example of integrated technology innovation is that service providers are adopting a
process to provide integrated solutions for flow assurance and production chemistry.
Another example of innovation is finding new uses for existing technology: a subsea
scraper launcher historically used for pipeline dewatering after a hydrotest and for wax
maintenance scraping; now is used in GoM for hydrate mitigation by untreated produced
fluid displacement.
Some operator companies, particularly the ones with offshore assets name flow assurance
among the technologies strategically important for the growth, along with seismic exploration and drilling wellwork (Murphy, 2015).
We have at our disposal the same number of solutions: chemical (alter interface), mechanical (displace, scrape or jet), thermal (heat or cool), and process (separate, depressurize or
pump), but just as there can be an infinite number of melodies with only seven musical notes,
the industry can combine technologies to move to new harmonious solutions, driven by cost
in the coming decades.
When a project is borderline economic, a flow assurance specialist can act as an architect
arranging the solutions together to help find a field development concept for stable uninterrupted production and make the project economic. Conversely, if the project design is “goldplated” with multiple risk management margins and allowances even a strong project can
become uneconomic and not pass the capital allocation sanction review. It is important to
keep track of all safety margins added to the design, particularly so in flow assurance and in
production chemistry calculations.
References
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sintef.no/home/sintef-energy/xergi/xergi-2010/artikkel6/. (Accessed 10 November 2017).
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1. Introduction
Conoco, 2016a. News release. conocophillips.com/newsroom/Documents/2016/2016_0204.pdf. (Accessed 17
November 2017).
Conoco, 2016b. Annual report 2015. static.conocophillips.com/files/resources/conocophillips_2015_annualreport.
pdf. (Accessed 17 November 2017).
Cullen, H.L., 1989. Inquiry in to Piper Alpha Disaster (part II).
DOE, EIA refinery yield data, 2017, 2019. US Department of Energy. tonto.eia.doe.gov/dnav/pet/pet_pnp_pct_dc_
nus_pct_m.htm (Accessed 10 November 2017); https://www.eia.gov/dnav/pet/pet_pnp_pct_dc_nus_pct_m.
htm (Accessed 4 April 2019).
Economides, M.J., Oligney, R.E., 2000. The Color of Oil: The History, the Money and the Politics of the World's Biggest
Business. Round Oak Publishers, p. 88.
Encyclopedia Mythica English dictionary. https://pantheon.org/articles/n/na_kika.html. (Accessed 4 December
2019).
Geohelp, 2017. History of the World Petroleum Industry, The virtual Geology Department, (for years 1814, 1818).
www.geohelp.net/world.html. (Accessed 10 November 2017) — for Ohio, Kentucky.
Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gas transmission lines. Ind. Eng. Chem. 26(8),
851–855.
Hu, Y., Makogon, T.Y., Karanjkar, P., Lee, K.H., Lee, B.R., Sum, A.K., 2017a. Gas hydrates phase equilibria and formation from high concentration NaCl brines up to 200 MPa. J. Chem. Eng. Data 62, 1910–1918.
Hu, Y., Makogon, T.Y., Karanjkar, P., Lee, K.H., Lee, B.R., Sum, A.K., 2017b. Gas hydrates phase equilibrium with
CaBr2 and CaBr2 + MEG at ultra-high pressures. J. Nat. Gas Eng. 2, 42–49.
Hu, Y., Makogon, T.Y., Karanjkar, P., Lee, K.H., Lee, B.R., Sum, A.K., 2018. Gas hydrates phase equilibria for structure
I and II hydrates with chloride salts at high salt concentrations and up to 200 MPa. J. Chem. Thermodyn. 117,
27–32.
Lebedev, A., 2010. Scale buildup inside a heat exchanger tube. https://upload.wikimedia.org/wikipedia/commons/0/06/Limescale-in-pipe.jpg. (Accessed 4 November 2019).
Makogon, Y.F., 1965. Образование гидратов в газоносном пласте в условиях многолетней мерзлоты. Газовая
промышленность, 5, издательство Недра (Hydrate formation in gas bearing strata in permafrost regions, Gazovaya
Promyshlennost, Izd. Nedra 5).
Makogon, T.Y., 2017. Process safety of hydrate deposition in orifices during a blowdown of line plugged with hydrate. In: Proceedings 9th International Conference on Gas Hydrates, Denver, Colorado.
Minami, K., 2017. SPE flow assurance technical section meeting, personal communication.
Morais, J.M., 2013. PETRÓLEO EM ÁGUAS PROFUNDAS: Uma história tecnológica da PETROBRAS na exploração
e produção offshore, Instituto de Pesquisa Econômica Aplicada. www.ipea.gov.br/agencia/images/stories/
PDFs/livros/livros/livro_petrobras_aguas_profundas. (Accessed 10 November 2017); http://www.ipea.gov.br/
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Murphy, 2015. Murphy.com. (Accessed October 2015).
Neto, J.B.O., 2006. O processo de aprendizado tecnológico na trajetória do sistema de produção flutuante empreendido pela petrobrás em seu programa de capacitação tecnológica em águas profundas – PROCAP, Masters thesis. Universidade Federal do Parana. http://www.economia.ufpr.br/Dissertacoes%20Mestrado/117%20-%20
José%20Benedito%20Ortiz%20Neto.pdf. (Accessed April 4, 2019).
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no/globalassets/project/oilandgas/pdf/flow.pdf. (Accessed November 10, 2017).
Oil150, 2017. Early crude oil production levels and pricing, (for years 1858–95). www.oil150.com/about-oil/early-crude-oil-production/ (Accessed 10 November 2017), for United States, Canada, Russia.
Riazi, M.R. (Ed.), 2016. Exploration and Production of Petroleum and Natural Gas. ASTM International manual,
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Said, K., 1937. Ali und Nino, publisher E. P. Tal & Co / Verlag.
Shaleprofile, 2017. shaleprofile.com. (Accessed 16 November 2017).
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issue-2/transportation/special-report-worldwide/near-term-pipeline.html. (Accessed 17 October 2014).
Smith, C.E., 2013. Worldwide Pipeline Construction: Crude, products plans push 2013 construction sharply higher,
02/04/2013. www.ogj.com/articles/print/volume-111/issue-02/special-report--worldwide-pipeline-construction/
worldwide-pipeline-construction-crude-products.html. (Accessed 17 October 2014).
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TSP, 2017, Historical Energy Production Statistics, (for years 1900–2014), www.tsp-data-portal.org/EnergyProduction-Statistics#tspQvChart, (Accessed 10/10/2017).
US EIA, 2017, United States Energy Information Administraion Historical Statistics, (for years 1981–2010), https://
www.eia.gov/beta/international/data/browser/, (Accessed 10/10/2017).
USAID, 2008, Natural gas value chain: pipeline transportation, www.sari-energy.org/PageFiles/What_We_Do/
activities/GEMTP/CEE_NATURAL_GAS_VALUE_CHAIN.pdf (Accessed 17 October 2014), http://sari-­
energy.org/oldsite/PageFiles/What_We_Do/activities/GEMTP/CEE_NATURAL_GAS_VALUE_CHAIN.pdf.
(Accessed 8 April 2019).
C H A P T E R
2
Initial diagnosis and solution of flow
assurance production problems in
operations
O U T L I N E
Field or laboratory tests for initial solid
samples identification
Field laboratory initial tests for solid
samples identification
Field analysis
Laboratory analysis
40
40
40
40
Typical blockage remediation plan
42
An operator may interpret the telltale signs of flow assurance problems to help identify
them first and then select the best solution. We can attribute characteristics of flow assurance
issues to the two parameters usually measurable in the field: pressure and time.
Pressure measurement is commonly available in the field production systems. Operations
usually have a limited instrumentation installed on production systems, but most systems
have the pressure measured at the tree upstream and downstream of the choke, and some
have gauges downhole in a well which measure pressure in real time or as a retrievable
recorder. Some chemical skids may have a chart recorder. Any additional available measurements such as temperature, water cut, flow rate, ultrasonic or dielectric signal will help verify
whether the initial identification of flow assurance issues makes physical sense.
Time is the other parameter commonly measurable in the field. It may be possible to tell
which problem is likely taking place by evaluating the time it took for the readings to change.
Both time and pressure need to be evaluated together.
Hydrate plugs can develop as quickly as in tens of minutes, or as slowly as in days. Scale
restriction may form as quickly as in 1 day, or build over the period of weeks. This distinction
of time can be used to help differentiate between different types of blockages when conditions for several different blockage types are present in the production system simultaneously.
Table 2.1 suggests a preliminary list of possible causes for a pressure change in a flowing
system, depending on how quickly that change occurred.
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00002-6
35
© 2019 Elsevier Inc. All rights reserved.
36
2. Initial diagnosis and solution of flow assurance production problems in operations
The most common differential pressure increase or no flow during a restart of a shut-in
system can be caused by a hydrate formed after MEG supply failure, scale after water breakthrough, by a wax or asphaltene partial restriction cemented by a hydrate, a waxy gel, or by
a closed valve.
Other types of pressure behavior on a relative timescale with possible causes are described
below.
Restriction may be partial or complete. If there is pressure communication through a restriction, solvent should be injected if safe to do so, in order to retain the pressure communication.
Below is provided a short summary of the general characteristics of each type of flow assurance issues, deposits or flow restrictions. Additional characteristics of the flow assurance
problem may be obtained from deposits collected at a separator inlet screen, or from the
observation of system behavior. Some general characteristics listed below may be used to
confirm the possible cause.
Asphaltene—hard and dark in color, heavier than water. Occurs in both light and heavy
oils. Common locations are in reservoir, in well production tubing, at subsurface safety
valve, in tree and in flowline.
Bacterial deposit—can be a soft accumulation in pipe or process equipment, or a hard
biodome inside a line pipe. Typical location is in surface water processing equipment.
Corrosion products—usually nonmagnetic. Can occur in any part of the production
system from well bottomhole to export pipeline when a chemical is present which takes
TABLE 2.1 Types of pressure behavior on a relative timescale with possible causes
Type of differential
pressure change
Time of differential pressure change
Minutes to hours
Hours to days
Days to weeks
Weeks to months
Wax, liquid (water or
condensate) holdup
in long export line
Single increase
Mechanical, stuck
Scale, hydrate
scraper, closed valve, plugging a gas line
leak with seawater
ingress
Asphaltene, liquid
holdup in intrafield
line
Multistep increase
Hydrate plugs
forming in oil line
Multiple hydrate
plugs dissociating
Sand in intrafield
line
Single peak
Water hammer,
liquid surge
Injector well damage Waxy gel breaking
with relief
Multiple oscillations
Slugging, well liquid Severe or terrain
loading, choke PID
slugging
controller
Single decrease
Leak, hydrate plug
movement
Hydrate with wax
compaction
Hydrate forming in a Scale formation
shut line
damage
Multistep decrease
Controlled
depressurization
Single trough
Asphaltene
formation damage
with subsequent
relief downhole
Pressure buildup
from gas hydrate
deposit
Reservoir depletion
2. Initial diagnosis and solution of flow assurance production problems in operations
37
electrons from the production system wall material and dissolves it. Iron sulfide (black
powder) can be pyrophoric when exposed to air.
Diamondoids deposition (adamantane, diamantane, triamantane)—looks as a white
solid. Diamondoid deposits commonly occur in gas and gas condensate pipelines.
Emulsions are fluid but can be very viscous if stabilized by solids. Stability is caused by
asphaltenes, chemical inhibitors, mineral fines or waxes. Emulsions commonly occur
from wellbore to surface or topsides process equipment, but can also be present in
reservoir.
Erosion of pipes, pipe elbows or valves—caused by droplets and solids. Typically occurs at
locations where flow changes direction. Erosion corrosion can occur where a fluid flow at
high velocity strips away the protective film of corrosion product or inhibitor from a pipe
wall. Flow assurance solids such as hydrate can contribute to corrosion and to erosion.
Fines produced from reservoir accumulation in lines or process equipment—common
in weakly consolidated reservoirs such as deepwater Gulf or Mexico, South America
or West Africa. Usually mineral fines accumulate in locations where flow velocity is
insufficient to fluidize and carry the solids.
Flow-induced vibration or pulsation of flow line or jumper—caused by higher than
designed flow. Can occur in jumpers and locations where flow changes direction and
bracing is insufficient to keep the flow path rigid, usually above flow rates of 2 mbd/in.2
or 58 GPM/in.2.
Foaming—can be caused by high flow, shear, incompatible fluids, improperly mixed
chemicals. Can occur downhole, in flowlines or in process equipment.
Holdup of liquids in flow lines or in pipe lines—can be caused by flow velocity
insufficient to sweep liquids as in flow turndown scenario, or triggered by pressure
oscillations. Usually occurs in low spots and can cause terrain slugging.
Hydrate blockage—occurs in vertical, horizontal and inclined lines. Accumulates in
low spots. Occurs where five conditions are met: high pressure, low temperature,
presence of water (as liquid, vapor or ice), presence of hydrocarbon (gas or oil with
dissolved gas), and flow shear insufficient to sweep the solids. Hydrate is usually more
thermodynamically stable than ice and can form in LNG process equipment. Hydrate is
translucent and usually dissociates with bubbles when exposed to atmosphere.
Ice blockage—can occur in low-flow or dead leg line pipe. Also can happen downstream
of a flow restriction, or in flare relief lines when two streams, cold and moist, combine.
Injectivity damage for injector wells—caused by biofilm or unfiltered solids or high
dosage chemicals. Can occur over time as unfiltered solids accumulate in the injection
well perforations, or from a sudden flow rate change as solids settled in the water
injection pipeline get fluidized and transported downhole.
Joule-Thomson cooling or J-T heating of produced fluids—caused by thermodynamic
response of hydrocarbon fluid to pressure change. Saturated fluid below the bubble point
pressure experience J-T cooling upon pressure decrease. Undersaturated or supercritical
fluid experiences heating upon pressure decrease as in well flow.
Loading of wells with liquids during multiphase flow occurs when gas kinetic energy is
insufficient to overcome liquid gravity. Typically occurs when gas flow velocity is below
2 m/s or 7 ft/s but depends on interfacial entrainment of liquid by gas (related to surface
tension).
38
2. Initial diagnosis and solution of flow assurance production problems in operations
Mercury accumulation in flow lines, process equipment and product streams—occurs
where mercury or organomercury is not soluble in the produced stream, usually at low
temperature. Mercury is a shiny liquid. Organomercury is clear volatile liquid, strong
neurotoxin and easily penetrates some PPE such as latex gloves. Mercury compounds in
hydrocarbons commonly occur in continental rim areas.
Naphthenates deposition in flow lines and process equipment occurs when produced
fluids have both natural acids dissolved in oil and metals such as calcium dissolved in
water. Deposits are highly viscous.
Oil quality noncompliance due to water content—occurs in surface process equipment
due to insufficient residence time or insufficient temperature to resolve water-in-oil
emulsion.
Productivity damage for producer wells—occurs when solids or liquids adsorb on
rock surface and reduce the pores cross section area and permeability. Deposits may be
organic such as asphaltenes, heavy oil fractions and inorganic such as sand or scale. Flow
shear and pressure drop caused by higher flow velocity in the near-wellbore zone may
cause asphaltenes precipitation. Subsequent well workover with an acid may further
destabilize asphaltenes.
Sand deposition in lines, process equipment or valves. Sand can be produced from
wells where rock consolidation or cementing was lost, such as in wells ramped up
quickly, or wells which have experienced reverse flow (bullheading) through a gravelpack completion. Cementing of sand grains in near-wellbore zone can be lost during
production of gas hydrate deposits where hydrate was the cementing agent but
dissociated to recover natural gas. Also cementing can be lost in regular oil or gas wells
if a chemical which can dissolve water such as methanol or methanol-based chemical is
pumped to and stays in the perforations. Methanol dehydrates rock, and sand production
may start or productivity damage may occur.
Scale deposition and scale products accumulation in flow line and process equipment—
happens when temperature, pressure and composition of both produced hydrocarbons
and produced water are such that all mineral dissolved in water at reservoir conditions
cannot remain dissolved in water at wellbore, flowline or separator conditions. Seawater
injection can cause barite scale deposition. Barite has toxic barium ions but is nearly
insoluble in water so does not affect health. Barium carbonate scale is toxic and strontium
sulfate scale can be radioactive.
Slugging: severe (terrain-induced) and hydrodynamic (gas flow-induced)—results in
significant pressure oscillations and in impacts of liquid slugs at bends and process
equipment. Typically occurs in near-horizontal gas and gas condensate production
both onshore and subsea, and in horizontal-come-vertical flow geometries such as in
deepwater multiphase tiebacks and in shale horizontal well production. Terrain-induced
or severe slugging is caused by insufficient energy of gas to lift liquids from a low spot
such as riser base, similar to well liquid loading. Hydrodynamic slugging occurs during a
change in gas flowrate (usually ramp-up or increase) when gas at higher velocity sweeps
liquid from its steady-state holdup locations and brings the surge of liquid to a bend or to
an outlet. Slugging can occur with time period of minutes to days.
Souring of produced fluids can occur when water injected into the reservoir to maintain
reservoir pressure brings sulphates which is food for sulfate-reducing bacteria present in
2. Initial diagnosis and solution of flow assurance production problems in operations
39
the reservoir. SRB bacteria flourish in reservoir zone with temperature between 10 and
50 °C and generate sour chemicals. Seawater treated with desulfation has less impact
on souring. Usually it takes several years for sour components to migrate through the
reservoir to producer wells. Faster souring may occur if there is streaming from injector
to producer wells.
Stuck scraper during pipeline commissioning or during flow line maintenance—can
occur when the energy of fluid propelling the scraper (a piston) is insufficient to
overcome the viscosity or Young's modulus of material being scraped. Can also happen
when a scraper gets tilted in a valve cavity, in a wye or on a deposit or obstruction and
loses seal against pipe wall allowing propelling fluid to freely bypass it.
Sulfur deposition in well tubing or in flow line—occurs when solubility of elemental
sulfur S8 in produced fluid at reservoir conditions is higher than at well or flowline
conditions. Elemental sulfur is yellow, not transparent and in its solid form is not toxic.
Underdeposit corrosion generally occurs from neglect for regular maintenance cleaning
of the flowline during its operation, or from inability to clean the line if it was designed
without such ability. Deposits of sand, precipitated wax, asphaltene, scale and their
combinations occur where flow velocity is low, usually less than 1 m/s. Deposits prevent
corrosion inhibitor from reaching the pipe wall, or allow bacteria to grow depending on
conditions.
Viscous oil or viscous emulsion flow—usually occurs in wells where viscosity at reservoir
conditions exceeds 200 cP. Significant pressure drop reduces production from such wells
and may require artificial lift.
Wax deposition—can occur in subsea, deepwater and onshore fluids when flowing oil
or condensate cools below temperature of normal (straight chain) paraffin wax freezing
or crystallization. Wax appearance temperature depends on content of normal paraffins
and typically ranges from 10 to 50 °C. Wax is a soft pliable material. Typical wax melting
temperature ranges from room temperature (for a waxy gel) to over 80 °C (for a wax
deposit aged 2+ years).
Wax deposition from gas is less common than from oil but possible when reservoir
fluid and hydrocarbon condensate liquid contain normal paraffins heavier than C18.
Wax deposition requires both a heat loss and replenishment of waxy components to be
present, thus a wax deposit can only form during flow. Without flow, wax can precipitate
in the liquid but cannot be replenished. Without heat loss, wax cannot precipitate.
Water quality noncompliance due to organic content—occurs in topsides or surface
process equipment due to insufficient residence time or insufficient temperature to
resolve oil-in-water emulsion or due to high concentration of water-soluble organic
(negatively charged acid groups or aromatic) components which cannot be separated by
mechanical means and require water clarifier (reverse demulsifier) chemical and water
polisher (sorbent) filter. Offshore discharge of water with oil causes a sheen layer on
seawater with colors. Water with water-soluble organics causes a gray sheen. Either can
result in a noncompliance.
Each of the possible flow assurance issue causes needs to be evaluated to determine if the
production system entered the pressure-temperature-composition conditions for stability
of each cause. If samples are available for laboratory analysis, the sample identification
should be performed.
40
2. Initial diagnosis and solution of flow assurance production problems in operations
Field or laboratory tests for initial solid samples identification
Once a closed valve was ruled out as the possible cause of a suspected blockage,
the separator inlet strainer should be inspected for any accumulated solids. Solids carried by produced fluids to the separator may help understand what processes happen
upstream.
Field laboratory initial tests for solid samples identification
Solids can be analyzed to help identify a flow assurance problem and develop the best
solution. Although a specialized lab testing is preferred, a number of tests can be performed
in the field to analyze the solid deposit using readily available chemicals such as water, table
salt, diesel fuel, and simple instruments such as polarized sunglasses.
Field analysis
Very preliminary analysis may be performed in the field using just water if getting the
sample to the lab is prohibitively far or would take a long time.
Hydrate: use an inverted graduated transparent cylinder to measure the volume of gas
from a known volume of hydrate sample. Place a sample into the graduated cylinder
filled with water. Place the upside-down graduated cylinder containing sample into an
upright glass filled with water. If enough gas evolves from the sample to displace all
water from the cylinder, it is hydrate.
Wax: if the sample floats in water it is likely wax.
Viscosity: use a calibrated cup viscometer with a hole of a known diameter in the bottom
to measure time of sample outflow.
Asphaltene: check sample density. If the sample sinks in water it is likely asphaltene.
Laboratory analysis
Table 2.2 lists a number of simple tests which can be conducted in the field, ordered from
simple to more complex.
Any preliminary analysis information should be shared with the professional laboratory
along with the sample as the initial measurements on solids which rapidly dissociate or melt
can make a difference in the proper identification of the flow assurance issue.
Inspired by The total systems approach process, Baker Hughes Inc., 2013.
Note: As sample can release a poisonous vapor, all tests must be done in a vent hood!
If a partial solid residue remains during any test it may be filtered, weighed and subjected
to additional tests.
100 °C temperature was selected for ease of obtaining this temperature in the field conditions using boiling water (at sea level); at elevation the water will boil at a lower temperature,
but the test results will remain valid.
CPM (cross-polarized microscope) is useful for analysis of paraffin wax and other
solids.
TABLE 2.2 Simple tests to help identify a solid
Ice
White
Stable
Hydrate
White
Diamondoid
Place in
xylene or
toluene
0.86 mg/L
Place in 11%
HCl acid
1.05 mg/L
Place in
15 wt% NaCl
1.12 mg/L
See in CPM
Falls
Falls
Floats,
dissolve
Floats,
dissolve
Light
Melts with Floats, active
gas bubbles release of gas
bubbles
Falls, releases
gas bubbles
Falls, releases
gas bubbles
Floats,
dissolve with
gas bubbles
Floats,
dissolve with
gas bubbles
No light
White
Stable
Sublimate
Dissolve
Dissolve
Paraffin wax
White, brown,
black
Stable
Floats, dissolve Falls, slowly
dissolve
Falls, dissolve
Halite Scale
White
Stable
Falls, solid
Solid
Solid
Carbonate Scale
White, brown
Stable
Falls, solid
Falls
Falls
Dissolve with
gas bubbles
Falls
Barium Sulfate scale
White, brown
Stable
Falls, solid
Falls
Falls
Falls
Falls
No light
Calcium Sulfate
scale
White, brown
Stable
Falls, solid
Falls
Falls
Slowly
dissolve
Falls
No light
Iron sulfide
Black
Heats or
ignites
Falls, solid
Falls
Falls
Dissolve,
releases H2S
Falls
No light
Naphthenate
Brown, white
Stable
Stable
Falls
Floats
Floats
No light
Corrosion products
Brown
Stable
Falls, solid
Falls
Falls
Falls, dissolve
Falls
No light
Asphaltene
Black, glossy
Stable
Falls, solid
Falls
Falls, dissolve
Falls
Falls
No light
350 °C coked
asphaltene
Black
Stable
Falls, solid
Falls
Falls
Falls
Falls
Light
Sand
Brown
Stable
Falls, solid
Falls
Falls
Falls
Falls
No light
Floats, melt
with little or
no gas release
Floats
Floats
Floats
Light
Slowly
dissolve
Field or laboratory tests for initial solid samples identification
Color
Expose to
air
Place in
Heat to 100 °C/ kerosene
place in
or diesel
boiling water 0.82 mg/L
41
42
2. Initial diagnosis and solution of flow assurance production problems in operations
In absence of a proper laboratory CPM, a field-grade cross-polarized microscopy may be
performed using two polarizer camera filters or two pairs of polarized eyeglasses. A thin
sample of solid (such as wax) is placed between the two polarizers, and polarizers are turned
relative to each other until no visible light passes through the assembly. Some crystals such
as wax or ice can rotate the plane of light polarization, which can be observed in CPM as
light passing through the crossed polarizers. A light shining through the sample in a CPM
helps tell whether this flow assurance sample is one of the deposits which can rotate light
polarization.
Typical blockage remediation plan
1. Gather system knowledge: fluids, samples, profile, insulation, internal and ambient
conditions
identify possible incompatibilities (wet gas + cold T, methanol + brine, LDHI + CI,
etc.) in system
identify probable locations (T < T_solid, jumpers/low spots, riser base, chokes), model
pressure
identify line MAOP (take into account design corrosion rates, performed inspections)
2. Review remediation plan: SMEs, services, logistics (access points, deck space, vessels)
clarify blockage(s′) properties (dP1-dP2, permeability, consistency)
how to reverse cause (P↓, T↑, flow back, solvent), possibility of transient movement
check accessibility w.r.t different remediation technologies, availability of vendors,
regional HSE
3. Organize: Asset Operations Manager in charge, specialists and services in support
designate accountabilities, appoint Project Manager
state primary and additional objectives, metrics; contracts and service agreements
4. Plan the Actions being honest about time and budget:
allow 2× time for every “if” (e.g., if permeable plug, if sea is calm, if through gaslift)
assess economics for each route
pick one with least uncertainty (ifs), then best economics
line up and inform your picked solvent or technology vendor(s)
5. Execute the plan:
interface management is key; Project Manager to keep vendors informed of status/
plan
simultaneous operations may affect timing—plan ahead
enforce time limit for execution based on asset value
6. Learn:
record blockage frequency, downtime, record what worked/didn't work
new designs to increase NPV reducing downtime by accommodating remediation plan
update remediation plans for this and other assets: who you're gonna call?
Key suggestions: Be prepared for a blockage, understand your system and resources.
C H A P T E R
3
PVT and rheology investigation
O U T L I N E
Phase behavior
Fluid characterization
Viscosity
Lumping for different fluids
Solid-liquid equilibrium
Additional laboratory studies
PVT tuning
43
Fluid sampling
44
Onshore vs deepwater
44
Special considerations for H2S samples 44
Special considerations for mercury samples 44
Sampling hydrocarbon fluid
45
Quality of fluid samples
Oil sample quality checks
Hydrocarbon fluid sample quality checks
Water sample quality checks
45
45
45
50
Drilling and wellwork fluids formulation
and safety
51
Fluid characterization
Fluid properties and measurements
51
51
52
56
56
57
59
60
Fluid physical properties
61
Non-Newtonian behavior
63
Emulsion characteristics
64
Biodegradation
65
References
65
Further reading
66
This chapter is at the beginning of the book because thermodynamic fluid characterization
also known as PVT represents the third most important characteristic of petroleum production after reservoir characterization and well drilling, and the most important one for flow
assurance and for production chemistry. Good understanding of fluid properties allows a
flow assurance engineer to develop a technically feasible and economically optimal set of
strategies to overcome a variety of problems listed in the first two chapters.
Phase behavior
Flow assurance analyzes the flow of fluids and associated solids at a range of pressure and
temperature conditions. Properties of fluids vary with both temperature and pressure.
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00003-8
43
© 2019 Elsevier Inc. All rights reserved.
44
3. PVT and rheology investigation
Pressure
Undersaturated
Liquid
Reservoir
Early Life
Dense Phase
Wellhead
Early Life
Reservoir
Late Life
Vapor +
Saturated Liquid
Separator Separator
Late Life Early Life
Vapor
Wellhead
Late Life
Temperature
FIG. 3.1 Fluid behavior shown on a phase diagram versus time and location in the production system.
A phase diagram in Fig. 3.1 helps illustrate fluid phases which are stable at different temperatures and pressures. A simple vapor-liquid equilibrium or VLE phase diagram is usually
plotted in two dimensions on the scales of pressure and temperature, and illustrates just two
phases, liquid and gas.
Fluid sampling
Onshore vs deepwater
Majority of onshore fluid samples are collected at the surface. Sampling conditions at the
test separator should always be recorded.
Deepwater exploration fluid samples are normally collected downhole to preserve the
fluid phase state.
A number of special containers are used for sampling such as MPSR, etc.
Special considerations for H2S samples
Containers for H2S collection should have internal lining which prevents H2S adsorption
on steel. Without such lining the H2S molecules adsorb on container walls and subsequent
sample analysis may show little or no H2S present in the fluid whereas in the reservoir H2S
would be in greater quantity.
Special considerations for mercury samples
Sample containers for fluids which may contain mercury should also be specially prepared.
Mercury similarly may adsorb on container walls making the fluid sample not representative.
A good summary of sampling techniques and in situ analysis is provided by Fiotodimitraki
(2016).
Quality of fluid samples
45
Laboratories for the sample collection should be validated, and personnel involved in actual sampling should be aware of the proper well flow duration requirements before the
sampling takes place, to ensure that the sample is not contaminated with drilling mud and
that sample itself is uniform and representative of the reservoir fluid.
Sampling hydrocarbon fluid
API Recommended Practice 44 provides detailed recommendations on how to conduct the
sampling for typical hydrocarbon fluids. Sampling specialists and laboratories would have
additional procedures on how to properly collect and transport samples of fluids which may
contain small amounts of hydrogen sulfide or mercury.
Information whether a sampling program should have provisions for H2S or mercury may
be obtained from regional analog fluids, from the analysis of samples collected earlier in the
same region about which published information is available or from geologic analysis which
provides indications whether similar rock structures may contain certain minerals which get
dissolved by the reservoir fluid.
Quality of fluid samples
Quality of the samples is of the most critical importance to the preconcept and concept
evaluation phases of a project when the technical feasibility of developing an asset is evaluated. A flow assurance specialist should be able to use a few simple quality checks to find the
most representative samples or to compensate for sample contamination.
Oil sample quality checks
Collecting a surface sample from a separator onshore is much simpler than collecting a
downhole sample from an openhole wellbore in deepwater. Thus a close attention must be
paid to quality checks of the samples collected downhole.
Several initial checks are described below. These checks omit the sampling process and
conditions, container preparation and sample transfer and instead focus on the measured
properties control which allows the flow assurance specialist to review data in the laboratory
reports for the factors which can affect flow assurance work.
Hydrocarbon fluid sample quality checks
1. Check for GOR range
GOR of the samples collected from similar depths of the same reservoir should be fairly
constant, within a few hundred scf/stb. If GOR of some of the samples differs significantly
from the rest, particularly if GOR is lower than the average, it may indicate that some of the
gas was lost during downhole sample collection or transfer.
In this case the reservoir fluid sample composition should be checked for methane
content.
46
3. PVT and rheology investigation
If the low GOR sample shows methane content relatively lower than in other samples, this
may indicate gas loss during sample recovery to surface. Usually the low quality samples are
not used. However, if very few samples are available, it may be possible to offset the loss of
gas which could occur during or after sampling and see if GOR may be matched by adding
methane back to the composition.
Conversely, if GOR of a downhole sample is significantly higher than the rest of the samples, it may indicate gas coning and intake at the sampling depth. This may happen in saturated reservoirs where a gas cap is present or pressure is at or below the bubble point, and
should not be the case in reservoirs with undersaturated fluid or dense phase. If GOR of one
of the samples is higher than the average, the sample may have been collected near a gas cap
if reservoir is saturated and free gas exists.
An example of a GOR check is shown below.
Fluid A-1 from 3050 m depth in well A has a GOR of 800 scf/stb, fluid B-2 from 3060 m in
well B has a GOR of 810 scf/stb. Fluid B-1 from 3055 m in well B has a GOR of 600 scf/stb.
It is possible that the sample container B-1 lost some gas during sample transfer from well
bottomhole to the lab. Laboratories record and report the pressure which the beneficiated
sample exhibited at opening of the container to verify whether pressure is similar to the other
containers and if any part of the sample may have been lost.
2. Check for drilling mud contamination
Oil based drilling muds typically are formulated with diesel fuel, kerosene or another
available fraction of hydrocarbons. This hydrocarbon base of the mud would usually have
increased content of hydrocarbons in the range between C16 and C20. Some synthetic muds
can be formulated to have only even-numbered paraffins such as C16 and C18 dominate the
composition. The presence of these paraffins can be noticed in gas chromatography analysis as an increased content relative to the composition of all paraffins on a logarithmic plot.
These components are not expected to be present at the increased content in a reservoir
fluid and can affect its properties. Additional steps are required to de-contaminate the
sample or to find the sample with the least drilling mud contamination. Contamination
level with a drilling mud below 1–2 wt% is considered acceptable for a PVT analysis.
An example of a mud contamination check is shown below.
Log10 plot of a GC analysis of sample A-1 composition in Fig. 3.2 shows a linear trend of
C10+ component mass percent versus carbon number.
Log10 of A-1 component mass %
0.6
0.5
0.4
0.3
0.2
0.1
0
C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35
FIG. 3.2 Example of a fluid with little to no contamination with oil-based drilling mud.
47
Quality of fluid samples
Log10 of A-2 component mass %
0.6
0.5
0.4
0.3
0.2
0.1
0
C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35
FIG. 3.3 Example of a fluid with some contamination with oil-based drilling mud seen as peaks at C16 and C18.
Note that mud carbon numbers may vary such as C14 and C16 or C18 and C20, etc.
Log10 plot of a GC analysis of sample A-2 in Fig. 3.3 has two significant deviations from a
linear trend at carbon numbers C16 and C18.
It is known that the wells were drilled with an oil-based mud.
The sample A-2 is likely contaminated with hydrocarbon components from the drilling mud.
This is important for reservoir modeling because PVT properties of a sample contaminated
with drilling mud would differ from the properties of the reservoir fluid.
This is also important for flow assurance because components C16 and C18 would affect
solubility of wax components C18 and C20, so prediction of wax deposition using data from a
contaminated sample would be less accurate.
For the purpose of wax deposition analysis it is possible to remove the artificially introduced parts of the components from the composition analysis to get a better prediction of
wax deposition from a decontaminated sample.
However, reservoir modeling requires a more thorough process of removing the oil-based
mud contamination and tuning the fluid properties.
3. Quality of PVT analysis can be examined by checking material balance of components in
the Differential Liberation or multistage separation tests for oil-dominated fluids or in the
constant volume depletion for gas condensates and volatile oils
Amounts of mass or moles of individual components from separated gas and liquid should
add up to the amounts in the original sample.
Also a mass balance or mole balance check may also be used to verify that measured oil
density and calculated gas density are consistent with the measured GOR.
An example of a material balance check for a typical PVT report is shown below.
Usual reservoir fluid composition as in Table 3.1 and PVT summary provides mole percentages for an oil sample from a differential liberation test.
TABLE 3.1 Example fluid composition as a reservoir fluid, liquid and gas
Reservoir fluid
Liquid
Gas
Symbol
Component
Name
Mole %
Mole %
Mole %
N2
Nitrogen
0.41
0.00
0.69
CO2
Carbon dioxide
0.29
0.01
0.48
(Continued)
48
3. PVT and rheology investigation
Component
Reservoir fluid
Liquid
Gas
Mole %
Mole %
Symbol
Name
Mole %
C1
Methane
41.53
0.25
69.99
C2
Ethane
5.40
0.29
8.92
C3
Propane
6.60
1.32
10.24
iC4
i-Butane
1.31
0.59
1.80
nC4
n-Butane
3.38
2.13
4.24
iC5
i-Pentane
1.35
1.59
1.18
nC5
n-Pentane
1.68
2.32
1.23
iC6
i-Hexanes
3.04
6.20
0.86
C7+
Heptanes +
35.00
85.31
0.36
Gas-oil ratio
876
scf/stb
Gas gravity
0.874
(Air = 1.00)
Gas MW
25.2
g/mol
Oil density
884
kg/m3
Oil MW
194.9
g/mol
28.5
°API
TABLE 3.2 Quality check example
x/z
y/z
C1
0.00602
1.685288
C2
0.053704
1.651852
C3
0.2
1.551515
iC4
0.450382
1.374046
nC4
0.630178
1.254438
iC5
1.177778
0.874074
nC5
1.380952
0.732143
Component mole % in liquid relative to % in total fluid, and mole % in vapor relative to % in total fluid.
From the PVT report we can prepare a table as in Table 3.2 of vapor Y relative to reservoir
fluid Z and of liquid X relative to reservoir fluid Z components.
The plot of the vapor (y/z) vs liquid (x/z) in Fig. 3.4 should be close to linear if sampling
in the well, sample beneficiation in the lab, and the lab tests were all performed correctly. If
there are significant deviations, particularly in the light hydrocarbons, this may indicate a
low quality sample and possible loss of light ends, if there is too little methane, or sampling
of only gas if there is too much methane. In such case the history of sample collection should
be reviewed to see if sufficient time was allowed for a well flow before sample collection (also
called conditioning a well).
49
Quality of fluid samples
Material Balance Plot for C1-C5
components mole % in vapor vs in
liquid. Slope ~1/GOR
1.8
1.6
1.4
y/z
1.2
1
0.8
y = -0.6926x + 1.6891
0.6
0.4
0.2
0
0
0.5
1
1.5
x/z
FIG. 3.4
Material balance plot for methane to pentane. Abscissa shows mole % ratio from Table 3.2 of each component in liquid. Ordinate shows mole % ratio from Table 3.2 of each component in vapor.
Linearity of the plot confirms that the sample quality is good and it can be used for flow
assurance analysis.
It is also possible to verify the gas oil ratio measured in the lab using information from the
plot. A linear curve fit for the plot provides a slope. This slope is a ratio between vapor components and liquid components. The slope is inversely proportional to the GOR, which can
be estimated using the following equations. Units of each parameter are presented for clarity.
GOR ( scf / stb ) = 0.159 ( m 3 / bbl ) 35.3 ( scf / m3 ) Volumetric gas ratio ( m 3 gas / m 3 oil )
∗
∗
Volumetric gas ratio ( m 3 gas / m 3 oil ) = Molar vapor ratio ( mol gas / mol oil )
∗
Gas molar volume ( L gas / mol gas ) / Oil molar volume ( L oil / mol oil )
Molar vapor ratio ( mol gas / mol oil ) = −1 / slope
Gas molar volume ( L gas / mol gas ) = Gas MW ( g gas / mol gas ) / Gas density ( g gas / L gas )
Oil molar volume ( L oil / mol oil ) = Oil MW ( g oil / mol oil ) / Oil density ( g oil / L oil )
Gas density ( g gas / L gas ) = Gas gravity ( ( g gas / L gas ) / ( g Air / L air ) ) ∗11.225 ( g Air / L Air )
Oil density ( g oil / L oil ) = 141.5 / ( Oil API° + 131.5 ) ∗ 1000
Calculation of GOR is provided below:
Slope = −0.692
Molar vapor ratio = −1 / −0.692 = 1.445 ( mol gas / mol oil )
50
3. PVT and rheology investigation
Gas molar volume = 25.2 / ( 0.874∗1.225 ) = 23.5 ( L gas / mol gas )
Oil molar volume = 194.9 / ( 141.5 / ( 28.5 + 131.5 ) ∗ 1000 ) = 0.220 ( L oil / mol oil )
Volumetric gas ratio = 1.445∗ 23.5 / 0.220 = 154.3 ( m 3 gas / m 3 oil )
GOR = 0.159∗ 35.3∗ 154.3 = 866 ( scf / STB ) .
The value of GOR estimated from the material balance is in fair agreement with the
­reported value of 876 scf/STB. This also confirms quality of the sample.
Water sample quality checks
The quality of the water sample is important for various production chemistry analyses.
The following initial quality checks may be done by a specialist to verify sample data.
1. Ionic balance
Ionic balance is the similarity of the combined weight of positive ions and the combined
weight of negative ions. Ionic balance indicates that sampling and lab analysis of the water
was performed correctly.
2. Drilling mud contamination
Most modern deepwater wells are drilled using an oil-based drilling mud, which keeps
water emulsified. This limits the exposure of water-sensitive rock such as water-swelling
clays to water, and also limits the exposure of the sample water to the mud water.
Most non-deepwater wells are drilled using a simpler water-based drilling mud.
If a water based drilling mud was used, brines used to weigh the mud could contact and
contaminate the downhole water sample with ions such as sulfate which originates from seawater carrier for salt, and with barite from salts which do make the mud heavy.
Typical reservoir water would have sulfate SO42− under 200 mg/L because sulfate SO42−
ions convert to sulfide S2− and precipitate as iron sulfide FeS, zinc sulfide ZnS or other minerals in reservoir over geologic times. Seawater would typically have around 2600 mg/L SO42−.
Any reservoir water with SO42− greater than 200 mg/L may be contaminated with water from
the drilling mud. The reservoir water samples with the lowest SO42− concentration should be
selected for further analysis.
3. Other salts
The following salts may be used to weigh the mud:
calcium chloride CaCl2
calcium bromide CaBr2
zinc bromide ZnBr
potassium formate KHCO2
cesium formate CsHCO2 for HPHT wells and reservoirs
Scale saturation index may be used to check water sample quality. Downhole samples with
scale saturation index below zero or saturation ratio below one calculated at reservoir conditions should be used as this indicates that water sample is not oversaturated with minerals.
The saturation index is calculated using any of the available scale prediction methods.
Bicarbonate HCO3 concentration will decrease after sampling due to HCO3 conversion to
carbonic acid H2CO3 and to CO2 and evolution of CO2.
Fluid characterization
51
Extreme cases
In rare cases the bicarbonate concentration may reach nearly 10,000 mg/L in some reservoirs which have high CO2 content. This indicates that reservoir water is saturated with CO2.
Reservoir water chemistry may change if seawater is introduced. CO2 will dissolve in seawater lowering its pH and making it acidic. Acidic seawater can dissolve carbonate minerals in
the reservoir and as pressure drops in or near the wellbore, dissolved minerals can precipitate
out of water solution causing solid scale deposition.
Drilling and wellwork fluids formulation and safety
Salts make the drilling muds and completion or wellwork fluids heavy in order to use hydrostatic pressure of the mud to counteract the potentially high pressure of reservoir fluids.
Overbalanced and underbalanced drilling are not in the scope of this work. Salts also help
control hydrate formation which can plug flow paths and stop circulation during wellwork.
All reservoirs differ in their many parameters. The two parameters we review in this section are rock consolidation and pressure.
Consolidation defines how strong is the rock and how much pressure it takes to fracture it.
Consolidation of mudstone or sandstone may be weak.
Pressure in some known reservoirs can be very high, up to 29,000 psi or almost 2000 bar.
When well and reservoir pressure dictate the need to prevent hydrate formation yet the
consolidation of the reservoir rock is weak, then the use of salt may create a wellwork fluid
which is too heavy and could lead to an uncontrolled fracture of the weakly consolidated
rock. In extreme cases this is manifested as hydrocarbon seeps at seabed around the wellbore.
To avoid such events, the wellwork fluid has to be formulated with both salts and other hydrate inhibitors to maintain both the desired mud weight and the hydrate inhibiting properties. A specialized series of lab measurements at up to 30,000 psi (2000 bar) were completed at
the Colorado School of Mines (Hu et al., 2017a,b) which provide hydrate stability conditions
with a variety of salts and inhibitors commonly used in wellwork fluids.
Fluid characterization
After the sample quality is verified, a flow assurance specialist can use the PVT report information to characterize the fluid for predictive use with an equation of state.
The objective for the fluid characterization process is to find the parameters for the selected
equation of state which will accurately predict properties of vapor, liquid and undersaturated
fluid phases along the range of temperature and pressure of interest for the subsequent multiphase flow assurance analysis. Key predicted parameters which must match the laboratory
measurements closely include density, saturation pressure, gas oil ratio and viscosity.
Fluid properties and measurements
Selection of the equation of state most appropriate for fluid characterization would determine the accuracy of fluid properties calculation. Equations of state are cubic equations
relating pressure (P), volume (V) via compressibility (Z) and temperature (T) in a mixture of
52
3. PVT and rheology investigation
components as a function of energy of interaction between components (A) and of molecular
size (B).
Peng Robinson or PR EOS and its updated versions PR78, PR78 Peneloux work more accurately with liquid-dominated systems and are equally as good for gas systems. Most hydrocarbon reservoir fluids are at present characterized using the PR78 EOS with the density
correction developed by Peneloux and coauthors in Peneloux et al. (1982).
Soave Redlich Kwong or SRK EOS works well for gas dominated fluids because the
Soave variant of the Redlich Kwong EOS can underpredict liquid compressibility by 10–20%
whereas the PR EOS predicts liquid compressibility a little better.
Polynomial form of P-R E.O.S. is
Z 3 + ( B − 1) Z 2 + ( A − 3B2 − 2B ) Z + ( B3 + B2 − AB ) = 0
(
A = 0.45724α Pr / Tr2
α = 1 + ( 0.37464 + 1.54226ω − 0.26992ω 2 ) ( −1Tr0.5 )
B=
)
2
P
bP
= 0.07780 r
RT
Tr
P
Pr =
Pc
T
Tr =
Tc
Values of acentric factor w, critical pressure and temperature Tc and Pc are known for each
component. EOS calculates compressibilities of vapor and liquid for a given pressure and
temperature.
Fluids with high CO2 or other polar or associating components content may be modeled
with specialty variants of the equations of state.
Recent equations of state CPA (cubic plus association) and SAFT (self associating fluid theory) include an additional parameter of association between molecules. These methods are
useful for polar components such as water, CO2, aromatics and asphaltenes.
Other more complex equations of state are seldom used because a fully compositional
model requires fast calculation of fluid properties, and the main demand for fluid properties
is in reservoir simulation.
Fluid characterization used for reservoir simulation is then usually transferred for further
fluid analysis in flow assurance and in production chemistry in order to assure flow in the
multiphase production system and surface process facilities.
Fluid characterization
Sometimes the composition analysis data are limited and reported in a form of true boiling
point analysis of volume % hydrocarbon vs temperature, with density data for the fractions
unavailable.
In order to model such fluid with EOS, it has to be converted from volume % to mass %
distribution for hydrocarbon fractions.
53
Fluid characterization
Group contribution method (Joback and Reid, 1987) may be used to estimate boiling point
of a one specific hydrocarbon molecule.
However, this method would require estimating properties for hundreds of hydrocarbon
molecules to find boiling point cuts which would introduce inaccuracy by developing a correlation from a correlation.
Katz and Firoozabadi (1978) report boiling points for up to C45 and interaction coefficients
for n-C4 and heavier for use with Peng-Robinson-AGA procedure to find fluid properties.
This method was adopted by Pedersen (Pedersen, 1989) to correlate Tb with MW and SG.
Correlation is used up to C45, then adds 6K for each carbon number.
Tb  ° R  = 97.58 MW ^ 0.3323 SG ^ 0.04609
However, this method does not provide a formula directly usable by an engineer to correlate carbon number with boiling point as it requires density of each fraction.
An additional correlation was developed here based on 188 hydrocarbons including n-­alkanes,
isoalkanes and aromatics which relates carbon number to boiling point, applicable to C5+.
Tb [ K ] = 240.71∗ LN ( carbon # ) − 90.5, for C 5 +
Boiling temperatures [K] for C1–C4 are 111.15, 180.82, 236.75, 276.15.
This formula may be used when composition analysis is reported in a form of true boiling
point analysis of volume % hydrocarbon vs temperature.
Conversion of TBP data from volume to weight fractions facilitates the further fluid characterization by permitting conversion of boiling point to carbon number.
Inverse form of the correlation shown in Fig. 3.5 is:
carbon # = 1.455 exp ( Tb [ K ] / 240.69 ) , for C 5 +
or
(
)
carbon # = exp ( Tb [ K ] + 90.5 ) / 240.69 .
1000
y = 240.69ln(x) - 90.295
R² = 0.969
Boiling Temperature, K
900
800
700
600
500
400
300
200
100
0
1
10
100
Carbon Number
FIG. 3.5 Correlation of boiling temperature versus carbon number for pentane and heavier hydrocarbons.
54
Correlation Boiling Temperature, K
3. PVT and rheology investigation
1200
1000
800
600
400
200
0
0
200
400
600
800
1000
Data Boiling Temperature, K
1200
FIG. 3.6 Comparison of boiling temperature from correlation vs from data.
The correlation performs fairly well, within ±20% error vs data as shown in Fig. 3.6.
Density can be related to carbon number either by method of Whitson and Brule (2000) or
Pedersen (1989).
Additional correlation in Fig. 3.7 for 115 n-alkanes, isoalkanes and aromatics is proposed,
applicable to C5+:
SG at 20° C  = 0.0661∗ Ln ( carbon # ) + 0.59 for C5 +
Specific gravities for C3–C4 are 0.504, 0.63.
Inverse form of the correlation is:
or
(
)
carbon # = exp 15.129 SG at 20° C  / 7501, for C5 +
((
)
carbon # = exp SG at 20° C  − 0.59 / 0.0661
)
1.2
Density at 20°C, g/cm3
1
0.8
0.6
0.4
0.2
0
0
10
20
30
40
Carbon Number
FIG. 3.7 Correlation for hydrocarbon density vs carbon number.
50
60
55
Fluid characterization
Correlation Density at 20°C, g/cm3
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Data Density at 20°C, g/cm3
1.2
FIG. 3.8 Comparison of hydrocarbon density from correlation vs from data.
The correlation performs fairly well for paraffins and overall reasonably, within ±20% error vs data, except for heavy components such as fused polyaromatics like naphthalene, anthracene, or pyrene as shown in Fig. 3.8.
Combining the two equations,
(
((
)
)
exp ( Tb [ K ] + 90.5 ) / 240.69 = exp SG at 20° C  − 0.59 / 0.0661
or
)
( Tb [ K ] + 90.5 ) / 240.69 = ( SG at 20 C  − 0.59 ) / 0.0661
°
we get a simplified relationship between specific gravity at 20 °C and boiling temperature
of a hydrocarbon fraction at 1 atm, for C5+ or Tb > 309 K.
SG at 20° C  = 0.615 + Tb [ K ] / 3642 for C5 + or Tb > 309K
Once the specific gravity information is derived from the True Boiling Point analysis, the
critical properties for the Equation of State may be estimated by method of Riazi and Daubert
(1980)
Tc  ° R  = 24.2787 Tb  ° R 
0.58848
Pc [ psia ] = 3122810000Tb  ° R 
∗ SG  at 60° F 
−2.3125
0.3596
∗ SG at 60° F 
2.3201
Molecular weight may be estimated from SG using Pedersen (1989).
MW = 14∗ carbon number − 4
56
3. PVT and rheology investigation
Viscosity
A number of correlations exist for dead oil viscosity as function of temperature and density.
A summary overview of these correlations is provided in Bergman and Sutton (2007). Based
on over 9000 viscosity measurements from over 3000 oil samples, they proposed a correlation:
(
)
Viscosity [ cP ] = exp exp ( 22.33 − 0.194 ∗ ρ + 0.00033 ∗ ρ 2 − ( 3.2 − 0.0185 ∗ ρ ) ∗ Ln ( TLM + 310 ) ) − 1
ρ = density, [API°], TLM = log-mean temperature [°F] for fluid between inlet and outlet.
TLM = exp(average(Ln(TINLET),Ln(TOUTLET))).
A simplified correlation is proposed here for stock tank oil viscosity at 60 °F for initial estimates, based on their correlation. Measured data should be used when available.
(
)
STO Viscosity [ cP ] = exp 194.3 / ρ  API°  / 27.47
Pseudocomponents and lumping
In order to speed up the compositional analysis reservoir simulation specialists lump multiple components together. For example, components C12 through C15 may be lumped into
a single pseudo-component C12–C15, etc. Properties of such pseudocomponents including
critical temperature, critical pressure, acentric factor, molecular weight, boiling temperature
etc. are calculated using the EOS tuning process. In early days of computer application for
reservoir simulation as few as three or four components were used, as C1–C2, C3–C6 and C7+
in order to accelerate the vapor liquid equilibrium computation. Today using 15 pure components and 10 pseudocomponents is not uncommon. When two or more zones produce into
the same well tubing, each zone gets characterized with a different set of pseudocomponents.
This progressively increases the number of pseudocomponents and decreases the speed and
accuracy of fluid property prediction. Typically five or more pseudocomponents, in addition to pure components (from C1 to C7) provide adequate ability to characterize a hydrocarbon fluid while maintaining reasonable computation speed. Usually software optimizes the
lumping and pseudocomponent selection automatically, but this can be changed if necessary.
Lumping for different fluids
It is preferred to have the same set of pseudocomponents for all fluids. Dedicated PVT
tools which are used for fluid characterization for reservoir simulation have the capability to
lump and tune different but similar fluids using the same set of pseudocomponents, which
is preferred because it improves accuracy of blended fluid properties and improves computation speed.
The accuracy of fluid behavior prediction improves substantially if the binary interaction
parameters or kij are also supplied along with the properties of pseudocomponents and entered in the PVT simulation software. The binary interaction parameters are the additional
adjustable coefficients in the equations of state which allow a more accurate prediction of
fluid properties in multi-component mixtures.
Flow assurance specialists usually receive fluid characterization information from the reservoir engineers who used the fluid properties to model the multiphase flow in the reservoir. The range of temperatures of interest to reservoir engineers is usually different from
that of the flow assurance engineers. While XHPHT or extra high pressure high temperature
57
Fluid characterization
r­eservoirs may be as warm as 350–400 °F, the flow assurance systems may be exposed to
temperatures as low as 0°C to −40°C in Arctic onshore or subsea environments. Typical deepwater temperature is near +4 °C or 40 °F, and the fluid characterization developed for the reservoir engineers may predict fluid properties accurately at high temperatures, but noticeably
less accurately at lower temperatures.
Fluid characterization should be done with both temperature ranges in mind so that the
same parameters of the equation of state could apply to fluid property prediction by both
reservoir and flow assurance disciplines.
It is advisable to keep the same characterization of the fluid as the one used for reservoir
analysis even if there are some inconsistencies in the VLE or other properties of the fluids
at a different conditions, in order to maintain consistency of the project analysis. However,
if the discrepancy is very significant and the flow assurance results would be significantly
improved with more accurate fluid properties, the fluid may need to be re-characterized for
flow assurance analysis using the laboratory data from the PVT report. The degree of discrepancy is to be determined by each individual project.
Solid-liquid equilibrium
Flow assurance and production chemistry add a number of other liquid and solid phases
to the diagram such as water, sand, hydrate, asphaltene, scale. The graph below illustrates
a diagram where various phases coexist. Each phase has a label on the side of the boundary
curve where the phase or a phenomenon appears, for example ice is on the colder side of the
ice phase boundary.
A flow assurance specialist or a production chemist could use the phase diagram in Fig. 3.9
like a map in order to get reservoir fluids efficiently from point A (well perforations) to point
B (the separator). Fluid temperature is shown as increasing from reservoir past the wellhead
and to the phase envelope to illustrate that in dense phase fluids Joule-Thompson effect causes
Pressure
Reservoir
Early Life
Wellhead
Early Life
Reservoir
Late Life
Separator Separator
Late Life Early Life
Wellhead
Late Life
Temperature
FIG. 3.9 Phase diagram for various flow assurance issues. Fluid behavior and solid phases appearance are shown
on a phase diagram versus time and location in the production system. Each phase is expected to appear on the
labeled side of the curve.
58
3. PVT and rheology investigation
heating. This effect can cause a hot reservoir fluid become even hotter during production and
has to be taken into account for material selection and well design. In late life reservoir pressure
declines but reservoir temperature remains the same so additional phases may become stable
or unstable.
Several solid phases can be present simultaneously if there are both sufficient fluid and
appropriate conditions present to form those solids.
Solids usually form from liquids by crystallization or by amorphous freezing. Examples
of crystals are hydrate, ice, paraffin wax. Examples of amorphous solids are asphaltenes and
some forms of wax and naphthenates. Scales are also crystals.
In some cases petroleum solids can form from the gas phase such as diamondoids composed
of adamantane, diamantane and heavier molecules. Diamondoids are also crystals and they
photoluminesce (Clay et al., 2011) which may help identify them among other petroleum solids.
Naphthenates are liquid crystals or micelles (Havre, 2002). Naphthenates have complex
and little studied phase diagrams, and also can form amorphous solid films (Magnusson and
Sjöblom, 2008).
Two structures of hydrate commonly occurring in production operations are shown in
the figure above to illustrate that when water is abundant for a hydrate to form, the propane
and heavier components will be depleted first to form structure II hydrate, and if pressure
is still sufficient to form more hydrate, the lean gas can keep forming structure I. This can
happen when the number of moles of water is approximately six or more times greater than
the combined number of moles of light hydrate forming hydrocarbons such as methane, ethane and propane. Similarly, if all gas is consumed into an exothermic hydrate and water is
still present, ice can form if temperature is below freezing. Thermodynamically hydrate is
more stable than ice at higher pressure because pressure helps water molecules in hydrate
stay connected at higher temperatures, whereas in ice pressure distorts the crystal. However,
kinetically ice forms faster than hydrate because it takes several types of molecules to get
organized in order to form a hydrate crystal, while ice crystal forms with just water. Thus in
an LNG process ice can form together with hydrate from an off-spec stream of hydrocarbon
with a sufficient moisture content. Furthermore, in colder arctic environments hydrate can
be dissociated by pressure reduction, while ice cannot if ambient temperature is below 0 °C.
Depressurization is endothermic or consuming heat and should be done with care if ambient
temperature is below freezing as hydrate upon dissociation releases mainly pure water. If
fresh water released from dissociated hydrate converts into an ice blockage one would need
to wait for the summer.
Phase boundaries in the figure above are qualitative and intend to highlight the relative dependence of phase stability on changes in pressure or in temperature. For example, BaSO4 scale
is less sensitive to changes in pressure than to changes in temperature. As pressure increases,
less barite forms and as temperature increases, less barite forms. CaCO3 scale is sensitive to
changes in both temperature and pressure. As temperature increases, more calcite would form.
Also as pressure drops more calcite forms, mainly due to CO2 evolving from water and hydrocarbon phases. Carbon dioxide, if present in water and hydrocarbons, helps dissolve calcite in
water, not too dissimilar from resins stabilizing asphaltene in oil. CaCO3 also can form a film
on pipe surface which can reduce corrosion, unless the film gets sheared away by the flow.
There is a continuous interaction between solid and fluid phases. Solids can act as diffusion barriers or as capillary channels to conduct less or more molecules in the liquid or gas
Fluid characterization
59
phases. This alters the rate of processes such as corrosion or formation of hydrate, deposition
of wax or asphaltene.
One should keep in mind that predicted stability of a solid phase does not guarantee solid
formation at exactly the predicted condition because nucleation kinetics may be delayed, and
formation of a solid does not always lead to a deposition and a blockage.
At the same time, if a phase is not stable, it does not mean that it could not form in real
operations. The software predictions and laboratory measurements can provide a warning
for a specific set of conditions and fluid compositions. However, operations in the field can
show that reality is more complex because not all factors and phase transitions were taken
into account by a software or a lab such as reaction kinetics, solids nucleation and metastability, and the influence of one solid phase on another. As an example of such influence, in a
system where scale is not stable, a hydrate formation can remove some water from a system.
Hydrate consumes pure water and leaves salt in the remaining water. If a nearly saturated
brine is present and the hydrate forms, it will cause water to become supersaturated with
salt, leading to scale precipitation and deposition. Similarly, injection of methanol to inhibit
hydrate into a produced fluid, which included a brine nearly saturated with NaCl, had led
to a change is salt solubility and an unexpected halite scale blockage in a North Sea pipeline.
Additional laboratory studies
Additional laboratory studies which may accompany a PVT report may include:
Oil pour point temperature
Oil HTGC or high-temperature gas chromatogram to resolve amounts of wax-forming
components
Oil emulsion stability study
Oil TAN total acid number and TBN total base number analysis
Oil SARA or saturates, aromatics, resins, asphaltenes content analysis
Oil foaming study
Wax appearance temperature measurement in CPM or cross-polarized microscope or
DSC differential scanning calorimeter at stock tank conditions
Wax appearance temperature measurement at pressurized conditions with reservoir fluid
with either DSC or CPM
Wax deposition study in a bench-scale mini-loop or a filter-plug apparatus
Wax deposition study in a pilot-scale loop
Wax deposition study in a cold finger apparatus with effect of chemical inhibitors
Wax deposition study in a pressure cell
Wax content from a cold solvent filtration study
Wax dissolution study with dispersant chemicals or solvents
Wax melting study for hot-oiling process
Waxy gel strength test in a small diameter tube
Asphaltene titration study for stock tank oil
Asphaltene isothermal depressurization for live reservoir fluid under pressure
60
3. PVT and rheology investigation
Asphaltene deposition study in a pressure cell
Asphaltene deposition study in a mini-loop or a filter-plug apparatus
Corrosion rate metal loss study with a static cell
Corrosion rate study with a rotating linear polarization electrode at atmospheric pressure
to measure the effect of shear on chemical performance
Corrosion rate with a rotating electrode under high temperature and high pressure
Corrosion rate from analog field metal coupon weight loss
Scale precipitation study in a static cell
Scale deposition in a mini-loop at high temperature to mimic reservoir condition
Scale deposition in a mini-loop at low temperature to mimic wellhead & flowline condition
Hydrate stability study with reservoir fluid and formation water
Hydrate stability study with reservoir fluid and wellwork fluid
Hydrate deposition study in a pressure autoclave, a rocking cell, a flow wheel or a flow
loop, with or without chemical thermodynamic or kinetic inhibitors
Hydrate dispersion study in a rocking cell with antiagglomerant chemicals
Among the above tests, there are some indirect correlations:
Hydrate nonplugging oil tendency may be related to TAN acids content and surfactants
content as investigated by J. Sjoblom, where surfactants content may be analyzed based
on emulsion stability study
Naphthenate tendency may be related to TAN acids content
Asphaltene tendency may be determined from SARA analysis
Production chemicals viscosity as function of pressure and temperature
Production chemicals vapor pressure analysis
There are numerous alternatives available to measure wax appearance and wax disappearance temperatures, which should be used depending on fluid type (e.g. regular or biodegraded):
-
CPM—visual detection of microscopic crystals assisted by polarized visual or IR light
DSC—exothermic detection of solids, applicable to regular or biodegraded oils
Viscometer or rheometer—detect a change in slope of Ln(viscosity) vs temperature
Cold finger—visual detection of solids
Cold filter plug—pressure differential detection of solids
Cloud point—visual detection of crystals by eye—less accurate but field-usable
Ultrasound change in wave frequency with temperature—applicable to live oil (Jiang
et al., 2014)
- Light scattering—applicable to wax appearance and wax disappearance
Compressibility.
PVT tuning
Binary interaction parameters kij serve as the tuning factors for the equations of state when
properties of multicomponent mixtures are calculated. These BIPs are regressed for multiple
61
Fluid physical properties
(pseudo)component—(pseudo)component pairs to achieve the best fit between measured
data and predicted values. Each group of regression, such as on liquid density, can have its
own regression tolerance.
Typical tolerance targets for regression during PVT tuning shown in Table 3.3 are as follows:
TABLE 3.3 Tuning target tolerances
Density
+/− 1–5%
Pressure of liquid saturation with gas
+/− 2–10%
Gas-oil ratio or RS (solution ratio)
+/− 1–5%
Liquid viscosity
+/− 5–20%
Parameters and acceptable tolerances of the fluid characterization are also illustrated in
section 4.7 of the Phase Behavior monograph by Whitson and Brule.
Fluid tuning process is available in multiple commercially available software packages.
One would normally start with the most relaxed tolerances and repeat tuning the fluid several times while reducing the tolerance and noting the overall errors in property prediction at
different temperatures and pressures.
Default value for kij is zero because kij enters the equation of state in a form (1−kij), so a
default value gives a complete contribution of a given pair of components to the interaction
energy parameter in the equation of state. Normally the values of interaction energy (a) and
molecule size (b) are calculated from the properties of components such as critical pressure
and critical temperature which can be measured in the laboratory and acentric factor which
can be calculated from the molecular structure. BIPs (kij) provide the ability to adjust the contribution of each component's interaction energy (a).
Besides kij, there are also characteristic constant (kappa), volume shift parameters for density match improvement and other methods.
As a final resort, when tuning of the GOR or density cannot be achieved with the provided
composition, some of the component contents may be varied by 1–5%. This variation must be
documented in the fluid characterization report. Example component properties are shown
in Table 3.4.
Fluid physical properties
TABLE 3.4 Component properties
Formula
Name
Molecular weight
Density (g/L)
V (L/mol)
Melting point
g/mol
at 1 atm, 15.5 °C
Air
29
1.225
23.67
−215
N2
Nitrogen
28
1.183
23.68
−210
CO2
Carbon dioxide
44
1.869
23.55
−56.6
H2S
Hydrogen sulfide
34.1
1.451
23.49
−82
°C
(Continued)
62
3. PVT and rheology investigation
TABLE 3.4 Component properties—cont’d
Formula
Name
Molecular weight
Density (g/L)
V (L/mol)
Melting point
C1
Methane
16
0.679
23.63
−182.5
C2
Ethane
30.1
1.281
23.47
−182.8
C3
Propane
44.1
1.896
23.26
−188
iC4
i-Butane
58.1
2.524
23.03
−159.6
nC4
n-Butane
58.1
2.531
22.96
−140
iC5
i-Pentane
72.2
623.9
0.116
−160
nC5
n-Pentane
72.2
629.7
0.115
−130
iC6
i-Hexane
86.2
657.1
0.131
−153
nC6
n-Hexane
86.2
662.2
0.130
−95
C6
Methylcyclopentane
84.2
753.3
0.112
−142
C6
Benzene
78.1
885.3
0.088
5.5
C6
Cyclohexane
84.2
782.2
0.108
6.5
C7
Heptane
100
687.0
0.146
−90.5
C7
Methylcyclohexane
98.2
774.1
0.127
−126
C7
Toluene
92.1
870.1
0.106
−95
iC8
Iso-octane
114
702.6
0.163
−107
C8
Octane
114
706.0
0.162
−57
C8
Ethyl benzene
106
873.0
0.122
−95
C8
m-Xylene
106
866.9
0.122
−48
C8
p-Xylene
106
866.9
0.122
13
C8
o-Xylene
106
882.9
0.120
−25
C9
Nonane
128
720.7
0.178
−51
C10
Decane
142
732.6
0.194
−30
C11
Undecane
156
742.5
0.211
−26
C12
Dodecane
170
750.4
0.227
−10
C13
Tridecane
184
758.3
0.243
−5.5
C14
Tetradecane
198
765.2
0.259
5.9
C15
Pentadecane
212
771.2
0.275
10
C16
Hexadecane
226
775.1
0.292
18.2
C17
Heptadecane
240
779.5
0.309
22
C18
Octadecane
255
783.4
0.325
28.2
C19
Nonadecane
269
787.3
0.341
32.1
C20
Eicosane
283
785.6
0.360
36.8
63
Non-Newtonian behavior
TABLE 3.4 Component properties—cont’d
Formula
Name
Molecular weight
Density (g/L)
V (L/mol)
Melting point
C21
Heneicosane
297
793.5
0.374
40.5
C22
Docosane
311
795.6
0.390
44.4
C23
Tricosane
325
798.7
0.406
47.6
C24
Tetracosane
339
800.8
0.423
50.9
C25
Pentacosane
353
802.3
0.440
53.7
C26
Hexacosane
367
805.9
0.455
56.4
C27
Heptacosane
381
807.1
0.472
59
C28
Octacosane
395
806.9
0.489
61.4
C29
Nonacosane
409
808.5
0.506
64
C30
Triacontane
423
811.5
0.521
66
C40
Tetracontane
563
817.0
0.689
82
C50
Pentacontane
703
824.0
0.854
91
CH3OH
Methanol
32
795
−98
C2H6O2
MEG
62.1
1117
−12.9
Hydrate structure1
17.7
916 at 129 atm
−81 at 1 atm
Hydrate structure2
19.1
958 at 22 atm
−44 at 1 atm
Light n-paraffin wax
400
910
66
Microcrystalline wax
800
940
78
Asphaltene
700
1100
not applicable,
pyrolizes on
heating
Non-Newtonian behavior
Viscosity of oil is measured at a range of temperatures and pressures.
Viscosity of gas is usually calculated using a correlation.
Waxy crudes may also exhibit a pour point which can be measured and reported. The pour
point is a measure of temperature at which a fluid in an inclined flask does not flow for a
prescribed period of time.
Non-Newtonian fluid rheology behavior is observed in viscosity measurement if solids such as wax precipitate in the liquid. If viscosity is plotted against temperature for a
Newtonian fluid, usually a plot of natural logarithm of viscosity vs temperature is linear.
When solids are introduced, the viscosity increases. This is exhibited as a nonlinear plot of
logarithm of viscosity versus temperature.
This nonlinearity may be used as one of the methods to determine wax appearance temperature of the fluid if more accurate data are not available.
64
3. PVT and rheology investigation
There are various correlations for the effect of slurry solids volume fraction on viscosity.
Nuland and Vilagines (2001, BHRG) proposed to use such correlation for hydrate slurries,
which is based on the correlation by Mills (1985) for apparent shear viscosity, which in turn
was based on the works of Einstein and Batchelor.
µr =
1 −Φ

Φ 
1−

Φ
max 

where µ r = µslurry / µ fluid ,
Φ = solid volume fraction ,
Φmax = maximum packing solids colume fraction = 4 / 7 for spheres.
Other non-Newtonian behavior is also associated with wax crystals forming a gel. When slurry
becomes so concentrated that crystals overlap and form a network, a waxy “gel” forms. The term
gel is used in this context to signify that the whole fluid becomes nonflowing and non-Newtonian
in its rheology. A gel exhibits a yield stress, which means that some force needs to be applied to
disrupt the network before a gelled fluid starts to flow. In some cases waxy crudes with 3% or
greater wax content (measured by cold filtration) may exhibit gelling behavior.
Gel strength may vary depending on the cooling rate of the fluid. So, faster cooling (near a
pipe wall) results in smaller wax crystals and a weaker network. Conversely, core of the gelling waxy oil cools at a relatively slower rate and grows larger crystals which form a stronger
network. This effect becomes most pronounced in larger pipelines. It is not uncommon to see
in a medium-diameter 2-in. pipe gel test that gel breaks near the pipe wall circumference, and
the gelled oil core is extruded from the test pipe. To overcome the discrepancy between gel
strength measured in a small laboratory tube and observed in a large diameter pipeline, gel
strength may also be measured in a temperature-controlled rheometer with a cone-and-plate
geometry to accurately reproduce the cooling rate history of a large diameter pipeline to obtain a more accurate gel strength reading. Alternatively, larger size test tubes or field pilot test
sections may be used.
Emulsion characteristics
Emulsion stability is commonly measured and reported for new oil samples. The time it
takes to resolve an emulsion by gravity into oil and water layers is reported.
Emulsion stability is particularly important for offshore operations as residence time in a
separator is limited by size and weight of the separator to 5–10 min.
Water-in-oil emulsions are prepared by mixing for a prescribed time at several shear rates
and different water cuts and are allowed to resolve at different temperatures.
Foaming of the oil may also be reported if observed.
Formation of slop or solids-stabilized layer between oil and water layers may be reported
if observed.
Inversion point for an emulsion may be reported if observed at some water cut.
References
65
Oil-in-water emulsions are prepared at different water cuts between 50% and 90% at different shear rates for a prescribed time, and oil content of water is reported in ppm. The reported
oil content should include both oil and water-soluble organic components.
Rheology or viscosity of emulsions formed at different shear rates is reported for different
temperatures and water cuts.
Biodegradation
Crude biodegradation may be exhibited by the absence of n-paraffin peaks in gas chromatogram or in high-temperature gas chromatogram. Bacteria present in the reservoir consume normal paraffins and only branched or isomerized paraffins remain.
This makes wax deposition prediction more complex as most modern wax deposition
models are based on a solubility prediction method developed by Erickson (Erickson et al.,
1993) which is applicable to n-paraffins. It also makes some laboratory studies such as CPM
more complex as isomerized paraffins may form less crystalline and more amorphous solids
which would not rotate the plane of light polarization.
DSC or other methods to detect wax onset may then be used. Laboratory studies for the
wax deposition then become necessary if wax appearance temperature is in the range of operating temperatures.
References
Bergman, D.F., Sutton, R.P., 2007. A consistent and accurate dead-oil-viscosity method, SPE110194. In: SPE Annual
Technical Conference and Exhibition, Anaheim, 11-14 November.
Clay, W.A., Sasagawa, T., Iwasa, A., Liu, Z., Dahl, J.E., Carlson, R.M.K., Kelly, M., Melosh, N., Shen, Z.-X., 2011.
Photoluminescence of diamondoid crystals. J. Appl. Phys. 110 (9), https://doi.org/10.1063/1.3657522.
Erickson, D.D., Niesen, V.G., Brown, T.S., 1993. Thermodynamic measurement and prediction of paraffin precipitation in crude oil. In: SPE 26604, Annual Technical Conference and Exhibition, Houston, 3–6 October.
Fiotodimitraki, T., 2016. Quality controlled oil reservoirs PVT data. Masters thesis, University of Crete. Accessed
12/12/2018, dias.library.tuc.gr/view/manf/63591.
Havre, T.E., 2002. Formation of Calcium Naphthenate in Water/Oil Systems, Naphthenic Acid. Chemistry and
Emulsion Stability. Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of DOKTOR
INGENIØR Department of Chemical Engineering. Norwegian University of Science and Technology, Trondheim.
Hu, Y., et al., 2017a. Gas hydrates phase equilibria for structure I and II hydrates with chloride salts at high salt concentrations and up to 200 MPa. In: Physical Chemistry Chemical Physics. Royal Society of Chemistry.
Hu, Y., et al., 2017b. Gas hydrates phase equilibrium with CaBr2 and CaBr2 +MEG at ultra-high pressures. In: Physical
Chemistry Chemical Physics. Royal Society of Chemistry.
Jiang, B., et al., 2014. Measurement of the wax appearance temperature of waxy oil under the reservoir condition with
ultrasonic method. Petroleum exploration and Development 41 (4).
Joback, K.G., Reid, R.C., 1987. Estimation of pure-component properties from group-contributions. Chem. Eng.
Commun. 57, 233–243.
Katz, D.L., Firoozabadi, A., 1978. Predicting phase behavior of condensate/crude oil systems using methane interaction coefficients. J. Petrol. Tech. 20, 1649–1655. SPE-6721.
Magnusson, H., Sjöblom, J., 2008. Characterization of C80 naphthenic acid and its calcium. J. Dispers. Sci. Technol.
29 (3), 464–473.
Mills, P., 1985. Non-Newtonian behavior of flocculated suspensions. J. Physique Lett. 46, L-301–L-309.
Nuland, S., Vilagines, R., 2001. Gas hydrate slurry flow – A flow modeler looks at the state of slurry rheology modelling. In: BHRG Multiphase International Conference proceedings, Cannes, France.
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Pedersen, K.S., et al., 1989. Characterization of gas condensate mixtures. In: Chorn, L.G., Mansoori, G.A. (Eds.), C7+
Fraction Characterization. Taylor & Francis, New York, pp. 137–152.
Peneloux, A.E., Rauzy, E., Freze, R., 1982. Fluid Phase Equilib. 8, 7–23.
Riazi, M.R., Daubert, T.E., 1980. Prediction of the composition of petroleum fractions. Ind. Eng. Chem. Process. Des.
Dev. 19, 289–294.
Whitson, C.H., Brule, M.R., 2000. Phase Behaviour, Richardson (TX). Society of Petroleum Engineers.
Further reading
Landt, L., Kielich, W., Wolter, D., Staiger, M., Ehresmann, A., Möller, T., Bostedt, C., 2009. Intrinsic photoluminescence of adamantane in the ultraviolet spectral region. Phys. Rev. B 80, 205323.
Pedersen, K.S., et al., 1991. Wax precipitation from North Sea crude oils. 4: Thermodynamic modelling. Energy Fuel
5, 924–932.
Riazi, M.R., 1979. Prediction of Thermophysical Properties of Petroleum Fractions. PhD Thesis The Pennsylvania
State University, PA.
C H A P T E R
4
Hydraulic and thermal analysis
O U T L I N E
Introduction
68
Hydraulic restrictions boundaries and
management
Scope
Hydraulic analysis deliverables
Overall design
Other considerations
Typical pressure drop
Hydraulics technologies
68
69
69
70
71
71
73
Hydrodynamics of multiphase flow
Multiphase flow pressure
drop—Vertical vs Horizontal
Designing out severe slugging
Multiphase flow liquid
holdup—Vertical vs Horizontal
74
Thermal effects
Heat transfer
Joule-Thomson effect
81
81
84
Flow modeling
Correlations
Dimensionless numbers
Software
84
84
85
86
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00004-X
74
79
80
Erosion modeling
Multiphase production problems
87
87
Operation online monitoring for pipeline 88
Correlations
89
Software
89
Operation online monitoring for
well liquids loading and forming
blockages/restrictions
Correlations
Software
Design of oil/gas development
project
Hydraulic management
Water injection management
Flow restriction and blockage
monitoring
88
89
89
89
89
90
91
Machine learning and artificial
intelligence in flow network
optimization
91
References
92
Further reading
93
67
© 2019 Elsevier Inc. All rights reserved.
68
4. Hydraulic and thermal analysis
Introduction
Hydraulic analysis is used to calculate and optimize pressure loss, holdup accumulation,
vibration, water hammer and surge exceeding normal operating parameters during steady
and transient flow operations. Sensitivity to the amounts of produced water should include
an assumption for planned and deferred water injection for pressure support, based on reservoir simulation production profiles.
Thermal analysis predicts the temperature changes in the produced fluid and in the producton system as heat is lost to ambient cooling or to JT expansion in multiphase flow or
gained from JT heating in supercritical (dense phase) fluids. Thermal analysis in wells is also
related to mechanical integrity if annular spaces are filled with fluids with low compressibility.
Both thermal and hydraulic analysis are performed simultaneously, coupled through location
in the system. Fluid properties depend both on temperature and pressure, and proper fluid characteristics and phase transitions rely on accurate calculation of both temperature and pressure.
Hydraulic analysis results are supplied to operability design analysis which aims to ensure
that temperature, pressure and flow are within normal operating limits for the production
system at any stage in field development life.
Flow lines from trees to manifolds and from manifolds to hubs are usually routed predominantly uphill to minimize pressure losses due to terrain liquids holdup in low spots, in
order to maximize overall fluid recovery by limiting backpressure on wells, and also to avoid
slugging induced by liquid accumulation in low spots and to enable uniform subsea chemical
distribution in produced fluid, and to reduce fatigue from cyclic slug impacts on pipe elbows
at bends and crossings.
Detailed field layout should ensure that both production and chemical injection systems
can operate with acceptable pressure drop and chemical stability in subsurface, subsea, topsides and export systems conditions.
Single line tieback concepts are economically attractive and may be considered for early
production systems if reliable ways to mitigate the risk of solids restriction are in place.
Hydraulic restrictions boundaries and management
Besides the regular solid blockages which derive from a phase transition such as solid
crystallization of normal paraffins as wax there also may be hydraulic restrictions in the
pipelines. Such hydraulic restrictions may occur both with and without phase changes,
merely due to accumulation of a gas or a liquid in a pipe due to variations in geometry or
due to evaporation or condensation. Such examples may include water or liquid holdup in
a low spot creating resistance to flow, a viscous emulsion accumulation in a process vessel
reducing its effective volume or a vapor lock at the intake of a centrifugal pump breaking
fluid continuity. Each may restrict or interrupt flow. Additional cases of restrictions pertain
to fluids flowing outside their normal operating conditions. Such examples include production chemicals slack flow which may cause a blockage in a chemical delivery umbilical
tube. Slack flow is a generalization term which means the fluid flows at a pressure below
its vapor pressure or bubble point. This may occur in late life production in deep water
­operations when produced fluid has a lower density than the production chemical injected
at the subsea tree, and the flowing wellhead pressure is lower than the hydrostatic pressure
Hydraulic restrictions boundaries and management
69
of the p
­ roduction chemical. Normally the chemical backpressure is controlled by a chemical
injection valve, but a valve set for operation in early life at initially higher wellhead pressure
may need to be recalibrated for late life lower pressure, and if that maintenance is deferred
the chemical may experience vacuum conditions at the top of the umbilical riser, causing
carrier solvent in the chemical to vaporize and leaving the viscous or solid active ingredient
residue in the chemical tube gradually blocking it.
These static hydraulic restrictions such as a holdup may be easier to plan for than dynamic
flow resistances such as hydrodynamic slug flow because static restrictions are caused by
localized conditions such as pressure, temperature or geometry and thus can be designed
out of the planned system. Dynamic restrictions emerge during the course of production,
and planning of the optimum balance of the production system capacity versus its cost is the
main focus of hydraulic analysis in flow assurance which relies on the anticipated production
flow rates derived from reservoir modeling that carries inherent uncertainty. The same may
be said about hydraulic design of production chemical injection systems.
Scope
Hydraulic assessment and management has the principal priority in flow assurance work
scope. The flow assurance analysis relies on fluid properties from reservoir model or laboratory
data and on a production profile from a recent reservoir model, and latest surface geometry or
subsea bathymetry. Liquid holdup accumulations forming a hydraulic restriction to flow and
erosional velocity limits for liquid and gas production need to be evaluated. For a tieback to
an existing facility, matching of hydraulic and insulation performance should be included to
calibrate the effective roughness and thermal insulation U-value based on existing operations
data from operations and third party engineering vendor experience. Note that the theoretical
roughness and insulation values of a system provided by vendors may be more optimistic than
field performance under subsea or onshore operation. Actual insulation performance may be
affected by flooded sections in pipe-in-pipe insulation or water ingress into the wet polymeric
insulation. Actual roughness is affected by corrosion and erosion. Both insulation performance
and roughness become worse with time.
Hydraulic analysis deliverables
The engineering analysis needs to identify when the system selected in early design operates with a hydraulic restriction or excessive velocity threats, quantify the duration of system
operating with flow instability, and provide a design for the selected one or more technically
mature technologies to mitigate the identified threats and to remediate the hydraulic restriction, flow instabilities or surge.
Deliverables of hydraulic analysis include the recommended in-field flowline network and
export pipeline sizes with updated corrosion and erosion allowances to permit maximum
uninterrupted production during the life of field, maximum flow velocities for produced
fluids, mitigation method and intervention frequency for liquid inventory management in
flowlines based on transient modeling of scraping and estimated based on historic analogs,
liquid surge capacity for onshore or topsides facilities sizing, chemical injection requirements
(location, dosage, storage, compatibility with materials and with other chemicals) if a chemical is used to manage liquid inventory (such as a foamer).
70
4. Hydraulic and thermal analysis
Analysis provides gas and liquid flow velocity upper boundaries for erosion, flow induced
vibration, and thermal material limits for JT expansion cooling (e.g. gas in Deepwater riser).
No credit should be taken for ability to monitor erosion in a dry tree vs subsea tree system and the erosional analysis should provide the same gas and liquid flow velocity upper
boundaries. Guideline chosen for the project needs to be used for erosion engineering analysis. There are several erosion guidelines available such as DNV-0501, API-14E or NORSOK
P-001. Additional models such as SPPS are also used for analysis. A summary overview of the
models is presented by Arabnejad et al. (2015).
Hydraulic multiphase flow analysis needs to be aligned with surface or topsides process
design procedures to make sure the flow rates at the outlet of the production system are
compatible with the flow rates at the intake of the process system. A slug catcher may act as
a surge suppressor if the production system output may have sudden high flow rates such
as during scraping or severe slugging. An overview of occurrence and solutions for severe
slugging is presented by Montgomery (2002).
A turndown analysis indicates what lowest flow rate is sustainable in the production system. Deliverables of a turndown sensitivity study relative to the design production profile
indicate when produced fluid flow remains above slug flow onset, and when start-up or
ramp-up surge volume exceeds the facilities process capacity.
Analysis also provides updated steady state temperature and pressure profiles through
time, including turndown sensitivity relative to the design production profile.
Overall design
Overall design for hydraulic management needs to rely on using proven technology to
avoid holdup accumulation irreversible by normal operating procedure. Sensitivity to produced water cut should include an assumption for planned and deferred water injection for
pressure support, based on reservoir simulation production profiles.
Operations with flow instability may include producer or injector well transient operation such as cold or warm start-up, planned or unplanned shut-in, and steady operation.
During FEED phase, at least steady operation and start-up surge analyses need to be
performed. Depressurization analysis should be performed if hydrate management relies
on it.
Mitigation of severe slugging and liquid surges may include topsides choking, riser
base gas lift, sufficiently sized slug catcher, subsea pumping, pressure management, etc.
Use of novel methods such as actively controlled topsides choke valve for riser severe
slugging is growing in acceptance in Deepwater and may be considered as technically
mature.
Remediation methods used to control hydraulic losses may include scraping to sweep
accumulated liquids, drag reducing agent chemical injection, or foamer to control liquid
inventory. Mechanical removal of liquids with swabbing has not been widely used in
Deepwater, but has been used successfully in onshore wells, and may be applicable to dry
tree risers in late life. Mechanical methods to reduce flow line cross section such as velocity strings or a­ rtificial lift such as ESP or multiphase pumps to propel liquids may be used
both in onshore and offshore production. Combinations of the methods may also be used
such as an ESP on a coiled tubing velocity string in onshore wells or in offshore risers.
71
Hydraulic restrictions boundaries and management
EXA M PLES OF UNSTAB LE F LOW M I TI G ATI O N
An example of a Deepwater system properly designed for hydraulic management may be a flow
line selected with predominantly uphill geometry to mitigate terrain slugs to ensure flow stability
for a longer portion of the field life and with a separator sufficiently sized to receive liquid surges
in late life. Another example as in Table 4.1 is a single line tieback with an artificial lift to mitigate
severe slugging.
Other considerations
Transient commercially available or custom-developed models should to be used for hydraulic analysis, upon performance verification against publicly available or commercial
flow data sets and after approval of the relevant project authority.
In general it takes between 3 and 10 years to develop a multiphase flow analysis tool, so the
task is manageable for a capable individual in an academic setting or for a large corporation
research team.
Transient multiphase flow analysis is complex, and tools which have not been verified by
the user should not be considered for application in production system design. Verification
itself is a complex and time consuming undertaking, and it may need to be outsourced to
qualified engineering vendor which has experience in multiphase flow analysis but no vested
interest in a particular tool.
Impact on production should be determined and accounted for if the choking option was
selected in early design for slug mitigation.
Typical pressure drop
One commonly used frictional pressure drop correlation applicable to single-phase flow is
Darcy-Weisbach:
∆P [ Pa ] = Lf Moody ρV 2 / ( 2D )
L = pipe length [m], f = friction factor, ρ = fluid density [kg/m3], v = fluid velocity [m/s],
D = inside diameter [m].
TABLE 4.1 Examples of hydraulic instabilities and their mitigation and remediation
Hydraulic examples (from reservoir to
process)
Mitigation examples
Remediation examples
Flow instability in wet gas wellbore (i.e.,
FBHP < Lift curve minimum P)
Reduce wellhead choke opening
Reduce tubing size or use
Artificial lift (boost)
Flow instability in wet gas flowline (i.e.,
FWHP < P_dew)
Periodically sweep liquids to
slugcatcher
Use partial separation
Flow instability in riser (severe slugging) Reduce boarding choke opening
Artificial lift (gas lift or boost)
72
4. Hydraulic and thermal analysis
If the Reynolds number is below 2100, the laminar Moody friction factor as a function of
Reynolds number is
f Moody = 64 / Re
f Fanning = f Moody / 4
Many different friction factor correlations are available for turbulent flow but the simplest
of these is the Blasius (1913) correlation.
f Moody = 0.3164 Re −0.25
For turbulent flow it is convenient to determine friction factor f from a non-recursive formula (Swamee and Jain, 1976)
(
f Fanning = f Moody / 4 = 4 × log ( ε / ( 3.7 D ) + 5.74 / Re0.9 )
)
−2
.
ε = pipe wall roughness [m]; typical aged carbon steel roughness is 45 μm or 45 × 10−6 m. Re
is Reynolds number.
For hydraulically smooth pipes fFanning = 0.0791/Re0.25.
For flow analysis it is helpful to estimate shear of fluid acting either on a solid or on pipe
wall. We summarize several shear correlations.
Shear_rate γ [1/ s ] = shear_stressτ [ Pa ] / dynamic_viscosity µ [ Pa s ] ( for Newtonian fluids ) .
Shear rate for laminar flow γLaminar = 8 vAve/D.
Average flow velocity vAve = Q/A.
Shear stress exerted by flowing fluid on pipe wall τwall = D ΔP/(4L)
τ Laminar_ at_ wall = 8 µ VAve / D
τ Turbulent _at _wall = ρ V 2 fFanning / 2
τ wall = D∆P / ( 4L )
For single-phase flow we can illustrate that laminar pressure drop is inversely proportional to pipe diameter to the power 4, whereas turbulent flow is inversely proportional to
diameter to the power 5.
∆PLaminar = 32 µ Lv Ave / ( D 2 ) = 128 µ LQ / (π D 4 )
∆PTurbulent = 4Lρ v Ave 2 fFanning / ( 2D ) = 32 ρ LQ 2 f / (π 2 D 5 )
Other equations such as Weymouth or Panhandle may also be used to calculate pressure
drop in gas flow. Panhandle B formula (1956) is for gas flow with medium Reynolds number
values.
Q [ MMscf / d ] = 0.028ED 2.53
(( P
1
2
− P2 2 ) / ( S 0.961 ZTL )
)
0.51
Hydraulic restrictions boundaries and management
73
E = efficiency, typically E = 0.92; D = diameter [inch], L = length [miles], Z = gas compressibility at average conditions, T = inlet gas temperature [°R], S = gas gravity relative to air, P1
= upstream pressure, P2 = downstream pressure [psia].
Average conditions for gas compressibility are estimated as log-mean temperature and
line-average pressure.
TAVERAGE = TAMBIENT + ( TIN − TOUT ) / ln ( ( TIN − TAMBIENT ) / ( TOUT − TAMBIENT ) )
PAVERAGE = 0.667 ( PIN 3 − POUT 3 ) / ( PIN 2 − POUT 2 )
Compressibility may be estimated with McCain or Hanafy correlations. Alternatively it
may be looked up in property tables.
Typical pressure drop for a gas flow line from a well to a processing facility is around
0.5 bar per km or 12 psi per mile. For multiphase lines the pressure drop may be as high as
10 bar per km, but typically is less. If the pressure drop is higher than this, then the backpressure on the wells is high and reservoir may produce less. If the pressure drop is lower, then
the pipe may be oversized and capital cost may reduce profitability. Export pipelines will
have different pressure drops.
A similar performance comparison is possible for a multiphase flow line from a well to a
processing facility. The main objective of a multiphase flow calculation similarly is to find
pressure drop in a line of a given size. Secondary objective is to forecast conditions to minimize the occurrence of a slugging flow regime. Evaluation of a multiphase flow pressure drop
is more complex than for a single phase flow and involves series of formulaic or graphic-­
analytical computations, with or without account for the gas-liquid dispersion flow regime.
Virtually all multiphase flow pressure drop calculations are done by computer software, with
the account for the flow regime.
Hydraulics technologies
A number of technologies may help economically produce fluids from a distant asset.
Technologies which should be considered in formulating an asset development project concept may include the following:
•
•
•
•
•
•
•
•
•
•
•
•
•
Hydraulic lines of different size and insulation type and thickness
Slug catcher vessel
HIPPS system
Periodic scraping
Production chemical
Subsea booster pump
Subsea multiphase pump
Subsea gas separator if proven for use in the region
Subsea water separator if proven in the region
Riser base caisson gas separator if proven in the region
Downhole and/or riser base gas lift
Drag reducing agent chemical
Active heating of flowlines with electrical energy or with heating medium fluid
74
4. Hydraulic and thermal analysis
• Multiphase flow meter
• Water injection pump with limits per rock fracture gradient
Hydrodynamics of multiphase flow
Multiphase flow pressure drop—Vertical vs horizontal
Modern hydraulic analysis methods rely on software packages using mass and momentum conservation equations with equations closure relationships. The closure relationships
constitute the commercial know-how of the vendors. Closure relationships are correlations
based on experiments or field data, which complete the system of equations for conservation
of mass and momentum required to calculate fluid motion. The relationships are being continuously updated based on field measurements and research data. Software is also regularly
updated to improve the accuracy of predictions.
A good summary of the basis relationships in multiphase flow is given by Hetsroni (1982).
The book presents the equations for single phase flow, two-phase flow, flow with particles,
interaction of interface with particles, liquid film condensation, drag reduction and measurement techniques.
A good discussion of closure relationships is presented by Roullier et al. (2017). A more detailed description of the overall multiphase flow simulator design is provided by Jansen (2009).
The summary for multiphase flow pressure drop correlations for vertical flow is provided in
the monograph by Brill and Mukherjee (1999). Many of these correlations are still in use today.
Variety of flow regimes have been identified by researchers over the past century. Few key
ones are illustrated below in Fig. 4.1 for horizontal and vertical flow. Inclined flow researchers
occasionally use terms froth or pseudo-slug which have more gas entrained in liquid slug and
are similar to churn.
Each flow regime represents a progressively increasing level of energy dissipation, as reflected by higher amounts of liquid droplets entrained into the gas phase. With higher pressure, droplet entrainment increases.
Inclined flow tends to have a stratified flow pattern going downhill and slug flow uphill.
FIG. 4.1 Illustration of multiphase flow regimes.
Hydrodynamics of multiphase flow
75
The following images in Fig. 4.2 show the four slugs completely crossing the pipe
cross-section, moving from right to left, in a 6-in. multiphase flow loop donated to the
University of Tulsa with air and water. The images are frames from a video recorded for
seven seconds. The incomplete slugs and waves are not shown. The areas of churn at slug
fronts with high bubble entrainment and maximum energy dissipation are darker on these
images, whereas liquid without entrained bubbles is light and translucent. The longer slug
in the second image has two areas with bubble entrainment, which suggests this may be a
slug merged from two smaller slugs.
A video of slug flow in these frames is available on makogon.com/resources/6inchILOOP050101slugs.AVI and 6inchILOOP050101slugging.gif.
Images from this video may be used to train slug pattern recognition in machine learning.
Slug velocity may be determined from the video recorded in May of 2001.
Slug length and frequency are common parameters predicted by the multiphase flow correlations. Slug length may be of a slightly greater interest from the system integrity standpoint because knowing it helps one calculate the momentum of the moving slug and the force
with which the slug can impact on a pipe bend, a tee or an elbow in the flow path.
A simplified calculation for an average slug length is proposed as
L Slug [ ft ] = (D [ in ] )
2
where pipe inside diameter is in inches and average slug length is in feet, so a 10 in. inside
diameter pipe would produce 100 ft. or 30 m long slugs, on average. This may be used only as
a very rough approximation of the true slug length, just to find the order of magnitude for the
possible slugs in multiphase flow. The advantage is that this calculation is easy to remember
and thus use in the field or as needed. This proposed correlation is useful up to pipe diameters of 14 in. which covers a large portion of installed multiphase pipes.
A comparison of software predictions with field data for slugging observed in a 12-in.
flowline is shown in Fig. 4.3 below (updated, from Fairhurst, 2002). The proposed slug length
correlation has a reasonable agreement with the slug lengths observed in the field.
Some examples of models for slug frequency are presented in Hill and Wood (1990) and
Shea et al. (2004).
The Hill-Wood model the slug frequency as function of mixture velocity and liquid height
U mixture 2.68 h film /D
10
D
The Shea model of the hydrodynamic slug frequency as a function of liquid superficial velocity and dimensionless slug length L expressed in pipe diameters was used in a commercial
transient software simulator.
f slug = 0.275
f =
0.68USL
D1.2 L0.6
Application of correlations developed over the past decades for pressure drop and liquid
holdup should be chosen based on pipe diameter and inclination and target flow conditions
such as flow regime, viscosity.
76
4. Hydraulic and thermal analysis
FIG. 4.2 Examples of slugs flowing in a 6-inch flow loop (from right to left).
77
Hydrodynamics of multiphase flow
Slug Length Distribution
250
200
Number of Slugs
Observed
Software1
Software2
150
100
50
260
250
240
230
220
210
200
190
180
170
Slug Lengths ( m )
160
150
140
130
120
110
90
100
80
70
60
50
40
30
20
0
10
0
FIG. 4.3
Slug length distribution. (Updated from Fairhurst, P., 2002. Slugging prediction, Galveston flow assurance
forum, 17–19th September, 2002).
It was calculated using OpenFOAM CFD that the largest portion of pressure drop is in the
slug front as shown in Fig. 4.4 (Wenzel et al., 2016).
Among the correlations easiest to apply in a hand calculation was one developed by
Poettman and Carpenter (1952) for a pressure drop in vertical flow. The original work
was performed with the goal to reduce the horsepower required to lift reservoir fluid by
selecting appropriate well tubing size. Data gathered from 34 flowing oil wells and 15
gas lift wells with production tubing sizes of 2, 2.5 and 3 in. were correlated by at least 14
variables. Correlation is for gas-liquid ratios up to 5000 cubic feet of gas per barrel of total
liquid, liquid rates from 60 to 1500 barrels of total liquid per day. The authors assumed
that the energy losses for multiphase flow can be correlated by the well-known Fanning
equation
f =
2 gc Wf D
4u 2 ( h2 − h1 )
The correlation can be used for high flow-rate wells with dispersed bubble flow pattern
and is shown below:
2
fQmix
M2
dP
=ρ+
ρ
dh
7.4131010 ρ 2 D5
78
4. Hydraulic and thermal analysis
PRESSURE p [Pa]
PRESSURE DROP IN SLUG BODY
101000
100800
100600
100400
100200
PRESSURE p [Pa]
0
0.05
0.1
101000
0.15
0.2
0.25
0.3
0.35
POSITION [m]
100800
100600
100400
100200
FIG. 4.4 Numerical Simulation of the pressure drop in a slug body. (Reproduced with permission Wenzel, S., Czapp,
M., Sattelmayer, T., 2016. Numerical investigation of slug flow in a horizontal pipe using a multi-scale two phase approach to
incorporate gas entertainment effects. https://www.td.mw.tum.de/en/research/research-areas/projektbeschreibungen/­numericalinvestigation-of-two-phase-flow-in-horizontal-pipes-in-slug-flow-regime-with-special-consideration-of-the-entrainment/
(Accessed 1 June 2018)).
ρ = ρ mix = ρliquid ∗ volumeFractionliquid + ρ gas ∗ ( 1 − volumeFractionliquid )
M is the total mass, in pounds, of flowing oil, gas, and water associated with one stock
tank barrel flowing through the system. Change in pressure with distance in psi/ft. due to
flow resistance is proportional to density in lb./ft3, friction factor, volumetric flow rate, mass,
and pipe inside diameter in inches. The product QM is in pounds of mixture per day. Friction
factor f is determined from a graph plotted as f vs ρ v D and developed based on data from 49
wells on normal depletion and with gas lift.
The graph may be summarized by the following values in Table 4.2 read off the original
chart:
The authors designated Wf as energy losses due to irreversibilities of the fluid in flow such
as slippage, liquid hangup or frictional effects, in lbf ft/lbf.
Vm is the cubic feet of mixed gas, oil and water at pressure P per barrel of stock tank oil
based on the ratio of fluids flowing into and out of the flow string.
u is integrated velocity of homogeneous mixture in feet per second, average between P1
and P2.
gc is a gravitational conversion constant 32.174 lbm ft/(lbf s2).
