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PVTiReferenceManual

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ECLIPSE Pre- and Post-Processing Suite
ECLIPSE* reservoir simulation software
Reference Manual
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Table of Contents
List of Figures ..... ...................................................................................................................................................................7
List of Tables ...... ...................................................................................................................................................................8
Chapter 1 - Developments................................................................................................................ 9
Product Maintenance..............................................................................................................................................................9
Developments for 2004A ......................................................................................................................................................10
Chapter 2 - The Most Asked Questions About PVTi.................................................................... 13
Introduction ......... .................................................................................................................................................................13
Chapter 3 - Introduction ................................................................................................................. 25
General information ..............................................................................................................................................................25
Chapter 4 - Getting started............................................................................................................. 29
Starting PVTi ...... .................................................................................................................................................................29
Chapter 5 - Tutorials ....................................................................................................................... 31
Overview............. .................................................................................................................................................................31
Fluid Properties Estimation...................................................................................................................................................33
Creating a fluid system .........................................................................................................................................................36
Simulating experiments ........................................................................................................................................................42
Fitting an equation of state to experimental results ..............................................................................................................49
Exporting ECLIPSE Black Oil PVT tables.............................................................................................................................53
Converting a black oil run to compositional ..........................................................................................................................58
Workflow Tutorial .................................................................................................................................................................61
Multiphase Flash .................................................................................................................................................................69
Exporting an ECLIPSE Thermal model ................................................................................................................................73
Data analysis and quality control ..........................................................................................................................................77
Removing contamination from samples................................................................................................................................84
Converting old projects to the current version ......................................................................................................................87
Chapter 6 - Reference section ....................................................................................................... 89
General information ..............................................................................................................................................................89
Main PVTi window ................................................................................................................................................................90
The PVTi main module .........................................................................................................................................................91
The fluid model ... .................................................................................................................................................................98
COMB - Compositional Material Balance ...........................................................................................................................112
Simulation using PVTi ........................................................................................................................................................117
Regression in PVTi .............................................................................................................................................................126
Exporting keywords ............................................................................................................................................................133
VFP module ........ ...............................................................................................................................................................138
Utilities ................ ...............................................................................................................................................................144
Batch system and keywords ...............................................................................................................................................152
Error handling ..... ...............................................................................................................................................................165
Chapter 7 - Keywords ................................................................................................................... 167
PVTi keywords.... ...............................................................................................................................................................167
Keywords A-D..... ...............................................................................................................................................................168
ACF: Acentric factors......................................................................................................................................................... 169
ACHEUH: A-coefficient for Cheuh-Prausnitz BICs ............................................................................................................ 170
ALLDRY: Dry Gas Tables for Each Sample ...................................................................................................................... 171
PVTi Reference Manual
Table of Contents
3
BIC: Binary interaction coefficients .................................................................................................................................... 172
BLACKOIL: Start of the BLACKOIL section....................................................................................................................... 174
CALVAL: Specify calorific values....................................................................................................................................... 175
CHARACT: Components to be characterized.................................................................................................................... 176
CNAMES: Component names ........................................................................................................................................... 177
COATS: Blackoil tables...................................................................................................................................................... 178
COMB: Start of the COMB section .................................................................................................................................... 179
COMBINE: Group existing components ............................................................................................................................ 180
CORRACF: Splitting correlation for ACFs ......................................................................................................................... 181
CORRCP: Splitting correlation for critical properties ......................................................................................................... 182
DRYGAS: Dry gas tables................................................................................................................................................... 183
DEADOIL: Dead oil tables ................................................................................................................................................. 184
DEBUE: Select output to debug file ................................................................................................................................... 185
DEBUG: Select output to debug file................................................................................................................................... 186
DEFBIC: Default binary interaction coefficients ................................................................................................................. 187
DEGREES: Temperature convention ................................................................................................................................ 188
DIFFERENTIAL: Blackoil tables ........................................................................................................................................ 189
DREF: Reference densities ............................................................................................................................................... 190
Keywords E-K ..... ...............................................................................................................................................................191
ECHO: Insert PVI file into PVP file..................................................................................................................................... 192
EOS: Defines the required Equation of State .................................................................................................................... 193
EOSOUT: EoS data for ECLIPSE 300............................................................................................................................... 194
EXP: Experiments.............................................................................................................................................................. 195
EXPIND: Set Status of Experiments .................................................................................................................................. 200
FIT: Perform fit by regression ............................................................................................................................................ 201
FRAC: Specify plus fraction data ....................................................................................................................................... 202
FRAGOR: Blackoil tables................................................................................................................................................... 203
FVFREF: FVF reference conditions................................................................................................................................... 204
GI: Define GI nodes for E200 tables .................................................................................................................................. 205
GROUP: Start of the GROUP section................................................................................................................................ 206
GRBYALL: Start of the GROUP section ............................................................................................................................ 207
GRBYMIX: Start of the GROUP section ............................................................................................................................ 208
GRBYSAM: Start of the GROUP section........................................................................................................................... 209
GRPBYWGT: Grouping by molecular weight .................................................................................................................... 210
HYDRO: Define component as hydrocarbon or non-hydrocarbon..................................................................................... 211
KVTABLE: Request K-value table for ECLIPSE 300 output .............................................................................................. 212
Keywords L- O .... ...............................................................................................................................................................213
LBC: Lohrenz-Bray-Clark viscosities ................................................................................................................................. 214
LBCCOEF: Set non-default LBC coefficients..................................................................................................................... 215
LIVEOIL: Live oil tables ..................................................................................................................................................... 216
LNAMES: Specify library names........................................................................................................................................ 217
MAXIT: Max. number of regression iterations.................................................................................................................... 218
MAXSTEP: Maximum step size allowed in regression ........................................................................................................ 219
MDP: Data for Whitson splitting ......................................................................................................................................... 220
MESSAGE: Echo message to file and screen ................................................................................................................... 221
MINDELP: Minimum pressure difference........................................................................................................................... 222
MINSTEP: Minimum step limit allowed in regression ........................................................................................................ 223
MIX: Mix samples............................................................................................................................................................... 224
MODSPEC : Denotes start of the run specification section ............................................................................................... 225
MODSYS : Start of the MODSYS section......................................................................................................................... 226
MOSES : Blackoil tables................................................................................................................................................... 227
MW : Specify molecular weights....................................................................................................................................... 228
MWS : Define plus fraction mole weight for CMF splitting................................................................................................ 229
NCOMPS : Specify number of components ..................................................................................................................... 230
NEWPVI : Request new output PVI file ............................................................................................................................ 231
NEWPVO : Request new output PVO file......................................................................................................................... 232
NOECHO : No insertion of PVI file into PVP file ................................................................................................................ 233
OBS : Specify observations .............................................................................................................................................. 234
OBSIND : Specify observation weights ............................................................................................................................ 235
4
PVTi Reference Manual
Table of Contents
OMEGAA/B: Specify EoS omega values........................................................................................................................... 237
OPTIONS : Set various program options ......................................................................................................................... 238
OUTECL3 : Start of the OUTECL3 section ...................................................................................................................... 240
Keywords P- S .... ...............................................................................................................................................................241
PARACHOR : Define parachors ........................................................................................................................................ 242
PCRIT : Critical pressures ................................................................................................................................................ 243
PEARCE : Blackoil tables................................................................................................................................................. 244
PEDERSEN : Specify Pedersen viscosities ..................................................................................................................... 245
PRCORR : Peng-Robinson correction ............................................................................................................................. 246
PSEUCOMP : Start of the PSEUCOMP section.................................................................................................................. 247
RECOVERY : Liquid production for recovery estimates................................................................................................... 248
REGRESS: Start of the REGRESS section....................................................................................................................... 249
REGTARG : Regression target ........................................................................................................................................ 250
RTEMP : Reservoir temperature for ECLIPSE Compositional ......................................................................................... 251
RUNSPEC : Denotes start of the run specification........................................................................................................... 252
SALINITY : Specify sample salinity ................................................................................................................................. 253
SAMPLE : Specify fluid sample ........................................................................................................................................ 254
SAMPLES : Specify fluid samples.................................................................................................................................... 255
SAMPLES : Specify fluid samples.................................................................................................................................... 256
SAMTITLE : Specify titles of fluid samples....................................................................................................................... 257
SAVCOMP : Save compositions ...................................................................................................................................... 258
SCT : Defines Semi-Continuous Thermodynamics split................................................................................................... 259
SG : Specify specific gravity ............................................................................................................................................. 260
SIMULATE : Start of the SIMULATE section.................................................................................................................... 261
SPECHA-D: Specify specific heat capacity coefficients .................................................................................................... 262
SPLIT : Start of the SPLIT section................................................................................................................................... 263
SSHIFT : Dimensionless volume shifts for PR3 ................................................................................................................ 264
STCOND : Standard conditions......................................................................................................................................... 265
SYSTEM : Start of the SYSTEM section ........................................................................................................................... 266
Keywords T - Z ... ...............................................................................................................................................................267
TBOIL : Specify boiling points .......................................................................................................................................... 268
TCRIT : Specify critical temperatures............................................................................................................................... 269
THERMX : Thermal expansion coefficient for volume shifts............................................................................................... 270
TITLE : Specify run title ................................................................................................................................................... 271
TLOW : Define lowest temperature for VFP tables ............................................................................................................ 272
TREF : Specify reference temperatures............................................................................................................................ 273
UNITS : Specify unit conventions ..................................................................................................................................... 274
VAR : Specify regression variables ................................................................................................................................... 275
VCRIT : Specify volumes.................................................................................................................................................. 278
VCRITVIS : Specify volumes for LBC viscosity calculations ........................................................................................... 279
VERSION : Version of PVTi .............................................................................................................................................. 280
VFP : Start of the VFP section .......................................................................................................................................... 281
WAT100 : Output water properties .................................................................................................................................... 282
WAT200 : Output water properties .................................................................................................................................... 283
WAT300 : Output water properties .................................................................................................................................... 284
WATVFP : Output water properties .................................................................................................................................... 285
WETGAS : Wet gas tables.................................................................................................................................................. 286
WHIT : Defines Whitson splitting....................................................................................................................................... 287
WHITSON : Blackoil tables ................................................................................................................................................ 288
X/YMFVP: XMFVP and YMFVP ECLIPSE tables .............................................................................................................. 289
ZCRIT : Specify critical Z-factors...................................................................................................................................... 290
ZCRITVIS : Specify critical Z-factors for LBC calculations .............................................................................................. 291
ZI : Specify sample composition...................................................................................................................................... 292
ZMFVD : Composition versus depth table ......................................................................................................................... 293
Chapter 8 - Technical Description ............................................................................................... 295
Overview............. ...............................................................................................................................................................295
Theoretical background of PVT ..........................................................................................................................................296
PVTi Reference Manual
Table of Contents
5
Equation of state . ...............................................................................................................................................................317
Basic laboratory experiments..............................................................................................................................................339
Regression ......... ...............................................................................................................................................................348
Output for ECLIPSE simulators ..........................................................................................................................................354
Analysis techniques ............................................................................................................................................................371
Recommended PVT analysis for oil reservoirs ...................................................................................................................372
Recommended PVT analysis for gas condensate reservoirs .............................................................................................377
Consistency tests and correlations .....................................................................................................................................381
Fluid Properties Estimation .................................................................................................................................................384
Regression in PVT analysis ................................................................................................................................................386
Wax and asphaltene precipitation in PVTi ..........................................................................................................................394
Cleaning samples contaminated with oil-based mud..........................................................................................................398
Mixing and recombination of samples.................................................................................................................................400
ECLIPSE Thermal Export Module ......................................................................................................................................401
Appendix A - Units........................................................................................................................ 409
Units.................... ...............................................................................................................................................................409
Appendix B - Symbols.................................................................................................................. 413
Symbols .............. ...............................................................................................................................................................413
Appendix C - Bibliography........................................................................................................... 415
Appendix D - Index ....................................................................................................................... 421
6
PVTi Reference Manual
Table of Contents
List of Figures
Figure 5.1 ..........
Figure 5.2 ..........
Figure 5.3 ..........
Figure 5.4 ..........
Figure 5.5 ..........
Figure 5.6 ..........
Figure 5.7 ..........
Figure 5.8 ..........
Figure 5.9 ..........
Figure 5.10 ........
Figure 5.11 ........
Figure 5.12 ........
Figure 6.1 ..........
Figure 6.2 ..........
Figure 6.3 ..........
Figure 6.4 ..........
Figure 6.5 ..........
Figure 6.6 ..........
Figure 6.7 ..........
Fingerprint Plot .......................................................................................................................................39
Phase Plot ..............................................................................................................................................40
The plotted simulation results .................................................................................................................45
Plot of Oil FVF, Viscosity and Rs versus pressure for the output black oil property tables ....................55
Phase Diagram for Schrader Bluff Fluids ...............................................................................................70
The phase envelope plot. .......................................................................................................................78
The main display shows messages indicating the quality of the data.....................................................79
The main plot window after zooming in ..................................................................................................80
The plot of k values versus pressure. .....................................................................................................81
The Hoffman-Crump plot ........................................................................................................................82
Hoffman-Crump-Hocott plot. ...................................................................................................................83
The original sample, the cleaned sample and the estimated contaminant. ............................................85
The main PVTi window ...........................................................................................................................91
Fingerprint Plot .....................................................................................................................................109
Phase plot.............................................................................................................................................110
Ternary Plot .........................................................................................................................................111
Main display after performing material balance ....................................................................................113
COMB module - vapor versus pressure plot ........................................................................................114
The VFP module...................................................................................................................................138
PVTi Reference Manual
List of Figures
7
List of Tables
Table 5.1
Table 5.2
Table 5.3
Table 5.4
Table 5.5
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Table 6.9
Table 6.10
Table 6.11
Table 6.12
Table 6.13
Table 6.14
Table 6.15
Table 6.16
Table 6.17
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 7.5
Table 7.6
Table 7.7
Table 7.8
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 8.5
Table 8.6
Table 8.7
Table 8.8
Table 8.9
Table 8.10
Table 8.11
Table 8.12
Table A.1
Table A.2
Table A.3
8
The Fundamentals panel .........................................................................................................................34
Component and fluid definitions...............................................................................................................36
Program Options data ..............................................................................................................................38
Constant Composition Expansion experiment at 220o F (* indicates bubble point pressure)..................43
Differential Liberation Experiment at 220o F (* indicates bubble point pressure).....................................46
List of library components ........................................................................................................................95
Observation data....................................................................................................................................123
Set PVTi Program Options panel ...........................................................................................................145
Keywords for introducing sections .........................................................................................................156
RUNSPEC keywords .............................................................................................................................156
SYSTEM keywords ................................................................................................................................157
SPLIT keywords .....................................................................................................................................158
GROUP keywords..................................................................................................................................159
COMB keywords ....................................................................................................................................159
SIMULATE keywords .............................................................................................................................160
REGRESS keywords .............................................................................................................................160
BLACKOIL keywords .............................................................................................................................161
PSEUCOMP keywords ..........................................................................................................................162
OUTECL3 keywords ..............................................................................................................................162
VFP keywords ........................................................................................................................................163
APITRACK keywords .............................................................................................................................163
Error codes ............................................................................................................................................165
Output indices ........................................................................................................................................185
Output indices ........................................................................................................................................186
Required data for experiments...............................................................................................................195
Keyword arguments ...............................................................................................................................196
Restrictions for EXP keyword arguments...............................................................................................198
Component Types..................................................................................................................................211
Equation of State omega values ............................................................................................................237
Default limits for variables ......................................................................................................................276
Alkanes ..................................................................................................................................................298
Napthenes..............................................................................................................................................299
Aromatics ...............................................................................................................................................299
Physical properties.................................................................................................................................300
Multi-component (ii) mixtures .................................................................................................................300
CVD Report............................................................................................................................................309
Equation of State coefficients ................................................................................................................319
Equation of State constants ...................................................................................................................320
Parameter estimation data. N is the number of experimental points .....................................................335
Parameter Values for Pure Component Viscosity Correlation ...............................................................336
Physical Properties of Methane and Decane .........................................................................................337
PVTi defaults for Fluid Property Estimation ...........................................................................................385
Units .......................................................................................................................................................410
Constants ...............................................................................................................................................411
Conversion factors .................................................................................................................................411
PVTi Reference Manual
List of Tables
Developments
Chapter 1
Product Maintenance
Maintenance of this application is continuing until further notice.
PVTi Reference Manual
New developments
Product Maintenance
9
Developments for 2004A
ECLIPSE Thermal Export facility
For the 2003A version of PVTi a new ECLIPSE Thermal support module was available where
you were able to interactively develop a correlation which accurately predicted K-values for
each component in a given fluid. For the 2004A version this module has been extended to a full
export facility where you can write out files that are suitable for use as PVT input for ECLIPSE
Thermal. The motivation behind this is so that, just as you can export files to use as PVT input
for ECLIPSE BlackOil and ECLIPSE Compositional, they will now be able to do the same for
ECLIPSE Thermal.
PVTi will export a series of keywords when an export for ECLIPSE Thermal is performed. For
a workflow description and brief summary of these keywords see "Compositional Data for
ECLIPSE Thermal" on page 366. For a more technical outline of how the exported keywords
are used in ECLIPSE Thermal see "ECLIPSE Thermal Export Module" on page 401.
Export for API Tracking option in ECLIPSE
BlackOil
The API Tracking facility enables ECLIPSE BlackOil to model the mixing of different types of
oil, having different surface densities and PVT properties.
Without the API Tracking facility, the presence of different types of oil in the reservoir could be
handled with the aid of PVT region numbers. Oil in PVT region 1 would have its properties
determined from PVT table number 1, and so on. However, this method cannot model the
mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on the
properties associated with region 2.
The API Tracking facility essentially replaces the concept of PVT regions for oil. The PVT
tables used for determining the oil properties are selected at each time step according to the
average API of the oil in each grid block (or to be more precise, its average surface density).
For a overview of the workflow involved to export PVT tables suitable for use in ECLIPSE
BlackOil with the API Tracking option turned on see "Export for API Tracking option in
ECLIPSE BlackOil" on page 134. For a more technical description of the API Tracking model
in ECLIPSE as well as an explanation of how PVTi calculates suitable PVT tables see "Model
for API Tracking option in ECLIPSE BlackOil" on page 363.
Batch Mode
For the 2004A version of PVTi the batch mode has undergone a significant revamp. Over the
last few years the user interface of PVTi has evolved rapidly and the existing batch mode facility
no longer adequately supports more recent functionality. There have been 3 significant
modifications to the PVTi batch mode:
1
10
The way a batch mode is executed has changed. The new way to launch a batch mode run
on a PC is to use the command $pvti -batch filename where filename is the
name of your PVTi project. See "General information" on page 152 for more details on
running batch mode with other platforms.
New developments
Developments for 2004A
PVTi Reference Manual
2
The new batch mode now supports the majority of the functionality available in interactive
mode - namely splitting, grouping, regression, experiment simulation and export. Export
for ECLIPSE Thermal, PNA splitting and material balance checks are not currently
supported. For more details on the functionality constraints of the batch mode see
"Constraints on the workflow" on page 154.
3
It was felt that a more user friendly way of constructing the .PVI files suitable for batch
mode was needed since a batch mode file requires some extra sections than a standard
interactive mode PVI file does. A new option called Write Keywords for Batch Mode is
available on the Options panel. If this is turned on and a workflow is performed in
interactive mode and then the file saved, PVTi ensures that this file is then suitable for use
in a batch mode run. The batch mode run then reproduces the workflow and results that
were obtained in interactive mode. See"Preparing Batch Mode Files in Interactive Mode"
on page 153 for a detailed explanation of this facility.
For an overview of all aspects of the new batch mode facility see "Batch system and keywords"
on page 152.
Panel Addition/Modification
1
There is a new LBC Viscosity Coefficients panel available under the menu option Edit |
Fluid Model | LBC Viscosity Coefficients.... This panel shows, if using the LorentzBray-Clark (LBC) viscosity model, the current values of the five coefficients.
2
The Thermal Properties panel has been modified to include the new properties introduced
as a result of the new ECLIPSE Thermal export functionality. Specifically, the properties
Heat Cap. A and Heat Cap. B have been changed to Heat Cap. A/G and Heat Cap. B/H.
There is also a new property called Heat of Vaporization which corresponds to the
HEATVAPS keyword exported for ECLIPSE Thermal.
Component Constraints
1
It is now possible to read in projects where fluid samples can have up to 100 components.
However, no functionality involving the EoS flash can be used until a group operation has
been performed in order to reduce the number of components in all samples to <=50.
2
Two new components are available in the PVTi library - Benzene (C6H6) and Toluene
(C7H8). The short names for use in the fundamentals or components panel are BEN for
Benzene and TOL for Toluene. See "Library" on page 95 to view the components in the
PVTi library. To view the library within PVTi itself use the View | Library option.
New Keywords and sections
Keywords
There are two new keywords in PVTi 2004A.
1
EXPIND.
This is a list of integers - one for each experiment defined in the project - which specify whether
an experiment should be used (‘turned on’) or not used (‘turned off’) when performing a
regression.
PVTi Reference Manual
New developments
Developments for 2004A
11
2
HEATVAPS.
This keyword is used to store the Heat of Vaporization at the standard temperature for each
component.
Sections
There is a new section called APITRACK. This is used when preparing batch files if the API
Tracking export facility is to be made use of in batch mode. It is essentially the same as the
BLACKOIL section but has an extra keyword called SAMPLES, which records the samples for
which PVT tables will be exported.
Manual
12
1
The section "The Most Asked Questions About PVTi" on page 13 has been updated with
questions regarding the Batch Mode, ECLIPSE Thermal Export and API Tracking
functionality.
2
A number of the tutorials have been amended - in particular the tutorial entitled “Using the
ECLIPSE Thermal Support Module” has been replaced by a tutorial called "Exporting an
ECLIPSE Thermal model" on page 73.
New developments
Developments for 2004A
PVTi Reference Manual
The Most Asked Questions
About PVTi
Chapter 2
Introduction
This section has been designed as a reference section so that you can quickly access information
about common problems encountered with PVTi without having to spend time looking through
the manual for the relevant section. The questions in this section have been constructed using
the most common support issues and also the InTouch database. Cross-references are provided
where necessary so that readers can access the appropriate parts of the manual for more detailed
information on a particular topic if required.
The questions are:
•
"What is PVTi used for? Why do we need it?" on page 14
•
"Where do I start? How do I set up a project within PVTi?" on page 14
•
"How do I create an experiment along with a series of observations?" on page 15
•
"What are the data limitations in PVTi?" on page 16
•
"What is the Fluid Properties Estimation facility in PVTi?" on page 17
•
"How do I perform regression on multiple fluid samples?" on page 17
•
"What regression parameters should I choose?" on page 19
•
"What is the difference between normal regression, special regression and automatic (PVTi
selects) regression?" on page 18
•
"How does PVTi support gas condensate simulation?" on page 20
•
"Can Black Oil tables be extended above the liquid bubble point in PVTi?" on page 20
•
"Can PVTi be used if you know the composition of a fluid but do not have any
observations? And vice-versa?" on page 20
•
"What black oil correlations are available in PVTi?" on page 21
•
"How do I generate the asphaltene phase envelope using PVTi?" on page 21
•
"How does PVTi support ECLIPSE Thermal?" on page 22
•
"How do I Use PVTi’s Batch Mode?" on page 23
PVTi Reference Manual
The Most Asked Questions About PVTi
Introduction
13
•
"How Can I Export PVT Tables to use the API Tracking Functionality in ECLIPSE
BlackOil?" on page 23
What is PVTi used for? Why do we need it?
PVTi is a compositional PVT equation-of-state based program used for characterizing a set of
fluid samples for use in our ECLIPSE simulators.
We need PVTi because it is vital that we have a realistic physical model of our reservoir fluid
sample(s) before we try to use them in a reservoir simulation. PVTi can be used to simulate
experiments that have been performed in the lab on a set of fluid samples and then theoretical
predictions can be made of any observations that were performed during a lab experiment, in
order that we can test the accuracy of our fluid model.
Any differences between the measured and calculated data are minimized using a regression
facility which adjusts various Equation of State parameters. This ‘tuned’ model is then exported
in a form suitable for one of our ECLIPSE simulators.
What is especially important to note when using the ECLIPSE Compositional simulator is that
PVTi and ECLIPSE Compositional use the same flash algorithm. This is vital as the flash has
been used to simulate the experiments and predict values for experimental observations and is
therefore inherent within the fluid model itself which has been exported by PVTi. If ECLIPSE
Compositional used a different flash then the fluid model exported by PVTi would no longer be
valid.
Where do I start? How do I set up a project within
PVTi?
Defining a Fluid Sample
If you want to open a new project then start PVTi as instructed in "Getting started" on page 29
for your machine-type and choose a filename. PVTi starts; recognizes that it has a new project
and immediately opens the Fundamentals panel. This panel has been specifically designed to
make setting up a new project as easy as possible. Simply fill in the Components and ZI
columns with the component names and mole fractions respectively, which is the minimum
required to have a project within PVTi.
To fill in the component names simply type the standard shorthand names for the components
in your fluid, for example, C1, N2, CO2, H2S, IC5, etc. For more information on shorthand
names and component types see "Component types" on page 102. The mole fractions can be
entered as fractions or percentages by selecting the appropriate option on the panel. Also,
weight fractions/percentages can be entered for the components instead of mole fractions/
percentages.
Your Mole/Weight data must add up to 1 if entering as fractions and up to 100 if entering as
percentages. If they do not then PVTi asks you if you want it to renormalize your data when you
close the Fundamentals panel. If you want to add some components then select No,- otherwise
select Yes.
Warning
14
If you try to perform operations on a fluid with incorrectly normalized mole/
weight fractions then the operation may fail.
The Most Asked Questions About PVTi
Introduction
PVTi Reference Manual
Once the Fundamentals panel has been completed you will see have a sample called ZI on the
tree view on the left-hand side of the main window.This is the fundamental sample for the
project and the name ZI cannot be changed.
Creating Other Fluid Samples
Other fluid samples can be created in a project by selecting Edit | Samples | Name... . Simply
type in the name of the new fluid sample you want to create. The composition information can
then be entered for this fluid by selecting the Edit | Samples | Compositions... option.
Additional fluid samples to the project must always be subsets of the ZI sample in terms of the
component names, for example you cannot have a C8 component in an additional fluid sample
called OIL if C8 was not defined in the ZI sample. If you open the Edit | Samples |
Compositions... panel you can see why this has to be the case in PVTi.
Note
Just because a component is defined in the ZI sample it does not mean there has to be
any of it there. It only has to be defined in the ZI sample to be used in other fluid
samples. If the mole fraction of a C8 component in the ZI sample is set to be 0.0 then
the C8 component can then be use in the OIL sample and the mole fractions set as
required.
Once at least one fluid sample (the ZI sample) has been defined then any experiment supported
within PVTi can be simulated as well as operations such as phase plots, fingerprint plots and
splitting.
For more information on creating fluid samples see "Defining Samples" on page 107.
How do I create an experiment along with a series
of observations?
Creating Experiments
To create an experiment select the Edit | Experiments... option and the experiment Entry panel
opens. The existing experiments are listed and you can edit them by selecting one of them and
clicking the next button. To create a new experiment click add in the top left of the panel and
select the experiment you wish to create. Choose the fluid sample you want to perform the
experiment on and then navigate through the panels by filling in the required information and
then clicking next, which takes you to the next panel. The information generally consists of
temperature and/or pressure information but not always, it depends on the experiment.
Once an experiment has been created an experiment button, along with an experiment name,
appears below the fluid sample which the experiment was performed on.
Creating Observations
If there are no observations at all for a particular experiment then to create one you need to select
the Edit | Observations... option and the Observations panel appears.
On the Experiments column on the left-hand side there is a list of all the experiments that are
available within PVTi and * symbols are next to the ones that you currently have defined within
your project.
PVTi Reference Manual
The Most Asked Questions About PVTi
Introduction
15
If one of these experiments is selected then in the Experiment List column a list of all the names
of the experiments of that type in your project appears for example, BUBBLE5, DEW3, DL1.
If one of these is selected then all the possible observations available within PVTi for that type
of experiment are displayed in the Observation Type column. Again observation types with a
* next to them means that there are values already defined for this particular experiment in your
project. Simply click on one to see and edit the values. To create a new observation select the
one you want and then click on the + button on the top left of the panel. Values and weights can
then be entered for the observation.
Note
Currently defined observations for an experiment can be edited in the Observations
folder on the experiment Entry panel.
For more information on creating and editing experiments/observations see "Simulation using
PVTi" on page 117 and/or the tutorial "Simulating experiments" on page 42.
What are the data limitations in PVTi?
Pre-2003A
Up to and including the 2002A_1 release (pre-2003A) the following data constraints were
present in PVTi:
•
50 fluid samples
•
50 components per fluid sample* (see below)
•
50 experiments per fluid sample
•
300 observations per experiment
Note
*When a splitting operation was performed it was possible to have more than 50
components (up to 100 in fact) but the components had to be grouped back so that there
were less than 50 before any experiment simulation could take place.
2003A
These pre-2003A data constraints have been present in PVTi for 4 to 5 years and, in-line with
the huge increase in computing power in the last few years, we have decided to enhance the data
constraint capability of PVTi so that the following is now available:
•
100 fluid samples
•
100 components per fluid sample* (see below)
•
100 experiments per fluid sample
•
300 observations per experiment
Note
16
It is now possible to read in, save, split and group with fluids containing up to 100
components. However, the limit is still 50 components for any functionality involving
the EoS flash.
The Most Asked Questions About PVTi
Introduction
PVTi Reference Manual
What is the Fluid Properties Estimation facility in
PVTi?
The Fluid Properties Estimation (FPE) facility in PVTi is designed so that it can be used when
you have minimal data at your disposal, at the well-site for example. In this scenario, a full lab
analysis of multiple fluid samples from the reservoir has not yet been performed. Typically, just
a single sample would be available and minimal fluid behavior known for example, saturation
pressure at a particular temperature.
Specifically, the FPE facility assumes that a single fluid sample with compositional information
is available which includes a single plus fraction (for example C7+) component of which the
weight fraction is known. Typically, this weight fraction data is fairly accurate but the mole
weight, which is used to characterize the critical properties of the plus fraction, is not. The FPE
functionality allows you to perform a quick look simulation that regresses on the mole weight
of the plus fraction, and keep the weight fraction constant, in order to fit to a saturation pressure
observation at a particular temperature.
The FPE facility is available in the top right-hand corner of the fundamentals panel whenever a
new project is created. Alternatively it can be accessed using the Edit | Properties Estimation
(FPE)... option. For more information on this facility see "Fluid Properties Estimation" on
page 384. For an example of how it works see the tutorial "Fluid Properties Estimation" on
page 33.
How do I perform regression on multiple fluid
samples?
General
The fluid samples that PVTi performs regression on is determined by the structure of the tree
view on the left-hand side. By default, PVTi performs a regression on every experiment which
has observations defined, even if there are multiple fluid samples, each with their own
experiments. The reason for this is that, within a project, all fluid samples are considered to be
relevant to each other and so the same fluid model should be applied to all samples, even if the
compositional make-up of each sample is different
Note
If two of your fluid samples are not relevant to each other for example they come from
different wells/reservoirs then a separate project should be created for each one.
Disabling Experiments/Observations
You can prevent PVTi from including an experiment in the regression by right-clicking on the
experiment and selecting Don’t use in Regression. A cross appears on the experiment
indicating it is not currently available within the regression facility.
You can disable an observation so that it is not used within the regression by again right-clicking
and selecting Don’t use in Regression. Alternatively, by right-clicking and selecting Set
Weight and then entering zero the observation is also not included in the regression.
PVTi Reference Manual
The Most Asked Questions About PVTi
Introduction
17
Note
If an experiment is disabled then, as you would expect, all the observations are
automatically disabled.
Regression Weights
In general there will be a set of values in an observation. For example, if we have a differential
liberation (DL) experiment defined then a viscosity observation would have a value for each
pressure. We have two types of weight: there are single weights for each value of an observation
and global weights that apply to every value in an observation.
By right clicking on an experiment observation the global weight can be set. As mentioned
above, by setting this to zero none of the values in the observation would be used. Alternatively,
you may want to set a global weight for an experimental observation particularly high, for
example, matching the bubble point of a fluid is normally very important if one wants to ensure
that it is a single-phase liquid at the temperature and pressure of the reservoir.
Or maybe you do not trust the accuracy of a particular observation value, for example an oil
formation volume factor (FVF) value in a DL experiment.You may then not want to use a global
weight as all the other observation values look ok. In this case setting a single-value weight to
a very low value helps you match all the other values in the observation during regression as the
rogue, inaccurate value no longer inhibits convergence.
Both the single-value and global weights for an experimental observation can be set in the
Observations panel by selecting the Edit | Observations... option, highlighting the
appropriate observation and then simply typing in your chosen weights.
For a good example of how to use the regression facility, see the tutorial "Fitting an equation of
state to experimental results" on page 49.
What is the difference between normal regression,
special regression and automatic (PVTi selects)
regression?
There are 3 types of regression: normal, special and automatic. The difference between them
depends entirely on what kind of variables are being regressed on.
Normal regression parameters are equation of state variables relating to a particular component,
for example, critical pressure, P c , critical temperature, T c , acentric factor, ω . and the binary
coefficients. The full set of normal regression variables can be viewed using the regression
panel using the Run | Regression... panel. Select normal as the regression type and then click
variables - the upper table shows the single-valued normal regression parameters for each
component and the lower panel shows the binary coefficients table. For more information on
setting normal regression see "Setting normal variables" on page 127.
Special regression parameters are global Equation of State variables, for example, the thermal
expansion coefficient or the Cheuh-Prausnitz A factor for binary coefficients. There may also
be some splitting parameters available as special regression variables depending on whether a
multi-feed split has been performed on the plus fraction. See "Multi-feed Split (also called semicontinuous thermodynamic (SCT) split)" on page 106 for more details on this facility. For more
information on setting special regression variables see "Setting special variables" on page 128.
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The Most Asked Questions About PVTi
Introduction
PVTi Reference Manual
The automatic regression facility or PVTi Selects as it is called on the Regression panel
attempts to choose the best normal variables to regress on for you before actually doing the
regression and reporting the answer. It should be noted that there is no substitute for a good
engineer in the sense that one should not just use this automatic facility all the time in the belief
that PVTi will do all the work. For example, the automatic facility will not use special variables
to regress on and so it is up to you to decide whether this would be necessary or not.
However the automatic facility can still be a useful tool in obtaining a good match to PVT data.
The way the algorithm chooses the regression parameters is essentially based on 2 criterion. No
parameters are allowed to have more than a 90% correlation on any other parameter. Secondly,
no parameter is allowed to have less than 1% of the sensitivity of the most sensitive parameter
For a detailed discussion of the automatic regression algorithm see "A consistent methodology
that can be applied automatically" on page 389.
For more general information on the regression facility see "Regression in PVTi" on page 126.
What regression parameters should I choose?
It should be noted that there are no concrete rules for getting a good match to observations
relating to multiple fluid samples, but there are some general guidelines of what is often a good
idea, and what you should definitely not do.
Library components tend to have properties that are very well known and any of these will not
normally be good choices of regression variables. Properties of non-library components and
characterized components are much less well known and these are often good choices. In
general, the following set of variables are normally good things to initially regress on:
•
P c, T c and ω of any non-library component.
•
P c, T c and ω of any component with mole weight of C7 or heavier (as these are effectively
mixtures of different molecule types and so may differ from library values).
•
Ω A and Ω B of any component with mole weight C7 or heavier. Again because these are
mixtures.
•
No binary inter-active coefficients because of the risk of over-fitting.
•
No viscosity-specific parameters, again because of the risk of over-fitting.
The variables mentioned above are all normal regression variables. The following set of special
regression variables can also often prove useful to get a match between samples:
•
Do a multi-feed split to split the plus fraction into 2 or 3 pseudo-components. The α ,
SCTMW and Kw parameters, which control the splitting are then very good choices.
•
The Cheuh-Prausnitz A binary parameter if using Cheuch-Prausnitz binaries.
•
The mole weight of a plus fraction (if no split on the plus fraction has been performed).
For a detailed explanation of why some of the above are good and bad choices for regression
parameters, see "Regression in PVT analysis" on page 386. There are also more specific
guidelines for choosing regression parameters depending on whether one is dealing with an oil
reservoir, see "Recommended PVT analysis for oil reservoirs" on page 372 - or a gascondensate reservoir, see "Recommended PVT analysis for gas condensate reservoirs" on
page 377.
Finally, for a tutorial illustrating the use of the normal and special regression facilities in a
typical workflow see the new "Workflow Tutorial" on page 61.
PVTi Reference Manual
The Most Asked Questions About PVTi
Introduction
19
How does PVTi support gas condensate
simulation?
Gas condensate simulation is modeled in PVTi using the Constant Volume Depletion (CVD)
experiment. In most gas condensate reservoirs liquid does reach a high enough saturation to
become mobile as the pressure drops. Thus, gas and oil, to a good approximation, do not move
with respect to each other and so the CVD experiment models this behavior very well. Other
experiments that tend to be used for gas condensates are the dew point and constant composition
expansion experiments. For more information see "Gas condensate systems" on page 341.
A common failing when analyzing gas condensate reservoirs is to attempt to establish an
equation of state representation without a through examination of the data on which it is to
based. Things to check in the data are the characteristics of the heavy components (use a
fingerprint plot), material balance information and other information such as K-values and Zfactors. Once you are happy with the data that you will try to match there is a recommended
procedure, in terms of regression, which will work for most gas condensates. For a detailed
description on how to model gas condensates see the section entitled "Recommended PVT
analysis for gas condensate reservoirs" on page 377.
Can Black Oil tables be extended above the liquid
bubble point in PVTi?
Yes. You should make sure that the DL/CVD experiment you simulate in PVTi covers the full
range of pressure values you are likely to encounter within your reservoir. If ECLIPSE BlackOil
encounters a pressure outside the range in the black oil table you exported from PVTi then it
will have no choice but to try to extrapolate to estimate properties such as gas-oil ratio (GOR)
and formation volume factor (FVF). The extrapolation used is linear and uses the appropriate
quantities at the two highest pressures in the exported black oil table.
However, this extrapolation can sometimes run into difficulties as is common in any problem
when you are trying to gain information about unexplored parameter space. The normal error is
that ECLIPSE throws up negative compressibilities for your fluid. If this happens then be sure
to check your black oil tables covered the appropriate range of pressures.
For a thorough description of the black oil model used by PVTi and how the tables are extended
above the bubble point see "Blackoil model" on page 354.
Can PVTi be used if you know the composition of
a fluid but do not have any observations? And
vice-versa?
You know the fluid composition
If you have compositional information about the fluid, but no observations, then you can do
anything you want within PVTi except use the Regression facility. This is because the
Regression facility tries to minimize the differences between lab observations and PVTi’s
theoretical predictions and this is not a sensible operation if no observations are defined.
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The Most Asked Questions About PVTi
Introduction
PVTi Reference Manual
In fact, in PVT laboratories engineers tend to use the default fluid model (one that has not been
regressed on) for a given equation of state in PVTi to give them a ‘ball-park’ answer for their
particular experimental observation. This can give them some idea as to how to set their
experiment up as they now have information on the kind of answers they might expect to
measure.
You have observations
If you have observations but no compositional information at all then PVTi does have the
facility to convert black oil tables into a fully compositional model. To do this you must have
black oil tables that were exported by PVTi using the 2002A release or later. The tutorial entitled
"Converting a black oil run to compositional" on page 58 will explain this workflow in more
detail.
Note
If you have black oil tables exported from before and including 2001A_2 PVTi, or you
have no black oil tables at all then, unfortunately, PVTi will not be able to construct the
compositional model for you. !
What black oil correlations are available in PVTi?
PVTi is a compositional PVT program and at the moment does not support black oil correlations
within its functionality.
It can however export a black oil model, using the compositional model tuned by the user within
PVTi to a DL or CVD experiment, for the ECLIPSE BlackOil simulator by generating tables of
Rs, FVF, etc. as a function of pressure for a given reservoir temperature. To export a black-oil
model select File | Export Keywords... . If you want to export a black oil table from a DL
experiment then you generally use the Oil Reservoir... menu option and if you have a CVD
experiment then the Gas Reservoir...option is appropriate. For more information on exporting
keywords see the section entitled "Exporting keywords" on page 133.
How do I generate the asphaltene phase envelope
using PVTi?
Just like a phase curve has single phase regions for the vapor and liquid and a 2-phase region an
asphaltene phase envelope may exist for your fluid. The asphaltene phase envelope partitions
off a region in pressure-temperature space where an asphaltene phase exists, analogous to the
two-phase region in a standard phase curve.
The upper line partitioning a region in pressure-temperature space where an asphaltene phase
does and does not exist is called the Asphaltene Disappearance Pressure (WDP) line. The lower
line is called the Asphaltene Appearance Pressure (WAP) line. In PVTi 2003A both curves are
supported, whereas in PVTi 2002A/2002A_1 just the functionality for the appearance line is
available.
Unlike a standard phase curve though where, as long as you do not have a fluid consisting of a
single pure component, there will always be a two-phase region, this is not the case in terms of
an asphaltene phase envelope. Asphaltene may never be present no matter what temperature and
pressure your fluid is at.
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The Most Asked Questions About PVTi
Introduction
21
In order to try to generate one of the asphaltene curves a PNA split must first be performed on
the heaviest component/pseudo component. To do this select Edit | Fluid Model | Split | PNA
Distribution..., which does this split for you using correlations from within PVTi.
Now, to create the curve an asphaltene appearance/disappearance experiment must be
performed. This can be done using the instructions in this section on "How do I create an
experiment along with a series of observations?" on page 15. In the experiment entry panel tick
the appropriate box depending on whether you want the asphaltene disappearance/appearance
curve and enter the temperature values where you want the curve generated.
Caution
You cannot plot theoretical predictions from PVTi of an experimental unless at
least one observation has been defined.
Make sure there is at least one observation defined for this experiment and then right click on
the experiment and select plot. You can super-impose your curve onto a standard phase plot by
using the super-impose button on the toolbar.
Hint
There is a shortcut for doing standard phase plots. This is accessed by clicking and
holding the left mouse button down on the appropriate fluid sample icon and then
dragging the cursor into the plot viewer.
There is a more detailed section on the theory behind how PVTi models the presence of wax and
asphaltene phases in "Wax and asphaltene precipitation in PVTi" on page 394.
How does PVTi support ECLIPSE Thermal?
The 2004A release of PVTi contains a new module that is capable of exporting a series of
keywords in a file suitable for use in an ECLIPSE thermal simulation. Therefore, just as you
were previously able to export PVT files suitable for use in ECLIPSE BlackOil and ECLIPSE
Compositional they can now do the same for ECLIPSE Thermal.
In PVTi and ECLIPSE Compositional we deal with an isothermal flash. This means that, for a
particular cell in a simulation, we know the composition of the fluid and the pressure and
temperature. We try to minimize the Gibbs Free Energy in order to determine how each
component splits across the different phases present. In other words we try to find the K-values,
which are the unknown variables.
In fact, in ECLIPSE Compositional, the temperature of each cell in a particular PVT region is
assumed not to change over time. In ECLIPSE Thermal this is not the case. The temperature
is a free parameter, which needs to be determined by way of a different type of flash - one at
constant energy. What we are saying here is that we know the pressure, functional form of the
K-values (K=K(P,T)), and the total energy of the system and the temperature is unknown.
The new ECLIPSE Thermal Export facility allows you to export one of two keywords (KVCR
or KVWI) to model the functional form of the K-values for each component. Since, as just
explained, isothermal flashes are not performed in ECLIPSE Thermal, PVTi also provides
support in this export facility in terms of calculating density and enthalpies in the oil and gas
phases. In ECLIPSE Thermal the keywords PREFT, TREFT, DREFT and ZFACTOR are used
to calculate oil/gas densities and the keywords STCOND, SPECHA, SPECHB, SPECHG,
SPECHH and HEATVAPS are used to calculate oil and gas phase enthalpies. For a brief
summary of all the keywords exported for use in ECLIPSE Thermal see "Outline of keywords
for ECLIPSE Thermal" on page 367.
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Introduction
PVTi Reference Manual
For more detailed information on the new thermal module see "ECLIPSE Thermal Export
Module" on page 401. For workflow information and a summary of the exported keywords see
"Compositional Data for ECLIPSE Thermal" on page 366.
How do I Use PVTi’s Batch Mode?
The batch mode facility is accessed from the command line (if using a PC) using the command
‘$pvti -batch filename.pvi’ where filename is the rootname of your project. If using
a UNIX machine then use the command ‘@pvti -batch filename.pvi’. The
recommended way to prepare a file for use in the batch mode is as follows:
1
Open the project file in interactive mode which you wish to use.
2
Save the file using the File | Save (concise)... menu option.
3
Load this new ‘concise’ file back into PVTi and open the Set PVTi Program Options
panel by doing Utilities | Program | Options.... Set the last option Write Keywords for
Batch Mode to Yes.
4
Now perform the required workflow in interactive mode that you wish the batch mode to
reproduce e.g. simulation of experiment, splitting, grouping, export, etc.
5
When you have performed the workflow save the file using File | Save...
6
The saved file is now suitable for running in batch mode.
For a comprehensive review of the new batch mode functionality see "Batch system and
keywords" on page 152.
How Can I Export PVT Tables to use the API
Tracking Functionality in ECLIPSE BlackOil?
PVTi now has the capability to export multiple PVT Tables for use in ECLIPSE BlackOil’s API
Tracking. Without the API Tracking facility, the presence of different types of oil in the
reservoir could be handled with the aid of PVT region numbers. Oil in PVT region 1 would have
its properties determined from PVT table number 1, and so on. However, this method cannot
model the mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on
the properties associated with region 2
Just like exporting a standard black oil table a depletion experiment must be defined in order to
do API Tracking export. The workflow is as follows:
1
Use the File | Export Keywords | API Tracking option in ECLIPSE BlackOil... menu
option to open the Export Panel for API Tracking.
2
Select the samples you wish to use in the export and move them to the Use box.
3
Choose the keywords you wish to export. Normally the Live Oil (PVTO) and Dead Gas
(PVDG) keywords are used with the API Tracking option.
4
Select whether you wish to export a gas table for each sample or just a single gas table.
5
Select whether you wish to plot the tables in PVTi.
6
Select whether you wish to write to tables using full double precision numbers.
7
Select the separator you wish to use for the export.
8
Select the units you wish to export the table in.
PVTi Reference Manual
The Most Asked Questions About PVTi
Introduction
23
PVTi should then write the tables to a file and show them in the output display. This file is then
suitable to use as the PVT input for an API Tracking run in ECLIPSE BlackOil. For a similar
description of the API Tracking workflow see "Export for API Tracking option in ECLIPSE
BlackOil" on page 134. For a technical description of the API Tracking model in ECLIPSE as
well as an explanation of how PVTi calculates suitable PVT tables see "Model for API Tracking
option in ECLIPSE BlackOil" on page 363.
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The Most Asked Questions About PVTi
Introduction
PVTi Reference Manual
Introduction
Chapter 3
General information
The PVTi program is an Equation of State based package for generating PVT data from the
laboratory analysis of oil and gas samples. The program may be used through an interactive
menu system or run in a batch mode. An interactive session can be saved as a batch input file,
which contains commands to reproduce the interactive operations. Alternatively, a batch input
file can be run from an interactive session.
Equations of state and viscosity correlation
Four equations of state are available, implemented through Martin’s generalized equation. This
enables the Redlich-Kwong, Soave-Redlich-Kwong, Peng-Robinson and Zudkevitch-Joffe
equations to be used. Two 3-parameter extensions of the Peng-Robinson Equation of State are
also available, one based on a Peneloux et al. volume shift, the other being an implementation
of the Schmidt-Wenzel Equation of State 2-parameter Peng-Robinson. The Soave-RedlichKwong Equation of State similarly has a three-parameter extension.
Viscosities may be calculated using a method by Pedersen et al. based upon a corresponding
states comparison with methane, or by the Aasberg-Petersen model based upon a corresponding
states comparison with methane and decane, or by the Lohrenz-Bray-Clark method.
Fluid definition
Multiple fluid samples can be defined by specifying components as one of three types. Library
components require only that the appropriate component mnemonic be entered. Characterized
components define properties of plus fractions from a limited set of information. Finally all the
properties of a component can be defined, a facility which can be used selectively to edit the
properties of existing components.
PVTi Reference Manual
Introduction
General information
25
It is possible to group the components to reduce or pseudoise the fluid system (make a fluid
definition of the system using pseudo components), or to split the plus fraction into more
components, preserving molecular weight and mole fraction. Multiple samples having different
plus fraction properties, say mole weight and specific gravity, can be characterized by splitting
the plus fraction into two or more pseudo-components of fixed properties but variable
composition.
Fingerprint plots of mole fraction against molecular weight, or phase diagrams, are available.
Material balance checks
A compositional material balance can be performed on any gas condensate or volatile oil for
which a laboratory constant volume depletion or differential liberation experiment has been
performed. This can be used to estimate liquid compositions and hence K-values. The calculated
quantities can then be used to estimate the quality and consistency of the laboratory data.
Additionally, tests on recombination of separator data can be performed and estimates of
reservoir recovery can be made.
Simulation of experiments
Experiments may be performed on the fluid systems defined using the equation of state model.
Possibilities are:
•
saturation pressures
•
flash calculations
•
constant composition expansions
•
constant volume depletions
•
differential liberations
•
swelling tests
•
multi-stage separator simulations.
Other experiments available are:
26
•
composition versus depth
•
vaporization test
•
multiphase flash
•
critical point
•
saturation temperature
•
first contact miscibility
•
multiple contact miscibility (condensing and vaporizing).
•
wax appearance temperature
•
asphaltene appearance pressure
Introduction
General information
PVTi Reference Manual
Regression of equation-of-state to measured data
The equation of state model may be tuned by regression. The critical state data, Ω a and Ω b
values, interaction coefficients, δ ij , and volume shift parameters, s i (for the three-parameter
volume shift equations of state), may be matched to experimental data from the first eight of the
experiments mentioned in the previous paragraph. Additionally, depending on the use of certain
facilities and options, five special regression parameters are also available. These are the A
coefficient in the Cheuh-Prausnitz Bids, the thermal expansion coefficient in the modified
Peneloux et al. volume shift method, and three variables associated with the Modified Whitson
splitting technique (denoted Semi-Continuous-Thermodynamics), being the mole weight and
distribution skewness parameter (on a sample-by-sample basis) and the characterization factor
of the plus fraction.
Hint
Almost any result from the experiments mentioned can be used as an observation
against which to regress.
PVT data for ECLIPSE simulators
Black oil and equilibration tables for ECLIPSE can be prepared, using the liquid and gas
compositions obtained from constant volume depletion or differential liberation experiments
passed through a separator system using the Coats or Whitson and Torp methods.
Gas injection schemes can be modeled using the ECLIPSE pseudo-compositional model which
modifies the ECLIPSE black oil tables as a function of the volume of injected gas.
For use in ECLIPSE Compositional, either pseudoised/regressed equation of state data or
tabular data (either K-values or liquid and vapor mole fractions as a function of pressure) can
be output.
Black oil tables can also be generated for the Vertical Flow Performance (VFPi) program,
simulating the phase and volumetric change in the wellstream fluid by a constant composition
expansion experiment at two temperatures, the highest (reservoir) and lowest in the production
string.
Water properties may also be output for use in any of the above programs. Default values for
formation volume factor, compressibility, etc., are constructed using well-known correlations
from specification of the pressure, temperature, salt and gas content of the water, though these
may be changed.
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Introduction
General information
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Introduction
General information
PVTi Reference Manual
Getting started
Chapter 4
Starting PVTi
Windows platforms
ECLIPSE Program Launcher
1
Start the ECLIPSE Program Launcher.
2
Click on the PVTi button.
3
Select the version and working directories as required.
Command line
1
Type the command $PVTI in a command prompt window.
UNIX platforms
1
PVTi Reference Manual
Type the command @pvti at the command prompt.
Getting started
Starting PVTi
29
30
Getting started
Starting PVTi
PVTi Reference Manual
Tutorials
Chapter 5
Overview
The tutorials provide a step-by-step introduction to the functionality of PVTi.
Note
These tutorials are not intended to teach PVT analysis, but instead concentrate on
illustrating typical work-flows for PVTi.
Each tutorial is divided into a number of distinct sections intended to highlight a specific aspect
of the analysis process. To avoid repetition, later tutorials assume familiarity with some used in
the first tutorials, so it is strongly recommended that you work through them in the order they
are presented.
Available tutorials
The following tutorials are available:
•
"Fluid Properties Estimation" on page 33
•
"Creating a fluid system" on page 36.
•
"Simulating experiments" on page 42.
•
"Fitting an equation of state to experimental results" on page 49.
•
"Exporting ECLIPSE Black Oil PVT tables" on page 53.
•
"Converting a black oil run to compositional" on page 58.
•
"Workflow Tutorial" on page 61.
•
"Multiphase Flash" on page 69.
•
"Exporting an ECLIPSE Thermal model" on page 73.
•
"Data analysis and quality control" on page 77.
•
"Removing contamination from samples" on page 84.
PVTi Reference Manual
Tutorials
Overview
31
•
32
Tutorials
Overview
"Converting old projects to the current version" on page 87.
PVTi Reference Manual
Fluid Properties Estimation
This tutorial describes how to use PVTi for Fluid Properties Estimation.
The data for this tutorial is provided with the standard installation of PVTi in the directory:
$ECL/2014.1/pvti/tutorials
and you should copy the files from this directory to your local directory before starting the
tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 33
•
"Basic Information - Fundamentals" on page 33
•
"Flash calculations" on page 35
•
"Discussion" on page 35
Introduction
Fluid properties estimation can provide quick-look PVT tables at the well site.
A saturation pressure (bubble or dew-point) together with a reservoir composition are sufficient
inputs to provide a quick-look simulation, giving an initial estimation of fluid properties in
advance of a full fluid analysis in the lab.
After completing this tutorial you should be able to use PVTi as a simulation tool for fluid
properties estimation.
Basic Information - Fundamentals
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Enter FPE.PVI as the file name for the new project.
Hint
When a new, empty project is created in PVTi, the Fundamentals panel opens
automatically. To re-enter this panel at any later time, select PVTi: Edit |
Fundamentals...
The Fundamentals panel allows you to enter the minimum information required to create
a complete equation of state model.
3
Click on the Enter Weight Fractions check box.
Hint
PVTi Reference Manual
The mole fractions that you see in lab reports are derived from weight fractions and the
mole weights of the components. It is weight fractions that are actually measured.
PVTi allows a choice of either form in the Fundamentals panel.
Tutorials
Fluid Properties Estimation
33
4
Right-click in the table and select Table Import | From File.
a
Import the file FUNDAMENTALS.TXT .
b
In the Text Import Wizard switch on Ignore Records and set the number of records
to ignore to 2 (since we want to ignore the column headings).
The Fundamentals panel should now look like Table 5.1.
Table 5.1
Components
CO2
The Fundamentals panel
ZI
Weight Frac.
(percent)
(percent)
0.05
C1
6.25
C2
3.10
C3
3.27
IC4
0.89
NC4
2.44
IC5
1.11
NC5
1.09
C6
3.88
C7+
77.49
5
Spec Gravity
0.43
N2
Hint
Mol Weight
218
Only enter mole weights for components whose properties will be characterized, the
other components come from the library. Also, specific gravity is an optional
additional parameter that can be used in the characterization, if it is not specified it is
calculated using a correlation.
Click Apply
PVTi adds the mole fractions and the specific gravity of the plus fraction.
6
Click on the Fluid Properties Estimation (FPE) check box
The temperature and pressure fields are now active.
a
Enter a Temperature of 220 F.
This is the temperature of the saturation pressure (dew or bubble point) and the
temperature that is used in the generated depletion experiments.
b
Hint
c
34
Enter a Saturation Pressure of 2800 psia.
PVTi uses this saturation pressure to fit the fluid model. The weight of the plus-fraction
is varied, the weight fraction being constant, until the saturation pressure predicted by
the equation of state matches the entered pressure.
Enter a Maximum Pressure of 5000 psia.
Tutorials
Fluid Properties Estimation
PVTi Reference Manual
Hint
This is the maximum pressure in the depletion experiments that are created.
7
Set the Project Units to Field, this sets the units that are used on the plots.
8
Click OK.
This is all the information required to fit the equation of state and to generate the Constant
Composition Expansion (CCE), depletion experiment (either differential liberation or constant
volume depletion) and the optimized separator. After fitting the equation-of-state and creating
the experiments, default plots from the depletion experiments are drawn along with the phase
curve for the fitted fluid.
The methods used in Fluid Properties Estimation are explained in "Fluid Properties Estimation"
on page 384.
9
PVTi: Run | Simulate
This opens a complete report for the project including the results from all the created
experiments.
Hint
By clicking on one of the experiments in the sample tree with the right mouse button,
and selecting Report..., you can view the reports for individual experiments
separately.
Flash calculations
1
2
Right-click on ZI in the project tree-view and select Properties Estimation (FPE)...
a
Enter a temperature of 60 F
b
Enter a pressure of 15 psia
c
Click OK.
Right-click on the newly created Flash simulation (FLASH1) and select Report to see the
results of flashing the reservoir fluid to standard conditions.
This allows you to attempt any Flash calculation on the reservoir fluid.
Hint
The Properties Estimation panel can also be used to create additional separators,
saturation pressure or depletion experiments, for example at other temperatures.
Discussion
Fluid Properties Estimation is a useful tool, particularly in situations where full lab analysis of
the fluid is not available for a complete equation-of-state matching project.
For full details of the operations performed during fluid property estimation see "Fluid
Properties Estimation" on page 384.
During fluid properties estimation, the project created is a complete PVTi project. This means
that a more experienced user has access to the rich range of features within the product. At the
same time, the less experienced user can use PVTi for Fluid Properties Estimation without
requiring in-depth knowledge of equation-of-state methods or PVT analysis.
PVTi Reference Manual
Tutorials
Fluid Properties Estimation
35
Creating a fluid system
This tutorial describes how to specify fluid properties in PVTi. It covers the basic functionality
of PVTi; knowledge of this tutorial is assumed in the later tutorials, so you are advised to work
through them in order.
The data for this tutorial is provided with the standard installation of PVTi in the directory:
$ECL/2014.1/pvti/tutorials
and you should copy the files from this directory to your local directory before starting the
tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 36
•
"Defining a fluid" on page 36
•
"Selecting an equation of state" on page 38
•
"Program options" on page 38
•
"View fluid attributes" on page 39
•
"Saving the SYSTEM section for future use" on page 40
•
"Discussion" on page 41
Introduction
The PVT report for this fluid contains details of three experiments: a Constant Composition
Expansion experiment, a Differential Liberation experiment, and a Bubble Point experiment.
The later tutorials describe how the experimental results may be used to fit an equation of state
to the experimental behavior, and how this fitted equation of state can be used to generate PVT
tables for use in reservoir simulations.
This tutorial shows how to set up basic fluid properties in PVTi and how to display the phase
envelope for the defined fluid.
Defining a fluid
PVT analysis involves fitting an Equation of State to experimental data and then using this
Equation of State to produce PVT tables for use in reservoir simulations. The first step is to start
up PVTi, and import the component and fluid definitions.
Table 5.2 shows the component and fluid definitions that are used in this tutorial.
Table 5.2
36
Component and fluid definitions
Component
% Mole Fraction
CO2
0.91
N2
0.16
C1
36.47
Tutorials
Creating a fluid system
Mole Weight
Specific Gravity
PVTi Reference Manual
Table 5.2
Component and fluid definitions
Component
% Mole Fraction
C2
9.67
C3
6.95
IC4
1.44
NC4
3.93
IC5
1.44
NC5
1.41
C6
4.33
C7+
33.29
Mole Weight
Specific Gravity
218.0
0.8515
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Select PVTi: File | New...
3
Enter BLACK.PVI as the project name in the file selection window.
4
Click on Open on PC or OK on UNIX platforms.
Note
This has defined BLACK as the prefix for any files that are written by PVTi.
The Fundamentals panel opens so that basic project information can be entered.
1
Enter CO2, N2, C1 and C6 into the Components column.
2
Click Apply.
3
Click Yes so that PVTi fills in the library component names.
4
Enter the mole fractions from Table 5.2 and the details for the C7+ component into the
Fundamentals panel and click OK.
Note
The components for which no mole weight or specific gravity has been specified are
automatically set to use the PVTi component properties library (see "Component
types" on page 102.)
Hint
The component properties can be examined by selecting PVTi: Edit | Fluid Model |
Components.... This panel can also be used to add additional components, the select
alternative characterization methods and to manually defined component properties.
Hint
Only one sample, ZI, is defined in the Fundamentals panel. Additional samples can
be created using PVTi: Edit | Samples | Names... and mole fractions can be entered
using PVTi: Edit | Samples | Compositions...
PVTi Reference Manual
Tutorials
Creating a fluid system
37
Selecting an equation of state
In this tutorial, the three-parameter Soave-Redlich-Kwong equation of state (see "Equation of
state formulation" on page 318) is fitted to the results of experiments carried out on the fluid
defined in "Defining a fluid" on page 36. The Lohrenz-Bray-Clark correlations (see "Lohrenz,
Bray and Clark" on page 330) is used for viscosity.
1
PVTi: Edit | Fluid Model | Equation Of State...
This opens the Equation of State and Viscosity Correlation panel.
2
Select the 3-parameter Soave-Redlich-Kwong equation of state (SRK3).
3
Click on OK.
4
Click on OK to change the parameters to SRK3 defaults.
Program options
1
PVTi: Utilities | Program | Options...
This opens the Program Options panel.
2
Set the Separator GOR calculation to use Liquid at Stock Tank Conditions.
3
Set the Temperature-dependence for volume shifts to be calculated by Polynomial
correlations. (See "Shift parameters" on page 322.)
4
Set Treatment of Volume Shifts to Independent Variables and click on OK.
The Program Options panel should now contain the following data:
Table 5.3
Program Options data
Field
Data
Definition of Liquid Saturation in CCE
Sliq=Vliq/Vsat
Treatment of volume shifts
Independent variables
Separator GOR Calculation
Liquid at Stock Tank Conditions
Temperature-dependence for volume shifts
Polynomial correlations
Specify/Calculate density & molar volume units
user units
Binary Interaction Coefficients for EoS
Katz-Firoozabadi
Specific Heat Capacity Coefficients and Calorific Values
38
Calculated compositions
No Save to samples
Component Library
Katz-Firoozabadi
Experimental Compositions
Output to Screen/PVP
Experimental Results
Always Output to PVP
Plot Vectors
No Output to file
Print file output
A4 format
Definition of GOR in Diff Lib
Normal
Definition of Oil relative volume in Diff Lib
Oil FVF = Voil(p)/Voil(stc)
Black Oil Table Output
All Data
LBC viscosity coefficients
Keep Fixed
Tutorials
Creating a fluid system
PVTi Reference Manual
Table 5.3
Program Options data (Continued)
Field
Data
Flash Calculations
E300 Flash
Sample mole fractions when regressing
Keep Fixed
Phase plot algorithm
New Phase Plots
Write Keywords for Batch Mode
No
5
Click Yes in answer to the question Set volume shifts to the default values for this
dependence.
View fluid attributes
Now that a fluid has been defined, there are two plots available to review the fluid we have
entered. First is the fingerprint plot of mole fraction versus molecular weight; the second is a
phase plot.
1
Right-click on ZI in the project tree-view and select Fingerprint Plot from the pop-up
menu.
The plot should look like Figure 5.1.
Figure 5.1 Fingerprint Plot
2
PVTi: View | Samples | Phase Plot...
3
Request Sample ZI, 5 quality lines.
4
Click on OK.
PVTi Reference Manual
Tutorials
Creating a fluid system
39
The plot should look like Figure 5.2.
Figure 5.2 Phase Plot
Note
A default phase plot with a single quality line can be generated by dragging ZI from
the tree-view of the project (in the left pane of the main window), and dropping it on
to the main plot workspace.
Saving the SYSTEM section for future use
The fluid sample definition can output as the RUNSPEC and SYSTEM sections of a PVI file.
1
PVTi: File | Save (Concise)...
2
Call the file FLUID_DEF.PVI.
Hint
The complete project can be saved using PVTi: File | Save... This, effectively, saves
a history of the project. The original fluid description is saved, along with SPLIT or
GROUP sections for split and group operations you perform. By choosing to save
current modifications, the system is saved in its current state, after all splits, groups,
etc., have been performed. For work in progress it is usually better to use Save so that
past steps can be recovered. For a final fluid model, the Save (Concise) option allows
a complete description of the final model to be saved, without the steps taken to get
there.
This file can now be read in using the PVTi: File | Import | SYSTEM... option.
40
Tutorials
Creating a fluid system
PVTi Reference Manual
Discussion
In this tutorial a fluid was defined from data and an Equation of State was selected to describe
that fluid. This fluid definition provides the basic building blocks for further PVT analysis. The
fluid definition can be used in simulation studies to compare it with experimental results from
the reservoir fluid; see "Simulating experiments" on page 42. This definition can then be
adjusted so that it describes the experimental results; see "Fitting an equation of state to
experimental results" on page 49. The fitted fluid definition is finally used to generate PVT
tables for ECLIPSE ; see "Exporting ECLIPSE Black Oil PVT tables" on page 53, ECLIPSE
pseudo-compositional, VFPi and ECLIPSE Compositional.
PVTi Reference Manual
Tutorials
Creating a fluid system
41
Simulating experiments
This tutorial illustrates how experiments are simulated in PVTi. It covers the basic functionality
of PVTi. Knowledge of this tutorial is assumed in later tutorials, so you are advised to work
through them in order. The data for this project are provided in the standard installation of PVTi
in the directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 42
•
"Defining experiments for simulation" on page 43
•
"Plotting simulation results" on page 45
•
"Defining further experiments and observations" on page 45
•
"Defining further experiments and observations" on page 45
•
"Simulating all the experiments" on page 47
•
"Discussion" on page 48.
Introduction
This tutorial describes how experimental observations can be entered into PVTi and how the
experiments can then be simulated from an existing fluid definition.
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
File | Open...
3
Open the file FLUID_DEF.PVI that was created in the last tutorial. (Alternatively open
the supplied tutorial file FLUID_CORRECT.PVI).
Setting units
42
1
Utilities | Units...
2
Set the Unit Type to Field
3
Set the Temperature Unit Type to Fahrenheit
4
Set Mole Fraction or Percentage to Percentage
5
Set Absolute or Gauge Pressure to Gauge.
6
Click on OK.
Tutorials
Simulating experiments
PVTi Reference Manual
Defining experiments for simulation
In this part of the tutorial, the experimental results from the PVT report are brought into PVTi
ready for simulation. In this section data from a constant composition expansion experiment are
brought into PVTi. If you do not have access to a spreadsheet, type the numbers from the tables
into the data entry forms in PVTi at the appropriate points.
Table 5.4
Constant Composition Expansion experiment at 220o F (* indicates
bubble point pressure)
Pressure
Relative Volume
(PSIG)
(V(p)/V(pb)
5000.0
0.9453
4500.0
0.9541
4000.0
0.9638
3500.0
0.9746
3000.0
0.9867
2900.0
0.9893
2800.0
0.9920
2700.0
0.9948
2620
0.9970
2605
0.9974
2591
0.9978
2516.7*
1.0000
2401
1.0243
2253
1.0599
2090
1.1066
1897
1.1750
1698
1.2655
1477
1.4006
1292
1.5557
1040
1.8696
830
2.2956
640
2.9457
472
3.9877
1
PVTi: Edit | Experiments...
2
Experiment Entry: Add | Pressure Depletion | Constant Composition Expansion...
PVTi Reference Manual
Tutorials
Simulating experiments
43
Hint
The constant composition expansion or CCE experiment can sometimes be known as
a constant mass study in PVT Reports.
The differential liberation or DL experiment is also known as a differential
vaporization experiment in PVT Reports.
The multi-stage separator or SEPS experiments can also be called a separation test in
PVT Reports.
The Experiment Entry window now shows three folders: General, Observations and
Components. These folders are used to define the experiment entry form.
3
Select the Observations folder.
4
Click in the top left cell of the table and select Pressure from the drop-down list in that
cell.
5
In the second column select Relative Vol. from the drop-down list.
Hint
6
By making the column headings the same as those in Table 5.4, the task of data entry
is simplified. The ability to tailor the table means that data entry can then be further
accelerated by importing observations from a text file or the clipboard.
Click on Next.
The table now shows two folders. The Components folder has disappeared as there were
no component observations selected; the General folder now shows an entry field to select
fluid type and another to enter the temperature of the experiment.
7
In the General folder, enter the temperature from Table 5.4 (220 F).
8
Select the Observations folder.
The Observations folder now shows a two-column table with the columns selected
previously. The table resembles Table 5.4.
Table 5.4 is provided in the file CCE_TABLE.TXT
9
Right-click in the table and select Table Import | From file...
10 Select CCE_TABLE.TXT and click on Open.
11 In the Text Import Wizard turn on Ignore Records and set the number of records to ignore
to 1 (since we want to ignore the column headings).
The view of the table should no longer contain the first row.
12 Click on OK.
Note
The error message “Cannot delete rows from this table” appears This
is because the table has a fixed length and the file we are importing from has fewer
rows than the table. This message can be safely ignored.
13 Click on OK to remove the message “Cannot delete rows from this table”.
The table now contains the same information as Table 5.4. As the experiment information
is complete, the experiment can be created.
14 Click on Next to create the experiment.
44
Tutorials
Simulating experiments
PVTi Reference Manual
Hint
The data tree now shows the created experiment (CCE1). The asterisk (*) next to the
experiment’s name means that it is active. CCE1 has one observation node, for the
relative volume measurements.
15 Click Close to shut the panel.
Plotting simulation results
1
Click on the Relative Vol. observation in the Data Tree and drop it over the Main Plot
Window.
The Main Plot Window should now look like Figure 5.3.
Figure 5.3 The plotted simulation results
Defining further experiments and observations
In this section of the tutorial the other experiments are defined, along with their observations.
The equation of state is later fitted to these observations, and then the fitted equation is used to
generate tables for a fully compositional ECLIPSE simulation.
PVTi Reference Manual
Tutorials
Simulating experiments
45
Differential liberation experiment
The first experiment to be added is a differential liberation experiment (Table 5.5), as in
"Defining experiments for simulation" on page 43.
Table 5.5
Differential Liberation Experiment at 220o F (* indicates bubble point
pressure)
Gas
Gas
Volume
Relative Factor
Density
(rb/Mscf)
Pressure
(PSIG)
Oil
Volume
Factor
Gas
Solution
Deviation
GOR
Factor
(Mscf/stb)
Z
Reservoir
Oil
Density
(lb/ft3)
2516.7*
1.7493
1.1342
45.110
2350
1.7095
1.0526
0.8686
45.6688
0.7553
1.2574
2100
1.6535
0.9378
0.8692
46.5022
0.7547
1.4070
1850
1.6013
0.8309
0.8719
47.3311
0.7565
1.6006
1600
1.5523
0.7307
0.8767
48.1595
0.7614
1.8586
1350
1.5057
0.6361
0.8836
48.9920
0.7704
2.2164
1100
1.4609
0.5460
0.8926
49.835
0.7859
2.7411
850
1.4171
0.4591
0.9036
50.6992
0.8121
3.5773
600
1.3726
0.3732
0.9167
51.6076
0.8597
5.1050
350
1.3234
0.2824
0.9324
52.6319
0.9618
8.7518
159
1.2720
0.1960
0.9481
53.6731
1.1726
18.6846
0
1.1228
0.0
56.3229
1.8901
1
PVTi: Edit | Experiments...
2
Experiment Entry: Add | Pressure depletion | Differential Liberation...
3
In the Observations folder, set the table headings to match those in Table 5.5: Pressure,
Oil Rel. Vol., Gas-Oil ratio, Vapor Z-factor, Liquid Density, Gas Gravity, Gas FVF.
4
Click on Next
5
Enter 220 F as the temperature in the General folder.
The file DL_TABLE.TXT provides the table in Table 5.5.
6
Import the file DL_TABLE.TXT into the table in the Observations folder, remembering
to ignore the first line, which contains column headings.
7
Click on Next to create the experiment.
The Experiment Entry panel now shows that there are 2 experiments defined.
Defining the bubble point experiment
Finally, there is a bubble point experiment at 220o F to be added.
46
1
Experiment Entry: Add | Single Point | Bubble Point...
2
In the Observations folder set the first column heading to Sat. Pressure and the second
to Liquid Density
3
Click on Next
Tutorials
Simulating experiments
PVTi Reference Manual
4
Enter the temperature, 220o F in the General folder.
5
Select the Observations folder.
6
Enter the saturation pressure as 2516.7 psig and the liquid density as 45.11 lb/ft3.
7
Click on Next to create the experiment.
8
Click Close.
Simulating all the experiments
All the experiments have now been entered. In summary, then, the project should now contain
the following:
•
A fluid description (component properties and a sample defined by mole fractions of
components).
•
A Constant Composition Expansion experiment with observations of relative volume.
•
A Differential Liberation experiment with observations of: relative oil volume, solution
gas-oil ratio, Z-factors, oil density, gas gravity and gas formation volume factor.
•
A Bubble Point experiment at 220o F with observations of bubble point pressure and liquid
density.
Hint
1
The information about which experiments have been defined, and for which
observations have been entered for those experiments, is contained in the Data Tree.
PVTi: Run | Simulate
A simulation report, showing information on all the experiments, is displayed in the Output
Display panel.
2
Output Display: File | Close
Plotting all observations for an experiment
1
PVTi: View | Observations...
2
Select the Differential Liberation (DL1) experiment.
3
Click OK.
This plots each observed data set (as points) for the differential liberation experiment and
each calculated data set (as lines) generated by simulation.
Hint
4
Examine each of the plots and note how well (or badly) the simulation has matched the
data.
Hint
PVTi Reference Manual
Double-clicking on one of the small plots swaps it with the large plot.
You can right-click on an axis and select Show Edit Box from the drop-down menu.
This opens the Axis Property Editing panel. In this panel you can customize the axes,
for example by changing the units used in plotting.
Tutorials
Simulating experiments
47
In the next section, the match between calculated and observed data values are improved by
regression.
Saving the project for future use
The fluid sample definition can be output as the RUNSPEC, SYSTEM and SIMULATE sections
of a PVI file.
1
PVTi: File | Save (concise)...
2
Call the file SIMULATE_SECTION.PVI.
Discussion
In this tutorial an existing project was extended to include experiments. Constant Composition
Expansion, Bubble Point and Differential Liberation experiments were imported and simulated
for the defined fluid. The match between the experimental observations and the simulated
results was examined using the plotting facilities in PVTi. The fluid model can then be adjusted
so that it provides the best fit (in a least-squares sense) to the experimental observations (see
"Fitting an equation of state to experimental results" on page 49). The fitted fluid definition is
finally used to generate PVT tables for ECLIPSE (see "Exporting ECLIPSE Black Oil PVT
tables" on page 53).
48
Tutorials
Simulating experiments
PVTi Reference Manual
Fitting an equation of state to experimental results
This tutorial shows how a fluid definition can be fitted, by regression, to describe experimental
results. This tutorial covers basic functionality of PVTi and knowledge this tutorial is assumed
in later tutorials, so you are advised to work through them in order. The data for this project are
provided in the standard installation of PVTi under the directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 49
•
"Fitting an equation of state by regression" on page 49
•
"Discussion" on page 52
Introduction
This tutorial illustrates the fitting of the fluid definition to the experimental observations.
The fluid definition and experiments are read in from an existing PVI file and the regression
facilities in PVTi are used to generate an improved fit between the two.
Fitting an equation of state by regression
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
File | Open...
3
Open the file SIMULATE_SECTION.PVI created in the last tutorial. (Alternatively you
can use the file SIMULATE_CORRECT.PVI.)
Hint
The Data Tree shows the contents of the opened project.
Fitting an equation of state by regression
In this part of the tutorial, the equation of state is fitted to the observation data to produce a better
representation of the fluid. A sensitivity analysis is carried out to determine which attributes of
the fluid components improve the solution by the smallest change. The most sensitive attributes
are then adjusted slightly by regression to improve the equation of state model of the fluid.
The first step in designing any regression is to determine the parameter set that will be used.
There are certain steps an engineer can take to improve the performance of a regression. The
first step is to try to make all regression variables have similar sizes. This is done to prevent a
minor constituent of the fluid having its properties varied extensively to achieve a mathematical
fit, which is not a reasonable physical solution.
1
PVTi Reference Manual
Examine the fluid component data in "Component and fluid definitions" on page 36.
Tutorials
Fitting an equation of state to experimental results
49
Note
The idea here is to look for consecutive components that have small mole fractions.
These can be grouped together and treated as a single regression variable, forcing the
solution to be physically realistic.
Hint
The properties of C1 and C2 are well known and generally do not differ significantly
from the library properties.
Grouping the C3, IC4, NC4, IC5, NC5 and C6 components into a single regression variable
preserves monotonicity between the components, in addition to creating a variable that accounts
for 19.5% of the total composition.
Hint
The plus fraction (C7+) contains a mixture of components C7+ and higher, so its
properties may not be so well-determined. This makes the plus fraction an ideal
candidate for regression to fit the equation of state to the experimental results.
C7+ is the second regression variable.
Sensitivity analysis
Sensitivity analysis is used to establish which fluid properties most affect the difference
between the observed and simulated values. The sensitivities are calculated for critical
temperature and pressure for each experiment, for both regression variables. Finally the most
sensitive properties will be selected for use in the regression.
Hint
In any regression, having a few very sensitive parameters is preferable to having
hundreds of insensitive ones. Always look for parameters that can be discarded (this is
called conditioning the problem - an ill-conditioned problem is difficult to solve).
1
PVTi: Run | Regression... opens the Regression panel.
2
Select Normal as the Type of regression variables in the Variables section of the panel.
3
Click Variables.
The regression variables are numbered for each property. Entering 1 in the critical pressure
(Pcrit) column in the rows corresponding to C3, IC4, NC4, IC5, NC5 and C6 groups those
components into the first regression variable.
4
50
Fill in the table in the Select EOS parameters for regression panel with the following
data:
Mnem
Pcrit
Tcrit
C3
1
1
IC4
1
1
NC4
1
1
IC5
1
1
NC5
1
1
C6
1
1
C7+
2
2
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Fitting an equation of state to experimental results
PVTi Reference Manual
5
Leave the second part of the Select EOS parameters for regression panel blank.
6
Click on OK.
Hint
7
The second part of the Select EOS parameters for regression panel relates to
binary interaction coefficients.
Click Regression in the Report section of the panel
The Regression Report panel provides several views of the regression problem, designed
to give the best possible insight into creating a fluid model.
For a description of the Regression Report panel see "Regression Report" on page 130.
a
Select the Sensitivities folder.
The sensitivities for the first Pcrit parameter are generally lower than for the other
regression variables.
b
Select the Hessian folder.
The values in the leading diagonal dominate the matrix, except in the first row, the row
relating the first Pcrit parameter.
c
Select the Covariance folder
In this table the largest value is for the first Pcrit parameter, indicating that it is the least
well determined by the regression.
d
Select the Correlation folder.
There is a strong negative correlation between the two Pcrit parameters, indicating that
the regression would proceed better if only one of those two parameters were used.
From an examination of the information in the Regression Report panel, it can be seen
that the first Pcrit parameter is not likely to aid the regression, and it may hinder it.
Consequently that regression variable is removed before regression is started.
8
Close the Regression Report panel.
9
Click Variables in the Regression panel.
10 In the Select EOS parameters for regression panel click on Reset to clear all the cells
in the table.
11 Fill in the columns to describe the reduced set of regression variables with the following
data:
Mnem
Pcrit
Tcrit
C3
1
IC4
1
NC4
1
IC5
1
NC5
1
C6
1
C7+
1
2
12 Click on OK.
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Tutorials
Fitting an equation of state to experimental results
51
Viewing the regression progress
The results of regression are viewed in a similar way to the results of simulation.
1
Right-click on experiment DL1 in the project tree-view and select Plot from the pop-up
menu.
2
Click Run in the Regress section of the Regression panel.
This starts the regression.
3
Click on Regression in the Report section of the Regression panel.
a
Select the Modifiers folder.
The difference between the final and initial value of each regression variable is
displayed.
b
Select the Details folder.
An observation-by-observation breakdown of the final fit is shown, along with the total
fit to all data (both unweighted and incorporating the observation weights).
4
Examine the plots in the main window.
The observed data are plotted as points and the simulated data before and after regression
are plotted as lines.
The regression has improved the equation of state model, so the regression results can be
accepted.
Hint
Right-clicking on an experiment allows you to choose to turn off that experiment
during the regression process.
5
Click Accept in the Regress section of the Regression Panel.
6
Close the Regression Report and Regression panels.
Saving the project
1
PVTi: Save (concise)...
2
Call the file REGRESS_SECTION.PVI
The results of regression are the fluid definition (that is the SYSTEM section) of the newly
created PVI file. They can now be read in using the PVTi: File | Import PVI Section |
SYSTEM... option.
Discussion
In this tutorial a fluid definition, an Equation of State and some experiments along with their
observations were imported from an existing PVI file (the file created in "Simulating
experiments" on page 42). The definition was adjusted so that it provided the best fit (in a leastsquares sense) to the experimental observations ("Fitting an equation of state to experimental
results" on page 49). This fitted fluid definition can now be used to generate PVT tables for
ECLIPSE (see "Exporting ECLIPSE Black Oil PVT tables" on page 53).
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Fitting an equation of state to experimental results
PVTi Reference Manual
Exporting ECLIPSE Black Oil PVT tables
This tutorial provides a typical workflow for PVTi: producing PVT tables that are then used in
an ECLIPSE BlackOil simulation. The data for this project are provided with the standard
installation of PVTi under the directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 53
•
"Exporting water properties" on page 53
•
"Generating ECLIPSE Black Oil PVT tables" on page 53
•
"Importing the keywords into ECLIPSE Office" on page 56
•
"Discussion" on page 57
Introduction
Once the fluid description has been fitted to the experimental observations, it may be used in a
reservoir simulation. PVTi facilitates the transition between a fluid description and the PVT
keyword description required by the ECLIPSE family of simulators.
In this tutorial PVT tables are created for the fluid definition developed in the tutorials 2, 3 and
4. The output tables are then used in an ECLIPSE simulation.
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Open REGRESS_SECTION.PVI created in the last tutorial (alternatively, open
REGRESS_CORRECT.PVI).
Exporting water properties
The water properties exported from PVTi are generated by correlation. This is effectively
separate from the fluid model.
1
2
PVTi: File | Export Keywords | Water...
a
Enter a reservoir temperature of 220 F and an initial reservoir pressure of 2500 psig.
b
Click on OK
c
Enter the filename PVTW.PVO for the water keyword
Close Output Display panel.
Generating ECLIPSE Black Oil PVT tables
In order to generate ECLIPSE BlackOil simulation PVT tables, PVTi requires either a
Differential Liberation experiment or a Constant Volume Depletion experiment to be simulated
from the fitted equation of state. The PVT tables are generated off either of these experiments.
PVTi Reference Manual
Tutorials
Exporting ECLIPSE Black Oil PVT tables
53
1
Right-click on experiment DL1 in the sample tree and select Export Keywords... from the
drop-down menu
Hint
2
PVTi: File | Export Keywords | Oil reservoir... produces an export panel for all
available Differential Liberation experiments.
Select PVTO and PVDG (Live oil and dry gas) on the radio button menu.
The Separators drop-down menu becomes active. This is because the produced fluid from
the Differential Liberation experiment must be passed through a surface separator to
calculate, for example, surface gas-oil ratios. The default is a separator at Standard
Conditions. If any separator experiments were defined for this sample, they would also
appear here.
3
Click OK
4
In the File Selection box, enter ECLIPSE100 as the name of the export file.
The keywords are generated and the Display Output module shows the generated keywords.
Note
The comments prefixed with --PVTi that appear before each keyword are the concise
version of the current PVTi project. This is the minimum information PVTi requires to
create the tables. This information can be used to rapidly convert an ECLIPSE
BlackOil data-set to an ECLIPSE Compositional data-set.
Caution
Note
Avoid editing the --PVTi prefixed comments. Any changes may invalidate the
file, preventing PVTi from reading it.
If the sample has had to be swelled, the sample SWELLSAM will have been added to
the sample tree. This sample is the swelled sample that was obtained by swelling the
original sample with vapor that was split off just below the bubble-point of the fluid.
PVTi automatically swells the sample with the vapor from the bubble-point so that the
table can be extended to values above the original bubble point.
The information in the keywords is also shown in the main plot space, keyword PVTO is shown
in Figure 5.4.
54
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PVTi Reference Manual
Figure 5.4 Plot of Oil FVF, Viscosity and Rs versus pressure for the output black oil property tables
Generating ECLIPSE Black Oil equilibration
keywords
This is similar to the generation of PVT tables. To generate equilibration tables, a composition
versus depth experiment is required.
1
PVTi: Edit | Experiments...
2
Edit Experiments: Add | Composition with depth...
3
Click Next
4
In the General panel enter the reference properties for the sample:
a
Enter 220 F as the Temperature.
b
Enter 3580 psig as the Pressure.
c
Enter 9200 ft. as the Depth
5
In the Observations panel enter the depths 9000 ft. and 9400 ft.
6
Click Next
7
Click OK to allow PVTi to add extra points between the maximum and minimum depths.
8
Click Close
9
Right-click on the new experiment (COMPG1) in the sample tree and select Export
keywords... from the drop-down menu.
10 Select the RSVD/RVVD (black oil) on the Equilibration Keyword radio button.
11 Click OK.
PVTi Reference Manual
Tutorials
Exporting ECLIPSE Black Oil PVT tables
55
12 Enter the filename RSVD.PVO for the exported keyword.
Note
In this case, only RSVD is generated. This is because the reservoir is all initially in the
liquid phase. If there were a gas-oil contact, both RSVD and RVVD would have been
generated. If the reservoir were all in the gas phase, only RVVD would be generated.
Note
In the case of a single-phase fluid, the RSVD keyword can be wrongly named as RVVD
and vice versa. The workaround is to correct the name manually in the exported file.
13 PVTi: File | Exit.
Keywords have now been generated and can be incorporated into an ECLIPSE data-set using
ECLIPSE Office.
Importing the keywords into ECLIPSE Office
This section is not intended as a tutorial on using ECLIPSE Office. Refer to the "ECLIPSE
Office User Guide" for details on using the product.
1
Start ECLIPSE Office with a new case (call it PVTI_TUTORIAL.OFF) and import the
standard data set ECLIPSE100.DATA
2
Click ECLIPSE to let ECLIPSE Office know what type of data-set is being imported.
3
Open the Data Manager.
4
Open the PVT Sections.
5
PVT Section: File | Import | Append..., and import the PVT table keyword file
(ECLIPSE100.PVO). Click OK to remove the warning message.
6
PVT Section: File | Import | Append..., and import the water keyword file (PVTW.PVO).
Click OK to remove the warning message
Note
At this stage you may want to view the keywords or plot them. For details on how to
do this, refer the "ECLIPSE Office User Guide".
7
Close the PVT Section, saving the file with the new keywords.
8
Open the Initialisation Section
9
Initialisation Section: File | Import | Append..., and import the equilibration keyword file
(RSVD.PVO). Click OK to remove the warning message.
10 In the Equilibration Data Specification keyword, set the Rs/Pb v Depth Table to 1, so
that the imported RSVD keyword is used.
11 Close the Initialisation Section, saving the file with the new keywords.
12 Run the simulation.
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PVTi Reference Manual
Discussion
In this tutorial an existing fluid definition was imported into PVTi and exported as PVT tables
that were used in an ECLIPSE Black Oil reservoir simulation. The basic requirements are that
PVTi must simulate a Constant Volume Depletion or Differential Liberation experiment and a
Separator experiment to allow the generation of black oil tables from the fluid definition.
PVTi Reference Manual
Tutorials
Exporting ECLIPSE Black Oil PVT tables
57
Converting a black oil run to compositional
This tutorial provides an example conversion from ECLIPSE BlackOil to ECLIPSE
Compositional. This tutorial requires the use of ECLIPSE Office in combination with PVTi.
Note
Many conversion projects require conversion of SCHEDULE section keywords, which
is outside the scope of this tutorial. This tutorial covers conversion of fluid properties
and equilibration. Specifically, the PROPS and SOLUTION sections.
Note
Some familiarity with ECLIPSE Office is assumed for this tutorial.
The data for this project are provided with the standard installation of PVTi under the directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
Note
You should choose a short name for your directory and the name must not contain
spaces. You can use underscore characters. ECLIPSE does not recognize directory
names that are long or that contain spaces.
The tutorial is split into several sections:
•
"Introduction" on page 58.
•
"Exporting the fluid model" on page 59.
•
"Converting equilibration keywords" on page 59.
•
"Creating the ECLIPSE Compositional case" on page 60.
•
"Discussion" on page 60.
Introduction
In this tutorial, the black oil PVT tables (PVTO and PVDG) and the Equilibration table (RSVD)
are converted into a full compositional model and composition versus depth table (ZMFVD).
This allows the ECLIPSE data-set from the previous tutorials to be run as a full compositional
case.
Caution
58
The --PVTi comments written out with the keywords are used by PVTi to
reconstruct the original fluid model. Without these there is not enough information
to convert blackoil projects to compositional models. It is important that the lines
prefixed by --PVTi in the ECLIPSE data-set are not edited or moved around
in the file.
1
Start ECLIPSE Office with the project created in "Exporting ECLIPSE Black Oil PVT
tables" on page 53 or create a new project and load in the data-set
ECLIPSE100_FULL.DATA.
2
Select the case.
Tutorials
Converting a black oil run to compositional
PVTi Reference Manual
3
Click on the PVTi launch button.
4
Click Run.
Note
The launch button has a default selection of launching PVTi with the PVT section of
the current case. PVTi reads this PVT section, creating a PVI file from the --PVTi
comments.
Exporting the fluid model
The imported PVT section contains the samples from the original PVI file plus any experiments
that were needed to generate the keyword. In this case the experiments are a Differential
Liberation experiment and a separator.
1
PVTi: File | Export Keywords | ECLIPSE Compositional Fluid Model...
2
Select the fluid {None}.
This means that PVTi does not write out a ZI keyword for the ECLIPSE Compositional
fluid model. This is the correct selection in this case as the equilibration (RSVD) is used to
create a composition versus depth table (ZMFVD).
3
Enter the reservoir temperature as 220o F.
Hint
The reservoir temperature is the temperature in the Differential Liberation experiment
definition. You can right-click on the DL1 experiment and select Edit... from the dropdown menu to view the definition of the Differential Liberation experiment.
4
Click OK.
5
Export the fluid model to FLUID.PVO
6
PVTi: File | Exit (There is no need to save the PVI file as it can be created from the
ECLIPSE Office case).
Converting equilibration keywords
1
In ECLIPSE Office, click on the PVTi launch button.
2
Select Initialisation as the section to launch PVTi with.
3
Click Run.
Hint
Again, PVTi searches for the --PVTi comments and uses them to construct a PVI
project file.
4
In PVTi, right-click on the composition versus depth experiment COMPG1.
5
Select Export keywords... from the drop-down menu.
6
In the COMPG1 export panel, select ZMFVD (Compositional) on the radio button.
7
Click OK.
8
Export the keyword to the file ZMFVD.PVO.
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Tutorials
Converting a black oil run to compositional
59
9
PVTi: File | Exit (there is no need to save the PVI file as it can be created from the
ECLIPSE Office case).
Creating the ECLIPSE Compositional case
1
ECLIPSE Office: Case | Add Case | Clone .
This creates an identical copy of the original case.
2
Name the case COMPOSITIONAL, and click OK.
3
Select the newly created case.
4
ECLIPSE Office: Module | Data Manager...
5
Select the Case Definition.
6
In the Case Definition module, select Compositional on the Simulator radio button.
7
Click OK to the warning about changing between black oil and compositional cases.
8
In the PVT folder set the number of components to 11, and click OK.
9
In the Data Manager, select the PVT section.
10 PVT Section: File | Import | Append... and import the file FLUID.PVO.
11 PVT Section: File | Import | Append... and import the file ZMFVD.PVO.
12 PVT Section: Section | Keywords...
13 Delete the PVTO and PVDG keywords.
14 PVT Keywords: File | Close...
15 PVT Section: File | Close... and save the section with a new name.
16 In the Data Manager select the Initialisation section.
a
Delete the RSVD keyword.
b
In the EQUIL keyword set the Compositional init type to 1 (so that ZMFVD is used
for equilibration).
17 Initialisation Section: File | Close and save the section with a new name.
18 Run the simulation from the ECLIPSE Office Run Manager.
Discussion
In this tutorial, an ECLIPSE BlackOil simulation data-set was converted to ECLIPSE
Compositional using the integration of PVTi and ECLIPSE Office.
The insertion of the --PVTi comments into the keyword export from PVTi is a powerful tool,
not just for converting data-sets, but also for developing projects in either black oil or
compositional models.
60
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PVTi Reference Manual
Workflow Tutorial
Introduction
This tutorial illustrates a typical workflow for an oil or gas condensate. It involves splitting the
C7+ fraction into 2 pseudocomponents, special regression, normal regressing, grouping
components, and matching viscosity data.
We have an oil PVT case, with two fluid samples ZI and W2 (Well 2). There is a C7+
characterization with CO2 present. Well 2 has C7+ has a different MW and Specific Gravity,
but the C7+ has been characterized with the ZI fraction only at this point. They are going to
inject CO2 into this field, so there is a Swelling Test with CO2.
The files for this tutorial are provided in the default PVTi installation in the following directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
This tutorial contains the following sections:
•
"Comparing the Default EOS Calculations to the Observations" on page 61.
•
"Splitting the C7+ Component" on page 62.
•
"Special regression to adjust the tail in the splitting calculation" on page 63.
•
"Normal regression to fine tune 11 component match" on page 64.
•
"Grouping Like Components to Reduce Nc" on page 64.
•
"Regressing to match viscosities" on page 67.
•
"Discussion" on page 68.
Comparing the Default EOS Calculations to the
Observations
1
Start PVTi.
2
Open WORKFLOW.PVI.
3
Run the Simulations; to do this click GO.
4
Review the calculated and observed Bubble Point Pressures for fluid ZI and W2 in the
Output Display, that is the first and last experiments.
5
Close Output Display panel.
6
Plot the results one experiment at a time.
7
PVTi Reference Manual
a
Right-click on CCE1 - Plot.
b
After reviewing the plots clear the plots by clicking the Remove Plots button.
Review all the experiments by observing the plots noting how well PVTi has done in each
case in matching the observations.
Tutorials
Workflow Tutorial
61
Splitting the C7+ Component
Creating a phase plot
Before we split we will create a Phase Plot (P versus T)
1
Select View: Samples| Phase plot | ZI; click OK.
2
Rescale the y-axis as follows:
3
a
Double click on the y-axis.
b
Select range.
c
Click off Limit Range.
d
Enter 0.0 in upper Visible Range area.
e
Enter 3000 in lower Visible Range area.
f
Click OK.
Click the "Superimpose" button or select Options | Graph | Superimpose.
Splitting the C7+
1
Edit | Fluid Model | Split | Multi Feed....
We will split the C7+ into 2 Pseudo components.
2
Note the Mole Weight of the heaviest pseudo component.
3
Enter the following Specific Gravity and Molecular Weight of Samples Plus Fraction
for W2:
Molecular Weight
199
Specific Gravity
0.8338
4
Click OK.
The C7+ has been split.
5
Select Edit | Samples | Compositions.
Check the mole fractions of the 2 pseudo heavy components. The split creates FRC2 with
small mole fraction (0.0477). We would rather have a splitting that has more of the mole
fraction in the heaviest component so we will perform another split.
6
Close this project and do not save the project.
7
Open WORKFLOW.PVI again.
8
Plot the Phase Diagram.
9
Select the Split panel and repeat steps 1 to 3.
10 This time change the Mole Weight of Heaviest Pseudo Component to 300.
This gives us a larger mole fraction for FRC2.
11 Click OK.
12 Check the Samples.
The FRC2 mole fractions are 8.2% and 13.9%
62
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13 Create a Phase Plot superimposed on the unsplit plot.
The phase diagram has not changed much at the reservoir temperature, which indicates a
good splitting.
