PVTi
Introduction
 QHSE information
 Class Times:
 9:30 to 12:30 am
 1:30 to 4:30 pm
 Questions at any time
 Personal Introductions
 Login,
 Start PVTi
Course Summary: Main Topics




Introduction
Samples and Components
Experiments and Observations
Regression
 Quality Control of laboratory measurements
 Generating output for Eclipse
 Miscibility
Course Summary: Main Topics






Components and Pseudo-Components
Characterisation of + components
Splitting and Grouping
Ideal Gas Laws and Equations of State
Matching Equations of State
Material Balance Checks
Purpose of PVTi Course




Demonstrate the use of the PVTi package
Introduce PVT analysis
Simple examples to familiarise with PVTi
“Real” examples to illustrate:
 Quality control problems with PVT data
 Problems encountered when attempting to match an EOS.
 Create PTV data for simulation
Why use PVTi ?
 Who is interested in PVTi results ?
 Which part of the production process needs to have PVTi

results ?
What are the (P,T) conditions at which we need fluid
properties?
Uses of PVTi
 Need to predict:
 Composition of well stream v.s. time
 Completion design (wellbore liquids)
 Gas injection or re-injection
 Specification of injected gas- how much C3, 4, 5’s to




leave in
 separator configuration and conditions
 Miscibility effects
Amounts and composition of liquids left behind and its
properties: density, Surface Tension, viscosity.
Separator/NGL Plant Specifications
H2S and N2 concentration in produced gas
Product values v.s. time
Uses of PVTi
Transport
Refining
Surface Seperation
Sampling
Gas Injection
(Re-cycling)
Sampling
Multi-Phase
Flow
Miscible/Immisicible
Displacement
Sampling
Pressure Decline
Saturation Change
Near Wellbore Blockage
 Require knowledge of fluid behavior in reservoir, well and at surface
 Over a wide range of pressures, temperatures and compositions
Uses of PVTi
 To match an Equation of State to observations
 This is done to compensate for the inability to measure

directly all the things we need to know about the
hydrocarbons
To Create
 “Black-Oil” PVT tables for a Black Oil model
 “Modified Black-Oil” PVT tables for an E200 GI Pseudocompositional Model or an E200 Solvent Model
 Compositional PVT parameters for a Compositional Model
Uses of Compositional Simulation
Processes where
 EOR involves a miscible displacement
 Gas injection/re-injection into an oil produces large


compositional changes in the fluids
Condensates are recovered using gas cycling
Surface facilities department needs detailed compositions of
the production stream
Uses of Compositional Simulation
Reservoirs with
 Large compositional variations with depth or in x-y direction
 Large temperature variation with depth
Advantages of Compositional Simulation
Can account for effects of
 Phase behaviour
 Multi-contact miscibility
 Immiscible or near-miscible displacement behavior in

compositionally-dependent mechanisms such as
vapourization, condensation, and oil swelling
Compositional - dependent phase properties such as
viscosity and density on miscible displacement
Field Oil Production Rate
PVTi modules
The first few exercises will not need material balance checks, so
we will cover PVTi in the following order:
 The Main panel




Systems: define fluids and samples
Simulate: experiments and observations
Regress : match EoS
Export : results to simulators
 COMB : material Balance
PVTi modules
For the Systems, Regress and Simulate operations, we will:




Discuss the background to the expected input data
Summarise some theory
Demonstrate how to input the data
Go through one or more practical examples
Launching PVTi
Launching PVTi
The First Panel
 After launching PVTi and specifying the working directory, PVTi
asks for the name of the project.
The First Panel
This name will be used to create output files for this project:
 xxx.PVI are PVTi Input files. These are the ‘saved’ files from a


PVTi run
xxx.PVO are PVTi Output files that are in the format expected
by the Eclipse simulators
xxx.PVP are PVTi Print files that contain the results of the
experiments that have been run in PVTi
The Fundamentals Panel
 This panel is a quick way of entering a fluid composition.
The Main Panel
 If you choose “Cancel” then the Main Panel will appear
The Main Panel
 Once you have specified a project name, you may want to
choose units: Main Panel: Utilities | Units
The Components
 Before we input any fluid components, we should discuss
what we mean by a “component”.
Components Fundamentals
Outline
 Homologous Series
 Single carbon Numbers
 Components and Samples
 Phase plots and Ternary diagrams
 Splitting
 Grouping
Components Fundamentals
Background Topics:
 Gas Laws
 Non-Ideal Behavior
 Equations of State
 K-Values
 Flash
 Phase Envelopes
Components Fundamentals
Components and Samples
We need to define:
 What components and pseudo-components are present
 What samples we are dealing with
 How much of each component is in each sample
and to plot:
 fingerprint plots
 phase diagrams
Components Fundamentals
 We therefore need first to understand what we mean by
components and pseudo-components
Components Fundamentals
 Theoretical background
 What do we mean by “component”?
 What do we mean by C6? C30??
Homologous Series
 Compounds having a common basic characteristic
 Paraffin Hydrocarbons
 Cycloparaffins
 Aromatic Hydrocarbons
 Above Categories containing additional atoms:
 Sulphur
 Nitrogen
 Oxygen
 Metals
Paraffin Hydrocarbons
 Methane
H
|
H -- C -- H
|
H
 Ethane
H
H
|
|
H -- C ---- C ---- H
|
|
H
H
 Propane
H
H
H
|
|
|
H -- C ---- C ---- C ---- H
|
|
|
H
H
H
Paraffin Hydrocarbons
Cn H 2 n  2
 All the carbon-carbon bonds are single bonds
Paraffin Hydrocarbons
N
1
2
3
4
5
6
7
8
9
Alkane Name
Methane
Ethane
Propane
Butane
Pentane
Hexane
Heptane
Octane
Nonane
Formula
C1H4
C2H6
C3H8
C4H10
C5H12
C6H14
C7H16
C8H18
C9H20
MW
16
30
44
58
72
86
100
114
128
Hydrocarbons
 Problems start with C4H10
 Butane
 or Butane?
 iso- and normal-butane
H
H
H
H
|
|
|
|
H -- C ---- C ---- C ---- C ---- H
|
|
|
|
H
H
H
H
H
H H
|
|
|
H -- C ---- C ---- C ---- H
|
|
|
H H--C--H H
|
H
Isomers
 Approximate ratios
iC4:nC4 is 2:1
iC5:nC5 is 3:2
Hydrocarbons: C6
 Carbon atoms can form single, double bonds, rings
 C-C-C-C-C-C or C-C-C-C-C=C
 C-C-C-C-C


|
C
C-C-C-C-C
|
C
C
|
C-C-C-C
|
C
CH
HC
CH
HC
CH
BENZENE
CH
Cycloparaffins
 Cycloparaffins - chain structures of normal paraffins formed
into rings - all carbon-carbon bonds are still single
 At low carbon numbers Cycloparaffins are less stable than
normal paraffin counterparts - thus present in much smaller
amounts - but can have significant effect on phase behaviour
Aromatic Hydrocarbons
 Aromatic hydrocarbons - contain one or more benzene rings
 Stable rings with 3 carbon-carbon double bonds - C6H6
 Significant effect on phase behavior
Polynuclear Hydrocarbons
 Polynuclear Hydrocarbons - asphaltenes and high molecular
weight Cycloparaffins, having a number of carbon ring
structures attached together
 Tarry deposit in well tubing - held in solution by intermediates
- as soon as pressure falls and intermediates leave with gas
phase, asphaltenes drop out in tubing.
Carbon Numbers
 API is not a good measure of what hydrocarbons are
present in an oil
141.5

( API  131.5)
 Knowing that an oil is 5% C9 helps, but what do we mean
by C9? What are the properties of this C9?
Number of Isomers
 Number of isomers increases rapidly above SCN of 6
 Question:
How many isomers of C30 do you think there are?
Number of Isomers
 Number of isomers increases rapidly above SCN of 6
 Question:
How many isomers of C30 do you think there are?
 Answer:
between 1x109 and 3x109 isomers of C30
Identifying Components
 For the lower molecular weights, analytical methods can
identify individual components and isomers of these basic
components.
 As the molecular weights of the hydrocarbon components
rise, polymers are less easily discriminated using routine
analytical methods.
Identifying Components - SCN
 The composition of the higher molecular weights is reported



in terms of boiling point fractions = the amounts of fluid which
distil between two specified temperatures.
The temperature intervals chosen are between the boiling
points of each member of the series of normal paraffins
Fractions are referred to by the number of carbon atoms in the
relevant normal paraffin
These groups referred to as single carbon number (SCN)
groups
SCN Groups
 Proliferation of isomers with increasing carbon number makes
individual identification impossible.
 Introduce Single Carbon Number (SCN) Groups
 SCN group n: all hydrocarbons with
Tb (Cn )  Tb  Tb (Cn 1 )
 for instance Benzene (C6H6) is usually in SCN Group 7 as
its boiling point is higher than that of the paraffin Heptane
(C7H16).
Distribution of SCN Groups in a North
Sea Oil
Distribution of SCN Groups in a North Sea
Condensate
Identifying Components - SCN
 ONLY for an extremely paraffinic fluid would the SCN
groupings have the properties (MW, Tc , Pc, ...) of the
corresponding normal paraffin
 In general, we don’t know the properties of the mix of
components defined by any SCN >5.
 For instance the Lab report C6 is a mixture of C6H14, C6H13,
C6H12, etc and a mixture of all their isomers.
 PVTi has a “library” of typical SCN properties. These values
are used by default: Katz and Firoozabadi
Identifying Components - Plus Fraction
 All PVT reports have a component analysis up to some upper
carbon number to be specified by the owner of the fluid, say 6,
11, 19 or 29.
 Residual hydrocarbon fluid is usually referred to as the plus
fraction, i.e., C7+, C12+ C20+ or C30+.
Identifying Components - Plus Fraction
 Detailed component analysis is made of pure component and
SCN fractions up to a PLUS fraction