The summary and comparison with field data for multiphase flow pressure drop correlations for horizontal flow is provided by Al-Ne'aim et al. (1995).
TABLE 4.2 Values read from the friction factor chart by Poettman and Carpenter
Dρ v =
f =
1.4737 10 −5 M Q
D
2 gc Wf D
4u ( h2 − h1 )
2
= 7.413
1010 W f D5
Q Vm2 ( h2 − h1 )
2
155
28
8.25
2.5
1.65
0.8
0.001
0.01
0.1
1
10
100
79
Hydrodynamics of multiphase flow
Comparisons of multiphase flow correlations and related experimental work is provided
by Shea et al. (1997), and Carrascal (1996).
Slugging in itself is detrimental as it can reduce the production rate. Slugging also reduces production by increasing backpressure on the well. One reference to an example of
a severe slugging flow reducing production by 20% was shown in Montgomery (2002).
Slugging also causes periodic impacts at elbows which may affect mechanical integrity
(Hill and Wood, 1994).
Extremely long liquid slugs can be created when downward sloping pipelines lead to riser
pipes in deepwater operations. These “severe slugs” can cause serious upsets in separation
processes, high pipe vibration and stresses during the arrival stage, and paraffin deposition
problems near the riser base.
Designing out severe slugging
Production system may be designed to minimize severe slugging by routing the flow
predominantly uphill. This is the common design technique used by offshore operators.
However, in onshore production in shale wells it may be more beneficial to route the flowing
the lateral portion of the well downhill, in a so-called toe-up configuration. Although this
approach in shale causes more flow instability, it allows liquids to accumulate at the well heel
location which then may be lifted to surface using artificial lift methods.
A novel method to control slugging was recently proposed (Makogon et al., 2011,
US8393398). The system has no automation or moving parts and was shown in pilot-scale
tests to help reduce slugging. It may be installed during initial construction or retrofitted to
an existing system. After the concept model of severe slugging control method showed that
slugging was eliminated in a multiphase flow simulator, the pilot tests quantified the range
of the method performance in a 3-in. diameter 20 m pipeline—14 m riser or lateral-vertical
flow geometry.
The effect is shown in the charts below in Fig. 4.5 indicating flow regime maps without and
with the method installed.
Not all combinations of gas and liquid velocities were affected equally, but in multiple
cases the method was effective.
Flow stability was achieved at lower superficial gas velocities. Backpressure fluctuations
were reduced or eliminated as data in Fig. 4.6 shows. An example of complete elimination
shows backpressure fluctuation without and with the method implemented.
10
10
Severe
Slugging
Transition
Severe
Slugging
Transition
Stable
VSL [m/s]
VSL [m/s]
Stable
1
0.1
0.1
1
10
1
0.1
0.1
VSG, 0 [m/s]
FIG. 4.5 Effect of flowline geometry on severe slug suppression.
1
VSG, 0 [m/s]
10
80
4. Hydraulic and thermal analysis
40
VSL =0.9 m/s,
VSG =0.2 m/s
35
Pressure, [psia]
30
25
20
15
No Modification
10
Modification One
Modification Two
5
Modification 3
0
0
50
100
150
200
250
300
350
Time, [s]
FIG. 4.6 Effect of flowline arrangement on backpressure fluctuations.
Besides severe slugging or liquid loading control, the method may be extended to optimize
gas lift effectiveness as in riser-based gas lift systems. Method may help extend production of
tiebacks with terrain slugs or declining and water-producing fields by recovering loaded up
production stopped by severe slugging. Method may help reduce slug vibration by breaking
large slugs into smaller ones, or to homogenize multiphase flow at subsea boosting pump
intake. With no moving parts or electronics, the method is expected to have higher reliability.
Multiphase flow liquid holdup—Vertical vs horizontal
In steady state operation the holdup averaged over large length does not change in vertical or horizontal flow, however local holdup can change in slug or churn flow. Multiple
correlations have been developed to calculate the liquid holdup value in either vertical or
horizontal configuration. Liquid holdup and entrainment in vertical flow are related to the
liquid loading of wells.
A correlation developed by Turner et al. (1969) based on Hinze (1955) flow equations by
balancing gravity and drag forces acting on a droplet and updated by Coleman et al. (1991)
allows one to estimate the minimum gas velocity in a well at which liquid entrainment will
be sufficient to lift the liquids to surface. The Turner correlation was found to have a closer
match to field data in Marcellus shale (Child and Brauer, 2017). It may be used with wellhead pressures over 1000 psi or 70 bar to find the minimum gas velocity u in feet per second
to lift water or oil.
1
u = 1.912
1
σ 4 ( ρ L − ρG ) 4
1
ρG2
The density of gas is proportional to pressure, and densities of liquid may be assumed
as 45 lbm/ft3 for oil and 67 lbm/ft3 for salt water. As the typical surface tension for gas-oil is
Thermal effects
81
25 mN/m and 60–65 mN/m for gas-water, in field units these are 0.17 lbf/ft and 0.44 lbf/ft.
The authors suggested that heavier water is more likely to accumulate downhole, thus minimum gas velocity to lift water should be used. In an example calculation it equals about 7 ft/s
or 2 m/s for a well with 1000 psi upstream of the tree choke. As pressure drops to 500 psi gas
becomes less dense and can entrain less water so the minimum velocity increases to 10 ft/s
or 3 m/s.
A recent overview for multiphase flow correlations for inclined and horizontal flow in
pipelines is provided in Jerez-Carrizales et al. (2015).
The correlations implemented in commercial software have been extended to use 3-phase
correlations with water, and sometimes with entrained solid particles.
A solids transport model has been presented by Warner and Letizia (2001).
Transient pressure hydraulic analysis is associated with surge calculations and HIPPS
systems. HIPPS systems can provide economic alternative to installing a thick-wall pipeline rated to the maximum pressure which may be experienced in the production system.
Instead, only a portion of the system which will definitely experience high pressure will
have a pipe rated to higher pressure for example during a shut-in, whereas the portion
of the production system which will experience lower pressure during production can be
equipped with a pipe rated to a lower operating pressure. The two portions of the production system would be separated by a fast acting HIPPS valve which can close in a few
seconds. A short portion of the production system downstream of the HIPPS valve would
still be rated to the higher pressure to account for the pressure increase while the HIPPS
valve is closing. Flow assurance uses transient analysis to determine the length of the reinforced pipe downstream of the HIPPS valve. Flow assurance hydraulic analysis for HIPPS
for subsea and for onshore or topsides facilities may rely on API 17TR13, section 10.8, and
API 17O standards.
Flow energy dissipation in gas-dominated systems and in multiphase systems is influenced by conduit roughness. Values for commonly used materials are summarized in the
chapter on reference information.
Thermal effects
Heat transfer
Typical average values for seawater flow velocity is 0.1 m/s and for air 1 m/s. Typical
seawater temperature is 4 °C at depth greater than 1000 m worldwide. Actual values must be
obtained from the recent meteorology and oceanography (metocean) report for the region of
interest, with seasonal variation.
As produced fluids flow from a warm reservoir through progressively colder environment, heat transfer occurs by conduction and convection. Changes in produced fluid temperature cause phase transitions which cause multiphase flow, solids precipitation and other
engineering challenges. Insulation helps maintain heat in the produced fluid.
Thermal properties of various materials commonly used in production systems are summarized below. These values in Table 4.3 are indicative only. Actual values should be verified for
relevant conditions.
82
4. Hydraulic and thermal analysis
TABLE 4.3 Material properties for thermal analysis
Heat capacity
J/kg K
Density kg/m3
Conductivity W/m K
Carbon steel
45.3
460
7865
CRA cladding SS316
14.5
500
7990
Duplex steel
18.2
460
7833
Flexible carcass
11.6
502
4835
Flexible pressure sheath
0.415
2023
945
Flexible armor
0.93
502
7076
Flexible fabric tape
0.6
1366
761.5
Flexible outer sheath
0.386
2153
940
Fiberglass (shale onshore pipe)
0.04
700
1520
Adhesive
0.22
2182
900
Asphalt enamel
0.692
1400
1324
Concrete weight coating
2
980
3040
Heat capacity
J/kg K
Density kg/m3
Conductivity W/m K
Fusion bonded epoxy
0.3
1500
1300
Novolastic
0.167
2500
993
Polypropylene foam
0.174
1744
720
Polypropylene solid
0.254
2153
900
Polypropylene weight coat
0.35
1300
2000
Spray polyurethane foam
0.16
1500
750
Thermotite deep foam
0.177
2017
760
Thermal sprayed aluminum
237
1005
2713
Neoprene
0.265
1340
1400
Aerogel
0.02
2100
20
Rockwool
0.045
840
128
Nylon
0.195
1700
1050
Glass
0.289
2000
1300
Foam
0.18
886
790
High density polyethylene
0.259
1776
936
PIPE LAYERS
INSULATION LAYERS
83
Thermal effects
TABLE 4.3 Material properties for thermal analysis—Cont’d
Concrete
1.7
840
3040
Light cement
0.346
1256
800
Medium cement
0.692
1195
1400
Heavy cement
1.25
1256
1900
Conductivity W/m K
Heat capacity
J/kg K
Density kg/m3
Ice
2.16
2108
910
Wax
0.25
2400
900
Methane hydrate
0.68
2080
910
Asphaltene
0.756
1340
1200
Scale calcite
2.12
2500
2710
Salt, scale halite
5.4
880
2160
Marine growth hard clams
2.88
2000
1120
Marine growth soft sponges
0.58
4200
1000
Onshore soil
1.3
938
2400
Undisturbed subsea soil
1
938
2400
Sand
2
830
1600
Reservoir rock
2
880
2100
OTHER MATERIALS
FLUIDS
Conductivity
W/m K
Heat capacity
J/kg K
Density kg/m3
Expansion 1/C
Viscosity
N s/m2
Reservoir fluid
0.295
1963
760
0.000744
0.0092
Liftgas
0.043
2747
107
0.0005
1.58E-05
Brine
1.73
2897
1400
0.0005
0.0005
Air
0.026
1005
1.22
Diesel
0.141
2093
840
Water
0.59
4184
1000
Oil
0.15
2100
860
Methanol
0.204
2430
791
MEG
0.25
2350
1145
Drilling mud
0.141
2093
1200
Drilling base oil
0.141
2093
780
84
4. Hydraulic and thermal analysis
Joule-Thomson effect
Minimum temperature in the production system is expected to occur in one of the two
scenarios:
- During restart due to JT cooling across the choke (so-called chilly choke conditions).
- During system depressurization due to JT cooling across the flare system valve.
In the first case a reservoir is below the bubble point pressure, reservoir fluid is saturated
with gas, and the well is produced in multiphase natural depletion mode without artificial
lift. Fluid settles downhole in such a well during a shut-in, and gas remains near the wellhead
and cools down to the ambient temperature. During a restart, the gas is produced initially before the well unloads the liquids and multiphase production resumes. The initially produced
gas is at a high wellhead shut-in pressure and at low ambient temperature. Flow of such gas
across a partly opened wellhead tree choke causes it to expand and cool.
When pressure drop across the valve is less than approximately 50%, gas expands and its
temperature drops as described by a thermodynamic equation of state in proportion to the
change in pressure and compressibility, which in turn depends on pressure and temperature.
Reservoir may also be above the bubble point pressure. Then the JT effect will cause heating if
pressure downstream of the choke is still above the bubble point pressure. JT effect will cause
a combination of heating and then cooling if the pressure downstream of the choke is below
the bubble point pressure.
In the second case of flow to flare an operator may be requested to depressurize the system, for example to remedy or to prevent a hydrate blockage. Flare system is normally rated
to pressures much lower than the production system, so a greater pressure differential may
be expected. In case of depressurization there will always be JT cooling.
When the pressure drop is greater than 50%, for example from 50 bar upstream of the
valve to 10 bar downstream, critical flow or choked flow occurs as exiting gas velocity
approaches the speed of sound in gas at the outlet pressure and temperature, which limits
the cooling of the expanding gas. Typical coldest temperatures for hydrocarbon gas in critical flow downstream of a restriction is of the −50 °C order of magnitude, not much colder.
Flow velocity across a critical flow choke can then only be increased if pressure upstream
of the choke increases. The choked flow discharge velocity may limit the depressurization
flow rate.
In both cases flow from high to low pressure causes the fluid to change temperature which
may affect the integrity of materials in the production or the depressurization systems. The
materials are exposed to ambient temperature, which supplies heat and offsets the JT cooling.
A smaller valve opening may be used to limit the flow of cold gas mass in order to maintain
temperature of the system above the material minimum temperature limit.
Flow modeling
Correlations
A number of correlations have been developed over the years using various data sets to
more accurately predict pressure drop and liquid content in a flowing fluid system. Most of
85
Flow modeling
TABLE 4.4 Application of correlations to flow in cylindrical pipes
Correlation
Geometry
Development
Beggs-Brill (Beggs and Brill, 1973)
Inclined
Empirical
Duns-Ross (Duns Jr. and Ros, 1963)
Vertical
Empirical
Hagedorn-Brown (Hagedorn and Brown, 1965)
Vertical
Empirical
Mukherjee-Brill (Mukherjee and Brill, 1985)
Inclined
Empirical
Dukler (Dukler et al., 1964)
Vertical
Mechanistic
Aziz (Aziz et al., 1972)
Vertical
Mechanistic
Observation
Small diameter
Holdup model issues
the flow modeling today is performed using software. Discussion and review of various flow
correlations is available in literature such as (Brill and Mukherjee, 1999).
To name a few correlations as in Table 4.4 and their typical application to flow in cylindrical pipes,
A more detailed information on flow correlation is in the chapter on reference information.
Although each correlation had been fit to best accuracy to data available at the time,
broader application of two-phase flow correlations may provide ±50% accuracy in system
with different conditions.
At present both engineering firms and academia aim to use computational power to validate three-phase correlations against ever larger data sets, including tens of thousands of
flow cases (Roullier et al., 2017). This results in a more reliable predictive capability of software tools and more cost-effective production system design.
Dimensionless numbers
The dimensionless numbers more commonly used in flow assurance as in multiphase flow,
fluid interfaces or solids deposition modeling include:
Reynolds Re =
Prandtl Pr =
Froude Fr =
Mach =
Ma
Euler Eu =
ρ vD inertial force
=
µ
viscous force
momentum diffusion
µ
=
k / CP
thermal diffusion
v
( g D)
0.5
=
inertial force
gravitational force
compressible fluid velocity
v
=
vSound speed of sound in compressible fluid
∆P pressure force
=
= energy dissipation in fluid flow
ρ v2
inertial force
86
4. Hydraulic and thermal analysis
Grashof Gr =
Nusselt Nu
=
Lewis =
Le
L3 ρ 2 β g ∆T
µ2
=
buoyancy
viscous force
h d convective heat transfer
=
k
conductive heat transfer
a
Sc thermal diffusion
=
=
DAB Pr
mass diffusion
µ
viscous mass transfer
ρ
Schmidt Sc =
=
DAB diffusive mass transfer
Sherwood =
Sh
Weber We =
ρ v 2 Ddroplet
σ interface
=
K c L convective mass transfer
=
D
diffusive mass transfer
fluid inertia
= interaction of two fluids at interface
surface tension
Peclet Pe=
Pr
=
Re
HEAT
Pe=
Sc
=
Re
MASS
advective heat transfer
diffusive heat transfer
advective mass transfer
diffusive mass transfer
Graetz GzHEAT =
Gz MASS =
DHydraulic
L
DHydraulic
L
Re Pr
Re Sc
The use of dimensionless numbers may be useful in understanding flow characteristics. For
example Beggs and Brill used Froude number in coordinates to present a flow regime map.
Someday multiphase software tools will be able to plot each of these dimensionless values,
which may lead to new understanding of multiphase flow phenomena and improved machine learning pattern recognition.
Software
Software can be broadly classified as capable of solving steady state and transient flow motion. Both classes include both empirical and mechanistic models, with the possibility to use
two phase flow as in vapor-liquid, three as in gas-liquid-water or four phases with addition
of a drilling mud fluid. In some instances solids transport may be added so flow of up to five
phases may be modeled.
Flow modeling
87
Specialists working on hydraulic modeling for both projects and operations offshore prefer to
use transient multiphase simulators because the production system flow path geometry includes
multiple significant changes in elevation such as wellbore and riser. Transient multiphase software allows to build the system model once and perform many different studies for both steady
state and transient or time-dependent operations. Onshore systems specialists have a preference for steady state tools as onshore geometry is more uniformly flat, wells can be modeled as
sources, and large networks of onshore gathering pipelines with hundreds or thousands of wells
can be more reliably modeled and more accurately converged using steady state tools.
With the advent of en-masse long-reach horizontal wells the flow geometry in onshore
production systems becomes more reminiscent of subsea production, with a wellbore vertical
section similar to an offshore riser. Transient multiphase simulator tools can accurately capture and predict flow instability such as slugging or liquid loading in horizontal wells.
Both classes of software have been extensively verified against laboratory and field data
and updated over the past decades. These tools provide sufficient accuracy in most cases.
Accuracy of commercial tools makes flow assurance engineering more routine because the
used preferred correlations limit the need for the specialty knowledge of how to set up a
model for a given system.
Erosion modeling
Erosion modeling has to be performed to ensure that the production system remains intact.
Typical flow velocities (as an approximation) should be limited to 70 m/s for gas systems and 70 ft/s for multiphase systems where liquids are present. At higher velocities the
liquid droplets may impinge on the pipe wall and affect the layer of corrosion inhibitor or
corrosion product usually present inside a carbon steel pipe, which may accelerate the rate
of corrosion.
Several methods exist which allow to predict the erosional velocity limit for fluid motion.
Some of these include:
°
°
°
°
DNV-0501 guideline
API 17E guideline
NORSOK P-001
SPPS
An overview and comparison of six models for single phase and multiphase flow is available in the literature (Parsi et al., 2016). However, each company should perform own selection and validation of an erosion modeling tool for their use.
Multiphase production problems
The more common problems associated with multiphase flow include
°
°
°
°
Slug movement and impacts on structures
Increased pressure drop (depends on holdup and on flow regime) and lower production
Liquids holdup (cause for corrosion, equipment weight, need for scraping)
Solids deposition
88
4. Hydraulic and thermal analysis
Increased pressure drop is the most omnipresent effect of multiphase flow. Many operators
try to produce fluid in the same state it is in the reservoir, above the bubble point pressure
in order to avoid the increased pressure loss and reduced production associated with multiphase flow. Water injection is one of the methods to maintain the reservoir pressure.
Slug impacts at pipe elbows and tees occur much less often than the increased pressure
drop but these impacts affect production system integrity and have a greater consequence.
Thus this problem is listed at the top of the list.
Deposition of solids such as soft unagglomerated hydrate slush may be accelerated by slug
flow as hydrates are periodically compacted by slug impacts.
Operation online monitoring for pipeline
Online production monitoring tools have been in field use for several decades. These tools
allow the operator to be aware of the process parameters in every location of a production or
an export pipeline without distributed instrumentation. The pressure and temperature transmitters installed at the inlet and outlet of the system along with a detailed model tuned to the
historic flow data allows the monitoring tool to calculate pressure, temperature, flow rate and
liquid holdup at every location along the pipe line.
The production monitoring tools also can provide look-ahead modeling to forecast how
the system will respond to changes in operating parameters. For example, if a pipeline carrying fluid flow is operating in a steady state it may develop certain liquid accumulation or a
holdup. If the flow rate increases, some liquid will be swept downstream. The tool allows to
forecast the time of the swept liquid arrival to the pipe line outlet so that operator can prepare
capacity in the processing facility to accommodate the arriving liquid.
Correlations
The correlations used in the production monitoring tool are the same as the ones used in
multiphase flow analysis tools. Tuning of the correlations may be done individually for each
flow system where the monitoring tool is deployed, to increase it accuracy.
Software
Variety of online monitoring software tools exists based on multiphase flow simulators. A
comparison of some of the commercial flow simulators presented by Dhoorjaty et al. (2018)
shows relative agreement between the investigated commercial and academic models.
Operation online monitoring for well liquids loading and forming
blockages/restrictions
The production monitoring tools may be equipped with modules which detect deviations
from normal parameters and interpret these as blockages, leaks and other upsets in normal
production.
Design of oil/gas development project
89
Correlations
The correlations used for detection of blockages rely on the phase transition conditions
and blockage properties for the solids which are more likely to form in a given production
or export pipeline. For example, for the detection of a wax blockage, the wax appearance
temperature as a function of pressure would be used to tell the monitoring tool whether the
wax solid phase is possible or not at a given location in the pipeline. The deviation of pressure
drop may then be interpreted as wax or another type of restriction if wax is not thermodynamically stable at that location.
Software
The same production monitoring tools can be used to detect the onset of liquids loading
and the forming blockages.
Design of oil/gas development project
The following flow assurance analysis is usually required for the design of a new project.
✓ Steady state line sizing and transient evaluation
° for gas fields
° for gas condensate fields & for volatile oil
° for black oil fields
° for heavy/viscous oil and tar sands production
✓ Steady state line sizing and transient analysis for gas or water reinjection case;
✓ Steady state line sizing for production chemical distribution system
✓ Optimization for the flow assurance mitigation strategy, with account for other issues and
solids (wax, scale, asphaltene, slugs, sand, etc.) that might interfere in the normal production
Hydraulic management
Hydraulic design should optimize both frictional and hydrostatic pressure loss, holdup
accumulation, vibration, water hammer and surge exceeding normal operating parameters
during steady and transient operations. Sensitivity to produced water cut should include assumption for planned and deferred water injection for pressure support, based on reservoir
simulation production profiles.
Operability design should ensure temperature, pressure and flow are within normal operating limits for the system at any stage in field development life.
Flowlines from trees to manifolds and from manifolds to hubs should be routed predominantly uphill to minimize pressure losses due to terrain liquids holdup in low spots, in order
to maximize overall recovery, and to avoid slugging to enable uniform subsea chemical distribution in produced fluid.
Detailed field layout should ensure that both production and chemical injection systems
can operate with acceptable pressure drop and chemical stability in subsurface, subsea,
­topsides and export systems conditions.
90
4. Hydraulic and thermal analysis
Single line tieback concepts may be considered for early production systems.
Technologies which could be considered in formulating a conceptual hydraulic design of a
field development include the following:
•
•
•
•
•
•
•
•
•
•
•
•
Slug catcher or separator vessel(s)
Periodic scraping
Onshore or subsea compressors or booster pumps
Onshore or subsea multiphase pumps
Gas separator to minimize hydraulic loss or to reduce hydrate risk
Water separator to minimize hydraulic loss or to reduce hydrate risk
Downhole, wellhead and/or riser base gas lift
Caisson gas separator if subsea reservoir is insufficiently strong
Drag reducing agent chemical
Multiphase flow meter or virtual flow meter
Erosional limits for line sizing
Water injection pump pressure limits per rock fracture gradient
Designs specific to subsea in the United States may refer to the following API technical
reports:
Avoidance of Blockages in Production Control Systems, API 17TR5;
Attributes of Production Chemicals in Subsea Production Systems, API 17TR6;
High-Pressure High-Temperature (HPHT) Design Guidelines, API 17TR8;
HIPPS for subsea, API 17TR13, section 10.8, and API 17O.
Water injection management
Multiphase flow assurance specialist may consult with topsides process, completion, and
reservoir engineers to design an effective system for water injection. Produced water injection system should be separate from sea water injection system if produced water overboard
discharge is not permitted.
Injection water should be treated seawater and not produced water. Produced water injection wells are subject to faster degradation of injectivity than seawater injection wells.
The injection water pump sizing and discharge pressure should take into account rock
fracture gradient. Injection pump design should include flexibility for injection at or above
the reservoir fracture pressure if injection above the reservoir fracture pressure is permitted.
The water injection pipe line minimum flow velocity in turndown case should be over 5 ft/s.
Project may consider placing water injection pump and filtration equipment on seabed to
reduce the number of risers.
Water hammer effects shall be accounted for in the design of all process control for valves
and automation operation.
Injection water quality relies on not mixing produced water and seawater in the injection
system. Even with very high injection water quality, operations may need to clean the wells
periodically.
Injection wells should be isolated when not in service so that no cross-flow happens between injection wells on shut-in if several injection wells are fed from the same
manifold.
Machine learning and artificial intelligence in flow network optimization
91
Provision for water injection line and header maintenance scraping to sweep any bacterial
growth should be included, with ensuring that scraped solids do not enter the injection well
or header. Proven technologies for anti-bacterial coating should be considered for water injection lines.
Injection wells should have a provision for hydrate inhibitor injection as hydrocarbons
may migrate up the wellbore and form a solid hydrate blockage near mudline when the injection well is not flowing.
Flow restriction and blockage monitoring
Production control and automation system should be able to monitor for leading indicators of an imminent blockage and to mitigate it as early as is noticed by altering operating
parameters upon approval by operations manager or by solvent / chemical injection. If flow
restriction mitigation was unsuccessful or late, monitoring capability should assist in a safe
and systematic remediation of blockage.
Technologies which could be considered for monitoring of blockage in produced fluids
include:
•
•
•
•
•
•
•
•
•
•
•
•
pressure differential deviation
temperature deviation
flow deviation
vibration deviation
valve operability change
water composition and pH
chemical residuals
oil and water quality
gas dew point and moisture content
bacteria counts
asphaltene instability
solids TDS and TSS monitoring.
Emerging technologies which may be applicable on a case by case basis include ­gamma-ray
densitometer, ultrasound solids detection, and guided wave deposit detection. The large
number of monitored parameters make it conducive to implement flow and blockage monitoring with a machine learning method.
Machine learning and artificial intelligence in flow network optimization
The early development in the use of computer for network flow optimization came in the
form of spreadsheets with multiple runs indicating the hydraulic resistance of individual
components of the network. One early example of such spreadsheet was presented by Lezeau
and Leporcher nearly two decades ago (Lezeau and Leporcher, 2001). The methodology and
logic presented in their work still is generally applicable to a further implementation of the
network flow optimization process.
92
4. Hydraulic and thermal analysis
Accuracy of the individual components of the hydraulic model such as reservoir flow
resistance, wellbore flow resistance, tree choke flow resistance and gathering flowline and
riser flow resistance all play into the overall reliability of the prediction for network flow
optimization.
Eventually the process was developed to integrate the network model within a single
steady state multiphase simulator. There are numerous commercially available steady state
simulators which can handle the task of flow network optimization.
Present day simulation is seeing a growing adoption of methods based on machine
learning algorithms. Multiple operator corporations and service companies are developing
capability in this area and deploying their solutions as field application. In the machine
learning approach, a number of simulations is performed for the individual segments and
for the whole network to determine flow hydraulic loss for a given set of conditions. With
the data set developed for the flow resistance versus operating conditions, machine learning database is then trained on a part of the data set, with the remaining part of the simulations comprising the data set kept for verification or validation of the accuracy of the
trained database prediction. Modern tools such as Python 3.7 language and Pytorch library
for parallelizing the database training in order to save time, with appropriate integrated
development environment tool such as Jupyter, may be used to implement artificial intelligence for flow network optimization. Development tools keep evolving along with hardware and software, so newer ones may gain acceptance with time. Recent implementations
of machine learning also deal with virtual flow metering (Andrianov, 2018), choke control,
gas lift optimization, as well as the detection of flow assurance blockages building up in the
production system.
A comparison of various artificial intelligence methods for multiphase hydraulic calculations with field data is provided by Attia et al. (2015).
References
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diameter pipes and high flow rates. In: Presented at Middle East Oil Show, 11–14 March Bahrain.
Andrianov, N., 2018. A machine learning approach for virtual flow metering and forecasting. In: Proc. of 3rd IFAC
Workshop on Automatic Control in Offshore Oil and Gas Production, Esbjerg, Denmark, May 30–June 01.
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Attia, M., Abdulraheem, A., Mahmoud, M.A., 2015. SPE-175724, Pressure drop due to multiphase flow using four
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Further reading
93
Dhoorjaty, P., Erickson, D., Kowta, R., 2018. A comparative study of the performance of multiphase flow pipeline
simulators in a hilly terrain pipeline. In: BHRG Multiphase Conference, Banff.
Dukler, A.E., Wicks, M., Cleveland, R.G., 1964. Frictional pressure drop in two-phase flow: an approach through
similarity analysis. AlChE J. 10 (1), 44–51.
Duns Jr., H., Ros, N.C.J., 1963. Vertical flow of gas and liquid mixtures in wells. In: Proceedings of 6th World
Petroleum Congress, pp. 451–456.
Fairhurst, P., 2002. Slugging prediction, Galveston flow assurance forum, 17-19th September.
Hagedorn, A.R., Brown, K.E., 1965. Experimental study of pressure gradients occurring during continuous twophase flow in small-diameter vertical conduits. J. Pet. Technol, 475–484.
Hetsroni, G., 1982. Handbook of Multiphase Systems. Hemisphere Publishing Corporation, McGraw Hill Book Company.
Hill, T., Wood, D.G., 1990. A new approach to the prediction of slug frequency. In: SPE-20629, SPE ATCE, pp.
141–149.
Hill, T.J., Wood, D.G., 1994. Slug flow: occurrence, consequences and prediction. In: SPE-27960, In University of Tulsa
Centennial petroleum engineering Symposium.
Hinze, J.O., 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AICHE J. 3, 289.
Jansen Jeppe, M., 2009. Evaluation of a flow simulator for multiphase pipelines. Master of Science Thesis, Norwegian
University of Science and Technology.
Jerez-Carrizales, M., Jaramillo, J.E., Fuentes, D., 2015. Prediction of multiphase flow in pipelines: Literature review,
Ingeneria y Ciencia.
Lezeau, P., Leporcher, E., 2001. A spreadsheet tool to ease the selection of a Deepwater production network. In:
Proceedings 10th International Conference on Multiphase Flow, BHRg, Cannes France 13–15 June.
Makogon, T.Y., Estanga, D., Sarica, C., 2011. A new passive technique for severe slugging attenuation. In: 15th
Multiphase Production Technology Conference, Cannes, France: 15–17 June.
Montgomery, J.A., 2002. Severe slugging and unstable flows in an S-shaped riser. PhD Thesis, Cranfield University. p. 22.
Mukherjee, H., Brill, J.P., 1985. Pressure drop correlation for inclined two-phase flow. J. Energy Resour. Technol. 107,
549–554.
Parsi, M., Kara, M., Sharma, P., McLaury, B.S., Shirazi, S.A., 2016. Comparative study of different erosion model
predictions for single-phase and multiphase flow conditions. In: OTC-27233, Offshore Technology Conference,
2–5 May, Houston.
Poettman, F.H., Carpenter, P.G., 1952. API-52, The multiphase flow of gas, oil and water through vertical flow strings
with application to the design of gas-lift installations. In: Drilling and Production Practice. American Petroleum
Institute, p. 257.
Roullier, D., Shippen, M., Adames, P., Pereyra, E., Sarica, C., 2017. Identification of optimum closure relationships
for a mechanistic model using a data set for low-liquid loading subsea pipeline. In: SPE-187327, SPE ATCE, 9-11
October, San Antonio.
Shea, R.H., Rasmussen, J., Hedne, P., Malnes, D., 1997. Holdup predictions for wet-gas pipelines compared. Oil Gas
J. 95 (20).
Shea, R., Eidsmoen, H., Nordsveen, M., Rasmussen, J., Xu, Z., Nossen, J., 2004. Slug frequency prediction method
comparison. In: BHRG Multiphase Production Technology Proceedings, Banff, Canada.
Swamee, P.K., Jain, A.K., 1976. Explicit equations for pipe-flow problems. In: J or the Hydraulics Division, ASCE. Vol.
102, No. HY5, Proc. Paper 12146, May, pp. 657–664.
Turner, R.G., Hubbard, M.G., Dukler, A.E., 1969. Analysis and prediction of minimum flow rate for the continuous
removal of liquids from gas wells. J. Pet. Tech, 1475–1482.
Warner, A., Letizia, L., 2001. Hyprotech, Gas-liquid Sand flows in horizontal pipelines—a novel model. In: Proceedings
10th International Conference on Multiphase Flow, BHRg, Cannes France 13-15 June.
Wenzel, S., Czapp, M., Sattelmayer, T., 2016. Numerical investigation of slug flow in a horizontal pipe using a multiscale two phase approach to incorporate gas entrainment effects. https://www.td.mw.tum.de/en/research/
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Further reading
Makogon, T.Y., Brook, G.J., 2013. Device for controlling slugging. US Patent 8393398.
C H A P T E R
5
Flow restrictions and blockages in
operations
O U T L I N E
Frequency of blockages
97
Frequency of blockage remediations
Duration of hydrate and other
flowline remediation
97
Hydrate versus other flowline
remediation time
98
99
Blockage remediation
101
Hydrate of natural gas
Introduction
Gas hydrate formation
Hydrate propensity, subcooling,
supercooling and
overpressurization
Chemistry
Thermodynamic features
Stability
Problems related to hydrate formation
Hydrate plug formation mechanism
Calculating location of hydrate
blockage in a pipe
Prevention of hydrate formation
Hydrate dissociation
Hydrate blockage remediation
Comparative economics of hydrate
prevention methods
101
101
102
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00005-1
Environmental impacts of hydrate
remediation
Health impacts
Effect of hydrates on corrosion
Gas hydrate in wells and in nature
Hydrate management
Emerging technologies of hydrate
management
Modeling of gas hydrates
Case studies and process safety
Commissioning/dewatering of
pipelines to avoid hydrates
104
106
106
108
108
109
109
110
117
118
121
Asphaltenes
Introduction
Asphaltene chemistry
Reservoir and wellbore plugging
Prediction of asphaltene risk
Light oil and EOR
Gas condensate
Heavy oil
Role of asphaltenes in microbubble
capture
Asphaltene precipitation and deposition
in wells and pipelines
Monitoring and remote sensing of
asphaltenes
95
122
123
123
125
127
128
129
131
139
140
140
141
141
142
143
143
144
144
144
145
© 2019 Elsevier Inc. All rights reserved.
96
5. Flow restrictions and blockages in operations
Remediation of asphaltene plugging
Environmental impact of various
techniques
Modeling of asphaltenes
Prevention of asphaltenes
146
Effect of PVT conditions
Role of composition
Miscellaneous factors
Tubular plugging
Prevention techniques
Remediation techniques
Environmental impacts of remediation
techniques
Measurement techniques
Conventional techniques
Remote sensing and monitoring
Emerging techniques
Modeling
Comprehensive modeling
Waxy gels
Case studies
146
146
147
Bacterial growth
Topsides process equipment
Water injection wells
Bacterial growth management
148
148
148
148
Corrosion products
Transport of solid corrosion products
149
149
Diamondoids
149
Ice
150
Liquid holdup
Water in gas and oil lines
Condensate in gas lines
Steam (condensed water in oil
sands steam injection lines)
Liquid accumulation in horizontal
and vertical wells
150
150
151
Multiphase flow
Flow resistance of gas, oil and water
Vacuum condition and pressure surge
during stock oil flow
153
153
Sand transport
Minimum transport velocity
Erosional velocity limits
Liquid with solids (hydrate,
corrosion products, scale)
153
154
155
Paraffin wax
Introduction
Chemistry
Composition
Structure
Wellbore and reservoir plugging
156
156
159
159
160
160
151
152
153
156
161
163
163
163
164
167
168
168
171
171
171
171
173
174
176
Reservoir souring
Introduction
Mitigation of reservoir souring
Treatment of sour production
Modeling of reservoir souring
176
176
177
177
178
Scale
178
178
178
178
179
179
180
181
Description
Carbonate
Sulfate
Analysis
Prediction
Remedial actions
Scale prevention
Interaction of flow assurance issues
with and effects on produced
fluids and flow
181
Seven suggestions from operations in
deepwater and onshore
183
References
184
Further reading
188
There are many types of flow assurance restrictions. Some of the more frequently encountered ones include asphaltenes, waxes, hydrates, scale and sand.
Flow assurance issues which may impede flow include the following:
• Hydraulic liquids holdup
• Emulsions, foam
Frequency of blockage remediations
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
97
Water injectivity loss
Formation damage or compaction
Hydrate
Ice
Wax and gels
Scale
Sulfur deposition
Naphthenate
Asphaltene
Diamondoids
Heavy oil
Viscous oil
Bacterial growth
Corrosion products
Sand
Field layout with low spots
Choice of technology(ies) for managing each of these possible threats should be based on reservoir rock type, reservoir fluids chemistry, regional environmental regulations, regional waste
handling availability, and technology commercial availability in the region. Various combinations of available and permissible flow assurance technologies should be screened in preliminary concepts evaluation. Technologies may be changed or made complementary during the life
of field, for example, operations may choose to switch from AA to KHI as water cuts increase, or
from KHI to MEG as demand for system reliability increases. Details of addressing some of the
flow assurance risks below may serve for development of project-specific flow assurance.
Frequency of blockages
The sequence in Fig. 5.1 and in Table 5.1 below is based on the subjective survey from the
SPE Flow Assurance Forum held in USA in June 2015. Although the forum was attended by
flow assurance specialists from different continents, these values should be used as indicative
only as this survey represents a fairly small sample size for a proper statistical analysis.
Location and frequency of blockages were marked by the Forum participants based on
their knowledge of the industry.
Frequency of blockage remediations
Historically, the US Minerals Management Service had received and processed applications
for flowline remediation in deepwater. Between 1991 and 1998, 52 subsea flowlines were reported blocked with wax and hydrates (Alvarado, 1999, 2003). Of these, all hydrate blockages
were remediated, and approximately half of the pipelines plugged with wax were abandoned.
Since then, several long-reach coiled tubing technologies have been commercialized to
clear out blockages from pipelines by hydraulic jetting. Similarly, technologies for subsea
hydrate and other blockage remediation by a subsea pump depressurization have matured
and became a common practice.
Some information about the global use of subsea blockage remediation with a commercially available subsea pump equipment during the past decade from 2008 through 2017 was
98
5. Flow restrictions and blockages in operations
FIG. 5.1 Frequency of flow assurance issues as indicated by the participants at the 2015 SPE Flow assurance
Forum, representing both onshore, subsea and shale production.
TABLE 5.1 Perceived locations and frequency of flow assurance blockages
Location
Asphaltene
Wax
Hydrate
Scale & sand
Reservoir
1
0
1
4
Well
30
2
0
13
Flowline & riser
0
28
24
7
Injection line
0
2
4
0
Export line
0
2
6
0
Subsea process
0
0
0
0
Topsides process
3
0
0
7
Tree & manifold
0
0
2
0
shared by one of the technology providers (Oceaneering, 2018). This information may be
useful in comparison of various flow assurance strategies.
Blockages occur at all water depths. The information in the graphs below is a summary of
subsea remediation for hydrate remediation and for other flowline remediation over the recent
decade from 2008 through 2017.
Duration of hydrate and other flowline remediation
On average, hydrate remediation took 21 days; the duration was nearly independent of
water depth as shown in Fig. 5.2. Other flowline remediation average time was 25 days;
99
Frequency of blockage remediations
Days for subsea remediation
160
Hydrate remediation
140
Other flowline
remediation
Time (days)
120
Linear (hydrate
remediation)
100
Linear (other flowline
remediation)
80
60
40
20
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10,000
Water depth (ft)
FIG. 5.2 Days for remediation of subsea flow assurance blockages.
this duration showed an increasing trend with water depth. Remediation project cost may
include, besides renting specialized remediation equipment, hiring a support vessel to deliver the equipment to the flowline which may range from a service boat at approx. 50–100
thousand of US dollars per day to a workover rig or a drilling rig which may cost 300–600
thousand USD per day. Additional cost for staff, engineering support, chemicals and mobilization/demobilization should also be considered when a flow assurance strategy is selected.
Typical cost limit for a subsea remediation project has been around 20 million USD, but valuable high productivity assets may increase this limit. Costs are approximate and shown in
2018 US dollars. While costs tended historically to approximately double every 20 years due
to inflation, future costs in USD may vary.
Hydrate versus other flowline remediation time
With time the flowline remediation methods become more effective and take less time.
However, the time for hydrate remediation subsea keeps increasing from year to year as
shown in Fig. 5.3.
The actual frequency of blockages occurrence is an important input into risk models.
Recent changes in the price of the produced hydrocarbon commodity made operators optimize cost of new projects to ensure these are still profitable. One of such optimizations is
risk-based flow assurance, discussed further, when the production system is estimated to get
plugged once per a time period. A common flow assurance strategy is to build a dual multiphase pipeline tieback to a new field which can be scraped, and live produced fluids can be
displaced with stock tank crude to mitigate most flow assurance risks.
An example of a risk-based flow assurance strategy approach is to build a single multiphase flowline subsea tieback to a new field if the probable cost savings of not installing the
second line outweigh, by a pre-set margin, the probable operating cost losses from the unmitigated flow assurance risks.
It would be useful for such risk-based approach to know the relative frequency for
­remediation of certain types of flow assurance blockages. A summary Table 5.2 for hydrate
100
5. Flow restrictions and blockages in operations
Progress in subsea remediation time
160
140
Hydrate remediation
Other flowline remediation
120
Linear (hydrate remediation)
Time (days)
Linear (other flowline remediation)
100
80
60
40
20
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
Year of work start
FIG. 5.3 Progress in subsea remediation time.
TABLE 5.2 Frequency of hydrate blockage remediations by one service provider
Year
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
Number
6
3
14
7
7
12
14
10
5
11
remediation performed by one technology provider below may be indicative of the overall
frequency of flow assurance blockages.
While the average number of hydrate blockage remediation projects per year is 9 globally
for one service provider as shown in Fig. 5.4, this is a lower estimate. Some blockages remain
Hydrate remediations per year
16
14
12
10
8
6
4
2
0
2007
2008
2009
2010
2011
2012
2013
2014
FIG. 5.4 Trend of subsea hydrate remediations by one service provider.
2015
2016
2017
2018
Hydrate of natural gas
101
in a plugged pipeline until the regulatory requirements mandate the operator to remove the
blockage or to decommission the pipeline. Some blockages get remediated by operator companies through operating process parameters manipulation, with proper engineering support. Some blockages get remediated by other service providers. In rare cases, blockages have
been known to get remediated by a confluence of events triggered by a natural phenomenon
like a hurricane as discussed earlier in Chapter 1.
Historically, the number of hydrate blockages has been on an uptrend.
Blockage remediation
Production system should be designed for blockage remediation to enable the removal of
blockage(s) and to avoid secondary re-formation of solids. Access points and topsides deck
space should be designated for regionally available remediation equipment. System equipment should include provisions for flow reversal for blockage remediation such as a stuck
scraper.
Technologies which could be considered for remediation of blockage in produced fluids
include:
•
•
•
•
•
•
Solvent chemical
progressive scraping
depressurization from topsides
depressurization through gas lift line
subsea depressurization skid
dry tree coiled tubing jetting.
Field-proven technologies which may be applicable on a case by case economic basis include pressure pulsation, long reach coiled tubing, and active electric heating.
Hydrate of natural gas
Introduction
Hydrates are solid crystals combining water molecules and guest molecules in a proportion
of approximately 10 wt% gas and 90 wt% water. Flow assurance deals mainly with hydrates
of light hydrocarbons such as methane, ethane, propane and isobutane present in natural gas.
Hydrates were first observed and reported by Priestley (1778). The compound was named
by Davy.
After hydrates form, they get deposited on pipe wall or dispersed in hydrocarbon liquid or
in water. Hydrate acts as a solid restriction or as viscous slush creating resistance to fluid flow.
Both light and medium gas components can form hydrate crystals but hydrates of
­medium-sized molecules are less often encountered in production systems. Medium-small
molecules like neohexane can still fit in hydrate cells (Makogon, 1996) but in general larger
hydrocarbon molecules with 5 or more carbon atoms in a chain are too big to fit as guests in
the hydrate cells.
102
5. Flow restrictions and blockages in operations
Gas hydrate formation
The formation of gas hydrate usually begins at the interface of water-gas-solid or water-­
hydrocarbon-solid. This is called heterogeneous nucleation. The presence of a solid reduces
the time it takes to start the formation of the crystal, called an induction time. In reality this is
related to the reduction of the energy barrier as described in a book by Makogon (1974, 1981)
on pages 65 and 72 accordingly. Whether a small crystal nucleus continues to grow larger
than the critical radius or dissolve depends on the latent heat of crystallization Q, supercooling at which crystallization occurs and nucleus' specific surface energy σ:
(
logP [ bar ] = β + 0.0497(T   C  + k T   C 
2
)
Crystals don't start to form as soon as the hydrate stability condition is reached. It takes extra cooling below the stability temperature to help organize the water molecules into a lattice
of cells which can trap gas molecules. This extra cooling is known as subcooling or supercooling or propensity. These terms are used interchangeably. The greater the subcooling, or the
difference between hydrate equilibrium temperature and local temperature in the system, the
sooner the crystals will start to form.
Similarly Sloan (1990) in p. 83 also provides an expression referenced from prior publications for the critical size of hydrate crystal nuclei above which the crystal continues to grow
as a function of the surface tension σ and a change in Gibbs free energy.
rcr = −
2σ
∆g
Neither manuscript provided a clear indication of what the typical size for the critical
nucleus would be—whether it is of the order of magnitude of 10 Angstroms, 100, or 1000,
rightly so because the nucleus size depends on the process. Nonetheless knowing the order
of magnitude for this value is important for a general understanding of how hydrates form.
Koh et al. (1996, 2000) suggests the gas hydrate nucleus size is of the order of 1 nm. A molecular modeling work by Walsh et al. (2009) with TIP4P-ICE confirms critical nucleus is of the
nanometer scale.
The importance of microbubbles and nanobubbles of gas for hydrate formation was described by Makogon (1996), ICGH-2. The radius of such microbubbles was related to pressure
of gas in such bubbles and the surface tension through the Laplace's law and the van der
Waals equation. An example detailed calculation presented in that work showed the gas microbubble size at 4.3 nm or 0.0043 μm. Pressure inside such gas microbubbles was estimated
to be on the order of tens of MegaPascals or higher.
An important observation is made by Sloan (1990) in p. 74 that works by Angell and Speedy
and Angell (1976) indicated that concentration of hydrogen-bonded polyhedra is suggestive
of pre-nucleation phenomena.
Rahman and Stillinger (1973) showed that hydrogen-bonded water molecules is arranged
as polygons.
Makogon (1974, 1981) calculated from measurements the number of hydrogen bonds remaining in water after melting of ice and after dissociation of hydrate.
Number of hydrogen bonds in water is shown in Table 5.3.
103
Hydrate of natural gas
TABLE 5.3 Number of hydrogen bonds in water at different temperatures
Temperature (°C)
0
25
50
100
150
200
250
300
350
% broken H-bonds in water
9
11
13.8
20
26
34
45
61
86.5
Average number of water molecules in
a cluster
860
455
288
70
37
16
8
4
1–2
After reference Makogon, Y.F., 1974. Gidraty Prirodnogo Gaza (Hydrates of Natural Gas, in Russian). Nedra, Moscow.
Vast majority of water molecules are hydrogen-bonded to their neighbors, with only a
small portion of bonds broken due to conformational defects, for example if two neighboring
water molecules point their hydrogen atoms in each other's direction. Broken bonds between
neighboring water molecules are eventually restored due to molecules' reorientations and
rearrangements. Some bonds are strained because of the differences in molecular positions.
A conceptual schematic of water molecules interconnected into a network by hydrogen
bonds is shown below, with few bonds broken. The network is dominated, according to
Rahman and Stillinger, by hexagons and pentagons as shown in Fig. 5.5. The results shown in
Chapter 10 confirm this distribution.
The water molecules are predominantly bonded, but the network contains defects and
some bonds are strained. When sufficient amount of gas such as methane is dissolved in
FIG. 5.5 Network of hydrogen-bonded water molecules is dominated by hexagonal and pentagonal ring groups.
104
5. Flow restrictions and blockages in operations
FIG. 5.6 Hydrate crystal formed by a lattice of hydrogen-bonded water molecules around a gas molecule.
­ ater, methophobicity or repulsion of water molecules from methane helps reorganize the
w
water network by making hollows or cavities to contain methane molecules into a crystal
lattice as sown in Fig. 5.6 with a less strained arrangement of hydrogen bonds.
The method for modeling water properties with a computer and calculating the number of
polygons is discussed in Chapter 10.
Rate of hydrate formation in production systems, process equipment and in nature may be
limited by the availability of water molecules, gas molecules and by heat transfer away from
the crystallization front.
The rate of hydrate blockage formation in operating conditions may range from tens of
minutes in liquid-dominated multiphase flowing systems to days in gas systems, depending
on the limitations mentioned above. The changes in differential pressure or changes in the
amount or composition of water arriving to the system outlet within this timescale may be
indicative of hydrate formation.
The rate of hydrate formation observed in laboratory as shown in Fig. 5.7 conditions can
be as high as 1 mm/s (Makogon, 1999) when there are no limitations to heat or mass transfer.
The typical growth rate of methane hydrate at an interface with seawater is on the order of
5 mm/min (Makogon et al., 2000). The growth rate decreases by 60% to approximately 2 mm/
min with a thermodynamic inhibitor such as 5% methanol.
Hydrate propensity, subcooling, supercooling and overpressurization
In addition to subcooling, the overpressurization can measure how far in the hydrate stability region is the local condition.
Overpressurization may be a useful measure in laboratory evaluation of gas hydrates
(Talley, 2000). Overpressurization may help discern the performance of some LDHI chemicals
105
Hydrate of natural gas
FIG. 5.7 Fast hydrate growth at gas-water interface at 110, 150, and 190 s (Makogon, 1999).
such as KHI or kinetic hydrate inhibitors. While some KHIs may perform well at a high subcooling at lower pressures (e.g. below 50 bar), their performance may deteriorate at the same
subcooling but at higher pressures. Although the terms may be seen in use interchangeably,
there is a difference as shown in Fig. 5.8.
Due to the non-linearity of hydrate equilibrium curves plotted in pressure-temperature
coordinates, the hydrate propensity varies whether measured as subcooling or as overpressurization. It is possible to plot a hydrate curve as a straight line (Dendy Sloan, personal
communication, 1993; Makogon, 1994) by presenting data either in ln(pressure) versus 1/
Temperature coordinates or as a semi-logarithmic plot. To illustrate, after plotting methane
hydrate stability line in semi-log coordinates, the propensity differs for a fixed subcooling
and a fixed overpressurization.
Methane hydrate stability data (Deaton and Frost, 1946) are shown in the plot. Onset of
hydrate formation is shown from a laboratory experiment (Makogon and Holditch, 2001b,
Oil & Gas Journal, p. 45). The maximum propensity at which methane hydrate formation
started in a clean laboratory system observed in Fig. 1A of this work is approximately 7 °C or
Pressure (MPa)
10
1
265
CH4 hydrate stability data
constant subcooling 7 K
constant overpressurization 4 MPa
Makogon CH 4 subcooling
270
275
280
285
Temperature (K)
FIG. 5.8 Comparison of subcooling and overpressurization for methane hydrate.
290
106
5. Flow restrictions and blockages in operations
4 MPa. The graph illustrates that the constant overpressurization line corresponds to a lower
subcooling at higher pressures, which fits empirical observations for KHI performance. At
lower pressures, higher subcooling may be achieved for a set overpressurization before hydrates start to form. At higher pressures, hydrate starts to form at a lower subcooling for a set
overpressurization.
An observation was made in laboratory tests by Makogon and Sarkisyants (1966, p. 36) that
a hydrate formation condition for a multi-component gas mixture differed from the hydrate
dissociation condition. The start of hydrate formation was observed at temperatures lower than
hydrate equilibrium (dissociation) condition by 1–10 °C approximately as read from the graph.
Makogon (1974, 1981) also studied the effect of water preheating to reduce hydrogen bond
structure in water on subcooling required to start hydrate formation. Table 12 and Fig. 37
in this work show that subcooling ranged from 0.6 to 8.3 °C at 127 atm and from 3.0 to 8.2
at 75 atm for methane hydrate. For ethane hydrate, Table 13 in this [1974, 1981] work shows
that subcooling ranged from 1.5 to 8.6 °C depending on pressure. He found that preheating of
water had effect on subcooling, but preheating beyond 30–35 °C gave no extra effect.
This is relevant to flow assurance project design because some operator companies base
the hydrate risk mitigation on a fixed subcooling value. Some companies use a positive subcooling and take a calculated risk by allowing the system to operate inside the hydrate stability region by a fixed number of degrees in temperature. Some companies take a conservative
approach and use negative subcooling, designing the system operation to stay away from the
hydrate region by a fixed safety margin of a number of degrees. Overpressurization margin
could be a more appropriate measure for use in designing a production system for hydrate
risk management. Also it is not advisable to rely on positive subcooling or overpressurization
(i.e. to design a system to operate inside a hydrate region) as measured in clean laboratory
conditions because in field operations produced fluids introduce impurities and solid particles which act as crystal nucleation sites and allow hydrates to start forming more easily,
closer to the equilibrium than in a laboratory.
Chemistry
Gas hydrates are chemically neutral as no chemical reactions occur during their formation
or dissociation, only a fraction of hydrogen bonds between water molecules changes.
As hydrate may consume sour gas components such as CO2 and H2S, the overall pH of the
fluid may change as a result of hydrate formation.
Crystal surface of hydrate may be both electronegative and electropositive as shown in
Fig. 5.9, depending on which level the crystal surface is cleaved at.
sII hydrate {1,1,1} dominant plane is commonly seen in real crystals.
Chemical conformations, bonding energy and active sites can be viewed on crystals with
molecular modeling as shown in Fig. 5.10. This helps compare the effectiveness of chemicals
before lab synthesis and tests.
Thermodynamic features
Thermodynamically the gas hydrates act as solids with low compressibility. A summary
overview of phase diagrams for gas hydrates for various components, including several
Hydrate of natural gas
107
sII hydrate {1,1,1} dominant crystal plane commonly seen in real crystals. Model shows open large 51264
cavities. Red and blue sites represent variation in electronegativity.
FIG. 5.9
FIG. 5.10 Model of polyvinylpirrolidone KHI polymer adsorbed on sII {1,1,1} crystal surface of hydrate.
108
5. Flow restrictions and blockages in operations
­ uadruple points where ice, water, hydrate and vapor can coexist, is presented by Sloan
q
(1990). More rare quintuple points for hydrates also exist such as the one discovered at the
Colorado School of Mines for the coexistence of water, structure I hydrate, structure H hydrate, liquid hydrocarbon and vapor five phases at the same condition.
Pure gas hydrate has a relatively low electrical conductivity or high electrical resistivity
which is on the order of 20,000 Ωm (Dunbar, 2013). That property, combined with the speed
of sound different from that of surrounding rock is used to find location and saturation of gas
hydrate deposits in geophysical studies of natural deposits of gas hydrates. Typical electrical
resistivity of a gas hydrate deposit is of the order of 100 Ωm, seabed is 1 Ωm and seawater
0.36 Ωm. The compression wave speed of sound is reported at 3650 m/s, and the shear wave
speed measured simultaneously, is 1890 m/s (Waite et al., 1999).
Stability
Stability of gas hydrates varies with pressure and temperature. In general, hydrates are
more stable at low temperatures and high pressures. At lower temperatures water molecules
have less movement relative to each other. At higher pressure more guest molecules such as
methane are dissolved in water. Hydrogen bonds which hold together the water molecules in
the gas hydrate crystal are stable at lower temperature and at higher pressure.
As an example, a structure II hydrate commonly encountered in subsea production systems
typically would form at approximately 10 atm and 4 °C with fresh water without chemicals.
To make a formed gas hydrate unstable, one or more of the following is required: lower
pressure, higher temperature, fewer hydrogen bonds. Chemicals such as methanol act by
removing hydrogen bonds from the gas hydrate crystal. Methanol does that by making the
hydrogen bonds in water which makes up the gas hydrate crystal switch from hydrate to the
hydroxyl group OH in methanol where electronegative oxygen in methanol attracts electropositive hydrogens in water.
As 4 °C or 40 °F is a temperature usually found in deep water environment, production systems may require a depressurization to below 10 bar in order to dissociate any formed hydrate.
In some cases the depressurization needs to be to a lower pressure because some chemicals
such as kinetic hydrate inhibitors (KHI) stabilize hydrates (Makogon and Holditch, 2001b).
Problems related to hydrate formation
Gas hydrate formation creates mainly economic but also safety issues. In onshore production systems, both wells and gathering lines get plugged by gas hydrates. In subsea systems,
mainly trees, flowlines and risers get plugged. A blocked well or a flowline can no longer generate revenue. However, hydrates also have plugged process equipment and flare relief lines
which led to a loss of primary containment and release of hydrocarbons. Hydrates require
four conditions to form: low temperature, high pressure, water and light hydrocarbons such
as gas or live oil. These four conditions can be met in some process operations which leads to
partial or sometimes complete hydrate blockages.
A hydrate plug occupies nearly all cross-section of the pipe. A radiographic image in
Fig. 5.11 shows a hydrate plug in a USA onshore field pipeline.
Partly dissociated gas hydrate particles can also be transported to relief lines from elsewhere
in the plugged line and restrict or block the vent relief line. In one instance (Makogon, 2017)
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FIG. 5.11 A radiographic image of a hydrate plug in a field line.
the cross sectional area of a relief line was reduced by half, which increased the time of
depressurization.
Water expands more when it turns into hydrate than when it freezes as ice. Hydrates possess a significant mechanical strength. Image of a collapsed production tubing in Chapter 1
shows the expansion effect of hydrate formed at 8 °C in a well annulus at 1100 m depth.
Collapse pressure was estimated at >800 atm. Volumetric expansion of hydrate relative to
water can be easily calculated from the crystallographic measurements. Hydrate occupies
approximately 26% more volume than the water making up the hydrate.
Hydrate plug formation mechanism
The viscosity of the hydrate slurry is one reason for the plug formation. Pressure of the
reservoir fluids may be insufficient to move several hundred feet of a highly viscous non-­
Newtonian liquid through a flow line.
The other reason is agglomeration of hydrate particles and their adhesion to the flowline
walls.
Numerous field studies were dedicated to the subject. A 3-in. service flowline in the
Tommelitten field in Norway was purposely plugged with hydrates nearly 20 times to study
the process of hydrate plug melting.
The recent advancements in hydrate research at the CSM allowed us to select the reasonable average size of a hydrate particle at 40 μm [March 2005 meeting, Golden, Colorado]. The
significance of the hydrate particle size is in the hypothesis that particles larger than 40 μm
would, on average, be larger than the size of the momentum or velocity boundary sublayer
near a pipe wall and will be transported by flow. The model assumes that the settled (<40 μm)
particles remain stationary.
A more detailed method exists to estimate average hydrate particle size from the
Kolmogorov energy dissipation for a specified flow rate as discussed further in this chapter
in and below Fig. 5.29.
Calculating location of hydrate blockage in a pipe
1. Calculate hydrate stability envelope
Use the gas composition to calculate hydrate dissociation conditions envelope. Hydrate
can form and accumulate in locations where temperature is lower than the hydrate stability
temperature.
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5. Flow restrictions and blockages in operations
2. Build a multiphase flow model
Construct a multiphase model of a flow line to determine the areas of water holdup accumulation. Determine the superficial liquid flow velocity for these areas. One or more of these
areas are prone to hydrate plugging. The key factor is whether or not the formed hydrate
particles are carried out by the flow or remain in the “low spot.”
If hydrate conditions are present throughout the flowline, one may need to rely on the
segments of increased liquid holdup for prediction of the likely blockage location. Segments
with liquid holdups higher than in other locations of the flow line may be the likely locations
of hydrate accumulations. Multiple blockages may be present.
3. Establish the pipeline segment where hydrate conditions are present
Determine the pipeline segment where hydrate conditions are present. In most cases the
hydrate conditions are present in 100% of a shut-in flow line. Exceptions may include warmer
climates where some sections of the flow line are exposed to an ambient temperature warmer
than the hydrate conditions.
4. Determine hydrate particle mobility
Use a solids transport model to estimate the flow velocities required to avoid solids settling
out in two phase pipeline flow. Beggs and Brill flow and Thomas' friction velocity correlations
may be used to determine the minimum transport condition at the transition to intermittent
boundary line.
The Thomas' correlation based on the Oak Ridge National Lab work (1961, 1962) can be
separated into two models. The upper model is used when the particle diameter exceeds the
laminar sub layer thickness, the lower model is used when the particle diameter is less than
that of the laminar sub layer. Unfortunately it has been shown that the upper model is only
suitable for use with high superficial gas velocities and that it greatly over predicts the pressure drop at low superficial gas velocities. The new approach is that under conditions where
solids are larger than the laminar sub layer the maximum superficial liquid velocity predicted
by the lower model gives the highest superficial liquid velocity required to ensure particle
transport. This approach always gives conservatively high liquid velocities when compared
to all the values for three phase gas/liquid/solid flow.
The default value for the density of hydrate particles is 50 lb/ft3. The minimum frictional
pressure drop required to avoid settling can then be calculated.
Thomas (1961) indicates that Reynolds numbers as high as 2.9–3.6 × l04 are required to
prevent solids deposition.
A recent model for gas hydrate deposition from water saturated vapor in deadlegs was
presented by Zhang (2017), which allows to estimate hydrate plug potential by a different
mechanism of hydrate deposition by condensation from vapor in vertical short pipe sections
without flow.
Prevention of hydrate formation
Hydrate easily plugs production systems and should be either avoided or managed both
in flowing and shut production and injection systems.
On production system shut-in, the fluid cooldown time should be no less than a sum of
time to safe out the system by normal operating procedure plus the no-touch time. No-touch
time should be no less than 2 hours to allow operator to respond, to reset control systems and
Hydrate of natural gas
111
to restart process equipment (consult with operations representative). Pipeline with gas filled
state should be assumed for cooldown calculations, and hydrate curve for condensed (fresh)
water should be used to determine cooldown time.
For high acid gas content (>2 mol% H2S or CO2), high salinity (>100,000 TDS) and high
pressures (>10,000 psi) lab measurements should be used to verify hydrate stability conditions. Hydrate formation metastability and underinhibition should not be relied upon in normal operations.
On start-up, system should be thermally or chemically treated until system temperature
increases sufficiently to provide a safe-out time plus a no-touch time before re-entering hydrate conditions during an aborted start-up. For systems with on-demand active heating only
temperature of components without heating (jumpers, trees, risers) should be considered.
For flow assurance risk management strategies, minimum water cut threshold for chemical treatment such as 1% may be used if supported by appropriate multiphase laboratory
verification (flow loop or flow wheel) and by multiphase modeling to ensure that all formed
hydrate is fully dispersed and does not accumulate when water cut is less than 1%. Partial gas
separation may be used to avoid hydrate if supported by appropriate laboratory verification.
Several methods for hydrate prevention may be used:
Thermal methods
Thermal insulation or line burial is used in onshore and subsea production systems. When
the produced fluids remain outside the hydrate stability envelope throughout the whole length
of the production system, the use of hydrate inhibitor chemicals is unnecessary. In some cases
the insulation is used to prevent wax deposition and thus hydrate also gets prevented as the
temperature of hydrate stability is usually lower than the temperature of wax stability.
Dehydration
To prevent or to shift hydrate stability before it forms, the amount of water may be reduced
in a flowing gas stream. Typical dehydration of gas is to 6–7 pounds of water per million
standard cubic feet of gas. Modern equipment allows to achieve dehydration to 1–2 pounds
per MMSCF.
Similar to gas dehydration, a partial or complete water removal from oil systems may help
achieve the hydrate blockage-free production to a level where remaining water can be transported with the reservoir fluid, with or without the use of chemicals. Alternative to partial water removal may be partial gas removal from low GOR systems. If the amount of hydrate which
forms after a partial gas removal can be transported with the reservoir fluid, with or without
the use of chemicals, this approach may also help achieve the hydrate blockage-free production.
Chemical inhibition
Chemical inhibition serves the same purpose as dehydration: to prevent hydrate blockages. A variety of chemicals exist, in two broad categories these are thermodynamic inhibitors
and low dosage hydrate inhibitors (LDHI). Thermodynamic inhibitors act by altering water.
Low dosage inhibitors work by altering hydrate crystals.
• Thermodynamic inhibitors
Thermodynamic inhibitors connect to water molecules either by hydrogen bonds like alcohols as shown in Fig. 5.12 and glycols or by ionic bonds like salt ions as shown in Fig. 5.13.
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5. Flow restrictions and blockages in operations
FIG. 5.12 Methanol hydrogen bonding to water thus preventing water from entering hydrate.
FIG. 5.13 Salt ions of sodium chloride forming solvation shells of water molecules thus preventing water from
entering hydrate.
All thermodynamic inhibitors require high concentration in water to be effective in hydrate prevention. Their dosage usually ranges between 20 and 40 mass% in water. This means
that for every 60–80 tons of water there needs to be added 40–20 tons of a thermodynamic
inhibitor. This becomes prohibitively expensive in regular production unless the chemical can
be recovered and reused. The most commonly used chemical in oil production is methanol.
The most common chemical used in gas and gas condensate production is MEG or monoethylene glycol. MEG usually requires a higher dosage compared to methanol.
Other thermodynamic inhibitors which may be used, if economics is favorable or if environmental or safety regulations require it are ethanol, triethylene glycol, and diethylene glycol.
Salt is seldom used in oil and gas production but almost always used in well drilling and
completion work for two reasons: salt can add weight to the wellwork fluid and also provides
hydrate protection.
Thermodynamic inhibitors have no limitation on the amount of water they can protect
from hydrate. Water cut may be as high as 99% at which point the amount of gas dissolved in
the remaining 1% of produced hydrocarbon fluid may be insufficient to form an appreciable
amount of hydrate solids unless the water remains stagnant in the flowline as a holdup in
multiphase flow. If multiphase flow cannot sweep the stagnant water, with time the hydrocarbon gas flowing past the water holdup area will form gas hydrate, provided the pressure and
temperature are appropriate. If the flow velocity of the liquid layer is less than that required
to fluidize the hydrate solids, hydrates may accumulate into a blockage. Recent transient
multiphase flow simulators are capable of modeling this process of hydrate accumulation. As
with any software, the accuracy remains to be verified by the user.
Ions of salts attract several water molecules and form salvation shells.
Glycols such as monoethylene glycol (MEG) or triethylene glycol (TEG) are often used to
control hydrate in longer (>30 km) flow lines gathering gas from remote wells. Glycols are usually recovered by distillation and reused in the same field due to relatively high chemical cost.
Historic MEG reclamation efficiency was typically in the 70–92 wt% range, with losses to
salt removal which added a requirement of a logistical chain for delivery of fresh glycol to replenish the supply. Modern glycol recovery methods allow to reach MEG purity to 98 + wt%.
Over 99% of MEG is recovered and reused. In many cases the economics of hydrate control
with electrical heat and glycol are competitive.
Ethylene glycol is often preferred as hydrate inhibitor because it has:
‐ lower dosage requirement than the other glycols.
‐ lower viscosity than the other glycols.
‐ lowest molecular weight of the glycols.
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‐ less soluble in liquid hydrocarbons than the other glycols.
‐ freezing temperature of its water solution is lower than for the other glycols.
Thermodynamic inhibitor chemicals including methanol, glycols, salts inhibit hydrates
above and below 0 °C for any length of time. However, these chemicals are required in large
quantities, methanol is toxic, and glycols need to be recovered from produced fluids stream
to be economic. Kinetic inhibitors are not toxic and can work at any water cut (up to 100%).
However, these work only during production, for a limited time, with a limited subcooling
or overpressurization, and accelerate hydrates growth when they eventually stop working.
Properties of glycol mixtures with water are important for a preliminary conceptual design of hydrate inhibitor delivery systems. One set of such data set (Union Carbide, 1978),
updated for brevity, for density and viscosity may be used to check software correlations'
predicted values. However, the best, most cost-effective and most reliable validation of a
chemical property such as density or viscosity is by a laboratory measurement. Laboratory
measured values should be used for a detailed project design.
• Low-dosage inhibitors
Low dosage inhibitors typically require 0.5–3 vol% dosage in water which is much lower
than that for thermodynamic inhibitor chemicals. Cost of treatment though remains the same
due to higher cost of specialty components used to formulate the LDHI. Operator may save
cost on logistics of chemical delivery as less chemical volume needs to be transported. While
it is not uncommon to see a separate pipeline designed to deliver MEG from shore to the
production platforms, LDHI is nearly always delivered in chemical tanks also called totes to
the platform.
Low dosage inhibitors fall in two sub-categories: kinetic and anti-agglomerant types.
Kinetic inhibitors work by adsorbing on the critical size nuclei of hydrate as shown in Fig. 5.14
and preventing their further growth, as well as by blocking methane and other gas molecules
which are like building blocks from reaching the growing hydrate surface. Altering surface
energy of hydrate nucleus and steric blockage of diffusion of guest molecules are the mechanisms of KHI. Eventually the chemical dissolved in water runs out and the crystals proceed
to form. Effectively KHI chemicals delay the growth of hydrate solids.
Kinetic hydrate inhibitors or KHIs provide a delay on the order of hours to tens of hours, depending on pressure. The further into the hydrate stability region on a pressure-temperature
hydrate stability diagram is the operating point, the shorter is the KHI protection time.
There are two ways to measure how far is the operating point from the hydrate stability curve: overpressurization or the difference between the operating pressure and hydrate
FIG. 5.14
some time.
KHI polyvinylpyrrolidone (PVP) polymers adsorb on hydrate nuclei and disrupt crystal growth for
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5. Flow restrictions and blockages in operations
s­ tability pressure at an operating temperature, and supercooling or the difference between
the operating temperature and hydrate stability temperature at an operating pressure.
The higher the overpressurization, the sooner a KHI can fail. Similarly the higher the supercooling, the sooner a KHI can fail. Empirical evidence (Talley, 2000) suggests that overpressurization is more important to reducing KHI effectiveness time than supercooling.
The first of the two sub-categories, the KHI have no limitation on the amount of water
they can protect from hydrate. Operators use that property to deploy KHI in the areas of
high water production such as late life deepwater oil wells, gas and gas condensate production with limited residence time of water in the pipeline. KHIs are also deployed in regions
where environmental regulations preclude the use of more toxic thermodynamic inhibitors or
­anti-agglomerant chemicals because typically KHI chemicals are non-toxic.
KHI chemicals are usually short polymers or oligomers with carbonyl groups present in
the side chains. Some of the early KHI chemical active ingredients like PVP were same as
used in shampoos and other non-toxic products. Some details and examples of chemicals are
presented further.
AA chemicals are similar in their chemical structure to corrosion inhibitors, which can
be quite toxic and corrosive themselves, depending on concentration. An example of an AA
chemical is a quaternary ammonium salt.
AA chemicals work by allowing the hydrates to form, but control the solid surface to keep
the solids finely dispersed in a carrier fluid. This makes AA chemicals have no limitation on
the time of protection, similar to thermodynamic hydrate inhibitors like methanol but AA do
have a limit on the amount of water they can protect from a hydrate blockage. As the formed
hydrate solids need to be dispersed into a carrier fluid such as live liquid hydrocarbons produced from a well in order to be transported from the flowline where they form to the processing facility, there is a limitation for AA chemicals on the water cut which can be protected.
Typical water cut limit for AA chemical use is between 40 and 50 vol%. Water expands when
it transforms into gas hydrate similar to as when it freezes into ice. Actually water expands
more when it forms a hydrate. Ice takes approximately 1.11 volumes when 1 volume of water
freezes. Hydrate takes between 1.2 and 1.26 volumes, as calculated by the hydrate crystallographic unit cells size for different crystal structures when 1 volume of water forms a gas hydrate. The difference in expansion ratios between ice and hydrate is explained by the volume
of gas trapped inside the hydrate crystal lattice. The expanded volume of solids can be dispersed in a liquid hydrocarbon and remain fluid up to 50–60% solids volume which dictates
the AA chemical applicability limit of the water cut. There are specialty formulations which
increase the limit to 60–70% water cut but these systems are rare. In one instance a formulation was developed by Yale University team led by Prof. Firoozabadi which allows an AA
chemical to be effective up to 100% water cut by forming a water-in-oil-in-water dual reverse
emulsion. The formed hydrate slurry remains fluid but is understandably very viscous as
reported by oil majors who tested this method (Walsh, 2014). The water cut limit for normal
operating conditions is verified in a laboratory for a specific oil which will be produced. This
step saves operator cost as each crude may contain different amounts of naturally-occurring
hydrate dispersant chemicals which may reduce the required AA chemical concentration.
Some crudes known as self-inhibited possess a property to naturally disperse forming
hydrate particles. This is usually associated with acidic crudes. Studies of the properties of
naturally-inhibited crudes indicated that crudes with high TAN number reduced hydrate
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agglomeration. Examples of crudes with naturally occurring inhibiting properties have been
reported in the Gulf of Mexico and in the Campos basin of the Atlantic Ocean.
The amount of water becomes limiting for the deployment of an AA hydrate inhibitor as
the chemical delivery system is typically rated to supply a certain flow rate of the chemical,
based on the maximum pressure which a chemical pump can reach. Usually half-inch or 12mm diameter tubes are used to supply chemicals to subsea trees in deepwater application.
Other sizes such as quarter inch or 5/8 in. may be used as dictated by project economics. Once
the amount of the produced water exceeds the ability of the chemical system to deliver sufficient amount of chemical (between 0.5 and 3 vol% on water basis) the chemical applicability
range is exceeded. Operator may respond either by choking back production from a well
which produces too much water or by increasing chemical injection up to the pump limit, as
dictated by economics of each response.
Time does become a limitation for AA chemicals when the threshold water cut is exceeded.
In such cases AA may provide a temporary protection from a solid blockage for several hours.
It is imperative if a production system experiences a sudden increase in produced water cut,
such as water breakthrough in a well either on water injection pressure maintenance or on
natural reservoir depletion that such production system is treated upon an eventual shut-in
with a secondary risk mitigation method such as methanol injection or bullheading of live
produced fluids using stock oil from the gathering flowline into the well to a depth which is
warmer than the hydrate stability temperature. If a secondary measure is not implemented
after the primary measure fails, a flowline blockage is likely to form. Once the blockage fully
forms, the pressure communication between the processing facility and the wellhead tree is
lost, and the ability to respond by injecting methanol, stock oil or by depressurizing disappears. The temporary protection time for an AA chemical used outside its normal operating
conditions verified in a laboratory depends on few aspects: how quickly water normally dispersed as droplets in hydrocarbons drains from high to low spots thus creating excess water
available for hydrate formation, and how quickly hydrate solids grow and agglomerate in
the production system undertreated with an AA chemical. Hydrate can grow as rapidly as
1 mm per second in laboratory conditions at gas-water interface with sufficient cooling. In
production system the process is limited by both heat transfer (hydrate formation releases
heat) and by mass transfer (gas molecules need to diffuse from live oil to water, through a
growing layer of hydrate). Hydrate growth in stagnant conditions in cylindrical geometries
was investigated in the laboratory (Makogon, 1997). It was shown that hydrate grows more
intensively near the pipe wall, likely as a thin capillary channel between hydrate and pipe
wall provides a path for water molecules to migrate up toward hydrocarbons thus accelerating the mass transfer, and proximity to the cold pipe wall surface also accelerated the heat
transfer. The hypothesis for capillary water migration may be substantiated by the coloring
of hydrate with corrosion products in the stainless steel cell where hydrate formed with degassed distilled water. Increased corrosion in stainless materials observed during hydrate
formation as shown in Fig. 5.15 was mentioned earlier.
• Effect of underinhibition
In case of insufficient thermodynamic inhibitor such as glycol or methanol, hydrate will
start forming and accumulating in the process stream. Methanol leads to more solid agglomeration, whereas glycol leads to more slushy hydrate which can get displaced from pipeline
low spots downstream into pipeline slug catcher when flow rate increases (Dawson, 1999).
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5. Flow restrictions and blockages in operations
FIG. 5.15 Increased corrosion in stainless steel observed during hydrate formation (Makogon, 1997).
Methanol in small amounts (below 2 wt%) acts as a hydrate growth rate promoter and may
act as enhancer for methane and natural gas hydrate. The subcooling required to start hydrate
formation is reduced when a small amount of methanol is added to water, at pressures between 50 and 100 bar (Makogon, 1974, 1981).
In case of insufficient LDHI, hydrate plug forms more rapidly with too little kinetic inhibitor than without a kinetic inhibitor.
With too little antiagglomerant inhibitor formed hydrates agglomerate into a plug.
• Inhibitor evaporation to gas
Volatile inhibitors (methanol) can evaporate into the gas phase, leaving the water
underinhibited.
The method to estimate the rate of methanol loss from water to gas is provided by Sloan
(1990, 2000) as 1 pound of methanol per MMscf gas for every weight percent of methanol in
water phase, at pressures >1000 psi. For more accurate estimates, the following three correlations were offered by Sloan (2000):
(mol frac. methanol in gas/mol frac. methanol in water) = exp(8.412–7250/T[°R]) for
1000 psia.
(mol frac. methanol in gas/mol frac. methanol in water) = exp(6.852–6432/T[°R]) for 2000
psia.
(mol frac. methanol in gas/ mol frac. methanol in water) = exp(5.706–5738/T[°R]) for
3000 psia.
For glycol, 0.02 pounds of MEG is lost to gas per MMscf gas, at pressures >1000 psi.
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Pressure management and wellwork safety
Combination of salt and glycol or low dosage hydrate inhibitor may be used in wells where
pressure management is important. An example is weakly consolidated formations in Western
Atlantic deepwater. In cases of very high pressure reservoirs, wells during drilling and completion need to be protected from hydrate formation at the mudline hydrostatic pressure and
mudline ambient temperature which is usually +4 °C, sometimes lower. Hydrates are a concern because hydrocarbon fluid may migrate into the openhole wellbore, gas or dense phase
hydrocarbon may evolve from reservoir as hydrocarbon density is lower than that of a drilling
mud or a wellwork fluid. Gas or dense phase hydrocarbon can rise by buoyancy to the mudline and form a hydrate accumulation at cold temperature leading to stuck equipment.
The concentration of salt in wellwork fluid required to prevent hydrate at these conditions
can make the brine too heavy, which may make the wellwork fluid overbalanced and cause
uncontrolled fracturing of the reservoir. This may lead to uncontrolled release of hydrocarbons from the reservoir through the fractures to the environment. In order to avoid that, the
formulation of the wellwork fluids for weakly consolidated formations may combine salts
and glycols. Glycol adds less weight than salt to the wellwork fluid, but adds as much hydrate inhibition as salt. It is recommended that hydrate stability of a selected wellwork fluid
is measured in the laboratory. This is a relatively simple and fast measurement which allows
the driller to know the exact pressure at which hydrate would be stable at seabed temperature. The cost of a lab test to verify hydrate conditions with high salinity high pressure drilling mud or workover fluid system is immeasurably less than that of a deepwater well or of
the undesirable consequences.
In some cases low dosage hydrate inhibitors lose their effectiveness or get poisoned by
other chemical additives present in wellwork fluids. Again the effectiveness of low dosage
hydrate inhibitors in wellwork fluids should be verified in a lab.
SCSSV safety valve has to be set deeper than the produced fluid hydrate stability depth,
using temperature distribution from undisturbed well temperature log. Regional geothermal
gradient analog may be used if accurate well log data are unavailable.
Hydrate dissociation
Hydrate dissociates when the environment is not sufficient anymore to balance the force
of guest molecules' repulsion from water and the attractive force of hydrogen bonds holding
water molecules in a lattice around the guest molecules. This occurs when one or more of the
three events take place: pressure is reduced, temperature is increased, or water molecules are
dissolved into a solvent. The fourth method for a direct removal of guest molecules from the
hydrate lattice has not been invented yet.
The presence of additives such as kinetic hydrate inhibitors had been shown (Makogon
et al., 2000; Makogon and Holditch, 2001a) to cause a hysteresis in hydrate dissociation,
when higher temperature was required to dissociate hydrate formed with KHI. Makogon
and Holditch (2001b) reported up to 8.2 °C higher temperature of complete dissociation with
0.5% kinetic inhibitor. The temperature was increased very slowly at 1 °C/day or less. It
was hypothesized that KHI molecules adsorbed to the hydrate surface stabilize it like steel
bars would stabilize a concrete wall, and also decreased the water vapor pressure above the
hydrate.
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5. Flow restrictions and blockages in operations
Upon dissociation, gas evolves into the water layer present on the hydrate crystal surface
as nano-bubbles and micro-bubbles which coalesce into larger gas phase. The importance and
pressure of nano-bubbles of dissolved gas for hydrate formation was described by Makogon
(1996). The significance of nanobubbles and microbubbles during hydrate dissociation was
reported by Uchida et al. (2016a, b, c) who developed acronym MNB or micro- and nano-­
bubbles. They used a transmission electron microscope to confirm the existence of MNB after
hydrate dissociation, with most frequently observed size in 200–400 nm range, and Raman
spectrometer to estimate the pressure inside the MNB around 7 ± 5 MPa. The authors also described the importance of MNB for the memory effect of gas hydrate recrystallization (Uchida
et al., 2016a, b, c). The industrial application of MNB for wastewater purification and physiological promotion was evaluated with respect to NaCl effect (Uchida et al., 2016a, b, c). The
authors found that low concentrations of NaCl stabilize MNB for at least 1 week, but at salt
concentrations >100 mM the MNB decay faster.
Hydrate blockage remediation
The time to dissociate a hydrate blockage depends on the blockage location and on the
insulation of the pipeline containing the blockage.
As a preliminary estimate, a hydrate plug in an insulated deepwater flowline will take as
many days to fully dissociate by depressurization as is the pipe diameter in inches.
timedissociation ( days ) ≈ Inside Diameter ( in.)
This estimate is based on heat transfer, mass of hydrate and the time it takes for the energy for dissociation to transfer through the flowline insulation as the majority of deepwater
flowlines are thermally insulated. An operator should plan for at least this many days for a
hydrate removal, plus time for mobilization and demobilization of depressurization equipment. A more accurate analysis for the anticipated time to dissociate a hydrate plug by depressurization can be done with detailed heat transfer analysis.
Hydrate may be dissociated in many ways, but the common practice is to depressurize the
plugged flowline to a pressure below hydrate stability.
Usually the dissociation pressure at the plug location will be below 10 bar in deepwater
conditions because structure II hydrate forms most commonly in oil and gas production, and
its stability pressure is near 10 bar at the typical deepwater temperature of 4 °C.
Initial pressure communication through the plug may start at as early as one tenth of the
time of complete dissociation, provided that pressure at the hydrate remains below its stability pressure. Pressure of the hydrostatic head of the liquid column in a deepwater riser must
be taken into account when planning a hydrate remediation project.
Thermodynamics of hydrate dissociation are described to explain this. Water molecules in
a hydrate crystal lattice are held together by hydrogen bonds, just like bricks in a building a
held together by mortar. It takes 5 kcal per mol of water to break the hydrogen bonds. Thus
the process of hydrate dissociation is endothermic or consuming energy.
Energy is required to agitate the bonded water molecules in a hydrate lattice to a point
where the hydrogen bonds begin to break. The energy in a deepwater environment comes
from the cold seawater. Deepwater flowlines are usually insulated with approximately 3 in. of
insulation layer, designed to keep fluids warm during normal produciton. However, during
Hydrate of natural gas
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hydrate dissociation this insulation limits the heat which can enter the pipeline and dissociate
the hydrate. This insulation explains why it takes so long to dissociate hydrate in a subsea
flowline. Energy flows from a cold 4 °C seawater into the pipeline because hydrate gets even
colder when it dissociates and reaches the equilibrium temperature at the flowline pressure.
The dissociation temperature may be lower than the freezing temperature of water. Fresh
water is released from a melting gas hydrate. If the dissociation occurs in conditions where
ambient temperature is below the freezing temperature of water, the water released from
hydrate will freeze as ice and will remain as ice until the ambient conditions warm up above
the freezing temperature of water. This should be taken into account in arctic operations and
in permafrost regions. A consideration that a hydrate blockage cannot be dissociated in a
gas pipeline operated at below freezing conditions was first specified by Makogon in 1961; a
partial hydrate blockage may be removed either by heat or by addition of methanol to the gas
stream (Makogon, 1961).
When hydrate forms, it releases heat and thus limits the rate of hydrate growth. When hydrate melts, it consumes heat and limits the rate of hydrate dissociation. Hydrate dissociation
or formation is a phase transition process. It is similar to boiling of water phase transition:
temperature will remain fixed until the whole phase transition from liquid to vapor completes.
The hydrate melting temperature typically is close to the water freezing temperature.
Hydrate takes up energy from the water present in the flowline until water freezes, which
depending on salinity occurs between 0 and approx. −6 °C.
Chemicals may be used to help dissociate hydrate.
Their effectiveness by weight decreases as the molecule size increases.
For example, to prevent hydrate at 4 °C and 100 atm it takes around 30 wt% methanol,
45 wt% MEG and 60 wt% TEG (Wood Virtuoso GUTS 6.2 software).
However, toxicity and hazardousness decrease as the molecule size increases. Methanol
is flammable and poisonous, while TEG is toxic if ingested and may be combustible at high
temperature.
In each of these inhibitors the active components are the oxygen and hydroxyl groups O
and OH.
Methanol formula is CH3-OH.
MEG or mono-ethyleneglycol formula is HO-CH2CH2-OH and easy to remember as two
methanols CH3-OH.
TEG or tri-ethyleneglycol formula is HO-CH2CH2-O-CH2CH2-O-CH2CH2-OH and easy to
remember as three MEG.
Furthermore, the chemicals get diluted and become ineffective as hydrate dissociates and
water is released from melting hydrate.
In one instance, a hydrate blockage formed in a deepwater dry tree riser remained stable
for weeks despite MEG being placed on top of the hydrate plug. After few months of waiting,
coiled tubing was deployed to safely jet out the hydrate blockage with a lukewarm KCl brine.
Combinations of pressure, chemical and thermal methods as well as points of access to
deliver the solutions allow for a multitude of implementation options. Table 5.4 below summarizes over 50 ways to melt a hydrate plug, many of which have been attempted in the past.
Some methods are more effective than others and some are more novel than others. Technical
feasibility, safety, duration and economics of each option should be considered when ­planning
a removal operation. Two-sided depressurization is considered to be safer than other options.
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5. Flow restrictions and blockages in operations
TABLE 5.4 Methods to dissociate a hydrate plug
Depressurize
From upstream of line
With hydrate skid
Through service line
Through access wye
From downstream
Through topsides
With hydrate skid
Through service line
Coiled tubing jet
From middle of line
Manifold
From upstream
With hydrate skid
From downstream
Through topsides
Through PLET
From middle
Cut, set plug and lift line
Riser base PLEM
Manifold
Flow chemical
Methanol
From upstream
Through flowline
Through service line
Through chemical line
From downstream
Through flowline
Through service line
Through chemical line
Glycol
From upstream
Through flowline
Through service line
Through chemical line
From downstream
Through flowline
Through service line
Through chemical line
Brine
From upstream
Through flowline
Through service line
Through chemical line
From downstream
Through flowline
Through service line
Through chemical line
121
Hydrate of natural gas
TABLE 5.4 Methods to dissociate a hydrate plug—cont’d
Nitrogen
From upstream
Through flowline
Through service line
Through chemical line
From downstream
Through flowline
Through service line
Through chemical line
Helium
From upstream
Through flowline
Through service line
Through chemical line
From downstream
Through flowline
Through service line
Through chemical line
Heat
Active
Exothermic reaction
Mix reactive fluids
Sodium stick in well
tubing
Hot medium
Annulus for PIP line
Hot water tubing
Hot oil
Electric
EH for wet insulation
DEH for PIP
Heat traced pipe in pipe
Welding apparatus
Heating lamp
novel
Pressure pulsation
From topsides
Microwave
Deployed via coiled tubing
Comparative economics of hydrate prevention methods
There are several industry-accepted methods for design of production systems which prevent hydrate formation.
•
•
•
•
insulation
active heating
chemical
periodic remediation (onshore vs. offshore)
The relative cost of each method varies with time as new technologies become available.
Insulation method should be valued for either wet insulation or dry insulation.
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5. Flow restrictions and blockages in operations
Wet insulation is exposed to ambient elements. Wet insulation has to be more rigid and
thus is more thermally conductive and less efficient compared to dry insulation. Wet insulation may be used for multiphase pipeline tiebacks up to 20–30 miles. Wet insulation also is
limited by water depth to which it can be deployed depending on type of the material. Wet
insulation absorbs moisture from ambient elements with time, and its efficiency may be expected to decrease by 3–5%.
Dry insulation is contained in the annulus between two concentric pipes for a pipe-in-pipe
configuration. Having two pipes nearly doubles the cost but provides more effective insulation which can be deployed to greater seawater depths. Dry insulation may be effective to
tieback lengths of 30–40 miles.
For tieback lengths >40 miles actively heated insulated pipes are used. Cost of active heating adds the power generation equipment and platform, cables, subsea transformers, installation costs. Actively heated pipes are used seldom. To-date <30 subsea projects are known to
have actively-heated pipes.
Chemical inhibition is used as often as insulation. While oil-dominated systems (GOR
<6000 scf/stb) rely mainly on insulation and use chemicals such as methanol or LDHI
for short-term operations such as well startup or a planned shutdown, gas-dominated
systems rely on the continuous injection of glycols, KHI or seldom methanol in the uninsulated multiphase pipelines. The choice of glycols is dictated by economics. While glycols
can be economically recovered from produced water at the onshore or topsides facility
and re-used, the technology for economic recovery of LDHI or methanol chemicals is still
in development. Over 99% of gas production through multiphase pipelines uses glycols.
One example of methanol use with a recovery plant is the Malampaya gas condensate
field. Glycol regeneration plants product contains 70–80 wt% glycol and balance water.
The dilution needs to be accounted for in the design of the plant capacity to meet the field
glycol demand.
Local supply of an inexpensive hydrate inhibitor such as ethanol and its easy and reliable
delivery to the field can be deciding factors in selecting the hydrate prevention methods.
However, safety of the application of a method should be the main parameter for the selection of a hydrate prevention method.
Environmental impacts of hydrate remediation
Various chemicals may be used in hydrate remediation. However, it is expected that all
chemical will be captured and not released to the environment.
•
•
•
•
Glycols are less toxic and non-flammable.
Ethanol is less toxic unless it is denatured but is flammable.
Methanol is very toxic, flammable and will damage the environment if released.
Low-dosage inhibitors vary in their toxicity. Polymers composing the KHI chemicals
active ingredients are usually non-toxic or have low toxicity. Chemicals constituting AA
usually have high toxicity.
Each field abides by the regional environmental regulations. The use of chemicals for hydrate control has to be approved by the appropriate authority if this chemical can be released
to the environment.
Hydrate of natural gas
123
Health impacts
Health impact of each chemical considered for hydrate control is based on the toxicity of two
key components: active ingredients which control hydrate formation and the solvent used to
transport the active ingredient to the location of hydrate control. Health impact of a chemical
should be described in a Material Safety Data Sheet (MSDS) and such information must be
made available to the workers dealing with the chemical injection. Specialty Personal Protective
Equipment (PPE) must be made available to and used by the workers dealing with chemicals.
In one instance, an onshore field was in operation with hydrate control implemented by
methanol injection. An operator took some methanol to their garage for use as a vehicle antifreeze coolant. The garage got burglarized and the liquid in an unlabeled container got stolen
and mistakenly ingested which led to a fatality. The field then got converted to the use of a
kinetic hydrate inhibitor as a safer and more economic method for hydrate control. When
selecting the hydrate control strategy, eventualities in storage, delivery and staff awareness
must be also considered.
Effect of hydrates on corrosion
There are reports that hydrates may accelerate corrosion rate if formed at both the carbon
steel and stainless steel interfaces as illustrated in Figs. 5.16 and 5.17 (Makogon et al., 2000,
2002; Makogon and Makogon, 2004). It is hypothesized that one of the mechanisms is crevice
corrosion where hydrate forms a solid over the steel material, and the gap between the steel
wall and hydrate creates a crevice with a concentration difference leading to corrosion.
Stainless steel 316 exhibits corrosion during hydrate formation as shown in Fig. 5.18
(Makogon and Makogon, 2004).
FIG. 5.16 Carbon steel coupons immersed in the same water, without hydrate (left) and with hydrate (right)
formation (Makogon, personal communication, 1999).
FIG. 5.17
Stainless steel caliper develops corrosion with hydrate formation (Makogon, personal communication,
1999).
FIG. 5.18 Stainless steel 316 corrosion during hydrate formation. Photo by Yuri Makogon.
Hydrate of natural gas
125
FIG. 5.19 Cr 13 steel without and with hydrate formation. Photo by Yuri Makogon.
Cr 13 steel, as illustrated in Fig. 5.19, also shows higher corrosion rate with hydrate formation (Makogon, 1999; Makogon and Makogon, 2004; Makogon et al., 2000).
Gas hydrate in wells and in nature
Stability of naturally occurring gas hydrates in wells and in natural settings such as in
seabed, in permafrost and other locations is important in evaluation of seafloor stability and
drilling through hydrate-saturated zones. This method of hydrate stability evaluation is also
useful for subsea wells in checking whether the setting depth for a SCSSV safety valve is
sufficient to avoid hydrate formation during a prolonged well shut-in so that the safety valve
could remain operable and not blocked by formed hydrate.
The method for calculation of hydrate stability was developed by Makogon (1965, 1974
p. 151, 1981 p. 171, 1982 p. 303) where the hydrate stability curve is plotted together with
the geothermal temperature profile as function of depth or hydrostatic pressure. The same
method works equally well for subsea wells, onshore wells and permafrost soils. Example
schematic chart in Fig. 5.20 below illustrates that method for a wellbore, with pressure plotted
in reverse order. This chart shows depths where pressure is sufficiently high and temperature
sufficiently low for a hydrate to be stable. Below a certain depth, rock is too warm for hydrate
to be stable, and SCSSV safety valve may be set at or deeper than that depth. In the example
chart this corresponds to 900 m where two lines cross each other.
126
0
0
1
100
2
200
3
300
4
400
5
500
6
600
7
CH4 hydrate stability data
700
8
Geothermal profile T, K
800
9
900
10
1000
Depth (m)
Pressure (MPa)
5. Flow restrictions and blockages in operations
Temperature (K)
FIG. 5.20 Hydrate stability curve plotted together with the geothermal temperature profile shows where hydrate
can be stable in nature or in a producer or injector well.
Geothermal profile has to be measured for a specific well, or obtained from nearby wells.
In oil and gas wells the structure II hydrates are encountered most often, so the methane hydrate stability data should be substituted with structure II hydrate stability data for a specific
reservoir fluid. Each reservoir fluid is different, so the structure II hydrate stability will vary.
Typical depth for setting a SCSSV is between 2500 and 3000 ft. or 800 and 1000 m below
mudline in subsea oil and gas wells.
Existence of gas hydrate in nature had been proven experimentally in 1961 (Makogon).
Меssоyaha gas-hydrate deposit shown in Fig. 5.21 was discovered in 1967, with start of commercial production оn 12/24/1969.
Several hypotheses exist about the effect of naturally occurring methane clathrate hydrate
deposits on the warming period known as Paleocene-Eocene Thermal Maximum. Besides earth,
hydrate may also exist in cosmic bodies and in comets as shown in Fig. 5.22 where gradual heating of surface by the sun causes gas and particles to erupt. Similar thermodynamic reasoning
applies to the hydrate accumulations in permafrost regions (Chuvilin and Davletshina, 2018)
and to the recently observed craters on the Yamal peninsula where hydrate may dissociate, upon
warming, below permafrost causing pneumatic eruptions (Makogon and Makogon, 2017).
The methods for estimating the water content in rock pore which is in equilibrium with
ice or gas hydrate in sediments was described by Istomin et al. (2017). The authors show that
the water content measured with via pore water potential by the dew point method was in
good agreement with direct contact measurements. The non-clathrate water content was estimated at 2–5% in contact with clay materials in the range of −20 to −2 °C hydrate formation
temperature shift. A modern overview of the worldwide gas hydrate deposits geology and
development was presented by Voronin (2017). To-date only two countries Japan and China
have achieved gas production from hydrate subsea. Flow assurance also plays an important role in these projects for commercial production of natural gas from subsea gas hydrate
deposits. Multiphase flow, subsea processing, artificial lift, rate and locations of phase transitions, and the distribution and effects of chemicals have been evaluated in the production
system design.
Hydrate of natural gas
127
FIG. 5.21 Geographic location of the Меssоyaha natural gas hydrate deposit.
Hydrate management
Technologies which could be considered for management of hydrate in produced fluids
include:
• displacement of untreated produced fluid with stabilized crude or diesel
• bullheading of untreated produced fluid below SCSSV
128
5. Flow restrictions and blockages in operations
FIG. 5.22 Dynamics of the phases of the Halley comet surface eruptions hypothesis with pressures shown in MPa
(Makogon, personal communication, 1999).
•
•
•
•
•
•
•
•
•
•
•
•
•
insulation
active flowline heating by PIP heating medium circulation such as heated bundles
active flowline heating by wet insulation EH
active flowline heating by PIP DEH
active flowline heating by PIP heat tracing
hot water injection from aquifer
depressurization / blowdown to topsides
alcohol chemical
glycol chemical
AA LDHI chemical
KHI LDHI chemical
subsea water separation
partial subsea gas separation.
Emerging technologies of hydrate management
Biological techniques
Biological remediation of gas hydrates had been discussed for at least three decades.
Bacteria which digest hydrocarbons have been proposed to gradually consume a hydrate
blockage by digesting methane out of the hydrate thus destabilizing it. However, this method
had never been tested in the field.
Hydrate of natural gas
129
Cold flow
Cold flow had been proposed as a way to achieve chemical-free production in subsea systems. The concept involves forming a suspension of hydrate particles and recirculation of
a fraction of the stream with hydrate particles into the uninhibited produced fluid stream.
Hydrate particles from the recycle stream will act as nucleation sites for the conversion of
water in the main stream to hydrate. Hydrate will grow on the suspended particles without
adhesion to pipe walls. The recycle stream needs to be added at a position in a flowline where
produced fluid stream has cooled down to the hydrate formation condition. The cold flow
method had been evaluated in laboratory setting in 2003 and showed good results for both
hydrate control and promising results for wax deposit control. The results were published
(US7261810 patent, 2003; Wolden et al., 2005). However, economics of the cold flow approach
are constrained by the need for a recirculation pump located close to the wellhead, a recycle
stream pipeline and the increased viscosity of the hydrate suspension. The combination of
these requirements makes cold flow applicable only in a narrow range of flowline distances.
This method has not been tested in the field. Another implementation of cold flow with a field
pilot test was reported by Turner and Talley (2008).
Partial gas separation
Partial gas separation may be used to avoid hydrate if supported by appropriate laboratory verification. With low GOR oils, the amount of gas available to form hydrate is low.
Partial gas separation may remove enough gas from the hydrocarbon mixture to shift hydrate
equilibrium outside the operating envelope. The method can be modeled with PVT software
but the true shift of hydrate stability conditions should be validated in a laboratory.
Static mixer
Static mixer concept for hydrate control has been tested in the field with promising results. The summary of the method and the field test had been presented at the 2008 ICGH in
Edmonton, Canada (ICGH, 2008).
Modeling of gas hydrates
Currently several rigorous models are available for calculation of gas hydrate stability.
These models have been developed based on the van der Waals and Platteau 1959 work
which has been discussed in Sloan (1990).
Early practical examples of software implementation for modeling of hydrate stability
were developed by Robinson (1988) and Erickson (1983) with the source code presented in
the dissertation.
The working version of the software for use on PC computers is also available at the
Colorado School of Mines, as described in Chapter 11. This software should be able to help
achieve safe operation of production facilities and to raise awareness of operators about gas
hydrates.
A number of empirical correlations have been presented over the years.