14 Before we move on the regression save these results, using File | Save As, give the file the
name SPLIT.PVI.
Special regression to adjust the tail in the splitting
calculation
Before we regress we want to set the weights of the viscosity observations to 0, so they are not
included in the RMS. We will regress on the viscosity last, after we finish the phase behavior
match.
Hint
Regressing on the viscosity coefficients after the phase behavior of the fluid has been
matched is always strongly recommended.
We will also increase the weights of the Bubble Point Pressure (Sat. pressure) Observation as
this is a very important criterion to match.
1
Right-click on Vapor Visc and enter 0 as the Set Weight.
2
Right-click on Liquid Visc and enter 0 as the Set Weight.
Note
Setting the weight of an observation to zero turns off that observation.
3
Right-click on Z1 | BUBBLE1 | Sat pressure and enter 40 as the Set Weight.
4
Right-click on W2 | BUBBLE2 | Sat pressure and enter 40 as the Set Weight.
5
Select Run| Regression.
6
Click Special and then Variables
7
Select all 3 SCT variables and press OK.
8
Select Regress | Run.
a
9
Note the RMS in the Log area.
In the Regression panel click Simulation and observe the match of the 2 Bubble Point
pressure.
a
Or alternately select Report | Regression.
10 Under Details check the matches of the observations, especially the 2 bubble point
pressures, both should match very well. Look at the Modifiers to see the amount of change
in the parameters.
Note
You may also view the Sensitivities and the Hessian, Covariance and Correlation
matrices in the Report panel. These matrices are explained in the "Reference section"
on page 89.
Plotting the match
1
PVTi Reference Manual
Switch off Superimpose, click Remove Plots.
Tutorials
Workflow Tutorial
63
2
Right-click on each experiment CCE1, etc. click plot, view the match and then click
Remove Plots before proceeding to the next experiment.
Note the DL results are much improved.
The general rule is if this special regression improves the match of the phase behavior you
should accept the regression. If it does not improve it or makes it worse reject the regression. In
this case the match is improved so we will accept this regression.
3
Click Accept and close the Regression panel.
4
Save the results, select File | Save As and save as ALPHA.PVI.
Normal regression to fine tune 11 component
match
You can do some normal regression to fine tune this 11-component match. The Swelling and
Separator Experiments still need to match. Or you can group now and then do the normal
regression to finish matching the phase behavior. This tutorial will do the fine tuning using
Normal Regression before grouping.
1
Set weights on bubble point pressures, etc. Right click on Observation | Set Weight and:
a
Make sure the 2 bubble point pressure observations weights are still 40.
b
Set the Swelling Test | Saturation Pressure Weights to 10.
c
Select CCE and set the Liquid Density Weights to 5.
d
Set the Separator Exp | Gas-Oil-Ratio weights to 5.
2
Select Run | Regression.
3
Select Normal under the Variables section.
4
Click Variables box.
5
Refer to the procedure described in section "Normal Regression to fine tune match" on
page 65 for fine tuning this 11 component match.
Note
6
Do not attempt to get a perfect match since the grouping process described below
changes the match. The key here is to get the Swelling Test; Saturation Pressures to
match better before grouping.
Save this characterization with a new file name.
Grouping Like Components to Reduce Nc
We will group the 11 components into 6 components. Rules for grouping a fluid like this are as
follows:
64
•
Keep Methane C1 as a pure component.
•
Keep CO2 as a pure component - we will inject CO2.
•
Keep the two heavy pseudocomponents that you created by splitting (and did a special
regression on) as separate components.
Tutorials
Workflow Tutorial
PVTi Reference Manual
1
Before we group create a Phase diagram of component ZI and click the Superimpose
button.
2
Select Edit | Fluid Model |Group.
3
Type the following integers into the New Index column:
CO2
1
C1
2
C2
3
C3
3
IC4
3
NC4
3
IC5
4
NC5
4
C6
4
FRC1
5
FRC2
6
4
Click Update.
5
Check the component (Group) names. You change them if you do not like a particular
name.
6
Click Update again, and then click OK.
7
Click the Edit sample composition’s button to view the mole fractions of the new group.
The usual rule is if one of the group mole fractions is significantly smaller than the others
group it into one of its neighbor groups.
8
Plot a Phase diagram on top of the un-grouped diagram.
If they are close to each other then the grouping is good. Your phase match should still be
close to the observed data.
9
Click GO and view the bubble point pressures
10 Plot the experiments to see how much the grouping has changed the calculated results.
11 If the match looks reasonable save this characterization with a new file name.
12 If the match has changed substantially, close this project without saving and read in the
.PVI file from the save at the end of the previous section.
13 Re-group with a different selection of groups or number of pseudocomponents.
Normal Regression to fine tune match
The steps in the normal regression process are:
•
Choose high weights on experiments or observations to improve the of key data
•
Pick various combinations of parameters to regress on, try it, look at the results, reject the
regression and try a different combination
PVTi Reference Manual
Tutorials
Workflow Tutorial
65
•
Volume shift parameters may be dependent on Tc and Pc - so you cannot regress on them
separately. They may be independent in which case you can regress on them. If you are
having trouble matching liquid densities try making the volume shifts independent.
A review of the match of the observations shows that the Saturation Pressure for the Swelling
Experiment with CO2 contains the largest difference between the calculated and observed. We
will increase the weight for these results.
There are two ways to change the weight for experiments and observations:
1
2
To change the global weight for the experiment:
a
Right -click on the experiment and click on set weight -
b
Type in the new weight.
To change the weight on individual observations:
a
select Edit | Observations:
b
click on the experiment type,
c
click experiment list,
d
then observation type,
e
then click on the large G in the upper left corner of the panel.
Individual weights appear on the right most columns.
f
Insert weight values and click Apply.
Suggested weight values:
•
Swelling, saturation pressure = 10.
•
CCE, liquid densities = 5.
•
SEPS, Gas-Oil Ratio = 5.
•
Bubble point pressure = 40 (previously set).
Regression variable trial and error process
For the remainder of the phase behavior regression, it is a trial and error procedure. Below are
several suggested combinations of parameters to regress on. Remember a vertical column of
numbers in the Regression panel:
1
1
1
1
creates one regression variable for all four components.
To create 4 regression variables one should enter the following in the column:
1
2
3
4
Below are 3 combinations of suggested variables (with volume shift parameters "Independent")
after grouping the 11 components into 6. A variable should be defined for the contents of each
bullet point in the 3 combinations:
66
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PVTi Reference Manual
•
Omega A - C9+, C23+
•
Omega B - C9+, C23+
•
AcenFac - C9+, C23+
•
Shift - all components
•
BIC CO2 and C1, C2+, C5+, C9+, C23+
•
BIC C1 and C5+, C9+, C23+
or:
•
Omega A - C2+, C5+, C9+, C23+
•
Omega B - C2+, C5+, C9+, C23+
•
AcenFac - C2+, C5+, C9+, C23+
•
Shift - all components
•
BIC CO2 and C1, C2+, C5+, C9+, C23+
•
BIC C1 and C5+, C9+, C23+
or:
•
Tc - C9+, C23+
•
Pc - C9+, C23+
•
AcenFac - C9+, C23+
•
Sshift - all components
•
BIC CO2 and C1, C2+, C5+, C9+, C23+
•
BIC C1 and C5+, C9+, C23+
1
Try as many combinations as required to match the data to within the degree of accuracy
you think is needed. Remember the accuracy of most PVT observations is 5% to 10% or
about 20 Psi.
2
Once you have finished matching the phase behavior data, accept the results of the
regression and save the file.
Regressing to match viscosities
Now that we have a match of the phase behavior, we next need to match the viscosity
observations. First we need to remove the experiments that do not have viscosity data from the
regression process. Then in the CCE we need to set the viscosity observations weights to 1 and
the other observations to 0.
1
To remove an experiment from regression right click on the experiment and select Don't
use in regression. Do this for all experiments except CCE.
2
In the CCE experiment for all the observations (except for the Vapor visc. and Liquid
visc.) right click on the observation and select set weight.
a
Change the weight to 0.
3
For the Vapor visc. and Liquid visc. change the weight (using the same sequence) from 0
to 1.
4
Select Run | Regression.
5
In the Variable section click Normal then the Variables box.
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67
First iteration
1
In the Select EOS parameters for regression panel enter 1 in all the boxes under the
heading VcritV.
2
Click OK.
3
In the Regression panel click Run.
4
Plot the Liquid and Vapor viscosity and compare the new match with the observations.
Second iteration
1
In the Regression panel press Reject to return the characterization back to the preregression values.
2
In the Select EOS parameters for regression panel enter 1 in the first box, 2 in the
second box, 3 through 6 in the remainder of boxes under the heading VcritV.
3
Click OK.
4
In the Regression panel click Run.
5
Plot the Liquid and Vapor viscosity and compare the new match with the observations.
Note this new match is better than the first match.
6
Press Accept to accept these results.
7
Save this characterization with a new file name.
The phase matching process is now complete. You are ready to export the PVT properties or
characterization for ECLIPSE simulations.
Discussion
This tutorial illustrated a typical workflow for an oil or gas condensate. It involved splitting the
C7+ fraction into 2 pseudocomponents, special regression, normal regressing, grouping
components, and matching viscosity data.
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Multiphase Flash
Introduction
The multiphase flash experiment tends to find more than two phases in systems with
Asphaltene/Waxes and/or with CO2 rich fluids at low temperatures. This tutorial demonstrates
multiphase flashes with both systems. The files for this tutorial are provided in the default PVTi
installation in the following directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into the following sections:
•
"Asphaltene and wax system" on page 69.
•
"CO2 Rich Fluids" on page 70.
•
"Summary" on page 72.
Asphaltene and wax system
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Load MULTIPHASE-START1.PVI into PVTi.
3
View this oil composition by selecting Edit | Fundamentals and view the 10 component
oil.When finished click OK.
4
To add an experiment, click Edit | Experiments and then Add | Single Point | Multiphase
Flash.
5
a
Click Next> and then enter 50 F as the Temperature,
b
Click Observations, fill in 1000 Psia.
c
Click Next> and then Close.
To run the experiment (again) click GO.
The Output Display shows the results of the flash.You will see two phases, Liquid and
Vapor, and their properties and compositions.
Now we are going to split the C7+ fraction into Paraffin, Naphthalene, and Aromatic
components, then redo the multiphase flash.
6
Select Edit | Fluid Model |Split | PNA Distribution.
The C7+ fraction is now split.
7
To view the new characterization, select Edit | Fluid Model | Components.
You will see that there are three new user-defined components which have replaced the C7+
component.
8
Click on the Complete folder to view the critical properties of these components.
9
Click on OK to close the panel.
We are going to run the MFLASH experiment again and view the phases present.
10 Click on GO .
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69
The Output Display shows the following 4 phases: Liquid, Wax, Asphaltene Liquid, and
Vapor.
11 Note that the compositions of the Wax is 100% PC7+ and the Asphaltene Liquid is 90.23%
AC7+.
12 Close the project, do not save the changes.
CO2 Rich Fluids
Certain fluids with a high CO2 content at low reservoir temperatures partition into two liquid
phases or two liquid phases in equilibrium with a vapor phase. This tutorial demonstrates such
a system.
SPE 71485, (see [Ref. 1]) gives fluid characterizations that exhibit multiphase behavior. This
paper describes reservoir oil with 12 components. It has heavy components of C7-9, C10-13,
C14-19, C20-35, and C36+. It also describes an injection gas called MI (Miscible Injection)
that is a combination of CO2 and NGL. In the paper they use the Peng-Robinson Equation-ofState to calculate the phase behavior. They combine the reservoir oil and the MI gas in various
mixtures at 86 °F and present a diagram of the phases present, which is shown in Figure 5.5.
Figure 5.5 Phase Diagram for Schrader Bluff Fluids
We will attempt to verify the phases present with a 0.8 fraction of MI with PVTi multiphase
flash.
70
1
Load MULTIPHASE-CO2.PVI into PVTi.
This contains the fluids and characterization from the SPE paper,[Ref. 1].
2
View the compositions of the fluid sample by selecting Edit | Samples | Compositions.
3
Click OK to close the panel.
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PVTi Reference Manual
4
To create a mixture of 80% MI and 20% reservoir oil, select Edit | Samples | Mix.
5
In the Mix panel enter the following:
a
Mixing Type By: Mole Fraction of Sample 2
b
Fluid Sample 1: Z1
c
Fluid Sample 2: MI
d
New Sample Name: .8MI
e
Temperature: 86 F
f
Mole Fraction: 80 percent
6
Click OK.
7
To view the new sample, click Edit | Samples | Compositions.
Note the new sample has 65.209% CO2.
Now we will create multiphase flash experiments at a series of pressures (Temperature = 86
F) starting in the Liquid-Liquid region (1100 Psia) then through the Liquid-Liquid-Vapor region
and ending up in the Liquid-Vapor region (600 Psia).
8
Select Edit | Experiments and then Add | Single Point | Multiphase Flash.
9
Enter the following:
a
Fluid Sample: .8 MI
b
Temperature: 86 F
10 Select Observations and enter 1100 (psia) as Pressure.
11 Click Next> and Close.
We now have MFLASH1 defined.
12 To create additional MFLASH experiments at a series of lower pressure, right click on
MFLASH1 and select Clone.
13 Repeat for MFLASH2 through to MFLASH5.
We now have 5 MFLASH experiments defined.
14 To change the flash pressures right click on the MFLASH experiment and select Edit |
Observations | Pressure.
15 Enter the following pressure values:
a
MFLASH2: 1050 (psia)
b
MFLASH3: 1000 (psia)
c
MFLASH4: 900 (psia)
d
MFLASH5: 600 (psia)
16 To switch between MFLASH experiments press Next> and then Close.
17 To run all experiments and view results, click GO.
18 Observe the results in the Output Display.
Note as the pressure decreases the flashes proceeds from the L-L region to the L-L-V region
to the L-V regions, just as Figure 5.5 illustrates.
Note
PVTi Reference Manual
The MFLASH5 experiment can sometimes label both the phases as liquid. However,
one of them is clearly a vapor as the density value is 4.93598 lb./ft.3.
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Multiphase Flash
71
Note
If a standard two-phase flash is performed at the same temperature and pressure as with
the multiphase flash, then one obtains liquid and vapor phases with the same density
values as produced with the MFLASH5 experiment.
Summary
This tutorial demonstrated the multiphase flash experiment. It tends to find more than two
phases in systems with Asphaltene/Waxes and/or with CO2 rich fluids at low temperatures.
This tutorial demonstrates multiphase flashes with both systems.
References
Guler B. et al,
"Three- and Four-Phase Flow Compositional Simulations of CO2/NGL EOR"
[Ref. 1]
SPE 71485,
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PVTi Reference Manual
Exporting an ECLIPSE Thermal model
Introduction
This tutorial demonstrates using the new ECLIPSE Thermal export facility where a file can be
exported containing a fluid model suitable for use in ECLIPSE Thermal. For technical
information on the ELCLIPSE Thermal export facility see "ECLIPSE Thermal Export Module"
on page 401 and for more general workflow guidelines see "Compositional Data for ECLIPSE
Thermal" on page 366. The files for this tutorial are provided in the default PVTi installation in
the following directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into the following sections:
•
"Verifying the Validity of the Fluid Model" on page 73.
•
"Fitting the Component K-values" on page 74.
•
"Viewing the K-value Fits" on page 75.
•
"Exporting the Model" on page 76.]
Verifying the Validity of the Fluid Model
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Open THERMAL.PVI.
3
Open the Fundamentals panel by selecting Edit | Fundamentals....
From the tree view on the left side of PVTi you can see that there is a single sample in this
project called ZI. The Fundamentals panel shows the composition of this 3-component
fluid as being C1, C5 and C20+.
4
On the tree view there are two experiments defined, a Differential Liberation (DL1) and a
bubble point experiment (BUBBLE1). Right-click on the DL1 experiment and select Plot.
Three observations should have been plotted oil density, oil relative volume and oil
viscosity. You can see that the Equation of State (EoS) fluid model shows good agreement
with all 3 observations.
5
Right-click on the bubble point experiment and select Report.
You can see that the EoS model also gives good agreement with the observed bubble point
pressure of 1784.1749psia.
Since we have a good match for our EoS based fluid model we can now export the model
for use in an ECLIPSE simulation. We have relatively few components (<4) so this fluid
would be suitable for use in an ECLIPSE Thermal simulation.
Note
PVTi Reference Manual
Simulations using ECLIPSE Thermal tend to use fluids consisting of two or three
components.
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Exporting an ECLIPSE Thermal model
73
Fitting the Component K-values
1
Right-click on the sample ZI and select the Export ECLIPSE Thermal model...
2
On the panel that opens, enter the following:
a
1500 psia as the Maximum Pressure,
b
400 F for the Maximum Temperature,
c
1000 psia for the Minimum Pressure,
d
and 200 F in the Minimum Temperature box.
Note
3
The default values here are Pmax=1000psia, Pmin=50psia, Tmax=400F and Tmin=50F
and are considered reasonable max/min parameters within a reservoir. However, every
reservoir is different and any knowledge of these parameters for your particular
reservoir should be entered.
Enter 40 in the Enter Number of Flashes to be Performed box.
To model component K-values we can either export the KVWI keyword, which models them
using Wilson’s formula, or the KVCR keyword, which uses Crookston’s formula. Crookston’s
formula is in general much more accurate and we will use this. See "K-Values" on page 401 for
a more detailed description regarding the modeling of K-values.
4
Tick the box Export Crookston Coefficient? to tell PVTi that you wish to export the KVCR
keyword.
5
Since we are exporting the KVCR keyword we need to determine the values of the
coefficients of Crookston’s equation to export. Click Fit Crookston Coefficients on the
panel to open the Fit Crookston Coefficients panel.
This panel shows Crookston’s equation where p is the pressure, T is temperature and the
coefficients A-E are what we wish to determine values for.
Note
The Fit Crookston Coefficients panel enables you to calculate the optimum values of
the coefficients A-E in Crookston’s formula, so that the best fit is found to PVTi’s EoS
predicted K-values for each component over the temperature and pressure range
defined by the user.
6
A and D should already be active. Click on B to make coefficient B active also.
7
Select the Plot option in the Plot P, T Values Used in Fitting Crookston Coefficient?
box.
In order to find values for the chosen coefficients PVTi throws in 40 points at random
coordinates in the region you just defined in pressure-temperature space. The Plot option plots
these points on the screen for you after the fit has been performed. Ideally, we would like to them
superimposed on a phase plot.
8
Select PVTi: View | Samples | Phase Plot... and press OK to perform the phase plot.
9
Select PVTi: Options | Graph | Superimpose.
Hint
You can also access the Superimpose option using the toolbar.
10 Now click Apply on the Fit Crookston Coefficients panel to start the run.
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Once the run has finished a results panel appears. In the Coefficients folder the best fit
values of A, B and D are reported for each component.
11 Click on the Statistics panel.
The mean error and standard deviation (in %) are reported for each fit. The C1 and C5
components have been fitted very well (rms<1.5%) and the C20+ fraction has been fitted
reasonably well with an rms of somewhere between 7-9% (depending on the random
number generator on your machine).
Can we do better though?
Caution
Make sure you turn off the Superimpose option before moving to the next
section.
Viewing the K-value Fits
In the last section "Fitting the Component K-values" on page 74 we saw how to use the module
to calculate the optimum values of a chosen set of coefficients in Crookston’s equation in terms
of fitting to PVTi’s Equation of State based K-values. We saw, for the fluid ZI in the
THERMAL.PVI file, that the C20+ fraction had a reasonable fit when using just A, B and D. In
this section we will see how to interactively view the fits in order to better understand why
PVTi’s EoS K-values for this C20+ fraction has not been represented as well as the other
components.
1
Click the View Fit button on the Fit Crookston Coefficients panel.
The Plot K-values vs Temperature or Pressure panel opens.
Hint
Plots can either be performed of K-values versus pressure (at constant temperature) or
K-values versus temperature (at constant pressure).
First we will look at the K-value versus temperature fits, which are dictated by the D and E
coefficients (just D in our case).
2
Enter 1250psia in the Enter Constant Pressure box and 400F and 200F as the
Maximum and Minimum Temperatures respectively. Now click Apply.
The PVTi EoS-based K-values are shown by the points and the K-values calculated using
Crookston’s equation are shown by the curves.
3
Experiment by changing the value of the constant pressure in the range 1000<P<1500 (our
chosen pressure range) to see how well Crookston’s formula models the temperature
dependence of the K-values at a given pressure.
In general, for the C20+ component, the D coefficient, models the observations pretty well
over the whole pressure-temperature range, although using the E coefficient as well may
well help slightly
4
Click the Plot at Constant Temperature box and enter 300F.
5
Now enter the appropriate pressure range, which is 1500 psia and 1000 psia for the
maximum and minimum values. Click Apply.
6
Again, experiment by changing the value of the constant temperature in the range
200<T<400 to see how well Crookston’s formula models the pressure dependence of Kvalues.
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75
In particular it can be seen in the range 300<T<400 (for the C20+ component) that
Crookston’s formula struggles to model the pressure dependence at pressures at
P<1100psia when using just the A and B coefficients. Using the C coefficient may well
improve things significantly.
You can see in particular, the K-value versus pressure curve for the C20+ component
struggles to fit the observations.The problem is that the term A+B/P starts to run into
problems for pressure values <1100psia (due to the strongly negative value of B) and
therefore we require the C coefficient to get a good fit.
7
Close the Crookston Report panel and the Plot K-values vs Temperature or Pressure?
panel.
8
Switch on the C and E coefficients by ticking the appropriate boxes on the Fit Crookston
Coefficients panel. Now click Apply.
This run will take slightly longer, as the introduction of the C and E terms vastly increases
the amount of parameter space that PVTi must search.
9
Once the run has finished repeat steps 1-3.
This time, due to the introduction of the C coefficient in the fit, we have done a better job
in fitting the pressure dependence of Crookston’s equation. The introduction of the E
coefficient has also slightly improved the modeling of the C20+ K-value versus
temperature.
10 Click on the Statistics folder.
Overall, the introduction of the C and E coefficients has decreased the rms fit for the C20+
component from ~8% to ~5%.
Exporting the Model
Now we are satisfied with our K-value fits we can export our ECLIPSE Thermal PVT model.
Note
If we had decided to export the KVWI keyword (that is use Wilson’s formula to model
K-values) then we would not have needed to fit the coefficients of Crookston’s
equation and could have exported straight away from the Export for ECLIPSE
Thermal panel. Although this may be quicker, Crookston’s formula models K-values
much better and spending this extra time is worthwhile.
1
Click the OK button on the Export for ECLIPSE Thermal panel.
2
Choose a name for the file to be exported.
By default PVTi names it rootname.PVO, so in this case THERMAL.PVO if you do not
choose otherwise.
3
Click Save.
The ECLIPSE Thermal fluid model is written to the specified file. This file can now be used
to model PVT behavior as part of an ECLIPSE Thermal simulation.
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PVTi Reference Manual
Data analysis and quality control
This tutorial provides a typical workflow for PVTi in its role as a data quality assessment tool.
Experimental results from analysis of a hydrocarbon gas is used to analyze the data quality and
to modify spurious data. The data for this project are provided with the standard installation of
PVTi under the directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 77
•
"Material balance checking" on page 78
•
"The Hoffman-Crump-Hocott test for separator data" on page 82
•
"Recovery calculations" on page 83.
Introduction
In addition to allowing an equation of state to be fitted to laboratory results and facilitating the
generation of ECLIPSE BlackOil/ Compositional PVT data, PVTi also provides material
balance checks to assess data quality. For information on the calculations involved in material
balance checking see "Compositional material balance" on page 308.
Note
Problems with the observations in a PVT report equate to problems with the fitted fluid
model. It is therefore recommended that material balance checks are carried out on all
PVT data.
In this tutorial an existing project file (GAS.PVI) is read into PVTi and the data are checked
and modified for material balance errors.
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
PVTi: File | Open...
3
Open GAS.PVI
Hint
4
The Data Tree should show that there are three experiments, CVD1, defined with 10
different types of observations, SEPS1 with observations of fluid mole fractions
(liquid and vapor) and CCE1 with observation of Vapor Z-Factor.
Click and drag the ZI node from the Data Tree and drop it into the Main Plot Window.
The phase envelope should look like Figure 5.6.
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77
Figure 5.6 The phase envelope plot.
Note
This fluid system has no well-defined critical point.
Material balance checking
1
Right-click on CVD1 in the sample tree and select Material Balance...
This opens the Material Balance panel for this experiment.
2
Click Report to create a material balance report.
The experiment is performed and the Output Display window opens showing messages
that indicate the quality of the data. (Figure 5.7)
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PVTi Reference Manual
Figure 5.7 The main display shows messages indicating the quality of the data
Warning
Warning
Warning
Warning
- Sg of final stage liquid plus fraction is not defined
- Mw of final stage liquid plus fraction is not defined
- Viscosities of gas of at least one stage of CVD is not defined
- Mw of vapor plus fraction of at least one stage is not defined
- setting constant Mw(CN+) = of Mw(CN+) at Psat
Warning - Sg of vapor plus fraction of at least one stage is not defined
Warning - Composition of final stage liquid does not sum to 100%
Calculated liquid mole% of N2
at P= 6300.00000 is negative
Calculated liquid mole% of CO2 at P= 6300.00000 is negative
Calculated liquid mole% of IC4 at P= 6300.00000 is negative
Calculated liquid mole% of NC4 at P= 6300.00000 is negative
Calculated liquid mole% of IC5 at P= 6300.00000 is negative
Calculated liquid mole% of NC5 at P= 6300.00000 is negative
Calculated liquid mole% of C6
at P= 6300.00000 is negative
Calculated liquid mole% of N2
at P= 5700.00000 is negative
Calculated liquid mole% of CO2 at P= 5700.00000 is negative
Calculated liquid mole% of N2
at P= 5100.00000 is negative
Calculated liquid mole% of CO2 at P= 5100.00000 is negative
Calculated liquid mole% of N2
at P= 4500.00000 is negative
Calculated liquid mole% of N2
at P= 3800.00000 is negative
Calculated liquid mole% of N2
at P= 3100.00000 is negative
Calculated liquid mole% of N2
at P= 2400.00000 is negative
Calculated liquid mole% of N2
at P= 1700.00000 is negative
Calculated liquid mole% of CO2 at P= 1700.00000 is negative
Calculated liquid mole% of N2
at P= 1000.00000 is negative
Calculated liquid mole% of CO2 at P= 1000.00000 is negative
Calculated liquid mole% of N2
at P=
300.00000 is negative
Calculated liquid mole% of CO2 at P=
300.00000 is negative
The messages show that some mole fractions were calculated as negative, so there are
clearly problems with the data. PVTi supplies various options for plotting the data to
ascertain the source of the errors. The first type of data check to perform is to view the
pressure variation of the gas compositions.
3
Output Display: File | Close
4
Click Plot in the Material Balance panel.
a
Select Vapor Compositions v Pressure in the Select Plot Type panel and click on
Plot.
b
Click Close
5
PVTi: View | Rubberband Zoom In
6
Click and drag the mouse to define the zoom area to approximately cover the region 2800
to 6500 psia and 0.1 to 2 vapor composition. After zooming in, the plot window should look
similar to Figure 5.8.
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79
Figure 5.8 The main plot window after zooming in
Many of the components have non-monotonically varying gas compositions. In general, there
are several fluids or analyses available, and bad data can be discarded. However, if no other data
is available PVTi offers tools to make modifications to the bad data.
Modifying CVD data
1
Click Modify in the Material Balance panel.
2
Select fraction modifiers.
3
Enter the following values in for 6996 psia:
Component
N2
CO2
...
IC4
NC4
IC5
NC5
C6
Percentage
10
10
...
2
10
5
5
20
Note
80
The other components are modified in proportion to their existing mole fractions.
Placing a letter in the thin column to the left of each column of modifiers allows the
proportion of that component to be fixed and thus not modified in proportion to its
existing mole fraction.
4
Click on OK in the Set correction factors for CVD compositions panel.
5
Click Report in the Material Balance panel to create a new material balance report.
6
Click on Yes to modify the vapor and liquid compositions in CVD1.
7
Click on No if you want to save the modified compositions, but retain their original values
until after the modified results have been examined.
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Data analysis and quality control
PVTi Reference Manual
Now none of the liquid mole percentages are negative. So this change to the data can be
accepted.
8
Click Report in the Material Balance Panel
9
Click on Yes to modify the compositions.
10 This time, click on Yes so that the compositions are modified.
Plotting K values versus Pressure
1
Click Plot in the Material Balance panel.
2
Select K-values:(1) log (k) v Pressure plot in the Select Plot Type panel and click on
Plot.
The plot window should now look like Figure 5.9.
Figure 5.9 The plot of k values versus pressure.
The K-values should plot monotonically in that N2 should be the largest, followed by C1, etc.
This is clearly not the case, so although there are now no calculated negative compositions, the
modified fluid definition is not fully consistent.
The Hoffman-Crump plot
1
Select the K-values:(2) Hoffman-Crump Plot in the Select Plot Type panel and click on
Plot.
2
Click Close in the plot panel.
3
Click Close in the Material Balance Panel.
The plot window should look like Figure 5.10.
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81
Figure 5.10 The Hoffman-Crump plot
In this plot, one line is generated for each pressure stage. The Hoffman F coefficients
correspond to C1, C2 etc. and the lowest to C11, C12+. In general, these lines should be
monotonic with pressure, with the highest pressure at the top. This plot shows most of the error
to be in the first stage.
The Hoffman-Crump-Hocott test for separator data
Applying the Hoffman-Crump-Hocott test to separator gas and oil samples indicates whether or
not the streams are genuine equilibrium fluids.
1
Right-click on SEPS1 in the project tree-view and select Recombination... on the pop-up
menu.
2
Click Report to create a recombination report.
3
Output Display: File | Close
4
Click Plot.
The two lines on the Hoffman-Crump-Hocott plot (Figure 5.11) show the actual data and
the Standing estimates of K-values. They are used as a consistency check and, in this case,
give further evidence that the initial feed stream composition is in error.
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Figure 5.11 Hoffman-Crump-Hocott plot.
Recovery calculations
PVTi can allow recovery calculations to be performed if a valid Constant Composition
Expansion, Constant Volume Depletion and Separator test exist.
1
Right-click on CCE1 in the project tree-view and select Recovery... on the pop-up menu.
2
Click on Report to perform the recovery calculation.
Hint
This assumes that there is no direct production of reservoir liquid. If you want to
include direct production of reservoir liquid, you need a relative permeability table,
which you can enter be clicking on Rel. Perm.
Note
PVTi runs the material balance check on the Constant Volume Depletion experiment
selected, and performs recombination on the Separator selected, before performing the
recovery calculation.
Discussion
This tutorial has illustrated how fluids may be examined for consistency and, if necessary,
modified, within a PVTi project.
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Tutorials
Data analysis and quality control
83
Removing contamination from samples
Introduction
Oil-based muds are in widespread use and often contaminate PVT samples taken at the wellsite.
This tutorial involves the cleaning of a sample that is contaminated by an oil-based mud.
The PVI file CLEAN.PVI is used for this tutorial and is provided in the default PVTi
installation in the following directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 84
•
"Removing oil-based mud contamination by skimming" on page 84
•
"Removing oil-based mud contamination by subtraction" on page 85
•
"Discussion" on page 86
Removing oil-based mud contamination by
skimming
1
Start PVTi (if you are unsure about this see "Starting PVTi" on page 29).
2
Open CLEAN.PVI.
3
Right-click on the sample ZI and select Fingerprint plot from the drop-down menu.
In naturally occurring hydrocarbons there is expected to be semi-log straight-line behaviour
for components C8+ (around a mole weight of 100). From the fingerprint plot, there is
clearly not straight-line behavior for this fluid.
The contaminating mud, like many oil-based muds, has a composition containing
components C10-C23. In the skimming method, it is assumed that the composition is not
known.
4
Right-click on the sample ZI and select Clean... from the drop-down menu.
a
Enter CLEAN as the sample name for the cleaned sample.
b
Enter CONTAM as the sample name for the contaminant.
c
Click OK.
The sample has now been cleaned.
5
PVTi: Options | Graph | Superimpose - and ensure that the Superimpose option is on.
6
Right-click on the sample CLEAN and select Fingerprint plot from the drop-down menu.
7
Right-click on the sample CONTAM and select Fingerprint plot from the drop-down menu.
The plot should now look like Figure 5.12.
84
Tutorials
Removing contamination from samples
PVTi Reference Manual
Figure 5.12 The original sample, the cleaned sample and the estimated contaminant.
Removing oil-based mud contamination by
subtraction
When the composition of the contaminant is known, the subtraction method can give better
results than the simple skimming method.
1
Right-click on the sample MUD and select Fingerprint plot from the drop-down menu.
The true composition of the contaminant contains components lighter than C8 and also up
to the plus-fraction (C25+). The skimming method could not remove this contaminant
completely, but the subtraction method can.
2
3
PVTi Reference Manual
Right-click on the sample ZI and select Clean....
a
Enter CLEAN2 as the sample name for the cleaned sample.
b
Select Subtraction as the method.
c
Select MUD in the Contaminant drop-down.
d
Click OK.
Right-click on the sample CLEAN2 and select Fingerprint plot from the drop-down menu.
Tutorials
Removing contamination from samples
85
Discussion
This tutorial showed how a fluid can be cleaned of oil-based contaminants such as drilling
muds. For information on how the skimming and subtraction methods work see "Removing
contamination from samples" on page 84.
In general different PVT samples contain different levels of contaminant. It is usually best to fit
the PVT reports from a number of (contaminated) samples. Once a consistent fluid model has
been developed, the samples can be cleaned using either of the methods outlined in this tutorial.
The cleaned samples can then be used in reservoir simulations.
86
Tutorials
Removing contamination from samples
PVTi Reference Manual
Converting old projects to the current version
This tutorial demonstrates conversion of an old project to the current version of PVTi. This is
especially important for projects (PVI files) created with versions before 99B, as the default
Field units for Gas Formation Volume Factor were changed for that release. The files for this
tutorial are provided in the default PVTi installation in the following directory:
$ECL/2014.1/pvti/tutorials
and should be copied to the local directory before starting the tutorial.
The tutorial is split into several sections:
•
"Introduction" on page 87
•
"Preparing the PVI file for conversion" on page 87
•
"Converting the file" on page 88
•
"Discussion" on page 88.
Introduction
The VERSION keyword, introduced in 2000A, allows a systematic method for updating old
PVI files to be compatible with the latest version of PVTi. This tutorial describes how the
keyword can be used to convert an old PVI file into the current version.
Caution
Files in FIELD units containing Differential Liberation (DL) experiments that
have Gas formation volume factor (GFVF) observations must be updated to the
current version.
Preparing the PVI file for conversion
1
Start PVTi with a new project.
2
Click Cancel in the Fundamentals panel.
3
PVTi: Utilities | Text Editor
4
Select OLD.PVI as the file to be viewed
5
In OLD.PVI enter the VERSION keyword in the RUNSPEC section with a value of 98B.
Hint
If you are unsure of the form of the VERSION keyword see "VERSION" on page 280.
6
File | Save As...
7
Save the file with the name CONVERT.PVI
8
File | Close
Note
PVTi Reference Manual
You could now use the file CONVERT.PVI in a normal session and PVTi interprets it
according to the version specified by the VERSION keyword.
Tutorials
Converting old projects to the current version
87
In this tutorial we go one step further and convert the PVI file to the current version.
Converting the file
1
PVTi: File | Open
2
Select CONVERT.PVI as the file to open.
3
PVTi: File | Save As...
4
Save the file with the name NEW.PVI
Hint
You can compare the file NEW.PVI to OLD.PVI to see the differences (the DL
observation GFVF is converted from rb/stb to rb/Mscf and the heat capacity keywords
are added in the SYSTEM section).
Discussion
In this tutorial an old PVI file was converted to the latest version. This is important for files
using FIELD units, containing Differential Liberation (DL) experiments that have Gas
formation volume factor (GFVF) measurements as the units, for this type of observation was
changed in 99B from rb/stb to rb/Mscf to make PVTi’s units systems consistent with those of
the ECLIPSE simulators.
88
Tutorials
Converting old projects to the current version
PVTi Reference Manual
Reference section
Chapter 6
General information
•
"Main PVTi window" on page 90
•
"File" on page 92.
•
"View" on page 95
•
"The fluid model" on page 98
•
"COMB - Compositional Material Balance" on page 112
•
"Simulation using PVTi" on page 117
•
"Regression in PVTi" on page 126
•
"Exporting keywords" on page 133.
•
"Utilities" on page 144.
•
"Batch system and keywords" on page 152.
•
"Error handling" on page 165.
PVTi Reference Manual
Reference section
General information
89
Main PVTi window
General information
PVT analysis involves fitting an Equation of State to experimental data and then using the
Equation of State to produce PVT tables for use in reservoir simulations. PVTi contains
facilities to allow you to import experimental data, fit the data to an Equation of State, and
finally produce the PVT tables for reservoir simulation studies.
The menu bar of the main PVTi window has the following options:
90
•
"File" on page 92.
•
"Edit" on page 94
•
"View" on page 95
•
"Run" on page 96
•
"Utilities" on page 97
•
"Options" on page 97
•
"Window" on page 150.
•
"Help" on page 150.
Reference section
Main PVTi window
PVTi Reference Manual
The PVTi main module
The main module is shown in Figure 6.1.
Figure 6.1 The main PVTi window
Data Tree
Log Window
Equation of State
Main Plot Window and Sub-plots
The main window contains all the tools necessary for Equation of State model fitting.
Basic features
The Data Tree provides a view of the current project’s contents. Each fluid sample is identified
with its experiments as sub-nodes in the tree. Likewise, each experiment has its observations as
sub-nodes. The Log Window is updated with pertinent information relating to actions taken in
PVTi. The Equation of State, upon which the current fluid model is based, is indicated in the
status bar. The Main Plot Window and the Sub-plots provide an area for viewing project
information graphically.
PVTi Reference Manual
Reference section
The PVTi main module
91
File
The File menu allows you to open, close and save PVTi project files (PVI files) and import
sections from PVI files, and provides access to keyword export modules. Graph printing and
plotting facilities are also available from this menu.
•
To open this menu, select File from the main PVTi window.
The File menu consists of the following options:
•
New...
This creates a new PVTi project.
•
Open...
Opens a PVTi project (PVI) file. The complete file is read in and the most recent fluid
model, experiment descriptions, observations, etc., are restored. For more information on
the files PVTi creates see "Files created by PVTi" on page 93.
•
Close...
Closes the current project. If the project is not empty you are asked if you want to save
before closing.
•
Save...
Saves the current PVI file, overwriting the previously saved project.
•
Save As...
Saves the current project to a new PVI file.
•
Save (concise)...
Saves a concise version of the current project containing the latest version of the fluid
model plus any experiments and observations used in simulation and regression. No other
information is saved, therefore information regarding regression variables or split/group
sections will not be recorded by the Save (concise) option.
•
Export Keywords
This provides access to the Keyword Export modules. Currently PVTi supports export for
the ECLIPSE simulators and VFPi. See "Exporting keywords" on page 133.
•
Import
This option allows a section from a previous PVI project or ECLIPSE data-set to be
imported or a “concise” PVI project to be merged with the current project. The sections that
can be imported here are SYSTEM,GROUP, SPLIT,SIMULATE and REGRESS. See
"Reading the SYSTEM section from a PVI or DATA File" on page 98.
•
View PVI Section
This opens a particular section from a PVI file and displays the keywords in a text editor.
The sections that can be viewed this way are SYSTEM, GROUP, SPLIT, SIMULATE, and
REGRESS. See "Displaying the SYSTEM section from a PVI file" on page 98.
•
Exit
This exits PVTi. If there is an active project, you are asked whether you would like to save
the project before exiting.
92
Reference section
The PVTi main module
PVTi Reference Manual
Files created by PVTi
All files in PVTi use the project name as their base name. PVTi creates the following files:
•
PVI file, for example ALL.PVI
Input data file, although can be written by PVTi to save system specification or session.
•
PVP file, for example ALL.PVP
Main printed output file. In interactive mode a prompt to write results to this file follows
most operations.
•
PVO file, for example ALL.PVO
Output file. Used for the output of ECLIPSE Black Oil, GI option (pseudo-compositional)
or ECLIPSE 300 (equation of state) properties.
•
VEC file, for example ALL.VEC
Vectors file. Contains vectors of plots performed in a PVTi section in a form suitable for
inclusion into the GRAF program.
•
DBG file, for example ALL.DBG
Debug file. This is only present if debug has been written.
•
MES file, for example ALL.MES
Message file. A temporary file used throughout the program run to display results. This file
is deleted when you quit the program.
•
LOG files, for example ALL.LOG
Program Log File. This file exists in the startup directory of the program and contains a
summary of keywords read in, tasks performed, etc.
•
NEW files, for example ALL.NEW
New data file. This is a temporary file that holds the details of the new .PVI file. It is left
in the working directory if the program does not shut down cleanly.
Hint
•
The .NEW file contains all the changes made during the last session. If you change the
file extension to .PVI you can use it to recover the session.
REG files, for example ALL.REG
Regress Module file. This temporary file holds details of the quantities plotted in the
Regress module. It is left in the working directory if the program does not shut down
cleanly.
Only one project at a time can be in use with a single run of PVTi. To open another project, close
the current project, either by selecting the File | Open option (the program prompts you save
the session to a new .PVI file) or by using File | Close.
Note
PVTi Reference Manual
Although only one project may be in use by the program, different sections of different
.PVI files may be read in.
Reference section
The PVTi main module
93
Edit
The Edit menu allows entry and editing of the fluid model, samples, experiments, observations
and regression variables.
1
To open this menu, select Edit from the main PVTi window.
The Edit menu consists of the following options:
•
Fundamentals...
This opens the Fundamentals panel, See "Fluid Properties Estimation" on page 33.
•
Fluid Model
This opens the sub-menu of fluid model editing options.
•
Equation of State... This opens the Equation of State selection panel. See "Equation
of State" on page 100.
•
Components... This opens the component properties panel. See "Components" on
page 101.
•
Binary Interaction Coefficients... This opens the binaries panel. See "Binary
Interaction Coefficients" on page 104.
•
Volume Shifts... See "Volume shifts" on page 104.
•
Thermal Properties... See "Thermal properties" on page 104.
•
LBC Viscosity Coefficients... See "LBC Viscosity Coefficients" on page 104
•
Split This opens the sub-menu of options for splitting fluid components. See "Splitting
components" on page 105.
•
•
•
Constant Mole Fraction...
•
Whitson...
•
Multi-feed...
•
PNA Distribution
Group...
Samples.
This opens the sub-menu of sample entry and editing options.
•
•
Names... See "Sample names" on page 107.
•
Compositions... See "Sample compositions" on page 107.
•
Salinities... See "Sample salinities" on page 107.
•
Mix... See "Mixing samples" on page 108.
Properties Estimation (FPE)...
See "Fluid Properties Estimation" on page 33.
•
Experiments...
See "Defining Experiments" on page 117.
•
Observations...
See "Defining Observations" on page 122.
94
Reference section
The PVTi main module
PVTi Reference Manual
View
The View menu provides facilities for plotting and reporting.
1
To open this menu select View from the main PVTi window.
The View menu has the following options:
Samples: This option opens a sub-menu containing sample plot types.
•
•
Phase plot. See "Sample phase plot" on page 109.
•
Fingerprint plot. See "Sample fingerprint plot" on page 108.
•
Ternary plot. See "Sample ternary plot" on page 110.
•
Observations... This allows you to plot an observations against calculated values, or any
calculated values where corresponding observations do not exist.
•
Library. This option allows you to view the internal PVTi library. See "Library" on page 95.
Library
The properties of library components are preset by the program.
To display the current list of library components select View | Library...
Table 6.1
PVTi Reference Manual
List of library components
Mnemonic
Name
Mnemonic
Name
H2 O
Water
N2
Nitrogen
H2
Hydrogen
H2 S
Hydrogen Sulfide
CO2
Carbon Dioxide
CO
Carbon Monoxide
C1
Methane
C2
Ethane
C3
Propane
C4
Butane
iC 4
Iso-Butane
nC 4
Normal Butane
C5
Pentane
iC 5
Iso-Pentane
nC 5
Normal Pentane
C6
Hexanes
C6 H6
Benzene
C7 H8
Toluene
C7
Heptanes
C8
Octanes
C9
Nonanes
C 10
Decanes
C 11
Undecanes
C 12
Dodecanes
C 13
Tridecanes
C 14
Tetradecanes
C 15
Pentadecanes
C 16
Hexadecanes
C 17
Heptadecanes
C 18
Octadecanes
C 19
Nonadecanes
C 20
Eicosanes
C 21
C21’s
C 22
C22’s
Reference section
The PVTi main module
95
Table 6.1
List of library components (Continued)
Mnemonic
Name
Mnemonic
Name
C 23
C23’s
C 24
C24’s
C 25
C25’s
C 26
C26’s
C 27
C27’s
C 28
C28’s
C 29
C29’s
C 30
C30’s
C 31
C31’s
C 32
C32’s
C 33
C33’s
C 34
C34’s
C 35
C35’s
C 36
C36’s
C 37
C37’s
C 38
C38’s
C 39
C39’s
C 40
C40’s
C 41
C41’s
C 42
C42’s
C 43
C43’s
C 44
C44’s
C 45
C45’s
Note
For components C 6 to C 45 , the properties stored in the internal library correspond to
the “grouped” properties of Single Carbon Number Groups (SCN), [Ref. 5].
Obvious candidates for the pseudoisation of components for use in large regressions or
compositional simulation are iso-butane and normal butane, and iso-pentane and normal
pentane, into single butane and pentane components. A study of many PVT reports [Ref. 19]
has shown that the typical ratios of iC4 : nC 4 , iC5 : nC 5 are 0.67:0.33 and 0.60:0.40 respectively.
The library also contains two other components, with the mnemonics C4 and C 5 , whose
properties are mole-weighted averages of the respective iso and normal component properties.
Run
The Run menu provides simulation and regression facilities.
The following options are available:
•
Check Fluid System.
This provides a consistency check of the current fluid, the results of which are posted to the
log window. If there are a lot of fluid errors, the results are also displayed in a text window.
•
Save As Samples .
If this option is turned on, any samples created by an experiment can be saved as additional
project samples.
•
96
Simulate
Reference section
The PVTi main module
PVTi Reference Manual
This simulates all active experiments and then display the simulation results in a text editor.
PVTi has intelligent simulation, which means that the results of the last simulation run are
stored, and if no change has been made to the experimental data the simulation run is not
repeated, the results from the previous run being used. This keeps the time spent running
simulations to a minimum.
•
Regression...
This opens the Regression panel. See "Regression in PVTi" on page 126.
Utilities
The Utilities menu option provides access to miscellaneous information relating to the project
and program set-up.
•
Units...
See "Units..." on page 144.
•
Standard Conditions...
See "Standard conditions..." on page 145.
•
Program
This opens the sub-menu of program configuration options.
•
•
Options... This opens the Options panel which mimics the OPTIONS keyword in the
PVI file. See "Program options" on page 145.
•
Debug... See "Debug..." on page 150.
Text Editor
This opens the text editor used for displaying simulation results, etc. It can be used to view
any ASCII file.
Options
This menu provides options related to the plotting of graphs.
•
Add New Graph...
Adds a new graph to the existing plot windows.
•
Superimpose
When the superimpose option is switched on, indicated by a tick next to the menu option,
subsequent graphs are superimposed on the current main graph.
•
Tabulate...
This option creates a table showing the values plotted in the current main graph.
•
Remove All
This option deletes all graphs from the window.
PVTi Reference Manual
Reference section
The PVTi main module
97
The fluid model
Displaying the SYSTEM section from a PVI file
Displays a RUNSPEC/SYSTEM section present in the current PVI file.
1
To display PVI data, select PVTi: File | View PVI Section | SYSTEM.
Reading the SYSTEM section from a PVI or DATA File
Reads data from a PVI or DATA file. You can use this option to load the equation of state,
viscosity options and hydrocarbon system description from a PVTi PVI file or an ECLIPSE
Compositional (E300) DATA file.
Hint
You can load the first two sections of a PVI file as a system specification, rather than
using menu options. Additionally, you can choose to echo the contents of the whole
PVI file to the current print file, PVP.
Reading the PVT section from an E300 DATA file
1
PVTi: File | Import | ECLIPSE Compositional (*.DATA) and select the appropriate
DATA file.
PVTi searches for the required file and, if found, reads it looking for the number of EoS and
Equilibration regions in the ECLIPSE model. The number of reservoir EoS regions is
defined by the ninth entry of the TABDIMS keyword and the number of Equilibration
regions is defined by the first entry of the EQLDIMS keyword. If the ECLIPSE model has
just one of each region type then the program simply reads in the data. However if multiple
EoS or Equilibration regions are found then the program displays a prompt specifying the
numbers of each region found. You are asked to specify which EoS and/or Equilibration
region they wish to read in.
2
Select the number of the EoS and /or Equilibration region you wish to load.
Note
EoS regions each have an EoS model defined within them that is an EoS plus a list of
critical properties defined for each component. An Equilibration region is a group of
cells where the initial pressure and saturation is defined. PVTi needs to know which
Equilibration region to read in if there are any composition versus depth (specified by
the ZMFVD or COMPVD keywords) tables in the ECLIPSE file. There is one table for
each of the Equilibration regions. By specifying which Equilibration region to use this
tells PVTi which table to read in.
Reading the SYSTEM section from a PVI file
1
PVTi: File | Import PVI Section | SYSTEM and select the appropriate PVI file.
PVTi searches for the required file and, if found, reads it looking for all occurrences of the
required section. If there are no RUNSPEC or SYSTEM sections in the file then no further
action is required. However, if one of more sections of the required type are found in the
file, you must select which, if any, are required. The program displays a prompt specifying
the number of sections found.
2
98
Select the section you wish to load.
Reference section
The fluid model
PVTi Reference Manual
Note
If more than one section is found, the program offers the last section as the default,
although you can read any of the sections.
Hint
If you are uncertain as to the contents of the selected section, use File | View PVI
Section to display the section to the screen.
The syntax of the external file is similar to that of ECLIPSE. The data file is free format, except
for keywords, which must start in column 1. For further information on the keywords see "PVTi
keywords" on page 167. An example of such a file for a trivial two-component CO2 -isoButane
system is as follows:
-----RUNSPEC section: specific number of components and the EoS
---RUNSPEC
NCOMPS
2 /
EOS
PR /
------SYSTEM section: define hydrocarbon properties and composition
---SYSTEM
---Unit conventions
UNITS
METRIC
ABSOL
FRACTION /
DEGREES
KELVIN /
---Component names (library defaults)
LNAMES
CO2
IC4 /
---Overwrite default omega values by component
OMEGAA
0.4572
0.4572 /
OMEGAB
0.0778
0.0778 /
---Initial sample composition
ZI
0.6
0.4 /
---Binary Interaction Coefficients
BIC
2
1
1
0.13 /
/
---------------END
This defines the fluid, EoS etc.
COMB, SIMULATE, REGRESS, BLACKOIL sections may now follow
See examples in Appendix C
Note the following points:
PVTi Reference Manual
Reference section
The fluid model
99
•
Any characters following ---- are taken as comments. The data is free format, apart from
keywords which should start in column 1. You can split data over lines as required. The
forward slash (/) characters terminate data for a keyword.
•
You can specify repeat counts for any item. For example 3 * 1.0 implies three values of 1.0.
You can enter defaults by specifying a repeat count alone, such as 1*, or by the early
termination of a data list with a forward slash (/).
•
You may enclose character data such as component or experiment names in quotes. This is
optional and is only strictly required when the name contains embedded spaces or nonalphanumeric characters.
Equation of State
Hint
The default Equation of State is the Peng-Robinson three-Parameter equation. This is
suitable for most requirements, so generally you do not need to set the equation of
state.
This panel allows you to choose one of five main equations of state, to specify the required
viscosity correlation, and to decide whether or not to activate editing of specific heat capacities.
The equations of state are described in "Equation of state" on page 317; the viscosity options
are described in "Viscosity correlations" on page 330 and in [Ref. 5], [Ref. 7] & [Ref. 41].
The available equations of state are:
•
Peng-Robinson
•
Soave-Redlich-Kwong
•
Redlich-Kwong
•
Zudkevitch-Joffe
•
Schmidt-Wenzel
Choosing the Equation of State
1
PVTi: Edit | Fluid Model | Equation of State...
This opens the Equation of State and Viscosity panel, which gives you radio buttons for
selecting one EoS from the following list:
100
•
PR: 2-Parameter Peng-Robinson
•
SRK: 2-Parameter Soave-Redlich-Kwong
•
RK: Redlich-Kwong
•
ZJ: Zudkevitch-Joffe
•
PR3: 3-Parameter Peng-Robinson
•
SRK3: 3-Parameter Soave-Redlich-Kwong
•
SW: Schmidt-Wenzel.
2
Select the appropriate equation of state.
If you select either of the Peng-Robinson equations or the Schmidt-Wenzel equation, you
must also select whether you wish to use the correction to the dependence of the Ωa upon
acentric factor. The default is the modified (third-order in ω ) Peng-Robinson form.
3
Check the box for Yes, or leave it unchecked for No, as appropriate (see "Equation of state"
on page 317).
Reference section
The fluid model
PVTi Reference Manual
Three-parameter extension of the EoS
The three-parameter extensions of the EOS are:
•
PR3 - Peneloux et al. three-parameter EoS
•
SW - Schmidt-Wenzel EoS (implemented as a modified PR3)
•
SRK3 - Peneloux et al. three-parameter EoS.
The PR3 EoS is the default setting.
Hint
It has been our experience that the Peneloux et al. three-parameter equations of state,
PR3 and SRK3, generally give much better predictions of liquid properties and
saturations.
They also allow you an additional set of regression parameters, namely the component
volume shifts, making for an easier match to measured data.
Viscosity correlations
The Lohrenz-Bray-Clark, Pedersen and Aasberg-Petersen viscosity models are available. Select
the appropriate viscosity model.
Note
You can re-select the equation of state or viscosity correlation at any stage. However,
the default EoS parameters for each component are dependent upon the EoS, and the
program re-initializes these if you change the EoS. Alternatively you can manually
reset the parameters to the default values at any time.
Components
PVTi: Edit | Fluid Model | Components...
Fluid model components
This option allows you to enter component names and properties. Use this option to enter new
fluid components. You enter a mnemonic and a type, which determines how the program
interprets the component.
1
Select the Names folder.
2
To enter a component, click in an empty index field.
3
Enter the mnemonic for the component and select its type.
See "Component types" on page 102.
4
Click on Apply.
5
The other folders now have information in them:
PVTi Reference Manual
•
Complete shows all the properties of all components
•
Library shows the properties that were retrieved from the internal library
•
User shows user-defined properties
•
Characterization allows definition of fluid-model properties by characterization.
Reference section
The fluid model
101
Component types
Library
The PVTi program checks this against the internal library of names. If this exists in the internal
library, it adopts the internal description. If it does not recognize the mnemonic from amongst
the set described in the previous section, you must re-enter the mnemonic name or respecify the
component as a Char or User type, see below.
User
This option allows you to define components. Enter the required properties into the panel:
critical pressure and temperature, acentric factors, etc.
You should enter the components in order of increasing molecular weight, and nonhydrocarbons before hydrocarbons:
Non-Hydrocarbons
•
H2
•
H2 O
•
CO
•
N2
•
H2 S
•
CO 2
Hydrocarbons
•
C1
•
C2
•
CN+
Hint
By selecting PVTi: Run | Check fluid system the fluid is re-ordered into increasing
mole weights.
PVTi allows you to input a user component even if you know only the critical temperature and
pressure. It calculates the other properties as follows:
102
•
from T c and P c - Riazi-Daubert. For further information see [Ref. 30] and [EQ 8.11],
[EQ 8.12].
•
from T c and T b - Riazi-Daubert. For further information see [Ref. 30] and [EQ 8.11],
[EQ 8.12].
•
from T b , T b and Sg - Riazi-Daubert. For further information see [Ref. 30] and [EQ
8.33], [EQ 8.34].
•
ω
from P c , T b and T c - Edmister. For further information see [Ref. 30] & [EQ 8.10].
•
P
from Macleod and Sugden. For further information see [Ref. 14].
Tb
Sg
Mw
Reference section
The fluid model
PVTi Reference Manual
•
Vc
& Z c - Riazi-Dubert. For further information see [Ref. 12].
Use the Apply button to calculate the other properties of the component.
Characterization
If you give a characterization, you must generally specify at least two out of the following (these
are specified in the Characterization folder):
•
molecular weight M w ,
•
specific gravity S g ,
•
normal boiling point temperature T b ,
•
Watson characterization factor K w ,
•
reference temperature K
Hint
If you have more than two of the set M w , S g , T b and K w , we recommend that you enter
the best two first, as the order of entry decides which pair the program selects. For
example, if you enter M w , T b and K w then the program uses M w and T b .
Note
It is possible to perform a characterization by entering just the molecular weight,
whereupon the program estimates the specific gravity from a look-up of Single Carbon
Number (SCN) groups.
You can choose from the following correlations for estimating the physical properties and
acentric factors:
Critical properties
•
Kesler-Lee. See [Ref. 10].
•
Cavett. See [Ref. 11].
•
Riazi-Daubert. See [Ref. 12].
•
Winn. See [Ref. 43].
•
Pedersen. See [Ref. 43], [Ref. 41] and [Ref. 45].
Acentric factors
•
Kesler-Lee. See [Ref. 10].
•
Edmister. See [Ref. 14].
•
Thomassen. See [Ref. 30].
•
Pedersen. See [Ref. 43], [Ref. 41] and [Ref. 45].
Note
PVTi Reference Manual
When reading in a file the critical volumes (Vc) and critical Z factors (Zc) for each
component must satisfy the relation PcVc=ZcRTc (where Tc, Pc, R are the critical
temperatures, critical pressures and universal gas constant respectively). If this is not
the case then PVTi will alter the values of the relevant critical Z-factors in order that
this relation is satisfied.
Reference section
The fluid model
103
Binary Interaction Coefficients
This option enables you to enter the Binary Interaction Coefficients (BICs) for each component.
1
PVTi: Edit | Fluid Model | Binary Interaction Coefficients...
This displays the Binary Interaction Coefficients panel.
2
Enter the Binary Interaction Coefficients for each component.
3
Alter the Cheuh-Prausnitz-A coefficient as required.
4
Click on Reset to return the interaction coefficients to default values.
Volume shifts
Note
Volume shifts are only available if you use a three-parameter Equation of State.
Use this option to enter the dimensionless volume shifts. The actual volume shifts in the
equation of state are displayed beside them.
1
PVTi: Edit | Fluid Model | Volume Shifts... .
This displays the Volume Shifts and Thermal Expansion Coefficient panel.
2
Enter the volume shifts for the required components.
3
Click on OK.
Note
If the "Temperature dependence for volume shifts" on page 147 option is set then you
can enter a value for THERMX, the thermal expansion coefficient.
Thermal properties
Note
You can only use this option if the program option "Specify/Calculate density and
molar volume units" on page 147 is switched on. It can be switched on in the Equation
of State panel (see "Equation of State" on page 100).
Specific heat capacity coefficients and calorific values for each component are the thermal
properties used in PVTi.
1
PVTi: Edit | Fluid Model | Thermal properties....
This opens the Thermal Properties panel.
2
Amend the thermal properties for the components, as required.
3
Click on OK.
LBC Viscosity Coefficients
Note
LBC Viscosity coefficients are only available if you are using the LBC Viscosity
model.
Use the option to view or edit the LBC viscosity coefficients.
104
Reference section
The fluid model
PVTi Reference Manual
1
PVTi: Edit | Fluid Model | LBC Viscosity Coefficients....
This opens the LBC Viscosity Coefficients panel.
2
View or amend the coefficients as required.
3
Click on OK.
Splitting components
This menu allows for the automatic splitting of the plus fraction into a required number of subfractions for subsequent use in a large regression or for output to a compositional simulator such
as the one in ECLIPSE.
Splitting is also used to accommodate different plus-fraction properties for different fluid
samples. This process is often known as a multi-feed split.
This option allows you to input data for splitting the plus fraction. There are three methods
available from this option for splitting the plus fraction, which must be the last component:
•
Constant Mole Fraction splitting (CMF)
•
Whitson
•
Multi-feed split or Semi-Continuous Thermodynamic (SCT) splitting
1
To choose the splitting method, select PVTi: Edit | Fluid Model | Split and select the
splitting option.
Constant Mole Fraction (CMF)
1
Specify the number of pseudo-components you require. The default is N frac = 3 .
2
Give the specific gravity and required sub-fraction split.
By default, the program estimates the specific gravity of the plus fraction from the
reference density, if one was given, and uses a constant mole fraction split of 1 ⁄ N frac .
3
Specify the Whitson Alpha Factor and the Whitson ETA factor, as required.
4
Enter the Critical Props. Correlation and the Acentric Props. Correlation.
5
Give the compositions of the pseudo-components.
6
Click on OK.
Whitson or modified Whitson (Whitson)
1
Specify the first single carbon number (SCN) group to be included in the plus fraction split.
For example, enter 7 if plus fraction is C 7+ .
2
Give the molecular weight, specific gravity and the mole fraction of the plus fraction.
3
Enter the number of pseudo-components to be used after the regrouping of the Whitson
split.
For example, N MCN = 3 .
4
Specify the Critical Props Correlation and the Acentric Props. Correlation.
5
Select the grouping technique.
6
Choose whether you wish to plot a fingerprint of the Whitson split fractions.
7
Click on OK.
PVTi Reference Manual
Reference section
The fluid model
105
Multi-feed Split (also called semi-continuous thermodynamic (SCT) split)
1
Specify the number of pseudo-components for the split.
This value must be between two and five. The default is two.
2
Confirm the default minimum mole weight in the plus fraction (Whitson η -parameter) or
edit the data as required.
3
Confirm the default mole weight of the heaviest pseudo-component or edit the data as
required.
The default setting is twice the plus fraction mole weight.
4
Set the Critical Props. and Acentric Props. correlations.
5
Specify the group and the molecular weight of the sample’s plus fraction.
6
Amend the default names for the new components, if required.
The default names are FRC1, FRC2, etc.
Note
Note that splitting is not necessarily the opposite of grouping. Splitting the plus
fraction into two or more pseudo-components, followed by a re-grouping of those
pseudo-components back into a single plus fraction, generally results in a different set
of critical properties, etc., from those originally possessed by the plus fraction.
PNA Distribution
This splits all components heavier than the library C6 component into paraffinic (P),
naphthalenic (N), and aromatic (A) components. This is done according to the method outlined
in "The PNA distribution of heavy components" on page 394. The critical properties assigned
to the PNA components are those described in "Critical properties of PNA species" on
page 395.
Group
This menu allows for the automatic grouping of sub-fractions for subsequent use in a large
regression or for output to a compositional simulator such as the one in ECLIPSE.
This option allows you to choose components to group and perform the grouping operation. The
default scheme for grouping is to group to the default sample ZI using the mole fraction
weighting to group components. Other schemes of grouping include grouping by molecular
weight and by mixing rule, see [Ref. 44]. Also the sample to group to can be changed to any in
the defined set, or to an average of all samples.
To group components, select PVTi: Edit | Fluid Model | Group...
This displays the current component system, each component having an associated index. The
first time you enter this option, all these indices are set to 0, indicating that they do not belong
to any group.
1
To create a new pseudo component, give a new index of greater than zero to two or more
components.
2
Select the Grouping Technique.
3
Give the group or pseudo-component a new component mnemonic, if required.
Hint
106
Reference section
The fluid model
You can perform several groupings from the same original component description by
specifying the new components with ascending indices, 1, 2, etc.
PVTi Reference Manual
4
Click on the Update button to automatically display any of these new component names.
5
Click on the OK button to create the groups.
Note
Note that splitting is not necessarily the opposite of grouping. That is, splitting the plus
fraction into two or more pseudo-components, followed by a re-grouping of those
pseudo-components back into a single plus fraction, generally results in a different set
of critical properties, etc., from those originally possessed by the plus fraction.
Defining Samples
Sample names
1
PVTi: Edit | Samples | Names...
Defines sample names. Use this option to enter mnemonics for each component. You can enter
more than one sample for later use; to do this, reference each sample by its mnemonic, of up to
8 characters.
Note
Note that the mnemonic for the default sample is “ZI”, for “z initial”.
For alternative samples, you may specify a line of text to give additional information. For
example: from different depths in the hydrocarbon column, a “saved” calculated composition
from a simulation, etc.
Sample compositions
1
PVTi: Edit | Samples | Compositions....
Enter the compositions for each defined sample. PVTi ensures that they all add up to unity. If a
sample does not add up to unity, a message appears asking whether or not the program should
redistribute the difference across the components.
Sample salinities
1
PVTi: Edit | Samples | Salinities...
This option allows you to enter sample salinities. If you have entered H 2 O as a component then
use this option to add the salinity of each sample.
Note
PVTi Reference Manual
This information is used in the MFLASH experiment in the "Simulation using PVTi"
on page 117.
Reference section
The fluid model
107
Mixing samples
This option allows you to form a new sample by mixing any two existing samples. You can enter
the amount of each sample to mix either as the mole fraction of the second sample in the
resulting mixture, or as a volume of gas of the second sample as a ratio to the volume of the first
sample at its P sat or other pressure at the specified mix temperature. The latter case is useful
when considering lean gas injections into an oil.
The program produces the required mix provided that:
•
The two samples are different.
•
The amount of the second sample to mix is greater than zero.
•
The number of samples does not exceed the maximum allowed (50).
•
The name of the new sample is unique in the set.
1
To mix samples, select PVTi: Edit | Samples | Mix...
This activates the Mix Samples panel.
2
Select the Mixing Type.
3
Choose the fluid samples you wish to mix.
4
Enter the new sample name.
5
Enter the temperature with its units, and the mole fraction.
6
If you are mixing by GOR, give the GOR and the pressure for GOR oil volume
calculation
7
Click on OK.
If the sample is mixed by recombination, the GOR is taken as the stock tank GOR, the
conditions are separator conditions and the mixture is created such that the stock tank GOR
matches the required value.
Viewing samples
Sample fingerprint plot
This option allows you to generate fingerprint plots. This consists of plotting the logarithm of
the component mole fractions against the component molecular weights.
Hint
1
Fingerprint plots give an idea of the nature, that is condensate or volatile oil, of a given
fluid sample. Providing a reasonable split of the Heptanes plus is available, then a
condensate typically has straight line or down-turning slope proceeding towards the
heavier fractions, whilst a volatile oil has an up-turning slope as it usually contains
more heavy fractions.
To generate fingerprint plots, select PVTi: View | Samples | Fingerprint Plot.
This activates the Fingerprint Plot panel, which enables you to select the sample you
require to be used for the plot from a drop-down panel.
2
108
Select the sample you wish to plot and click on Apply. An example of a plot is shown in
Figure 6.2.
Reference section
The fluid model
PVTi Reference Manual
Figure 6.2 Fingerprint Plot
Sample phase plot
This option allows you to generate phase plots. This uses the equation of state model with the
current fluid description to obtain the bubble point and dew point lines. Where the two lines
meet is the critical point, at T = T c , p = p c . As part of the calculation process, an explicit
calculation is made of the position of the critical point. You can choose how many quality lines
(lines of constant vapor mole fraction) are required on the plot; this can vary between 0 and 9
(that is, 10%, 20%,..., 90%).
1
To generate phase plots, select PVTi: View | Samples | Phase Plot.
This activates the Phase Plot and Quality Lines panel.
2
Select the sample you wish to plot.
3
Enter the number of quality lines (from 1 to 9).
4
Decide whether or not to plot the Hydrate formation line.
5
Click on OK.
Hint
A default phase plot (with one quality line) can be generated by simply dragging a
sample name from the Data Tree and dropping it into the Main Plot Window.
Note
If depletion experiments or separators exist, they are plotted onto the phase plot too.
PVTi Reference Manual
Reference section
The fluid model
109
Figure 6.3 Phase plot
Sample ternary plot
This option allows you to create a ternary plot for a particular sample. The ternary plot panel
allows you to set: the sample to be plotted; the temperature and pressure for the plot; and the
grouping of the fluid components so as to create three components for the ternary plot.
1
To generate a ternary plot, select PVTi: View | Sample | Ternary Plot
2
Select the fluid sample for plotting
3
Enter a temperature and pressure.
4
Select the component groupings and the names of the grouped components.
Hint
110
Reference section
The fluid model
The default component groupings are: C1 and the non-hydrocarbons, C2-C6 and C7
and heavier hydrocarbons. This is typically the best choice, so you should only need to
change the groupings from the default in special cases.
PVTi Reference Manual
Figure 6.4 Ternary Plot
PVTi Reference Manual
Reference section
The fluid model
111
COMB - Compositional Material Balance
Introduction
Material balance checks provide an important tool in analyzing the quality of the data found in
a PVT report. In PVTi, material balance checking is provided for Constant Volume Depletion
(CVD) experiments, Separators by recombination, and the calculation of liquid and vapor
recovery.
Caution
It is important to always examine PVT laboratory data for material balance errors.
If the reported observations contain serious errors, these will be reflected in the
fitted equation of state model.
It is generally the case that for gas condensate and volatile oil samples, a constant volume
depletion experiment (CVD) is performed as part of a laboratory analysis. Using material
balance considerations, it is possible to calculate liquid compositions and hence K -values,
molar masses, densities, etc. This can be very useful for two reasons:
1
With appropriate separator data, estimates of oil and gas recovery can be performed without
recourse to an equation of state model.
2
The consistency checks provide a measure of the quality of laboratory data and
consequently its value or otherwise in any subsequent regression analysis.
Accessing material balance checks
The Material Balance panel can be found by selecting the experiment in the project tree-view,
right-clicking on it and selecting Material Balance... from the pop-up menu that appears.
A technical outline of the methodology used in the Material Balance panels can be found in
"Consistency checks and correlations" on page 308.
There are three different Material Balance panels: one for depletion (CVD), one for separators,
and one for Constant Composition Expansion (CCE). Each is described below.
Material balance for Constant Volume Depletion (CVD)
Experiments
Right-click on the experiment in the project-tree and select Material Balance... from the popup menu.
There are three buttons on this panel
•
Report
•
Plot
This gives access to the full range of material balance diagnostic plots. For more details on
these plots see "Consistency checks and correlations" on page 308.
•
112
Modify
Reference section
COMB - Compositional Material Balance
PVTi Reference Manual
Report
This option performs the material balance calculation and produces a report on any current
problems with the fluid.
Figure 6.5 Main display after performing material balance
Plot
Use this option to perform plots.
The set of plots available from this option are:
•
Vapor composition (input)
•
Liquid composition
•
K -values
•
Produced moles
•
Vapor moles left in cell
•
Liquid moles left in cell
PVTi Reference Manual
(1): log( K ) versus pressure
Reference section
COMB - Compositional Material Balance
113
•
Produced mass
•
Vapor compositions versus pressure
•
Liquid compositions versus pressure
•
Liquid volume in cell
•
K -values
•
Initial and recovered compositions
•
Final stage liquid composition
•
Calculated and correlated liquid density
•
Input and correlated vapor Z -factor
(2): Hoffmann plot
Figure 6.6 COMB module - vapor versus pressure plot
Modify
Use this option to modify data. Errors in the input data may become evident after you performed
the CVD material balance. You can use this option to rectify these errors. You may consider
changing the saturation pressure liquid saturations, Z -factors, etc.
Hint
114
You can avoid calculated liquid mole fractions remaining in the cell by changing the
composition of the feed stream (well stream) or one or more of the removed gas
streams.
Reference section
COMB - Compositional Material Balance
PVTi Reference Manual
Negative calculated liquid moles
Negative calculated liquid moles for a given component across a wide range of the sampled
pressure stages probably indicate errors in the wellstream composition (which is usually a
calculated recombination sample).
Errors at a lesser number of stages or at just one or two specific stages probably indicate a
measurement error on a given removed gas stream.
In either case, you can modify the well stream or removed gas stream compositions by
increasing (positive % or absolute value) or decreasing (negative % or absolute value) one or
more component compositions. The program automatically re-scales the remaining
(unmodified) compositions in the stream, according to their initial mole fraction, so that the total
mole fraction for the stream sums back to 100%.
If you require any of the compositions to remain fixed prior to the material balance calculation,
type any character in the field immediately preceding the Modifier field for that composition.
Separator recombination
Use this panel to directly test the quality of recombinations. To open this panel,
right-click on the separator experiment in the project-tree and select Material Balance... from
the pop-up menu.
Report
Use this option to test recombinations. It generates the calculated and Standing's K -values and
provides a report on the results.
Testing combinations
If sufficient volumetrics data has been entered in the previous item the recombined sample is
calculated and output to the report and PVP file.
The output details the calculated feed to either separator using the given values of GOR, oil
density and liquid and vapor compositions from each separator stage and is printed together
with the given feed composition for comparison.
Plot
Use this option to plot the recombination results. It produces a Hoffmann-Crump-Hocott plot,
which gives a measure of the quality of the separator data.
Constant Composition Expansion (CCE) recovery
calculations
Use this option to make estimates of the recovery of vapor and liquid from an initial reservoir
pressure in excess of the saturation pressure defined in the CVD experiment.
To open this panel, right-click on the CCE experiment and select Material Balance... from the
pop-up menu.
Note
PVTi Reference Manual
This option is only available if there are valid depletion and separators experiments in
the project, in addition to the CCE experiment.
Reference section
COMB - Compositional Material Balance
115
Rel. Perm.
Use this option to define liquid production. If oil is to be ‘produced’ in the recovery calculations
(using the method of Reudelhuber Hinds, [Ref. 37]), you must enter two points on the plot of
relative permeability versus total liquid saturation.
Report
Use this option to perform recovery calculations. It allows you to estimate recoveries of vapor
and liquid.
Plot
Use this option to produce a plot of the gas and oil recovered as a function of pressure.
116
Reference section
COMB - Compositional Material Balance
PVTi Reference Manual
Simulation using PVTi
Introduction
PVTi allows you to perform experiments on your defined hydrocarbon system. The experiments
available include:
•
Flash calculation
•
Bubble and dew point determination
•
Simulation of laboratory experiments such as constant composition expansion, constant
volume depletion, and differential liberation
•
Swelling tests
•
Separators
•
Variation of composition and pressure with depth
•
Vaporization tests
•
multiphase flash.
•
Wax appearance temperature
•
Asphaltene appearance pressure
Note
You can enter any experimentally determined observations available to compare with
the output produced by the Simulate module, apart from the multiphase flash
experiment.
Defining Experiments
1
PVTi | Edit | Experiments...
This opens the Define Simulate Experiments panel.
2
To add a new experiment select it on the Add menu. To edit an existing experiment, select
its name from the drop-down list, which appears in the panel, and click OK.
3
Once an experiment has been created for definition or selected for editing, you will see a
customizable form that can be tailored to suit your data. The information is entered in a
number of folders.
4
In the first folder, General, you can select various single-valued pieces of information for
entry. The required information is automatically selected and cannot be deselected, so an
information line informs that this data is required.
5
The second folder, Observations, shows a table where you can customize column
headings to match your observation data. If you are editing an existing experiment, the
observations in the currently defined set are already shown as column headings. In this way
you can match the data entry panel to your own data-set. If you forget to enter a required
quantity (for example Pressure in a Differential Liberation experiment - see "Differential
liberation" on page 119) PVTi warns you and does not create the customized entry form.
PVTi Reference Manual
Reference section
Simulation using PVTi
117
6
The third folder, Components, allows you to determine whether you enter componentbase data or not. Typical options here are for Liquid Mole Fractions, Vapor Mole Fractions
or K-values.
7
The fourth folder, Other, is used for miscellaneous observations that do not fit any of the
other categories. Currently this folder is only used by the Constant Volume Depletion
experiment for the Final Liquid Mole Fraction. When other experiments are being entered,
this folder does not appear.
8
Click Apply.
9
A customized form is now created, with the same folders as described above. Now the
folders contain data-entry fields and tables for observations. Once the data have been
entered, click on Apply to submit the data and create or edit the experiment.
10 Finally, Close becomes active and can be used to close the panel
Data requirements for the experiments
Flash calculation
For this experiment you must define the pressure and temperature of the flash.
The program performs a stability test and establishes the number of phases present prior to the
flash calculation.
Note
The gas-oil ratio reported by the calculation is defined as gas volume at standard
conditions divided by liquid volume at flash conditions. The gas volume is obtained
using a Z -factor of unity.
Bubble point pressure
For this experiment you must enter the temperature at which the bubble point is required.
Note
If the temperature is such that no bubble point can be found (above the critical
temperature) the program returns a warning message.
Dew point pressure
For this experiment you must supply the temperature and choose between normal or retrograde
dew points. The default dew point is retrograde.
Note
If the temperature is such that no dew point can be found (above the critical
temperature) the program returns a warning message.
Constant composition expansion
For this experiment you must specify a temperature and a series of pressures. Additionally you
must specify whether the fluid is oil or gas. You do not need to give a value at saturation
pressure.
118
Reference section
Simulation using PVTi
PVTi Reference Manual
Hint
You can apply this experiment to a liquid (bubble point) or vapor (dew point) system.
The program tests for both possibilities. It is also possible to perform a constant
composition expansion on a true one-phase system (SIN), such as an (dry) injection
gas above its cricondentherm.
Note
When obtaining relative volumes the program uses saturation volume as a
normalisation volume, if one exists, or the volume at the highest pressure, if not.
Constant volume depletion
For this experiment you must specify a temperature and a series of pressures. You do not need
to give a value at saturation pressure.
Hint
You can apply this experiment to a liquid (bubble point) or vapor (dew point) system.
The program tests for both possibilities. It is not, however, possible to apply this
experiment to samples that are above the cricondentherm.
Note
The relative volume reported by the program is the fraction of the cell filled with liquid
at the end of the constant volume step, that is after the original volume has been
restored by removing vapor.
Differential liberation
For this experiment you must specify a temperature and a series of pressures. You do not need
to give a value at the bubble point. PVTi provides this pressure point.
The program also provides automatically the last step in the differential liberation process, the
reduction to standard conditions. However, the program does not provide the pressure point at
standard pressure (usually 14.7psia) and at reservoir temperature and the user must enter this for
the final stage.
Note
You may only apply this experiment to a liquid (bubble point) system.
Hint
The relative volume reported by the program is the ratio of the oil volume at each step
to the oil volume at the final (standard conditions) step.
Note
There are alternative definitions of the GOR and the relative oil volume available using
the program options "Definition of GOR in Diff. Lib." on page 148 and "Definition of
Oil relative volume in Diff. Lib." on page 149.
Swelling test
A swelling test consists of adding increasing amounts of a lean gas to a reservoir fluid and
determining the swelling of the mixture relative to the original fluid composition.
For this experiment you must specify:
PVTi Reference Manual
Reference section
Simulation using PVTi
119
1
The nature of the original fluid type, OIL or GAS.
2
The composition of the lean gas to be added.
3
The reservoir temperature.
4
A set of either mole percentages of gas in the mixture or GORs (the volume of gas at STC,
that is 14.7 psi and 60 °F , per volume of oil at original saturation pressure or other specified
pressure).
Separators
Separators consist of a set of connected equilibrium flashes at user prescribed pressures and
temperatures.
For this experiment you must specify:
1
The composition of the feed stream from the defined sample mnemonics.
2
A number of stages (up to seven) for which you must give a pressure and temperature.
Additionally, you must connect the vapor and liquid outputs of each stream to some subsequent
stream. The default routing is to connect the liquid output of stage (j) to stage (j+1), and to take
the vapor output to stock tank conditions (as defined by the STCOND keyword or by the
Standard Conditions menu option under OPTIONS).
Note
A stage output can be fed back to any previous stage though not back to the current
stage. No stock tank stage is defined automatically, and whereas it is customary to
quote vapor properties at stock tank conditions, liquid properties will be quoted at the
“final stage” conditions. Therefore, if liquid properties at stock tank conditions are
required, this should be the final (additional) stage which must be defined by the user.
For example if we have a separator with 3 stages with the last stage being stock tank
conditions, then a liquid FVF at stage 1 of the separator will be the volume of liquid
divided by the final liquid volume (stock tank conditions in this case) after flashing the
liquid feed of stage 1 through the remaining 2 stages of the separator chain.
Hint
The "Definition of Oil relative volume in Diff. Lib." on page 149 program option
allows you to quote GORs as volume of gas at standard conditions per volume of stock
tank oil as opposed to the default calculation of volume of gas at standard conditions
per volume of separator liquid at separator conditions.
The program can calculate oil formation volume factors, that is the volume of reservoir fluid at
initial or bubble point conditions per stock tank volume (SRELV) and, by separator stage,
volume of separator liquid at separator conditions per stock tank oil volume (ORELV).
To use this option tick the box in the panel or use the FVFREF keyword in batch mode.
Variation of composition and pressure with depth
It is well known that composition varies with depth in a reservoir.
For this experiment you must specify:
120
1
A reference sample composition (from the currently defined sample mnemonics).
2
A reference depth, pressure and temperature for the sample.
3
A set of depths above and/or below the reference depth, at which you wish the program to
calculate the composition and pressure.
Reference section
Simulation using PVTi
PVTi Reference Manual
If during the increment up and/or down, either a genuine gas-oil contact is found or a transition
from gas to oil (or vice-versa) without passing through a contact (a “critical” transition), then
the program reports this depth.
Note
The assumptions made in the performance of this experiment, that there are no
asphaltenes and that the reservoir is in thermal, gravitational and diffusive equilibrium,
are probably not achieved in any real reservoir. However, despite these reservations,
this is a useful test of the depth-variation of a particular fluid.
Vaporization test
This is a somewhat specialised test performed for gas-injection on reservoir fluids, but in fact it
is rather similar to a swelling test.
For this experiment you must specify:
1
The composition of the reservoir fluid and injection fluid from the currently defined sample
mnemonics.
2
The reservoir pressure and temperature
3
The number of moles of injection gas to be added to the reservoir fluid.
Multiphase flash calculation
The inputs required for the multiphase flash experiment are the same as for the usual two-phase
flash experiment ([Ref. 36]). For this experiment you must define the pressure and temperature
of the flash. The program performs a stability test and establishes the number of phases present
prior to the flash calculation.
Note
The gas-oil ratio reported by the calculation is defined as gas volume at standard
conditions divided by liquid volume at flash conditions. The gas volume is obtained
using a Z -factor of unity. Note also no facility currently exists for comparing these
against observed values.
Note
If the sample you select for the experiment contains water, you should enter the salinity
in the PROPS section.
Saturation pressure calculation
This is essentially the same as the bubble and dew point calculations. For this experiment you
must enter the temperature at which the saturation point is required.
The calculation is particularly useful if you have no a priori information about whether the
saturation point is bubble or dew.
Note
PVTi Reference Manual
In the case of the dew point, program returns the retrograde (highest pressure) dew
point.
Reference section
Simulation using PVTi
121
Saturation temperature calculation
For this experiment you must specify the pressure. Since there are generally two saturation
temperatures (one from each side of the phase envelope), you must also specify which solution
is required - lower or higher.
Critical point calculation
This is a convenient way of obtaining the critical point of a sample, without generating a full
phase envelope. Enter the sample name for this experiment.
First contact miscibility pressure calculation
This calculation returns the lowest pressure at which the samples are directly miscible,
regardless of the proportions in which they are mixed. The method used to determine the
minimum pressure is described in the paper by Jensen and Michelsen, [Ref. 39]. For this
experiment specify the temperature and the names of the two samples.
Multiple contact miscibility pressure calculation
This calculation determines the lowest pressure at which two samples (one oil, one gas) are
always miscible (regardless of their relative proportions) after repeated contacts between them,
when only one of the samples is affected at each contact. When the sample affected is the gas,
this simulates a one-cell vaporizing drive. If the oil is affected each time, this mimics a one-cell
condensing driveways method used to determine the minimum pressure. This case is also
described in the paper by Jensen and Michelsen, [Ref. 38]. For this experiment, specify the
temperature and the names of the two samples. Give the drive to simulate.
Multiple contact test
This experiment simulates the multiple contact test where a series of flashes are performed on
mixtures of reservoir oil and injected gas.
For this experiment specify:
1
The oil and gas samples
2
The temperature and pressure of the test
3
The drive to simulate (either condensing where the remaining oil is kept after each flash
and contacted with the initial gas sample, or vaporizing where the remaining gas is kept
after each flash and contacted with the original oil sample)
4
The fractions of remaining oil/gas to be contacted with the original gas/oil at each stage.
Hint
You can use this experiment in the REGRESS section. For further information see
"Regression in PVTi" on page 126.
Defining Observations
Observations can be defined at the same time as the experiment; see "Defining Experiments" on
page 117.
1
PVTi: Edit | Observations...
This opens the Define Simulate Observations panel.
122
2
Choose the index of the experiment
3
Select abbreviation for the observation to be entered
Reference section
Simulation using PVTi
PVTi Reference Manual
4
Enter the data for this observation
5
If you are entering data for regression purposes, give weightings, either individual or
global, for the observation types.
The observations available vary with experiment type, but will be from the following set:
Table 6.2
Observation data
Abbreviation
Observation
Liquid Z-Factor
Liquid Z -factor
Vapor Z-Factor
vapor Z -factor
Liquid Density
Liquid density
Vapor Density
Vapor density
Liquid Mol. Wght. Liquid molecular weight
Vapor Mol. Wght
Vapor molecular weight
Liquid Visc.
Liquid viscosity
Vapor Visc.
vapor viscosity
Liquid Sat.
Liquid saturation
Vapor Sat.
Vapor saturation
Vapor Mol. Frac.
Vapor mole fraction
Sat. Pressure
Saturation pressure: gas - p dew , oil - pbub
Sat. Temperature
Saturation temperature: not currently available
Gas-Oil Ratio
GOR: SEPS - gas (STC)/oil (stage/STC); DL gas (STC)/oil (STC/ p sat )
Relative Vol.
Relative volume (SWELL = swelling factor)
Total Gas-oil ratio
Cumulative separator GOR: (Gas at STC/final stage Oil)
Ternary Plot
Ternary Plot (Multi-Contact Test and plotting only)
Mole. wght. plus
Mole weight of plus fraction (COMB Mat. Bal.)
Rel. oil sat.
Relative oil saturated volume ( B o ( p bub ) in DL)
K Values
K -values
Liquid mol. frac.
Liquid mole fraction
Vapor mol. frac.
vapor mole fraction
Total mol. frac.
Total mole fraction
Spec. grav. plus
Specific gravity of plus fraction (COMB Mat. Bal.)
Moles Recov.
Moles recovered from depletion experiment (CVD,DL)
Liquid mol. vol.
Liquid molar volume (specific volume)
Vapor mol. vol.
vapor molar volume (specific volume)
Final mol. wght.
liq. plus
Mole weight of liquid plus fraction (COMB Mat. Bal.)
Final spec. grav.
liq. plus
Specific gravity of liquid plus fraction (COMB Mat. Bal.)
Final liq. mol. frac. Liquid mole fraction of final stage of CVD (COMB Mat. Bal.)
PVTi Reference Manual
Total rel. vol.
Total (oil and gas) relative volume (DL)
Oil rel. vol.
Oil relative volume (DL, SEPS, vapor) (also see RVSAT)
Gas Gravity
Gas gravity (Differential Liberation)
Reference section
Simulation using PVTi
123
Table 6.2
Observation data (Continued)
Abbreviation
Observation
Gas FVF
Gas formation volume factor (DL)
Gas Vol. Ext.
Gas volume extracted (at STC) (DL)
2-phase Z
Two phase Z -factor (CVD)
Oil rel. FVF
Oil FVF from p init ⁄ p bub to p stock (SEPS)
Note
Note that not all the observed data types are available for all experiments.
Running a simulation
Note
1
Simulations are automatically run on creation, so the results are immediately available.
PVTi: Run | Simulate
When the simulation is complete the program displays a text module detailing the success
or otherwise of the runs. The PVTi main display window showing the experiment results
will resemble the following:
CCE :
Constant Composition Expansion
Soave-Redlich-Kwong (3-Parm) on Z1
Lohrenz-Bray-Clark Viscosity Correlation
Density units are
KG/M3
Viscosity units are
CPOISE
Surface Tension units are
DYNES/CM
Specified temperature
Deg K
377.5944
Liq Sat calc. is Vol oil/Vol Fluid at Sat. Vol
------------------- ----------------------- -----------Rel Volume
Vap Mole Frn
Pressure
Inserted ----------------------- -----------BARSG
Point
Observed Calculated
Calculated
------------------- ----------------------- -----------344.739
0.9189
0.9485
310.265
0.9278
0.9565
275.791
0.9379
0.9652
241.317
0.9492
0.9750
199.948
0.9623
0.9882
193.053
0.9651
0.9906
186.159
0.9681
0.9930
179.264
0.9711
0.9955
Hint
124
-----------Liq Density
-----------Calculated
-----------682.4368
676.7593
670.6133
663.9241
655.0453
653.4620
651.8460
650.1961
PVTi recognizes which experiment simulations are up to date and then only performs
necessary calculations. This means that to view the simulation results you should
always use PVTi: Run | Simulate.
Reference section
Simulation using PVTi
PVTi Reference Manual
Hint
If you click on an experiment in the sample-tree using the right mouse button, and
select Report... from the drop-down menu, you can see the report for that experiment
on its own.
Plotting simulation results
In addition to the simulation results tables, the results of simulations can be plotted. There are
two ways to do this.
Firstly, to view the comparison between the simulated results and the observations, simply drag
the appropriate observation from the Data Tree and drop it into the Main Plot Space.
Secondly, you can use the observation editor to plot any simulated quantity, not just those for
which there are observations. For information on the observation editor see "Defining
Observations" on page 122.
PVTi Reference Manual
Reference section
Simulation using PVTi
125
Regression in PVTi
Introduction
Performing a regression
To perform a regression you must specify:
•
The experiments to be used in the regression. You can choose from the experiments
mentioned in "Defining Experiments" on page 117.
•
The weighting for the observations associated with those experiments. You can use most of
the observations given in a laboratory experiment as observations to match against
predicted data.
•
The Equation of State parameters you wish to vary to match predicted to observed
quantities. Most of the Equation of State parameters are available as regression variables.
Note
The time taken for the regression operation rises rapidly with the number of variables
chosen, and the use of the minimum possible set is suggested. That said, any
combination of critical point data, Ωa and Ωb values, acentric factors, binary
interaction coefficients, δ ij and volume shift parameters (if the PR3 or SRK3 forms for
the Equation of State are being used) may be chosen to be modified. There is a
maximum total of 50 regression variables.
Regression function
The regression function to be minimized is the normalized root mean square (RMS) error of
predicted experiment results to the given (weighted) observed experiment results. See "Details
Folder" on page 131 for a description of the RMS value used.
Note
In order to run the regression, there must be at least as many observations as chosen
regression variables.
Regression Panel
1
To open the Regression panel select PVTi: Run | Regression...
2
Use this menu to set up and perform regression. To open this menu, select PVTi: Edit |
Regression
Variables
The Variables section has the following options:
•
Normal (component properties and BICs)
Normal variables are individual fluid component properties and binary interaction
coefficients. For further information see "Defining regression variables..." on page 127.
126
Reference section
Regression in PVTi
PVTi Reference Manual
•
Special (MW of characterized components etc.)
The special variables available depends on the project settings and the fluid model
properties. Typical special variables are the mole weight of the plus fraction or the CheuhPrausnitz coefficient for binary interaction coefficients. See "Setting special variables" on
page 128.
•
PVTi Selects
This sets up the regression variables according to the rules given in "Physical selection of
regression parameters" on page 386.
The two buttons are:
•
Variables... Opens a panel specific to the selection of variable types (see above).
•
Limits... Sets limits on regression variables. For further information see "Setting regression
limits" on page 129.
Report
The Report section has the following buttons:
•
Regression: Opens the Regression Report panel. See"Regression Report" on page 130.
•
Simulation: Opens the simulation report of all experiments.
Regress
The Regress section is for running regressions. The buttons in this section are:
•
Run: Perform regression. For further information see "Performing a regression" on
page 130.
•
Accept / Reject: Accept or reject the last regression. For further information see
"Accepting or reject regression results" on page 130.
Additional Information
Defining regression variables...
Use this option to define/re-define the set of variables for use in the regression. There may be
two sets of variables available for use in regression, depending on the state of the "Program
options" on page 145 and whether modified Whitson splitting (SCT) has been used on the plus
fraction. The two sets are denoted normal and special.
•
The normal variables are the component dependent ones, that is variables such as critical
properties, acentric factors, etc.
•
The special variables are system-wide or multi-component variables such as the thermal
expansion coefficient or the Cheuh-Prausnitz A -factor for binary interaction coefficients.
Setting normal variables
There are two panels for setting normal variables.
Use the first panel to define the EoS parameters, the parameters for the LBC viscosity
correlation and the volume shifts for the currently defined N c components.
PVTi Reference Manual
Reference section
Regression in PVTi
127
1
Enter integers for the EoS parameters:
a
Pc
b
Tc
c
ω
d
Ωa
Hint
2
Enter integers for the LBC viscosity parameters:
a
Ωb
b
Vc
c
Vc
Hint
3
If you wish to vary a given EoS parameter, say T c , of two or more components as
separate independent quantities, you should give them different values. For example
1,2,..., etc.
If you wish to vary the parameters as one or more groups of variables, you should give
the required group members the same integer. This may be particularly useful when
trying to vary V c values to match to viscosity data using the LBC correlation, for
example.
Enter integers for the volume shifts:
a
PR3
b
SRK3
Note
All of these data fields can take an integer value, 0,1,2,..., and so on. The default of
zero (or blank/null field) implies that the particular component’s EoS parameter is not
to be used in any subsequent regression.
Use the second panel to define the status of the lower half of the (symmetric, zero-diagonal)
matrix of binary interaction coefficients.
Note
Note that the rules regarding choice of groups for binary interaction coefficients are
slightly different in that groups may be specified down columns or along rows of the
lower half matrix but not both.
Setting special variables
1
128
Give the following information:
a
Plus fraction mole weight.
b
Plus fraction skewness.
c
Thermal expansion coefficient for volume shifts.
d
Pre-multiplying coefficient for Cheuh-Prausnitz BICs.
e
Characterization for SCT-splitting.
Reference section
Regression in PVTi
PVTi Reference Manual
Note
Note that the mole weight and skewness variables apply on a sample-by-sample basis,
therefore there must be the appropriate number of measurements defined to allow this
option to be used.
Setting regression limits
Use this option to change the regression control parameters.
1
Select PVTi: Edit | Regression | Limits...
This opens the Regression Controls panel where you can set the following options.
Maximum number of iterations
The maximum number of successive iterations that the regression uses. Enter the maximum
number of iterations. The default value is 10.
Maximum step limit
The maximum amount if change allowed in the regression vector during successive iterations.
Give the maximum step limit, if required.The default value is 0.100000. For further information
see "Regression" on page 348.
Minimum step limit
The minimum amount of change allowed in the regression vector during successive iterations.
Enter the minimum step limit, if required. The default is 0.000010. For further information see
"Regression" on page 348.
Regression target
The regression target is the size of the objective function at which the regression terminates as
having achieved a match of calculated to observed values. Enter the regression target. The
default value is 0.000001.
Hint
Normally you do not need to change any of these limits, except for the maximum
number of iterations (which might be reduced, especially for larger problems) and the
limits on some variables (for example to prevent violation of monotonicity
relationships).
Note
For all variables specified in the regression the program displays the lower and upper
limits.
Variable
VAR1
VAR2
:
:
PVTi Reference Manual
Lower limit
VAR1lo
VAR2lo
:
:
Upper limit
VAR1up
VAR2up
:
:
Reference section
Regression in PVTi
129
Note
For all the equation of state parameters, except the acentric factor and binaries, these
lower and upper limits are scaled (to unity) variables, with default settings of 0.5 and
1.5. That is, the program allows the variable to decrease/increase by up to 50% before
it terminates the regression.
Running a regression
Use this option to perform regression.
Note
This option is only available if you first define a set of experiments, observations and
variables.
Performing a regression
1
PVTi: Run | Regression
The program performs the regression after first checking that there are at least as many
regression points as variables.
Hint
The results of regression can be viewed in the Sensitivity Analysis panel. See
"Regression Report" on page 130.
Accepting or reject regression results
Use this option to accept or reject the last regression The program holds the regressed system in
memory. This allows you to examine the plots and experimental output and decide whether you
wish to accept or reject the regression.
Accepting/rejecting a regressed system
1
Examine the plots and experimental output
2
PVTi: Run | Regression | Accept/Reject
3
Accept or reject the regression as appropriate.
Regression Report
The regression report contains detail of the current fit between the model and the observations.
Also use this option to display the sensitivity matrix, that is the sensitivity of the program’s
predictions to each of the given regression variables. This panel also gives detailed descriptions
of the current fit and the conditioning of the regression problem. All the information required to
develop a mathematically sound regression problem is available through this panel. The hints
provided in this section help you interpret the wealth of information contained within the folders
of this panel.
Hint
130
Reference section
Regression in PVTi
In any regression, having a few very sensitive parameters is preferable to having
hundreds of insensitive ones. Always look for parameters that can be discarded. This
is called conditioning the problem - an ill-conditioned problem is difficult to solve.
PVTi Reference Manual
Details Folder
The first folder, Details, shows the current fit. The numbers at the top of the folder show the
Total (normalized) RMS fit and the Weighted (normalized) RMS fit.
Hint
The RMS values in PVTi are normalized (the difference between the observed and
calculated values is divided by the observed value) so that, for example, pressures
(which could be thousands of psi) are treated similarly to saturations (which are
between zero and one). To calculate the weighted RMS, each normalized difference is
multiplied by the assigned weighting. The default weight is 1 and so, initially, the two
RMS values are the same.
The remainder of this first folder shows the observations, their weighting in the regression, and
the percentage difference between the observed and calculated values.
Modifiers folder
The second folder, Modifiers, shows the selected regression parameters, the minimum and
maximum allowed values for each modifier, and the percentage change made to the modifier
during regression (initially this is zero as no regression has been run).
Sensitivities folder
The Sensitivities folder shows the sensitivity of each observation to changes in each regression
variable.
Hint
A large sensitivity indicates that changing that regression variable has a large effect on
the fit to that observation. Likewise, consider discarding regression variables to which
the observations are insensitive, since a large modifier is needed to obtain a fit and, in
general, large modifications lead to unrealistic fluid models.
Hessian folder
The Hessian matrix is a good indication of the conditioning of the inversion problem
(regression).
Hint
In a well-conditioned problem the leading diagonal of the Hessian matrix is dominant.
Specifically, look at an element on the leading diagonal. If it is larger than the other
values in that row (or column) of the Hessian, then it indicates that the regression is
likely to succeed.
Covariance folder
The Covariance matrix shows the likely scale of variation in the regression variables that will
occur during regression. The larger a value, the less well-determined the value of the regression
variable will be.
PVTi Reference Manual
Reference section
Regression in PVTi
131
Correlation folder
The Correlation matrix is very important as it can indicate links between regression variables
that are not obvious on first inspection. If two variables are strongly correlated (correlation close
to 1), they both move the fit in the same direction; and so changing one is similar, in effect, to
changing the other. If two regression variables are strongly anti-correlated, changing one has the
opposite effect to changing the other. This latter case can cause a difficulty in regression as the
two variables could be changed an unlimited amount in opposite directions without having a
noticeable effect on the fit.
Hint
132
Reference section
Regression in PVTi
Look at off-diagonal elements in the correlation matrix. If any are close to 1 or -1,
consider removing one of the two regression variables that are correlated. This
improves the likelihood of a good final fluid model being created.
(If the variables are of the same type, for example if they are both Tcrit, you could
consider combining them into a single regression variable.)
PVTi Reference Manual
Exporting keywords
General information
PVTi can be used to generated output for ECLIPSE BlackOil, ECLIPSE Gi option, ECLIPSE
Compositional, ECLIPSE Thermal, VFPi and the API Tracking option in ECLIPSE BlackOil.
The Export modules are used to produce models for the ECLIPSE simulators (see "Output for
ECLIPSE simulators" on page 354 for background information). You can generate data files for
exporting to ECLIPSE BlackOil , ECLIPSE Compositional, ECLIPSE Thermal, API Tracking
and VFPi from PVTi.
To open this menu, select PVTi: File | Export.
The Export menu has the following options:
•
ECLIPSE Compositional Fluid Model...
See "Export for ECLIPSE Compositional" on page 133.
•
ECLIPSE Thermal Fluid Model...
See "Export for ECLIPSE Thermal" on page 134.
•
API Tracking option in ECLIPSE BlackOil...
See "Export for API Tracking option in ECLIPSE BlackOil" on page 134.
•
Oil reservoir...
See "Export Oil Reservoir" on page 135.
•
Gas reservoir...
See "Export Gas Reservoir" on page 135.
•
Equilibration...
See "Export Equilibration" on page 136
•
Water...
See "Export Water" on page 136.
•
VFPi
Use this option to generate VFPi tables. For further information see "VFP module" on
page 138.
Export for ECLIPSE Compositional
Description
This panel exports the fluid model as keywords suitable for the ECLIPSE Compositional
PROPS section.
Units
Allows you to export in the ECLIPSE unit set of choice.
Sample
If a sample is selected, it will be exported in the ZI keyword.
PVTi Reference Manual
Reference section
Exporting keywords
133
Reservoir temperature
This is exported in the RTEMP keyword.
Export for ECLIPSE Thermal
This panel exports the fluid model as keywords suitable for the ECLIPSE Thermal PROPS
section.
Sample
The sample for which the keywords will be exported for.
Number of Flashes to be Performed
This number is used when calculating the coefficients of Crookston’s equation. You an usually
leave this set as the default value of 20.
Max/Min Pressure/Temperature
You are recommended to enter the maximum and minimum values of pressure and temperature
for your reservoir.
Export Crookston Coefficients
If the box is ticked then the coefficients of Crookston’s equation will be exported. If not then
Wilson’s formula is used to calculate K-values.
Units
Allows you to export in the ECLIPSE unit set of choice.
A detailed explanation of the workflow required for this export option is described in the
"Compositional Data for ECLIPSE Thermal" on page 366. For a technical review of PVTi’s
export facility for ECLIPSE Thermal see "ECLIPSE Thermal Export Module" on page 401.
Export for API Tracking option in ECLIPSE BlackOil
This panel can be used to export a series of black oil tables suitable for use with the API
Tracking option in ECLIPSE BlackOil.
Set of Fluid Samples
Select which set of fluid samples to export the black oil tables for.
Properties Keyword
This sets the keywords that are exported, for example Live Oil (PVTO) and Dry Gas (PVDG).
Hint
All the keywords are described in the "ECLIPSE Reference Manual".
Write Gas Tables for each Sample?
If exporting the PVDG (dry gas) or PVTG (wet gas) tables then you can specify whether to write
out a gas table for each sample. Often a table for each sample is only required for the oil
keywords in ECLIPSE. If No is selected then PVTi exports a gas table for the sample in the list
with the median vapor density at surface conditions.
134
Reference section
Exporting keywords
PVTi Reference Manual
Plot Results?
You can tell PVTi not to plot the tables if you wish. PVTi only has room for 8 plots so if there
are many samples in the list then it may be useful not to plot the tables.
Write Values to Double Precision?
You can ask for full double precision values if you wish, but the table columns may not be fully
aligned if this option is used.
Separator Experiment
You can select a separator in your project if you wish instead of the default standard conditions
separator (usually 14.7psia and 60F).
Table Generation Method
The algorithm used to generate the black oil tables. See "Output for ECLIPSE simulators" on
page 354.
Units
Allows you to export in the ECLIPSE unit set of choice.
Export Oil Reservoir
This panel exports keywords from a Differential Liberation experiment (that is, for an oil
reservoir).
The keywords are suitable for the ECLIPSE BlackOil and ECLIPSE Compositional PROPS
section.
Units
Allows you to export in the ECLIPSE unit set of choice.
Properties Keyword
This sets the keywords that are exported.
Hint
All the keywords are described in the "ECLIPSE Reference Manual".
Write Values to Double Precision?
You can ask for full double precision values if you wish.
Separator experiment
If creating tables for ECLIPSE BlackOil, the output from the Differential Liberation can be
passed through any separator. The default is to use a single stage at standard conditions (that is,
a stock-tank only - normally 14.7 psia, 60F).
Table generation method
See "Output for ECLIPSE simulators" on page 354.
Export Gas Reservoir
This panel exports keywords from a Constant Volume Depletion experiment (that is for a gas
reservoir).
PVTi Reference Manual
Reference section
Exporting keywords
135
The keywords are suitable for the ECLIPSE BlackOil and ECLIPSE Compositional PROPS
section.
Units
Allows you to export in the ECLIPSE unit set of choice.
Properties Keyword
This sets the keyword that is exported.
Hint
All the keywords are described in the "ECLIPSE Reference Manual".
Separator experiment
If creating tables for ECLIPSE BlackOil, the output from the Constant Volume Depletion can
be passed through any separator. The default is to use a single stage at standard conditions (that
is, a stock-tank only).
Table generation method
See "Output for ECLIPSE simulators" on page 354.
Injection fluid
For the Gi option only, this provides the injection sample to be used in creating the pseudocompositional keywords. See "Pseudo-compositional tables for ECLIPSE GI option" on
page 360.
Export Equilibration
This panel exports keywords from a Composition versus Depth experiment.
The keywords are suitable for the ECLIPSE BlackOil INIT section and ECLIPSE
Compositional PROPS section.
Units
Allows you to export in the ECLIPSE unit set of choice.
Properties Keyword
This sets the keyword that are exported.
Hint
All the keywords are described in the "ECLIPSE Reference Manual".
Separator experiment
If creating tables for ECLIPSE BlackOil, the output from the Composition versus Depth
experiment can be passed through any separator. The default is to use a single stage at standard
conditions (that is, a stock-tank only).
Export Water
Description
This panel exports water properties.
136
Reference section
Exporting keywords
PVTi Reference Manual
The keyword PVTW or PVTWSALT can be exported for the ECLIPSE simulators. The keyword
Hint
All the keywords are described in the "ECLIPSE Reference Manual". WATPVT is
described in the "VFPi User Guide".
Units
Allows you to export in the ECLIPSE Unit set of choice.
Reservoir temperature
This sets the reservoir temperature to be used in generating the keywords.
Reservoir pressure
See above.
Dissolved natural gas
If this option is checked, the properties account for the presence of dissolved gas in the water.
Brine
If this option is checked, salt concentration(s) can be accounted for.
VFPi
If this option is checked, the exported keyword will be WATPVT. The low temperature and low
pressure fields become active, these values correspond to the lower values to be used in the flow
table (for example, the top of the pipe).
For more information see "Water properties" on page 362.
PVTi Reference Manual
Reference section
Exporting keywords
137
VFP module
Introduction
The VFP module generates blackoil tables for VFPi. To open this menu, select PVTi: File |
Export | VFPi from the main PVTi window.
Figure 6.7 The VFP module
The VFP module has the following options:
•
File
This option allows you to read and display data from the PVI file. For further information
see "File" on page 139.
•
Edit
This option allows you to add a new graph and copy items to the clipboard.
•
View
This option allows you to control the appearance of the plot workspace.
•
138
Define
Reference section
VFP module
PVTi Reference Manual
This option allows you to define experiments and the method of calculation. For further
information see "Define" on page 141.
•
Generate
This option allows you to generate tables. For further information see "Generate" on
page 142.
•
Options
Allows the modification of the plot workspace.
•
Help
Gives you access to the on-line help for this module.
VFP toolbar
The module toolbar contains the following buttons:
Display section from PVI file. Use this option to display VFP sections from the PVI file.
For further information see "Display VFP section from PVI..." on page 140.
Read section from PVI file.
Use this option to load VFP sections from the PVI file. For further information see "Read
VFP section from PVI..." on page 140.
Experiments
Use this option to define VFP experiments. For further information see "Experiments..." on
page 141.
Generate.
Use this option to select the method of generation for the VFPi blackoil tables. For further
information see "Method" on page 142.
Simulate
Use this option to generate the tables. For further information see "Perform" on page 142.
View results
Use this option to review the tables.
View plots
Use this option to view plots of the tables. For further information see "Plot" on page 143.
File
Use this menu to read and display VFP sections from a PVI file.
The File menu has the following options:
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Reference section
VFP module
139
Display VFP section from PVI...
Use this option to display a VFP section from the current PVI file.
Displaying VFP sections
1
Select VFP | File | Display VFP section from PVI... .
2
Select the VFP section.
Read VFP section from PVI...
Use this option to read data from a PVI file. You can use this option to load all or part of the
data required for the VFP section. Additionally you can choose to echo (the contents of the
whole PVI file to the current printfile, PVP.
Loading PVI data
1
Choose VFP | File | Read VFP section from PVI... and select the appropriate PVI file.
PVTi searches for the required file, and looks for all occurrences of the required section. If
it finds more than one section of the required type in the file, you must select which section
you wish to read. The program displays a prompt specifying the number of sections found.
2
Select the section you wish to load.
Note
If the program does not find a VFP section in the PVI file it produces an error message
and stops processing.
Print preview
Previews the printed plot in the main module area.
Print layout
Allows you to set the text styles and sizes for printing.
Print setup
Sets up the printer specifications. This option is specific to Windows.
Print
Prints the whole module print area, the main window and allows you to set the print type, for
example color, postscript.
Close
Use this option to close the VFP module. To close the VFP module, select VFP | File | Close.
Note
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Reference section
VFP module
The data is not lost. If you reselect the module all data that was previously set is
available.
PVTi Reference Manual
Define
This menu allows you to set up experiments and the method of calculation. To open this menu,
select VFP | Define.
The Define menu has the following options:
•
Experiments...
Defines experiments. For further information see "Experiments..." on page 141.
•
Method...
Defines the method of calculation. For further information see "Method" on page 142.
Experiments...
Use this option to define experiments.
Defining experiments
1
Select VFP | Define | Experiments... .
This opens the Constant Composition Experiment panel.
2
Define a Constant Composition Expansion (CCE) experiment.
This is a depletion experiment where the moles entering the wellbore must leave the
wellbore. For further information on defining experiments see "Data requirements for the
experiments" on page 118.
Hint
The first temperature you give for the CCE should be the highest temperature in the
production string, which can safely be taken to be the reservoir temperature. The
second temperature you give should be the lowest temperature in the production string,
for example a sub-sea temperature of 4 °C .
Note
You do not need to give a saturation pressure as the program gives this data. It also
calculates undersaturated properties for all pressures. See "Output for ECLIPSE
simulators" on page 354 for further details
3
Define the separator conditions that take the reservoir liquid and/or vapor to surface
conditions to define the various ratios in the blackoil tables.
Note
Note that to comply with the blackoil definition strictly, the last stage in the separator
train should be at standard conditions.
4
Specify the composition of the injection gas using one of the currently defined sample
mnemonics.
5
Give the gas-oil ratios in which the lean gas is to be added to the reservoir fluid.
6
Press OK.
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141
Method
Use this option to select the method of calculation. You can choose from Coats, or Whitson and
Torp method. The default is the Whitson and Torp method
Choosing the method of calculation
1
Select VFP | Define | Method... .
This opens the Switch Method of Generation panel.
2
Choose the appropriate method.
For further information on the Coats method, [Ref. 3], or the Whitson and Torp method,
[Ref. 6], see "Output for ECLIPSE simulators" on page 354.
Generate
This menu allows you to generate blackoil tables for VFPi. To open this menu, select VFP |
Generate.
The Generate menu has the following options:
•
Perform
Generates the blackoil tables.
Perform
Use this option to generate blackoil tables.
Note
You must define a depletion experiment and the separator configuration (which only
need be a one stage default system to standard conditions) to generate the blackoil
tables.
Generating blackoil tables
1
Select VFP | Generate | Perform.
This generates the blackoil tables OILPVT and WGASPVT. The program also writes gas,
oil and water densities, at standard conditions, to the VFPi SURFDENS keyword.
Note
If the process is successful the program also writes the data to the PVO file which you
can add to an VFPi input file.
Note
Note each set of tables is repeated twice, for the set of pressure nodes defined on the
CCE experiment, at the specified high (reservoir) and low temperatures.
Water properties
1
142
Click Yes when asked if you wish to generate water properties, using the VFPi keyword
WATPVT.
Reference section
VFP module
PVTi Reference Manual
This opens a a series of data entry panels where you can enter the data necessary for the inbuilt correlations to generate the appropriate data.
Plot
Use this option to produce plots.
Producing plots
1
Select VFP | View | Plot.
You can generate any of the following plots:
•
oil formation volume factor, B o
•
gas formation volume factor B g
•
oil viscosity μ o
•
gas viscosity μ g
•
oil R s
Help menu
Gives access to help with PVTi.
Help
Opens the context-sensitive on-line help panel.
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Reference section
VFP module
143
Utilities
Introduction
This menu allows you to change or redefine various program settings. It has the following
options:
•
Units...
This allows you to set unit types. For further information see "Units..." on page 144.
•
Standard Conditions...
This allows you to set the standard temperature and pressure. For further information see
"Standard conditions..." on page 145.
•
Program Option
This allows you to change the program options For further information see "Program
options" on page 145.
•
Debug...
This allows you to set the debug flags. For further information see "Debug..." on page 150.
Units...
This option allows you to select various unit types. You can:
•
Choose the unit type within PVTi.
•
Choose the temperature unit type; this can be different from the one selected by the above.
•
Set mole fractions or percentages.
•
Select absolute or gauge pressures.
For further information on the units see "Units" on page 409.
Setting unit types
1
To define the units, select Utilities | Units. This opens the Set PVTi Unit Definitions panel.
Each unit type is selected by clicking on the corresponding radio button.
Choosing the unit type for PVTi
Select from Metric, Field, Lab and PVT-Metric.
Setting the temperature unit type
Select the temperature unit type from Kelvin, Celsius, Rankine and Fahrenheit.
Setting mole fractions or percentages
Select the required option.
Selecting absolute or gauge pressures
Select the required option.
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Standard conditions...
This option allows you to set the standard temperature and pressure.
Defining standard conditions
1
To set the standard conditions select Utilities | Standard Conditions....
This opens the Standard Conditions panel.
2
Enter the standard temperature.
3
Enter the standard pressure.
4
Click on OK.
Program options
This option allows you to set various program options. Various options which cannot be set
elsewhere in PVTi have been collected together under this option.
1
To set the program options, select Utilities | Program Option.
This opens the Set PVTi Program Options panel.
You can set the following:
Table 6.3
Set PVTi Program Options panel
Program Option
Available choices
"Definition of Liquid Saturation in CCE" on
page 146.
Sliq = Vliq/Vsat
See “Treatment of Volume Shifts” on page 146.
Independent variables
Sliq = Vliq/Vtot
Dependent
"Separator GOR Calculation" on page 147.
Separator Conditions
Stock Tank Conditions
"Temperature dependence for volume shifts" on
page 147
None
Linear expansion only
Polynomial correlations
"Specify/Calculate density and molar volume
units" on page 147
user units
"Binary interaction coefficients for EoS" on
page 147
Katz-Firoozabadi
"Specific heat capacity coefficients and calorific
values" on page 147
No Output of Values
"Calculated compositions" on page 148
No save to samples
gm/cc and cc/gm-mole
Cheuh-Prausnitz
Output Values to Screen/PVP
Allow Optional Save to Samples
"Component Library" on page 148
Katz-Firoozabadi
Old PVTi Library
"Experiment compositions" on page 148
Output to Screen/PVP
No Output to Screen/PVP
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Reference section
Utilities
145
Table 6.3
Set PVTi Program Options panel (Continued)
Program Option
Available choices
"Experiment results" on page 148
Always Output to PVP
Optionally Output to PVP
Never Output to PVP
"Plot vectors" on page 148
No Output to file
Output to Graf .VEC files
"Print file output" on page 148
A4 format
132 characters wide
"Definition of GOR in Diff. Lib." on page 148
Normal
No Last Stage
Incremental
Volume of Oil at Pbub
"Definition of Oil relative volume in Diff. Lib." on Oil FVF = Voil(p)/Voil(stc)
page 149
Oil FVF = Voil(p)/Voil(pbub)
"Black oil table output" on page 149
All Data
Truncation at Saturation Pressure
"LBC viscosity coefficients" on page 149
Keep Fixed
Allow Change when Regressing
"Flash calculations" on page 149
E300 Flash
Old PVTi Flash
"Sample mole fractions when regressing" on
page 149
Keep Fixed
"Phase Plot Algorithm" on page 149
New Phase Plots
Allow Change
Old Phase Plots
"Write Keywords for Batch Mode" on page 149
No
Yes
Definition of Liquid Saturation in CCE
The definition of liquid saturation in the Constant Composition Expansion experiment varies
from laboratory to laboratory. The standard definition is to quote liquid saturation as volume of
liquid at pressure p per volume of fluid at saturation volume (usually referred to as the cell
volume). However, some laboratories refer to Sliq as the volume of liquid at pressure p per the
total volume of fluid at pressure p .
1
Select the appropriate option from the available list.
Treatment of Volume Shifts
Available options are Dependent and Independent. Dependent means that you cannot
regress on the volume shifts. They are defined as a function of the other critical properties for
each component and so if critical properties change, for example during a regression, then the
volume shifts are dynamically altered to stay consistent with the new component data.
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Utilities
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If you use the Independent option then you are allowed to regress on the volume shifts of the