C7+
- old/cheap
C12+
C20+
C30+
- expensive
 Mole Weight of C+ fraction made by freezing point depression
or boiling point elevation.
Identifying Components - Plus Fraction
 For C7+, C12+ C20+ or C30+ only a limited set of information
available, usually the molecular weight MN+ and sometimes the
specific gravity N+
 For use in an EOS model, we need the EOS parameters such
as Tc, Pc, , etc.,
 These are obtained from correlations depending on MN+ and
N+, for example the Kesler-Lee Correlation.
 This is called “Characterization of the Plus fraction”.
Identifying Components
 We don’t know the properties of the SCNs.
 We don’t know the properties of the plus fraction.
 Therefore we can’t predict fluid behavior.
 This is where regression comes in: we adjust the fluid
properties to match the observations.
We will do this later in the Regression Module.
Defining Components
Edit | Fluid Model |Components gives a choice of:
 built-in library properties
 Characterising
 defining your
own
Default is “Library”
except for the
last component
Defining Components
“Characterise” gives a choice of methods:
Characterisation of + Component
 Must specify MW
 Specify density if available, otherwise PVTi uses correlation

which can be displayed [Sg v MW]
- see next slide.
[Characterise] will generate properties of + component
 Looking ahead to regression … the properties of the +
component are the least well-known and therefore the best
candidates for adjustment
Defining Components
If Specific gravity (Sg) is not available, a corellation will give Sg
from the Molecular Weight (MW).
Defining Components
 The “Complete” tab shows the properties of each components
and pseudo-component.
Property Trends - Pure H/C Components
 Properties increasing with increasing molecular weight






Tc Critical Temperature
Tb Normal Boiling Point
Vc Critical Volume
 Acentric Factor
o Liquid Density
Pa Parachor
Property Trends - Pure H/C Components
 Properties decreasing with increasing molecular weight
 Pc Critical Pressure
 Zc Critical Z-Factor
The Fluid Model
 Having defined our components and pseudo-components, we
can define what our sample is made of.
Samples in PVTi
 Main Panel | Edit: Samples: Names
Samples in PVTi
 Edit | Samples | Compositions
Samples in PVTi
 Checks that sum(zi)=1
Systems: Samples, Phase Plots
Samples, Phase Plots
Samples in PVTi
 You can’t change the name of the default sample ZI, but you
can have as many other samples as you want.
 Note the difference between “components” and “samples”:
you can have
 a component called CO2 and
 a sample called CO2.
- Discuss
Tutorials: Exercise 1
 Creating a Fluid System
 Defining a fluid
 Defining a fluid sample
 Selecting an EoS
 Program Options
 Viewing fluid attributes (Phase Plots)
 Saving Systems section
Tutorial: Phase Plot Result
Exercise 2
Model Oil - Three Components
 For demonstration purpose define oil composed of
 C1
 C6
 C12
 Use PVTi Default Values
Model Oil - Three Components
 We will look at the change in the phase plot as the fluid
composition changes.
Model Oil - Three Components




Clear all pictures
Click on “superimpose plots”
Add a new component C12
Create 7 new samples
Model Oil - Three Components
 Define compositions of new samples
C1 = 80% to C1 = 20%
with the remaining % divided between C6 and C12
All other % = 0
 So for example
Sample 1 is 80% C1, 10%C6, 10%C12
Sample 2 is 70% C1, 15%C6, 15%C12
Sample 3 is 60% C1, 20%C4, 20%C12
etc…
Model Oil - Three Components
 Plot phase diagrams
 Comment on:
 Shape
 Position of Critical Point
 Fluid type at 550 K
 Psat at 550 K as a function of C1 concentration
Model Oil - Three Components
Model Oil - Three Components
Phase Envelopes for Reservoir Fluids
- C is Critical Point
Oil and Gas Compositions
Dry Gas
Gas
Condensate
Volatile Oil
Oil
N2
6%
CO2
2%
2%
1%
1%
C1
82%
80%
69%
36%
C2 – C6
10%
13%
14%
20%
5%
16%
33%
C6
Exercise 2A





Clear all plots
Plot with 1 Quality Line
Select “Superimpose plots”
Change EoS
Compare new phase plot
Reservoir Temp = 150 o C
Fluid ZI: 80% C1, 10% C6, 10% C12
Splitting and Grouping
Splitting
 Our objective is to match all the available observations with

the minimum number of (pseudo-)components.
We therefore want to group components
but …
 We may need to split the “+” component before we start
Splitting
 “Insufficient description of heavier hydrocarbons reduces the


accuracy of PVT predictions” (Whitson C.H., SPEJ, p. 683,
Aug. 1983)
Condensates and Volatile Oils are particularly sensitive to plus
fraction composition and properties
Laboratories tend to give very limited analysis to the plus
fraction, i.e., MN+, N+
Splitting the plus Fraction
 From Standard C7+, C12+, C20+ analysis:
 The heavier ends tend to remain in solution during CVD

Experiment
 There is a wide distribution of heavy components in the
plus fraction
No EOS model using a single component for such a plus
fraction could hope to adequately model the above process,
even with tuning.
C7+ Component Splitting
•
Original Distribution of Components
Mole
Fraction
C7+
Molecular Weight
Distribution of SCN Groups in a North
Sea Oil
C7+ Component Splitting
 Know Mole Weight and density (specify gravity) of plus
fraction
 Whitson splitting calculation uses three parameter probability
density function
 Procedure Splits C7+ fraction into many(30-40) small SCN, then
groups into 2, 3 or 4 components
Fingerprint Plot
Idealised fingerprint plot
Original C7+ component has high mole fraction
Mole
Original C7+
Fraction
Molecular Weight
Whitson Splitting
Original C7+ component split into several new (red) fractions
Mole
Fraction
OriginalC
7+
C7+
Molecular Weight
Splitting Procedure
 Specify MN+, N+, zN+
 Assume constant Watson factor Ki=KN+(MN+, N+)
 Specific gravity
 i  Tb1,/i 3 / Ki

where Tbi, are SCN group values (Whitson)
Mole weights
b c
M i  aTb, i i
 Calculate mole fractions from cumulative probability integral
Analysis of Plus Fraction
 Require model to relate mole composition to mole weight
 Whitson, 3 parameter PDF
(M  )
p( M ) 
( 1)
exp[ 
  ( )
(M  )

]
where
  is skewness
  is normalization
  is minimum Mw in plus faction
 where  defines the form of the distribution (approx.
between 0.5 to 2.5)
Analysis of Plus Fraction Contd.
 Where  is defined as
  M c    / 
7
 And the gamma function

    
0
 1 
e d
Fingerprint Plot
Split Components
Split Components
Grouping after Whitson Splitting
Grouping after Whitson Splitting
 Whitson splitting takes C7+ SCN into SCN 7, 8, 9, 10,…45.
 Regrouped according to Sturges rules, giving a reduced
number of Multiple Carbon Number (MCN) groups of Nn where:
N n  Integer[1  3.3 log 10 (M  N )]
 N and M are the first and last carbon numbers in the plus

fractions.
N is usually 7, M is 45 here.
Grouping after Whitson Splitting
 Example:
 Oil is described by up to C45
 How many components should we split C7+ into?
 M=45, N=7
 Nn= Integer[1+3.3 log(45-7)] = 6
Grouping after Whitson Splitting
 The mole weights separating each MCN group are given by
  1
M M 