Katz had developed a graphical method to find hydrate formation conditions for natural
gases with various gravities (Katz, 1945; Katz et al., 1959). A detailed example of this method
allowing one to calculate the gas gravity and to find the appropriate hydrate conditions is
also presented in Sloan (1990).
130
5. Flow restrictions and blockages in operations
1000
Pressure (bar)
100
4
10
1
–10
–5
0
5
10
15
20
25
30
Temperature (°C)
FIG. 5.23 Hydrate stability conditions. Redrawn from Makogon Y.F., Sarkisyants G.A., 1966. Prevention of Hydrate
Formation in Production and Transport of Gas. Nedra Publisher, Moscow, 188 pp.
We reproduce the Katz method in Fig. 5.23 below to facilitate a quick estimate of hydrate
stability from known gas gravity in absence of a computer software or a calculator. As a check
point, methane hydrate stability at 0 °C is 26 bar.
Makogon and Shalyaho (1972) and Makogon (1974, 1981, 1997) provided a simple
equation method for the gas specific gravity range of 0.6–1 for hydrocarbon hydrates
from 0 to 25 °C:
(
logP [ bar ] = β + 0.0497 T [°C ] + k ( T [°C ])
2
)
Graphs for the coefficients β and k were digitized and fitted by Elgibaly and Elkamel (1997)
β = 2.681 − 3.811SG + 1.679 SG2
k = −0.006 + 0.011SG + 0.011 SG2
Hydrate of natural gas
131
SG is gas specific gravity relative to air.
The Makogon correlation had been found as best simple correlation in Gjellesvik (2011),
corresponding surprisingly well with results from software simulator in many situations.
Gas gravity is calculated from gas composition as follows:
 mol% N 2 × 28 + mol% CO 2 × 44



 + mol% CH 4 × 16 + mol% C 2 H6 × 30 
Gas gravity =  + mol% C 3 H8 × 44 + mol%iC 4 H10 × 58  / 28.96 / 100


 +mol% C 4 H10 × 58 + mol%iC 5 H12 × 72 
 +mol% C H × 72 + mol% C H × 86 
12
6
14
5


Case studies and process safety
Multiple cases are known where blockages formed, and more emerge on an almost daily
basis. Liquid loading and hydrate plugging are primary sources of unplanned losses in onshore wells.
Historically, majority of blockages have been dissociated but there are several examples
in the North Sea and several in the Gulf of Mexico where hydrate blockage remained in the
well or the flowline as it was uneconomic to attempt to or to carry on the hydrate removal
operation.
There were 16 reported cases of hydrate blockages in flowlines reported to US MMS between 1991 and 1998. In comparison there were 39 paraffin blockages.
Operators in general found it difficult to determine the position of these blockages.
All 16 hydrate blockages were removed successfully. Of these 12 were complete blockages,
5 were offshore GOM.
There was only one reported instance of hydrate in a multiphase flowline (GOM). This was
a complete hydrate blockage following a shut-in. It was removed with coiled tubing/jetting
glycol.
Of the other 15, 5 were in condensate lines, one was in a gas lift injection line and the others
were in gas lines.
The Staffa 8″ flowline which suffered 2 complete blockages in the North Sea, was believed
to be a combination of wax and hydrate. The water cut in this flow line was surprisingly low
(<1%). Staffa field was eventually abandoned following two pipeline blockages with a combined wax hydrate plug. The nature of the 8″ multiphase flowline was such that the fluids
cooled to seabed temperatures within the first 2 miles from the tree having a further 4 miles
before reaching the Ninian platform. The fluids arrived well below the wax appearance temperature of the oil. Round trip scraping was not possible. The subsea line was also undulating
and at one point crossed another flowline, both exposing it to additional cooling and introducing restrictions into the flow path. Following the first blockage in June 1993 which could
not be removed, 2 km of the line was cut out and replaced. After a further occurrence the field
was abandoned in November 1994 (Gluyas and Underhill, 2003).
A large number of hydrate blockages case studies is described in the SPE Hydrate
Engineering monograph (Sloan, 2000).
Instead, we will focus on the hydrate incidents associated with process safety because
these involve multiple steps leading to the event. Case studies below focus on process safety
132
5. Flow restrictions and blockages in operations
and deal with either blockage causing a leak, a leak leading to blockage or a projectile movement. In several cases projectile movement allowed to expand knowledge about hydrate effects on process safety.
There are multiple experiences of hydrate projectile movement, both in subsea lines, offshore topsides process facilities, onshore process facilities and onshore pipelines, some impacting on pipe elbows, some on closed or partly opened valves. In some cases this resulted
in a significant pipe movement observed by ROV camera subsea or by personnel on topsides,
in some cases this resulted in a loss of primary containment and hydrocarbons leak, and in
some cases both onshore and offshore this resulted in a pipe rupture and a severe leak of
hydrocarbons. In one instance the formed flammable vapor cloud offshore did not result in a
FPSO catastrophe as wind direction was away from the source of ignition.
18 February 1957 Europe pipeline
Operator noticed inlet pressure increase in a gas condensate field 32 cm gathering network
pipeline while production rate reduced. Following management's command to maintain the
production rate overriding operator's objection, the operator increased inlet pressure which
led to line rupture and ignition as shown in Fig. 5.24. The rupture point was approximately
700 m upstream of the gathering network connection node point. The connection point was at
the crest of a hill. Next day the ruptured pipeline was repaired and the production resumed.
Nine days later another gathering network pipeline ruptured and ignited, downstream of
and close to the connection node point. The connection point valve was closed. A slug of condensate discharged from the ruptured segment downstream of the connection point. The slug
fell on a group of repair workers which caused multiple injuries and eight fatalities. Hydrate
blockages were later determined to be the causes of the pipeline ruptures.
FIG. 5.24 First encounter with real consequences of gas hydrates plug effect on process safety, 1957 (Makogon,
personal communication, 2018).
Hydrate of natural gas
133
FIG. 5.25
Marha well drilling rig covered with gas hydrates after a blowout. Photo by Yuri Makogon, 1963, personal
communication, 1999.
1963 Europe onshore
Marha well drilling rig got covered with gas hydrates after a blowout as shown in Fig. 5.25.
T = −57 °C. The blowout gradually sealed itself. Sample placed in water in an upside-down
glass actively offgassed as a hydrate. As the air temperature warmed up to −40° hydrate
converted to ice.
According to Makogon and Omelchenko (2012), the Markha River field not the Markha
well should be considered the first discovery of a gas hydrate field in 1963. The well reached
a gas deposit at 1830 m depth, with reservoir temperature of no greater than 3.8 °C.
January 1966 Europe LPG storage tank valve
3/4 in. sampling valve in LPG storage sphere had a faulty handle. Operator used a 2 in.
drain valve to take LPG sample rather than using 3/4 in. sampling valves. A solid plug of ice
or hydrate stopped the flow which suddenly cleared with a large release of propane which
ignited.
134
5. Flow restrictions and blockages in operations
December 1980 US North onshore
At an oil sands plant, possible hydrate formation in the compressor second stage discharge
caused piping rupture due to blockage, and a fire.
May 1987 Europe well
A gas condensate well integrity loss during a productivity test led to a blowout, uncontrollable for the previous several years.
After many attempts, an intercept well made a connection, and the injected 40 m3 kill fluid
got lifted by gas and failed to stop the flow.
144 m3 of ice-cold water was then injected from a nearby lake into the well which formed a
hydrate blockage in the blowout well and stopped gas flow after 80 min.
1997 US onshore
In the onshore gas pipeline a blockage was formed on purpose, then allowed to disband
from the pipe and move through the pipe. The estimated peak speed of the hydrate projectile movement through a gas condensate pipeline was in excess of 300 ft/s (Xiao et al., 1998).
The field test was designed with a long straight section of pipe to avoid any impacts on pipe
elbows.
July 1988 Europe offshore topsides condensate line
Normal process of water removal from condensate was altered for equipment maintenance.
A condensate transfer line got plugged.
The line leaked releasing condensate which ignited and led to a loss of platform and 167
lives.
Hydrate was considered among three other causes. Investigation deemed that hydrate did
not contribute to the incident.
August 2012 US North gas purge line
A 4 in. natural gas liquids gas purge line was washed with soapy hot water, then nitrogen
purge was performed to displace water.
A 10 bbl methanol pill was injected on the upstream end, but it was not pushed the length
of the line.
Pipe is undulating because the pipe supports are prone to subsidence due to freeze/thaw
cycles which is common in permafrost areas.
The line looks like a roller coaster with lots of high points and low points that could easily
collect a full diameter of water.
Radiograph inspection confirmed a hydrate plug. Pipe was depressurized in August to
remove hydrate.
Learning: it's not recommended to wash gas lines with water in cold conditions.
April 1997 US North well valve
Hydrate or ice plug formed in a well needle valve during well wireline service preparation.
A heater trunk was suspended from the companion valve to thaw out the needle valve
plug.
After 20 min, operator attempted to open the needle valve again and saw no pressure.
After an additional 5 min, operator opened the needle valve again and some gas began
bleeding off.
Then, suddenly, the hydrate plug released and the gas escaped very rapidly.
The gas hit a slop bucket that the operator was holding and knocked it out of his hand into
the corner of the wellhouse.
Hydrate of natural gas
135
A flash fire occurred while the gas was escaping. The flame slightly affected the operator's
hair. Service crew stopped the job and exited the unit.
The flame extinguished itself and no additional gas was escaping. The operator reentered
the wellhouse to shut the needle valve.
The operator was in the appropriate position (out of the line of fire) at the time of incident
and was wearing all appropriate PPE (suit, safety glasses, hardhat, etc.).
Learning: grounding strap should be attached from the slop bucket to the wellhead.
October 2004 Canada underground tank
Water dump valve on inlet separator stuck open and high level shutdown on the water
tank failed causing water and condensate to leave process equipment.
Liquid was contained onsite in bermed area around tank.
Learning: Process problem caused formation of hydrate in water boot, causing valve to
stick and float to malfunction.
November 2009 US North oil line
Operator discovered an oil spill from the line along the pipeline road and instructed facility controls to conduct an Emergency Shut Down and initiate the Emergency Action Plan.
Two weeks prior, operations lead identified a low temperature condition on one of the two
parallel lines entering the facility.
Operators bled down pressure on both ends of the low temperature line to evaluate flow
conditions.
A rapid drop in pressure at each end indicated the line had ceased flow and had blockages
close to each end.
According to hydrate handling procedures, the facility prepared a temporary line thawing
procedure and staff began conducting a risk assessment of the temporary thawing procedure.
The line failed 3 days later before the risk assessment and the thawing procedure could be
completed.
Line failure was at the 6 o'clock position limiting environmental impact.
Based on temperature monitor analysis, the failed line flow stopped and production diverted to the parallel larger line without recognition.
The surface mounted temperature monitor on the pipeline was located inside the enclosed
facility. This condition created an inability to accurately reflect pipeline temperatures due to
process equipment heat.
A solid plug of ice caused the failure.
October 2004 Europe onshore oil line
A hydrate formed in a remote gathering oil line with water cut below 5%, blocking the
flow. The line in marshy area was found ruptured.
After repair and environmental cleanup the production resumed with methanol inhibition.
Methanol was later replaced with hot water to keep fluids outside of hydrate conditions.
January 2009 Africa offshore flowline
During a production restart following a week-long shut down, operator noticed a higher
than usual riser base pressure.
Operator shut the system back down, believing that there could be a blockage forming in
the riser.
Initial analysis concluded that the riser was not blocked, but high pressure was caused by
large quantities of liquid accumulated in the flow line during the shutdown.
136
5. Flow restrictions and blockages in operations
Riser base valve was shut to isolate the flow line from the riser. Riser contents were treated
with methanol injected at the riser base.
Fluids displaced from the top of the riser during the injection of methanol showed that
there had been some oil at the top of the riser, with the rest of the riser filled by seawater.
After displacement of riser with methanol the riser base valve was opened but a “greater
than hydrostatic” pressure differential between the flow line low point and the riser base did
not disappear.
A differential pressure of up to 30 bar has been retained by the blockage.
It was determined that a combination of system failures allowed seawater to enter the
flowline through spare manifold slots, which were corrected.
Hydrate was dissociated by depressurizing through riser base gas lift system.
August 2008 Africa offshore topsides flare line
Prolonged flaring of uninhibited cold gas from glycol contactor into the wet gas flare line
simultaneously with wet gas from slugcatchers caused ice/hydrate blockage in the flare line.
Wet gas flare line became overpressured causing reverse rupture of safety bursting discs
and the flow of gas into the cooling water, heating medium and oil production systems.
The bulk of the gas got discharged overboard, resulting in the formation of a significant
gas cloud. Prior HAZOP did not identify blockage potential.
February 2008 Africa onshore process plant pipe
Six high pressure header main inlet valves were closed.
Each valve was fitted with a 1 in. bypass line and ball valve to facilitate opening the valves
when flow need to be redirected.
Operator used a spare manifold slot to control the low pressure compressor by recycling
gas from high pressure line to low pressure line by partially opening the equalization bypass
valve and the low pressure valve of the same unused slot.
The equalizing 1 in. bypass line valves were subjected to frequent temperature change by
opening the valves to recycle gas.
Hydrate formation and subsequent movement due to differential pressure resulted in the
manifold pipe work moving 3–5 in., causing excess stress on a weak point in the system (1 in.
equalizing valve).
Three of the 1 in. valves failed, two immediately and one a few moments later, the bodies
breaking apart at the screwed connection with the balls being ejected from the valves, resulting in a significant gas release.
February 2005 Europe onshore
In preparation for a planned regeneration of molecular sieve dryer the dryer has to be
emptied by removing the liquid propane butane fraction to a drum.
Control room operator found no flow to the drum after he had opened the two necessary
motor valves. Then of the two valves he closed one positioned near to the drum.
After a field operator had inspected the status of both valves he tried to check whether
flow to flare is possible or not by opening a 1 in. pipe to cold flare.
The origin of this pipe is between the two valves. Nearly instantaneously a leak occurred
at a 2 in. valve gasket of the closed valve near to the drum, followed by release of propane
butane.
Operator mentioned no flow to the drum. Field operator reported a bump just after cold
flare valve opened. Both findings are explainable by a plug.
Hydrate of natural gas
137
The plug moved driven by a pressure differential of 35 bar with high velocity to the closed
valve near to the drum.
The impact created additional forces to the bolts, reduction of surface pressure to the gasket and finally a leak.
No foreign body was found but ice or hydrate can form solid bodies. The line including the
two valves is a local low point.
If free water is present it will accumulate there. Water has been found once in the past.
Temperatures in February were low and the line toward the two valves is not trace heated.
September 1998 Australia onshore process plant
Hydrate inhibition was originally designed for methanol, but eventually switched to
glycol.
A 3 °F safety margin was built into the glycol calculation per operator practice.
In June (winter) hydrate formed in the slug catchers receiving a mixture of gas, condensate,
water and glycol at gas production and processing facilities.
Liquids from the slugcatchers carried over into gas plants GP2 and GP3, again causing
shutdowns.
About 10 days before the June hydrate incident, substantial amount of aquifer water entered the pipeline from the operation of some high-GOR wells.
Significant increase in individual pipeline flowrates feeding into the slugcatchers due to
gas demand increase during a holiday, caused liquids lying in the pipelines to be swept from
the pipelines into the slugcatchers.
Significant amounts of methanol were used to clear hydrate in slugcatchers.
The TRC3B valve had been giving trouble for some time before the accident.
TRC3B valve was a control system designed to regulate the temperature of condensate in
the bottom of Absorber B.
TRC3B valve repair was done in March. On that occasion the TRC3B valve was not closing
fully. One of the block valves was also not closing fully.
Repairs were effected by injecting methanol into the process, apparently in the belief that
a hydrate was causing the problem.
Whatever the cause, the injection of methanol appeared to solve the problem.
In September, explosion and fire with loss of 2 lives occurred as GP905 heat exchanger
ruptured.
A physical connection was drawn between the two events concerned the presence of molecular sieve dust found in GP903B heat exchanger when it was opened for inspection after
the September incident.
The compound used in the molecular sieves, or dehydrators, is damaged by contact with
methanol, large quantities of which were injected into the slugcatchers during the hydrate
incident in June.
Methanol would have entered the dehydrators as methanol vapor leading to a possible
breakdown of the molecular sieve particles and an accumulation of molecular sieve dust in
GP903 heat exchanger. Investigation deemed that hydrate did not contribute to the incident.
January 2009 US refinery flare line
A freeze-related restriction developed in the gas flare line in US between flare knock out
drum and flare stack which caused a high purge gas pressure alarm. Operator observed that
the high pressure alarm for the flare knock out drum was also active, which confirmed that
138
5. Flow restrictions and blockages in operations
the restriction existed in the uninsulated inlet line leading from the knock out drum to the
flare stack.
January 2001 Canada well
A plug developed in sour gas well tree during well workover to repair tubing to annulus leak under cold weather conditions −15 °C. Pressure in the tubing/casing annulus was
2100 psi. Prior to running a wireline punch tool, attempt to pressure test well lubricator was
unsuccessful as operator found tree valves frozen. Steam was applied to thaw the valves.
After thawing the tree, the wireline lubricator was found to be plugged.
Well valves were then closed and the lubricator pressure bled off. The lubricator assembly
was then removed from the tree and laid down on the catwalk.
Steam was applied to the lubricator to thaw it out and remove the stuck tools when a loud
boom was heard. The bottom section of the lubricator was removed to inspect what had happened and it was observed that the tubing punch was missing. While applying steam to the
outside of the lubricator, trapped pressure inside the lubricator was released and the tubing
punch shot out of the lubricator and hit the engineer's shack 28 m away, embedded in the vertical metal pole of the propane tank skid within 1.5 ft of two 400 lb. propane tanks. The tubing
punch fired on contact with the skid.
After this occurred, the supervisor returned and installed the drag cap on the remaining
sections of the lubricator string. All personnel were going to the doghouse for a meeting to
discuss what had just happened when a second bang was heard. The remaining tool string
shot through the drag cap 100 m into a field, passing within 2 ft of 3 workers walking to the
doghouse. The two remaining sections of the lubricator assembly recoiled across the catwalk
hitting the xmas tree and bending the upper master valve stem. The lower master valve remained undamaged and the well remained secure.
June 2008 US onshore gas plant
A cryogenic service instrument valve failed to close when solids suspected of being hydrates
cut into the Teflon valve seat. Process equipment did have hydrate problems prior to this event.
Hydrates may have formed as a result of maintenance activities that used water to hydrotest
the cryogenic equipment. Although systems were purged with warm nitrogen after hydrostatic
testing, inadequate purging may have left water. A hydrocarbon leak in an instrument loop
caused an uncontrolled release of cryogenic fluid. After the plant emergency shutdown of the
train, the contents of train were manually depressurized to flare to reduce the amount of hydrocarbon leaking to the atmosphere. As a result, the flare piping fell below its design temperature.
Train was injected with methanol and drained out of the exchangers prior to startup. Learning:
using water for hydrotesting in cryogenic service requires robust drying to prevent hydrate.
April 1991 US refinery
Hydrates of isobutane caused the blockage of a pump. After isolation by valve closure,
the pump was removed and hydrate melted by steam. A butane cloud was released from
a hydrocracker and ignited by a fired heater. After repairs, methanol is added to the rundown lines. TDC alarms on propanizer flows alert the operators to the formation of hydrates.
Piping has been changed to balance the flow in the overhead lines.
February 2005 US onshore pipe
A hydrate plug was formed on purpose in a gas pipeline, with undulating profile, to validate methods of hydrate plug location prediction, hydrate location detection, and hydrate
Hydrate of natural gas
139
removal. During depressurization, gas flow carried partially dissociated hydrate slush to the
vent line where slush deposited inside the 2-in. transition nipple and at the end of the vent
stack. The hydrate deposited on the vent stack end got sheared off from the vent pipe wall by
gas flow and formed a projectile which flew in the air for 4 s to an estimated height of 20 m.
Approximately half of the nipple cross section area, initially clear, was found to be filled with
hydrate.
May 2003 US onshore
Operator was cycling a well on which a plunger lift had been installed. The pressure in the
well decreased rapidly, and operator shut in the well. As the operator walked away from the
well, the plunger lift assembly on top of the wellhead blew off the wellhead lubricator.
Plunger in the well or hydrate in the well was driven up the well bore by well pressure and
impacted the plunger assembly with enough force to dislodge it from the wellhead. Hydrate
plug in tubing was considered as the cause. There were no injuries and no environmental
damage.
Commissioning/dewatering of pipelines to avoid hydrates
During commissioning of the newly installed pipelines, they are hydro tested to check
if the pipes can hold water before they can hold hydrocarbons. Displacing water from the
pipeline after the hydrotest is usually accomplished with scrapers, and drying the remaining
water with nitrogen. Remaining water can also be inhibited with glycol.
Several multiphase flow considerations are present:
•
•
•
•
multiphase flow in dewatering lines
nitrogen requirements
scraping efficiency
tools and methods to verify the line is dry
A water sweeping scraper can have a very tight seal against the pipe wall. However, water
will remain in the pipe wall roughness. Also some water will bypass the scraper cups. For
long distance pipes the amount of water trapped in pipe wall roughness can be substantial.
For example, assuming a perfect scraper seal against pipe wall and a 45-μm roughness typical for a carbon steel, in an 18-in. diameter pipe wall roughness there is 33 liters of water per
kilometer or 0.33 barrels per mile.
Gas dew point analyzer is used to check nitrogen arriving from the dried pipeline for moisture content in order to detect the absence of water in the pipeline.
Alternatively, a water detector scraper may be used to check for the presence of water
holdup in a pipeline as shown in Fig. 5.26.
Water detection scraper after deployment in an 18 × 20 inch multidiameter oil export pipeline indicated some water presence. The detector at the scraper front as shown in Fig. 5.27
is a pre-weighed PVC fitting with inserted plastic tie-strap for mounting on the scraper and
filled with molten sugar (caramelized sugar candy). Sugar dissolves in proportion to the time
of contact with water which is measured by weight on arrival. While soluble in water, sugar
does not dissolve in oil or refined products such as gasoline. Identical detector was fitted on
the scraper back, which indicated little to no contact with water.
140
5. Flow restrictions and blockages in operations
FIG. 5.26 Foam scraper for a 4 in. pipe equipped with water detection, a soluble material (sugar) at front and back.
FIG. 5.27 Water detection scraper after deployment in an 18 × 20 inch multidiameter oil export pipeline.
Asphaltenes
Introduction
Asphaltenes are high molecular weight (300–800, typically 700+ g/mol) hydrocarbons
with polarity (Sheu, 2002). When destabilized, asphaltenes flocculate and deposit from oil
onto production system surfaces, restricting flow, blocking sensors and limiting operability
of valves.
Asphaltenes
141
Asphaltene deposits can occur in the reservoir, well tubing, flowlines, risers, strainers, separators, pumps and other locations.
The nature of asphaltenes has been investigated by Katz and Beu (1945). They determined
that the asphaltene particles size is less than 65 Angstroms (0.0065 μm).
Asphaltene chemistry
Asphaltens do not have a specific chemical structure. Instead the asphaltenes are characterized as a fraction of hydrocarbons which is soluble in toluene but insoluble in light hydrocarbons such as pentane or heptane.
Various structures of asphaltenes have been proposed and substantiated with laboratory
analysis. However these vary with oil deposits around the world. One common characteristic
is multiple fused benzyl rings and presence of heteroatoms such as N, O, S and metals V, Fe,
Ni. The average ratio of carbon to hydrogen atoms in asphaltenes is 1.1. This helps distinguish asphaltene deposits from paraffin wax which mainly contain saturated hydrocarbons
with the C:H ratio of 2.
It is thought that asphaltenes flocculate and deposit mainly due to electrostatic and van der
Waals attraction between various parts of the asphaltene molecules and the surfaces. Recent
study (Arsalan, 2015) measured by inverse gas chromatography the Lifshitz-van der Waals
(non-polar interaction with n-alkanes) component of surface energy for asphaltene at 0.313 J/
m2. The polar component could not be measured due to very strong interaction with the polar
probes (dichloromethane as acid and ethyl acetate as base molecules).
Resin molecules (fraction insoluble in propane and butane but soluble in pentane) help
stabilize asphaltenes in reservoir crude oil.
Reservoir and wellbore plugging
In an undersaturated reservoir all molecules are dissolved in a liquid phase. As reservoir
fluid moves toward wellbore, oil pressure and density decrease, lighter components expand
first due to their higher compressibility. Resins are more soluble in light components and are
stripped away from asphaltenes. Flocculation of asphaltenes occurs at the upper onset pressure (see Fig. 3.9 in Chapter 3). Asphaltenes then can deposit in wellbores or in reservoir pores
(Haskett and Tartera, 1965; Alkafeef et al., 2003; Mansoori et al., 1986; Thaver et al., 1999).
There is a severe shortage of published field data on asphaltene deposition. Many research
works rely on the sole 1965 paper providing a caliper measurement of asphaltene deposit in
one well. Other papers exist which detail asphaltene deposition with fewer detail (Lichaa,
1977; Tuttle, 1983; Von Albrecht et al., 1977).
Asphaltenes get destabilized, flocculate and deposit for the following reasons:
‐
‐
‐
‐
‐
‐
‐
CO2 flooding—due to change in acidity and strong polar interaction with asphaltene.
light oil flooding—due to solvation of resin molecules away from asphaltene.
gas lift—due to heavy ends from gas dissolving into oil and reducing oil density.
mixing of incompatible fluid streams—due to light ends dissolving in heavier oil.
acidizing—due to change in acidity.
electric charge on surfaces—due to polar attraction of asphaltene.
shear—accelerating deposition rate.
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5. Flow restrictions and blockages in operations
Asphaltenes can also alter reservoir effective permeability if more viscous emulsions with
water are stabilized by asphaltene particles, without asphaltene deposition on rock pores.
Asphaltenes may become unstable and precipitate from oil in the wellbore. This usually
occurs after the reservoir pressure drops substantially so that produced fluid enters the upper
asphaltene instability envelope while it is in the wellbore. This may also happen during a
temporary high well drawdown condition.
Destabilized asphaltenes precipitate and may deposit on tubing wall or in SCSSV downhole valve. Removal of deposited asphaltene has to be done either by dispersant chemical,
if effective in laboratory tests, or by solvent soak with toluene or another aromatic solvent.
Prediction of asphaltene risk
A quick screening for asphaltene precipitation may be done using SARA analysis of crude
oil which subdivides the oil into four groups: saturates, aromatics, resins and asphaltenes.
Laboratories have a detailed sequence of solvents used to determine the SARA fractions as
each one has its own solubility characteristics. Asphaltenes are stabilized by resins and are
soluble in aromatics, so a higher content of resins and aromatics will reduce the risk of asphaltene precipitation.
Oil is considered stable and have low asphaltene risk if either the Resin/Asphaltene ratio > 10 or Aromatics/Saturates ratio > 2.
A similar method for asphaltene stability derived from the Hirschberg model (Hirschberg
et al., 1984) is known as deBoer plot which compares reservoir fluid undersaturation and density. Asphaltenes are generally stable (pose low risk) if the undersaturation, calculated as the
difference between the initial reservoir pressure and the bubble point pressure is <5000 psi or
if the live oil density is >0.75 g/cm3 (not the stock oil density).
Both the SARA ratios and the deBoer plot are qualitative only and may serve as a preliminary indicator of the asphaltene risk.
Laboratory tests are more reliable in identifying the conditions of asphaltene instability
and the rate of asphaltene deposition.
Asphaltene onset pressure can be measured by isothermal depressurization of a live oil
sample in a visual cell in infrared light. As oils are translucent to infrared light, a camera can
detect the appearance of solids as pressure goes below the upper instability envelope.
If several asphaltene onset pressures are measured at different temperatures, the asphaltene
instability phase envelope may be constructed to find pressure and temperature conditions
where the risk of asphaltene precipitation is minimal, and possibly design the production
system to avoid entering the asphaltene instability conditions.
Core flood test can predict the conditions and rate of formation damage due to asphaltene
plugging of rock pores.
Laboratories should also be used to check the effectiveness of asphaltene inhibitor or disperant chemicals. The chemical testing process requires adequate amount of oil samples, so
the exploration well sampling program should be planned with anticipation of such needs.
Wang and Buckley (2001) have developed asphaltene instability test (ASIST) method
which allows to rely on laboratory measurement of asphaltene instability in stock oil by measuring refractive index, capillary tube flow pressure drop, near infrared light scattering or
microscopic observation at atmospheric pressure to predict instability at other conditions.
Asphaltenes
143
The plot of the square root of molar volume of n-alkane precipitants (such as n-C5, n-C7 up
to n-C15) versus the precipitation onset parameter has a linear shape and is the asphaltene
instability trend. The linear trend is used to predict asphaltene precipitation at high pressure
conditions. The precipitation onset parameter is calculated from the measurements by correlations derived from the Flory-Huggins polymer theory. The method has been gradually
gaining acceptance as the predictive technique for oilfield projects.
PC-SAFT or the perturbed chain statistical associating fluids theory is another method
used to estimate phase equilibria and asphaltene precipitation conditions. The method was
developed by Gross and Sadowski (2001) for chain molecules based on SAFT (Chapman
et al., 1988). The liquid phase is modeled as pseudocomponents, and asphaltenes as pseudocomponents with same size or a range of sizes. Despite its promising nature as an equation
of state, the relative difficulty in implementing this method and the requirement to regress
the equation of state parameters for each oil based on laboratory measurements of asphaltene
titration makes this a research method.
Of the above methods the asphaltene onset pressure method has seen the most use in project design work as it is a direct laboratory measurement. Nonetheless, laboratory methods
may have results of varying precision which may be affected by drilling mud contamination
and should be complemented with predictive methods such as ASIST or PC-SAFT for asphaltene risk analysis.
Light oil and EOR
Enhanced oil recovery can be accomplished by light oil miscible flooding, CO2 flooding or
water flooding.
Light oil solubilizes resins which causes asphaltene flocculation. Injection of light oil
may destabilize asphaltenes, similar to titration by n-paraffins. Laboratory tests should be
able to tell whether miscible flood would not cause reduced permeability due to solids
precipitation.
CO2 flooding increases the acidity which leads to asphaltene flocculation (Srivastava et al.,
1999).
Another study (Srivastava et al., 1995) indicated that asphaltene began to flocculate at
about 42 mol% CO2 concentration in oil.
Water flooding, if applied after the reservoir pressure dropped below the bubble point, at
some later time after the start of production may cause asphaltene deposition in the reservoir
as it is re-pressurized. As the gas cap light ends get redissolved in oil due to pressure maintenance, the light ends solvate resins which destabilizes asphaltenes.
Gas condensate
Gas condensate and light oils can cause asphaltene deposition from heavy oils when comingled from several production streams. Caution should be used in combining production
from several wells into the same flowline, or several flowlines into the same separator.
In some hydrocarbon fluids condensate may be carried by gas as droplets rather than by
being dissolved in gas. Such condensate can contain asphaltenes which can precipitate in
high shear locations of the production system such as the choke.
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5. Flow restrictions and blockages in operations
Heavy oil
Heavy oils have asphaltenes stabilized by other molecules. When light oil or condensate
is added, the solubility of lighter resins in heavy oil changes and asphaltenes can flocculate.
Light oils (reservoir fluid density below 0.75 g/cm3) are more likely to have asphaltene
instability (pose high risk) than heavy oils.
Role of asphaltenes in microbubble capture
Asphaltenes are polar compounds and adsorb on microbubbles of water. This leads to
stabilization of water-in-oil emulsion.
An early warning of an imminent asphaltene issue is an increase in emulsion stability in
separators if nothing else changed. Precipitated asphaltenes stabilize emulsions. As the asphaltenes precipitate in the separator, they can also precipitate and deposit in other parts of
the production system.
Asphaltene precipitation and deposition in wells and pipelines
If the upper asphaltene instability envelope on the pressure-temperature phase diagram is
crossed while oil is flowing in the pipeline, then asphaltenes will precipitate there. Although
precipitation does not necessarily lead to deposition, it usually does.
Asphaltenes deposited in the pipelines need to be removed by routine maintenance scraping. If this is not or cannot be done as in single flowline tiebacks, the deposited asphaltenes
may lead to accumulation of other solids such as waxes or hydrates or sand, depending on
conditions. Asphaltenes cannot be removed by heating, and solvent soaks require large quantities of solvent and downtime.
Asphaltene dispersant chemicals, if successfully identified and selected for a given crude
oil, may be useful in reducing the need for scraping. However, the effectiveness of asphaltene dispersants is still not as certain as for scale or hydrate inhibitors, and require further
research.
Thus the single unscrapable flowlines may be a poor choice for asphaltene-prone crudes
unless a service pipeline is available for periodic deployment of aromatic solvent for deposit
removal, and field economics allow for a regular downtime for solvent soaks.
The profile of an asphaltene deposit in a wellbore was reported with depth and time by
Haskett and Tartera (1965). The variation of asphaltene deposit thickness in a well tubing
with depth and time is approximately redrawn from their work as shown in Fig. 5.28.
One important parameter from this work is the time it takes to plug the well with asphaltenes. While few months is a relatively short time, it is still longer compared to days it
takes for a scale to plug production or hours for a hydrate.
This parameter, time to form a blockage, may be used to help an operator distinguish
between the nature of blockages. The longest time to form a plug is wax, which may take
months to years to form a complete blockage.
Other reports such as (Kabir et al., 2001) show asphaltene deposition characteristics.
Asphaltenes
145
6500 ft
7000 ft
7500 ft
8000 ft
8500 ft
9000 ft
FIG. 5.28 Variation of asphaltene deposit location and thickness in a well tubing of 4.5 in. nominal size with depth
and time (redrawn, from Haskett and Tartera, 1965): Red outline 29 Jan, Orange outline 18 Feb, Yellow outline 9 Mar,
Green outline 12 Apr, Blue outline 8 May.
Monitoring and remote sensing of asphaltenes
• Currently used techniques
Asphaltene detection in production systems is mainly limited to observation of solids accumulated in separator inlet strainer or in scraper receiver. Loss of operability of control equipment such as SCSSV which have to be periodically tested per regulatory requirements may
also indicate asphaltene deposition, but it could also be caused by scale deposition. Hydrate
is unlikely because SCSSVs are set in a well at a depth warmer than the hydrate stability temperature for the water hydrostatic pressure.
• Emerging techniques
Additional early warning of asphaltene deposition may be if a sensor transmitter such as
pressure or a temperature gauge reading appears to drift to a lower value. Asphaltene may
be depositing over the probe and altering its actual condition; the gauge reading is true of the
changed conditions, but biased by the deposited layer of solids.
• Integrated systems
Integrated production monitoring systems rely on correlating readings from all available
pressure, temperature gauges and flow meters to show the most likely flow rate in the production system. Integrated systems may have additional monitoring software modules to detect and interpret deviations from steady values as a flow restriction. Systems may be trained
146
5. Flow restrictions and blockages in operations
to distinguish between types of restrictions based on pressure, temperature, flow rates of oil,
gas and water, and on the deviation trend signature indicative of the solid type.
Remediation of asphaltene plugging
Deposited asphaltenes may be removed from the flow system by several methods:
• Chemical techniques
Toluene soak can dissolve asphaltene deposits in risers, flowlines, wells and reservoirs
pores, provided that the solvent chemical can reach the asphaltene buildup.
• Mechanical techniques
Topsides asphaltene removal from separators, heat exchangers and other process equipment may be safer, cheaper and faster than the use of flammable toxic solvent.
Scraping is also a mechanical method of removing asphaltenes from production flowlines.
• Novel materials
Non-stick coatings have been shown to reduce asphaltene adhesion. Effectiveness of different coatings should be verified in laboratory for a specific oil.
• Emerging techniques
Pressure pulsation is an effective novel method either for a complete removal of pliable
asphaltene deposit from a flowline or for opening a communication channel through an asphaltene blockage so that a solvent could be circulated through the blockage. However, composite blockages for example of a less pliable hydrate and asphaltene may be more difficult
to remove using this method.
Environmental impact of various techniques
Each method carries its own set of risks for an operator. Such risks and hazards have to be
identified in a review. Mitigation plan should be developed for the credible risks to minimize
potential environmental impact should a treated production system lose continuity.
Modeling of asphaltenes
• Reversible thermodynamics
Asphaltene precipitation (flocculation) is usually reversible within small excursion into
the asphaltene instability phase envelope. If asphaltenes precipitate as pressure is decreased,
they get re-solubilized when pressure increases again.
The Flory-Huggins solubility model of asphaltenes is
((
)
Vol.fraction_of_asphaltene_in_oil = exp − 1 − Vasp / Voil − Vasp / RT
T ( d _ asp − d _ oil )
2
)
with units T [K], V [m3/mol], where Vasp is molar volume of asphaltene, Voil is molar volume of oil, d_asp is solubility parameter of asphaltene, d_oil is solubility parameter of oil, R
is universal gas constant, and T is system temperature.
At the asphaltene solubility limit (flocculation), the solubility of asphaltene in oil equals
the volume fraction of asphaltene in live oil. The Hirschberg model is an example of using an
equation of state to predict reversible flocculation of asphaltene in oil.
Asphaltenes
147
• Irreversible thermodynamics
In cases when pressure excursion into the asphaltene instability envelope is significant, resins may flow away from flocculating asphaltene particles and be unavailable to re-­solubilize
asphaltenes if pressure were to increase again. In this case the flocculation process becomes
irreversible, and flocculated asphaltenes are more likely to deposit on production system surface such as on well tubing walls or in a separator. A model which accounts for the stabilizing
effect of resins was developed by Pan and Firoozabadi (1998). Once asphaltenes deposit on
a surface of a rock in the reservoir or on steel or polymeric production system surface, the
solubility loss becomes irreversible and an increase in pressure above the upper asphaltene
instability envelope or a decrease in pressure below the lower asphaltene instability boundary would not lead to redissolution of the precipitated asphaltene. Asphaltene deposition tool
ADEPT was developed to forecast the rate of asphaltene deposition.
Prediction of asphaltene solids precipitation may be done with the ASIST method based on
laboratory measurements. Precipitation may be reversible, but not always is.
Prediction of asphaltene deposition may be done with the ADEPT method. Deposition is
usually irreversible. Unlike wax deposits which can be redissolved by increasing temperature
(e.g. by hot oiling) or hydrate deposits which can be dissociated by either pressure reduction
or by temperature increase (slowly), the asphaltene deposit does not respond to a change in
either pressure or temperature. Asphaltene pyrolizes at very high temperatures of over 500 °C
which cannot be practically achieved in production systems. Solvent, mechanical removal or
flow path replacement (either by pipe section replacement or reservoir re-fracturing) may be
the only methods to restore production after irreversible asphaltene deposition.
Prevention of asphaltenes
Production operation should avoid or control asphaltene formation and accumulation
which is usually irreversible by normal operating procedure. Asphaltene flocculation may be
reversible with pressure but should not be relied upon in production.
Pressure threshold for the start of chemical treatment with asphaltene inhibitor, dispersant
or solvent may be used if supported by live fluid laboratory data. Chemical injection for asphaltene treatment should be set shallower than the scale treatment injection depth because
scale deposit may be more difficult to remedy. While asphaltene may be dissolved by toluene, barite scale cannot be easily dissolved and requires either mechanical milling or costly
chelant treatment. Note that acid workover for scale formation damage tends to destabilize
asphaltene which can form a deposit or a stable emulsion.
Asphaltene inhibitor effectiveness is measured in a high pressure laboratory cell
equipped with infrared light and meter. A reduction in the amount of asphaltene deposited
on the cell walls after depressurization, determined by light absorbance, and the amount
precipitated in oil, determined by filtration of live oil, indicate chemical effectiveness (Yin
et al., 2000).
Technologies which could be considered for management of asphaltene in produced fluids
include:
• asphaltene dispersant/inhibitor chemical from topside, wet tree or downhole
• avoid commingling of dissimilar produced hydrocarbon fluids
• pressure maintenance above asphaltene onset pressure AOP
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5. Flow restrictions and blockages in operations
• periodic scraping
• periodic solvent wash
Following remediation technologies could also be considered.
• solvent soak
• coiled tubing to jet out the deposit, especially in a riser.
Bacterial growth
Topsides process equipment
Bacteria present in the production fluid may grow inside process vessels and restrict the
flow and the vessels' capacities. Periodic biocide treatment or mechanical removal may be
required for maintenance of the process vessels.
Water injection wells
Various bacteria may be present in the lower temperature reservoirs. However, their activity is subdued by the high reservoir temperature. As water is injected to maintain reservoir
pressure, it usually cools down to the ambient temperature of the water injection pipeline.
Injection of a colder water into the reservoir lowers the temperature near the wellbore and
activates the indigenous bacteria which may include sulphate reducing and nitrate reducing
bacteria.
In some cases the bacteria may grow close to the well perforations and cause resistance to
flow or injectivity damage.
If filtered seawater is injected, it contains sulphate SO4 ions dissolved in sea water. Sulphate
reducing bacteria produce H2S which causes reservoir fluid souring and corrosion issues in
the producer wells. Sulphate reducing bacteria activity is mitigated by either water desulphation treatment or by injection of nitrate into the injection water.
If nitrate chemical is injected into the injection water, the nitrate reducing bacteria are activated more than the sulphate reducing ones and take over the favorable temperature space.
Their products are less harmful to the reservoir and producer wells.
One way to mitigate the low temperature impact of water injection is to preheat the water
downhole by drilling the injection well deeper than required and allowing water to flow
down the tubing and up the annulus, using reservoir heat to warm it up before entering the
reservoir through perforations. Injecting hotter water through perforations reduces the zone
of favorable temperature and prevents bacterial accumulation at perforations and injectivity
damage. The extra cost of a deeper well has to be weighed against lower cost of desulphation
equipment or chemical injection such as THPS biocide or calcium nitrate to control bacterial
growth downhole.
Bacterial growth management
Bacterial growth effects should be controlled within normal operating procedure.
Diamondoids
149
Production system should make identification of waste streams and their regulatory classification/disposal more straightforward. System operability should be reviewed to understand how wastes are generated, identify the chemical components and develop appropriate
disposal plan.
Technologies which could be considered for management of bacterial growth in produced
fluids include:
•
•
•
•
•
•
•
•
Biocide glutaraldehyde chemical
biocide THPS chemical
chlorination
periodic scraping
desulphation for injection water for controlling reservoir souring
nitrate chemical for injection water for controlling reservoir souring
preventing comingling of injection seawater and produced water
Provision for water injection line scraping to sweep any bacterial growth
It is noted that efficiency of biocides isothiazolinone and 2,2-dibromo-3-nitrilopropionamide
(DBNPA) may drop by half or more in presence of O2 scavengers (Folwell, 2017), so that a
compatibility test should be performed.
Corrosion products
Transport of solid corrosion products
Carbon steel pipelines are corroding both from inside and from outside. Temperature,
pressure, composition and shear of the produced multiphase fluids flowing inside the pipeline determine the rate of steel corrosion. Corrosion rates of <0.1 mm/yr may be deemed
acceptable yet some corrosion products enter the flow and may accumulate in the pipeline.
A 24″ pipeline and a corrosion rate of 3 mils per year (MPY), will result in almost a barrel of
material loss per kilometer pipe length.
Accumulation of the corrosion products may be managed either by periodic maintenance scraping or by keeping the flow velocity above the rate where transported solids
settle out.
The flow rate for minimum transport velocity of corrosion products is similar to sand and
is on the order of 1 m/s in near-horizontal pipelines. The models for solids transport velocity
are similar to those for sand transport.
Diamondoids
Diamondoids are a class of polycyclic hydrocarbons which can be transported by gas in the
vapor phase from the reservoir. When flowing conditions change, diamondoids may deposit
as solids in the production systems.
The most common diamondoids are adamantane C10H16, diamantane C14H20 and triamantane C18H24. Their densities are 1.07, 1.21 and 1.24 g/cm3.
150
5. Flow restrictions and blockages in operations
Diamondoids are translucent crystals and are may be observed in natural gas production.
Diamondoids may also form gas hydrates. A study by Lederhos et al. (1992) showed that
adamantane can fit in the largest 51268 cavity of structure H hydrate. As structure H hydrate is
mainly observed in natural environments and not in production systems.
A study on diamondoid molecules is published by Mansoori (2007) provides more detailed properties of diamondoids.
Ice
Ice formation in multiphase flow assurance is relevant not only to Arctic and permafrost
areas, but also to regular production where Joule-Thomson cooling can cause ice solids formation at chokes and at other flow restrictions.
The presence of solids such as ice alters the erosional consideration of flow design and the
solids-free formulas may no longer apply.
Ice can also form in stagnant parts of the system which are thought to be flowing. This may
occur in parallel or looped line configuration where flow rate is not monitored in each leg of the
flow network. Ice, like hydrate, expands upon freezing into a solid. Ice expands by around 9%
relative to the original volume of water. In comparison, hydrate expands even more by approximately 26% to make room for the guest molecules. Similar to the automobile engine blocks,
which can get cracked by ice if water is used as engine coolant, ice can rupture the pipeline.
Ice can be managed by heat tracing the line to keep pipe walls from reaching the freezing
temperature. Ice may also be managed by the addition of salt or antifreeze chemicals in static
systems. However, the chemical route can be prohibitively costly or difficult to implement in
flowing systems.
Unlike hydrate solids, ice cannot be melted by pressure reduction. If an ice blockage
formed in the pipe, it either needs to be warmed up or chemically dissolved, or mechanically
jetted out with brine or milled.
Hydrate however, can be converted to ice when ambient temperature is below freezing
(e.g. 0 °C) and pressure is below hydrate stability. Caution should be taken while developing
a hydrate blockage dissociation plan in regions with cold ambient temperatures to avoid converting a hydrate plug into an ice plug because an ice plug may remain stable as long as the
environment remains below 0 °C.
Liquid holdup
Water in gas and oil lines
Water is heavier than hydrocarbons and may accumulate in the gathering lines or in the
export lines. Accumulation of water increases hydraulic resistance to flow, increases the potential for pipe wall corrosion and increases the possibility of hydrate formation.
Systems are normally designed to minimize the accumulation of liquid while increasing the
pipeline throughput by minimizing the pressure drop through a pipeline. When ­hydrocarbon
Liquid holdup
151
flow velocity is sufficient, water holdup gets swept by the shear stress exerted on water by the
flowing hydrocarbon. Water may also be mechanically removed from the flow systems which
don't have sufficient flow velocity by scraping.
Condensate in gas lines
Hydrocarbon deposits have various condensate-gas ratio or CGR. Fluids with a higher
CGR are likely to condense more liquid hydrocarbons. Pipelines are designed to maximize
throughput and to reduce condensate holdup. Significant accumulation of condensate in a
low spot may lead to the onset of terrain induced slugging. Therefore lines are predominantly
routed to avoid passing through low spot locations.
In tiebacks to offshore facilities it may be more economic to install a longer pipeline to
avoid a low spot because terrain slugging requires a larger size separator or slug catcher
in the topsides process system. Larger topsides equipment requires more deck space and
weighs more which may lead to a greater increase of the host facility cost compared to the
extra cost of a longer line.
Steam (condensed water in oil sands steam injection lines)
Steam transmission lines are used in one of the costliest methods of hydrocarbon extraction, the steam assisted gravity drainage, or SAGD. Steam generated at a central facility is
distributed to the injection wells through pipelines.
Phase transitions important for this single-component system are condensation and evaporation. Condensation occurs as superheated steam gradually cools down and water begins
to condense in the transmission pipelines due to ambient cooling. Any condensed water acts
as a restriction to flow and reduces the throughput capacity of the steam transmission lines.
Majority of steam distribution systems are designed to deliver superheated steam without
condensed water because the hydrocarbon bitumen has to be heated to 150–300 °C to become
mobile and steam has to be hotter than this.
Superheated steam may come in contact with a pool of cold fluid, either condensed water or condensed hydrocarbon. A sudden condensation of superheated steam leads to steam
hammer.
Works by Irani and Carlson (Irani, 2013; Carlson, 2012) describe the process.
In some cases the condensed water may exist in various locations of the steam generation
system. It may be a manifold near the plant with a low spot or a pipeline with a low spot used
to collect steam generated from several units to the distribution line. Sequential startup of
multi-unit systems should be prepared for the possibility of condensed water accumulation
near the cold non-operational unit. Valve opening sequence should be planned so as to avoid
the possibility of steam hammer. If a valve to a new unit is opened suddenly, superheated
steam from the operational units may reach the condensed water and suddenly condense
causing steam hammer.
System design should avoid low spots and account for the potential locations of condensed
fluids to reduce the possibility of steam hammer.
152
5. Flow restrictions and blockages in operations
Liquid accumulation in horizontal and vertical wells
In vertical multiphase flow of gas and liquid the liquid phase may be transported as a film
on the tubing wall or as droplets carried with the gas. There are film models and droplet models which allow to predict the liquid accumulation in vertical flow. As soon as liquid starts
to accumulate in tubing, the flow from a well begins to have additional resistance to flow.
Eventually the well becomes filled with liquid or loaded up.
There are droplet models and film models for liquids transport with gas flow.
Droplet models include Turner et al. (1969) correlation and its modification by Coleman
et al. (1991). Film models include Barnea (1986) and Luo et al. (2014) models.
Both droplet and film models account for shear stress exerted by gas on the liquid surface.
Recent reviews of film models are in works (Shi et al., 2015; Chen et al., 2016).
Droplet models are among the most widely used in operations due to their simplicity.
Typical accuracy of empirical models fitted to data from wells producing some fluid in some
region may be as accurate as ±20%. Usually these correlations require operator adjustment
for a given field. Simpler models are more conducive to operational adjustment.
In addition to the empirical models there are also rigorous multiphase flow models which
are available commercially. The rigorous models are tuned to data sets for multiphase flow
of various mixtures of water, liquid hydrocarbons and gas. The empirical models may reach
accuracy of +/− 10% when all parameters are accurately determined.
Turner et al. (1969) correlation is the most widely known droplet correlation for liquid
loading onset. In its development both the film and droplets were considered, and droplet
mechanism fit the 106 field operating data better.
For vertical flow, the liquid accumulation starts when largest droplets are not carried up by
the gas flow. Terminal velocity of a particle falling in gas is determined by the balance of shear
force acting on the projection of the particle surface area, buoyancy of the particle in gas, and
the force making the particle fall.
F _ drag = C _ drag v 2 density _ gas Area _ particle / 2
3
For spheres, mass m = π Dparticle
density_particle / 6 and the area is projected area = π Dp2article / 4
v = ( 4 gD _ particle ( density _ particle − density _ gas ) / ( 3density _ gas C _ drag ) )
0.5
Turner assumed C_drag = 0.44. In field units, the Turner correlation for droplet unloading
minimum gas velocity is
((
)
2
Vgas _ min [ ft / s ] = 1.92 ρliquid − ρgas σ / ρgas
)
0.25
Surface tension σ [dyne/cm], density ρ [lb/ft3]. σWater-Gas ~ 60 dyne/cm; σCondensate-Gas ~ 20
dyne/cm.
Coleman et al. (1991) updated the Turner correlation to
((
)
2
Vgas _ min [ ft / s ] = 0.8 × 1.92 ρliquid − ρgas σ / ρgas
)
0.25
Belfroid et al. (2008) further updated the Turner correlation for use in horizontal wells
by using Fiedler shape function, based on laboratory tests with a 2 in. I.D. flow loop. The
153
Sand transport
c­ orrelation allows to estimate the minimum gas velocity to unload liquid in lateral sections of
deviated or near-horizontal wells. Belfroid presented the correlation in metric units.
0.5
Vgas _ min [ m / s ] = 3.1A ρgas
(( ρ
liquid
) )
− ρgas gσ
0.25
× ( sin ( 1.7ω ) )
0.38
/ 0.74
ω = deviation from horizontal (0° = horizontal), A = tube area [m2], surface tension σ
[N/m], density ρ [kg/m3], g = gravity acceleration [m/s2]. The correlation shows zero velocity
at ω = 0°.
Multiphase flow
Flow resistance of gas, oil and water
Hydraulic resistance to flow is composed of frictional pressure drop and hydrostatic pressure drop. Most production systems operate in turbulent flow regime. As shown in Chapter 4,
turbulent pressure drop is proportional to diameter to the power of 5. Presence of liquids in
the line reduces the effective cross-section of pipe available for transport of the less viscous
fluid such as gas, which increases the pressure drop.
Vacuum condition and pressure surge during stock oil flow
In oil export pipelines going through mountainous terrain or in deepwater displacement
of the flowline live oil with stock oil there may be a vacuum condition at the highest point of
the flow system.
If pressure at the bottom of the riser or at a pumping station downstream of a mountain
is lower than hydrostatic head pressure for stock oil, vacuum may occur at the riser top or at
the crest of the mountain.
Vacuum condition has to be taken into account for design of flexible lines and flexible parts
and materials on topsides system.
Vacuum can occur at top of chemical injection lines causing flashing off of solvent and
deposition of active ingredient in the chemical tubing.
Deadheading or higher than normal flowing pressure may occur during start of stock oil
flow to move the stationary fluids in the pipeline or in the flowline. Pressure surge also occurs
during sudden valve closure.
Sand transport
Fine sand particles get produced with the fluid into the wellbore and production system
despite downhole sand screens and gravel pack well completions.
Maintenance scraping is one way to remove sand from production flowlines. High flow
velocity is another way to transport sand to the separator, from which it can be mechanically
removed during periodic maintenance.
Sand production from wells is one of the hindrances to subsea separation for oil fields.
Sand may also get produced from gas wells if rock consolidation is weak.
154
5. Flow restrictions and blockages in operations
Rock consolidation can be weakened in permafrost and Arctic wells by repeated hydrate
formation and dissociation over geologic time. Hydrate expands upon formation relative to
the water volume and crushes the rock pore matrix. Also if methanol is allowed to contact
rock near perforations, it dehydrates the rock and dissolves the cement holding consolidated
particles together. Sand production may hinder gas production from natural hydrate reservoirs if a complete physical and chemical understanding of the historic and technological
processes is not achieved.
Sand may also get produced from regular gas wells if well drawdown is too high.
Minimum transport velocity
If the liquid flow velocity falls below 1 m/s, solids are likely to accumulate in near-­
horizontal pipelines.
The following single phase Newtonian fluids transport methods are available.
Thomas (1961).
Turian et al., 1987.
Oroskar and Turian, 1980.
Wicks, 1971.
Wicks (1968) presented sand transport study in 1 and 6 in. pipes with water, kerosene and
simulated crude oil. The model is only applicable to high sand concentrations up to 0.01
volume fraction and should not be used for subsea pipeline transport where solid loading is
typically below 0.01 lb/bbl or approximately 10−8 volume fraction. However, it may be useful
for lines which already have sand deposited.
Thomas (1961) indicates that solids are less likely to settle at Reynolds>36,000.
The work by Bbosa et al. (2017) extends the transport velocity prediction method to
non-Newtonian slurry.
Multiphase transport models were presented by.
King et al., 2001.
Al-lababidi et al., 2012.
Ibarra et al., 2014.
Yan (2010) presents results of sand transport study in multiphase 2, 3 and 4 in. pipes inclined from 0 to 20°.
Sand transport in vertical flow has multiple technology areas to rest on such as catalyst
fluidized bed models, drill cuttings transport.
One of the easier methods to estimate sand transport velocity is to find sand falling velocity in a fluid.
Vertical velocity in gas is a free fall velocity with gas resistance and depends on particle
drag coefficient and cross-sectional area, and on gas density.
V _ particle = ( 2 × mass _ particle × g / ( density _ gas × C _ drag × Area _ particle ) )
0.5
As sand particles are rough and irregularly shaped, C_drag is usually 1.15 or higher at high
Re > 100. At low flow velocities the Stokes' solution gives C_drag = 24/Re.
155
Sand transport
Stokes equation (1851) for particle settling velocity in a fluid shows dependence on particle
diameter D:
Ws = D2 × ( density _ particle − density _ fluid ) × g / ( 18 × viscosity )
which is valid where density_fluid × Ws × D/viscosity <1.
Measurements for particles transport in vertical gas-liquid flow are presented by Toda
et al. (1982).
Biot and Medlin (1985) discuss the applicability and methods for applying the settling
velocity calculations for solids transport in vertical flow with small and large particle
concentrations.
Wang et al. (2014) discuss drag on sand particles in liquid and multiphase flow.
Erosional velocity limits
Several guidelines are available to help determine the maximum fluid velocity at which it
is safe to operate a pipeline, without erosion of the pipe wall material.
The Norwegian NORSOK P-001 standard was developed before 1996 to replace individual
oil company specifications on erosion. The new P-002 standard (2014) replaces the P-001.
API RP 14E (2017) recommended practice has been historically widely used due to its ease
of application and relative conservatism, providing a solution which is highly unlikely to
result in an erosional rupture and accident.
Typical safe limit recommendation for C = 100 holds for solids-free fluid flow. However,
operating companies report (Mansoori et al., 2013; Salama, 2000) that the use of the API-14E
guideline is overly conservative and provide field observations that higher C-factors may be
acceptable. While the onshore erosion consequences may be more easily managed, the API14E is specifically for offshore platform systems where reliability is more important.
(
V _ maximum [ ft / s ] = C / fluid _ density lb / ft 3 
)
0.5
C = 100 lbm0.5/ft0.5 s for continuous flow in carbon steel, 125 for intermittent flow excursion
to a higher rate, and 200 in corrosion resistant material.
The C = 100 factor corresponds to approximately 12–14 ft/s flow velocity.
Note that in metric units the C factor will differ from that in the field units.
C = 122 kg0.5/m0.5 s for continuous flow in carbon steel.
A recent clarification by API (2017) states that pipes with a pressure rating over 10,000 psi
are outside the scope of this guideline.
A more recent 2015 DNV guideline is available.
A good discussion on erosion in elbows in hydrocarbon production systems is available
from the UK Safety office (2003).
While there are guidelines for erosional velocity limits in steel pipes, there is a shortage
in agreement on erosional guidelines in non-metallic pipes such as fiberglass pipes. The
NORSOK P-001 guideline provides maximum velocity recommendation for glassfiber-­
reinforced pipe at 6 m/s, same as for steel pipe. DNV-O501 specifies that K-constant for a fiber
pipe be three to six times lower than for a steel pipe. Fiberglass pipe manufacturers provide
their own recommendations, some recommending higher velocities.
156
5. Flow restrictions and blockages in operations
Each company has to perform their own research if they intend not to use the recommended safe limit.
Liquid with solids (hydrate, corrosion products, scale)
We propose several methods for calculation of shear stress in multiphase flow with solids
such as gas hydrates as shown in Fig. 5.29. Shear affects performance of antiagglomerant
chemicals in two ways: (1) it breaks up water droplets into size of few microns (see size estimate in Autoclave section) and (2) it keeps hydrate agglomerates dispersed (shear-degraded).
Hence shear stress should be consistent across test methods. The following cases are illustrated: pipeline fluid wall shear stress, Flowloop fluid wall shear stress, Flowwheel fluid wall
shear stress, Rocking cell—shear from rolling ball and Autoclave impeller energy dissipation.
The example shows that turbulent shear stress can be maintained equal in field operating
conditions and in laboratory tests.
The formulas used above are:
τ w _ lam [ Pa ] = 8 µ [ Pa s ]V [ m / s ] / D [ m ] = 32 µ [ Pa s ] Q m 3 / s  / π D3 ( m 3 )
τ w _ tur [ Pa ] = 0.5 f ρ kg / m 3  V 2 m 2 / s 2 
V = average velocity = Q/A, flowrate divided by the cross-sectional area, μ = viscosity,
ρ = density.
These are simplified calculations and use friction factor f = 0.316/Re0.25 (Blasius smooth
pipe) for consistency because most tests as in a rocking cell have smooth surfaces.
Effective diameter for the rocking cell calculation is used as = (4 × AANNULUS/π)0.5 where
annulus area is opening between test tube and ball.
Dissipation energy for the Autoclave calculation is = power per unit mass = Power/ρ
Vol_Liq.
Turbulent microscale for water droplets breakup by the Autoclave impeller.
η = ( kinematic _ viscosity 3 / dissipation _ energy )
0.25
according to the Kolmogorov (1941) turbulent energy dissipation.
Paraffin wax
Introduction
Paraffin wax deposition is one of the most common flow assurance issues. Petroleum fluids by their nature commonly contain straight molecular chain or normal paraffins. Normal
paraffins deposits are known as macrocrystalline wax. Such deposits contain normal paraffins, branched paraffins which co-deposit with normal paraffins, occluded precipitated asphaltenes, resins, sand, oil and other solids which may be present such as rust, scale.
Normal paraffins crystallize at higher temperatures because they have straight molecular
chains, which get easily organized into crystals as illustrated in Fig. 5.30.
Paraffin wax
FIG. 5.29 Examples of shear calculation for various hydrate tests.
157
158
5. Flow restrictions and blockages in operations
FIG. 5.30 Illustration of paraffin wax crystal with normal paraffin molecules organized together.
Molecules of various size crystallize as their crystallization temperature is reached. Largest
n-paraffins crystallize at higher temperatures, and usually determine the measurable parameter called the wax appearance temperature. The parameter is subjective and depends on the
laboratory's ability to detect the crystallization either by light, heat, force or pressure. Some
objectivity is added because modern laboratory equipment has relatively comparable sensitivity levels.
There are several mechanisms for deposition of paraffins on walls of pipe or well tubing:
thermal and Brownian diffusion, and shear dispersion and settling. The most common one is
thermal diffusion. Paraffins will not deposit if temperature is above crystallization temperature. Paraffins will have almost no deposition on a pipe wall if there is no temperature difference between pipe wall and bulk oil because there is no driving force for paraffin molecules
to move toward the pipe wall. Normal paraffin molecules are usually driven from solution
in oil toward the pipe wall by the concentration difference in laminar flow and by turbulent
eddies in turbulent flow. When molecules reach the laminar sublayer, the diffusion mechanism starts.
In turbulent flow there are three sublayers: concentration sublayer, thermal sublayer and
flow or momentum sublayer. Thermal sublayer should be used because it is at this boundary where the transition to wax crystallization can occur. Concentration sublayer is slightly
smaller than thermal sublayer due to kinetic delay effects of wax crystallization.
The most illustrative description of the three sublayers was shown by Incropera et al.
(2007). I update the illustration from that work here as shown in Fig. 5.31 to reflect the relative
thicknesses of the sublayers as described in Bird et al. (1960). Understanding the difference
between the three boundary layers is very important to the physical effects involved in wax
deposition.
Diffusion coefficient is assumed constant.
Velocity
Temperature
Concentration
Velocity
boundary
layer
Temperature
Concentration
boundary
boundary
layer
layer
FIG. 5.31 Illustration of boundary layers in flow of a mixture of hydrocarbons past a surface with component
precipitation.
Paraffin wax
159
Molecules diffuse from areas with high concentration to low concentration. Concentration
of n-paraffins can become low near a pipe wall if the wall is cold which affects solubility of
n-paraffins in oil. At low temperature, n-paraffins crystallize and precipitate out from solution as solids, which causes concentration to decrease. This in turn causes diffusion from high
concentration to low concentration areas.
Besides thermal diffusion there is also shear dispersion mechanism for deposition of paraffins. Dispersion also depends on fluid cooling down below the paraffin crystallization temperature, but does not require diffusion or temperature difference. Dispersion requires flow.
Flow causes dispersion and movement of precipitated solids from area of high content (bulk
of oil) to the periphery of flow (pipe wall or well tubing). Dispersion contributes between 1
and 10% of deposition. This means that even in a perfectly insulated pipes flowing oil with
precipitated wax crystals, there will still be adhesion and accumulation of precipitated wax
crystals on pipe walls. Regular maintenance for removal of wax deposits may be accomplished with scraping such pipe line.
Brownian diffusion and settling are commonly ignored in wax deposition analysis.
Brownian diffusion is eclipsed by flow turbulence. Gravity settling is only observed in static
non-flowing systems such as shut-in pipes or storage tanks, and settled wax particles are
usually easily re-dispersed when flow resumes.
Branched or isomerized paraffins also can form wax. Such wax is observed in biodegraded
oils where normal paraffins have been isomerized by bacteria. While the degree of crystallinity is less or absent, such wax also can deposit as solids on cold surfaces when there is a
temperature difference between bulk oil and pipe wall.
Chemistry
Wax is usually composed of n-paraffins which are inert, apolar and non-reactive at normal
production operation conditions.
Composition
Besides the solid crystalline matrix made up of normal paraffins, the wax deposits may
contain occluded oil, sand, precipitated asphaltenes, resins, corrosion products, and other
materials.
The measurements of mass fractions for asphaltenes, resins and solid hydrocarbons
was reported for samples deposited at various depths (Liushin and Iksanova, 1965) for
the Bavlinskoye, Romashkinskoye and other fields. The summary table is shown below in
Table 5.5.
Similar data were compiled for eight oil fields. Authors note that the solid hydrocarbons
extracted from oils of different fields significantly differ in fractional composition, such as in
heavy high-temperature melting solid hydrocarbons. Authors suggest that the intensity of
paraffin deposition is directly proportional to the content of high-melting temperature hydrocarbons in oil, all other parameters being equal. The authors also discuss the differences
in properties and crystallization habits of macrocrystalline (paraffinic) and microcrystalline
(isoparaffinic) wax. Authors note that strength of paraffinic wax deposits increases with an
increase of n-paraffin content in oil and decreases with an increase of aromatic content in oil.
160
5. Flow restrictions and blockages in operations
TABLE 5.5 Data for paraffin deposits collected from various depths of the same well
Composition (wt%)
Paraffin sample
depth (m)
Asphaltenes
Resins, via
silica gel
Solid
hydrocarbons
Melt
temperature
(°C)
Residue (oils)
(wt%)
Loss (wt%)
36
2.2
8.9
64.8
72
21.8
2.3
88.5
1.7
6.2
65.7
72
22.0
4.4
133.5
1.6
7.9
64.0
74
26.3
0.2
193.5
2.3
6.4
59.1
75
28.7
3.5
328.5
2.1
5.9
53.8
75
33.9
4.3
448.5
2.7
7.8
49.1
77
35.0
5.4
Structure
Wax crystal habit depends on the cooling rate. Fast cooling leads to many small crystals.
Slow cooling leads to fewer large crystals. Wax usually crystallizes as 2-dimensional platelets.
Wellbore and reservoir plugging
Deposit thickness was reported for wellbores and surface gathering lines for Devonian
paraffinic oil production in Tatarstan, Russia (Mazepa, 1965) as shown in Fig. 5.32. The author
also reported the microphotographic research on adhesion on a steel plate of precipitated
paraffin particles flowing in oil. The study indicated that particles sized between 0.002 and
0.2 mm adhered to the steel plate.
Production operating parameters for the above wells are summarized in Table 5.6 below.
The wells 4136 and 4138 were producing undersaturated oil, at pressure above the bubble
point. The author (Mazepa, 1965) produced the first proof that paraffin deposition may occur
from undersaturated flowing oil. Additional results for 40 wells were also presented in this
work.
The author indicates that the relatively low length of sections with wax deposition for
low-rate wells was caused by the stratified multiphase flow of oil and gas. This flow regime
ended at a relatively short distance from wellheads. The stratified flow in the gathering lines
was confirmed in the field using radioactive density meter, sample valves, and transparent
spools installed on the pipelines. The critical flow rate at which the stratified flow may still
occur was determined from the critical Froude parameter (which accounts for the effect of
gravity on flow).
Q 2 = Frcrit ( 1 − Gas fraction ) π 2 g D5 / 16
2
Frcrit = ωc 2 / ( gν )
Q = oil flow rate, D = pipe diameter, ωc = mixture velocity, g = gravity acceleration, and
ν = hydraulic depth.
161
Paraffin wax
FIG. 5.32
Wax deposit thickness profiles in wells and in surface gathering lines (updated from Mazepa, 1965).
Distances are shown in meters.
TABLE 5.6 Production operating parameters for the waxy wells
Well parameters
Field
Well
Q (ton/d)
Gathering lines parameters
P_buffer
(atm)
L (m)
D
(in.)
P (atm)
Burial (m)
Deposit
length (m)
Zaj-Karatayskaya 4028
75
17
600
2.5
17
0
400
Aznakayevskaya 4138
15
80
500
2.5
80
0
300
Aznakayevskaya 4136
26
79
500
2.5
79
0
350
Pavlovskaya
32
4
400
4
4.0/5.0
0
75/100
3901
The calculated critical flow rate of 70 tons/day was close to the observed value of 60 tons/
day.
Effect of PVT conditions
Temperature has the largest effect on the solubility of n-paraffin molecules in oil. When
temperature decreases, the molecules move slower and at some temperature may align together and form a solid crystal of wax. The heavier molecules with longer carbon chains
162
5. Flow restrictions and blockages in operations
crystallize first, at higher temperatures, and the short molecules crystallize last, at lower
temperatures.
Wax crystals typically contain molecules with carbon chains as short as 18 carbons, or
C18H38, octadecane. Crystals may contain n-paraffins as large as C100 but these molecules exist in oils in very low quantities. More commonly, the heaviest n-paraffins present in a wax
deposit are in the C40–C60 range. This range of the typical heaviest molecules determines
the typical wax appearance temperature (WAT), or the temperature at which the heaviest
n-paraffins begin to crystallize as wax at around 30 °C. There are oils with WAT as high as
50 °C, which contain high concentration of normal paraffins. Oils with high n-paraffin content
usually also exhibit high pour-point temperature and gelling issues, when the whole oil turns
into a ­solid-like non-Newtonian liquid.
The pressure also has an effect on the solubility of n-paraffin molecules in oil. When pressure is high, more gas molecules are dissolved in oil. These light molecules help solubilize
the longer n-paraffin molecules in oil. WAT decreases with pressure until the bubble point.
The WAT temperature is usually the lowest at the bubble point pressure. Above the bubble
point pressure, molecules get compressed in undersaturated oil and molecules come together
to crystallize easier, so WAT increases with pressure. Wax solubility models can capture this
effect as shown in Fig. 5.33.
FIG. 5.33 Effect of pressure on WAT in a low wax content crude.
Paraffin wax
163
Role of composition
The presence of light hydrocarbons and aromatic compounds helps solubilize the heavy
n-paraffin molecules in crude oil. The WAT and wax deposition both decrease with an increase in the content of hydrocarbons lighter than C17 and aromatic components in oil.
The composition of crude oil can be analyzed for the purposes of wax prediction very
roughly with a thermogravimetric analyzer, roughly with boiling point fractionation, detailed with gas chromatograph and very detailed with a high temperature gas chromatograph
(HTGC). In a HTGC, a small amount of oil or wax deposit is dissolved under a vent hood in
a volatile solvent such as toluene (less toxic) or carbon disulfide (very toxic). The dissolved
sample is then injected in a temperature-controlled vaporizer and flown through an adsorption coil in carrier gas to the flame ionization detector where all molecules are dissociated into
ions to analyze mass of the components in the stream. Time of elution is calibrated to normal
paraffins of known molecular weight, and composition of the sample is determined based on
calibration. The heaviest commercially available calibration sample is C60. Analysis of elution
times for heavier components are based on logarithmic extrapolation.
Oil WAT increases with an increase of heaviest components content.
Majority of petroleum analyses for wax is done with GC or HTGC. In some cases laboratory data are supplied as true boiling point distribution. In order to use the oil composition in
a predictive tool one needs to convert the boiling point temperature of a fraction to molecular
weight of a fraction. The method proposed for doing this was presented in Chapter 3.
Miscellaneous factors
Oil-based drilling muds may be used in deepwater wellwork. Oil-based drilling muds
contain n-paraffins such as C14, C16 and C18. Oil samples contaminated with large amounts of
drilling mud may be inappropriate for PVT analysis of oil thermodynamic properties such as
bubble point, density or gas oil ratio. However, it may still be possible to use such samples for
paraffin analysis with decontamination. The amount of components is expected to decrease
logarithmically with molecular weight. Components of oil-based drilling mud will be seen in
HTGC data as outlier peaks, and it is possible to subtract the extra peaks from the composition to make it usable for paraffin deposition analysis.
Tubular plugging
• Effect of PVT conditions
It was demonstrated (Mazepa, 1965) than wax can deposit from both saturated oil (multiphase flow of oil and gas) and undersaturated oil (single phase flow). As fluids flow up the
wellbore, pressure decreases and the wax appearance temperature also decreases. However,
ambient temperature also becomes lower. The colder ambient conditions cause wax to precipitate. In some cases vacuum insulated tubing (VIT) or downhole electric heating cables were
used to maintain heat in the flowing crude to avoid wax deposition.
• Role of composition
The presence of water helps retain heat in flowing produced fluid and reduces the amount
of wax deposition. Water is also denser than oil and creates additional shear on the wax deposit, partly removing it.
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5. Flow restrictions and blockages in operations
The presence of gas decreases the temperature of the produced fluid by J-T cooling due to
gas expansion. Addition of gas lift gas also decreases the temperature of the fluid. The presence of light hydrocarbons helps solubilize n-paraffins in oil, but the effect of cooling usually
causes more wax deposition with presence of gas.
• Miscellaneous factors
Wax deposit in flexible risers may reduce the potential for adhesion of other solids. Wax is
made of hydrocarbons, so hydrophilic compounds such as gas hydrates may have less possibility of adhesion and plugging in annular flow regime in vertical or near-vertical risers when
some wax deposit is present. However, the wax deposit may trap sand and water and cause
other integrity issues. Wax deposits may be prevented with insulation, mechanical removal,
solvents or active heating.
Prevention techniques
Operations should avoid wax formation and accumulation irreversible by normal operating procedures. This may be accomplished by keeping oil at temperature above the wax
appearance temperature when system is flowing.
Wax appearance temperature should be used as higher of the measurements from DSC
and CPM or high pressure CPM if available. In case of high content of microcrystalline (biodegraded, isoalkane) wax in oil, high pressure DSC WAT should be used instead of high
pressure CPM.
Technologies which could be considered for management of wax and gels in produced
fluids include:
•
•
•
•
•
•
•
•
•
•
•
insulation
periodic scraping
wax inhibitor chemical
pour point depressant chemical
wax dispersant chemical
active flowline heating by PIP heating medium circulation
active flowline heating by wet insulation EH
active flowline heating by PIP DEH
active flowline heating by PIP heat tracing
hot water injection from aquifer if proven in the region
low rate flow circulation in a shut line to prevent gel from setting
Following remediation technologies could also be considered.
•
•
•
•
dry tree wireline scraping
hot oiling
wax solvent wash
coiled tubing to jet out the deposit, especially for a riser
Several techniques are discussed in more detail.
• Wireline scraping
Wireline scraping of wax in well tubing is a commonly used mechanical wax removal
method. Onshore wells use a timer-actuated motor to lower and lift a wireline with a cutter
Paraffin wax
165
FIG. 5.34 A wireline scraper used to scrape wax in a deepwater dry tree well.
through a lubricator. This method in onshore wells encounters operational issues such as
wireline tearing or cutter sticking, which are resolved by a well service crew.
In deepwater subsea production only dry tree wells are conducive to wireline cutting of
wax. A cutting tool on a string as shown in Fig. 5.34 is lowered from topsides into the tubing
and mechanically removes the wax deposit. In a subsea tree, access to the well is significantly
more complicated and requires the use of a workover rig, which makes wax removal by cutting in subsea tree wells uneconomic.
• Scraping
Scraping is the most common way to remove wax deposits from gathering flowlines and
from export pipelines.
Wax scraping requires a careful balance of forces acting on a scraper, in order to not break
the scraper or not to make it stuck on the wax deposit in a pipeline.
Typical forces acting on a scraper include:
‐ Force of scraper friction on pipe wall, which depends on scraper size relative to the pipe size.
‐ Force required to cut the wax from pipe wall, which is a function of wax content, which
in turn is a function of time. The diffusion of normal paraffin molecules into the porous
wax deposit causes the deposit to harden with time.
‐ Force required to propel the wax cuttings in front of the scraper, which depends on
scraper efficiency in removing wax and on the oil bypass of the scraper from back to
front, which depends on scraper size relative to the pipe size.
The sum of these forces should not exceed the value recommended by the manufacturer,
typically 30–40 psi, otherwise the scraper may get deformed and stuck in a pipeline.
Scraping typically removes up to 50% of a wax deposit per pass. Data on the wax removal
efficiency by scraping were measured by Wang et al. (2001, 2008) for cup and disk scraper
types.
166
5. Flow restrictions and blockages in operations
Typical scraping velocities are between 1 and 3 m/s. The faster the scraper moves, the
more its cutting surfaces deform and the less efficient is the scraping run in removing wax.
Therefore an operational experience can show the optimum balance between the duration of
the scraping run and the amount of wax removed per run. In some cases only the soft layer
of wax gets scraped by the scraper while the aged harder underlying layer gets left behind.
If a pipeline carrying waxy crude has not been scraped for an extended time (over 6 months)
it is likely that the amount of accumulated wax is too great to be handled by a single full-­
diameter scraper. In such cases the progressive scraping is implemented when softer material
(lower durometer) scrapers are used for initial scraping of wax, then progressively larger and
harder scrapers are used to remove the remaining wax deposit.
One way to avoid wax deposition in a pipeline and to reduce or eliminate the need for
scraping is cooling of the crude to ambient environment temperature before sending it
through the pipeline. No wax will deposit on the pipe wall by diffusion since there is no
temperature difference between the fluid and the pipe wall. However, this requires additional equipment or a length of pipeline and may be uneconomic. A pre-cooling system could
include a heat exchanger with non-stick cold surfaces which would pre-cool the crude and
send all precipitated solids with the flow. Prior laboratory tests indicated that wax sticks to
almost any material which can be withstand harsh production system conditions and erosion,
so such pre-cooling heat exchanger is not technically achievable yet. An oleophobic non-stick
surface could possibly be made of polyacrylonitrile polymer modified by oxyfluorination to
improve its antifouling, possibly with embedded SiO2 nanoparticles, or periodically actively
heated to melt off the deposited wax.
Even if the hydrocarbon liquid is pre-cooled, precipitated wax may still accumulate in the
pipeline by the dispersion mechanism discussed in Burger et al. (1981). An example of wax
from a line where the main wax deposition mechanism is by dispersion is shown in the image
below in Fig. 5.35.
FIG. 5.35 A 48-in. diameter scraper used to scrape wax in an oil export pipeline.
Paraffin wax
167
• Vacuum insulation tubing
Vacuum insulation tubing (VIT) is an effective albeit costly method to reduce heat transfer
in a well downhole. As the temperature difference between hot oil and colder ambient conditions is the main driving force for wax deposition, the effective insulation prevents wax
deposition.
Vacuum insulated tubing is relatively costly at over USD 100/ft.
• Electrical heat
Electrical heat has been used to effectively remove wax deposits from well tubing. Several
studies found the downhole electrical heating method to be most cost-effective in onshore
applications if the commercial cost of electric power is low in the region.
Subsea systems have used actively heated pipelines of the EH (electrical heating or pipe
and cable), DEH (direct electrical heating or pipe in pipe) and ETHPIP (electrically trace
heated pipe in pipe) mainly for hydrate control, but wax deposition also benefits from the
active heating.
• Comparative economics of prevention techniques
Scraping is the second most common method of wax management, after pipe insulation.
Pipe may be insulated either by addition of insulating layer, by burial underground or both.
Scraping frequency optimization is one of the most profitable technology studies for an operator. A justified reduction of downtime for scraping by reduction of the frequency of maintenance scraping brings substantial uptime and revenue to the operator.
Remediation techniques
Wax tends to deposit as fluid flow rate declines and the fluid cools to conditions below the
wax appearance temperature. Once the wax deposits, there are several methods to remove it.
• Mechanical
Mechanical removal of wax is accomplished by scraping, wireline scraping, coiled tubing
jetting or pressure pulsation.
• Thermal
Thermal removal may include hot oiling and SGN exothermic chemical reaction. Hot oiling is not always effective as the fluid has to be hotter than the wax dissolution temperature.
Wax dissolution temperature is a temperature at which a concentrated wax deposit dissolves
in crude oil. It may be 10–40 °C higher than the wax appearance temperature. Hot oil may
cool below the wax dissolution temperature while still flowing to the deposit.
SGN chemical reaction is seldom used as it requires to simultaneously time the arrival of
two chemicals at the wax deposit location. The chemicals have different viscosity, and the
lower viscosity fluid catches up to the higher viscosity fluid. Upon mixing, they react exothermically to produce nitrogen and release heat which dissolves the wax deposit.
• Chemical
Chemical removal may be accomplished with a solvent or a dispersant. Solvent efficiency
in wax removal depends on its composition (diesel, xylene, kerosene) and temperature.
Temperature of the solvent is a process-safety related issue. Volatility and ignition temperatures must be closely evaluated before the selection of the chemical solvent.
Water-based dispersant may help remove non-aged wax deposits from wellbores by a surfactant mechanism.
168
5. Flow restrictions and blockages in operations
• Comparative economics of remediation techniques
Regional availability and operator experience with a wax removal technique are often
more important than the relative cost savings or effectiveness because safety of a method
application should increase with the operator's familiarity with the method.
Mechanical methods are usually the most cost-effective ones for wax removal. While
scraping and wireline scraping are commonly used to maintain production operations, the
coiled tubing jetting is used to clear wax from completely plugged pipes and for hydrocarbon
removal during pipeline decommissioning.
Environmental impacts of remediation techniques
• Thermal
Thermal methods are usually cost-effective for downhole onshore well applications because earth around the wellbore provides heat retention. Hot oiling is usually ineffective in
offshore wells or in flowlines both onshore and offshore because of the requirement for the
high initial temperature of the heating medium (hot oil) and the significant heat loss to the
ambient environment.
Thermal methods such as hot oiling may not be applicable in cold regions production such
as permafrost areas.
• Mechanical
Mechanical methods such as scraping, wireline cutting or jetting can be applied in onshore
wells and in flowlines both onshore and offshore. Un-scrapable lines may require solvent
remediation of wax deposit.
• Chemical
Lab selection of solvent should focus on chemical compatibility with the production system including valve seals material. Chemical should also be effective in dissolving samples
of wax from a given field in the least amount of time at the lowest operationally possible temperature. Higher temperature usually increases the solvent effectiveness, but it also increases
the flashing off of solvent vapor which may create environmental and safety hazards.
Measurement techniques
Laboratory measurements focus on determination of conditions, usually temperature but
sometimes both pressure and temperature at which solid paraffins start to precipitate from
oil, and on the comparison of amounts of wax deposition with various additives.
Finding the temperature of wax precipitation may be done with a number of methods,
categorized in Table 5.7 below.
An example in Table 5.8 below illustrates how the mass of a paraffin deposit from a cold
finger laboratory test as shown in Fig. 5.36 may be used to estimate the wax diffusion coefficient, in order to test other diffusion coefficient evaluation methods such as flow loop deposit
measurement. The initial rate of deposition is used to calculate flux in this method.
Compositional analysis of oils or wax deposits is performed using HTGC, described earlier.
The amount of wax deposition can be measured quantitatively using in a laboratory using
the methods of a cold finger, cold plate, rotating shear cell, flow loop or in field conditions using
flow spools. The methods of cold finger or a mini-flow loop can be used to compare the effects
of various chemical additives on the mass, consistency and melting point of the wax deposit.
169
Paraffin wax
TABLE 5.7 Methods to find the temperature of wax precipitation
Type
Method
Optical
Visual—deposit in laboratory cold finger or flow loop equipment or in the field separator inlet
strainer, scraper receiver or bypass spool pipe at various temperatures.
Visual polarized light microscopy, atmospheric and pressurized. Polarized light is only applicable to
n-paraffin waxes because these crystals can rotate the plane of light polarization. Amorphous wax
such as from biodegraded crudes cannot be detected by CPM
Infrared or visual light transmission. Infrared light is more applicable to crude oils as crudes are
translucent to infrared light
Heat
Differential scanning calorimeter to detect heat released by crystallization of paraffins, atmospheric
and pressurized
The DSC method is applicable to both n-paraffins (macrocrystalline wax) and isomerized paraffins
(microcrystalline and amorphous wax) because heat of fusion is released by both
Mechanical Viscometer to detect transition to non-Newtonian fluid behavior with appearance of solids
Rheometer to detect transition to non-Newtonian fluid behavior with appearance of solids
Pressure
Cold filter plug to find onset of wax deposition by measuring pressure drop
TABLE 5.8 Procedure to calculate wax diffusion coefficient from a deposition experiment data such as a
laboratory cold finger
Flux = D (C_WAT − Cwall)/L_diff
- Assume Fick's law
V_sample, mL
166
Estimated
Depth, in.
2.6
Assume +1 in. from U tube to flask bottom to allow for stirrer
Flask area, cm
24.8
= V_sample/depth
Flask ID, cm
5.6
Diameter calculated from area
L_deposit, in.
4
Estimated from image
L_vertical, in.
1
Estimated from image
0.25
Estimated from image
Area_deposit, in.
3.14
= pi × OD × L
Circumference, in.
4
to estimate radius of cold finger
R, in.
0.636
radius of cold finger
Stirrer RPM, 1/min
100
estimated
Flow velocity past finger, in./
min
400
= 2 × pi × R × RPM 16.9
cm/s
Viscosity of stock oil @ 36 °C, cP
40.995
per lab data
kg/m s
2
OD_finger, in.
2
3
Density oil, g oil/cm oil
2
0.85
0.040995
0.40995
g/cm s
3
850
kg/m
4.82E-05
m2/s
Kinematic viscosity, cm /s
0.482
= viscosity/
density
Viscous sublayer, cm
0.330
= 11.6 × kinem.visc/flow velocity
(Continued)
170
5. Flow restrictions and blockages in operations
TABLE 5.8 Procedure to calculate wax diffusion coefficient from a deposition experiment data such as a
laboratory cold finger—cont’d
Flux = D (C_WAT − Cwall)/L_diff
- Assume Fick's law
Oil heat capacity, J/kg K
1917
per PVT tool at 1 bar, 36 °C
Oil thermal conductivity, W/m K 0.152
per PVT tool at 1 bar, 36 °C
Reynolds
22
= dens.oil × flow velocity × OD_finger/viscosity
Prandtl
517
= viscosity × heat capacity/thermal conductivity
Thermal sublayer, cm
0.001386 delta_thermal/L = 0.664 Pr^(−2/3)/sqrt(Re)
Flow sublayer, cm
0.1263
WAT, °C
36
Distance fraction
0.8
= 1-(Thot − WAT)/(Thot − Twall)
L, cm
0.6
= R_flask-R-OD
L diffusion, cm
0.00139
Using thermal sublayer
Flux, g/in.2/h
0.01215
= mass_initial_deposition/time_initial_deposition/area_deposit
Flux, g/cm2/s
5.2E-07
T, °C
40
Hot oil temperature
Twall, °C
20
Cold finger temperature
T_WAT, °C
36
T_BP237
−32
delta_flow = 0.37 diam_finger^(4/5) *(kinem visc/veloc)^0.2
Wax content measurement temperature
C_WAT, wt% = g wax/g oil × 100 6.2
Maximum concentration of wax in oil at WAT 36 °C
C_BP237 (−32 °C)
0
Zero concentration of wax in oil at −32 °C
C_20°C = Cwall, wt%
4.74
=(Twall − T_BP237)/(T_WAT − T_BP237) × C_WAT
C_WAT, g wax/cm3 oil
0.053
Cwall, g wax/cm3 oil
0.040
C_WAT-Cwall, g wax/cm3 oil
0.012
D = Flux × L_diff/(C_WAT
− Cwall)
5.9E-08
cm2/s
FIG. 5.36 Wax deposit on a typical U-shaped cold finger test.
Paraffin wax
171
A good overview of some of the experimental laboratory techniques used for wax and
waxy oils analysis is presented in Zhu et al. (2008).
Conventional techniques
The common methods for wax control include insulation, mechanical removal and chemical inhibition. The relative cost-effectiveness of each method depends on the availability and
the number of competing vendors present in a region.
Remote sensing and monitoring
Remote sensing of wax deposition is relatively difficult as the deposit is usually thin and
affects the frictional pressure drop mainly by an increase in pipe wall roughness, particularly
in multiphase flow.
The remote sensing methods for wax detection include ultrasonic measurement through a
pipe wall, optical detection and indirect methods such as a change in readings of instrumentation where a wax deposit could cover and insulate temperature or pressure probe.
Technologies such as virtual metering which combine the readings from all available pressure and temperature gauges in wellbore, tree and flowline may be able to detect the deviation in pressure drop from normal, which may be indicative of wax deposition. Such remote
monitoring should be done with a complete analysis of the possibility of other solids or liquids accumulation which may affect the pressure drop in a monitored section of production
system.
Emerging techniques
The method of magnetic treatment of oils to reduce the deposition of wax has been discussed for over 50 years. The method is not 100% reliable despite field data sets which show
its effectiveness in some wells. The method may affect kinetics of wax crystallization, similar
to the cold flow technique, promoting precipitation of wax as crystals in flowing produced
fluid and effectively decreasing the amount of n-paraffins dissolved in oil and available for
deposition in wells and flowlines. The method reportedly is only effective in waxy oils where
polar components such as flocculated asphaltenes are present. As this method does not provide a complete reliability, it found little commercial application in the field.
Jetting using coiled tubing has been in use for several years to clear and decommission unscrapable subsea pipelines plugged with wax. A plugged subsea line is usually cut and raised
to surface, one end at a time, for cleaning with a coiled tubing jet.
Pressure pulsation for wax remediation has also been used with recent success. Wax blockage gets displaced from a pipe. Adequate downstream storage should be provided to capture
the displaced wax.
Modeling
Historic scraping models are based on flowloop tests performed with dead oil. Wax ages
in field pipeline differently than in a laboratory flowloop. Fluids in multiphase flowlines
are “live” and behave very differently from “dead oil” or stock tank crude as shown in
Figs. 5.37–5.39.
A proper scraping model should be based on a balance of forces acting on the scraper so
that the scraper does not get stuck. These include the friction of scraper on the pipe wall,
172
5. Flow restrictions and blockages in operations
Wax content
T = 26°F
T = 50°F
0 .1
1
Time (days)
10
FIG. 5.37 Laboratory wax deposit wax content—model oil (Makogon, 2003).
Wax content
T = 70°F
T = 60°F
0
0.1
1
10
100
Time (days)
FIG. 5.38 Laboratory wax deposit wax content—stock tank crude oil (Makogon, 2003).
FIG. 5.39 Field wax deposit wax content—live crude oil (Makogon, 2003).
Paraffin wax
173
the cutting of wax from the pipe wall and the pushing of wax cuttings ahead of the scraper.
The wax cutting force had been measured at the University of Tulsa. The same laboratory
provided an estimate of the amount of wax removed by a scraper. Typically 30–50% of wax is
removed in one scraping run when softer polymer cup scrapers are used. The rest of the wax
is smeared on the pipe wall. Subsequent scraper runs remove additional amounts of wax.
When more rigid K-disk scrapers are used, the wax removal may increase to 50–60% per run.
Comprehensive modeling
Models of wax deposition reproduce and model physical processes which occur in a pipe
during the process of n-paraffins diffusion to and inclusion in the solid deposit on a pipe wall.
Wax deposition is driven by diffusion of heavy normal paraffins to the cold surface.
Diffusion is caused by the difference in concentration of normal paraffin molecules dissolved
in the bulk of oil at high temperature and near the cold surface where these molecules come
out of solution as crystals. The straight chain normal paraffin molecules are more easily organized into regular crystal structures than the branched isomer paraffins. This affects their tendency to crystallize and their solubility in hydrocarbon liquids. As some paraffin molecules
precipitate, their concentration in liquid decreases, and other molecules diffuse from liquid
to take their place.
When there is no difference in temperature, there is no driving force for normal paraffin
molecules to diffuse, and no wax deposition on a surface occurs. Nonetheless, when there is
a uniform cooling of fluid, without flow, the normal paraffins still precipitate as crystals and
usually settle at the bottom of the fluid because solids are usually denser than liquid from
which they form (except aqueous solids such as ice or hydrate).
The rate of diffusion of normal paraffins to the cold surface limits the growth rate of a wax
crystal in a deposit.
Similar to settling mobility of particles, diffusion of solids in liquid may be estimated by
Stokes-Einstein equation. Einstein's equation (1905) comes from the solute diffusion coefficient, derived from Stokes's law for a sphere of diameter D moving in a liquid, and van't
Hoff's law for the osmotic pressure:
Diffusion Coefficient_particle = k × T/(3 × π × viscosity_fluid × D)
where k = 1.381 × 10−23 J/K, the Boltzmann constant.
However, the Einstein relation is only valid for small values of particle concentrations.
Dissolved particle movement due to collisions with other molecules can be estimated from
the same equation as:
( position − position _ 0 ) / ( time − time _ 0 ) = k × T / ( 3 × π × viscosity _ fluid × D )
2
Hayduk and Minhas (1980) method for evaluating diffusion coefficients in hydrocarbon
fluids fit laboratory data better than other correlations. That's why this diffusion correlation
may be preferred for use in wax deposition modeling.
As oil cools down, heavier n-paraffins become less soluble in oil, and partly precipitate out
of oil as solid crystals. In order to evaluate the amount of paraffins dissolved in oil at various conditions, the solubility correlations were developed. Several recent solubility correlations for waxy paraffins in hydrocarbons have been developed such as Won (1986), Erickson
174
5. Flow restrictions and blockages in operations
et al. (1993), Pedersen (1995), Lira-Galeana et al. (1996), Coutinho et al. (2001), and EscobarRemolina et al. (2009). The relative comparison (Huang et al., 2015) of precipitated wax of
some of the above solubility models shows that the Erickson model predicts on average more
precipitated wax and is more conservative than the Coutinho method. Both models allow
tuning to WAT.
The solubility models evaluate the solid-liquid equilibrium for each component (such as
n-C30) as function of the heat of fusion ΔH fi and the melting point T fi.
((
)(
Si / Xi = ( γ i L / γ i S ) exp ∆H i f / RT 1 − T / Ti f
))
γLi and γSi are activity coefficients of component i in liquid and solid phases. The melting
point for normal paraffins depends on the molecular weight.
Ti f = 374.5 + 0.02617 MWi − 20172 / MWi
In comprehensive models the multiphase or single phase flow model which calculates hydraulic frictional and hydrostatic pressure drops is coupled through time with heat transfer
from oil to surroundings and with mass transfer which calculates the radial diffusion of wax
components in crude oil as a function of pressure and temperature. This coupling is done
for several sections of the pipeline. Changes in composition of oil are tracked from section to
section. Two-dimensional models keep track of both longitudinal and radial distribution in
wax components. Circumferential variation in properties is commonly ignored because heat
transfer is calculated axisymmetrically.
An overview of wax deposition laboratory measurements and modeling methods was presented by Theyab (2017).
The models allow to evaluate the rate, location and amount of wax deposited on a cold
surface such as well tubing or pipe wall.
There are commercial wax deposition models, proprietary in-house models developed by
operator companies, and university research models some of which were in part derived
from the proprietary company models. A comparison of field data and commercial models'
predictions was presented by Giacchetta et al. (2017).
Waxy gels
In normal production, wax deposits contain some solid wax crystals and some liquid occluded
within the porous wax matrix. Solids content in a deposit usually ranges from 10 to 50 vol%.
Waxy gels form when the whole bulk of fluid converts, upon cooling, into a solid-like
material. In a waxy gel, the amount of wax is sufficient to form a network of solid crystals
interconnected so that it behaves like a solid. Solid content in a gel typically ranges from 3 to
10 vol%. The pores are occupied by liquid.
Both wax deposit and wax gel have the same structure. Waxy oils which can form a gel,
contain enough normal paraffins to build a network of crystals in the whole volume of the
liquid after cooling. The oils which form a deposit do not have enough normal paraffins to
fill the whole volume with crystals after cooling, but gradually build the deposit on the pipe
or a well tubing wall.
Paraffin wax
175
Waxy gels may form in the pipeline when the normal paraffin content of the components
heavier than C18 is usually greater than 3 wt%. Oils with lower wax content are less likely to
form gels.
One method to characterize gelling tendency is pour point measurement. A stock tank oil
sample is chilled to a set temperature in a flask, which is then tilted 90°. No fluid movement
for at least 5 s represents the condition when the pour point temperature was reached, and
the liquid has gelled.
The term gel is used qualitatively only to represent a formation of interconnected matrix of
solid crystals made of normal paraffins.
While illustrative, the use of the term “gel,” for example in (Singh et al., 2001), to describe the initial wax deposit on a cold surface can be misleading. The term “gel” in wax
terminology should be used for near-uniform transformation of a waxy hydrocarbon liquid into a solid-like material when it is not flowing and its temperature falls below the
pour point temperature. In the initial deposit the wax crystals interconnect and form a
lattice which has a certain mechanical strength. Just as in the regular deposit, the strength
depends on the shear stress exerted on the deposit by the fluid flowing past the deposit.
Higher flow velocity results in a more solid wax deposit, able to withstand shear of the
faster flow. A proper characteristic for initial wax deposit should be not the aspect ratio of
a crystal but a mechanical strength measurement of a deposit. While it is a technical impossibility at present to measure the aspect ratio of an individual micron-sized wax crystal
inside a pipeline, one can measure the force it takes to remove the deposit off a pipe wall
using a scraper.
Conversely, stronger flow results in weaker waxy gels. For example, one method to prevent gelling of a waxy crude at temperatures below its pour point, is to maintain flow circulation, however slow. The flow will keep disrupting the networks forming between the few
crystals, and as none of the crystals can deposit and take hold on the pipe wall due to the lack
of temperature differential driving force, no deposition or gelling would occur. Such method
has been used on a gravity-based offshore platform oil offloading system in the Northern
Atlantic.
Waxy gels are characterized by their strength, or by the yield stress required to break the
interconnected matrix of wax crystals in the gel. The strength of a gel can be measured in a
stress-controlled rheometer or in a model pipe. In a rheometer the yield stress is a direct measurement. In a model pipe, the pressure required to restart the flow of a gelled oil or the gel
break pressure is measured, which then is translated into the yield stress
Differential Pressure [ Pa ] = 4 × Yield _ stress [ Pa ] × Pipe _ Length [ m ] / Pipe _ Diameter [ m ]
Studies have reported that the scale-up of the gel break pressure to larger diameter pipes
using the above equation provides conservative estimates. Several multi-year industrial research Joint Industry Projects have developed improved correlations for gel strength prediction using small size laboratory equipment such as 0.25 in. test loop. However, it would be
easier to measure gel strength more accurately in larger laboratory equipment, such as a test
loop of at least 2 in. diameter, with appropriate insulation layers and appropriate thermal
history of the oil cooldown. Laboratories aiming to improve gel break pressure correlations
176
5. Flow restrictions and blockages in operations
should be equipped with 2 or 3-in. diameter wax equipment which could adequately measure the relevant processes.
Gels may be weaker if their cooling rate is non-uniform. Some parts of the gel may break
first, if the crystals making up the network are smaller as caused by the faster cooldown.
Usually, the faster the cooling rate, the smaller are the crystals, the weaker is the gel. This
is observed in laboratories where gel usually breaks at the pipe wall first, where the heat
transfer was the greatest.
In insulated or buried pipes the cooling rate may be more uniform, leading to the uniform
gel strength. Axial center of the pipe may have mechanical deformation of the gel due to its
cooling, and thermal expansion or contraction.
Gels may also be weakened by presence of gas pockets in the pipe.
Typical gelling crudes contain at least 3 wt% wax, as measured by the cold filter method.
Crudes with lower content of normal paraffins are less likely to gel because not enough
solid crystals precipitate on cooling to ambient temperature to form a network. As with any
natural material, a gelling oil may contain less than 3 wt% normal paraffins, but a higher
fraction of isomerized or biodegraded alkanes, which can still solidify into amorphous solids
and cause gelling. Crudes containing more than 5% wax (normal paraffins) may be expected
to have gelling issues.
A correlation between wax content and pour point temperature was presented by Baha
et al. (2018).