components. PVTi also de-couples the dependence of the volume shifts on the critical
parameters so that a change in Tc, Pc, etc. does not effect a volume shift value.
1
Select the appropriate option from the available list.
The default setting is the Dependent option.
Separator GOR Calculation
Some laboratories choose to quote separator liquid volumes at stock tank conditions, rather than
the actual pressure and temperature of the separator stage at which the liquid is produced.
1
Select the appropriate option from the available list.
The default setting is the volume quoted at the separator conditions.
Temperature dependence for volume shifts
The volume shift corrections applied to the three-parameter PR3 and SRK3 equations of state
assume that the mis-match in predicted and measured liquid density at some reference
conditions on a component-by-component basis can be used to correct volumes at all other
pressures and temperatures. In an attempt to account for the known temperature dependence,
two methods are available for modifying the volume shifts.
You can modify the shifts by applying linear thermal expansion to all components, with an
attempt at correction for molecular weight, or calculated for light components as a polynomial
involving temperature, with heavy components being modified by thermal expansion, but
without a correction for molecular weight. The methods are described in "Three-parameter
equation of state" on page 321.
1
Select the appropriate option from the available list.
Specify/Calculate density and molar volume units
Overriding the current units convention, you may specify that liquid and gas densities should be
output in units of gm/cc and molar volumes in cc/gm-moles.
1
Select the appropriate option from the available list.
Binary interaction coefficients for EoS
As an alternative to the BICs of Katz and Firoozabadi, the correlation of Cheuh and Prausnitz
(see "Binary interaction coefficients" on page 337) can be used to calculate hydrocarbonhydrocarbon BICs. If selected, the pre-multiplying A - coefficient can be used as a special
regression variable, especially useful for matching saturation pressures.
1
Select the BIC coefficients you wish to use.
Specific heat capacity coefficients and calorific values
The calculation of ideal gas specific heat in ECLIPSE Compositional can be accomplished by
switching on this flag, which then outputs the coefficients used in the temperature-dependent
expansion on a component-by-component basis. Calorific values of the components of the
system are also output to ECLIPSE Compositional using this option.
1
Switch on the output of the coefficients and calorific values, if required.
PVTi does not produce the coefficients and calorific values, by default.
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Reference section
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147
Calculated compositions
Compositions calculated during an EoS simulation of an experiment can be saved to be used
later as samples for further experiments, phase plots, etc. This might be useful in swelling tests,
separator calculations or estimating the variation of composition with depth.
1
Select the save samples option, if required.
PVTi does not save these samples, by default.
Component Library
This option allows you to specify the component library to use. The choice is between the KatzFiroozabadi and the Oil PVTi Library. The Katz-Firoozibadi is the default and recommended
choice. (Benzene and toluene are taken from Perry [Ref. 67].)
Experiment compositions
This option allows you to turn off lengthy output to the print file of liquid and vapor
compositions calculated in experiments.
1
Switch off the output of the liquid and vapor compositions if they are not required.
PVTi prints the liquid and vapor compositions to the screen and PVP file, by default.
Experiment results
On definition of fluid properties, completion of experiments, etc., you can optionally choose to
write all the data to the PVP print file.
1
Select the appropriate output option.
By default, PVTi always writes all the data to the PVP print file; however, you can choose
to make this write optional or never done.
Plot vectors
For more advanced graphical manipulation of PVTi plots, you may choose to output data
vectors to a file in GRAF user vector format. The vectors are written when the plots are
performed.
1
Choose whether you wish to produce the vectors.
PVTi does not produce these vectors by default.
Print file output
Use this option to determine the format of the print (PVP) file.
1
Select the appropriate option from the available list.
PVTi uses A4 as the default paper size format for this file.
Definition of GOR in Diff. Lib.
This option allows you to alter the definition of the GOR calculation in a differential liberation
experiment. Three alternative definitions are available:
148
•
Normal where the last stage to standard conditions is removed with the volume of gas being
normalized to the volume of oil at reservoir conditions
•
The GOR is defined in increments, that is, at each stage of the depletion process.
•
The GOR is the default GOR but normalized to the volume of oil at its bubble point
pressure rather than at STC.
Reference section
Utilities
PVTi Reference Manual
See "Differential liberation" on page 340 for the precise definitions of these quantities.
1
Select the appropriate option from the available list.
PVTi uses option 1 by default.
Definition of Oil relative volume in Diff. Lib.
This option allows you to define an alternative definition for the relative oil volume in a
differential liberation experiment. When turned on, the option normalizes the volume of oil at
each stage to the volume of initial oil at its bubble point rather than standard pressure. Refer to
"Differential liberation" on page 340 for a precise definition of the alternative.
1
Select the appropriate option from the available list.
Black oil table output
Switching to the Truncation at Saturation Pressure option outputs and plots only the black
oil table data relating to pressure values at the saturation pressure and below.
If the default of All Data is used then for pressure values above the saturation pressure, PVTi
swells the fluid with vapor in order to raise PSAT to the required value.
1
Select the appropriate option from the available list.
PVTi outputs all data to the blackoil tables by default.
LBC viscosity coefficients
This option allows the coefficients used in the LBC viscosity correlation to vary when
regressing to any viscosity observations.
1
Choose whether you wish to vary the coefficients.
PVTi fixes the coefficients by default.
Flash calculations
This option allows the Flash and Psat algorithms to be changed from the default ECLIPSE
Compositional algorithms to the old PVTi (pre-99B) algorithms.
1
Choose to use the old PVTi algorithms for Flash and Psat.
Sample mole fractions when regressing
This option allows you to vary mole fractions of components in any sample when using the
special regression variables CHARMF and/or MIXING.
Note
This option must be set in the ON state for you to use these regression variables. You
must have characterized and/or user components, or be mixing samples, for the
variables to become of use.
Phase Plot Algorithm
This option allows the phase plot algorithm to be changed from the default New Phase Plots
to the pre-2000A Old Phase Plots algorithm.
1
Choose to use the old pre-2000A phase plot algorithm.
Write Keywords for Batch Mode
This option allows a .PVI file to be prepared for use in batch by writing extra keywords.
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Reference section
Utilities
149
1
Choose to instruct PVTi to write out the extra keywords required for use in batch mode. By
default this option is disabled.
This option cannot be saved, which means every time you open a project it is disabled by
default. The reason for this is that when this option is enabled it writes many more keywords
than is necessary in interactive mode. You could easily forget that a project had this option
enabled when opening an existing project meaning that many more keywords than necessary
would continue to be written to the PVI file.
Debug...
This option sets the debug flags.
Note
This is a programmer test facility to request additional information from the program
at a debug level. You do not need to set one or more of the debug flags unless help is
required in tracing an apparent anomaly.
Monitor option
This is a programmer test facility to trace the root of a problem in the program at a subroutine
level.
Note
You do not need to need to set this flag ON unless asked to do so.
Window
This menu allows you to control the size and appearance of the program windows. To select this
menu, select Window from the main PVTi window.
Tile
This puts all the visible windows into a “tiled” formation.
Cascade
This puts all the visible windows into a “cascade” formation.
Minimize children
This option minimizes all windows except the main PVTi window.
Restore children
This opens all minimized windows so that they are visible.
Help
This menu gives you access to the help for PVTi. To select this menu, select Help from the main
PVTi window.
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Help
This opens the on-line help panels.
ToolTips enabled
The ToolTips provide a single line of text about each toolbar button when the mouse pointer is
stationary over the icon. This option turns the ToolTips feature on and off.
About PVTi -...
This provides brief information on the program code version.
Right mouse button menu
Clicking the right mouse button on one of the buttons in the project tree displays a popup menu
that provides short-cuts to some of the common operations used in PVTi.
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151
Batch system and keywords
This section focuses on the batch mode functionality of PVTi. First of all a general overview is
given of the batch mode. The next section explains the new functionality for PVTi 2004A,
which enables you to set up a batch mode file in interactive mode. The third section list all of
the different keywords supported within the batch mode. The 3 sections are:
•
"General information" on page 152.
•
"Preparing Batch Mode Files in Interactive Mode" on page 153.
•
"Overview of all supported keywords in Batch Mode" on page 155.
General information
For the 2004A version of PVTi the batch mode has undergone a significant revamp. Over the
last few years the user interface of PVTi has evolved rapidly and many of the PVTi sections are
now no longer written out to the PVI file as they are no longer required when PVTi reads in a
file. For example a BLACKOIL section is no longer written out by PVTi when black oil tables
are exported using the user interface. Although they can be inserted into the file manually it was
felt that a more user friendly way of constructing the .PVI files containing all the appropriate
sections required for the batch mode was needed.
The next section outlines how it is now possible to perform a workflow interactively in order
for PVTi to be able to reproduce this workflow in batch mode at a later time.
The way in which you run a file in batch mode has also changed. Pre-2004A you had to enter
the keyword TESTCASE anywhere in the RUNSPEC section of the PVI file. You then launched
batch mode the command line, for example using $pvti filename (if using a PC).
This has changed for the 2004A release. It was felt that opening files and adding keywords and
then remembering to remove them at a later data was cumbersome. The new way to run in batch
mode is to launch PVTi from the command line and specify the word ‘-batch’ before the
filename in the line command instruction.
Hint
To launch the file TEST.PVI to run in PVTi’s batch mode on a PC use the command
‘$pvti -batch TEST.PVI’. On a UNIX machine ‘@pvti -batch
TEST.PVI’ runs the file TEST.PVI in batch mode.
Sometimes users have more than 1 version of PVTi installed. It is also possible to specify which
version of PVTi to use on the command line using the -ver command.
Hint
152
On a PC, to specify the 2004A version of PVTi to run the file TEST.PVI in batch
mode, use the command ‘$pvti -ver 2004a -batch TEST.PVI’.
Reference section
Batch system and keywords
PVTi Reference Manual
Preparing Batch Mode Files in Interactive Mode
Overview
As explained in the previous section this new functionality introduced for PVTi 2004A enables
you to generate files suitable for batch mode using PVTi’s interactive mode. The idea is that you
would go through a pre-defined workflow in interactive mode and then subsequently be able to
make PVTi automatically perform this workflow in the batch mode.
Note
The workflow must be pre-defined. The batch mode is not designed to be able to
reproduce workflows where you have been experimenting with a particular project.
1
Start PVTi in interactive mode with the file that you eventually wish to run in batch mode.
2
Save the file concisely by doing File | Save (concise)....
This erases the history of any workflows stored in the file.
3
Open the Options panel using the File | Utilities | Program | Options....
4
In PVTi 2004A a new option has been added at the bottom called Write Keywords for
Batch Mode. Select Yes and then close the panel.
5
Perform the required workflow and, when finished, save the file (but not concisely) using
the File | Save... option.
Note
6
The file must not be saved concisely as this would erase all the history in the .PVI file
that PVTi uses to reproduce your workflow in batch mode.
The final task is to actually run the file in batch mode. To do this on a PC launch PVTi from
the command line using the statement ‘$pvti -batch filename’ where filename is
the name of your PVTi project, for example TEST.PVI.
Note
The word ‘-batch’ can be put after or before the filename but it has to be somewhere
on the command line in order to tell PVTi to run in batch mode.
When you are running in batch mode the program automatically sends printed output such as
experiment simulation results to a print file with the same root name as the input .PVI file. For
example, if the input file is CRUDE.PVI, the print file is CRUDE.PVP. See "PVI file" on
page 155 for further information. In batch mode all the experiments are automatically simulated
in the project by default. If any regression is to be performed in the batch mode then the
experiment simulation is performed after this has been done.
If keywords are exported for ECLIPSE during the batch run then .PVO files are created as
normal, but they are named using a convention that is outlined in the next section.
A file is also created called BATCH_OUT.PVI. This is a saved version of your project after all
the steps in the workflow have been performed. It can be useful to have this file after the batch
run has finished if the fluid model has changed (for example during regression) in your project
during the course of the workflow
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Batch system and keywords
153
Constraints on the workflow
In this new interactive approach to creating batch mode files there are constraints on the
workflows that you can perform. However, despite these constraints, all of the commonly used
functionality within PVTi is supported.
Regression
You are allowed a maximum of two REGRESS sections in the batch mode file. This is so that
regression on both special and normal variables is possible. Any further regression sections are
ignored by the batch mode.
Splitting/Grouping
You are allowed two GROUP sections and two SPLIT sections in the file. If there are REGRESS
sections then one SPLIT and one GROUP section is allowed before the first REGRESS section
and one SPLIT and one GROUP section is allowed after this REGRESS section.
Export
It is assumed that all exports would be performed at the end of the workflow. An unlimited
amount of export sections (such as BLACKOIL, OUTECL3 sections) are allowed as long as they
are after the last REGRESS section. Because multiple exporting is allowed a naming convention
has been invented to stop PVTi just writing each exported .PVO file over the top off the last one
that was written out.
The naming convention depends on what kind of export is being performed:
BLACKOIL
If a BLACKOIL section has been read in the .PVI file then the naming convention of the .PVO
file is “filename_samplename_experimenttype_keyword1keyword2.PVO”
where:
filename is the rootname of the project,
samplename is the sample name used for the export,
experimenttype is the type of depletion experiment used in the export,
keyword1 is the name of the first keyword exported
and keyword2 is the name of the second keyword exported.
For example if the file CRUDE.PVI was used to export sample ZI based on experiment DL1
using Live Oil and Dry Gas keywords then the name of the produced file would be
CRUDE_ZI_DLLIVEDRY.PVO.
OUTECL3
If an OUTECL3 section has been read in the .PVI file then the naming convention of the
outputted .PVO file is filename_samplename_FLUIDMODEL.PVO.
APITRACK
If an APITRACK section has been read in the .PVI file then the naming convention of the
outputted .PVO file is filename_experimenttype_APITRACK.PVO.
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Overview of all supported keywords in Batch
Mode
Listed below is a summary of all the keywords supported in a .PVI file using the batch mode:
Note
The COMB, PSEUCOMP and VFP sections-type keywords cannot currently be
prepared in a .PVI file for batch mode using interactive mode.
•
"PVI file" on page 155.
•
"Keywords introducing sections" on page 156.
•
"RUNSPEC section keywords" on page 156.
•
"SYSTEM section keywords" on page 157.
•
"SPLIT section keywords" on page 158.
•
"GROUP section keywords" on page 159.
•
"COMB section keywords" on page 159.
•
"SIMULATE section keywords" on page 160.
•
"REGRESS section keywords" on page 160.
•
"BLACKOIL section keywords" on page 161.
•
"PSEUCOMP section keywords" on page 162.
•
"OUTECL3 section keywords" on page 162.
•
"VFP section keywords" on page 163.
PVI file
The PVI file consists of a number of sections, each introduced by a section keyword.
•
The first section must be RUNSPEC, which specifies the number of components, the
equation of state option and the run title.
•
The SYSTEM section must follow the RUNSPEC section.
•
Other sections may be in arbitrary order, and may occur more than once.
Using the PVI file
After each operation that redefines the system, which may be by splitting, grouping or
regression, the program rewrites the audit trail. When you exit from a session you can choose
to write the audit trail to a PVI file. This creates new sections with the names MODSPEC and
MODSYS (corresponding to RUNSPEC and SYSTEM). The program treats these new sections in
the same manner as the original definitions. When you load a PVI file created in a previous
PVTi session the program automatically searches for the RUNSPEC and any subsequent
MODSPEC sections.
The PVTi keywords are described in detail in Chapter 7.
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Reference section
Batch system and keywords
155
Keywords introducing sections
Each of the sections in a PVI file has a specific keyword to introduce it into the file. Table 6.4
details these keywords.
Table 6.4
Keyword
Keywords for introducing sections
Comments
Details
RUNSPEC
This must be the first section.
See "RUNSPEC" on page 252
SYSTEM
This must follow the RUNSPEC
section.
See "SYSTEM" on page 266
SPLIT
See "SPLIT" on page 263
GROUP
See "GROUP" on page 206
COMB
See "COMB" on page 179
SIMULATE
See "SIMULATE" on page 261
REGRESS
See "REGRESS" on page 249
BLACKOIL
See "BLACKOIL" on page 174
VFP
See "VFP" on page 281
PSEUCOMP
See "PSEUCOMP" on page 247
OUTECL3
See "OUTECL3" on page 240
Keywords by section
Each of the main sections, for example the RUNSPEC section, has its own specific keywords.
Note the following:
•
The keywords UNITS, DEGREES and STCOND are normally be specified in the SYSTEM
section, but can occur elsewhere, and can occur more than once.
•
The keywords DEBUG and OPTIONS can be specified in the RUNSPEC section or in the
SYSTEM, COMB, SIMULATE or REGRESS sections.
•
The keyword MESSAGE can be specified anywhere, its function being merely to echo the
argument to the print file at the time of a batch run.
RUNSPEC section keywords
Table 6.5 details the keywords specific to the RUNSPEC section.
Table 6.5
156
RUNSPEC keywords
Keyword
Comments
Details
EOS
Selects the equation of state.
See "EOS" on page 193
LBC
Selects Lohrenz-Bray-Clark
viscosities.
See "LBC" on page 214
NCOMPS
Sets the number of components.
See "NCOMPS" on page 230
NEWPVI
Outputs a new PVI file at the end of the See "NEWPVI" on page 231
batch run.
PEDERSEN
Selects the Pedersen viscosity
correlation.
Reference section
Batch system and keywords
See "PEDERSEN" on page 245
PVTi Reference Manual
Table 6.5
RUNSPEC keywords (Continued)
Keyword
Comments
Details
PRCORR
Selects the modified Peng-Robinson
equation.
See "PRCORR" on page 246
TITLE
Sets the run title.
See "TITLE" on page 271
ECHO
Includes the PVI file in the PVP file.
See "ECHO" on page 192
NOECHO
Does not include the PVI file in the
PVP file.
See "NOECHO" on page 233
DEBUG
Sets the Debug flags.
See "DEBUG" on page 186
DEBUE
Sets Debug flags.
See "DEBUE" on page 185
OPTIONS
Sets Options flags.
See "OPTIONS" on page 238
VERSION
Indicates the version of PVTi
See "VERSION" on page 280
SYSTEM section keywords
"The fluid model" on page 98 explains how to set up the SYSTEM keywords using menu
options. Table 6.6 details the keywords specific to the SYSTEM section.
Table 6.6
SYSTEM keywords
Keyword
Comments
Details
DEGREES
Specifies the temperature
convention.
See "DEGREES" on page 188
STCOND
Specifies the standard conditions.
See "STCOND" on page 265
UNITS
Specifies the unit convention.
See "UNITS" on page 274
CNAMES
Sets the component names.
See "CNAMES" on page 177
LNAMES
Sets the library component names.
See "LNAMES" on page 217
CHARACT
Specifies the characterisation of the
components.
See "CHARACT" on page 176
SCT
Defines the Semi-ContinuousThermodynamic split.
See "SCT" on page 259
ACF
Defines the acentric factors.
See "ACF" on page 169
ACHEUH
Defines the Cheuh-Prausnitz A coefficient.
See "ACHEUH" on page 170
BIC
Defines the binary interaction
coefficients.
See "BIC" on page 172
CALVAL
Defines the calorific values.
See "CALVAL" on page 175
DEFBIC
Defines the default binary interaction See "DEFBIC" on page 187
coefficients.
DREF
Defines the reference densities.
See "DREF" on page 190
LBCCOEF
LBC
Specify the viscosity coefficients.
See "LBCCOEF" on page 215, "LBC"
on page 214
MW
Specifies the molecular weights.
See "MW" on page 228
OMEGAA
Specifies non-default Ω a values
See "OMEGAA/B" on page 237
(optional).
PVTi Reference Manual
Reference section
Batch system and keywords
157
Table 6.6
SYSTEM keywords (Continued)
Keyword
Comments
Details
OMEGAB
Specifies non-default Ω b values
See "OMEGAA/B" on page 237
(optional).
PARACHOR
Specifies parachors.
See "PARACHOR" on page 242
PCRIT
Defines the critical pressures.
See "PCRIT" on page 243
SPECHA,B,C,D
Defines the specific heat capacity
coefficients.
See "SPECHA-D" on page 262
SSHIFT
Specifies dimensionless volume
shifts for PR3 EoS.
See "SSHIFT" on page 264
TBOIL
Specifies boiling points (for ZJ
equation).
See "TBOIL" on page 268
TCRIT
Defines the critical temperatures.
See "TCRIT" on page 269
THERMX
Specifies thermal expansion
coefficient for volume shifts.
See "THERMX" on page 270
TREF
Defines the reference temperatures.
See "TREF" on page 273
VCRIT
Specifies the critical volumes.
See "VCRIT" on page 278
VCRITVIS
Defines critical volumes used in
LBC viscosity correlation.
See "VCRITVIS" on page 279
ZCRIT
Specifies critical Z -factors.
See "ZCRIT" on page 290
ZCRITVIS
Defines critical Z -factors used in
LBC viscosity correlation
See "ZCRITVIS" on page 291
ZI
Defines sample composition
(primary sample).
See "ZI" on page 292
SAMPLES
Defines other samples, lean gas for
swelling test.
See "SAMPLES" on page 255
SAMTITLE
Defines long titles for other samples. See "SAMTITLE" on page 257
HYDRO
Specifies hydrocarbon/Nonhydrocarbon.
See "HYDRO" on page 211
SALINITY
Defines the salinity of specified
samples.
See "SALINITY" on page 253
MIX
Allows mixing of two samples to
form a new sample.
See "MIX" on page 224
SPLIT section keywords
Table 6.7 details the keywords specific to the SPLIT section.
Table 6.7
Keyword
158
SPLIT keywords
Comments
Details
CORRACF
Selects the acentric factor correlation.
See "CORRACF" on page 181
CORRCP
Selects the critical property correlation.
See "CORRCP" on page 182
FRAC
Sets the number and distribution of new plus
fractions.
See "FRAC" on page 202
Reference section
Batch system and keywords
PVTi Reference Manual
Table 6.7
SPLIT keywords (Continued)
Keyword
Comments
Details
MDP
Sets the molar distribution parameters.
See "MDP" on page 220
MWS
Specifies the plus fraction molecular weight.
See "MWS" on page 229
SG
Specifies the plus fraction specific gravity.
See "SG" on page 260
SCT
Defines the Semi-ContinuousThermodynamic split.
See "SCT" on page 259
WHIT
Defines a Whitson splitting.
See "WHIT" on page 287
GROUP section keywords
Table 6.8 details the keywords for the GROUP section.
Table 6.8
GROUP keywords
Keyword
Comments
Details
COMBINE
Specifies fractions to be grouped
together.
See "COMBINE" on page 180
GRPBYSAM
Specifies which sample to group to.
See "GRBYSAM" on page 209
GRPBYWGT
Specifies grouping by molecular
weight.
See "GRPBYWGT" on page 210
GRPBYMIX
Specifies grouping by mixing rule.
See "GRBYMIX" on page 208
GRPBYALL
Specifies grouping to average of all
samples.
See "GRBYALL" on page 207
COMB section keywords
The "COMB - Compositional Material Balance" on page 112 allows you to set up the COMB
keywords using menu options. Table 6.9 details the keywords for the COMB section.
Table 6.9
PVTi Reference Manual
COMB keywords
Keyword
Comments
Details
EXP
Defines experiments.
See "EXP" on page 195
OBS
Defines observations.
See "OBS" on page 234
OBSIND
Defines the weight for individual observations.
See "OBSIND" on page 235
COATS
Requests Coats’ method for blackoil tables.
See "COATS" on page 178
PEARCE
Requests Pearce’s method for blackoil tables.
See "PEARCE" on page 244
WHITSON
Requests Whitson’s method for blackoil tables.
See "WHITSON" on page 288
RECOVERY
Sets the liquid production relative permeability for
recoveries.
See "RECOVERY" on page 248
Reference section
Batch system and keywords
159
SIMULATE section keywords
"Simulation using PVTi" on page 117 describes how to set up the SIMULATE keywords using
menu options. Table 6.10 details the keywords for the SIMULATE section.
Table 6.10
SIMULATE keywords
Keyword
Comments
Details
EXP
Defines experiments.
See "EXP" on page 195
OBS
Defines observations.
See "OBS" on page 234
OBSIND
Defines the weight for individual observations.
See "OBSIND" on page 235
FVFREF
Sets the reference values for FVF calculations.
See "FVFREF" on page 204
SAVCOMP
Saves the information for calculated compositions.
See "SAVCOMP" on page 258
REGRESS section keywords
"Regression in PVTi" on page 126 describes how to set up the REGRESS keywords using menu
options. Table 6.11 details the keywords for the REGRESS section.
Table 6.11
160
REGRESS keywords
Keyword
Comments
Details
EXP
Defines experiments.
See "EXP" on page 195
OBS
Defines observations.
See "OBS" on page 234
OBSIND
Defines the weight for individual observations. See "OBSIND" on page 235
VAR
Defines variables.
FVFREF
Sets the reference values for FVF calculations. See "FVFREF" on page 204
FIT
Perform regression.
See "FIT" on page 201
MAXIT
Specifies the maximum number of iterations.
See "MAXIT" on page 218
MAXSTEP
Specifies the maximum regression step limit.
See "MAXSTEP" on page 219
MINSTEP
Specifies the minimum regression step limit.
See "MINSTEP" on page 223
REGTARG
Specifies the regression target.
See "REGTARG" on page 250
Reference section
Batch system and keywords
See "VAR" on page 275
PVTi Reference Manual
BLACKOIL section keywords
This section allows you to generate output for ECLIPSE Black Oil. The "Exporting keywords"
on page 133 describes how to set up the BLACKOIL keywords using menu options. Table 6.12
details the keywords for the BLACKOIL section.
Table 6.12
BLACKOIL keywords
Keyword
Comments
Details
UNITS
Defines the units to use in the export.
See "UNITS" on
page 274
EXP
Defines experiments.
See "EXP" on page 195
Note you can only define CVD, DL and SEPS.
PVTi Reference Manual
COATS
Requests Coats’ method for blackoil tables.
See "COATS" on
page 178
WHITSON
Requests Whitson and Torp’s method for blackoil
tables.
See "WHITSON" on
page 288
DIFFERENTIAL
Requests Differential method for blackoil tables.
See "DIFFERENTIAL"
on page 189
FRAGOR
Requests Fragor method for blackoil tables.
See "FRAGOR" on
page 203
MOSES
Requests Moses method for blackoil tables.
See "MOSES" on
page 227
LIVEOIL
Generates tables with live oil.
See "Live oil tables" on
page 216
DEADOIL
Generates tables with dead oil.
See "DEADOIL" on
page 184
WETGAS
Generates tables with wet gas.
See "WETGAS" on
page 286
DEADGAS
Generates tables with dead gas.
See "DRYGAS" on
page 183
WAT100
Outputs water properties.
See "WAT100" on
page 282
MINDELP
Specifies minimum compressibility test pressure
difference.
See "MINDELP" on
page 222
Reference section
Batch system and keywords
161
PSEUCOMP section keywords
The "Exporting keywords" on page 133 describes how to set up the PSEUCOMP keywords using
menu options. This section allows you to generate output for ECLIPSE Black Oil options. Table
6.13 details the keywords for the PSEUCOMP section.
Table 6.13
PSEUCOMP keywords
Keyword
Comments
Details
EXP
Defines experiments.
See "EXP" on page 195
Note you can only define CVD and SEPS.
GI
Defines GI nodes for the GI option tables.
See "GI" on page 205
WAT200
Outputs water properties.
See "WAT200" on page 283
MINELP
Specifies minimum compressibility test
pressure difference.
See "MINDELP" on page 222
COATS
Requests Coats’ method for blackoil tables.
See "COATS" on page 178
WHITSON
Requests Whitson and Torp’s method for
blackoil tables.
See "WHITSON" on page 288
OUTECL3 section keywords
This section allows you to generate output for ECLIPSE Compositional. The "Exporting
keywords" on page 133 describes how to set up the OUTECL3 keywords using menu options.
Table 6.14 details the keywords for the OUTECL3 section.
Table 6.14
OUTECL3 keywords
Keyword
Comments
Details
UNITS
Specifies the units to use in the export.
See "UNITS" on page 274
SAMPLE
Specifies the fluid sample to use in the
export.
See "Specify fluid sample" on
page 254
RTEMP
Defines the reservoir temperature.
See "RTEMP" on page 251
NEWPVO
Defines a rootname for the export file.
See "Request new output PVO
file" on page 232
EOSOUT
Requests equation of state data for
ECLIPSE Compositional.
See "EOSOUT" on page 194
WAT300
Outputs water properties.
See "WAT300" on page 284
EXP
Defines experiments.
See "EXP" on page 195
Note you can only define COMPG or
CVD.
162
KVTABLE
Requests K -value table for ECLIPSE
Compositional.
See "KVTABLE" on page 212
XMFVP
Requests XMFVP and YMFVP tables for
ECLIPSE Compositional.
See "X/YMFVP" on page 289
YMFVP
Requests XMFVP and YMFVP tables for
ECLIPSE Compositional.
See "X/YMFVP" on page 289
ZMFVD
Requests ZMFVD table for ECLIPSE
Compositional.
See "ZMFVD" on page 293
Reference section
Batch system and keywords
PVTi Reference Manual
VFP section keywords
This section allows you to generate output for VFPi. The "VFP module" on page 138 describes
how to set up the VFP keywords using menu options. Table 6.15 details the keywords for the
VFP section.
Table 6.15
VFP keywords
Keywords
Comments
Details
EXP
Defines experiments.
See "EXP" on page 195
Note you can only define CCE and SEPS.
COATS
Requests Coats’ method for blackoil tables.
See "COATS" on
page 178
WHITSON
Requests Whitson and Torp’s method for blackoil
tables.
See "WHITSON" on
page 288
WATVFP
Outputs water properties.
See "WATVFP" on
page 285
TLOW
Defines lowest temperature in the production string.
See "TLOW" on
page 272
APITRACK section keywords
This section allows you to generate a series of black oil tables suitable for use with the API
Tracking option in ECLIPSE BlackOil. The "Export for API Tracking option in ECLIPSE
BlackOil" on page 134 describes how to set up the APITRACK keywords in interactive mode
using the appropriate panel. details the keywords for the APITRACK section...
Table 6.16
APITRACK keywords
Keyword
Comments
Details
UNITS
Defines the units to use in the export.
See "UNITS" on page 274
EXP
Defines experiments.
See "EXP" on page 195
Note you can only define CVD, DL and
SEPS.
PVTi Reference Manual
SAMPLES
The list of samples to export tables for.
See "SAMPLES" on page 256
COATS
Requests Coats’ method for blackoil tables.
See "COATS" on page 178
WHITSON
Requests Whitson and Torp’s method for
blackoil tables.
See "WHITSON" on page 288
DIFFERENTIAL
Requests Differential method for blackoil
tables.
See "DIFFERENTIAL" on
page 189
FRAGOR
Requests Fragor method for blackoil tables.
See "FRAGOR" on page 203
MOSES
Requests Moses method for blackoil tables.
See "MOSES" on page 227
LIVEOIL
Generates table with live oil.
See "Live oil tables" on
page 216
DEADOIL
Generates tables with dead oil.
See "DEADOIL" on page 184
Reference section
Batch system and keywords
163
Table 6.16
164
APITRACK keywords (Continued)
Keyword
Comments
Details
WETGAS
Generates tables with wet gas.
See "WETGAS" on page 286
DRYGAS
Generates tables with dry gas.
See "DRYGAS" on page 183
ALLDRY
Generates gas tables for each sample.
See "ALLDRY" on page 171
Reference section
Batch system and keywords
PVTi Reference Manual
Error handling
Keyword errors
If an error occurs during keyword input, the program displays the offending line with ?
characters under the field that is causing difficulties.
The error numbers given by the program may be of two types:
•
Up to and including 100.
These are errors detected within the PVTi data parser. Descriptions of these errors are given
in Table 6.17.
•
Above 100
System data errors, usually caused by internal read operations used to convert a character
to its value.
Table 6.17
PVTi Reference Manual
Error codes
Error code
Description
1
Unable to read next line from data file.
2
Length of current line is zero.
3
Quote misplaces in stack or data field.
4
/ character found in the wrong place.
5
Data field length greater than 24.
6
End of file reached.
7
Invalid character found.
8
Zero length stack found.
9
Stack length 1 with illegal character.
10
Incorrect stack pointers.
11
Failed to find * character in repeated data field.
12
Multiplier for repeated data field has more than 24 characters.
13
Error after internal read of multiple value.
14
Negative multiplier for repeated data field.
15
* character found as first token in stack.
16
Unrecognisable character for number in repeated data field.
17
Single field has the wrong data type.
18
Empty token next on stack.
19
Unknown data type.
20
Data read which is not of the type expected and which cannot be easily converted.
21
Error in internal read to convert character data to number.
22
Repeated data has field length of more than 24 characters.
23
Error in internal read of repeated data multiplier.
24
More than one exponential character found.
Reference section
Error handling
165
Table 6.17
166
Error codes (Continued)
Error code
Description
29
Previous data type of repeated field not compatible for current repeated data field.
30
Error in internal read of previous repeated data field.
31
Unable to convert current value due to error in previous repeated data field.
32
Values for margin setting not valid.
33
Zero length string found internally.
Reference section
Error handling
PVTi Reference Manual
Keywords
Chapter 7
PVTi keywords
This chapter contains details of all the keywords in PVTi. The keywords are listed in
alphabetical order.
•
"Keywords A-D" on page 168
•
"Keywords E-K" on page 191
•
"Keywords L- O" on page 213
•
"Keywords P- S" on page 241
•
"Keywords T - Z" on page 267
PVTi Reference Manual
Keywords
PVTi keywords
167
Keywords A-D
This section contains the A-D keywords.
The other PVTi keywords are listed as follows:
"Keywords E-K" on page 191
"Keywords L- O" on page 213
"Keywords P- S" on page 241
"Keywords T - Z" on page 267.
168
Keywords
Keywords A-D
PVTi Reference Manual
ACF
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Acentric factors
Specifies the acentric factors for the components in the system. The keyword is followed by N c
values, and terminated with a slash character (/), where N c is the number of components
specified in the RUNSPEC section.
Example
ACF
.22500
.20100
.34540
.57400
.80160
/
PVTi Reference Manual
.40000E-01
.22230
.38610
.61270
.84160
.13000E-01
.25390
.42510
.64860
.88300
.98600E-01
.30070
.46220
.68550
.92410
.15240
.27420
.49840
.72460
1.0590
.18480
.30560
.53420
.76340
Keywords
ACF
169
ACHEUH
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
A-coefficient for Cheuh-Prausnitz BICs
Specifies the value of the A -coefficient (pre-multiplying) of the Cheuh-Prausnitz binary
interaction coefficients for hydrocarbon-hydrocarbon interactions. Its value generally lies
between 0.1 and 0.5.
Note
Only available if OPTIONS flag 6 is active.
Example
--Default value:ACHEUH
0.15 /
170
Keywords
ACHEUH
PVTi Reference Manual
ALLDRY
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
Dry Gas Tables for Each Sample
This keyword requests that ECLIPSE BlackOil dry gas tables be output for each sample. If this
keyword is not present then a dry gas table is written out for the sample with the median vapor
density at surface conditions.
The keyword ALLDRY has no arguments.
VFP
X APITRACK
PVTi Reference Manual
Keywords
ALLDRY
171
Binary interaction coefficients
BIC
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies binary interaction coefficients. There are two possible formats for this keyword.
First format
•
The keyword should be followed by up to ( N c -1) lines of data followed by a forward slash
character (/).
•
Each line should consist of three integers followed by the set of binary interaction
coefficients between two specified components, terminated with a forward slash character
(/). The first integer specifies the index of the first component and the second and third
integers the lower and upper indices of the other component.
Second format
The program uses this format when saving.
This format in effect displays the lower triangle of the BIC matrix, and there is no need for the
first three columns informing the program of the component and the lower and upper indices.
PVTi assumes the coefficients are read in as second, third component, etc., by row with the
columns as the first, etc., component.
Note
For both formats the interaction coefficient between any given component and itself
must be zero. PVTi always ensures that this is the case.
Examples
First format
Binary interaction coefficients for a six component system.
BIC
2 1
3 1
4 1
5 1
6 1
/
1 -0.02000
2 0.10000
2 0.13000
2 0.13500
5 0.12700
/
0.03600
0.05000
0.08000
2*
/
/
/
2*0.0600
/
Here there are zero binary interaction coefficients between components 4 to 3, 5 to 3,4 and 6 to
2,3.
172
Keywords
BIC
PVTi Reference Manual
Second format
The same system of BICs appears as follows:
BIC
-0.02000
0.10000
0.13000
0.13500
0.12700
/
PVTi Reference Manual
0.03600
0.05000
0.08000
2*
2*0.0600
Keywords
BIC
173
BLACKOIL
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
174
Keywords
BLACKOIL
Start of the BLACKOIL section
This is a delimiter keyword, specifying the start of the BLACKOIL section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used to generate blackoil tables for any of the currently defined fluid samples by
simulating reservoir depletion with a constant volume depletion or differential liberation. Tables
are generated that can then be input into ECLIPSE BlackOil.
PVTi Reference Manual
CALVAL
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify calorific values
Specifies the calorific values for the components in the system. The keyword is followed by N c
values, where N c is the number of components specified in the RUNSPEC section. It is
terminated with a / character. The current units convention is used.
The default is kJ ⁄ kg -ml kJ/kg-ml. For alternatives a UNITS keyword should have been
previously read. For further information see [Ref. 39].
Example
For a two component C1/I-C4 system, using PVT-Metric units:
-- Calorific Values kJ/kgmol
CALVAL
8.130000000E+02 2.659000000E+03
PVTi Reference Manual
/
Keywords
CALVAL
175
CHARACT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Components to be characterized
Specifies the components that are to be defined by characterization. This keyword is followed
by up to N c lines (or as many non-blank components as in the CNAMES keyword, below), each
terminated with a / character. The last line of data is followed by a / character.
Each line begins with the mnemonic of the component to be characterized, followed by five
items of data:
•
Molecular weight M w
•
Specific gravity Sg
•
Normal boiling point temperature T b
•
Watson characterisation factor K w
•
Reference temperature T ref
•
Two strings which specify the characterisation procedure required for:
•
Critical properties.
Kesler-Lee (K), Cavett (C), Riazi-Daubert (R), Winn (W) or Pedersen (P)
•
Acentric factor.
Kesler-Lee (K), Edmister (E), Thompson (T) or Pedersen (P).
Generally, you must provide two out of the four data items M w , S g , T b and K w to characterize a
component. If more than two items are available, give the “best” two items since the order of
entry dictates which two are used. It is possible to perform a characterization with a minimum
data entry of M w ; the program estimates the specific gravity from a Single Carbon Number
(SCN) table look-up. See [Ref. 18].
Note
If no reference temperature is specified it is given the value of the standard
temperature.
Example
Characterizes two plus fractions, the first of which has known specific gravity and normal
boiling point temperature, the second of which has only molecular weight. Riazi-Daubert
critical properties and Edmister acentric factor correlations to be used:
CHARACT
C7+1 1*
C7+2 200.0
/
0.7500
/
390.0
2*
R
E
/
If more than two of the four items, M w , Sg , T b and K w are available, then the program uses the
first two, that is given data for M w , T b and K w , then PVTi uses M w and T b .
176
Keywords
CHARACT
PVTi Reference Manual
CNAMES
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Component names
Specifies the mnemonics associated with the components in the system that are either to be
characterized or fully user defined. This keyword is followed by N c component names, where
N c is the number of components specified in the RUNSPEC section. It is terminated with a /
character.
Define library components using the LNAMES keyword. Any system containing both library and
characterisation/user defined components should contain both LNAMES and CNAMES with the
default specification 1*, where appropriate.
The program translates the component names into upper case on input. The length may be up to
72 characters, but a limit of four is suggested to fit into the program output formats.
Example
For a nine-component condensate system, the first five being from library, the last four to be
user defined:
CNAMES
5*
LNAMES
CO2 N2
PVTi Reference Manual
C4-6 C7+1 C7+2 C7+3
C1
C2
C3 4*
/
/
Keywords
CNAMES
177
Blackoil tables
COATS
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
178
Keywords
COATS
Specifies that the Coats method for the generation of blackoil tables is used in preference to the
Whitson and Torp method. By default, the program uses the Whitson and Torp method.
The keyword COATS has no arguments.
PVTi Reference Manual
COMB
RUNSPEC
SYSTEM
SPLIT
GROUP
X COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the COMB section
This is a delimiter keyword, specifying the start of the COMB section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used for data and consistency checking of laboratory data of gas condensates and
volatile oils. Material balance is performed on any Constant Volume Depletion data, to calculate
liquid compositions, K-values, densities, etc. Additionally, tests of separator recombination data
are available, as well as estimates of recovery, and generation of blackoil tables without
recourse to the equation of state.
PVTi Reference Manual
Keywords
COMB
179
COMBINE
RUNSPEC
SYSTEM
SPLIT
X GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Group existing components
Requests the grouping of a range of existing components into a new combined fraction. This is
done by specifying a group index for each existing component. PVTi groups together
components with the same group index.
Components not to be grouped may be ignored, or given a group index of zero.
Note
The group index has no significance other than to identify sets of components.
You may enter a name for the new fractions. By default the program uses GRP1, GRP2 and
GRP3 as the group names.
The form of the keyword is:
COMBINE
icl1 icu1 ifr1 zfr1
icl2 icu2 ifr2 zfr2
/
/
/
where:
•
icl1 is a lower existing component index;
•
icu1 is an upper existing component index;
•
ifr1 is a group index;
•
zfr1 is the mnemonic for a fraction.
Example
In a 19-component system, group the components 10 to 14 inclusive, and the components 15,
17 and 18. Accept default names for the fractions:
COMBINE
10 14 1
15 15 2
17 18 2
/
180
Keywords
COMBINE
/
/
/
PVTi Reference Manual
CORRACF
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Splitting correlation for ACFs
Specifies the correlation to be used for calculating the acentric factors of characterized split
fractions. It should be either Kesler-Lee (K), Edmister (E), Thomassen (T) or Pedersen (P) [Ref.
13], [Ref. 14], [Ref. 30] & [Ref. 41] respectively. It must be terminated with a forward slash (/
) character.
The default is Kesler-Lee (K).
Example
Edmister correlation required:
CORRACF
E /
PVTi Reference Manual
Keywords
CORRACF
181
CORRCP
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Splitting correlation for critical properties
Specifies the correlation to be used for calculating the critical properties of characterized split
fractions. It should be one of Kesler-Lee (K), Cavett (C) Riazi-Daubert (R), Winn (W), or
Pedersen (P) [Ref. 10], [Ref. 11], [Ref. 12], [Ref. 42] , [Ref. 43], and [Ref. 41] respectively. It
should be terminated by a forward slash (/) character.
The default is Kesler-Lee (K).
Example
Cavett correlation required:
CORRCP
C /
182
Keywords
CORRCP
PVTi Reference Manual
DRYGAS
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Dry gas tables
This keyword requests that ECLIPSE BlackOil dry gas tables be output.
The keyword DRYGAS has no arguments.
X APITRACK
PVTi Reference Manual
Keywords
DRYGAS
183
DEADOIL
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Dead oil tables
This keyword requests that ECLIPSE BlackOil dead oil tables be output.
The keyword DEADOIL has no arguments.
X APITRACK
184
Keywords
DEADOIL
PVTi Reference Manual
DEBUE
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Select output to debug file
Requests that additional output from the PVTLIB annex be directed to the DBG debug file. The
keyword is followed by up to eight integers in the range one to eight, terminated with a forward
slash (/) character. The indices request the following output:
Table 7.1
Output indices
Index
Output from
0
No debug
1
Full debug (see below)
2
Flash stability routines
3
Flash split routines
4
Newton routines
5
Fugacity routines (enter as -1 to obtain fugacities of components, batch
mode only)
6
Water EoS routines
7
p sat routines
8
Critical point routines
9
Phase plot generator
Example
Request debug from Newton and p sat routines:
CORRCP
C /
PVTi Reference Manual
Keywords
DEBUE
185
Select output to debug file
DEBUG
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Requests that additional output from PVTi be directed to the DBG debug file. The keyword is
followed by up to 16 integers in the range one to 16, terminated with a forward slash (/)
character. The indices request the following output:
Table 7.2
Output indices
Index
Output from
1
Array allocation routines
2
Phase plots
3
Zudkevitch-Joffe equation of state
4
Regression
5
Parser
6
Characterization/Splitting
7
Experiments (not p sat )
8
Observations
9
Saturation pressure/temperature
10
Flash routine
11
Newton routines
12
Fugacity evaluation (set as -1 to obtain Fugacities of components - batch
mode only)
13
Stability Check/Michelsen
14
Opening/closing of files
15
Regression output
16
LBC coefficients with regression
17
COMB routines
Example
Request debug from Flash and Michelsen routines only:
DEBUG
9* 10 2* 13 /
186
Keywords
DEBUG
PVTi Reference Manual
DEFBIC
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Default binary interaction coefficients
Specifies that default binary interaction coefficients are required. These are only available
between library/library and library/characterization components.
The keyword DEFBIC has no arguments.
PVTi Reference Manual
Keywords
DEFBIC
187
DEGREES
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Temperature convention
Specifies the temperature convention to use. The keyword is followed by a character string
identifying the convention, which may be one of the following four:
•
KELVIN
Degrees Kelvin
•
CELSIUS
Degrees Celsius
•
RANKINE
Degrees Rankine
•
FAHRENHEIT
Degrees Fahrenheit.
Only the first character is significant, and may be lower or upper case. The default temperature
convention is degrees Kelvin.
Note
This keyword must follow the UNITS keyword.
Example
Set to degrees Fahrenheit:
DEGREES
F /
188
Keywords
DEGREES
PVTi Reference Manual
DIFFERENTIAL
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Blackoil tables
Specifies that differential black oil tables are generated. By default, the Whitson and Torp
method of composite black oil table generation is used.
The keyword DIFFERENTIAL has no arguments.
PVTi Reference Manual
Keywords
DIFFERENTIAL
189
Reference densities
DREF
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the reference densities for the components in the system. The keyword is followed by
N c values, and terminated with a forward slash (/) character, where N c is the number of
components specified in the RUNSPEC section.
Note
•
These reference densities are only required if the Zudkevitch-Joffe or three-parameter
Peng-Robinson equations have been selected (although it is good practice to always
enter them), and are associated with the reference temperatures specified with the
TREF keyword.
UNITS: METRIC: kg/ m 3 FIELD: lb/cu ft LAB: gm/cc PVT-M: kg/ m 3
Note
Example
For a two-component CO2/I-C4 system:
DREF
777.00
190
Keywords
DREF
557.00
/
PVTi Reference Manual
Keywords E-K
This section contains the E-K keywords.
The other PVTi keywords are listed as follows:
"Keywords A-D" on page 168
"Keywords L- O" on page 213
"Keywords P- S" on page 241
"Keywords T - Z" on page 267.
PVTi Reference Manual
Keywords
Keywords E-K
191
Insert PVI file into PVP file
ECHO
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
192
Keywords
ECHO
This keyword inserts the PVI input file into the PVP print file.
The keyword ECHO has no arguments.
PVTi Reference Manual
EOS
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Defines the required Equation of State
Defines the required equation of state from the list:
•
PR Two-parameter Peng-Robinson.
•
PR3 Three-parameter Peng-Robinson.
•
RK Redlich-Kwong.
•
SRK Soave-Redlich-Kwong.
•
SRK3 Three-parameter Soave-Redlich-Kwong.
•
SW Schmidt-Wenzel.
•
ZJ Zudkevitch-Joffe.
The default is PR3.
Example
EOS
PR3
PVTi Reference Manual
/
Keywords
EOS
193
EOSOUT
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
194
Keywords
EOSOUT
EoS data for ECLIPSE 300
Requests that equation of state data be output to the PVO file for inclusion in ECLIPSE
Compositional. The EOSOUT keyword has no arguments.
By default, if this keyword is omitted and no other keywords are in the OUTECL3 section, EoS
data is automatically output to the PVO file.
PVTi Reference Manual
EXP
X
X
X
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Experiments
Specifies the experiments to be performed. Up to 100 experiments plus one set of BLACKOIL
calculations can be defined.
The form of the keyword and associated data is:
EXP
<no>1
<no>2
:
<samp>1
<samp>2
<type>1
<type>2
<data>1
<data>2
/
/
where:
•
<no> specifies the experiment number, usually increasing sequentially from 1;
•
<samp> specifies the mnemonic of the required sample composition for this experiment;
•
<type> specifies the experiment type. One of: FLASH, BUBBLE, DEW, CCE, CVD, DL,
SWELL, SEPS, COMPG, TERN, vapor, MFLASH, CRIT, TSAT, FCMP, MCMP, PSAT, MCT.
In the above, a forward slash (/) character terminates entry of experiments, and the form of the
<data> depends on the particular experiment type:
Table 7.3
Required data for experiments
Experiment Data
FLASH
T
BUBBLE
T
DEW
IRT
P
T
CCE
FLUID
T
P
P2...
...PN
CVD
FLUID
T
P1
P2...
...PN
DL
T
P
P2...
...PN
SWELL
FLUID
YMF
T
[PRESS P]
STYPE
X1...
...XN
SEPS
T1
P1
L1
V1
(option 1)
T2
P2
L2
V2
.
.
.
.
TN
PN
LN
VN
SEPS
T1
P1
FL11
FV11
FV1N
(option 2)
T2
P2
FL21
FV21...FL2N
FV2N
.
.
.
.
.
TN
PN
LN
FVN1...FLNN FVNN
COMPG
FLUID
T
P
D
D1
TERN
T
P
ZG1
ZG2
ZG3
IG2...
...IGN
T
P
M1... ...MN
VAPOR
FLUID
YMF
MFLASH
T
P
IG1
CRIT
PVTi Reference Manual
Keywords
EXP
195
Table 7.3
Required data for experiments (Continued)
Experiment Data
TSAT
P
TSAT
FCMP
YMF
T
MCMP
YMF
ICORV
PSAT
T
MCT
YMF
FCMP
T
MCMP
PSAT
ICORV
T
P
FL2...FLN-1N
(option 1)
MCT
MCT
(option
1)
YMF
ICORV
T
P
FV2...FVN-1N
(option 2)
MCT
(option
2)
TCLOUD
T
P
PCLOUD
T
P
where:
Table 7.4
Keyword arguments
Keyword
arguments
Data requirements
T
Single temperature entry
P
Single pressure entry
IRT
Retrograde (IRT=1) or normal (IRT=0) dew point
FLUID
GAS or OIL system
PI
I’th pressure
YMF
Mnemonic of gas sample composition defined in SAMPLES or ZI.
STYPE
Specifies subsequent data is MOLE fraction of gas in the mixture or GOR
gas volume at STP in the oil at original pressure or other pressure.
ICORV
Condensing (ICORV=0) or vaporizing (ICORV=1) multiple contact
miscibility pressure required
XI
Mole fraction or GOR (see STYPE) for step I.
MI
Number of moles added cumulatively at step I.
TI
Temperature of I’th separator stage.
LI
Destination of liquid output from stage. Default is next stage, I+1.
VI
Destination of vapor output from stage. Default is the cumulative vapor
output, 0.
Note, for separators, cumulative output stage is labelled 0, with vapor at
STC, liquid at final stage conditions.
196
Keywords
EXP
FLIJ
Fraction of liquid output from stage I to stage J. Default is 1.0 to the next
stage.
FVIJ
Fraction of vapor output from stage I to stage J. Default is 1.0 to the
cumulative vapor output, 0.
D
Reference depth.
PVTi Reference Manual
Table 7.4
Keyword arguments (Continued)
Keyword
arguments
Data requirements
DI
Depth I.
ZGI
Names of the I’th ternary group.
IGI
Ternary group index (1-3) for component I.
Example
Consider the following experiments:
1
Dew point pressure at 200 °F , no pressure estimate given;
2
Swelling test at 200 °F , injection gas composition specified in SAMPLES with mnemonic
ZINJ, four stage addition with given mole percentage of gas in reservoir fluid;
3
Constant composition expansion of condensate (GAS) at 200 °F , pressures in psi;
4
Constant volume depletion of condensate at 200 °F , pressures in psi;
5
2-stage separator at 500 psi, 125 °F and 50 psi, 90 °F with second stage fed from liquid
output of stage one;
6
Composition with depth: a volatile oil (OIL) at reference conditions of 220 °F , 4000 psi and
7500 ft. Require compositions and pressures at 7000, 7100,..., 8000 ft;
7
Ternary diagram calculation for an eight component system, explicit grouping;
8
Ternary diagram calculation for an eight component system, default grouping;
9
First contact miscibility pressure at 160 °F on ZI, injecting ZINJ;
10 Multiple contact miscibility pressure at 160 °F on ZI, injecting ZINJ, vaporizing drive;
11 Multiple contact miscibility pressure at 160 °F on ZI, injecting ZINJ, condensing drive;
12 Multiple contact test at 121.1 °F and 2738 psi on ZI, injecting ZINJ, condensing drive. At
each stage all of the remaining oil from the flash is contacted with one mole of ZINJ.
PVTi Reference Manual
Keywords
EXP
197
EXP
1 ZI
2 ZI
DEW
SWELL
1
GAS
3
CCE
GAS
ZI
200.0
ZINJ
MOLE
200.0
/
200.0
0.1271
6000.0
2000.0
3000.0
0.3046
5000.0
1000.0
2400.0
4 ZI CVD
GAS 200.0
-- old format for SEPS
5 ZI SEPS
125.0
500.0 2
90.0 50.0
0
7 ZI TERN
N2C1 C2C5 C6+ 1 1 2
8 ZI TERN /
9 ZI FCMP ZINJ 160.00 /
10 ZI MCMP ZINJ 1 160.00 /
11 ZI MCMP ZINJ 0 160.00 /
12 ZI MCT
ZINJ 0 121.10 2738.0
/
Note
0.5384
4000.0
0.6538
3000.0
1800.0
1200.0
0
0 /
2 2 2 3 3
/
/
/
/
1.0 1.0 1.0 1.0
/
At pressures above the saturation pressure where no compositional changes take place,
the Constant Volume Depletion (CVD) and the Differential Liberation (DL) are
effectively a Constant Composition Expansion (CCE) experiment.
Restrictions
The EXP keyword arguments are subject to restrictions in the BLACKOIL, COMB, OUTECL3,
REGRESS and VFP sections:
Table 7.5
Restrictions for EXP keyword arguments
Section
Experiment
BLACKOIL
CVD, DL & SEPS only.
PSEUCOMP
CVD & SEPS only.
COMB
CVD, SEPS & CCE only.
OUTECL3
CVD & COMPG only.
REGRESS
Not COMPG, TERN, MFLASH, CRIT, TSAT, FCMP, MCMP.
VFP
CCE & SEPS only.
BLACKOIL section
In the BLACKOIL section, to generate blackoil tables you must define a depletion experiment
and a separator network.
Number these experiments; 1 (CVD or DL) and 2 (SEPS).
198
Keywords
EXP
PVTi Reference Manual
COMB section
In the COMB section, you are restricted to the above experiments for the material balance (CVD),
recombination of separator data (SEPS) and recovery calculations (CCE).
Number these experiments 1 to 3, in any order.
OUTECL3 section
In the OUTECL3 section, you are restricted to a CVD for the purposes of generating either
KVTABLE or XMFVP and YMFVP tabular data.
Note
Only two pressures should be entered, the maximum and minimum pressures required
in the table. The other pressures are calculated by interpolation (up to 50 pressures in
all).
You can also specify a COMPG experiment for the purpose of generating ZMFVD tables for
ECLIPSE Compositional.
Note
Only two depths should be entered, the maximum and minimum depths required in the
table. The other depths are calculated by interpolation (up to 50 depths in all).
Number these experiments 1 (CVD) and 2 (COMPG).
VFP section
In the VFP section, to generate blackoil tables you must define a depletion experiment and a
separator network.
Number these experiments 1 (CCE) and 2 (SEPS).
PVTi Reference Manual
Keywords
EXP
199
EXPIND
X
X
X
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Set Status of Experiments
This keyword is used to set the status of a particular experiment, necessary when performing a
regression operation. The keyword is a list of integers, one for each experiment, where a 0
means the experiment is not to be used in a regression (‘turned off’) and a 1 means the
experiment is to be used in a regression (‘turned on’).
Example
We have 20 experiments in total in our project and wish that they all be ‘turned on’ during
regression except the 5th, 10th, 14th, 16th and 18th, which will be ‘turned off’:
OPTIONS
1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1/
200
Keywords
EXPIND
PVTi Reference Manual
FIT
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Perform fit by regression
This keyword requests that a regression operation, previously specified using the EXP, OBS and
VAR keywords, be carried out.
The keyword FIT has no arguments.
PVTi Reference Manual
Keywords
FIT
201
Specify plus fraction data
FRAC
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the number and relative compositions of the plus fraction splitting. You specify the
number of fractions required, the relative composition of the fractions, and the mnemonics to
be associated with the split fractions (optional), terminated with a / character.
Example
Split the plus fraction into three sub-fractions:
FRAC
3 0.72
202
Keywords
FRAC
0.23
0.05
C7+1
C7+2
C7+3
/
PVTi Reference Manual
FRAGOR
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Blackoil tables
Specifies that the Fragor method for the generation of composite from differential blackoil
tables is used.
By default, the program uses the Whitson and Torp method of composite black oil table
generation.
The keyword FRAGOR has no arguments.
PVTi Reference Manual
Keywords
FRAGOR
203
FVFREF
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
X SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
FVF reference conditions
The reference conditions for the liquid formation volume factors from Pinit/Pbub to Pstock
(mnemonic SRELV) calculation in separator experiments may be input here.
For each SEP experiment, a reference temperature and pressure are required. If the reference
pressure is zero, the saturation pressure at the reference temperature will be used.
Each record must be terminated with a / character. The set of records must end with a blank
record, containing only a slash (/).
Note
If reference conditions are not entered for a SEP experiment, no FVFs are calculated
for that experiment. This includes the FVFs at each stage, and the ORELV mnemonic,
as well as SRELV.
Example
FVFREF
2 220.0
4 200.0
7 210.0
/
204
Keywords
FVFREF
4000.0
0.0 /
/
/
PVTi Reference Manual
GI
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
X PSEUCOMP
OUTECL3
VFP
Define GI nodes for E200 tables
Specifies the lean gas injection sample and the GI nodes (gas-oil ratios) for the generation of
ECLIPSE pseudo-compositional tables. This keyword is followed by a mnemonic specifying
the fluid sample (defined on the SAMPLES keyword) and up to ten GI values, terminated with
a / character.
Example
Inject sample ZINJ at GI’s of 0.1, 0.2, 0.3 mscf/rb:
GI
ZINJ
PVTi Reference Manual
0.1
0.2
0.3
/
Keywords
GI
205
Start of the GROUP section
GROUP
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
206
Keywords
GROUP
This is a delimiter keyword, specifying the start of the GROUP section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used to define data necessary for the grouping of components into pseudocomponents.
PVTi Reference Manual
GRBYALL
RUNSPEC
SYSTEM
SPLIT
X GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the GROUP section
This keyword specifies that the grouping of components specified by the COMBINE keyword
be performed with respect to an average of all samples rather than to the default ZI sample.
The keyword GRBYALL has no arguments.
PVTi Reference Manual
Keywords
GRBYALL
207
GRBYMIX
RUNSPEC
SYSTEM
SPLIT
X GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
208
Keywords
GRBYMIX
Start of the GROUP section
This keyword specifies that the grouping of components specified by the COMBINE keyword
be performed using a molecular weighting, rather than the default mole fraction approach.
The keyword GRBYMIX has no arguments.
PVTi Reference Manual
GRBYSAM
RUNSPEC
SYSTEM
SPLIT
X GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the GROUP section
This keyword specifies that the grouping of components specified by the COMBINE keyword
be performed with respect to the named sample, rather than to the default ZI sample.
Example
Group to sample ZINJ
PVTi Reference Manual
GRPBYSAM
ZINJ
/
Keywords
GRBYSAM
209
GRPBYWGT
RUNSPEC
SYSTEM
SPLIT
X GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
210
Grouping by molecular weight
This keyword specifies that the grouping of components specified by the COMBINE keyword
be performed using a molecular weighting, rather than the default mole fraction approach.
The keyword GRBYWGT has no arguments.
Keywords
GRPBYWGT
PVTi Reference Manual
HYDRO
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Define component as hydrocarbon or nonhydrocarbon
Specifies whether a component is a hydrocarbon or a non-hydrocarbon. The keyword is
followed by up to N c (the number of components in the fluid system) flags indicating the
component types and terminated by a forward slash (/) character.
The available flags are given in Table 7.6.
Table 7.6
Component Types
Type
Flag in HYDRO
Non-hydrocarbon
N
Hydrocarbon
H
Paraffin
P
Cyclic-hydrocarbon (naphthalene)
C
Aromatic
A
By default, all components are assumed to be hydrocarbons, except for specific nonhydrocarbons in the “LIB” set, that is, CO2 , H2 S , H 2 O , N 2 , H 2 and CO .
Example
An 11 component system consisting of CO2, N2, C1, C2, C3, IC4, NC4, IC5, NC5, C6, C7+:
HYDRO
N N 9*H
PVTi Reference Manual
/
Keywords
HYDRO
211
KVTABLE
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
212
Keywords
KVTABLE
Request K-value table for ECLIPSE 300
output
Requests that a K -value table, consisting of the K -value of each component at a set of pressures,
be output to the PVO file. The keyword KVTABLE takes no arguments.
Note
Your must also define a Constant Volume Depletion (CVD) experiment with the EXP
keyword and associated data in order that the KVTABLE can be generated.
Note, also, that only two pressures need be defined in the CVD; these should be the
maximum and minimum required.
PVTi Reference Manual
Keywords L- O
This section contains the L-O keywords.
The other PVTi keywords are listed as follows:
"Keywords A-D" on page 168
"Keywords E-K" on page 191
"Keywords P- S" on page 241
"Keywords T - Z" on page 267.
PVTi Reference Manual
Keywords
Keywords L- O
213
Lohrenz-Bray-Clark viscosities
LBC
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
214
Keywords
LBC
Specifies that the Lohrenz-Bray-Clark viscosity correlation is to be used, rather than the
Pedersen method. The LBC correlation is the default and is used if neither of the LBC or
PEDERSEN keywords is used.
The keyword LBC has no arguments.
PVTi Reference Manual
LBCCOEF
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Set non-default LBC coefficients
Enables the default coefficients used by the Lohrenz-Bray-Clark viscosity correlation to be
modified. This should only be done with great care: the viscosity is obtained from a fourth order
polynomial in reduced density and must clearly not go negative.
There are five coefficients with default values of 0.1023, 0.023364, 0.058533, -0.040758 and
0.0093324. Any coefficient not specified with LBCCOEF takes these default values.
Example
Reset two of the LBC coefficients
LBCCOEF
1* 0.025 1* -0.04 0.01
PVTi Reference Manual
/
Keywords
LBCCOEF
215
LIVEOIL
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Live oil tables
This keyword requests that ECLIPSE BlackOil live oil tables be output.
The keyword LIVEOIL has no arguments.
X APITRACK
216
Keywords
LIVEOIL
PVTi Reference Manual
LNAMES
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify library names
Specifies the mnemonics associated with the components in the system that are to be taken from
the internal library. A system containing both library and characterized/user defined
components should contain both LNAMES and CNAMES with the default specification, 1*,
where appropriate.
The component names are translated into upper case on input. The length may be up to 72
characters, but a limit of four is suggested to fit into the program output formats.
Each record is terminated with a slash (/).
Example
For a nine-component condensate system, with the first five from library and the last four userdefined:
CNAMES
5* C4-6 C7+1 C7+2 C7+3 /
LNAMES
CO2 N2
C1
C2
C3 4*
PVTi Reference Manual
/
Keywords
LNAMES
217
Max. number of regression iterations
MAXIT
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies maximum number of function evaluations in the non-linear regression step. This does
not include the initial stage required in setting up the numerical Jacobian.
The default is 50.
The record is terminated with a slash (/).
Example
MAXIT
40 /
218
Keywords
MAXIT
PVTi Reference Manual
MAXSTEP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Maximum step size allowed in regression
At each step of the regression, a maximum step size, or trust region radius is maintained. This
is allowed to vary during the regression, depending upon how successfully the behavior of the
regression function is predicted. However, a maximum trust region radius is also imposed.
MAXSTEP allows this to be reset.
The variables upon which this limit acts are scaled to unity in the case of
p c , T c , V c , Z c , Ω a , Ω b , and are the actual values for binary interaction coefficients and acentric
factors. Thus a maximum step of 0.1 corresponds to a change of 10% in a critical temperature.
The default is 0.1.
The record is terminated with a slash (/).
Example
MAXSTEP
0.2 /
PVTi Reference Manual
Keywords
MAXSTEP
219
Data for Whitson splitting
MDP
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the α (shape factor) and η (lowest mole weight) parameters used in the Whitson
probability density function used to characterize plus fractions.
Default values are 1.0 and 97.0 respectively.
The record is terminated with a slash (/).
Example
Change η to 92.0, leave α unchanged:
MDP
1* 92.0
220
Keywords
MDP
/
PVTi Reference Manual
MESSAGE
X
X
X
X
X
X
X
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Echo message to file and screen
Echoes a single line to the screen and print file when a PVI input file is read. The MESSAGE
keyword can occur anywhere after the first keyword, RUNSPEC, and takes the form:
Example
PVTi Reference Manual
MESSAGE
Message to echo goes here
Keywords
MESSAGE
221
MINDELP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
X PSEUCOMP
OUTECL3
VFP
Minimum pressure difference
Specifies the minimum pressure step to allow during the automatic insertion of pressure nodes
into pressure depletion experiments following blackoil table total compressibility tests.
Note
This keyword must be placed after the keywords defining the depletion and separator
experiments.
The default is one atmosphere.
The record is terminated with a slash (/).
Example
MINDELP
14.7 /
222
Keywords
MINDELP
PVTi Reference Manual
MINSTEP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Minimum step limit allowed in regression
At each step of the regression, a maximum step size, or trust region radius is maintained. This
is allowed to vary during the regression, and may be reduced
•
if the function is poorly predicted
•
if error conditions occur in the regression functional
•
if the solution attempts to cross a lower or upper limit.
If the step size limit falls below a minimum value, for any reason, the regression terminates, as
further progress is unlikely to be made. This minimum value may be reset with the MINSTEP
keyword.
Note
This is not the minimum step that may be taken; it is the minimum upper limit imposed
on a step.
The default is 0.00001.
The record is terminated with a slash (/).
Example
MINSTEP
0.000001
PVTi Reference Manual
/
Keywords
MINSTEP
223
Mix samples
MIX
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
This keyword allows two samples to be mixed to form a new one. The inputs are the two sample
names, the new sample name, the type of mixing and the amount of mixing. The types of mixes
are as follows:
•
MOL specifies that the mixing amount given is the mole fraction of sample two in the
mixture with sample 1.
•
If the mixing method is GOR, then the amount is given as the gas volume at standard
conditions of sample two as a ratio of the volume of the initial sample. The latter is useful
for consideration of mixing of lean gases in oil samples.
Note
•
Mixing is only performed if:
- the two samples are different
- the amount to mix is greater than zero
- the name of the new sample is different from any other sample
- the mixing does not take the number of samples over the program limit.
For the GOR option, the volume of the initial sample is usually the volume at its P sat at
the specified temperature. However, an alternative pressure can be specified; this is shown
in Example 2, below.
Each record must be terminated with a slash (/).
The set of records must end with a blank record, containing only a slash (/).
Examples
Example 1
Mix sample Z1 with Z2 to form Z3. The amount to mix is such that sample Z2 is 0.45 of the
mole fraction in the new sample Z3.
MIX
Z1
/
Z2
Z3
80.000 MOL
0.45
/
Example 2
Mix sample T1 with T2 to form T3. The amount to mix is represented as a GOR of 5.0 MSCF/
stb, and the volume of the first sample T1 is measured at a pressure of 5000 PSI at the mix
temperature of 670 °F . If the saturated volume of T1 was required then the PRES could be set
as 0.0, or those two items removed from the keyword.
MIX
T1
/
224
Keywords
MIX
T2
T3
670.0
PRES 5000.0
GOR 5.0 /
PVTi Reference Manual
MODSPEC
x RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Denotes start of the run specification section
Any split, group, regress or user change of the fluid system causes a new RUNSPEC/SYSTEM
section to be appended to the audit trail, which can be saved on exit from PVTi to a PVI file.
These new sections are labelled with the keywords MODSPEC and MODSYS to indicate they are
modified definitions. They are interchangeable with RUNSPEC and SYSTEM.
This section defines the number of components, equation of state and viscosity option, run title
and name of any new output file.
The keyword MODSPEC has no arguments.
PVTi Reference Manual
Keywords
MODSPEC
225
MODSYS
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
226
Keywords
MODSYS
Start of the MODSYS section
MODSYS is a delimiter keyword, specifying the start of the MODSYS section, which defines the
component properties and the fluid sample compositions.
As for MODSPEC, the MODSYS keyword denotes a modified fluid system that was saved from
a previous PVTi session following on from a split, group, regress or manual change of the fluid
system originally defined with RUNSPEC and SYSTEM. The MODSYS section generally follows
the MODSPEC section.
The keyword is interchangeable with SYSTEM.
PVTi Reference Manual
MOSES
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Blackoil tables
Specifies that the Moses method for the generation of composite from differential blackoil
tables is used. By default, the program uses the Whitson and Torp method of composite black
oil table generation.
The keyword MOSES has no arguments.
PVTi Reference Manual
Keywords
MOSES
227
Specify molecular weights
MW
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the molecular weights for the components in the system. The keyword is followed by
N c values, where N c is the number of components specified in the RUNSPEC section.
The set of records must be terminated with a forward slash (/) character.
Example
Molecular weights for 15-component system:
MW
44.010
58.124
209.26
228
Keywords
MW
28.013
72.151
281.29
16.043
72.151
462.30
30.070
86.178
44.097
106.09
58.124
152.68
/
PVTi Reference Manual
MWS
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Define plus fraction mole weight for CMF
splitting
This keyword specifies the mole weight of the plus fraction in the Constant Mole Fraction
splitting algorithm. The keyword is followed by a single real number for the mole weight and a
forward slash (/) character.
Example
Plus fraction mole weight of 140.0:
MWS
140.0
PVTi Reference Manual
/
Keywords
MWS
229
NCOMPS
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
230
Keywords
NCOMPS
Specify number of components
Specifies the number of components in the sample. This keyword must be entered in the
RUNSPEC section. The maximum value available for NCOMPS is usually 100. This is set by a
parameter in the source code, and can be increased at specific request.
Example
NCOMPS
20 /
PVTi Reference Manual
NEWPVI
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Request new output PVI file
Allows you to output the current system description at the end of a batch run if it is thought that
the system changes during the run (because of splitting/grouping and/or regression). The
keyword is followed by the required filename root (that is the file name less any prefix or suffix)
and is terminated with a forward slash (/) character.
Example
Write out new PVI file with name SAVE:
NEWPVI
SAVE /
PVTi Reference Manual
Keywords
NEWPVI
231
NEWPVO
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
Request new output PVO file
Allows you to name the export file produced in batch mode when there is an OUTECL3 section
present. The keyword is followed by the required filename root (that is the file name less any
prefix or suffix) and is terminated with a forward slash (/) character.
Example
Write a PVO file with name SAVE:
NEWPVO
SAVE /
232
Keywords
NEWPVO
PVTi Reference Manual
NOECHO
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
No insertion of PVI file into PVP file
This keyword requests that the PVI input file is not to be inserted into the PVP output file. This
is the default condition.
The keyword NOECHO has no arguments.
PVTi Reference Manual
Keywords
NOECHO
233
Specify observations
OBS
RUNSPEC
SYSTEM
SPLIT
GROUP
X COMB
X SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the observations associated with experiments performed individually or as part of a
regression analysis.
Note
This keyword can only be specified if the EXP keyword and associated experiments
have already been defined.
•
In the SIMULATE section, this keyword provides the means of supplying experimentally
determined data for comparison purposes in output.
•
In the REGRESS section, this keyword provides the experimental data to be regressed
against.
The form of the keyword and its associated data is:
OBS
no
mnem
mnem
no
mnem
mnem
weight
weight
data
data
/
/
:
/
weight
weight
data /
data
/
:
/
/
where:
no
specifies the experiment number given in the EXP keyword
mnem
specifies the observation mnemonic (see below)
weight
global weight to be given to subsequent data.
Several observations can be associated with a given experiment, each of which must be
terminated with a forward slash (/) character. The entry of observations for a particular
experiment is then terminated with a forward slash (/) character. A forward slash character (/)
also terminates the entry of all observations.
234
Keywords
OBS
PVTi Reference Manual
OBSIND
RUNSPEC
SYSTEM
SPLIT
GROUP
X COMB
X SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify observation weights
Specifies the individual observation weights associated with observations defined with an OBS
keyword.
Note
Note that the OBS keyword must exist in the section of the PVI file before the OBSIND
keyword is inserted.
If no OBSIND keyword is used the individual observation weights take the value of the global
observation weight defined for each mnemonic in OBS.
The form of the keyword and its associated data is:
OBSIND
no
mnem
mnem
:
data
data
/
/
data
data
/
/
/
no
mnem
mnem
:
/
/
where:
no
specifies the experiment number given in the EXP keyword ("EXP" on page 195);
mnem
specifies the observation mnemonic (see OBS keyword, "OBS" on page 234);
data
individual weights to be given to each point described in the previous OBS keyword.
Example
Observation weights for the experiments defined for the EXP keyword
(compare with example in OBS keyword description):
1
Saturation pressure and vapor Z -factor of dew point
2
Saturation pressure and swelling factor (relative volume) at each stage of swelling test
3
Relative volumes at each stage of CCE, vapor Z -factors at pressures above saturation
pressure only
4
Liquid saturation, vapor Z -factor and gas mole fractions at each stage of CVD (nine
component system)
5
GOR at each stage and stock tank GOR (in Mscf/stb) from two stage separators.
PVTi Reference Manual
Keywords
OBSIND
235
OBSIND
1 PSAT 50.0 /
ZV
1.0 /
/
2 PSAT 10.0 10.0 10.0 10.0 /
RELV 1.0 1.0 1.0 1.0 /
/
3 RELV
1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0
2.0 2.0 3.0 4.0
ZV
1.0 1.0 1.0 1.0 1.0 1.0 10*
/
4 SL
1.0 1.0 1.0 1.0
/
ZV
1.0 1.0 1.0 1.0
/
YMF 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
1.0 1.0 1.0 1.0 1.0 /
/
5 GOR
100.0 10.0 /
TGOR 10.0
/
/
/
236
Keywords
OBSIND
/
/
PVTi Reference Manual
OMEGAA/B
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify EoS omega values
These keywords specify non-default Ω a and Ωb values for the components in the system. Each
keyword is followed by N c values, where N c is the number of components in the system, and is
terminated with a forward slash (/) character. You need only specify these keywords if you wish
to override the default equation of state values, which are as follows:
Table 7.7
Equation of State omega values
Equation
OMEGAA
OMEGAB
RK
0.4274802
0.08664035
SRK
0.4274802
0.08664035
ZJ
0.4274802
0.08664035
PR
0.457235529
0.07776074
Example
Ωa
and Ωb values for two component system:
OMEGAA
0.457 0.456
OMEGAB
0.0780
PVTi Reference Manual
0.0781
/
/
Keywords
OMEGAA/B
237
OPTIONS
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Set various program options
This keyword is used to set the various program options. Each option is described in "Program
options" on page 145. As from the release of PVTi 2004A there are 21 options with each option
specified by an integer (usually 0 or 1).
Note
Upon program start-up, most options are OFF, specified by an option value 0 (zero).
Options 2 and 7 are the only ones that are on (=1) by default.
To subsequently turn any option ON, specify an the integer 1 (but be careful of the special
options below). The vector of integers is terminated with a / character.
Special option settings
Option 4
Temperature dependence of volume shifts (when using a three-parameter EoS) takes the
following arguments:
•
0 - No temperature dependence;
•
1 - Apply linear thermal expansion to all components;
•
2 - Use polynomial correlations and thermal expansion.
Option 11
Optional printing of results to the PVP file also takes specific arguments:
•
0 - ALways print;
•
1 - OPTionally print (that is user prompted);
•
2 - NEVer print.
Option 14
Alternative definitions of GOR in differential liberation experiments also takes specific
arguments:
238
Keywords
OPTIONS
•
0 - Default definition;
•
1 - Last stage removed and oil volume at its bubble point pressure;
•
2 - Incremental GOR;
•
3 - As default but volume of oil at its bubble point pressure rather than stock tank
conditions.
PVTi Reference Manual
Example
Separator liquid volumes to be output at stock tank conditions. Cheuh-Prausnitz BICs required.
Optional printing of results to PVP file:
OPTIONS
0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 /
PVTi Reference Manual
Keywords
OPTIONS
239
OUTECL3
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
240
Keywords
OUTECL3
Start of the OUTECL3 section
This is a delimiter keyword, specifying the start of the OUTECL3 section.
Note
If present, this section must not appear before the SYSTEM section.
The section is used in generating output data for inclusion into the ECLIPSE compositional
model. Either equation of state or pressure-dependent tabular data can be generated.
PVTi Reference Manual
Keywords P- S
This section contains the P-S keywords.
The other PVTi keywords are listed as follows:
"Keywords A-D" on page 168
"Keywords E-K" on page 191
"Keywords L- O" on page 213
"Keywords T - Z" on page 267.
PVTi Reference Manual
Keywords
Keywords P- S
241
PARACHOR
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Define parachors
Specifies the parachors for the components in the fluid system. The keyword is followed by up
to N c values (the number of components specified in the RUNSPEC section) and terminated by
a forward slash (/) character.
Units
Should be consistent to obtain surface tensions in dyne/cm.
Example
Parachors from [Ref. 18] for N2, C1, C2 and C3:
PARACHOR
41.0 77.0 108.0 150.3 /
242
Keywords
PARACHOR
PVTi Reference Manual
PCRIT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Critical pressures
Specifies the critical pressures for the components in the system. The keyword is followed by
N c (the number of components in the system) values, and terminated with a forward slash (/)
character.
•
UNITS: bars (METRIC), psi (FIELD), atm (LAB), atm (PVT-M).
Example
For a two-component system, using atm:
PCRIT
72.90
PVTi Reference Manual
36.00
/
Keywords
PCRIT
243
PEARCE
RUNSPEC
SYSTEM
SPLIT
GROUP
X COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
244
Keywords
PEARCE
Blackoil tables
Specifies that the Pearce method for generating blackoil tables is used in preference to the
Whitson and Torp or Coats method. By default, the program uses the Whitson and Torp method.
The keyword PEARCE has no arguments.
PVTi Reference Manual
PEDERSEN
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify Pedersen viscosities
Specifies that the Pedersen corresponding state viscosity correlation is to be used, rather than
the default Lohrenz-Bray-Clark method.
The keyword PEDERSEN has no arguments.
PVTi Reference Manual
Keywords
PEDERSEN
245
PRCORR
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
246
Keywords
PRCORR
Peng-Robinson correction
This keyword requests that a modified form of Peng-Robinson equation of state is to be used.
This changes the usual form of the Ω a value as a function of the component acentric factor.
The keyword PRCORR takes no arguments, and has no effect on equations of state other than
the Peng-Robinson.
PVTi Reference Manual
PSEUCOMP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
X PSEUCOMP
OUTECL3
VFP
Start of the PSEUCOMP section
This is the delimiter keyword specifying the start of the PSEUCOMP section used for the
generation of ECLIPSE pseudo-compositional tables.
This section performs a depletion experiment to define fluid properties in the reservoir and then
passes the liquid and vapor through a separator network to surface conditions to define standard
blackoil tables. Then a series of gas injections are performed and modified blackoil tables
generated with the various mixtures.
PVTi Reference Manual
Keywords
PSEUCOMP
247
RECOVERY
RUNSPEC
SYSTEM
SPLIT
GROUP
X COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Liquid production for recovery estimates
The presence of the RECOVERY keyword turns on the ability to calculate liquid production by
the method of Reudelhuber and Hinds ([Ref. 37]) in the COMB section recovery calculations. It
should be followed by the coordinates of two points on the curve of relative permeability versus
total liquid saturation. The order of entry is the minimum and maximum relative permeabilities,
and then the total liquid saturations for the minimum and maximum points.
Example
RECOVERY
<RPMIN> <RPMAX> <SRPMIN> <SRPMAX> /
248
Keywords
RECOVERY
PVTi Reference Manual
REGRESS
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the REGRESS section
This is a delimiter keyword, specifying the start of the REGRESS section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used to perform a regression of the equation of state parameters such as to
minimize the difference between observed and calculated results of the following experiments:
•
equilibrium flash
•
bubble and dew point evaluation
•
saturated pressure
•
constant composition expansion
•
constant volume depletion
•
differential liberation
•
swelling test
•
vaporization test
•
multi-stage separator networks
•
the multi-contact test.
PVTi Reference Manual
Keywords
REGRESS
249
REGTARG
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Regression target
This quantity allows the default regression target to be changed. The regression target is applied
to the sum of squares of the differences between the calculated and observed values. If a solution
is found for which the residual approaches zero, the regression returns successfully when the
sum of squares falls below this value. If there is a non-zero residual minimum this limit is
applied to the derivatives of the residual at the minimum.
•
DEFAULT: 0.000001.
The record is terminated by a forward slash (/) character.
Example
RETARG
0.1D-8
250
Keywords
REGTARG
/
PVTi Reference Manual
RTEMP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
Reservoir temperature for ECLIPSE
Compositional
This keyword defines the reservoir temperature to be used in an ECLIPSE Compositional
simulation by including it along with the EoS data, which is output on the PVO file. It is
followed by a single real number and terminated with a forward slash (/) character. It should be
in the current PVTi unit set: it may be converted on output into an appropriate ECLIPSE
Compositional unit set.
Example
Specify a reservoir temperature of 200 °F :
RTEMP
200.0
PVTi Reference Manual
/
Keywords
RTEMP
251
RUNSPEC
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
252
Keywords
RUNSPEC
Denotes start of the run specification
This keyword opens the run specification section, and is normally the first keyword in the input
data file. This section defines the number of components, equation of state and viscosity option,
run title and name of any new output file.
PVTi Reference Manual
SALINITY
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify sample salinity
For systems containing water, this specifies the salinity of any sample. The data are only used
in the multiphase flash experiment.
The record is terminated by a forward slash (/) character.
•
UNITS: ppm (parts per million).
Example
RTEMP
200.0
PVTi Reference Manual
/
Keywords
SALINITY
253
SAMPLE
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
Specify fluid sample
This keyword is specifies the fluid sample to use in the exportation of a fluid model for use in
an ECLIPSE Compositional simulation.
APITRACK
254
Keywords
SAMPLE
PVTi Reference Manual
SAMPLES
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify fluid samples
This keyword defines different composition fluids. Up to 50 different samples can be defined
on all platform types. This maximum number can be changed on request, please contact us for
advice if this situation arises. Each composition must be given a unique mnemonic to
distinguish it from all others.
Note
Note that the default sample composition is given by the ZI keyword and is given the
mnemonic of ZI.
Thus, each line consists of the composition mnemonic followed by up to N c mole fractions,
which should sum to unity, followed by a forward slash (/) character. The last composition
should be followed by another forward slash (/) character.
The composition of the lean gas injection fluid used in a swelling test should be defined under
this keyword.
Example
Lean gas composition for swelling test:
SAMPLES
ZINJ 2*
/
PVTi Reference Manual
0.9468
0.0527
0.0005
4*
/
Keywords
SAMPLES
255
SAMPLES
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify fluid samples
If this keyword is in the APITRACK section and not the SYSTEM section then it specifies the
fluid samples involved when exporting a series of black oil tables to be used with the API
Tracking option in ECLIPSE BlackOil.
X APITRACK
256
Keywords
SAMPLES
PVTi Reference Manual
SAMTITLE
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify titles of fluid samples
This keyword defines a long description to be associated with each alternative sample, so as to
give more information about the origin of the samples, etc. The description must be enclosed in
quotes.
Each record is terminated by a forward slash (/) character. The set of records must be ended by
a blank record, containing only a slash.
Note
This keyword should not precede the SAMPLES keyword.
Example
Second sample from deeper in the column. Lean gas composition for swelling test:
SAMTITLE
Z2
‘Second sample from deeper in the column’ /
ZINJ ‘Lean gas composition for swelling test’ /
/
PVTi Reference Manual
Keywords
SAMTITLE
257
SAVCOMP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
X SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Save compositions
If you have turned on the OPTIONS switch for saving compositions calculated during
experiments, this keyword may be used in the SIMULATE section to save compositions to
named samples. Each line in this section contains the experiment number, the fluid type required
(from XMF, YMF, ZMF, for liquid, vapor and total compositions), the stage of the experiment if
it is a multi-stage experiment, and the sample name required. The stage index should be omitted
if the experiment is not a multi-stage experiment. In the particular case of the stock tank stage
of a SEPS experiment, you should enter ST for the stage indicator.
Each record is terminated by a forward slash (/) character. The set of records must be ended by
a blank record, containing only a slash.
Example
Save the total composition for experiment 4, a COMPG experiment, at stage (here depth) 4, and
label it Z80. Save the liquid output from stage 3 of experiment 2, a SEPS experiment, and label
it S23, and the stock tank vapor output of the same experiment, labelling it ST2:
SAVCOMP
4 ZMF 4 Z80 /
2 XMF 3 S23 /
2 YMF ST ST2 /
/
258
Keywords
SAVCOMP
PVTi Reference Manual
SCT
RUNSPEC
X SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Defines Semi-Continuous Thermodynamics
split
This keyword requests the modified Whitson method, here denoted the Semi-ContinuousThermodynamics (SCT) split. This method has the advantage that it can take multiple plus
fraction definitions from multiple samples and split them into a consistent set of pseudocomponents with mole fractions adjusted between the different samples to honour moles and
mole weights.
Each record is terminated by a forward slash (/) character. The set of records must be ended by
a blank record, containing only a slash.
The keyword is followed by N samp + 1 lines of information, where N samp is the number of already
defined samples, including the default sample ZI.
•
The first line of data specifies the mnemonic of the heavy end to split, the number of
pseudo-components required (which must be between two and five), the minimum mole
weight in the plus fraction (the Whitson η -parameter) and the mole weight of the heaviest
pseudo-component required. As a default, the heaviest pseudo-component weight could be
set to 1.5 and 2.0 times the heaviest plus fraction mole weight.
•
Next follows N samp lines of data, one for each sample currently defined. On each line should
be the sample mnemonic, the skewness parameter (Whitson α -parameter), the sample plus
fraction mole weight and specific gravity.
Example
The default and one alternative sample from different depths in the hydrocarbon column, and
therefore different mole weights and specific gravities for the C7+ plus fraction. Different
compositions are on the ZI and SAMPLES keyword, sample ZALT, which preceded this
keyword and data. Three pseudo-component split requested with minimum and maximum mole
weights of 90.0 and 300.0. Different skewness parameters reflects compositional grading in
fluid from top (ZI - low Alpha) to bottom (ZALT - high Alpha).
SCT
C7+ 3
ZI
ZALT
/
PVTi Reference Manual
90.0
1.10
2.30
300.0
130.0
150.0
/
0.75
0.80
/
/
Keywords
SCT
259
Specify specific gravity
SG
RUNSPEC
SYSTEM
Z SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
260
Keywords
SG
Specifies the specific gravity (with respect to water at standard conditions) for the plus fraction
to be split. The record is terminated by a forward slash (/) character.
Example
SG
0.86 /
PVTi Reference Manual
SIMULATE
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
X SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the SIMULATE section
This is a delimiter keyword, specifying the start of the SIMULATE section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used to define any of the following experiments:
•
equilibrium flash
•
bubble and dew point evaluation
•
constant composition expansion
•
constant volume depletion
•
differential liberation
•
swelling test
•
vaporization test
•
multi-stage separator networks
•
multiphase flashes
•
ternary diagrams
•
saturated pressure and temperature
•
critical point
•
compositional gradient
•
minimum miscibility pressures
all using the equation of state model.
PVTi Reference Manual
Keywords
SIMULATE
261
SPECHA-D
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify specific heat capacity coefficients
Specifies the specific heat capacity coefficients for the components in the system. The keywords
are followed by N c values, and terminated with a / character, where N c is the number of
components specified in the RUNSPEC section.
Note
The values are output only in EoS data for ECLIPSE Compositional input files and
only if OPTION number 7 is turned on.
Example
For a two component system, in PVT-Metric units:
-- Specific Heat Coefficients A kJ/kgm/K
SPECHA
5.409000000E+00 -4.224000000E+00 /
-- Specific Heat Coefficients B kJ/kgm/K
SPECHB
1.781000000E-01 3.063000000E-01 /
-- Specific Heat Coefficients C kJ/kgm/K
SPECHC
-6.938000000E-05 -1.586000000E-04 /
-- Specific Heat Coefficients D kJ/kgm/K
SPECHD
8.713000000E-09 3.215000000E-08 /
262
Keywords
SPECHA-D
PVTi Reference Manual
SPLIT
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Start of the SPLIT section
This is a delimiter keyword, specifying the start of the SPLIT section.
Note
If present, this section must not appear before the SYSTEM section.
This section is used to define data necessary for the splitting of the plus fraction, assumed to be
the last component.
PVTi Reference Manual
Keywords
SPLIT
263
SSHIFT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
264
Keywords
SSHIFT
Dimensionless volume shifts for PR3
This keyword defines the dimensionless volume shift parameters used in the three-parameter
Peng-Robinson equation of state. The keyword is followed by N c real numbers and terminated
with a / character, where N c is the number of components.
Example
SSHIFT
0.15 0.05
-0.05
-0.03
-0.01
0.01
0.05
0.12
/
PVTi Reference Manual
STCOND
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Standard conditions
Specifies the current standard conditions. This is followed by the standard temperature and
pressure values. The record is terminated by a forward slash (/) character.
Example
Standard conditions in degrees Fahrenheit and psia:
PVTi Reference Manual
STCOND
60.0 14.7
/
Keywords
STCOND
265
SYSTEM
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
266
Keywords
SYSTEM
Start of the SYSTEM section
This is a delimiter keyword, specifying the start of the SYSTEM section. This section generally
follows the RUNSPEC section.
This section is used to define the component properties and the fluid sample compositions.
PVTi Reference Manual
Keywords T - Z
This section contains the T-Z keywords.
The other PVTi keywords are listed as follows:
"Keywords A-D" on page 168
"Keywords E-K" on page 191
"Keywords L- O" on page 213
"Keywords P- S" on page 241.
PVTi Reference Manual
Keywords
Keywords T - Z
267
Specify boiling points
TBOIL
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the boiling point temperatures for the components in the system. The keyword is
followed by N c values, where N c is the number of components specified in the RUNSPEC
section, and terminated with a / character. The current temperature convention is used. The
default is degrees K , and for alternatives a DEGREES keyword should have been previously
read.
Note
Boiling points are only required if the Zudkevitch-Joffe equation has been selected.
Example
For a two component CO2/I-C4 system, using degrees K :
TBOIL
194.70
268
Keywords
TBOIL
261.30
/
PVTi Reference Manual
TCRIT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify critical temperatures
Specifies the critical temperatures for the components in the system. The keyword is followed
by N c values, where N c is the number of components specified in the RUNSPEC section, and
terminated with a forward slash (/) character. The current temperature convention is used.
•
DEFAULT: degrees K . For alternatives a DEGREES keyword should have been previously
read.
Example
For a two component CO2/I-C4 system, using degrees K :
TCRIT
305.6 408.1 /
PVTi Reference Manual
Keywords
TCRIT
269
THERMX
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Thermal expansion coefficient for volume
shifts
Specifies the value of the volume expansion coefficient which may be applied to the threeparameter equations of state (PR3, SRK3) volume shifts.
It is terminated with a forward slash (/) character.
Note
The specified value is only used if the appropriate OPTIONS switch is in force.
Example
Default value with temperature in degrees Centigrade, that is THERMX in °C –1 :
THERMX
0.0005
270
Keywords
THERMX
/
PVTi Reference Manual
TITLE
X RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify run title
This keyword introduces the title of the run, which appears on the header of each section of the
PVP output file. The line following the title keyword is taken as the title to be used.
Note
The syntax is slightly different from that of other keywords, in that no terminating
forward slash (/) character is required.
Example
TITLE
18 component condensate test
PVTi Reference Manual
Keywords
TITLE
271
Define lowest temperature for VFP tables
TLOW
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
X VFP
PVT properties for VFPi must be defined at least for two temperatures. The highest temperature,
assumed to be reservoir temperature, is set on the constant composition expansion (CCE)
experiment definition under the EXP keyword. The lowest temperature in the production string
is defined using this keyword.
It is terminated with a forward slash (/) character.
Example
Production string runs through deep sea-water at 40 °F
TLOW
40.0 /
272
Keywords
TLOW
PVTi Reference Manual
TREF
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify reference temperatures
Specifies the reference temperatures for the components in the system. The keyword is followed
by N c values, where N c is the number of components specified in the RUNSPEC section, and
terminated with a forward slash (/) character. The current temperature convention is used.
•
DEFAULT: degrees K . For alternatives a DEGREES keyword should have been previously
read.
Note
These reference temperatures are only required if the Zudkevitch-Joffe equation has
been selected.
Example
For a two component CO2/I-C4 system, using degrees K :
TLOW
40.0
PVTi Reference Manual
/
Keywords
TREF
273
Specify unit conventions
UNITS
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
APITRACK
This keyword specifies which unit convention is required, and sets flags to specify whether
absolute or gauge pressures, and mole fractions or mole percentages, are to be used.
The UNITS keyword is followed by a character string identifying the units convention, which
may be one of the following four:
•
METRIC: Metric unit system
•
FIELD: Field units
•
LAB: Laboratory units
•
PVT: PVT-metric units (metric units with pressures in atm).
Only the first character is significant, and case is not significant.
•
DEFAULT: PVT-metric.
The pressure switch is one of the two following strings:
•
ABSOL: Absolute pressure
•
GAUGE: Gauge pressure.
•
DEFAULT: ABSOLute pressures.
The mole composition switch is one of the following strings:
•
FRAC: Compositions as fractions of unity
•
PERC: Compositions as percentages of a hundred.
•
DEFAULT: FRACtions.
Example
Set to field units:
UNITS
F /
274
Keywords
UNITS
PVTi Reference Manual
VAR
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
X REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify regression variables
Specify variables for regression. The keyword is followed by a number of lines of data, each
specifying variables to be added to the regression set. The data is terminated by a blank record
(a single forward slash (/) character).
The keyword thus takes the form:
VAR
S1
S2
S3
:
/
1
I1
I2
I3
:
J1
J2
J3
:
K1
K2
K3
:
L1
L2
L3
:
IND1
IND2
IND3
:
LL1
LL2
LL3
:
UL1/
UL2 /
UL3 /
:
The strings S1,S2... identify variables for regression, the indices I1, J1 (and K1, L1 for
binaries) identify component ranges, lower and upper.
Possible strings identifying variables (that is, S1, S2 etc.) are:
•
TCRIT: Critical temperatures
•
PCRIT : Critical pressures
•
VCRIT: Critical volumes in LBC viscosity correlation
•
ZCRIT: Critical Z -factors in LBC viscosity correlation
•
ACF: Acentric factors
•
OMEGAA: Ω a values
•
OMEGAB: Ω b values
•
SSHIFT: Volume shift parameter
•
BIC : Binary interaction coefficients
In all cases except BIC, the lower and upper component indices should be specified. In the
case of BIC, lower and upper index ranges should be given, that is, in four values. For
example BIC 1 3 7 8 contains the BICS for (1, 7), (1, 8), (2, 7), (2, 8), (3, 7) and (3, 8).
2
PVTi Reference Manual
The indices IND1, IND2, etc., specify the variable index as applied to the particular
variable. “Special” regression variables are available and are:
•
SCTALF: SCT Splitting parameter
•
SCTMW: SCT plus fraction weight
•
SCTKW: SCT Watson K factor
•
THERMX: Thermal expansion coefficient
•
CHEUHA: Cheuh-Prausnitz BIC coefficient
•
CHARMW: Molecular weights of characterized components
•
CHARMF: Mole Fractions of characterized and/or user components for any sample
•
MIXING: The mixing factor between two samples when using the MIX keyword.
Keywords
VAR
275
Note
In the case of SCTKW, THERMX, CHEUHA and MIXING the component and variable
indices are redundant as the variable applies to all components.
In the case of SCTALF and SCTMW, the I1 and K1 indices refer to the sample rather
than component range.
For the CHARMF two other sets of indices are needed to indicate the range of samples
over which the particular variable applies. This follows the syntax of the BIC
keyword. For example, CHARMF 1 2 4 5 contains the mole fractions for
components 4 and 5 for samples 1 and 2.
The quantities LL and UL specify limits imposed on the variables during the regression. All
variable limits are applied as a percentage of the current value, scaled to unity. Thus a maximum
value of 1.5 corresponds to allowing a 50% increase in any variable; a negative value implies
that the variable is allowed to change sign (restricted set!). Defaults are as follows:
Table 7.8
Default limits for variables
Variable
Lower limit
Upper limit
pc
0.5
1.5
Tc
0.5
1.5
Vc
0.5
1.5
Zc
0.5
1.5
Ωa
0.5
1.5
Ωb
0.5
1.5
ω
0.5
2.0
BIC
-5.0
+5.0
si
-5.0
5.0
SCTALF
0.5
5.0
SCTMW
0.9
1.1
SCTKW
0.75
1.25
CHEUHA
0.5
1.25
THERMX
-5.0
5.0
CHARMW
0.9
1.1
CHARMF
.75
1.25
MIXING
.75
1.25
Grouped regression variables can be defined by giving them the same variable index.
276
Keywords
VAR
PVTi Reference Manual
Examples
Example 1
Regression variables are the critical temperature for component 1, the Ωa values for
components 2 and 3, the binary interaction coefficient for components 1 and 10, and the volume
shift parameters for components 4 and 6 to 10 as a first grouped variable, and components 1 to
3 and 5 as a second grouped variable. Default limits are taken for all components except the
binary, which is restricted to a lower limit of 30% and an upper limit of 200% of the current
value:
VAR
TCRIT
OMEGAA
BIC
SSHIFT
SSHIFT
SSHIFT
SSHIFT
/
1
2
1
1
4
5
6
1
1 /
3
1 /
1 10 10 1 0.30 2.00
3
1 /
4
2 /
5
1 /
10
2 /
/
That is a total of five variables.
Example 2
The default settings for the first five special regression variables with a system of three samples
is as follows:
VAR
’SCTALF’
’SCTALF’
’SCTALF’
’SCTMW’
’SCTMW’
’SCTMW’
’SCTKW’
’CHEUHA’
’THERMX’
/
Note
PVTi Reference Manual
1
1
1
2
2
2
3
3
3
1
1
1
2
2
2
3
3
3
0.750000
0.500000
-5.000000
0.500000
0.500000
0.500000
0.900000
0.900000
0.900000
1.250000 /
1.500000 /
5.000000 /
5.000000
5.000000
5.000000
1.100000
1.100000
1.100000
/
/
/
/
/
/
The special regression variables SCTALF and SCTMW cannot be grouped into one
variable and must be entered in the manner shown above, that is one variable for each
sample.
Keywords
VAR
277
Specify volumes
VCRIT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the critical volumes for the components in the system. The keyword is followed by N c
values, where N c is the number of components specified in the RUNSPEC section, and
terminated with a forward slash (/) character.
The critical volumes are in volume per mole at critical pressure and temperature.
•
UNITS:
3
m /kg-mole (METRIC),
cc/gm mole (LAB),
cub ft/lb mole (FIELD),
3
m /kg-mole (PVT-M).
VCRIT values may be entered as an alternative to ZCRIT values - that is one of VCRIT or
ZCRIT should be entered. If VCRIT values are entered, critical Z -factors are obtained
internally using the usual relationship:
p crit V crit
Z crit = ------------------- ,
RT crit
[EQ 7.1]
where R is the gas constant.
Example
For a 20-component system, in field units:
VCRIT
1.5057
4.0847
7.8058
13.779
/
278
Keywords
VCRIT
1.4417
4.9337
8.8374
4.759
1.5698
4.9817
9.8465
15.684
2.3707
5.8948
10.830
16.018
3.2037
6.0710
11.799
16.018
PVTi Reference Manual
VCRITVIS
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify volumes for LBC viscosity
calculations
Specifies the critical volumes for the components in the system, to be used in the LBC viscosity
calculation only. The keyword is followed by N c values, where N c is the number of components
specified in the RUNSPEC section, and terminated with a forward slash (/) character.
The critical volumes are in volume per mole at critical pressure and temperature.
•
UNITS:
3
m /kg-mole (METRIC),
cc/gm mole (LAB),
cub ft/lb mole (FIELD),
3
m /kg-mole (PVT-M).
VCRITVIS values may be entered as an alternative to ZCRITVIS values; that is, one of
VCRITVIS or ZCRITVIS should be entered. If VCRITVIS values are entered, critical Z factors are obtained internally using the usual relationship:
p crit V critv
Z critv = --------------------- ,
RT crit
[EQ 7.2]
where R is the gas constant.
Note
If VCRITVIS or ZCRITVIS is not entered then values entered with VCRIT or
ZCRIT are used in the viscosity correlation. The form of VCRITVIS is the same as
that of VCRIT.
Example
For a 20-component system, in Field units:
VCRITVIS
1.5057
4.0847
7.8058
13.779
/
PVTi Reference Manual
1.4417
4.9337
8.8374
14.759
1.5698
4.9817
9.8465
15.684
2.3707
5.8948
10.830
16.018
3.2037
6.0710
11.799
16.018
Keywords
VCRITVIS
279
VERSION
x RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
280
Keywords
VERSION
Version of PVTi
This keyword indicates the version of PVTi that created the PVI file.
Caution
Files in FIELD units containing Differential Liberation (DL) experiments that
have Gas Formation Volume Factor (GFVF) observations must be updated to the
current version. See "Converting old projects to the current version" on page 87
for a tutorial on converting old-version PVI files.
VERSION
2001A /
PVTi Reference Manual
VFP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
X VFP
Start of the VFP section
This is a delimiter keyword, specifying the start of the VFP section.
Note
This section must follow the SYSTEM section.
This section is used to generate blackoil tables for VFPi, for any of the currently defined fluid
samples, by simulating phase and volumetric changes in the wellbore with a constant
composition expansion and separator flash at high (reservoir) and low temperatures. Tables are
generated that can then be input into VFPi.
PVTi Reference Manual
Keywords
VFP
281
WAT100
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Output water properties
Specifies the following for calculation of water properties within a black oil table generation for
ECLIPSE Black Oil:
It is terminated with a forward slash (/) character.
1
Temperature at which water properties are required
2
Pressure at which water properties are required
3
Flag for salt dissolved in water (Y for Yes, N for No)
4
Flag for keyword required (S for PVTW, M for PVTWSALT)
5
Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl))
6
Flag for gas dissolved (Y for gas, N for no gas)
7
Salinities. This can have just one value if the PVTW keyword is required, but up to ten
values if PVTWSALT is required (zero salinities can be defaulted with *). Units are given
by the above flag.
Examples
Example 1
For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F ,
pressure 5514.7 psi.
--Water properties requested for E100
WAT100
200.00000 5514.70000 Y S P Y
10000.0000
/
Example 2
For PVTWSALT output, salt present with salinities 10, 20 and 30 gpl, with no gas dissolved.
Temperature 200 °F , pressure 5514.7 psi.
-- Water properties requested for E100
WAT100
200.00000 5514.70000 Y M G N
10.0000
20.0000
30.0000 7*
/
282
Keywords
WAT100
PVTi Reference Manual
WAT200
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
X PSEUCOMP
OUTECL3
VFP
Output water properties
Specifies the following for calculation of water properties within a black oil table generation for
ECLIPSE.
It is terminated with a forward slash (/) character.
1
Temperature at which water properties are required
2
Pressure at which water properties are required
3
Flag for salt dissolved in water (Y for Yes, N for No)
4
Flag for keyword required (S for PVTW, M for PVTWSALT)
5
Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl))
6
Flag for gas dissolved (Y for gas, N for no gas)
7
Salinities. This can have just one value if the PVTW keyword is required, but up to 10 values
if PVTWSALT is required (zero salinities can be defaulted with *). Units are given by the
above flag.
Examples
Example 1
For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F ,
pressure 5514.7 psi.
--Water properties requested for E200
WAT100
200.00000 5514.70000 Y S P Y
10000.0000
/
Example 2
For PVTWSALT output, salt present with salinities 10, 20 and 30 gpl, with no gas dissolved.
Temperature 200 °F , pressure 5514.7 psi.
-- Water properties requested for E200
WAT200
200.00000 5514.70000 Y M G N
10.0000
20.0000
30.0000 7*
/
PVTi Reference Manual
Keywords
WAT200
283
WAT300
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
Output water properties
Specifies the following for calculation of water properties within a run involving EoS output for
ECLIPSE Compositional.
It is terminated with a forward slash (/) character.
1
Temperature at which water properties are required
2
Pressure at which water properties are required
3
Flag for salt dissolved in water (Y for Yes, N for No)
4
Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl))
5
Flag for gas dissolved (Y for gas, N for no gas)
6
Salinity, units of which are given by the above flag.
Example
For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F ,
pressure 5514.7 psi.
--Water properties requested for E300
WAT300
200.00000 5514.70000 Y P Y
10000.0000
/
284
Keywords
WAT300
PVTi Reference Manual
WATVFP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
X VFP
Output water properties
Specifies the following for calculation of water properties within a run involving black oil
output for the VFPi program.
It is terminated with a forward slash (/) character.
1
Highest temperature at which water properties are required
2
Highest pressure at which water properties are required
3
Lowest temperature at which water properties are required
4
Lowest pressure at which water properties are required
5
Flag for salt dissolved in water (Y for Yes, N for No)
6
Flag for units of salinity (P for Parts per million, G for grammes per liter)
7
Flag for gas dissolved (Y for gas, N for no gas)
8
Salinity, units of which are given by the above flag.
Example
For PVTW output, salt present of salinity 10000 poem, with gas dissolved. Calculated at
temperatures 200 °F and 80 °F , pressure 6000.0 psi.
--Water properties requested for VFP
WATVFP
200.00000 6000.00000
80.00000 6000.00000
/
PVTi Reference Manual
Y P Y
10000.0000
Keywords
WATVFP
285
WETGAS
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
X BLACKOIL
PSEUCOMP
OUTECL3
VFP
Wet gas tables
This keyword requests that ECLIPSE BlackOil wet gas tables be output.
The keyword WETGAS has no arguments
X APITRACK
286
Keywords
WETGAS
PVTi Reference Manual
WHIT
RUNSPEC
SYSTEM
X SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Defines Whitson splitting
This keyword defines data specific to the Whitson splitting algorithm. The method consists of
taking the single plus fraction consisting of SCN groups N+ with composition, mole weight and
specific gravity z N+ , M N+ , γ N+ and splitting from SCN group N to some large carbon number,
say 45, and then re-grouping to a user specified number of pseudo-components N grp .
The keyword is followed by an integer to specify the first SCN group in the plus fraction, three
real numbers for the composition, mole weight and specific gravity and an integer to specify the
required number of pseudo-components on re-grouping, all terminated with a forward slash (/)
character.
Example
Split C 7+ with z7+ = 0.1 , M 7+ = 140.0 , γ 7+ = 0.85 into three pseudo-components:
WHIT
7 0.10
PVTi Reference Manual
140.0
0.85
3
/
Keywords
WHIT
287
WHITSON
X
X
X
X
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
288
Keywords
WHITSON
Blackoil tables
Specifies that the Whitson and Torp method for the generation of blackoil tables is used in
preference to the Coats method. By default, the program uses the Whitson and Torp method.
The keyword WHITSON has no arguments.
PVTi Reference Manual
X/YMFVP
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
XMFVP and YMFVP ECLIPSE tables
Requests that XMFVP and YMFVP tables, consisting of the liquid and vapor mole fractions of
each component at a set of pressures, be output to the PVO file. The XMFVP and YMFVP
keywords have no arguments.
Note
PVTi Reference Manual
You must also define a Constant Volume Depletion (CVD) experiment via the EXP
keyword and associated data in order that the XMFVP and YMFVP tables can be
generated.
Only two pressures need be defined in the CVD, which should be the maximum and
minimum required.
Keywords
X/YMFVP
289
Specify critical Z-factors
ZCRIT
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the critical Z -factors for the components in the system. The keyword is followed by
N c values, where N c is the number of components specified in the RUNSPEC section, and
terminated with a / character.
ZCRIT values may be entered as an alternative to VCRIT values, but one of VCRIT or ZCRIT
should be entered. If ZCRIT values are entered, critical volumes are obtained internally using
the usual relationship:
RT crit Z crit
V crit = ----------------------- ,
p crit
[EQ 7.3]
where R is the gas constant.
Example
For a CO2/Methane/Ethane/I-C4 system:
ZCRIT
0.2709
290
Keywords
ZCRIT
0.2809
0.2808
0.279
/
PVTi Reference Manual
ZCRITVIS
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specify critical Z-factors for LBC
calculations
Specifies the critical Z -factors for the components in the system to be used in the LBC viscosity
correlation only. The keyword is followed by N c values, where Nc is the number of components
specified in the RUNSPEC section, and terminated with a forward slash (/) character.
ZCRITVIS values may be entered as an alternative to VCRITVIS values, but one of
VCRITVIS or ZCRITVIS should be entered. If ZCRITVIS values are entered, critical
volumes are obtained internally using the usual relationship:
RT crit Z critv
V critv = ------------------------- ,
p crit
[EQ 7.4]
where R is the gas constant.
If VCRITVIS or ZCRITVIS is not entered then the values entered with VCRIT or ZCRIT are
used. The form of ZCRITVIS is the same as that of ZCRIT.
Example
For a CO2/Methane/Ethane/I-C4 system:
ZCRIT
0.2709
PVTi Reference Manual
0.2809
0.2808
0.279
/
Keywords
ZCRITVIS
291
Specify sample composition
ZI
RUNSPEC
X SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
OUTECL3
VFP
Specifies the mole fractions for the components in the system. The keyword is followed by N c
values, and terminated with a forward slash (/) character, where Nc is the number of components
specified in the RUNSPEC section.
Example
For a two-component CO2/I-C4 system, 60/40 mixture:
ZI
0.6
292
Keywords
ZI
0.4 /
PVTi Reference Manual
ZMFVD
RUNSPEC
SYSTEM
SPLIT
GROUP
COMB
SIMULATE
REGRESS
BLACKOIL
PSEUCOMP
X OUTECL3
VFP
Composition versus depth table
Requests that a ZMFVD table for ECLIPSE Compositional input, consisting of the composition
of each component at a set of depths, be output to the PVO file. The ZMFVD keyword takes no
arguments.
Note
PVTi Reference Manual
You must also define a COMPG experiment using the EXP keyword and associated data
in order that the ZMFVD table can be generated.
Only two depths need be defined in the experiment, which should be the maximum and
minimum required.
Keywords
ZMFVD
293
294
Keywords
ZMFVD
PVTi Reference Manual
Technical Description
Chapter 8
Overview
This section of the manual contains information on the following:
•
"Theoretical background of PVT" on page 296.
•
"Analysis techniques" on page 371.
•
"Regression in PVT analysis" on page 386
•
"Wax and asphaltene precipitation in PVTi" on page 394
•
"Cleaning samples contaminated with oil-based mud" on page 398
•
"Mixing and recombination of samples" on page 400
PVTi Reference Manual
Technical Description
Overview
295
Theoretical background of PVT
Introduction
This section of the manual contains information on the following:
•
"General background" on page 296.
•
"Properties of pure components and mixtures" on page 297.
•
"Characterization, splitting and grouping" on page 301.
•
"Material balance" on page 317.
•
"Flash calculations" on page 317.
•
"Equation of state formulation" on page 318.
•
"Multiphase flash" on page 324.
•
"Viscosity correlations" on page 330.
•
"Binary interaction coefficients" on page 337.
•
"Blackoil systems" on page 339.
•
"Gas condensate systems" on page 341.
•
"Process simulation" on page 343.
•
"Gas injection processes" on page 344.
•
"Variation of composition with depth" on page 346.
•
"Practical considerations" on page 348.
•
"Theoretical model" on page 351.
•
"Blackoil model" on page 354.
•
"Pseudo-compositional tables for ECLIPSE GI option" on page 360.
•
"Compositional data for ECLIPSE Compositional" on page 361.
•
"Water properties" on page 362.
•
"Model for API Tracking option in ECLIPSE BlackOil" on page 363.
•
"Compositional Data for ECLIPSE Thermal" on page 366.
General background
Both in the fully compositional and extended black oil formulations of reservoir simulation, an
accurate description of the hydrocarbon system and its properties is important.
In the compositional case the phase behavior of the hydrocarbon system is an integral part of
the simulation. Equal phase fugacity conditions or flash calculations are used to determine the
phase split and composition.
In the black-oil and extended black-oil formulations averaged properties of the oil and gas
phases such as Bo (oil volume factor), Rs (solution gas-oil ratio), B g (gas volume factor) and R v
(condensate gas ratio) are obtained through laboratory experiments or by using an equation of
state description of the hydrocarbon system.
296
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Laboratory tests
Information on oil and gas properties is normally obtained through laboratory tests upon oil and
gas samples. These yield:
1
The mole fraction distribution of lighter components
2
The mole fraction, molecular weight and specific gravity of the residual
3
Pressure-volume relationships obtained through depletion and expansion experiments.
The mole distribution of the lighter components is usually obtained through gas
chromatography, providing a quantitative separation of the lighter components into pure
compounds with known properties. The heavier components are then lumped into pseudocomponents, for example a C7+ fraction containing hydrocarbons with carbon numbers from
seven upwards.
Beside this simple laboratory analysis more complex methods for analyzing oil and gas samples
are coming into use. In these methods the residual (C7+ fraction) is split up into sub-fractions
through a distillation of the residual. The boiling point of each of these sub-fractions is then used
to assign pseudo component properties through empirical correlations.
Expansion experiments are often carried out on oil and gas samples from the reservoir to
evaluate volume factors in conditions that reflect the depletion process in the reservoir as
closely as possible.
On the basis of these experimental data, a model composition of the hydrocarbon mixture can
be developed and used in combination with an equation of state model to calculate additional
oil and gas properties at reservoir conditions and at surface conditions.
The oil and gas volume factors used in black oil type models depend on the process facilities
and configuration. The equation of state model allows black oil tables to be evaluated for
various process facilities and configurations.
An excellent summary of many of the features required to build up an understanding of fluid
phase behavior from sampling considerations through laboratory techniques to the use of
Equations of State can be found in the text of Pedersen et al.[Ref. 30], and McCain, [Ref. 33].
Properties of pure components and mixtures
All petroleum accumulations have hydrocarbons as their predominant constituents. The
chemistry of the carbon atom is the richest of all the known elements making it difficult to
assign simple rules to the volumetric behavior of petroleum mixtures. In order to understand the
behavior of mixtures, let us firstly consider the pure components making up a typical petroleum.
This section contains information on:
•
"Pure components" on page 297.
•
"Pure component properties" on page 300.
•
"Multi-component mixtures" on page 300.
Pure components
The natural gas and crude oil found in underground natural deposits are mixtures of a large
number of different hydrocarbon components and some additional non-hydrocarbons such as
CO2 , H 2 S , N 2 , H 2 and CO .
PVTi Reference Manual
Technical Description
Theoretical background of PVT
297
Hydrocarbon groups
Hydrocarbons are usually divided into groups based on characteristics in molecular structure.
The most important of these groups are:
Alkanes or paraffins
Alkanes or paraffins are very stable chemical compounds. The chemical formula for compounds
in the group is C n H 2n + 2 . The group contains hydrocarbon components such as:
Table 8.1
Alkanes
Formula
Name
C1 H4
Methane
C2 H6
Ethane
C3 H8
Propane
C 4 H 10
Butane
C 5 H 12
Pentane
C 6 H 14
Hexane
C 7 H 16
Heptane
C 10 H 22
Decane
Each of these molecules can exist as a single straight chain of carbon atoms attached to three
(end carbons), or two (non-end carbons) hydrogen atoms (except Methane, which has four
attached hydrogens).
Isomers
For molecules containing four carbons or more, additional structures other than the straight
chains are possible. The number of these branched molecules or isomers increases with
increasing carbon number.
•
Butane has one isomer in addition to the straight-chained normal-Butane, the branched
molecule iso-Butane.
•
Pentane has two isomers in addition to the normal-Pentane, known as iso- and neo-Pentane.
The neo- isomer (cross-shaped) is rarely found in naturally-occurring petroleum. Most
fluid analyses include the iso- and normal- components of Butane and Pentane.
•
Hexane (six carbon atoms) has four isomers in addition to the normal-Hexane.
Note
298
The number of isomers increases rapidly with carbon number making the
identification of the increasingly small concentration of these isomers impossible.
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Napthenes or cycloparaffins
Napthenes are characterized by the chemical formula C n H2n . Important members in this family
are:
Table 8.2
Napthenes
Formula
Name
C3 H6
Cyclopropane
C 5 H 10
Cyclopentane
They share the same formula as the alkenes, which are the same as the alkanes except that one
or more pairs of carbon atoms are linked by double bonds with the consequent loss of one or
more hydrogen atoms.
Note
Alkenes and their triple bond equivalents, the alkynes, are rarely found in naturally
occurring petroleum.
Any one of the hydrogens can be replaced by a methyl-( CH3 ) or higher group, for example
C 7 H 14 , Methylcyclohexane.
Aromatics
The third family of hydrocarbons are aromatics. These are ring-type structures. Some of the best
known members of this family are:
Table 8.3
Aromatics
Formula
Name
C6 H6
Benzene
C7 H8
Toluene
SCN groups
All of napthenes, aromatics, more complicated hydrocarbons (polynuclear molecules),
hydrocarbons compounds containing other species, namely Nitrogen, Sulphur, Oxygen and
certain trace metals, are all capable of existing as isomers. Identification of even a relatively
small number of the possible isomers within a petroleum mixture is a complicated and therefore
expensive task.
It is standard practice within the petroleum industry to lump all isomers together on the basis of
the boiling point of the molecule.
Single Carbon Number (SCN) groups are defined for components, for example hexanes,
heptanes, etc. Components are pure hydrocarbon components with normal boiling point
temperatures, that is at one atmosphere pressure, between consecutive normal-paraffin boiling
points.
For example, the SCN hexanes group consists of those hydrocarbons that boil between the
normal boiling points of n-pentane and n-hexane.
PVTi Reference Manual
Technical Description
Theoretical background of PVT
299
Pure component properties
Each of the pure components, which is now taken to include SCN groups for hexane and above,
in a hydrocarbon mixture is characterized by specific physical properties such as:
Table 8.4
Physical properties
Term
Nomenclature
Tc
Critical temperature
pc
Critical pressure
Vc
Critical volume
Zc
Critical Z -factor
Mw
Molecular weight
ω
Acentric factor
Tb
Normal boiling point
ρ ref
Reference density (usually specified at a reference temperature)
T ref
Reference temperature
[P]
Parachor (see surface tensions)
The component library in PVTi contains properties for some of the more common pure
components.
Multi-component mixtures
As mentioned previously, natural gas and crude oil contains literally thousands of different
components. No attempt is usually made to identify all the hydrocarbons beyond C 5 : rather,
SCN groups denoted hexanes, heptanes, etc., are used. Even so, you may be left with ten or more
components in any given petroleum mixture.
To describe a multi-component system thermodynamically using an equation of state model, the
system must be defined in terms of the properties of the components and their mole fractions in
the mixture.
The terms and nomenclature used to characterize multi-component mixtures may be
summarized as follows, where the subscript i denotes the i th component:
Table 8.5
300
Multi-component (ii) mixtures
Term
Nomenclature
n
Number of components in the mixture
T c, i
Critical temperature
p c, i
Critical pressure
M w, i
Molecular weight
ωi
Acentric factor
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Table 8.5
Multi-component (ii) mixtures (Continued)
Term
Nomenclature
xi
Mole fraction in the liquid phase
yi
Mole fraction in the vapor phase
zi
Mole fraction in the mixture as a whole
p
Pressure of the mixture
T
Temperature of the mixture
V
Mole fraction of the vapor phase
L
Mole fraction of the liquid phase
Note
Not all of the parameters listed above are independent.
The thermodynamic behavior of a multi-component mixture depends strongly on composition,
pressure and temperature.
Phase diagrams
In terms of a phase diagram plotted against pressure and temperature, the upper part of the phase
envelope, up to the critical point, represents the bubble-point curve.
From the critical point the phase envelope continues as dew point curve. The phase envelope
encircles the two phase region in the phase diagram.
A phase diagram is often characterized by the maximum pressure, the cricondenbar, and the
maximum temperature, cricondentherm.
The area within the phase envelope bounded by a vertical line through the critical point and the
line represented by the cricondentherm is the retrograde area. A reduction of pressure into this
area results in retrograde condensation.
For the RK and ZJ equations of state the critical point calculation implements the theory
developed in [Ref. 50].
For the PR and SRK equations of state the calculations use the theory developed in the followup paper in [Ref. 47].
Characterization, splitting and grouping
This section of the manual contains information on:
•
"Components" on page 301.
•
"Characterization" on page 302.
•
"Splitting" on page 303.
Components
All components in PVTi are labeled as being one of three possible types:
•
PVTi Reference Manual
LIB: Library
Technical Description
Theoretical background of PVT
301
•
CHAR: Characterization
•
USER: User defined
LIB components
Lib components are the commonly occurring hydrocarbons C 1 , C 2 ,..., C 45 and the specific nonhydrocarbons H2 O , H2 S , CO2 , N 2 , H 2 and CO .
CHAR components
Components designated as CHAR are typically the last component in a PVT report and as such
comprise the plus fraction, that is, contains all remaining hydrocarbons. For such fractions, a
laboratory would typically measure only the mole weight and specific gravity, denoted here by
M N+ , γ N+ , where N is the number of the first carbon group in the fraction.
User components
User components are those for which you must supply all the data necessary to define the
equation of state parameters, that is T c , pc , Vc , M w and ω .
Characterization
Clearly, correlations are required that are capable of generating the critical properties and
acentric factors from just the mole weight and specific gravity.
In general, any p - V - T report gives at least the mole weight of the plus fraction. If this is the
only information available, PVTi estimates a value of the specific gravity from known (SCN)
distributions. Otherwise, any two out of the four of M w , γ , T b , K w is sufficient to characterize
a component.
PVTi employs five sets of correlations for generating critical properties by:
•
Kesler and Lee [Ref. 10]
•
Cavett [Ref. 11]
•
Riazi and Daubert [Ref. 12]
•
Winn [Ref. 42] and [Ref. 43]
•
Pedersen [Ref. 41].
It also uses four sets of correlations for acentric factors by:
•
Lee and Kesler [Ref. 13]
•
Edmister [Ref. 14]
•
Thomassen [Ref. 30]
•
Pedersen [Ref. 41].
Watson characterization factor
In many of these correlations, a quantity often quoted is the Watson characterization factor,
denoted K w which is defined as:
T bi = ( K w γ i )
3
[EQ 8.1]
where:
•
302
T bi
is the normal boiling point temperature (in degrees Rankine)
Technical Description
Theoretical background of PVT
PVTi Reference Manual
•
γi
is the specific gravity of the i th component.
Splitting
The plus fraction often has an importance that appears to far outweigh its relatively small mole
fraction of a fluid sample. In particular, saturation pressure calculations can be extremely
sensitive to the mole fraction and properties of the plus fraction. More accurate predictions
requiring less regression of equation of state parameters can be achieved if a thorough
description of the plus fraction can be made.
Ideally, a complete true-boiling-point distillation (TBP) should be made that yields not only the
detailed composition of the plus fraction but also the boiling points, specific gravities and
molecular weights of the constituent components. However, this analysis is rarely performed
and so a general procedure to describe the distribution of components and properties within a
plus fraction is required.
Three techniques are available within PVTi for the splitting of the plus fraction into subfractions:
•
Constant Mole Fraction (CMF);
•
Whitson.
•
Semi-Continuous Thermodynamics (Modified Whitson)
All of these techniques rely on a probability density function (PDF) to relate mole fraction to
mole weight. This approach is due to Whitson [Ref. 4].
Probability density model
The PDF used by Whitson to describe the relation between mole fraction and mole weight is a
three-parameter gamma function:
(M – η)
(α – 1)
(M – η)
exp ------------------β
------------------------------------------------------------------p(M) =
α
β Γ(α)
[EQ 8.2]
where:
•
α, β, η
are parameters defining the distribution
•
Γ
is the gamma-function
•
α
gives a measure of the shape of the distribution
•
η
is the lowest mole weight in the plus fraction
•
β
is a normalization condition that can be determined from the condition:
[EQ 8.3]
M N + – η = αβ
where M N + is the average mole weight of the plus fraction.
The cumulative probability function, P ( X ≤ x ) is the integral of p ( x ) from η to x :
P(X ≤ x) =
x
η p ( x ) d x
[EQ 8.4]
that is evaluated numerically from:
∞
P(X ≤ x) = e
–y