M l  M N exp 
ln
  N n M N 
l
 MN and MM are the mole weights of the first and last carbon
numbers in the plus fraction.
Grouping after Whitson Splitting
 Same example:
 Oil is described by up to C45, C7+ is split into 6 pseudo
components,
 Upper molecular weight of first pseudo-component ML = 96
[exp(1/6) ln(539/96)] = 128
 Similarly for the other 5 pseudo components
Grouping After Whitson Splitting
 In practice, 3 is usually a good choice
Grouping
Grouping
 The number of grouped ‘pseudo-components’ needed in a
compositional simulation depends on the process that is
modelled:
 For depletion, 2 pseudo-components may be enough
(Black-oil model)
 For miscibility, more than 10 components may sometimes
be needed.
 In general, 4 to 10 components should be enough to describe
the phase behaviour
Why Grouping or Pseudoization?
 PVTi calculations tend to go as Nc3
May make analysis of large PVT report impractical
 Compositional simulator uses same EOS model as PVTi
Flash calculations can take 50% of simulation time
 Reduce number of equations  reduce number of
components
Rules for Grouping
 Basis for grouping
 similar properties, eg MW
 same log(K) versus p trend
 insensitivity of experiments to trial grouping
 Obvious candidates
 iC4 and nC4  C4
 iC5 and nC5  C5
 Add N2 to CH4, CO2 to C2H6 (at low concentrations)
Grouping
 Add N2 to CH4, CO2 to C2H6
Molecule
 N2
 CO2
Molecular weight
28
44




16
30
44
58
CH4
C2H6
C3H6
C4H8
K-values v.s. Pressure
Tutorial: Exercise 3: Grouping
 Make sure you frequently SAVE
 Reduce number of components from 16 to 9
 Is the phase plot the same?
 Reduce to 7 then 5
 Is the phase plot the same? In the region of interest?
 How low can you get?
Exercise 3: Splitting and Grouping




Reload original data
Try splitting the C12+
Group into fewer pseudo components
Did splitting help?
Exercise 3: Splitting and Grouping
 Load data from COMB.PVI
 Change Type of component C12+ from “User” to




“Characterise”
Change MW of C12+ from 161 to 165
Change Specific Gravity from 0.805 to 0.807
Save then Characterise
Group into fewer pseudo components
(Reservoir Temperature = 220F)
Some Theory...
 Flash calculations
Flash Calculation
Feed this container with N moles of fluid - composition
CO2 N2 C1 C 2-3C 4-6 C 7-10 C 11-15
C 16-20 C 20+ (know Zi mole fraction feed)
Flash: Determine amount, properties and
composition of the vapor and liquid at
EQUILIBRIUM
Temperature and
Pressure Set
FLASH
 Most EoS calculations are based on the flash
 The same flash library is used in both PVTi and ECLIPSE 300
 The flash is used to either: determine number of phases present and their split
 iterate in P or T to find Psat or Tsat
 Most of the CPU time in ECLIPSE 300 can be spent on the
flash calculations.
Flash and Saturation Pressure
 Flash: know {zi} and (p,T)
 Unknowns: {Ki} and V
 Psat: know {zi} and (T,V)
 Unknowns: {Ki} and P, (Psat)
Bubble Point Pressure
 Specify temperature and feed composition of OIL
 PVTi returns pressure where phase transition occurs.
Dew Point Pressure
 Specify temperature and feed composition of GAS
 PVTi returns pressure where phase transition occurs.
Flash and Saturation Pressure
 1 mole of fluid, composition {zi}, flashed to
 L moles liquid, of composition {xi}
 V moles vapor, of composition {yi}
where
L V  1
Lxi  Vyi  zi
x
i
i 1
y
i 1
i
1
i
1
z
i 1
1
BEWARE of Notation
 V = Mole fraction in Vapor
 This is NOT the same V that appears in
PV=RT
The V here is the volume at pressure P and temperature T
BEWARE of Notation
 zi is mole fraction of component i in sample
 Z is compressibility form PV=ZRT
Flash and Saturation Pressure
 K-Values: Ki = yi/xi, gives
zi
xi 
1  V ( K i  1)
K i zi
yi 
1  V ( K i  1)
 Flash: know {zi} and (p,T)
 Unknowns: {Ki} and V
 Psat: know {zi} and (T,V)
 Unknowns: {Ki} and P, (Psat)
Flash: K-values
 K-values = Equilibrium Constants
yi
Ki 
xi
V yi
L xi
Flash: K-values
 Constant K - values
 yi=Kixi table look-up on i
 K-values function of (P,T) Isothermal
 yi=Ki(P)xi table look-up on i and Pressure
 K-values function of (P,T,yi,xi) and isothermal
 yi=Ki(P,yi,xi)xi
PR Calculated K-Values at 100o C
1000.00000
100.00000
10.00000
C1
C3
C6
C10
C15
C20
C30
K-Values
1.00000
0.10000
0.01000
0.00100
0.00010
0.00001
0
20
40
60
80
100
120
Pressure (barsa)
140
160
180
200
PR Calculated K-Values at 400o C
1000.00
C1
C3
C6
C10
C15
C20
C30
100.00
K-Values
10.00
1.00
0.10
0.01
0
20
40
60
80
100
120
Pressure (barsa)
140
160
180
200
Flash Equation
 In the flash calculation: we know the feed mole fractions zi and
we have an estimate of the component K-Values Ki
 We don’t know the molar fraction of vapour V.
 This can be found from solving the FLASH Equation
(Rachford-Rice Equation) :
zi ( K i  1)
0

i 1 1  V ( K i  1)
nc
i  1,2,3, ... n c
Development of Flash Equation
 See if you can derive this expression as homework
zi ( Ki  1)
( yi  xi )  
0

i 1
i 1 1  V ( K i  1)
N
N
Flash - General Theory - 1
 Given estimates for zi and Ki
 The Flash Equation gives solutions for V, L, xi and yi
zi Ki  1
g V   
0
i 1 1  V  Ki  1
nc
 Next look at the properties of this equation.
Flash - General Theory - 2
zi Ki  1
g V   
0
i 1 1  V  Ki  1
nc
 The root(s) of this equation will give the value of V for the
hydrocarbon mixture.
 Notes: g() is a monotonically decreasing function of  and
g() has the following asymptotes:
 = 1/(1-Ki)
i = 1,2,3,…nc
Flash - General Theory - 3
 If Kl = Largest K - value and Ks = Smallest K - value
 Then a necessary but not sufficient condition for the existence
of a root between 0 and 1 is that of 0 and 1 be included in the
interval
1 
 1
,
1  Kl 1  Ks 
Flash - General Theory - 4
 The solution of EQ 60 has 3 possible cases
 Case 1: g (0) > 0, g (1) < 0 Root in (0,1)
 Case 2: g (0) < 0
Root  Case 3: g (1) > 0
Root > 1
 Case 1: Yields a root of g (V) between (0,1) Thus, 2 phases are


present.
Case 2 and 3: Root > 1 or Root < 0
Thus, we have a SINGLE PHASE
Flash by Successive Substitution
 Given T, P, Zi
 Obtain an initial estimate of Ki from Wilson’s Formula



1

exp 5.371  i 1 

Tri 


Ki 
Pri
OR from the previous flash results
 Solve for V from
zi K i  1
g V   
0
i 1 1  V K i  1
nc
Flash by Successive Substitution
 Solve for xi, yi from
xi  zi / 1  V  Ki  1
i  1,2 ,...... nc
yi  Ki zi / 1  V  Ki  1 i = 1,2 ,..... nc
 Use EOS to find ZL, ZV, then calculate fugacities of each
component in each phase fiL, fiV
Flash by Successive Substitution
 Test for Convergence
 Calculate
nc

i 1
2
 f iL


 f  1
 
 iV

 If No go to calculate a new Ki (next slide)
 If Yes Equilibrium Found
 ~ 10 12
Flash by Successive Substitution
 If flash has not converged then calculate new estimate of Kvalue by the equation:
K
NEW
i
K
OLD
i
 f iL 
 
 f iV 
 Then recalculate V from expression g(V)=0
 Called successive substitution
 Recall fiL/fiV=1 at equilibrium
 Acceleration techniques for Kinew available
Flash Summary






Guess Ki
Solve Rachford-Rice equation to get V
From V get L, xi and yi
From EoS, get ZL, ZV,
From V, L, xi, yi, ZL and ZV calculate fiL, fiV
Test for convergence
 either converged
 or recalculate Ki and start again.
Flash Example Problem
C1 + C3 + C10 System
P,T known
V
L
Flash Example Problem
Total moles of C1, C3, C10 in “grid block” is
Known
Moles of Component i
Zi 
Total Moles
Component 1: C1
Component 2: C3
Component 3: C10
Z1 = 0.8
Z2 = 0.1
Z3 = 0.1
Flash Example Problem
We have an estimate of the K-values
yi
Ki 
xi
C1: K1 = 11
C3: K2 = 1
C10: K3 = 0.1
most of C1, in gas phase
equally divided between liquid and gas
most of C10 in liquid phase
L (liquid fraction) and V (vapor fraction) are unknown.
Flash Example Problem
 Z1=0.8, Z2=0.3, Z3=0.1
 K1=11, K2=1, K3=0.1
zi Ki  1
g V   
0
i 1 1  V Ki  1
nc
 How many phases?
 What is V?
 L? xi, yi?
Flash Example Problem
Substitute for zi and Ki and develop an algebraic expression
for g(V) = …..
zi K i  1
g V   
0
i 1 1  V  Ki  1
3
Flash Example Problem
Z 3 ( K 3  1)
Z1 K1  1
Z 2 K 2  1
g V  