Case studies
The following is a MMS record that describes how a wax buildup can contribute to a process safety event.
Fire No. 87
Date: 15-Nov-2000 Operator: _____
Area: South Pelto Operation: Production
Remarks: Two operators noticed liquid falling from the still column on the glycol reboiler
and began to shut in the glycol reboiler when they noticed a small fire coming from the
flange on the glycol reboiler stack. The fire was extinguished immediately using a 30-lb fire
extinguisher and a firehose. There were no injuries or pollution. The investigation findings
showed that because of the well's paraffin content, the glycol contactor was contaminated
with condensate and paraffin from the high-pressure separator due to foaming. The paraffin
plugged the ceramic saddles in the still column of the reboiler causing the condensate in the
still column not to drain back into the reboiler. This caused condensate to escape through the
top of the still column onto the stack. The hot flange ignited the condensate.
Reservoir souring
Introduction
Reservoir souring introduces hydrogen sulfide into the produced fluid stream, which affects the corrosion potential of the production system materials and may alter the equilibrium
of some flow assurance solids such as gas hydrates.
Reservoir souring
177
Both sulfate-reducing bacteria (SRB) and nitrate-reducing bacteria (NRB) may already be
present in the reservoir. Bacterial activity may be subdued due to high reservoir temperature.
Bacteria become more active in the temperature range between 10 °C and 70 °C. As water is
injected into the reservoir, it usually lowers the temperature. Fresh water is seldom available
offshore, so seawater may be injected. Seawater carries dissolved sulfate ions SO42− with it
into the reservoir. Seawater usually contains 0.26 wt% of sulfate. Along with lowering the
temperature to a more comfortable range, seawater also brings food for the sulfate-reducing
bacteria.
SRB bacteria become more active and release H2S which over several years migrates with
the reservoir fluid to the producer wells and causes increased H2S concentration in the produced fluids.
Mitigation of reservoir souring
Usually generation of H2S by SRB bacteria is prevented or reduced by reduction of their
activity. This is accomplished by either addition of calcium nitrate to the injection water in 70–
80 mg/L dosage in order to activate the NRB and thus suppress the activity of SRB. Another
method is the removal of sulfate ions in topsides desulphation plant. Desulphated seawater
is injected into the reservoir without activating the bacteria.
Batch deployment of biocides such as THPS at 300–500 ppm is used. Acrolein is very rarely
used.
An alternative method may be to suppress the bacterial activity by allowing the injected
seawater to warm up to reservoir conditions. Injected seawater is usually cold as it flows
through water injection pipeline exposed to ambient seabed temperature, which is commonly
around 4 °C. Water gains some heat while flowing down the injection well from heat exchange
with rock. If well were drilled deeper than the perforation depth, and injected water flowed
down the tubing to the bottomhole and up through annulus to the injection perforations, it
would gain more heat from the rock. However, such method may be expensive to implement
due to the offshore well drilling cost.
Treatment of sour production
Wells which are already producing H2S are commonly treated with H2S scavenger chemicals. Usually triazine is used at 20–40% active component dissolved in toluene or similar
solvent as H2S scavenger.
Usually H2S is dealt with in one of the following methods: corrosion inhibitor is injected
to protect production systems made of carbon steel; use of corrosion-resistant alloy (CRA) for
the production system construction; injection of H2S scavenger chemical; amine scrubbing.
The first three methods are applicable between reservoir and separator. Amine scrubbing can
only be done in a surface or topsides process equipment.
The capital cost of H2S scavenger chemicals is usually low, with low space requirement.
However, the operating cost is high and can reach $10/pound of sulfur. The economic limit
for H2S scavenger deployment is usually $3000–4000/day. Chemical demand may be as high
as 20 pounds of H2S scavenger to remove 1 pound of H2S.
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5. Flow restrictions and blockages in operations
Modeling of reservoir souring
Souring is modeled by commercial models which account for fluid inflow such as from a
water injection well, and temperature distribution in the reservoir between the injector and
producer wells.
Scale
Solid scale deposits form when ions dissolved in water reach a saturation concentration,
and are no longer soluble in water. Due to a great variety of ions, and their ability to combine
as ionic compounds, there are several scales which can be encountered in petroleum production systems. Commonly encountered scales are calcium carbonate, calcium sulfate, barium
sulfate and halite.
Description
Scale is composed primarily of insoluble barium, calcium, and strontium compounds that
precipitate from the produced water due to changes in temperature and pressure. Radium is
chemically similar to these elements and, as a result, it is possible that radium can form part of
the scales. The API PUBL 7103 Management and disposal alternatives for naturally occurring
radioactive material (NORM) wastes in oil production and gas plant equipment found that
the highest concentrations of radioactivity are in the scale in wellhead piping and in production piping near the wellhead.
Carbonate
Carbonate is among the more commonly occurring scales, and the ones easiest to treat.
Solubility of calcium carbonate scale decreases with temperature, so more calcium carbonate deposits at high temperature. High temperature conditions may exist downhole and at
electrical submersible pumps running dry or hot.
Downhole pressure changes may cause evolution of CO2 from produced water, which alters the content of HCO3– ion, which in turn leads to the formation of CaCO3 or calcite scale.
Scaling index (tendency to precipitate scale) for calcite is lower at high pressure and higher
at low pressure.
Calcite scale from formation water can form and deposit in wells and in production flowlines. When seawater is injected, calcite can also deposit in reservoir causing formation damage because seawater has very low HCO3 (bicarbonate) content. If seawater is injected in a
carbonate reservoir with high CO2 content, its acidity will increase as sour CO2 dissolves in
seawater. Acidic seawater will dissolve carbonate rock and gain Ca2+ and HCO3– ions. As reservoir fluid approaches producer well, its pressure drops which causes calcite precipitation in
the near-wellbore area and formation damage (Braden and McLelland, 1993; Lu et al., 1997).
Sulfate
Calcium sulfate or gypsum is another scale which can form in wells and flowlines.
Scale
179
Solubility of sulfate scale in water increases with temperature, so more calcium sulfate deposits at lower temperatures. However, the brine instability or scaling index of sulfate scale
may increase with temperature.
Barium sulfate or barite can form downhole in reservoir, wells, in flowlines and in topsides
process equipment. Solubility of barite scale usually increases with temperature, so more barite can deposit at a lower temperature.
Barite forms when ions from formation water and from injected seawater combine. Barite
scaling index is usually the highest in the 40–70% seawater range.
Sulfate scale deposition can be very rapid. In one example offshore North Sea, production
system got completely blocked in 1 day after the seawater breakthrough, without scale mitigation (Kelland, 2014).
Analysis
Scale laboratory tests generally fall in one of the two categories: static bottle test and dynamic tube plugging test.
The static test is used to determine the effectiveness of scale inhibitors with limited laboratory equipment. Brines used in the test can represent formation water if carbonate deposits
are studied or a blend of formation water and seawater if sulfate deposits are studied.
The brines are made up of a cationic solution and anionic solution. Chemical inhibitor is
usually added to the anionic solution. The brines are maintained at a fixed temperature and
atmospheric pressure to simulate the production system thermal condition. After a set time
such as 12–16 h, samples are collected from each test bottle liquid phase to find the desired
cations' concentration using titration, inductively coupled plasma atomic emission spectroscopy (ICP-AES) or atomic absorption spectroscopy (AAS). Absence of ions indicates that they
have precipitated as scale. Relative ability of chemicals to retain ions in solution is proportional to chemical effectiveness for a given brine at a given temperature.
The dynamic tube plugging test uses a blend of saturated brines injected into a tube maintained at a set pressure and temperature. The dynamic test can be used to measure the effectiveness of chemical inhibitors in prevention of precipitation, adhesion and accumulation
of deposits inside steel tubes in flowing conditions. The required solutions are prepared by
dissolving salts in distilled water, same as before a static test. Two complex solutions are prepared in order to keep deposit forming cations (solution 1) separate from the deposit forming
anions (solution 2), so that to get the desired brine when the two are blended. It is desirable
that both solutions would be charge-balanced and have the same ionic concentration. This is
accomplished by the adjustment of NaCl content in the solutions.
Special considerations are made when preparing solutions for sulfate deposits such as the
sequence in which salts are dissolved in each solution.
A pump is used to flow the blend of two solutions through the tube, and pressure differential is monitored to compare the effectiveness of chemicals relative to a brine without
chemical additives.
Prediction
Scale precipitation prediction is based on the analysis of combined solubility of all ions
soluble in water. Several commercial models are available for scale stability prediction.
180
5. Flow restrictions and blockages in operations
Free government-developed models for ion solubility in water at reservoir conditions are
also available for use.
Scale becomes an issue when water or another solvent can no longer dissolve the ions
when conditions such as temperature, pressure or composition change.
There are two common metrics of brine supersaturation: Saturation ratio (SR) and
Saturation index (SI).
Saturation of salts dissolved in water may be expressed as a saturation ratio which is determined by the activity coefficients of ions and the solubility product of scale.
SR = ( acation aanion ) / K solubility product
Thermodynamically scale precipitation is possible when SR > 1 but it takes time for ions to
find each other and combine which is represented as kinetics of the process.
For calcium carbonate scale the SR > 1.2 causes scale deposition when water temperature
Twater > 100 °C. Under pressure water boils at >100 °C but loses some of its ability to dissolve
carbonate ions and ions diffuse in hot water more rapidly. At lower temperature the saturation ratio SR must reach 2–3 for calcite scale to appear.
For barium sulphate scale to become an operational issue, both the saturation ratio must
be >3 and the scale precipitation amount must be >50 mg/L (Graham et al., 2005; Simpson
et al., 2005).
Brine instability is also reported as Saturation Index (SI).
SI = log 10 ( acation aanion / K solubility product )
When SI > 0 or SR > 1 then aqueous brine is saturated with ions. Various scales precipitate
at different SI. For example, calcite precipitation is expected when SI > 1, barite when SI > 0.5.
Location of scale deposition usually coincides with the location of precipitation.
Rate of scale deposition is usually measured in a laboratory.
An approximate correlation may be made between the rate of calcite scale deposition and
the saturation index based on results presented by Setta et al. (2012).
Calcite Scaledeposition rate ( inches / yr ) = 3.3 × ( Saturation Index − 0.9 )
This correlation is only applicable to calcite because barite uses a different threshold for its
saturation index.
Remedial actions
Scale remediation methods depend on its composition. Halite scale is water-soluble. Halite
scale blockage formed in a North Sea pipeline downstream of a methanol injection port was
cleared by water circulation.
Carbonate scales are soluble in acids. Mild acids such as citric or acetic as well as strong
acids as hydrochloric can be used to dissolve carbonate scale.
Calcium sulfate (gypsum) is also soluble in acids such as hydrochloric or sulfuric.
Interaction of flow assurance issues with and effects on produced fluids and flow
181
Solubility of scales in acids usually increases with temperature. Laboratory verification
of scale type and selection of the best solvent is required for efficient remediation of formed
scale deposits.
Barium sulfate scale is insoluble in water or acid and has to be removed by chelant chemical treatment, or by mechanical milling.
Scale may be controlled by optimization of operating pressure or temperature to reduce or
prevent scale precipitation, or by injection of chemical inhibitors.
Scale inhibitors are usually deployed downhole in the deepest chemical injection location.
Inhibitors may be deployed as periodic batch treatments via annulus, as continuous treatment via chemical injection tubing, as periodic treatment by squeeze into reservoir rock, and
as periodic treatment with solid soluble material placed in well sump.
Scale prevention
Scale management aims to mitigate the risk of scale restriction by physical or chemical
means. Physical means include avoiding comingling of incompatible fluids from multiple
zones.
Scale potential should be evaluated based on laboratory measurements of water samples
collected under pressure and properly preserved upon depressurization. In absence of water
samples from exploration/appraisal wells, one may utilize high pressure water chemistry
from analog fields.
Technologies which could be considered for management of scale in produced fluids
include:
•
•
•
•
Scale inhibitor chemical on topsides, at tree, or downhole
pressure maintenance to reduce carbonate evolution
desulphation of injection water
preventing comingling of incompatible fluids.
Note that scale inhibitor chemical deployment downhole may be accomplished continuously by injection via capillary tube, periodically by squeeze into the formation, periodically
by soluble pellets in sump, or initially by proppant pellets impregnated with chemical.
Some examples of scale inhibitor chemicals include phosphonate, polyacrylic acid, polyvinylsulphonic acid or phosphinopolycarboxylic acid.
Following remediation technologies could also be considered as a back-up.
• acid or water solvent wash, depending on scale type
• coiled tubing to mill out the deposit, especially for a wellbore or a riser for insoluble
scales
Interaction of flow assurance issues with and effects on produced
fluids and flow
The issue of interaction of flow assurance issues is an interesting one, and was brought into
a separate section rather than listing the likely interactions individually for each issue.
182
5. Flow restrictions and blockages in operations
The complexity of interactions is potentially as intricate as a game of chess. In chess, there
are 32 pieces which may interact at certain conditions. The objective of a game of chess is to
foresee these interactions. In flow assurance, the phases and processes are as numerous:
Water phase/ice.
Gas phase.
Hydrocarbon phases and batch flow.
Hydraulic performance.
Thermal performance.
Emulsions.
Foam.
Subsea or topsides separation.
Water treatment.
Water or gas injection performance.
Hydrate.
Wax and gels.
Scale.
Sand.
Sulfur deposition.
Naphthenate.
Asphaltene.
Heavy oil.
Viscous oil.
Bacterial growth in process systems/reservoir souring.
Corrosion.
H2S CO2 sour gases.
Mercury & organomercury, arsenic selenium/heavy metals.
Blockage monitoring/flow monitoring & optimization.
Blockage remediation.
Subsea and riser considerations.
Field layout/wellbore trajectory optimization.
Commingled production from various producing zones.
Cross-flow between wellbores through manifold.
Fracture gradient of injection wells and rock consolidation.
Materials erosion properties.
It does not mean that an engineer skilled in flow assurance will be good at playing chess.
Nonetheless, the complexity of possible interactions and their consequences is not too dissimilar. Fortunately, most fields in development do not possess all of the above issues at the
same time. However, some assets like in Paleogene possess many. We will try to outline some
of the possible interactions.
Hydrate
Gas hydrates interaction may come from one or more of the following effects:
‐ Hydrates create a flow restriction; it may alter pressure and temperature distribution in a
flowing system leading to changes in stability of other flow assurance phases.
Seven suggestions from operations in deepwater and onshore
183
‐ Mechanical movement; hydrate plugs have been known to move and scrape wax
deposit from a pipe wall into a solid wax blockage, which could not be removed by
depressurization.
‐ Mechanical expansion; hydrate expands more than ice relative to liquid water upon
freezing; hydrate formed downhole has been known to crush well tubing. Mechanical
expansion also affects rock consolidation in natural environments as hydrate formation
and dissociation over geologic times affected sediment strength.
‐ Hydrate formation introduces solid particles, which may lead to increased
erosion-corrosion.
‐ Hydrates are water-based compounds and remove water from produced stream;
removal of water may cause other water-dissolved materials to precipitate; It was
confirmed experimentally (Hu et al., 2018) that solid halite scale does precipitate out of
water solution after hydrate formation consumes some water. It is also hypothesized
that chemical inhibitors formulated in water may precipitate out of solution as water
molecules are removed into hydrate.
‐ Hydrates consume light hydrocarbons and sour gases. Change in the amount of
dissolved methane may affect asphaltene stability; change in CO2 content may affect
carbonate scale stability; change in H2S content may affect corrosion.
‐ If dissociated in Arctic or other sub-zero environments by depressurization, hydrate will
convert to an ice plug and remain as ice until the warm season; in Arctic subsea with
−2 °C seawater temperature time to a warm season may take a while.
Seven suggestions from operations in deepwater and onshore
FA is prediction and management of physical and chemical behavior of produced fluids to
ensure uninterrupted operation. The following are suggested as seven rules of a successful
flow assurance engineer (both multiphase and production chemistry).
1. Keep track of your fluids.
Double check what's being injected and whether it's compatible with the fluids and materials in place. Chemical tanks may get re-badged or de-badged en-route or at the blending
plant.
2. No inhibitor gives 100%.
Even after passing lab tests for one set of fluids, inhibitors may underperform in changed
fluids.
3. Displace while you still can.
Use a proven method to safe-out systems from hydrate even if another issue (scale etc.) is
suspect.
4. All models approximate.
A recent comparison across commercial and in-house software packages brought up dissimilarities and gaps in inhibition prediction for brines+MEG.
5. Unplug from downstream.
In a short system (a jumper) a solid month-old hydrate blockage was unplugged after
methanol was injected in reverse to the original flow.
184
5. Flow restrictions and blockages in operations
6. Establish and update safe limits in labs.
Use available labs to periodically verify performance for adequate treatment because fluids change. A pre-deployment lab test of acidic scale dissolver gave optimal contact time.
7. When in doubt read the procedure and err on the side of safety.
Cost of lost production and involving additional resources trying to remediate a previouslyformed blockage can outweigh the benefit from operating beyond established safe limits.
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189
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2003, Puerto Vallarta, Mexico.
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natural gas to form solid gas hydrate deposits in earth crust at certain thermodynamic conditions (temperature up
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Sloan, E.D., 1998. Clathrate Hydrates of Natural Gases. Marcel Dekker, New York.
Thomas, D.G., 1962. Transport characteristics of suspensions. Part VI. Minimum transport velocity for large particle
size suspensions in round horizontal pipes. AIChE J. 8 (3), 373–378.
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Resour. Technol. 127 (4).
Annual Statistical Review of World Energy, BP, 2018.
API PUBL 7103. Management and disposal alternatives for naturally occurring radioactive material (NORM) wastes
in oil production and gas plant equipment.
C H A P T E R
6
Production chemistry and fluid quality
O U T L I N E
Sampling fluids
Quality: 4Cs of production
chemicals
Laboratory verification of chemical
performance
Pass/fail criteria for hydrate, wax,
asphaltene, scale, corrosion
chemicals
Lab equipment requirements
Test procedures
Chemical injection systems
191
Emulsions, foam, topsides separation,
water treatment management
195
192
Naphthenate management
Properties of naphthenates
197
197
193
Heavy oil management
198
Viscous oil management
198
Mercury management
199
Sulfur deposition
199
DRA
199
Chemical characteristics
200
193
193
193
194
Comparative economics of production
chemicals
194
Chemical tubing blockage
200
Product fluid quality
Hydrocarbon oil
Hydrocarbon gas
Produced water
194
195
195
195
Dosage selection and optimization
200
Chemical data
200
References
203
Sampling fluids
All containers should be clean from contamination.
Containers for live hydrocarbons should be sufficient in size to allow to perform the required flow assurance and production chemistry tests. The sampling program should be
coordinated with the flow assurance and production chemistry specialists to determine the
required amount of samples.
Handbook of Multiphase Flow Assurance
https://doi.org/10.1016/B978-0-12-813062-9.00006-3
191
© 2019 Elsevier Inc. All rights reserved.
192
6. Production chemistry and fluid quality
Water should be sampled without leaving un-filled space for air on top of the sampling
bottle. Water should be filled to overflow the bottle and the cap placed on it quickly to limit
exposure to air.
The water sample should be buffered as early as possible to preserve the dissolved ions.
H2S or mercury can adsorb to steel container walls. This adsorption would reduce the
quantity of either component in the sample and may give an erroneous measurement indicating that there is no presence of these compounds in the sample.
Sampling containers where H2S or mercury are expected to be present due to regional or
geologic analogs should have special inside liner coating which would prevent adsorption of
either H2S or Hg to the container steel wall.
Sampling method recommendations for petroleum fluids are summarized in the API recommended practice 44 (API, 2003).
Quality: 4Cs of production chemicals
The production chemicals quality may be described with the following characteristics:
• Compatibility
Chemicals should be compatible with each other without a significant loss of
effectiveness, and with the production system materials such as valve elastomeric seals
without degrading or dissolving them.
• Consistency (stability)
Chemical should remain of the same consistency and fluidity over the range of
temperatures and pressures in the production system.
Chemicals should retain their consistency for at least 6 months because chemical injection
may not occur for and extended time while chemical may remain in the injection tubing
at elevated pressure and temperature such as downhole before being injected into the
produced fluid.
Consistency should also remain at reduced pressure such as vacuum. Chemicals are
usually formulated in solvents such as toluene, glycol or methanol. Carrier solvents
may be heavier than the live produced fluid. Hydrostatic pressure of the chemical may
be higher than of the produced fluid at the injection point. In some cases in deepwater
the heavier chemical may fall down the riser portion of the injection tubing and create
vacuum condition. In vacuum, the solvent would flash off or evaporate and leave the
heavier active components which may lead to plugging the chemical tubing.
• Cleanliness
Chemical should be clean and filtered because the presence of even minute quantities of
solids could plug off the chemical injection valve or port.
• Concentration
Chemicals should be effective in fairly low concentrations to remain economic and not
affect the separation process significantly.
Typical dosages of chemicals were shown in Chapter 1. Chemicals are usually injected
in 50–500 ppm concentration (0.005–0.05 wt%). Hydrate control chemicals are used in
much higher concentrations ranging from 10,000 to 400,000 ppm (1 to 40 wt%). Chemical
Laboratory verification of chemical performance
193
injection at higher dosage may become uneconomic. The operating expenditure for the
use of production chemistry may add between $0.1 and $2/bbl lifting cost, depending on
the scope and severity of flow assurance and production chemistry issues.
Laboratory verification of chemical performance
Pass/fail criteria for hydrate, wax, asphaltene, scale, corrosion chemicals
Laboratories are used to ensure the chemical performance alone and in a blend with other
chemicals which are planned for injection in a given well or flowline. The criteria for chemical
performance are subjective for each company and laboratory and there is no standard metric
for these. Joint industry projects developed such criteria but their adoption remains gradual.
Some of the chemical performance criteria are suggested below.
Hydrate thermodynamic inhibitor has to completely prevent formation of hydrate solids.
Hydrate kinetic inhibitor has to completely prevent formation of hydrate for at least the
time of residence of fluids in production system at the highest pressure in the system.
Hydrate antiagglomerant chemical has to prevent agglomeration of hydrate and its adhesion to an optical window in a pressurized rocking cell, stirred vessel, flow loop or in a
rotated wheel.
Wax inhibitor has to reduce the mass of wax deposition by at least 50% at the temperature
differential between wax appearance temperature and ambient temperature in the planned
production system at atmospheric pressure in a cold finger, shear cell or flow loop test or at
high pressure (rare shear cell apparatus).
Asphaltene inhibitor has to prevent or reduce the amount of precipitated solids.
Asphaltene dispersant has to prevent adhesion of flocculated asphaltenes on the test cell
walls.
Scale inhibitor has to prevent precipitation of solids by retaining the scale-forming cations
in test solution in a static bottle test as indicated by their residual concentration.
Scale inhibitor has to prevent or reduce deposition of solids in test tubing in a dynamic
loop test as indicated by pressure drop across the loop.
Corrosion inhibitor has to reduce the rate of metal loss so that penetration rate is below 1
mil (0.001 in.) per year. In some cases rates as high as 4 mpy are considered acceptable, depending on the design life of the system.
Lab equipment requirements
Lab equipment should be able to reproduce as closely as possible the pressure and temperature in the production system, and not allow any leaks of test fluids or ambient fluids
across the test apparatus boundary. In some cases it is impractical to use pressurized equipment, then atmospheric pressure is used as in emulsion or some scale or wax tests.
Test procedures
Test procedures for corrosion are documented by NACE.
194
6. Production chemistry and fluid quality
Test procedures for some of the scale tests are also available from NACE, but in many cases
are developed or updated by companies or laboratories individually.
Test procedures for the majority of other flow assurance issues are developed by companies or laboratories individually.
Some test standards as ASTM D97 for waxy oil pour point are adopted or modified.
Both laboratories and test equipment vendors may recommend the test procedures. Every
test procedure should be reviewed by operator company specialists to ensure that it adequately reflects the operating conditions expected in the planned production system.
Chemical injection systems
Chemicals are usually deployed through chemical trunkline with branch lines equipped
with metering valve systems. Chemicals may also be deployed with point-to-point chemical
lines for systems which require high reliability of chemical delivery.
Chemicals may be delivered into the lower wellbore with downhole chemical injection,
into the upper wellbore with injection above SCSSV or from tree, into the tree, into the jumper
with injection from tree or a dedicated line, into the flowline or riser with a dedicated line,
and topsides.
Chemicals may also be deployed into the reservoir with injection water through a water
injection pipeline, into the reservoir with squeeze treatment through a service flowline.
Processing equipment may be located on surface (onshore or topsides offshore), subsea
(separation, boosting, pumping) or subsurface (downhole separation or homogenizing, or
subsea caisson separation). Chemicals may need to be injected into processing equipment by
the point-to-point method.
Comparative economics of production chemicals
Typical dosages of chemicals in the 50–500 ppm range were shown in Chapter 1. In most
cases the initial production starts at elevated chemical dosage to ensure the reliable startup
of production.
Subsequent periodic reviews of chemical effectiveness and economics may be done
to check whether the injected dosage for each chemical is sufficient, too high or too low.
This should be done in concert for all chemicals injected at a facility because many chemicals may affect each other's performance. So, an increase of corrosion inhibitor dosage may lead to reduced performance of demulsifier, low dosage hydrate inhibitor and
some other chemicals. This may lead to loss in separated water quality and incidents of
noncompliance.
Product fluid quality
The product of petroleum production includes hydrocarbon oil, hydrocarbon gas and produced water.
Emulsions, foam, topsides separation, water treatment management
195
Hydrocarbon oil
Water content specification applies to sales oil. In the USA the crude oil should have a
water content under 5000 ppm or 0.5 wt%. Some contracts vary and the water content may be
lower at 2000 ppm or higher at 10,000 ppm or 1 wt%.
Methanol is soluble up to 1% in crude oil. Methanol content in USA oil is regulated by
contract with the receiving refinery. Some refineries cannot process oil with high methanol
content.
In Russia separation processes may vary, and oil may contain up to 1% water. The maximum salt content of product oil is set to 300 mg/L and is rated into three categories by a state
standard. Methanol content in oil is not regulated.
Hydrocarbon gas
Gas is expected to have water content below 6–7 pounds per MMScf.
Produced water
Water discharge requirements include hydrocarbon content and toxicity.
In the US Gulf of Mexico the allowed oil and grease hydrocarbon content limit in produced water averaged over 30 consecutive days is 29 mg/L. The temporary excursion limit
is 42 mg/L which allows for slightly-off-spec water discharge. This temporary excursion is
allowed only during any 24-h period. Once the limit is exceeded and the regulatory agency
notices that, usually in a form of a sheen, usually silvery in color and well seen from aerial
vehicle such as a helicopter.
The difficulty in obtaining the discharge water specification is that it includes both
­water-insoluble and water-soluble organics. While the former may be separated by regular
means as free water knockout, flotation cell and electrostatic treater, the latter may not because organics are dissolved in water. This requires the injection of water clarifier chemicals.
The water may also contain hydrocarbons in form of a reverse emulsions. In a reverse emulsion a droplet of water is covered by a shell of hydrocarbon material, which is suspended
in bulk water. Reverse demulsifier chemicals (also called water polishers) also help remove
hydrocarbons from water. Reverse emulsions and water soluble organics usually manifest
themselves in form of a greyish color sheen on water near the discharge point.
Toxicity test is performed with shrimp in the water sample and survival rate is monitored
over several hours.
Emulsions, foam, topsides separation, water treatment management
Emulsions and foams both increase resistance to flow and should be avoided in wells and
flowlines.
Separation management is complementary to the topsides process design in controlling
emulsion or foam formation by physical or chemical means. Physical means include avoiding
flow shear or incompatible fluids comingling.
196
6. Production chemistry and fluid quality
Produced water should be discharged overboard, if regional regulations permit. No commingling of produced water with seawater should be allowed on a regular basis because of
compatibility issues and potential for scale deposition.
Topsides process design should include:
• Chemical injection points to deliver required chemicals
• Sampling points to monitor chemical performance and fluid characteristics.
Technologies which could be considered in formulating fluid handling concept of flow
assurance include the following:
•
•
•
•
•
•
•
•
•
•
Emulsion breaker chemical
Defoamer chemical
Oxygen scavenger chemical
Reverse demulsifier water clarifier chemical
Hydrocyclone equipment to separate water
Vacuum de-aeration equipment
Filtration equipment for produced water reinjection
Desulphation membranes equipment for pressure maintenance water injection
Separator equipment
Flotation cell equipment
Note that topsides process technologies should be verified by trials as mutually compatible, for example triazine injected for scavenging H2S from gas may result in scale deposition,
corrosion inhibitor can adversely affect emulsion separation, etc.
Emulsion breaker and reverse demulsifier chemicals are perhaps the most important
chemical category after the corrosion inhibitor because they ensure quality of the product
stream. When separation is inefficient, it may leave hydrocarbons, both regular organics and
water-soluble organics in water. Disposal of produced water stream with off-specification
residual components in it may lead to either plugging of the produced water reinjection wells
or to sheen on seawater if water is discharged overboard.
In USA, the BOEM regularly monitors the performance of production facilities separation
and issues warnings of non-compliance if they observe it or shut-in the facility. The data on
the incidents of non-compliance (INC) are publicly available and may serve as the lagging
indicator of which operator needs help with their production chemistry operation. Periodic
reviews of chemical effectiveness discussed above may serve as the leading indicator of production chemistry performance. The up to date reports of INC for USA operators (BOEM,
2019) are in www.data.boem.gov/Company/INCs/Default.aspx.
The number of both warnings and shut-ins shown in Figs. 6.1 and 6.2 have both been on
a decreasing trend in the past. It may be a coincidence that there is a peak in non-­compliance
with water quality specification, which is 29 ppm hydrocarbons in discharged water or
42 ppm momentary excursions, for a 30 day average and daily maximum, respectively, in the
year when petroleum commodity price was low.
The method required to monitor hydrocarbon compounds in produced water is the Federal
EPA Method 1664 (2010). This regulatory compliance method is a weight-based method which
relies on solvent extraction of oil and grease hydrocarbons with hexane followed by solvent
evaporation and weight analysis of the residue.
197
Naphthenate management
BOEM INC warnings per facility
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
2011
2012
2013
2014
2015
2016
2017
2016
2017
FIG. 6.1 BOEM warnings per facility between 2012 and 2016.
BOEM INC component shut-in per facility
2.00
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
2011
2012
2013
2014
2015
FIG. 6.2 BOEM component shut-ins per facility between 2012 and 2016.
Naphthenate management
Calcium naphthenate is one of the concerns in production chemistry which may plug production systems and process equipment. Naphthenate precipitates when naphthenic acid reacts with metal ions such as calcium or sodium.
Properties of naphthenates
Naphthenate density ranges between water and oil densities. Naphthenates may collect at
oil-water interface and behave as surfactants by stabilizing emulsions.
198
6. Production chemistry and fluid quality
Calcium naphthenate is a calcium soap of naphthenic acids in crude oil, and appears as a
light brown gel.
Sodium naphthenate looks like white gel or clear dark brown liquid. Sodium naphthenate
behaves as an emulsifier and as a mild detergent.
Naphthenic acids molecular weight ranges from 120 to over 700 g/mol. Naphthenic acids
may be present in immature heavy oils. Paraffinic crudes usually have low acid content.
Naphthenate potential can be evaluated with laboratory measurements of oil and water
samples collected under pressure and properly preserved as needed upon depressurization.
ARN-acid is the naphthenate of concern for the calcium naphthenate issue.
The naphthenate potential is analyzed based on the total acid number (TAN), the CO2 content in the reservoir oil and bicarbonate ion HCO3− in reservoir brine. Total acid number can
be determined by thermometric titration.
Naphthenate restriction may be controlled by chemical or physical means. Physical means include avoiding incompatible fluids commingling, if it is practical to have segregation with a sliding sleeve completion or having separate wells and flowlines for different incompatible reservoirs.
Technologies which could be considered for management of naphthenates in produced
fluids include:
•
•
•
•
Naphthenate inhibitor chemical
Preventing exposure of oil to calcium-rich water
Acetic acid chemical
Selection of a different emulsion breaker chemical to remedy separation threats
Heavy oil management
Heavy oil increases the backpressure on reservoir which reduces production by high
density.
Technologies which could be considered for management of heavy oil in produced fluids
include:
• Artificial lift
• Preliminary water knock-out or subsea water separation
• Multiphase pumping.
Viscous oil management
Viscous oils increase the backpressure on reservoir which reduces production by high viscosity. In some countries the oil is considered to be viscous when its viscosity at reservoir
conditions exceeds 200 cP.
Technologies which could be considered for management of viscous oil in produced fluids
include:
• Multiphase pumping
• Drag reducing agent chemical
DRA
199
• Active heating
• Emulsion breaker chemical to reduce emulsion viscosity
• Emulsifier chemical to form water-external emulsion.
Mercury management
Mercury content in produced fluids affects the environment and personal health through
discharge streams such as de-oiled filtered produced water. Mercury also can accelerate corrosion of metals such as aluminum and cause integrity issues in process equipment components made of aluminum.
Mercury in produced fluids is usually associated with production in North Sea and regions
near continental rim such as Northern Australia or Indonesia.
Mercury management aims to reduce the mercury impact on health, safety and environment and material integrity.
Technologies which could be considered for management of mercury in produced fluids
include:
• Mercury removal from gas unit including recommended location and technology
• Mercury monitoring system including sample locations and appropriate
equipment
Materials in production systems containing mercury should avoid aluminum, brass, nickel
alloys as suitable for the expected mercury level.
Sulfur deposition
Sulfur may be carried from reservoir in gas phase. As pressure and temperature in wellbore change, sulfur may deposit in well tubing.
Sulfur deposition depends on both temperature and pressure.
Elemental sulfur solubility in gas decreases very roughly tenfold for every 25 °C or for
every 100 bar.
DRA
Drag reducing agents are long polymeric chains which help reduce turbulence at the pipe
wall by affecting turbulent eddy size and reducing fluid drag on pipe wall.
Being long chains, the DRA chemicals suffer from shear degradation when long molecules get sheared and broken by the flow. The location of DRA chemical injection should be
downstream of any equipment which causes high shear such as valves, chokes, etc. to avoid
chemical degradation.
Typical dosage of DRA chemicals is described in Chapter 1.
200
6. Production chemistry and fluid quality
Chemical characteristics
Chemicals may be formulated in carrier solvents such as methanol, toluene, glycol or water. Concentration of active components usually varies from 10% to 40%. Bulk properties of
chemicals such as density, viscosity, vapor pressure and resistance to flashing off of solvent
mainly depend on the properties of the carrier solvent.
Some characteristics of chemicals are available in literature, which may be used for a preliminary hydraulic design of the chemical injection system.
A more robust process is to get the chemical characteristics including density, viscosity
and vapor pressure as function of both temperature and pressure from the potential chemical
suppliers at an early stage of project design, after the scope of potential flow assurance issues
is understood based on appraisal well samples or regional analogs.
Chemical tubing blockage
Vapor pressure of a chemical is an important characteristic because vacuum can occur at
top of chemical injection lines causing flashing off of solvent and deposition of active ingredient in the chemical tubing, leading to its plugging. Plugged chemical tubing may be remediated with solvent circulation if there is flow communication through the blockage, or using a
pressure pulsation blockage removal method.
Chemical tubing may also be blocked with flow assurance solids such as hydrates when
pressure in the chemical tubing is less than in the production system. Such difference
in pressures may occur when production is shut in, and chemical is less dense than the
produced fluids. Untreated or undertreated produced fluid may migrate across the check
valve(s) as all valves have some leakage, and form a blockage in the chemical tubing. An
example of a hydrate blockage inside methanol tubing was discussed earlier in Chapter 1.
Dosage selection and optimization
Dosage selection is performed with account to potential loss of chemical effectiveness
when other chemicals are injected, and to project economics. Chemicals performance is tested
at several concentrations both without and with other chemicals, and the lowest concentration which is sufficiently effective is selected.
Chemical data
• Density of MEG is shown in Fig. 6.3
• Viscosity of MEG is shown in Fig. 6.4
Table 6.1 shows estimated properties of production chemicals at atmospheric pressure and room
temperature. Note that viscosity and density will increase at higher pressure and lower temperature;
data should be obtained from chemical vendors.
Chemical data
FIG. 6.3 MEG specific gravity (relative to water density at 60 °F) (updated from Union Carbide, 1978)
201
202
6. Production chemistry and fluid quality
FIG. 6.4 MEG viscosity (updated from Union Carbide, 1978).
203
References
TABLE 6.1 Chemical properties
Chemical
Viscosity, cP
Density, kg/m3
Asphaltene inhibitor or dispersant
35
910
Corrosion inhibitor
100
960
Defoamer
10
950
Emulsion breaker
100
930
Glycol (MEG)
35
1110
H2S scavenger (triazine)
20
1120
LDHI chemical (AA)
15
800
Methanol
1
790
Naphthenate dispersant/acetic acid
200
1050
Scale inhibitor
30
1020
Wax inhibitor or pour point
depressant
100
880
References
API, 2003. Sampling petroleum reservoir fluids. In: American Petroleum Institute Recommended Practice 44, second
ed. April.
BOEM, 2019. www.data.boem.gov/Company/INCs/Default.aspx. (Accessed January 1, 2019).
EPA, 2010. Method 1664, Revision B: n-Hexane Extractable Material (HEM; Oil and Grease) and Silica Gel Treated
n-Hexane Extractable Material (SGT-HEM; Non-polar Material) by Extraction and Gravimetry, February. United
States Office of Water Environmental Protection Agency (4303).
Union Carbide, 1978. Glycols.
C H A P T E R
7
Flow assurance deliverability issues
O U T L I N E
Flowline design process
205
Optimization of flowline sizes
206
Artificial lifting
206
Topsides equipment and arrival
pressures
207
Cold flow and emulsion
Heavy oil viscosity
Emulsion rheology
207
208
208
References
209
Further reading
209
Flowline design process
Flowline design is in the realm of pipeline engineers, but is done in collaboration with
flow assurance specialists. The flow assurance analysis helps indicate whether the pipe is
sufficiently large or too large for the life of the project and whether flow is likely to be stable
or intermittent. Flow assurance also helps forecast the amount of liquids arriving into the
process equipment at various stages of the project life.
Pipeline sizing considerations are usually based on two boundary conditions: pressure
and velocity.
Pressure in a pipeline should not to exceed the pipe design pressure.
Usually the MAOP is set with a safety margin of between few bar and up to 10% lower
than the design pressure, to allow for pressure surges during transient flow events such as
production startup or shutdown.
Velocity in a pipeline should not exceed the erosional velocity. Maximum velocity is determined based on operator internal design considerations for erosion, fluid corrosivity, or on
recommended guidelines provided by API, DNV or NORSOK. Regional regulatory requirements may prescribe which method to use for the flow velocity considerations.
In some cases, velocity should not drop below a certain minimum threshold to ensure
produced solids such as sand are transported by the flow. Typical minimum liquid v
­ elocity
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205
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206
7. Flow assurance deliverability issues
expected to transport sand in a near-horizontal pipe is 1 m/s. This value may differ at
­various operator companies. In some production systems operating in stratified multiphase flow regime, the chemical inhibitors are injected and are carried in the liquid phase.
Sufficient gas flow velocity is required to entrain liquid droplets and wet the perimeter
of the flowline so that all parts of the production system are treated with the injected
chemicals.
The minimum gas flow velocity consideration is important when top of the line corrosion (TOLC) is expected to be an issue. In multiphase flow with stratified flow regime,
as flowing produced fluid cools down, water may condense from the gas stream and accumulate as droplets on top of the flow line. Freshly condensed water has no inhibitor
chemicals in it. This brings the concerns of corrosion and hydrate formation. Corrosion
risk may be mitigated by maintaining gas velocity above the minimum value. Hydrate risk
may be mitigated by injection of a volatile hydrate inhibitor such as methanol. It should
be noted that methanol may absorb oxygen from air if kept in a storage tank without a gas
blanketing system. Oxygen thus brought into the system with methanol may increase the
rate of corrosion.
Routing of flowlines should avoid significant elevation changes. It may be more profitable
to increase the line length in order to keep the line mostly flat rather than build it straight over
a mountain or through a canyon. Analysis of the relative cost of extending the flowline length
should be performed together with the flowline size and flow rate optimization to find the
relative impact of a hill or canyon crossing on the backpressure and delivery of wells over the
life of field.
Optimization of flowline sizes
Flowline sizes may be optimized to provide target flow rates over the life of field.
Larger diameter pipelines result in lower pressure drop, but also cost more. In multiphase
flow the liquids accumulation as holdup in low and uphill sections of oversized lines also acts
as a hydraulic restriction and increases pressure drop.
Flow assurance can develop a flow performance analysis, correlating both pressure drop
and liquid holdup with the flow rate and flowline size. There is expected to be a flowline size
when pressure drop and holdup are low. This size is optimal for the operation as it would
reduce the back pressure and increase production from wells over the life of field, and reduce
liquid surge into process equipment.
Artificial lifting
Artificial lift design is in the realm of production engineers, but should be done in collaboration with flow assurance specialists (Table 7.1).
When reservoir pressure is or becomes low, there are several methods which allow to add or
to periodically accumulate the energy in order to lift heavier liquids from reservoir to surface.
Some of the artificial lift methods are listed in the table below. Absence of moving parts
should improve equipment reliability.
207
Cold flow and emulsion
TABLE 7.1 Artificial lift methods categorized by energy introduction, application location and presence of
moving parts
Artificial lift method
Add or accumulate energy
to flow
Application
Moving parts
Gas lift
Add
Well
No
Plunger lift
Accumulate
Well
Yes
Velocity string
Accumulate
Well
No
ESP
Add
Well
Yes
Progressive Cavity Pump
Add
Well
Yes
Jet pump
Add
Well or flowline
No
Swabbing
Add
Well
Yes
Multiphase pump
Add
Flowline
Yes
Topsides equipment and arrival pressures
Topside equipment should be rated to the pressures expected at the wellhead.
In cases of high pressure high temperature (HPHT) reservoirs, the shut-in wellhead
pressure may be significantly higher than the flowing wellhead pressure and the process
equipment pressure rating. In such field development designs the high integrity pressure
protection system (HIPPS) with fast-acting valves (can go from fully open to fully closed in
approximately 3 s) may be installed to protect the equipment from pressure. A certain length
of reinforced pipe rated to the maximum wellhead pressure, usually less than 1000 m long
is installed downstream of HIPPS valves. The remainder of the pipe and process equipment
may be rated to a lower pressure to reduce capital cost.
Flow assurance can develop a fast transient flow performance analysis to estimate the maximum pressure observed downstream of the HIPPS valve while it closes. The fast transient
HIPPS analysis can help ensure that the length of a reinforced pipe is sufficient to contain the
produced fluid pressure during the time while the well stops and the HIPPS system actuates.
Cold flow and emulsion
Cold flow is a technology concept which has been evaluated between 10 and 20 years ago.
The premise of cold flow is to eliminate the use of the highest dosage and costly hydrate control chemicals by routing of the production fluids so as to induce precipitation of solids in a
controlled way that said solids would not plug the production system.
This may be accomplished by recycling some of the production fluids cooled to ambient
temperature back to the vicinity of the wellhead. The cooled produced fluid would already
contain small crystals of gas hydrate and paraffin wax. Injection of the recycle stream at the
wellhead would serve to provide crystal seeds on which wax and hydrate would grow from
the well stream fluid, instead of on the pipe wall. The method had been validated and demonstrated to work in a pilot scale equipment in Tiller, Norway (Argo et al., 2004).
208
7. Flow assurance deliverability issues
Another cold flow design is static mixer. The static mixer design has been validated in
the field (Turner and Talley, 2008) to control the hydrate formation and to keep hydrates dispersed and flowing.
None of the cold flow methods have been implemented for continuous field use due to
novelty and lack of historic performance. Operators are not yet certain whether either cold
flow technique can deliver 100% reliability over the life of field. Cold flow technology may be
useful where the use of chemicals is restricted by local regulation.
Heavy oil viscosity
Heavy oils provide increased resistance to flow not only by being heavy but also by having
higher viscosity.
Over 20 methods are available in literature for estimating oil viscosity. These methods have been
summarized by Bergman and Sutton (2007) who correlated dead oil viscosity with temperature
and density based on 9837 viscosity measurements from 3047 fluids which ranged in API gravity
from 0.45° to 135.9°. The Bergman and Sutton correlation was discussed earlier in Chapter 3.
A recent correlation for estimating the viscosity of heavy oil in mixtures with water has
been presented by Wen et al. (2016). The method proposed by Wen may be used together with
the correlation provided by Bergman and Sutton (2007).
Emulsion rheology
Oil and water emulsion may be more viscous than just oil by a factor of 10 or more. Several
correlations for emulsion viscosity had been developed including Smith & Arnold, Woelflin
Loose, Woelflin Medium and Woelflin Tight.
Emulsions may exhibit peak viscosity around 50–85% water cut. The inversion point from
oil-external to water-external emulsion depends on the character of the crude, the character
of the brine, and the degree of emulsification. The inversion points corresponds to maximum
viscosity (Fig. 7.1).
Emulsion Viscosity
Effective Emulsion Viscosity, cP
100,000
10,000
1000
Smith & Arnold
Woelflin Loose
Woelflin Medium
Woelflin Tight
100
0.0
0.1
0.2
0.3
0.4
Water Cut
FIG. 7.1 Effective emulsion viscosity correlations comparison.
0.5
0.6
0.7
0.8
Further reading
209
References
Argo, C.B., Bolavaram, P., Hjarbo, K.W., Makogon, T.Y., Oza, N., Wolden, M., Lund, A., Larsen, R., 2004. Method and
System for Transporting Flows of Fluid Hydrocarbons Containing Wax, Asphaltenes, and/or Other Precipitating
Solids. (WO2004059178).
Bergman, D.F., Sutton, R.P., 2007. A consistent and accurate dead-oil-viscosity method, SPE110194. In: SPE Annual
Technical Conference and Exhibition (Anaheim, 11–14 November).
Turner, D.J., Talley, L.D., 2008. Hydrate inhibition via cold flow—no chemicals or insulation. In: 6th International
Conference on Gas Hydrates, Vancouver, July 6–10.
Wen, J., Zhang, J., Wei, M., 2016. Effective viscosity prediction of crude oil-water mixtures with high water fraction.
J. Pet. Sci. Eng. 147, 760–770.
Further reading
Bradley, H.B., 1987. Petroleum Engineering Handbook. Society of Petroleum Engineers, Richardson, TX (Chapter 19).
Woelflin, W., 1942. The viscosity of crude-oil emulsions. In: Drill. and Prod. Prac., API, pp. 148–153.
C H A P T E R
8
Flow assurance stability issues
O U T L I N E
Severe slugging
Phenomena description
Prediction methods
Suppression techniques
211
211
212
213
Transient operation
Shut-in and start-up
Rate ramp-up and ramp-down
213
213
214
Slugging in gathering lines
214
Calculation of slug impact force on
Tees and Elbows
214
Calculation of pressure surge on sudden
flow shut-in
215
Vacuum condition in flow
216
References
216
Further reading
216
Severe slugging
Phenomena description
The issue of severe slugging has several impacts on production system. Periodic slugging
causes mechanical integrity issues as slugs of liquid impact on bends of the flow lines. Slug of
a large volume may cause a production facility shutdown if it overfills the separator capacity.
Slug flow also causes periodic increase of backpressure on wells which reduces the overall
production rate and may lead to lower ultimate recovery of hydrocarbons from the reservoir.
A detailed description of severe slugging issues is provided by Hill and Wood (1994). The
authors provide the correlations for slug frequency, average and maximum possible slug
length and discuss the design of slugging systems.
The authors report the “best fit” average slug frequency correlation as:
( Fs D / Vm ) ∗ (1 − 0.05 VSG ) D0.3 = −24.729 + 0.00766 exp
( 9.91209∗ Hle∗ (1 − 0.068 / VSL ) ) + 24.721 exp
( 0.20524∗ Hle∗ (1 − 0.068 / VSL ) )
∗
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212
8. Flow assurance stability issues
Fs = slug frequency per hour; D = pipe diameter, m; Vm = mixture velocity, m/s; VSG =
superficial gas velocity, m/s; Hle = equilibrium stratified liquid holdup; VSL = superficial
liquid velocity, m/s.
Prediction methods
Flow regime map
Flow regime map is plotted in coordinates of superficial liquid velocity vs. superficial gas
velocity, on a log-log scale.
A flow regime map would be expected to have the following form (Fig. 8.1).
Stability limits
Multiple additional works on severe slugging are available in the literature such as
Montgomery (2002). The author indicates that severe slugging causes a 20% drop in production, and results in separator trips/shutdowns. The stability criterion proposed by the
author:
U GL S ≤ U GB S∗ ( 1 − g εLP L P sin θ ( ρL − ρG ) / ( PS + ρL g h R ) )
UGLS = inlet gas velocity.
UGBS = gas velocity entering the riser base, m/s.
g = gravity acceleration, m/s2.
εLP = pipeline liquid holdup, calculated using Taitel (1986) method.
LP = downhill pipe length upstream of the lowest point.
θ = inclination from horizontal at riser base downstream of the riser lowest point.
PS = separator pressure.
ρL = liquid density.
ρG = gas density.
hR = riser height.
FIG. 8.1. Typical multiphase flow regime map.
Transient operation
213
The author indicates the stability criterion is that in order to prevent a bubble penetrating
the riser base, the inlet gas velocity must be lower than some critical gas velocity, which depends on the ratio of the hydrostatic head in the pipeline and riser.
The Boe criterion for the occurrence of severe slugging is commonly used in the industry.
The Boe criterion provides an estimate of the minimum liquid velocity at which pressure
increase due to liquid accumulation in vertical part of the multiphase flow system is higher
than pressure increase due to gas compression in horizontal part of the system.
U L S ≥ PP U G S / ( ρL g ( 1 − εL ) L sin α )
ULS = liquid superficial velocity.
PP = pipe pressure.
UGS = gas superficial velocity.
ρL = liquid density.
g = gravity acceleration.
εL = pipeline or tubing liquid holdup.
L = length of downhill pipe upstream of the lowest point.
α = inclination of pipe upstream of the lowest point.
Boe estimated the holdup based on no-slip condition: ε L = U L S / ( U L S + U G S )
The Boe criterion is a straight line in ULS vs. UGS coordinates. Unstable flow is at values
above the line.
Additional work which provides stability criterion on horizontal-vertical flow systems includes Zakarian (2000). Author developed a stability criterion and validated it with laboratory analysis.
Suppression techniques
Slug mitigation options (Montgomery, 2002) include: gas lift, choke control and separation.
Choke control, separator pressure and gas lift are named as slug mitigation options in
(Sancho, 2015). The author also provides a severe slug classification into four categories.
A novel method for slug suppression by dividing large liquid slugs into smaller parts
which would be more easily accommodated by the separator was proposed (Makogon et al.,
2011) which was discussed in Chapter 4.
Transient operation
Shut-in and start-up
On production shut-in, liquids redistribute according to gravity in the production system. This affects the cooldown of the produced fluids. Water tends to retain more heat. As
water drains to and accumulates in the low spots, this may provide additional time before
hydrates begin to form. However, system insulation is usually designed to provide sufficient
cooldown time in the gas-filled sections of the flowline. Gas has the least heat capacity of the
produced fluids. Sections of flowline filled with gas cool down the fastest. Typical insulation
214
8. Flow assurance stability issues
thickness in subsea flowlines is 3 in., which provides sufficient time for the operator to take
preventive action to manage the risk of flow assurance blockages in the system.
Startup of production is a transient operation which can cause a surge of liquids settled in
the low spots of the production system to arrive in the separator and stop the production if
separator is not sufficiently large to hold the arrived liquids. Transient multiphase simulation
tools are available to estimate the volume of liquid surge at different well ramp-up rates during
a start-up.
Rate ramp-up and ramp-down
Production operator may increase or decrease wells' production rate according to the field
development plan.
During a flow rate ramp-up an event similar to a liquid surge during start-up may be
expected. Higher flow rate sweeps liquid holdup accumulated in the flow line; the liquid
travels to the separator and temporarily increases the liquid rate.
During a flow ramp-down, less liquid is expected to be produced to the process facilities.
At lower flow rate more liquid will accumulate in the flow line.
Slugging in gathering lines
Gathering lines carrying multiphase fluids may also experience slugging when slugs originate in a wellbore as the well starts to be loaded with liquids.
Choke opening or artificial lift methods may be used to reduce the liquid loading in wells
and slugging in the gathering lines.
Lowering production tubing into the Boycott range may also help stabilize wells production and extend well life.
If no method works to mitigate the slugging, then flowline restraints or bracing for the
flowlines should be used as recommended by Hill and Wood (1994) to help with the loads on
the pipework.
Calculation of slug impact force on Tees and Elbows
Slugs traveling at high velocity through a production flow line carry a substantial momentum M and impact the pipe locations with change in direction with a significant force. Slugs
are known to have knocked flow lines off their support stands and caused significant (greater
than 1 pipe diameter) movement.
Slugging has led to loss of integrity as in-field pipelines made of fiber epoxy got disconnected from the Tee at the location of slug impacts.
Liquid slug is pushed through a flow line by gas. Liquid slug travels at nearly the velocity
of gas which pushes the slug like a piston.
A simplified correlation for slug length based on pipe diameter was proposed in
Chapter 4.
L [ ft ] = (D [ inch ])2
Calculation of pressure surge on sudden flow shut-in
215
The force of slug impact may be calculated if one knows slug density, gas velocity, pipe size
and angle of the pipe bend.
Force of slug impact on a bend may be estimated as:
F = ∆Μ / ∆t = ρ V 2 A ( 2 − 2 cos θ )
0.5
ρ = liquid slug density, kg/m3.
V = gas or slug velocity, m/s.
A = pipe cross section area, m2.
θ = bend angle.
M = momentum, kg m/s.
t = time, s.
Time may be estimated based on slug velocity and slug length.
The calculated force value should be multiplied with a suitable dynamic load factor (DLF).
A DLF of 2.0 is commonly used.
Experimental data on slug forces at pipe bends from several researchers was presented and
summarized in the works of Hou et al. (2014) and Tay and Thorpe (2015).
Calculation of pressure surge on sudden flow shut-in
Flowing mass of liquid carries a substantial momentum. When flow path becomes suddenly blocked, a pressure is expected to increase. Transient single phase flow simulators are
commonly used to estimate the pressure change during such event. A simple albeit somewhat
conservative method to calculate pressure surge is based on Joukowski.
∆P = ρ C ∆V
ΔP = change in pressure, Pa.
ρ = density of flowing fluid, kg/m3.
c = speed of sound in fluid at operating pressure and temperature, m/s.
ΔV = change in flow velocity, m/s.
c = (K*/ρ)0.5.
K* = K/(1 + D K/(e E)).
D = pipe diameter, m.
e = wall thickness, m.
E = wall elasticity modulus, Pa = kg/(ms2).
K = fluid bulk modulus, Pa = kg/(ms2).
Some values for materials commonly used in production systems are shown below.
ESTEEL = 200 * 109 Pa.
EFIBERGLASS = 17 * 109 Pa.
EHDPE = 0.8 * 109 Pa.
KWATER = 2.15 * 109 Pa.
KOIL = 1.7 * 109 Pa.
KGLYCOL + WATER = 3.4 * 109 Pa.
216
8. Flow assurance stability issues
Vacuum condition in flow
Vacuum condition and pressure surge may occur during stock oil flow.
In oil export pipelines going through mountainous terrain, or in deepwater during displacement of the flowline live oil with stock oil there may be a vacuum condition at the highest point of the flow system.
If pressure at a pipeline pumping station downstream of a mountain or at the bottom of the
flowline riser is lower than hydrostatic head pressure for stock oil, vacuum may occur at the
crest of the mountain or at the riser top.
Vacuum condition has to be taken into account for design of flexible lines and flexible parts
and materials on topsides system.
Vacuum can also occur at top of chemical injection lines causing flashing off of solvent and
deposition of active ingredient in the chemical tubing.
Higher than normal flowing pressure or deadheading may occur during start-up of stock
oil flow to move the stationary fluids in the pipeline or in the flowline such as during dead
oil displacement.
References
Hill, T.J., Wood, D.G., 1994. Slug flow: occurrence, consequences and prediction. In: SPE 27960, University of Tulsa
Centennial Petroleum Engineering Symposium, Tulsa, 29–31 August.
Hou, D.Q., Tijsseling, A.S., Bozkus, Z., 2014. Dynamic force on an elbow caused by a traveling liquid slug. J. Press.
Vessel. Technol. 136.
Makogon, T.Y., Estanga, D., Sarica, C., 2011. A new passive technique for severe slugging attenuation. In: 15th
Multiphase Production Technology Conference, Cannes, France, 15–17 June.
Montgomery, J.A., 2002. Severe Slugging and Unstable Flows in an S-Shaped Riser. PhD. Thesis, Cranfield University.
Sancho, A.M., 2015. Severe Slugging in Pipelines. Master Sc. Thesis, Instituto Superior Tecnico, Lisboa.
Taitel, Y., 1986. Stability of severe slugging. Int. J. Multiphase Flow 12 (2), 203–217.
Tay, B.L., Thorpe, R.B., 2015. Statistical analysis of the hydrodynamic forces acting on pipe bends in gas–liquid slug
flow and their relation to fatigue. Chem. Eng. Res. Des. 104, 457–471.
Zakarian, E., 2000. Analysis of two-phase flow instabilities in pipe-riser system. In: Proceedings PVP2000, ASME
Pressure Vessels and Piping Conference, July 23–27, Seattle.
Further reading
Boe, A., 1981. Severe Slugging Characteristics, Part I, Flow Regime for Severe Slugging, Presented at Special Topics
in Two-Phase Flow, Trondheim, Norway.
Joukowsky, N., 1898. “Über den hydraulischen Stoss in Wasserleitungsröhren.” (“On the hydraulic hammer in water
supply pipes.”). Mémoires de l'Académie Impériale des Sciences de St.-Pétersbourg (1900), Series 8 9 (5), 1–71. (in
German); Sections presented to the Division of Physical Sciences of O.L.E., 26 September 1897, to the PhysicalMathematical Commission of the Society, 30 January 1898, to the Polytechnic Society of the Moscow Imperial
Institute, 21 February 1898; complete paper to the Russian Technical Society, 24 April 1898, to the PhysicalMathematical Division of the Academy of Sciences, 13 May 1898. Also: Жуковский, Н.Е. (1899). “О гидравлическом
ударе в водопроводных трубах.” (“On hydraulic hammer in water mains.”), Proc., 4th Russian Water Pipes
Congress, pp. 78–173, printed in Moscow (1901), April 1899, Odessa, Russia.
C H A P T E R
9
Flow assurance integrity issues
O U T L I N E
Corrosion
Introduction
Types of corrosion
Corrosion monitoring methods
Currently used corrosion control
techniques
217
217
218
218
Integrated models
219
Erosion
220
References
220
219
Corrosion
Introduction
Besides mechanical impacts on pipe walls and process equipment by liquid slugs and
moving flow assurance plug projectiles, the production system also experiences chemical
degradation by corrosion.
Corrosion management is the domain of corrosion engineers. Corrosion system design
should be done in collaboration with flow assurance specialists.
Numerous flow parameters which are used to estimate the rate of corrosion can be derived
from flow assurance analysis, including:
multiphase flow regime,
liquid and gas flow velocities and densities,
liquid and gas pressure and temperature,
rate of liquid droplets entrainment by gas flow,
location and rate of water condensation from gas,
location and composition of water holdup,
shear stress exerted by gas or liquid flow on the pipe wall,
flow velocities at the chemical injection quill locations,
locations of solid deposits.
Handbook of Multiphase Flow Assurance
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217
© 2019 Elsevier Inc. All rights reserved.
218
9. Flow assurance integrity issues
Types of corrosion
A large amount of NACE literature on corrosion exists. General details on corrosion are
available (Fontana 1975; Dillon 1982).
Two key categories of corrosion are:
physico-chemical corrosion.
microbially influenced corrosion.
Some of the common types of physico-chemical corrosion include:
Uniform—caused by electrochemical reaction leading to dissolution of metal;
Galvanic—may occur due dissimilar weld material and pipe material;
Pitting—localized corrosion enhanced by localized difference in ion concentration;
Crevice—when a gap between pipe wall and another material such as flow assurance
deposit creates a localized difference in ion concentration;
Intergranular—when metallurgy has dissimilar grains of metal present;
Stress corrosion cracking—due presence of chloride ions released from fluid. May occur in
stainless steels such as chemical injection systems or sour service systems (Fischer et al., 2016).
Hydrogen embrittlement—may occur due hydrogen evolution in the system and ingress
into metals due to its small molecule size.
Microbially influenced corrosion (MIC) affects the rate of corrosion processes due to a biofilm formation on a surface of pipe.
MIC may occur in crude pipelines near the locations of water holdup in low spots, which
relates the MIC to flow assurance hydraulic analysis.
A recent overview of MIC in petroleum systems is provided by Al-Saleh et al. (2011).
Corrosion monitoring methods
There are several methods in the operations to monitor corrosion rate listed:
Weight loss coupons.
Electrical resistance probes.
Linear polarization resistance (LPR).
Field signature method (FSM).
Electrochemical noise.
Flexible UT Mats.
Ultrasonic pipe thickness measurement.
ILI in-line inspection with magnetic flux leakage intelligent scraper tool.
Radioactive methods.
Indirect monitoring may also be done by
Ultrasonic sand detection.
Process stream analysis.
Corrosion monitoring can provide data for tuning of the integrated multiphase flow and
corrosion models. An overview summary of corrosion monitoring methods is available in
Hedges and Bodington (2004).
Corrosion
219
Currently used corrosion control techniques
Corrosion prevention is accomplished by several methods simultaneously: use of corrosion inhibitor chemicals, use of maintenance scraping to remove water holdup from the pipelines, use of corrosion-resistant materials.
Corrosion inhibitor chemicals are among the most widely used methods of corrosion
methods. Chemicals performance is evaluated in laboratory by tests and in field by in-line
inspection.
Lab methods aim to measure:
Inhibitor efficiency;
Inhibitor partitioning behavior between hydrocarbon and water;
Compatibility with other production chemicals;
Film stability and persistence;
Optimum concentration.
Inhibitor efficiency may be measured with:
Bubble test apparatus;
Rotating electrode, including rotating disk (laminar flow) and rotating cylinder
(turbulent flow, high shear);
Jet impingement test;
Recirculating flow loop, which allows to make tests at a controlled shear stress;
In-line inspection (ILI) uses magnetic flux leakage probes installed circumferentially on a
ILI tool which records wall thickness along the whole perimeter and length of the tested pipe.
Integrated models
Multiphase flow models can be combined with corrosion rate models to provide an integrated assessment of the expected corrosion rates for a given flow scenario. There are commercial tools available which allow to estimate corrosion rate.
Alternatively it is possible to find multiphase flow parameters and then use these in the
corrosion rate prediction model. Commercial multiphase flow simulators have modules of
published corrosion models such as NORSOK M-506, deWaard-95 and Top-Of-the-LineCorrosion (Wang and Nesic, 2003). The first two are for CO2 based corrosion, and the TOLC
is for condensed fresh water corrosion. The use of these built-in modules for corrosion rate
assessment may be limited if corrosion engineers at operator companies develop and maintain in-house corrosion rate prediction models. The limitation for the use of multiphase tools’
corrosion modules for corrosion rate prediction is the limited ability to tune the model input
parameters. It may be useful as an initial check of the corrosion rate. Nonetheless, multiphase flow modeling tools are very useful and indispensable in analyzing the two parameters which are required by the corrosion specialists: thermal conditions of flowing fluids and
shear rates exerted by fluids on pipe wall. Both of these are parameters used in the in-house
models. Temperature determines both the corrosive species’ diffusion and corrosion reaction
rate and the condensation rate of fresh water. Shear affects the corrosion inhibitor layer and
the protective corrosion product layer. Some operators, to derive the desired shear and temperature distribution, as well as flow regime, attempt to couple the in-house corrosion rate
220
9. Flow assurance integrity issues
correlations with multiphase flow models such as point or drift flux slip, with varying success. The uncertainty in corrosion rate prediction keeps the ILI inspection service companies
in demand. In some instances, best available in-house models for US-based and UK-based
integrated operators underpredicted the corrosion rate in deepwater dense fluid production
and in onshore sour service production. Other companies deploy artificial intelligence to fit
measured rates to corrosion models. Comparison of which flow parameters (calculated with
a commercial multiphase flow simulator) have the most impact showed that holdup and inside heat transfer were top (Liao et al., 2012).
Erosion
Besides mechanical degradation of pipe wall surface, erosion by impingement of liquid
droplets or solids such as sand or hydrates affects the integrity of the protective corrosion
inhibitor film or of a corrosion product layer formed on a passivated pipe wall. This may lead
to localized pitting corrosion.
References
Al-Saleh, M.A., Sanders, P.F., Ibrahim, T.M., Sorensen, K.B., Lundgaard, T., Juhler, S., 2011. Microbially influenced
corrosion assessment in crude oil pipelines. In: NACE-11227, Corrosion-2011, 13–17 March, Houston.
Dillon, C.P. (Ed.), 1982. Forms of Corrosion, Recognition and Prevention. Vol. 7. NACE.
Fischer, D., Li, C., Huang, W., Sun, W., 2016. Investigation of the sulfide stress cracking and stress corrosion cracking
behaviors of duplex and lean duplex stainless steel parent and welded materials in sour service. In: NACE-20167325, Corrosion 2016, 6–10 March, Vancouver.
Fontana, M.G., 1975. The Eight Forms of Corrosion, Process Industries Corrosion. NACE, pp. 1–39.
Hedges, W., Bodington, A., 2004. A comparison of monitoring techniques for improved erosion control: a field study.
In: NACE-04355, Corrosion 2004, 28 March-1 April, New Orleans.
Liao, K., Yao, Q., Wu, X., Jia, W., 2012. A numerical corrosion rate prediction method for direct assessment of wet gas
gathering pipelines internal corrosion. Energies 5, 3892–3907.
Wang, S., Nesic, S., 2003. On coupling CO2 corrosion and multiphase flow models. In: Paper 03631, Corrosion 2003,
NACE International.
C H A P T E R
10
Research methods in flow assurance
O U T L I N E
Hydrate stability and crystal growth
Importance of studying gas
hydrates
Gas hydrates as an industrial
hazard
Hydrates as an environmental
buffer for holding Ch4, Co2
Industrial applications for gas hydrates
Hydrates as a source of hydrocarbon
fuel
Properties and structures of gas
hydrates
Thermodynamics of hydrate formation
Kinetics of hydrate formation
Phase transitions in gas hydrates
Methane hydrate experiments
Xenon sI and xenon + neohexane
sH hydrate experiments
Evaluation of experimental results
Evaluation of the biomolecular
computer studies
222
Molecular modeling
Comparison of chemical performance
on a solid surface
Computer study of hydrate inhibition
mechanism
251
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Docking of macromolecules on hydrate
and ice
Studying of kinetic inhibitor interaction
with water: solvation of the
polymer in the bulk water
Summary of computer modeling
Summary of the experimental
and computer model work
222
223
223
224
226
228
233
234
235
236
241
249
250
251
252
Experimental and computer study of the
effect of kinetic inhibitors on
clathrate hydrates
Crystallographic information
about hydrates
Hydrate crystal growth
Inhibition of hydrate formation
Computer modeling of hydrates: solid
solution models
Potential models
Structures of liquid water and
hydrate
Thermodynamic properties
Translational and vibrational spectra
Stability of gas hydrates
Early modeling of hydrate growth
Inhibition of hydrate growth
Research objectives
221
253
262
279
280
280
284
286
287
290
290
290
292
293
293
294
296
297
© 2019 Elsevier Inc. All rights reserved.
222
10. Research methods in flow assurance
Experimental study of hydrate
crystal growth
299
Morphology of hydrate crystals
299
Effect of adding kinetic hydrate
inhibitors on the morphology of
growing hydrate
304
Effect of NaCL salt on THF hydrates 308
THF + water + inhibitors solution
with NaCL salt
312
Growth rate measurements
312
Computer modeling of interaction
between a hydrate surface and an
inhibitor
Organization of this section
Early modeling of clathrate
hydrates at CSM
Studies of monomers adsorption
on hydrate with cerius2
Using the hand-written software
for studying interaction of water
and monomers
Adsorption of inhibitor polymers
on hydrate
Using the computer to design inhibitors
312
312
313
313
320
329
336
Summary of simulations
Summary from the adsorption
simulation results
Conclusions about kinetic
inhibition mechanism
Recommendations
338
340
341
341
Flow loop tests
341
Bench scale tests
Paraffin cold fingers
Paraffin cross-polarized microscope CPM
Rheology
DSC
Raman spectroscopy
342
342
342
343
343
343
Computer code
Program for generating radial
distribution function in water
Program for h bonded rings count
in water
Monte carlo program for polymer
adsorption on hydrate
343
References
436
Further reading
441
343
346
367
Hydrate stability and crystal growth
This section describes measurement of thermodynamic equilibria for methane sI hydrate
formation, which were measured in a temperature interval of 190–262 K. No structural hydrate
phase transition occurred in the studied region. Methane hydrate remained as structure I.
Thermodynamic equilibria of xenon sI hydrate and xenon + neohexane sH hydrate formation were studied. The temperature interval was from 228 to 288 K for sI hydrate and from 233
to 288 K for sH hydrate. A quintuple point sH-sI-Lw-Lh-V was determined to be at 281.5 K.
Importance of studying gas hydrates
Gas hydrates are inclusion crystalline compounds. Hydrates may form when a mixture
of water and gas molecules is subjected to specific temperature and pressure. Usually, the
pressure of gas hydrate formation is high (above 10 psi) and temperature is low (below 50 °F).
Temperature and pressure of hydrate formation may be dependent or independent variables,
depending on the number of components and phases in system.
Gas hydrates have an increasingly important place in the oil and gas industry. They may
serve in the future as the principal source of hydrocarbon fuel. One of the estimates suggests
that gas hydrate deposits worldwide are about 2 × 1016 m3 or 7 × 105 Tcf. This is roughly two
times the amount of carbon in all other known fossil fuel deposits.
Hydrate stability and crystal growth
223
Currently, gas hydrates are considered to be an industrial nuisance. Hydrate plugs forming in the pipelines prevent the normal operation of gas and oil production facilities. To date
the worldwide expenditures on hydrate prevention through methanol injection into the pipeline are over $150,000,000 (Long et al., 1994).
Gas hydrates as an industrial hazard
The normal operating conditions during oil and gas production establish the thermodynamic conditions favorable for hydrate formation. Gas is transported from the well at high
pressure. Water coming from the production well is also present in the pipeline. When the
temperature of the pressurized gas-water mixture falls below the equilibrium value, thermodynamic conditions are established for gas hydrate to form.
Formation of hydrate consumes gas and water present in the pipeline. Bulk of the forming hydrate eventually adheres to the pipeline walls and narrows the flow channel. This results in the
further pressure increase in the pipeline in front of the hydrate and accelerates growth of hydrate
on the wall of pipeline. With time hydrate plugs the pipeline and stops its normal operation.
Usually, after the hydrate formation pressure in the pipeline is lowered below equilibrium
pressure and hydrate is allowed to dissociate into gas and water. Sometimes, however, the
hydrate plugging of the pipeline may result in serious damage to the producing facilities and
cause a disaster.
Such was the case at the Piper Alpha oil rig in the North Sea (Cullen, 1990). The explosion at
that platform had happened on 6 July 1988. It caused the death of 167 persons, injury and trauma
to many of the survivors, and destruction of the platform. The economic estimate (Lovegrove,
1990) was that the British Government will have lost $2.8 billion in revenues. Cost of the platform
for Occidental Petroleum (Caledonia) LTD which operated the platform was $0.5 billion.
The investigation on the accident had shown that one possible cause of the explosion was
plugging of the condensate pump with gas hydrates and the following gas leak.
Finally, gas hydrates within the foundation sediments of deep water offshore structures may
present a hazard to the foundation of pipelines and other production facilities (Makogon, 1988).
Hydrates as an environmental buffer for holding CH4, CO2
Interest on environmental aspects of gas hydrates is mostly related to the greenhouse effect
of methane and carbon dioxide. These gases may form hydrates at conditions existing on earth.
Greenhouse gases are transparent to the infrared solar radiation on its way to earth. They
absorb the energy of this radiation after it reflected from the earth surface. This causes the
temperature increase in the atmosphere.
Atmospheric temperature affects the stability of methane and natural gas hydrates located widely on earth. More methane is released into the atmosphere as hydrate decomposes.
Hypothetically, this may result in a runaway global warming (Fig. 10.1).
Methane has a greenhouse effect which is 21 time stronger than that of carbon dioxide
(Englezos, 1993a). Several scenarios of global warming were proposed. The annual atmospheric temperature increase ranged from 0.006 °C/year to 0.08 °C/year for the catastrophic
scenario (Englezos, 1993b). Industrial development has been accompanied by a release of
greenhouse gases into the atmosphere. Atmospheric temperature increase during the past
century is attributed to artificial activity. Electric power plants are among the most active sites
releasing CO2, another important greenhouse gas.
224
10. Research methods in flow assurance
Runaway.
Methane
hydrate
decomposition
Temperature
increases
Release of a
greenhouse
gas.
More hydrate
decomposition.
Enhancement of
global warming.
FIG. 10.1 Scenario of a runaway global warming.
It was noticed, however, that similar fluctuations of atmospheric temperature are not uncommon in past years. Large amounts of greenhouse gases were and are released into the
atmosphere during volcanic eruptions. It should also be noticed that, to date nature had the
ability to equilibrate the conditions on earth.
Another approach is to treat gas hydrates as an environmental buffer for storing excess
greenhouse gases. When the gas concentration in atmosphere reaches a certain value, formation of gas hydrate becomes more favorable than its further decomposition. Such mechanism
allows the atmosphere to store the excess of greenhouse gas in form of hydrate (Fig. 10.2).
Industrial applications for gas hydrates
Many applications for gas hydrates were described earlier (Makogon, 1981, 1985; John, 1993).
These applications are based on the change of properties of hydrate formers in hydrate state.
The specific volume of water increases by 26–32% during formation of gas hydrate and only
by 9% during freezing (Makogon, 1985), while the specific volume of gas changes by several orders of magnitude. This permits the storage of large amounts of natural gas in the hydrate state.
Gas molecules are packed much closer together in hydrate than in gaseous state. Pressure
of gas can be increased by passing it through a hydrate state and decomposing the gas hydrate in a limited volume.
Only molecules of a particular size may form gas hydrate. Also various compounds require different thermodynamic conditions in order to form hydrate. Separation techniques
may be based on these properties of gas hydrate.
Water enrichment with D2O may utilize the fact that heavier isotopes of water form hydrate easier than the lighter ones (Makogon, 1985).
Hydrate stability and crystal growth
225
Methane
hydrate
decomposition
Tempertature
increases
Release of a
greenhouse
gas.
No runaway.
Increase of methane
concentration in
atmosphere.
Formation of
methane hydrate
to remove excess gas
from atmosphere.
FIG. 10.2 Schematic of greenhouse effect damping with hydrate.
Hydrate may be used as a heat accumulator. The hydrate formation is accompanied with
release of energy on the order of 400 kJ/kg (Makogon, 1985). In the reverse direction, to dissociate a hydrate one has to introduce the same amount of heat.
Electric conductivity of hydrate is lower than that of the initial solution. The sound velocity in hydrate is higher by 60–100% than that in gas saturated rock (Makogon, 1985). These
properties of hydrate provide the effective means for surveying gas hydrate deposits.
Gas hydrates may be applied in biotechnology. Modification of activity of enzymes encapsulated in reverse micelles may be done through pressure manipulations (John, 1993).
Formation of gas hydrates in the water-in-oil microemulsions or reversed micelles leads to
removal of intramicellar water and a consequent decrease in micelle size.
Gas hydrate can be used as a means of disposal of carbon dioxide. Power plants generate
CO2 and excessive amounts of this gas may increase the greenhouse effect. It is estimated that
the contribution of carbon dioxide has reached 71% of all greenhouse gases (Tomisaka et al.,
1990).
A hypothesis is being developed (Aya et al., 1991) that carbon dioxide expelled into deep
water (below 2750 m) will form a hydrate under high hydrostatic pressure. CO2 hydrate is
denser that the sea water and it will settle on the bottom of the ocean (Fig. 10.3). Assumption
of stability of sea conditions has been made (Fig. 10.4).
226
10. Research methods in flow assurance
CO2 tanker
more than
3000 m.
CO2 discharge pipe
FIG. 10.3 Conceptual view of CO2 disposal at ocean bottom.
Hydrates as a source of hydrocarbon fuel
Hydrates of natural gas are widely spread around the globe. The techniques of gas extraction from hydrate already exist (Makogon, 1981) and are being improved. Locations of
hydrates are found in all continents in the world. It can be seen that hydrates are often encountered in offshore regions as well as onshore.
Gas hydrates store a tremendous amount of gas. Over 170 volumes of gas at standard temperature and pressure may be enclathrated by water. Fig. 10.4 demonstrates that the amount
of gas in gas hydrate is sufficient to support its own combustion while melting the hydrate
crystal. Natural gas hydrates are a potential source of fuel for the future.
One of the most recent illustrations of the influence of natural hydrates on the environment may be viewed in the several unexplained vertical near-cylindrical caverns or craters of
approx. 100 ft in size which have suddenly appeared in area of northern Russia called Yamal
(Fig. 10.5). Makogon and Makogon (in Riazi 2016, p.429) hypothesize that this may have
been brought about by warming of the upper lithological permafrost cover thus destabilizing
gas hydrate deposit trapped under the icy permafrost cover, which is impermeable to gas.
As permafrost temperature remained below ice freezing but above hydrate stability, gas released from a hydrate lens deposit accumulated under the permafrost cover. Pressure of the
gas released from hydrate built up until it equaled the geostatic overburden pressure of the
permafrost cap still frozen and impermeable and led to a pneumatic explosion. Gas would
escape to the atmosphere and the soil and still stable ice from permafrost would form edges of
crater or fall to the bottom of the crater. The lower estimate of the amount of gas released from
hydrate may be easily calculated from measuring the depth and diameter of the vertical near-­
cylindrical crater by equating the pressure exerted by overburden permafrost soil column
Hydrate stability and crystal growth
227
FIG. 10.4 Burning methane hydrate (U.S. Geological Survey, 2016).
of typical density to the pressure exerted from below the overburden by gas released from a
hydrate lens deposit of similar diameter by warming in a confined volume. Gas would be released as temperature exceeds equilibrium. Geothermal profile of temperature for permafrost
areas may be found in the literature. The upper estimate of the amount of gas released may
be higher as the hydrate deposit could be thicker and the remainder of hydrate could dissociate without overburden pressure stabilizing it. Hydrate content in lenses is usually high, up
to 100% hydrate so using the volume of gas released from hydrate of 164 m3 methane /m3
hydrate is not unreasonable. Satellite measurements at time of the craters’ appearance have
228
10. Research methods in flow assurance
c­ onfirmed spikes of methane content in atmosphere over the area coinciding with approximate time of the event, substantiating this hypothesis. Unexplained ice also has been found
by explorers at the bottom of the several noticed craters, further substantiating this hypothesis
because hydrate dissociation is endothermic, and upon dissociation at atmospheric pressure
water released from hydrate would convert to ice. Warming of the atmosphere may gradually
bring more dissociation of some portion of the natural gas hydrate deposits existing onshore
which are estimated at 3% of the global hydrate amount releasing methane and setting off a
chain reaction. Eventual warming of the oceans may similarly destabilize, with time, some
of the oceanic sediment natural gas hydrate, estimated at 97% of the global hydrate amount.
However, if other natural phenomena such as methane solubility in seawater plays a role,
the process would eventually over geologic times balance out. Makogon et al. (1972) showed
that at T and P corresponding to the hydrate equilibrium, the solubility of methane in water decreases abruptly, by a factor of 3 to 5. Makogon et al. (2004) confirmed these data and
showed that at a pressure of 75 bar the solubility of methane in water changes from 4 cm3/g
without hydrate to 0.22 cm3/g above hydrate. This difference in concentrations of methane in
water creates the driving force for methane diffusion from the atmosphere into the hydrate.
Based on gas solubility without hydrate, seawater can dissolve 4 cm3 methane / gram water.
Estimating global ocean at 1.34 × 109 km3 = 1.34 × 1024 g, and global reserve of gas in natural
hydrate deposits at 1.5 × 1016 m3 = 1.5 × 1022 cm3, then 0.28% of the ocean can dissolve all gas
released from all the natural hydrate. Nonetheless, dynamics of gas dissolution may be slow
and depend on pressure and temperature. While the above estimate is encouraging that the
ocean can dissolve the methane from hydrate, more detailed research is needed to confirm
the rate of methane dissolution in the ocean because global ocean temperatures vary laterally
and with depth.
Properties and structures of gas hydrates
A gas hydrate is a crystalline compound in which water molecules enclathrate one or more
types of guest molecules. Such inclusion compounds are formed when the appropriate thermobaric conditions were applied to the gas-water system. An extensive review of common
types of hydrate crystals and their properties is available (Sloan, 1990). Also a list of the more
rare hydrate structures was presented by Dyadin et al. (1991).
Hydrate crystalline structures are composed of guest and water molecules. Water molecules arrange themselves in polyhedra encapsulating the guest molecules. Oxygen atoms of
water molecules are positioned in the vertices of such polyhedra (Fig. 10.6).
Such polyhedra or cavities share faces to form the crystalline lattice. Different combinations of cavities produce different hydrate structures (Fig. 10.7). Geometric properties of hydrate crystals are presented in Table 10.1.
Most often in nature hydrates of cubic structure I (sI), (Fig. 10.8) and cubic structure II (sII),
(Fig. 10.9) are formed. These two hydrate structures are formed with three types of cavities:
512, 51262, and 51264. These numbers represent the types of faces and numbers of these faces
forming a cavity. Thus, 512 represents twelve pentagonal faces forming a dodecahedron.
Cubic structure (sI) hydrate is formed when 512 and 51262 cavities come together. sI hydrate
may be formed with molecules ranging in size from methane (0.436 nm diameter) to triethylene oxide (0.61 nm diameter).
Hydrate stability and crystal growth
229
FIG. 10.5 Yamal crater (Yamal, 2015). Photo by Prof. Bogoyavlenski; reproduced with permission.
FIG. 10.6 Water molecules enclathrating the methane guest molecule and forming a 512 cavity. Dashed lines represent hydrogen bonds.
230
10. Research methods in flow assurance
FIG. 10.7 Schematic of sI and sII hydrates formation.
Cubic structure (sII) hydrate is formed when 512 and 51264 cavities arrange themselves in a
lattice. sII hydrate may be formed with molecules ranging in size from argon (0.38 nm diameter) to isobutane (0.65 nm diameter).
Hexagonal structure hydrate (sH) was discovered recently (Ripmeester et al., 1987). This
hydrate is composed of the three types of cavities: 512, 435663, and 51268, forming a lattice
shown in Fig. 10.10. Sizes of molecules which may participate in sH hydrate range from that
of argon (0.38 nm diameter) to hydrogen sulfide (0.46 nm) and from the size of cyclohexane
(0.75 nm) to that of methylcyclohexane (0.86 nm diameter).
Any molecule that is of the abovementioned size or smaller may be a simple or binary hydrate former. The exception to this statement are the molecules with a size smaller than argon.
These very small molecules can't form hydrate because they cannot stay in the cavity formed
231
Hydrate stability and crystal growth
TABLE 10.1 Geometry of hydrate structures.
Hydrate crystal structure
I
II
5
5 6
5
435663
51268
2
6
16
8
3
2
1
0.391
0.433
0.3902
0.4683
0.391
0.406
0.571
Effective free diameter, nm
0.51–0.52
0.57
0.48–0.50
0.69
–
–
–
Number of water molecules per
unit cell
46
136
34
Space group
Pm3n
Fd3m
P6/mmm
Crystal system
cubic
cubic
Hexagonal
Lattice parameter, nm
1.2
1.71
a = 1.22; c = 1.02
5
Number of cavities per unit cell
Average cavity radius, nm
a
a
12 2
12
H
5 6
Cavity type
12
12 4
From Istomin et al. (1988), assuming the van der Waals radius of water being equal 0.14 nm.
FIG. 10.8 Stereoscopic view of sI. Obtained with Hyperchem® software.
FIG. 10.9 Stereoscopic view of sII. Obtained with Hyperchem® software.
12
232
10. Research methods in flow assurance
y
x
framework viewed along [001]
FIG. 10.10 Stereoscopic view of sH. Source: Meier, W. M., Olson, D. H. 1987. Atlas of Zeolite Structure Types. 2nd
revised ed. London: Butterworth.
by water. Small size allows these molecules to escape from the cavity. And in case the small
guest molecule prefers to stay inside, it will not provide sufficient support to the surrounding
water molecules and the cavity will collapse.
Hydrates may form from pure components as well as from the mixtures of hydrate formers.
Structure I and II hydrates may form with pure gases. Examples may be methane forming
structure I hydrate and nitrogen forming structure II hydrate. However, structures I and II
may be formed with mixtures of gases as well. Structure H hydrate must be formed with a
mixture of components. The variation in size of sH hydrate is so large that the hydrate cavities cannot be stabilized by guest molecules of one size.
Not every cavity is occupied in hydrate by a guest molecules. In order for the hydrate to
be stable the occupancy of the hydrate lattice must be high. For this requirement to be met it
is necessary to have sufficient availability of the guest molecules of appropriate size. In case
of structure II hydrate there should be enough methane molecules to fit into the small 512
cavities and propane molecules to stabilize the large 51264 cavities.
Gas hydrates may change their structure depending on thermodynamic conditions and composition of hydrate former. The van der Waals and Platteeuw (1959) statistical thermodynamics
model is most frequently used in fitting and in predicting the equilibrium conditions of hydrates
formation. A recent use of the model by Lundgaard and Mollerup (1992) suggested an unusual
prediction of the phase diagrams of methane hydrates, obtained via minimization of the Gibbs free
energy of the system. One of the predictions of Lundgaard and Mollerup was that a slight mismeasurement of the unit crystal cubic side (by as little as 0.002 nm in 1.2 nm) could cause a structural
transition (I to II) on the three phase (I-H-V) hydrate equilibrium line at a temperature of 170 K.
Such a transition would not be unique because cyclopropane and trimethylene oxide have
the ability to form either structure I or II hydrates, depending on thermodynamic conditions.
The simple hydrates of cyclopropane were shown to undergo structural transition in the temperature range of 257.1–274.6 K based on data by Hafemann and Miller (1969) and Majid et al.
(1969). Hydrates of trimethylene oxide undergo phase transition between 252.4 and 260.1 K as
determined by Hawkins and Davidson (1966).
Several other works (e.g., Holder and Hand (1982), Adisasmito and Sloan Jr. (1992), etc.)
provided experimental evidence for structure I - structure II transition for hydrates of natural
gas mixtures at temperatures above the ice point. However, for gas mixtures, the phase transition occurs as a principal function of gas composition.
Hydrate stability and crystal growth
233
Thermodynamics of hydrate formation
Hydrate formation without inhibitors
The phase equilibria of gas hydrates are of the most industrial and academic interest.
Thermodynamic conditions at which hydrates form from pure water are usually described by
a pressure-temperature diagram. An univariant curve describes the equilibrium for hydrate
formation from binary mixture water-hydrate former. The univariant curve is prescribed by
the Gibbs's phase rule:
2+C = F+P
(10.1)
where C = number of components, F = number of degrees of freedom, P = number of phases.
The three phase line (V, Lw, H) for Structure I hydrate of methane will serve as an example:
2 + 2 ( methane + water ) = 1 + 3 ( vapor + hydrate + liquid )
(10.2)
This gives only one degree of freedom for hydrate formation equilibrium.
A large amount of hydrate equilibrium data for natural gases was compiled by Sloan
(1990). He analyzed the sI and sII hydrate equilibria for pure hydrate formers and their multicomponent guest mixtures.
Data for sH hydrate of methane and adamantane was reported by Lederhos et al. (1992).
Data for other hydrate structures have not been reported in the recent literature.
Usually, as temperature of the system goes down, a lower pressure is required to form gas
hydrate. This can be shown from the Clausius-Clapeyron equation.
d ( ln P ) / d ( 1 / T ) = −∆ d H / ( ZR ) .
where ΔdH is the enthalpy of hydrate dissociation. Hydrate consumes heat on dissociation
and ΔdH is greater than zero. Thus the slope of ln P against 1/T is negative.
This also can be explained from an entropic viewpoint. At lower temperature water molecules vibrate less and become more ordered. The entropy of the system decreases. According
to the equation:
G = U + PV − T S,
(10.3)
if the volume stays constant and temperature decreases, then the pressure must also decrease
in the closed system (U = const) at equilibrium (G = const).
Hydrate formation with inhibitors
There are four basic methods of prevention of hydrate formation. These include removal
of water from the system, raising the system temperature above equilibrium, decreasing the
system pressure below equilibrium, and introduction of an inhibitor.
Thermodynamic inhibitors such as alcohols or glycols are widely used in gas and oil industry
to prevent hydrate formation. When an inhibitor is added to the gas-water system, lower pressure
is required to form hydrate compared to a system without an inhibitor, at the fixed temperature.
Makogon (1981, p. 133) reported that, “With an increase in concentration of alcohols in
water, a breakdown is observed in the structural organization of water and in the clathrate-­
forming aggregates. As a result, the probability of hydrate formation is reduced”. This observation suggests that the thermodynamic inhibitors change the structure of water away from
that favoring hydrate formation as a part of their effect. A result from a neutron diffraction
study (Soper and Finney, 1993) of a 1:9 M ratio methanol-water mixture concludes that the
234
10. Research methods in flow assurance
HH pair correlation function doesn't change much from that for the pure water. This work
also showed the experimental evidence that water molecules form a disordered hydrogen
bonded cage around the methanol molecule.
The water structure can be described not only by the pair correlation function but also by the
structure of hydrogen bonded network in water. No difference can be seen for the pair correlation
function of pure water and water + hydrate inhibitor solution. The changes in hydrogen bonded
network of aqueous inhibitor solution were significant compared to pure water. Formation of the
hydrogen bonded cage around the inhibitor monomers was also noticed in computer simulation.
Phase equilibria data for hydrate formation with inhibitors is available in the literature.
Sloan (1990) reviewed the data for pure hydrate forming natural gases and their mixtures.
There has been some contradiction in the literature on the effect of hydrate equilibrium with
low concentrations of alcohol. Makogon (1981, p. 134) and Berecz and Balla-Achs (1983, p. 102)
reported that at concentrations below approximately 5 wt% of methanol in water the onset of
hydrate formation can occur at a higher temperature, thus reducing the subcooling required to
start hydrate formation. A hypothesis was suggested by Makogon (1981) that this may happen
due to inclusion of the methyl CH3 radical in voids in the structure of water.
It was also reported later (Svartas and Fadnes, 1992) that methanol inhibited the hydrate
formation over the whole range of concentrations. Only a few data points in this work, which
indicated the opposite effect, were related to an experimental error.
Another interesting concept discussed in the literature is whether methanol molecules can
or cannot participate in the hydrate structure. NMR and dielectric study of ethylene oxide
and tetrahydrofuran hydrates was performed (Davidson et al., 1981). The results show no
sign of enclathration of methanol.
The opposite was suggested by computer studies performed on water-methane-methanol
mixtures (Wallqvist, 1992) at 270 K. He made a simulation of a single unit cell of sI methane
hydrate with a varying number of methane molecules substituted by methanol molecules.
He reported that small amounts of methanol can be incorporated into the hydrate structure.
A 4 wt% methanol solution hydrate was reported to be stable, whereas a 7 wt% solution hydrate melted. Experimental evidence for the formation of a solvation shell of water molecules
around methanol molecules is drawn from a neutron diffraction study (Soper and Finney,
1993) of a 1:9 M ratio methanol-water mixture.
Kinetics of hydrate formation
Studying the kinetics of hydrate formation allows one to determine two attributes of hydrate formation. One is how soon hydrate will start forming (induction time) since the system
was placed in appropriate thermodynamic conditions. The other attribute is the growth rate
at which liquid water or ice will be converted into a solid hydrate.
Interest in this area of hydrate research has previously been purely academic. Today industry is seeking the new chemicals which allow operation of a gas-water system at conditions
where hydrate would normally form, so that it stays in a metastable state without aggregating to a large hydrate mass.
Experimental data for kinetics of hydrate formation are available in the literature for temperatures above and below the ice point. Falabella (1975) studied the formation of hydrates of
different gases and mixtures of gases at low sub-zero temperatures. The work on kinetics of
hydrate formation have been reviewed (Sloan, 1990).
Hydrate stability and crystal growth
235
Rates of linear hydrate growth may reach up to 103 nm/s as reported by Makogon (1974,
p. 74). This allows one to estimate the time required to orient one layer of water molecules into
hydrate lattice. Taking the size of water molecule as its van der Waals diameter of 0.29 nm, it
takes 290 μs for water molecules to position themselves from bulk water into the crystalline structure. This scale of time is about 10 times larger than time scale of usual computer simulations in
regular computers using distributed processing or GPUs with CUDA or similar parallel coding
and achievable in supercomputers. This indicates that, most likely, kinetics of hydrate formation
will be studied experimentally and using computer molecular modeling in the near future.
In experimental work kinetics of gas hydrate formation may be affected by many different
factors. Among these are:
(a) Subcooling, or lowering the system temperature below the equilibrium value for a
given pressure. Different shapes of hydrate crystals were obtained by Makogon (1981,
pp. 88–100) depending on the amount of subcooling.
(b) Overpressurizaton, or increase of the system pressure above its equilibrium value for a
set temperature. This is another measure of subcooling.
(c) Rate of cooling, or gradient of temperature decrease of the system in time.
(d) Stirring rate. Effect of turbulence in the hydrate system on kinetics of crystallization,
the crystal size distribution and the duration of the induction period was described by
Englezos et al. (1987).
(e) Previous temperature of water available for hydrate formation. This effect was studied
by Makogon (1981, pp. 63–72).
(f) Presence of the sites for hydrate nucleation like steel walls of the reactor or pipeline, or
particles of silica or bentonite.
(g) Preliminary saturation of water with hydrate forming gas. Dissolution of gas in water is
a diffusion process if no mixing were applied to the system. Rate of gas dissolution may
be monitored and subtracted from total gas consumption during the experiment.
Kinetics of hydrate formation is strongly affected by so- called kinetic inhibitors. The
mechanism of kinetic inhibition is by adsorption to hydrate nuclei and by sterically blocking
guest molecules from reaching the hydrate surface. Kinetic inhibitors are usually polymeric
molecules of high molecular weight having the ability to hydrogen bond with water.
• Comparison of chemical performance on a crystal solid surface and laboratory methods
Phase transitions in gas hydrates
For a single guest component hydrate, a solid phase transition can be indicated by a sharp
change of slope in the three-phase, univariant pressure-temperature equilibrium line shown
as a discontinuity in a plot of d(ln P) against d(1/T). This slope change is due to the change
in the enthalpy of hydrate formation, ΔdH, determined by the Clausius-Clapeyron equation
applied to a univariant system.
d ( ln P ) / d ( 1 / T ) = ∆ d H / ( ZR )
(10.4)
The univariant Clausius-Clapeyron equation is given in the above equation where P and T
are absolute pressure and temperature of hydrate equilibrium with vapor and ice, ΔdH is the
enthalpy of dissociation of hydrates to ice and vapor, Z is the compressibility of the gas, and
236
10. Research methods in flow assurance
R is the universal gas constant. If ΔdH/Z were constant over the temperature range, a plot
of ln P against 1/T would be linear within a single structure. On the other hand, a non-linear
plot might indicate either a hydrate crystal structure change, or a variable ΔdH/Z.
Methane hydrate experiments
Data in the literature for methane hydrate
Experimental equilibrium data for methane hydrate formation below the ice point were
available from multiple sources: Deaton and Frost Jr. (1946) at 273 to 262.4 K, Roberts et al.
(1940) at 259.1 K, and Falabella (1975) at 148.8 to 193.2 K. However these data sets did not
cover the temperature range 193–259 K. Linear fits for the available semilogarithmic data sets
at temperature above and below 210 K are shown in Fig. 10.11. Fitted lines intersect at an
angle which suggested a transition between structures I and II. Such phase transition was
suggested in the work by Lundgaard and Mollerup (1992). The paucity of measurements
in the temperature range of 193–259 K suggested an experiment to determine whether this
transition might occur.
FIG. 10.11
Frost Jr. (1946).
Methane hydrates equilibrium data. □—data by Falabella (1975). △—data by Deaton and
Hydrate stability and crystal growth
237
FIG. 10.12 Schematic of the apparatus.
Experimental equipment and procedure for methane hydrate
A schematic of the experimental equipment is given in Fig. 10.12. The apparatus was built
around a stainless steel spherical cell of 5.08 cm internal diameter rated for 10.1 MPa. The cell
was filled with 150 stainless steel balls of 0.31 cm diameter, needed for surface renewal. A
Thermolyne orbital shaker with 0.4 cm amplitude was used to agitate the stainless steel balls
inside the cell at 16.7 rps. A cylinder of 99.9% pure methane from Matheson Inc. was used as
a gas supply without further purification. The volumetric unit and the vent chamber shown
on the diagram were not used in this set of experiments. Pressure was monitored via Heise
gauges rated at 13.43 and 2.01 MPa. A Barocel differential electronic manometer (0.267 MPa
full scale, 0.133 Pa resolution) was used at low pressures. A grease-sealed glass flask attached
to the water and hydrocarbon inlet was used to vacuum distill water into the steel cell.
The cell was immersed in an 8 l Neslab ethanol stirred bath. The bath was cooled using the
Neslab cryocool CC-100 II 2-stage immersion cooler. The minimal attainable temperature was
180 K. The operating temperature was maintained with the Neslab temperature controller
with ±0.3 K stability at temperatures below 260 K and ±0.1 K at higher temperatures and a
600 W immersion heater. Temperatures were measured with an Omega platinum resistance
thermometer with ±0.1 K accuracy. The shaker frequency was selected to provide maximum
cell agitation without excessive vibration.
The lines and cell were evacuated to 4 Pa. Water (degassed, deionized) was vacuum distilled
into the cell which was partially immersed in liquid N2. After the vacuum distillation process
was complete, lines were re-evacuated. The bath was set to a constant experimental temperature.
Fig. 10.13 presents a schematic of the experimental procedure. The gas was admitted into
the system, and 8–10 min were allowed for pressure and thermal equilibrium without agitating the cell. After the system had stabilized, the shaker was started and the pressure drop was
monitored as hydrates formed.
238
10. Research methods in flow assurance
Pressure
hydrates
form
hydrates
form
Peq
error
in data
hydrates
decompose
hydrates
decompose
0
0
Time
FIG. 10.13 Schematic of experimental procedure.
When the pressure approached a near-equilibrium value (in several hours), some gas was
vented from the system to decrease the system pressure below the expected equilibrium
value. The hydrates which had previously formed, dissociated causing the pressure to increase and to approach the equilibrium value. After pressure stabilization at some new level,
the system pressure was increased again.
This process was repeated in successive approximations until the differential between the
formation and dissociation pressure reached 1–2% of the absolute pressure, as shown on the
right in Fig. 10.13. The arithmetic average of the upper and lower pressure approximations
was taken as the equilibrium value.
Results and discussion for methane hydrate data
The new equilibrium measurements are presented in Table 10.2 and in Fig. 10.14 along with
those of previous researchers. The two extremes of our measurements (at 262.4 and 190.15 K)
fit smoothly with previous results of Falabella (1975), and Deaton and Frost Jr. (1946), respectively. This agreement suggested the validity of the apparatus and experimental procedure.