α+j
y
-----------------------------Γ(α + j + 1)
[EQ 8.5]
j=0
PVTi Reference Manual
Technical Description
Theoretical background of PVT
303
where y = ( x – η ) ⁄ β
The frequency, f i of a component i having mole weight boundaries M i – 1 , M i is given by the
integral:
fi =
Mi
M
p ( M ) dM
[EQ 8.6]
i–1
= P ( M ≤ M i ) – P ( M ≤ Mi – 1 )
[EQ 8.7]
and the mole fraction z i is related to its frequency by:
zi = zN + fi
[EQ 8.8]
The average mole weight in the same interval is given by:
P ( M ≤ M i ,α + 1 ) – P ( M ≤ M i – 1 ,α + 1 )
M i = η + αβ -----------------------------------------------------------------------------------------------P ( M ≤ M i ,α ) – P ( M ≤ M i – 1 ,α )
[EQ 8.9]
where the P ( X ≤ x ) functions all use the same value of β regardless of the value of α , (that is α
or α + 1 ) and where z N + is the total mole fraction of the plus fraction.
In the absence of any other data, you should assume that α is unity. The parameter η is the
minimum mole weight that occurs in the plus fraction, therefore if the plus fraction were C 7+ ,
then a good estimate to η is 92.0.
Generally, Whitson recommends:
η = 14n – 6
[EQ 8.10]
where n is the first SCN group in the plus fraction, for example 7.
Note
Both splitting techniques available in PVTi use the Whitson PDF to define the mole
fraction/mole weight distribution of the plus fraction, however, they differ slightly in
the way they sub-divide into the required number of pseudo-components.
Constant mole fraction, CMF
In this technique, you select the number of pseudo-components required from the split. From
this PVTi calculates the mole fraction to be assigned to each of the pseudo-components, scaled
to unity.
Note
By default equal mole fractions are assigned.
Generally, you may consider skewing the distribution thus: highest mole fraction for the lightest
pseudo-component to smallest mole fraction for the heaviest pseudo-component.
Hint
If you have evidence on the shape of the plus fraction distribution, it may be prudent
to manually change the skewness parameter α , that is less than unity for a condensate
and greater than unity for a crude oil.
The value of the minimum mole weight in the plus fraction η rarely needs changing from its
(calculated) default value.
304
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Knowing the required mole fraction split, PVTi then integrates the PDF from η up to some mole
weight M 1 such that integral gives the correct first mole fraction, and then similarly for the
remaining pseudo-components.
Knowing the mole weight boundaries, the program can calculate the average mole weights of
the pseudo-components, estimate the specific gravities from the SCN distributions and calculate
the critical properties, etc., from the various correlations currently in force.
Whitson
The Whitson technique consists of splitting the plus fraction into SCN groups N (the first in the
plus fraction) to some high number, for example 45.
The mole weight boundaries are estimated from the user specified plus fraction mole weight and
specific gravity from which one can calculate a plus fraction Watson factor:
0.15178 – 0.84573
[EQ 8.11]
K w, N+ = 4.5579M w, N+ γ N+
Assuming that an average Watson factor K w, N+ can be applied to each individual SCN groups,
the SCN groups’ specific gravities can be estimated from equation (1), namely:
1⁄3
T b, i
γ i = --------------K w, N+
[EQ 8.12]
where the T b, i are the normal boiling point temperatures of the SCN groups, which in fact define
the SCN groups. That is SCN C 6 is all hydrocarbons that have normal boiling point
temperatures between those of normal- C 5 and normal- C 6 , etc.
Then, with known boiling points and specific gravities, mole weights can be estimated using the
Riazi-Daubert correlation, which is of the general form:
b c
[EQ 8.13]
θ = aT b γ
where θ is the property to be evaluated, say M w and ( a ,b ,c ) are tabulated coefficients, see [Ref.
4].
With average mole weights for the SCN groups, the boundary mole weights are estimated from:
1
M i = --- ( M i – 1 + M i )
2
[EQ 8.14]
These can then be used to integrate the PDF to give mole fractions for each of the SCN groups.
Hint
Generally, you will not want to work with 20-30 additional components. Therefore the
SCN groups are pseudoised down into Multi-Carbon Number (MCN) groups. A
method for estimating the required number of MCN groups is that due to Sturge’s,
discussed in [Ref. 4]. However, this often predicts the use of four or five pseudocomponents. It has been our experience that two or three pseudo-components is
sufficient for most purposes.
Multi-carbon number (MCN) groups
In evaluating the properties of the MCN groups from the basis SCN groups, simple mole
weighted averages are taken, that is.:
i = lN
1
M l = --zl
PVTi Reference Manual
 zi Mi
[EQ 8.15]
i = l1
Technical Description
Theoretical background of PVT
305
where the summation is performed over the SCN groups i in the MCN group l and z l is the
mole fraction of the l th MCN group.
Modified Whitson splitting (1988)
The Constant Mole Fraction (CMF) and Whitson Splitting methods described above both
consist of a continuous molar distribution model, which is subsequently discretized into a set of
pseudo-components.
Another method to effect the discretization is to use quadrature methods; in particular, integrals
of the form:
∞
0
N
 wi f ( xi ) ,
–x
f ( x )e dx =
[EQ 8.16]
i=1
where the weighting factors w i and quadrature points x i are determined from a class of Laguerre
polynomials for a given order N , see [Ref. 31].
For our mole weight/mole composition model, we can associate the quadrature points xi with
pseudo-component mole weights M i = η + βx i and the mole fractions z i = w i f ( xi ) .
To account for compositional variations with depth, Whitson extended the standard model to
account for these variations, or plus fraction mole weight and skewness parameter. Since
different plus fraction mole weights and skewness parameters lead to different β parameters,
the following modification was introduced:
β0
β = --------------------------[ 1 + ln ( δ ) ]
[EQ 8.17]
where β 0 and δ are parameters in the modified distribution function p0 ( M ) given by:
(α – 1)
α
– ( M – η ) ( 1 + ln ( δ ) )
(M – η)
- = p(M)
p 0 ( M ) = -------------------------------exp ---------------------- ----------------------------α
[ ( M – η ) ⁄ β0 ]
β0
β0 Γ ( α )
δ
[EQ 8.18]
that is numerically identical to the original function p ( M ) , see[EQ 8.2].
To determine the mole fraction, we integrate the PDF by Gaussian quadrature by making the
following transformation:
M–η
x 0 = -------------β0
[EQ 8.19]
with dM = β0 dx to give:
∞
0
( α – 1 ) –x0
x0
e
--------------------------------------------------dx = 1
x
–α 0
Γ ( α )δ 0 ( 1 + ln ( δ ) )
[EQ 8.20]
Comparing with [EQ 8.16], we have:
(α – 1)
α
( 1 + ln ( δ ) )
x0
f ( x0 ) = ---------------------------------------------x
Γ ( α )δ 0
[EQ 8.21]
and thus the mole fraction and mole weight are given by:
306
z i = w i f ( x 0i )
[EQ 8.22]
M i = η + β 0 x 0i
[EQ 8.23]
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Procedure
The procedure for using this method is particularly attractive.
Firstly we choose the number of pseudo-components required, N , which is normally in the
range 2 ≤ N ≤ 5 : this then fixes the values of weights and points, w i and xi .
The minimum mole weight η is chosen as before.
Next we specify β 0 which is done by selecting the maximum mole weight component to be
used: Whitson recommends M N = 500.0 but we prefer 2 × M N+ . Either way we now have:
MN – η
β 0 = ----------------x 0N
[EQ 8.24]
Next we estimate a value for the skewness parameter, which as before is taken as unity in the
absence of any other information. Then to satisfy the total number of moles and mass, we
calculate:
β0
δ = exp  ----- – 1
β