0
1  V K1  1 1  V ( K 2  1) 1  V K 3  1
0.811  1
0.11  1 0.1(0.1  1)


0
1  V 11  1 1  V 1  1 1  V 0.1  1
8
 0.09
g V  

1  10V 1  0.9V
Flash Example Problem
Step 1 - Check to see if Case 1 (root in [0,1])
or Case 2 (root <0) {no need to solve for V here}
or Case 3 (root > 1) - {no need to solve for V here}
Flash Example Problem
8
 0.09

1  10V 1  0.9V
Test g 0
8 0.09
g 0  
 7.91  0 OK
1
1
8
0.09
8 0.09
g1 

 
 0.72727  0.9  0.17273  0 OK
1  10 1 0.09 11 0.1
g V  
We have Case 1: Root in [0,1]
Flash Example Problem
g V


8
0.09

 0
1  10V
1  0.9V
8
0.09

1  10V
1  0.9V
81  0.9V

 1  10V  0.09
8  7 .2V  0.09  0.9V
7 .91  8.1V
7 .91
V 
 0 .97654 97 .65% vapor
8 .1
L= 1-V = 0 .02346 2.34% L iquid
Flash Example Problem
L+V=1
(1)
Lxi + Vyi = Zi
(2)
1. Develop equations for xi and yi
HINT: Substitute (1) and (2)
AND: Remember Ki = yi/xi
2. Then solve for C1, C3, and C10 mole fractions in the
liquid and vapor.
Flash Example Problem
1. Develop equations for xi and yi
1  V xi
 Vyi  Z i
yi
also K i 
xi
Zi
therefore xi 
1  V K i  1
Ki Zi
and yi 
1  V K i  1
Flash Example Problem
2. Then solve for C1, C3, and C10 mole fractions in the liquid and
vapor.
0.8
for C1 : x1 
 0.0743
1  0.976510 
110.8
y1 
 0.817
1  0.976510 
0.1
for C3 : x2 
 0.1
1  0.97651  1
y2  K1 x1  10.1  0.1
Flash Example Problem
C10: x3  1  x1  x2  1  0.743  01
.  0.823
y3  1  y1  y2  1  0.817  01
.  0.083
Flash Summary






Guess Ki
Solve Rachford-Rice equation to get V
From V get L, xi and yi
From EoS, get ZL, ZV,
From V, L, xi, yi, ZL and ZV calculate fiL, fiV
Test for convergence
 either converged
 or recalculate Ki and start again.
Ternary Diagrams
Ternary Diagrams
 Ternary Diagram - pictorial display of 3 component groupings
 Mainly used for analysis of MISCIBILITY.
 3 groupings are light, intermediate and heavy
 Only approximate view - depends on grouping
Ternary Diagram
100% methane
Vapor Phase Composition: y
tie lines connect liquid
and vapor phases in
equilibrium
z
Plait Point: tie line length = 0
30% C1, 60% C4, 10% C12
Liquid Phase Composition: x
extension of critical tie line
100% C12
100% C4
20% C1, 20% C4, 60% C12
Ternary Diagrams at 150°C and 200 Bar
A1
A5
A3
A7
Two Phase Envelope at Various Pressure
330 bars
300 bars
Fluid A4
200 bars
150 bars
Two Phase Envelope at Various Pressures
150 bars
50 bars
110 bars
Exercise: Ternary Diagrams
 View
| Samples
| Ternary Plot
Exercise: Ternary Plots
 Simulate: Go (Simulate:Perform)
 Simulate: Define: Observations:
 Try
different
pressures
Exercise: Ternary Plots
 What is Psat?
 How can you check this?
Ternary Diagrams
500 K,
200 bars
Ternary Diagrams
Ternary Diagrams
Some more Theory...
Equations of State Overview
PVT Review - Pure Component Behavior
Boyle’s Law
Pressure
For a fixed mass of
gas at constant
temperature
1/Volume
pV = Constant
Boyle’s Law
 Boyle’s Law is based on observations made around 1660, that
for a fixed mass of gas at a fixed temperature, the product of
pressure and volume is a constant:

pV = constant
Charles’ Law
 Over a century later (1787) it was observed that for a fixed
mass of gas at constant pressure, the volume varies linearly
with temperature
 If the gas had a volume Vo at 0o C, then at a temperature T:
V = Vo(1+aT)
Charles’ Law
 The gradient, a, is found to have the value 1/273
 as a consequence, when T= -273oC the gas volume will become zero.
 By re-specifying a temperature scale T’ with the same spacing of degrees
as the centigrade scale, but starting with 0 at -273oC the
volume/temperature relationship becomes:
V
V
T
273
0
PVT Review - Pure Component Behavior
Charles’ Law
Temperature
For a fixed mass of
gas at constant
pressure
Volume
V / T = Constant
Ideal Gas Law
 Boyle’s Law: fixed mass of gas at constant temperature
 pV = constant
 Charles’ Law: fixed mass of gas at constant pressure
 V/T = constant
 Combining gives the Ideal Gas Law
 pV = nRT
n = number of moles
 R = 10.372 psia /ft3 / lbmole
 R = 0.0821 Barsa / m3 / kgmole
Assumptions and Limitations
 Assumptions of the Ideal Gas Law
 pV = nRT
 Molecules are point-like, i.e. zero volume
 No inter-molecular forces
Limitations:
 Gases are not infinitely compressible
 No account of change of phase
 Adequate only for low pressure gases
Real Gas Law
 If the prediction of changes of state are not important, we can
relate the volume of a real gas at one set of T and P conditions
to another set using of Z-factors or compressibility factors.
 The Z-factors are functions both of T and P and of the gas
involved. The Z-factor at standard conditions (60 F, 14.7 psia)
is equated to 1.
 The method is applicable to both pure components and to gas
mixtures.
Compressibility - Z-factor
 PV=nRT
 PV=ZnRT
Ideal Gas
Real Gas
Z = compressibility
 Definition of compressibility:
Z=PV/RT i.e. deviation from ideal behaviour
Non-Ideal Behavior - Z-Factor
 We can relate the volume of gas at one pressure to the volume
at another pressure:
p1V1 p2V2

T1Z1 T2 Z 2
Equation of State
 To modify the ideal gas EOS to account for departures from

ideal behavior and to account for phase changes, we need a
more complex equation.
Various attempts were made in the latter half of the
19th Century, the most famous being the Van der Waals
equation
Equation of State
 Ideal Gas Law => Van der Waals (1873)
a 

 p  2  V  b  RT

V 
a: attractive force
b: co-volume
Equations of State (EoS)
 An Equation of State (EoS) is an analytic expression relating



pressure to volume and temperature
PV=ZRT is an equation of state
Common EoS are PR, SRK
 These are cubic in Z
None completely satisfactory for all engineering applications
Equation of State
PV  nRT Ideal Gas
PV  ZnRT Real Gas, Z  compressib ility
RT
a
P

Van der Waals
V  b V V 
RT
a(T)
P

Soave - Redlich Kwong
V  b V V  b 
RT
aT 
P

Peng - Robinson
V  b V V  b   bV  b 
Pure Components
 Given Tc, Pc, , Zc, Vc one can predict
 Volume (or the density) that a mass of pure component will
take at any P and T
 The pressure or temperature at which the component
changes phase
 Other thermodynamic properties of the component
PVT for Mixtures
 Oil field hydrocarbons are mixtures of many components.
 To determine the pressure in a fixed volume with a fixed
number of moles of each component at a fixed temperature,
the EOS used must be solved for the mixture.
 so we need a value for a and b in the equation
RT
a(T)
P

V  b V V  b 
for the mixture
PVT for Mixtures
.  Use PVTi to obtain initial Tc, Pc, , Wa , Wb … for each
component
 Equations are used to calculate a and b for the mixture from
the known data and mixing rules.
 We can then Flash (solve the EoS) to obtain L,V and xi,yi and
fluid properties
 We then compare these calculated fluid properties with
observed values from experiments
 We then update Tc, Pc, , Wa , Wb … to get a better match.
 Details later in the course
Exercises: Theory
 Exercise 1: Real Gas Behaviour
 Exercise 2 Phase Behaviour of a pure component
Properties of Pure Substances
PVT Relation of a Pure Substance
From Adkins
“Equilibrium
Thermodynamics”
Most useful projections of the PVT surface
p
From Adkins
“Equilibrium
Thermodynamics”
p
C
solid
T
liquid
vapour
C
V
Tc
Ttr
P-T Diagram for Pure Component
Critical
Point
Solid+
Solid
Liquid
Liquid
Pressure
Vapor
Triple
Point
Temperature
P-T Diagram for Water
Pressure
Isothermal compression causes melting
Solid
Critical
Point
Liquid
Vapor
Triple
Point
Temperature
Law of Corresponding States
 Law of corresponding states (applied to gases) means that the
same real gas compressibility factor (Z-Factor) can be applied
to different gases when they are in the reduced condition.
 Reduced properties Pr = P/Pc, Vr=V/Vc, Tr=T/Tc
 That is Z is unique to a given P/Pc and T/Tc
 Systems are in corresponding states if two of their reduced
variables are equal.
Properties of Mixtures
Z-Factor- Kay Mixing Rule
 1936 - experimental work by Kay, and correlations based on
his data, proved the extension of the Law of corresponding
states to the treatment of gaseous mixtures, specifically
hydrocarbon gas mixtures.
Kay’s Mixing Rule
 For certain purposes, a mixture of gases can be considered as