The other values fit smoothly into the temperature gap, as complements to existing data.
Reproducibility of the measurements was also determined by duplicate runs at 243, 208, 198,
and 190 K, with the largest variation of 2.5% at 198 K.
239
Hydrate stability and crystal growth
TABLE 10.2 Methane hydrate equilibrium.
Data by
T equil, K
P equil, MPa
Error, MPa
190.15
8.471E-02
±0.001
8.572E-02
±0.001
1.349E-01
±0.001
1.365E-01
±0.001
2.336E-01
±0.002
2.278E-01
±0.002
218.15
3.666E-01
±0.005
243.15
9.825E-01
±0.01
9.991E-01
±0.01
9.823E-01
±0.01
9.805E-01
±0.01
262.4
1.847E+00
±0.06
148.8
5.30E-03
159.9
1.21E-02
168.8
2.11E-02
178.2
4.20E-02
191.3
9.01E-02
193.2
1.01E-01
262.4
1.79E+00
264.2
1.90E+00
266.5
2.08E+00
268.6
2.22E+00
270.9
2.39E+00
273.7
2.77E+00
274.4
2.90E+00
275.4
3.24E+00
275.9
3.42E+00
277.1
3.81E+00
279.3
4.77E+00
Present work
198.15
208.15
Falabella (1975)
Deaton and Frost Jr. (1946)
set 1
set 2
Continued
240
10. Research methods in flow assurance
TABLE 10.2 Methane hydrate equilibrium.—cont’d
Data by
T equil, K
P equil, MPa
280.4
5.35E+00
280.9
5.71E+00
281.5
6.06E+00
282.6
6.77E+00
284.3
8.12E+00
285.9
9.78E+00
259.1
1.65E+00
Error, MPa
Roberts et al. (1940)
FIG. 10.14 Methane hydrates equilibrium data. □—data by Falabella (1975). △—data by Deaton and Frost Jr.
(1946), ◊—data by Roberts et al. (1940), ⊙—present work data (1992).
Hydrate stability and crystal growth
241
We used the Clausius-Clapeyron equation and the hydrate heat capacity by Handa (1986)
in order to show that a smooth equilibrium line is expected with the absence of a phase transition in the region. Justification for use of this equation for univariant systems over a narrow
temperature range comes from the fact that ΔdH and z do not change rapidly with temperature. Total change in ΔdH over the studied temperature interval was 22% of the initial value.
Eq. (10.4) can be used to determine the enthalpy of dissociation of the hydrate systems, as
validated by Handa (1986). This equation shows that the slope of the logarithm of the hydrate
equilibrium pressure versus inverse equilibrium temperature is proportional to ΔdH. When a
plot of ΔdH against T is monotonic and continuous, then a plot of ln[P] against 1/T will have
no slope discontinuity. It is also known that.
ΔH depends on T as follows:
T0
∆d H ( T ) = ∆d H ( T0 ) + ∫ ∆CP dT
(10.5)
T
From this dependence it is seen that if a plot of ΔCp against T is smooth, then, so is ΔdH
against T in the absence of a phase transition. ΔCp was evaluated using the stoichiometric
formula:
∆CP = CP ( Hydrate ) − 6CP ( Ice ) − CP ( Gas )
(10.6)
assuming that the unit cell of sI hydrate crystal is formed by six ice molecules and one gas
molecule at the most probable 96% occupation of cavities by guest molecules. Cp(Hyd) values
were taken from Handa (1986), and Cp(Ice) and Cp(Gas) were extrapolated from literature
values (Handbook of Chemistry and Physics, 1988; Friend et al., 1989) available for the region
(23–271 K). Since both heat capacities of ice and methane do not deviate substantially from
straight lines over the temperature region of interest, the conclusion may be drawn that ΔdH
and consequently the slope of ln(P) against 1/T should be continuous. This fact may be supported by the experimental evidence from the work of Majid et al. (1969) for cyclopropane
hydrates, where the sharp changes of slope of the hydrate equilibrium line were observed in
the hydrate structural transition region.
The absence of slope discontinuities in the entire subzero methane hydrates equilibrium
line suggested that there was no structural transition of the structure I hydrates to structure
II in the region of interest.
Xenon sI and xenon + neohexane sH hydrate experiments
Data in the literature for Xe hydrates
The second part of research on the low temperature apparatus was performed with a mixture of hydrate formers. Pure xenon and xenon + neohexane were chosen as the structure I and
structure H hydrate formers, respectively. Pure xenon is only capable of forming sI hydrate.
Data for sI hydrate of xenon were published by Aaldijk (1971). One unpublished data point by
Dyadin et al. is at a much higher pressure. No previous phase equilibrium data was available
for sH hydrate of this two guest mixture. An investigation of a temperature - pressure phase
diagram of sH hydrate was the main purpose of this work.
242
10. Research methods in flow assurance
Apparatus used for xenon hydrate formation
A xenon gas hydrate may form from ice as well as from liquid water. In order to study
thermodynamic properties of gas hydrate below ice point the low temperature apparatus has
been used. A schematic diagram of the apparatus was previously shown in Fig. 10.12.
A spherical stainless steel reactor of spherical shape rated to 1500 psia was used to form
hydrate. One hundred and fifty stainless steel balls of 1/8 in. diameter were placed inside
the reactor. A reactor with stainless steel balls was shaken by the Thermolyne orbital shaker
in order to mix the contents and renew the hydrate formation surface. Reactor maintenance
consisted of regular cleaning with acetone, alcohol, and, sometimes, nitric acid to remove the
fouling from the walls of the reactor and steel balls.
The reactor was immersed in the constant temperature methanol bath. The temperature
of the bath was maintained within ±0.3 K at temperatures below 260 K, and within ±0.1 K at
higher temperatures by the Neslab on/off temperature controller. Cooling was provided by a
Neslab CC-100 II low temperature cooler.
The pressure of the reactor was sensed by two Heise gauges and by a Barocel manometer.
The Heise gauges were Bourdon tubes with ranges 0–2.07 MPa ±1.38 kPa and 0–13.79 MPa
±13.79 kPa. The Barocel manometer was a differential electronic manometer with the range
0–2000 Torr ± 0.001 Torr (0–0.267 MPa ± 0.133 Pa).
Water and liquid hydrocarbon were supplied to the reactor by vacuum distillation.
Evacuation of the apparatus was provided by the Trivac vacuum pump generating a vacuum
to 4 Pa. The cold trap was placed between the apparatus and the vacuum pump in order to
prevent pollution of the apparatus tubing with vacuum oil and to collect some of the waste
liquid after the experiment. The cold trap was cooled by the Flexi-cool cooler to 263 K.
Experimental procedure
A typical experiment started with evacuation of all tubing and the reactor. Stabilization
of the pressure with the vacuum pump valved off indicated complete removal of water and
hydrocarbon liquid.
A weighed sample of degassed water was vacuum distilled into the reactor immersed
into the cold bath by evaporation from the inlet flask and condensation on the cold walls
of ­reactor. Vacuum distillation transported 98–99% of liquid into the reactor which was determined by weighing the reactor before and after distillation. Non-condensed vapor was
evacuated. Liquid hydrocarbon was then, if required, distilled into the reactor, which was
immersed into liquid nitrogen. All lines were evacuated after the distillation was complete.
Xenon of 99.999% purity purchased from Matheson Gas Products, Inc. was used in this
set of experiments. The gas pressure was set and gas was allowed to cool in the stationary
reactor for 10 min. The pressure was then adjusted to the starting value and the shaker was
started. Pressure was monitored with intervals of 10–30 min and recorded into the notebook
for further analysis. A typical curve of pressure versus time is shown in Fig. 10.15, similar to
that of Fig. 10.13. Gas was partially vented after hydrate formation rate approached zero and
hydrate decomposed. Pressure was then increased to the lowest point in the previous formation cycle and hydrates formed.
This process was repeated until the differential between the lower formation and upper
decomposition pressures narrowed to 7–14 kPa. The arithmetic average of the two values of
243
Hydrate stability and crystal growth
Pressure, torr
800
run 39 10 / 9 / 92
xenon–neohexane
Structure I equilibrium pressure
700
T=–10°C, Tamb=75°F
s.s.balls=150, D=1/8in.
shaking rate=970rpm
stirring rate=1000rpm
99.999 xenon
7:1 water–neohexane
m water = 1g
600
500
0
500
1000
1500
2000
Time, min.
FIG. 10.15 Typical hydrate equilibrium run.
decomposition and formation pressures in the end of experimental curve (see Fig. 10.13) was
taken as the equilibrium pressure of hydrate formation at the given conditions. This procedure provides a more rapid approach to equilibrium.
Upon completion of the experiment gas was vented into the atmosphere. Water, and the
hydrocarbon liquid, if any, were evacuated from the reactor and lines.
Results
A set of data for pure Xe sI hydrate formation conditions was generated. Experiments
were run with 1 g of water in the reactor at constant temperatures of 228, 273, 283, and 288 K.
Data are presented in Table 10.3 along with the data by Aaldijk (1971). Fig. 10.16 shows the
equilibrium data for xenon sI hydrate formation. The change of equilibrium line slope in
Fig. 10.16 at sub-zero temperatures is attributable to the change of heat capacity as discussed
in Eq. (10.6).
A set of data for Xe + neohexane liquid sH hydrate formation conditions was generated.
Xenon (effective diameter 0.458 nm) fits only into small (512) and medium (4351263) cavities
of sH hydrate (see Table 10.1). Neohexane (effective diameter 0.773 nm) can fit only into the
large (435663) cavity of sH hydrate. At complete occupancy of cavities, the unit cell of sH
244
10. Research methods in flow assurance
TABLE 10.3 Pure xenon sI hydrate equilibrium.
Data by
T equil, K
P equil, MPa
Error, KPa
228.15
0.01620
±0.1135
273.15
0.1551
±1.216
283.15
0.4263
±1.723
288.15
0.6984
±0.1723
289.07
0.784
283.62
0.4465
278.66
0.269
273.15
0.153
262.16
0.0932
252.49
0.0594
232.88
0.0212
227.29
0.01512
CSM
Aaldijk (1971)
Miller (Amer, 1981)
Dyadin (1994), Dyadin et al. (unpublished)
337
250,000
hydrate, composed of 34 water molecules, may enclathrate at most 1 neohexane molecule
and 5–6 xenon molecules. Experiments were run with 1–2 g of water and a higher than stoichiometric amount of neohexane, (0.15–1 g) in order to avoid disappearance of liquid hydrocarbon phase. Experimental data are presented in Table 10.4. In order to ensure repeatability,
runs at four out of ten temperatures were repeated.
Results and discussion for xenon hydrate data
Fig. 10.17 shows the superimposed data sets for pure xenon and xenon+neohexane mixture hydrates. A crossover of equilibrium curves can be seen in the temperature interval
around 281.5 K. This indicates a presence of a quintuple point for a vapor-liquid1-­liquid2-sI
hydrate-sH hydrate system. This is the first quintuple point observed for sH hydrate.
­
Fig. 10.18 shows the enlarged crossover area.
At temperatures above the crossover, the xenon + neohexane hydrate formation line has a
slightly higher pressure, but is parallel to the pure xenon hydrate formation line. Crossover
and a change in slope of equilibrium pressure line for xenon + neohexane hydrate clearly indicates the phase transition of sH hydrate into sI hydrate in this temperature interval. Fig. 10.18
shows this phenomenon more clearly.
A program utilizing the SRK EOS was written in Turbo Pascal, allowed the calculation
of vapor and liquid composition of xenon + neohexane mixture. It indicated that liquid
Hydrate stability and crystal growth
245
FIG. 10.16 Equilibrium data for pure xenon sI hydrate. □—CSM data (1992). △—data by Aaldijk (1971).
­ ydrocarbon phase was present in the system at the studied conditions. Results of this calcuh
lation are presented in Table 10.5.
Justification for elevation of sI hydrate equilibrium line for the three-component mixture
above the sI line for the two component mixture was done using a two-step process. The first
step used PHAS_88 program by DB Robinson Research LTD. to calculate the vapor phase compositions of two- (water + xenon) and three-component (water + xenon + neohexane) systems
with known total compositions. The second step used HYDR_88 program by DB Robinson
Research LTD. to estimate sI hydrate equilibrium pressure for the two- and three-component
systems with known total compositions.
Hydrate equilibrium requires the fulfillment of the three conditions: equal temperature,
pressure, and chemical potential in hydrate and in other phases. In case of two component
system a certain pressure of xenon is required in the vapor to form hydrate. If a third v
­ olatile
component is added (like neohexane) which cannot participate in sI hydrate, the partial
­pressure of xenon will decrease due to the presence of neohexane in the vapor. Hydrate will
form only if the partial pressure of xenon in the vapor mixture is equivalent to the pressure of
TABLE 10.4 Xenon + neohexane hydrate equilibrium.
Temperature (K)
Pressure (MPa)
233.15
0.0145
±0.0011
253.15
0.0464
±0.0001
263.15
0.0785
±0.0017
273.15
0.1333
±0.0010
0.1315
±0.0001
0.1819
±0.0010
0.1813
±0.0005
278.15
0.2412
±0.0003
280.65
0.3447
±0.0010
0.3427
±0.0057
283.15
0.4525
±0.0010
285.65
0.5742
±0.0019
288.15
0.7242
±0.0032
0.7238
±0.0052
0.7296
±0.0016
275.65
FIG. 10.17 Data for pure xenon and for xenon + neohexane mixture. □—Present work data for pure xenon,
△—data by Aaldijk for xenon (1971), ⊙—present work data for xenon + neohexane.
Hydrate stability and crystal growth
247
FIG. 10.18
Data for pure xenon and for xenon + neohexane mixture above 273 K. □—Present work data for pure
xenon, △—data by Aaldijk for xenon (1971), ⊙—present work data for xenon + neohexane.
TABLE 10.5 Calculated phase composition for the xenon + neohexane system.
T, K
x Xe
y Xe
278.15
0.06957
0.92354,
280.65
0.09655
0.93963
283.15
0.12222
0.94818
285.65
0.14837
0.95379
288.15
0.18293
0.95943
Liquid and vapor phase composition at equilibrium conditions based on program calculation for
Xe + neohexane system.
pure xenon above sI hydrate. Thus a higher total pressure was required in the 3 component
mixture to offset the neohexane concentration in the vapor.
Table 10.6 presents how the xenon vapor concentration is reduced by the addition of neohexane to the system. The bottom section of the table shows the normalized reduction of
concentration to vary between 4% and 9%.
248
10. Research methods in flow assurance
TABLE 10.6 Calculated vapor phase composition.
3 component vapor phase composition at equilibrium conditions based on EquiPhase
program calculation for Xe + neohexane + water system
T, K
y H2O
y neoC6
y Xe
278.15
0.003516
0.0795
0.917
280.65
0.002924
0.0627
0.9344
283.15
0.002639
0.05375
0.9436
285.65
0.002469
0.04788
0.9496
288.15
0.002262
0.04202
0.9557
2 component vapor phase composition at equilibrium conditions based on EquiPhase
program calculation for Xe + water system
T, K
y H2O
y Xe
278.15
0.003575
0.9964
280.65
0.00299
0.997
283.15
0.002713
0.9973
285.65
0.002551
0.9974
288.15
0.002354
0.9976
Change in vapor xenon concentration as a result of adding neohexane in the system
T, K
△y/(y3 component)
278.15
0.086587
280.65
0.066995
283.15
0.05691
285.65
0.050337
288.15
0.043842
In the second part, higher sI hydrate equilibrium pressures in a three-component system
were predicted, compared to the two-component system. Although the predicted pressures
were underestimated by 7–8%, the predicted pressure differences for the two- and three-­
component systems were comparable to the differences measured experimentally as indicated in Fig. 10.19. This figure presents the experimental and calculated univariant sI hydrate
lines. Table 10.7 presents the calculations and experimental data. The reader may notice that
the normalized pressure and compositional differences have similar values in the last five
lines of Tables 10.6 and 10.7. This similarity reflects the change in partial pressure as a function of composition (pA = yA*P). If yA decreases the total pressure must increase proportionally
in order to maintain the same partial pressure (uncorrected fugacity).
Hydrate stability and crystal growth
249
FIG. 10.19
Calculated and experimental data for pure xenon and for xenon + neohexane mixture above 273 K.
□—CSM data for pure xenon (1992), △—data by Aaldijk for xenon (1971), ⊙—CSM data for xenon+neohexane
(1992), - -, HYDR_88 program predicted data.
Evaluation of experimental results
Study of the phase transition possibility for methane hydrate at subzero temperatures was
investigated. Results of this study are summarized earlier in this chapter. It was shown that
in the temperature interval of 154–273 K no sI to sII structural transition of the hydrate happened. It is possible, however, that the structural transition may occur at temperatures below
154 K where no experimental data exist.
Experiments on xenon sI and xenon + neohexane sH hydrate equilibria resulted in a generation of two phase diagrams in the temperature region of 228–288 K. It was found from the
generated equilibrium curves that a quintuple point sH-sI-Lw-Lh-V point should be present
in the temperature interval of 278–283 K. This phase diagram does not violate the Gibbs's
phase rule.
250
10. Research methods in flow assurance
TABLE 10.7 Hydrate equilibrium calculation.
Hydrate equilibrium for Xe + neohexane + water system
T, K
P, kPa
Pcalc
278.15
241.25
264.22
280.65
344.74
333.38
283.15
452.52
421.12
285.65
571.21
532.8
288.15
733.593
673.68
sI hydrate equilibrium for Xe + water system
T, K
P, kPa
278.15
N/A
280.65
N/A
283.15
426.2743
285.65
N/A
288.15
698.4332
Pcalc
396.2
640.66
Normalized changes in xenon pressure required as a result of
having neohexane in the system.
T, K
△P/P(3 component)
278.15
N/A
280.65
N/A
283.15
0.057999
285.65
N/A
288.15
0.047928
Evaluation of the biomolecular computer studies
Simulation of the macromolecules docking on the surface of water crystals showed the
preferential orientations and interaction energies between macromolecules and the surface. It
was concluded from the resulting low energies of interaction that Winter Flounder polypeptide biomolecule, PVP and PVCap molecules are able to adsorb on ice, sI and sII hydrate surfaces. Very high interaction energy was shown for the VC-713 polymer which suggests that
it cannot dock on water crystals. The reason for inability of VC-713 to dock on water crystal
is considered to be the DMAEMA (dimethylaminoethylmethacrylate) monomers presence in
the polymer chain. This monomer acts as a buffer between polymer and crystal.
Verification of the water models was performed. The simple point charge (SPC) water model
was shown to adequately represent the structural and thermodynamic properties of real water.
SPC water model is recommended as a choice among all water models available in SYBYL.
Molecular modeling
251
Study of structural changes in the water hydrogen bonding network incurred by the hydrate inhibitors was done. A new method of analyzing the structure of water was used in this
study. The results of simulation are in qualitative agreement with the experimental performance of the studied compounds.
Limitations of this study are (1) the docking was performed in vacuo; (2) PVP, PVCap, and
PVCA inhibitors were simulated as single monomers; (3) Scaling of the dielectric interactions
was used in inhibitors effect on water structure study.
A potentially better hydrate inhibitor was suggested based on the computer simulation
results. Molecular dynamics simulation proved not only to replicate the real experimental
data, but to predict the new compounds as well.
This study suggests that the following properties should be present in a good hydrate inhibitor:
1. Presence of a carbonyl group (active site) to introduce structural changes into the water.
2. Presence of a strongly electronegative atom such as nitrogen next to the carbonyl group
in order to enhance the electron cloud of the carbonyl oxygen (electron donating site).
3. Ring structure holding the active and the electron donating sites in order for electron
sharing to be smoothly equilibrated.
4. A polymer chain holding the rings with active and electron donating sites to add a
pattern to the active groups.
The potential new kinetic inhibitors may have the structure similar to cyanuric acid and
its derivatives.
Mechanism of the kinetic hydrate inhibition is most likely in the structural rearrangement of
water molecules. Kinetic inhibitors decrease the number of H bonded polygons driving the structure of water away from that favoring hydrate and making the formation of hydrate unfavorable.
Several recommendations can be made for the future studies.
Simulation
1. Use oligomers rather than monomers of inhibitor
2. Try solutions of these inhibitors with different concentrations
3. Hydrate the species before docking on the hydrate surface
4. Look at docking on different surfaces of the hydrate crystal lattice
Experimental
1. Pinpoint the xenon-water-neohexane system quintuple point location above 0 °C.
2. Chromatographic analysis is needed for liquid and vapor phases composition in the
xenon-water-neohexane system.
Molecular modeling
Comparison of chemical performance on a solid surface
Computer simulations can be used to gain an understanding of the hydrate inhibition
mechanism. Docking simulation of hydrate inhibitors on surfaces of ice and gas hydrates of
sI and sII reveals the energy with which they adsorb. Inhibitor chemicals included the Winter
Flounder polypeptide biomolecule, PVP, PVCap, and VC-713. Modeling of water and ice was
done using the SPC water model. A study was done of the effect of hydrate inhibitors on the
252
10. Research methods in flow assurance
structure of water using a polygons counting approach. A potential new hydrate inhibitor
was proposed, based on this study.
Computer study of hydrate inhibition mechanism
Overview of the computer simulations
Reasons for the computer study
The mechanism for kinetic inhibition of hydrates can be studied on a micron scale when
hydrate nuclei are sterically prevented by polymeric inhibitors from agglomeration. It also
can be viewed on the scale of nanometers when the inhibitor affects the microstructure of
water and defers hydrate formation.
Today's experimental techniques do not allow the dynamic study of the properties of materials in time on a microscopic basis. Computer simulation (molecular dynamics) is a widely
used tool which possesses several advantages over the real experiment. The first advantage
is the ability to look into the dynamics of the processes on a scale of angstroms. Other advantages include 100% repeatability, ease of modification of parameters, and a safe environment.
Among the disadvantages are the use of simplified, theoretical models of the real processes,
high computing and data storage requirements, and computational round-off errors.
Modern high-powered computers permit more complex simulations, such as phase behavior and structural properties of fluids and solids. Examples of computational research
are discussed in an ever increasing number of publications. Guidelines for writing the computer simulation programs may be found in books by Allen and Tildesley (1987) and by Haile
(1992). Many commercial software packages for state-of-the-art simulations are available,
such as BIOSYM®, SYBYL®, and HyperChem®.
SYBYL® is an extensive suite of software focused on computational molecular and biomolecular design. A modular program, SYBYL® features software for applications in drug
design, biochemical research, homologous chemical modeling, property prediction, molecular dynamics, polymer research, and conformational analysis. SYBYL® includes a molecular
spreadsheet which can store the obtained information. A molecular spreadsheet allows the
analysis of stored information using one or more parameters. SYBYL® functions in a number
of modes: command line, graphical, and a combined mode which mixes command line access
with graphical selection of objects directly from the screen.
The central role of SYBYL® is to enable the researcher to answer the question: “What
chemical structure or structures should I synthesize next in order to more fully understand
my research problem or produce more active agents?” The search for the best gas hydrate
inhibitor requires the answer of this question. In order to synthesize a chemical to prevent
hydrate formation completely, the mechanism of hydrate inhibition has to be known. It is necessary to determine the function of the kinetic inhibitors in preventing hydrates' formation.
SYBYL® has been used previously to model SPC water. The results of previous simulations
(Clark, 1992) are in good agreement with the original SPC model results (Berendsen et al., 1981).
Results of the computer simulation
This work attempted to provide a qualitative explanation of kinetic inhibition phenomena
for hydrate formation. Two hypotheses for the inhibition mechanism were tested.
Molecular modeling
253
The first hypothesis was based upon a similarity to the inhibition of ice growth. Polypeptides
present in the blood of the winter flounder allows it to survive the Arctic sea temperatures of
270.9 K. The structure of this polypeptide is described later in this chapter. It was shown (Knight
et al., 1993) that polypeptide adsorption on the ice surface prevents further crystal growth. We
hypothesized that adsorption on the hydrate surface might prevent hydrate growth just as in
ice. This hypothesis is addressed in Section “Docking of macromolecules on hydrate and ice”.
The second hypothesis was that hydrate inhibition is not the result of a crystal surface
interaction, but that of interaction with the bulk liquid. The hypothesis was that the polymer changes the structure of water, making hydrate formation entropically unfavorable.
This hypothesis is addressed in Section “Studying of kinetic inhibitor interaction with water:
Solvation of the polymer in the bulk water”.
Docking of macromolecules on hydrate and ice
Introduction
The first portion of the computer study was directed to provide evidence for (or against) the
adsorption hypothesis. Evidence was obtained that some of the polymeric hydrate inhibitors
with relatively simple structures like polyvinylpyrrolidone (PVP) and polyvinylcaprolactam
(PVCap) might adsorb on the surface of hydrate crystal. This adsorption was hypothesized to
be similar to adsorption of the winter flounder polypeptide on a plane of growing ice.
Method of research
The molecular simulation program SYBYL® (version 6.01), a product of Tripos Associates,
Inc., was used to perform the docking studies. Docking of the winter flounder polypeptide
was simulated on three different surfaces of ice-I, and on crystal surfaces of sI and sII hydrate. The sequence of the aminoacids chemical formula of the winter flounder polypeptide
is shown here. Docking of the hydrate inhibitor polymers VC-713, PVP, PVCap shown in
Fig. 10.20 was performed on crystal surfaces of sI and sII hydrate. The crystal surface and
each macromolecule were docked in vacuo and the intermolecular energy was estimated for
different conformations.
Adsorption energy was the main parameter studied in this calculation. The energy of adsorption is a measure of the interaction between the inhibitor and the water crystal (ice or
gas hydrate). Both the polymer (inhibitor macromolecule) and the site (hydrate or ice crystal) were positioned by SYBYL® in the two separate molecular areas. The interaction of the
polymer with hydrate was calculated on an atom-to-atom and charge-to-charge basis which
accounted for each water molecule in the hydrate lattice. The interaction energy accounts for
the steric (van der Waals) and electrostatic (Coulombic) interactions.
The energy of interaction is zero at infinite separation of the site and the polymer, and it is
a potential function of distance between interacting sites. A review of potential functions was
presented by Prausnitz et al. (1986, sec. 5.5). The lowest interaction energies obtained in this
study cannot be viewed as absolute minima. The number of possible configurations of polymer on the crystal surface is nearly infinite, only limited by computer precision. The energies
obtained energies represent local minima in energy and the best attempt of the author within
the available resources.
254
10. Research methods in flow assurance
FIG. 10.20 Chemical structures of PVP, PVCap and VC-713.
Surfaces of sI and sII empty hydrate lattices, and hexagonal ice lattice were prepared using
SYBYL® by inputting the coordinates of the oxygen and hydrogen atoms and connecting
them into water molecules. Coordinates were generated using the Fortran program which
replicated the X-ray diffraction data for crystal unit cell in x, y and z directions. A surface of
any size and thickness could be generated. Size of the surface was made 5 × 5 × 1 sI unit cells
for sI hydrate, 4 × 4 × 1 sII unit cells for sII, and 9 × 9 × 2 repeat units for ice. The dimension of
the surface was 6.1 nm or more along x and y axes. Such sizes were chosen in order to accommodate the winter flounder polypeptide (5.9 nm length), 9-link chain of the VC-713 polymer
(6.1 nm length) and to reduce computation time.
The polymer chain of VC-713 and winter flounder polypeptide were generated using the
Hyperchem® release 2.0 program for Windows made by Autodesk, Inc. Potential energies of
the macromolecules were minimized in vacuo before transferring to the IBM RS-6000 workstation. After transferring to the IBM workstation an overall energy minimization was done.
Molecular modeling
255
The winter flounder polypeptide sequence of the aminoacids in standard nomenclature is:
DTASDAAAAAALTAANAAAAAKLTADNAAAAAAATAA,
where the letters represent D—aspartic acid, T—threonine, A—alanine, S—serine, L—leucine,
N—asparagine, and K—lysine.
The structures of these aminoacids can be found in every recent organic chemistry textbook. These structures are described in Table 10.8. The VC-713 polymer chain was built as a
repeating sequence of monomers present in the real polymer:
− ( vinylpyrrolidone − vinylcaprolactam − DMAEMA )x − .
The molecules were then transferred from the 486 PC to the IBM workstation in Brookhaven
format. PVP and PVCap chains were also 9 repeat units long. Fig. 10.20 shows polymer structures. These polymers were built using the SYBYL’ program.
The studied macromolecule and the crystal surface were read into SYBYL’. Charges for
water molecules in the crystal and for the macromolecules were computed using the method
by Pullman (Berthod and Pullman, 1965). Macromolecule was equilibrated in vacuo. Periodic
boundary conditions were set up around the system, and a lattice of the intermolecular potential energy field was precalculated for various relative positions of the macromolecule and
the crystal surface. Six variables define a position and orientation of the rigid polymer chain
in space. Docking of macromolecules on the crystal surface was performed by varying the
x, y, z, Θ and Φ variables for the macromolecule. Coordinates x, y and z specify the center of
the macromolecule relative to the crystal surface, Θ is the angle between the center line of the
TABLE 10.8 Structure of aminoacids composing the winter flounder polypeptide.
General aminoacid formula:
Aminoacid
R radical
D aspartic acid
CH2CO2H
T threonine
A alanine
CH3
S serine
CH2
L leucine
CH2CH(CH3)2
N asparagine
CH2CONH2
K lysine
(CH2)4NH2
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10. Research methods in flow assurance
macromolecule and the initial position on the crystal surface, and Φ is the angle of the macromolecule rotation about its center line relative to the initial position. The macromolecule was
flat, relative to the surface, keeping the sixth variable 0 fixed. The intermolecular energy (potential energy between molecules in current conformation relative to infinitely distant molecules) was monitored during the docking. The conformation with the lowest intermolecular
energy was chosen as the preferred orientation of the macromolecule on the crystal surface.
A typical value of the interaction energy prior to the relaxation of the macromolecule on the
crystal surface was of the order of tens of kilocalories per mole. The energy of the whole system was minimized (the macromolecule was relaxed on the crystal surface). The final system
energies are given in Table 10.9.
Data analysis
One run was performed for each polymer chain. For each run the following final values
were inspected:
(a) The number of hydrogen bonds between the macromolecule and water molecules
of the crystal. Hydrogen bonds were defined by the following default values stored
in SYBYLQ two water molecules were found to be hydrogen bonded if the length of
hydrogen bond were less than or equal to 0.285 nm and the HO-----H angle >120%.
TABLE 10.9 Analysis of macromolecules docking on crystals.
Intermolecular
energy, kcal/mol
Number of
hydrogen bondsa
Pattern of
adsorption sites
Winter flounder polypeptide on
ice 011
1742
4 (100%)
Yes (1.69 nm)
ice 101
−19,850
4 (100%)
Yes (1.69 nm)
ice 110
−19,924
4 (100%)
Yes (1.69 nm)
sI hydrate
−5245
0 (0%)
Yes (1.69 nm)
sII hydrate
−12,696
4 (100%)
Yes (1.69 nm)
sI hydrate
751,600
0 (0%)
Some (3.69 nm)
sII hydrate
731,594
1 (33%)
No
sI hydrate
−5065
0 (0%)
Yes (0.6 nm)
sII hydrate
−12,495
1 (33%)
Some (1.87 nm)
sI hydrate
−5057
0 (0%)
Yes (0.6 nm)
sII hydrate
−12,504
0 (0%)
No
VC-713 on
PVP on
PVCap on
a
Percentage of bonding at available sites on macromolecule.
Molecular modeling
257
FIG. 10.21 Conformation of the winter flounder polypeptide docked on ice (surface 1). Dashed lines represent
hydrogen bonds. Winter flounder polypeptide is hydrogen bonded by four hydroxyl OH groups to oxygens of water
molecules in ice.
(b) Conformation geometry, repeating of docking sites on the crystal, if any. Some
macromolecules exhibited a regular, periodic geometric fit of adsorption groups and
adsorption sites. This can be best seen with winter flounder polypeptide in Fig. 10.21.
Macromolecules retained the regular coil conformation.
(c) The energy of intermolecular interaction. The energies after the final minimization were
compared. Very high positive energies indicated that adsorption was impossible. This is
the case for VC-713.
The results of the analysis are presented in Table 10.9.
Discussion of polymers docking
The docking of winter flounder polypeptide was performed on five types of crystal surface:
100, 010 and 001 surfaces of ice, and 001 surfaces of sI and sII hydrate. The best results were
obtained for docking of the winter flounder polypeptide on ice surfaces. This was an anticipated outcome because the winter flounder polypeptide prevents the blood of this fish from
freezing at sub-zero temperatures down to 270.9 K by adsorbing on ice crystals and preventing them from growing further (Knight et al., 1993). Docking of the polypeptide on hydrate
sI and sII shows that interaction energies are low (−5245 and −12,696 kcal/mol, accordingly).
The winter flounder polypeptide may have a similar effect on the growth of hydrate by preventing bulk hydrate formation. Edwards (1993) presented results for the winter flounder
polypeptide docking on hydrate sI. He suggested that this polypeptide adsorbs on sI hydrate
in [110] direction based on the similarity of polypeptide hydroxyl groups spacing (1.686 nm)
and distance between second nearest large cavity neighbors in sI hydrate (1.697 nm). Winter
flounder polypeptide adsorption on all water crystals shows the repetitive pattern of adsorption sites locations. See Figs. 10.22–10.25.
The main result of this study was that the polymers PVP and PVCap may inhibit hydrate
growth by adsorbing on the hydrate crystal, as indicated by their low adsorption energy.
However, adsorption is, probably, not the inhibition mechanism of VC-713, because the adsorption energy of VC-713 was high. Docking of VC-713 polymer on sI and sII hydrates resulted in very high interaction energy (over 730,000 kcal/mol). The high energy indicates that
adsorption of VC-713 on hydrate surface is energetically unfavorable. This high energy is
thought to be the consequence of DMAEMA group which sterically prevents the adsorption.
This result suggests that the mechanism of kinetic inhibition for the VC-713 polymer may not
258
10. Research methods in flow assurance
FIG. 10.22 Conformation of the winter flounder polypeptide docked on ice (surface 2). Dashed lines represent
hydrogen bonds. Winter flounder polypeptide is hydrogen bonded by four hydroxyl OH groups to oxygens of water
molecules in ice.
FIG. 10.23 Conformation of the winter flounder polypeptide docked on ice (surface 3). Dashed lines represent
hydrogen bonds. Winter flounder polypeptide is hydrogen bonded by four hydroxyl OH groups to oxygens of water
molecules in ice.
FIG. 10.24 Conformation of the winter flounder polypeptide docked on sI hydrate. Dashed lines in the polypeptide and the hydrate represent hydrogen bonds. Winter flounder polypeptide is not hydrogen bonded to water
molecules in hydrate.
Molecular modeling
259
FIG. 10.25 Conformation of the winter flounder polypeptide docked on sII hydrate. Dashed lines represent hydrogen bonds. Winter flounder polypeptide is hydrogen bonded by five carbonyl CO groups to hydrogens of
water molecules in hydrate.
be through adsorption of the polymer on the hydrate surface. VC-713 may work in solution
by restructuring of the bulk water and making it difficult for the water molecules to arrange
into the hydrate crystal. This alternative hypothesis was investigated in the second part of
the computer studies (Section “Studying of kinetic inhibitor interaction with water: Solvation
of the polymer in the bulk water”). Locations of adsorption sites of VC-713 have little or no
pattern. See Figs. 10.26 and 10.27.
Docking of PVP polymer gave results very similar to those for the winter flounder
polypeptide. An optimal fit of PVP on hydrate surfaces is energetically favorable (−5065
to −12,495 kcal/mol). PVP may be inhibiting hydrates through adsorption on any growth
site and changing the hydrate surface properties. Adsorption sites of PVP on sI hydrate
show the pattern in locations. See Figs. 10.28 and 10.29.
Docking of PVCap polymer produced results very similar to those of PVP. Low interaction
energies (−5057 to −12,504 kcal/mol) and presence of adsorption sites on sI can be seen.
See Figs. 10.30 and 10.31.
Fig. 10.32 shows separate macromolecules. Numbers in Fig. 10.32 show the distance between repeating groups which may participate in hydrogen bonding.
FIG. 10.26
Conformation of the VC-713 polymer docked on sI hydrate. Dashed lines represent hydrogen bonds.
VC-713 is hydrogen bonded by one carbonyl CO group to hydrogen of water molecule in hydrate.
FIG. 10.27 Conformation of the VC-713 polymer docked on sII hydrate. Dashed lines represent hydrogen bonds.
VC-713 is hydrogen bonded by one carbonyl CO group to hydrogen of water molecule in hydrate.
FIG. 10.28 Conformation of the PVP polymer docked on sI hydrate. Dashed lines in the hydrate lattice represent
hydrogen bonds. PVP is not hydrogen bonded water molecules in hydrate.
FIG. 10.29
Conformation of the PVP polymer docked on sII hydrate. Dashed lines represent hydrogen bonds.
PVP is hydrogen bonded by one carbonyl CO group to hydrogen of water molecule in hydrate.
FIG. 10.30 Conformation of the PVCap polymer docked on sI hydrate. Dashed lines in the hydrate lattice represent hydrogen bonds. PVCap is not hydrogen bonded to water molecules in hydrate.
Molecular modeling
261
FIG. 10.31
Conformation of the PVCap polymer docked on sII hydrate. Dashed lines in the hydrate lattice represent hydrogen bonds. PVCap is not hydrogen bonded to water molecules in hydrate.
FIG. 10.32 Examples of natural antifreeze polypeptide and of kinetic hydrate inhibitors.
Conclusions for docking study
Molecular mechanics was used for examining potential kinetic inhibitors' interaction with
ice or gas hydrate surface. Docking of the winter flounder polypeptide on three surfaces of
ice Ih and surfaces of sI and sII hydrates was performed. Adsorption energy is favorable.
Simulation provides some insight into the ice inhibition mechanism. Energies for VC-713
docking on water crystals are shown to be unfavorable. Long DMAEMA groups sterically
hinder the ability of a VC-713 polymer chain to lie flat on adsorption site. Results for the other
kinetic hydrate inhibitors PVP and PVCap are very similar to the results for winter flounder
262
10. Research methods in flow assurance
polypeptide. Docking may well be the mechanism of hydrate inhibition by these polymers.
However, there is a contradiction between the difference in performance of these polymers in
inhibiting hydrate formation and similarity of results of the docking study. This suggests that
a more detailed study of adsorption of inhibitors on hydrate in water solution is necessary.
Studying of kinetic inhibitor interaction with water: Solvation of the polymer
in the bulk water
Introduction
Structural changes in liquid water were investigated in the second part of the computer
studies of gas hydrate inhibition. This testing of the second kinetic hydrate inhibition mechanism hypothesis (destruction of structure in the bulk water) was performed using molecular
dynamics. Different polymers or their monomers were solvated in SPC water, depending on
the desired polymer concentration. Effects of each polymer on the structure of water was obtained by comparing it with the structure of pure SPC water at the same conditions.
The work was started with selecting the SPC water model for use after the comparison of
water models available in SYBYIT. Melting point of the SPC water model was fit to 200 K as
reported (Karim et al., 1990) by scaling of the electrostatic interactions. This was followed by
determination of the structure of water at 203 and 220 K (scaled 277 and 298 K). Simulation of
the polymer solutions and analysis of the structure of solvent concluded this work. Initially
the models of water available in SYBYL were verified by comparing the oxygen‑oxygen
radial distribution function of simulated and real water at 298 K, with results presented in
Fig. 10.33. The radial distribution function (RDF) measures local density as a function of distance. RDF can be viewed as the probability of finding a water molecule at a certain distance
from a particular water molecule. Integration of the area under the first peak represents the
number of the nearest neighbors. The best fits of simulation to data were obtained for the SPC
(simple point charge) and the TIP3p (transferable intermolecular potential 3 point) models.
Based on this result the SPC water model was selected. A comparison of oxygen- hydrogen
radial distribution functions for the SPC model and water was made. The oxygen-hydrogen
radial distribution function indicates the average length of hydrogen bonds in water through
the position of the first peak. A good comparison was obtained between the experimental
data (Soper and Phillips, 1986) and the simulation results (Fig. 10.34). This completed the
verification of the water model radial distribution function. The most interesting outcome of
this part of the work is that the kinetic inhibitors affect the structure of hydrogen bonded network of water molecules in such a way as to make hydrate formation more difficult. This was
discovered through the counting of rings in three dimensional hydrogen bonded network of
water in a fashion similar to that described by Rahman and Stillinger (1973). The structure of
water can be described as a network of hydrogen bonds connecting almost all water molecules, with only a small number of molecules free of the network. At higher temperatures, the
energy of hydrogen bonding (approximately 5 kcal/mol) is insufficient to keep the moving
water molecules together and the network of hydrogen bonds becomes very loose. As the
temperature decreases, water molecules vibrate less and a dense network of dynamic hydrogen bonds is formed. Hydrogen bonds in this network are arranged in rings which form
and rearrange with time. Rings sizes are measured in terms of the number of participating
water molecules. The most probable sizes of hydrogen bonded rings are 5 and 6. For a comparison, water molecules in ice (hexagonal Ih) are arranged exclusively as 6-membered rings,
Molecular modeling
263
FIG. 10.33 RDF oxygen‑oxygen for all water models available in SYBYL® compared with experiment.
which is determined by the molecular structure of water, which is in turn determined by the
electron cloud configuration. Rings of these sizes dominate the structure of water (Rahman
and Stillinger, 1973; Speedy et al., 1987). Water molecules usually participate in several rings
simultaneously. A schematic of the network of hydrogen bonds between water molecules is
shown in Fig. 10.35. Near the freezing point almost all water molecules are hydrogen bonded
to the common network. In order to form ice, all rings of a size other than 6 must rearrange
and form 6-membered rings. Since 5- and 6-membered rings are the most numerous in the
network, little rearrangement is required. At very fast cooling rates, though, the network does
not rearrange and water freezes into amorphous ice. This is a common outcome of attempts
at computer simulations of freezing the water. Similarly, substantial water structure is already
present before gas hydrate is formed. Dissolved guest molecules are driven into the lattice of
water molecules arranged mostly in 5- and 6-membered rings. It should be noted that 5- and
6- membered rings are the only ones present in the structure of gas hydrate. The aqueous
solutions of polymers used as gas hydrate inhibitors were simulated for VC-713, PVP, PVCap
264
10. Research methods in flow assurance
FIG. 10.34 Oxygen‑hydrogen radial distribution function for SPC water model simulation (this work)—solid
line, and experiment (Soper and Phillips, 1986)—line with circles.
and a prospective chemical ­polyvinyl cyanuric acid (PVCA). The structure of the new chemical is presented in Fig. 10.36. The last three inhibitors were simulated as single monomers
in order to match the <1.0% weight concentration used in real experiments, and to use effectively the computer resources. The number of 5- and 6-membered rings in the pure water
simulation were compared with those of aqueous polymer/monomer solutions. For the polymer/monomer solutions there was a dramatic decrease of the number of hydrogen bonded
rings in the water structure. It was hypothesized that this disappearance of hydrogen bonded
rings changes the water so that it cannot form gas hydrate without rearrangement of hydrogen bonds, which will require both energy and time. This is in a qualitative agreement with
the time dependent performance of kinetic inhibitors. There has been an experimental study
of the effectiveness of kinetic inhibitors monomers. This study indicated that monomers need
to be about 10 times more concentrated in water to inhibit hydrate growth as the polymer.
265
Molecular modeling
d
e
c
f
b
a
g
h
FIG. 10.35 Schematic hydrogen bonded network, updated from (Rahman and Stillinger, 1973). Polygon a-b-cd-e-f-g-h is short-circuited by the bond c-g and will not be counted in water structure. Two polygons a-b-c-g-h and
c-d-e-f-g will be counted instead.
FIG. 10.36 Structure of the proposed monomer.
266
10. Research methods in flow assurance
Verification of water models
In order to verify that water properties are represented adequately by the model, comparison of the three models available in SYBYL against the experimental data was done.
These models are SPC (simple point charge), TIP3p (transferable intermolecular potential
3 point charge) and the proprietary Tripos model. All these models are the three-center
models of water. Radial distribution function was chosen as the check parameters for the
comparison. Default parameters preset in SYBYIT were used for these simulations. These
include the 0.8 nm interaction cutoff and 10 nm Ewald summation of electrostatic interactions radii. All atoms in water molecules had partial charges on them. Charges for the SPC
and TIP3p models were set as the default ones, and for the Tripos model charges were set
equal to +0.41 on each hydrogen and − 0.82 on oxygen as in the SPC model. As the result
of this part, the SPC water model was chosen as the best to simulate the structure of real
water.
The importance of having charges on the atoms of water cannot be underestimated. A
run was performed by mistake for the Tripos water model without charges. A change of the
radial distribution function was very significant compared to the correct simulation and the
experimental data.
Procedure of water models verification
A lattice of 216 (6 × 6 × 6) water molecules was set up for each model with the density
of 1.0 g/cc. Periodic boundary conditions were applied. Charges on the SPC water molecules were set as precomputed (+0.41 on each hydrogen and −0.82 on oxygen). Values of
the charges are the fractions of the electron charge (4.8 × 10w esu). The physical significance of the charges in an electroneutral molecule is the distribution of an electron cloud
between the atoms of this molecule. In every simulation the system potential energy
was minimized prior to the run. Conjugate gradient minimization routine of SYBYLF
was used.
The initial part of each run was equilibration of the water in the periodic box. It consisted
of four stages:
(1) 1000 time steps in microcanonical NVE ensemble (constant number of particles N,
constant volume V, and constant energy E) to equilibrate kinetic and potential energies
of water and to melt the water lattice.
(2) 1000 time steps in canonical NTV ensemble (constant N, constant temperature T,
constant V) to set the temperature to 300 K.
(3) 1000 time steps in microcanonical NVE ensemble.
(4) The last part was the data collection part of 10,000 time steps in NVE ensemble. Each
time step equals 1 fs or 10−15 s. Default parameters preset in SYBYL’ were used for these
simulations.
Each simulation in this part used the previous starting velocities of atoms. This means that
the initial kinetic energy or the temperature of the system had to equilibrate from the initially
minimized value (effectively ~0 K). The implementation of molecular dynamics in SYBYL allows a choice of force fields (as it is also done in the SYBYL energy minimization facility) and
uses the Verlet (1967), also known as the Leapfrog method, for the integration of the equations
of motion. In each simulation the TRIPOS forcefield was used.
Molecular modeling
267
Analysis of the water structure for different models
After the runs were finished, an ASCII file with coordinates of particles in time was generated and processed by a Fortran program (see Computer Code section) to obtain the oxygen- oxygen radial distribution function (RDF). RDF is an indicator of density fluctuations of
system. RDF for three water models were compared against X-ray diffraction experimental
data (Narten and Lewy, 1971). Experimental data are available for water at a density (1.01 g/
cc) and temperature (298 K) which is close to the simulation conditions. Comparison shows
that SPC and TIP3p models are in good agreement with experiment whereas the Tripos model
doesn't represent the water structure very well.
Runs for SPC and TIP3p water were continued up to 50,000 fs (50,000 time steps for TIP3p
water and 76,923 time steps for SPC water). This difference is explained by 1 fs time step for
TIP3p model and 0.65 fs time step required for SPC water model. RDF for these runs were
generated and are presented in Figs. 10.37 and 10.38. After the SYBYL® implementation of
FIG. 10.37 RDF oxygen‑oxygen for TIP3p model and water at 298 K. ***, Narten and Lewy (1971), _ _ _ , this work.
268
10. Research methods in flow assurance
FIG. 10.38 RDF oxygen‑oxygen for SPC model and water at 298 K. ***, Narten and Lewy (1971), _ _ _, this work).
SPC model was proven to be adequate, a study of the melting point was performed. It was
determined that the ice lattice loses its structure (melts) at a temperature of 200 K (scaled
273 K) which is reported in the literature (Karim et al., 1990) when the dielectric function is
scaled by a factor of 1.535. The oxygen‑oxygen RDF for the SPC water model at 220 K (scaled
298 K) is shown in Fig. 10.39 to provide a better agreement with experimental data (Narten
and Lewy, 1971) and an excellent fit to the more recent neutron diffraction data (Soper and
Phillips, 1986). These comparisons indicate that SPC water model is a good representation of
the structural properties of the real water.
Hydrogen bonded network of water
Determination of the water hydrogen bonding structure
Water molecules are hydrogen bonded to each other and form a three-dimensional network of ring-like structures. An example of the water structure was shown in Fig. 10.35 as
first described by Rahman and Stillinger (1973). They used the ST2 four-point pair potential
Molecular modeling
269
FIG. 10.39 RDF oxygen‑oxygen for SPC model and water at 220 K (298 K scaled) with scaled dielectric function.
♦♦♦, Narten and Lewy (1971), _ _ _, this work).
water model to simulate liquid water at a temperature of 283 K and a density of 1.0 g/cm3.
They used the adaptation of the program written by Dr. Lester Guttman to enumerate the
distribution of hydrogen bond polygons. The results for water structure from their simulation
are shown in Fig. 10.40.
In order to process the results of SYBYL® simulations, a program for determining the hydrogen bond patterns in water was independently written in Pascal. This program allows to
determine the number distribution of H-bonded water molecules arranged in polygon ringlike structures. This program is very computationally intensive due to the multi-branch loop
algorithm of search and validation of hydrogen bonded polygons. The code is presented in
the Computer Code section. The search part consists of exhaustive search of the honeycomb-­
like hydrogen bonded patterns. When the pattern closes or comes to the starting point in
a certain number of steps (between 3 and 15), a 3- to 15-sided polygon is said to be found.
270
10. Research methods in flow assurance
Normalized number of
polygons per molecule
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10
11
Number of water molecules in hydrogen bonded polygon
FIG. 10.40 Distribution of hydrogen bonded polygons in water at 283 K (Rahman and Stillinger, 1973).
The validation part checks for the short circuits of other hydrogen bonds crossing the found
polygon. A visual explanation of short circuited polygons is presented in Fig. 10.35. If no
short circuits are found, a polygon is counted. Also this program checks for the “penetration”
polygons which go across the periodic boundary conditions implied in this search. Some of
such polygons do not close into a loop and are discarded. An example of a faulty polygon
may be a chain of hydrogen bonds going across the simulation box and crossing the periodic
boundary only once (shown in Fig. 10.41). Due to the limited number of water molecules allowed to form a hydrogen bonded ring, this periodic boundary penetration effect decreases
with the size of simulation box.
The program to count the hydrogen bonded polygons has been extensively tested and
shown to be valid. A relatively short program was written in Turbo Pascal in order to help
visually verify the validity of counted polygons. This program allows to see a projection of
each 3-dimensional hydrogen bonded ring pattern separately. An example of a valid pattern
crossing the boundaries of the simulation box is shown in Fig. 10.42. The faulty polygon pattern shown in Fig. 10.41 was drawn in Paintbrush for Windows, while the valid polygon is a
typical output of the visualization program.
Derivation of hydrogen bond connectivity
Data for the ring counting program was supplied from another program written in Fortran
which translates the SYBYL® simulation coordinate output file into a list of pairs of hydrogen
bonded molecules for a given time “snapshot”. Two water molecules were considered to be
Molecular modeling
271
FIG. 10.41 Example of an invalid hydrogen bonded polygon crossing the periodic boundary an odd number
of times.
FIG. 10.42 Example of a valid hydrogen bonded polygon crossing the periodic boundary an even number
of times.
272
10. Research methods in flow assurance
hydrogen bonded if the distance between oxygens was less then 0.35 nm and the hydrogen
bond (O-H-----O) angle was not <145°. These values differ from the arbitrary default values
of 0.285 nm and 120° and were selected as to accommodate two criteria discussed in each of
the following paragraphs.
The first criterion is to match the number of hydrogen bonds in real water at a temperature
of 298 K. The value from the literature is 89% of unbroken hydrogen bonds (Makogon, 1974,
1981) at this temperature. The number of nearest neighbors reported by Jorgensen et al. (1983) is
3.54 for the SPC model at these conditions. This can be translated into 88.5% hydrogen bonding
because a 100% hydrogen bonded water molecule (like in the ice lattice) has 4 nearest neighbors
or 4 hydrogen bonds. Results of the SYBYL® simulation at the same temperature with scaling
of the dielectric function produced the average value of 83.1% hydrogen b
­ onding. The number
of hydrogen bonds oscillated during the run to within ±4% of the average value.
The second criterion in selecting hydrogen bond parameters is to reduce the number of
hydrogen bonded trigons which are configurationally and energetically unfavorable. A study
was performed on dependence of the number of hydrogen bonds in simulated water as a
function of the allowed oxygen‑oxygen distance and hydrogen bond angle. The simulation
results are presented in Fig. 10.43. This plot shows the percentage of hydrogen bonds in ­water
depending on the hydrogen bond length and angle. Values of over 100% mean that water
molecules have more than four hydrogen bonds on average.
The size distribution of hydrogen bonded polygons in water oscillated in time, with examples of such oscillations shown in Fig. 10.44 for the final 10 model outputs (1500 timesteps
between each) of the run. This means that the structure of hydrogen bonded network is constantly changing.
Distribution of H bonding in water
140
120
100
80
% of H bonds 60
40
20
0
4
3.75
O-O Maximun Distance, A
3.5
3.25
3
2.75
2.5
2.25
2 170
165
160
155
150
120
O-H---O Angle,
degrees
FIG. 10.43 Percentage of unbroken hydrogen bonds in water as a function of OO distance and OH O angle.
A 100% value was assigned to the average of four shared hydrogen bonds per molecule. Values of over 100% mean
that water molecules have more than four hydrogen bonds on average.
273
Molecular modeling
Number of hydrogen
bonded rings
6
140
120
100
5
78
80
9
60
10
40
4
20
0
1
2
3
4
5
6
Time (90+n) ps
7
8
9
10
FIG. 10.44
Variation of the numbers of the hydrogen bonded polygons in water at model time 91–100 ps. Columns
in each histogram represent four- to ten-membered hydrogen bonded rings.
Results of hydrogen bonded water network study
A run was made to determine the distribution of hydrogen bonded rings in SPC water.
This simulation was run for 80,000 fs, including three 10,000 timesteps equilibration periods
in NVE, NTV and NVE ensembles without scaling of the dielectric constant. The simulation
box consisted of 318 SPC water molecules with the default charges on them. The water molecules geometries were restrained using the SHAKE algorithm which allowed the increased
time step size of 1 fs. All the subsequent simulations used the SHAKE algorithm. The results for the distribution of hydrogen bonded rings in SPC water at the temperature of 298 K
are shown in Fig. 10.45. It can be seen from this figure that the maximum size of hydrogen
bonded polygons is 14 for the used parameters. The important outcome of this calculation is
that the 5- and 6-membered rings dominate the structure of water. This result is similar to the
results from the study of water structure by Rahman and Stillinger (1973) which was shown
in Fig. 10.40.
It should be noticed that gas hydrates have only 5- and 6-membered rings in their ideal
lattice structure. This suggests that the larger part of the hydrogen bonded network of ­water
molecules is already present in the bulk of water. Hydrate formation only reorganizes it
somewhat around apolar molecules. Studying the effect of macromolecules in redistribution
of hydrogen bonded rings in water was the next step in this study.
274
10. Research methods in flow assurance
Normalized number
of hydrogen bonded rings
per molecule
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9 10 11 12 13
Number of water molecules in hydrogen bonded ring.
14
15
FIG. 10.45 Distribution of hydrogen bonded polygons in water at 298 K dominated by pentagons and hexagons.
Effect of macromolecules on the structure of water
Several polymers are known to be gas hydrate formation inhibitors. When certain polymers are introduced into water, hydrate formation is deferred for some time on the scale of
minutes to hours. The testing of the hypotheses for the mechanism of inhibition is a topic of
this section.
The first hypothesis was the docking of polymer chains on the growth sites of hydrate.
This presumes the irreversible adsorption as in the case of winter flounder polypeptide.
The other mechanism can be sought as change of the water structure by the polymer away
from that favoring hydrate formation (i.e., decreasing the number of 5- and 6-membered rings
in water). This hypothesis can fit into the kinetic nature of inhibition since water molecules
can reorganize with time back to an abundance of 5- and 6-membered polygons. A number of
simulations was run to test the second hypothesis. The main outcome of this part of research
is that the relative computer simulation performance of inhibitors is in accord with the real
experiments. In addition a new inhibitor was designed via computer which outperformed
PVCap by nearly a factor of two.
Effect of VC-713 Inhibitor
A 9 repeat unit, 28 monomer chain of VC-713 polymer composed of 596 atoms was solvated
in 827 SPC water molecules. Initial conformation of the polymer was the same as shown in
Fig. 10.32. Atoms of the polymer did not have charges on them. Charges on the atoms of ­water
275
Molecular modeling
molecules were standard for the SPC model. The whole system was electroneutral. Scaling of
the dielectric function was not used in this run in order to match the conditions of the pure
water simulation at 300 K. The potential energy of the whole system was minimized using
the Conjugate Gradient method. The simulation run included the equilibration for 10,000 fs in
microcanonical ensemble (NVE), 10,000 fs in canonical ensemble (NTV) to set the temperature
to 300 K, and 10,000 fs (NVE) steps. The data collection was made for the subsequent 90,000 fs
of the run in NVE ensemble.
Analysis of the ten final timesteps data was performed. Distribution of the hydrogen
bonded rings in the VC-713 in water solution is given in Table 10.10 along with that for the
pure water at the same conditions. Fig. 10.46 shows the distribution of hydrogen bonded
polygons for the VC-713 in water solution. An overall decrease in the number of hydrogen
bonded rings in the VC-713 solution was 25% compared to pure water.
Effect of PVP inhibitor
High pressure experiments in the CSM hydrate lab use low concentrations of polymers.
For the comparability of results it was decided to use a similar polymer concentration in
computer simulations. A single monomer of PVP was solvated in 907 water molecules to
produce the concentration of 0.7 wt%. Atoms in the monomer had the charges computed
TABLE 10.10 Normalized number of hydrogen bonded
polygons for VC-713 and water.
H bonded
VC-713
Water
Polygon size
T = 298 K
T = 298 K
1
0
0
2
0
0
3
0
0
4
0.032044
0.034591
5
0.193471
0.251572
6
0.23942
0.257862
7
0.137243
0.144654
8
0.061669
0.059748
9
0.045345
0.044025
10
0.03023
0.056604
11
0.050314
12
0.037736
13
0.040881
14
0.009434
15
0
Temperatures in the table indicate the simulation values.
276
10. Research methods in flow assurance
Normalized number
of hydrogen bonded rings
per molecule
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
Number of water molecules in hydrogen bonded ring.
10
FIG. 10.46 Distribution of hydrogen bonded polygons in water + VC-713 solution at 298 K.
by the Pullman method. Water molecules had the standard SPC charges. In this simulation
the dielectric function was scaled by a factor of 1.535. Simulation temperature of 203 K is
equivalent to 277 K, the temperature being used in real experiments. Potential energy of the
system was minimized. Simulation was run in an NVT ensemble for 100,000 fs. Number of
hydrogen bonded rings was oscillating in a fashion similar to the pure water. The values of
hydrogen bonded ring distributions averaged over the last ten timesteps of the run are given
in Table 10.11. The total number of hydrogen bonded polygons in PVP solution increased by
1% compared to pure water. The number of hydrogen bonds was oscillating about the average value of 87% bonding within ±2%.
A separate run was made with 318 SPC water molecules in order to obtain the distribution
of hydrogen bonded polygons sizes at a temperature of 203 K (equivalent to 277 K). The number of polygons increased by 15% compared to the 298 K pure water run. Results for the run
presented in Table 10.11 show that the number of hydrogen bonds averaged to 87.2% ± 2%.
A shell of irregularly hydrogen bonded water molecules was found to encage the PVP
monomer. Experimental evidence for the formation of a solvation shell around PVP side
groups is available from several sources (Johari, 1990; Maeda et al., 1993). Three water molecules were hydrogen bonded to the carbonyl oxygen of the inhibitor. This fact shows that PVP
is a local hydrogen bond maker.
277
Molecular modeling
TABLE 10.11 Normalized number of hydrogen bonded polygons for pure water and water + polymer
solutions.
H bonded
polygon size
PVP T = 277 K
PVCap T = 277 K
PVCA T = 277 K
Water T = 298 K
Water T = 277 K
1
0
0
0
0
0
2
0
0
0
0
0
3
0.000331
0.000539
0.000236
0
0.000629
4
0.040684
0.038814
0.029222
0.036164
0.045912
5
0.199338
0.150045
0.119089
0.158176
0.193082
6
0.248732
0.197574
0.144619
0.182075
0.253774
7
0.178611
0.133603
0.115397
0.139937
0.184277
8
0.122933
0.094519
0.086174
0.116038
0.110063
9
0.093275
0.074124
0.059544
0.083019
0.083019
10
0.059757
0.045553
0.04077
0.073899
0.062264
Total
0.94366
0.734771
0.595051
0.789308
0.933019
Temperatures in the table indicate the values scaled to natural values with respect to the ice melting point.
Effect of PVCap Inhibitor
For comparability of results, the same weight concentration of polymer (0.7%) was used.
A single monomer of PVCap was solvated in 1113 water molecules to produce the desired
concentration. Atoms in the monomer had the charges computed by the Pullman method
and SPC water molecules were used. In this simulation the dielectric function was scaled by
a factor of 1.535. The simulation temperature was set to 203 K (equivalent to 277 K) and the
potential energy of the system was minimized. Simulation was run in an NVT ensemble for
100,000 fs. The number of hydrogen bonded rings oscillated slightly in a fashion similar to
the pure water. The values of hydrogen bonded ring distributions averaged over the last ten
timesteps of the run were given in Table 10.11. The total number of hydrogen bonded polygons in PVCap solution decreased significantly; 21% less polygons were counted compared
to pure water. The number of hydrogen bonds oscillated about the average value of 87%
bonding within ±2%. A shell of irregularly hydrogen bonded water molecules was found
around the PVCap monomer, similar to PVP. Only one water molecule was hydrogen bonded
to the carbonyl oxygen of the inhibitor. PVCap is not a strong hydrogen bond maker, probably, due to its larger size compared to PVP and larger steric hindrance for water molecules to
hydrogen bond.
Effect of PVCA Inhibitor
A new monomer was proposed based on studying the features of hydrate inhibitors. It
was decided that the carbonyl group included in a ring structure next to the nitrogen atom
is the active group of the polymer. Nitrogen plays the role of electronegativity enhancer for
the oxygen of a carbonyl group. Increasing the number of the carbonyl groups in a monomer
278
10. Research methods in flow assurance
ring should enhance the inhibiting properties of the polymer. The name PVCA in the title of
this paragraph stands for poly(vinyl cyanuric acid) because the structure of the proposed
monomer is close to the structure of cyanuric acid. Structure of the proposed monomer was
shown in Fig. 10.36.
For the comparability of results, the same weight concentration of polymer of 0.7% was
used. A single monomer of PVCA was solvated in 1273 water molecules to produce the
desired concentration. Atoms in the monomer had the charges computed by the Pullman
method and SPC water molecules were used. In this simulation the dielectric function was
scaled by a factor of 1.535. Simulation temperature was set to 203 K (equivalent to 277 K) and
the potential energy of the system was minimized. The simulation was run in an NVT ensemble for 100,000 fs.
The number of hydrogen bonded rings oscillated in a fashion similar to the pure water. The
values of hydrogen bonded ring distributions averaged over the last ten timesteps of the run
were given in Table 10.11. The total number of hydrogen bonded polygons in PVCA solution
decreased by 36.2% compared to pure water at the same conditions. The number of hydrogen
bonds was oscillating about the average value of 86.7% bonding within ±3%.
A shell of irregularly hydrogen bonded water molecules was found around the PVCA
monomer, similarly to PVP and PVCap. Four water molecules were hydrogen bonded to the
three carbonyl oxygens of the inhibitor. PVCA is a rather strong local hydrogen bond maker,
since it has three times as many active carbonyl groups as other inhibitors. On an overall basis, a slight decrease in the number of hydrogen bonds was noticed.
Overview of inhibitor simulation
A novel method of analyzing the structure of water was used in this research. The performance of simulated hydrate inhibitors was similar to performance in physical experiments,
thus showing the validity of computer simulation as a tool for designing new chemicals.
The following suggestions can be made based on this study. A common feature shared by
all these polymers is a presence of a lactam ring in side groups. The group common to all
lactam rings is the >CO (carbonyl) group. The high electronegativity of the carbonyl oxygen may affect the surrounding water molecules and disrupt the hydrogen bonded network
between them.
In order to increase the inhibiting effect of the polymer, the number of carbonyl groups can
be increased. The nitrogen atom present in the lactam ring next to the carbonyl group plays an
important role of enhancing the charge on oxygen. If nitrogen in the lactam ring is replaced by
CH, the negative charge on the carbonyl oxygen calculated in SYBYL® increases from −0.388
to −0.349, an 11% change. If a second nitrogen atom is introduced into the lactam ring next
to the carbonyl group, the negative charge on oxygen decreases to −0.418. These calculations
were made using SYBYL® by building the polymer structure and letting the program assign
charges to the atoms using Pullman method (Berthod and Pullman, 1965).
Irregularly hydrogen bonded water molecules were found to form a solvation shell around
the inhibitor molecules. Some of the water molecules were hydrogen bonded to the carbonyl
oxygen. Three water molecules were found hydrogen bonded to the oxygen of PVP in the final timestep of the simulation. One water molecule was hydrogen bonded to PVCap oxygen.
Four water molecules were hydrogen bonded to PVCA having three carbonyl groups on the
ring. The diameter of the solvation shell around the inhibitor is the van der Waals diameter of
the polymer groups plus van der Waals diameter of hydrogen in water. No apparent structure
was noticed in these solvation shells.
279
Molecular modeling
Normalized number
of hydrogen bonded rings
per molecule
Normalized number of H bonded rings
0.3
0.25
SPC water T=203 (scaled 4C)
PVP monomer in SPC water
0.2
PVcap monomer in SPC water
PVCA monomer in SPC water
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10
Number of water molecules in H bonded ring
Number of water molecules in Hydrogen bonded ring.
FIG. 10.47
temperature.
Comparison of inhibitors' performance in altering the water structure at +4 °C scaled model
Fig. 10.47 shows the distributions of hydrogen bonded polygons on the same plot for ­water,
PVP, PVCap and the new proposed inhibitor PVCA. PVCA shows the largest decrease in the
number of hydrogen bonded polygons. It is expected to be a good gas hydrate inhibitor.
Summary of computer modeling
It was determined that SPC and TIP3p models for water incorporated in SYBYL® give adequate representation of the structural properties of water. Simulation results for the structure
of water compare well with previous data.
Docking studies of the hydrate inhibitors showed that PVP and PVCap will be able to adsorb on the hydrate surfaces, whereas VC-713 will not due to the very high interaction energy.
Similarity of the docking results for PVP and PVCap and the difference in real life performance may be explained by very similar structure of these polymers with only difference in
the side group ring size. The difference in real performance also may suggest that docking is
not the inhibition mechanism for at least one of these polymers.
Molecular dynamics simulation for kinetic inhibitors effects on water structure mirror the
experimental results. PVP is shown to have a weaker effect on the structure of water than
PVCap, VC-713 and PVCA. The largest decrease in the number of hydrate-favoring 5- and
6-membered rings was obtained with the newly proposed chemical, PVCA. The tools for
analyzing the structure of water were used successfully to predict the possible new hydrate
inhibitor.
280
10. Research methods in flow assurance
Summary of the experimental and computer model work
The first part of the work was experimental. A question about the possibility of the phase
transition of methane hydrate was solved negatively. The second part was also experimental. The study of xenon sI and xenon + neohexane sH hydrates was done. A quintuple
point sH-sI-Lw-Lh-V was shown to occur in the temperature interval around 281.5 K in
xenon + neohexane system.
The last part of the work was performed on the IBM RS-6000 model 550 computer with
128 Mb RAM using the SYBYL 6.01 software. Docking of macromolecules on hydrate and ice
surfaces showed that Winter Flounder polypeptide, PVP and PVCap chains may adsorb on
ice and hydrates, whereas VC-713 may not. SPC water model was adequately representing
the structural and thermodynamic properties of the real water. Study of the influence of gas
hydrate inhibitors on the structural properties of water allowed to propose a new kinetic hydrate inhibitor. A hypothetical explanation of the hydrate inhibition mechanism was stated.
Experimental and computer study of the effect of kinetic inhibitors on
clathrate hydrates
This part of research work consists of an experimental and theoretical investigation of
interaction between clathrate hydrates and kinetic inhibitors. There is experimental and computational evidence in support of the hypothesis that kinetic inhibitors act by adsorbing with
their side groups inside or near the incomplete large cavities on a hydrate surface and block
adsorption of guest molecules into hydrate cavities.
Experiments showed that single crystals of THF hydrate grew as octahedra with {111} crystallographic faces. A change in morphology of a THF hydrate crystal was observed upon addition of a hydrate inhibitor whereupon an octahedral crystal became planar with {111} faces
due to inhibitor adsorption on hydrate.
Computer modeling of inhibitor adsorption on the hydrate surface showed that polymers
strongly adsorb in a flat (train) conformation at the periphery of large open hydrate cavities.
Adsorbed polymers inhibit adsorption of guest molecules at the growing hydrate surface.
The computer was used to design more effective hydrate inhibitors.
The pressure and temperature at which hydrate forms determine the ratio of guest molecules to water molecules. Generally, hydrate formation is favored at high pressures and at
low temperatures, and the water-guest ratio is close to 6.
The first documented formation of clathrate hydrate dates about 200 years back when
SO2 hydrates (Priestley, 1790) and Cl2 hydrates (Davy, 1811) were formed. However, only the
growth of gas and oil industry caused hydrates to gain industrial importance when they were
found to plug natural gas pipelines (Hammerschmidt, 1934).
The molecules which form clathrates range in size from hydrogen (Vos et al., 1993) to ethylcyclohexane (Thomas and Behar, 1994). Sizes of these molecules are estimated as 3.0 and
9.7 Å, respectively. The highest pressures for which hydrate formation data were reported
are 2 GPa for nitrogen (van Hinsberg et al., 1993), 30 GPa for hydrogen (Vos et al., 1993), and
1.5 GPa for argon and krypton (Dyadin et al., 1996).
Currently, the main task at hand is to understand the formation of gas hydrates and to
be able to prevent their formation and promote their decomposition in industrial facilities.
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
281
The importance of studying and improving methods for hydrate inhibition is great. The
annual cost of hydrate prevention in gas and oil production through methanol injection
alone is over $500,000,000 (Sloan, 1996a). A 1988 accident which may have resulted from
hydrate formation at the Piper Alpha platform in the North Sea cost 167 people's lives and
£3.3 billion in damage and losses (Cullen, 1990; Lovegrove, 1990).
Existence of gas hydrates in nature was proven in 1965 (Makogon, 1965).1 Natural gas
production from the Messoyakh a hydrate deposit in Siberia started in 1969 (Makogon, 1981,
2010). Currently, Japan, China and other countries are considering the possibility of producing natural gas from their offshore in-situ deposits of gas hydrates. Hydrates can store a tremendous amount of gas. Over 170 volumes of gas at standard T, P can be enclathrated by one
volume of ­water. The reserve of carbon in gas hydrate deposits was estimated to be twice that
in all other fossil fuel deposits (Makogon, 1982; Kvenvolden, 1994). These resources can be
recovered worldwide once economic methods of production have been developed. The map
in Fig. 10.48 compiled from maps by Kvenvolden (1988, 1994) shows the locations of hydrate
deposits on earth. Hydrates are situated in offshore regions under the sea where hydrostatic
pressure of water provides hydrate stability, and in permafrost regions where low temperatures stabilize hydrates.
FIG. 10.48 Hydrate locations in the world.
1
Hereinafter references (Makogon) are due to Dr. Yuri F. Makogon. Taras Makogon's works are denoted
(T.Y. Makogon).
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10. Research methods in flow assurance
Environmental aspect of gas hydrates is related to the greenhouse effect of methane and
carbon dioxide. Hydrates of these two gases can exist on earth at subsea T, P. If a temperature of the sea bottom increases above methane hydrate stability limit, it causes hydrate to
release methane. Methane has a greenhouse effect which is 21 times stronger than that of carbon dioxide (Englezos, 1993a). As more methane is released, the greenhouse effect increases
temperature further which may cause a runaway global warming (Leggett, 1990). The 1996
Conference in Brussels on the Global Environment has reiterated that natural hydrates of
methane can contribute to a greenhouse effect (Sloan, 1996b).
Offshore gas hydrate deposits may release natural gas if the sea water temperature at the
bottom rises above hydrate stability limit. It was shown that a model ship floating on a water
will sink if the water becomes foam because of the natural gas bubbles released from decomposing hydrate (Makogon, 1996a,b). A series of photographs in Fig. 10.49 shows such a
process. In the image 1 the ship is floating on the water. In image 2 the gas starts to rise from
a system of pipes on the bottom of the pool simulating natural gas discharge. The ship is
still afloat. In image 3 the ship has sunk. The ship model is 2 m long. Ocean can be in contact
with gas hydrate (Makogon, 1982) which may release gas upon dissociation as shown further
(Fig. 10.50).
Existence of gas hydrates in space is reasonable to expect at low temperatures. It was proposed that the core of the Halley's comet consists of clathrate hydrate when an anomalous
behavior of eruptions was observed at the surface of the comet (Makogon, 1987).
Three forms of clathrate hydrates which are studied the most in the western hemisphere
are known as structure I (sI), structure II (sII) and structure H (sH). All these hydrates contain
a common basic “building block” water cavity—the 512 cavity which has 12 pentagonal faces.
The 512 cavity is composed of 20 water molecules held together by hydrogen bonds.
Hydrogen bonding is weaker than chemical bonding. The magnitude of hydrogen bonds
is about 5 kcal/mol (Sloan, 1990) for bonding between water molecules, which is weak compared to hundreds of kcals/mol for covalent bonds. However, in the laboratory it is important
to remember that hydrogen bonds are stronger than van der Waals bonds. Organic solvents
containing chlorine atoms, like chloroform, can hydrogen bond to compounds containing
carbonyl groups, like acetone, in a fairly exothermic reaction which can heat the system to
spontaneous combustion.
Properties of hydrates as solids are not very different from those of ice. The specific volume
of water increases by 26% upon transition to a hydrate phase, while such an increase for ice
is only 9%. The specific volume of gas changes in such transition by several orders of magnitude. The electric conductivity of hydrate is lower than that of the initial solution. The sonic
velocity in hydrate is 60–100% higher than that in gas saturated rock (Makogon, 1985). These
properties of gas hydrates provide effective means for surveying gas hydrate deposits.
Several applications for gas hydrates described earlier (Makogon, 1981, 1985; John et al.,
1994) are based on the change of properties of hydrate forming gases in the hydrate state. Gas
molecules are packed much closer together in hydrate than in gaseous state.
Storage and main-line transportation of natural gas in the hydrate state may be profitable
in some regions of the world (Makogon, 1970; Smirnov and Dyachenko, 1989; Gudmundsson
and Borrehaug, 1996). The original idea belongs to Mr. Kalina (Makogon, 1996a) A method
of container and briquette transportation of gas in hydrate state from Siberia to Europe was
ruled out because it required a rate of hydrate formation of 11 m3 of solid hydrate per second.
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
FIG. 10.49 Ship sinking in a foam caused by decomposed hydrates. Courtesy of Yuri Makogon, OTRC.
283
284
10. Research methods in flow assurance
Depth (km)
Ocean
1
2
4
1
Hydrate
3
5
6
7
2
Hydrocarbon
migration routes
75°
70°
65°
60°
North latitude
FIG. 10.50
Relation between the Arctic Ocean and hydrate zone: (1) ocean; (2) cryolite; (3) hydrate formation
zone; (4) gas; (5) hydrocarbons; (6) hydrocarbon source; (7) hydrocarbon migration (Makogon, 1982).
Only molecules of a particular size can form clathrate hydrate. Also different compounds
have different conditions of hydrate formation. Separation techniques such as water enrichment with D2O use these properties of hydrates (Makogon, 1985).
Hydrates consume heat during decomposition. This suggested their use in a cold-storage
process (Mori and Mori, 1989; Mori, 1995). Currently, this process has been used to cool air
at one of the Tokyo subway stations (Sloan, 1996c). Many more aspects of clathrate hydrates
such as molecular structures, phase equilibria, kinetics, statistical thermodynamics, omitted
here, are described in detail in the monograph by Sloan (1990).
Crystallographic information about hydrates
The three common forms of clathrate hydrates known as structure I (sI), structure II (sII)
and structure H (sH) are shown in Fig. 10.51. Structures I and II are cubic crystals. sI hydrate
is a Pm3n body-centered cubic structure with a 12 Å unit cell size. Its unit cell is formed as a
result of the linkage of faces of two dodecahedral cavities (512) with interstices composed of
six large 51262 cavities which have twelve pentagonal and two hexagonal faces.
Structure II hydrate is a Fd3m face centered cubic diamondoid structure with a 17.1 Å
unit cell size. Its unit cell is formed as a result of the linkage of faces of sixteen dodecahedral cavities (512) with interstices composed of eight large 51264 cavities which have twelve
pentagonal and four hexagonal faces. Generally, small molecules like methane form sI
hydrates while larger molecules like propane form sII hydrates with the exception of the
smallest hydrate formers like argon and krypton which also form sII hydrates. The monograph by Sloan (1990) provides a comprehensive review of these conventional hydrate
structures.
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
285
FIG. 10.51 Common clathrate cavities and hydrates of structure I, structure II and structure H.
Structure H hexagonal hydrate (sH) was discovered by Ripmeester et al. (1987) as a double
hydrate - it required two kinds of molecules to be stable: a small molecule like xenon or methane and a larger molecule like methylcyclohexane. sH hydrate is composed of three different
types of cages: the 512 cage which is common to sI and sII hydrates, a small 435663 cage which
has three square faces, six pentagonal, and three hexagonal faces, and a large 51268 cage with
twelve pentagonal and eight hexagonal faces. Ripmeester and Ratcliffe (1990) used X-ray
powder diffraction and NMR techniques to determine 24 molecules ranging in size from 7.5
to 8.6 Å which were enclathrated in sH hydrate along with smaller guests (xenon or hydrogen sulfide). The identified guest molecules include methyl substituted alkanes and cycloalkanes, many of which are known to be present in petroleum and are also found in significant
amounts in crude oil reservoirs.
The first phase equilibrium data on sH were reported from CSM laboratory by Lederhos
et al. (1992), which also represents the first instance of methane in the smaller sH cavities. sH
hydrates had been previously formed, but not recognized as sH hydrate by Palmer (1950) and
in the Kobayashi hydrate research group. Recently, an extensive set of sH hydrate equilibrium measurements for the binary systems of large sH forming hydrocarbons with methane
was compiled in CSM hydrate lab by Mehta (1996). His work also has two data sets in which
the small sH guest molecules were nitrogen and xenon.
286
10. Research methods in flow assurance
Hydrate crystal growth
It is difficult to study the growth of the natural gas hydrate crystals, both because pressures
above atmospheric are required and because the hydrocarbon “guest” molecules are sparingly soluble in water, so that crystallization occurs mainly at the gas-liquid interface (Long,
1994). It is more convenient to use tetrahydrofuran (THF) as a hydrate former because it is
completely miscible in water. Clathrate hydrates of THF melt at 4.38 °C at atmospheric pressure (Erva, 1956). The THF hydrate is known to have a cubic structure (face-centered cubic,
diamondoid) (Palmer, 1950) and is classified as a structure II hydrate (Mak and McMullan,
1965). There are no published data about the shape of single THF hydrate crystals. A study of
shape of the negative crystals of THF hydrates (McLaurin and Whalley, 1988) showed that the
voids melted in a THF hydrate had an octahedral shape.
A phase diagram of aqueous THF solution (Fig. 10.52) indicates that the THF hydrate has
the highest melting temperature of about 4.4 °C at the composition of about 80 wt% water
and 20 wt% THF. This composition corresponds to the molar composition of the THF hydrate where every mole of THF is enclathrated by 17 mol of water. The eutectic point where
two solid phases coexist is at −1.0 °C and 0.9 wt% THF (Erva, 1956). Another hydrate former
­having a hydrate melting temperature above the ice point at atmospheric pressure is ethylene
FIG. 10.52 Phase diagram of aqueous THF solution.
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
287
oxide (11.1 °C (Glew and Rath, 1966) which forms sI. H2S forms sII hydrate at 0.5°C (Ward
et al., 2015) at atmospheric pressure.
A study of natural gas hydrate crystals growth for sI, sII and sH was recently performed
by Smelik and King (1997). In their work crystals of methane hydrate (sI), methane + propane
hydrate (sII), and methane + methylcyclopentane hydrate (sH) were grown in a visual reactor
under pressure. Structure I crystals generally exhibited {110} and in some cases {100} faces.
Structure II crystals grew as octahedra exhibiting {111} faces. Structure H crystals grew as
hexagonal prisms with {001}, {110}, and {120} faces.
Similar work on the growth of the cubic type crystals of pyrite was performed by
Murowchick and Barnes (1987). They studied the effects of temperature and degree of supersaturation on morphology of pyrite crystals. Two types of crystal growth were observed:
surface-­controlled growth when the rate of growth is limited by the rate at which components are incorporated into the growing surface, and the diffusion-controlled growth when
the growth rate is limited by the rate at which nutrient components diffuse to the surface.
Growing faces of the crystals were smooth in the surface-controlled regime, when the nutrients were equally available to faces, edges and vertices of the crystal. In the diffusion-­
controlled case protrusions such as vertices and edges were in contact with a nutrient-­richer
solution. Growth at the end of protrusions was favored over growth on the flat surface. Such
a mechanism resulted in striated and dendritic growth.
Inhibition of hydrate formation
Hydrates of natural gas can plug flow channels (wells and pipelines) during production
of natural gas. There are four classical methods for preventing hydrate formation in a system
containing a hydrocarbon gas: increasing temperature of the system, decreasing system pressure, removing water from the system, or adding inhibitors of hydrate formation.
“Thermodynamic” hydrate inhibitors such as alcohols, glycols or salt are commonly used
to avoid hydrate formation in gas and oil industry for systems where dehydration or heating
are impossible or not economic. Such inhibitors shift the thermodynamic stability boundary
of hydrates to higher pressure or lower temperature by aggregating with water molecules
and preventing their arrangement into a hydrate lattice (Sloan, 1990). This method is not always the best environmental or economic solution for preventing hydrate plugs.
Recently, the CSM Center for Hydrate Research proposed an alternative method of inhibiting gas hydrates. It was found that certain polymers, when added to water, will delay the
conversion of gas and water into hydrate. The induction time for the onset of hydrate formation is generally unpredictable, or stochastic at fixed conditions. The same stochastic behavior
is observed for the onset of freezing in a pure water system seeded with AgI crystals (Barlow
and Haymet, 1995). However, the hydrate induction time is a function of supersaturation or
pressure (Herri et al., 1996).
Numerous researchers have reported that additives affect the crystal morphology. Michaels
and Colville (1960) reported that surfactants inhibit certain faces of adipic acid crystals growing from aqueous solution. Cationic surfactants caused greater reduction in the growth rate of
{010} and {110} faces. Anionic surfactants had such effect on the {001} face. These effects were
related to the hydroxyl density on the crystal faces.
288
10. Research methods in flow assurance
Knight and coworkers have reported inhibition of ice growth by an antifreeze glycopeptide biomolecule which adsorbs in certain orientations on ice crystals (Knight et al., 1991,
1993). The ice crystallization rate in presence of such glycopeptides is up to five times greater
than in pure water (Harrison et al., 1987).
Bromley et al. (1993) has reported that diphosphonates caused morphology change in
barite crystals. L-leucine was documented to adsorb on glycine crystals and to inhibit their
growth (Li et al., 1994). Chen et al. (1994) has studied the adsorption of additives on chloronitrobenzene crystals. He found that the crystal morphology was modified. In general, it can be
stated that certain additives adsorb on growing crystals and block crystal growth.
The so-called “kinetic” inhibitors do not always inhibit hydrate formation completely, as
thermodynamic inhibitors do. However, kinetic inhibitors can delay the formation of hydrate
for a period longer than the residence time of the water phase in a pipeline. Kinetic inhibition
is currently applied in petroleum industry together with thermodynamic inhibitors to delay
hydrate formation in wells and in pipelines (Lederhos et al., 1996). Bloys and Lacey (1995)
reported successful KHI application to a production system with residence time of 120 h or
5 days.
Several successful kinetic inhibitors were found by an extensive screening of the commercially available chemicals (Long et al., 1994; Lederhos, 1996). Over 1500 chemicals were
tested for their effectiveness of hydrate inhibition in a THF screening apparatus. If a chemical
inhibited hydrate growth in the THF screening apparatus, it was then tested in a high pressure apparatus with natural gas. Delay time before visible hydrate formation was determined
as the effectiveness of hydrate inhibition was measured at 0 °C, which is 4.4 K lower than
the equilibrium temperature of THF hydrate melting at atmospheric pressure. The relative
performance of several inhibitors in terms of natural gas consumption versus time in a high
pressure apparatus is presented in Fig. 10.53. While the initial rate of hydrates formation is
high, the overall conversion rate is lowered by inhibitors.
O

Generally, kinetic inhibitors are polymer molecules having an amide ( C N) linkage
in their side groups. Both poly-N-vinyl pyrrolidone (PVP) and poly-N-vinyl caprolactam
(PVCap) shown in Fig. 10.54 have rings of carbon atoms as their side groups. It was determined that the ring structure is not imperative to an effective inhibitor. A kinetic inhibitor
poly(N,N-diethyl acrylamide) (PNNDEAM) differs from PVP by position of the carbonyl
(CO) group and by the absence of a covalent bond between the two carbons opposite from
the nitrogen atom in the pyrrolidone ring. Hydrogen bonding ability is a necessary but not a
sufficient property of a kinetic inhibitor. Poly(vinyl alcohol) (PVA) has a hydrogen bonding
capability with the hydroxyl (OH) group; however, it is not a hydrate inhibitor.
One successful inhibitor is VC-713, a copolymer of about 30% vinyl-pyrrolidone, as in
PVP; 60% of vinyl-caprolactam, as in PVCap, and about 10% of dimethylaminoethylmethacrylate (DMAEMA). The composition of this copolymer indicated the study of copolymer
of PVP and PVCap monomers in order to improve the kinetic inhibitor's performance. With
50% caprolactam +50% pyrrolidone this copolymer provided a larger hydrate formation
than PVCap or VC-713 alone, but with 75% caprolactam +25% pyrrolidone the copolymer
performed like PVCap (Figures 40, 41 in the Center for Hydrate Research Report) (Annual
Report, 1993).
Gas Consumption (gmol)
0.6
0.5 wt% Polymer + 3.5 wt% Sea Salt,
P=1000 psig, and T=39.2 F
0.5
Sea Water
0.4
0.3
PNNDMAM
0.2
PNEAM
PVCAP(BASF,92K)
0.1
VC-713(70K)
0.0
0
400
800
1200
Time (min)
FIG. 10.53 Natural gas consumption due to hydrate formation with different kinetic inhibitors.
FIG. 10.54 Monomers of some of the studied chemicals (PVP, PVCap and PVA).
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10. Research methods in flow assurance
Computer modeling of hydrates: Solid solution models
An extensive review of the effort of the hydrate computational community was presented
by Tse at the First Conference on Natural Gas Hydrates in the New York Academy of Sciences
in 1993 (Tse, 1994). He emphasized the success of the van der Waals and Platteeuw solid
solution model (van der Waals and Platteeuw, 1959) in describing the stability of clathrate
hydrates. That model uses statistical thermodynamics and Langmiur adsorption theory to
calculate the adsorption of guest molecules in hydrate cavities assumed to be spherical. The
model is used to predict temperature and pressure of hydrate stability based on empirical
Langmiur constants.
The spherical cell approximation used in the original model can be replaced by localized
water sites (Tester et al., 1972). Tse stated that the dissociation pressure and guest occupancy
calculated with this method for several clathrate hydrates are similar to those calculated with
the spherical cell approximation. Rodger (1989) discussed the possibility of including the
effects of hydrate lattice thermal motion on the small cavity potential in sI in the model of
cavity-guest interactions.
Potential models
Proper choice of the potential model determines the success of a simulation. TIP4P
(Jorgensen et al., 1983) and SPC (Berendsen et al., 1981) potentials for water are the most
accurate in predicting such properties of liquid water as density, structure (in terms of radial
distribution functions), and intermolecular energy (Jorgensen et al., 1983). These models are
comparable to or better than other models in predicting heat of vaporization, heat capacity,
thermal expansivity, and isothermal compressibility of liquid water.
The TIP4P and SPC models predict dielectric relaxation times, which is a measure of the
hydrogen-bond rearrangement dynamics, of 6.3 and 11 ps (Ohmine and Tanaka, 1993) which
compare favorably with the experimental value of 8–9 ps (Bertolini et al., 1982).
Water molecules show the strongest preference for participation in 4 hydrogen bonds in
the ST2 (Stillinger and Rahman, 1974) potential model which uses a tetrahedral charge distribution. Radial distribution function for this potential shows the greater structure than for the
potentials with 3-point charge distributions.
Recently, a new potential model (Kumagai et al., 1994) was developed for water in
clathrate hydrates which includes 2-body guest-guest, host-host and guest-host interactions and 3-body intramolecular host interactions. This potential is being used with
some success in Japan to model hydrates (Itoh et al., 1996). However, this potential model
does not explicitly include the hydrogen bonding host-host or guest-host interactions.
The long-range attractive part of the potential is represented by Coulombic charge-charge
attraction.
Structures of liquid water and hydrate
The classic work on the structure of water molecules in liquid water by Rahman and
Stillinger (1973) used the ST2 potential model to estimate the hydrogen-bond connectivity
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
291
FIG. 10.55 Number of hydrogen-bonded polygons in liquid water at 283 K (Rahman and Stillinger, 1973).
distribution. They have reported that the structure of liquid water is dominated by pentagons
and hexagons, followed by heptagonal hydrogen bonded water rings (Fig. 10.55). The same
structure of water was confirmed by other simulations (Makogon, 1994; Head-Gordon, 1995).
Ohmine and Tanaka (1993) using the TIPS2 (Jorgensen et al., 1983) potential report that there
exist collective motions and energy fluctuations associated with the hydrogen bond network
rearrangements in liquid water. Koga and coworkers (Koga et al., 1994) indicate that the hydrogen bond network is severely modified by methanol. At least 70% of methanol molecules
placed in hydrate cavities had one or more hydrogen bonds to water molecules. In methylamine hydrate almost all molecules had four hydrogen bonds, while in methanol hydrate
only 86% of molecules had four hydrogen bonds.
A recent publication by Koga and Tanaka (1996) examines the waiting time distributions
for rearrangements of water connectivity in a clathrate hydrate. They report that this distribution is of a power-law form at short times (to 20 ps) and exponential at longer times
when events are uncorrelated to each other. Two types of connectivity rearrangements are
discussed: thermally excited defects induced in a perfect region and defects caused by defects
in the connectivity of neighboring molecules. The second type of rearrangements is reported
responsible for the power-law region of the waiting time distribution. The dipole autocorrelation function, a quantity associated with dielectric relaxation (see above) was found to
exhibit power-law behavior when the waiting time for rearrangements was a strong powerlaw function.
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10. Research methods in flow assurance
Thermodynamic properties
Computer models can predict some properties of solids (e.g., ice). TIP4P potential gives
a very accurate prediction of the vibrational density of states for ice Ih (Tse, 1994). This
agreement with experimental data (Fig. 10.56) for ice may suggest that predictions for
hydrates will also be acceptable. By using the SPC model Tse was able to model well the
heat capacities of ice Ic, empty sI hydrate lattice, and sI methane hydrate (Tse et al., 1983a).
However, the density of ice under pressure is overestimated using the TIP4P model (Tse
and Klein, 1988).
The large thermal expansivity of hydrate (compared to ice) has been qualitatively reproduced by a constant pressure molecular dynamics (MD) of sI hydrate of ethylene oxide
(Tse et al., 1987). The large thermal expansion is rationalized as an excluded volume effect when the guest-host interactions weaken the host-host interactions. Wallqvist (1991)
reports the MD study using the SPC potential of phase separation in methane-water system. Upon addition of methanol to the simulated system he observed a weak preferential
solvation of the methyl part of methanol in hydrocarbon core. This effect increased with
pressure. At even higher pressure methane became completely miscible in water as water
formed clusters around separate methane molecules, resembling a mixture of LennardJones molecules.
Density
of States
0.150
0.125
0.100
0.075
0.050
0.025
0.0
0
5
10
15
20
25
30
35
40
Frequency (cm–1)
FIG. 10.56
(Tse, 1994).
Theoretical TIP4P (solid line) and experimental (dashed line) vibrational density of states for ice Ih
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
293
Translational and vibrational spectra
The frequency distribution functions obtained by Fourier transformation from time correlation functions can be compared to experimental spectra as these become available. Simulated
translational (motion) and librational (rotational oscillation) spectra were compared for ice,
empty hydrate lattice and methane hydrate using MD simulation (Tse et al., 1983a). It was
noted that long-range electrostatic interactions are important for correct calculation of a translational spectrum. Vibrational (translational oscillation) spectrum for methane guest was partitioned into contributions from large and from small cavities.
In a MD simulation of xenon sI hydrate vibrational and librational spectra (Tse et al., 1983b)
were calculated. Simulators were able to predict the gap separating the two modes of motion
in spectra obtained by infrared (IR) spectroscopy.
Tse reports (Tse et al., 1984) that the vibrational frequency distribution functions for the
host molecules are broadly similar for hydrates enclathrating different guest molecules. The
oscillatory motions correlation time for tetrafluoromethane of 5 ps are remotely comparable
with experimental value of 13.6 ps (Davidson et al., 1977). The same modeling work reports
the existence of preferred orientations for ethylene oxide and cyclopropane molecules in large
sII cavities. A recent polarized Raman spectroscopy work (Tomoko, 1996) reports the existence of preferred orientation for CO2 molecules in hydrate cages.
In 1987 the simulated vibrational spectrum of a sII hydrate lattice with krypton guests (Tse
and Klein, 1987) was found to be similar to that of a sI host lattice; the translational spectrum
was different. The frequencies of krypton translation in hydrate cavities were calculated to be
9 and 34 wavenumbers. These values were compared to the experimental frequency of guest's
rattling motion in β-quinol hydrate of 36 wavenumbers.
One of the most recent MD works from Hokkaido University (Itoh et al., 1996) studies
the stretching and bending frequencies of CO2 in large and small cavities of sI hydrate. The
Kumagai (Kumagai et al., 1994) potential was used. The higher frequencies in small cavities
were attributed to guest-host van der Waals interactions. Only qualitative agreement with
experimental spectra was achieved.
Stability of gas hydrates
As simulated by Rodger (1991, 1992) the stability of hydrate lattice analyzed in terms of
mean square displacement (MSD) of oxygen atoms of waters and cavity radial distribution
function (CRDF) increased with the number of cavities filled with guests. In one simulation
melting of the empty hydrate lattice was observed. The importance of guest-host repulsive
interactions for hydrate stability was emphasized.
Tanaka and Kyohara (1993a) have studied the contributions of guest-host interactions, the
free energy of guest vibration, and change in energy of host vibrations through coupling with
guest on the stability of hydrate. They found that the presence of guests causes an increase
in most of the vibrational frequency peaks. These shifts are reported to be thermodynamically unfavorable to hydrate stability as the chemical potential of water in host lattice was
decreased.
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10. Research methods in flow assurance
However, this shift prevents hydrate lattice from collapsing in terms of kinetic stability.
The cause of hydrate instability was attributed to the increase in low and intermediate frequency oscillatory motions of hosts. In their subsequent study (Tanaka and Kyohara, 1993b)
compared intermolecular host-host vibrations in hydrates of propane, xenon and methane. It
was shown that motion of propane guest in a large hydrate cavity does not couple with the
host motion. Thus the fixed lattice approximation can be used to simulate methane and xenon
guests motions inside large cages.
Effect of pressure on the stability of xenon and argon hydrates was reported by Tanaka and
Nakanishi (1994). Chemical potential of water was calculated from the general partition function and used in the generalized van der Waals and Platteeuw model to calculate hydrates
stability. At high temperatures good agreement with experiment was found.
In a simulation of hydrate stability encaging highly polar guests (Koga et al., 1994) it was
found that amine hydrates are stable because guests don't form hydrogen bonds to hosts,
while in alcohol hydrate many guest-host hydrogen bonds are formed. In an MD simulation
using the SPC water model Westacott and Rodger (1994) showed that the stability of sI hydrate calculated in terms of Gibbs free energy of the host lattice increased with the number of
guests. Shape of the hydrate lattice was not affected by the inclusion of guests in small cavities, but changed when the large cavities were filled with Lennard-Jones guests. Guest-guest
and guest-host radial distribution function (RDF) and cavity RDF (CRDF) were used to show
that guest-host repulsions are more important than the attractive interactions for use with
van der Waals and Platteeuw theory (Rodger, 1994a,b).
Wallqvist (1994) studied the effects of methanol on sI hydrate unit cell stability using MD
with SPC water model. From calculated CRDF he showed that guest molecules increased
hydrate stability, compared to empty lattice. Addition of methanol molecules to the mixture
broadened and lowered the CRDF which indicated a decrease in hydrate stability.
Thermodynamic stability of ethane, ethylene, and CO2 hydrates (Kvamme and Tanaka,
1995) was found to be in qualitative agreement with experiments in the sub-zero temperature region. The addition of a virial coefficient to the equation for calculation of guest chemical potential matched the predicted pressures with experimental values for ice-hydrate
equilibrium region. At water temperatures predicted values were in a qualitative agreement
with data.
A MD simulation of sII hydrates (Hirai et al., 1996a) was performed to investigate stability of CO2 hydrate relative to argon hydrate and an empty hydrate lattice. The authors observed broadening of the cavity RDF and higher MSD for host molecules in hydrate with CO2
guests, compared to reference systems. Although the host molecules retained their positions
throughout the simulation (no melting has occurred), the conclusion was that CO2 hydrate
will be thermodynamically unstable. This conclusion appears questionable.
Early modeling of hydrate growth
The dynamic growth studies reviewed in this section are questionable attempts at modeling real-world hydrate growth. Computer modeling of hydrate growth is nonsense due
to the simulation times involved—much too short compared to real world growth times.
Rates of axial volume-diffusion hydrate growth reported by Makogon (1981) range from ca.
0.6 to 3 mm/h for different gases which is 1600–8300 Å/s. Molecular dynamics computer
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
295
simulations in modern computers are typically limited to times of the order of hundreds
of microseconds (10−4 s) or tens of milliseconds for supercomputers. This time frame allows the use of supercomputers for simulated growth. However, with the advent of GPUs
and parallel programming such as CUDA, the task is now becoming within reach of more
researchers.
Since in a real crystal growth the preferred growth sites are steps or kinks, an idea may be
recommended for future work that the hydrate growth be stimulated in a crystal kink site.
This could be attempted using a (2 × 2 × 2) periodic MD simulation box composed of 7 crystalline hydrate unit cells and one melted unit cell. However, such a simulation is not currently
feasible because of the reasons mentioned above.
Computer modeling of crystal growth has been done since 1972 when growth of the {001}
face of a Kossel crystal surface had been simulated using the Monte Carlo (MC) method
(Gilmer and Bennema, 1972). In 1993 Clancy (Baez and Clancy, 1994) used the SPC/E
(Berendsen et al., 1987) potential in an attempt to utilize the memory effect of a recently
melted hydrate (Makogon, 1981) for hydrate growth. A simulation box with ca. 3000 water
molecules and a stoichiometric number of guests was seeded with a spherical crystal of hydrate (245 water molecules + guests) and the simulation was allowed to proceed. After 1/5th
of the simulation time the number of water molecules in a hydrate cluster had stabilized at
ca. 400 molecules.