[EQ 8.25]
and calculate the mole fractions and mole weights. Finally, the average plus fraction mole
weight is checked:
 zi M i
M N+ =
[EQ 8.26]
i------------------=1
N
 zi
i=1
and the δ is adjusted if [EQ 8.26]does not equate to the measured value.
The appeal of this model is it allows a variable plus fractions mole weight and skewness
parameter by sample composition. That is different plus fraction mole weight and mole fraction,
but allows us to use a common set of pseudo-components with fixed mole weights and hence
critical properties.
Hint
Having used this procedure to characterize the plus fraction(s), you can then use the
special regression facility, which allows the sample plus fraction mole weights and
skewness parameters to be variables.
In particular, where there is a known variation of composition with depth and you have
at least two samples from different depths in the hydrocarbon column, this technique
can be used with some success, see [Ref. 32].
Special regression facility
An additional special regression facility has been added to this model to allow different
characterizations of the split pseudo-components from this technique.
Having obtained mole fractions and mole weights from the above method, a variant on the
Watson K factor may be derived, denoted Fc .
This is then used to estimate specific gravities and hence critical properties, acentric factors,
etc., as per the original Whitson model. The additional feature is the new characterization factor,
F c , which can be regressed, that is:
tot
cal
reg
[EQ 8.27]
Fc = Fc × Fc
PVTi Reference Manual
Technical Description
Theoretical background of PVT
307
reg
where Fcal
is
c is the value calculated by the Whitson model, that is assuming SCN-cuts, and F c
the potentially regressable function which defaults to unity. This allows you to make your fluid
more or less aromatic with respect to the standard distribution (equivalent to a K w ∼ 12.0 ), which
in turn yields different critical properties, etc., and hence different fluid behavior.
Grouping
Grouping of components is performed by one of three techniques:
•
Molar averaging
•
Weight averaging
•
Mixing rule.
All of these are explained in the comprehensive text of Joergensen and Stenby [Ref. 44].
Consistency checks and correlations
PVT analysis of reservoir fluids is usually performed so that a model fluid, be it blackoil,
compositional or otherwise, can be constructed for use in a reservoir simulator.
This analysis requires that an equation of state model is used to match measured data from
laboratory experiments.
Any uncertainties in the laboratory data, brought about by inconsistencies in the laboratory
measurements but more likely due to problems encountered in the taking of the fluid samples,
feed through into a poor fluid model.
Consistency tests
Most fluids that show some form of compositional behavior, namely gas condensates and
volatile oils, are subject to a constant volume depletion experiment (CVD) as part of their
analysis. For further information see "Compositional material balance" on page 308.
A material balance calculation can be performed using the data that is generated from such an
experiment from which quantities such as liquid compositions, K -values, molecular weights
and densities of vapor and liquid, etc., can be evaluated. This data can then be examined to look
for any inconsistencies, such as lack of monotonicity.
Additional data often given in a laboratory PVT report are separator compositions for the liquid
and vapor streams. If such data is available, then K -values can be constructed and plotted
against theoretical fits, again as a test of consistency.
Finally, estimates of recovery of gas and oil from the reservoir can be made as well as generation
of blackoil tables, without recourse to the use of the equation of state model.
Compositional material balance
Several authors have published models for testing the consistency of laboratory CVD data, [Ref.
19] and [Ref. 6].
This section of the manual contains information on:
308
•
"Consistency checks and correlations" on page 308.
•
"Liquid compositions and K-values" on page 310.
•
"Physical properties" on page 312.
Technical Description
Theoretical background of PVT
PVTi Reference Manual
•
"Correlations" on page 312.
•
"Recombination of separator data" on page 315.
•
"Recovery calculations" on page 316.
Note
The model employed in PVTi was adapted from a program developed by Pearce [Ref.
20].
A typical laboratory CVD report might be as follows [Ref. 6]:
Table 8.6
CVD Report
Equilibrium vapor Pressures (psi)
Equil
Liquid
Component
714.7
6764.7 5514.7 4314.7 3114.7 2114.7 1214.7 714.7
Carbon Dioxide
2.37
2.40
2.45
2.50
2.53
2.57
2.60
.59
Nitrogen
0.31
0.32
0.33
0.34
0.34
0.34
0.33
.01
Methane
73.19
75.56
77.89
79.33
79.62
78.9
77.8
12.42
Ethane
7.80
7.83
7.87
7.92
8.04
8.40
8.70
3.36
Propane
3.55
3.47
3.40
3.41
3.53
3.74
3.91
2.92
isoButane
.71
.67
.65
.64
.66
.72
.78
.91
n-Butane
1.45
1.37
1.31
1.30
1.33
1.44
1.56
2.09
isoPentane
.64
.59
.55
.53
.54
.59
.64
1.4
n-Pentane
.68
.62
.58
.56
.57
.61
.66
1.6
Hexanes
1.09
.97
.88
.83
.82
.85
.9
3.68
Heptanes plus
8.21
6.2
4.09
2.64
2.02
1.84
2.12
71.01
Total
100.00
100.00
100.00
100.00
100.00
100.00
100.00
100.00
Mw(C7+)
184.0
160.0
142.0
127.0
119.0
115.0
114.0
213.0
Sg(C7+)
.816
.799
.783
.770
.762
.758
.757
.833
Zvap
1.238
1.089
.972
.913
.914
.937
.960
Nprod
0.000
9.024
21.744
38.674
55.686
72.146
81.301
Sliq
0.00
14.1
19.70
21.60
21.30
20.20
19.3
This gas condensate with an assumed reservoir composition equal to composition at the first
pressure, which corresponds to the saturation pressure of the fluid, psat = 6764.7 psia is put
through the stages of the CVD.
The CVD consists of reducing the pressure to the required stage pressure, and then removing
gas so that the volume remaining in the cell is equal to volume at the saturation pressure.
At each stage, the composition, mole weight and specific gravity of the plus fraction (denoted
Mw and Sg), the vapor Z -factor (denoted Zvap), the number of moles produced (denoted
Nprod) and the liquid saturation (denoted Sliq), are measured.
The subsequent analyses used to generate liquid compositions, K -values, volumes, masses and
densities follow those of Whitson and Torp [Ref. 6].
PVTi Reference Manual
Technical Description
Theoretical background of PVT
309
Liquid compositions and K-values
Cell compositions
A material balance performed on the total moles and individual components is:
n tj = n lj + n vj
[EQ 8.28]
n tj z ij = n lj x ij + n vj y ij
[EQ 8.29]
where:
•
n tj , n lj , n vj
are the total, liquid and vapor moles at stage j
•
( p = p j ) and z ij , x ij , yij are the total, liquid and vapor mole fractions of component i .
Starting with one mole of fluid at the saturation pressure (first stage in the reported CVD), the
number of moles remaining the cell after the j th stage is:
j
n tj = 1 –
 Δnpk
[EQ 8.30]
k=2
where n pk is the number of moles of gas produced at stage, denoted Nprod in the table above,
so that Δn pk is the incremental gas recovered during the kth stage, that is, reducing the pressure
from p k – 1 to p k .
Similarly, the mole fraction of the i th component remaining in the cell after the j th stage is:
j
n tj z ij = z i1 –
 Δnpk yik
[EQ 8.31]
k=2
Cell volumes
To convert moles and mole fractions to volumes, one must have some reference volume, such
as the volume of the cell.
For a gas condensate, the cell volume, for one mole, can be calculated from the real gas law:
Z 1 RT
V cell = ------------p1
[EQ 8.32]
where:
•
Z1
and p1 are the vapor Z -factor and pressure at the first (saturation) pressure
•
R
•
T is the temperature at which the CVD is performed, assumed constant throughout the
experiment.
is the universal gas constant
For a volatile oil, a CVD report gives the molecular weight and density of the bubble point
liquid, M w1 and ρ 1 , and thus the cell volume, again for one mole, is calculated as:
M w1
V cell = ---------ρ1
[EQ 8.33]
Knowing the cell volume and the liquid saturation at the j th stage, S lj (denoted Sliq in the table
above), the volume of the cell occupied by liquid is:
V lj = S lj V cell
310
Technical Description
Theoretical background of PVT
[EQ 8.34]
PVTi Reference Manual
and thus the volume of the cell occupied by gas is:
[EQ 8.35]
V vj = ( 1 – S lj )V cell
Moles and mole fractions
The number of moles of vapor remaining in the cell at the j th stage can be determined from the
real gas law:
p j V vj
n vj = -----------Z j RT
[EQ 8.36]
Thus, the composition of the liquid remaining in the cell at the j th stage can be determined from:
n tj z ij – n vj y ij
x ij = ------------------------------n tj – n vj
[EQ 8.37]
Equilibrium K-values
The K -values can now be estimated from the ratio of the vapor and liquid mole fractions:
y ij
K ij = ----x ij
[EQ 8.38]
The best test of the consistency of the CVD data is to plot the logarithm of the p j K ij product
against the characterization factor F , [Ref. 20], where:
1 1
F = b i  ------- – ---
 T bi T
[EQ 8.39]
where T is the reservoir or CVD experiment temperature and bi is the Hoffmann-Crump-Hocott
b -factor
for the i th component, which is given by:
( log ( p ci ) – log ( p ref ) )
b i = ---------------------------------------------------1
1
 ------ – -------
 T bi T ci
[EQ 8.40]
Here:
•
T ci
and T bi are the critical and normal boiling point temperatures
•
p ci
is the critical pressure (in psia)
•
p ref
is the reference pressure, usually 14.7 psia.
Plots
As pointed out by Bashbush, [Ref. 19], the curves should plot in a parallel-like trend, that is,
there should be no humps in any individual curve or crossing of any pair or pairs of curves.
The highest curve should belong to nitrogen, followed by methane and carbon dioxide.
Then depending on the fluid composition, either ethane or hydrogen sulphide should be plotted
followed by the curves for the remaining hydrocarbon components in order of increasing
molecular weight.
Finally, it should be noted that the iso- components of butane and pentane should plot above
their corresponding normal components. This plot is available from PVTi.
PVTi Reference Manual
Technical Description
Theoretical background of PVT
311
Other useful plots consists of fingerprint plots of the liquid composition remaining in the cell at
the end of the CVD (the last column in the above table) and the equivalent calculated liquid
composition, and the calculated liquid compositions as a function of pressure. Both of these
plots are available from PVTi.
Physical properties
As well as performing material balances on moles and mole fractions, material balance can be
done on the total, liquid and vapor masses:
m tj = m lj + m vj
[EQ 8.41]
The total mass remaining the cell at the j th stage is given by:
j
m tj = M s –
 Δnpk Mvk
[EQ 8.42]
k=2
where M s and M vk are the initial or saturation pressure molecular weight and the vapor
molecular weight at the kth stage, respectively, both of which can be evaluated from Kay’s rule:
Nc
M vj =
 yij Mi
[EQ 8.43]
i=1
where M i is the molecular weight of the i th component.
Vapor molecular weight is calculated from:
m vj = n vj M vj
[EQ 8.44]
And liquid molecular weight from the mass balance:
m lj = m tj – m vj
[EQ 8.45]
Now, knowing the masses and volumes of liquid and vapor in the cell at each stage, one can
calculate densities from ρ = m ⁄ V
Plots of these quantities are available from PVTi.
Correlations
Alani-Kennedy liquid densities
The liquid molar volume of a pure hydrocarbon component is given by the smallest real positive
root of the Van der Waal’s equation:
a
RT =  p + -----2- ( V – b )