a single gas having properties which are the sum of the mole
fraction weighted properties of the individual gas
components.
The most common application of this rule is the computation
of pseudo-reduced temperatures and pressures for a gas
mixture in order to calculate Z-factors: i.e.
N
T
Tpr   zi
Tci
i 1
Z-Factor - Kay Mixing Rule
 The pseudo-criticals, denoted Ppc, Tpc and Vpc, are used in the
same way as Pc and Tc in the determination of Z -factors.
 This can be done from the now famous chart generated by
Standing in 1942.
 Various numerical methods also exist, among the more
popular being the Yarborough-Hall method, which formed the
basis of calculation of the HP-41-C fluids pack.
 The use of such correlations has been superseded by EOS
modelling in programs such as PVTi
Raoult’s Law Non-ideal Solution Behavior
Vapor Pressure of Pure A
Z
Liquid Composition
Vapor Pressure of Pure B
X
Y
Mixture Vapor Pressure
100
50
Mole Percent of Component A
0
Raoult’s Law Non-Ideal Solution Behavior
 Guide to Vapor Pressure Vs. Mole Percent of Component A
 Dotted line represents ideal solution behavior
 Liquid of composition x is in equilibrium with vapor of
composition y
 If this vapor condenses it gives a liquid with the same
composition, ie., z
 Comments: Principle of distillation - azeotropic mixture
(Gin: 43% ethyl- alcohol)
 Component with highest vapor pressure has lowest boiling
point.
Dalton’s Law of Partial Pressures
 Dalton’s Law of partial pressures states that the partial
pressure due to a gas within a mixture of gases is the same
pressure as would be measured if it alone were present under
the same conditions as the mixture.
Dalton’s Law of Partial Pressures
 If perfect gas properties are assumed, then
N i RT
pi 
VT
where
 pi is the partial pressure in the gas mixture due to component i
 Ni is the number of moles of component i in the gas mixture
Dalton’s Law of Partial Pressures
 Also p  NT RT
T
VT




where
VT is the total volume occupied by the gas mixture
NT is the total number of moles in the mixture
R and T are the gas constant and absolute
temperature respectively.
Amagat’s Law
 The partial volume of a gas in a mixture of gases is defined as
that volume which the gas would occupy if it alone were
present at the same temperature and pressure as the mixture
of the gases.
 (For an ideal gas this follows directly from Dalton’s Law of
partial pressures).
Dalton’s Law with Raoults’s Law
 It can be seen therefore that
pi
Ni

 yi
pT NT
 where yi is the mole fraction of component i in the gas.
Combining this with Raoults’s Law gives:
xi poi  pi  pT yi
Dalton’s Law with Raoults’s Law
 Rearranging gives
yi poi

xi pT
 ie., the molar ratio of a component (vapor to liquid) is equal to
vapor pressure/total pressure for each component.
Raoult’s + Dalton’s Law Modified
 Dalton’s Law and Raoult’s Law (below) can be rewritten in
terms of fugacities, thus allowing the original formulations to
be used and yet taking account of the non-ideal behavior.
pi  xi poi  fi  xif
K-Values
 The term yi/xi, which is the ratio of the mole fraction of
component i in the vapour, to its mole fraction in the liquid is
known as the equilibrium constant or K value.
yi poi

 Ki
xi pT
Equations of State
Equations of State (EOS)
 An Equation of State (EOS) is an analytic expression relating



pressure to volume and temperature
Best method for handling large amounts of PVT data
Efficient and versatile means of expressing thermodynamic
functions in terms of PVT data
None completely satisfactory for all scientific and engineering
applications
Equations of State
 Ideal Gas Law
 Combination of Boyle’s and Charles’ Laws
pV  RT
 Adequate only for low pressure gases
 Van der Waals (1873)
a
( p  2 )V  b   RT
V
 a: attractive force
 b: co-volume
Phase Change in EOS
 In order to model the phase behaviour of real fluids, it is

necessary to account for attractive and repulsive forces
between molecules.
Thus, the pressure exerted between the molecules by a real
fluid has two components:
 where prep and patt are the repulsive and attractive pressure
terms
p p
rep
p
att
Phase Change in EOS
 The most famous relationship for describing the energy of
interaction between molecules is that due to Lennard-Jones:
 1 2 
 (r )   12  6 
r 
r
 where r is the intermolecular separation and 1,  2 are
constants
Van der Waals EOS
 In terms of the Lennard-Jones potential equation ,
 the r12 term has been replaced by a “hard-sphere”

approximation in the form of the b parameter
whereas the attractive r6 term is accurately represented by the
a/V2 term since the volume V ~ r3.
Critical Point
 Definition: The intensive properties of the vapor and liquid
become equal
 Intensive properties - independent of the amount of substance
 Extensive properties - dependent on the amount of substance
in the system, e.g. heat content, volume internal energy.
Critical Point
 At the critical point on mole of substance occupies a critical
volume,Vc
 The three critical constants of any gas are NOT related by gas
law.
 Critical coefficient, (RTc)/(pcVc) for ideal gas should be = 1, but
normally between 3 and 3.5
Most useful projections of the PVT surface
p
From Adkins
“Equilibrium
Thermodynamics”
p
C
solid
T
liquid
vapour
C
V
Tc
Ttr
P-V Behavior of Cubic EOS
Van der Waals EOS
 At critical point
 Critical isotherm is a point of inflection
 p

 V


Tc  0

 2 p 
 2 Tc  0
 V 
As a cubic in volume, three real equal roots

RT

V  b 
p

3
 2 a
ab
V  V 
0
p
p

 Apply above conditions at Critical Point
At Critical Point
RTc
2a
 P 
 3 0

 
2
 V T (Vc  b) Vc
c
 2P 
RTc
3a
 2  
 4 0
3
 V T (Vc  b) Vc
c
Van der Waals EOS
3 RTc
Vc 
8 pc
27 R 2Tc2
a
64 pc
b
1 RTc
8 pc
R 2Tc2
or W a
pc
or W b
RTc
pc
By comparison with Real Gas Law
And by definition
W
V dW
a
WVb dW
Z
27

64
1

8
V dw
c
3

8
Van der Waals EOS
 Working with cubic EOS, more convenient to work in terms of
the Z -factor rather than volume. Replacing V in equation
RT
a
p
 2
V  b  V
 by ZRT/p and rearranging gives:
Van der Waals EOS
where
Z 3  B  1Z 2  AZ  AB  0
ap
27 pr
0 pr
A  2 2  Wa 2 
RT
Tr
64 Tr2
bp
B
RT
pr 1 pr
 W

Tr 8 Tr
0
b
 This Equation yields 1 or 3 Real Roots depending on the No.
of Phases in the system.
Non-Ideal Behavior
a
(p 
)(V  b)  RT
2
T V  C 
Clausius (1880)
A
(P 
)(V  b)  RT Berthelot (1878)
2
TV
p(V  b)  Re
(
a
)
VRT
Dieterici (1899)
Redlich-Kwong EOS
 First major improvement on Van der Waals EOS
RT
a
p

V  b V V  b
where
a  ac (T )
 (T )  Tr1/ 2
 Soave modification
 1/ 2  1  m( )(1  Tr1/ 2 )
Where m( ) is polynomial in Acentric factor
Redlich-Kwong EOS
2
2
c
RT
ac  0.42748...
,
pc
W  0.42748
RTc
b  0.08664...
,
pc
W  0.08664
0
a
0
b
Redlich-Kwong EOS


Z 3  Z 2  A  B  B 2 Z  AB  0
where
ap
0 pr
A  2 2 or W a 2  Tr 
RT
Tr
bp
B
RT
pr
or W
Tr
0
b
 This Equation yields 1 or 3 Real Roots depending on the No.
of Phases in the system.
Soave-Redlich-Kwong (SRK) EOS
 As for R-K EoS with modified 

  1  m  1  Tr

m   0.480  1.574  0.176
2
where m() is polynomial in acentric factor
 1/2 is linear in Tr1/2 with negative slope
Acentric Factors
 The Acentric factor of a component is a log function of the
component vapour pressure at a reduced temperature of 0.7:
  (log 10 P  1);
s
r
at Tr  0.7
 Originally formulated by Pitzer et al (J. Am. Chem. Soc., 77,
p.3427, 1955) it is a measure of the non-sphericity of the
component molecule, and hence an indicator of the degree of
non-ideal behaviour to be expected from the component.
Peng-Robinson (EOS) PR
 Most widely used 2-parameter (a,b) EOS
RT
a
p