An experimental study and computer modeling of the memory effect of hydrate lattices
was performed on sI and sII by Handa and colleagues (Handa et al., 1991). They discovered
that a compressed empty hydrate lattice was able to recover its crystalline structure after
pressure was released. It was proposed from the MD results that under pressure the water
molecules collapse around the guest molecules, and repulsive guest-host forces are responsible for the recovery of crystal structure when pressure is released.
Recently, hydrate growth was modeled with some success by Hirai (Hirai et al., 1996b).
He used the Kumagai (Kumagai et al., 1994) two- and three-body potential to model
host-host and guest-host interactions in a periodic box with side of two unit cells length.
Positions of the Ar guest molecules were held constant. He observed the formation of sI
hydrate lattice around guests in the simulation box after a 165 ps MD simulation. As the
simulation progressed, the number of pentagonal hydrogen bonded rings increased to ca.
330, and number of hexagonal rings decreased to ca. 50. This distribution in 8 sI hydrate
unit cells is 384:48.
A number of commercial software packages are available. The Cerius2 program utilizes the
Bravais Friedel Donnay Harker method to predict the faces on a growing crystal. This method
is a geometrical calculation that uses the crystal lattice and symmetry to generate a list of
possible faces and their relative growth rates. From this, crystal morphology can be deduced.
Bravais and Friedel (Bravais, 1913; Friedel, 1907) observed that the center-to-face distance for
a given plane tended to be related to the inverse-plane spacing:
D~
where
1
d
D—crystal center-to-face distance,
d—lattice-plane spacing (thickness of unit cell in a direction normal to plane).
296
10. Research methods in flow assurance
This can be easily rationalized by assuming that growth involves the consecutive addition
of growth planes of molecules. If energetic effects are discounted, the ease of adding a plane
is proportional to its thickness. Thus, a thinner plane grows faster and has a larger centerto-­face distance. Donnay and Harker (1937) refined this approach by developing rules that
related the crystal symmetry to the possible growth planes.
The Cerius2 program was used to report correctly the shapes of sI and sII single hydrate
crystals as regular octahedron and rhombic dodecahedron, respectively. These shapes were
also observed experimentally (Larsen et al., 1996; Makogon et al., 1997). sH hydrate crystal
was predicted to grow as a hexagonal prism. All calculated shapes were later confirmed by
the work of King (Smelik and King, 1997).
Inhibition of hydrate growth
Effects of additives on crystal growth from aqueous solutions have been studied previously for calcium sulphate (McCartney and Alexander, 1958), adipic acid (Colville, 1958),
ice Ih (Knight et al., 1991), glycine (Li et al., 1994). However, such experiments for clathrate
hydrates have started just recently for sII (Makogon et al., 1997), and sI (Larsen et al., 1996)
hydrates. Computer simulations have predated experimental work in this area.
In 1993 Edwards has presented the results obtained with the Cerius and CHARMm software for the adsorption of polar fish glycopeptides on hydrate and ice (Edwards, 1994). He
indicated that the optimum spacing for the polypeptide adsorption was on {100} face of sI
hydrate in a ⟨110⟩ direction. He reported that 15 hydrogen bonds formed from aminoacid side
chains and some carboxyl groups to the hydrate surface. This number is qualitatively higher
than the fraction of hydrogen bonds measured between poly(methyl methacrylate) carbonyl
groups and hydrogen terminated {100} silanol (silicon oxide) surface measured as 0.09–0.13
(Zazzera et al., 1993).
Intramolecular motions of hydrophilic polymers like poly(dimethylacrylamide)
(PNNDMAM) in aqueous solution are measured to be of the timescale which can be modeled by computers, ca. 3.4 ns (Soutar et al., 1996). Such simulation using MD would be long.
Usually adsorption of flexible polymer chains on surfaces is modeled by self-avoiding Monte
Carlo technique using the cubic lattice for positioning polymer links in solution modeled by
vacuum (Konstadinidis et al., 1992; Zhan et al., 1993; Zajac and Chakrabarti, 1994). Such simulations are suitable for calculation of the surface coverage with polymer segments and radii
of gyration. Cubic lattice allows to simulate polymer only as a chain of segments with a discrete attractive, repulsive or neutral potential (e.g., -kT, 0, 0.5 kT, kT). No atomic information
can be modeled using the lattice model.
However, more complicated methods involving chain rotations and cooperative motions
have to be used if polymer links are composed of multiple atoms (e.g., pyrrolidone). A pivot
algorithm for polymer chain rotations was reintroduced by Madras and Sokal (1988). The
algorithm makes very bold changes in polymer backbone conformation. Many such moves
get rejected because polymer segments overlap. However, the few moves which are accepted
produce such changes in conformation which would have taken many regular movements
of polymer segments on the cubic lattice. MC simulations involving pivot moves were used
to study adsorption of monomers, homopolymers and copolymers on interfaces (Clancy and
Webber, 1993, 1997).
Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates
297
Adsorption of PVP of different chain lengths on sI hydrate was modeled using MC module
of the commercial software Cerius2 (Carver et al., 1996). It was found that the adsorption of
rigid PVP chains of 1, 2, 4, and 8 mers on hydrate was energetically favorable. Formation of
loops in adsorbed state was reported for a rigid PVP octamer. Monomers were found to adsorb on an edge of a partially completed large cavity by forming two hydrogen bonds.
A similar work was performed at CSM using the Cerius2 software to form monomers of
inhibitors on hydrates. This work gave us preliminary results about locations of inhibitor
monomers adsorption on sII hydrate. In our work the monomers were found to adsorb both
inside the hydrate cavities and on their periphery. The monomers adsorbed in the partial hydrate cavity had their carbonyl (CO) oxygens pointed at hydrogens on the hydrate surface
indicating hydrogen bonding.
Koh et al. (1996)) has presented time-resolved NMR measurements for hydrate structure in
presence of PVP and tyrosine. No definitive conclusion was made about where PVP adsorbs
on sII hydrate.
Kvamme and colleagues have presented their results on molecular dynamics simulation of
PVP in water and water/hydrate systems on both International hydrate conferences. The first
work (Kvamme, 1994) indicated that a PVP monomer hydrogen-bonded to water in solution
via its carbonyl group gradually changes its bond towards the water in hydrate. The continued work (Kvamme et al., 1996) simulated behavior of PVP as side group ring without the
backbone part. The inhibitor was observed to orient perpendicular to the hydrate surface.
As a general conclusion, various characteristics of liquid water, ice and clathrate hydrates
obtained through modeling are summarized in Table 10.12. At present, potential models need
improvement in order to be able to truly simulate gas hydrate behavior.
Over the last 6 years all commercially available chemicals have been tested, and there
is a need to predict new chemicals which can be synthesized and then tested in a screening a­ pparatus. The goal of this work is the design of kinetic inhibitors using computer
­modeling. Therefore the mechanism of kinetic inhibition of gas hydrates formation is of
critical i­ nterest. No experimental information was available to-date about the mechanism of
kinetic i­ nhibition. Three hypotheses for the kinetic inhibition mechanism were developed at
CSM (Long, 1994):
(1) A classical inhibition mechanism through adsorption of an inhibitor molecule on the
growing surface of a crystal and preventing hydrate growth.
(2) Modification of the structure of water in vicinity of an inhibitor to make it unfavorable
for hydrate formation. This hypothesis originated from CSM (Makogon, 1994).
(3) A mass transfer limitation caused by polymeric chains preventing agglomeration of
hydrate.
Research objectives
The present work analyzed experimental and computer modeling evidence for the adsorption hypothesis. There were eight research objectives for this work:
1. Design and use a new apparatus to determine preferred growth planes of sII hydrate,
2. measure the effects of kinetic inhibitors and/or NaCl at different concentrations on
hydrate growth and on the preferred direction of a sII hydrate crystal growth,
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10. Research methods in flow assurance
TABLE 10.12 Modeling of hydrate-related substances on computers.
Can be modeled well on computers
Can't be modeled well on computers
1. Density of water
1. Density of ice under pressure
2. Dynamic structure of liquids
2. Heat of water vaporization
3. Static structure of solids
3. Thermal expansivity
4. Intermolecular energy
4. Isothermal compressibility
5. vdW&P hydrate stability
5. Oscillations of guest in hydrate
6. Dielectric relaxation time
6. Stretching and bending frequencies of CO2 guest in
hydrate
7. Number of hydrogen bonds
7. Thermodynamic hydrate stability
8. Vibrational spectrum for ice
8. Rates of hydrate formation, nucleation and growth.
9. Heat capacities of ice and hydrate
10. Phase separation
11. Vibrational, librational spectra for water in hydrate
12. Preferred orientations of guest
13. Translational spectra of guest
14. Effect of pressure on hydrate
15. Stability of polar guest hydrate
16. Stability of hydrate with methanol
17. Crystal growth
18. Hydrate structure recovery after restoring pressure
19. Shapes of hydrate single crystals
20. Polymer adsorption on surfaces
3. use molecular modeling to determine the preferred sites of monomer adsorption on
hydrate surface,
4. model the inhibitor adsorption on an active growing site of sI, sII and sH hydrates, and
measure the adsorption properties for different inhibitors (energy, hydrogen bonding,
location, monomer orientation),
5. modify the Monte Carlo computer program written by Prof. Haile to study the
adsorption of polymers on the preferred sites on hydrate determined in item above,
6. develop a correlation between the adsorption properties of hydrate inhibitors,
7. use the computer to predict new, more effective kinetic inhibitors, and.
8. test new inhibitors in single crystal growth studies.
Experimental study of hydrate crystal growth
299
Experimental study of hydrate crystal growth
Morphology of hydrate crystals
The main objective of this part of research was to study the shape of hydrate crystal, the
morphology of crystal faces, and the growth rate of hydrate crystals, with respect to the following variables:
(1)
(2)
(3)
(4)
temperature;
concentration of added kinetic inhibitors;
molecular weight of added kinetic inhibitor;
concentration of NaCl salt added (with and without added kinetic inhibitor).
An elementary principle of crystal growth is that the slowest growing crystal faces are preserved, and the faces which grow fast grow out of existence as illustrated in Fig. 10.57. Thus
a control experiment of growing a single crystal from pure hydrate melt gives information
about the orientations with the slowest growth kinetics. Additives may produce new slowest-­
growing faces, in which case one discovers the surface orientations to which they adsorb.
This technique has been used successfully for the antifreezes evolved by polar fish to prevent
ice crystal growth in their blood (Harrison et al., 1987; Knight et al., 1991; Knight et al., 1993).
A visual apparatus for observation of the THF hydrate growth was constructed. The apparatus (Fig. 10.58) consisted of a transparent Plexiglas cooling jacket with inserted glass sample
tube containing a glass pipette. The test solution was placed inside a sample tube and cooled
below the hydrate melting point. Then the glass pipette was placed into the solution, and a
copper wire cooled with liquid nitrogen or with ice water was inserted into the pipette in
order to initiate hydrate formation inside the pipette. The pipette served as a conduit for the
growing crystal. The hydrate crystal grew to the edge of the pipette and a small area of the
crystal became exposed to the solution in the test tube. Hydrate started to grow as a single
crystal on the tip of the pipette in the test solution inside the test tube.
A study of the effect of temperature on crystal growth was performed. From equilibrium
considerations, the temperature at the growing crystal surface equals to the equilibrium
temperature of hydrate decomposition. The greater the temperature difference between the
crystal surface and the bulk solution, named supercooling, the greater the driving force for
hydrate nucleation, and the faster the crystal growth. The heat of crystal nucleation ΔdH is
dissipated into the bulk solution via convective flow of solution near the crystal. Since there
is no mass transfer change in growth from THF hydrate melt, the growth is heat-transfer
limited. Crystal growth experiments held temperature, pressure, and composition constant.
FIG. 10.57 Disappearance of a fast-growing crystal face (long arrow).
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10. Research methods in flow assurance
FIG. 10.58 Single crystal apparatus schematic.
It was observed that the morphology of a hydrate crystal changed with the set temperature.
At moderate amounts of supercooling (1.4–3.4 K below the equilibrium melting temperature)
a hydrate crystal preferred to grow as a regular polyhedron, whereas at large supercooling
(4 K or more) the hydrate grew simultaneously as several crystals with defects. The least visible amount of defects was obtained at a 1.4 K supercooling for a THF hydrate crystal.
The hydrate crystal morphology was also dependent on supersaturation of THF. At concentrations of THF in water varying >15% from stoichiometric, the growth habit was changed
into thin hexagonal plates (Larsen et al., 1996). In water-rich solutions the growing plane was
thin. In water-poor solutions the hydrate crystal began as 2-D plane but thickened with time
into a three-dimensional crystal.
Growth of hydrate crystals was recorded by the Olympus SZ-CTV microscope on videotape with magnification of up to 50. Each test was repeated at least twice. All runs without NaCl were 100% repeatable, while in the presence of NaCl in the solution, variations in
growth occurred. The THF sII hydrate crystal was a regular octahedron as shown in Fig. 10.59
with a digitized video image presented in Fig. 10.60. This shape is common for face-centered
cubic crystals such as pyrite (Murowchick and Barnes, 1987), and it was identical to the shape
of sII N2/O2 hydrate (Fig. 10.61) (Nakahara et al., 1988). The shape of the THF hydrate crystals
clearly indicates their cubic nature.
For comparison, sI hydrates of ethylene oxide grow as rhombic dodecahedra (Larsen et al.,
1996). The first formation of single crystals of sI (ethylene oxide) and sII (THF + hydrogen
sulfide) hydrates was reported by McMullan and Jeffrey (1965a,b). They used the crystals
Experimental study of hydrate crystal growth
301
FIG. 10.59 Octahedral crystal shape of the THF hydrate.
FIG. 10.60
Single crystal of THF hydrate grown (a) at 1 °C (supercooling of 3.4 K), and (b) at 3 °C (supercooling of
1.4 K). Diameter of the pipette shown hereinafter is ca. 2 mm.
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10. Research methods in flow assurance
FIG. 10.61 Crystal of air hydrate inclusion in Antarctic ice (Nakahara et al., 1988).
for X-ray determination of its structure. The shapes of the single crystals were not reported
though. The initial growth of single crystals of sH (methane + methylcyclopentane) hydrate
is due to Smelik and King (1997). sH crystals grew as hexagonal prisms.
By definition, a cubic crystal must have four three-fold rotational axes of symmetry. The
regular octahedral crystal can have four unique axes drawn, as shown in Fig. 10.62, around
which the crystal can be rotated 3 times through angles of 120°; the axes of rotation are la. After each rotation the crystal would be congruent to the initial
beled with the sign
orientation.
An octahedral THF hydrate crystal shown in Fig. 10.59 had eight triangular faces. The
triangular faces of the octahedron were identified as the {111}-type crystallographic planes
by similarity with other octahedral crystals. No single crystal X-ray measurements were
made specifically to locate the {111} plane on THF hydrate crystals. A {111} plane is defined
by making a unit step from the crystal center along each of the three crystallographic axes
(⟨100⟩, ⟨010⟩, and ⟨001⟩ directions) and drawing a plane through the three reached points
(Fig. 10.63). This plane produces an equilateral triangle when it crosses a cube representing a cubic unit cell. The other seven triangular faces in an octahedral crystal represent the
{111}, {111}, {111}, {111}, {111}, {111}, and {111} planes. The observed {111} planes exhibited
the slowest growth rate.
Experimental study of hydrate crystal growth
303
FIG. 10.62 Three-fold axes of rotation drawn through a regular octahedron.
FIG. 10.63 Three crystallographic axes drawn as dotted lines through a THF hydrate crystal and defining the
<100>, <010>, and <001> directions. The shaded face represents the {111} plane.
The fastest hydrate growth occurred in the directions of crystal vertices. These directions
are collinear with the <100>, <010>, and <001> axes. Since the growth rate in other directions
is slower, the largest dimension of the crystal is along the directions of fastest growth. Thus
we obtain six vertices of an octahedron.
It is important to notice that the {111} faces which grow the slowest are the planes which
contain all of the hexagonal rings in the 51264 cavities of THF sII hydrate. The hexagonal faces
are contained only in the large cavities of the hydrate.
Since the {111} faces containing the hexagonal rings grow the slowest, the large cavities
are also the slowest to grow, compared to the small 512 cavities. We hypothesize that the
completion of the large cavities may be slowed because hydrogen bonds are more strained in
hexagonal rings than in pentagonal rings. Normally water hydrogen-bonds are oriented at
tetrahedral 109.48° angles, like in ice. In pentagonal faces which predominate in the hydrate
the angles between hydrogen bonds are only slightly strained at 108°, while hexagonal faces
cause a substantial bending of the hydrogen-bonds between the water molecules at 120°.
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10. Research methods in flow assurance
Effect of adding kinetic hydrate inhibitors on the morphology of growing hydrate
THF + water + inhibitors solution without salt
The next step in studying hydrate crystal growth was to identify the effect of inhibitor
polymers on the morphology and the growth rate of THF hydrate crystals. The following chemicals were tested: poly(vinylpyrrolidone), poly(vinyl-caprolactam) and a random
copolymer of vinylpyrrolidone, vinylcaprolactam, and dimethylaminoethylmethacrylate.
These compounds are referred to as PVP, PVCap, and VC-713 respectively. These chemicals
provide hydrate inhibition in both THF and natural gas systems, showing that the THFwater system is a good model for structure II hydrate formation from natural gas (Lederhos
et al., 1996).
In this work concentrations of 0.5 wt% and 0.1 wt% were tested at temperatures of +1, +2,
and +3 °C. We studied the solutions of PVP, PVCap, or VC-713 of both high (89 K or higher)
and low (10 K or less) molecular weights. The studied polymeric inhibitor chemicals were
obtained from BASF. Solid samples of the investigated inhibitors were dissolved in deionized
water obtained from IBM Labs. If an inhibitor was available in an alcohol solution, the solvent
was removed by evacuation.
An unusual phenomenon was observed when we added kinetic inhibitors to the aqueous
THF solution. The shape of the THF hydrate crystal grown in the presence of these chemicals
changed from octahedral (3-D) to planar hexagonal (2-D) (Figs. 10.64 and 10.65). Faces of the
hexagonal plate were postulated to be {111} since the angles at which faces meet are same as
in an octahedral crystal. Another evidence supporting the hypothesis that the planar crystal
faces are {111} is the growth of a plane on an octahedral crystal grown without an inhibitor
and then moved into inhibited solution (Larsen et al., 1996, this work). The plane is parallel
to the {111} face of the octahedral crystal from which it grew (Fig. 10.66) which also indicates
a {111} plane.
The same effect was observed both at a 0.5 wt% concentration and at the lower concentration of 0.1 wt% of these chemicals in the test solution. All crystals grown in the presence of
hydrate inhibitors had visible defects. After hydrate crystals reached the sample tube walls,
hydrate also started to grow on the tube walls.
We hypothesize that the polymer chains of kinetic inhibitors adsorbed on the {111} surface
of the THF hydrate by hydrogen-bonding and blocked the further crystal growth. One possible explanation of the preference of the inhibitor adsorption towards the {111} face is that {111}
is the only surface available for adsorption since it's the slowest-growing face and other faces
have insufficient area for polymer adsorption on them. Another explanation may appeal to
the nature of {111} face. Inhibitor may adsorb stronger to {111} face compared to the other
faces because of a higher density of adsorption sites on that face.
We observed that the hydrate crystal growth was not completely inhibited by the kinetic
inhibitors at the concentrations listed above at the supercooling of 3.4 K, while at a lower
supercooling of 1.4 K the growth can be inhibited completely at a certain inhibitor concentration (Larsen et al., 1996; Makogon et al., 1997). The formed planar crystals grew in thickness,
as well as along the edge. This observation suggests that the adsorbed polymer allows for
hydrate growth beneath it. Otherwise, the polymer molecules must have been occluded by
the growing hydrate; however, the NMR study of hydrates by Ripmeester (1995) does not
confirm the occlusion phenomenon.
Experimental study of hydrate crystal growth
305
FIG. 10.64 Planar crystal of THF hydrate grown (a) with 0.5 wt% of high molecular weight PVP in solution at 1 °C
(supercooling of 3.4 K), and (b) with 0.1 wt% of high molecular weight PVP in solution at 3 °C (supercooling of 1.4 K).
In case of VC-713 inhibition at 3.4 K supercooling, the plane of hydrate did not grow
thicker. Instead, other planes and defects appeared on the surface of the original plane. With
VC-713 hydrate crystals simultaneously started to grow on sample tube glass walls without
the original crystal plane reaching the glass walls.
The problem of the two-dimensional growth is interesting because the plate perimeters
also appear to be {111} based on observing a thick hydrate plates which grew from a solution
with 0.1 wt% PVP of high molecular weight. However, at higher inhibitor concentrations in
306
10. Research methods in flow assurance
FIG. 10.65
Side view of the planar crystal of THF hydrate grown (a) with 0.5 wt% of high molecular weight PVP
in solution at 1 °C (supercooling of 3.4 K), and (b) with 0.1 wt% of high molecular weight PVP in solution at 3 °C
(supercooling of 1.4 K).
the hydrate melt the plate perimeters may no longer be {111}, but of a different crystallographic orientation. Why do the plate faces grow much more slowly than the perimeters,
when they all are {111}?
One hypothesis would appeal to stacking faults providing reentrant edges that encourage nucleation of new layers (Hamilton and Seidensticker, 1960; Wagner, 1960; van de Waal,
1996). Stacking faults on {111} are very likely in structure II hydrates, since in certain positions
Experimental study of hydrate crystal growth
307
FIG. 10.66
An octahedral crystal of THF hydrate formed at 1 °C and then placed in a melt with 0.5 wt% PVP
exhibits a planar continued growth (supercooling of 3.4 K).
a {111} surface has six-fold symmetry, while the crystal itself has a three-fold symmetry axis
normal to that plane.
A second possible mechanism might appeal to a time-dependence of the inhibitor adsorption. If adsorption requires reorientation of the inhibitor molecules to conform with some
feature of the face, then there may not be time for that to occur at the rapidly growing plate
edges, whereas the inhibited plate faces remain slow-growing. This has some precedent in
the effect of kinetic inhibitors on ice growth. It has been reported that one of these changes
the growth habit completely in free growth at low supercooling but does not change it in the
faster growth at high supercooling (Harrison et al., 1987), and Knight has observed the same
phenomenon for several other of the kinetic ice “antifreezes”. It is hard to relate this effect
to polymer diffusivity in hydrate melt since the diffusivities of kinetic inhibitors in water are
unknown.
Preliminary experiments have shown that the plate-like habit found at low concentrations
of kinetic inhibitors is a transition to complete inhibition of crystal growth at higher inhibitor
concentration. Complete inhibition is also a function of supercooling, and a long series of experiments was performed by Roar Larsen at CSM to quantify this as a function of type, molecular weight, concentration of the inhibitor, and the THF concentration in the water solution.
During these tests a single crystal of THF with an octahedral shape was grown in the aqueous THF solution. Then this crystal was transferred into the aqueous THF solution containing
a kinetic inhibitor. As one example, 0.75 wt% VC-713, of 70,000 molecular weight, inhibits
growth completely (growth rate undetectable: less than about 0.01 mm/h over 25 h at a supercooling of 1.4 K) where the uninhibited linear growth rate of the octahedral crystals was
about 5 mm/h (Larsen et al., 1996).
As controls for the experiments with inhibitors, we performed growth experiments with
other additives that do not provide kinetic inhibition: polyvinyl alcohol, urea, hydroxyethylcellulose, and polyacrylamide (Long et al., 1994). These chemicals were chosen from a list of
non-inhibitors because they are soluble in water. Two of these also have a vinyl backbone and
308
10. Research methods in flow assurance
have pronounced effects on water hydrogen bonding (Makogon, 1994). The plate-like habit
was not found at chemical concentrations of 0.5 wt% and a supercooling of 3.4 K.
It follows from these results that the inhibitors can adsorb on {111} surfaces of hydrate.
This is a fundamental issue for understanding hydrate growth inhibition at the molecular
scale. Preferential adsorption of kinetic inhibitor on hydrate {111} faces was recently proven
experimentally (Larsen, 1996).
Effect of NaCl salt on THF hydrates
A set of experiments was performed with NaCl in solution at 1 °C (3.4 K supercooling).
NaCl is a known thermodynamic hydrate inhibitor (Sloan, 1990). The presence of NaCl in water solution improves kinetic inhibitors' performance (Long, 1994). In present work it was also
determined that hydrate growth can be stopped completely if salt is added to the solution.
The synergism of salt with kinetic inhibitors may be explained using Langmiur adsorption isotherm. It was hypothesized (Long et al., 1994) that hydrate growth involves adsorption of guest molecules onto labile hydrate cavities. The rate of attachment to the surface
should be proportional to a driving force times an area. The driving force is the concentration
in the fluid, and the area is the amount of bare surface. If the inhibition is performed only
by the polymer adsorbed on hydrate, the rate of coverage with guest molecules at pseudo-­
equilibrium would be equal to the rate of desorption from the surface, (if desorption does
occur for all polymer segments).
Desorption = Adsorption
(
)
(
)
kGuest ΘGuest + k Poly Θ Poly = k′Guest CGuest 1 − ΘGuest − Θ Poly + k′Poly CPoly 1 − ΘGuest − Θ Poly ,
where
θi—fraction of the surface covered with species i,
k′i, ki—pseudo-equilibrium adsorption and desorption rate constants.
Rearrangement leads to the Langmiur isotherm expression:
ΘGuest =
KGuest CGuest
,
1 + KGuest CGuest + K Poly CPoly
where
Ki =
k ′i
.
kGuest
If the inhibition is performed by the kinetic inhibitor adsorbed on hydrate and salt ions
with shells of water molecules blocking some adsorption sites, the Langmiur isotherm expression would look like:
ΘGuest =
KGuest CGuest
.
1 + KGuest CGuest + K Poly CPoly + KSalt CSalt
An extra term in the denominator decreases the coverage of the hydrate surface with guest.
Results of investigating the hydrate growth habits with and without salt are summarized
in Table 10.13.
309
Experimental study of hydrate crystal growth
TABLE 10.13 Summary of THF hydrate crystal growth at 1 °C (3.4 K supercooling).
Chemical
MW
Concentration, wt%
THF + water
PVP
PVCap
VC-713
Shape
No salt
3.5 wt% salt
3-D
2-D
low
0.1
3-D
2-D
~10 K
0.5
2-D
No growth
high
0.1
|
2-D
360 K
0.5
|
No growth
low
0.1
|
|
~5 K
0.5
|
↓
high
0.1
|
2-D
92 K
0.5
|
No growth
low
0.1
|
|
~10 K
0.5
|
↓
high
0.1
|
No growth, 2-D
70 K
0.5
↓
No growth
The melting temperature of THF hydrate melting was lowered from 4.4 to 2.2 °C by adding
3.5 wt% NaCl. This change in equilibrium temperature is similar to the change in temperature
of ice melting with addition of 3.5 wt% NaCl of 2.1 °C (CRC Handbook, 1988).
In the presence of NaCl the hydrate crystals grew as almost defect-free hexagonal flat
planes. The THF hydrate crystal growth rate with salt was higher than that with the kinetic
inhibitors present. A digitized image of a THF hydrate crystal growing in a 3.5 wt% solution
of NaCl in water + THF mixture is presented in Fig. 10.67.
The concentration of NaCl at which the hydrate started to grow as a plane was determined
to be 3.0 wt% NaCl in a mixture of THF and water at 1 °C. This was determined by growing
the THF hydrates in solutions with different NaCl concentrations. Supercooling was variable
during this set of experiments. Fig. 10.68 presents the images of THF hydrates grown in solutions with different concentrations of NaCl without kinetic inhibitors. It appears that the borderline concentration of planar crystal growth is between 2 and 3 wt% NaCl in hydrate melt.
Salt readily ionizes in water and aggregates water molecules in solvation shells around
ions. The presence of solvated ions near a hydrate crystal causes a hindrance for the water
and THF molecules adsorbing on the hydrate surface. Transition to a planar crystal growth
habit caused by NaCl observed at 3 wt% NaCl can be attributed to shifting the growth mechanism to a diffusion-controlled type. Planar crystal growth would be preferred in such case.
The rate of crystal growth can be limited either by the rate at which components are incorporated into the growing surface (surface-controlled growth) or the rate at which those
nutrient components diffuse to the surface (diffusion-controlled growth) (Murowchick and
Barnes, 1987). In a THF hydrate the nutrients (water and THF) are evenly distributed around
the crystal, and the corners and edges do not protrude into regions of higher supersaturation.
This results in a regularly shaped polyhedral crystal.
FIG. 10.67 Planar crystal of THF hydrate grown with 3.5 wt% NaCl in hydrate melt at 1 °C (3.4 K supercooling).
0.25 wt. % NaCl
0.5 wt. % NaCl
1.0 wt. % NaCl
2.0 wt. % NaCl
3.0 wt. % NaCl
5.0 wt. % NaCl
FIG. 10.68 THF hydrate morphology at different NaCl concentrations in hydrate melt at 1 °C (3.4 K supercooling).
Experimental study of hydrate crystal growth
311
If the diffusion of nutrients to the crystal is hindered by the inhibitor adsorbed to the crystal face, then the diffusion-controlled growth occurs. In such case any protrusion of the crystal
surface may encounter more nutrient. Growth at the end of the protrusion will be favored
over growth on flat crystal face. It was observed that in case of thin planar crystal growth in
presence of PVCap or VC-713 the growth rate at the edge of the plane was faster than at the
crystal face by at least an order of magnitude.
Change of crystal habit from octahedral to planar at non-stoichiometric hydrate melt
compositions described above (Larsen et al., 1996) can also be attributed to a transition to
a diffusion-­controlled growth. As the concentration of either nutrient (water or THF) drops
near the growing surface, a planar crystal growth becomes preferred.
There are three common types of crystal growth mechanisms illustrated in Fig. 10.69:
(1) Screw-dislocation. This is growth around a defect in a spiral direction. Such growth
of crystals results in acicular, or needle-like growth. It occurs at very low degrees
of supersaturation. Acicular crystal growth is seldom observed experimentally.
Murowchick and Barnes (1987) have observed acicular growth of pyrite only once in a
set of 70 experiments. We observed such growth only once in all experiments (Fig. 10.70)
with aged PVCap solution.
(2) Layer-by-layer. This type of growth occurs at moderate degrees of supersaturation.
Such mechanism involves two-dimensional nucleation and lateral spreading from these
nuclei on surface. Growth steps are visible on the crystal surface in Figs. 10.60 and 10.64.
The large steps indicate a high nucleation rate causing the spreading layers to pile up on
one another.
(3) Continuous. In this type of growth building blocks attach to any crystal surface
when the nucleation rate is extremely high. This occurs at very high degrees of
supersaturation and when heat of crystallization is low. A product crystal does not show
any crystal faces and looks like a boulder (Myerson, 1993).
It was experimentally observed at CSM Hydrate Center that polymers of lower molecular
weight (MW) have better performance than those of higher MW. Diffusivity of lower MW
polymers is higher than that of polymers with higher MW. Lower MW inhibitors can reach
hydrate surface and block its growth faster than higher MW ones.
(A)
FIG. 10.69 Mechanisms of crystal growth.
(B)
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10. Research methods in flow assurance
FIG. 10.70 Needle-like growth of THF hydrate crystals.
THF + water + inhibitors solution with NaCl salt
A set of experiments was performed with 3.5 wt% of NaCl and kinetic inhibitors in the
solution at 1 °C. In 7 out of 12 tests the kinetic inhibitors (PVP, PVCap, VC-713) with 3.5 wt%
NaCl in the tested solution inhibited hydrate growth completely for at least 30 min after the
hydrate nucleation. In the remaining 5 cases the hydrate growth was planar.
Growth rate measurements
Measurements of hydrate growth rate through a capillary were not reproducible. It is recommended not to use narrow conduits for hydrate growth rate experiments.
Computer modeling of interaction between a hydrate surface
and an inhibitor
Organization of this section
This section deals with computer simulation of hydrate inhibition. Within we attempt to
determine the mechanism of kinetic inhibition and to explain why some inhibitors are better
than others. The section contains five main subsections:
1. Early modeling of clathrate hydrates at CSM.
2. Studies of inhibitor adsorption on hydrate using commercial software Cerius2.
3. Using hand-written software for studying interaction of monomers with water and with
hydrate.
4. Adsorption of inhibitor polymers on hydrate.
5. Using the computer to design new inhibitors.
Computer modeling of interaction between a hydrate surface and an inhibitor
313
Early Modeling of clathrate hydrates at CSM
Computer modeling of clathrate hydrates was performed in our lab for the last 5 years.
Long (1994) determined that the coordination number of water molecules around apolar
guest molecules in liquid water is quantized in a series (20, 24, 28, 36, 40) as a function of the
apolar guest size. The first four numbers in this series correspond to the numbers of water
molecules in 512, 51262, 51264, and 51268 hydrate cavities.
Pratt (1994) studied hydrate-liquid interface properties. He found that water molecules in
the liquid near the interface align themselves to resemble the hydrate lattice. He also used
cluster-cluster aggregation and diffusion-limited aggregation (DLA) fractal models to simulate hydrate growth. The DLA growth resembled the hydrate growth observed in brine
(Burruss, 1993) as spikes of hydrate grew to the source of hydrate forming molecules.
Molecular simulation studies performed in CSM laboratory aimed at revealing the mechanism of kinetic inhibition of hydrates were reported by Makogon (1994). Adsorption of inhibitor species on a surface of hydrate and changing the hydrogen bond structure of water
were identified as possible mechanisms of inhibition. The 1994 work was performed using
the commercial software package SYBYL made by Tripos, Inc. The present work studies the
adsorption mechanism more in-depth.
Studies of monomers adsorption on hydrate with Cerius2
In our initial simulation work the Cerius2 package was used for modeling the inhibitor
adsorption on {100} and {111} planes of sI and sII hydrates.
The DREIDING forcefield (Mayo et al., 1990) used in simulations was developed and validated by Mayo, Olafson and Goddard for predicting structures and dynamics of organic compounds involving H, C, N, O, F, P, S, Cl, and Br. The authors found that the forcefield produced
excellent structural results for 76 tested organic compounds, rotational barriers of a number of
molecules, and relative conformational energies of a number of molecules. This forcefield was
adopted for use in a commercial molecular modeling package Cerius2 by MSI-Biosym.
The {111} plane was identified as the preferred THF hydrate growth site by our single crystal experiments described in prior sections of this chapter. All hexagonal rings of hydrogen-­
bonded water molecules present in the structure II hydrate lie in the {111} planes (Fig. 10.71).
Since H2O in hexagonal rings have bonds stretched at 120° (more than in pentagons (108°) or
the normal water angle (104.5°) or tetragonal angles (109.5°)) it is thought that hexagonal ring
formation may be difficult and therefore limiting.
Adsorption of the inhibitor monomers of PVP and PVCap and of a non-inhibitor monomer of
PVA was modeled using the “sorption” Monte-Carlo algorithm in the Cerius2 program at constant volume and temperature. The interactions between the hydrate surface and an inhibitor
monomer were modeled with the DREIDING forcefield which involved Lennard-Jones and electrostatic interaction. No adsorption simulations were done using molecular dynamics (MD).
The hydrate surface was generated from a hydrate unit cell information using the geometric
rules. The sI and sII unit cell data with positions of oxygens and hydrogens of water molecules
in the hydrate lattice were taken from Sparks (1991). During the simulation positions of water
molecules in the hydrate surface were fixed to represent an empty solid hydrate lattice.
Preparation of the monomer for simulation started with its energy minimization and charge
equilibration in the Cerius2 program. The total charge on the monomer was neutral. After the
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10. Research methods in flow assurance
FIG. 10.71 Hexagonal rings (shaded) lie in the {111} plane of sII outlined by dashed triangle. Dark circles represent oxygens of water molecules.
geometry and charge equilibration, the monomer was solvated in 100 SPC water molecules
and run through a 10 ps (ps) MD equilibration in a microcanonical NVE ensemble. Molecular
dynamics timestep was set to 0.001 ps. The initial configuration was an energy minimum, and
the starting velocities of atoms were assigned by doubling the required temperature of 300 K
which resulted in an equilibrated simulation temperature of about 350 K.
After the system's energy equilibration the solvation box was removed and monomer was
moved to its initial position above hydrate surface. In a MC simulation the monomer moved
about the hydrate surface like a probe. Motion of monomer about the hydrate surface was
controlled by the Metropolis Monte-Carlo algorithm.
A rigorous testing procedure was adopted. Adsorption of inhibitor monomers was modeled on different surfaces of sI and sII hydrates sliced in increments of 1 Å from the unit cell origin, so that all possible hydrate surfaces were tested. The monomer could adsorb either on the
upper or the lower surface of a hydrate slab (Fig. 10.72) because of the periodic boundary conditions, so that two hydrate surfaces were tested at the same time. The study of the inhibitor
adsorption on different hydrate surfaces was performed for the monomers of PVP and PVCap.
The results for a PVP monomer strongest adsorption (energy minimum) are presented in
Table 10.14, and for a PVCap monomer in Table 10.15.
Study of different hydrate surfaces allowed us to make several conclusions:
(1) There is an energy difference (at most 36% for PVCap on sII {111}) between adsorption
of either PVP or PVCap on different hydrate surfaces. On all surfaces the monomers
adsorbed with a favorable (negative) energy. The possibility of adsorption of the
inhibitor on a certain hydrate face is governed by the stability and availability of that
face for adsorption.
Computer modeling of interaction between a hydrate surface and an inhibitor
8Å
FIG. 10.72 A 8 Å thick slice of hydrate with upper and lower surfaces available for inhibitor adsorption.
TABLE 10.14 Energies of adsorption of a PVP monomer on different surfaces.
E min, kcal/mol
Preferred site of adsorption
0 and 6 Å
−13.36
6 Å slice above large cage
1 and 7 Å
−10.85
7 Å slice above large cage
2 and 8 Å
−14.25
2 Å slice below large cage
3 and 9 Å
−12.64
3 Å slice below large cage
4 and 10 Å
−11.83
4 Å slice below small cage
5 and 11 Å
−14.40
11 Å slice above large cage
0 and 6 Å
−16.46
6 Å slice above large cage
1 and 7 Å
−14.76
1 Å slice below large cage
2 and 8 Å
−12.53
2 Å slice below large cage
3 and 9 Å
−12.51
3 Å slice below small cage
4 and 10 Å
−11.86
4 Å slice below small cage
5 and 11 Å
−14.40
11 Å slice above large cage
12 and 17 Å
−12.97
12 Å slice below large cage
13 and 18 Å
−11.51
13 Å slice below large cage
14 and 19 Å
−15.35
14 Å slice below large cage
15 and 20 Å
−13.22
15 Å slice below large cage
16 and 0.22 Å
−13.43
16 Å slice below small cage
0 and 9 Å
−13.96
0 Å slice below large cage
1 and 10 Å
−11.67
1 Å slice below small cage
2 and 11 Å
−15.68
2 Å slice below small cage
Surface
sI (1,0,0) sliced at
sI (1,1,1) sliced at
sII (1,0,0) sliced at
315
316
10. Research methods in flow assurance
TABLE 10.14 Energies of adsorption of a PVP monomer on different surfaces.—cont’d
Surface
E min, kcal/mol
Preferred site of adsorption
3 and 12 Å
−15.91
12 Å slice above large cage
4 and 13 Å
−15.72
13 Å slice above large cage
5 and 14 Å
−14.90
5 Å slice below large cage
6 and 15 Å
−13.61
6 Å slice below small cage
7 and 16 Å
−15.81
7 Å slice below small cage
8 and 17 Å
−12.34
17 Å slice above large cage
0 and 5 Å
−15.99
0 Å slice below large cage
1 and 6 Å
−12.13
1 Å slice below small cage
2 and 7 Å
−14.47
7 Å slice above large cage
3 and 8 Å
−11.90
8 Å slice above large cage
4 and 9 Å
−15.76
4 Å slice below large cage
10 and 15 Å
−12.17
15 Å slice above small cage
11 and 16 Å
−12.48
11 Å slice below small cage
12 and 17 Å
−11.76
12 Å slice below small cage
13 and 18 Å
−16.92
13 Å slice below large cage
14 and 19 Å
−12.83
14 Å slice below large cage
20 and 25 Å
−15.53
20 Å slice below small cage
21 and 26 Å
−13.46
21 Å slice below small cage
22 and 27 Å
−13.02
22 Å slice below small cage
23 and 28 Å
−14.49
28 Å slice above large cage
24 and 29 Å
−13.55
24 Å slice below large cage
sII (1,1,1) sliced at
(2) It was noticed that the monomers tend to adsorb in such an orientation that the ring
group of a monomer would be inside a partial hydrate cage at the surface, while
the backbone part of a monomer would be outside of the cage. Oxygen atoms of the
monomers were usually hydrogen bonded to hydrogens of water molecules on the
hydrate surfaces.
(3) The large hydrate cavities (51262 for sI and 51264 for sII) are preferred for adsorption since
the monomers adsorbed more frequently near the large than the small cavities.
(4) On the average for all surfaces PVCap adsorbed 10% stronger than PVP on sII {111} faces
which are usually encountered in industry.
For the further simulations one hydrate surface was selected. This was a sII {111} surface
sliced at depths of 8 and 13 Å. The reason for selecting this surface was the presence of open
Computer modeling of interaction between a hydrate surface and an inhibitor
317
TABLE 10.15 Energies of adsorption of a PVCap monomer on different surfaces.
Surface
E min, kcal/mol
Preferred site of adsorption
0 and 9 Å
−15.02
9 Å slice above large cage
1 and 10 Å
−10.32
1 Å slice below small cage
2 and 11 Å
−12.46
11 Å slice above small cage
3 and 12 Å
−15.99
12 Å slice above large cage
4 and 13 Å
−13.91
4 Å slice below large cage
5 and 14 Å
−16.18
14 Å slice above large cage
6 and 15 Å
−13.58
6 Å slice below small cage
7 and 16 Å
−12.83
7 Å slice below large cage
8 and 17 Å
−12.71
8 Å slice below large cage
0 and 9 Å
−16.46
9 Å slice above large cage
1 and 8 Å
−14.04
8 Å slice above large cage
2 and 10 Å
−14.62
2 Å slice below small cage
3 and 11 Å
−16.19
3 Å slice below large cage
4 and 12 Å
−15.18
4 Å slice below large cage
5 and 13 Å
−17.11
5 Å slice below large cage
6 and 14 Å
−13.49
6 Å slice below small cage
7 and 15 Å
−16.80
7 Å slice below large cage
16 and 23 Å
−16.08
16 Å slice below small cage
17 and 24 Å
−15.72
17 Å slice below large cage
18 and 25 Å
−15.46
18 Å slice below large cage
19 and 26 Å
−16.28
19 Å slice below large cage
20 and 27 Å
−13.30
27 Å slice above large cage
21 and 28 Å
−12.84
21 Å slice below small cage
22 and 29 Å
−14.10
22 Å slice below small cage
sII (1,0,0) sliced at
sII (1,1,1) sliced at
large cavities which would represent adsorption sites for tested monomers on one side of the
surface, and open small cavities on the other side.
The simulation length was set at 100,000 MC attempted moves which was sufficient for
the system energy equilibration. This involved about 50,000 translation attempts and 50,000
rotation attempts about half of which were accepted. The acceptance ratios were set to 0.5 as
recommended by Prof. Haile.
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10. Research methods in flow assurance
Simulation results included a graphical image showing the position of an adsorbed inhibitor on hydrate with a sample output shown in Fig. 10.73, and a histogram distribution of
adsorption energies during the simulation (Fig. 10.74). Hydrogen bonding was not explicitly
included in the calculation. The presence of hydrogen bonds was determined postfactum
from geometric position of inhibitor relative to the surface.
Relative positions of the histograms shown in Fig. 10.74 indicate that PVCap and PVP have
similar adsorption capacities, and that PVA adsorbs weaker than PVP or PVCap.
The results of simulating adsorption of PVP, PVCap and PVA monomers ten times each
indicated that the strongest energy of adsorption was exhibited by PVP (Table 10.16). The adsorption energies of inhibitors (PVP and PVCap) were more favorable than of a non-inhibitor
(PVA). Adsorption of several other chemicals was tested on the same surface. These results
are also summarized in Table 10.16.
The obtained results indicate that the adsorption energy of PVCap monomer is 0.5%
weaker than that of PVP. The weaker adsorption of PVCap monomer can be explained by a
40% larger hydrocarbon part of its side group compared to PVP and the same sizes of polar
amide groups. The experiments clearly show that PVCap (10,000 MW) is a better hydrate
kinetic inhibitor than PVP (350,000 MW) (Lederhos et al., 1996). This suggests that the adsorption energy is not the only parameter which defines a good inhibitor.
The modeling work reported by Rodger (1994a,b) also stated that adsorption of PVP on
different surfaces of sI and sII hydrates was energetically favorable, but no comparison was
FIG. 10.73 Monomer of PVCap adsorbed on the {111} surface of sII hydrate. Hydrogen bonds are shown by
dashed lines.
319
Computer modeling of interaction between a hydrate surface and an inhibitor
FIG. 10.74 Histogram distributions of adsorption energy during the simulation for different monomers on sII
{111} slice of hydrate (surfaces at 8 Å and 13 Å from origin).
TABLE 10.16 Averaged results of docking study on {111} face of sII hydrate.
Polymer IUPAC name
E adsorption (kcal/
mol) average value
Preferred site of
adsorption
PVCap
Poly(1-vinyl-azepan-2-one)
−16.31
Near an open 51264 cage
PVP
Poly(1-vinyl-pyrrolidin-2-one)
−16.39
Near an open 51264 cage
PVA
Poly(vinyl-alcohol)
−11.0
Near an open 51264 cage
#1
Poly(1-vinyl-piperidin-4-one)
−20.87
Near a completed 512
cage
#3
Poly(1-acryloyl-piperidin-4-one)
−17.54
Near an open 512 cage
PAM
Poly(acrylamide)
−14.99
Near an open 512 cage
Succinimide
Poly(1-vinyl-pyrrolidine-2,5-dione) −14.68
Near an open 512 cage
Monomer
Chemical
structure
done with PVCap. The work reported by Rodger was done using both commercial software
packages Cerius2 and MOPAC, and non-commercial code. A more recent work from the same
group (Carver et al., 1996) also reported that a monomer of PVP can adsorb with its pendant
group or with its backbone part in a partially completed hydrate cavities. However, in their
work the authors didn't discard the runs where the monomer entered the hydrate cavity with
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10. Research methods in flow assurance
its backbone pointing into cavity rather than only its side group. Such a conformation is improbable in a real polymer system from steric considerations.
The results of our simulations performed using Cerius2 have shown that monomers of
both inhibitors and non-inhibitors exhibit favorable but different energies of adsorption on
hydrate surface (no polymer evidence presented yet). Non-inhibitors poly(vinylalcohol),
poly(acrylamide) and poly(N-succinimide) adsorbed with a 9–48% weaker interaction than
PVP or PVCap.
Simulating the motion of a water molecule around a fixed monomer of PVP was done
using the Cerius2 to determine whether the carbonyl group of inhibitors or a nitrogen atom
interact with water. Monte Carlo simulation of a single water molecule near the PVP monomer has indicated that even without explicitly calculated hydrogen bonding water is most
likely to be near the carbonyl oxygen of PVP. Fig. 10.75 shows the locations of the water molecule center of mass during the simulation. The more dense region near the double-bonded
carbonyl oxygen indicates that water preferred to associate with this part of a PVP monomer.
The less dense regions near the hydrocarbon parts of the monomer represent a hydrophobic
solvation shell around the monomer.
Using the hand-written software for studying interaction of water and monomers
Some force fields (CHARMm, DREIDING) use a hydrogen bond potential to describe
i­nteractions between atoms involved in hydrogen bonds. The used module of the Cerius2
­program didn't have explicit hydrogen-bonding between the hydrate surface and an ­inhibitor
FIG. 10.75 Association of water molecule with the carbonyl group of a PVP monomer.
Computer modeling of interaction between a hydrate surface and an inhibitor
321
­ onomer although it used the DREIDING forcefield. In Cerius2 hydrogen bonding was
m
modeled by the charge-charge interaction. This is a common approach for simulation of
­water-based systems (Jorgensen et al., 1983; Rodger, 1994b). However, this approach does not
give a complete set of water-water interactions and results in lower ice melting temperature
(e.g., 200 K for SPC water). The major reasons for writing our own code were to improve the
potential model by adding the hydrogen bonding interaction and to be able to sample any
variable at any time during the simulation neither of which could be explicitly done using
Cerius2.
The main Monte-Carlo routine was written by Professor James Haile of the Clemson
University while on sabbatical at the CSM. Hydrogen bonding interaction of up to 5 kcal/mol
was included in the hand-written code for the simulation of chemicals' interactions with a
SPC-water-based (Berendsen et al., 1981) hydrate surface along with the dispersion (LennardJones) and electrostatic (Coulombic) interactions. The SPC water potential were validated
along with other water potentials by Jorgensen et al. (1983) and is widely used for water
simulations. Relative magnitudes of all interactions used in the hand-written code are shown
in Fig. 10.76. The hydrogen bonding was implemented as a distance and angle dependent interaction based on the Lennard-Jones 12–10 potential. The donor-acceptor distance cutoff was
set to 4 Å and a spline function was applied to the hydrogen-bonding potential in the interval
between 3.5 and 4 Å to avoid an abrupt potential cutoff. A hydrogen bond was strongest at
a 180° donor‑hydrogen-acceptor angle and at a 2.8 Å donor-acceptor distance. More specific
details of the simulation can be found in the Computer Code section which contains the polymer adsorption simulation code.
Testing the simulation code
Prior to using the code, its components were tested:
(1) The interaction potentials were calculated by hand for a test pair of molecules and were
found to be same as calculated by the program.
FIG. 10.76 Relative magnitudes of the Lennard-Jones, electrostatic and hydrogen-bond potentials.
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10. Research methods in flow assurance
(2) The rotation and translation algorithms were tested for proper reorientation and
positioning of monomers using a set of discrete angles (0,45, 90°) and steps in each
dimension.
(3) The sampling bin size of the radial correlation function was optimized. The area of
produced correlation function was integrated to yield a normalized value of 100 as
required.
(4) Proper functioning of cubic and rhombic periodic boundary conditions was verified.
(5) It was shown that the starting position of a moving molecule near the fixed molecule
does not affect the resulting strength or place of adsorption by performing 8 simulations
of one water molecule moving around a fixed PVP monomer.
The following variables were also tested: position of hydrate slice; thickness of slice; length
of equilibration; attractive effect of non-bonded interactions; number of runs required for
each slice; size of the hydrate surface (1 × 1 or 2 × 2 unit cells area).
Using the simulation code
After testing the code, the simulation of water molecule movement around a fixed inhibitor monomers was done to compare it with the results obtained using Cerius2. In 10 trial runs
the sufficient equilibration “time” for the running-average energy was determined to be at
most 26,000 steps. Simulations consisted of 200,000 move attempts with radial correlation
functions analysis output every 100,000 steps.
The temperature was fixed at 273.15 K. Charges on the water molecule were set to the
DREIDING forcefield values of −0.68 on oxygen and 0.34 on each hydrogen. The resulting
dipole moment was 2.01 Debyes, which is close to the experimental value of 1.85 Debyes for
water in the gas phase. The SPC parameters for water were adopted in later simulations.
Charges on the vinylpyrrolidone monomer were calculated using the QEq charge equilibration method available in the Cerius2 program. The QEq charge calculation method was
proposed and validated by Rappe and Goddard (1991). Their method showed excellent
agreement of calculated dipole moments with experimental data for 20 salts and 7 simple
organic compounds like water or methane. Also comparison of the QEq method with other
methods (like AMBER2) showed acceptable agreement for 18 simple organic compounds and
several polypeptides.
In our work for a PVP monomer the dipole moment vector was found to lie close to the
plane of the pyrrolidone ring, pointing from the oxygen atom towards the nitrogen atom.
The following monomers were tested using the hand-written code: vinylpyrrolidone,
vinylcaprolactam, vinyl-N,N-dimethylacrylamide, vinyl-N-acrylamide, and vinyl-alcohol
(a.k.a. ethanol). It was found that the water molecule always moves close to the carbonyl
­oxygen of the pyrrolidone ring. The peak of the Owater-Opyrrolidone radial correlation function
was found to be between 2.9 and 3.0 Å (Fig. 10.77). Investigation of the effect of the initial
water position with respect to the PVP monomer in the simulation box was done by running
eight simulations; in each simulation the water molecule was initially placed in a different
­octant. The final running- average energies were found to have a maximum standard deviation of 6.2% after 200,000 steps. The OO radial distribution peak was between 2.9 and 3.0 Å
in all cases. Thus it was determined that the starting position of the water molecule in the
simulation box does not affect the results.
323
Computer modeling of interaction between a hydrate surface and an inhibitor
4.00
N
1
C
O
3.00
2
3
Distance from oxygen to
Oxygen
Nitrogen
2.00
Carbonyl
carbon
Carbon 1
Carbon 2
Carbon 3
1.00
0.00
0.00
2.00
4.00
6.00
8.00
FIG. 10.77 PVP Monomer atom-water oxygen pair correlation functions overlapping for a 100,000 step and a
500,000 step MC simulations.
In order to determine that the run time was sufficiently long to sample all energy states,
the radial distribution functions between water oxygen and the atoms of the pyrrolidone ring
were compared for an average of eight 100,000 steps runs with an average of eight 500,000
steps runs. The distribution functions (Fig. 10.77) precisely overlap, having no variation in
shape. The only difference between the two sets of runs was the smaller statistical deviation
for the 500,000 runs shown as error bars on peak of the oxygen‑oxygen line. The running-­
average energies of interaction between water and the monomer were also different by <1%.
This indicated that the water-monomer simulation length of 100,000 steps was sufficient for
sampling the most probable energy states.
The running-average energies averaged over 8 runs are presented for the studied monomers in Table 10.17. Vinyl-alcohol (ethanol) had the strongest interaction with water, followed
by the monomers of PVCap, PNDMAm, PVP, and PNAm. Since ethanol is a known thermodynamic inhibitor (Sloan, 1990), this outcome is not very surprising. The other monomers'
interaction with water reflect their polymers' inhibition performance in natural gas systems
in the correct order of the decreasing effectiveness.
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10. Research methods in flow assurance
TABLE 10.17 Energies of interaction between water and monomers.
Monomer name
Final running-average energy, kcal/mol
Vinylpyrrolidone
−7.86
Vinylcaprolactam
−8.11
Vinyl-N-dimethylacrylamide
−7.62
Vinyl-N-acrylamide
−7.06
Vinyl-alcohol (a.k.a. ethenol)
−8.57
Adsorption of monomers on discrete hydrate surface
The next step in using the hand-written code was to modify it for studying monomer adsorption on a hydrate surface consisting of discrete water molecules. The subroutine for constructing the {100}, {110}, and {111} slices of structure I and structure II hydrates was written
and extensively tested.
Since a long-range charge-charge interaction is used in this study, thickness of the hydrate
slice becomes an important factor. Interaction energy was compared for a PVP monomer
above a hydrate surface for hydrate surfaces of different thickness. This study indicated that
after the hydrate thickness reaches 8 Å, further increase in the interaction energy is insignificant for {111} or {100} of sII. The results of this study are presented in Fig. 10.78 as the fraction
of the interaction energy versus the hydrate slab thickness. 100% of the interaction energy
was taken at a hydrate slab thickness of 100 Å. Hydrate slabs with thicknesses of 3, 5, 8, 9, 10,
12, 15, 20, 24, 30, 40, and 100 Å were tested for hydrates of sI and sII both for {100} and {111}
faces. Each slice was prepared three times with its surface at three equally spaced positions in
the unit cell (e.g., for sII {111} face at 0, 10, and 20 Å), and the results were averaged.
In cubic unit cells the particles (atoms, ions or molecules) are arranged similarly at some
intervals. Distance between planes with similarly arranged particles is called interplanar
spacing. Interplanar spacing for a cubic unit cell in the <100> direction equals to the unit
cell side length (Myerson, 1993) which is 17.1 Å for sII. Interplanar spacing in ⟨110⟩ direction
equals 2 / 2 unit cell side lengths. Interplanar spacing in ⟨111⟩ direction equals 3 / 3 unit
cell side lengths (Fig. 10.79). For example, in a sII hydrate the shortest distance between parallel planes containing hexagonal rings of water molecules is 3 / 3 times 17.1 Å.
Simulations of monomer adsorption were run on hydrate surfaces of a fixed thickness of
8 Å, but sliced at different depths. For sI the {110} face is the one which is exhibited in a single
crystal. The interplanar spacing for this face is 8.49 Å. Eight surfaces from 0 to 7.43 Å of the
unit cell origin with increments of 1.06 Å were studied for this face. For the sII {111} face the
interplanar spacing is 9.87 Å. Ten surfaces from 0 to 8.89 Å were studied.
Each simulation was conducted 10 times in order to sample the potential space sufficiently.
Results after 4–5 runs usually reproduced themselves. Initially, strong forces (Coulombic and
hydrogen-bonding) were turned off and the monomer was moving about the periodic hydrate surface in order to assume a random position and orientation above the surface. Then
these forces were turned on, and the monomer was allowed to equilibrate for 50,000 MC
attempts. After that, the simulation variables were sampled for 100,000 steps.
sII-111
sII-100
1.00
sI-111
Fraction of Energy
0.90
sI-100
0.80
0.70
0.60
0
16
32
48
64
Hydrate surface Thickness, A
80
96
FIG. 10.78 Energy of interaction between monomer and hydrate as a function of hydrate thickness.
29.62
17.1
FIG. 10.79 Positions of equivalent {111} surfaces in a sII cubic unit cell. Distance between neighboring
planes is 29.62 Å •
1
3
.
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10. Research methods in flow assurance
In order to avoid the physically unrealistic results the monomer's orientation was restricted
so that it points with its backbone part away from the hydrate surface. The nitrogen-backbone
covalent bond axis was allowed to vary between 0° (normal to surface) and 90° (flat on surface) with respect to the plane of hydrate surface.
The main variables monitored during the simulation of monomers' adsorption on sI and
sII hydrates were: (1) running-average energy, (2) number of hydrogen bonds, and (3) correlation functions between selected monomer atoms and a hydrate surface. It was found that
only on some slices monomer preferred to adsorb into a partially completed cavity. In other
cases the monomer was adsorbed on the surface without entering the cavity. Large cavities
were a preferred adsorption site, compared to the small cavities (Table 10.18).
A sample orientation of a PVCap monomer adsorbed in a hydrate cavity is shown in
Fig. 10.80. It supports the finding of the previous work with the Cerius2 program that inhibitor monomers can enter the partially completed hydrate cavities because they don't experience steric hindrance of a polymer backbone. For a polymer such entrance may be possible
if a side group is properly oriented with respect to the hydrate surface and its neighboring
segments don't hinder its entrance into a cavity.
Selected results of the simulation of PVP, PVCap and PVA monomers adsorption on hydrates are presented in Table 10.19. In the first row of the column the average of running-­
average energies for all hydrate surfaces is shown. According to these results, PVP should be
the best inhibitor since it adsorbs 6.5% stronger than PVCap, but PVCap actually is (Lederhos
et al., 1996). This result is the same as from Cerius2 which indicated that the adsorption e­ nergy
TABLE 10.18 Locations of inhibitor monomers' adsorption (averaged over
180 runs for each chemical).
Fraction of monomers adsorbed
On surface
Into cavity
Average for PVP and PVCap
0.56
0.44
PVP
0.48
0.52
PVCap
0.64
0.36
FIG. 10.80 Monomer of PVCap adsorbed into the large cavity of sII hydrate.
327
Computer modeling of interaction between a hydrate surface and an inhibitor
TABLE 10.19 Some properties of monomers' adsorption on hydrates.
PVP on sI
{110} face
PVP on sII
{111} face
PVCap on sI
{110} face
PVCap on sII
{111} face
PVA on sI
{110} face
PVA on sII
{111} face
Average energy of
adsorption for all surfaces
−21.45
−27.51
−21.32
−25.71
−19.22
−24.83
Average energy of
adsorption on surfaces
with pattern
−21.60
−28.15
−20.09
−26.16
−18.94
−25.32
Average energy at depth
0Å
−25.88
−29.41
−25.00
−28.80
−23.44
−29.14
1
−23.33
−27.83
−21.98
−25.85
−21.85
−23.31
2
−22.56
−27.20
−21.41
−24.79
−19.55
−21.25
3
−16.49
−26.15
−15.24
−26.00
−16.68
−24.89
4
−18.92
−29.04
−20.09
−24.56
−14.98
−28.23
5
−18.18
−27.97
−17.12
−28.94
−16.20
−23.96
6
−23.14
−28.15
−24.58
−26.46
−19.06
−21.92
7
−23.11
−26.57
−25.17
−23.28
−21.99
−21.33
8
–
−26.09
–
−25.80
–
−23.24
9
–
−26.73
–
−22.62
–
−30.99
Average elevation of
2.20
monomer above surface, Å
1.53
2.79
2.41
0.93
0.61
Average number of H
bonds (HB) to surface
1.26
1.06
1.18
1.03
1.21
1.04
% runs with 0 HB
2.5
17
1.25
18
0
19
With 1
68.75
60
80
51
78.75
58
With 2
28.75
23
18.75
31
21.25
23
Property
of PVCap monomer is 0.5% weaker than that of PVP. The larger hydrocarbon part of PVCap's
side group compared to PVP caused weaker adsorption of PVCap monomer. The monomer
adsorption energy is not the only parameter which defines a good inhibitor.
The second row presents the average of energies only for those surfaces on which locations
of monomer made a recognizable pattern (e.g., only above the large cavities of hydrate). The
next rows show the running-average energies for each surface of hydrate, averaged over 10
runs. Average elevation of the monomer is measured by the position of the nitrogen atom in
the monomer above the hydrate surface. The numbers of hydrogen bonds between monomers and the surface are analyzed in the last rows of Table 10.19.
Comparison and contrast with experimental results
The main attention in the simulations was given to the adsorption on the {111} face of sII
both because sII is the industrially encountered hydrate for which the chemicals are being developed, and because the {111} face was shown experimentally to dominate in the sII hydrate.
328
10. Research methods in flow assurance
The adsorption energy exhibited by PVCap monomer is weaker than that of PVP, although
PVCap is a better inhibitor than PVP. The weaker adsorption of PVCap monomer can be
explained by the larger hydrocarbon part of its side group compared to PVP and the same
sizes of polar amide groups. Both PVP and PVCap adsorbed to hydrate stronger than a non-­
inhibitor PVA.
After averaging the results for all 300 runs for the adsorption of PVP, PVCap, and PVA
monomers on sII {111} surfaces it was found that if a monomer adsorbed to the hydrate surface with two hydrogen bonds (e.g., stronger), it was at a larger distance from surface than
if it were adsorbed with one or no hydrogen bonds (Table 10.20). This suggests that strong
adsorption through hydrogen bonding cannot occur inside a hydrate cavity because there are
no water hydrogens pointing inward the cavity. On the hydrate surface and on periphery of
the cavities the hydrogens pointing away from the surface are present.
Another observed property of monomers adsorption (Fig. 10.81) is that the distance between hydrate surface and N atom distance for PVP, PVCap and surface-to-COH distance for
PVA varied with the hydrate surface type. All monomers adsorbed closer to surface on sII
compared to sI. The variation between the monomers can be attributed to their difference in
size. PVCap adsorbed farther from surface than PVP or PVA monomers. The smallest monomer, PVA, which is the poorest inhibitor, adsorbed closest to both sI and sII hydrate surfaces
on average, and in some simulations entered open hydrate cavity.
TABLE 10.20 Averaged position of reference atom (nitrogen for PVCap and PVP
and hydroxylated carbon for PVA) above surface vs. number of hydrogen bonds.
Number of hydrogen bonds
0
1
2
Average elevation of reference atom
above hydrate surface
0.52
1.70
1.84
3.5
3
2.5
Elevation, A
2
1.5
1
0.5
0
–0.5
–1
PVCap sI
PVCap sII
PVPsI
PVPsII
PVA sI
PVA sII
FIG. 10.81 Surface-to-N atom distance for PVP, PVCap and surface-to-COH distance for PVA.
Computer modeling of interaction between a hydrate surface and an inhibitor
329
It can be concluded from the monomer study that both inhibitors (PVP and PVCap) and
non-inhibitors (PVA) adsorbed to the hydrate surface. Difference in the strength of adsorption
was not large (under 10%), but the difference in inhibition is great (inhibitor vs. non-inhibitor).
Adsorption of inhibitor polymers on hydrate
Simulating the adsorption of short polymer chains on hydrate called for a serious modification of the program. The Monte Carlo moves of rotation and translation were already
present in the simulation. In order to obtain realistic conformations of the polymer chain on
hydrate surface, the polymer backbone had to be flexible. Molecular dynamics was ruled
out because the results would not be directly comparable to the previously obtained data for
monomers. Lattice Monte Carlo is a widely used model for studying polymer adsorption on
solids. However, this approach requires prior knowledge or an assumption of the adsorption
strength for each segment, and atomically correct polymer chains could not be simulated.
The pivot Monte Carlo method was used for obtaining a new conformation of a polymer by
making a bold change in backbone structure. Many of the pivot attempts got rejected because of
the higher energy final state, but the accepted move produces an “essentially new” configuration
(Madras and Sokal, 1988). This algorithm allowed us to use the existing Monte Carlo code and
run simulations with atomically correct polymer chains and hydrate surfaces. Extensive validation of the polymer adsorption program was not done since it included the already validated
monomer adsorption program and a new pivot-move part. Several trial runs were done to ensure
the proper functioning of the added pivot-move part of the simulation. Tests were performed
with 10-­segment polymers of PVP and PVA as simple but representative chemicals. The chains
segments reoriented in proper directions and the polymer chain wasn't broken by this motion.
The sII {111} surface was selected for studying the adsorption of short polymers because of
sII hydrates' industrial significance and because our single crystal experiments indicated that
the {111} face dominates the sII THF hydrate.
From the monomer studies it was found that the strength of adsorption on sII {111} face varied with the surface distance (depth) from unit cell origin. A study of hydrate surface stability
was done using Cerius2 in order to determine the most stable hydrate surface for polymer
adsorption. A one-water-molecule-thick 5 Å {111} slice of hydrate was cut from the sII unit cell
at different positions, and the surface potential energy was calculated. We used DREIDING
interaction parameters with hydrogen bonding potential well depth set to 5 kcal/mol and SPC
Lennard-Jones and charge parameters for atoms in water. Two valleys were found at about 3
and 7 Å from the unit cell origin. These locations correspond to the surfaces where the large
and the small cavities get completed (Fig. 10.82). The same study was repeated for 8.5 Å thick
slices of hydrate. The most stable slice was the one with its surface 7 Å from the unit cell origin.
This surface exhibits completed small 512 cavities and open 51264 cavities. The most stable surface was adopted for studying adsorption of polymers.
The same procedure was used to compare relative stabilities of {100}, {110}, and {111} hydrate surfaces of sII. It was found that in each of the three directions the number of water
molecules falling into a 5 Å-thick slab of hydrate varies, so the potential energies were normalized by the number of water molecules. The equilibrium shape of a crystal is that of its
minimum energy. This is called the Wulff condition (Myerson, 1993). {111} planes show the
most ­stability (Fig. 10.83) which possibly explains why they are observed experimentally;
same result was obtained for non-normalized surface energies.
330
10. Research methods in flow assurance
0.00
True stability (5A thick)
Surface potential energy, kcal/mol
Studied slice stability (8.5 Å thick)
–400.00
–800.00
Large
cavity
completed
–1200.00
Small
cavity
completed
–1600.00
-2000.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
Distance from the unit cell origin to the surface top, Å
FIG. 10.82 Stability of sII {111} hydrate surfaces sliced at different depths from unit cell origin.
Preparation of the short polymer chain for simulation started with its construction in a
syndiotactic conformation, energy minimization and charge equilibration in the Cerius2 program. The total charge on the polymer was neutral. After the geometry and charge equilibration, the polymer was solvated in 350–500 SPC waters and run through a short (10–20 ps)
MD equilibration with 1 fs timesteps allowing the polymer to relax an assume the solvated
configuration. Afterwards, the solvation box was removed and polymer was saved in a. MSI
format. From the. MSI file the hand written program placed the polymer in its initial position
above hydrate surface.
In a MC simulation three types of moves were attempted per each cycle: (1) translation of
the whole chain, (2) rotation of the whole chain, and (3) pivot move of some randomly chosen
part of the chain with respect to the other part.
For shorter 3-segment and 5-segment chains 50,000 equilibration cycles and 50,000 run
cycles were performed. For longer 8-segment chains the equilibration length was increased
to 100,000 cycles to allow for energy equilibration. All comparisons were made for the same
molar concentrations of polymers; weight concentrations differed.
Motion of polymer about the hydrate surface was controlled by the Metropolis MonteCarlo algorithm based on the sum of the intramolecular polymer energy and the adsorption energy. Modifying the acceptance ratio can decrease the length of system equilibration
331
Computer modeling of interaction between a hydrate surface and an inhibitor
–4
111
Surface potential energy per molecule, kcal/mol
100
110
–6
–8
–10
–12
Large
cavity
completed
Small
cavity
completed
–14
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17
Distance from the unit cell origin to the surface top, Å
FIG. 10.83 Stability of sII {100}, {110}, and {111} hydrate surfaces sliced at different depths from unit cell origin.
(Allen and Tildesley, 1987). We varied the acceptance ratios of translation, rotation and
pivot attempts between 0.125, 0.125, 0.125 and 0.5, 0.5, 0.5 respectively.
Acceptance ratios of 0.25, 0.125, and 0.25 for translation, rotation and pivot attempts respectively were found to give the fastest potential energy equilibration. After equilibration,
the ratios were set to 0.35, 0.25, and 0.35 respectively to make less bold moves of polymer and
allow relaxation of polymer on the surface.
The temperature was set to 723 K for the equilibration part and was halved to 361 K during
the run period. The initial 25,000 cycles of the run period were allocated for re-equilibration of
the polymer at the new temperature, and only the final 25,000 cycles were analyzed.
The seven monitored variables were:
(1) step sizes and acceptance ratios for the elementary moves of translation (Å), rotation
(radians) and pivot (radians);
(2) position of the reference atom (central carbon of backbone) averaged over 1000 cycle
intervals;
(3) number of intramolecular polymer hydrogen bonds and number of hydrogen bonds
between polymer and hydrate averaged over 1000 cycle intervals;
(4) polymer end-to-end distance averaged over 1000 cycle intervals;
332
10. Research methods in flow assurance
(5) intramolecular polymer energy averaged over 1000 cycle intervals;
(6) the potential energy of adsorption averaged over 1000 cycle intervals;
(7) running-average energy of the system.
Each polymer adsorption simulation was repeated 4 times with different random number
generator seeds, and the results were averaged.
Visual images of the simulated system were stored every 10,000 cycles. From these images
it was possible to see the conformation of a short polymer chain on hydrate surface and orientations of each side group relative to the surface.
For trimer, pentamer and octamer adsorption three conformations were: (1) laying flat
with the backbone parallel to the surface (train), (2) with some part of the chain adsorbed and
the other part not adsorbed (tail), and (3) with two ends of the chain adsorbed (loop). The
preferred conformation was a train for most polymers (Table 10.21). An example of a polymer
adsorbed on hydrate is presented in Fig. 10.84.
TABLE 10.21 Properties of short polymers' adsorption on {111} face of sII hydrate for each of 4 repeated
simulations.
Conformation
Tail
Loop
Adsorption site
12 4
In 5 6 cavity
Above 51264 cage(s)
Periphery of 51264
Chemical name
Flat
PVCap trimer
****
PVCap pentamer
**
**
PVCap octamer
***
*
PVP trimer
****
PVP pentamer
***
*
**
****
PVP octamer
***
*
**
****
PVA trimer
***
*
*
PVA pentamer
***
*
****
PVA octamer
**
new-PVP octamer
*
new-PVCap trimer
****
new-PVCap pentamer
***
new-PVCap octamer
****
8-ring-PVCap-8mer
*
*
new-2-PVP-octamer
***
new-2-PVCap-8mer
***
new-3-PVP octamer
***
Average fraction
0.72
***
***
***
**
*
***
**
*
***
**helix
*
**
****
*
***
****
*
***
**
*
***
****
**
****
****
****
**
*
****
*
*
***
****
*
***
**
*
0.18
0.10
0.15
****
***
****
0.25
0.60
One large star indicates a result for one simulation (e.g., PVCap trimer adsorbed flat in all 4 runs).
Small stars indicate that there were two major adsorption sites in one simulation (e.g., part of the PVCap trimer adsorbed in a cavity
and the rest on periphery of a cavity in 3 runs and only on periphery in 1 run).
Computer modeling of interaction between a hydrate surface and an inhibitor
333
FIG. 10.84 Octamer of PVP adsorbed on sII {111} face. (a) Top view (along <111> direction), (b) side view (along
<110> direction); one side group is adsorbed into an open 51264 cavity.
Formation of a loop or a tail conformation was observed less often. Most polymers prefer
to adsorb flat on the surface because each segment is strongly attracted to the surface by electrostatic interaction. Hydrogen bonding increases the attraction. Intramolecular hydrogen
bonding was observed in several simulations for PVA chains.
The preferred adsorption sites for all simulated polymers were categorized in three types:
(1) in-cavity, when a side group of a polymer adsorbed inside an open hydrate cavity, (2)
above an open hydrate cavity, and (3) on cavity periphery, or as combinations of these three
types. Since a hydrate cavity doesn't have water molecules whose hydrogens point inward
that cavity, the hydrogen atoms are only available for hydrogen bonding on the periphery of
an open cavity.
Monomer adsorption simulations showed that for PVP and PVCap on average 0.44 monomers adsorbed in an open cavity and 0.56 on the periphery of a cavity (Table 10.18). In simulation of octamers at most one side group adsorbed in a cavity. For PVP and PVCap octamers
the average fraction of the side groups adsorbed in cavity changed to 0.0625 per monomer
unit, or 0.5 per chain. For all polymers adsorption of a side group in cavity was observed in
29% of all runs, and only for chemicals having carbonyl (CO) groups. Most polymer chains
adsorbed at the periphery of an open 51264 cavity, or both at the periphery and above cavity.
In the polymer adsorption simulations we were primarily interested in the strength of adsorption to the surface and in the number of hydrogen bonds between the chain and the surface. It
was found that known inhibitor polymers (new-3-PVP, PVP and PVCap) adsorbed stronger than
non-inhibitors (PVA) (Fig. 10.85). Strongly adsorbing impurities are expected to have a much
greater effect on the growth rate of crystals than impurities that adsorb weakly (Myerson, 1993).
334
10. Research methods in flow assurance
polymer type
0
–20
Eadsorption (kcal/mol)
–40
–60
–80
–100
–120
std.dev.
std.dev.
ave
–140
FIG. 10.85 Strengths of adsorption for all simulated chemicals.
Guest molecules adsorption on a hydrate surface
In order to investigate the hypothesis of an adsorbed inhibitor hindering building blocks from
reaching the growing crystal surface, a separate set of MC simulations was performed. Water was
assumed to be abundant near the hydrate surface. Guest molecules adsorption on a hydrate surface was modeled with a bare hydrate surface and with a hydrate surface having a preadsorbed
polymer. Position of the preadsorbed polymer was obtained from the polymer adsorption runs.
The guest molecule selected to be a guest molecule was prepared using Cerius2, and small
partial charges were assigned to its atoms. Monte Carlo simulation for methane used the same
program as was used for polymer adsorption except the pivot moves were discarded completely, and rotation moves were attempted once in 10 cycles. Methane is a spherical molecule
and its rotations were almost always accepted so that acceptance was monitored only for translational moves. Methane molecule was atomically correct (e.g., had explicit carbon and four
hydrogens with non-zero Lennard-Jones diameters). It could interact both with the hydrate surface and with the polymer fixed on surface. Only Lennard-Jones and electrostatic interactions
between methane and hydrate/polymer were calculated. Hydrogen bonding was neglected.
Validation of the methane adsorption model
In the hand-written code we used only the nonbonded interactions in DREIDING which
consist of van der Waals or dispersion (Evdw), electrostatic (EQ), and explicit hydrogen bond
(Ehb)terms (Fig. 10.79):
Enb = Evdw + EQ + Ehb .
At one atmosphere the volume occupied by 1 mol of methane is 22.4 l. This translates to
37,191 Å3 per methane molecule at 1 atm. The volume of the simulation box above the hydrate
surface was 7597 Å3 which is 5 times smaller than the volume per molecule of methane at one
atmosphere. This suggests that the pressure in the simulation can be estimated as 5 atm.
335
Computer modeling of interaction between a hydrate surface and an inhibitor
Simulations for methane adsorption on hydrate surface indicate that methane condenses
at a temperature of 100 K. Vapor pressure calculation was performed for methane using the
empirical equation obtained from the reference (Reid et al., 1987). Vapor pressure of 5 atm is
exerted at 90.1 K which is close to the value of 100 K obtained in the simulation. However, the
freezing temperature of methane is 90.7 K which means that instead of condensing, methane
freezes at this temperature. The model closely reflects the methane phase transition at 100 K
as compared to the empirical value of ca. 90 K.
Simulation of methane adsorption
Simulations were performed for a range of temperatures from 100 K to 400 K in 50 K increments. Length of simulations included 50,000 equilibration cycles and 50,000 run cycles. Each
simulation was repeated 4–8 times, and the results were averaged.
It was found that the adsorption of methane in hydrate cavities had changed with the
presence of a polymer on the hydrate surface (Fig. 10.86). Different polymers had different
effects on the methane adsorption. The largest decrease in methane adsorption was caused by
PVCap, followed by PVP and PVA.
1.00
Fraction of simulation CH4 spent in cavities
no polymer
pvcap
pvp
0.80
pva
0.60
0.40
0.20
0.00
100.00
200.00
300.00
400.00
Temperature, K
FIG. 10.86 Adsorption of methane on bare sII {111} hydrate surface and with octamers of PVCap, PVP and PVA.
336
10. Research methods in flow assurance
The curves in Fig. 10.86 are only meaningful up to the temperature of about 200–250 K
above which hydrate would normally melt. The empty hydrate lattice was artificially fixed
in place and could not melt. It was determined that the SPC ice loses its structure (melts) at
a temperature of 200 K (Karim et al., 1990). The difference in chemical potential between ice
and an empty sI hydrate lattice is only 0.31 kcal/mol (Tse et al., 1986).
For sII hydrate the difference is even less at 0.25 kcal/mol, which is less than one hydrogen
bond's strength.
There are several MD simulation estimates of hydrate stability limit ranging from 205 K
(Tse et al., 1983b) to 330 K (Forrisdahl et al., 1996). Tse and coworkers have observed in their
MD study of sI hydrate using SPC model that translational frequency spectra for empty hydrate lattice at 110 K was different from that at 205 K indicating a possible phase transition.
A recent study by Forrisdahl et al. (1996) of hydrate stability with methane guests in an NVT
MD used SPC model for water. The authors indicate that the hydrate stability limit of 330 K
is an overestimate of an experimental value. Guest molecules significantly stabilize empty
hydrate lattice (Rodger, 1991; Tse, 1994).
In the present work we assume that the SPC empty hydrate lattice melting temperature is
same as for SPC ice, i.e., empty hydrate lattice would melt at about 200 K and the results for
higher temperatures would be for unstable hydrate.
The shape of curves in Fig. 10.86 is attributable to the nature of methane interaction with
the hydrate surface and/or the adsorbed polymer. Without polymer on the surface at low
temperature limit methane condenses and doesn't move out of a hydrate cavity. The number
of cycles which methane spent outside hydrate cavities increased with temperature.
In presence of a polymer at 100 K temperature methane condensed on the polymer and
spent less time in hydrate cavities. This results in low adsorption of guest into open cavities.
At 150 K there is a peak in adsorption curves. Methane which mostly adsorbed on polymer
at 100 K is now able to desorb from polymer and reach the hydrate surface. The temperature
is still sufficiently low for methane's thermal motion to overcome the attraction of hydrate
cavities. Methane mostly remains adsorbed in hydrate cavities. This results in a peak in adsorption curves.
At 200 K methane doesn't adsorb in cavities as often because of a higher temperature and
its higher thermal motion. At temperatures above 200 K methane adsorbs less on hydrate and
moves in and out of hydrate cavities. The fraction of methane adsorption on hydrate is higher
with polymers present than on a bare surface because polymer creates additional attraction
for methane towards the hydrate.
Using the computer to design inhibitors
The properties which define a good inhibitor are:
(1) Blocking of guest molecules adsorption on hydrate. This requires (a) relatively large
steric size of a side group (8–12 atoms excluding hydrogens and backbone atoms)
and (b) presence of hydrophobic part in side group for attracting hydrocarbon guest
molecules.
(2) Strong adsorption to surface. In all simulations inhibitors adsorbed stronger than
non-inhibitors. This requires a polar part in side group (like CO) sufficient to make
adsorption and hydrogen bonding of the hydrophobic side group on hydrate favorable.
337
Computer modeling of interaction between a hydrate surface and an inhibitor
(3) Coverage of the surface. It was found that most polymers adsorb on periphery of
large hydrate cavities where water hydrogens pointing from surface are available
for hydrogen bonding. The largest amount of supercooling showed by PVCap was
35 °F for a 1600 MW polymer (Annual Report, 1996). This corresponds to a short
11-segment polymer. Shorter polymers adsorb flat on the surface and cover larger
area. However, a polymer shouldn't be too short because then it could desorb from
hydrate.
Several new chemicals were tested in simulation for the strength of adsorption on hydrate
and for the ability to block methane adsorption on hydrate. These results are summarized in
Table 10.22. Curves for selected chemicals are shown in Fig. 10.87. Growth rates are controlled
by the energetics of molecule attachment to the crystal surface (Hartman and Bennema, 1980).
Thus the adsorbed impurity or inhibitor additive hindering methane adsorption onto hydrate crystal changes the hydrate growth rate. Performance of New-3-PVP a.k.a. UA-210 was
close to that of PVCap in simulation. This was confirmed experimentally.
TABLE 10.22 Averaged results of docking octamers on {111} face of sII hydrate.
Polymer
Chemical
structure
E adsorp., kcal/ Number
mol (average
of H
Polymer IUPAC name value)
bonds
Dipole moment Volume of
of a monomer, a monomer,
Debye
Å3
PVCap
Poly(1-vinyl-azepan2-one)
−69.8
1.85
3.56
150.4
PVP
Poly(1-vinylpyrrolidin-2-one)
−92.9
3.03
3.52
113.9
PVA
Poly(vinyl-alcohol)
−67.7
1.75
2.86
53.1
New-pvp
Poly(1-vinylpyrrolidine-2,3-dione)
−91.7
1.48
5.53
141.0
New-pvcap
Poly(3-vinyl-[1,3]
oxazepane-2,7-dione)
−122.8
2.58
7.09
138.7
8-ring-pvcap
Poly(3-vinyl-[1,3]
oxazocane-2,8-dione)
−88.6
2.00
6.95
155.4
New-2-pvp
Poly(4,4-dimethyl3-vinyloxy-dihydrofuran-2-one)
−84.1
1.88
5.85
153.5
New-2-pvcap
Poly(1-acryloylazepan-2-one)
−102.5
1.75
3.06
165.6
New-3-pvp
Poly(1-acryloylpyrrolidine-2-one)
−92.0
2.00
2.03
131.9
338
10. Research methods in flow assurance
1.00
Fraction of simulation CH4 spent in cavities
no polymer
PVCap
PVP
0.80
new-3-PVP
new-2-PVP
new-2-PVCap
0.60
0.40
0.20
0.00
100.00
200.00
300.00
400.00
Temperature, K
FIG. 10.87 Methane blocking performance of commercially available or feasible chemicals.
Poly(1-acryloyl-azepan-2-one) (also named new-2-pvcap) and poly(4,4-dimethyl-3-­
vinyloxy-dihydro-furan-2-one) (new-2-pvp) are potentially good inhibitors and their synthesis is under way.
Summary of simulations
The following conclusions can be made from the Monte Carlo simulation results:
(1) All studied chemicals (both inhibitors and non-inhibitors) adsorbed on hydrate surface
with favorable energies. More polar chemicals adsorbed stronger. Adsorption strength
increased with the number of hydrogen bonds from polymer to surface. Comparison
of adsorption between monomers and polymers (Table 10.23) shows that both groups
have inhibitors adsorbing stronger to hydrate. However, the adsorption strengths of
PVCap and PVA polymers are very close, but their inhibition performances are different.
Adsorption strength should not be used as the only criterion for finding good inhibitors.
(2) Simulation performance of chemicals in blocking methane adsorption on the hydrate
is strongly related to the gas consumption performance of chemicals. Chemicals with
339
Computer modeling of interaction between a hydrate surface and an inhibitor
TABLE 10.23 Adsorption strengths of existing monomers and 8-segment polymers.
polymer IUPAC name
Monomer
E adsorp.,
kcal/mol
Polymer
E adsorp.,
kcal/mol
Inhibitor as a
polymer
PVCap
Poly(1-vinyl-azepan-2-one)
−16.31
−69.8
Best
PVP
Poly(1-vinyl-pyrrolidin-2-one)
−16.39
−92.9
Good
PVA
Poly(vinyl-alcohol)
−11.0
−67.7
Non-inhibitor
New-3-pvp
Poly(1-acryloyl-pyrrolidine-2-one)
−92.0
Good-best
Succinimide
Poly(1-vinyl-pyrrolidine-2,5-dione)
Chemical
name
(3)
(4)
(5)
(6)
(7)
Chemical
structure
−14.68
Non-inhibitor
larger side groups block CH4 adsorption better (Fig. 10.88) for two reasons: (a) their
larger steric size helping block CH4 motion, and (b) their larger hydrocarbon part of side
group attracting CH4 from water.
Polymers prefer to adsorb flat on hydrate surface near the periphery of open large
cavities where hydrogen bonding is likely.
The fraction of polymer segments adsorbed to surface is over 0.86 since both in “tail”
and “loop” conformations about half of segments was adsorbed.
Adsorbed segments' orientation relative to surface was not definitive. Segments were
observed with polar groups both pointing to and away from the surface. This may be
explained by the rigid backbone-side group bond unable to rotate in simulation (e.g.,
CHN bond in PVP).
Poly(1-acryloyl-azepan-2-one) (new-2-pvcap) and poly(4,4-dimethyl-3-vinyloxydihydro-furan-2-one) (new-2-pvp) are potentially good inhibitors.
The length of polymer chain sufficient to distinguish between good and poor inhibitors
was found to be 8. Shorter chains do not reflect the inhibitors' performance. Length of
each simulation was 100,000–150,000 cycles which was at least 10 h of run-time on the
fastest available computers as of 1996.
Summary based on experiments with THF hydrate growth
1. THF hydrate single crystals grow as regular octahedra from stoichiometric water + THF
solution (hydrate melt) exhibiting triangular {111} faces.
2. Increasing the degree of supercooling of hydrate melt results in an increasing amount of
visible defects on hydrate surface.
3. Transition of THF hydrate crystal shape from octahedral to planar can be caused by the
following three methods:
(a) Addition of kinetic inhibitors to the hydrate melt;
(b) Addition of 3 wt% NaCl or more to the hydrate melt;
(c) Changing the supersaturation of THF in hydrate melt.
340
10. Research methods in flow assurance
Fraction of methane adsorbed on hydratesurface
0.80
PVA
0.60
PVP
0.40
PVCap
N3PVP
0.20
N2PVP
N2PVCap
0.00
40.00
80.00
120.00
160.00
200.00
Monomer size, ų
FIG. 10.88 Methane blocking performance of chemicals sampled at 200 K is proportional to the monomer size.
4. Faces of the planar THF hydrate crystals are also {111}.
5. Complete inhibition of hydrate growth can be achieved by adding both kinetic inhibitor
and NaCl to the hydrate melt.
Summary from the adsorption simulation results
1. All studied chemicals (both inhibitors and non-inhibitors) adsorbed on hydrate surface
with favorable energies. More polar chemicals adsorbed stronger. Adsorption strength
increased with the number of hydrogen bonds from polymer to surface. Carbonyl oxygen
of inhibitors hydrogen bonds to the hydrate surface. However, it seems clear that neither
strength of adsorption nor steric fit alone determine the best inhibitors.
2. Simulation performance of chemicals in blocking methane adsorption on the hydrate is
strongly related to the experimental hydrate inhibition performance of chemicals and to
the size of inhibitor's side group.
3. Monomers of inhibitors can adsorb in partially completed hydrate cavities or on
periphery of these cavities. Polymers prefer to adsorb flat on hydrate surface near the
periphery of open large cavities where hydrogen bonding is likely. Large open 51264
cavities are a preferred site for monomer adsorption.
4. Fraction of polymer segments adsorbed to surface is over 0.86 since both in “tail” and
“loop” conformations about half of segments was adsorbed.
Flow loop tests
341
5. Adsorbed segments orientation relative to surface was not definitive. Segments were
observed with polar groups both pointing to and away from surface. This may be
explained by the rigid backbone-side group bond unable to rotate.
6. New simulated chemicals show both strong adsorption on hydrate and significant
blocking of methane adsorption in cavities. New-2-PVP and New-2-PVCap are
potentially good inhibitors and were recommended for synthesis.
7. Length of polymer chain sufficient to distinguish between good and poor inhibitors was
found to be 8. Shorter chains do not reflect the inhibitors' performance. Length of simulation
was 100,000–150,000 cycles which is at least 10 h of run-time on the CSM fastest computers.
Conclusions about kinetic inhibition mechanism
(1) Experiments with single THF hydrate crystals indicate a change in crystal growth habit
upon addition of kinetic inhibitors to the hydrate melt. This phenomenon is explained
by adsorption of polymeric chains on {111} faces of sII hydrate.
(2) Computer simulations show that polymer chains adsorb on hydrate surface with
favorable energies.
(3) Computer simulations show that polymer chains also block guest molecules from
hydrate surface. Polymer chains adsorbed on hydrate decrease the adsorption of guest
molecules into open hydrate cavities. It is likely that methophilic part of inhibitors
accumulate hydrocarbon molecules on them producing additional deficit of guest
molecules near hydrate surface.
Recommendations
(1) Make and test the new-2-PVCap and new-2-PVP.
(2) Design chemicals with side groups having a polar hydrogen-bonding part and an apolar
methophilic part.
(3) Monomer size should be in the range 140–170 Å3 which is close to the size of PVCap
monomer. Further increasing the monomer size may decrease performance.
Flow loop tests
Flow loops are a complex yet relatively easy to construct laboratory equipment. The key
components include: a pump, tubing, and a cooling system. The following studies may be
performed with a flow loop:
• Paraffin deposition
• Hydrate formation
• Multiphase flow
Some additional considerations need to be made for each of the equipment types.
• Paraffin deposition
Paraffin deposition loop requires a heated tank to dissolve any formed wax solids
before oil is recirculated into the loop. The tank volume should be at least 10 times and
preferably 100 times as large as the volume of the loop piping. Oil in the tank should be
heated to just above the wax appearance temperature.
342
10. Research methods in flow assurance
Cooling system for the loop should be able to maintain a length of tubing chilled to a temperature below the wax appearance temperature.
Wax loop may be equipped with removable or transparent pipe spools to observe wax
solids either as final deposit or during flowing or non-flowing conditions.
• Hydrate formation loop requires a gas compression/charge system to supply gas and
pressurize the loop before the test start and after hydrate formation consumes gas.
Pressure control system should maintain set pressure irrespective of temperature changes
or gas consumption into hydrates.
Either rotating vane or progressive cavity pump is required to circulate water with gas
hydrate particles. Hydrate solids can be broken up by the pump impeller. Low shear type
pumps are preferable for a hydrate loop in order to better evaluate the hydrate slurry flow.
• Multiphase flow loop requires a gas compressor in addition to a liquid pump, and a
separator to allow recirculation of the test fluids. Temperature control may not be as
important as for the paraffin and hydrate loops.
Flow loops allow to study formation of solid (wax or hydrate) or liquid (slug) obstructions
to flow. However, flow loops require costly maintenance and are only suited for universities
or research companies which work on joint industry projects.
Bench scale tests
A variety of bench scale laboratory tests may be done to research the growth of flow assurance solids. The more common ones are listed below.
Paraffin cold fingers
A cold finger may be assembled with a relatively low cost. The main parts include a flask to
hold heated oil, a stirred heater, a magnetic stirrer, a steel tube, rubber hoses and a cold bath
with a water pump or a temperature-controlled circulating cooler. Oil in the flask should be
heated to just above the wax appearance temperature.
The cold bath with ice water may be used to approximate the deepwater temperature
which is close to 4 °C, or as low as −2 °C in Arctic subsea.
Cold finger will show how much wax deposits at different wall temperatures and with
different chemical additives.
Paraffin cross-polarized microscope CPM
A CPM may also be assembled at a relatively low cost. The main parts include a microscope, a cooling stage made of quartz glass and two polarized lenses. The use of quartz glass
is important as it does not rotate the plane of light polarization. A temperature-controlled
cooler will be required for chilling oil sample to induce wax crystallization.
CPM will show how wax crystal form at different cooling rates and with different chemical
additives.
Computer code (Makogon, 1994, 1997)
343
Rheology
A stress-controlled rheometer can tell at what conditions the flow in presence of solids
begins and ends. This information can be used to help design production systems and to
compare the effects of chemicals on flow assurance solids.
A rheometer may range in cost from few to ten CPMs.
It is impossible to assemble a stress-controlled rheometer without highly specialized machining equipment and detailed knowledge of its design.
DSC
A differential scanning calorimeter is an expensive piece of laboratory equipment and may
cost as much as two rheometers. This apparatus can tell how much heat is released during
crystallization of flow assurance solids such as hydrate or wax. This information may be useful in planning the heat transfer characteristics of a production system. One usually wants to
retain heat in the system. However, if a blockage such as hydrate already formed, heat from
ambient environment is required to melt it.
It is impossible to assemble a computer-controlled differential scanning calorimeter.
However, it may be possible to assemble a calorimeter using a well-insulated flask and thermometer, and to use compounds such as cyclopentane which form hydrates at atmospheric
pressure to get qualitative understanding of the heat released during hydrate formation, or
heat consumed during hydrate dissociation.
Raman spectroscopy
A Raman spectrometer may is perhaps the most expensive apparatus and may cost as
much as ten differential scanning calorimeters.
Raman spectroscopy allows one to investigate the environment in which molecules exist. It
can tell whether a gas molecules is inside a small or a large cavity of a hydrate crystal.
It is impossible to assemble a Raman spectrometer without highly specialized machining
and optical equipment and a detailed knowledge of its design.
Computer code (Makogon, 1994, 1997)
Program for generating radial distribution function in water
c
c
c
c
c
This program generates radial distribution function for water MD box.
Input is a name of coordinates file generated by Sybyl named rdf.crd
and a number of molecules and timesteps in the system.
Output will be sent to the file rdf.dat as g(r) vs. r.
Vary shell thickness to achieve smooth g(r).
implicit real*8(a−h,o−z)
real*8 x(1000),y(1000),z(1000),rdf(1000)
344
10. Research methods in flow assurance
open(unit=1,file="rdf.crd",status="old")
open(unit=2,file="rdf.dat",status="unknown")
write(*,'($,"Enter number of molecules in the system: ")')
read(*,*) k
write(*,'($,"Enter density of the system (g/cc):
")')
read(*,*) density
write(*,'($,"Enter number of timesteps in the run:
")')
read(*,*) l
write(*,'($,"Enter number of eqilibration timesteps: ")')
read(*,*) le
3 format(3F12.6)
6 format(6F12.6)
side=(dfloat(k)/density)**(1.D0/3.D0)
sigma=1.D0/side
rdel=0.04D0
!shell thickness
rdel=rdel*sigma
do j=1,1000
rdf(j)=0
end do
do i=0,l
!start of cycle on time
read(1,*)t
write(*,*)i,t
read(1,3)x(1),y(1),z(1)
read(1,6)t1,t2,t3,t4,t5,t6
if((k/2.−k/2).EQ.0.)then
m=int(k/2−1)
do j=1,m
!start of read cycle
n=j*2
!on molecules
n1=n+1
read(1,6)x(n),y(n),z(n),t1,t2,t3
read(1,6)t4,t5,t6,x(n1),y(n1),z(n1)
read(1,6)t1,t2,t3,t4,t5,t6
end do
!end of read cycle on mol−s
read(1,6)x(k),y(k),z(k),t1,t2,t3
read(1,6)t1,t2,t3,xmin,ymin,zmin
read(1,6)t1,t2,t3,t4,t5,t6
read(1,6)t1,t2,t3,t4,t5,t6
read(1,6)t1,t2,t3,t4,t5,t6
read(1,6)xmax,ymax,zmax
else
m=int(k/2)
do j=1,m
!start of read cycle
n=j*2
!on molecules
n1=n+1
read(1,6)x(n),y(n),z(n),t1,t2,t3
Computer code (Makogon, 1994, 1997)
read(1,6)t4,t5,t6,x(n1),y(n1),z(n1)
read(1,6)t1,t2,t3,t4,t5,t6
end do
!end of read cycle on mol−s
read(1,6)xmin,ymin,zmin,t1,t2,t3
read(1,6)t1,t2,t3,t4,t5,t6
read(1,6)t1,t2,t3,t4,t5,t6
read(1,6)t1,t2,t3,xmax,ymax,zmax
endif
c
c
if(i.GE.le) then
c Data analysis for timestep i starts here
xbox=xmax−xmin
ybox=ymax−ymin
zbox=zmax−zmin
do 100 j=1,1000
x(j)=x(j)/xbox
y(j)=y(j)/ybox
z(j)=z(j)/zbox
100
continue
!If acquisition time came
!Start of data analysis
!Find box sides sizes
!Nullify shells array
!and normalize box size to 1
do 200 ii=1,k−1
!outer loop over spheres II
do 200 j=ii+1,k
rx=x(ii)−x(j)
ry=y(ii)−y(j)
rz=z(ii)−z(j)
c Apply minimum image criteria (periodic conditions)
if (RX.GT.0.5D0) RX=RX−1.D0
if (RY.GT.0.5D0) RY=RY−1.D0
if (RZ.GT.0.5D0) RZ=RZ−1.D0
if (RX.LT.−0.5D0) RX=RX+1.D0
if (RY.LT.−0.5D0) RY=RY+1.D0
if (RZ.LT.−0.5D0) RZ=RZ+1.D0
RIJ=DSQRT(RX*RX+RY*RY+RZ*RZ)
c
IF (RIJ.LE.0.5D0) then
ishell=int(rij/rdel)+1
rdf(ishell)=rdf(ishell)+1.D0
endif
200
continue
endif
!End of data analysis
end do
!End of cycle on i (time)
c Here goes the normalization of counter for radial distribution function
345
346
2
700
10. Research methods in flow assurance
Pi=3.14159265
nrdels=0.5D0/rdel
origns=k/2
rdelsi=rdel/sigma
format(2F12.6)
do 700 j=1,nrdels
radius=rdelsi*dfloat(j)
volshl=4.D0*PI*(RADIUS**3−(RADIUS−RDELSI)**3)/3.D0
GR=rdf(j)/(density*origns*volshl*(l−le+1))
write(2,2)radius*(xbox+ybox+zbox)/3.D0/side,gr
continue
close(1)
close(2)
end
Program for h bonded rings count in water
program ringcode;
{written for AIX 3.2.3 Pascal}
{General description
This program is used to count the distribution of n–membered
ring-like paths in the network of H bonds between water molecules.