V
[EQ 8.46]
that contains the two unknown parameters ( a ,b ) .
Alani and Kennedy, [Ref. 20], inserted known values of T , p and V into [Ref. 16] for two
pressures for a variety of hydrocarbons. Thus they were able to observe the variations of ( a ,b )
from which they derived:
a = K exp ( n ⁄ T )
[EQ 8.47]
b = mT + C
[EQ 8.48]
where:
312
Technical Description
Theoretical background of PVT
PVTi Reference Manual
•
( n ,K ,m ,C )
are tabulated constants for the hydrocarbons
•
C 1 , C 2 ,..., C 6 :
•
C 7+ can be calculated from given correlations in molecular weight and specific gravity of
the plus fraction and temperature (see [Ref. 22]).
the coefficients for the plus fraction
The ( a ,b ) coefficients for a hydrocarbon mixture are given by Kay’s rule:
C N+
a mix =
C N+
 xi ai
b mix =
C1
 xi bi
[EQ 8.49]
C1
where xi are the liquid mole fractions.
Note
The non-hydrocarbons N 2 , CO2 and H 2 S are added into the C 1 fraction.
Vapor Z-factor
The vapor Z -factor, Z vap , can be estimated from the correlation due to Dranchuk, Purvis and
Robinson [Ref. 21]:
0.27p r
Z vap = --------------ρr Tr
[EQ 8.50]
where T r and p r are the reduced temperature ( = T ⁄ T c ) and reduced pressure ( = p ⁄ pc ) , and ρ r
is the pseudoreduced density, which is found by iteratively solving:
[EQ 8.51]
f ( ρr ) = 0
where:
6
3
2
3
2
2
f ( ρ r ) = Aρ r + Bρ r + Cρ r + Dρ r + Eρ r ( 1 + Fρ r ) exp ( – F ρ r ) – G
[EQ 8.52]
and:
A = 0.06423
[EQ 8.53]
B = 0.5353T r – 0.6123
[EQ 8.54]
0.5783C = 0.3151T r – 1.0467 – --------------2
Tr
[EQ 8.55]
D = Tr
[EQ 8.56]
0.6816
E = --------------2
Tr
[EQ 8.57]
F = 0.6845
[EQ 8.58]
G = 0.27T r
[EQ 8.59]
with the initial estimate for the pseudoreduced density of:
0.27p r
ρ r0 = --------------Tr
[EQ 8.60]
Pseudo-critical temperatures and pressures
Pseudo-critical temperatures and pressures for a fluid mixture can be calculated from one of two
methods:
PVTi Reference Manual
Technical Description
Theoretical background of PVT
313
•
Kay’s rule
•
Wichert and Aziz Correlation.
Kay’s rule has been stated already, being a mole fraction weighted sum of the appropriate
quantity.
The correlations due to Wichert and Aziz, [Ref. 22], correct for the presence of the so-called
sour gases, CO2 , H2 S and N 2 .
The pseudo-critical temperature and pressure of the hydrocarbon portion of a condensate is
given by:
HC
HC 2
[EQ 8.61]
HC
HC 2
[EQ 8.62]
HC
= 187 + 330γ g – 71.5 ( γ g )
HC
= 706 + 51.7γ g – 11.1 ( γ g )
Tc
pc
where γ HC
is the hydrocarbon gas gravity that is related to the mixture gas gravity, γ mix
by:
g
g
mix
HC
γg
γ g – 0.9672y N – 1.5195y CO – 1.1765y H S
2
2
2
= -----------------------------------------------------------------------------------------------------------1 – y N – y CO – y H S
2
2
[EQ 8.63]
2
with:
mix
γg

yi Mi
= ------------------M air
[EQ 8.64]
and M air is the molecular weight of air (= 28.97).
The pseudo-critical temperature and pressure for the mixture, including non-hydrocarbons, is:
HC
T pc = ( 1 – y N – y CO – y H S )T c + 227.3y N + 547.6y CO + 672.4y H
2
2
2
2
2
[EQ 8.65]
2S
and
HC
p pc = ( 1 – y N – y CO – y H S )p c + 493.0y N + 1071.0y CO + 1306.0y H
2
2
2
2
2
2S
[EQ 8.66]
The correction to T pc and ppc in the presence of sour gas ( CO2 and H2 S ), due to Wichert and
Aziz, is:
ε = 120 [ ( y CO + y H S )
2
0.9
2
– ( y CO + y H S )
2
2
1.6
0.5
] + 15 ( y H
2S
4.0
– yH S )
2
[EQ 8.67]
to give:
[EQ 8.68]
T∗ pc = T pc – ε
and
p pc ( T pc – ε )
p∗ pc = ----------------------------------------------------T pc + y H S ( 1 – y H S )ε
2
[EQ 8.69]
2
Gas viscosity
The dynamic gas viscosity of a hydrocarbon gas at a temperature T can be estimated from a
correlation due to Lee, Gonzalez and Eakin, [Ref. 23]:
C
μ g = A exp ( Bρ )
[EQ 8.70]
where:
314
Technical Description
Theoretical background of PVT
PVTi Reference Manual
–4
1.5
10 ( 9.4 + 0.02M w )T
A = ---------------------------------------------------------( 209.0 + 19.0M w + T )
[EQ 8.71]
986.0
B = 3.5 + ------------- + 0.01M w
T
[EQ 8.72]
C = 2.4 – 0.2B
[EQ 8.73]
and:
pM w
ρ = ----------ZRT
[EQ 8.74]
where ρ is measured in g/ cm3 .
Recombination of separator data
In most laboratory PVT reports, the well stream fluid used as the basis for the experiments is
generally a recombined sample of separator gas and oil. The rates of production of the two
phases are also recorded and the ratio of gas rate to oil rate defines the separator gas-oil ratio
(GOR).
Generally, the separator is operating at some pressure and temperature above what would be
considered as standard conditions, such as 60 °F , 14.7 psia, in which case the separator oil is
almost certainly not be stable at standard conditions since it probably still contains dissolved
gas. The best laboratory analyses contain a mole fraction analysis of the separator oil and gas
and the stabilized, standard conditions, oil and gas.
Any available gas and oil compositional analysis can be used to generate a set of K -values.
These K -values can be plotted using the Hoffmann-Crump-Hocott construction, see [Ref. 19]
and"Correlations" on page 312.
An analysis of sets of K -values from many fluid samples by Standing, [Ref. 24], indicated that
for pressures less than 1000 psia, compositional dependency in K -values, usually indicated by
the apparent convergence pressure of the log ( K ) versus log ( p ) plot, is small and can often be
neglected.
Noting this, Standing fitted the following form:
1 ( a + cF )
K = --- 10
p
[EQ 8.75]
with:
–4
–8 2
[EQ 8.76]
a = 1.20 + 4.5 ×10 p + 15.0 ×10 p
–4
–8 2
[EQ 8.77]
c = 0.89 – 1.7 ×10 p – 3.5 ×10 p
where F is the Hoffmann et al. characterization factor, refer to [EQ 8.39].
As most separators are operated at pressures less than 1000 psia, the so-called Standing K values provide a reasonable test of the quality of the calculated separator data and can be used
as an alternative for blackoil table generation etc., when no such actual data is available.
The feed to each stage of the separator can be calculated given the compositions of liquid and
vapor resulting from the separator flash, the GOR and the liquid density. It can be shown that
the phase split β is given by F ⁄ ( 1 + F ) where:
( GP std M )
F = -------------------------( RT std ρ oil )
•
PVTi Reference Manual
[EQ 8.78]
where:
Technical Description
Theoretical background of PVT
315
•
G
is the GOR (gas at STC, oil at stage conditions)
•
M
is the molar weight of oil, that is
 xi Wi
i
•
d ρ oil is the density of the separator oil.
Given β , the feed z i can be found from z i = βyi + ( 1 – β )xi .
Recovery calculations
For reservoirs whose initial pressure, p init , is greater than its saturation pressure, psat , estimates
of fluid recovery can be made if the Z -factors in the range p init ≥ p ≥ psat are known.
Note
Above the saturation pressure, no compositional changes in the fluid take place so for
a unit volume of the fluid at isothermal conditions:
n1 Z1
n2 Z2
----------- = ---------p1
p2
[EQ 8.79]
Starting with 100 moles of fluid at the initial reservoir pressure, the number of moles at some
pressure p j above the saturation pressure is:
left
nj
rem
= 100 – n j
[EQ 8.80]
where:
rem
nj
pj Z1
= 100  ----  -----
 Z j  p 1
[EQ 8.81]
At pressures below the saturation pressure, the produced moles are known from the CVD
experiment.
The fluid at each stage can then be flashed to surface conditions, using separator or Standing’s
K -values to get the volumes of liquid and vapor that could be expected at the surface, assuming
100% efficiency in the separators.
An option exists to produce liquid along with gas, in a ratio defined by input relative
permeabilities, using the technique described in Reudelhuber and Hinds, refer to [Ref. 37].
316
Technical Description
Theoretical background of PVT
PVTi Reference Manual
Equation of state
General information
PVTi allows you to fit data to an Equation of State. See "The fluid model" on page 98 and
"Batch system and keywords" on page 152 for further information on how to define Equations
of State in PVTi.
This section of the manual contains information on:
•
"Material balance" on page 317.
•
"Flash calculations" on page 317.
•
"Equation of state formulation" on page 318.
•
"Surface tensions" on page 321.
•
"Three-parameter equation of state" on page 321.
•
"Binary interaction coefficients" on page 337.
Material balance
We consider a hydrocarbon system consisting of one mole of mixture or feed of composition z i .
In general, this consists of:
•
L
moles of liquid of composition xi
•
V
moles of vapor of composition y i
•
at some pressure and temperature, p and T .
The conditions exist that:
[EQ 8.82]
L+V = 1
 xi =  yi =  zi = 1
[EQ 8.83]
Lxi + Vy i = z i
[EQ 8.84]
i
i
i
Flash calculations
For a thermodynamic system to be in equilibrium it is further required that the fugacities in the
liquid and vapor phases must be equal for each component:
[EQ 8.85]
f iL = f iV
The equations [EQ 8.82] to [EQ 8.85] in the unknowns L , V , x i and yi may be solved to find
the equilibrium state of a system of known composition z i .
The fugacities are functions of temperature, pressure and composition (see "Equation of state
formulation" on page 318),
f i = f i ( T , p, x i)
PVTi Reference Manual
Technical Description
Equation of state
317
The fugacities can be calculated directly from an equation of state. Defining equilibrium
constants K i for each component as:
yi
K i = ---xi
the mole fractions of each component in the liquid and vapor phases are defined as:
zi
x i = ------------------------------------[ 1 + ( K i – 1 )V ]
[EQ 8.86]
and
Ki zi
y i = ------------------------------------[ 1 + ( K i – 1 )V ]
[EQ 8.87]
The flash calculation determining the equilibrium conditions in the two-phase region is
performed in two stages:
Use Michelsen’s stability criterion, [Ref. 16], to establish how many phases are present. The
stationary condition used to determine the Gibb’s energy minimum is obtained using successive
substitution accelerated with the general dominant eigenvalue method, [Ref. 8], switched to
BFGS minimization near the minimum, [Ref. 9].
If two phases are present, solve the phase split calculation to obtain equal fugacity liquid and
vapor states. The solution variables used are Ji = log ( K i ) and the vapor mole fraction. The
stability check provides an initial set of values, which are refined using accelerated successive
substitutions, and finally solved using a full Newton-Raphson method.
In the case of finding a saturation pressure, that is a bubble point for an oil or a dew point for a
condensate, the same N -fugacity equations are used, [EQ 8.85], and a constraint based upon the
difference in the sum of vapor and liquid mole fractions, [EQ 8.83]. Rather than iterating to find
the vapor fraction, V , or liquid fraction L = 1 – V , from [Ref. 1], V is set to 0 (zero - bubble
point) or 1 (one - dew point) and we vary pressure until the set of conditions is satisfied.
Equation of state formulation
The fugacities and Z -factors used in the flash calculations are obtained from the equation of
state.
The four equations of state implemented in PVTi are:
•
(RK) Redlich-Kwong
•
(SRK) Soave-Redlich-Kwong
•
(ZJ) Zudkevitch-Joffe
•
(PR) Peng-Robinson
The equations of state listed above are implemented using the formulation presented by Martin,
[Ref. 2], and Coats, [Ref. 3].
The equation of state for a real fluid is:
PV = nRTZ
[EQ 8.88]
where P is the pressure, V the volume, n the number of moles, R the universal gas constant, T
the temperature and Z is obtained from the solution of the cubic equation:
3
2
Z + E2 Z + E1 Z + E0 = 0
[EQ 8.89]
with
318
Technical Description
Equation of state
PVTi Reference Manual
[EQ 8.90]
E 2 = ( m 1 + m 2 – 1 )B – 1
2
[EQ 8.91]
E 1 = A – ( 2 ( m 1 + m 2 ) – 1 )B – ( m 1 + m 2 )B
and
2
[EQ 8.92]
E 0 = – [ AB + m 1 m 2 B ( B + 1 ) ]
The coefficients m1 and m2 depend upon the equation used:
Table 8.7
Equation of State coefficients
value
Mnemonic
Equation of state
m1
RK
Redlich-Kwong
0
1
SRK
Soave-Redlich-Kwong
0
1
ZJ
Zudkevitch-Joffe
0
1
PR
Peng-Robinson
1+
2
m2
1–
value
2
The cubic equation for the Z -factors may be solved to obtain Z -factors for liquid and vapor
phases. Generally three solutions are obtained. The distinction between the liquid and vapor
phase is then made by choosing the smallest root as the Z -factor for the liquid phase and the
largest root as the Z -factor for the vapor phase.
Fugacity coefficients are calculated using:
fi
( Z + m2 B )
Bi
2S i B i
A
ln  ------- = – ln ( Z – B ) + ---------------------------- ------- – ----- ln ------------------------- + ----- ( Z – 1 )
 px i
( m 1 – m 2 )B A
( Z + m1 B )
B
B
[EQ 8.93]
where
Si =
 Aij xj
n
A =
[EQ 8.94]
n
  ( xj xk Ajk )
[EQ 8.95]
j = 1k = 1
n
B =
 ( xj Bj )
[EQ 8.96]
j=1
A jk = ( 1 – k jk ) ( A j A k )
1--2
[EQ 8.97]
and kjk are binary interaction coefficients, normally between hydrocarbons and nonhydrocarbons.
These four equations, [EQ 8.94] to [EQ 8.97], express the mixing laws used in all the equations
of state.
The variables A j and B j are defined by the following equations:
p rj
A j = Ω A ( T, j ) -----2
T rj
[EQ 8.98]
and
p rj
B j = Ω B ( T, j ) -----T rj
PVTi Reference Manual
[EQ 8.99]
Technical Description
Equation of state
319
and ΩB ( T, j ) used in equations [EQ 8.98] and [EQ 8.99] are functions of the acentric
factor ω and the reduced temperature T rj .
Ω A ( T, j )
For Redlich-Kwong
1
– --2
Ω A ( T, j ) = Ω A T rj
[EQ 8.100]
Ω B ( T, j ) = Ω B
[EQ 8.101]
0
0
For Soave-Redlich-Kwong
Ω A ( T, j ) = Ω A 1 + ( 0.48 + 1.57ω j –
0
Ω B ( T, j ) = Ω B
0
2 
0.17ω j )  1

–
2
--1- 
2
T rj
[EQ 8.102]

.
[EQ 8.103]
For Zudkevitch-Joffe
1
– --2
Ω A ( T, j ) = Ω A F aj ( T )T rj
[EQ 8.104]
Ω B ( T, j ) = Ω B F bj ( T )
[EQ 8.105]
0
0
For Peng-Robinson
1
--- 
2 
2
Ω A ( T, j ) = Ω A 1 + ( 0.37464 + 1.54226ω j – 0.2669ω j )  1 – T rj
0


Ω B ( T, j ) = Ω B
2
[EQ 8.106]
[EQ 8.107]
0
The normal PR form can be optionally modified for large acentric factor, using the factor
2
3
rather than ( 0.37464 + 1.54226ωj – 0.2699ω 2j ) for
ω j > 0.49 . This correction is invoked by use of the PRCORR keyword or interactively from the
Equation of State panel. For further information see "The fluid model" on page 98.
( 0.379642 + 1.48503ω j – 0.164423ω j + 0.016666ω j )
ΩA
0
and Ω B0 are constants depending upon the equation of state:
Table 8.8
Equation
ΩA
RK, SRK, ZJ
0.4274802
0.086640350
PR
0.457235529
0.077796074
Note
320
Equation of State constants
0
ΩB
0
In the program, these default values may be over-written on a component basis either
interactively, or by the use of the OMEGAA and OMEGAB keywords.
Technical Description
Equation of state
PVTi Reference Manual
Zudkevitch-Joffe equation
The Zudkevitch-Joffe equation contains additional temperature factors, denoted F aj ( T ) and
F bj ( T ) , multiplying the usual RK temperature dependence. These are adjusted to match the purecomponent fugacity values along the vapor pressure line, and to observe the correct component
liquid density.
In the program the required variation of component saturation pressure and liquid density with
temperature are obtained using correlations of Reidel, and Gunn and Yamada. These
correlations require the input of the normal boiling point and the reference liquid density at a
specified reference temperature.
Surface tensions
The surface tension between the liquid and vapor phase of a multi-component mixture can be
estimated by the Macleod-Sugden relationship, [Ref. 18]:
1--4
σ mix
Nc
=
 [ Pi ] ( ρm
Liq
Vap
[EQ 8.108]
xi – ρm yi )
i=1
where [ P i ] is the parachor of the i th component, see [Ref. 18], which has a liquid and vapor mole
Vap
fraction of xi and yi respectively, and the liquid and vapor molar densities are ρ Liq
m and ρ m
respectively. If the parachors are assigned values consistent with [Ref. 18] and the molar
volumes are expressed in gmoles/ cm3 then the surface tension σ have units of dynes/cm.
Three-parameter equation of state
The traditional weakness of the so-called two-parameter equation of state, such as the PengRobinson, Redlich-Kwong, etc., above, is their poor prediction of liquid properties, especially
liquid densities and saturations.
Peneloux et al., [Ref. 25], proposed a molar volume correction for the SRK Equation of State,
which is also applicable to any cubic Equation of State. This technique, referred to as volume
translation, adds a third parameter to the Equation of State, which greatly improves liquid
properties estimations.
Note
In PVTi, this correction is available for the Peng-Robinson and the Soave-RedlichKwong Equation of State.
For a mixture of N components, the phase volume, Vmol,p , is given by:
N
EoS
V mol,p = V mol,p –
 zi ci
[EQ 8.109]
i=1
where:
PVTi Reference Manual
EoS
•
V mol,p
is the molar volume of the phase
•
p
•
z i = ( x i ,y i )
•
c ri
= (liquid, vapor) predicted by the traditional (two-parameter) Equation of State
are the liquid and vapor mole compositions
constitute a set of volume corrections.
Technical Description
Equation of state
321
The component corrections are usually related to the set of dimensionless shift parameters, s i ,
by:
c ri
s i = -----bi
[EQ 8.110]
where:
RT ci
b i = Ω b, i ----------- .
p ci
[EQ 8.111]
See [Ref. 25].
Shift parameters
No Temperature Dependence (“None”)
In the simplest case, where the Volume Shift dependence is “None”, the Shift parameters for the
inorganic and light hydrocarbon components are calculated using the temperature-dependent
correlations given by Søreide, [Ref. 34].
The functional form of these polynomials depends on whether the PR or SRK EOS is being used
and on whether the reduced temperature, Tr (= T ⁄ T crit ) is less than or greater than 1. For this
simple case, where there is no temperature dependence on the Volume Shifts a value of Tr=0.7
is used in the equations.
In the case of the PR EOS the equation take the form:
s i = T r – 0.741
1.355
– 0.164 + 0.479ω i + 0.428 exp [ 25.33 ( T r – 1 ) ]
[EQ 8.112]
+ 0.587ω i + 0.369 exp [ 10.369 ( T r – 1 ) ]
[EQ 8.113]
and for the SRK EOS:
s i = T r – 0.904
3.713
where, for each component, s i is the dimensionless Volume Shift, ω i the acentric factor and,
as mentioned above, T r =0.7.
For heavier components ( M w > 90 ) the shifts are estimated on a component by component basis
as the difference in the calculated single component molar volume using the two-parameter
Equation of State at the components reference pressure and temperature (often 60 °F and 14.7
psia), and the reference molar volume (mole weight divided by reference density).
The shift parameters of the heavier components are potential regression variables and are added
to the allowed set if you request either the PR3 or the SRK3 Equation of State. Experience has
shown that simultaneous matches to saturation pressure and density can be achieved more easily
as a result, and therefore the use of these Equations of State in PVTi is recommended.
One obvious deficiency of this model is that the shift coefficients, ci , are only valid at one
temperature. If one attempts to model the change of molar volume of a pure component, such
as Hexane, with temperature using, say, the PR3 Equation of State, and compares that against
the known thermal expansion coefficient, see [Ref. 18], one will find a discrepancy.
In an attempt to overcome this deficiency, two options have been added to PVTi whereby
temperature-dependence is introduced using differing methods which are now outlined.
Linear Expansion Only
In this model, the volume shifts of all the components are modified with a linear thermal
expansion coefficient, κ , using the equation:
322
Technical Description
Equation of state
PVTi Reference Manual
[EQ 8.114]
c i ( T ) = c ri ( T ri, P ri ) [ 1 + κ i κ ( T – T ri ) ]
where cri ( T ri, P ri ) for a particular component is the dimensional volume shift specified in
equation [EQ 8.109]. Physically these cri coefficients correspond to the difference in volume of
1 mole of a particular component at temperature T and pressure P (pressure at standard
conditions - usually 60F), and 1 mole of that component at its reference temperature and
pressure, T ri and P ri .
The κ i coefficients are determined using a formula which is a fitted functional (of mole weights)
of the first ten paraffins from [Ref. 17] and is given by:
[EQ 8.115]
κ i = 0.9 – 0.002MW i, MW i < 200
κ i = 200, MW i ≥ 200
is a special regression function in PVTi, and takes the default value of 0.0005 °C –1 ,
determined from a fit to a crude oil. Physically, it represents a thermal expansion factor, and has
keyword THERMX within PVTi.
κ
Polynomial Correlations
If the temperature dependence of the Volume Shifts is set to Polynomial Correlations then the
equations of Soreide are used which were introduced in the case of Tr<1 in equations [EQ 8.112]
and [EQ 8.113]. When the None option was set we always set Tr=0.7 and so these equations
were fine. However, if a temperature above Tc is supplied to the algorithm with the Polynomial
Correlations option set so that Tr>1, then PVTi chooses from a set of equations depending on
the mole weight of the component. These equations can be found in [Ref. 34].
Note
The Soreide correlations only cover light components up to C 6 .
For heavier components ( M w > 90 ) the thermal expansion scheme outlined in the "Linear
Expansion Only" on page 322 is applied. However, since the scheme is now applied to regions
where the fitted functional κ i is no longer valid, κ i is set to unity, and the thermal expansion
factor, κ , applies directly. For this reason it is often a good choice as a regression variable for
heavy hydrocarbon components if one is finding difficulty matching liquid densities.
The Linear Expansion Only model has some advantages in that since the modification to
volume shifts is linear, the volume shifts may be regressed for all components.
For the Polynomial Correlations model, since the correlations of Søreide are not linear, you
cannot regress the shift parameters of lighter components to which the correlations have been
applied.
Hint
PVTi Reference Manual
However, an inspection of the behavior of volume shifts with temperature, as given in
[Ref. 36], shows that volume shifts generally do not obey a linear relation with
temperature, and for this reason, the second method often gives better results and is the
recommended choice.
Technical Description
Equation of state
323
Note
If the volume shifts are Dependent, then they are calculated so that the calculated
reference density (the density at the reference temperature and standard conditions
pressure) is guaranteed to match the observed value. This means that the volume shifts
are dependent on the critical properties and acentric factor of the component. If the
volume shifts are Independent this guarantee is broken and the volume shifts can be
varied during regression. In this situation they are not affected by changes in the
critical properties or acentric factors.
Multiphase flash
Standard algorithm
The conventional two phase flash calculation starts with a stability test for the feed composition,
based on Michelsen’s (1982) stability criterion, . If unstable, a flash phase split calculation is
performed to determine the two phase compositions. The multiphase flash continues in a stepwise fashion: if any one of the current N phases exhibits instability, an N+1 phase flash split
calculation is performed, the resulting tested for stability. The maximum allowed number of
phases is five, after that is reach no more phases are split off.
Options with the Multiphase flash
The Multiphase flash has three modes:
1
Conventional two phase mode.
2
Three phase mode, one of which is restricted to water.
3
The full multiphase flash mode.
This is the default. In this mode there are now two different ways of performing a
multiphase flash calculation.
a
The standard method. This method is the one that was in use for the 2002A release and
initially assumes a single phase equal to the feed. Stability checks are performed and
subsequent phases are split off if the system is unstable.
b
Instead of the flash starting with the feed an initial guess/guesses can be used assuming
there are 4 phases present, which are initially undetermined.
Stability analysis
The stability of each phase present in a multiphase regime can be tested with the Michelsen
analysis, [Ref. 16], precisely as for the two phase case, using the Gibbs energy tangent plane
distance criterion. However, the initial estimates for phases that will be split off are not limited
to the vapor/liquid equilibrium phases characterised by the Wilson K-values: additional
estimates are chosen from the following phases:
324
•
Each inorganic component
•
Lightest hydrocarbon
•
Heaviest hydrocarbon
•
Ideal gas
•
Arithmetic mean of existing phases.
•
Wax - prediction of cloud point - SPE 27629
Technical Description
Equation of state
PVTi Reference Manual
The solutions method used for Michelsen stability criterion is a Successive substitution with
GDEM (general dominant eigenvalue method) follow by BFGS if that does not work. These
trial phases are tested in turn until one indicates instability, in which case the whole system is
unstable, and the algorithm proceeds to split of that phase, provided that phase does not already
exist. If none of the trial phase indicates instability, the state is assumed to be stable.
Phase Split Calculations
The multiphase flash calculations are based on Gibbs energy minimisation of the system, and is
fully defined by the multiphase flash equation and the Gibbs energy stationary point criterion.
Systems of Equations
Material Balance, Mass conservation equations or consistency equations
Consider a hydrocarbon system consisting of one mole of mixture or feed of composition { z i }.
In general, this will consist of { β m } moles from each of the M phases, with composition { z im },
at some pressure P and temperature T.
Mass conservation gives:
 βm
= 1
[EQ 8.116]
 zim
= 1
[EQ 8.117]
m
i
 βm zim
= zi
[EQ 8.118]
m
These consistency rules can be checked at the end of the multiphase flash calculation.
Defining the multiphase equilibrium ‘K’-values as:
z ij
K ij = ----------z ir ( i )
Where r ( i ) is the reference phase index chosen for component i, usually so that the largest
amount of component i is in the reference phase.
Gibbs Energy Stationary Conditions
The solution of the multiphase flash satisfies the consistency equations and is the absolute
minimum of the Gibbs free energy.
The reduced Gibbs energy of an M phase system is written as:
G
g° = ------- =
RT
  βm zim ln ( fim )
i
[EQ 8.119]
m
th
where f im is the fugacity coefficient in the i component and the m
fugacties are calculated from the equation of state.
th
phase. Where the
The first derivative with respect to the scaled mole numbers Θ jk = β k z jk ⁄ z j can be written in
various forms:
g· ° = z j ( ln f jk – ln f jr ( j ) )
PVTi Reference Manual
[EQ 8.120]
Technical Description
Equation of state
325
= z j ( ln z jk – ln z jr ( j ) + ln Φ jk – ln Φ jr ( j ) )
[EQ 8.121]
= z j ( ln K jk + ln Φ jk – ln Φ jr ( j ) )
[EQ 8.122]
where Φ jk is the fugacity coefficient of component j in the k’th phase. In equilibrium, the Gibbs
energy is at a minimum, and the first order stationary condition thus implies fugacity balance
between like components in all phases.
The second derivative of the Gibbs free energy is:
δ mk – δ mK  δ ij
∂ ln Φ im
g··° = z i z j  -------------------------  ------- – 1 + ------------------ –

  z im
βm
∂z im
∂ ln Φ iM
δ Mk – δ MK  δ ij
–  --------------------------  -------- – 1 + ------------------- –

  z iM
βM
∂z jM
∂ ln Φ im

 zpm -----------------∂z pm 
p
∂ ln Φ iM
-
 zpM -----------------∂z pM 
p
where K = r ( k ) , M = r ( m ) and δ ij is the Kronecker delta and the fugacity coefficient
derivatives are calculated from the Equation of State being used.
Finding Stationary solutions
Starting from initial conditions provided by the stability analysis (or input directly), the general
algorithm is repeating cycle of the following:
•
iterate forward to new J = ln ( K ) values
•
solve the multiphase flash equation for new beta-values
•
update the compositions. Checking to see solution is consistent, that is mole fractions have
to add up to one.
The algorithm has two attempts at converging to a local minimum. First method updates with
direct or successive substitution with GDEM of the J-values. If it does not converge that is the
fugacity balance equation residuals fails to meet a specified tolerance, it proceeding to a try
continuing the convergence with Newton-Raphson/Murray method.
Successive Substitution (SS)
The SS part incorporates the General Dominant Eigenvalue Method (GDEM) acceleration
algorithm. For details see Crowe and Nishio. The variable used are the J-values themselves,
updated from the second form of the first derivative given in equations [EQ 8.120], [EQ 8.121]
and [EQ 8.122]. The reference phase for each component is chosen as the phase with the highest
mole fraction of that component, so as to scale each K value close to and below one.
Newton-Raphson (NR)
The NR part uses a Murray decomposition of the Gibbs Hessian to ensure positive definiteness
of the Jacobian, and therefore progress towards a minimum. Occasionally, a cubic trace back
augmented line search in the Newton direction indicated is required when the Gibbs free energy
is found not to decrease.
The variables used are the scaled mole numbers, and the reference phase is the same as in the
SS, that is, the phase with the highest mole fraction.
326
Technical Description
Equation of state
PVTi Reference Manual
Trace Elements
If a phase possesses a near-zero component composition, then the variable for that component
and phase can be dropped from the variable list (that is not changed in the SS or NR) and its
value calculated after each iteration by invoking fugacity balance between it and the fugacity of
a variable that was update in the usual way. In doing so, the trace element fugacity coefficient
is calculate by setting its composition to zero. If the component transcends the numerical zero
boundary, its variable is reintroduced into the variable set ready for the next iteration.
4-Phase Guess Method
Instead of doing a phase split method we can used initial guesses to obtain a different initial
starting points for the find stationary solutions using SS and NR, which might converge to a
different stationary state. See Trebble ([Ref. 62]).
There are various initial guesses that can be implemented.
•
Wilson initiation, proposed by Wilson ([Ref. 1])
•
Wilson and Antonie
•
NISA (Non-Iterative Stability Analysis)
•
Wilson and Stability
•
NISA and Stability
•
Liquid-Liquid Initiation
•
Trebble’s Vapor-Liquid-Liquid Initiation
•
Liquid-Vapor and Wax
•
Wax and Liquid-Liquid-Vapor Initiation.
•
Five phase initial guess.
It was found that for a flash with wax that the wax initial guess did give a lower Gibbs free
energy some of the time. For the wax initial guess we assume the composition of the liquid
phase is the same as the feed. We then workout based on the wax, heavier liquid and vapor K
values by:
o
ln y i = ln x i + ln Φ i, V ( x i ) – ln Φ i, L
[EQ 8.123]
o
ln x 2i = ln x i + ln Φ i, L ( x i ) – ln Φ i, L
[EQ 8.124]
o
ln x 3i = ln x i + ln Φ i, W ( x i ) – ln Φ i, L
[EQ 8.125]
o
where Φ denotes pure fugacity, L,V and W denote liquid, vapor and wax. y i component in the
vapor phase. x i , x 2i and x 3i are the components in the lightest liquid, the heavier liquid and
the wax phase.
Both result using the initial guess and standard algorithm can pass the stability test, so in the
multiphase where it is possible for wax to form, we do both the four phase wax initial guess and
the standard multiphase flash and compare results, taking the one with the lowest Gibbs free
energy.
In the case of the debug option switching on all the initial guesses and in the case for the wax
possible case fail to give an answer which pass the stability test, then all initial guesses are tried
and compared and the result with the minimum Gibbs free energy taken as the answer.
PVTi Reference Manual
Technical Description
Equation of state
327
Treatment of water systems
Water systems need to be given special treatment because of the inapplicability of the Equations
of State generally used for any phase, liquid or vapor, containing water. The current lines of
attack at this problem are
•
Lattice-gas models
•
local composition models
•
different mixing rules
•
use of henry’s law rather than an Equation of State
•
modification of commonly used Equations of State
Lattice-gas models and local composition models have attracted attention through their strong
theoretical basis, incorporating hydrogen-bonding and electrolyte thermodynamics
respectively. Relaxation of the commonly used symmetry condition for τ ij s yielding different
mixing rules, is attractive for similar reasons. As yet though, these approaches have found little
application, and are not easily incorporated into existing Equation of State packages.
Henry’s Law, based essential on ‘look-up’ fugacites for given solutes and solvent, has had a
longer history of application to engineering ‘rule-of-thumb’ problem, but is difficult to
incorporate in a GEM multiphase algorithm, requires significant amounts of data, uses nonexact models for pressure and salinity corrections, and is restricted to specific solvents and
solutes.
The Valderrrama-Patel-Teja Equation of State is a 3 degree Equation of State that has extra
terms involving the compressibility factor, and has had some success in dealing with water
systems. Again, this has not had wide use, and again, has still to be corrected for salinity. The
most common approach in the literature is to use the more popular Equations of State, but with
some modification, particularly to the τ ij s used. The Peng-Robinson Equation of State has
received this treatment, using T-dependent τ ij s between water and most SCN groups. The
‘PRW’ Equation of State is used here details are given in "Peng-Robinson and Water Equation
of State" on page 329.
The multiphase flash allow three separate treatments for systems containing water that produce
a water phase, each based on the PRW Equation of State:
•
maintain the water phase as pure
•
allow CO 2 only to dissolve
•
allow all components to dissolve
If the given system contains water the stability analysis attempts specifically to split off a water
phase before any other. A full Michelsen stability analysis is not required:- each of the above
options describe a water-dominated phase, so it is enough to compare the activity of water in a
pure water phase with that in the feed mixture, and reintroduce the impurities required by the
option at a later stage. In terms of fugacities, a pure water phase will split off if and only if
fugacity of water in the feed is greater than fugacity of a pure water ( f w ( feed ) > f w ( pure ) ) or:
ln ( Φ w ) feed + ln ( z w ) feed > ln ( Φ w ) pure
where the w denotes the component index of the water. The difference between the options is
then implemented in the ‘bring-back’ treatment for trace components used in the phase split
calculations, either none, CO 2 only, or all.
328
Technical Description
Equation of state
PVTi Reference Manual
Water- CO 2 bic-fitting
A particular modification to the use of PWR Equation of State is made when only CO2 is
dissolved in water, in allowing for salinity effect CO 2 solubility decrease with salinity, but the
PRW Equation of State makes no allowance for this. It has been possible, however, to establish
a polynomial form for the H 2 O – CO 2 τ ij by iterating adjusting (with a NR scheme) the
H 2 O – CO 2 τ ij until the solubility predicted by the flash calculation matches experimentally
determined solubilities. With a set of such τ ij s one can fit a 3 degree surface polynomial in p,
T, S (salinity):
τ H O – CO = f 1 P, T ) + Sf 2 P, T )
2
2
f i = a 1i + a 2i T + a 3i P + a 4i TP + a 5i T
2
2
3
+a 6i P + a 7i T P + a 9i T + a 10i P
2
3
where a linear correction for salinity is assumed.
Peng-Robinson and Water Equation of State
The treatment of water systems is based on the PRW (Peng-Robinson and Water) equation of
state. The original PR Equation of State has the form (for the usual symbols):
RT
a(T)
P = ------------ – ------------------------------------------------V – b V(V + b) + b(V – b)
a =
  xi xj ( 1 – δij ) ( ai aj )
j
i
b =
1⁄2
 xi b i
i
a i = a ci α i
2 2
R T ci
a ci = 0.45724 ---------------P ci
α
1⁄2
1⁄2
= 1 + κ ( 1 – Tr
)
2
κ = 0.37464 + 1.54226ω i – 0.26992ω i
RT ci
b i = 0.07780 ----------P ci
Two modification are made for water systems. Firstly, for the water component in any phase, a
correction is made to improve predicted water vapor pressures:
α
1⁄2
= 1.0085677 + 0.82514 ( 1 – T r
1⁄2
when T r
1⁄2
)
< 0.85
Secondly, in the aqueous liquid phase, a temperature-dependent interaction parameter is used,
so that the mixing rules change slightly to:
PVTi Reference Manual
Technical Description
Equation of state
329
a =
  xi xj ( 1 – τij ( T ) ) ( ai aj )
i
1⁄2
j
when T r ≥ 0.85 , or the phase is not the aqueous liquid phase, the original PR Equation of State
is used.
The temperature τ ij s required may be found from the published curves given by Peng &
Robinson. The following forms have been derived:
τ C ↔ H O = 1.659T r P rw – 0.761
1
2
τ C ↔ H O = 2.109T r P rw – 0.607
2
2
2 2
τ C ↔ H O = – 18.032T r P rw + 0.9441T r P rw – 1.208
3
2
τ C ↔ H O = 2.800T r P rw – 0.488
4
2
Tc
τ C ↔ H O =  0.4 ------ T r P rw – 0.8 , n > 4
n
2
 P c
τ N ↔ H O = 0.402T r – 1.586
2
2
τ H S ↔ H O = 0.22T r – 0.19
2
2
2
τ CO ↔ H O = – 0.074T r + 0.478T r – 0.503
2
2
The general C n form, was fitted here.
Viscosity correlations
Three correlations are available in PVTi for the estimation of viscosities, namely that due to
"Lohrenz, Bray and Clark" on page 330, [Ref. 7], the method due to "Pedersen et al." on
page 331 (PED), [Ref. 5] and [Ref. 36], and also that of "Aasberg-Petersen et al" on page 333,
[Ref. 63].
Lohrenz, Bray and Clark
The most widely used correlation for the prediction of liquid and vapor viscosities in reservoir
simulators is that due to LBC.
The viscosity being related to a fourth-degree polynomial in reduced density, ρ r = ρ ⁄ ρ c :
–4 1 ⁄ 4
[ ( η – η∗ )ξ + 10 ]
2
3
4
= a1 + a2 ρr + a3 ρr + a4 ρr + a5 ρr
[EQ 8.126]
where
a 1 = 0.1023000
a 2 = 0.0233640
a 3 = 0.0585330
a 4 = – 0.0407580
a 5 = 0.0093324
330
Technical Description
Equation of state
[EQ 8.127]
PVTi Reference Manual
and η∗ is the low-pressure gas mixture viscosity. ξ is the viscosity-reducing parameter, which
for a fluid mixture is given by:
1⁄6
N

ξ =
–1 ⁄ 2
N

z i T ci
i=1
i=1
–2 ⁄ 3
N

z i M wi
[EQ 8.128]
z i p ci
i=1
The critical density ρ c is evaluated from:
N
ρc =
–1
Vc

= 

 i = 1, i ≠ C

( z i V ci ) + z C
7+
V cC
7+
7+
 –1



[EQ 8.129]
where the critical volume of the plus fraction is found from:
V cC
7+
= 21.573 + 0.015122M wC – 27.656γ C + 0.070615M wC γ C
7+
7+
7+
7+
[EQ 8.130]
The dilute gas mixture viscosity is as given by Herning and Zippener, [Ref. 28]:
N
–1
N

η∗ =
1⁄2
z i η i∗ M wi
i=1

1⁄2
[EQ 8.131]
z i M wi
i=1
where the dilute gas viscosities of the individual components, ηi∗ are derived from expressions
due to Stiel and Thodos, [Ref. 29]:
– 5 1 0.94
η i∗ = 34 ×10 ---- T ri
ξi
[EQ 8.132]
T ri < 1.5
–5 1
0.625
η i∗ = 17.78 ×10 ---- ( 4.58T ri – 1.67 )
ξi
[EQ 8.133]
T ri > 1.5
where
1⁄6
–1 ⁄ 2 – 2 ⁄ 3
[EQ 8.134]
ξ i = T ci M wi p ci
Hint
By making the viscosity a function of the fourth power of density, results are very
sensitive to small differences in estimation of density. It is not unusual for this
technique to predict a viscosity only 50% of the measured viscosity. Small changes in
critical volumes or critical Z -factors remedy the error but it is recommended that they
are changed as a single group, from [EQ 8.130].
Pedersen et al.
Viscosities can be calculated from a modified form of the corresponding states method. A group
of substances obey the corresponding states principle if the functional dependence of the
reduced viscosity, η r , say, on reduced density and temperature, ρ r and T r , say, is the same for
all components within the group, namely:
[EQ 8.135]
η r ( ρ, T ) = f ( ρ r ,T r )
in which case comprehensive viscosity data is only needed for one component of the group,
which is denoted as the reference substance, to be given the subscript ( o ) all other components
are identified with the subscript ( x ).
Generally, the critical viscosity, ηc , is not known but it can be estimated from the inverse of [EQ
8.135]),
–1 ⁄ 2 2 ⁄ 3 –1 ⁄ 2
Vc Mw
[EQ 8.136]
η r ( ρ, T ) = η ( ρ, T )T c
PVTi Reference Manual
Technical Description
Equation of state
331
Thus, the viscosity of component x at temperature T and a pressure with density ρ , is given by:
1⁄2
–2 ⁄ 3
1⁄2
T cx V cx M wx
η r ( ρ ,T ) = ----------- ------------- ------------ η o ( ρ o ,T o )
T co V co M mo
[EQ 8.137]
where ρ o = ρρ co ⁄ ρ cx , T o = TT co ⁄ T cx and ηo is the viscosity of the reference substance at T o and
ρo .
Oil mixtures contain a range of components with molecular weights ranging from 16 (Methane)
to about 1100 ( C 80 ). It cannot be expected for C 1 and C80 to belong to a group where a simple
corresponding states principle applies. Generally, a third parameter must be added to account
for the shape of the molecules, such as the acentric factor.
Pedersen et al., [Ref. 5], presented a corresponding states principle depending on reduced
temperature and reduced pressure, η r = f ( p r, T r ) where:
η
η r = ηξ = ------------------------------------–1 ⁄ 6 2 ⁄ 3 1 ⁄ 2
Tc pc Mw
[EQ 8.138]
The deviation from the simple corresponding states principle is expressed in terms of a
rotational coupling coefficient, denoted α , to give:
–1 ⁄ 6
2⁄3
1⁄2
p c, mix M w, mix α mix
T c, mix
η mix ( p, T ) = ------------------------ ---------------------- ------------------------- ----------- η o ( p o, T o )
T co
p co
M wo
αo
[EQ 8.139]
where
p co α o
p o = p ------------------------p c, mix α mix
[EQ 8.140]
T co α o
T o = T -------------------------T c, mix α mix
[EQ 8.141]
The critical temperature and volume for unlike pairs of molecules are given by:
T c, ij = ( T c, i T c, j )
1⁄2
1 1⁄3
1⁄3 3
V c, ij = --- ( V c, i + V c, j )
8
[EQ 8.142]
[EQ 8.143]
where the critical volume of a component can be expressed in terms of the critical temperature
and pressure using the real gas law and the critical Z -factor.
Assuming a constant Z c for all components,[EQ 8.143] becomes:
T c, i 1 ⁄ 3  T c, j 1 ⁄ 3 3
1
V c, ij = --- constant   ---------
+ --------
 p c, j 

p c, i 
8
[EQ 8.144]
The mixture critical temperature is found from:
  zi zj Tc, ij Vc, ij
T c, mix =
i------------------------------------------------= 1j = 1
N N
[EQ 8.145]
  zi zj Vc, ij
i = 1j = 1
Combining [EQ 8.143] and [EQ 8.145] gives:
332
Technical Description
Equation of state
PVTi Reference Manual
  zi zj
c, i
T
------- p c, i
1⁄3
c, j
T
------- p c, j
1⁄3 3
[ T c, i T c, j ]
1⁄2
[EQ 8.146]
= 1j = 1
T c, mix = i---------------------------------------------------------------------------------------------------------------N N
T c, i 1 ⁄ 3 T c, j 1 ⁄ 3 3
z i z j  ---------  ---------
 p c, i   p c, j

i = 1j = 1
and the mixture critical pressure is evaluated from:
8
  zi zj
c, i
T
------- p c, i 
1⁄3
c, j
T
------- p c, j 
1⁄3 3
[ T c, i T c, j ]
1⁄2
[EQ 8.147]
i = 1j = 1
p c, mix = ------------------------------------------------------------------------------------------------------------------2
N N

1⁄3 T
1 ⁄ 3 3
T
c
,
i
c
,
j


z i z j  ---------  ---------
 p c, i  p c, j


i 1 j 1


The mixture mole weight is given by:
–4
M w, mix = 1.304 ×10 ( M w
2.303
– Mn
2.303
[EQ 8.148]
) + Mn
where M w and M n are the weight average and number average mole weights, respectively.
This mixing rule is derived empirically on the basis of available viscosity data and assigns a
larger influence to heavier components.
The α -parameter for the mixture is found from:
– 3 1.847
α mix = 1.0 + 7.378 ×10 ρ r
0.5173
[EQ 8.149]
M w, mix
where the α of Methane, the reference substance, is given by:
1.847
[EQ 8.150]
α 0 = 1.0 + 0.031ρ r
Note
The constants and exponents in equations [EQ 8.149] and [EQ 8.150] have been found
from fitting to experimentally determined viscosity data.
It has been our experience that the method of Pedersen gives much better prediction of
viscosities than does the method of Lohrenz, Bray and Clark. Neither method is particularly
good but typical errors based on un-regressed Equation of State data are, LBC ∼ 50 % and
PED ∼ 90 % of the reported values. However, you should treat experimentally measured
viscosities with some caution, as viscosities are often calculated.
Aasberg-Petersen et al
The Aasberg-Petersen model is also based on the principle of corresponding states, but uses two
references fluids, methane and decane, instead of just the one (methane) in the case of the
Pedersen et al. model. The usual problem with the Pedersen model is that inaccurate predictions
occur for fluids with components that are significantly different in molecular weight to the
reference component (methane).
The idea of this model is to use a heavier second reference component and effectively create an
optimum reference component by using the molecular weight of the fluid as an interpolation
parameter between the two reference components. Decane is chosen as the second reference
component because it is the heaviest alkane for which a significant amount of experimental
viscosity data is known. Methane is a natural choice as the first reference component because
of its presence in large mole fractions in most reservoir fluid mixtures
The interpolation law is used to calculate the reduced viscosity of the optimum reference
component (denoted with the subscript x) using the reduced viscosities of methane and decane
and is obtained using the following expression:
PVTi Reference Manual
Technical Description
Equation of state
333
η r2
MW x – MW 1
ln η rx = ln η r1 + ------------------------------- ln  --------
MW 2 – MW 1  η r1
[EQ 8.151]
MW is the molecular weight and subscripts 1 and 2 refer to the reference components. The
functional form of equation [EQ 8.151] was originally suggested by Teja and Rice (1981), [Ref.
64], using the acentric factor instead of MW. This is not possible in the present work, since the
acentric factor decreases with increasing molecular weight for heavy oil fractions.
The reduced properties are determined from:
E
E r = ------, E = T, P, η
Ec
[EQ 8.152]
Subscripts r and c indicated reduced and critical properties respectively. The following
expression is used to evaluate the critical viscosity (Pedersen et al. 1989):
ηc = C ⋅
1
--- 2
--- – 1
--2 3 6
MW P c T c
[EQ 8.153]
C is a constant. From equations [EQ 8.151], [EQ 8.142] and [EQ 8.143] the following equations
may be derived for determination of the viscosity:
η cx η 1 ( T 1, P 1 ) η 2 ( T 2, P 2 )η c1 K
η x = ----------------------------------- ----------------------------------η 1 ( T 1, P 1 )η c2
η c1
[EQ 8.154]
MW x – MW 1
K = ------------------------------MW 2 – MW 1
[EQ 8.155]
η 1 and η 2 are evaluated at conditions corresponding to the reduced temperature and pressure of
component x:
T ci T
T i = -----------, i = 1, 2
T cx
[EQ 8.156]
P ci P
P i = -----------, i = 1, 2
P cx
[EQ 8.157]
The model outlined in the above is extended to mixtures using the same mixing rule as the
Pedersen et al. model, that is equations [EQ 8.146] and [EQ 8.147]. The mixture molecular
weight is calculated using the formula:
MW mix = MW n + 0.00867358 ( MW w
where
1.56079
– MW n
1.56079
)
[EQ 8.158]
[EQ 8.159]
N
2
 zi MWi
=1
MW w = i-------------------------N
 zi MWi
i=1
and
N
MW n =
 zi MWi
[EQ 8.160]
i=1
334
Technical Description
Equation of state
PVTi Reference Manual
The constants in equation [EQ 8.142] are determined by regression using experimental viscosity
data for binary mixtures and oils.
The following equations are used for determination of the viscosity of the reference
components:
η 0 = η k ( T ) + ρη 1 ( T ) + η 2 ( ρ, T )
9
 GVi T
ηk ( T ) =
[EQ 8.161]
(i – 4)
--------------3
[EQ 8.162]
i=1
T 2
η 1 ( T ) = A + B C – ln  ---
 F
[EQ 8.163]
j4
η 2 ( T, ρ ) = H 2 exp  j 1 + ----

T
[EQ 8.164]
H 2 = – 1 + exp ρ
0.1 
j7 
j3 
j
0.5 
- + θρ  j 5 + ---6- + ---- j 2 + -------
1.5
T T 2


T 
[EQ 8.165]
where
[EQ 8.166]
( ρ – ρc )
θ = ------------------ρc
These equations were originally developed by Hanley et al. (1975), [Ref. 65], to correlate the
methane viscosity. For methane the values of the GVi parameters in equation [EQ 8.152] given
by Hanley et al. were maintained. For decane GV4-GV9 are equal to zero and GV1-GV3 were
taken from the DIPPR tables (1985). All the parameters in equations [EQ 8.59]-[EQ 8.165] were
estimated. In Table 8.9, data of the parameter estimation are given and Table 8.10 lists all
parameters for the pure component viscosity correlation. Of the parameters in Table 8.10 are
used the viscosity is obtained in μP if the density is given in g/cm3.
Table 8.9
PVTi Reference Manual
Parameter estimation data. N is the number of experimental points
Methane
Decane
N
881
252
T-range (K)
91-523
244-477
P-range (atm.)
0-680
0-1000
Dev. (%)
3.1
3.8
Technical Description
Equation of state
335
Table 8.10
Parameter Values for Pure Component Viscosity Correlation
Methane
Decane
GV1
-209097
0.2640
GV2
264276
0.9487
GV3
-147282
71.0
GV4
47164
0.0
GV5
-9491.9
0.0
GV6
1220.0
0.0
GV7
-96.28
0.0
GV8
4.274
0.0
GV9
-0.0814
0.0
A.100
23946
0.00248
B
343.79
81.35
C
0.4487
5.9583
F
168.0
490.0
j1
-22.768
-11.739
j2
30.574
16.092
j3
-14929
-18464
j4
1061.5
-811.3
j5
-1.4748
1.9745
j6
290.62
898.45
j7
30396
119620
The density of the reference components as a function of the pressure and temperature is also
required in equations [EQ 8.48] and [EQ 8.165]. For methane, as with the Pedersen model, the
33-parameter MBWR-equation given by McCarthy (1974), [Ref. 66], was used to calculate the
density. For decane we decided to used the flash available within PVTi to obtain the density at
a given pressure and temperature.
336
Technical Description
Equation of state
PVTi Reference Manual
Finally, the following physical properties for methane and decane were used in Table 8.11 below
when required.
Table 8.11
Physical Properties of Methane and Decane
Methane
Decane
Tc
190.55
617.40
Pc
45.39
20.18
MW
16.043
142.284
ω
0.008
0.484
ρc
0.1649
0.2269
The predictions of the Aasberg-Petersen model have been shown to agree well with
experimental data over large pressure and temperature ranges. In particular this model is able to
handle mixtures with CO2, paraffinic and aromatic components with better accuracy than the
Pedersen model. A better match is also obtained than the Pedersen model for heavier oils, where
the size and shape of the molecules differ substantially from the single reference component
(methane).
Note
It should be noted that the Aasberg-Petersen model is not recommended for fluids with
large concentrations of napthalenic components.
Binary interaction coefficients
Strictly, binary interaction coefficients are interpreted as accounting for polar forces between
pairs of molecules.
Another interpretation is they account for tertiary and higher-order interactions in the cubically
(in volume) truncated form of the Second Virial Equation:
RT a
p = ------- + -----2- + …
V V
[EQ 8.167]
Eitherway, they might be thought of as the fiddle-factors for the equation of state. Strictly, they
should be determined for all possible binary mixtures of hydrocarbons and non-hydrocarbons
by tuning their value to get a match between experimental and theoretical (Equation of State)
behavior. Thus, each new Equation of State requires that a completely new set of binaries be
developed: a laborious task indeed. This is the main reason why the Soave-Redlich-Kwong and
Peng-Robinson Equations of State tend to dominate in reservoir applications.
Caution
Many authors have suggested that binaries are the obvious Equation of State
parameter to adjust to match Equation of State to laboratory results, especially the
Methane to plus-fraction binary. However, Pedersen et al., [Ref. 30], have shown
that this is problematic.
Given that our preferred Equation of State is the Peng-Robinson, we derive binaries from one
of two sources.
PVTi Reference Manual
Technical Description
Equation of state
337
The current default is to assume they are zero for all hydrocarbon-hydrocarbon interactions
except for Methane to heavier hydrocarbons that vary like:
KC
1,
j
[EQ 8.168]
= 0.14γ j – 0.06
where γ j is the (liquid) specific gravity of the heavier component. In addition, the hydrocarbon
to non-hydrocarbon interactions take certain fixed values, see [Ref. 4].
The alternative set, activated by the appropriate option switch is a set due to Cheuh and
Prausnitz, see [Ref. 32].
The hydrocarbon to non-hydrocarbon interactions are as above but the hydrocarbon to
hydrocarbon binaries are given by:
1⁄6 6
 2 ( V c, i V c, j ) 
-
K i, j = A 1 –  --------------------------------- V 1c, ⁄i3 + V 1c, ⁄j3 
[EQ 8.169]
where V c, i is the molar volume of the i th component and A is a special regression variable which
is generally in the range 0.15 ≤ A ≤ 0.25 .
There is some appeal in using the pre-multiplying coefficient to regress all binaries together.
This preserves symmetry, which might be lost using the Methane to plus fraction binary
approach of [EQ 8.169], which (see [EQ 8.169] and [Ref. 28]) can lead to strange results.
These particular binaries are also given a temperature dependence by the use of an additional
multiplying factor that has the form:
1.0 + TC ( T – T std )
[EQ 8.170]
where TC has the fixed value of 0.0025.
338
Technical Description
Equation of state
PVTi Reference Manual
Basic laboratory experiments
Introduction
This section describes the basic laboratory experiments and how PVTi attempts to simulate
them. More detail on experimental methods can be found in the excellent text by Pedersen et al.
[Ref. 30].
Schematic diagrams of the apparatus used for the standard laboratory techniques to be described
here can be found in the above text.
See "The fluid model" on page 98 and "Batch system and keywords" on page 152 for further
information on defining experiments in PVTi.
This section contains information on the following:
•
"Blackoil systems" on page 339.
•
"Gas condensate systems" on page 341.
•
"Gas injection processes" on page 344.
•
"Process simulation" on page 343.
Blackoil systems
Essentially two experiments are performed on black or crude oil systems:
•
"Bubble point evaluation" on page 339
•
"Differential liberation" on page 340 (sometimes referred to differential expansion).
Bubble point evaluation
Laboratory experiment
1
Having charged the PVT cell with the reservoir fluid, the system is left to come into
equilibrium at the required (reservoir) temperature and pressure or some higher pressure
where the fluid is a single phase liquid, whereupon the fluid volume is noted.
2
The pressure is then dropped (at constant temperature) and the new fluid volume is
recorded. The bubble point pressure is then readily found from the discontinuity in the
pressure/volume relationship where the first bubble of gas is evolved from the liquid. Since
gases are more compressible than liquids, reduction in pressure and liberation of gas results
in an increase in rate of volume expansion of the (two phase) fluid.
PVTi
1
PVTi finds the bubble point by taking one mole of the reservoir fluid and using estimates
for the K -values, constructs vapor compositions at a set of pressures, testing for the stability
of the second (vapor) phase using the method of Michelsen [Ref. 16].
2
Once the highest-pressure, two-phase state has been found, the N equal fugacity conditions
and the one mole fraction constraint (see "Material balance" on page 317 and "Flash
calculations" on page 317) are used to solve for the N + 1 unknowns of N K -values and the
bubble point pressure by iteration.
PVTi Reference Manual
Technical Description
Basic laboratory experiments
339
Differential liberation
Having found the bubble point pressure, the crude oil would normally then be subject to this
experiment.
Laboratory experiment
1
Starting from the bubble point pressure, the pressure is dropped by several hundred psia,
whereupon a volume of gas is evolved that is removed from the cell at the (new) constant
pressure. This process is repeated several times noting the volume of gas evolved (at
reservoir and surface conditions) and the volume of liquid remaining.
2
The volume of liquid remaining at the last stage, which should be at standard or
atmospheric pressure, is then reduced to standard or atmospheric temperature and remeasured. This liquid is discharged and its density is obtained. The density of the liquid at
the other pressure (and temperature) stages can be calculated from mass balance knowing
the volumes and molecular weight of the removed gas streams.
The data usually quoted is:
•
Bo
Oil formation volume factor
•
Bg
Gas formation volume factor
•
Rs
Gas-oil ratio
•
ρo
Oil density
•
γg
Gas gravity (density)
•
Zg
Gas deviation factor
•
μo
Oil viscosity
•
μg
Gas viscosity
where:
Vo ( p )
B o ( p ) = ------------std
Vo
[EQ 8.171]
Vg ( p )
B g ( p ) = ---------------std
Vg ( p )
[EQ 8.172]
i = std
1
R s ( p ) = -------std
Vo
 Vg
std
(i)
[EQ 8.173]
i=p
and
Mg ( p )
γ g = --------------M air
[EQ 8.174]
Here, Vo , Vg are volumes of oil and gas, M g , M air are mole weights of hydrocarbon gas and
air, the superscript std implies standard conditions, and the summation for the gas-oil ratio
is taken over the volumes of evolved gas from the current pressure, p to the final pressure
at std .
340
Technical Description
Basic laboratory experiments
PVTi Reference Manual
PVTi
1
In PVTi, the experiment is simulated by firstly locating the bubble point pressure, as above.
Then one mole of bubble point fluid is dropped in pressure and a flash calculation is
performed to determine the phase split and the volumes of oil and gas. All the gas is
removed and the liquid composition forms the feedstream for the next pressure depletion
stage, etc.
Note
The "Definition of GOR in Diff. Lib." on page 148 program option allows three further
definitions of the GOR.
The first removes the stage to standard conditions and normalizes gas volumes to the
volume of oil at reservoir conditions, that is:
i = plast
1
R s ( p ) = --------------------------V o ( T, p bub )

std
[EQ 8.175]
Vg ( i )
i=p
where T is the temperature of the depletion experiment, and p last is the last pressure stage
specified.
2
The second definition specifies the GOR as an incremental one, that is:
std
Vg ( p )
R s ( p ) = ---------------std
Vo
3
[EQ 8.176]
The third definition is the same as the default but the volume of oil is at its bubble point
pressure rather than at stock tank conditions, that is:
i = std
1
R s ( p ) = --------------------------V o ( T, p bub )
 Vg
std
[EQ 8.177]
(i)
i=p
The program option "Definition of Oil relative volume in Diff. Lib." on page 149 allows an
alternative definition of the oil relative volume where the volume of oil is normalized to the
initial volume of oil at reservoir rather than standard conditions:
Vo ( p )
B o ( p ) = --------------------------V o ( T, p bub )
[EQ 8.178]
Gas condensate systems
Essentially three experiments are performed on gas condensate systems:
•
"Dew point evaluation" on page 342.
•
"Constant composition expansion" on page 342.
•
"Constant volume depletion" on page 343.
Hint
PVTi Reference Manual
It is not uncommon for CCEs to be performed on all fluids, and it is recommended to
perform CVDs on more volatile oils.
Technical Description
Basic laboratory experiments
341
Dew point evaluation
Laboratory experiment
This experiment is generally more difficult than the bubble point evaluation and consequently
subject to larger uncertainties.
1
Most condensate systems are relatively compressible above the dew point so that the
appearance of a heavier, less-compressible second liquid phase cannot be identified on a
pressure/volume relationship. This means the dew point must be found by eye, by visual
determination of the pressure when the first drop of liquid is formed in the cell.
Note
This can be affected by imperfections or grease in the cell, poor experimental
procedures, etc., and it is not uncommon for errors of 100 psia to be associated with
this measurement.
PVTi
In PVTi, this experiment is simulated in much the same way as the bubble point evaluation
except that the trial second (liquid) phase is heavier than the original fluid.
1
The same stability test is done to find the highest two phase state and the same set of
equations and variables iterated to solution.
2
As an alternative to this high-pressure dew point, usually referred to as the retrograde dew
point, the low-pressure or normal dew point can be found by starting low in pressure and
iterating higher.
Constant composition expansion
Laboratory experiment
This experiment is often done while trying to find the dew point of a gas (or bubble point of a
volatile or even crude oil).
1
It consists of varying the pressure and measuring the resulting volume of the single phase
fluid above saturation pressure, and volumes of vapor and liquid (and total) phases below it.
2
For the single phase state, the vapor Z -factor or liquid density can be calculated from the
other fluid properties.
These data items are reported along with the relative volume, being the volume of the fluid at
any given pressure per the volume of the fluid at the saturation pressure.
PVTi
In PVTi, the CCE is simulated by:
342
1
Finding the saturation pressure which for one mole of feedstream defines the cell or control
volume.
2
Then at pressures above the saturation pressure it is sufficient to find the single phase liquid
or vapor Z -factor to calculate the volumetric behavior.
3
Below the saturation pressure, the feedstream is flashed at each required pressure stage to
determine the phase split and other volumetric properties.
Technical Description
Basic laboratory experiments
PVTi Reference Manual
Constant volume depletion
Laboratory experiment
The CVD is the most useful, and probably the most difficult experiment to perform on a gas
condensate (and increasingly on volatile oils).
1
It consists of starting with a volume of fluid at its saturation pressure, which again defines
the cell or control volume for the experiment.
2
Then the pressure is dropped by several hundred psia, or so, whereupon the fluid becomes
two phase and expands in volume.
3
Any excess volume over and above the cell volume is removed by taking off gas which is
analysed compositionally and volumetrically as well as noting the number of moles.
4
In addition, the percentage of liquid in the remaining fluid, the cell volume, defines the
liquid saturation.
Generally reported is:
S liq :
Liquid saturation;
N pro :
Moles of vapor removed;
Z gas :
Z -factor of removed vapor;
y i, j :
Composition of each removed vapor stream;
and occasionally:
x i, N :
vap
M N+ :
vap
γ N+ :
Composition of liquid stream left in cell at last pressure stage;
Mole weight of removed vapor plus fraction;
Specific gravity of removed vapor plus fraction.
PVTi
In PVTi this experiment is simulated by:
1
First finding the saturation pressure. The volume occupied by one mole of fluid at its
saturation pressure then defines the cell or control volume.
2
At some pressure less than the saturation pressure, the fluid is flashed into two phases and
any excess gas is removed to return the volume to the control volume.
3
The number of moles of vapor and its properties are noted.
4
The composition of the remaining fluid is calculated by volumetric balance and this forms
the feedstream for the next pressure stage, and so on.
Process simulation
For the purposes of process-type simulation and/or for the definition of blackoil tables for
reservoir modeling, separator tests are performed to see what phase splits are achieved when a
fluid is flashed at a series of pressures and temperatures in some prescribed sequence.
PVTi Reference Manual
Technical Description
Basic laboratory experiments
343
Laboratory experiment
1
Most laboratory analyses consist of the reservoir fluid being flashed in a cell at some
specified pressure and temperature, and (generally) the liquid output being fed to a second
(and possibly third) cell at some reduced pressure and temperature: the last stage cell
usually being at standard conditions.
Volumes of gas evolved from each stage are generally collected together and the properties
of the resulting mixture are quoted/evaluated at standard conditions.
PVTi
1
In PVTi this process is simulated by a set of flash calculations at the required set of
pressures and temperatures, taking the reservoir fluid as the feedstream and routing the
liquid and vapor outputs to other stages.
2
The default output streams are liquid to the next stage and vapor to the stock-tank
accumulation, but PVTi is capable of solving feedback loops, where, for example, vapor
output is routed back to an earlier stage.
3
In addition, a user option allows the output streams to be split and directed to more than one
other stage.
Optimized separators
In the Fluid Properties (FPE) workflow, PVTi offers the automatic generation of the optimum
separator configuration for a fluid. The optimum separator configuration is defined as the twostage separator for which the stock-tank formation volume factor (Bo) is minimized.
Given the reservoir temperature and the maximum separator pressure, the following separator
chain is constructed:
1
A separator stage at some temperature below the reservoir temperature and some pressure
below the highest separator pressure. This stage is optimized.
2
A second stage at standard conditions, the liquid output from Stage 1 passes into this second
stage.
3
The stock tank. The vapor output from Stages 1 and 2 both pass into the vapor stock tank
and the liquid output from Stage 2 passes into the liquid stock tank.
A special regression procedure is used to determine the optimum temperature and pressure for
Stage 1, such that Bo is minimized in the stock tank. This point coincides with minimum Total
Gas-Oil Ratio and minimum stock tank vapor Gravity.
Note
If no maximum pressure is supplied, it is assumed that the maximum separator
pressure available is 1440 psia (source: Oil Phase).
For more information on fluid properties estimation see "Fluid Properties Estimation" on
page 384.
Gas injection processes
PVTi has several simulations available for investigating gas injection processes.
The three that correspond closely to laboratory experiments are:
•
344
"Swelling test" on page 345
Technical Description
Basic laboratory experiments
PVTi Reference Manual
•
"Vaporization test" on page 345
•
"Multiple contact test" on page 346
In addition, PVTi has available: a ternary diagram, and first and multiple contact minimum
miscibility pressure experiments by one-cell simulation.
Note
These have no equivalent in the laboratory.
Swelling test
Laboratory experiment
1
The swelling test consists of finding the saturation pressure and hence volume of a reservoir
fluid.
2
Followed by adding, in a series of steps, prescribed volumes (or moles) of lean injection
gas, re-pressuring the resulting mixture to return to a single phase system and measuring
the new saturation pressure and volume.
The data quoted is the set of saturation pressures for the original fluid and the mixtures and the
ratio of the saturation volume of the mixtures to the saturation volume of the original fluid,
usually referred to as the swelling factor.
PVTi
In PVTi this is simulated by:
1
Firstly finding the saturation pressure of one mole of the required reservoir fluid and hence
the saturation volume.
2
Then prescribed volumes of a lean injection gas are added as a GOR (volume of injection
gas at standard conditions per volume of original reservoir fluid at its Psat or other
prescribed pressure) or a mole% (moles of lean gas per moles of mixture) to give a new
fluid composition.
3
The saturation pressure and volume of the new mixture are found, and hence the swelling
factor.
Vaporization test
This is similar to the swelling test, except that it is performed at constant volume and pressure.
Laboratory experiment
1
A volume of reservoir fluid at some pressure and temperature, usually below the saturation
pressure and hence two phase, is contacted by a series of lean gas injections.
2
After each contact, a volume of (enriched) gas and/or liquid is removed to return the system
to the original volume. The composition of the removed gas is measured.
The experiment seeks to measure the extent of vaporization of intermediate and heavy
components from the reservoir liquid phase by stripping into the injected gas stream.
In PVTi, the procedure is as follows.
1
PVTi Reference Manual
One mole of reservoir fluid at a prescribed pressure and temperature is flashed to calculate
the phase split and volumes of liquid and vapor.
Technical Description
Basic laboratory experiments
345
2
Lean gas is then added in a series of steps of moles, to give a new mixture composition
which is flashed at the same pressure and temperature, and any excess fluid volume
removed.
3
The composition of the removed stream is noted and the resulting mixture is then subject
to further lean gas injections.
Multiple contact test
PVTi
1
In condensing drive mode the initial reservoir oil (the mole fraction can be specified) is
contacted with one mole of injection gas at a specified temperature and pressure.
2
This mixture is then flashed and a specified fraction of the resulting oil is then contacted
with one mole of the initial injection gas. This process is repeated at each stage of the test.
The vaporizing drive follows the same procedure as that of the condensing drive except that it
is a specified fraction of the resulting gas from each flash that is contacted with one mole of
reservoir oil.
A special ternary plot is available for this experiment that plots the compositions at each stage
of the oil and gas resulting from each flash, and these points effectively mark the boundary of
the two-phase region at the specified conditions.
Variation of composition with depth
PVTi
Although not a laboratory experiment, the estimation of the variation of a fluid’s composition
with depth is of great possible value.
1
On purely thermodynamic principles, fugacity in an isothermal system that can be expected
to vary with depth according to:
Mi g ( h – h0 )
ln f i = ln f i, 0 + ----------------------------RT 0
2
Assuming thermodynamic equilibrium in the fluid at some reference height h0 (namely
the equal fugacity conditions and mole composition constraints of "Material balance" on
page 317 and "Flash calculations" on page 317), the N -equations, defined in [EQ 8.179],
and a further mole constraint equation can be used to determine the N -compositions and
pressure, z i , p , from the reference composition and pressure, z i, 0 , p 0 .
Note
346
[EQ 8.179]
However, the compositional gradient experiment assumes many conditions: namely
thermal, gravitational and diffusive equilibrium. Any or all of these conditions can be
violated in a given reservoir, thus invalidating the use of [EQ 8.179]).
Technical Description
Basic laboratory experiments
PVTi Reference Manual
Note
The existence in some reservoirs of a temperature gradient indicates a lack of global
thermodynamic equilibrium, but may still allow a steady-state situation, in which the
mass flux is zero (that is hydrostatic equilibrium), whilst the energy flux is not. As yet,
there is no consensus on how to treat such temperature gradients. The temperature
gradient element has been implemented in PVTi for the compositional gradient
experiment since 2002a. It is suitable for gentle temperature gradients. The algorithm
is essentially the same as that described in Pedersen's SPE paper 84364 "Simulation of
Compositional Gradients in Hydrocarbon Reservoirs Under the Influence of a
Temperature Gradient".
With the above caveats, the experiment may still be of use in the prediction of the existence and
possible location of either gas-oil contacts or so-called critical transitions. This latter transition
consists of the grading of a fluid from an oil to a gas, or vice-versa, without passing through a
gas-oil contact. This occurs when an over-pressured reservoir has a fluid composition at some
depth whose critical temperature is equal to the reservoir temperature at that depth. There is
evidence that such behavior exists in some North Sea fields.
Critical point experiment
This experiment calculates the critical point of the given sample.
FCMP experiment
Refer to Jensen and Michelsen [Ref. 38] and Pedersen et al. [Ref. 30] for detail.
MCMP experiment
Refer to Jensen and Michelsen [Ref. 38] and Pedersen et al. [Ref. 30] for detail.
Tsat experiment
Refer to Michelsen [Ref. 15] for further details.
PVTi Reference Manual
Technical Description
Basic laboratory experiments
347
Regression
Introduction
This section of the manual contains information on:
•
"Practical considerations" on page 348.
•
"Theoretical model" on page 351.
Practical considerations
There are no set rules for how to do regression of an equation of state model to match to
laboratory measurements.
The paper by Coats and Smart, [Ref. 27], contains an appendix on the choice, selection and
range limits of regression variables.
However, the Coats and Smart model is limited in its choice of regression variables to the Ωa ’s,
Ω b ’s and the binary interaction coefficients.
Another limitation of their model is the use of the standard two-parameter equation of state. It
is well known that the two-parameter Equation of State is in error in prediction of liquid
properties by as much as 10%. Therefore, to get matches to saturation pressures and densities it
becomes necessary to change the properties of “well-defined” components, say Ωa ( C 1 ) and
Ωb ( C1 ) .
Such a problem is avoided in PVTi by use of the PR3 or SRK3 Equation of State, which allows
the volume shift parameter to be a possible regression variable.
Additionally, rather than varying just the Ωa ’s and Ωb ’s, PVTi allows you to change the critical
pressures and temperatures. This has the advantage in that monotonicity tests can readily be
applied to the set of T c ’s, p c ’s,..., etc., for the hydrocarbon components to ensure that critical
temperatures increase with increasing mole weight, critical pressures decrease (except C 1 , C 2 ,
C 3 ) etc. For further information on performing a regression in PVTi see "Regression in PVTi"
on page 126 and "REGRESS section keywords" on page 160.
The present section also contains information on:
•
"Consistency and quality of measured data" on page 348
•
"Plus fraction" on page 349
•
"Performing regressions in PVTi" on page 350.
Consistency and quality of measured data
As a first step, before any regression is considered, as many tests as possible should be
performed to test the consistency and quality of the measured data. Clearly it is not possible to
match to an inconsistent PVT report, yet our experience is that all reports are flawed to a greater
or lesser degree.
The cause of these errors may be numerous. For example:
•
348
Poor sampling and/or collection
Technical Description
Regression
PVTi Reference Manual
•
Bad laboratory procedures
•
Simple typing mistakes in reporting (for example a composition does not add up to 100).
It is most likely to be a combination of all these effects. However, an equation of state model
cannot be used in isolation from measured data as no two fluids are ever likely to be the same.
PVTi provides you with the ability to check the consistency of CVD reports in the COMB section.
For further information see "COMB - Compositional Material Balance" on page 112 and
"COMB section keywords" on page 159. This test should always be done if the data is available;
the results may be surprising.
Simple tests like checking compositions sum to 100% often reveal errors.
Another useful check is to plot pressure-dependent data, for example liquid dropout from a
CVD, relative volumes from a CCE, etc., to see if they are smoothly varying. One way this can
be done is to enter this and other data as OBS to compare with the Equation of State predicted
values from the experiments in the SIMULATE section. For further information see "Simulation
using PVTi" on page 117 and "SIMULATE section keywords" on page 160.
Generally, the properties of the multi-stage experiments vary smoothly (apart from
discontinuities in vapor/liquid properties across a saturation pressure boundary), so that vapor
Z -factors, etc., that decrease, increase and decrease again as pressure drops in a CVD, probably
indicates data error.
Check the definitions of measured data. It has been our experience that what one laboratory may
call liquid saturation in a CCE experiment, for example liquid volume divided by volume of the
fluid at the saturation pressure, may be different to that from another laboratory, say liquid
volume divided by the current cell volume.
Check that a consistent set of units is being used. The saturation density of a crude oil is often
quoted as a specific volume in units of ft 3 /lb , for example.
Plus fraction
Having determined that the data is reliable, or having rejected either poor data or adjusted it to
be consistent, one will usually find that the Equation of State predictions differ from the
measured data.
Most of this error can probably be associated with the incomplete fluid description, namely the
failure to fully characterize the plus fraction, for example C 7+ , although some error has to be
associated with the inadequacies of a cubic Equation of State.
Clearly, the plus fraction, consisting as it does of many hundreds or possibly thousands of
components, cannot be represented by just one component without some modification. Even
then, just to represent a C 7+ of a condensate or volatile oil, which may be 5-20 mole percent of
the fluid, by a single component with regressed properties may be insufficient for describing a
multi-pressure process.
On some CVD analyses the mole weight and specific gravity of the produced gas plus fraction
are measured and reported.
In such a case you may note that the plus fraction gets lighter as one would expect. Then it is
clearly not adequate to represent the plus fraction by a single component and one should
consider splitting it into two or three pseudo-components, say using the techniques available in
PVTi.
The properties of the plus fraction, or its pseudo-components if splitting has been performed are
the obvious candidates for regression. However, one should avoid regressing the property of a
component with a small mole fraction, say 1%.
PVTi Reference Manual
Technical Description
Regression
349
This can be avoided by using the group facility in regression in which an Equation of State
property of two or more components can be treated as a single variable. This grouping of
components for regression should be borne in mind if the aim of the PVTi analysis is to produce
a pseudoised set of components for a compositional simulation.
Finally, one should always use the minimum set of variables possible.
It is not possible to say what this set is for any given fluid/measurement set, but the symptoms
of redundant variables are easy to spot; for example, one or more of the variables is hitting one
of its limits, or there is bouncing of the reported Rms error within a small range.
If the regression facility from an interactive session is being used, you have the option (as
default) of rejecting the latest regression and restoring the pre-regression Equation of State.
This makes it possible to vary the set of variables and test the success, or otherwise, of a given
set of variables in a limited number of iteration steps, for example, 10. The sensitivity of the
observations to which one is attempting to match as a function of the regression variable set is
output both to the screen and to the PVP printable. This gives a direct measure to the relative
importance, or otherwise, of a given variable.
Performing regressions in PVTi
Whilst not being complete, the following may be of assistance:
350
1
Always use one of the three-parameter Equation of State. We suggest the Peng-Robinson
Equation of State (PR3). The extra degree of freedom allows the possibility of matching
saturation pressure using critical properties etc., and then independently matching to
saturation density (liquid) or Z -factor (gas) using the volume shifts.
2
Consider splitting the plus fraction for volatile fluids, that is gas condensates and volatile
oils. Genuinely, crude oils are often well described by a single plus fraction, such as the C 7+
reported. Dry gases do not have a significant quantity of plus fraction to affect results. Of
all the splitting algorithms currently available, the best appears the modified Whitson
method, otherwise referred to as Semi-Continuous-Thermodynamics (SCT). The use of
this model allows the use of the special regression parameters: sample by sample plus
fraction mole weight, probability density function skewness parameter and overall PNAdistribution.
3
There is strong evidence to suggest that the adjustment of one or two binary interaction
coefficients to create an un-symmetric pattern is very dangerous, see [Ref. 30]. The
alternative is to select the Cheuh-Prausnitz BICS (see "Binary interaction coefficients" on
page 337) using the appropriate “options” switch, and then regress the pre-multiplying A coefficient to adjust the binaries.
4
As an alternative to 3., one might consider other properties. If the SCT-splitting has been
activated, one might consider the mole weight and skewness parameter or the overall
characterization of the plus fraction. These techniques have the advantage of preserving
monotonicity of all the key Equation of State variables, critical temperatures and pressures,
and acentric factors. If choosing the critical properties or acentric factors, one should start
with just those of the plus fraction, or the pseudo-components split from it.
If this is not sufficient, remember that any SCN-group in your sample analysis (for example
C 6 , C 7 ,...) are subject to uncertainty because of their PNA-content. One should not have to
consider changing properties associated with C 1 , C 2 ,..., and so on. However, if you have a
significant mole percentage of inorganics in your fluid or they are being injected into your
fluid, it may be appropriate to adjust the set of inorganic-hydrocarbon binaries, probably as
a single group change.
Technical Description
Regression
PVTi Reference Manual
5
Critical volumes or Z -factors (equivalent variables) are only needed for the Lohrenz-BrayClark (LBC) viscosity correlation.
Note
The LBC correlation can be as much as 150% in error and is regularly 50% in error.
The Pedersen correlation appears to be much better (and is insensitive to Vc , Z c ). This
having been said, the fact that Z c ’s or V c ’s affect only LBC viscosities means they can be
regressed independently of all other variables/results. If doing this, it is suggested they be
regressed simultaneously as a single group because of the LBC functional form, [EQ
8.126].
PVTi now has independent sets of critical volumes and Z -factors, one set are used in the
LBC viscosity correlation and can be selected as regression variables, the other for use in
the equation of state. The latter are not available for regression as they do not affect results.
6
For characterized components try using the molecular weight of these components. This is
available as a special variable and must not be used in conjunction with Tcrits etc., as
changing the molecular weight of each characterized component changes most of the
properties by way of the characterization technique anyway. The use of this variable is a
very powerful alternative one to the approach of Tcrits, Pcrits and acentric factors etc. as
described above
All observations entered into PVTi can be assigned a weighting factor that multiplies the
measured minus calculated residuals, see [EQ 8.181].
Clearly, some observations are more important than others and should be given a higher weight
to account for this.
As a general rule, the saturation pressure should be given the highest weight followed by
saturation density and then other quantities.
Users who have performed several material balance calculations on CVD experiments will
probably recognize that mole compositions should generally be given low weights, if they are
to be used at all.
The only way to perform regression is by trial and error.
Define your experiments and associated (consistent and reliable) observations and save them to
a PVI file prior to starting regression.
Include different sets of variables, experiments and observations. Use engineering judgement to
decide when the best match has been achieved to the maximum amount of data while
remembering to maintain monotonicity and physical consistency in one’s Equation of State
model.
Theoretical model
Generally the results of an equation of state model must be tuned by regression of one or more
variables, x = ( x1, …, x N )T to a set of laboratory experiments, y = ( y1, …, y M )T
˜
˜
[EQ 8.180]
where M ≥ N and:
yi = yi ( x )
˜
or in residual form:
[EQ 8.181]
ri ( x ) = wi [ ( y i – yi ( x ) ) ⁄ yi ]
˜
˜
PVTi Reference Manual
Technical Description
Regression
351
where w i is the weighting factor applied to the i th item of observed (or measured) data, yi .
This section of the manual contains information on:
•
"Regression algorithm" on page 352.
•
"First and second order derivatives" on page 352
•
"Trust region" on page 353
•
"Termination conditions" on page 353
Regression algorithm
The regression algorithm in PVTi seeks to minimize the least squares residual ( l 2 norm) given
by the objective function:
M
1
f ( x ) = --2
˜
 ri ( x˜ )
2
1
T
= --- R ( x ) R ( x )
2 ˜
˜
[EQ 8.182]
i=1
where R ( x ) is the residual function.
˜
The minimum of f ( x ) occurs at some x∗ , where:
˜
˜
[EQ 8.183]
∇f ( x∗ ) = 0
˜
Since f ( x ) is generally non-linear in the set x , [EQ 8.183] must be solved iteratively. Applying
˜
˜
Newton’s method gives:
–1
[EQ 8.184]
x j + 1 = x j – ( ∇2f ( x j ) ) ∇f ( x j )
˜
˜
˜
˜
First and second order derivatives
The first and second derivatives of the objective function can be readily evaluated, see Dennis
and Schnabel, [Ref. 9].
It is possible to construct a numerical approximation to the first derivative using two function
evaluations. That is with the current values of the variables, x , and shifted values x + δx .
˜
˜
˜
A similar procedure to evaluate the second derivative becomes prohibitively expensive and so
an approximation is generated, see [Ref. 9].
The advantage of this pseudo second-order method is that it ensures that the algorithm proceeds
towards a genuine minimum.
A function of a single variable, say g ( x ) , has a minimum at the point xm if g' ( xm ) = 0 and the
second derivative g'' ( x m ) is positive.
For a multi-variate function like the objective function, f , the equivalent requirement is that the
matrix ∇2f ( x ) is positive definite.
˜
A matrix is positive definite if it is symmetric and all its eigenvalues are positive.
The approximation used to construct the second derivative ensures the symmetry condition. The
program can correct for the lack of positive eigenvalues by adding a multiple of the identity
matrix.
352
Technical Description
Regression
PVTi Reference Manual
Trust region
The algorithm only approaches the true solution rapidly if the current estimate xj is close to the
˜
actual solution x∗ . Generally, the objective function at any iteration j is only an approximation
˜
to the true solution. Therefore, it helps to identify a region surrounding the current solution, in
which we trust our second order approximation to model the actual second order problem.
PVTi employs the trust region model by defining a step length, δ c , which is a measure of the
region in which our model can be thought to be representative.
Ideally, the step-size, which is determined automatically subject to certain maximum and
minimum sizes, decreases as the iterations proceed to convergence.
The program uses the value of the current step length to adjust the second order derivative
matrix, so that a zero or small value of δ c causes PVTi to solve the full Newton problem, refer
to [EQ 8.184].
If following the evaluation of a step, the program determines that the objective function would
not decrease, then the algorithm has a procedure for cutting back the step so that it ensures a
decrease in f .
Termination conditions
A variety of termination conditions from the regression algorithm are possible.
Note
The required condition is that the residual goes to some small value, such as 10 –6 , but
this is rarely achieved for larger problems.
An alternative is that the gradient of the objective function goes to zero, indicating that the
regression is approaching a minimum and no further improvement can be expected.
As a result of one or more steps made by the algorithm, one or more of the selected regression
parameters can be pushed out of physical range.
What constitutes a physical range is debatable, but it is suggested that an increase or decrease
in excess of 50% of the original value causes termination. You can change these limits but care
should be taken.
You can request a premature termination by allowing only a small number of iterations, say five
or ten.
Hint
This is a good practice to follow for any regressions which involve several variables,
experiments and observations.
Finally, if any errors are detected in any of the experiments during the regression, then
depending on their nature, the program may terminate the regression.
PVTi Reference Manual
Technical Description
Regression
353
Output for ECLIPSE simulators
General information
Our suite of reservoir simulation software supports five different models for fluid behavior.
There is the ECLIPSE extended blackoil model, the pseudo-compositional model (GI option),
the ECLIPSE compositional model., the ECLIPSE Thermal model and the API Tracking option
used in ECLIPSE BlackOil.
p -V -T
data suitable for use in any of these models can be generated from the PVTi package.
Each of the models and typical output is discussed in the appropriate section.
This section of the manual contains information on:
•
"Blackoil model" on page 354.
•
"Differential and composite from differential tables" on page 359.
•
"Pseudo-compositional tables for ECLIPSE GI option" on page 360.
•
"Compositional data for ECLIPSE Compositional" on page 361.
•
"Water properties" on page 362.
•
"Model for API Tracking option in ECLIPSE BlackOil" on page 363.
•
"Compositional Data for ECLIPSE Thermal" on page 366.
Blackoil model
ECLIPSE has a so-called extended blackoil model. That is, in addition to the standard blackoil
parameters, Rs , B o and B g , it contains the parameter R v for modeling oil vaporization in the gas
stream.
Methods of obtaining black oil tables from compositional data are described by Whitson and
Torp, [Ref. 6] and Coats, [Ref. 3].
In both cases the basis of the method is a constant volume depletion experiment, used to supply
reservoir liquid and vapor compositions at a series of pressures. (In the case of crude oil
samples, a differential liberation process is used in the same way.)
The blackoil model, used by ECLIPSE, can be viewed as a two-component compositional
model. The “components” are stock tank oil and stock tank gas that are assumed to be invariant
and are assigned constant densities.
PVT model
The actual form of the PVT model for the hydrocarbons depends on whether:
354
•
There is or could be liquid and/or vapor in the reservoir during its production.
•
The reservoir phases produce stock tank oil and/or gas on flashing to surface conditions.
Technical Description
Output for ECLIPSE simulators
PVTi Reference Manual
Reservoir fluids
Assuming the stock tank fluids are constant, the reservoir fluids, named liquid and vapor to
distinguish them from the surface fluids which are designated as oil and gas, are generally a
combination of the stock tank fluids.
The amount of surface gas dissolved in the reservoir liquid is given by the Gas-Oil-Ratio
(GOR), denoted Rs , which has units of sm3 /sm3 (metric), mscf/stb (field) or scm 3 /scm 3 (lab).
The volume of surface oil vaporized in the reservoir vapor is given by the Condensate-GasRatio (CGR), denoted Rv , which has units of sm3 /sm 3 (metric), stb/mscf (field) or scm 3 /scm 3
(lab).
The model uses formation factors to account for changes in volume when the fluids are
transferred from the reservoir to the surface. The factors for the liquid and vapor are denoted,
Bo
and Bg , and given units of rm3 /sm 3 (metric), rb/stb (field) or rm3 /sm 3 (lab), and rm3 /sm3
(metric), rb/mscf (field) or rcm 3 /scm 3 (lab), respectively.
The model assumes that the reservoir has been depleted to a pressure below the saturation
pressure (liquid bubble point or vapor dew point) and consequently has become two phase.
One mole of reservoir vapor and liquid occupies the volumes V gr and Vor , respectively. If each
of these volumes are then flashed through some separator system (two stages are indicated
above but this can be variable) to stock tank conditions, then most generally each reservoir
phase partitions into the streams named stock tank gas and oil.
Stock tank components
If the one mole of reservoir vapor, volume V gr , gives N gg moles of stock tank gas of volume Vgg
and N og moles of stock tank oil of volume Vog , whilst the one mole of reservoir liquid, volume
V or , gives N go moles of stock tank gas of volume V go and N oo moles of stock tank oil of volume
V oo , then conservation of mass requires that:
M gr = M og + M gg
[EQ 8.185]
M or = M go + M oo
[EQ 8.186]
where ( M gr, M or ) are the reservoir molar masses and ( M og, M gg ) , ( M go, M oo ) are the corresponding
actual surface masses after flashing.
Since ρ = M ⁄ V , we can write equations [EQ 8.185] and [EQ 8.186] as:
ρ gr V gr = ρ og V og + ρ gg V gg
[EQ 8.187]
ρ or V or = ρ go V go + ρ oo V oo
[EQ 8.188]
or:
1
ρ gr = ------ ( ρ gg + R v ρ og )
Bg
[EQ 8.189]
1
ρ or = ------ ( ρ oo + R s ρ go )
Bo
[EQ 8.190]
where:
V go
R s = -------V oo
PVTi Reference Manual
V og
R v = -------V gg
[EQ 8.191]
Technical Description
Output for ECLIPSE simulators
355
V or
B o = -------V oo
Note
V gr
B g = -------V gg
[EQ 8.192]
Strictly, the blackoil model requires that the stock tank “components” are constant and
invariant with time.
CVD process
In the Coats method, only the reservoir vapor is taken through the separator, the oil B o and R s
values being obtained by solving the mass conservation equations:
ρ sto V 2 ( b g S g + b o R s S o ) 2 = ρ sto V 1 ( b g S g + b o R s S o ) 1
[EQ 8.193]
ρ stg V 2 ( b g R v S g + b o S o ) 2 = ρ stg V 1 ( B g R v S g + b o S o )1
[EQ 8.194]
for each expansion step of the CVD process from V 1 to V2 , where ρ sto and ρ stg are fixed surface
densities, and b o = 1 ⁄ Bo , b g = 1 ⁄ B g .
The stock tank densities are obtained from the output of the separators at the saturation pressure.
Solving these equations yields values at all pressures except the saturation pressure, at which
the Whitson method can be used.
Alternatively, a small initial pressure step from the saturation pressure may be specified.
Note
The constant volume expansion method is usually applied to condensates, but can also
be used for volatile oils.
Differential liberation
The differential liberation approach is only suitable for oils.
In this case, the analogue of the Whitson method runs both reservoir oil and vapor through the
separators as before.
The analogue of the Coats method uses the conservation equations, [EQ 8.193] & [EQ 8.194]
(although in this case S g1 is zero for each step), ρ sto and ρ stg are obtained from the reservoir oil
at the saturation pressure.
ECLIPSE 100 tables
For both processes, you can produce the ECLIPSE live oil, wet gas, dead oil and dry gas tables.
The respective keywords are PVTO, PVTG, PVDO, and PVDG.
In addition, the model calculates the density of the oil, water and gas phases at stock tank
conditions (final stage separator) for the saturation point fluid, and output under the DENSITY
keyword. These values are important as the reservoir properties are calculated using the R s , Rv ,
B o , B g from the stock tank volumes and densities.
Hint
356
The "Choosing the unit type for PVTi" on page 144 program option gives you a choice
of outputting and plotting all the data (saturated and undersaturated) or just the
saturated data.
Technical Description
Output for ECLIPSE simulators
PVTi Reference Manual
An example of a typical set of blackoil data (for a volatile oil fluid) is shown below:
-- Blackoil tables for sample ZI at T = 176.00000 deg F
-- With Peng-Robinson (three-parameter) EoS
-- And Lohrenz-Bray-Clark viscosity correlation
-- ECLIPSE 100 DENSITY data
-- Surface densities of oil, water and gas:
-- Units of FIELD
DENSITY
50.74699
62.42797
0.05842 /
-- Two stage separator at
-- Pressures
214.69590
14.69590
-- Temperatures
100.00010
60.00001
-- Pressures in PSIA
Temperatures in deg F
--ECLIPSE 100 PVTG data
--(Constant volume depletion)
--Units are FIELD
--Method used: Whitson and Torp
PVTG
-PRES
RV
BG
VISC
-PSIA
STB/MSCF
RB/MSCF
CPOISE
1114.69590
0.00099
2.43709
0.0139554
--Saturated
0.00000
2.43919
0.0139489
/ --Dry gas
1814.69590
0.00276
1.43004
0.0166381
--Saturated
0.00099
1.43350
0.0165733
--Undersat gas
0.00000
1.43543
0.0165380
/ --Dry gas
2514.69590
0.00736
1.02359
0.0206166
--Saturated
0.00276
1.02929
0.0202678
--Undersat gas
0.00099
1.03150
0.0201382
--Undersat gas
0.00000
1.03272
0.0200669
/ --Dry gas
3214.69590
0.01695
0.82309
0.0257392
--Saturated
0.00736
0.82851
0.0246867
--Undersat gas
0.00276
0.83111
0.0242117
--Undersat gas
0.00099
0.83211
0.0240316
--Undersat gas
0.00000
0.83267
0.0239322
/ --Dry gas
3914.69590
0.03492
0.71605
0.0321610
--Saturated
0.01695
0.71725
0.0297284
--Undersat gas
0.00736
0.71789
0.0285431
--Undersat gas
0.00276
0.71820
0.0279877
--Undersat gas
0.00099
0.71831
0.0277758
--Undersat gas
0.00000
0.71838
0.0276584
/ --Dry gas
4077.56801
0.04108
0.69977
0.0339734
--Psat
0.03492
0.69960
0.0329685
--Undersat gas
0.01695
0.69910
0.0306120
--Undersat gas
0.00736
0.69884
0.0293996
--Undersat gas
0.00276
0.69871
0.0288303
--Undersat gas
0.00099
0.69867
0.0286129
--Undersat gas
0.00000
0.69864
0.0284924
/ --Dry gas
PVTi Reference Manual
Technical Description
Output for ECLIPSE simulators
357
4614.69590
0.04109
0.65591
0.0368566
--Generated
0.03492
0.65447
0.0357868
--Undersat gas
0.01695
0.65029
0.0332692
--Undersat gas
0.00736
0.64806
0.0319664
--Undersat gas
0.00276
0.64699
0.0313522
--Undersat gas
0.00099
0.64658
0.0311171
--Undersat gas
0.00000
0.64635
0.0309867
/ --Dry gas
--ECLIPSE 100 PVTO data
--(Constant volume depletion)
--Units are FIELD
--Method used: Whitson and Torp
PVTO
-RS
PRES
BO
VISC
-MSCF/STB PSIA
RB/STB CPOISE
0.49137
114.6959 0.34107 0.30770
--Saturated
1814.69590 1.32574 0.33605
2514.69590 1.31260 0.36369
3214.69590 1.30116 0.39067
3914.69590 1.29106 0.41705
4077.56801 1.28887 0.42310
4614.69590 1.28206 0.44285
/
0.79978
1814.69590 1.49404 0.23723
--Saturated
2514.69590 1.47369 0.26054
3214.69590 1.45641 0.28344
3914.69590 1.44147 0.30594
4077.56801 1.43827 0.31112
4614.69590 1.42836 0.32808
/
1.16269
2514.69590 1.67183 0.18640
--Saturated
3214.69590 1.64551 0.20520
3914.69590 1.62331 0.22377
4077.56801 1.61862 0.22806
4614.69590 1.60421 0.24214
/
1.63520
3214.69590 1.90440 0.14692
--Saturated
3914.69590 1.87000 0.16174
4077.56801 1.86286 0.16517
4614.69590 1.84116 0.17646
/
2.34029
3914.69590 2.25803 0.11383
--Saturated
4077.56801 2.24611 0.11645
4614.69590 2.21050 0.12507
/
2.56913
077.56801 2.37483 0.10661
--Psat
4614.69590 2.33394 0.11462
/
2.66303
4614.69590 2.37492 0.10622
--Generated
5151.82379 2.33402 0.11423
/
/
Both the PVTO and PVTG tables are extended to include properties of the undersaturated oil and
gas, respectively.
In the case of the PVTG table the model computes, at all values of Rv between the saturated
value and the dry gas value ( Rv = 0.0 ), a value for Bg by adding sufficient stock tank oil to the
stock tank gas (both from the flash of the saturated gas to stock tank) to give the required R v and
then taking the ratio of this fluid's volume at reservoir and stock tank volumes.
358
Technical Description
Output for ECLIPSE simulators
PVTi Reference Manual
In the case of the PVTO table, the model compresses the saturated fluid from a given Rs node at
all pressures from the saturated pressure up to the highest pressure. The ratio of these volumes
to the resulting stock tank oil volume (from flashing the saturated oil) gives the undersaturated
B o values.
Monotonicity and compressibility tests
If you specify a highest pressure that is higher than the saturation pressure fluid, then PVTi
increases the saturated pressure of the sample to a value above the maximum pressure used in
the depletion experiment by mixing the sample with a lighter gas sample.
The gas sample used is the vapor split-off obtained from performing a p sat calculation on the
original sample.
The model mixes this vapor with the sample and performs a new p sat calculation on the new
sample.
It then mixes the resulting vapor split off with the new sample and repeats the process until a
p sat forms that is higher than the maximum pressure stage. If this process is successful you can
save the final sample and use it in the calculation of the black oil tables.
Alternatively if you do not want to swell the sample, PVTi allows you to select to truncate the
blackoil tables at the saturation pressure.
Note
Oil and gas properties below the saturation point generated as described above are also
subjected to the ECLIPSE total compressibility test.
Note
If negative compressibilities are detected, PVTi (with confirmation) solves for
intermediate points, which provide the necessary resolution to pass the compressibility
test.
Differential and composite from differential tables
As an alternative to the composite tables described above, you can produce a differential black
oil table.
This technique involves simulating a differential liberation experiment, and the values of Bo and
R s are taken to be the normal definitions of oil formation volume factor and gas-oil ratio,
respectively, as defined in this experiment.
Note
These definitions are detailed in the manual (refer to "Basic laboratory experiments"
on page 339 and "Gas condensate systems" on page 341, and to equations [EQ 8.171]
and [EQ 8.173]). The quantities are known here as B Do and RDs .
From these differential quantities, it is possible to estimate composite values of Bo and R s using
a number of formulae.
Two of the more popular methods are due to Moses, and Fragor [Ref. 40] (both now termed CM
and CF respectively).
PVTi Reference Manual
Technical Description
Output for ECLIPSE simulators
359
Both methods start by estimating a value for Bo and R s at the saturated pressure ( p sat ) of the
CM
initial oil. This oil is passed through a separator chain and the values of B CF
o ( p sat ) and B o ( p sat )
are given by the oil formation volume factor from the separator. Likewise the values of R CF
s ( p sat )
and RCM
s ( p sat ) are given the value of the gas-oil ratio from the separator.
Once these two values are computed, the rest of the values from the lowest pressure up to psat
are found from the following formulae.
Firstly the Fragor definitions:
CF
D
( B o ( p sat ) – 1 ) ( B o ( p ) – 1 )
CF
B o ( p ) = 1 + ----------------------------------------------------------------D
( B o ( p sat ) – 1 )
[EQ 8.195]
and
CF
D
R s ( p sat )R s ( p )
CF
R s ( p ) = -------------------------------------D
R s ( p sat )
[EQ 8.196]
The Moses expressions are given by:
CM
D
B o ( p sat )B o ( p )
CM
B o ( p ) = --------------------------------------D
B o ( p sat )
[EQ 8.197]
and
CM
 B o ( p sat )
CM
CM
D
D
-
R s ( p ) = R s ( p sat ) – ( R s ( p sat ) – R s ( p ) )  ---------------------- BD