(V  b) (V  m1b)(V  m2b)
where
m1  2  2
m2  2  2
 and
a  ac ( , T )

  1  m  1  Tr

Peng-Robinson (EOS) PR

 

Z  1  B Z  A  3B  2B Z  AB  B  B  0
3
2
2
2
3
where
ap
0 pr
A  2 2 or W a 2  Tr  , where W 0a  0.45724
RT
Tr
bp
B
RT
pr
0
or W
, where W b  0.07780
Tr
0
b
 This Equation yields 1 or 3 Real Roots depending on the No.
of Phases in the system.
Zudkevich-Joffe (ZJ) EOS
 Omega parameters become temperature dependent
 Wa and Wb obtained for each pure substance from saturated
liquid density and equalisation of fugacities
 Omegas are taken as temperature independent above Tc
Comparison of EOS
 Van der Waals, Redlich-Kwong, Peng-Robinson, etc., are two
parameter, ie (a,b) EOS
Z
VdW
c
 0.375
Z
RK
c
 0.333...
Z
PR
c
 0.307...
 But hydrocarbons have Zc< 0.29
 Introduce Third Parameter - Variable Z-Factor
3-Parameter EOS
 Peneloux et al., Fluid Phase Equil., 8, pp. 7-23, 1982 - “volume


shift” technique.
Calculate fugacities, etc., as for 2-parameter EOS
Shift volumes, and hence Z-factors
N
 where
V (3)  V ( 2)   xi ci
i 1
ci  Vi
EoS
( pst , Tst )  Vi
Obs
( pst , Tst )
Volume Shift Technique
 Van Der Waal’s loop
 Areas above and below p = pv line
are equal.
 Therefore equal liquid and gas
fugacity: equilibrium system
 Shifting the equal area plot left or
right, on volume axis does not
change the equal area (fugacity)
balance
Phase Behavior – SPE Monograph vol. 20
Mixing Rules
 In multicomponent systems mixing rules have to be applied
 Most EOS use original Van der Waals mixing rules:
 Quadratic mixing rule for A:
N
N
a   xi x j ai a j (1  kij )
i 1 j 1
where kij are binary interactiv e coefficien ts
and kii  0 and kij  k ji
Mixing Rules
 Linear mixing rule for B:
N
b   xi bi
i 1
Default Binaries for PR
 Katz and Firzoobadi
 Experimentally determined for Non-Hyd:Hyd
 Hyd:Hyd all zero except between C1 and CN+
k C1 , j  0.14γ j  0.06
Binaries for PR
Cheuh-Prausnitz
 Can be set with the appropriate option switch
 Theoretical consideration
ki, j
  2(V V )1 / 6  B 
c ,i c , j

 

 A 1
1
/
3
1
/
3
  Vc ,i  Vc , j  


Cheuh-Prausnitz BIC
 Where Vc,i is the critical molar volume of the ith component
 Generally B is set to 6.0 and A is adjusted to match the

measured saturation pressure
Good match is usually obtained with 0.15A0.25.
 There appears some physical justification for this model in
that the cube root of the volume is the “radius” of the
molecule, thus equation for kij is some weighted average of
the proximity with which two unequal species can come
into contact.
Mixing Rules
 kij interaction Coefficients to the Peng-Robinson equation of
state according to Prausnitz
C1
C2
C3
I-C4
n-C4
I-C5
n-C5
C6
C7
C8
C9
C10
N2
CO2
C2
0
C3
0.017
0
i-C4
0.03
-0.005
-0.008
n-C4
0.027
0.01
0.003
-0.002
I-C5
0.009
0.012
n-C5
0.027
0.028
C6
0.04
-0.04
-0.004
C7
0.037
0.007
0.007
C8
0.052
0.018
0
C9
0.05
0
0
C10
0.042
0.014
0
N2
0.031
0.042
0.094
0.017
-0.007
0.004
0
0
0.008
0.149
0.048
CO2
0.124
0.131
0.135
0.127
0.11
0.113
-0.012
Phase Diagrams of Mixtures of Ethane and nHeptane
Composition
1400
Pressure, psia
4
1200
5
3
1000
No.
1
2
3
4
5
6
7
8
9
10
Wt % ethane
100.00
90.22
70.22
50.25
29.91
9.78
6.14
3.27
1.25
n-Heptane
2
800
1
6
600
7
8
400
9
10
200
0
100
200
300
400
Temperature, °F
500
Generalized Cubic EOS
(Van der Waals Type)
RT
a
P
 2
V  b V  uV  w
 In 2-parameter forms of the equation u and w are related to b
 In 3-parameter form u and w related to b and a 3rd parameter c
(or some properties such as acentric factor)
Parameters for General Cubic EOS
Generalised Equation of State
 Martin’s generalised form:
Z 3  E2 Z 2  E1Z  E0  0
with
E2  (m1  m2  1) B  1
E1  A  (2(m1  m2 )  1)B 2  (m1  m2 ) B
E0  [ AB  m1m2 B 2 ( B  1)]
Generalised Equation of State
 Martin’s generalised form:
Z  E2 Z  E1Z  E0  0
3
2
with
EoS
m1
R-K
0
1
0
1
1 2
1 2
Z-J
P-R
E2  (m1  m2  1) B  1
E1  A  (2(m1  m2 )  1)B 2  (m1  m2 ) B
E0  [ AB  m1m2 B 2 ( B  1)]
m2
Predicted Dew Point Pressures by
Various EOS
 PR(BIP) = PR +BI
Parameters
 VPT = Valderrama,
Patel, Teja
 mPR = modified PR
 EXP = experimental
 PR = PengRobinson
Equilibrium Ratios Predicted by
Various EOS
Measured and Predicted Condensate
Drop-out by Various EOS
EoS Conclusion
 Need to match EoS to observations
Simulate, Regress Outline





Experiments and observations
Laboratory Measurements
CCE
CVD
DL
 Regression: which variables? When? How?
 Regression weights
Description of main PVTi
Experiments
Multi-Stage Pressure Experiments
 Standard lab experiments
 Constant Composition Expansion (CCE)
 All fluids
 Constant Volume Depletion (CVD)
 Gas condensates and volatile oils
 Differential liberation
 Crude (black) oils
Constant Composition Expansion
 Specify a temperature and a series of pressures
 Pick: OIL, GAS or SIN (true one-phase system, such as dry
gas above the cricondotherm)
 Saturation volume will be used as a normalization volume
Constant Composition Expansion
At p > psat there are no compositional
changes and CVD and DL are
equivalent to CCE
Vapor
Vapor
Cell
Volume at
Dew Point
Vapor
Liquid
p>pdew
Vapor
pdew
p<pdew
Liquid
p<<pdew
Constant Volume Depletion
 Specify a temperature (below cricondotherm) and a series of
pressures
 Applies to both oil and condensate systems
 Vapor removed to restore cell to original volume
 Relative volume reported is the fraction of the cell filled with
liquid after the gas is removed
Constant Volume Depletion
Withdrawn
Gas
Withdrawn
Gas
Vapor
Vapor
Cell
Volume at
Dew Point
Vapor
Vapor
Liquid
p>pdew
pdew
p<pdew
Liquid
p<<pdew
Differential Liberation
 Specify a temperature and a series of pressures.
 Applied to oil only
 All gas is removed at each pressure step
 Last pressure step will be a reduction to standard conditions automatic.
Differential Liberation
Withdrawn
Gas
Schematic Diagram of
Differential Liberation
Withdrawn
Gas
Vapor
Vapor
Liquid
Liquid
Liquid
Liquid
p>pbub
pbub
p<pbub
Liquid
p<<pbub
Cell
Volume at
Bubble Point
Swelling Test
 Specify temperature, reservoir fluid and lean gas to be mixed
with reservoir fluid.
 Gas added amounts specified
 Mole percentages of gas in the mixture
 GOR (volume of gas at STC/volume of oil at original
saturation pressure)
Swelling Test
 Either specify a Mole% of a gas or a GOR, where
mole%  M 
GOR  G 
N gas
N gas  N res
st
V gas
o
Vres ( p sat
)
 For mixture
zimix  (1  M ) zires  Mzigas
Two Phase Z-Factor
 Can use 2 -phase Z factors in simulation to avoid using gas in
oil / oil in gas formulation.
 2 phase Z factor - only present in CVD experiment. It is really a
measure of the compressibility of the two fluids together, i.e.,
the liquid/gas
 uses PV = ZnRT equation
Two Phase Z-Factor
 Two Phase Z factor
= Pressure(i) x Total Volume ( liquid & gas )
/ ( moles of liquid & gas(i) ) x Reservoir Temperature
Separators
 Separators consist of a set of flashes at user-specified
pressures and temperatures.
 Specify
 Number of stages
 Pressure and Temperature of each stage
 Connection of vapor and liquid outputs of each stage
 Final stage is stock tank conditions – needs to be specified
Observation Mnemonics