Program expects the input as the list of pairs of numbers of H bonded
oxygens as nhb array[1..n,1..2] where 1..n is the total number of
H bonds and 1..2 means that 2 water molecules represented by oxygen
atoms are connected by one H bond. The list of H bonds must be sorted
in an increasing order (for example see test array nhb2).
Output of the program is the number of unique non short circuited
closed paths. This distribution is stored in array rdist. Numbers
should be divided by 2 because each path is counted clockwise and
counterclockwise. List of atoms present in every such ring–path is
in the array ring.
Method of work
Briefly: find and test. Program searches all the possible paths
from a given point which will return to start in no more that nmax
steps. Then the ring–path is checked for short circuiting bonds.
A short circuit is defined here as a path between two points of a
ring–path, shorter or equal than the shorter distance in a ring-path
between these two points. If short–circuit is of the same length as
the shorter path in the ring, then ring–path is considered to be
short–circuited only if the number of atom in position 2 of short
circuit is greater than that of atom in position 2 in ring. Or if
Computer code (Makogon, 1994, 1997)
347
ring–path is divided by short-circuit into two equal halves, atom
in position 2 of short-circuit must be greater than both #2 and
#-1 in the ring-path.
Example:
^6
/|\
1 / 8 \5
| | |
| | |
2 \ 7 /4
\|/
v3
A ring-path was found: 1-2-3-4-5-6. It will be
shortcircuited by path 3786. Here is how: Shortcircuits
are possible between points 3 and 6 in ring. 3 is less
than 6, thus search was started at point 3. Found
possible short-circuit is 3-7-8-6 which doesn't
belong to the ring and doesn't "backbite" on itself.
Point #1 in ring-path and in short-circuit is point 3.
Points #-1 and #2 in the ring-path are points 2 and 4.
In order to be a valid short circuit, number of point #2 in shortcircuit must be greater than both #-1 and #2 in the ring-path,
which is true: 7>2, 7>4. Conclusion: ring-path 1-2-3-4-5-6 is short- circuited and
is not counted. Such approach will give 4 good ring-paths: 1-2-3-7-8-6, 1-6-8-7-32, 3-4-5-6-8-7, and 3-7-8-6-5-4. This is a correct answer of 2 rings (counted twice
each).
Another example:
1-----5
A ring-path 1-2-6-4-5 is not short-circuited. Possible
| /\
points are 5 and 6. 5<6, then search from 5. Shorter
| / \
distance in ring-path is 6-4-5 (2 bonds), compared to
| <3 >4
5-1-2-6 (3 bonds). Search for paths between 5 and 6 of
| \ /
length 2 at most. Found 5-3-6(2 bonds). Compare point #2
|__\/
in short-circuit(point 3) and #2 in ring-path (point 4).
2
6
Number of #2 in short-circuit is lesser than of #2 in
ring-path (3<4). This doesn't qualify for a short-circuit.
Conclusion:ring-path 1-2-6-4-5 is not short-circuited. Such approach will give 4
good ring-paths: 1-2-6-4-5, 1-5-4-6-2, 3-5-4-6, and 3-6-4-5. This is a correct
answer of one 4-membered and one 5-membered ring (counted twice).}
%CHECK off
label 1,2,3;
const nmax=10;
{maximum ring size}
ngrand=3000;
{maximum number of bonds to search}
{
nhb2:array[1..12,1..2]of integer=((1,2),(1,3),(1,5),(1,6),(2,4),}
{
(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6));
}
348
10. Research methods in flow assurance
var ring:array[1..ngrand,1..nmax]of
integer; {array of ring atoms numbers}
i,j,jc,k,l,m,m1,m2,
{counter variable}
itime,ntime,nequil,
{timestep}
n,
{number of H bonded oxygens}
natom,
{largest number of the atom}
nbond,
{number of studied bond}
npass,
{number of PBC penetrations for ring}
npass1,
{plane of 1st PBC penetration}
npass2,
{plane of 2nd PBC penetration}
nr,
{counter of links in tempor. chain}
nnext,
{number of next search O}
dist,
{distance between points in ring}
ntot:integer;
{counter of rings found}
rin,
{temporary ring array}
rdist:array[1..nmax]of integer;
{ring size histogram array}
nhb:array[1..ngrand,1..2]of integer; {list of H bonds}
bonds:array[1..nmax]of integer; {list of bond numbers for temp. ring}
order:array[1..ngrand]of integer;{order of connectivity for members}
pass:array[1..ngrand]of integer; {bond across periodic boundary}
rinm:array[1..nmax]of integer;
{next-pointer for current link}
rinn:array[1..nmax]of boolean;
{next-ptrs for bonds in temp.ring}
closed,
{indicator of ring closure}
contin,
{use same bond to seek other rings}
short,
{indicator of short circuited ring}
nothere,
{atom not in ring,also dummy in CleanUp}
found,
{found next link}
npb,
{1st penetration of PBC occurred}
deadend1,deadend2:boolean;
{indicators of unconnected bond}
f,f1,f2:text;
{data file variables}
ttyin, ttyout:text;
{terminal input/output}
{variables used in CheckShort procedure}
is,js,ks,
{counters}
ns,
{number of links found}
nstart,
{number of starting bonds}
snext,
{number of point to search}
start,finish,
{short path terminals}
ps,
{position of start}
pf,
{position of finish}
start1,start2
{ring neighbors of start}
:integer;
sbond:array[1..100] of integer;
{list of start bonds, 100 is arbitrary}
Computer code (Makogon, 1994, 1997)
srin,
{temporary list of short circuit}
srinm,
{list of next:pointers}
sbonds
{list of bond numbers for short circ.}
:array[1..nmax div 2] of integer;
srinn:array[1..nmax div 2] of boolean;
{flags of next-pointers}
proceed,
{all checked fine}
scontin,
{use same bond to seek short circuit}
snothere,
{atom not in short circuit}
sfound
{found next link}
:boolean;
Procedure Output;
var io,jo:integer;
begin
rewrite (f1, 'NAME=ring.out');
for io:=1 to ntot do
begin
for jo:=1 to nmax do
if ring[io,jo]<>0 then
write(f1,ring[io,jo]:4,' ');
writeln(f1);
end;
close(f1);
end;
Procedure Choice;
label C1,C2;
var kc,ic,jc,jc2:integer;
begin
if closed then kc:=nr
else kc:=nr−1;
for ic:=1 to kc do
begin
rinn[ic]:=False;
rinm[ic]:=0;
for jc:=bonds[ic]+1 to n d
begin
nothere:=False;
if (nhb[jc,1]=rin[ic]) then
begin
{Used to determine branching and to
define the next-branch in the path
for each point in the ring.}
{counters}
{If ring is not complete then don't}
{seek branches at last point reached}
{Specify no branching at nhb[nbond,1]}
{See if choices are present: }
{if a bond from list i+1..n has a }
{check point and not in ring itself.}
{one end of the bond fits}
349
350
10. Research methods in flow assurance
nothere:=True;
for jc2:=1 to ic do
if nhb[jc,2]=rin[jc2] then
begin
nothere:=false;
goto C1;
end;
end;
if (nhb[jc,2]=rin[ic]) then
begin
{other end of the bond fits}
nothere:=True;
for jc2:=1 to ic do
if nhb[jc,1]=rin[jc2] then
begin
nothere:=false;
goto C1;
end;
end;
if nothere then
begin
rinn[ic]:=True;
rinm[ic]:=jc;
goto C2;
end;
{Found a branch. Record its position.}
C1: end;
C2:end;
end;
{end of loop on bonds}
{end of loop on ring links}
{exit from procedure}
Procedure SChoice;
label C1,C2;
var kc,ic,jc,jc2:integer;
{similar to Choice,used by CheckShort}
begin
for ic:=1 to ns do
begin
srinn[ic]:=False;
srinm[ic]:=0;
for jc:=sbonds[ic]+1 to n do
begin
nothere:=False;
if (nhb[jc,1]=srin[ic]) then
begin
nothere:=True;
for jc2:=1 to ic do
{counters}
{specify no branching at nhb[nbond,1]}
{see if choices are present:
}
}
{if a bond from list i+1..n has a
{check point and not in ring itself }
{one end of bond fits}
Computer code (Makogon, 1994, 1997)
if nhb[jc,2]=srin[jc2] then
begin
nothere:=false;
goto C1;
end;
end;
if (nhb[jc,2]=srin[ic]) then
begin
{other end of bond fits}
nothere:=True;
for jc2:=1 to ic do
if nhb[jc,1]=srin[jc2] then
begin
nothere:=false;
goto C1;
end;
end;
if nothere then
begin
{found branch in short circuit path}
srinn[ic]:=True;
{Record its position.}
srinm[ic]:=jc;
goto C2;
end;
C1: end;
{end of loop on bonds}
C2:end;
{end of loop on ring links}
end;
{exit from procedure}
Procedure CleanUp;
{Used to remove useless bonds from list}
label C2;
var i,j,k,l,m1,m2:integer;
begin
{delete all parallel (double) bonds}
begin
for i:=1 to ngrand do
begin
ring[i,1]:=0;
{use array ring as tempor. storage}
end;
k:=0;
{reset counter of repeating bonds}
for i:=1 to n−1 do
for j:=i+1 to n do
{find repeated bonds}
if ((nhb[i,1]=nhb[j,1])and(nhb[i,2]=nhb[j,2]))or
((nhb[i,1]=nhb[j,2])and(nhb[i,2]=nhb[j,1])) then
351
352
10. Research methods in flow assurance
begin
k:=k+1;
ring[k,1]:=j;
end;
repeat
{remove duplic.from list of rep.bonds}
begin
nothere:=true;
for i:=1 to k−1 do
for j:=i+1 to k do
if ring[i,1]=ring[j,1] then
begin
nothere:=false;
for l:=j+1 to k do
ring[l−1,1]:=ring[l,1];
k:=k−1;
end;
end
until nothere;
{reset change indicator}
for i:=1 to k do
{remove repeated bonds from the list}
begin
for j:=ring[i,1]+1 to n do
begin
nhb[j−1,1]:=nhb[j,1];
nhb[j−1,2]:=nhb[j,2];
pass[j−1]:=pass[j];
end;
nhb[n,1]:=0;
nhb[n,2]:=0;
pass[n]:=0;
n:=n−1;
{decrease by 1 number of bonds}
for j:=i to k do
ring[j,1]:=ring[j,1]−1;
{correct values in ring[k,1]}
end;
writeln(ttyout,'All duplicate bonds eliminated');
end;
begin
repeat
C2:begin
nothere:=true;
for i:=1 to n do
{discard all dead–end bonds which
don't participate in rings}
{reset change indicator}
Computer code (Makogon, 1994, 1997)
begin
m1:=nhb[i,1];
{remember atoms in bond under question}
m2:=nhb[i,2];
deadend1:=true;
deadend2:=true;
for j:=1 to n do
if i<>j then
{seek same atoms in other bonds}
begin
if (nhb[j,1]=m1)or(nhb[j,2]=m1) then
deadend1:=false;
if (nhb[j,1]=m2)or(nhb[j,2]=m2) then
deadend2:=false;
end;
if deadend1 or deadend2 then
begin
{delete bond with a dead end oxygen}
nothere:=false;
for j:=i+1 to n do
begin
nhb[j−1,1]:=nhb[j,1];
nhb[j−1,2]:=nhb[j,2];
pass[j−1]:=pass[j];
end;
nhb[n,1]:=0;
nhb[n,2]:=0;
pass[n]:=0;
n:=n−1;
{decrease number of H bonds}
goto C2;
end;
end;
end
until nothere;
writeln(ttyout,'All dead-end tails eliminated');
end;
end;
Procedure CheckShort;
{searches a path from rin[j] to rin[k]
of length <= dist}
label S1,S2,S3,S4;
var is,js,ks:integer;
begin
short:=false;
ns:=0;
if rin[j]<rin[k] then
{determine starting and ending }
353
354
begin
start:=rin[j];
ps:=j;
finish:=rin[k];
pf:=k;
if (j=1)or(j=nr) then
begin
if j=1 then
begin
start1:=rin[2];
start2:=rin[nr];
end;
if j=nr then
begin
start1:=rin[1];
start2:=rin[nr−1];
end;
end
else
begin
start1:=rin[j−1];
start2:=rin[j+1];
end;
end
else
begin
start:=rin[k];
ps:=k;
finish:=rin[j];
pf:=j;
if (k=1)or(k=nr) then
begin
if k=1 then
begin
start1:=rin[2];
start2:=rin[nr];
end;
if k=nr then
begin
start1:=rin[1];
start2:=rin[nr−1];
end;
end
else
10. Research methods in flow assurance
{points of expected short circuit}
{and find neighbors in ring for start}
{as start1 and start2}
Computer code (Makogon, 1994, 1997)
begin
start1:=rin[k−1];
start2:=rin[k+1];
end;
end;
{search for bonds starting sh. circt}
nstart:=0;
for is:=1 to n do
begin
if (nhb[is,1]=start) then
if ((nhb[is,2]<>start1)and(nhb[is,2]<>start2)) then
begin
{found such bond}
nstart:=nstart+1;
sbond[nstart]:=is;
{record new starting bond}
end;
if (nhb[is,2]=start) then
if ((nhb[is,1]<>start1)and(nhb[is,1]<>start2)) then
begin
{found such bond}
nstart:=nstart+1;
sbond[nstart]:=is;
{record new starting bond}
end;
end;
{search for bonds starting sh. circ.}
for is:=1 to nstart do
begin
for js:=1 to nmax div 2 do
begin
srin[js]:=0;
sbonds[js]:=0;
srinn[js]:=false;
srinm[js]:=0;
end;
ns:=1;
srin[ns]:=start;
sbonds[ns]:=sbond[is];
snext:=nhb[sbond[is],1];
if snext=start then
snext:=nhb[sbond[is],2];
{search continuation of start bonds}
{reset temporary variables}
{reset list of bonds in short circuit}
{If length of short-circuit is same as dist, then
only point snext >start1 and/or snext > start2 can yield a successful
short circuit. Check if ring halves are of different or same size
(if nr odd −>halves can't be equal in size, even−>can be equal halves)
and compare snext to start1,2 of shorter or of both halves of the ring.
Then proceed as in main routine until ns>=dist or found finish.}
355
356
10. Research methods in flow assurance
proceed:=false;
if ((nr mod 2)=0)and(dist=(nr/2)) then
begin
{dist is same as equal halves of ring}
if (snext>start1)and(snext>start2) then
proceed:=true;
{snext can start a good short circuit}
end
else
begin
{different halves of ring}
if ps<pf then
begin
if (rin[ps+dist]=finish)then
begin
{shorter
if rin[ps+1]=start2 then
begin
{shorter
js:=start1;
start1:=start2;
start2:=js;
end;
end
else
begin
{shorter
if rin[ps+1]=start1 then
begin
{shorter
js:=start1;
start1:=start2;
start2:=js;
end;
end;
end
else
begin
if (rin[ps–dist]=finish)then
begin
{shorter
if rin[ps−1]=start2 then
begin
{shorter
js:=start1;
start1:=start2;
start2:=js;
end;
end
else
begin
{shorter
if rin[ps−1]=start1 then
begin
{shorter
half is increasing positions}
half must start with start1}
half is decreasing positions}
half must start with start1}
half is increasing positions}
half must start with start1}
half is decreasing positions}
half must start with start1}
Computer code (Makogon, 1994, 1997)
js:=start1;
start1:=start2;
start2:=js;
end;
end;
end;
if snext>start1 then
proceed:=true;
end;
{snext can start a good short circuit}
repeat
S4: begin
{search for sh.circ. starting with snext}
if order[snext]=2 then
begin
{easy find: only one possibility}
sfound:=true;
ns:=ns+1;
srin[ns]:=snext;
for js:=1 to n do
begin
if (nhb[js,1]=snext)and(nhb[js,2]<>srin[ns−1])then
snext:=nhb[js,1];
if (nhb[js,2]=snext)and(nhb[js,1]<>srin[ns−1])then
snext:=nhb[js,1];
end;
if snext=srin[ns] then
snext:=nhb[js,2];
sbonds[ns]:=js;
end
else
{search the tedious way}
for js:=1 to n do
if (nhb[js,1]=snext)or(nhb[js,2]=snext) then
begin
sfound:=false;
if nhb[js,1]=snext then
begin
{one of atoms in bond fits}
snothere:=true;
for ks:=2 to ns do
{see if link was found already}
if srin[ks]=nhb[js,2] then
snothere:=false;
for ks:=1 to pf-1 do
{see if link is in the ring}
if rin[ks]=nhb[js,2] then
snothere:=false;
{avoiding test of finish position}
if pf <> nr then
for ks:=pf+1 to nr do
357
358
10. Research methods in flow assurance
if rin[ks]=nhb[js,2] then
snothere:=false;
if snothere then
begin
{new point in short circuit found}
sfound:=true;
ns:=ns+1;
srin[ns]:=snext;
{write to short circuit array}
sbonds[ns]:=js;
{write to short circ. bonds list}
snext:=nhb[js,2];
{define next atom for search}
goto S2;
end;
end;
if nhb[js,2]=snext then
begin
{another atom in bond fits}
snothere:=true;
for ks:=2 to ns do
{see if link was found already}
if srin[ks]=nhb[js,1] then
snothere:=false;
for ks:=1 to pf−1 do
{see if link is in the ring}
if rin[ks]=nhb[js,1] then
snothere:=false;
{avoiding test of finish position}
if pf <> nr then
for ks:=pf+1 to nr do
if rin[ks]=nhb[js,1] then
snothere:=false;
if snothere then
begin
{new point in short circuit found}
sfound:=true;
ns:=ns+1;
srin[ns]:=snext;
{write to short circuit array}
sbonds[ns]:=js;
{write to short circ. bonds list}
snext:=nhb[js,1];
{define next atom for search}
goto S2;
end;
end;
end;
{end of loop on js over all bonds}
if (not sfound)and(ns<dist) then {**may have problem here later}
begin
ns:=ns+1;
srin[ns]:=snext;
end;
S2:
if (snext=finish) and (ns=dist) and proceed then
begin
Computer code (Makogon, 1994, 1997)
short:=true;
goto S1;
end;
if (snext=finish) and (ns<dist) then
begin
short:=true;
goto S1;
end;
if ns<dist then goto S4;
SChoice;
scontin:=false;
ks:=1;
for js:=1 to ns do
{get number of links to use in new path}
if srinn[js] then
{from old path}
begin
ks:=js;
scontin:=true;
end;
ns:=ks;
if(not scontin)or(ns=1)then goto S3;
{if no branches left,goto next sbond}
for js:=ns+1 to nmax div 2 do
begin
{reset the rest of temp. short circ.}
srin[js]:=0;
sbonds[js]:=0;
srinn[js]:=false;
srinm[js]:=0;
end;
found:=true;
snext:=nhb[srinm[ns],1];
if srin[ns]=snext then
snext:=nhb[srinm[ns],2];
sbonds[ns]:=srinm[ns];
goto S2;
end;
{end of repeat–loop}
until ns>=dist;
{end search not giving short circuit}
{
{
{
{
if not proceed then goto S3;
SChoice;
ns:=dist−1;
goto S2; }
{program never gets here}
{this part was intended to continue}
{search if ring weren't closed}
359
360
10. Research methods in flow assurance
S3:
end;
S1:
end;
{end of overall loop on is}
{end of CheckShort}
Procedure Conti;
var j:integer;
begin
contin:=false;
jc:=1;
for j:=1 to nr do
if rinn[j] then
begin
jc:=j;
contin:=true;
end;
nr:=jc;
{get # of links to use in new ring}
{use same bond to search other rings}
end;
Procedure Conti2;
var j:integer;
begin
for j:=nr+1 to nmax do
begin
rin[j]:=0;
{reset the rest of tempor.ring array}
bonds[j]:=0;
rinn[j]:=False;
rinm[j]:=0;
end;
nbond:=rinm[nr];
{define number of new bond}
found:=true;
nnext:=nhb[nbond,1];
{set next atom to search for}
if rin[nr]=nhb[nbond,1] then
nnext:=nhb[nbond,2];
bonds[nr]:=nbond;
end;
begin
{n:=12;
{for i:=1 to n do
{ for j:=1 to 2 do
{
nhb[i,j]:=nhb2[i,j];
{start of the main routine}
{number of H bonded pairs}
{readin data from array in test mode}
}
}
Computer code (Makogon, 1994, 1997)
termin(ttyin);
{send input/output to tty terminal}
termout(ttyout);
writeln(ttyout,'Program starting');
reset(f, 'NAME=ring.dat');
rewrite(f2, 'NAME=ring.hst');
write(ttyout, 'Enter the number of timesteps ? ');
readln(ntime);
write(ttyout, 'Enter the number of equilibration timesteps ? ');
readln(nequil);
read(f,i,j);
if (i<>1234)or(j<>5678) then writeln(ttyout,'Error at start of ring.dat');
for itime:=1 to ntime do
begin
writeln(ttyout,'Timestep ',itime);
n:=0;
{read in H bond data from a file}
ntot:=0;
{number of rings found}
found:=False;
while not eof(f) do
begin
read(f,i,j);
if (i=1234)and(j=5678) then goto 3;
n:=n+1;
nhb[n,1]:=i;
nhb[n,2]:=j;
end;
3:
writeln(ttyout,n,' bonds read');
if itime<=nequil then n:=0;
{if in equilibration discard bonds}
for i:=1 to ngrand do
{Find bonds which went through PBC}
pass[i]:=0;
{reset pass array}
for i:=1 to n do
if (nhb[i,1]<0)or(nhb[i,2]<0)then {if pass flag is present in data}
begin
if nhb[i,1]<0 then
pass[i]:=1;
if nhb[i,2]<0 then
begin
pass[i]:=2;
if nhb[i,1]<0 then
pass[i]:=3;
end;
nhb[i,1]:=abs(nhb[i,1]);
361
362
10. Research methods in flow assurance
nhb[i,2]:=abs(nhb[i,2]);
end;
CleanUp;
{remove repeated and unconnected bonds}
writeln(ttyout,n,' bonds left');
for i:=1 to nmax do
{clear the ring and rdist arrays}
begin
rdist[i]:=0;
bonds[i]:=0;
for j:=1 to ngrand do
ring[j,i]:=0;
end;
natom:=0;
for i:=1 to n do
begin
if nhb[i,1]>natom then
natom:=nhb[i,1];
if nhb[i,2]>natom then
natom:=nhb[i,2];
end;
{determine the largest atom number}
for i:=1 to natom do
{get order of connectivity for members}
begin
order[i]:=0;
for j:=1 to n do
{search for atom of number i in bonds}
if (nhb[j,1]=i)or(nhb[j,2]=i)then
order[i]:=order[i]+1;
end;
for i:=1 to n−2 do
{loop over all bonds, 1..n−2}
begin
{writeln(ttyout,'Counting rings for bond #',i);}
for j:=1 to nmax do
begin
rin[j]:=0;
bonds[j]:=0;
rinn[j]:=False;
{reset next-pointers of tempor. ring}
rinm[j]:=0;
end;
nr:=1;
nbond:=i;
{get number of currently studied bond}
rin[nr]:=nhb[nbond,1];
{start temporary chain}
bonds[nr]:=nbond;
{modify list of bonds in ring}
nnext:=nhb[i,2];
Computer code (Makogon, 1994, 1997)
repeat
begin
found:=false;
closed:=false;
for j:=i+1 to n do
{search for next link}
begin
if (nhb[j,1]=nnext)or(nhb[j,2]=nnext) then
begin
nbond:=j;
if nhb[j,1]=nnext then
begin
nothere:=true;
for k:=1 to nr do
if nhb[j,2]=rin[k] then
nothere:=false;
if nothere then
begin
nr:=nr+1;
if nr>nmax then goto 1;
rin[nr]:=nnext;
bonds[nr]:=nbond;
nnext:=nhb[j,2];
found:=true;
goto 1;
end;
end
else
begin
nothere:=true;
for k:=1 to nr do
if nhb[j,1]=rin[k] then
nothere:=false;
if nothere then
begin
nr:=nr+1;
if nr>nmax then goto 1;
rin[nr]:=nnext;
bonds[nr]:=nbond;
nnext:=nhb[j,1];
found:=true;
goto 1;
end;
end;
end;
{one of atoms in bond fits}
{verify that atom not present in ring}
{found same atom in ring before}
{add to temporary chain}
{define next atom for search}
{another atom in bond fits}
{verify that atom not present in ring}
{found same atom in ring before}
{add to temporary chain}
{define next atom for search}
363
364
10. Research methods in flow assurance
end;
if(not found)and(nr<nmax) then
begin
nr:=nr+1;
closed:=false;
rin[nr]:=nnext;
Choice;
end;
{end of j–loop}
1:if found and (nr<nmax) then
{found next link – exit j–loop}
begin
if nr>=2 then
{if more than 2 molecules, }
begin
{then check for ring closure}
closed:=false;
for j:=1 to n do
if ((nhb[j,1]=rin[1])and(nhb[j,2]=nnext))or
((nhb[j,2]=rin[1])and(nhb[j,1]=nnext)) then
begin
closed:=true;
{nnext closed ring, add it to rin}
nbond:=j;
nr:=nr+1;
rin[nr]:=nnext;
bonds[nr]:=nbond;
Choice;
end;
end;
short:=false;
if closed and(nr>3) then
begin
npass:=0;
for j:=1 to nr do
if pass[bonds[j]]<>0 then
npass:=npass+1;
if npass=1 then short:=true;
if npass=2 then
begin
npb:=false;
for j:=1 to nr do
if pass[bonds[j]]<>0 then
if npb then
npass2:=pass[bonds[j]]
else
begin
npb:=true;
{check for ring short–cicuitedness}
{for rings of size 4 or more}
{count number of passes through PBC}
{one pass means ring is pass–chain}
Computer code (Makogon, 1994, 1997)
npass1:=pass[bonds[j]];
end;
if npass1<>npass2 then short:=true;
end;
if short then
begin
Conti;
{if no branches left go to next link}
if (not contin)or(nr=1) then goto 2;
Conti2;
goto 1;
{see if this is a new ring}
end;
for j:=1 to nr−1 do
{between positions j and k of ring}
begin
{where k>j, shorted by one bond}
if j=1 then
m1:=nr−1
else
m1:=nr;
for k:=j+2 to m1 do
if (order[rin[k]] >2) and (order[rin[j]] >2) then
begin
for m2:=1 to n do
{seek one-bond short circuits}
if ((nhb[m2,1]=rin[j])and(nhb[m2,2]=rin[k])) or
((nhb[m2,2]=rin[j])and(nhb[m2,1]=rin[k])) then
begin
short:=true;
Conti;
{no branches left goto next link}
if (not contin)or(nr=1) then goto 2;
Conti2;
goto 1;
{see if this is a new ring}
end;
end;
end;
for j:=1 to nr−1 do
{between positions j and k of ring}
begin
{where k>j}
if j=1 then
m1:=nr−1
else
m1:=nr;
for k:=j+2 to m1 do
if (order[rin[k]] >2) and (order[rin[j]] >2) then
begin
if (k−j)<(nr/2)then
dist:=k−j
365
366
10. Research methods in flow assurance
else
dist:=nr−(k−j);
Checkshort;
if short then
begin
Conti;
{if no branches left goto next link}
if (not contin)or(nr=1) then goto 2;
Conti2;
goto 1;
{see if this is a new ring}
end;
end;
end;
end;
{end of short circuit check}
if (not short)and closed then
{found a new ring * * * * * * * * *}
begin
{add nnext to rin}
ntot:=ntot+1;
{increase counter of found rings}
rdist[nr]:=rdist[nr]+1;
{modify distribution histogram}
for j:=1 to nr do
ring[ntot,j]:=rin[j];
{move rin to ring}
nr:=nr−1;
{cut by 1 to avoid short circuits}
closed:=false;
{reset closed variable}
found:=false;
{reset found variable}
Conti;
{if no branches left goto next link}
if (not contin)or(nr=1) then goto 2;
Conti2;
goto 1;
{see if this is a new ring}
end;
{end of found a new ring * * * * *}
end;
{end of code starting at label 1:}
if (nr>nmax) or (not found) then
begin
Choice;
nr:=nmax−1;
Conti;
if (not contin)or(nr=1) then goto 2; {no branches left,goto nextlink}
Conti2;
goto 1;
{see if this is a new ring}
end;
end
{end of repeat-loop}
until (nr>nmax) or (not found);
{terminate search not going anywhere}
2:
Output;
end;
{end of i-loop}
Computer code (Makogon, 1994, 1997)
367
if itime>nequil then
begin
write(f2,'Step ',itime:4,' : ');
write(ttyout,'Step ',itime:4,' : ');
for i:=1 to nmax do
begin
write(f2,rdist[i]:3,' ');
write(ttyout,rdist[i]:3,' ');
end;
writeln(f2);
writeln(ttyout);
end;
end;
{end of itime loop}
close(f2);
end.
Monte Carlo program for polymer adsorption on hydrate
Files required for using this program include:
– pm3n.hyd or fd3m.hyd - sI or sII unit cell data;
– .MSI Cerius2® file - polymer coordinates and charges;
The above files are available on crystal.mines.edu computer.
Input file is optional and can be piped to the program instead of manually inputting the
simulation parameters.
C
version 1.0
C
Monte Carlo for monomer against a rectangular lattice
C
surface of water molecules
C
J. M. Haile February 1996
C
version 2.0
C subroutine for generating the hydrate surface was added and the
C boundary conditions routine was modified to be able to handle
C rhombic boundaries
Taras Makogon, April 1996
C
C
version 3.0
C all subroutines were rewritten for polymer simulation
C The program was used on IBM RS-6000, IBM-PC and SGI computers.
C The I/O statements which need to be chosen for different FORTRAN
C compilers are commented out with “ccc” or are right next to those.
C
T. Makogon, September 1996
C-------------------------------------------------------------------
368
10. Research methods in flow assurance
IMPLICIT REAL*8(A-H,O-Z)
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
C ... Initialization
C
CALL POLY
CALL RUNPAR
CALL SURFCE
CALL LJPARM
CALL INIPOS
CALL ENPOLY
CALL RESTARTCHECK(Nstart)
IF(Nstart.ne.1) goto 10
CALL GRAPHDATA
C ... Equilibration
CALL REINIT
10 IF(Neq.eq.1) goto 20
CALL CYCLES(Nstart,Ndead)
Nstart=1
Kcyc=0
Neq=1
Temp=Temp*0.5
Tk=Tk*0.5
CALL CRASHSAVE
C ... main process
CALL REINIT
20
CALL CYCLES(Nstart,Ncycle)
C
normalize the z(backbone) and other data
CALL SUMMARY
C
STOP
END
C
C------------------------------------------------------------------C
SUBROUTINE POLY
C
This subroutine arranges atoms into monomer groups by doing a chain
c
search.
c
*** The condition of this search – polymer backbone can consist ***
c
*** only of carbon or oxygen atoms. Carbons should be CH2 or CH.***
c
*** Side groups can't start with a −CH2− or a −CH− carbon***
Computer code (Makogon, 1994, 1997)
c
*** C=O or CR1R2R3 are allowed|
c
c
if O is present in backbone, it must be positioned before the C
c
which is connected to a side group
c
c
e.g.
H3C − O − CH − CH2 − O − CH ----c
side
side
c
c
if O is present in side group and in backbone then backbone must have
c
at least two carbons between backbone oxygens (as in figure above)
c
and side group can't be -OH
c
C-----arrays info:------c
nbonds(i)
– number of covalent bonds found to atom (i)
c
nrawatom– current MSI value of irawatom(i)
c
n2atom – MSI number of atom bonded to nrawatom
c
chain(i)– number of an atom in backbone
c
listwait(i)
– list of atoms waiting for side group search
c
ibonddata(i,j) – number of atom bonded to atom i by bond j
c
irawbond(i,j)
– MSI numbers of atoms (j=1,2) bonded by bond (i)
c
irawatom(i)
– MSI number of atom (i) in a molecule
c
iatomtype(i,j) – j=1:type of atom (i){H=1;C=2;O=3;N=4}; j=2:monomer #
c
nbondfound
– number of found bonds in molecule
c
natom
– number of found atoms in molecule
c
ngroups – number of monomers
c
atomdata(i,j)
– j=1..4: X,Y,Z,charge for atom (i)
c
monodata(i,j)
– list of atoms (j) in monomer (i)
c
monocount(i)
– number of atoms in monomer (i); also contains info
about backbone
implicit real*8 (a–h,o–z)
implicit integer(i–n)
integer*2 nrawatom,n2atom,listwait(100),chain(100)
COMMON
COMMON
COMMON
COMMON
COMMON
C
/bonds
/raw
/types
/atoms
/chain
/
/
/
/
/
ibonddata(1000,4),nbonds(1000)
irawbond(1000,2),irawatom(1000)
iatomtype(1000,2),nbondfound,natom,ngroups,ncall
atomdata(1000,4),atomdata2(1000,4)
monodata(100,100),monocount(99),nbackbone
CALL READMSI
calculate the total charge and number of oxygen atoms in molecule
c=0.D0
no=0
do i=1,natom
iatomtype(i,2)=0
369
370
C
C
10
C
c
c
10. Research methods in flow assurance
c=c+atomdata(i,4)
if (iatomtype(i,1).eq.3) no=no+1
end do
if charge is not exactly zero, redistribute the difference
between all atoms and subtract the computational error from the last atom
if(abs(c).gt.1.D0) print *,' WARNING: Non-zero Total Charge'
if(c.ne.0.D0) then
delc=c/natom
c=0.D0
do i=1,natom
atomdata(i,4)=atomdata(i,4)−delc
c=c+atomdata(i,4)
end do
atomdata(natom,4)=atomdata(natom,4)−c
endif
write(*,10)no
Format(' Number of oxygen atoms=',I4)
print *,'Please enter the number of monomers in chain'
read (*,*)ngroups
arrange data on atom connectivity
do i=1,natom
nbonds(i)=0
nrawatom=irawatom(i)
do j=1,nbondfound
if (irawbond(j,1).eq.nrawatom) then
nbonds(i)=nbonds(i)+1
see what is the atom number on the other end of bond
do ii=1,natom
if(irawatom(ii).eq.irawbond(j,2))n2atom=ii
end do
ibonddata(i,nbonds(i))=n2atom
endif
if (irawbond(j,2).eq.nrawatom) then
nbonds(i)=nbonds(i)+1
see what is the atom number on the other end of bond
do ii=1,natom
if(irawatom(ii).eq.irawbond(j,1))n2atom=ii
end do
ibonddata(i,nbonds(i))=n2atom
endif
end do
end do
Computer code (Makogon, 1994, 1997)
C*******************************************************************
c
if backbone contains atoms other than C or O, obtain the needed
c
info from user (which types are there; in what order are they
c
connected
C*******************************************************************
C
distinguish which are the backbone atoms
nbackbone=0
c
first, find the terminating carbon of CH3 group
do i=1,natom
ntype=0
do j=1,nbonds(i)
ntype=ntype+iatomtype(ibonddata(i,j),1)
end do
if(ntype.eq.5.and.iatomtype(i,1).eq.2) then
nend=i
goto 20
endif
end do
20
nbackbone=1
chain(1)=nend
c
find the backbone atom next to CH3 – check that it's not a hydrogen
do i=1,4
if(iatomtype(ibonddata(chain(1),i),1).ne.1)then
nbackbone=2
chain(2)=ibonddata(chain(1),i)
endif
end do
c
find the following backbone atoms
25
do i=1,nbonds(chain(nbackbone))
morecanfind=0
natm=ibonddata(chain(nbackbone),i)
c
it's a carbon
if(iatomtype(natm,1).eq.2.and.natm.ne.chain(nbackbone–1))then
c
check that it isn't a side group carbon
isum=0
do j=1,4
if(iatomtype(ibonddata(natm,j),1).eq.1)isum=isum+1
end do
if(isum.eq.2.or.isum.eq.1) then
morecanfind=1
nbackbone=nbackbone+1
chain(nbackbone)=ibonddata(chain(nbackbone-1),i)
goto 30
endif
endif
371
372
c
c
30
10. Research methods in flow assurance
it's an oxygen
if(iatomtype(natm,1).eq.3.and.natm.ne.chain(nbackbone-1))then
check that it isn't a side group oxygen - that it isn't -OH
if(iatomtype(chain(nbackbone-1),1).ne.3.and.
&
iatomtype(ibonddata(natm,1) ,1).ne.1.and.
&
iatomtype(ibonddata(natm,2) ,1).ne.1) then
morecanfind=1
nbackbone=nbackbone+1
chain(nbackbone)=ibonddata(chain(nbackbone-1),i)
goto 30
endif
endif
end do
if(morecanfind.eq.1) goto 25
C
C
c
c
c
c
c
c
c
atmono=nbackbone/ngroups
if(atmono.ne.int(atmono)) then
print *,'Non-integer number of backbone atoms per monomer'
print *,'Please input this number (e.g. 2 for a vinyl chain)'
read (*,*)atmono
endif
assign numbers to backbone atoms
do i=1,nbackbone
nmono =i
=int(i/atmono+0.5D0) - this formula can be used to assign monomer numbers
iatomtype(chain(i),2)=nmono
assign monomer numbers to backbone nearest neighbors
do j=1,nbonds(chain(i))
natm =ibonddata(chain(i),j)
check that the backbone neighbor isn't a next/previous backbone atom
ibone=0
do k=1,nbackbone
if(natm.eq.chain(k))ibone=1
end do
if(ibone.eq.0) then
iatomtype(natm,2)=nmono
assign monomer numbers to side groups
if it's not a hydrogen, and atom isn't in backbone, it's a side group
if(iatomtype(natm,1).ne.1) then
reset counters of atom being tested and those waiting for testing
ntest=1
nwait=1
store the side group first atom as nside
nside=natm
listwait(nwait)=nside
Computer code (Makogon, 1994, 1997)
c
50
c
c
c
c
c
C
C
cycle through the wait list and search for other side group atoms
do l=1,nbonds(listwait(ntest))
look at the atoms connected to current atom
natm=ibonddata(listwait(ntest),l)
see that it's not already in wait list and not a backbone atom
nstatok=1
do m=1,nwait
if(listwait(m).eq.natm.or.natm.eq.chain(i)) nstatok=0
end do
if(nstatok.eq.1) then
nwait=nwait+1
listwait(nwait)=ibonddata(listwait(ntest),l)
endif
end do
ntest=ntest+1
check that there are more atoms to test
if(ntest.le.nwait) goto 50
all side group atoms were found - assign their monomer numbers
do l=1,nwait
iatomtype(listwait(l),2)=nmono
end do
end of the side group routine
endif
endif
end do
end do
assign atoms to their monomers by numbers
do i=1,99
monocount(i)=0
monodata(100,i)=0
do j=1,100
monodata(i,j)=0
end do
end do
do i=1,natom
nmono=iatomtype(i,2)
monocount(nmono)=monocount(nmono)+1
monodata(nmono,monocount(nmono))=i
end do
store the backbone information in the 100th element of monodata(i,j)
do i=1,nbackbone
monodata(100,i)=chain(i)
end do
RETURN
END
373
374
10. Research methods in flow assurance
C
C------------------------------------------------------------------C
SUBROUTINE READMSI
implicit real*8 (a-h,o-z)
character*80 cc
character*20 f1,f2,f3
character*1 aaa
character*12 fname2
character*8 fname
COMMON /fname / fname
COMMON /raw / irawbond(1000,2),irawatom(1000)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
print *,'Enter the name of the .MSI file without extension:'
read(*,'(A8)')fname
print *,'input was', fname
fname2 = fname(1:index(fname,' ')-1)//'.msi'
open(unit=1,file=fname2,status='unknown')
open(unit=2,file='atoms.dat',status='unknown')
open(unit=3,file='bonds.dat',status='unknown')
C
10
C
C
11
12
C
nbondfound=0
natom=0
read a line
read (1,'(80A)')cc
check for end of file attribute: ) in position 1
if(cc(1:1).eq.')') goto 100
scan the line for Bond statements
nfound=0
do i=80,1,-1
ncc=i
if(cc(i:i).ne.' ') goto 11
end do
if(ncc.gt.4) then
if(cc(ncc-3:ncc).eq.'Bond')then
nbondfound=nbondfound+1
read (1,'(80A)')cc
check for end of file attribute: ) in position 1
if(cc(1:1).eq.')') goto 100
do i3=1,77
if(cc(i3:i3+3).ne.'Atom') goto 15
n1=index(cc,'Atom') +6
n2=index(cc,')') -1
nn=0
Computer code (Makogon, 1994, 1997)
15
C
16
22
C
C
24
C
do j=n1,n2
nn=nn+10**(n2-j)*(ichar(cc(j:j))-48)
end do
nfound=nfound+1
irawbond(nbondfound,nfound) = nn
end do
if(nfound.lt.2) goto 12
goto 90
endif
endif
scan the line for Atom statements
do i=80,1,-1
ncc=i
if(cc(i:i).ne.' ') goto 16
end do
if(ncc.gt.4) then
if(cc(ncc-3:ncc).eq.'Atom')then
natom=natom+1
n1=index(cc,'(') +1
n2=index(cc,'Atom') -2
nn=0
do j=n1,n2
nn=nn+10**(n2-j)*(ichar(cc(j:j))-48)
end do
irawatom(natom)=nn
read (1,'(80A)')cc
check for end of file attribute: ) in position 1
if(cc(1:1).eq.')') goto 100
if(cc(8:8).eq.'C')goto 24
if(cc(8:8).eq.'X')goto 26
if(cc(8:8).eq.'F')goto 28
goto 30
get atomic charge
aa=0.d0
n1=index(cc,'Charge') +7
n2=index(cc,'.') +1
n3=index(cc,')') -1
do j=n2,n3
aa=aa+10.D0**(n2-j-1)*(ichar(cc(j:j))-48.D0)
end do
if (cc(n1:n1).eq.'-') aa=-aa
nfound=nfound+1
atomdata(natom,4) = aa
goto 30
get atomic coordinates
375
376
26
C
28
C
30
90
10. Research methods in flow assurance
n1=index(cc,'XYZ') +5
n2=index(cc,')') -1
nspace1=index(cc(n1:n2),' ')+n1-1
nspace2=index(cc(nspace1+1:n2),' ')+nspace1
ndot1=index(cc(n1:nspace1-1)
,'.')+n1-1
ndot2=index(cc(nspace1+1:nspace2-1),'.')+nspace1
ndot3=index(cc(nspace2+1:n2)
,'.')+nspace2
f1='(F15.11)'
f2='(F15.11)'
f3='(F15.11)'
aaa='2'
if(ndot1.eq.n1-1) then
write(f1,'(I2)')nspace1-n1
aaa=f1(2:2)
f1='(F'//aaa//'.0)'
endif
if(ndot2.eq.nspace1) then
write(f2,'(I2)')nspace2-nspace1-1
aaa=f2(2:2)
f2='(F'//aaa//'.0)'
endif
if(ndot3.eq.nspace2) then
write(f3,'(I2)')n2-nspace2
aaa=f3(2:2)
f3='(F'//aaa//'.0)'
endif
read(cc(n1:nspace1-1),
f1)atomdata(natom,1)
read(cc(nspace1+1:nspace2-1),f2)atomdata(natom,2)
read(cc(nspace2+1:n2),
f3)atomdata(natom,3)
nfound=nfound+1
goto 30
get atom type
n1=index(cc,'FFType') +8
iatomtype(natom,1)=0
if(cc(16:16).eq.'H') iatomtype(natom,1)=1
if(cc(16:16).eq.'C') iatomtype(natom,1)=2
if(cc(16:16).eq.'O') iatomtype(natom,1)=3
if(cc(16:16).eq.'N') iatomtype(natom,1)=4
if(iatomtype(natom,1).eq.0) print *,'ERROR: Atom type unknown'
nfound=nfound+1
goto 30
check if all atomic parameters were read
if(nfound.lt.3) goto 22
endif
endif
goto 10
Computer code (Makogon, 1994, 1997)
C
100
output data to files
do i=1,nbondfound
write (3,'(2I8)')irawbond(i,1),irawbond(i,2)
end do
do i=1,natom
write (2,'(4F10.5)')(atomdata(i,j),j=1,4)
end do
close (1)
close (2)
close (3)
return
end
C
C------------------------------------------------------------------C
SUBROUTINE RUNPAR
IMPLICIT REAL*8(A-H,O-Z)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /NCC / Kacct, Kaccr, Kaccp
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /PROPTY/ Bmax, Gmax, Rdel
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /NHB / nhb(100),nhbpoly,nhbcurr(100)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /bonds / ibonddata(1000,4),nbonds(1000)
C
pi = 3.14159265358979d0
Kcyc=0
C ... identify monomer atom that serves as origin for body frame
Norgn=monodata(100,(int(nbackbone/2)+1))
C ... identify atoms whose position vectors will be used
C
to monitor the polymerend-to-end distance during the run
M1 =monodata(100,1)
M2 =monodata(100,nbackbone)
C ... temperature & gas constant (kcal/(mol K))
R = 0.001987D0
Print *, ' '
Print *, ' Enter the simulation temperature in K'
Read *, Temp
print *,'input was', temp
Tk = R*Temp
C
377
378
10. Research methods in flow assurance
CALL RUNLEN
C ... acceptance ratios for translation, rotation, pivot
Acctrn = 0.25D0
Accrot = 0.125D0
Accpiv = 0.25D0
Kacct = 0
Kaccr = 0
Kaccp = 0
C hydrogen bonds counters
do i=1,nbackbone
nhb(i)=0
end do
C ... maximum step sizes (Angstroms and degrees to radians)
Deltrn = 1.0D0
Delrot = 12.D0*PI/180.D0
Delpiv = 12.d0*pi/180.d0
C
C ... Coulomb unit conversion
Co =332.0637D0
C
C ... top cell boundary (not for periodic boundaries _ Xmaxh)
Bmax =15.D0
CC
CC ... shell thickness for g(z) & max elevation to sample
cCRdel = 0.1D0
cCGmax = 10.D0
CC
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE RUNLEN
IMPLICIT REAL*8(A-H,O-Z)
real*4 ra,randseed
COMMON /CRASH / ncrash, ncalls
COMMON /rans / randseed
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
C
C ... Number of dead cycles & run cycles
Print *, ' '
print *,'Is it a crash recovery? (No- 0, Yes- #of random calls)'
read *, ncrash
print *,'input was', ncrash
ncalls=0
Computer code (Makogon, 1994, 1997)
C assume that equilibration was not done yet
Neq=0
C
randomize number generator
Print *, ' '
Print *, ' Enter a seed for random number'
read *,randseed
print *,'input was', randseed
call srand(randseed+0.)
ccc
CALL SEED(randseed+0.)
C
if (ncrash.GT.0) then
do NNRn=1,ncrash-1
ra=roulet()
end do
endif
C
Print *, ' '
Print *, ' Enter number of equilibration cycles'
Read *, Ndead
print *,'input was', ndead
C
Print *, ' '
Print *, ' Enter number of run cycles'
Read *, Ncycle
print *,'input was', ncycle
C
Print *, ' '
Print *, ' Enter print interval, in cycles'
Read *, Kprint
print *,'input was', kprint
C
Print *, ' '
Print *, ' Enter interval for graphical output'
Read *, Kdprnt
print *,'input was', kdprnt
C
Print *, ' '
RETURN
END
C
C------------------------------------------------------------------C
REAL*8 FUNCTION ROULET()
IMPLICIT REAL*8(A-H,O-Z)
REAL*4 aa
COMMON /CRASH / ncrash, ncalls
379
380
ccc
10. Research methods in flow assurance
call random(aa)
aa=rand()
bb=dble(aa)
roulet = bb+bb-1.D0
ncalls=ncalls+1
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE CYCLES(N1,Ntimes)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
C
C ... main Monte Carlo simulation loop
C translation move attempt
DO 100 Kcyc = N1, Ntimes
CALL NEWPOS
CALL ENERGY(Ener)
CALL DECIDE(Ener, 0)
C rotation move attempt
CALL NEWORI
CALL ENERGY(Ener)
CALL DECIDE(Ener, 1)
C pivot move attempt
CALL NEWPIV
CALL ENERGY(Ener)
CALL DECIDE(Ener, 2)
C adjust maximum step sizes, based on move acceptances
IF (MOD(Kcyc,10) .EQ. 0) CALL ADJUST
C ... output information for the POSVIEW and POS2BMP programs
IF(MOD(Kcyc,Kdprnt).EQ.0) CALL GRAPHDATA
C
IF(MOD(Kcyc,Kprint).EQ.0) then
CALL PRTOUT
CALL CRASHSAVE
CALL SAMGOZ
endif
C
100
CONTINUE
C
RETURN
END
C
Computer code (Makogon, 1994, 1997)
C------------------------------------------------------------------C
SUBROUTINE NEWPOS
IMPLICIT REAL*8(A-H,O-Z)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
C
C
identify call type (translation move)
ncall=1
C ... translate entire polymer
Xstep = Deltrn*ROULET()
Ystep = Deltrn*ROULET()
Zstep = Deltrn*ROULET()
C
DO 100 I = 1, Natom
xn(I) = xms(I) + Xstep
yn(I) = yms(I) + Ystep
zn(I) = zms(I) + Zstep
100 CONTINUE
CALL PBC
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE PBC
IMPLICIT REAL*8(A-H,O-Z)
INTEGER A,AP
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
COMMON /side / side, unitside
COMMON /diag / diag
COMMON /PROPTY/ Bmax, Gmax, Rdel
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /SURF1 / a, ap
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
C
C if chain goes over the top boundary, push it back in
C
IF (zn(Norgn) .GT. Bmax) THEN
381
382
10. Research methods in flow assurance
delta = zn(Norgn) - Bmax + 3.D0
DO 470 I = 1, Natom
470
zn(I) = zn(I) - delta
ENDIF
C if chain goes deeper than 6 A into the surface, push it to 3 A above surface
C
IF (zn(Norgn) .LT. -6.D0) THEN
delta = -zn(Norgn) + 3.D0
DO 475 I = 1, Natom
475
zn(I) = zn(I) + delta
ENDIF
C apply periodic boundaries to vertical walls
C--------------[100]--------------if (AP.eq.1.or.ap.eq.3) then
C we are dealing with [100] or [110] hydrate surface -rectangular box BC
C ... apply periodic boundaries to entire chain in x & y
C
directions, based on position of origin of body frame
C
IF (xn(Norgn) .GT. xmax) THEN
DO 480 I = 1, natom
480
xn(I) = xn(I) - xmax
ENDIF
C
IF (xn(Norgn) .LT. 0.D0) THEN
DO 485 I = 1, natom
485
xn(I) = xn(I) + xmax
ENDIF
C
IF (yn(Norgn) .GT. ymax) THEN
DO 490 I = 1, natom
490
yn(I) = yn(I) - ymax
ENDIF
C
IF (yn(Norgn) .LT. 0.D0) THEN
DO 495 I = 1, natom
495
yn(I) = yn(I) + ymax
ENDIF
endif
C --------------[111]-------------if(ap.eq.2) then
C we are using the [111] hydrate surface - apply rhombic BC
C
RT2 = side
RRT2 = 1.0D0 / RT2
RT3 = 1.732050807568877D0
Computer code (Makogon, 1994, 1997)
RRT3 = 1.D0/RT3
RT32 = RT3/2.D0
RRT32 = 1.D0/RT32
DXms = rt2*DNINT(Xn(Norgn)*rrt2 -RRT3*Yn(Norgn)*rrt2)
:
+ rt2*DNINT(RRT32*Yn(Norgn)*rrt2)*0.5D0
DYms = rt2*DNINT(RRT32*Yn(Norgn)*rrt2)*RT32
if(DXms.ne.0.D0 .OR. DYms.ne.0.D0) then
do 498 i=1, natom
Xn(I) = Xn(I) - DXms
498
Yn(I) = Yn(I) - DYms
endif
endif
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE NEWORI
IMPLICIT REAL*8(A-H,O-Z)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
common /matrix/ r11,r12,r13,r21,r22,r23,r31,r32,r33,r41,r42,r43
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
common /rotate/ A1,A2,A3,v1,v2,v3,alpha
C
C
identify call type (rotation move)
ncall=2
C ... get random numbers to determine axis of rotation
delx = ROULET()
dely = ROULET()
delz = ROULET()
c
choose angle of rotation; and two coordinates on rotation axis
alpha=DELROT*ROULET()
a1=xms(Norgn)
a2=yms(Norgn)
a3=zms(Norgn)
v1=a1+delx
v2=a2+dely
v3=a3+delz
c
c
prepare the rotation matrix
call Initrotate(A1,A2,A3,v1,v2,v3,alpha)
383
384
10. Research methods in flow assurance
call Initrotate
c
do i=1,natom
xn(i)=xms(i)*r11+yms(i)*r21+zms(i)*r31+r41
yn(i)=xms(i)*r12+yms(i)*r22+zms(i)*r32+r42
zn(i)=xms(i)*r13+yms(i)*r23+zms(i)*r33+r43
end do
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE NEWPIV
C
this subroutine is used to rotate any number of 3D points about axis
c
passing through 2 points with coordinates (a1,a2,a3) and (v1,v2,v3).
c
angle of rotation ALPHA is in radians
implicit real*8 (a-h,o-z)
real*4 ran
integer*2 ncenter,ncenter2
common
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
common
C
c
/matrix/
/types /
/chain /
/NWPOS /
/STEPS /
/SPACE /
/center/
/rotate/
r11,r12,r13,r21,r22,r23,r31,r32,r33,r41,r42,r43
iatomtype(1000,2),nbondfound,natom,ngroups,ncall
monodata(100,100),monocount(99),nbackbone
xn(1000), yn(1000), zn(1000)
Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
xms(1000), yms(1000), zms(1000)
ncenter,ncenter2
A1,A2,A3,v1,v2,v3,alpha
identify call type (pivot move)
ncall=3
choose angle of rotation; and two backbone atoms as rotation axis
ran=roulet()
alpha=DELPIV*ran
ran=(roulet()+1.)*0.5
ncenter=int(nbackbone*ran)+1
ncenter2=ncenter+1
if(ncenter.gt.nbackbone/2) ncenter2=ncenter-1
a1=xms(monodata(100,ncenter))
a2=yms(monodata(100,ncenter))
a3=zms(monodata(100,ncenter))
v1=xms(monodata(100,ncenter2))
v2=yms(monodata(100,ncenter2))
v3=zms(monodata(100,ncenter2))
Computer code (Makogon, 1994, 1997)
c
c
c
c
c
c
prepare the rotation matrix
call Initrotate(A1,A2,A3,v1,v2,v3,alpha)
call Initrotate
see which end of the chain are we rotating
if(ncenter.gt.nbackbone/2) then
do i=ncenter,nbackbone
do j=1,monocount(i)
x=xms(monodata(i,j))
y=yms(monodata(i,j))
z=zms(monodata(i,j))
xn(monodata(i,j))=x*r11+y*r21+z*r31+r41
yn(monodata(i,j))=x*r12+y*r22+z*r32+r42
zn(monodata(i,j))=x*r13+y*r23+z*r33+r43
end do
end do
assign new coordinates to the non-moving part of the chain
do i=1,ncenter2
do j=1,monocount(i)
xn(monodata(i,j))=xms(monodata(i,j))
yn(monodata(i,j))=yms(monodata(i,j))
zn(monodata(i,j))=zms(monodata(i,j))
end do
end do
the Origin atom was moved, so check if it has crossed the PBC
CALL PBC
else
do i=1,ncenter
do j=1,monocount(i)
x=xms(monodata(i,j))
y=yms(monodata(i,j))
z=zms(monodata(i,j))
xn(monodata(i,j))=x*r11+y*r21+z*r31+r41
yn(monodata(i,j))=x*r12+y*r22+z*r32+r42
zn(monodata(i,j))=x*r13+y*r23+z*r33+r43
end do
end do
assign new coordinates to the non-moving part of the chain
do i=ncenter2,nbackbone
do j=1,monocount(i)
xn(monodata(i,j))=xms(monodata(i,j))
yn(monodata(i,j))=yms(monodata(i,j))
zn(monodata(i,j))=zms(monodata(i,j))
end do
end do
385
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10. Research methods in flow assurance
endif
C
return
end
C
C------------------------------------------------------------------C
c
Subroutine Initrotate(A1,A2,A3,v1,v2,v3,alpha)
Subroutine Initrotate
implicit real*8 (a-h,o-z)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
common /rotate/ A1,A2,A3,v1,v2,v3,alpha
common /matrix/ r11,r12,r13,r21,r22,r23,r31,r32,r33,r41,r42,r43
c
cal=dcos(alpha)
sal=dsin(alpha)
cal1=1.d0-cal
rho=dsqrt((v1-a1)*(v1-a1)+(v2-a2)*(v2-a2)+(v3-a3)*(v3-a3))
if(rho.eq.0.d0) then
theta=0.d0
cph=1.d0
sph=0.d0
else
if(v1.eq.a1) then
if(v2.ge.a2) theta=0.5d0*pi
if(v2.lt.a2) theta=1.5d0*pi
else
theta=datan((v2-a2)/(v1-a1))
if(v1.lt.a1) theta=theta+pi
endif
cph=(v3-a3)/rho
sph=dsqrt(1.d0-cph*cph)
endif
cth=dcos(theta)
sth=dsin(theta)
cph2=cph*cph
sph2=1.d0-cph2
cth2=cth*cth
sth2=1.d0-cth2
r11=(cal*cph2+sph2)*cth2+cal*sth2
r12=sal*cph+cal1*sph2*cth*sth
r13=sph*(cph*cth*cal1-sal*sth)
Computer code (Makogon, 1994, 1997)
r21=sph2*cth*sth*cal1-sal*cph
r22=sth2*(cal*cph2+sph2)+cal*cth2
r23=sph*(cph*sth*cal1+sal*cth)
r31=sph*(cph*cth*cal1+sal*sth)
r32=sph*(cph*sth*cal1-sal*cth)
r33=cal*sph2+cph2
r41=a1-a1*r11-a2*r21-a3*r31
r42=a2-a1*r12-a2*r22-a3*r32
r43=a3-a1*r13-a2*r23-a3*r33
return
end
C
C------------------------------------------------------------------C
SUBROUTINE ENPOLY
c
Initial setup of the Epoly and Esurf arrays.
c
Calculation of the initial intramolecular polymer energy is done
c
with 1-2 backbone group exclusion
implicit real*8 (a-h,o-z)
integer a, ap
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi, Tk,Temp
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /bonds / ibonddata(1000,4),nbonds(1000)
COMMON /NHB / nhb(100),nhbpoly,nhbcurr(100)
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /SURF1 / a, ap
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3), qw(3)
C
C Calculate intramolecular polymer energy
nhbpoly=0
do I=1,nbackbone-2
do ii=i+2,nbackbone
Ener = 0.D0
do J=1,monocount(i)
do jj=1,monocount(ii)
natom1 = monodata(i,j)
387
388
C
C
C
C ...
C ...
C ...
C ...
10. Research methods in flow assurance
natom2 = monodata(ii,jj)
x =xn(natom1)
y =yn(natom1)
z =zn(natom1)
xx=xn(natom2)
yy=yn(natom2)
zz=zn(natom2)
rsq=(x-xx)**2+(y-yy)**2+(z-zz)**2
r=dsqrt(rsq)
Ehb = 0.D0
Elj = 0.D0
Coulombic interaction
Ecou = Co*atomdata(natom1,4)*atomdata(natom2,4)/R
Lennard-Jones interaction
IF (R .LE. Rcut) THEN
Itype=iatomtype(natom2,1)
R6red=(RR(Itype,natom1)*RR(Itype,natom1)/Rsq)**3
Elj = DD(Itype,natom1)*R6red*(R6red-2.D0)
hydrogen-bond interaction, if applicable
ndon=0
IF(rhb(natom1).eq.2.8D0.and.rhb(natom2).eq.0.01D0) then
ndon=monodata(i,j)
nacc=monodata(ii,jj)
endif
IF(rhb(natom2).eq.2.8D0.and.rhb(natom1).eq.0.01D0) then
ndon=monodata(ii,jj)
nacc=monodata(i,j)
endif
IF(ndon.gt.0) then
check if within switching distance
Swtchr = 1.D0
IF (Rsq .GT. Rsqon) CALL SWITCH(Rsqon,Rsqoff,Rsq,Swtchr)
get hydrogen atom vector
Xh = xn(ibonddata(nacc,1)) - xn(nacc)
Yh = yn(ibonddata(nacc,1)) - yn(nacc)
Zh = zn(ibonddata(nacc,1)) - zn(nacc)
Rhsq = Xh*Xh + Yh*Yh + Zh*Zh
get donor-acceptor distance
Xah= xn(ndon) - xn(nacc)
Yah= yn(ndon) - yn(nacc)
Zah= zn(ndon) - zn(nacc)
Rahsq = Xah*Xah + Yah*Yah + Zah*Zah
cos**2 of HB angle
Chbsq = (Xh*Xah + Yh*Yah + Zh*Zah)**2/(Rhsq*Rahsq)
IF (Chbsq . LT. Casqof) goto 10
Computer code (Makogon, 1994, 1997)
C
Rsqred = Rhb(ndon)*Rhb(ndon)/Rsq
Ehb = Dhb(ndon)*Rsqred**5*(5.D0*Rsqred -6.D0)*Chbsq*Swtchr
nhbpoly=nhbpoly+1
ENDIF
ENDIF
10
Ener = Ener + Ecou + Elj + Ehb
end do
end do
Epoly(i,ii) = Ener
end do
end do
C
C
C Calculate interaction of polymer with the surface
Erun = 0.D0
C outer loop over all polymer segments
DO j=1,nbackbone
Esurf(j)=0.d0
do jj=1,monocount(j)
natom1 = monodata(j,jj)
nhbcount=0
Ener=0.D0
C ...inner loop over water molecules
DO 20 Iw = 1, Nwatrs
C ... loop over all atoms on each water molecule
DO 20 I = 1, 3
Ehb = 0.D0
Elj = 0.D0
Xi = xw(Iw,I)
Yi = yw(Iw,I)
Zi = zw(Iw,I)
Qi = qw(I)
C
Xij = Xi - xn(natom1)
Yij = Yi - yn(natom1)
Zij = Zi - zn(natom1)
C
C ... minimum image distances in x & y to keep surface under chain
if (ap.eq.1.or.ap.eq.3) then
C we are dealing with the [100] or [110] hydrate surface-rectangular box
IF (Yij .GT. ymaxh) Yij = Yij - ymax
IF (Yij .LT.-ymaxh) Yij = Yij + ymax
IF (Xij .GT. xmaxh) Xij = Xij - xmax
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10. Research methods in flow assurance
IF (Xij .LT.-xmaxh) Xij = Xij + xmax
endif
if(ap.eq.2) then
C We are using [111] surface - rhombic boundaries
if (Yij .GT. ymaxh) then
Yij = Yij - ymax
Xij = Xij - xmaxh
endif
if (Yij .LT.-ymaxh) then
Yij = Yij + ymax
Xij = Xij + xmaxh
endif
IF (Xij .GT. xmaxh) Xij = Xij - xmax
IF (Xij .LT.-xmaxh) Xij = Xij + xmax
endif
Rsq = Xij*Xij + Yij*Yij + Zij*Zij
Rij = DSQRT(Rsq)
Ecou = Co*Qi*atomdata(natom1,4)/Rij
C collect cutoff-dependent interactions
IF (Rij .LE. Rcut) THEN
C set itype for SPC water hydrogen
itype=5
C if oxygen, set itype for SPC water oxygen
if(i.eq.3)itype=6
R6red = (RR(Itype,natom1)*RR(Itype,natom1)/Rsq)**3
Elj
= DD(Itype,natom1)*R6red*(R6red - 2.D0)
C
C ... collect hydrogen-bond interaction, if applicable
IF (iatomtype(natom1,1).eq.3) THEN
IF (I.EQ.3.and.Rsq.LT.Rsqoff) CALL HBOND(Xi,Yi,Rsq,Iw,J,Ehb)
ENDIF
C end of collecting cutoff-dependent interactions
ENDIF
Ener = Ener + Ecou + Elj + Ehb
20
CONTINUE
Esurf(j)=Esurf(j)+Ener
end do
end do
C
Epold=0.D0
do 50 i=1,nbackbone-2
do 50 j=i+2,nbackbone
50 Epold=Epold+Epoly(i,j)
Computer code (Makogon, 1994, 1997)
60
Eold=0.D0
do 60 i=1,nbackbone
Eold=Eold+Esurf(i)
Eold=Eold+Epold
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE ENERGY(Ener)
IMPLICIT REAL*8(A-H,O-Z)
integer a, ap
integer*2 ncenter,ncenter2
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
COMMON /side / side, unitside
COMMON /diag / diag
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /bonds / ibonddata(1000,4),nbonds(1000)
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /NHB / nhb(100),nhbpoly,nhbcurr(100)
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi, Tk,Temp
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3), qw(3)
COMMON /SURF1 / a, ap
COMMON /center/ ncenter,ncenter2
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
C
C Calculate interaction of polymer with the surface.
C Outer loop over all polymer segments
C
set temporary surface energies to accepted values
do 100 i=1,nbackbone
100 Es(i)=Esurf(i)
c determine which segments were moved and need new energy calculation
ni = 1
nii= nbackbone
if(ncall.eq.3) then
ni = 1
nii= ncenter
if(ncenter.gt.nbackbone/2) then
ni = ncenter
391
392
10. Research methods in flow assurance
nii= nbackbone
endif
endif
C
outer loop over polymer segments
DO j = ni , nii
Es(j)=0.d0
nhbcount=0
do jj=1,monocount(j)
natom1 = monodata(j,jj)
Ener=0.D0
C ...inner loop over water molecules
DO 200 Iw = 1, Nwatrs
C ... loop over all atoms on each water molecule
DO 200 I = 1, 3
Ehb = 0.D0
Elj = 0.D0
Xi = xw(Iw,I)
Yi = yw(Iw,I)
Zi = zw(Iw,I)
Qi = qw(I)
C
Xij = Xi - xn(natom1)
Yij = Yi - yn(natom1)
Zij = Zi - zn(natom1)
C
C ... minimum image distances in x & y to keep surface under chain
if (ap.eq.1.or.ap.eq.3) then
C we are dealing with the [100] or [110] hydrate surface-rectangular box
IF (Yij .GT. ymaxh) Yij = Yij - ymax
IF (Yij .LT.-ymaxh) Yij = Yij + ymax
IF (Xij .GT. xmaxh) Xij = Xij - xmax
IF (Xij .LT.-xmaxh) Xij = Xij + xmax
endif
if(ap.eq.2) then
C We are using [111] surface - rhombic boundaries
if (Yij .GT. ymaxh) then
Yij = Yij - ymax
Xij = Xij - xmaxh
endif
if (Yij .LT.-ymaxh) then
Yij = Yij + ymax
Xij = Xij + xmaxh
endif
IF (Xij .GT. xmaxh) Xij = Xij - xmax
Computer code (Makogon, 1994, 1997)
IF (Xij .LT.-xmaxh) Xij = Xij + xmax
endif
Rsq = Xij*Xij + Yij*Yij + Zij*Zij
Rij = DSQRT(Rsq)
Ecou = Co*Qi*atomdata(natom1,4)/Rij
C
c
c
IF (Rij .LE. Rcut) THEN
set itype for SPC water hydrogen
itype=5
if oxygen, set itype for SPC water oxygen
if(i.eq.3)itype=6
R6red = (RR(Itype,natom1)*RR(Itype,natom1)/Rsq)**3
Elj = DD(Itype,natom1)*R6red*(R6red - 2.D0)
C
C ... collect hydrogen-bond interaction, if applicable
C
IF(iatomtype(natom1,1).eq.3) then
IF (I.EQ.3) THEN
IF (Rsq .LT.Rsqoff) CALL HBOND(Xi,Yi,Rsq,Iw,natom1,Ehb)
IF(Ehb.ne.0.D0) nhbcount=nhbcount+1
ENDIF
ENDIF
C
ENDIF
Ener = Ener + Ecou + Elj + Ehb
200 CONTINUE
nhb(j)=nhb(j)+nhbcount
nhbcurr(j)=nhbcount
Es(j)=Es(j)+Ener
end do
end do
C
count the total polymer-surface energy
Ener=0.D0
DO j=1,nbackbone
Ener=Ener+Es(j)
end do
RETURN
C
END
C
C------------------------------------------------------------------C
SUBROUTINE ENERGYP(Ener)
IMPLICIT REAL*8(A-H,O-Z)
integer a, ap
393
394
10. Research methods in flow assurance
integer*2 ncenter,ncenter2
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
COMMON /side / side, unitside
COMMON /diag / diag
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /bonds / ibonddata(1000,4),nbonds(1000)
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /NHB / nhb(100),nhbpoly,nhbcurr(100)
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi, Tk,Temp
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3), qw(3)
COMMON /SURF1 / a, ap
COMMON /center/ ncenter,ncenter2
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
C
C Move was a pivot - find intramolecular polymer energy for the moved segments
nhbpoly=0
C set the temporary array EP of segment interaction energies to accepted values
do 10 i=1,nbackbone-2
do 10 j=i+2,nbackbone
10 Ep(i,j)=Epoly(i,j)
C assign boundaries for loops over moved (ncenter), unmoved (ncenter2) segments
ni = ncenter
nii= ncenter2
if(ncenter.gt.nbackbone/2) then
ni = ncenter2
nii= ncenter
endif
C loops over moved and unmoved segments
do i = 1 , ni
do ii=nii, nbackbone
c if the pair of groups is a neighboring pair in backbone, skip the pair
if(abs(i-ii).eq.1)goto 35
Ener = 0.D0
do j=1,monocount(i)
do jj=1,monocount(ii)
natom1 = monodata(i,j)
natom2 = monodata(ii,jj)
x =xn(natom1)
y =yn(natom1)
z =zn(natom1)
Computer code (Makogon, 1994, 1997)
C
C
C
C
C
C
C
C
xx=xn(natom2)
yy=yn(natom2)
zz=zn(natom2)
rsq=(x-xx)**2+(y-yy)**2+(z-zz)**2
a quick test for close contacts (1.5 A)
if (rsq.lt.2.25)then
Ener=1.D8
return
endif
r=dsqrt(rsq)
Ehb = 0.D0
Elj = 0.D0
Coulombic interaction
Ecou = Co*atomdata(natom1,4)*atomdata(natom2,4)/R
Lennard-Jones interaction
IF (R .LE. Rcut) THEN
Itype=iatomtype(natom2,1)
R6red=(RR(Itype,natom1)*RR(Itype,natom1)/Rsq)**3
Elj = DD(Itype,natom1)*R6red*(R6red-2.D0)
intramolecular hydrogen-bond interaction, if applicable
IF (Rsq.LT.Rsqoff) then
ndon=0
IF(rhb(natom1).eq.2.8D0.and.rhb(natom2).eq.0.01D0) then
ndon=natom1
nacc=natom2
endif
IF(rhb(natom2).eq.2.8D0.and.rhb(natom1).eq.0.01D0) then
ndon=natom2
nacc=natom1
endif
IF(ndon.ne.0) then
... check if within switching distance
Swtchr = 1.D0
IF (Rsq .GT. Rsqon) CALL SWITCH(Rsqon,Rsqoff,Rsq,Swtchr)
... get hydrogen atom vector
Xh = xn(ibonddata(nacc,1)) - xn(nacc)
Yh = yn(ibonddata(nacc,1)) - yn(nacc)
Zh = zn(ibonddata(nacc,1)) - zn(nacc)
Rhsq = Xh*Xh + Yh*Yh + Zh*Zh
... get donor-acceptor distance
Xah= xn(ndon) - xn(nacc)
Yah= yn(ndon) - yn(nacc)
Zah= zn(ndon) - zn(nacc)
Rahsq = Xah*Xah + Yah*Yah + Zah*Zah
... cos**2 of HB angle
395
396
C
C
C
C
10. Research methods in flow assurance
Chbsq = (Xh*Xah + Yh*Yah + Zh*Zah)**2/(Rhsq*Rahsq)
IF (Chbsq . LT. Casqof) goto 30
calculate Ehb from the LJ 12-10 potential,angle coefficient,and spline if any
Rsqred = Rhb(ndon)*Rhb(ndon)/Rsq
Ehb = Dhb(ndon)*Rsqred**5*(5.D0*Rsqred -6.D0)*Chbsq*Swtchr
IF(Ehb.ne.0.D0) nhbpoly=nhbpoly+1
ENDIF
ENDIF
ENDIF
30
Ener = Ener + Ecou + Elj + Ehb
end loops over segment atoms, assign temporary interaction value for the pair
end do
end do
Ep(i,ii) = Ener
35 end do
end do
ended loops over moved/unmoved segments
calculate total polymer intramolecular energy
Ener=0.D0
do 50 i=1,nbackbone-2
do 50 j=i+2,nbackbone
50 Ener=Ener+Ep(i,j)
return
end
C
C------------------------------------------------------------------C
SUBROUTINE HBOND(Xi,Yi,Rsq,Iw,J,Ehb)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3),qw(3)
C
C ... check if within switching distance
Swtchr = 1.D0
IF (Rsq .GT. Rsqon) CALL SWITCH(Rsqon,Rsqoff,Rsq,Swtchr)
C set hydrogen bond donor parameters
Xa = xn(J)
Ya = yn(J)
Za = zn(J)
RRhb = RHB(J)
DDhb = DHB(J)
C
Computer code (Makogon, 1994, 1997)
C ... check only closer hydrogen atom on water for HB angles
C
CALL HBIMGE(Xi,Yi,Xa,Ya,Za,Xah,Yah,Zah,Iw,K)
C
C ... get water-bond vector
Xh = xw(Iw,3) - xw(Iw,K)
Yh = yw(Iw,3) - yw(Iw,K)
Zh = zw(Iw,3) - zw(Iw,K)
Rhsq = Xh*Xh + Yh*Yh + Zh*Zh
C
C ... get hydrogen-acceptor distance
Rahsq = Xah*Xah + Yah*Yah + Zah*Zah
C
C ... cos**2 of HB angle
Chbsq = (Xh*Xah + Yh*Yah + Zh*Zah)**2/(Rhsq*Rahsq)
IF (Chbsq . LT. Casqof) RETURN
C
Rsqred = RRhb*RRhb/Rsq
Ehb = DDhb*Rsqred**5*(5.D0*Rsqred -6.D0)*Chbsq*Swtchr
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE SWITCH(Xon,Xoff,xxx,Swtch)
IMPLICIT REAL*8(A-H,O-Z)
Top = ((Xoff-xxx)**2)*(Xoff +2.D0*xxx -3.D0*Xon)
Swtch = Top/(Xoff-Xon)**3
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE HBIMGE(xi,yi,xa,ya,za,Xah,Yah,Zah,Iw,K)
IMPLICIT REAL*8(A-H,O-Z)
integer a, ap
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
COMMON /side / side, unitside
COMMON /diag / diag
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3), qw(3)
COMMON /SURF1 / a, ap
DIMENSION xwxa(2), ywya(2), zwza(2)
C
C
for hydrogen bonding, apply minimum imaging to all 3 atoms
397
398
C
C
C
10. Research methods in flow assurance
of a water, based on whether an image is used for the
oxygen atom
Xij = xi - xa
Yij = yi - ya
C
DO 12 K = 1,2
xwxa(K) = xw(Iw,K) - xa
ywya(K) = yw(Iw,K) - ya
zwza(K) = zw(Iw,K) - za
12
CONTINUE
C do actual adjustment of hydrogens' positions
if (ap.eq.1) then
C we are dealing with [100] or [110] hydrate surface - a rectangular box
IF (yij .GT. ymaxh) THEN
ywya(1) = ywya(1) - ymax
ywya(2) = ywya(2) - ymax
ENDIF
C
IF (yij .LT.-ymaxh) THEN
ywya(1) = ywya(1) + ymax
ywya(2) = ywya(2) + ymax
ENDIF
C
IF (xij .GT. xmaxh) THEN
xwxa(1) = xwxa(1) - xmax
xwxa(2) = xwxa(2) - xmax
ENDIF
C
IF (xij .LT.-xmaxh) THEN
xwxa(1) = xwxa(1) + xmax
xwxa(2) = xwxa(2) + xmax
ENDIF
endif
C
if(AP.EQ.2) THEN
C We are using [111] surface - rhombic boundaries
IF (Yij .GT. ymaxh) then
ywya(1) = ywya(1) - ymax
ywya(2) = ywya(2) - ymax
xwxa(1) = xwxa(1) - xmaxh
xwxa(2) = xwxa(2) - xmaxh
Xij = Xij - xmaxh
ENDIF
C
Computer code (Makogon, 1994, 1997)
IF (Yij .LT.-ymaxh)
ywya(1) = ywya(1) +
ywya(2) = ywya(2) +
xwxa(1) = xwxa(1) +
xwxa(2) = xwxa(2) +
Xij = Xij + xmaxh
ENDIF
then
ymax
ymax
xmaxh
xmaxh
C
IF (xij .GT. xmaxh) THEN
xwxa(1) = xwxa(1) - xmax
xwxa(2) = xwxa(2) - xmax
ENDIF
C
IF (xij .LT.-xmaxh) THEN
xwxa(1) = xwxa(1) + xmax
xwxa(2) = xwxa(2) + xmax
ENDIF
C
endif
C
Rah1sq = xwxa(1)**2 + ywya(1)**2 + zwza(1)**2
Rah2sq = xwxa(2)**2 + ywya(2)**2 + zwza(2)**2
K = 1
IF (Rah2sq .LT. Rah1sq) K=2
C
C ... reverse vector for subsequent dot product
Xah = -xwxa(K)
Yah = -ywya(K)
Zah = -zwza(K)
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE GRAPHDATA
C This subroutine writes a coordinate file from which a bitmap can be generated
C by the POS2BMP program.
IMPLICIT REAL*8(A-H,O-Z)
CHARACTER*12 fname
character*4 form
integer a,ap,ndig
COMMON /bonds / ibonddata(1000,4),nbonds(1000)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
399
400
10. Research methods in flow assurance
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
/chain / monodata(100,100),monocount(99),nbackbone
/NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
/NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
/WPOS / xw(6000,3), yw(6000,3), zw(6000,3),qw(3)
/SURF1 / a, ap
/NWPOS / xn(1000), yn(1000), zn(1000)
/BDIST / xmax, ymax, xmaxh, ymaxh
/ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
/NHB / nhb(100),nhbpoly,nhbcurr(100)
/POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
/PROPTY/ Bmax, Gmax, Rdel
/STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
/ZSAVE / zrun(100),epolymer,Erun
/SPACE / xms(1000), yms(1000), zms(1000)
/RATIOS/ Ratiot, Ratior, Ratiop
C
set the name of the .POS file to a current MC move number
if(Kcyc.eq.0) then
ndig=1
else
ndig=int(log(dble(Kcyc))/log(10.D0))+1
endif
form='(I'//char(ndig+48)//')'
write(fname,form)Kcyc
fname = fname(1:ndig)//'.pos'
IF(Neq.eq.0)fname = fname(1:ndig)//'e.pos'
open(unit=1,file=fname,status='unknown')
C
coordinates for YX polymer
scale=240/ymax
write(1,'(F4.0)')scale
nxoff=60
nyoff=240
if(ap.eq.2)then
nxoff=160
nyoff=240
endif
write(1,'(3I4)')natom
do i=1,natom
ir=iatomtype(i,1)*scale/15
iix=int(yn(i)*scale)+nxoff
iiy=int(xn(i)*scale)+nyoff
write(1,'(5I4)')ir,iix,iiy,nbonds(i),iatomtype(i,1)
do j=1,nbonds(i)
ix=int(yn(ibonddata(i,j))*scale)+nxoff
Computer code (Makogon, 1994, 1997)
iy=int(xn(ibonddata(i,j))*scale)+nyoff
write(1,'(2I4)')ix,iy
end do
end do
iix=int(yn(monodata(100,1))*scale)+nxoff
iiy=int(xn(monodata(100,1))*scale)+nyoff
write(1,'(3I4)')iix,iiy,nbackbone
do i=2,nbackbone
ix=int(yn(monodata(100,i))*scale)+nxoff
iy=int(xn(monodata(100,i))*scale)+nyoff
write(1,'(2I4)')ix,iy
end do
C
data for YX surface
ir=int(scale/3.d0)
nxoff=60
nyoff=240
if(ap.eq.2)then
nxoff=160
nyoff=240
endif
write(1,'(2I4)')ir,nwatrs
do i=1,nwatrs
iix=int(yw(i,2)*scale)+nxoff
iiy=int(xw(i,2)*scale)+nyoff
write(1,'(2I4)')iix,iiy
ix=int(yw(i,3)*scale)+nxoff
iy=int(xw(i,3)*scale)+nyoff
ixw1=int(yw(i,1)*scale)+nxoff
ixw3=int(yw(i,3)*scale)+nxoff
iyw1=int(xw(i,1)*scale)+nyoff
iyw3=int(xw(i,3)*scale)+nyoff
write(1,'(6I4)')ix,iy,ixw3,iyw3,ixw1,iyw1
end do
C
data for YZ polymer
nxoff=320
nzoff=-240
if(ap.eq.2)then
nxoff=480
nzoff=-240
endif
do i=1,natom
ir=iatomtype(i,1)*scale/15
iix=int(yn(i)*scale)+nxoff
401
402
C
C
10. Research methods in flow assurance
iiz=int(zn(i)*scale)+nzoff
write(1,'(5I4)')ir,iix,-iiz,nbonds(i),iatomtype(i,1)
do j=1,nbonds(i)
ix=int(yn(ibonddata(i,j))*scale)+nxoff
iz=int(zn(ibonddata(i,j))*scale)+nzoff
write(1,'(2I4)')ix,-iz
end do
end do
iix=int(yn(monodata(100,1))*scale)+nxoff
iiz=int(zn(monodata(100,1))*scale)+nzoff
write(1,'(3I4)')iix,-iiz,nbackbone
do i=2,nbackbone
ix=int(yn(monodata(100,i))*scale)+nxoff
iz=int(zn(monodata(100,i))*scale)+nzoff
write(1,'(2I4)')ix,-iz
end do
data for YZ surface
ir=int(scale/3.D0)
nxoff=320
nzoff=-240
if(ap.eq.2)then
nxoff=480
nzoff=-240
endif
write(1,'(I4)')ir
do i=1,nwatrs
iix=int(yw(i,2)*scale)+nxoff
iiz=int(zw(i,2)*scale)+nzoff
write(1,'(2I4)')iix,-iiz
ix=int(yw(i,3)*scale)+nxoff
iz=int(zw(i,3)*scale)+nzoff
ixw1=int(yw(i,1)*scale)+nxoff
ixw3=int(yw(i,3)*scale)+nxoff
izw1=int(zw(i,1)*scale)+nzoff
izw3=int(zw(i,3)*scale)+nzoff
write(1,'(6I4)')ix,-iz,ixw3,-izw3,ixw1,-izw1
end do
current simulation information
Deno = 3.D0*DFLOAT(Kcyc)
if(kcyc.eq.0)deno=1.D0
Eave = Erun/Deno
Epol = Epolymer/Deno
nbb=nbackbone
nhbs=0
do 10 i=1,nbackbone
Computer code (Makogon, 1994, 1997)
10
NHbs=nhbs+nhbcurr(i)
Deno = 1.D0/(kprint*3.D0)
Rave=dsqrt(zrun(4)*deno)
Eplmave=zrun(8)*deno
Esrfave=zrun(9)*deno
Ecurave=zrun(7)*deno
90
write(1,*)' Kcyc <Re-e> <Ecur> <Epol> <Esur> Xpos
Ypos Zpos
&HBp HBs Epoly Esurf'
WRITE(1,90) Kcyc,rave,Eplmave,Esrfave,Ecurave,
& xms(Norgn),yms(Norgn),zms(Norgn),NHbpoly,NHBs,Epol,Eave
write(1,'(A20,99I2)')' Segments H bonds: ',(nhbcurr(i),i=1,nbb)
FORMAT(I7,F6.2,3F7.2,2F7.2,F6.2,I4,I4,2F7.2)
close(1)
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE DECIDE(Ener, Iflag)
IMPLICIT REAL*8(A-H,O-Z)
real*4 ran
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /PROPTY/ Bmax, Gmax, Rdel
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /chain / monodata(100,100),monocount(99),nbackbone
C obtain a sum of intramolecular and intermolecular energies for MC check
Enerp=Epold
IF(Iflag.eq.2) CALL ENERGYP(Enerp)
Ener=Ener+Enerp
C MC check
IF (Ener .LT. Eold) THEN
CALL ACCEPT(Ener, Iflag)
CALL ZSAMPLE
RETURN
else
Delu = (Ener - Eold)/Tk
IF (Delu .LT. 75.D0) THEN
Ran=(roulet()+1.)*0.5
IF (DEXP(-Delu) .GT. Ran) THEN
CALL ACCEPT(Ener, Iflag)
CALL ZSAMPLE
403
404
10. Research methods in flow assurance
RETURN
ENDIF
ENDIF
ENDIF
ENDIF
C
C
C ... Reject proposed move
Erun = Erun + Eold
CALL ZSAMPLE
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE ACCEPT(Ener, Iflag)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /NCC / Kacct, Kaccr, Kaccp
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
C
C
assign new values for polymer segments-surface interactions
do 10 i=1,nbackbone
10
Esurf(i)=Es(i)
c
20
C
30
C
assign new values for the intramolecular polymer segments interactions
if(Iflag.eq.2)then
Epold=0.D0
do 20 i=1,nbackbone-2
do 20 j=i+2,nbackbone
Epoly(i,j)=Ep(i,j)
Epold=Epold+Epoly(i,j)
endif
assign new coordinates to polymer
DO 30 I = 1, natom
xms(I) = xn(I)
yms(I) = yn(I)
zms(I) = zn(I)
CONTINUE
Computer code (Makogon, 1994, 1997)
Erun = Erun + Ener
Eold = Ener
C
C
If acceptance is a translation, increase translation acceptance counter
IF (Iflag .EQ. 0) Kacct = Kacct + 1
C If acceptance is a rotation, increase rotation acceptance counter
IF (Iflag .EQ. 1) Kaccr = Kaccr + 1
C If acceptance is a pivot, increase pivot acceptance counter
IF (Iflag .EQ. 2) Kaccp = Kaccp + 1
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE ADJUST
IMPLICIT REAL*8(A-H,O-Z)
COMMON /RATIOS/ Ratiot, Ratior, Ratiop
COMMON /NCC / Kacct, Kaccr, Kaccp
COMMON /PROPTY/ Bmax, Gmax, Rdel
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
C
C ... Adjust maximum translational step size
Ratiot = DFLOAT(Kacct)/DFLOAT(Kcyc)
IF (Ratiot .GT. Acctrn) deltrn=1.01D0*deltrn
IF (Ratiot .LT. Acctrn) deltrn=0.99D0*deltrn
IF (deltrn .GT. 3.0D0) deltrn=3.0D0
C ... Adjust maximum rotational step size
Ratior = DFLOAT(Kaccr)/DFLOAT(Kcyc)
IF (Ratior .GT. Accrot) delrot = 1.01D0*delrot
IF (Ratior .LT. Accrot) delrot = 0.99D0*delrot
IF (delrot .GT. 3.D0) delrot = 3.D0
C ... Adjust maximum pivot step size
Ratiop = DFLOAT(Kaccp)/DFLOAT(Kcyc)
IF (Ratiop .GT. Accpiv) delpiv = 1.01D0*delpiv
IF (Ratiop .LT. Accpiv) delpiv = 0.99D0*delpiv
IF (delpiv .GT. 3.D0) delpiv = 3.D0
C
RETURN
END
C
C------------------------------------------------------------------C
405
406
10. Research methods in flow assurance
SUBROUTINE REINIT
IMPLICIT REAL*8(A-H,O-Z)
COMMON /PROPTY/ Bmax, Gmax, Rdel
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /NCC
/ Kacct, Kaccr, Kaccp
COMMON /NHB / nhb(100),nhbpoly,nhbcurr(100)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
C
Erun = 0.D0
Epolymer=0.D0
10
do 10 i=1,100
nhb(i)= 0
C
Kacct = 0
Kaccr = 0
Kaccp = 0
C ... acceptance ratios for translation, rotation, pivot
if(Neq.eq.1) then
Acctrn = 0.35D0
Accrot = 0.25D0
Accpiv = 0.35D0
endif
C
C ... output column headings
open(unit=1,POSITION='APPEND',file='output.dat',status='unknown')
ccc
open(unit=1,access='APPEND',file='output.dat',status='unknown')
write(1,'(A80)')' Cyc Dtr Rtr Dro Rro Dpv Rpv <Xc> <Yc> <Zc> HB
&p HBs <R> <Epol> <Esur> <Ecur>'
write(1,'(A80)')' x1K A nrm rad nrm rad nrm Angs Angs Angs <cu
&r><cur> A kcal/m kcal/m kcal/m'
close(1)
write(6,'(A80)')' Cyc Dtr Rtr Dro Rro Dpv Rpv <Xc> <Yc> <Zc> HB
&p HBs <R> <Epol> <Esur> <Ecur>'
write(6,'(A80)')' x1K A nrm rad nrm rad nrm Angs Angs Angs <cu
&r><cur> A kcal/m kcal/m kcal/m'
C
RETURN
END
C
C------------------------------------------------------------------C
Computer code (Makogon, 1994, 1997)
SUBROUTINE PRTOUT
IMPLICIT REAL*8(A-H,O-Z)
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
/ESAVE /
/NATOMS/
/NHB /
/POTPAM/
/PROPTY/
/STEPS /
/ZSAVE /
/SPACE /
/NRUN /
/chain /
/RATIOS/
Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
Norgn, Nwatrs, M1, M2, M3, M4
nhb(100),nhbpoly,nhbcurr(100)
Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
Bmax, Gmax, Rdel
Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
zrun(100),epolymer,Erun
xms(1000), yms(1000), zms(1000)
Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
monodata(100,100),monocount(99),nbackbone
Ratiot, Ratior, Ratiop
C
C ... run-monitor data
C ... Note: Three configurations are sampled per cycle
C
c
c
c
c
c
c
c
zrun(1..3)
zrun(4)
zrun(5)
zrun(6)
zrun(7)
zrun(8)
zrun(9)
-
x,y,z(norgn)
R^2 end-to-end
H bonds between polymer segments
H bonds between polymer and surface
Total energy
Epoly
Esurf
ncyc=Int(kcyc*0.001)
rt=ratiot/acctrn
rr=ratior/accrot
rp=ratiop/accpiv
Deno = 1.D0/(kprint*3.D0)
xave=zrun(1)*deno
yave=zrun(2)*deno
zave=zrun(3)*deno
hbpave=zrun(5)*deno
hbsave=zrun(6)*deno
Rave=dsqrt(zrun(4)*deno)
Eplmave=zrun(8)*deno
Esrfave=zrun(9)*deno
Ecurave=zrun(7)*deno
C print MC run-time info
open(unit=1,POSITION='APPEND',file='output.dat',status='unknown')
ccc
open(unit=1,access='APPEND',file='output.dat',status='unknown')
407
408
20
10. Research methods in flow assurance
write(1,20)ncyc,deltrn,rt,delrot,rr,delpiv,rp,xave,yave,zave,
&hbpave,hbsave,rave,Eplmave,Esrfave,Ecurave
write(6,20)ncyc,deltrn,rt,delrot,rr,delpiv,rp,xave,yave,zave,
&hbpave,hbsave,rave,Eplmave,Esrfave,Ecurave
FORMAT(I4,6F4.1,2F6.1,F5.1,F5.2,F5.1,F5.1,F6.1,2F7.1)
close(1)
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE SAMGOZ
C
c
c
c
this subroutine writes the following to a ALLDATA.DAT file
nbackbone, Running-average # of H-bonds from each segment to surface;
Epoly, Esurf, total energy for the whole simulation, and
total Esurf for the print interval, and current Esurf for each segment.
IMPLICIT REAL*8(A-H,O-Z)
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /NHB
/ nhb(100),nhbpoly,nhbcurr(100)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
deno=1/(kcyc*3.d0)
E1=Erun*deno
Esur=Erun-Epolymer
E2=Esur*deno
E3=Epolymer*deno
E4=zrun(9)/(Kprint*3.D0)
ccc
open(unit=1,POSITION='APPEND',file='alldata.dat',status='unknown')
open(unit=1,access='APPEND',file='alldata.dat',status='unknown')
write(1,'(I7,4F8.2,I3,99F6.1,99F4.1)')Kcyc,E3,E2,E1,E4,nbackbone,
& (deno*nhb(i),i=1,nbackbone),(Esurf(i),i=1,nbackbone)
close(1)
c re-zero the current period counters
do i=1,100
zrun(i)=0.D0
end do
RETURN
Computer code (Makogon, 1994, 1997)
END
C
C------------------------------------------------------------------C
SUBROUTINE ZSAMPLE
IMPLICIT REAL*8(A-H,O-Z)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /NHB
/ nhb(100),nhbpoly,nhbcurr(100)
c zrun(1..3) - x,y,z(norgn)
c zrun(4)
- R^2 end-to-end
c zrun(5)
- H bonds between polymer segments
c zrun(6)
- H bonds between polymer and surface
c zrun(7)
- Total energy
c zrun(8)
- Epoly
c zrun(9)
- Esurf
C ... accumulate positions of backbone atoms
zrun(1) = zrun(1)+xms(Norgn)
zrun(2) = zrun(2)+yms(Norgn)
zrun(3) = zrun(3)+zms(Norgn)
zrun(4) = zrun(4)+ (
& (xms(M1)-xms(M2))*(xms(M1)-xms(M2))+(yms(M1)-yms(M2))*
& (yms(M1)-yms(M2))+(zms(M1)-zms(M2))*(zms(M1)-zms(M2)) )
zrun(5) = zrun(5)+nhbpoly
zrun(7) = zrun(7)+Eold
zrun(8) = zrun(8)+Epold
zrun(9) = zrun(9)+Eold-Epold
10
do 10 i=1,nbackbone
zrun(6) = zrun(6)+nhbcurr(i)
zrun(i+10)=zrun(i+10)+zms(i)
C accumulate polymer intramolecular energy
Epolymer=Epolymer+Epold
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE SUMMARY
409
410
10. Research methods in flow assurance
IMPLICIT REAL*8(A-H,O-Z)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
C print average elevations of backbone atoms
print *,'Backbone segments` elevation above surface:'
deno= 3.D0*DFLOAT(Kprint)
write(*,'(99F4.1)') (zrun(i)/deno,I=11,10+nbackbone)
print *,'Simulation is complete'
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE INIPOS
IMPLICIT REAL*8(A-H,O-Z)
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /offset/ xo,yo,zo,phi,theta,xi
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /iori / iori
COMMON /NHB
/ nhb(100),nhbpoly,nhbcurr(100)
C
C
move the chain so that the origin atom Norgn is at (0,0,0)
dx=atomdata(Norgn,1)
dy=atomdata(Norgn,2)
dz=atomdata(Norgn,3)
DO I=1,natom
atomdata(I,1)=atomdata(I,1)-dx
atomdata(I,2)=atomdata(I,2)-dy
atomdata(I,3)=atomdata(I,3)-dz
end do
C
Print *, ' '
Print *, ' Enter position (x,y,z) for origin of monomer'
Read *, xo, yo, zo
write(*,'(A10,3F8.3)')' input was', xo, yo, zo
Print *, ' '
Computer code (Makogon, 1994, 1997)
C
C ... initial Euler angles
phi
=0.D0
theta =0.D0
xi
=0.D0
Print *, '
Specify orientation of monomer (enter 1)'
Print *, '
OR use default orientation (enter zero)?'