o ( p sat )
[EQ 8.198]
PVTi can provide all four types of black oil output, that is, the usual composite, the differential,
and the two composite from differential tables.
Note
The output form for the differential and composite from differential tables is by way
of the PVTO/PVDO and PVDG keywords only.
Pseudo-compositional tables for ECLIPSE
GI option
At pressures less than the saturation pressure, psat , compositional effects become important.
Limitations of the ECLIPSE blackoil model
360
1
The blackoil approximation, discussed in the previous section, models compositional
changes by making the parameters, Rs , B o , R v , and B g all functions of pressure, which it
determines from the reservoir and surface properties of the liquid and vapor phases.
2
The extended blackoil treatment, that is variable R v as available in ECLIPSE, cannot model
gas injection into condensates at pressures less than psat , without careful consideration (see
keyword VAPPARS in the "ECLIPSE Reference Manual"). Lean gas injected into a
saturated reservoir fluid causes the stripping of the light and intermediate components from
the reservoir fluid, resulting in an enriched gas phase and a depleted liquid phase.
Technical Description
Output for ECLIPSE simulators
PVTi Reference Manual
3
To model this process accurately requires a detailed fluid description and the use of a fully
compositional simulator using a many-component model of the fluid. However, such is
generally impractical, especially using a fully implicit formulation since the number of
equations, which need to be solved increases with the product of the number of components
and the number of gridblocks.
ECLIPSE GI option
One possible solution to this problem is to extend the three-parameter blackoil model as used in
ECLIPSE BlackOil, that is p , S w and So , by adding a fourth parameter/equation.
In the ECLIPSE pseudo-compositional model, this fourth parameter, denoted GI, is the
cumulative gas volume, which has passed over the volume of reservoir liquid in a gridblock. As
such, GI is equivalent to a gas-oil ratio of volume of injection gas at standard conditions to
volume of oil at reservoir conditions:
gas
V stc
GI = --------oil
V res
[EQ 8.199]
This model determines the oil volume at reservoir conditions, V oil
res , for the first stage of gas
addition, from the GI=0.0, that is the standard blackoil model. It then calculates the gas volume
at standard conditions, Vgas
stc , from the gas law:
add
n ZRT stc
gas
V stc = -------------------------p stc
[EQ 8.200]
where n add is the number of moles of gas added. By convention, at standard pressure and
temperature, p stc = 14.7 psia, T stc = 60.0 °F , and the gas-compressibility factor, Z = 1 .
Having defined a Constant Volume Depletion (CVD) experiment and a separator network with
the last stage corresponding to stock tank conditions, the model then performs a calculation of
the conventional extended blackoil tables. This defines the GI=0.0 data.
It then adds lean gas to the reservoir fluid in a series of stages and generates the blackoil table
with the mixture. The ratio of the non-zero GI blackoil properties and the GI=0.0 properties
defines a set of GI-multipliers. This gives a two-dimensional set of tables in ( p , GI) to describe
the fluid behavior.
Detailed evaluations of the model’s performance have been undertaken and with favourable
conditions and tuning against a full compositional treatment, this model can give reliable
predictions.
Compositional data for ECLIPSE Compositional
You can run ECLIPSE Compositional in one of three modes:
•
Blackoil - As ECLIPSE 100
•
K -value
•
Compositional - Equation of state.
- Specify K -values at given pressures
It is envisaged that generally you will want to run ECLIPSE Compositional in compositional
(Equation of State) mode.
PVTi Reference Manual
Technical Description
Output for ECLIPSE simulators
361
However, in blackoil mode, ECLIPSE 300 reads the same PVTO and PVTG tables as used in
ECLIPSE BlackOil.
In K -value mode, you must specify a set of K -values for each component at a set of pressures
spanning the operating pressure region. You can generate these, as in PVTi, by performing a
CVD experiment on the reservoir fluid.
Compositional mode
The Equation of State mode is essentially the same as that employed by PVTi for its flash,
saturation pressure, etc., calculations.
You must specify the number of components, the Equation of State required (the same set as
available in PVTi), and the critical properties, acentric factors, binary interaction coefficients,
compositions, etc.
Clearly, the more components used, the more accurate the simulation (assuming the component
set has been optimised to measured data); however, such simulations require more CPU time.
Hint
If running ECLIPSE Compositional in fully implicit mode, more than six or seven
components may become prohibitive for all but the largest of supercomputers or
workstations, in which case you should consider pseudoisation of this fluid system to
fewer components.
Water properties
ECLIPSE and VFPi consider water to be non-volatile (only exists as liquid water) and
immiscible with the hydrocarbon phases (water cannot dissolve in the hydrocarbons or viceversa). This simplifies the PVT treatment of water.
If water is present, the variation of water volume in the reservoir with pressure, V w ( p ) , is defined
with respect to the volume of water at surface conditions, Vstw , by the formation volume factor,
B w , where:
Vw ( p )
B w ( p ) = --------------V stw
[EQ 8.201]
which has units of rm3 /sm 3 (metric), rb/stb (field) or rcm3 /scm3 (lab).
Note
Note that VFP only supports metric and field units.
Within the models, B w is defined in terms of the Bw at some reference pressure, p ref :
B w ( p ref )
B w ( p ) = ----------------------------2
(1 + X + X )
[EQ 8.202]
where
X = C w ( p – p ref )
[EQ 8.203]
and C w is the water compressibility which is defined as:
1 dB w
C w = – ------  ---------
B w  dp  p = pref
362
Technical Description
Output for ECLIPSE simulators
[EQ 8.204]
PVTi Reference Manual
that has units of barsa–1 (metric), psia –1 (field) or atmos–1 (lab).
Water viscosity is modeled in the same way as the formation volume factor:
μ w ( p ref )
μ w ( p ) = ---------------------------2
(1 + Y + Y )
[EQ 8.205]
where
[EQ 8.206]
Y = C μw ( p – p ref )
and C μw is the water viscosibility which is defined as:
1 dμ w
C μw = – ------  ---------
μ w  dp  p = p ref
[EQ 8.207]
that also has units of barsa–1 (metric), psia –1 (field) or atmos–1 (lab).
An additional complication can arise if the effect of salt (brine) concentration is to be modeled
(ECLIPSE BlackOil and GI option only). See the keyword PVTWSALT in the "ECLIPSE
Reference Manual" for further details in this case.
Note
Correlations for generating default values for all the above correlations can be found
in [Ref. 33].
Model for API Tracking option in ECLIPSE
BlackOil
For further information on the ECLIPSE keywords referenced in this section see the "ECLIPSE
Reference Manual".
Introduction
The API Tracking facility enables ECLIPSE BlackOil to model the mixing of different types of
oil, having different surface densities and PVT properties.
Without the API Tracking facility, the presence of different types of oil in the reservoir could be
handled with the aid of PVT region numbers. Oil in PVT region 1 would have its properties
determined from PVT table number 1, and so on. However, this method cannot model the
mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on the
properties associated with region 2.
The API Tracking facility essentially replaces the concept of PVT regions for oil. The PVT
tables used for determining the oil properties are selected at each time step according to the
average API of the oil in each grid block (or to be more precise, its average surface density). A
mass conservation equation is solved at the end of each time step to update the oil surface
density in each grid block, to model the mixing of the different oil types.
When using ECLIPSE BlackOil, the API Tracking facility is turned on by the keyword API in
the RUNSPEC section. In dead oil systems the keyword RSCONSTT cannot be used with API
tracking, but RSCONST (defining a uniform Rs value over the whole field) can be used.
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Using PVTi to Export the Tables
PVTi can be used to export the black oil tables in the required form outlined in the next few
sections. Simply open the Export Panel for API Tracking option panel by using File | Export
| API Tracking option in ECLIPSE BlackOil....
The user needs to select the samples for which the export is required. This is done by selecting
a set of samples and dropping them in the use box. Next, the required keywords to export need
to be specified in the normal way.
Hint
Since the API Tracking functionality in ECLIPSE models the mixing of live oil
properties the usual procedure in PVTi is to use the API Tracking export facility to
write out a series of tables containing the PVTO (live oil) and PVDG (dead gas).
You can then specify whether they want a gas table for each sample. Normally the API Tracking
option in ECLIPSE only uses a different oil table for each sample and just a single gas table is
used, as explained in the next section, and so this is the default. If this default option is used then
PVTi exports a single gas table for the sample with the median gas density at surface conditions.
The separator and units to use for the export can be specified in the normal way. You can also
specify a few other straightforward options such as whether to write to full double precision and
whether to plot the tables.
When the export is performed PVTi orders the tables so that the oil surface densities increase
monotonically with table number, which is a requirement of ECLIPSE. Each table also has
comments associated with it specifying which sample the table is linked to and what the oil
surface density is for this particular table.
ECLIPSE requires that the Rs ranges of any live oil tables are the same. To ensure this is the
case PVTi analyzes all the samples you selected and calculates the Rs at the maximum pressure
in the DL experiment. PVTi then finds the sample with the maximum Rs and then uses linear
extrapolation to extend the black oil tables of the other samples so that the Rs ranges for all the
samples are the same.
See the next few sections for technical details of ECLIPSE’s API Tracking option.
The PVT properties
Two or more sets of PVT tables should be supplied, each set being associated with a particular
value of the API. The oil property tables are entered in the usual way (with keyword PVTO or
PVCO for live oil problems, or keyword PVDO for dead oil problems), but with the requirement
that all the PVTO or PVCO tables must have the same upper and lower Rs values. From these
tables, ECLIPSE constructs a set of internal tables that have a common set of Rs nodes, which
includes the Rs nodes of all the input tables. This allows ECLIPSE to use an efficient method of
interpolating between tables, for intermediate values of the API. The restriction that the upper
and lower Rs values must be the same for each table prevents extrapolation of the input data
during this process, which may cause unphysical behavior.
The API values associated with each PVT table are set using the keyword GRAVITY, which
inputs the oil, water and gas gravities for each PVT table number. The API values are converted
internally to oil surface densities, using the formula given in "Conversion factors" on
page 1236. The oil API values must decrease monotonically with the table number.
Alternatively the surface densities associated with each table number can be input directly using
the keyword DENSITY. In this case the oil surface densities must increase monotonically with
the table number.
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The PVT properties of water and gas are not affected by the API Tracking option. The same
number of tables must be entered in all the PVT data keywords and the ROCK keyword, but
normally only the first table is actually used in all except the oil PVT data. The unused PVT and
rock compressibility tables can be defaulted by typing a single slash (/) on a new line for each
unused table in the keyword.
Grouping tables into PVT regions
The API Tracking facility over-rides the concept of PVT table regions for oil. The tables used
to determine the oil PVT properties are selected according to the surface density of the oil in the
grid block, instead of the block’s PVT region number. Thus the PVTNUM keyword in the
REGIONS section is not normally required with the API tracking facility.
If however the concept of PVT regions for different types of oil is still required in an API
Tracking run, the oil PVT tables can be partitioned into groups for use in different regions of the
reservoir. The keyword APIGROUP must be entered, to specify the maximum number of groups
of oil PVT tables. The grouping of the oil PVT tables is then determined by the order in which
they are entered. Within each group, the oil API gravities should decrease (or the oil surface
densities should increase) monotonically with the table number. A break in the required
monotonicity is taken to indicate that the subsequent tables belong to the next API group. An
error is flagged if the total number of API groups exceeds the maximum specified in the
APIGROUP keyword.
The separate groups of oil PVT tables can then be used in different areas of the reservoir. The
REGIONS section keyword PVTNUM is used to specify which API group is to be used for each
grid block. For example, a cell in PVTNUM region 2 will use the second API group to obtain the
oil properties.
For water and gas PVT properties, the PVTNUM regions correspond to the actual table numbers,
as in runs that do not use API tracking. So a cell in PVTNUM region 2 still uses table number 2
for its water and gas properties.
Setting the initial conditions
The initial API distribution throughout the reservoir is specified in the SOLUTION section. If
the initial conditions are determined by equilibration, the API can vary with depth
independently in each equilibration region. Keyword APIVD supplies a table of API values
versus depth for each equilibration region.
When setting the initial conditions by enumeration (keywords PRESSURE, SWAT etc.), the
keyword OILAPI is used to supply the initial API values for each grid block.
The API tracking calculation
The initial API values in the grid blocks are immediately converted into oil surface density. The
hydrostatic pressure gradient calculation takes account of the varying surface density of the oil.
The variation of other PVT properties with surface density (bubble point pressure, formation
volume factor and viscosity) is handled by interpolating between PVT tables. The two adjacent
PVT tables whose oil surface densities straddle the oil surface density value in the grid block
are located, and their properties ( 1 ⁄ B o , 1 ⁄ ( Bo μo ) ) are interpolated linearly in oil surface density.
To calculate the bubble point, the two PVT tables corresponding to oil surface gravities either
side of the current grid block API value are located. The bubble point is then obtained by
linearly interpolating between the bubble points in these PVT tables at the given grid block
dissolved gas-oil ratio.
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The oil surface density in each grid block and well is held constant over the time step. When a
converged solution for the time step has been found, and the inter-block flows determined, a
mass conservation equation is solved to update the oil surface densities. The new densities are
used in the next time step.
The oil surface densities are converted back into API values for the output reports. The
mnemonic OILAPI in the RPTSCHED keyword provides an output of the grid block API
values, and the well reports include the API values in the wells.
API tracking in wells
The oil surface density in each well is calculated at the end of the time step to reflect a flowweighted average surface density of the inflowing oil. A crossflowing well will reinject oil of
this average surface density back into the formation. However, the hydrostatic head calculation
in the wellbore will be based on a (more accurate) flow-weighted average of upstream
connection inflows if WELSPECS item 12 is ‘SEG’, allowing the oil density to vary with
position in the wellbore. (The pre-98A treatment of wellbore hydrostatic head, which uses the
well’s average oil surface density, can be restored if required by setting switch 35 in the
OPTIONS keyword.)
If the well uses a VFP table to calculate the tubing pressure losses, this should be calculated
using a suitable value of the oil surface density. However, it is possible to take account of the
variation of the well’s producing API over time by defining the fifth lookup variable, the ALQ,
to represent the surface density of the produced oil (see keyword WALQCALC). The VFP table
should be prepared using the same definition of the ALQ, with values spanning the expected
range of oil surface densities. The VFPi program contains an option to prepare tables with
variable oil surface density.
Behavior in wet gas systems
By default, in wet gas systems, the surface density property (API) of the oil is transported in
both the oil and gas phases, that is the API is interpreted as a property of the oil component
rather than the liquid oil phase.
By using OPTIONS switch 58 this behavior can be modified. When the switch is set greater
than zero the API property will only be transported in the liquid oil phase. In this case the API
property can be thought of as a heavy component which does not vaporize. Care needs to be
taken when using this option as it is possible to vaporize all the oil in a cell, leading to high
surface densities and negative API values.
Compositional Data for ECLIPSE Thermal
Introduction
This introduction contains a brief outline of the reason for the introduction of this module.
366
•
"Outline of keywords for ECLIPSE Thermal" on page 367 contains a brief description of
the keywords exported.
•
"Workflow" on page 368 section gives step-by-step instructions of how to perform a typical
export for use in ECLIPSE Thermal.
•
"Some handy hints for fitting the Crookston coefficients" on page 369 gives some hints and
tips on how to export Crookston coefficients that provide accurate approximations to
PVTi’s EoS K-values.
Technical Description
Output for ECLIPSE simulators
PVTi Reference Manual
For the 2003A version of PVTi a new ECLIPSE Thermal support module was available where
you were able to interactively develop a correlation which accurately predicted K-values for
each component in a given fluid. For the 2004A version this module has been extended to a full
export facility where you can write out files that are suitable for use as PVT input for ECLIPSE
Thermal. The motivation behind this is so that, just as you can export files to use as PVT input
for ECLIPSE BlackOil and ECLIPSE Compositional, they will now be able to do the same for
ECLIPSE Thermal.
When you use this new export facility, they now have a choice of keywords to export regarding
K-values - namely the KVCR keyword (which was available in 2003A PVTi) or the KVWI
keyword which is tells ECLIPSE Thermal to use a simplified version of Crookston’s equation
called Wilson’s formula. In addition PVTi also exports a series of other keywords enabling
ECLIPSE Thermal to calculate properties of the feed fluid such as oil density, gas density and
oil/gas phase enthalpies.
For a technical description of how these keywords exported by PVTi are used in ECLIPSE
Thermal see "ECLIPSE Thermal Export Module" on page 401. For a summary and brief outline
of the nature of these keywords see the next section.
Outline of keywords for ECLIPSE Thermal
1
STCOND - the standard temperature and pressure used in PVTi
2
NCOMPS - the number of components in the fluid.
3
CNAMES - the names of each component.
4
MW - the molecular weight of each component.
5
TCRIT - the critical temperature of each component.
6
PCRIT - the critical pressure of each component.
7
TREFT - the ECLIPSE Thermal reference temperature at which the reference density,
DREFT, is calculated.
Note
In general the quantities TREFT, PREFT, DREFT are not the same as the related
quantities of reference temperature, TREF and references density, DREF used in
PVTi. Please see
8
ACF - the acentric factors of the components.
9
SPECHA - oil phase specific heat first coefficients.
10 SPECHB - oil phase specific heat second coefficients.
11 SPECHG - gas phase specific heat first coefficients.
12 SPECHH - gas phase specific heat second coefficients.
13 HEATVAPS - heats of vaporization at the standard temperature.
14 CREF - component isothermal compressibilities in the oil phase.
15 THERMEX1 - component thermal expansion coefficients in the oil phase.
16 ZFACTOR - the gas Z factor for each component.
17 KVWI - tells ECLIPSE Thermal to use Wilson’s formula to estimate K-values.
18 KVCR - tells ECLIPSE Thermal to use Crookston’s equation to estimate K-values. This
keyword contains the values of the coefficients (A-E) for each component.
19 ZI - the feed mole fractions of each component
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The keywords STCOND, SPECHA, SPECHB, SPECHG, SPECHH, HEATVAPS, CREF,
THERMEX1, ZFACTOR, KVWI and KVCR are only exported for ECLIPSE Thermal and not for
ECLIPSE Compositional. See "ECLIPSE Thermal Export Module" on page 401 for a technical
description of how the values contained in these keywords are used to calculate K-values, oil/
gas densities and oil/gas enthalpies for each component.
Workflow
1
To access the Thermal Support module select Edit | Samples | ECLIPSE Thermal
Support | Export for ECLIPSE Thermal.... Alternatively right- click on a fluid sample
of interest and select Export ECLIPSE Thermal Model....
2
In the panel type in the maximum and minimum values of the pressure in your reservoir
and also the maximum and minimum temperature.
3
Select the sample you wish to export the model for by using the drop-down menu.
4
You need to decide if you want to estimate K-values in ECLIPSE Thermal using
Crookston’s equation or using Wilson’s formula. Wilson’s formula gives much less
accurate results than Crookston’s formula but if you have time constraints then much less
work is involved in exporting this information from PVTi. If you want to use Wilson’s
formula then your work is finished and you do not need to go though steps 5-12. Simply
select which units you want to export and click OK.
Hint
If you have time and you know the rough limits on temperature and pressure within
your reservoir then Crookston’s equation will, in general, give you much more
accurate estimates of K-values than Wilson’s formula.
5
If you want to export coefficients for Crookston’s equation then tick the box entitled Export
Crookston Coefficients?
6
Now enter how many flashes you want to perform.
Unless you have very large ranges in temperature or pressure in your reservoir then the
default of 20 is probably fine. These flashes generate K-values using PVTi’s EoS algorithm
at random points in the region defined by your maximum pressure and temperature. The
generated K-values are the “observations” used when trying to optimize the values of the
coefficients in Crookston’s equation.
7
Click the Fit Crookston Coefficients button.
Another panel opens.
8
Select the coefficients to optimize. As a rule always start with B and D or A,B and D. Now
click Apply and PVTi attempts to use a minimization algorithm to calculate the best values
of your chosen coefficients that gives the most accurate prediction of K-values for each
component.
9
Once PVTi has finished a results window opens with two folders. The Coefficients folder
enables you to see the coefficient values derived by PVTi for each component. The
Statistics folder enables you to observe the mean rms of the fit (in %) and the standard
deviation (in %) of the fits for each component over the specified temperature and pressure
range.
10 To view your fit click View Fit on the Fit Crookston Coefficients panel. Another panel
opens. You are able to view the results by plotting K-values as a function of temperature (at
constant pressure) or pressure (at constant temperature). Type in the appropriate
information and click Apply.
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11 PVTi now show you the observations it was fitting to for each component, that is the Kvalues found using the Equation of State based flash (the points) and the curves, which are
the predictions of the K-values found using Crookston’s formula.
12 Once you are happy with your results close the Fit Crookston Coefficients panel and click
OK on the Export for ECLIPSE Thermal panel. A File | Save panel opens. Choose the
name of the file you want to save it as and click Enter. A text file is created and shown in
the output display containing the exported keywords. This file can be used as the PVT input
in an ECLIPSE Thermal simulation.
Note
The default file extension when exporting for ECLIPSE Thermal is .PVO. The save
panel assumes you want to call your exported file filename.PVO where
filename.PVI is the name of your PVTi project file.
See the next section for some hints on performing the optimization of the Crookston
coefficients.
Some handy hints for fitting the Crookston coefficients
The goal of this optimization is to allow you to interactively develop a correlation that
accurately predicts K-values for each component in a given fluid over a specified range of
temperature and pressures. The functional form of the correlation used by PVTi is given by
Crookston’s equation which is:
B
–D
K ( P, T ) =  A + --- + CP exp  -------------


 T – E
P
[EQ 8.208]
You are able to specify which coefficients to use in equation [EQ 8.208] (as already explained
in the previous section) and PVTi calculates the values of these coefficients which give the best
fit to the PVTi flash for each component over the pressure and temperature range. The following
things may help you in your workflow:
1
Try doing a phase curve first of your fluid to get an idea of the pressure and temperature
range where your sample is two-phase. PVTi does not use any regions of pressuretemperature space where the fluid is single phase.
2
When choosing the values of the max/min temperature and pressure consider the following:
3
PVTi Reference Manual
a
The default values of Pmax=1000psia, Pmin=50psia, Tmax=400F and Tmin=50F are
considered to be reasonable variations of conditions within a reservoir.
b
Make sure you alter these values to suit your particular reservoir. Try to make the
region that is defined by your values as small as possible. For example if you think that
the maximum temperature in your reservoir is going to be 300F then do not leave the
default value in the panel (400F).
c
If the region you define is too big then Crookston’s formula may have trouble getting
good fits to the EoS based K-values. This is because K-values are really a function of
the fluid composition as well as the pressure and temperature. See "K-Values" on
page 401 for an explanation of why this is so.
The number of flashes variable is set by default to 20. PVTi randomly throws this number
of points into your defined region and flashes are performed at each (P,T) coordinate in
order to obtain K-values. These are the observations. You are probably fine using 20 as this
value. If your region is particularly big (which is not recommended) then you may want to
increase this. By the same token, decreasing this value will speed up the calculations
significantly, but the fits may be less accurate.
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369
4
The A and D coefficients are turned on by default. You can turn them off if you want to but
experience shows that you will almost always need them to get the best fits to the
observations. In theory, turning all of the coefficients on should give the best fits. In
practice, although you will do this most of the time, you will find:
a
this slows the application down as it increases the parameter space to search. If you
want to get a feel for how the module works start with A, B and D turned on.
b
the algorithm finds the nearest local minimum of the objective function. This may not
be the global minimum. PVTi uses an intelligent guess and the idea is that it starts in
the parameter space reasonably close to the global minimum so that this is the nearest
local minimum. When all 5 coefficients are switched on this initial guess technique is
not always guaranteed to give as good a guess as when less coefficients are selected.
5
When you view the fits, check to see how good they are when you use a constant value of
temperature that is halfway between the maximum and the minimum one. In theory the
pressure part of Crookston’s equation should show the best fit here. If the functional form
of the line plots looks wrong for even a single component then you probably need another
pressure coefficient in order to match all the components for this particular fluid. Check in
the same way for the temperature part of Crookston’s equation and turn E on as well if the
D coefficient is having trouble fitting the observations
6
In terms of the rms values you should expect in the fits, this depends on how large a region
you define and how many components are in your fluid. If the region is, say 1000 psia high
and 200K wide, then you should expect fits on the observations of 2-3% on average.
For more technical information on the ECLIPSE Thermal export facility see "ECLIPSE
Thermal Export Module" on page 401.
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Analysis techniques
Introduction
•
"Recommended PVT analysis for oil reservoirs" on page 372.
•
"Recommended PVT analysis for gas condensate reservoirs" on page 377.
•
"Consistency tests and correlations" on page 381.
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Technical Description
Analysis techniques
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Recommended PVT analysis for oil reservoirs
Oil reservoirs
Oil reservoirs have been divided into three classes in the following discussion:
Under-saturated reservoirs
Refers to those reservoirs that are under-saturated not only at the time of their discovery but also
throughout their development.
Note
This class does not include reservoirs whose pressures fall below the bubble point at
some time during their development, or reservoirs that are subject to gas injection.
Under-saturated reservoirs can be represented by two-phase (oil and water) simulation models,
usually using the black oil formulation. For further information see "Under-saturated
reservoirs" on page 374.
Saturated black oil reservoirs
Refers to those reservoirs whose pressures fall below the bubble point somewhere in the oil
column during development, but that can be modeled sufficiently accurately using the black oil
formulation.
Note
All reservoirs with initial gas-caps are regarded as saturated (but may not be
adequately represented by the black oil formulation).
For further information see "Saturated blackoil reservoirs" on page 375.
Volatile oil reservoirs
Refers to those reservoirs in which phase behavior effects are important. These generally
require extensive use of a PVT program and compositional modeling for accurate
representation.
Note
Volatile oil usually refers to a reservoir fluid whose critical temperature is only slightly
above the reservoir temperature under initial conditions.
For further information see "Volatile oil reservoirs" on page 376.
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Black oil or compositional simulation
You can generate both black oil tables (for black oil simulation) and equation of state data (for
compositional simulation) using the PVTi package. In some cases you can generate black oil
tables from laboratory results alone, rather than using the full equation of state model. See
"COMB - Compositional Material Balance" on page 112 and "COMB section keywords" on
page 159.
Oil reservoirs
Almost all under-saturated reservoirs, and most saturated oil reservoirs where the reservoir fluid
has a critical temperature far above the reservoir temperature, do not normally require the
complexity of compositional simulation, and a black oil formulation is normally of sufficient
accuracy.
Note
Such a formulation does not allow the stock tank oil density or gas density to vary with
time.
You may wish to consider using compositional simulation if miscible or semi-miscible
processes are involved.
Volatile oil reservoirs
For volatile oil reservoirs it may be possible to obtain some sort of approximation to reservoir
fluid behavior during depletion using a black oil formulation, providing that this has been
modified to allow the gas phase to contain some vaporized oil (variable Rv ).
In general, however, a compositional simulation is required for accurate treatment. This applies
even for depletion of the reservoir.
A compositional approach is essential for reservoirs where gas injection is planned.
Compositional grading with depth
Many oil reservoirs exhibit some kind of grading of fluid properties with depth.
If you use the black oil formulation, then you can often represent the effects of this grading by
a variation of solution gas-oil ratio with depth.
However, if the stock tank oil API varies with depth, and it is necessary to model the variation
of API with time, then you should use a variable oil API option in the black oil runs.
Where part of the fluid column is near critical conditions you would use an initial compositional
gradient with depth in a compositional simulation.
Some reservoirs may grade from a gas condensate to a volatile oil without an initial phase
transition or contact of any kind. Others may have gas-liquid or even liquid-liquid interfaces.
You can simulate this process with the COMPG experiment in PVTi. One of the quantities output
to the PVP file is the API, which you then use as the basis for constructing the API versus depth
variation. For further information see "Defining Experiments" on page 117.
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Technical Description
Recommended PVT analysis for oil reservoirs
373
Under-saturated reservoirs
For under-saturated reservoirs, it is not often that an equation of state representation is of
particular value, although you may find the PVTi program useful for separator calculations.
Although it is possible to derive black oil tables from equation of state models, for this
application it is better to derive them from laboratory data for the following reasons:
Laboratory analyses generally have sufficient information to derive the PVT tables directly.
It is often difficult to characterize reservoir oils accurately. This leads to difficulty in
establishing an equation of state model that satisfactorily matches the measured data.
To establish a black oil PVT model of a single sample from an undersaturated reservoir the
following procedure is recommended:
1
From the laboratory report take the saturation pressure (bubble point) of the sample, the
reservoir density at that pressure, and the compressibility (as a function of pressure) above
the saturation pressure.
2
If the field is under production there is normally data available on the producing GOR for
the field separator conditions, the gas gravity ( γ g , air = 1), and the stock tank oil gravity
(API).
3
Ensure that the GOR and gas gravity include all the separator and stock tank gases. If they
do not then you can often make reasonable estimates. You can then combine this data with
the reported oil density to give the formation volume factor ( Bo ) at the saturation pressure
p b as follows (in field units):
γ g ⋅ GOR ⋅ 0.00122
141.5
1
B o ( p b ) = -------- ---------------------------------- + ---------------------------------------------ρ res ( 131.5 + API )
5.6146
[EQ 8.209]
where ρ res is the reservoir density in gm/cc, and the GOR in scf/rb.
4
You can find the oil formation volume factor at pressures higher than the saturation pressure
using the compressibility factor in the PVT report.
5
If the field has only been tested and there is no data on producing GOR and gas gravity then
often a separator test for appropriate separator conditions are reported. This supplies a
formation volume factor for bubble point oil at these conditions of separation. You can use
the reported compressibilities to derive formation volume factors at higher pressures.
If a separation test is reported and the field is under production, then you should rationalize
the formation volume factors derived from point 2 with the separator test.
6
If no separation test was performed by the laboratory and there is no production data, then
you can either use a suitable set of correlations, or, if the sample is a re-combination, it may
be possible to use the re-combination data to derive data at separation conditions using
PVTi, providing it is possible to characterize the fluid.
Note
It is important to avoid using what is often referred to as the formation volume factor
(it is actually a relative volume) during a differential liberation experiment. The oil
remaining at the end of this experiment has a completely different composition from
stock tank oil and this formation volume factor is usually higher (by as much as 10%)
than the correct value.
For the simulation of undersaturated reservoirs this differential liberation experiment
is usually superfluous, although laboratories often perform it anyway.
If there are a number of samples you should follow the above procedure for each one.
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7
Then determine if there evidence of an API gradient by plotting stock tank oil density
against depth.
8
If there is no such evidence take the most appropriate sample (or average of samples). This
becomes the PVT representation of the reservoir oil.
If the reservoir has an API gradient the following additional stages are recommended:
9
Draw a representative curve through the API versus depth plot. Use this to represent the
model API versus depth relationship of the reservoir oil.
10 There are a number of ways of allocating PVT properties as functions of API gravity. By
suitable plots, such as saturation pressure against depth, formation volume factor for a
common pressure against depth, and formation volume factor against pressure, you can
find a method appropriate to that particular reservoir. You may find it necessary to use
correlations to extrapolate to depths above and below the range of sample data.
Saturated blackoil reservoirs
Most of the stages for "Under-saturated reservoirs" on page 374 are appropriate for these
reservoirs.
In addition you must generate a table of solution gas-oil ratio, oil and gas formation volume
factor, and oil and gas viscosities below the bubble point.
Normally, you can derive this data from the separation test and differential liberation
experiments performed in the laboratory.
Note
Again it must be stressed that you should not use differential liberation data alone.
What is often referred to as the formation volume factor during the liberation makes
no reference to separator conditions.
To be completely accurate the laboratory should perform a separation test on the fluid resulting
from each pressure stage of the differential liberation experiment.
In practice this is rarely done, and the volumetric data is determined from the single separation
test (at the bubble point pressure), and the relative volumes and gas volumes of the differential
liberation experiment.
The correct oil formation volume factor is this relative volume, divided by the relative volume
of the bubble point fluid (during the same differential liberation), multiplied by the correct oil
formation volume factor of the bubble point fluid for the separator conditions operating. This
derivation, of course, uses the black oil approximation that the stock tank oil density is
unchanging.
Solution gas-oil ratio is derived in a similar way, the value at the bubble point pressure being
exactly that derived from the separator test ( R s ( p b ) ).
Simple material balance of gas and oil shows that the correct gas-oil ratio ( Rs ) at a pressure
below the bubble point is given by:
R s = R s ( p b ) – ( R s' ( p b ) – R s' )B o' ( p b ) ⁄ B o ( p b )
[EQ 8.210]
where Rs' and Bo' refer respectively to the reported solution gas-oil ratio and formation volume
factor from the differential liberation experiment.
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Technical Description
Recommended PVT analysis for oil reservoirs
375
As well as API plots against depth for different samples, plots of producing gas-oil ratio and
formation volume factor against depth (for a consistent pressure) may indicate a solution gasoil ratio for a such a reservoir.
Volatile oil reservoirs
A differential liberation experiment, or a constant volume depletion experiment, or both, may
have been performed on a volatile oil sample. In practice, during depletion, some intermediate
process occurs in the reservoir because gas migrates away from the oil, although it might be
argued that enough gas will be trapped near the oil for a constant volume depletion experiment
to be most representative. A swelling test may also have been performed if gas re-injection is
planned.
You should subject the results of any constant volume depletion experiment to the same analysis
as for a gas condensate fluid sample, as described in "Recommended PVT analysis for gas
condensate reservoirs" on page 377.
The objective of the PVT analysis is to generate an equation of state model of the reservoir,
which you then use for compositional simulation. If it is felt that the depletion experiment is a
good enough representation then you can generate a black oil table from the equation of state
model.
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Recommended PVT analysis for oil reservoirs
PVTi Reference Manual
Recommended PVT analysis for gas condensate
reservoirs
Introduction
•
"Blackoil or compositional simulation" on page 377.
•
"Data analysis" on page 378.
•
"Compositional grading with depth" on page 378.
•
"Data analysis" on page 378.
•
"Equation of state model" on page 379.
Blackoil or compositional simulation
For most gas condensate reservoirs the liquid that condenses in the pore spaces during depletion
does not reach a high enough saturation to become mobile. Gas and oil do not move with respect
to each other, and they therefore stay in equilibrium. It is possible to model this type of reservoir
behavior quite accurately by the constant volume depletion (CVD) experiment performed in the
laboratory.
For further information on defining experiments in PVTi see "Defining Experiments" on
page 117.
For a straightforward gas condensate, a black oil formulation, modified to include a variable Rv
vapor oil-gas ratio, can therefore do a reasonable job of modeling simple depletion.
Although the black oil formulation nominally constrains stock tank oil and gas to have
unvarying compositions and densities, it is possible to reproduce the compositional data
available for the original constant volume depletion experiment for surface facility calculations
by post-processing black oil output.
However, if the gas condensate becomes very rich, perhaps grading to a volatile oil, then it
requires a fully compositional simulation to model it.
This is also the case when you wish to consider almost any other development scenario than
depletion, except, perhaps, pressure maintenance by water injection.
Dry gas cycling, in particular requires fully compositional modeling for accurate predictions of
the phase effects when dry gas contacts condensed reservoir oil. The extended black oil
formulation allows dry gas to pick up oil until the gas becomes saturated, an optimistic
approximation to the actual reservoir behavior.
When you generate black oil tables from a CVD experiment by PVTi, the program includes dry
gas properties in the table, allowing gas cycling to be modeled.
Note
PVTi Reference Manual
The results of such modeling are to over-estimate the condensate recovery from the
field by a few percent for full and partial pressure maintenance. Low pressure
recycling will probably be very poorly modeled.
Technical Description
Recommended PVT analysis for gas condensate reservoirs
377
Compositional grading with depth
Where part of the fluid column is near critical conditions an initial compositional gradient with
depth would be used in a compositional simulation. Reservoirs may grade from a gas
condensate to a volatile oil without a phase transition or contact of any kind. More often there
is an oil-rim, which can exist even without critical conditions being approached. For further
information on defining experiments in PVTi see "Defining Experiments" on page 117.
Provided reservoir fluids are not close to critical conditions, a reasonable approximation to
recovery can often be made using a black oil formulation, by modeling the dew point variation
and ignoring the condensate-gas ratio. The black oil formulation cannot normally reproduce,
simultaneously, the variation in dew point pressure and in condensate-gas ratio.
Data analysis
A common failing when analyzing gas condensate reservoirs is to attempt to establish an
equation of state representation without thorough analysis of the data on which it is to be based.
A thorough comparison of samples, analysis of inter- and intra- sample consistency, and
clarification of the aims of establishing an equation of state model, allows you to determine
which data is worth trying to match, what components to use, and how best to establish a
matched model.
You should closely scrutinize all the available samples. Some of the questions that should be
answered are as follows:
1
Are the samples properly constituted (examine recombination data and compare with
correlations)?
2
Have experiments been performed consistently and accurately (examine compositional
material balances)?
3
Are other experimental data such as Z -factors, implied K -values and liquid densities
reasonable (correlations and tests of consistency)?
4
What are the characteristics of the heavy fractions (fingerprint plots)?
During this analysis it may seem reasonable to establish alternative (modified) data by adjusting
sample data to achieve material balance consistency and a reasonable fluid description. This can
be a useful exercise but a good appreciation of the main sources of inaccuracy is required for it
to be successful.
If the sample is a recombination, the report usually contains recombination data that can be used
for calibrating correlations, to obtain an analysis of separation using the COMB section of PVTi.
For further information see "COMB - Compositional Material Balance" on page 112 and
"COMB section keywords" on page 159.
It is possible to obtain gas and condensate recovery estimates for different abandonment
pressures by combining this with constant composition data above the dew point, and CVD data
below the dew point.
After you have analyzed each sample individually you should examine all the samples together
by, for example, plotting dew point pressures and condensate-gas ratios against sampling depth,
comparing compositions, fingerprint plots etc.
Before rejecting any particular sample that appears to be anomalous, you should investigate the
source of anomalies. Such an investigation may be useful in making recommendations
concerning sampling techniques or laboratory analysis.
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Recommended PVT analysis for gas condensate reservoirs
PVTi Reference Manual
Equation of state model
When a good overall view of the reservoir field has been gained, it is then possible to establish
PVT models. If depletion is planned it may not be necessary to establish an equation of state
model. If the basic (or modified) laboratory data is of sufficient quality you can use to establish
black oil tables. Normally, however, you establish equation of state models.
For further information on fitting data to an EoS in PVTi see "Equation of State" on page 100.
Different engineers have their own methods of establishing an equation of state model, but a
suggested approach is as follows:
1
Establish a model based upon as many components as the data defines, using correlations
where necessary. Split the last component (the plus fraction) into, say, three further
fractions, using one of the splitting options. The modified Whitson (Semi-ContinuousThermodynamics (SCT)) is recommended. For further information see "Multi-feed Split
(also called semi-continuous thermodynamic (SCT) split)" on page 106.
2
Previously, it was recommended that the binary interaction coefficient between Methane
and the plus fraction be varied to match the dew point pressure. This practice is no-longer
recommended. Adjusting binaries to match saturation pressure at just one temperature
often massively distorts the phase envelope at other (generally lower) temperatures, see
[Ref. 30].
Instead, it is now recommended to use one of the following approaches:
a
If using Cheuh-Prausnitz BIC’s, try the (pre-multiplying) A -coefficient. This adjusts
ALL hydrocarbon-hydrocarbon binaries by the same amount, maintaining symmetry
and monotonicity. For further information see "Viscosity correlations" on page 101.
b
Having performed an SCT-split, regress on the plus fraction mole weight, PVTi’s
internal correlations then convert this modified mole weight into critical properties,
etc., which are monotonic and consistent.
c
If the above are unavailable, critical temperature of plus fraction usually requires
changing less than any other individual EoS parameter.
3
Compare this first model with the data to be matched. This usually comprises the
volumetric data associated with constant volume and constant composition experiments,
separator data and swelling test data. As well as the volumetric data, it is important to
compare compositional data, although the possible inaccuracies in reported compositions
should be considered here.
4
Attempt to establish a model that is a good match with only a minimal modification of the
data. Such modifications may be made manually or semi-automatically but you should
obtain a good understanding of the effects of each modification.
The emphasis is on the modification (preferably consistently) of individual component
descriptions, especially those of the heavy components which are poorly defined. The
splitting of the plus fraction may be a suitable modification to make.
Other properties to consider are the critical temperature and pressure of the plus fraction
along with its acentric factor. Additionally, because of the generally uncertain ParaffinicNapthanic-Aromatic (PNA) of the Single Carbon Number (SCN) groups, that is hexanes,
heptanes, etc., these are a better option for a more limited change.
If such a minimal set of modifications does not give a satisfactory match then a full regression
procedure may be necessary as described for pseudoization below. Ideally this full regression
will not be necessary before pseudoization.
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Technical Description
Recommended PVT analysis for gas condensate reservoirs
379
1
Generate a black oil table from this many-component model from a simulated CVD
experiment. For further information on defining experiments in PVTi see "Defining
Experiments" on page 117.
2
Decide upon an appropriate set of pseudo-components, bearing in mind the objectives of
the study. Use the grouping option to generate the pseudo-component model from the
many-component model. In many cases about six pseudo-components is appropriate.
3
Compare the predictions of the pseudo-component model with the laboratory data.
4
Use the automatic regression procedure to modify the representation. The emphasis now is
on obtaining a good match to the data and the results of the many-component model. Fairly
coarse matching parameters may be required.
Modify parameters for which a small change has a large effect. (The matrix of sensitivities
produced by the regression algorithm may be useful here.) You should try several sets of
regression parameters and you should compare the predictions over the whole area of
interest (including mixing of dry and wet gases) with the predictions of the manycomponent model and with the data (where available).
When pseudoizing, the ideal grouping results in minimal predictive change from the
original system. This is not always possible and some small changes in the group properties
may be necessary.
5
If there are problems matching reservoir data and separator data simultaneously then it is
possible to divorce the two in ECLIPSE for compositional simulation, using different Ω
values and binary interaction coefficients for the separators, or using K -values for the
separators.
It is also possible to account for temperature variation using the temperature-dependent
volume shift. By matching separator volumetric properties first, that is at or near surface
temperature where the volume shifts are actually defined, you can then attempt to match to
reservoir volumetric properties, at the elevated reservoir temperature, by using the thermal
expansion coefficient that is available as a regression variable.
One advantage of the above procedure is that it addresses directly one of the main problem areas
in this type of work: the characterization of the heavy fractions.
These components have an effect on fluid behavior that far outweighs their sometimes small
mole fractions. You always rationalize any splitting performed with any true boiling point
(TBP) distillation data available, fingerprint plots, correlations etc.
A second advantage of the recommended procedure is that it allows (through the manycomponent model) a good understanding of the character of the fluid.
A third advantage is that if it is possible to obtain a good match to the laboratory data with
minimal modification of the pure many-component equation of state model then it is more likely
that accurate predictions are obtained away from the measured data.
Note
380
A cubic equation of state can only supply approximations to the behavior of fluids.
This must be borne in mind when matching laboratory data, but especially when
extrapolating outside the area of data control. By the same token, laboratory analyses
of samples only normally supply an approximation to the sample behavior and the
sample itself is only an approximation to the reservoir fluid.
Technical Description
Recommended PVT analysis for gas condensate reservoirs
PVTi Reference Manual
Consistency tests and correlations
Introduction
During initial data analysis a number of tests are available in the COMB (COmpositional
Material Balance) section of the program for examining the consistency and quality of a
particular laboratory sample.
For further information see "COMB - Compositional Material Balance" on page 112 and
"COMB section keywords" on page 159.
This section contains information on the following:
•
"Compositional material balances during the CVD experiment" on page 381.
•
"Fluid density correlations" on page 381.
•
"Viscosity calculations" on page 382.
•
"Separator calculations" on page 382.
•
"K-value checks" on page 382.
•
"Recovery calculations" on page 383.
Compositional material balances during the CVD
experiment
From the volumetric and gas compositions reported during the various pressure stages of the
CVD experiment it is possible to make deductions about the composition and density of the
remaining liquid at each stage. For further information on defining experiments in PVTi see
"Defining Experiments" on page 117.
If the moles of liquid remaining after the last stage is reported (which, unfortunately, is not
always the case) it is possible to combine this with the fractions recovered at each stage to
compare the initial and recovered compositions.
This overall comparison can be revealing in terms of laboratory accuracy and the desirability of
making modifications to the basic data before making a match.
Fluid density correlations
It is possible to compare the liquid density calculated from compositional material balance with
calculated values using the Alani-Kennedy correlation, [Ref. 22].
Several correlations are available for the gas phase.
It is possible to compare the pseudo-critical temperature and pressures (the internal correlation
uses the Wichert-Aziz correction for sour gases). You can compare these pseudo-critical
properties with those calculated using a correlation based on the hydrocarbon molecular weight.
It is possible to compare a representation of the Standing-Katz Z -factor correlation by
Dranchuk et al., [Ref. 21], using the Benedict-Webb-Rubin equation of state with laboratory
measured Z -factors.
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Technical Description
Consistency tests and correlations
381
K-value checks
The Hoffmann-Crump-Hocott (HCH) technique consists of plotting the logarithm of the
product of the K -value and the pressure against a characterization factor for each component.
HCH found that at any given pressure this data plotted close to a straight line, at least for the
pure components. It is possible to check K -values derived from the (calculated) liquid and
(reported) gas compositions during the various stages of the CVD experiment. For further
information on defining experiments in PVTi see "Report" on page 113.
This technique is also useful for checking the recombination of samples. It forms the basis of
Standing’s method for performing separator calculations, discussed later.
Another good check of the K -values from a CVD experiment is to plot them against the
logarithm of pressure for each component. This allows an estimation of the apparent
convergence pressure, which then allows cross-checking against NGAA tables.
Viscosity calculations
Laboratories generally do not have the equipment for measuring gas viscosities and usually
calculate viscosities based on the Carr, Kobaysahi and Burrows correlation. Other correlations
exist, such as the "Lohrenz, Bray and Clark" on page 330 method and the "Pedersen et al." on
page 331 corresponding states technique. These different correlations often yield markedly
different predicted viscosities.
Ideally, a consistent correlation should be used throughout the reservoir engineering analysis,
from the well test analysis used to derive permeabilities to the reservoir simulation. ECLIPSE
accepts a set of critical volumes (entered with VCRITVIS or ZCRITVIS), which are only used
for viscosity calculations, in order that significant changes in Vc values used to match viscosity
correlations do not effect the remainder of the simulation.
Separator calculations
Standing evolved a method for calculating K -values for separators, based on the HCH method.
For each component, a b -factor is calculated at the separator temperature.
HCH suggested that this b -factor is based on pure component normal boiling points and critical
temperatures.
Standing suggested a slightly different set but this probably only applied to the particular oil he
was considering. b -factors obtained by the HCH method may be used in PVTi to generate
separator K -values.
An alternative is to use those derived from recombination data, though these should first be
checked against those obtained using the HCH method.
From the K -values derived in this way, PVTi can calculate the condensate and oil recoveries for
a given separator system. Separator liquid densities are based on the Alani-Kennedy correlation
(see "Alani-Kennedy liquid densities" on page 312)and stock tank densities are calculated using
Amagat's law (addition of specific volumes).
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Consistency tests and correlations
PVTi Reference Manual
Another method of calculating recovery factors is to assume stabilized liquid consists of, say,
the Pentanes plus fraction, whilst the stabilized gas consists of the other, lighter components.
With these assumptions, recoveries down to the last pressure in the CVD experiment are
commonly reported in laboratory analyses in units of gallons of condensate per mscf of wet gas.
Laboratories calculate these using Amagat’s law. You can perform these calculations in PVTi
using input specific gravities and molecular weights.
Recovery calculations
From input CCE, CVD data and the separation system, PVTi can calculate gas and condensate
recovery factors from any supplied initial reservoir pressure to any supplied abandonment
pressure, for a depletion scenario.
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Technical Description
Consistency tests and correlations
383
Fluid Properties Estimation
Introduction
Fluid properties estimation is used in situations where a full equation of state matching across
numerous samples is not available.
Typically, there is only one sample and limited information about the fluid behavior. From this,
fluid properties estimation simulates typical experiments and provide analysis of the fluid ahead
of full laboratory experiments.
Minimum information
In fluid property estimation the following data provide sufficient information to construct a
complete set of example experiments:
•
Weight percentage of each component (or mole fractions)
•
The mole weight of the plus fraction
•
A saturation pressure (bubble or dew point)
•
The maximum pressure to use when constructing a depletion experiment (the default is to
use the saturation pressure.
Fitting to saturation pressure
The plus fraction mole weight is used to characterize the critical properties of the plus-fraction.
In general, the weight fraction of the plus-fraction is well known, but the appropriate mole
weight to use in characterizing the critical properties is not.
By varying the weight of the plus-fraction, whilst maintaining the weight fraction constant,
PVTi is able to determine the most appropriate mole weight to use in characterizing the critical
properties. This gives a good fit to the entered saturation pressure and creates a fluid model that
can be used for fluid properties estimation.
Generation of pressure depletion experiments
In generating pressure depletion experiments, PVTi begins by creating the Constant
Composition Expansion (CCE). There are up to ten pressure steps from the maximum entered
pressure down to the saturation pressure, and up to ten pressure steps from the saturation
pressure down to standard pressure. If no maximum pressure was provided, the CCE starts at
the saturation pressure.
If the saturation pressure was a bubble point, a Differential Liberation (DL) experiment is
created, otherwise a Constant Volume Depletion (CVD) experiment is created. The DL or CVD
has the same pressure steps as the CCE previously created.
384
Technical Description
Fluid Properties Estimation
PVTi Reference Manual
Optimized separator
An optimized separator calculation can be performed. The method for this is discussed in
"Optimized separators" on page 344.
Technical Information
The default settings for the PVTi fluid properties estimation are in Table 8.12.
Table 8.12
PVTi defaults for Fluid Property Estimation
Property
Value
Equation of state
Peng-Robinson 3-parameter (corrected)
Library for component properties
Katz-Firoozabadi
Correlations for plus-fraction properties
Kesler-Lee
Viscosities
Lohrenz-Bray-Clark
The equation-of-state and the viscosity model can be changed using PVTi: Edit | Fluid Model
| Equation of State...
The component library in use can be selected in PVTi: Utilities | Program | Options...
The correlation used for the plus-fraction can be changed in PVTi: Edit | Fluid Model |
Components...
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Technical Description
Fluid Properties Estimation
385
Regression in PVT analysis
Introduction
The goal of PVT analysis is to provide a tuned Equation of State that can model the reservoir
fluid in simulations. The selection of regression parameters is crucial in determining the quality
of the tuned fluid model.
This chapter discusses the selection of regression variables in PVT analysis and consolidates
traditional variable selection, based on physical principles ("Physical selection of regression
parameters" on page 386), with variable selection based on mathematical analysis of the
problem ("Mathematical analysis of the regression problem" on page 388). "A consistent
methodology that can be applied automatically" on page 389, describes how information in the
preceding two sections are used by the PVTi Quick Fit option.
Fundamentally, the fitting process twists
the standard cubic-equation of state to fit the supplied data. Across the temperature and pressure
ranges of the observations the fitted model may be useful, at very different temperatures and
pressures the model may not be representative of the fluid behavior at all.
Note
Always use data at reservoir conditions, such as depletion experiments, and at surface
conditions, such as separator tests, when fitting a fluid model that is to be used in
reservoir simulation.
In "Weighting observations for regression" on page 390, there is a discussion on weighting the
observation data to get the desired fit.
This chapter does not contain a mathematical description of the Levenberg-Marquardt
algorithm, that can be found in "Weighting observations for regression" on page 390.
Physical selection of regression parameters
The traditional, chemistry-centered approach to equation-of-state fitting relies on first
determining which parameters are least well defined. Parameters that are not known accurately
are candidates for fitting.
Critical properties
For pure library components, particularly the non-hydrocarbons and lighter hydrocarbons, the
acentric factor (ω) and critical temperature (Tc) and pressure (Pc) are well known. It is generally
not justifiable to tune these properties.
Hint
386
It is very unlikely that the Pc, Tc and ω of H2O, H2S, N2, CO2, CO, C1, C2, C3, IC4,
NC4, IC5, NC5, and C6 differ from the library values. So do not use them in
regression.
Technical Description
Regression in PVT analysis
PVTi Reference Manual
The critical properties of the heavier components are less well determined. The plus-fraction is
a mixture of many different hydrocarbons and usually the properties are determined by
correlations based on mole weight and specific gravity of the plus fraction as a whole.
Consequently the critical properties are only as good as the characterization method that
generated them.
Hint
The Pc, Tc, and ω of the plus fraction usually come from characterization. This means
that they are not well determined, making them ideal candidates for tuning.
Pedersen et al. have suggested that the molecular weights of the characterized components
might be a good choice of regression variable as this varies Pc, Tc and ω consistently, in line
with the chosen characterization method, see [Ref. 59].
Binary interaction coefficients
The binary interaction coefficients are introduced into the cubic equation-of-state to account for
the effect of polar forces in the interactions between components. This means that for non-polar
interactions, such as those between hydrocarbons, the binary interactions are close to zero.
There are lots of binary interaction coefficients, generally there is insufficient PVT data to
justify tuning all of them. Over-fitting, fitting the data more closely than is justified, can lead to
a fluid model that is not physically valid outside the range of the data being fitted. In the
reservoir simulator you model many compositions outside the observed PVT data-set. Over
tuning, particularly using the binary interactions, can cause serious convergence problems.
Caution
Careless tuning of binary interaction coefficients often leads to a fluid model that
has convergence problems in compositional simulations.
The basic cubic equation-of-state uses the acentric factor to consider slight deviations in
molecule shape; the assumption is that all molecules are close to being spherical. The binary
interaction coefficient between light components and the heaviest hydrocarbon can be used to
compensate for the non-sphericity of the heavy hydrocarbon molecules.
ΩA and ΩB coefficients
The default values of ΩA and ΩB are based on the following assumptions:
1
The critical isotherm of a component has a slope of zero and an inflection point at the
critical point. In layman’s terms this means that the component is pure.
2
That the determination carried out, for the limited number of pure components available,
can be extrapolated to all heavier and lighter components.
3
The values were valid for pure-component density and vapor pressure below critical
temperature.
In developing his equation of state, Tareq Ahmed explained why these basic assumptions are
violated in many fluid models, see [Ref. 61]:
1
Pseudo-components and the plus fraction are not pure components, so assumption 1 is
violated by these.
2
The heavier hydrocarbons and light components may not have the same ΩA and ΩB as the
pure components tested. Specifically, assumption 2 might not be true.
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Technical Description
Regression in PVT analysis
387
3
Light components such as methane and nitrogen are well above their critical points at
temperatures typically encountered in PVT studies. Assumption 3 does not apply to these
components.
Hint
The assumptions upon which the default ΩA and ΩB constants are based do not hold
for light components, pseudo-components, and the plus fraction. This makes them
candidates for regression.
Lohrenz-Bray-Clark viscosity coefficients
The Lohrenz-Bray-Clark viscosity correlation is a fourth order polynomial in density.
Consequently it is very sensitive to the density of the fluid. In PVTi there is the option to regress
on the critical volume or Z-factor used in calculating each component’s contribution to the total
viscosity.
Hint
Varying the critical volume and Z-factor are equivalent in this case, so it is futile to
vary both at once.
This critical volume or Z-factor is only used to calculate the viscosity, so remember that in a
regression only the viscosity observations themselves are used to tune these parameters.
Caution
As only a few observations apply to the tuning of the critical volumes for
viscosity, make sure that there are no more than one or two regression variables of
this type in a regression run. It is much better to put all critical volumes for
viscosity into one regression variable than to vary all of them at once.
There is another option in PVTi that allows the constants used in the fourth order polynomial in
density to vary.
Caution
This option is available so that the original Lohrenz-Bray-Clark analysis can be
repeated with new data-sets. It should only be used if you have a large number of
samples and lots of viscosity observations. Fitting too many parameters to too few
observations leads to convergence problems for the fluid in a compositional
simulator.
Mathematical analysis of the regression problem
In this section the analysis of the regression problem is based upon the need to create a solvable
mathematical system of equations. The physical reasons for changing parameters were laid out
in the previous sections, this defined a set of candidates for regression. The mathematical
analysis indicates which candidates should be regressed together in a single regression run.
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Regression in PVT analysis
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Understanding the Levenberg-Marquardt algorithm
The Levenberg-Marquardt algorithm, like many non-linear regression algorithms, starts from
the assumption that the non-linear problem can be solved as a set of small linear steps. This, in
effect, means that the problem must not be too non-linear. The regression can be helped by
designing the problem, that is choosing regression variables, such that the problem is not too
non-linear. What is meant by too non-linear? It is more straightforward to start from the linear
problem and bend the rules a little. The characteristics of the linear problem are:
1
No regression parameters are numerically redundant
2
All regression parameters are independent
High sensitivities
The first rule means that interest should focus on the most sensitive parameters, those for which
a small change has a large effect on the fit.
The Hessian tab of the Sensitivity Analysis panel gives an indication of the sensitivity of the
different parameters. The values along the leading diagonal of the Hessian matrix are most
useful, a high value means high sensitivity.
Hint
By removing insensitive regression variables from the set, the problem becomes less
non-linear and thus more solvable.
Kai Liu has reported success with an automatic regression technique based solely on selecting
the eight most sensitive regression parameters, see [Ref. 61].
Correlations between parameters
The second rule means that there should be no very strong correlations between parameters. A
strong correlation means that the effect of a change in one parameter is the same as, or opposite
to, the effect of changing another.
The Correlation Sensitivity Analysis panel shows the correlations between parameters. A
value close to 1 indicates a strong correlation, which means changing one parameter has the
same effect as changing the other. A value close to -1 indicates a strong anti-correlation, which
means changing one parameter has the opposite effect to changing the other.
Hint
Amalgamating strongly correlated regression variables of the same type (for example
Tc) in a single regression variable or removing one of the two strongly correlated
variables makes the problem less non-linear and thus more solvable.
A consistent methodology that can be applied
automatically
This section describes how the rules laid out in "Physical selection of regression parameters" on
page 386 and "Mathematical analysis of the regression problem" on page 388 can be applied to
a automated regression system.
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Technical Description
Regression in PVT analysis
389
Note
By their nature automatic regression schemes do not make judgement calls that an
experienced engineer would make.
The choice of regression variables
From the rule-of-thumb guidelines given in "Physical selection of regression parameters" on
page 386, the following set of properties was determined as begin available candidates for
regression:
1
Tc, Pc and ω of any non-library component.
2
Tc, Pc and ω of any component with mole weight of C7 or heavier. (As these are effectively
mixtures of different molecule types and so may differ from library values).
3
ΩA and ΩB of any component with mole weight of C7 or heavier. Again because these are
mixtures.
4
No binary interaction coefficients because of the risk of over-fitting.
5
No viscosity-specific parameters, again because of the risk of over-fitting.
This gives a large number of regression variables, many of which are very closely interrelated.
The next step is to apply a mathematical analysis onto this set.
Reducing the set of regression variables
From "Mathematical analysis of the regression problem" on page 388 it is clear the problem can
be made more solvable by selecting those parameters with high sensitivities and low intercorrelations.
From the discussion, the following rule was created:
•
Regress using the set of variables with the highest total sensitivity, for which no correlation
between parameters is greater than 0.9 or less than -0.9; and for which the lowest sensitivity
is at least 1% of the highest sensitivity.
The total sensitivity of the set of variables was taken to be the sum along the leading diagonal
of the Hessian. The sensitivity of a regression variable was taken to be the value on the leading
diagonal of the Hessian relating to that variable.
Note
This method takes no advantage of amalgamating regression variables of the same type
into a single variable.
Weighting observations for regression
The least-squares fit to the observation data is not necessarily the goal of equation-of-state
fitting. To be precise, the goal is to create a fluid model that behaves like the reservoir fluid.
There are aspects of the reservoir fluid that the model must capture accurately.
PVTi allows the weighting of regression variables so that additional importance can be attached
to some measurements over others.
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Regression in PVT analysis
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Matching saturation pressure
Usually, it is important to match the fluid’s saturation point within the depletion experiment.
This value is closely related to the gas-oil contact in the reservoir and can strongly affect the
initial fluids in place calculation.
Hint
Use the saturation pressure measurement from the depletion experiment to create a
dew-point or bubble-point experiment. Weight the observation of saturation pressure
very high (1000+).
Matching surface densities or GOR
The separator densities or GOR strongly determine the total oil and gas produced. Also it is
worth remembering that the depletion experiment often has 20 or more stages, whereas the
surface separator is unlikely to have more than 2 or 3 stages. This means there are usually lots
more observations for the reservoir depletion process than for the produced oil and gas.
Hint
Weight the separator densities or GOR highly (500+) to guarantee that the right amount
of oil and gas are produced.
Guiding the regression
Sometimes a fluid does not seem to fit the observations. In this situation, the regression weights
can be used to guide the regression algorithm.
For example, an excellent fit may have been achieved for the bubble point using the method
described in "Matching saturation pressure" on page 391, but there may be difficulty in fitting
the liquid saturation below the bubble point.
PVTi allows the weighting of individual observations for this purpose.
In this situation, by weighting the observations for which the fit is worst by the highest amount,
the regression is forced to take more account of the data as a whole.
Hint
Weight the worst-fit observation the most and successive observations less and less
through to the best fit observations that retain their original weighting of 1. This guides
the regression to take more account of the worst parts of the fit.
Caution
PVTi Reference Manual
Be aware of the errors in the observed data and do not be tempted to over-fit.
Models that are over-fitted cause convergence problems in compositional
simulations.
Technical Description
Regression in PVT analysis
391
SmartOpt - Systematic MAtrix Reduction
Technique for Optimization
This algorithm performs a rapid and exhaustive search of the sensitivity matrix described in
"Reducing the set of regression variables" on page 390. As the non-linear regression is,
effectively, a succession of linear steps, the problem must be designed such that it is only weakly
non-linear.
The number of combinations of regression variables that could be used for regression is 2N
where N is the number of regression variables. For even 20 regression variables this would be
1,048,576 combinations, for 30 variables the number of combinations is more than a billion. To
calculate the correlations between parameters, a matrix inversion is required, clearly several
million matrix inversions is impractical. By re-designing the problem, however, a fast and
efficient exhaustive search can be made to find the most sensitive regression matrix representing
a weakly non-linear problem.
A starting point - the most sensitive single variable
If the run is made with just one regression variable, there are no other variables so correlation
is not an issue. The starting point then is to find the single most sensitive variable. This gives us
an initial estimate of the best sensitivity - no combinations with lower sensitivity than this need
be tried.
Ordering for speed
The Hessian is reformed with the most sensitive variable in the first row, down to the least
sensitive variable in the final row. As is explained in the next section, this gives an important
speed increase.
Searching all combinations
The speed in this method relies reducing the time spent analyzing combinations that do not turn
out to be the best one.
The first test to be applied, then, is the sensitivity difference - no parameter should have less
than 1% the sensitivity of the most sensitive parameter. As the combination is constructed, it is
tested against this criterion. If it fails, the search knows that any combination with a less
sensitive parameter will also fail. The re-ordering of the Hessian means that it is easy to skip the
other combinations that are not allowed.
The next test to be applied is that of highest sensitivity. If the sensitivity of the constructed
combination is less than the current best candidate, the search moves on the next combination.
Again, by having the Hessian ordered, it can be quickly determined whether the sum of all
remaining parameters would be higher than the highest sensitivity. If not, the search can skip
the set of parameters that cannot form a matrix with a high enough sensitivity to be considered.
Finally the correlations are tested. This is because the calculation of correlations requires the
Hessian to be inverted. Again as the correlations are calculated, as soon as a single correlation
is discovered that exceeds 90%, the search moves on to the next combination.
If the construction of the correlations completes without discovering a correlation greater than
90%, this combination must be the best one found yet and so it is stored and the search
continues.
This method is very fast and guaranteed to find the best matrix according to the criteria:
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Regression in PVT analysis
PVTi Reference Manual
1
Highest total sensitivity (determined as the sum along the leading diagonal of the Hessian).
2
Lowest sensitivity is not less than 1% of the highest sensitivity (again sensitivity refers to
the terms along the leading diagonal of the Hessian).
3
No correlations more than 90%.
These criteria could be adjusted, though you must take care that the criteria you choose define
a weakly non-linear problem, otherwise the effort of analysis will not show any benefit for the
regression.
PVTi Reference Manual
Technical Description
Regression in PVT analysis
393
Wax and asphaltene precipitation in PVTi
Introduction
The solid precipitation model in PVTi handles waxes as a solid solution and asphaltenes as an
additional liquid phase.
The wax model assumes that paraffins and naphthalenes can precipitate as a solid solution. In
the asphaltene model it is assumed that the heaviest aromatic component will form an
asphaltenic liquid phase.
To use the solid precipitation model, the paraffin, naphthalene and aromatic fractions for each
carbon number are needed. These can be entered by hand, if known, or generated from the
correlations described in "The PNA distribution of heavy components" on page 394 and
"Critical properties of PNA species" on page 395.
The theory behind the wax model is explained in "Wax precipitation" on page 395.
The PNA distribution of heavy components
In PVTi, the components heavier than C6 may be split into their paraffinic (P), naphthalenic (N)
and aromatic (A) constituents. This is an important part of solid precipitation as it is the P and
N species, which generally form wax and the heaviest aromatic is the major constituent (by
weight) of the asphaltenic liquid phase.
The PNA distribution is then estimated as described by Nes and Westerns, see [Ref. 48].
v = 2.51 ( n – 1.4750 ) – ρ + 0.8510
w = ρ – 0.8510 – 1.11 ( n – 1.4750 )
3660
A% = 430v + -----------MW
( for v < 0 )
3660
A% = 670v + -----------MW
( for v > 0 )
10000
R = 820w + --------------MW
( for w > 0 )
10600
R = 1440w + --------------MW
( for w < 0 )
N% = R – A%
P% = 100 – R
[EQ 8.211]
Where P%, N% and A% are the percentages of paraffinic, naphthalenic and aromatic
constituents respectively; ρ is the liquid density in gcm-3 at 20oC and 1 atm, and n is the
refractive index of the true boiling point (TBP) fraction.
n
is given by Riazi and Daubert’s correlation, see [Ref. 49]:
n =
+ 2I
1
--------------
 1–I
[EQ 8.212]
where I is a characterization factor given by:
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Technical Description
Wax and asphaltene precipitation in PVTi
PVTi Reference Manual
– 0.02269
I = 0.3773T B
Hint
SG
0.9182
If a full PNA specification of the sample is available, the mole fractions can be used in
the normal way, over-riding the default estimates from this splitting procedure. First
enter the single carbon number (SCN) fluid; perform the PNA split, then type in the
measured mole fractions.
Critical properties of PNA species
In PVTi the critical properties of the PNA species are set up using the correlations of Riazi and
Al-Sahhaf, see [Ref. 50], which are all of the form:
ln ( θ ∞ – θ ) = a – bMW
c
[EQ 8.213]
where MW is the mole weight of the hydrocarbon and the constants a, b, c and θ∞ have been
determined for various basic properties of PNA species (refer to the reference for tables of their
values).
Note
The critical properties of the PNA species can be tuned just as for any other
components.
In addition to the usual set of critical properties, the melting points of the PNA species are also
determined, for use in the wax precipitation.
For paraffins, the melting point is given by the correlation of Won (1986), see [Ref. 51]:
f
20172
T = 374.5 + 0.02617MW – --------------MW
[EQ 8.214]
For naphthalenic and aromatic species, the melting point is given by (Pan, Firoozabadi and
Fotland, 1997 - see [Ref. 52]):
f
T = 333.45 – 419e
– 0.00855MW
[EQ 8.215]
where, in each equation, MW is the mole weight of the hydrocarbon.
Wax precipitation
In PVTi it is considered that the paraffinic and naphthalenic species of components heavier than
C15 can form waxes and that the heaviest aromatic component forms the asphaltenic liquid
phase.
Chemically, the waxes that drop out of hydrocarbon fluids at lower temperatures, are known to
contain paraffins and, to a lesser extent, naphthalenes.
In PVTi the method of Pedersen et al. (see [Ref. 55]) has been improved to use the paraffin and
naphthalene components, rather than a “wax forming component”. This means that the critical
properties correlations for the paraffins and naphthalenes, as given by the correlations in
"Critical properties of PNA species" on page 395, are used in determining the solid
precipitation.
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Technical Description
Wax and asphaltene precipitation in PVTi
395
The wax is modeled as a solid-solution and so we can apply an adjusted liquid fugacity and
solve for the wax phase using a full multiphase equation-of-state flash calculation. For nonPNA species the solid fugacity is e50 , which effectively means that they cannot form wax.
The adjustment to the liquid fugacity is given by:
f
f
f
f
Δh i 
T i Δc Pi 
T i Δc Pi  T i
S
L
f pure i ( P,T ) = f pure i ( P,T ) × exp ---------f  1 – ----- – -----------  1 – ----- – ----------- ln  -----
R
R
T
T
 T