ZL - Liquid Z-factor
 MWV - Vapor molecular
weight
ZV - Vapor Z-factor
DNL - Liquid density
DNV - Vapor density
MWL - Liquid molecular
weight




VSL - Liquid viscosity
VSV - Vapor viscosity
SL - Liquid saturation
SV - Vapor saturation
Observation Mnemonics
 VMF - Vapor mole fractions
 PS - Saturation pressure: gas - Pdew, oil - Pbub
 FSGOR - GOR: in SEPS - gas(STC)/oil(stage/STC); in DL 
gas(STC)/oil(STC/Psat)
RV - Relative volume (in SWELL=swelling factor)
Observation Mnemonics
 TGOR - Cumulative separator GOR: (Gas at STC/final stage




Oil)
TERN - Ternary Plot
MWP - Mole weight of plus fraction (in COMB Mat Bal)
RVSAT - Relative oil saturated volume (Bo(Pbub) in DL)
KV - K-values
Observation Mnemonics





XMF - Liquid mole fraction
YMF - Vapor mole fraction
ZMF - Total mole fractions
SGP - Specific gravity of plus fraction (in COMB Mat Bal)
RECOV - Moles recovered from depletion experiment (CVD,
DL)
Observation Mnemonics
 MOLVL - Liquid molar volume (specific volume)
 MOLVV - Vapor molar volume (specific volume)
 LMWP - Mole weight of liquid plus fraction (in COMB Mat Bal)
Observation Mnemonics
 LSGP - Specific gravity of liquid plus fraction (in COMB Mat



Bal)
LXMF - Liquid mole fraction of final stage of CVD (in COMB
Mat Bal)
TRELV - Total (oil and gas) relative volume (DL)
ORELV - Oil relative volume (DL, SEPS, VAPOUR)
Observation Mnemonics





GGRAV - Gas gravity (DL)
GFVF - Gas formation volume factor (DL)
GVEXT - Gas volume extracted (at STC) (DL)
2PZ - Two phase Z-factor (CVD)
SRELV - Oil FVF from Pinit/Pbub to Pstock (SEPS)
Tutorials: Exercise 2
 Simulation Section
 Defining experiments
 Simulating experiments
 Plotting results
 Defining further experiments
 Simulating all the experiments
Exercise 2: CCE RV results
Exercise 2: DL FSGOR results
Regression
Regression
 Why Regress EOS parameters?
Regression
 Why Regress EOS parameters?
 Incomplete fluid description
 Limitations of cubic EOS
 Problems of regression
 Multi-variable
 Non-linear
Prior to Regression
 Check measured data for consistency and quality
 Compositions sum to 100%?
 Pressure-dependent data: correct trends?
 Material balance on CVD?
 Property definitions?
 Consistent units?
 Plus fraction description?
 EOS: Use three-parameter model - extra degree of freedom in
si (Volume Shift Parameter)
Rules for Regression
 Vary properties of poorly defined components, i.e., plus
fraction(s)
 Choose as few properties as possible
 “Bouncing” Rms or
 Variables  limits 
 Redundancy in variable set: “trial and error” to find
optimum set or sensitivity matrix Aij = ri/xj
 Ensure variable monotonicity
Variable Choice
 (Tc, pc), or Omegas of plus fraction(s): saturation pressure,
liquid dropout, etc.
 Volume shift: Z-factors, densities, etc.
 Zc or Vc for LBC viscosity Do this last!
 Consider Experiment set
 Observation set and weights
 Variable set and limits
Rms Error
 Set of variables:
x  ( x1 , x2 ,..., xN )
 Define Residuals:
obs
calc
ri ( x)  yi  yi ( x)
 where M < N
 then, “Rms Error”
1 M 2
f ( x)   ri ( x)
2 i 1
T
(i  1,2,..., M )
Minimization of f
 Minimum of f(x) requires f(x)=0
 Solve by globally convergent: Newton
 Ensure is minimum from properties of 2f(x) matrix
 Evaluate matrices by numerical differencing:
hence work/iteration ~N+1
Process: Grouping and Regression
Check data using all components
Regress
Group “similar” components
Does it make a difference in range of interest?
 Phase envelope
 Ternary
Can you match?
 Simulate PVT experiments
 Adjust: Tc,Pc,,Kij, Wa, Wb, by regression
 Poor match
re-adjust pseudo components start again
 Similar match continue
 Better match
Great!
Regression
Regression
 Special Regression
Details
Sensitivities
Hessian Matrix
 Used to examine the
conditioning of the regression
problem
 ‘Good’ Hessian - diagonal
elements dominate and are
roughly equal in size
 Ill-conditioned Hessian - may
result in slow convergence of
a regression
 Ill-conditioned Hessian fixed
by removing redundant
parameters - reducing interdependence between
parameters
Covariance Matrix
 Calculated as inverse of Hessian
matrix
 Used to infer how well
determined the parameters are
for the current match
 Larger diagonal elements associated with less well
determined parameters
 Off-diagonal elements parameter co-variances
(measure of how well one is
known given the other)
Correlation Matrix
 Used to indicate the degree of



association between changes in one
parameter with changes in another (1<= =>+1)
-1 indicates - increase in one
parameter has exactly the opposite
effect (decrease) in another
+1 indicates an increase in one
parameter has exactly the same effect
as an increase in the other (they are
correlated)
0 indicates they are independent of
one another
Tutorials: Exercise 3
 Regression
 Fitting an EoS by regression
 Regression using the special variables
Exercise: PVT Analysis of an Oil
Investigate the oil properties of the fluid
6 components -
T = 38 0 C
Name
CO2
N2
C1
Mole fraction
0.01
0.01
0.10
C3
C10
C15
0.10
0.30
0.48
Exercise: PVT Analysis of an Oil
 Look at:
 Phase plot
 Ternary Diagram
 Check oil? Gas? How near critical? Psat?
Exercise: PVT Analysis of an Oil
Determine MCMP at the given temperature with
1. Methane
2. Solvent (60% C1, 40% C3)
3. CO2
4. N2
Method:
1) Draw ternary diagram at different pressures, MCMP= tangent
over reservoir point (for C1)
2) swelling Test : Define Swelling experiment
3) MCMP experiment
Viscosity Correlations
Viscosity Correlations
 Cannot predict viscosities from EOS: phase flow property
 Two most widely used correlations
 Lohrenz-Bray-Clark (LBC)
 Pedersen et al
 Aasberg-Petersen – not yet available in Eclipse Compositional
 LBC OK for gases and volatile oils, very poor for heavier oils
 Pedersen better for gases and oils, but not good for heavy oils (presence
of asphaltenes)
 AP Good over large P and T ranges. Can handle mixtures of CO2, paraffinic
and aromatic components. Better than Pedersen for heavy oils
 Can only regress with LBC
Pedersen et al
 Based on Corresponding States Method (CSM)
 A group of substances obey CSM if functional dependence

of “reduced” quantity on other reduced quantities is the
same for all components in the group
Pedersen (most commonly used)
mr = f(Tr, Pr)
 Alternative Ely and Hanley (not in PVTi)
mr = f(Tr, r)
Aasberg-Petersen
 Uses 2 reference fluids rather than the 1 for Pedersen –

Methane and Decane
Interpolation law to compute reduced viscosity of optimum
reference component
 Better than Pedersen for heavy oils, since the size and shape
of the molecules differ substantially from that of methane
 Not recommended for fluids with a lot of napthalenes
Lohrenz-Bray-Clark
 Viscosity a parameterized function of reduced density

r 
c
1 

 c    xiVc ,i 
Vc  i 1

N
where critical density
 To give
  a1  a2  r  a3   a4   a5 
2
r
3
r
4
r
1
Viscosity Regression
 First regress everything else
 Ensure that regression is performed on liquid and vapour
viscosities simultaneously
 Then adjust the critical volume of the plus fraction
Miscibility
Miscibility
 An oil-gas displacement is immiscible if the oil and gas
segregate into separate phases.
Oil-gas relative permeabilities and capillary pressures are
used.
 A displacement is miscible if the mixture of oil and gas forms
a single hydrocarbon phase.
Oil-gas relative permeabilities and capillary pressures are not
needed.
What is Miscibility
 Under normal conditions, oil & gas reservoir fluids form



distinct, immiscible phases
Immiscible phases are separated by an interface
 associated with inter-facial tension (IFT)
 when IFT=0, fluids mix => MISCIBILITY
residual oil saturation to gas (and water) directly proportional
to IFT
miscible displacement characterized by low/zero residual oil
saturations
Miscible Conditions
 Establishment of miscibility depends on
 pressure (MMP)
 fluid system compositions
 Miscibility normally determined by laboratory measurement
 Miscibility difficult to predict analytically
 complex phase behavior
 derivation of surface tension
Miscible Processes
 Three basic types of miscible process
 first-contact miscibility
 condensing-gas drive
 vaporizing-gas drive
Compositional Processes
 First Contact Miscible
 LPG slugs - designed to achieve first - contact miscibility with
oil at leading edge of slug and with driving gas at trailing edge
Compositional Processes
Example Oil:
C1 - 31%
Injection gas: C1
nC4 - 55%
C10 - 14%
Pressure/Composition Diagram
for Mixtures of C1 with C1/nC4/C10 Oil.
4000
Cricondenbar (3250 psig)
Pressure
Psia
Bubble Pts
0
0
Dew pts
100
50
Volume % Methane
Compositional Processes
 Rule: For 1st Contact Miscible - Pressure of Displacement
must be above Cricondenbar
First Contact Miscibility
 Pressure > MMP
 All points between solvent and reservoir oil lie in single phase