Read *, Iori
print *,'input was', iori
IF (Iori .EQ. 1) THEN
Print *, ' '
Print *, ' Enter initial Euler angles in degrees'
Print *, '
phi, theta, xi = '
Read *, phi, theta, xi
print *,'input was', phi, theta, xi
CALL INIORI(xo,yo,zo, phi,theta,xi)
ENDIF
C
default Euler angles
IF (Iori .EQ. 0) THEN
Print *, ' '
Print *, 'Using phi = 0, theta = 0, xi = 0'
Print *, ' '
Cphi = 1.D0
Sphi = 0.D0
Cthe = 1.D0
Sthe = 0.D0
Cxi = 1.D0
Sxi = 0.D0
10
DO 10 I = 1, natom
xms(I) = atomdata(I,1) + xo
yms(I) = atomdata(I,2) + yo
zms(I) = atomdata(I,3) + zo
xn(I) = xms(I)
yn(I) = yms(I)
zn(I) = zms(I)
CONTINUE
CALL ENERGY(Ener)
Eold = Ener
C
ENDIF
C
RETURN
411
412
10. Research methods in flow assurance
END
C
C------------------------------------------------------------------C
SUBROUTINE INIORI(xo,yo,zo,phi,theta,xi)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /NWPOS / xn(1000), yn(1000), zn(1000)
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /EANEW / Cphin,Sphin,Cthen,Sthen,Cxin,Sxin
C ... convert angles to radians
Rphi = phi*PI/180.D0
Rthe = theta*PI/180.D0
Rxi = xi*PI/180.D0
C ... trig functions of initial Euler angles
Cphi = DCOS(Rphi)
Sphi = DSIN(Rphi)
Cthe = DCOS(Rthe)
Sthe = DSIN(Rthe)
Cxi = DCOS(Rxi)
Sxi = DSIN(Rxi)
C ... store as new angles for XFORMB
Cphin = Cphi
Sphin = Sphi
Cthen = Cthe
Sthen = Sthe
Cxin = Cxi
Sxin = Sxi
C
C ... xform new orientation to space-fixed frame
C
DO 100 I = 1, natom
CALL XFORMB(atomdata(I,1),atomdata(I,2),atomdata(I,3),xx,yy,zz)
xms(I) = xo + xx
yms(I) = yo + yy
zms(I) = zo + zz
xn(I) = xms(I)
yn(I) = yms(I)
zn(I) = zms(I)
Computer code (Makogon, 1994, 1997)
100 CONTINUE
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE XFORMB(xc,yc,zc,xx,yy,zz)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /EANEW / Cphin,Sphin,Cthen,Sthen,Cxin,Sxin
C
a11 = Cphin*Cthen
a21 = Cthen*Sphin
a31 = Sthen
C
a12 = -Sphin*Cxin - Sthen*Cphin*Sxin
a22 = Cphin*Cxin - Sthen*Sphin*Sxin
a32 = Cthen*Sxin
C
a13 = Sphin*Sxin - Sthen*Cphin*Cxin
a23 = -Cphin*Sxin - Sthen*Sphin*Cxin
a33 = Cthen*Cxin
C
xx = a11*xc + a12*yc + a13*zc
yy = a21*xc + a22*yc + a23*zc
zz = a31*xc + a32*yc + a33*zc
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE CRASHSAVE
IMPLICIT REAL*8(A-H,O-Z)
real*4 randseed
integer a, ap
character*8 fname
COMMON /fname / fname
COMMON /CRASH / ncrash, ncalls
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /NCC
/ Kacct, Kaccr, Kaccp
COMMON /NHB
/ nhb(100),nhbpoly,nhbcurr(100)
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /SURF1 / a, ap
COMMON /SURF2 / b, c
413
414
10. Research methods in flow assurance
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
C
50
c
/NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
/SPACE / xms(1000), yms(1000), zms(1000)
/iori / iori
/offset/ xo,yo,zo,phi,theta,xi
/ZSAVE / zrun(100),epolymer,Erun
/chain / monodata(100,100),monocount(99),nbackbone
/types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
/STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
/rans / randseed
/POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
/RATIOS/ Ratiot, Ratior, Ratiop
open(unit=1,file='SAVEFILE.',status='unknown')
write (1,'(A8)') fname
write (1,'(I9)') ngroups
write (1,*) Temp
write (1,'(I12)') ncalls+1
write (1,*) randseed
write (1,'(I9)') ndead
write (1,'(I9)') ncycle
write (1,'(I9)') kprint
write (1,'(I9)') kdprnt
write (1,'(I2)') a
write (1,'(I2)') ap
write (1,*) b
write (1,*) c
write (1,*) xo,yo,zo
if(Iori.eq.1) then
write (1,*) 1
write (1,*)phi,theta,xi
else
write (1,*) 0
endif
write (1,'(2I9)') KCYC,Neq
write (1,'(4F32.18)') EOLD,Epold,ERUN,epolymer
E segments
do 50 i=1,nbackbone-2
write (1,'(99F23.18)') (Epoly(i,j),j=i+2,nbackbone)
write (1,'(99F23.18)') (Esurf(i),i=1,nbackbone)
write (1,'(3I16)') Kacct, Kaccr, Kaccp
write (1,'(6F24.18)') Deltrn,Delrot,Delpiv, Ratiot, Ratior, Ratiop
write (1,'(99I10)') (nhb(i),i=1,nbackbone)
write (1,'(99F27.18)') (zrun(i),i=1,100)
write (1,'(2999F22.18)') (xms(i),yms(i),zms(i),i=1,natom)
write blank spaces to fill the write buffer and force a write to disk
Computer code (Makogon, 1994, 1997)
c
write (1,'(1000X)')
close (1)
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE RESTARTCHECK(Nstart)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /CRASH / ncrash, ncalls
COMMON /ESAVE / Eold,Epold,Epoly(99,99),Ep(99,99),Esurf(99),Es(99)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
COMMON /NCC
/ Kacct, Kaccr, Kaccp
COMMON /NHB
/ nhb(100),nhbpoly,nhbcurr(100)
COMMON /NRUN / Ncycle,Ndead,Kprint,Kdprnt,Kcyc,Neq
COMMON /SPACE / xms(1000), yms(1000), zms(1000)
COMMON /ZSAVE / zrun(100),epolymer,Erun
COMMON /STEPS / Deltrn, Delrot, Delpiv, Acctrn, Accrot, Accpiv
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /RATIOS/ Ratiot, Ratior, Ratiop
C
40
Nstart=1
if (ncrash.GT.0) then
read (*,'(2I9)') Kcyc,Neq
Nstart=Kcyc+1
read (*,'(4F32.18)') EOLD,Epold,ERUN,epolymer
E segments
do 40 i=1,nbackbone-2
read (*,'(99F23.18)') (Epoly(i,j),j=i+2,nbackbone)
read (*,'(99F23.18)') (Esurf(i),i=1,nbackbone)
read (*,'(3I16)') Kacct, Kaccr, Kaccp
read (*,'(6F24.18)') Deltrn,Delrot,Delpiv,Ratiot, Ratior, Ratiop
read (*,'(99I10)') (nhb(i),i=1,nbackbone)
read (*,'(99F27.18)') (zrun(i),i=1,100)
read (*,'(2999F22.18)') (xms(i),yms(i),zms(i),i=1,natom)
write(6,'(A80)')' Cyc Dtr Rtr Dro Rro Dpv Rpv <Xc> <Yc> <Zc> HB
&p HBs <R> <Epol> <Esur> <Ecur>'
write(6,'(A80)')' x1K A nrm rad nrm rad nrm Angs Angs Angs <cu
&r><cur> A kcal/m kcal/m kcal/m'
call prtout
c re-zero the current period counters after prtout
do i=1,100
zrun(i)=0.D0
end do
415
416
10. Research methods in flow assurance
endif
RETURN
END
C
C------------------------------------------------------------------C
DOUBLE PRECISION FUNCTION ANGL(Cb,Sb)
real*8 cb,sb,pi
pi=datan(1.d0)*4.d0
if(cb.ge.0.d0) then
angl=180.D0/pi *dasin(sb)
else
angl=180.d0/pi *(pi-dasin(sb))
endif
return
END
C
C------------------------------------------------------------------C
SUBROUTINE LJPARM
IMPLICIT REAL*8(A-H,O-Z)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
C
C ... cutoff distance (A) for LJ potential
C
Rcut = 8.5D0
C
C ... set LJ parameters for atoms on solid water surface
C
Parameters for SPC (Berendsen, et al., Intermolecular Forces, 1981)
DDhwa = 0.000D0
RRhyd = 0.000D0
DDoxy = 0.1625D0
RRoxy = 3.1656D0
C Assign the polymer-water interaction parameters
C ... outer loop over one water molecule
DO 10 I = 1, 3
Di = DDhwa
Ri = RRhyd
itype=5
IF (I.EQ.3) THEN
Computer code (Makogon, 1994, 1997)
Di = DDoxy
Ri = RRoxy
itype=6
ENDIF
C ... inner loop over polymer molecule
DO 10 J = 1, natom
CALL LJMORE(Dj,Rj,J)
DD(Itype,J) = DSQRT(Di*Dj)
RR(Itype,J) = 0.5D0*(Ri+Rj)
10
CONTINUE
C Assign the intramolecular polymer interaction parameters
DO 20 i = 1, natom
CALL LJMORE(Dj,Rj,i)
DDhyd = 0.0152D0
RRhyd = 3.195D0
DD(1,i) = DSQRT(DDhyd*Dj)
RR(1,i) = 0.5D0*(RRhyd+Rj)
DDcar = 0.0951D0
RRcar = 3.8983D0
DD(2,i) = DSQRT(DDcar*Dj)
RR(2,i) = 0.5D0*(RRcar+Rj)
DDoxy = 0.0957D0
RRoxy = 3.4046D0
DD(3,i) = DSQRT(DDoxy*Dj)
RR(3,i) = 0.5D0*(RRoxy+Rj)
DDnit = 0.0774D0
RRnit = 3.6621D0
DD(4,i) = DSQRT(DDnit*Dj)
RR(4,i) = 0.5D0*(RRnit+Rj)
20 CONTINUE
C
CALL HBPARM
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE LJMORE(Dj,Rj,J)
IMPLICIT REAL*8(A-H,O-Z)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
C Parameters from Dreiding Forcefield (J.Phys Chem., 94, 8897-8909, 1990)
417
418
10. Research methods in flow assurance
DDhyd
RRhyd
DDcar
RRcar
=
=
=
=
0.0152D0
3.195D0
0.0951D0
3.8983D0
C
C ...
C ...
C ...
C ...
C ...
C
DDoxy = 0.0957D0
RRoxy = 3.4046D0
DDnit = 0.0774D0
RRnit = 3.6621D0
hydrogen
IF (iatomtype(j,1) .EQ. 1) THEN
Dj = DDhyd
Rj = RRhyd
ENDIF
carbon
IF (iatomtype(j,1) .EQ. 2) THEN
Dj = DDcar
Rj = RRcar
ENDIF
oxygen
IF (iatomtype(j,1) .EQ. 3) THEN
Dj = DDoxy
Rj = RRoxy
ENDIF
nitrogen
IF (iatomtype(j,1) .EQ. 4) THEN
Dj = DDnit
Rj = RRnit
ENDIF
add more atoms types here if needed
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE HBPARM
IMPLICIT REAL*8(A-H,O-Z)
COMMON /types / iatomtype(1000,2),nbondfound,natom,ngroups,ncall
COMMON /LJPAM / DD(6,1000), RR(6,1000), DHB(1000), RHB(1000)
COMMON /NATOMS/ Norgn, Nwatrs, M1, M2, M3, M4
COMMON /POTPAM/ Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
COMMON /WPOS / xw(6000,3), yw(6000,3), zw(6000,3), qw(3)
COMMON /atoms / atomdata(1000,4),atomdata2(1000,4)
COMMON /chain / monodata(100,100),monocount(99),nbackbone
Computer code (Makogon, 1994, 1997)
C
C ... H-Bond LJ parameters & cutoffs
DHBoxy = 5.D0
RHBoxy = 2.8D0
DHBhyd = 5.D0
RHBhyd = 0.01D0
Rsqon = 3.5D0*3.5D0
Rsqoff = 4.D0*4.D0
Casqof = (DCOS(222.D0*PI/180.D0))**2
C
C ... assign hydrogen-bond parameters
C
DO 10 J = 1, natom
DHB(J) = 0.D0
RHB(J) = 0.D0
c assign parameters for oxygens not in backbone
notbackbone=1
do i=1,nbackbone
if(monodata(100,i).eq.j)notbackbone=0
end do
IF (iatomtype(j,1).EQ.3.and.notbackbone.eq.1) THEN
DHB(J) = DHBoxy
RHB(J) = RHBoxy
ENDIF
c assign parameters for hydrogens with charge >0.3
IF (iatomtype(j,1).EQ.1.and.atomdata(j,4).gt.0.3D0) THEN
DHB(J) = DHBhyd
RHB(J) = RHBhyd
ENDIF
10
CONTINUE
C
C ... point charges on water atoms
qw(1) = 0.41D0
qw(2) = 0.41D0
qw(3) = -0.82D0
C
RETURN
END
C
C------------------------------------------------------------------C
SUBROUTINE SURFCE
IMPLICIT REAL*8(A-H,O-Z)
COMMON /BDIST / xmax, ymax, xmaxh, ymaxh
419
420
10. Research methods in flow assurance
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
COMMON
/side /
/diag /
/NATOMS/
/WPOS /
/SURF1 /
/SURF2 /
/POTPAM/
/types /
side, unitside
diag
Norgn, Nwatrs, M1, M2, M3, M4
xw(6000,3), yw(6000,3), zw(6000,3),qw(3)
a, ap
b, c
Casqof,Co,Rsqon,Rsqoff,Rcut,Pi,Tk,Temp
iatomtype(1000,2),nbondfound,natom,ngroups,ncall
C
C START OF THE HYDRATE SURFACE CODE
C***************************************************************
real*8 x1(6000),y1(6000),z1(6000)
real*8 x2(6000),y2(6000),z2(6000)
real*8 x3(6000),y3(6000),z3(6000)
character Screen(80,25)
integer*1 RemFlag(6000)
integer A,AP,BFlag
real*8 B,C,D
C
A- type of hydrate 1=sI, 2=sII
C
AP-type of surface 1=[100], 2=[111], 3=[110]
C
B- Z-distance from 000 to top surface, Angstroms
C
C- thickness of hydrate slice, angstroms
C
D- angle of [111] block rotation during Y transformation
C within program all distances are normalized by unit cell length,
C e.g. side of a rhombus for [111] surface has length 1.414.
Nlines=20
C request input of hydrate type
write(*,*)'Which hydrate would you like to use: 1)sI or 2)sII ?'
10
read(*,*)A
if (a.ne.1.and.a.ne.2) then
write(*,*)'Please re-enter the hydrate type'
goto 10
endif
C
C request input of slice direction
write(*,*)'Which surface: 1) [100], 2) [111] or 3) [110] ?'
20
read(*,*)AP
if (ap.ne.1.and.ap.ne.2.and.ap.ne.3) then
write(*,*)'Please re-enter the surface type'
goto 20
endif
C
if(a.eq.2) then
Computer code (Makogon, 1994, 1997)
C use sII - prepare variables
unitside=17.1D0
side=unitside
npts=136
endif
C
if(a.eq.1) then
C use sI - set variables
unitside=12.D0
side=unitside
npts=46
endif
C
if(ap.eq.2) then
C using [111] surface - prepare variables
side=side*Dsqrt(2.D0)
diag=unitside*Dsqrt(3.D0)
ietc=111
nx=1
ny=1
nz=2
xmax = unitside * Dsqrt(2.D0)
ymax = unitside * Dsqrt(1.5D0)
xmaxh = xmax/2.D0
ymaxh = ymax/2.D0
endif
C
if (ap.eq.1) then
C using [100] surface - prepare variables]
diag=unitside
ietc=100
xmax = unitside
ymax = unitside
xmaxh = xmax/2.D0
ymaxh = ymax/2.D0
nx=0
ny=0
nz=0
endif
C
if (ap.eq.3) then
C [110] surface
diag=unitside * Dsqrt(2.d0)
ietc=110
xmax=unitside
421
422
10. Research methods in flow assurance
ymax=unitside * Dsqrt(2.d0)
nx=0
ny=1
nz=0
xmaxh=xmax * 0.5D0
ymaxh=ymax * 0.5D0
endif
C
C
C user dialog requesting surface dimensions
if (A.EQ.2) then
C input slice position for sII hydrate
write(*,*)'Using structure II hydrate',ietc,' slice'
write(*,*)'Reading the unit cell data from the file fd3m.dat'
write(*,*)' z ^'
write(*,*)' | unit cell'
write(6,30)diag
write(*,*)' | |'
write(*,*)' |____________|top position'
write(*,*)' |^ |'
write(*,*)' | thickness |'
write(*,*)' |______v_____|'
write(*,*)' | |'
write(*,*)' 0-|------------|---> x'
write(*,*)' 0'
write(*,*)'Enter the distance from 0 to top surface in Z direction
% - '
if(a.eq.1) then
write(6,31)diag
else
write(6,32)diag
endif
open(unit=1,file='fd3m.hyd',status='old')
C set flag that B is within limits
read(*,*) B
BFlag=0
do while (b.LT.0.)
b=b+diag
bflag=1
end do
do while (b.GT.diag)
b=b-diag
bflag=1
end do
Computer code (Makogon, 1994, 1997)
if (bflag.eq.0) then
write(6,34)B
else
write(6,35)B
endif
C end of check for proper slice position input
else
C input slice position for sI hydrate
write(*,*)'Using structure I hydrate',ietc,' slice'
write(*,*)'Slice size for sI will be increased to 2x2x1'
write(*,*)'Reading the unit cell data from the file pm3n.dat'
write(*,*)'
z ^'
write(*,*)'
|
unit cell'
write(6,30)diag
write(*,*)'
|
|'
write(*,*)'
|____________|top position'
write(*,*)'
|
^
|'
write(*,*)'
| thickness |'
write(*,*)'
|______v_____|'
write(*,*)'
|
|'
write(*,*)'
0-|------------|---> x'
write(*,*)'
0'
write(*,*)'Enter the distance from 0 to top surface in Z direction
% - '
if(a.eq.1) then
write(6,31)diag
else
write(6,32)diag
endif
open(unit=1,file='pm3n.hyd', status='old')
30
FORMAT(F6.2,'|____________')
31
FORMAT(1X,'Choose from 0 to',F8.4,' Angstroms')
32
FORMAT(1X,'Choose from 0 to',F7.3,' Angstroms')
read(*,*) B
C set flag that B is within limits
BFlag=0
do while (b.LT.0.D0)
b=b+diag
bflag=1
end do
do while (b.GT.diag)
b=b-diag
bflag=1
end do
423
424
10. Research methods in flow assurance
if (bflag.eq.0) then
write(6,34)B
else
write(6,35)B
34
FORMAT(1X,'Position set to ',F10.6)
35
FORMAT(1X,'Position reset to ',F10.6)
endif
C end of check for proper slice position input
endif
C
write(*,*)'Enter desired slice thickness in Z direction:'
read(*,*) C
C read in the unit cell
do i=1, npts
read(1,*)ii,x1(i),y1(i),z1(i),x2(i),y2(i),z2(i),
- x3(i),y3(i),z3(i)
end do
C ------------[111]------------------if(ap.eq.2) then
C if constructing the [111] surface, the unit cell will be
C replicated 12 times for slicing
do 45 ix=0, nx
do 45 iy=0, ny
do 45 iz=0, nz
do 45 i=1, npts
x1(i+ix*6*npts+iy*3*npts+iz*npts)=x1(i)-ix
y1(i+ix*6*npts+iy*3*npts+iz*npts)=y1(i)-iy
z1(i+ix*6*npts+iy*3*npts+iz*npts)=z1(i)-iz
x2(i+ix*6*npts+iy*3*npts+iz*npts)=x2(i)-ix
y2(i+ix*6*npts+iy*3*npts+iz*npts)=y2(i)-iy
z2(i+ix*6*npts+iy*3*npts+iz*npts)=z2(i)-iz
x3(i+ix*6*npts+iy*3*npts+iz*npts)=x3(i)-ix
y3(i+ix*6*npts+iy*3*npts+iz*npts)=y3(i)-iy
z3(i+ix*6*npts+iy*3*npts+iz*npts)=z3(i)-iz
45
continue
C determine which molecules should be sliced off in [111]
do i=1,npts*12
remflag(i)=0
C check the cell in direction of equation 1: -2x+y+z=1
xyz=-x1(i)-x1(i)+y1(i)+z1(i)
c correct computational error
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.GT.1.D0) remflag(i)=1
Computer code (Makogon, 1994, 1997)
C check the cell in direction of equation 2: x-2y+z=1
xyz=x1(i)-y1(i)-y1(i)+z1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.GT.1.D0) remflag(i)=1
C check the cell in direction of equation 3: x-2y+z=-2
xyz=x1(i)-y1(i)-y1(i)+z1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.LE.-2.D0) remflag(i)=1
C check the cell in direction of equation 4: -2x+y+z=-2
xyz=-x1(i)-x1(i)+y1(i)+z1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.LE.-2.D0) remflag(i)=1
C check the cell in direction of equation 5: x+y+z=1
xyz=x1(i)+y1(i)+z1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.GT.1.D0) remflag(i)=1
C check the cell in direction of equation 6: x+y+z=-2
xyz=x1(i)+y1(i)+z1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.LE.-2.D0) remflag(i)=1
end do
C move the unremoved molecules to the front of coordinate arrays
nrem=0
do i=1,npts*12
if(remflag(i).eq.0) then
x1(i-nrem)=x1(i)
y1(i-nrem)=y1(i)
z1(i-nrem)=z1(i)
x2(i-nrem)=x2(i)
y2(i-nrem)=y2(i)
z2(i-nrem)=z2(i)
x3(i-nrem)=x3(i)
y3(i-nrem)=y3(i)
z3(i-nrem)=z3(i)
else
nrem=nrem+1
endif
enddo
C modify the number of molecules in [111] slice
npts=npts*12-nrem
C reorient the basic [111] block to align the top surface with
C the x-y plane at position z=0 and with center at x=0, y=0
do i=1, npts
425
426
10. Research methods in flow assurance
C shift the block up by 1/2 unit cell to put block center at 000
z1(i)=z1(i)+0.5D0
z2(i)=z2(i)+0.5D0
z3(i)=z3(i)+0.5D0
C rotate the [111] block around Z for +45 degrees
tempx=x1(i)
x1(i)= x1(i)*DCOS(Pi/4.D0)+y1(i)*DSIN(Pi/4.D0)
y1(i)=-tempx*DSIN(Pi/4.D0)+y1(i)*DCOS(Pi/4.D0)
tempx=x2(i)
x2(i)= x2(i)*DCOS(Pi/4.D0)+y2(i)*DSIN(Pi/4.D0)
y2(i)=-tempx*DSIN(Pi/4.D0)+y2(i)*DCOS(Pi/4.D0)
tempx=x3(i)
x3(i)= x3(i)*DCOS(Pi/4.D0)+y3(i)*DSIN(Pi/4.D0)
y3(i)=-tempx*DSIN(Pi/4.D0)+y3(i)*DCOS(Pi/4.D0)
C rotate the [111] block around Y for -54.74 degrees
D=-DACOS(1.D0/DSQRT(3.D0))
tempx=x1(i)
x1(i)= x1(i)*DCOS(D)+z1(i)*DSIN(D)
z1(i)=-tempx*DSIN(D)+z1(i)*DCOS(D)
tempx=x2(i)
x2(i)= x2(i)*DCOS(D)+z2(i)*DSIN(D)
z2(i)=-tempx*DSIN(D)+z2(i)*DCOS(D)
tempx=x3(i)
x3(i)= x3(i)*DCOS(D)+z3(i)*DSIN(D)
z3(i)=-tempx*DSIN(D)+z3(i)*DCOS(D)
C rotate the [111] block around Z for -30 degrees
tempx=x1(i)
x1(i)= x1(i)*DCOS(-Pi/6.D0)+y1(i)*DSIN(-Pi/6.D0)
y1(i)=-tempx*DSIN(-Pi/6.D0)+y1(i)*DCOS(-Pi/6.D0)
tempx=x2(i)
x2(i)= x2(i)*DCOS(-Pi/6.D0)+y2(i)*DSIN(-Pi/6.D0)
y2(i)=-tempx*DSIN(-Pi/6.D0)+y2(i)*DCOS(-Pi/6.D0)
tempx=x3(i)
x3(i)= x3(i)*DCOS(-Pi/6.D0)+y3(i)*DSIN(-Pi/6.D0)
y3(i)=-tempx*DSIN(-Pi/6.D0)+y3(i)*DCOS(-Pi/6.D0)
C shift the block down by sqrt(3)/2 unit cell to locate top at z=0
z1(i)=z1(i)-0.5D0*DSQRT(3.D0)
z2(i)=z2(i)-0.5D0*DSQRT(3.D0)
z3(i)=z3(i)-0.5D0*DSQRT(3.D0)
end do
C end of slicing of the basic [111] block
endif
C ------------[100]----------------if (ap.eq.1) then
Computer code (Makogon, 1994, 1997)
C shift the [100] cell down to locate top at z=0
do i=1,npts
z1(i)=z1(i)-1.D0
z2(i)=z2(i)-1.D0
z3(i)=z3(i)-1.D0
end do
endif
C ------------[110]------------------if (ap.eq.3) then
C if constructing the [110] surface, the unit cell will be
C replicated 2 times for slicing
do 46 iy=0, ny
do 46 i=1, npts
x1(i+iy*npts)=x1(i)
y1(i+iy*npts)=y1(i)-iy
z1(i+iy*npts)=z1(i)
x2(i+iy*npts)=x2(i)
y2(i+iy*npts)=y2(i)-iy
z2(i+iy*npts)=z2(i)
x3(i+iy*npts)=x3(i)
y3(i+iy*npts)=y3(i)-iy
z3(i+iy*npts)=z3(i)
46
continue
C determine which molecules should be relocated in [110]
do i=1,npts*2
remflag(i)=0
C check the cell in direction of equation 1: x+y=1
xyz=x1(i)+y1(i)
c correct computational error
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.GT.1.D0) then
x1(i)=x1(i)-1.D0
y1(i)=y1(i)-1.D0
x2(i)=x2(i)-1.D0
y2(i)=y2(i)-1.D0
x3(i)=x3(i)-1.D0
y3(i)=y3(i)-1.D0
endif
C check the cell in direction of equation 2: x-y=1
xyz=x1(i)-y1(i)
if(abs(xyz-dnint(xyz)).lt.1d-10) xyz=dnint(xyz)
if(xyz.GT.1.D0) then
x1(i)=x1(i)-1.D0
427
428
10. Research methods in flow assurance
y1(i)=y1(i)+1.D0
x2(i)=x2(i)-1.D0
y2(i)=y2(i)+1.D0
x3(i)=x3(i)-1.D0
y3(i)=y3(i)+1.D0
endif
end do
C modify the number of molecules in [110] slice
npts=npts + npts
C reorient the basic [110] block to align the top [110] surface with
C the x-y plane at position z=0 and with center at x=0, y=0
do i=1, npts
C shift the block down by 1/2 unit cell to put block center at 000
z1(i)=z1(i)-0.5D0
z2(i)=z2(i)-0.5D0
z3(i)=z3(i)-0.5D0
C rotate the [110] block around Z for +45 degrees
tempx=x1(i)
x1(i)= x1(i)*DCOS(Pi/4.D0)+y1(i)*DSIN(Pi/4.D0)
y1(i)=-tempx*DSIN(Pi/4.D0)+y1(i)*DCOS(Pi/4.D0)
tempx=x2(i)
x2(i)= x2(i)*DCOS(Pi/4.D0)+y2(i)*DSIN(Pi/4.D0)
y2(i)=-tempx*DSIN(Pi/4.D0)+y2(i)*DCOS(Pi/4.D0)
tempx=x3(i)
x3(i)= x3(i)*DCOS(Pi/4.D0)+y3(i)*DSIN(Pi/4.D0)
y3(i)=-tempx*DSIN(Pi/4.D0)+y3(i)*DCOS(Pi/4.D0)
C rotate the [110] block around Y for -90 degrees
D=-Pi/2.D0
tempx=x1(i)
x1(i)= x1(i)*DCOS(D)+z1(i)*DSIN(D)
z1(i)=-tempx*DSIN(D)+z1(i)*DCOS(D)
tempx=x2(i)
x2(i)= x2(i)*DCOS(D)+z2(i)*DSIN(D)
z2(i)=-tempx*DSIN(D)+z2(i)*DCOS(D)
tempx=x3(i)
x3(i)= x3(i)*DCOS(D)+z3(i)*DSIN(D)
z3(i)=-tempx*DSIN(D)+z3(i)*DCOS(D)
C shift the block down by sqrt(2)/2 unit cell to locate top at z=0
z1(i)=z1(i)-0.5D0*DSQRT(2.D0)
z2(i)=z2(i)-0.5D0*DSQRT(2.D0)
z3(i)=z3(i)-0.5D0*DSQRT(2.D0)
C shift the block by 1/2 unit cell to locate edge at x=0
x1(i)=x1(i)+0.5D0
x2(i)=x2(i)+0.5D0
Computer code (Makogon, 1994, 1997)
x3(i)=x3(i)+0.5D0
C shift the block by sqrt(2)/2 unit cell to locate edge at y=0
y1(i)=y1(i)+0.5D0*DSQRT(2.D0)
y2(i)=y2(i)+0.5D0*DSQRT(2.D0)
y3(i)=y3(i)+0.5D0*DSQRT(2.D0)
end do
C end of slicing of the basic [110] block
endif
C correct the upper surface position
C top boundary is strict, i.e. z.GE.0. is shifted.
do i=1,npts
z1(i)=z1(i)+(diag-B)/unitside
z2(i)=z2(i)+(diag-B)/unitside
z3(i)=z3(i)+(diag-B)/unitside
if(z1(i).ge.0.D0) then
z1(i)=z1(i)-diag/unitside
z2(i)=z2(i)-diag/unitside
z3(i)=z3(i)-diag/unitside
endif
end do
C add more unit cells in height if needed
nadd=0
CC=C
do while (CC.gt.diag)
nadd=nadd+1
do i=1,npts
x1(i+nadd*npts)=x1(i)
y1(i+nadd*npts)=y1(i)
z1(i+nadd*npts)=z1(i)-diag/unitside*nadd
x2(i+nadd*npts)=x2(i)
y2(i+nadd*npts)=y2(i)
z2(i+nadd*npts)=z2(i)-diag/unitside*nadd
x3(i+nadd*npts)=x3(i)
y3(i+nadd*npts)=y3(i)
z3(i+nadd*npts)=z3(i)-diag/unitside*nadd
end do
CC=CC-diag
end do
npts=npts+npts*nadd
C Correct the slice thickness to requested value. Adjust lower surface.
C Lower boundary is relaxed i.e. z.LT.-C is removed
do i=1,npts
429
430
10. Research methods in flow assurance
remflag(i)=0
if(z1(i).lt.(-C/unitside)) then
remflag(i)=1
endif
enddo
nrem=0
do i=1,npts
if(remflag(i).eq.0) then
x1(i-nrem)=x1(i)
y1(i-nrem)=y1(i)
z1(i-nrem)=z1(i)
x2(i-nrem)=x2(i)
y2(i-nrem)=y2(i)
z2(i-nrem)=z2(i)
x3(i-nrem)=x3(i)
y3(i-nrem)=y3(i)
z3(i-nrem)=z3(i)
else
nrem=nrem+1
endif
end do
npts=npts-nrem
C
C
C
C
C
c
C
C
if desired, the unit cell will be enlarged to a NxMx1 surface size
currently set to enlarge [100], [110] and [111] sI surfaces
to
2x2;
2x1;
2x2 respectively.
For a sII[111] surface a 2x2 enlargement is done for polymers with >8 units.
replicate molecules in xyz arrays and adjust surface parameters
if(ap.eq.1.and.a.eq.1) then
C for [100] (ap=1)
do 461 ix=0, 1
do 461 iy=0, 1
do 461 i=1, npts
x1(i+ix*2*npts+iy*npts)=x1(i)+ix
y1(i+ix*2*npts+iy*npts)=y1(i)+iy
z1(i+ix*2*npts+iy*npts)=z1(i)
x2(i+ix*2*npts+iy*npts)=x2(i)+ix
y2(i+ix*2*npts+iy*npts)=y2(i)+iy
z2(i+ix*2*npts+iy*npts)=z2(i)
x3(i+ix*2*npts+iy*npts)=x3(i)+ix
y3(i+ix*2*npts+iy*npts)=y3(i)+iy
z3(i+ix*2*npts+iy*npts)=z3(i)
461
continue
Computer code (Makogon, 1994, 1997)
npts=npts*4
side=side*2.D0
xmaxh = xmax
ymaxh = ymax
xmax = xmax + xmax
ymax = ymax + ymax
endif
if(ap.eq.3.and.a.eq.1) then
C for [110] (ap=3)
do 462 ix=0, 1
do 462 i=1, npts
x1(i+ix*npts)=x1(i)+ix
y1(i+ix*npts)=y1(i)
z1(i+ix*npts)=z1(i)
x2(i+ix*npts)=x2(i)+ix
y2(i+ix*npts)=y2(i)
z2(i+ix*npts)=z2(i)
x3(i+ix*npts)=x3(i)+ix
y3(i+ix*npts)=y3(i)
z3(i+ix*npts)=z3(i)
462
continue
npts=npts + npts
xmaxh= xmax
xmax = xmax + xmax
endif
if((a.eq.1.and.ap.eq.2).or.
(a.eq.2.and.ap.eq.2.and.ngroups.gt.8)) then
C for [111]
do 463 ix=0, 1
do 463 iy=0, 1
do 463 i=1, npts
x1(i+ix*2*npts+iy*npts)=x1(i)+(ix*xmax+iy*xmaxh)/unitside
y1(i+ix*2*npts+iy*npts)=y1(i)+iy*ymax/unitside
z1(i+ix*2*npts+iy*npts)=z1(i)
x2(i+ix*2*npts+iy*npts)=x2(i)+(ix*xmax+iy*xmaxh)/unitside
y2(i+ix*2*npts+iy*npts)=y2(i)+iy*ymax/unitside
z2(i+ix*2*npts+iy*npts)=z2(i)
x3(i+ix*2*npts+iy*npts)=x3(i)+(ix*xmax+iy*xmaxh)/unitside
y3(i+ix*2*npts+iy*npts)=y3(i)+iy*ymax/unitside
z3(i+ix*2*npts+iy*npts)=z3(i)
463
continue
npts=npts*4
C adjust parameters for [111]
&
431
432
10. Research methods in flow assurance
side=side*2.D0
xmaxh = unitside * Dsqrt(2.D0)
ymaxh = unitside * Dsqrt(1.5D0)
xmax = 2.D0 * xmaxh
ymax = 2.D0 * ymaxh
C now center a [111] surface
do i=1,npts
x1(i)=x1(i)-xmaxh/unitside*0.75D0
y1(i)=y1(i)-ymaxh/unitside*0.5D0
x2(i)=x2(i)-xmaxh/unitside*0.75D0
y2(i)=y2(i)-ymaxh/unitside*0.5D0
x3(i)=x3(i)-xmaxh/unitside*0.75D0
y3(i)=y3(i)-ymaxh/unitside*0.5D0
end do
endif
C check if geometries of water molecules are still intact
do i=1, npts
d1=(x1(i)-x2(i))**2+(y1(i)-y2(i))**2+(z1(i)-z2(i))**2
d1=dsqrt(d1) * unitside
d2=(x1(i)-x3(i))**2+(y1(i)-y3(i))**2+(z1(i)-z3(i))**2
d2=dsqrt(d2) * unitside
if(d1.gt.1.1.or.d2.gt.1.1.or.d1.lt.0.9.or.d2.lt.0.9) then
write(*,*)'Error in water geometry O-H bond length ',d1,d2
endif
end do
write(6,47)npts
format(1X,'A surface consisting of',I5,' water molecules was gener
%ated')
write(*,*)'Top surface was placed at z=0'
if (ap.eq.1) then
C
write(6,49)side,side,C
write(6,49)xmax,ymax,C
write(6,48)xmaxh,ymaxh
else
C
write(6,49)side*sqrt(2.),side*sqrt(1.5),C
write(6,49)xmax,ymax,C
write(*,*)'Center of the surface is at x=0, y=0'
endif
48
FORMAT('Center of the surface is at x=',F5.2,', y=',F5.2)
49
FORMAT(' Maximum surface size along axes x=',F6.2,', y=',F6.2,
_', z=',F6.2)
C code for writing the water box coordinates to a file surface.dat
C
open(unit=2,file='surface.dat',status='unknown')
47
Computer code (Makogon, 1994, 1997)
C
do i=1, npts
C
write(2,50)i,x1(i),y1(i),z1(i),x2(i),y2(i),z2(i),x3(i),y3(i),z3(i)
C
end do
C50
format(I3,9F8.4)
C***************************************************************
C END OF THE HYDRATE SURFACE CODE
Nwatrs=npts
C move the water coordinates to the water array and scale the coordinates
C ... positions of oxygen atoms
DO 100 I = 1, Nwatrs
xw(I,3) = x1(i) * unitside
yw(I,3) = y1(i) * unitside
zw(I,3) = z1(i) * unitside
C ... positions of hydrogens
xw(I,1) = x2(I) * unitside
yw(I,1) = y2(I) * unitside
zw(I,1) = z2(I) * unitside
C
xw(I,2) = x3(I) * unitside
yw(I,2) = y3(I) * unitside
zw(I,2) = z3(I) * unitside
100
CONTINUE
C code for writing the water box coordinates to a file surface.dat
C
open(unit=2,file='surface.dat',status='unknown')
C
do i=1, npts
C
write(2,50)i,xw(i,3),yw(i,3),zw(i,3),xw(i,1),yw(i,1),zw(i,1),
C
_ xw(i,2),yw(i,2),zw(i,2)
C
end do
C50
format(I3,9F8.4)
C
C some code to print the surface positions visually on screen
do 110 i=1,80
do 110 j=1,25
110
screen(i,j)=' '
if (ap.eq.1.or.ap.eq.3)then
C construct a [100] or a [110] surface
do 115 i=1,Nwatrs
if(zw(i,3).ge.-5.D0) then
C for oxygens
nx=+nint(xw(i,3)*2.D0)
ny=25-nint(yw(i,3))
C and for hydrogens
lx=nint(xw(i,2)*2.D0)
ly=25-nint(yw(i,2))
mx=nint(xw(i,1)*2.D0)
433
434
115
10. Research methods in flow assurance
my=25-nint(yw(i,1))
if(nx.lt.1.or.nx.gt.80.or.ny.lt.1.or.ny.gt.25)goto 115
if(lx.lt.1.or.lx.gt.80.or.ly.lt.1.or.ly.gt.25)goto 115
if(mx.lt.1.or.mx.gt.80.or.my.lt.1.or.my.gt.25)goto 115
screen(lx,ly)='.'
screen(mx,my)='.'
screen(nx,ny)='o'
endif
continue
screen(1,1)='2'
screen(2,1)='4'
screen(1,5)='2'
screen(2,5)='0'
screen(1,9)='1'
screen(2,9)='6'
screen(1,13)='1'
screen(2,13)='2'
screen(1,17)='8'
screen(1,21)='4'
screen(1,25)='0'
screen(8,25)='4'
screen(16,25)='8'
screen(24,25)='1'
screen(25,25)='2'
screen(32,25)='1'
screen(33,25)='6'
screen(40,25)='2'
screen(41,25)='0'
screen(48,25)='2'
screen(49,25)='4'
screen(56,25)='2'
screen(57,25)='8'
screen(64,25)='3'
screen(65,25)='2'
screen(72,25)='3'
screen(73,25)='6'
endif
if(ap.eq.2) then
C construct a [111] surface
do 120 i=1,Nwatrs
if(zw(i,3).ge.-5.D0) then
C for oxygens
nx=40+nint(xw(i,3)*2.D0)
ny=13-nint(yw(i,3))
Computer code (Makogon, 1994, 1997)
C and for hydrogens
lx=40+nint(xw(i,2)*2.D0)
ly=13-nint(yw(i,2))
mx=40+nint(xw(i,1)*2.D0)
my=13-nint(yw(i,1))
if(nx.lt.1.or.nx.gt.80.or.ny.lt.1.or.ny.gt.25)goto 120
if(lx.lt.1.or.lx.gt.80.or.ly.lt.1.or.ly.gt.25)goto 120
if(mx.lt.1.or.mx.gt.80.or.my.lt.1.or.my.gt.25)goto 120
screen(lx,ly)='.'
screen(mx,my)='.'
screen(nx,ny)='o'
endif
120
continue
screen(2,1)='1'
screen(3,1)='2'
screen(2,5)='8'
screen(2,9)='4'
screen(2,13)='0'
screen(2,17)='-'
screen(3,17)='4'
screen(2,21)='-'
screen(3,21)='8'
screen(2,25)='-'
screen(3,25)='1'
screen(4,25)='2'
screen(7,25)='-'
screen(8,25)='1'
screen(9,25)='6'
screen(15,25)='-'
screen(16,25)='1'
screen(17,25)='2'
screen(23,25)='-'
screen(24,25)='8'
screen(31,25)='-'
screen(32,25)='4'
screen(40,25)='0'
screen(48,25)='4'
screen(56,25)='8'
screen(64,25)='1'
screen(65,25)='2'
screen(72,25)='1'
screen(73,25)='6'
endif
C now print the constructed surface
435
436
130
135
C
10. Research methods in flow assurance
do 130 j=1,25
write(6,135)(screen(i,j),i=1,79)
format(79A)
RETURN
END
C
C------------------------------------------------------------------C
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Ward, Z.T., Deering, C.E., Marriott, R.A., Sum, A.K., Sloan, E.D., Koh, C.A., 2015. Phase equilibrium data and model
comparisons for H2S hydrates. J. Chem. Eng. Data 60(2), 403–408.
Yamal,
2015.
http://siberiantimes.com/PICTURES/SCIENCE/Yamal-crater-November-2014/Yamal-craterBogoyavlensky/inside_yamal_hole_gv_bogoyavl.jpg (Accessed 4/29/2015).
Westacott, R.E., Rodger, P.M., 1994. Direct free energy calculations for clathrate hydrates. Ann. N. Y. Acad. Sci. 715,
537.
Zajac, R., Chakrabarti, A., 1994. Kinetics and thermodynamics of end-functionalized polymer adsorption and desorption processes. Phys. Rev. E 49 (pt. A), 3069.
Zazzera, L., Tirrell, M., Evans, J.F., 1993. In situ study of poly(methyl methacrylate) adsorption from solution onto
chemically modified Si(100) surfaces by internal reflection infrared spectroscopy. J. Vac. Sci. Technol. 11, 2239.
Zhan, Y., Mattice, W.L., Napper, D.L., 1993. Monte Carlo simulation of the adsorption of diblock copolymers from a
nonselective solvent. I. Adsorption kinetics and adsorption isotherms. J. Chem. Phys. 98, 7502.
Further reading
BIOSYM software, 1994. BIOSYM Technologies, Inc., San Diego, CA.
Buerger, M.J., 1960. Crystal-Structure Analysis. Wiley, New York.
Englezos, P., et al., 1992. Atmospheric climate changes and the stability of the in-situ methane hydrates in the Arctic.
In: Proceedings of the Second (1992) International Offshore and Polar Engineering Conference (June 14–19, 1992),
San Francisco, USA. pp. 644–652.
442
10. Research methods in flow assurance
Handa, Y.P., et al., 1992. Structural transition of xenon and krypton as a function of gas composition. J. Phys. Chem.
94, 4363–4365.
HyperChem. AUTODESK, Inc., Sausalito, CA.
Kvenvolden, K.A., 1993a. International Conference on Natural Gas Hydrates. Abstracts. (June 20–24, 1993) The
New York Academy of Sciences. 12.
Kvenvolden, K.A., 1993b. Worldwide distribution of subaquatic gas hydrates. Geo-Mar. Lett. 13, 32–40.
Sloan Jr., E.D., 1990. Clathrate Hydrates of Natural Gases. Marcel Dekker, New York.
SYBYL software, 1994. Tripos Associates, Inc., St. Louis, MO.
C H A P T E R
11
Toolkit
O U T L I N E
Free modeling tool for hydrate stability
calculation
443
Free modeling tool for chemical injection
distribution system
443
Free modeling tool for single phase fluid
flow use for water injection system 444
Free modeling tool for scale stability
444
Free hydrate plug remediation software
447
Free LNG cryogenic heat exchangers
solids deposition
448
Free gas, gas condensate and LNG
thermodynamic property calculator 448
There is a number of software tools which have been made available to public domain
through partial funding by the USA Government or other entities. These software tools are
free as of the date of publication.
Free modeling tool for hydrate stability calculation
Software for hydrate stability calculation is available from the Colorado School of Mines
Center for Research on Hydrates as shown in Fig. 11.1.
The software is appropriate and sufficiently accurate for hydrate prediction in systems
with moderate pressure and salinity.
The software is available at: http://hydrates.mines.edu/CHR/Software_files/CSMHyd.
zip. It can run under Windows 10 (with right click—Properties-Compatibility-Windows XP enabled) or earlier operating systems.
Free modeling tool for chemical injection distribution system
The EPANET2 single phase hydraulic network analysis tool is available from United States
Environmental Protection Agency.
Handbook of Multiphase Flow Assurance
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444
11. Toolkit
FIG. 11.1 Hydrate stability and inhibitor dosage software.
The tool is designed for use with water distribution networks as shown in Fig. 11.2.
As it provides the ability to update fluid viscosity, it can be used for chemical injection distribution system analysis. Frictional pressure drop is evaluated with the HazenWilliams, Darcy-Weisbach, or Chezy-Manning methods. The model also has many
additional capabilities such as chemical growth or decay reaction in the flowing fluid,
pump curves, etc.
The software allows to model chemical injection into the fluid stream and track chemical
concentration in the network, and is available at: https://www.epa.gov/water-research/
epanet
Free modeling tool for single phase fluid flow use for water injection system
The EPANET2 tool may also be used for single phase flow networks as shown in Fig. 11.3.
The software is available at: https://www.epa.gov/water-research/epanet
Free modeling tool for scale stability
PHREEQC water ion saturation analysis tool is available from United States Geological Survey
as shown in Fig. 11.4.
Free modeling tool for scale stability
445
FIG. 11.2 Example of EPANET2 network flow tool (United States Environmental Protection Agency).
FIG. 11.3 Example of EPANET2 tool use for water injection network (United States Environmental Protection Agency).
446
11. Toolkit
FIG. 11.4 Scale mineral solubility software.
The tool calculates scale saturation index for the following minerals:
CaSO4
Aragonite
BaSO4
CaCO3
SrSO4
CO2
CaMg(CO3)2
Fe(OH)3
FeOOH
CaSO4*2H2O
NaCl
Fe2O3
FeSO4*7H2O
FeCO3
SrCO3
KCl
BaCO3
as well as scale mass fraction, water density, water activity and ionic strength.
Free hydrate plug remediation software
447
The software is available at: https://wwwbrr.cr.usgs.gov/projects/GWC_coupled/
phreeqc/ or https://www.usgs.gov/software/phreeqc-version-3
Several flow assurance packages from the University of Western Australia are described in
www.fsr.ecm.uwa.edu.au/what-we-do/software/ including.
Free hydrate plug remediation software
HyPRISM allows components up to C70+ and calculates hydrate, oil and gas and properties at the user-specified P and T and the P and T of hydrate stability as shown in Fig. 11.5.
HyPRISM also calculates the pressure in the system after dissociation of hydrate to help
determine if it is safe to heat up a closed system containing hydrate.
Software is available at: www.fsr.ecm.uwa.edu.au/wp-content/uploads/2017/10/
HyPRISM.zip
FIG. 11.5 Hydrate plug remediation model.
448
11. Toolkit
Free LNG cryogenic heat exchangers solids deposition
CryoFAST estimates risk of deposition for hydrocarbon solids such as solid hexane in cryogenic heat exchangers as shown in Fig. 11.6.
Software is available at: www.fsr.ecm.uwa.edu.au/wp-content/uploads/2017/10/
CryoFAST.zip
Free gas, gas condensate and LNG thermodynamic property calculator
Thermofast allows components up to C19 and calculates oil and gas properties at the
­user-specified P and T as shown in Fig. 11.7.
Software is available at: www.fsr.ecm.uwa.edu.au/wp-content/uploads/2018/07/
ThermoFAST-FULL.zip
FIG. 11.6 LNG process solid deposition software.
Free gas, gas condensate and LNG thermodynamic property calculator
FIG. 11.7 Fluid PVT flash property calculation software.
449
C H A P T E R
12
Flow assurance modeling
Flow assurance model relies on system description including
• Reservoir characterization
• PVT fluid characterization
• Material characteristics
The sequence of flow assurance modeling in time follows the exploration process.
1. At the time of selection of region for exploration, find analog fluids to estimate
properties.
– Only analog fluids may be available for flow assurance study.
estimate density ±10°API.
estimate viscosity @ T_reservoir ±10 cP.
estimate wax appearance temperature ±20 °C.
estimate rock material and consolidation.
limited understanding about porosity, permeability, aquifer presence and strength,
water composition, GOR, hydrate, asphaltene, etc.
Appropriate flow assurance work at this stage: none.
What minimum work could be done:
– estimate hydrate curve based on guessed GOR and analog composition, using PVT
modeling tools.
– estimate scale tendency based on analog water composition.
– estimate wax appearance temperature based on analog fluid.
– estimate asphaltene tendency based on deBoer plot and/or SARA ratio.
– prepare a list of flow assurance laboratories and chemical supplier candidates.
2. By the time exploration well is in place.
– First fluids are available
Measure P_res, P_sat, GOR, density, viscosity, AOP, WAT, SARA;
Limited understanding about aquifer pressure support strength, reservoir
compartmentalization, water composition.
Basic understanding of wax, asphaltene onset pressure, GOR, hydrate conditions,
porosity, permeability, fines and sand from side core plugs.
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452
12. Flow assurance modeling
Appropriate flow assurance work at this stage:
Line sizing and preliminary routing using a steady state flow tool, insulation
requirement to avoid wax/hydrate for steady state flow in early or late life.
Erosion velocity limits for mid life plateau production and for late life with increased
gas.
Identify flow assurance threats (slugging in early or late life, hydrate, asphaltene, wax,
scale, diamondoids.
3. Appraisal well is in place and flow test performed.
– More live fluids are available for tests.
– Possibly a drill stem test.
Obtain water composition, sufficient oil sample for hydrate plugging evaluation,
asphaltene deposition.
Some understanding of reservoir compartmentalization.
Limited understanding about aquifer.
Appropriate flow assurance work:
Concept evaluation.
Line sizing update, using multiphase flow models for transient analysis.
Wells placement, flowlines layout, rock consolidation which determines well ramp-up
time.
Develop several concepts with transient analysis (startup based on ramp-up for one
well, cooldown shutdown, blowdown separator sizing, slugging separator sizing.
4. Concept selection
Decide on host facility as FPSO, semi-submersible, spar, island, etc. based on country risks.
Decide on water injection program.
Decide on gas lift or boosting based on NPV of incremental fluids recovery vs. capex
and opex.
Appropriate flow assurance work:
Evaluate technical possibility of mitigating flow assurance threats (slugging in early or
late life, reservoir souring from water injection).
Erosion velocity limits in risers or flowlines for gas lift.
Network flow analysis using flow model for steady state flow rates and or transient
multiphase flow simulators for transient startup and shutdown sequencing.
Support of operating procedures development.
C H A P T E R
13
Risk analysis
O U T L I N E
Introduction
453
Project cost optimization CapEx vs OpEx 453
Historic frequency of blockages based on
remediation
453
Modeling dynamic behavior
454
Integration of various precipitation
phenomena
454
Impact on overall planning
454
Introduction
Several operator companies are migrating their project development approach from flow
assurance issues prevention to issue risk probability management. This approach allows
to defer cost for the facility development while possibly increasing the operating cost and
difficulty.
Project cost optimization CapEx vs OpEx
Projects tend to be CapEx-lean and OpEx heavy due to the uncertainty in reservoir performance. If reservoir is a strong producer and the produced commodity market is expected to
be strong, then additional facilities may be developed.
Historic frequency of blockages based on remediation
The risk-based approach to flow assurance relies on historic frequency of blockages to
forecast the future probability of a blockage.
Historic blockage frequencies and trends were presented in Chapter 5.
Handbook of Multiphase Flow Assurance
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454
13. Risk analysis
Modeling dynamic behavior
Probabilities of individual flow assurance issues should be tabulated along with the impact of such an event. Individual risks should be integrated in a dynamic field development
model to evaluate a range of probabilistic scenarios for reaching the target profitability performance for the field.
Time-dependent events such as aquifer water breakthrough or injection water breakthrough should be reflected by the increased risk to project performance.
After the project starts, with time, more understanding of the relative weights and consequences for individual flow assurance risks becomes available. Risk based model should be
kept updated to both optimize the risk evaluation for the existing field and to serve as probability basis for the future fields.
Integration of various precipitation phenomena
All flow assurance and production chemistry issues should be evaluated simultaneously.
The likelihood of one issue may increase the probability of a different issue. An example from
a West African subsea tieback operation shows that a wax deposition risk was not managed
and wax was allowed to deposit and remain in the pipe as it was not causing a significant
hydraulic resistance to flow. A hydrate plug then formed, became solid. During pressure
changes attempting to resolve the blockage, the hydrate plug became mobile and scraped
wax off the pipe wall like a pig, compacting it into a secondary blockage. While hydrate could
be dissociated by depressurization, the paraffin blockage could not. This caused a significant
downtime to gradually dissolve the paraffin blockage with a solvent.
A similar example from USA deepwater shows a flowline where asphaltene was allowed
to deposit, which provided local restrictions in the pipe cross-section and promoted hydrate
accumulation and blockage.
Impact on overall planning
The combined field development plan should be prepared with input from and interaction
with flow assurance and production chemistry specialists, as well as corrosion engineers.
A systematic approach to risk analysis of the individual flow assurance issues and their
integration in a field development model can be used to support investment decisions.
C H A P T E R
14
Case studies/reference material
O U T L I N E
PVT gas properties
455
Advanced flow assurance fluid properties 463
Abbreviations and definitions
460
Flow correlations
464
Monitoring and instrumentation for
flow assurance
465
Units and conversions
465
Standard temperature and pressure
467
Regulatory requirements and
environmental law which
may affect flow assurance
460
Pipe roughness
463
Sample requirements
463
PVT gas properties
We present several tables with properties evaluated with PR78 EoS for methane, lean gas, rich
gas and retrograde gas as shown in Tables 14.1–14.4. The properties include density, viscosity
and Z-factor for compressibility, and aim both to illustrate how these properties vary in different
fluid types and to serve as initial estimate values for a gas of similar gravity. Gas gravity is relative to air density 1.225 kg/m3.
Methane, gravity = 0.554.
Lean gas, gravity = 0.588.
Components: nitrogen, H2S, methane, ethane, propane, hexane;
4.283, 0.0001, 92.41, 3.242, 0.036, 0.023 mol
Rich gas, gravity = 0.995.
Components: nitrogen, CO2, H2S, methane, ethane, propane, iC4, nC4, iC5, nC5, hexane, heptane;
0.13, 3.5, 4.9, 46.4, 21.4, 16.9, 1.8, 3.8, 0.49, 0.47, 0.16, 0.003 mol
Gas from volatile oil/retrograde condensate, gravity = 0.787.
Components: nitrogen, CO2, methane, ethane, propane, iC4, nC4, iC5, nC5, hexane, heptane;
0.93, 0.32, 71.9, 14.4, 7.6, 0.82, 2.2, 0.47, 0.6, 0.42, 0.2, 0.05 mol
Handbook of Multiphase Flow Assurance
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456
14. Case studies/reference material
TABLE 14.1 Variation of methane properties with temperature and pressure
Density, kg/m3
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.7178
0.6788
0.606
0.5244
0.4622
50
41.22
37.92
32.49
27.18
23.51
100
92.25
82.58
68.16
55.48
47.31
200
184.8
166.5
136.7
109.9
92.84
500
301.5
286.8
257.2
222.0
194.72
1000
369.5
359.4
338.0
309.7
284.74
2000
–
416.9
402.8
383.3
365.0
Viscosity, cP
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.0102
0.0107
0.01179
0.01327
0.01467
50
0.01105
0.01147
0.01239
0.0137
0.01492
100
0.01348
0.01351
0.01396
0.01491
0.01593
200
0.0213
0.01969
0.0181
0.01779
0.01822
500
0.04052
0.03698
0.03119
0.02641
0.02423
1000
0.06317
0.05843
0.04985
0.04087
0.03484
2000
–
0.09363
0.08134
0.06781
0.05758
Z factor
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.9972
0.9976
0.9984
0.9991
0.9995
50
0.8682
0.8928
0.931
0.9637
0.9826
100
0.7758
0.8201
0.8876
0.9444
0.9767
200
0.7744
0.8136
0.8849
0.9537
0.9954
500
1.187
1.181
1.176
1.18
1.186
1000
1.937
1.884
1.79
1.692
1.623
2000
–
3.249
3.004
2.734
2.532
457
PVT gas properties
TABLE 14.2 Variation of lean gas properties with temperature and pressure
Density, kg/m3
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.7623
0.7209
0.6435
0.5569
0.4909
50
43.91
40.37
34.55
28.89
24.97
100
98.49
88.03
72.54
58.96
50.25
200
196.5
176.9
145.3
116.7
98.53
500
318.1
302.7
271.7
234.7
205.97
1000
389
378.4
356.1
326.5
300.34
2000
–
438.3
423.7
403.3
384.2
Viscosity, cP
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.01048
0.011
0.01211
0.01363
0.01506
50
0.01137
0.0118
0.01274
0.01408
0.01533
100
0.01393
0.01394
0.01437
0.01533
0.01637
200
0.02221
0.02046
0.01871
0.01833
0.01874
500
0.04212
0.03843
0.03236
0.02732
0.025
1000
0.06546
0.06056
0.05166
0.04234
0.03606
2000
–
0.09686
0.08413
0.07015
0.05959
Z factor
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.9971
0.9976
0.9984
0.9991
0.9995
50
0.8654
0.8906
0.9297
0.9631
0.9823
100
0.7717
0.8169
0.8857
0.9436
0.9765
200
0.7738
0.8129
0.8844
0.9539
0.996
500
1.195
1.188
1.182
1.186
1.191
1000
1.954
1.9
1.804
1.704
1.634
2000
–
3.281
3.033
2.759
2.554
458
14. Case studies/reference material
TABLE 14.3 Variation of rich gas properties with temperature and pressure
Density, kg/m3
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
1.289
1.218
1.086
0.9391
0.8272
50
70.91
72.82
73.92
55.23
45.5
100
–
–
204.7
126.9
97.6
200
–
–
–
252.7
197.1
500
–
–
–
399.3
354.2
1000
–
–
–
–
453.9
2000
–
–
–
–
533.6
Viscosity, cP
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.009187
0.009678
0.01074
0.01223
0.01366
50
0.01148
0.01186
0.01255
0.0134
0.01456
100
–
–
0.0256
0.01728
0.01702
200
–
–
–
0.03102
0.02456
500
–
–
–
0.05883
0.04665
1000
–
–
–
–
0.07412
2000
–
–
–
–
0.1189
Z factor
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.9917
0.9929
0.9949
0.9968
0.9979
50
0.7168
0.7167
0.7311
0.8475
0.9071
100
–
–
0.5281
0.7379
0.8457
200
–
–
–
0.7407
0.8377
500
–
–
–
1.172
1.165
1000
–
–
–
–
1.819
2000
–
–
–
–
3.094
459
PVT gas properties
TABLE 14.4 Variation of volatile oil / retrograde condensate properties with temperature and pressure
Density, kg/m3
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
1.02
0.9648
0.8609
0.7446
0.6565
50
59.83
57.74
50.72
40.79
34.58
100
206
157.9
116.8
87.12
71.47
200
317.4
288
231
175.6
143.1
500
–
–
361
316.4
278.7
1000
–
–
–
405
376.8
2000
–
–
–
475.7
457.1
Viscosity, cP
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.009451
0.009937
0.01098
0.01244
0.01382
50
0.01109
0.01138
0.01208
0.01325
0.01445
100
0.02586
0.01847
0.01563
0.01542
0.0161
200
0.04581
0.03874
0.02811
0.0219
0.02041
500
–
–
0.05382
0.04157
0.03421
1000
–
–
–
0.06635
0.05493
2000
–
–
–
0.1069
0.09058
Z factor
Temperature, °C
Pressure, atm
0
15.56
50
100
150
1
0.9945
0.9953
0.9967
0.998
0.9988
50
0.7671
0.7886
0.8444
0.9105
0.9476
100
0.492
0.5982
0.7341
0.8527
0.9172
200
0.6435
0.6698
0.7446
0.8483
0.9212
500
–
–
1.197
1.183
1.184
1000
–
–
–
1.848
1.752
2000
–
–
–
3.146
2.887
460
14. Case studies/reference material
Gas phase envelopes
300
METHANE
LEAN GAS
RICH GAS
RETROGRADE
250
Pressure (atm)
200
C
150
100
C
C
C
50
0
–200
–150
–100
–50
0
50
100
Temperature (°C)
150
200
250
300
FIG. 14.1 Comparison of phase envelopes for methane, lean gas, rich gas, and retrograde fluid.
The difference of retrograde fluid may be seen in the location of its critical point, where
liquid and vapor densities are the same, on the P-T graph, being on the low temperature side
of the phase envelope as shown in Fig. 14.1.
Abbreviations and definitions
Commonly used abbreviations, acronyms, and definitions as as well as some of the industry standards applicable to flow assurance are are shown in Tables 14.5 and 14.6.
Regulatory requirements and environmental law which may affect flow
assurance
Regional regulatory requirements have to be identified at the project consideration stage
because of their high impact on the project. A list of applicable regulatory requirements have
to be included as a list in the basis of design document. Examples of requirements that may
affect flow assurance include:
•
•
•
•
Guidelines or restrictions on production and chemical use methods
Guidelines on use of gas gradient for shut-in tubing pressure calculation
Imposed chemical restrictions or toxicity limits
Waste management/handling regulations
Regulatory requirements and environmental law which may affect flow assurance
461
TABLE 14.5 Abbreviations, acronyms, and definitions
Acronym or name
Description
AA
Anti-agglomerant chemical
AAPG
American Association of Petroleum Geologists
AI
Asphaltene inhibitor chemical
AOP
Asphaltene onset pressure
ARN
Tetra-carboxylic naphthenic acid (old Norwegian arn, eagle)
Blockage
A restriction impermeable to flow
BOD
Basis of design
CI
Corrosion inhibitor chemical
CPM
Cross-polarized microscope
D
Diameter
Deepwater
Projects in water deeper than 1000 ft
DEH
Direct electrical heating
DF
Defoamer chemical
DSC
Differential scanning calorimeter
DSP
Decision support package
DTHYD
Difference between hydrate stability and ambient temperature
EB
Emulsion breaker chemical
EtOH
Ethyl alcohol chemical
FBHP
Flowing bottomhole pressure
FBHT
Flowing bottomhole temperature
FIV
Flow induced vibration
FWHP
Flowing wellhead pressure
FWHT
Flowing wellhead temperature
GOR
Gas oil ratio
GUTS
Grand unified thermodynamic simulator software
HPHT
High pressure high temperature
HTGC
High temperature gas chromatograph
JT
Joule-Thomson cooling effect
KHI
Kinetic hydrate inhibitor chemical
LDHI
Low dosage hydrate inhibitor chemical (KHI or AA)
MAOP
Maximum allowable operating pressure
Continued
462
14. Case studies/reference material
TABLE 14.5 Abbreviations, acronyms, and definitions—Cont’d
Acronym or name
Description
MARS
Multiple Application Reinjection System intervention interface for trees
MEG
Mono ethylene glycol chemical
MEOH
Methyl alcohol (methanol) chemical
NORM
Naturally occurring radioactive materials, such as strontium sulfate scale
PLET
Pipeline end termination
PPD
Pour point depressant chemical
PVT
Pressure volume temperature
Q
Flow rate
Restriction
Accumulation of material in a flow channel limiting flow
ROV
Remotely operated vehicle
Safe-out time
Time after a shut-in required to bring the system to a condition safe from
flow assurance threats arising from cooling to ambient, e.g. by displacement,
depressurization, heating or chemical treatment.
SCSSV
Surface-controlled subsurface safety valve
SGN
Nitrogen generation system
SI
Scale inhibitor
SITP
Shut in tubing pressure
SME
Subject matter expert
SOP
Site operating procedure
TDS
Total dissolved solids
TEG
Triethyleneglycol chemical
THPS
Tetrakis (hydroxymethyl) phosphonium sulfate biocide chemical
TSS
Total suspended solids
VIT
Vacuum-insulated tubing
WAT
Wax appearance temperature
•
•
•
•
•
•
•
•
Discharge fluid property requirements
Flaring restrictions and requirements
Local content requirements for labor and materials
Automated valve closure requirements such as HIPPS
Maintenance, inspection and testing frequency requirements
Metering and calibration requirements
Guidelines or restrictions on handling of produced water
Restrictions on injection at or above reservoir fracture pressure
463
Advanced flow assurance fluid properties
TABLE 14.6 Some of the industry standards applicable to flow assurance
Document No.
Description
API 17TR14
Flow Assurance Considerations in Subsea Production Systems
API 17TR5
Avoidance of Blockages in Production Control Systems
API 17TR6
Attributes of Production Chemicals in Subsea Production Systems
API 17 TR13
General Overview of Subsea Production Systems—Section 10.8 HIPPS
API 17O
Recommended Practice for High Integrity Pressure Protection Systems (HIPPS)
ASME B31.3
Process Piping, ASME Code for pressure piping, An American National Standard
Pipe roughness
Typical roughness of pipe materials is shown in Table 14.7.
Sample requirements
Usual samples required for basic flow assurance analysis are shown in Table 14.8.
Advanced flow assurance fluid properties
Fluid properties required for more advanced flow assurance analysis are shown in
Table 14.9.
TABLE 14.7 Pipe roughness
Material
Roughness, microns
Carbon steel, low-carbon steel
45
Stainless steel (hot rolled)
450
Stainless steel (cold drawn)
40
Duplex stainless steel
40
Glass-lined carbon steel (new)
5
Glass-lined carbon steel (old)
50
Galvanized carbon steel
150
Epoxy lined pipe
150
Fiber pipe, plastic pipe
15
Glass reinforced epoxy
5
Titanium
45
464
14. Case studies/reference material
TABLE 14.8 Basic sample requirements for flow assurance analysis
Black oil
Compositional analysis to C36+ with C7-C9 aromatics broken out
Constant composition expansion at reservoir temperature
Constant composition expansion at wellhead temperature and at
temperature between wellhead and reservoir (optional)
Differential liberation
Oil viscosity
Separator test
Volatile oil
Compositional analysis to C36+ with C7-C9 aromatics broken out
Constant composition expansion at reservoir temperature
Constant composition expansion at wellhead temperature and at
temperature between wellhead and reservoir (optional)
Differential liberation and/or constant volume depletion
Oil viscosity
Separator test
Retrograde condensate
Compositional analysis to C36+ with C7-C9 aromatics broken out
Constant composition expansion at reservoir temperature
Constant composition expansion at wellhead temperature and at
temperature between wellhead and reservoir (optional)
Constant volume depletion
Oil viscosity of separator liquid at reservoir temperature (optional)
Wet and dry gases
Compositional analysis
TABLE 14.9 Advanced fluid properties required for flow assurance analysis
Advanced fluid properties for flow assurance
Dead oil WAT
Dead oil HTGC
Dead oil pour point
Dead oil gel strength
Live oil high pressure CPM
Live oil AOP isothermal depressurization
Dead oil refractive index with n-C5/n-C7 titration
Dead oil viscosity as a function of temperature
Live oil viscosity as a function of temperature
H2S, CO2 and mercaptan content
Mercury, Arsenic, Selenium metals content
Total acid number
Total base number
Dead oil ARN acid content
Connate water composition, especially barium content
Water TDS
Sulfur content in oil
Flow correlations
Pressure drop in single phase liquid turbulent flow.
Darcy's equation.
Pressure drop in gas flow.
Panhandle equation.
465
Units and conversions
Gravity driven flow is characterized by Froude (pronounced fru:d) formula
Fr = v/(g D)^0.5.
Fr < 1 stratified smooth.
Fr < 2 stratified wavy.
Fr > 2 stratified mist.
Fr > 12 mist.
Froude allows an important insight at energies of entrainment and deposition. V = 2√gD
is a transition where flowing gas starts to entrain liquid. This may be of use for TOLC corrosion inhibition.
Flow correlations applicability to vertical or horizontal flow is shown in Table 14.10.
Monitoring and instrumentation for flow assurance
Possible locations for produced fluids monitoring instrumentation are shown in Table 14.11.
Units and conversions
Acceleration of gravity (standard) near 45° latitude; gravity near equator is 0.25% less and
gravity in polar regions is 0.25% more.
g = 32.17 ft/s2 = 9.807 m/s2
Avogadro's number
NA = 6.023 * 1023 molecules/g-mole
Newton's conversion constant
gc = 32.17 lbm-ft/lbf s2 = 1.000 kg m/N s2
TABLE 14.10 Flow correlations applicability to vertical or horizontal flow
Near-vertical
liquid
dominated
flow
Inclined liquid Near-horizontal Near-vertical
Near-horizontal
dominated
liquid
gas dominated gas dominated
flow
dominated flow flow
flow
Ansari
+
−
+
−
−
Beggs and Brill
+
+
+
+
+
Duns & Ross
+
+
+
+
+
Govier, Aziz and
Forgasi
+
+
+
+
+
Gray
−
−
+
−
−
Hagedorn and Brown
+
−
+
−
−
Mukherjee and Brill
+
+
+
+
+
Oliemans
−
−
−
+
+
Orkiszewski
+
−
+
−
−
466
14. Case studies/reference material
TABLE 14.11 Possible locations of instrumentation for fluids conditions monitoring
Temperature
Reservoir
Pressure
Downhole T,
Distributed (fiber)
temperature
Downhole pressure
Tree
Yes
Yes—standard equipment
upstream and downstream
of the tree choke
Jumper
Yes
Manifold
Yes
Yes
Distributed (fiber)
temperature
Riser
Topsides
Composition GC
Water injection or producer
wells may be converted
into monitoring wells
Wellbore
Flowline
Sand/
acoustic
Resistivity
corrosion
monitor or
coupon
Yes
Export line
Yes onshore
Riser base pressure
Yes
Yes
Yes
Yes at each end
Heat of fusion of water at 1 atm, 0 °C
79.7 cal/g = 144 Btu/lbm
Heat of vaporization of water at 1 atm, 100 °C
540 cal/g = 972 Btu/lbm
1 J/kg K = 2.3886 * 10−4 Btu/lbm °F
1 cal = 4.184 J
1 Btu = 1055 J
1 N = 1 kg m/s2
1 N = 100,000 dyne
1 N = 0.22481 lbf
1 N = 0.1019501 kgf
1 psi = 6894.73 Pa
1 psi = 0.07029264 kg/cm2
1 kg/cm2 = 98,066 Pa
1 Pa = 1 N/m2
1 Pa = 1 kg/(m s2)
1 Pa = 1.01973E-05 kg/cm2
1 bar = 100,000 Pa
Yes onshore
Yes
Online
Gas chromatograph
Standard temperature and pressure
467
1 atm = 101,325 Pa
1 Torr = 1 mmHg
1 atm = 760 mmHg
1 ft = 0.3048 m
1 ft = 12 in
1 mile = 5280 ft
1 Nautical mile = 1852 m
1 US offshore block = 9 sq. Nautical miles
1 acre = 43,560 sq. ft
1 W/(m2 K) = 0.1761 Btu/(h ft2 °F)
1 W/(m K) = 0.57782 Btu/(h ft °F)
1 W = 1 J/s = 3.4123 Btu/h
1 kg = 2.2046 lbm
1 pound = 16 oz = 453.592 g
1 ton = 1000 kg
1 US ton = 907.185 kg
1 imperial ton = 1016.05 kg
1 m3 = 6.2898 bbl
1 bbl = 158.987 L = 0.158987 m3
1 bbl = 9702 in3
1 gal = 3.78541 L
1 gal = 231 in3
1 gal = 4 quarts = 8 pints = 128 fluid ounces = 768 teaspoons
1 L = 1000 cm3
1 m3 = 1000 L = 35.3134 ft3
1 cP = 0.001 Pa s
Standard temperature and pressure
There is no internationally accepted standard for STP. In 1980 GPA adopted 15 °C,
101.3250 kPa (abs) as standard conditions for SI units. Thus standard molar volumes are:
23.645 std. m3/kmol at 15 °C (288.15 K), 101.3250 kPa
GPA SI standard conditions.
379.49 std. ft3/lb. mol at 60 °F (519.67 °R), 14.696 psia.
Index
Note: Page numbers followed by f indicate figures and t indicate tables.
A
Acrolein, 177
Activity coefficients, 174, 180
Alcohol
chemical, 128
hydrate, 294
prevent hydrate formation, 233
thermodynamic inhibitors, 111, 233, 287
American Association of Petroleum Geologists
(AAPG), 461–462t
American Petroleum Institute, 12
Anionic surfactants, 287
Anti-agglomerant (AA) chemical, 114, 193, 461–462t
Anti-bacterial coating, 91
Artificial lift method, 206, 207t, 214
Asphaltene dispersant, 144, 147, 193
Asphaltene instability test (ASIST) method, 142–143, 147
Asphaltenes, 36
chemical structure, 141
deposition, 144
enhanced oil recovery, 143
environmental impact of, 146
gas condensate, 143
inhibitor, 193
irreversible thermodynamics, 147
light oil effect, 143
mass fractions, 159
microbubble capture, role, 144
monitoring, 145–146
precipitation, 142–144
prevention of, 147–148
remediation of, 146
remote sensing of, 145–146
reservoir, 141–142
reversible thermodynamics, 146
wellbore plugging, 141–142
ASTM D97 test, 194
B
Bacterial deposit, 36
Bacterial growth
management, 148–149
periodic biocide treatment, 148
water injection wells, 148
Barium sulfate, 10, 41t, 178–181
Barocel differential electronic manometer, 237
Bench scale tests, 342–343
Biodegradation, 65
BIOSYM®, 252
Biotechnology, gas hydrates in, 225
Black oil, 464t
Blockages, 453–454. See also Hydrate blockage
chemical tubing, 200
extreme cases, 15–16
natural gas production, 20
in onshore wells, 16
production monitoring tools
correlations, 89
software, 89
remediation plan, 42
Boiling point analysis, 52–53
Boltzmann constant, 173
Bravais Friedel Donnay Harker method, 295
Brownian diffusion, 158–159
C
Calcium cabonate, 10, 178, 180
Calcium naphthenate, 197
Calcium sulphate, 296
CapEx and OpEx, 452
Carbonate, 178
Carbon dioxide
disposal at ocean bottom, 225, 226f
greenhouse effect, 223–224, 224–225f, 282
Carbon steel pipelines, 23, 149
Cationic surfactants, 287
Cavity radial distribution function (CRDF), 294
Cerius2 program, 295–296
CGR. See Condensate-gas ratio (CGR)
CHARMm software, 296
Chemical delivery system, 13, 13–14t
Chemical injection distribution system, EPANET2 tool,
443–444, 445f
Chemical injection systems, 194
Chemical potential, 245–247, 293–294, 336
Chemical tubing blockage, 200
Chilly choke conditions, 84
Clathrate hydrates. See also Gas hydrates
characteristics, 297, 298t
cold-storage process, 284
469
470
Clathrate hydrates (Continued)
computer modeling at CSM, 313
crystal growth (see Hydrate crystal growth)
forms of, 282
structure H, 285
structure I, 284
structure II hydrate, 284
hydrate growth, 294–296
kinetic inhibitors and
computer modeling, 280
interaction between, 280
pressure and temperature, 280
THF hydrate crystal, 280
separation techniques, 284
size, 284
thermodynamic properties, 292
translational and vibrational spectra, 293
Clausius-Clapeyron equation, 233, 235
Cleanliness, production chemicals, 192
Cloud point, 60
Cold filter plug, 60
Cold finger, 60, 342
Cold flow method, 207–208
Cold-storage process, 284
Commercial software packages, 295
Compatibility, production chemicals, 192
Computer coded program
counting H bonded rings in water, 346–367
generating radial distribution function in water,
343–346
Monte Carlo program for polymer adsorption on
hydrate, 367–436
Concentration, production chemicals, 192–193
Condensate-gas ratio (CGR), 151
Conference in Brussels on the Global Environment, 282
Consistency, production chemicals, 192
Core flood test, 142
Correlations, 464–465, 465t
blockages, production monitoring tools, 89
flow modeling, 84–85
pipeline, production monitoring tools, 88
Corrosion, 37
control techniques, 219
flow parameters, 217
hydrate formation
carbon steel coupons, 123f
Cr 13 steel, 125f
stainless steel caliper, 124f
stainless steel 316 exhibits corrosion, 124f
inhibitor, 193
management, 217
monitoring methods, 218
products, 36–37, 149
risk, 206
Index
test procedures, 193
types, 218
Corrosion-resistant alloys (CRA), 23, 177
CRDF. See Cavity radial distribution function (CRDF)
Cross-polarized microscope (CPM), 8, 40, 42, 60, 342
Crude biodegradation, 65
Crude oil, 5. See also Asphaltenes; Naphthenic acids
composition of, 163
live, 172f
methanol solubility in, 195
SARA analysis, 142
stock tank, 172f
water content, 195
CryoFAST, 448, 448f
D
Deepwater production
challenges, 30–31
fluid sampling, 44–45
operations, 29, 183–184
Diamondoids, 37, 149–150
Differential scanning calorimeter (DSC), 60, 343
Diffusion-limited aggregation (DLA) fractal models,
313
DMAEMA monomers, 250
Drag reducing agents, 199
DREIDING forcefield, 313
Droplet models, 152
Dynamic field development model, 454
Dynamic tube plugging test, 179
E
Electric conductivity, 225, 282
Electric power plants, 223
Emulsion, 37, 182, 195
breaker, 13, 13–14t, 196
characteristics, 64–65
and cold flow, 207–208
rheology, 208, 208f
viscosity, 208, 208f
Enhanced oil recovery (EOR), 143
Enthalpy, 233, 235–236, 241
Entropy, 233
EOR. See Enhanced oil recovery (EOR)
EPANET2 tool
chemical injection distribution system, 443–444,
445f
for water injection system, 444, 445f
Equilibrium line, 232, 235, 241, 243, 245
Erosion, 37, 220
F
The Flory-Huggins solubility model, 146
Flow assurance
Index
advanced fluid properties, 463
background, 17–21
basis of design, 21–22
blockages, 2–3
correlations, 464–465, 465t
data mining, 28
definitions, 2, 21
design chemical injection program, 15
flow restrictions, 2–3
fluid characterization, 22
hardware cost, 24–26
hydrates and electrical heating, 3
ice blockages, 5
industry standards to, 463t
integrity issues
corrosion (see Corrosion)
erosion, 220
internal boundaries, 12
issues, 12
lack of training/experience, 15
measuring system, 30
monitoring, 28
multiphase technology & OLGA, 3
operations, 28–29
operator error, 15
outlooks, 30–31
pipe roughness, 463
prevention methods, 13
problems, 5–10
process safety, 30
produced fluids monitoring instrumentation, 465
production chemistry items, 10, 11–12t
project design, 14
PVT-related fluid analysis, 22
regional regulatory requirements, 460
sample requirements, 463
standard temperature and pressure, 467
systematic approach, 29–30
units and conversions, 465–467
Flow assurance model
concept selection, 452
exploration, 451–452
flow test, 452
material characteristics, 451
PVT fluid characterization, 451
reservoir characterization, 451
Flow-induced vibration, 37
Flowline deliverability issues
arrival pressure, 207
artificial lift methods, 206, 207t
cold flow and emulsion, 207–208
design process, 205–206
emulsion rheology, 208, 208f
heavy oil viscosity, 208
471
optimization of sizes, 206
topsides equipment, 207
Flow loop tests, 341–342
Flow modeling
correlations, 84–85
dimensionless numbers, 85–86
erosion modeling, 87
multiphase production problems, 87
software, 86–87
Flow rate, 3, 35, 37, 70, 77, 88, 115, 145–146, 149, 160,
167, 206, 214
Fluid characterization process
group contribution method, 53
laboratory studies, 59–60
lumping, 56–57
oil viscosity, 56
properties and measurements, 51–52
pseudocomponents, 56
PVT tuning, 60–61
solid-liquid equilibrium, 57–59
Fluid physical properties, 61–63, 61–63t
Fluid quality
BOEM component shut-ins per facility, 196, 197f
BOEM warnings per facility, 196, 197f
emulsions and foams, 195–196
hydrocarbon gas, 195
hydrocarbon oil, 195
produced water, 195
topsides process design, 195–196
water treatment management, 195–196
Fluid sampling
deepwater samples, 44
H2S sample collection, 44
hydrocarbon fluid, 45
mercury samples, 44–45
onshore samples, 44
quality checks, 45–51
Fluid velocity, 155
Fluid viscosity, 444
Foaming, 37, 64
G
Gas condensate, 143
ThermoFast, 448, 449f
Gas dew point analyzer, 139
Gas-dominated systems, 122
Gas hydrate formation
chemistry, 106
flow restriction, 182
light hydrocarbons and sour gases, 183
mechanical expansion, 183
mechanical movement, 183
of microbubbles, 102
of nanobubbles, 102
472
Gas hydrate formation (Continued)
solid particles, 183
water-based compounds, 183
in wells and in natural settings, 125–126
Gas hydrates
annual cost for preventing, 280–281
applications, 282
deposition, 222
greenhouse effect, 223–224, 224–225f, 282
industrial applications, 224–225, 226–227f
as industrial hazards, 223
kinetics
experimental studies, 235
factors, 235
growth rate, 234
inhibitors, 235
locations in world, 281, 281f
in nature, 281
offshore deposits, 282, 283–284f
in oil and gas industry, 222
phase transitions in, 235–236
pressure and temperature of, 222
properties and structures, 282
crystalline compound, 228
cubic structure I and II, 228, 230, 231f
geometric properties, 228, 231t
guest and water molecules, 228, 229f, 232
hexagonal, 230, 232f
pure components, 232
sI and sII hydrate formation, 228, 230f
small size, 230–232
thermodynamics model, 232
related substances on computers, 297, 298t
reserve of carbon in, 281
as source of hydrocarbon fuel, 226–228, 229f
in space, 282
stability, 293–294
storage and main-line transportation, 282
at thermodynamics conditions
with inhibitors, 233–234
without inhibitors, 233
Gas oil ratio (GOR), 122
liquid components vs.vapor components, 49
reservoir fluid sample, 45
Geothermal profile, 126, 126f
Gibbs free energy, 102
Gibbs's phase rule, 233
Global warming, 223, 224f
Glycols
combination of salt and, 117
modern recovery method, 112
prevent hydrate formation, 233
properties, 113
reboiler, 176
Index
regeneration plants product, 122
thermodynamic inhibitors, 111, 115
types, 112
Grease-sealed glass flask, 237
Greenhouse effect, 223–224, 224–225f, 282
Gypsum, 178, 180
H
Halley comet hypothesis, 128f
Hardware cost
infrastructure-led exploration, 24
Na-Kika semi-submersible platform, 25
net present value, 24
Heat accumulator, hydrate as, 225
Heavy oil, 143–144
management, 198
viscosity, 208
Heterogeneous nucleation, 102
High integrity pressure protection system (HIPPS), 73,
81, 207, 462, 463t
High pressure high temperature (HPHT) reservoirs, 23,
56–57, 207, 461–462t
High temperature gas chromatograph (HTGC), 163, 168
The Hill-Wood model, 75
Hirschberg model, 142, 146
Historic pigging models, 171–173
H2S samples, 44
HTGC. See High temperature gas chromatograph
(HTGC)
Hydrate blockage
calculating location in pipe, 109–110
case studies in flowlines, 131
causes of pipeline ruptures, 132
characteristics, 37
multiple, 16
onshore field, 15–16
partial, 16
rate of, 104
remediation
dissociation temperature, 119, 120–121t
melting temperature, 119
versus other flowline time, 99–101
preliminary estimation, 118
prevention of, 110–117
projects, 100–101
rate of, 104
regional environmental regulations, 122
Hydrate control chemicals, 192–193
Hydrate crystal growth
computer modeling, 295
in directions of crystal vertices, 303
at gas-liquid interface, 286
inhibition, 296–297
measurements, 312
Index
mechanism, 311, 311f
morphology
axes of rotation, 302, 303f
effect of temperature, 299–300
face-centered cubic crystals, 300, 302f
{111} faces, 303
fast-growing crystal face, 299, 299f
kinetic hydrate inhibitors effect, 304–308, 305–307f
NaCl salt effect on THF hydrates, 308–311, 309t,
310f, 312f
octahedral crystal shape of sII, 300, 301f, 302, 303f
single crystal of THF, 300, 301f
variables, 299
visual apparatus, 299, 300f
natural gas, 287
recorded by Olympus SZ-CTV microscope, 300
tetrahydrofuran, 286–287, 286f
THF + water + inhibitors solution with NaCl salt,
312
types of, 287
Hydrate formation loop, 342
Hydrate inhibition
computer modeling
clathrate hydrates at CSM, 313
comparison and contrast results, 327–329, 328f,
328t
design inhibitors, 336–338, 337t, 338f
guest molecules adsorption, 334
methane adsorption model, 334–335
monomer adsorption with Cerius2 program,
313–320, 314–315f, 315–317t, 318–320f, 319t
Monte Carlo simulation, 338–340, 339t, 340f
short polymer adsorption, 329–336, 330–331f, 332t,
333–334f
simulation of methane adsorption, 335–336, 335f
software for water and monomers interactions,
320–329, 321f, 323f, 324t, 325–326f, 326–327t
computer simulations (molecular dynamics)
reasons for, 252
results, 252–253
formation
affecting crystal morphology, 287–288
kinetic inhibitors, 288, 289f
thermodynamic hydrate inhibitors, 287
Hydrate prevention method
active heating, 122
biological remediation, 128
chemical inhibition, 111–116, 122
cold flow, 129
commissioning/dewatering, 139
dry insulation, 122
gas dehydration, 111
partial gas separation, 129
pressure management, 117
473
static mixer concept, 129
thermal insulation, 111
wellwork safety, 117
wet insulation, 122
Hydrates
computer modeling, 290
definition, 101
dissociation, 117–118
docking of macromolecules on, 253–262, 254f,
255–256t, 257–261f
formation, 8f, 9
gas hydrate, 102–104
kinetic inhibitor, 193
management, 127–128
risk, 206
structures, 290–291, 291f
Hydrate-saturated zones, 125
Hydrate stability
calculation, free modeling software tool, 443, 444f
computer studies, evaluation of, 250–251
gas hydrates (see Gas hydrates)
methane hydrate (see Methane hydrate)
xenon sI and xenon + neohexane sH hydrate
experiments (see Xenon sI and xenon +
neohexane sH hydrate experiments)
Hydrate thermodynamic inhibitor, 193
Hydraulic restrictions
assessment and management, 69
deliverables of, 69–70
design, 70–71
frictional pressure drop, 71
hydraulic restrictions, 68–74
mitigation examples, 71, 71t
network flow optimization process, 91–92
remediation examples, 71, 71t
technologies, 73–74
work scope, 69
Hydrocarbon fluid sample, 45
Hydrocarbon gas, 195
Hydrocarbon oil, 195
Hydrogen bonded network, 268–273, 270–271f
Hydrogen bonding, 282
HYDR_88 program, 245
HyperChem®, 252
Hyperchem® release 2.0 program, 254
HyPRISM, 447, 447f
I
Ice
blockage, 37
characteristics, 297, 298t
docking of macromolecules on, 253–262, 254f,
255–256t, 257–261f
formation, 150
474
Index
Ice (Continued)
growth inhibition, 253
modeling of, 251–252
xenon gas hydrate formation, 242
ILX. See Infrastructure-led exploration (ILX)
Indirect corrosion monitoring methods, 218
Induction time, 102
Infrastructure-led exploration (ILX), 24–25
Inhibitor chemicals, corrosion, 219
In-line inspection (ILI) tool, 219
Integrated models, 219–220
Integrity issues
corrosion
control techniques, 219
flow parameters, 217
management, 217
monitoring methods, 218
types, 218
erosion, 220
Irreversible thermodynamics, 147
Isoparaffinic, 159
J
Joukowski equation, 215
Joule-Thomson cooling effect, 37, 70, 84, 150
K
Katz method, 130
Kerosene lamps, 17
Kinetic hydrate inhibitors (KHI), 104–105, 108, 113, 117,
123
Kinetic inhibitors, 235, 251
Kolmogorov energy dissipation, 109
L
Lactam ring, 278
Laminar flow, 72, 158, 219
Laplace's law, 102
LDHI. See Low dosage hydrate inhibitors (LDHI)
Lean gas
critical point location, 460, 460f
density, 457t
gas gravity, 455
viscosity, 457t
Z factor, 457t
Liberation test, 47, 47–48t
Light oil, 143
Liquid holdup
condensate-gas ratio, 151
liquid accumulation, 152–153
steam transmission lines, 151
Liquid slug, 214
Liquid water
characteristics, 297, 298t
structures, 290–291, 291f
LNG cryogenic heat exchangers
CryoFAST, 448, 448f
LNG liquefaction process, 29
LNG thermodynamic property, ThermoFast, 448, 449f
Low dosage hydrate inhibitors (LDHI), 104–105, 111
M
Macrocrystalline wax, 156, 159, 169t
Material Safety Data Sheet (MSDS), 123
MEG. See Monoethylene glycol (MEG)
Mercury
accumulation, 38
management, 199
samples, 44–45
Methane
critical point location, 460, 460f
density, 456t
gas gravity, 455
greenhouse effect, 282
viscosity, 456t
Z factor, 456t
Methane hydrate
burning, 225, 227f
experiments
Clausius-Clapeyron equation, 241
equilibrium data, 236, 236f, 238, 239–240t, 240f
equipment and procedure, 237–238, 237–238f
measurements, 238
results, 238–241
stoichiometric formula, 241
greenhouse effect, 223–224, 224–225f
phase transition, 249
Methanol-water mixture, 233–234
Microbially influenced corrosion (MIC), 218
Microbubbles, 102, 118
Microcrystalline, 159
Molecular modeling
chemical performance on solid surface, 251–252
hydrate inhibition (see Hydrate inhibition)
Monitoring instrumentation, 465
Monoethylene glycol (MEG)
density, 200
specific gravity, 201f
viscosity, 200, 202f
Monte Carlo computer program, 298, 367–436
Monte Carlo (MC) method, 295, 329
Multiphase flow
flow resistance, 153
hydrodynamics
design technique, 79–80
Fanning equation, 77
liquid holdup, vertical vs. horizontal, 80–81
pressure drop, vertical vs. horizontal, 74–79
slugging/liquid loading control, 80
loop, 4, 75, 342
Index
models, 219
vacuum condition, 153
N
Na-Kika semi-submersible platform, 25
Nanobubbles, 102, 118
Naphthenates
calcium, 197
deposition, 38
management, 197–198
properties, 197–198
Naphthenic acids, 198
Natural gas hydrates
calculating location, 109–110
chemical reactions, 106
corrosion effect, 123–125
crystal growth, 287
environmental impacts, 122
formation of, 102–104
gas dehydration, 111
gas hydrate stability, 129–131
health impact, 123
overpressurization, 104–106
plug formation, 109
problems related, 108–109
propensity, 104–106
stability of, 108
subcooling, 104–106
supercooling, 104–106
thermodynamic features, 106–108
Natural gas production, 281
Neslab cryocool CC-100 II 2-stage immersion cooler, 237
Neslab on/off temperature controller, 242
Newtonian fluids transport methods, 154
Nitrate-reducing bacteria (NRB), 148, 177
Non-stick coatings, 146
NRB. See Nitrate-reducing bacteria (NRB)
O
Offshore production
design technique, 79
drilling rig, 19f
operations, 28
Oil/gas development project
blockage monitoring, 91
flow restriction, 91
hydraulic design, 89–90
water injection management, 90–91
Oil-in-water emulsions, 65
Oil quality noncompliance, 38
Omega platinum resistance thermometer, 237
Online monitoring software tools, 88
Onshore production
challenges, 30–31
operations, 28
475
Operations
deepwater production, 29
offshore production, 28
onshore production, 28
P
Paraffin wax, 159
Brownian diffusion, 159
chemistry, 159
cold finger, 342
composition, 159, 163
comprehensive modeling, 173–174
conventional techniques, 171
cross-polarized microscope, 40, 342
deposition, 5–6
deposition loop, 341
deposits collection data, 160t
emerging techniques, 171
environmental impacts of, 168
historic pigging models, 171–173
laboratory measurements, 168–171
management of, 164
miscellaneous factors, 163
monitoring, 171
operating parameters, 160, 161t
PVT conditions, 161–162
remediation techniques, 167–168
remote sensing, 171
structure, 160
thermal diffusion, 159
waxy gels, 174–176
wellbores and surface gathering lines,
160–161, 161f
Periodic biocide treatment, 148
Petroleum
fluids, 156, 192
industry, 20
production
global, 17
large scale, 17
Ludvig Nobel, 20
product, 194
quality
hydrocarbon gas, 195
hydrocarbon oil, 195
produced water, 195
reservoirs, 9–10
solids, 58
use of, 17
Petroleum Jelly, 20
Phase diagram/phase map, 29
PHAS_88 program, 245
PHREEQC water ion saturation analysis tool, 444, 446f,
447
Physico-chemical corrosion, 218
476
Pipeline
gas hydrate formation, 223
production monitoring tools
correlations, 88
software, 88
Piper Alpha offshore platform, 15–16
Pipe roughness, 463
Poly(N,N-diethyl acrylamide) (PNNDEAM), 288
Poly(vinyl alcohol) (PVA), 288, 289f
Poly-N-vinyl caprolactam (PVCap) inhibitor,
288, 289f
chemical structures, 253, 254f
conformation of, 260–261f
effect on water structure, 277, 277t
Poly-N-vinyl pyrrolidone (PVP) inhibitor, 288, 289f
adsorption, 297, 313, 318
chemical structures, 253, 254f
conformation, 260f
docking, 259, 279
effect on water sturcture, 275–276, 277t
molecular weight, 305f
results for, 314
Potential models, 290
Pressure volume temperature (PVT)
crude biodegradation, 65
emulsion characteristics, 64–65
fluid characterization process, 51–61
fluid physical properties, 61–63, 61–63t
fluid sampling, 44–45
gas properties, 455–460
GOR range, 45–50
non-Newtonian fluid, 63–64
phase behavior, 43–44, 44f
quality checks, samples, 45–51
simulation software, 56
true boiling point analysis, 55
tuning, 60–61
wellwork fluids formulation, 51
PROCAP 1000, 5
Produced water, 195
Production chemicals
characteristics, 200
chemical injecting system, 194
chemical performance
asphaltene dispersant, 193
asphaltene inhibitor, 193
corrosion inhibitor, 193
criteria for, 193
hydrate antiagglomerant chemical, 193
hydrate kinetic inhibitor, 193
scale inhibitor, 193
wax inhibitor, 193
chemical tubing blockage, 200
4Cs quality, 192–193
Index
dosage selection and optimization, 200
effectiveness and economics of, 194
estimated properties, 203t
lab equipment requirements, 193
MEG data
density, 200
specific gravity, 201f
viscosity, 200, 202f
operating expenditure, 192–193
sampling fluids, 191–192
test procedures, 193–194
Production issues
blockage remediation plan, 42
causes of
asphaltene, 36
bacterial deposit, 36
corrosion products, 36–37
diamondoids deposition, 37
emulsions, 37
erosion of pipes, pipe elbows or valves, 37
fines production, 37
flow-induced vibration, 37
foaming, 37
hydrate blockage, 37
ice blockage, 37
Joule-Thomson cooling, 37
liquids holdup in flow lines, 37
loading of wells, 37
mercury accumulation, 38
naphthenates deposition, 38
oil quality noncompliance, 38
pressure-temperature-composition
conditions, 39
productivity damage, 38
sand deposition, 38
scale deposition and scale products accumulation,
38
slugging, 38
souring of produced fluids, 38–39
stuck pig, 39
sulfur deposition, 39
underdeposit corrosion, 39
viscous oil/viscous emulsion flow, 39
water quality noncompliance, 39
wax deposition, 39
differential pressure change, 35–36, 36t
hydrate plugs, 35
pressure measurement, 35
solid samples identification, 40
field analysis, 40
field laboratory initial tests, 40
laboratory analysis, 40–42, 41t
time, 35
Production monitoring tool, 88
Index
Pullman method, 275–276, 278
PVCA inhibitor, 277–278, 277t
PVT. See Pressure volume temperature (PVT)
Q
Quality checks
hydrocarbon fluid sample, 45–50
oil sample, 45
water sample, 50–51
R
Radial distribution function (RDF), 262–264
Raman spectroscopy, 343
Research objectives, 297–298
Reservoir souring
commercial models, 178
mitigation of, 177
treatment, 177
Retrograde gas, 464t
critical point location, 460, 460f
density, 459t
gas gravity, 455
viscosity, 459t
Z factor, 459t
Reverse demulsifier chemicals, 195–196
Reversible thermodynamics, 146
Reynolds number, 72
Rheology, 64–65, 343
Rich gas
critical point location, 460, 460f
density, 458t
gas gravity, 455
viscosity, 458t
Z factor, 458t
Risk analysis, flow assurance
bowtie, 22
economic balance, 24
product value, 24
Risk probability management
blockage, 453–454
dynamic field development model, 454
prevention, 453
project cost optimization CapEx vs. OpEx, 453
wax deposition, 454
S
SAGD. See Steam assisted gravity drainage (SAGD)
Sand deposition, 38
Sand transport
erosional velocity limits, 155–156
liquid with solids, 156
minimum transport velocity, 154–155
multiphase transport models, 154
SARA analysis, 142
Scale deposition, 38
Scale inhibitor, 193
Scale saturation index, 50
PHREEQC, 444, 446f, 447
SCSSV safety valve, 117, 125
SGN chemical reaction, 167
The Shea model, 75
Simple point charge (SPC) water model, 250
melting point, 250
simulation results, 262–264, 264f
Slack flow, 68–69
Slugging
hydrodynamic, 38
impact, 214–215
pressure surge calculating method, 215
severe, 38, 211–213
Boe criterion for, 213
flow regime map, 212, 212f
frequency correlation, 211
impact on production system, 211
periodic, 211
stability criterion, 212–213
suppression techniques, 213
transient operation
flow rate ramp-up and ramp-down, 214
in gathering lines, 214
shut-in and start-up production, 213–214
vacuum condition in flow, 216
Software packages, 74, 86–87
Software tools
CryoFAST, 448, 448f
CSMHYD, 443, 444f
EPANET2 tool, 443–444, 445f
for hydrate stability calculation, 443, 444f
HyPRISM, 447, 447f
PHREEQC, 444, 446f, 447
Thermofast, 448, 449f
Solid scale
calcium sulfate, 178–179
carbonate, 178
laboratory tests, 179
management, 181
precipitation prediction, 179–180
remediation methods, 180–181
Solid solution models, 290
SPE Hydrate Engineering monograph, 131
Spherical stainless steel reactor, 237, 242
Spreadsheet, 91
SRB. See Sulfate-reducing bacteria (SRB)
Static bottle test, 179
Steam assisted gravity drainage (SAGD), 151
Stress-controlled rheometer, 343
Sulfate, 178–179
Sulfate-reducing bacteria (SRB), 177
477
478
Sulfur deposition, 39, 199
SYBYL®, 252–253
T
Tetrahydrofuran (THF) hydrate, 286–287
hydrate crystal morphology, 339–340
NaCl salt effect, 308–311, 309t, 310f
needle-like growth, 311, 312f
octahedral crystal shape, 300, 301f, 302, 303f
single crystal, 300, 301f
visual apparatus, 299, 300f
Thermal effects
heat transfer, 81, 82–83t
Joule-Thomson effect, 84
Thermodynamic hydrate inhibitors, 287
Thermodynamics, of hydrate formation
with inhibitors, 233–234
without inhibitors, 233
ThermoFast, 448, 449f
Thermolyne orbital shaker, 242
Tiller multiphase flow loop, 4
TIP3p (transferable intermolecular potential 3 point)
model, 262–264, 266–268, 279
Toluene soak, 146
Top of the line corrosion (TOLC), 206
Topside equipment, 207
Topsides process design, 195–196
Transient operation
flow rate ramp-up and ramp-down, 214
in gathering lines, 214
shut-in and start-up production, 213–214
Trivac vacuum pump, 242
Tubular plugging
composition role, 163
miscellaneous factors, 164
PVT conditions, 163
U
Univariant curve, 233
V
Vacuum
condition, 216
at stock oil flow, 216
Vacuum insulation tubing (VIT), 163, 167
Vaseline, 20
VC-713 inhibitor, 305, 312
adsorption energy, 257–259
chemical structures, 253, 254f
conformation of, 259–260f
docking, 261–262
effect on water structure, 274–275, 275t, 276f
polymer chain of, 254
Index
Viscosity, 56
emulsion, 208, 208f
heavy oil, 208
lumping, 56
of MEG, 200, 202f
pseudocomponents, 56
Viscous oil
characteristics, 39
management, 198–199
VIT. See Vacuum insulation tubing (VIT)
VLE phase diagram, 44
Volatile oil, 464t
W
WAT. See Wax appearance temperature (WAT)
Water and liquid hydrocarbon, 242
Water injection system, EPANET2 tool, 444, 445f
Water-in-oil emulsions, 64, 144
Water-methane-methanol mixtures, 234
Water models, kinetic inhibitor interaction with
hydrogen bonded network
connectivity, 270–272, 272–273f
outcomes, 273
schematic of, 262–264, 265f
structural determination, 268–270, 270–271f
macromolecules effect
hypothesis, 274
PVCA inhibitor, 277–278, 277t
PVCap inhibitor, 277, 277t
PVP inhibitor, 275–276, 277t
VC-713 inhibitor, 274–275, 275t, 276f
monomer structure, 262–264, 265f
overview, 278–279
oxygen-oxygen radial distribution function, 262–264,
263f
SPC water model (see Simple point charge (SPC)
water model)
verification
analysis, 267–268, 267–269f
comparison between SPC, TIP3p and proprietary
Tripos model, 266
procedure, 266
Water quality noncompliance, 39
Water sample, 192
drilling mud contamination, 50
ionic balance, 50
rare cases, 51
scale saturation index, 50
Water structure, 234, 251
Wax appearance temperature (WAT), 6–8, 131, 158, 162,
167
Wax deposition, 39
Wax dissolution temperature (WDT), 6–8
Wax formation, prevention techniques
479
Index
comparative economics of, 167
electrical heat, 167
management of, 164
mechanical wax removal method, 164–165, 165f
pigging, 165
remediation technologies, 164
vacuum insulation tubing, 167
Wax inhibitor, 193
Wax loop, 342
Wax, remediation techniques
chemical removal, 167
comparative economics of, 168
mechanical removal, 167
thermal removal, 167
Wet and dry gases, 464t
Winter flounder polypeptide
adsorption of, 253, 257
aminoacids structure, 255, 255t
chemical formula, 253
conformation on, 257, 257–259f
docking of, 253, 257, 261–262
Hyperchem® release 2.0 program, 254
sequence of aminoacids, 255
X
Xenon sI and xenon + neohexane sH hydrate
experiments
calculated phase composition, 244–245, 247t
crossover of equilibrium curves, 244, 246–247f
equilibrium calculation, 248, 249f, 250t
equilibrium data, 243–244, 244t, 245f, 246t
equipments, 237f, 242
literature data, 241
procedure, 242–243, 243f
two phase diagrams, 249
two-step process, 245
vapor phase composition, 245–247
XHPHT reservoirs, 56–57