RT i 
[EQ 8.216]
where Δh fi is the enthalpy of fusion for component i; ΔcPi is its heat capacity of fusion; and Tfi
is its melting point temperature.
Enthalpy of fusion
The enthalpy of fusion for paraffins comes from the correlation by Won [Ref. 51]:
f
f
[EQ 8.217]
Δh i = 0.1426MW i T i
For napthalenes the correlation of Lira-Galeana et. al. (1996) [Ref. 56] was used:
f
f
[EQ 8.218]
Δh i = 0.0527MW i T i
For aromatics the correlation of Pan et al. [Ref. 52] was used:
f
f
[EQ 8.219]
Δh i = 11.2T i
Heat capacity of fusion
The heat capacity of fusion for all P, N, A species is given by the correlation of Pedersen et
al.[Ref. 57]:
–4
Δc Pi = 0.3033MW i – 4.635 × 10 MW i T
[EQ 8.220]
The asphaltenic liquid phase
The asphaltenic phase is known to form at temperatures higher than the melting point of the
heavy aromatic molecule that is the solid asphaltene. Maximum precipitation occurs close to the
bubble point of the liquid and the precipitated phase is a thick, black liquid, see [Ref. 58]. After
filtering, an asphaltene deposit is recovered.
In PVTi there are a special set of default binary interaction coefficients introduced for the
interactions between the heaviest aromatic component and the light components. This is based
on the critical volumes of the components and takes a similar form to that of the CheuhPrausnitz binary interactions :
1⁄6
1⁄6 θ
 2V ci V cj 
-
k ij = A 1.0 –  ---------------------------- V 1ci⁄ 3 + V 1cj⁄ 3
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Technical Description
Wax and asphaltene precipitation in PVTi
[EQ 8.221]
PVTi Reference Manual
where kij is the binary interaction coefficient between the ith and jth components; Vc is the
critical volume of the ith or jth component; A is the Cheuh-Prausnitz parameter, which can be
varied as a special regression variable, the value used for interactions with the heaviest
hydrocarbon is 10A; θ has been fitted using a number of asphaltene data-sets and is 6.0 for
interactions involving hydrocarbons with mole weights less than that of SCN C7. It is zero for
interactions involving hydrocarbons C7 and heavier, except for the heaviest aromatic
component for which it is 12.0.
This scheme is identical to the Cheuh-Prausnitz scheme for hydrocarbons up to C6, when the
PNA split is not made, the Cheuh-Prausnitz binaries are the same as in pre-2002A versions of
PVTi.
For P, N and all A species apart from the heaviest aromatic, the binary interactions are zero. The
strong interactions between the heaviest aromatic component and the light components creates
the conditions for a precipitating asphaltenic liquid phase, which maximizes near the bubble
line. Thus mimicking the behavior witnessed in laboratory tests.
Discussion
PVTi uses a consistent, single fluid model for all calculations, so the critical properties used in
matching, say, the differential liberation experiment, are used in calculating the wax appearance
temperature. Consequently all the observations, including those of the solid phase, can be
regressed at once, leading to a more consistent and complete single description for use in both
reservoir and process simulations.
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Technical Description
Wax and asphaltene precipitation in PVTi
397
Cleaning samples contaminated with oil-based mud
Introduction
Oil-based muds are in widespread use and often contaminate PVT samples taken at the wellsite.
PVTi offers two methods for cleaning oil-based muds, "Removing oil-based mud contamination
by skimming" on page 398 describes a method that can be used when the composition of the
contaminant is not known. If the contaminant composition is known, "Removing oil-based mud
contamination by subtraction" on page 399 provides an accurate method for removing the
contaminant.
The methods used in PVTi are based on the work of Gozalpour et al, see [Ref. 53].
Removing oil-based mud contamination by
skimming
In naturally occurring hydrocarbon fluids, a semi-log straight-line relationship is seen between
increasing mole fraction and increasing mole weight for components C8 and heavier, see [Ref.
56].
Many oil-based muds contain components in the range, C10 - C23, any contamination of the
reservoir fluid, therefore, appear as a positive deviation from the semi-log straight-line
behavior.
The assumptions made for the skimming method are: firstly, that the semi-log straight-line
behavior is exhibited by the fluid; and that there are uncontaminated components, heavier than
the heaviest contaminated component. The second assumption is required for the straight-line
to be constructed.
The method involves constructing the straight-line between the C8 component and the
uncontaminated heavy components. This line then gives the reservoir fluid and the excess molefractions provide the composition of the contaminating oil-based mud.
In PVTi the light-end point is the first component with a mole weight heavier than 100 (if library
components are used this is C8). The heavy end point is the lowest mole-fraction before the
plus-fraction.
Caution
It is important that the sample being cleaned has heavier components than the oilbased mud, so that there is an uncontaminated point to use in constructing the
straight line.
If the composition of the oil-based mud is known, it is better to use the subtraction method
described in "Removing oil-based mud contamination by subtraction" on page 399.
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Technical Description
Cleaning samples contaminated with oil-based mud
PVTi Reference Manual
Removing oil-based mud contamination by
subtraction
As described in "Removing oil-based mud contamination by skimming" on page 398, there is a
semi-log straight-line relationship amongst the heavier components in a naturally occurring
hydrocarbon fluid that can be exploited to allow the removed of oil-based mud contamination.
The subtraction method is applicable when the composition of the contaminant is known.
In this case, a small amount of the contaminant is subtracted from the sample. The resultant
sample is tested for RMS fit to a semi-log straight-line defined as the same line used in the
skimming method.
A numerical optimization is performed to find the amount of contaminant that must be removed
to minimize this RMS fit.
Note
The restriction that the oil-based mud contain components C10 - C23 does not apply
here. The mud can be of any composition.
Note
The assumption that there are uncontaminated components, heavier than the oil-based
mud components, is not necessary for this method.
Hint
If the composition is known, the subtraction method is a better choice than the
skimming method.
PVTi Reference Manual
Technical Description
Cleaning samples contaminated with oil-based mud
399
Mixing and recombination of samples
Introduction
PVTi offers both sample mixing and sample recombination. There is a subtle difference between
mixing and recombining. In mixing, you provide a mole fraction or gas-oil ratio for the mix;
these are used and the mixed sample is created directly. In recombining, you enter a target gasoil ratio for the mixture. In that case the proportion of mixing is determined iteratively using the
scheme outlined in "Recombination" on page 400.
Mixing
Mixing is an addition of the two samples. If the mole fraction of the second sample is specified,
the mixture is a weighted sum. If gas-oil ratio (GOR) is specified, this value is first translated
to a mole fraction at the temperature and pressure requested.
The conversion from GOR to mole fraction (MF) is as follows:
n Assuming n moles of Sample 2 are mixed with 1 mole of Sample 1, then F = -----------
1+n
RT
F 
std
- where R is the universal gas constant, Tstd and
- -----------------The GOR is then given by GOR =  ----------1 – F P std V oil
Pstd are standard temperature and pressure respectively and Voil is the oil volume at the
temperature and pressure you specified. If you do not specify the pressure, it is taken as the
saturation pressure of the sample
Recombination
In recombination, the aim is to create a mixture with the stock tank gas-oil ratio specified.
In this case, the temperature and pressure you enter are used as the first stage in a two-stage
separator. The second stage is always at standard conditions. The GOR you enter is the target
GOR for the mixture. This is used as an initial guess and the fluids are mixed in the usual way
(see "Mixing" on page 400). When this mixture is passed through the separators, a stock-tank
GOR is calculated. A regression is performed, adjusting the mixing combination until the stocktank GOR is equal to the target value you requested.
The mix applied at each iteration is recorded in the log window.
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Technical Description
Mixing and recombination of samples
PVTi Reference Manual
ECLIPSE Thermal Export Module
Introduction
In PVTi and ECLIPSE Compositional we deal with an isothermal flash. This means that, for a
particular cell in a simulation, we know the composition of the fluid summed over all the phases
and the pressure and temperature. We try to minimize the Gibbs Free Energy in order to
determine how each component splits across the different phases present. In effect we try to find
the K-values, which are the unknown variables.
ECLIPSE Compositional assumes that the temperature of each cell stays constant over time,
even if there is a distribution of temperatures across the cells to start with. It is assumed that if
a particular drop of fluid moves from one cell with temperature, T1 to another cell with
temperature T2 that the fluid takes on the temperature T2. When the Thermal option is used in
ECLIPSE Compositional this is not the case. Thermal diffusion is allowed to take place over
time, which means that the temperature in each cell is a free parameter that needs to be
determined using a different type of flash; one at constant energy. We therefore know the
pressure, functional form of the K-Values (K=K(P,T)), and the total energy of the system but the
temperature is unknown.
The long-term goal of this ECLIPSE Thermal module is to use PVTi’s powerful Equation of
State (EoS) functionality to provide extensive support for the Thermal option in the ECLIPSE
Compositional simulator. The first step was to introduce functionality into PVTi 2003A to
calculate an optimal K-value functional relation. This can then be used within ECLIPSE
Thermal to perform these flashes at constant energy.
For PVTi 2004A the module has been extended to write out a whole file containing a series of
keywords that can be used as the PVT input for an ECLIPSE Thermal simulation. In addition
to the standard keywords written out for an ECLIPSE Compositional run, for example acentric
factors (ACF), critical temperatures (TCRIT) etc., PVTi writes out additional keywords that
enables ECLIPSE Thermal to calculate accurate values for K-values oil/gas densities and oil/
gas phase enthalpies.
•
"K-Values" on page 401, "Oil Density" on page 403,
•
"Gas phase density" on page 404,
•
and "Enthalpy" on page 405 explain how the relevant keywords are used in ECLIPSE
Thermal to calculate the appropriate quantities.
For a brief non-technical summary of these keywords see "Outline of keywords for ECLIPSE
Thermal" on page 367.
K-Values
For PVTi 2004A you have the option of either using Crookston’s equation (the KVCR keyword)
or Wilson’s formula (the KVWI keyword).
Hint
PVTi Reference Manual
In fact Wilson’s formula is a simplified version of Crookston’s equation, which is
explained below.
Technical Description
ECLIPSE Thermal Export Module
401
The coefficients of Crookston’s equation are written out by PVTi using the KVCR keyword. The
general functional form of the K-Value correlation we use is given by Crookston’s formula:
–D
B
K ( P, T ) =  A + --- + CP exp  -------------


 T – E
P
[EQ 8.222]
If a simplified version of equation [EQ 8.222] is used, given by setting A, C, E=0 that is:
B
D
K ( P, T ) =  --- exp  – ----
 P
 T
[EQ 8.223]
then B and D can be calculated by using at least two experimentally determined observations.
Alternatively, Wilson’s formula can be used to estimate K-Values, which is given by the
formula:
Pc
Tc
K ( P, T ) =  ------ exp 5.372697 ( 1 + ω )  1 – -----
 P

T
[EQ 8.224]
where P, T are the pressure and temperature and K , P c , T c and ω are the K-value, critical
pressure, critical temperature and acentric factor respectively for a particular component. In fact
Crookston’s equation is a generalized form of Wilson’s formula, which can be obtained by
setting:
A = 0
B = Pc
C = 0
Tc
D = 5.372697T ( 1 + ω )  ----- – 1
T

E = 0
in equation [EQ 8.222].
There are also tabulated values for B and D for certain components. The central problem we face
though is that K-values for a particular component are not functions of just temperature and
pressure, as Wilson’s formula would suggest, but also of the types and quantities of other
substances present. Consider the following. If we have a fluid of say 50% methane and 50%
decane then each component has its own K-value at a particular temperature and pressure. If
we now add, say toluene, to the mixture then the K-values of methane and decane changes and
we also have the K-value for the new component. This illustrates that changing the composition
of a fluid clearly effects the K-values of respective components.
Also, for heavier hydrocarbon components (anything above about C7), the K-values are an
increasing monotonic function of pressure. It is clear that Wilson's formula is completely
inadequate here as K=Pc/P is clearly a decreasing monotonic function of pressure. The full
Crookston expression can cope with such components by using the A and C terms.
PVTi can provide valuable assistance here because it provides its own experimental data using
the flash; as we know that the flash accurately reproduces experimental observations. The
ECLIPSE Thermal export facility then calculates the values of a chosen set of Crookston
coefficients so that the correlation best approximates a set of flashes performed by PVTi in the
pressure and temperature range you specified.
This correlation is unique to the fluid sample and specified pressure and temperature range and
ensures that the Thermal option in ECLIPSE Compositional is using accurate approximations
to component K-values.
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Technical Description
ECLIPSE Thermal Export Module
PVTi Reference Manual
Oil Density
PVTi writes out the keywords PREFT, TREFT, DREFT, CREF and THERMEX1, which
ECLIPSE Thermal uses internally to calculate the oil density of the fluid at a specified pressure
and temperature. For further information on the ECLIPSE keywords referenced in this section
see the "ECLIPSE Reference Manual".
Algorithm
ECLIPSE Thermal calculates the molar oil density b o of the fluid using the following set of
equations:
bo
is given by:
b o = 1 ⁄ V oil
[EQ 8.225]
where the molar specific volume Voil of the oil phase is calculated using Amagat’s law of partial
volumes:
Nc
V oil =
c
 x Voil
c
[EQ 8.226]
c=1
c
and x is the mole fraction of component c in the oil phase. The component oil phase volume
V oil
c
is given by:
c
c
MW
V oil = -----------c
ρ
[EQ 8.227]
where MW c is the molecular weight of component c given by the MW keyword, and the
component oil phase density ρ c is given by:
c
ρ
ref
ρ = --------------------------------------------------------------------------------------------( 1 + C T1 ( T – T ref ) ) ( 1 – C p ( P – P ref ) )
c
The reference density ρ
c
ref
[EQ 8.228]
is defined by ECLIPSE Thermal’s DREF keyword (or PVTi’s
DREFT keyword); the standard temperature and pressure, T ref and Pref are defined by keywords
TREF (TREFT in PVTi) and PREF (PREFT in PVTi); the thermal expansion coefficient C T1 is
defined by the THERMEX1 keyword; and the component isothermal compressibility C P is
defined by the CREF keyword.
The quantities C T1 and C p are defined by the usual thermodynamic relations:
1 ∂V
C T1 = --- -----V ∂T P = PREF
[EQ 8.229]
1 ∂V
C p = – --- -----V ∂P T = TREF
[EQ 8.230]
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Technical Description
ECLIPSE Thermal Export Module
403
Remarks
It is important to note that PVTi’s DREF, TREF keywords are, in general, not the same as
ECLIPSE Thermal’s DREF, TREF keywords.
PVTi’s DREF, TREF
In PVTi the reference density DREF is an observed/measured quantity of each component at the
reference temperature, TREF and standard pressure (14.7 psia). DREF is then used in
conjunction with PVTi’s predicted density at these conditions (using a 2-parameter equation of
state) to calculate volume shifts for each component. Volume shifts were introduced as a “third
parameter” into EoS models to improve calculations of liquid density. Therefore the standard
values of TREF for each component in the literature are chosen such that this component is in
the liquid phase at the temperature TREF and standard pressure.
ECLIPSE Thermal’s DREF, TREF, PREF
In ECLIPSE Thermal it can be seen from equation [EQ 8.227] that we require knowledge of a
reference density measured at a reference pressure and temperature. The reference density is
used along with the isothermal and isobaric expansion coefficients (CREF and THERMEX1) to
extrapolate linearly in order to obtain the density of the oil given an arbitrary temperature and
pressure. PVTi’s reference quantities are not used because they may be very different to the
conditions in the reservoir; and so it would be unreasonable to expect accurate answers using a
linear extrapolation.
In order to obtain reference parameters that are typical of the conditions in the reservoir PVTi
calculates the quantities TREFT, PREFT and DREFT. TREFT and PREFT are the average of the
maximum and minimum reservoir temperatures/pressures respectively. You input these extreme
reservoir values of temperature and pressure on PVTi’s Export for ECLIPSE Thermal panel.
DREFT for each component is then the density calculated by PVTi’s EoS model at pressure
PREFT and temperature TREFT. Assuming that the component is in the liquid phase at these
conditions then DREFT is a good point to perform linear extrapolation using [EQ 8.227] to find
the density of the component at an arbitrary temperature and pressure in the reservoir.
However, if the component is not in the liquid phase (which is the case for lighter components)
at the initial values of TREFT and PREFT then we set TREFT=TREF (PVTi’s TREF) and
PREFT=14.7psia, which we know guarantees that the component is in the liquid phase. We then
use [EQ 8.227] to extrapolate to reservoir conditions and calculate the properties of the
component. These lighter components contribute a relatively small amount to the overall
density of the fluid and we have found this approach to give accurate values of oil density.
The isothermal compressibility and thermal expansion coefficient are calculated by PVTi using
[EQ 8.228]and[EQ 8.229] with the appropriate values of TREFT and DREFT
TREFT, PREFT, DREFT are the same as ECLIPSE Thermal’s TREF, PREF, DREF. PVTi uses
alias names because, as explained, it has already has definitions for TREF and DREF. ECLIPSE
Thermal automatically recognizes these aliases and knows that it is dealing with its own internal
keywords.
Gas phase density
PVTi writes out the keywords TREFT, PREFT, DREFT and ZFACTOR, which ECLIPSE
Thermal uses internally to calculate the molar gas phase density of the fluid at a specified
pressure and temperature.
404
Technical Description
ECLIPSE Thermal Export Module
PVTi Reference Manual
Algorithm
The molar density of the gas phase bg is given by:
b g = 1 ⁄ V gas
[EQ 8.231]
where the molar specific volume Vgas of the gas phase is
Nc
V gas =
c
 y Vgas
c
[EQ 8.232]
c=1
assuming no water is present. yc is the mole fraction of component c in the gas phase. Each
hydrocarbon component gas phase molar volume V gas c is obtained from the gas law,
c
c
[EQ 8.233]
PV gas = Z RT
where Z c is specified with the ZFACTOR keyword. See the "ECLIPSE Reference Manual".
Remarks
The algorithm outlined above assumes that Z c does not change as a function of temperature.
Z
c
is calculated by PVTi for each component by performing an EoS flash on a fluid consisting
purely of the relevant component. If a single gas phase is found then Z c is set to the value of the
Z-factor returned by PVTi’s EoS code. If a liquid phase is returned then Z c is set to ECLIPSE
Thermal’s default value of 0.96.
Enthalpy
•
"Algorithm" on page 405 outlines the three different approaches ECLIPSE Thermal can
take in calculating oil and gas phase enthalpies.
•
"Remarks" on page 405 then explains which of these approaches PVTi supports.
For further information on the ECLIPSE keywords referenced in this section see the "ECLIPSE
Reference Manual".
Algorithm
ECLIPSE Thermal calculates the enthalpy of the oil phase using a mole fraction weighted
average of the component enthalpies:
Nc
H oil =
x
c=1
c
c
⋅ MW ⋅ H
c
[EQ 8.234]
oil
where xc is the mole fraction of component c in the oil phase and MW c is the component
molecular weight given by the MW keyword.
The enthalpy of the hydrocarbon components in the gas phase is calculated using a mole fraction
weighted average of the component enthalpies:
PVTi Reference Manual
Technical Description
ECLIPSE Thermal Export Module
405
Nc
y
H gas =
c
c
⋅ MW ⋅ H gas
c
[EQ 8.235]
c=1
c
where y is the mole fraction of component c in the gas phase.
The component enthalpies in the oil and gas phases are calculated from component specific
heats and heats of vaporization. Specific heat values must be given for each hydrocarbon
component in at least one fluid phase. If they are only specified in one phase, then the heat of
vaporization should be given. The following options are therefore available for the fluid phase
enthalpies:
1
Set the specific heat of components in the oil and gas phases and the heat of vaporization
at the standard temperature.
2
Set the specific heat of components in the oil phase and the heat of vaporization as a
function of temperature.
3
Set the specific heat of components in the gas phase and the heat of vaporization as a
function of temperature.
Solid phase enthalpies are only required in simulations where a solid phase is present.
Specific heats
The specific heats C coil , C cgas of a component c in the oil and gas phases are given by
c
c
c
C oil = C oil + C oil ⋅ ( T – T st )
1
2
c
c
c
C gas = C gas + C gas ⋅ ( T – T st )
1
2
where the oil phase coefficients are defined by keywords SPECHA and SPECHB and the gas
phase coefficients are defined by keywords SPECHG and SPECHH.
T st
is the standard temperature defined by STCOND. The specific heats must always be positive.
If oil phase specific heats are defined, the molar enthalpy of component c in the oil phase is:
c
H oil =
c
2
1 c
= C oil ⋅ ( T – T st ) + --- ⋅ C
⋅ ( T – T st )
1
2 oil 2
c
 Coil dT
T st
[EQ 8.236]
For temperatures above the critical temperature, T > T ccrit , the oil phase molar enthalpy is set
equal to the gas phase molar enthalpy.
If gas phase specific heats are defined, the molar enthalpy of component c in the gas phase is
c
c
c
H gas = H vaps +
 Cgas dT
[EQ 8.237]
T st
c
c
2
1 c
= H vaps + C gas ⋅ ( T – T st ) + --- ⋅ C
⋅ ( T – T st )
1
2 gas 2
where Hcvaps is the heat of vaporization at the standard temperature, defined by HEATVAPS.
If a solid phase is simulated, the molar enthalpy of component c in the solid phase is
c
H sol =
c
 Csol dT
T st
406
c
2
1 c
= C sol 1 ⋅ ( T – T st ) + --- ⋅ C
⋅ ( T – T st )
2 sol 2
Technical Description
ECLIPSE Thermal Export Module
[EQ 8.238]
PVTi Reference Manual
Heat of vaporization
A temperature dependent heat of vaporization ΔHc ( T ) can be specified instead of either the oil
or gas specific heat.
If the specific heat of a component c in the oil phase is not specified, then the oil phase enthalpy
is calculated from the gas component enthalpy by
c
c
c
H oil = H gas – ΔH ( T )
[EQ 8.239]
Alternatively, if the specific heat of a component c in the gas phase is not specified, then the
gas phase enthalpy is calculated from the oil component enthalpy
c
c
c
H gas = H oil + ΔH (T)
[EQ 8.240]
The heat of vaporization is given by [Ref. 56]:
c B
c
ΔH ( T ) = A ⋅ ( 1 – T ⁄ T crit )
c
ΔH ( T ) = 0
T < T crit
c
T ≥ T crit
c
[EQ 8.241]
[EQ 8.242]
where the constant A is defined by the HEATVAP keyword, the exponent B is defined by the
HEATVAPE keyword, and T crit c is the component critical temperature defined by the TCRIT
keyword.
Heats of vaporization are usually obtained at the normal boiling point T nb . The constant A ,
defined by the HEATVAP keyword can be found by inverting :
c
ΔH ( T nb )
A = ---------------------------------------B( 1 – T nb ⁄ T crit )
[EQ 8.243]
where ΔHc ( T nb ) is the heat of vaporization at the normal boiling point. The exponent B for each
component, entered with keyword HEATVAPE, is usually set to a value in the range 0<B<=1.
Remarks
PVTi uses the oil and gas phase component specific heat coefficients (SPECHA, SPECHB,
SPECHG and SPECHH) and the heats of vaporization at the standard temperature (HEATVAPS)
for each component. As explained in the previous section, the oil and gas phase enthalpies are
then calculated using [EQ 8.236] and [EQ 8.237].
In the future this functionality could be extended so that you could specify in PVTi which of the
three options to calculate enthalpies you wish to take advantage of in ECLIPSE Thermal. PVTi
would then export the relevant keywords depending on which option you had selected.
PVTi Reference Manual
Technical Description
ECLIPSE Thermal Export Module
407
408
Technical Description
ECLIPSE Thermal Export Module
PVTi Reference Manual
Units
Appendix A
Units
General information
This option allows the current unit and temperature conventions to be changed. The options
available are:
•
Metric unit system
•
Field units
•
Laboratory units
•
PVT-metric units
The temperature conventions are:
•
Degrees Kelvin
•
Degrees Celsius
•
Degrees Rankine
•
Degrees Fahrenheit
Any of the unit conventions are compatible with any of the temperature options. The unit
conventions may be changed at any point in a session, existing quantities being converted to the
new units. PVT-metric units are the same as metric, except in that pressure is measured in
atmospheres. In addition, it is possible to enter mole compositions as fractions (of unity) or
percentages (up to 100%), and pressures can be specified in absolute or gauge units.
PVTi Reference Manual
Units
Units
409
The units for each data quantity are given in the table below.
Table A.1
Units
Quantity
Metric
Field
Lab
PVT-M
Length
metres
feet
cms
metres
days
days
hours
days
gm ⁄ cc
kg ⁄ m
Depth
Time
Density
Pressure
kg ⁄ m
3
lb ⁄ ft
3
3
barsa
psia
atma
atma
Pressure difference
bars
psi
atm
atm
Compressibility
1 ⁄ bars
1 ⁄ psi
1 ⁄ atm
1 ⁄ atm
Viscosity
cPoise
cPoise
cPoise
cPoise
Permeability
mDarcy
mDarcy
mDarcy
mDarcy
Liquid surface volume
sm
3
stb
scc
sm
3
Gas surface volume
sm
3
mscf
scc
sm
3
Reservoir volume
rm
3
rb
rcc
rm
3
stb ⁄ day
scc ⁄ hour
sm ⁄ day
Gas surface volume rate sm 3 ⁄ day
mscf ⁄ day
scc ⁄ hour
sm ⁄ day
Reservoir volume (rate)
rb ⁄ day
rcc ⁄ hour
rm ⁄ day
(absolute)
Liquid surface volume
rates
Formation volume
factor (liquid)
Gas-oil ratio
Oil-gas ratio
Volume
Specific volume
Energy
Enthalpy
Specific heat
Units
Units
3
rm ⁄ day
3
3
3
rb ⁄ mscf
rcc ⁄ scc
rm ⁄ sm
3
3
mscf ⁄ stb
scc ⁄ scc
sm ⁄ sm
3
3
stb ⁄ mscf
scc ⁄ scc
sm ⁄ sm
cc
m
sm ⁄ sm
sm ⁄ sm
m
3
3
rm ⁄ sm
3
ft
3
m ⁄ kg
-ml
3
3
ft ⁄ lb
kJ
-ml
cc ⁄ gm
btu
kJ ⁄ kg
-ml
kJ ⁄ kg
– ml
⁄K
Thermal conductivity
kJ ⁄ m ⁄ d ⁄ K
Gas-oil ratio (oil at
reservoir)
sm ⁄ rm
Gauge pressure
Surface tension
Transmissibility
410
3
m ⁄ day
-ml
J
btu ⁄ lb
-ml
btu ⁄ lb
– ml
⁄R
3
3
3
3
3
3
3
3
m ⁄ kg
-ml
kJ
J ⁄ gm
-ml
J ⁄ gm
– ml
kJ ⁄ kg
⁄K
J ⁄ kg
-ml
– ml
⁄K
btu ⁄ ft ⁄ d ⁄ R
J ⁄ cm ⁄ h ⁄ K
kJ ⁄ m ⁄ d ⁄ K
mscf ⁄ rb
scc ⁄ rcc
sm ⁄ rm
barsg
psig
atmosg
atmosg
dyne ⁄ cm
dyne ⁄ cm
dyne ⁄ cm
dyne ⁄ cm
cPrb ⁄ d ⁄ psi
cPcc ⁄ h ⁄ a
cPm ⁄ d ⁄ a
3
3
3
cPm ⁄ d ⁄ bar
3
3
3
PVTi Reference Manual
A number of constants that depend upon the unit convention are used. These are:
Table A.2
Constants
Quantity
Metric
Field
Lab
PVT-M
Gravity constant
0.000098066
0.00694444
0.000967841
0.0000967841
Darcy constant
0.00852702
0.00112712
3.6
0.00864
Atmos. pressure
1.01325
14.6959
1.0
1.0
Density of air
1.2232
0.076362
0.0012232
1.2232
Gas constant R
0.083143
10.732
82.055776
0.08205576
Standard conditions are taken as one atmosphere and 60 °F .
Some useful conversion factors
The following table contains conversion factors.
Table A.3
Conversion factors
Quantity
Conversion factor
Length
1m
= 3.28084 ft
1ft
= 0.30480 m
Volume
1ft
Mass
3
3
= 35.3146600 ft
= 6.2898110 bbl
3
3
= 0.02831685 m
= 0.1781076 bbl
1m
= 2.20462300 lb
1kg
1lb
Density
= 0.45359237 kg
3
= 0.06242797 lb ⁄ ft
= 1.0E-3 gm ⁄ cc
= 16.0184600 kg ⁄ m 3
= 0.01601846 gm ⁄ cc
1 bar
= 14.5037700 psi
= 0.986923 atm
1 psi
= 0.06894757 bar
= 0.068046 atm
1kg ⁄ m
1lb ⁄ ft
Pressure
Gas-oil
3
3
3
1m ⁄ m
3
1 mcf ⁄ bbl
Gravities API
Temperatures
= 5.614583E-3 mcf ⁄ bbl
= 178.1076000 m 3 ⁄ m 3
(141.5/liq.grav.)-131.5
T
(deg K )
= T (deg R )/1.8
Conversion of gas moles to volumes at Z=1
The volume occupied by one mole of gas, with an ideal gas Z -factor of unity, at temperature T
(deg R ) and pressure p (psia), is:
Vmolar = RT ⁄ p = 379.39445 at p = 14.70 psi, T = 519.67 deg R
Vmolar = RT ⁄ p = 23.650203 at p = 1.013 bar, T = 288.15 deg K
PVTi Reference Manual
Units
Units
411
The number of moles in unit volume V of gas with an “ideal gas” Z -factor of unity, at
temperature T and pressure p , is:
lb-moles = p ⁄ RT = 0.002635779 at p = 14.70 psi, T = 519.67 deg R
kg-moles = p ⁄ RT = 0.042282930 at p = 1.1013 bar, T = 288.15 deg K
412
Units
Units
PVTi Reference Manual
Symbols
Appendix B
Symbols
f iL
Fugacity of component i in the liquid phase
f iV
Fugacity of component i in the vapor phase
Ki
Equilibrium constant of component i
L
Mole fraction of liquid phase
m1
Constant in Martins equation of state.
m2
Constant in Martins equation of state.
p
Pressure of mixture.
p ci
Critical pressure of component i .
p ri
Reduced pressure of component i : p ri = ------i .
T
Temperature of mixture.
Tc
Critical temperature of component i .
T ri
Reduced temperature of component i : T ri = ------i- .
V
Mole fraction of vapor phase.
xi
Mole fraction of component i in the liquid phase.
yi
Mole fraction of component i in the vapor phase.
Z
Z -factor in equation of state.
δ ij
Binary interaction coefficient.
ΩA
PVTi Reference Manual
p
p ci
T
T ci
i
Omega- A values for each component.
Symbols
Symbols
413
ΩB
ωi
414
Symbols
Symbols
i
Omega- B values for each component.
Acentric factor for component i .
PVTi Reference Manual
Bibliography
Appendix C
Wilson, G.
“A Modified Redlich-Kwong Equation of State, Application to General Physical Data
Calculations”.
[Ref. 1]
Paper No. 15C Ohio, presented at the AIChE 65th National Meeting, Cleveland. May 4-7, (1969).
Martin, J.J.
“Cubic Equations of State - Which?”
[Ref. 2]
IEC Fundamentals, Vol. 18, Page 81 , May, (1979).
Coats, H.
“Simulation of Gas Condensate Reservoir Performance”,
[Ref. 3]
SPE paper no. 10512, presented at the Sixth SPE Symposium on Reservoir Simulation, New
Orleans , January 31st - February 3rd, (1982).
Whitson, C.H.
“Topics on: Phase Behaviour and Flow of Petroleum Reservoir Fluids”,
[Ref. 4]
Ph.D. Thesis, The University of Trondheim, Norwegian Institute of Technology, Department of
Petroleum and Chemical Engineering, August, (1983).
Pedersen, S.K.,
Fredenslund, Aa.,
Christensen, P.L., and
Thomassen, P.
Whitson, C.H., and
Torp, S.B.
Lohrenz, J.,
Bray, B.G., and
Clark, C.R.
Crowe, C.M., and
Nishio, M.
“Viscosity of Crude Oils”,
[Ref. 5]
Chemical Engineering Science, Vol. 39, Page 1011-1016 , No. 6, (1984)
“Evaluating Constant-Volume Depletion Data”,
[Ref. 6]
J. Pet. Tech. Page 610-620. March, (1983)
“Calculating Viscosity of Reservoir Fluids from their Composition”,
[Ref. 7]
J. Pet. Tech. Page 1171 , (1964); Trans., AIME,. 231.
“Convergence Promotion in the Simulation of Chemical Processes - The General Dominant
Eigenvalue Method”,
[Ref. 8]
AIChEJ, Vol. 23, No. 3 , Page 528-529. May (1975)
PVTi Reference Manual
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415
Dennis, J.E., and
Schnabel, R.B.
“Numerical Methods for Unconstrained Optimisation and Non-linear Equations”,
[Ref. 9]
Prentice-Hall Inc., New Jersey, (1983)
Kesler, M.G., and
Lee, B.I.
“Improved Predictions of Enthalpy of Fractions”,
Hydro. Proc. Page 153-158 , March (1976)
Cavett, R.H.
“Physical Data for Distillation Calculations - Vapor-Liquid Calculations”,
[Ref. 10]
[Ref. 11]
Proc. 27th API Meeting, San Francisco, Page 351-366, (1962)
Riazi, M.R., and
Daubert, T.E.
“Simplify Property Predictions”,
[Ref. 12]
Hydro. Proc. Page 115-116 , March (1980)
Lee, B.I., and
Kesler, M.G.
“Improved Vapor Pressure Predictions”,
Hydro. Proc. Page 163-167. July (1980)
Edmister, W.C.
“Applied Hydrocarbon Thermodynamics”,
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[Ref. 14]
Part 4: Compressibility Factors and Equation of State, Pet. Refiner , Page 173-179 , April, (1958)
Michelsen, M.L.
“The Isothermal Flash Problem. Part I. Stability”,
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Fluid Phase Equilibria, Vol. 9 , Page 1-19, , (1982)
Katz, D.L. et al.
“Handbook of Natural Gas Engineering”,
[Ref. 16]
McGraw-Hill Company , Page 129, (1982)
Reid, R.C,
Prausnitz, J.M., and
Sherwood, T.K.
Bashbush, J.L.
“The Properties of Gases and Liquids”,
[Ref. 17]
McGraw-Hill Company, Third Edition, (1977)
“A Method to determine K-values from Laboratory Data and its Applications”,
[Ref. 18]
SPE 10127 , (1981)
Hoffmann, A.E.,
Crump, J.S., and
Hocott, C.R.
Alani, G.H., and
Kennedy, H.T.
Dranchuk, P.M.,
Purvis, R.A., and
Robinson, D.B.
Wichert, E., and
Aziz, K.
Lee, A.L.,
Gonzalez, M.H., and
Eakin, B.E.
416
Equilibrium Constants for a Gas-Condensate System”,
[Ref. 19]
Trans. AIME., 198 , Page 1-10.
“Volumes of Liquid Hydrocarbons at High Temperatures and Pressures”,
[Ref. 20]
Page Trans. AIME, 219, Page 288-292 , (1960)
“Computer Calculations of Natural Gas Compressibility Factors using the Standing and Katz
Correlation”,
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Institute of Petroleum Technical Series, No. IP 74-008, (1974).
“Calculate Zs for Sour Gases”,
[Ref. 22]
Hydrocarbon Processing, 51, Page 119 , May (1972)
“The Viscosity of Natural Gases”,
[Ref. 23]
J. Pet. Tech. Page 997-1000 , August, (1966)
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PVTi Reference Manual
Standing, M.B.
“A Set of Equations for Computing Equilibrium Ratios of a Crude Oil/Natural Gas System at
pressures below 1000 psia”,
[Ref. 24]
J. Pet. Tech. Page 1193-1195 , September (1979)
Peneloux, A.,
Rauzy, E., and
Freze, F.
Søreide, I.,
Reffstrup, J., and
Whitson, C.H.
“A Consistent Correction for Soave-Redlich-Kwong Volumes”,
[Ref. 25]
Fluid Phase Equilibria 8 , Page 7-23, (1982)
“Procedures for Reservoir Fluid Characterisation using an Equation of State Model”, [Ref. 26]
, Report RE 88-8, Laboratory for Energetics, Danish Tech. Univ., Lyngby.
Coats, K.H., and
Smart, G.T.
“Application of a Regression-Based EOS PVT Program to Laboratory Data”,
SPE Res. Eng. Page 277-299 , May (1986)
Herning, F., and
Zippener, L.
“Calculation of the Viscosity of Technical Gas Mixtures from the Viscosity of the Individual
Gases”,
[Ref. 28]
[Ref. 27]
Gas u. Wasserfach 79, Page 69-73, (1936)
Stiel, L.I., and Thodos,
G.
Pedersen, K.S.,
Fredenslund, Aa., and
Thomassen, P.
Abramowitz, M., and
Stegun, I.A.
“The Viscosity of Nonpolar Gases at Normal Pressures”,
[Ref. 29]
AIChEJ , Page 611-615 , (1961)
“Properties of Oils and Natural Gases”,
[Ref. 30]
Gulf Publishing Company, Houston , (1989)
Handbook of Mathematical Functions
[Ref. 31]
New York , Page 923, (1972)
Whitson, C.H.,
Anderson, T.F., and
Søreide, I.
“ C 7+ Characterisation of Related Equilibrium Fluid using the Gamma Distribution”, [Ref. 32]
Paper in C 7+ Characterisation, Edited by Mansoori G.A., and Chorn L.G., Taylor and Francis, New
York, (1989).
McCain, W.D.
“The Properties of Petroleum Fluids”,
[Ref. 33]
PennWell Publishing Company, Second Edition, Tulsa , (1990)
Søreide, I.
“Improved Phase Behaviour Predictions of Petroleum Reservoir Fluids from a Cubic Equation
of State”,
[Ref. 34]
Ph.D. Thesis, The University of Trondheim, Norwegian Institute of Technology, Department of
Petroleum and Chemical Engineering , April (1989)
Søreide, I., and
Whitson, C.H.
“Peng-Robinson Predictions for Hydrocarbons, CO2 , N 2 , and H2 S With Pure Water and NaCl Brines”,
[Ref. 35]
Fluid Phase Equilibria, Vol. 77 , Page 217-240, (1992)
Pedersen, S.K., and
Fredenslund, Aa.
“Chemical Engineering Science”,
[Ref. 36]
Vol. 42, No. 1 , Page 182-186, (1987)
PVTi Reference Manual
Bibliography
417
Reudelhuber, F.O., and
Hinds, R.F.
“A Compositional Material Balance Method for Prediction of Recovery from Volatile Oil
Depletion Drive Reservoirs”,
[Ref. 37]
Petroleum Transactions, AIME, Vol. 210 , Page 19, (1957)
Jensen, F., and
Michelsen, M.L.
Gmehling, J.,
Onken, U., and
Arlt, W.
“Calculation of First Contact and Multiple Contact Minimum Miscibility Pressures”, [Ref. 38]
In Situ, 14(1) , Page 1-17, (1990)
“Vapor-Liquid Equilibrium Data Collection DECHEMA Chemistry Data Series”,
[Ref. 39]
DECHEMA, Frankfurt/Main, (1981)
Fragor Reference Manual Vol. 2.4, Chapter 5
[Ref. 40]
J. Pet. Tech. Page 720-723 , July 1986.
Pedersen K.S.,
Thomassen P, and
Fredenslund Aa
Winn F.W.
“Characterisation of Gas Condensate Mixtures”,
[Ref. 41]
Adv. Thermodynamics 1 , Page 137, (1989b)
“Physical Properties by Monogram”,
[Ref. 42]
Pet. Refiner 36 , Page 157-159, (1957)
Sim W.J. and
Daubert T.E.
“Prediction of vapor-Liquid Equilibrium of Undefined Mixtures”,
Ind. Eng. Chem. Process. Des. Dev. 19 , Page 386-393, (1980)
Joergensen, M. and
Stenby, E.H
“Optimisation of pseudo-component selection for compositional studies of reservoir
fluids”,
[Ref. 43]
[Ref. 44]
SPE 30789, 70th Annual SPE Technical conference & exhibition. Dallas TX , (1995)
Pedersen, K.
Unpublished
[Ref. 45]
1997
Michelsen, M.L. and
Heidemann, R.A.
Heidemann, R.A. and
Khalil, A.M.
Nes, K. and Westerns,
H. A. van
“Calculation of critical points from cubic 2-constant equation of state”,
[Ref. 46]
AIChE Journal (Vol 27 No3) , Page 769, (1980)
“The Calculation of Critical Points”,
[Ref. 47]
AIChe Journal 26 No 5 , Page 521, (1981)
“Aspects of the Constitution of Mineral Oils”,
[Ref. 48]
Elsevier, New York, (1951)
Riazi, M. R. and
Daubert, T. E.
“Prediction of the composition of petroleum fractions”,
Ind. Eng. Chem. Process Des. Dev., Vol. 19, Page 289 -294, , (1980)
Riazi, M. R. and AlSahhaf, T. A.
“Physical properties of n-alkanes and n-alkylhydrocarbons: Application to petroleum
mixtures”,
[Ref. 50]
[Ref. 49]
Ind. Eng. Chem. Res., Vol. 34, Page 4145 -4148, (1995)
Won
[Ref. 51]
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PVTi Reference Manual
Pan, H., Firoozbadi, A.
and Fotland, P.,
Gozalpour, F., Densh,
A., Tehranio, D. H.,
Todd, A.C. and Tohidi,
B.,
Katz, D.
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SPE Prod. and Fac - SPE 36740, Page 250, (, 1997)
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oil-based mud”,
[Ref. 53]
SPE 56747, (1999)
“Overview of Phase Behavior in Oil and Gas Production”,
[Ref. 54]
JPT, Page 1205-1214, , (1983)
Pedersen, K. S.
“Prediction of cloud point temperatures and amount of wax precipitation”,
[Ref. 55]
SPE 27629, (1995)
Lira-Galeana, C.,
Firoozbadi, A., and
Prausnitz, J. M.
Pedersen, K. S.,
Skovborg, P. and
Ronningsen, H. P.
Rydahl, A. K.,
Pedersen, K. S., and
Hjermstad, H. P.
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[Ref. 56]
AIChE J., Vol. 42, Page 239, (1995)
“Wax precipitation from North Sea crude oils. 4. Thermodynamic Modeling”,
[Ref. 57]
Energy and Fuels, Vol. 5 (6), Page 924, (1991)
“Modeling of live oil asphaltene precipitation”,
[Ref. 58]
“Properties of Oils and Natural Gases”,
[Ref. 59]
Chapter 10, ISBN 0-87201-588-2,
Ahmed, T.
SPE 18532
[Ref. 60]
Liu, K.
SPE 66363
[Ref. 61]
Trebble, M.A.
“A preliminary evaluation of two and three phase flash initiation procedures”,
[Ref. 62]
Fluid Phase Equilibria. 53, Page 113-122, , (1989)
Aasberg-Petersen, K.
“The Viscosity of Hydrocarbon Fluids”,
[Ref. 63]
Fluid Phase Equilibria. 70, Page 293-308, (1991)
Teja, A.S. & Rice, P.
“Generalised Corresponding States Method for the Viscosities of Liquid Mixtures”,
[Ref. 64]
“Ind. Eng. Chem. Fundam., 20, Page 77, (1981)
Hanley, H.J.M.,
McCarty, R.D. &
Haynes, W.M.
McCarthy, R.D.,
“Equation of the Viscosity and Thermal Conductivity Coefficients of Methane”,
[Ref. 65]
Cryogenics, 15, Page 413,(1975),
“A Modified Benedict-Webb-Rubin Equation of State for Methane Using Recent Experimental
Data”
[Ref. 66]
Cryogenics, 14, Page 276 , (1974)
PVTi Reference Manual
Bibliography
419
Green, Don W.; Perry,
Robert H.
420
Perry’s Chemical Engineers’ Handbook (8th Edition)
[Ref. 67]
McGraw-Hill, (2008)
Bibliography
PVTi Reference Manual
AIndex
Index
A
Acentric factors. . . . 103, 169
Alani-Kennedy liquid densities312
Alkanes . . . . . . . . . . . . . 298
Aromatics. . . . . . . . . . . . 299
Asphaltene and Wax System 69
CCE . . . . . . . . . . . . . . . . 342
CVD . . . . . . . . . . . . . . . 343
Cell compositions . . . . . . 310
Cycloparaffins . . . . . . . . 299
Cell volumes . . . . . . . . . . 310
Celsius . . . . . . . . . . . . . . 409
CHAR components . . . . . 302
Characterization. . . . . . . . 176
Cheuh-Prausnitz . . . 147, 170
CMF. . . . . . . . . . . . . . . . 304
CO2 Rich Fluids . . . . . . . . 70
B
Binary Interaction
Coefficients104, 172, 319, 337
Coefficients default . 187
Black oil tables
differential. . . . . . . . 189
Blackoil
Compositional simulation373
Appendix D
Coats . . . . . . . . . . . . 27, 178
COMB section
keywords . . . . . . . . . 159
Command line . . . . . . . . . . 29
Components . . . . . . . . . . 230
Compositional
Blackoil . . . . . . . . . . 373
grading with depth . . 373
D
Data analysis . . . . . . . . . . 77
DBG file . . . . . . . . . .93, 186
Dead oil tables .171, 184, 216
Debug . . . . . . . . . . . . . . 150
Default Binary Interaction Coefficients
187
Dew point . . . . . . . . . . . 342
Differential black oil tables189
Dry gas tables. . . . . . . . . 183
Condensate systems . . . . . 342
BLACKOIL section
keywords . . . . . . . . 161
E
Consistency tests . . . . . . . 308
correlations . . . . . . . 381
ECLIPSE 300. . . . . . . . . 194
Boiling point temperatures 268
Constant Mole Fraction105, 303 to 304
Edmister . . . . .103, 176, 302
Bubble point pressure . . . 340
Conversion factors . . . . . . 411
EoS
Correlation . . . . . . . . . . . 182
C
Calorific values. . . . 147, 175
Cascade . . . . . . . . . . . . . 150
Cavett . . . . . . 103, 176, 302
PVTi Reference Manual
Critical pressures . . . . . . . 243
omega values . . . . . 237
regression to measured data27
Critical temperatures . . . . 269
Equation of state. . . .193, 317
fitting to experimental results49
Critical viscosity . . . . . . . 331
Equilibrium K-values . . . .311
Critical volumes. . . . . . . . 278
Experiments . . . . . . . . . . 195
Critical Z-factors . .290 to 291
Export . . . . . . . . . . . . . . 136
Index
421
Equilibration. . . . . . .136
Gas Reservoir . . . . . .135
Oil Reservoir . . . . . .135
VFP . . . . . . . . . . . . .138
Export modules . . . . . . . .133
K
Katz-Firoozabadi . . . . . . 147
Kelvin . . . . . . . . . . . . . . 409
Kesler-Lee . . . 103, 176, 302
Keyword errors . . . . . . . . 165
F
Keywords
PVTi. . . . . . . . . . . . 167
Fahrenheit . . . . . . . . . . . .409
K-value checks . . . . . . . . 382
Mole weight of the plus fraction229
Molecular weights . . . . . . 228
Monitor option. . . . . . . . . 150
MOSES keyword . . . . . . . 227
Moses method . . . . . . . . . 227
Multi-feed Split . . . . . . . . 105
MW keyword . . . . . . . . . 228
MWS keyword . . . . . . . . 229
Field units . . . . . . . . . . . .409
Fluid definition . . . . . . . . .25
Fourth-degree polynomial .330
Fragor method . . . . . . . . .203
L
N
Napthenes . . . . . . . . . . . . 299
Laboratory experiments . . 339
NCOMPS keyword . . . . . 230
Laboratory units . . . . . . . 409
NEW . . . . . . . . . . . . . . . . 93
LBC viscosity correlation 149
NEW files . . . . . . . . . . . . . 93
G
Lee-Kesler . . . . . . . . . . . 302
NEWPVI keyword .231 to 232
LIB components . . . . . . . 302
Newton-Raphson . . . . . . . 318
Gas formation volume factor340
Library components. . . . . . 95
NOECHO keyword . . . . . 233
Gas gravity (density). . . . .340
Linear thermal expansion coefficient322
Non-hydrocarbon. . . 102, 211
Gas viscosity . . . . . . 314, 340
Liquid formation volume factors204
Gas-oil ratio. . . . . . . . . . .340
definition . . . . . . . . .148
Liquid saturation . . . . . . . 146
Fugacities . . . . . . . . . . . .317
GI
nodes . . . . . . . . . . . .205
GOR
definition . . . . . . . . .148
GRAF . . . . . . . . . . . . . . .148
GROUP section . . . . . . . .159
keywords . . . . . . . . .159
LNAMES keyword . . . . . 177
LOG files . . . . . . . . . . . . . 93
Lohrenz-Bray-Clark214 to 215, 245
O
OBS keyword . . . . . . . . . 234
Observations . . . . . . . . . . 234
OBSIND keyword . . . . . . 235
M
Oil density. . . . . . . . . . . . 340
Oil formation volume factor340
Martin . . . . . . . . . . . . . . 318
Oil viscosity . . . . . . . . . . 340
Material balance checks . . . 26
OMEGAA, OMEGAB keywords237
Maximum step size . . . . . 219
On-line help . . . . . . . . . . 151
MES file. . . . . . . . . . . . . . 93
Opening a project. . . . . . . . 95
H
Metric units . . . . . . . . . . 409
OPTIONS keyword . . . . . 238
Michelsen’s stability criterion318
OUTECL3 keyword . . . . . 240
Hoffman-Crump plot . . . . .81
Mixing . . . . . . . . . . . . . . 224
Hydrocarbon . . 102, 211, 298
Mnemonics. . . . . . . . . . . 177
OUTECL3 section . . . . . . 162
keywords . . . . . . . . . 162
Grouping . . . . . . . . . 106, 180
components . . . . . . .206
Modified form of Peng-Robinson246
Modified Whitson . . . . . . 303
I
Individual observation weights235
Internal library . . . . . . . . .217
Isomers . . . . . . . . . . . . . .298
422
Index
Modified Whitson Splitting306
P
MODSPEC keyword . . . . 225
PARACHOR keyword . . . 242
MODSYS keyword . . . . . 226
Paraffins . . . . . . . . . . . . . 298
Molar volume correction . 321
PCRIT keyword. . . . . . . . 243
Mole fractions. . . . . . . . . 292
PEARCE keyword . . . . . . 244
PVTi Reference Manual
Pedersen. . . . . 103, 176, 302
Reference temperatures . . 273
Single Carbon Number . . 103
PEDERSON keyword . . . 245
REGRESS section . . . . . . 160
keywords . . . . . . . . . 160
Soave-Redlich-Kwong 25, 318
Regression
operation . . . . . . . . . 201
target . . . . . . . . . . . . 250
variables . . . . . . . . . 275
SPECHA,B,C,D keyword 262
REGTARG keyword. . . . . 250
SPLIT keyword . . . . . . . 263
Reservoir temperature . . . 251
SPLIT section
keywords . . . . . . . . 158
Peneloux . . . . . . . . . . . . 321
Peneloux et al. volume shift 25
Peng-Robinson . . . . . 25, 318
modified form of . . . 246
Phase diagrams . . . . . . . . 301
Plus fraction splitting. . . . 202
PRCORR keyword . . . . . 246
Pressure nodes
automatic insertion. . 222
Probability density model. 303
Program options . . . 145, 238
PSEUCOMP keyword . . . 247
PSEUCOMP section . . . . 162
keywords . . . . . . . . 162
Reudelhuber and Hinds . . 248
Riazi-Daubert . 103, 176, 302
RTEMP keyword . . . . . . . 251
RUNSPEC . . . . . . . . . . . 155
RUNSPEC keyword. . . . . 252
RUNSPEC section
keywords . . . . . . . . . 156
Søreide . . . . . . . . . . . . . 322
Specific heat. . . . . . . . . . 147
Specific heat capacity coefficients262
Splitting. . . . . . . . . . . . . 105
SSHIFT keyword . . . . . . 264
Standard conditions. . . . . 265
Standard pressure . . . . . . 145
Standard temperature . . . 145
STCOND keyword . . . . . 265
Surface tension . . . . . . . . 321
Pseudo-compositional tables247
Swelling test. . . . . . . . . . 345
Pseudo-critical
temperatures, pressures313
S
SYSTEM . . . . . . . . . . . . 155
Pseudoise
definition . . . . . . . . . 26
SALINITY keyword . . . . 253
Pseudoised
EoS data . . . . . . . . . . 27
SYSTEM section
keywords . . . . . . . . 157
SAMPLES keyword254 to 256
Sample composition . . . . . 255
Pure . . . . . . . . . . . . . . . . 297
SAMTITLE keyword . . . . 257
Pure components. . . . . . . 300
Saturated black oil reservoirs372, 375
PVI file . . . . . . . . . . . . . . 93
Saturation
liquid. . . . . . . . . . . . 146
PVO file. . . . . . . . . . . . . . 93
SYSTEM keyword . . . . . 266
T
TBOIL keyword . . . . . . . 268
SAVCOMP keyword . . . . 258
TCRIT keyword . . . . . . . 269
Saving compositions . . . . 258
Temperature convention . 188
Schmidt-Wenzel. . . . . . . . . 25
Thermal expansion . . . . . 147
SCN . . . . . . . . . . . . . . . . 103
THERMX keyword. . . . . 270
SCN groups. . . . . . . . . . . 299
Thomassen. . . .103, 176, 302
SCT keyword . . . . . . . . . 259
Tiled . . . . . . . . . . . . . . . 150
SCT split. . . . . . . . . . . . . 259
TITLE keyword . . . . . . . 271
Semi-Continuous Thermodynamics105,
303
split . . . . . . . . . . . . . 259
TLOW keyword . . . . . . . 272
Separator liquid volumes . 147
True-boiling-point distillation303
R
SG keyword . . . . . . . . . . 260
Trust region radius . .219, 223
Shift parameters. . . . . . . . 322
Two-parameter equation of state321
Rankine . . . . . . . . . . . . . 409
SIMULATE. . . . . . . . . . . 261
Recovery calculations . . . 383
SIMULATE keyword . . . . 261
RECOVERY keyword . . . 248
Redlich-Kwong. . . . . 25, 318
SIMULATE section
keywords . . . . . . . . . 160
U
Reference densities . . . . . 190
Simulation of experiments . 26
Undersaturated reservoirs 372
PVP file . . . . . . . . . . . . . . 93
PVT data for ECLIPSE simulators27
PVTLIB annexe . . . . . . . 185
PVT-metric units . . . . . . . 409
Q
Quality control . . . . . . . . . 77
PVTi Reference Manual
ToolTips . . . . . . . . . . . . 151
TREF keyword . . . . . . . . 273
Index
423
Unit convention . . . . . . . .274
View menu . . . . . . . . . . . . 95
Watson characterization factor302
Unit types . . . . . . . . . . . .144
Viewing the K-value Fits . . 75
WATVFP keyword . . . . . . 285
UNITS keyword. . . . . . . .274
Viscosities . . . . . . . . . . . 331
Wet gas tables . . . . . . . . . 286
UNIX . . . . . . . . . . . . . . . .29
Viscosity calculations . . . 382
WHIT keyword . . . . . . . . 287
UNIX platforms . . . . . . . . .29
Volatile oil reservoirs 372, 376
User components . . . . . . .302
Volume expansion coefficient270
Whitson . . . . . 105, 303, 305
probability density function220
splitting . . . . . . . . . . 287
Volume shift
corrections . . . . . . . 147
Whitson and Torp . . . . . . 288
V
Volume shift parameters
dimensionless . . . . . 264
WHITSON keyword . . . . 288
Vapor Z-factor . . . . . . . . .313
Volume translation . . . . . 321
Window . . . . . . . . . . . . . 150
Whitson-Torp . . . . . . 27, 178
VAR keyword . . . . . . . . .275
Windows platforms . . . . . . 29
VCRIT keyword. . . . . . . .278
Winn. . . . . . . . 103, 176, 302
VCRITVIS keyword. . . . .279
VEC file . . . . . . . . . . . . . .93
VERSION keyword . . . . .280
VFP . . . . . . . . . . . . . . . .138
section . . . . . . . . . . .163
VFP keyword. . . . . . . . . .281
VFP section
keywords . . . . . . . . .163
VFP Tables . . . . . . . . . . .366
VFPi . . . . . . . . . . . . 133, 272
424
Index
W
WAT100 keyword . . . . . . 282
WAT200 keyword . . . . . . 283
Z
WAT300 keyword . . . . . . 284
ZCRIT keyword. . . . . . . . 290
Water properties
ECLIPSE 100 . . . . .
ECLIPSE 300 . . . . .
ECLIPSE GI option .
VFPi. . . . . . . . . . . .
ZCRITVIS keyword. . . . . 291
282
284
283
285
Z-factors, critical . .290 to 291
ZI keyword . . . . . . . . . . . 292
ZMFVD keyword . . . . . . 293
Zudkevitch-Joffe 25, 318, 321
PVTi Reference Manual
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