region
Need high concentrations of solvent - expensive
Multi-Contact Miscibility
 Pressure < MMP
Condensing - Gas Drive Process
 Injection gas is enriched with intermediate components such


as:
C2, C3, C4 etc
Mechanism:
 Phase transfer of intermediate MW hydrocarbons from the
injected gas into the oil. Some of the gas “Condenses” into
the oil.
 The reservoir oil becomes so enriched with these materials
that miscibility results between the injection gas and the
enriched oil.
Multiple Contact Experiment
Injection Gas
Injection Gas
Injection Gas
Injection Gas
oil
Equilibrium Oil Transferred to Next Cell
Condensing Gas Drive
Condensing Gas Drive Miscibility
Mixing 1:
Mixing 2:
Mixing 3:
Mixing 4:
Injection gas with Reservoir Oil
Mixture M1 splits into L1 and V1
(liquid and Vapor)
Injection gas with Liquid L1
Mixture M2 splits into L2 and V2
Injection gas with Liquid L2
Mixture M3 splits into L3 and V3
Injection gas with Liquid L3
Mixture M4 splits into L4 and V4
V1
V2
V3
G
V4
The enriched Liquid Li position moves toward
the Plait Point until a line connecting the
injection gas and the enriched liquid lies
only in the single phase region.
reservoir oil
injection gas
M1
L1
M M4
M2 3
L2
L3
Plait Point
L4
o
extension of critical tie line
Condensing Gas Drive Miscibility
Miscibility developed at the
trailing edge of the injection
gas
gas compositions with NO
multiple contact miscibility
gas compositions with
multiple contact miscibility
line from reservoir oil tangent
to 2 phase envelope
O
reservoir oil
extension of critical tie line
gas compositions with
first contact miscibility
Condensing - Gas Drive




Pressure < MMP
Solvent and oil not miscible initially
Solvent components transfer to liquid oil phase
Repeated contact between oil and solvent moves system
towards plait (critical) point (dynamic miscibility)
Condensing - Gas Drive
 For systems with oil composition to left of tie line, solvent

composition must lie to right
Field behaviour is more complicated
 continuous, not batch, contact
 both phases flow
 actual phase behaviour more complicated, especially near
plait point
Slim Tube Apparatus
Condensing - Gas Drive Process
 As P increases the two phase region becomes smaller. At
some point gas A is to the right of the limiting tie line and
MCM develops.
miscible
95-98%
X
X
X
X
X
X
X
X
Oil Recovery
%
X
X
Minimum Miscibility Pressure
(MMP)
P
 Results from slim tube displacements at various pressures
Slim Tube Recovery of a North Sea Oil
at 100o C
Procedure to Find Minimum Enrichment
Vaporizing Gas Drive Process
 Injection Gas - Lean Gas, C1, CO2, N2
 For vaporizing gas drive - multiple contact miscibility
 Mechanism: Intermediate hydrocarbon components in the oil

vaporize to enrich the gas.
As the leading edge of the gas slug becomes sufficiently
enriched, it becomes miscible with the reservoir oil.
Vaporising Gas Drive
Injection Gas
Equilibrium Gas Transferred to Next Cell
oil
oil
oil
oil
oil
oil
Vaporizing Gas Drive
oil
Vaporizing Gas Drive Miscibility
Mixing 1:
Mixing 2:
Mixing 3:
Mixing 4:
Mixing 5:
Injection gas with Reservoir Oil
Mixture M1 splits into L1 and V1
(liquid and Vapor)
Gas Mix V1 with reservoir oil
Mixture M2 splits into L2 and V2
Gas Mix V2 with reservoir oil
Mixture M3 splits into L3 and V3
Gas Mix V3 with reservoir oil
Mixture M4 splits into L4 and V4
Gas Mix V4 with reservoir oil
Mixture M5 splits into L5 and V5
The enriched Gas Vi position
moves toward the Plait Point
until a line connecting the
enriched gas and the
reservoir oil lies
only in the single
phase region.
injection gas
G
M1
V1
o
V2
V3
o
M2
V4
o
M3
V5
M4
o
o
M5
L1
L2
L3
L4
L5
o
reservoir oil
Vaporizing Gas Drive Miscibility
injection gas
Miscibility developed at the
leading edge of the injection
gas
G
For MCM in a Vaporizing Gas Drive
The Reservoir Oil composition MUST
lie to the right of the limiting tie line
2000 psia: Miscibility?
3000 psia: Miscibility?
4000 psia: Miscibility?
Vaporizing Gas Drive Process
 To experimentally determine the MMP for given [oil, injection gas]
combination in a slim tube, the process and results are similar to
the condensing gas drive discussion
Condensing/Vaporizing Gas Drive
 Vaporizing gas drive not strictly valid for real reservoir fluids
 Injection gas does not generally contain middle heavy

fractions which are present in the oil
More realistic process is called Condensing/Vaporizing Gas
Drive since contains some of both processes
Condensing/Vaporizing Gas Drive
 Injection gas enriches the oil in the light intermediate range
 Also, it strips the heavier fractions
 Thus, reservoir in contact with fresh gas initially becomes
lighter, but as it contacts more gas and loses the middle
intermediates and lighter heavies, it tends to get heavier
Condensing/Vaporizing Gas Drive
 This heavier oil becomes LESS miscible with the injection gas
 The bubble point and the dew point curves on the
pseudoternary diagram initially converge and the diverge
Condensing/Vaporizing Gas Drive
injection gas
G
Figure from Aaron Zick’s Paper
Condensing/Vaporizing Gas Drive
 Forward moving gas (like a Vaporizing Gas Drive) becomes


richer in the middle intermediates and heavier fractions
At the same time looses the light intermediates
The forward moving gas becomes more similar to the
reservoir oil
Condensing/Vaporizing Gas Drive
 In Real situation miscibility (or near miscibility) achieved
within a transition zone
 Front of transition zone = Vaporizing Gas Drive (VGD)
 Tail of transition zone = Condensing Gas Drive (CGD)
Condensing/Vaporizing Gas Drive
Transition Zone
Injection Gas
CGD
VGD
Reservoir Oil
Vaporizing and Condensing Gas Drive:
Summary
 When a gas in injected into an oil the resulting displacement
can be:
 Vaporizing Drive: N2, CO2, C1, flue gas, dry separator gas
 Condensing Drive: Rich separator gas, C1 enriched with C2,
C3, C4, etc.
Vaporizing and Condensing Drive
 Where does the miscibility occur?
 Leading Edge or trailing edge?
 Which recovers most reservoir oil?
 Why is not used more often?
Vaporizing and Condensing Gas Drive:
 Minimum Miscibility Pressures can be obtained from ternary
diagram, or ...
First Contact Miscibility Pressure
Experiment
 Specify a temperature and two named samples
 Calculates the lowest pressure at which the samples will be
directly miscible (always one phase) in all proportions.
Minimum Miscibility Pressure
 If at a low pressure the oil and gas separate into two phases
then the displacement is called Immiscible.
 If the experiment is repeated at ever increasing pressure until
oil and gas become, the pressure where this first occurs is
called the Minimum Miscibility Pressure.
Miscibility Exercise
 PVTi Fluid Development
PVTi Class Exercise
 “Exercise Document”
 Determine MMP
PVTi Workshop: Fluid 1
 6 components 




 Slim Tube Units
 Tslimtube = 38 0 C
CO2
N2
C1
C3
C10
C15
0.01
0.01
0.10
0.10
0.30
0.48
 Determine MCMP at the slimtube temperature with
 N2 ,
 CO2,
 Methane, and
 Solvent (60% C1, 40% C3)
 Record the results for future use.
PVTi Workshop: Fluid 2
 6 components 




 Field Units
 Tslimtube = 180 0 F
CO2
N2
C1
C3
C10
C15
0.01
0.01
0.75
0.17
0.04
0.02
 Calculate Dew Pt., Ternary Diagram.
 Run swelling experiments with N2 and Methane to determine the
effect of gas added to the dew point pressure. Plot the Dew Point
pressure of mixtures of the Condensate with increasing mole
fractions of N2 and C1.
 Record the results for future use.
COMB, Export Module Outline
 PVTi COMB module
 COmpositional Material Balance
 Understanding Laboratory PVT Report
 Recombination of Samples
 Details of CVD Experiments
 Hoffman Crump Hocott Analysis
 Two Phase Z-Factors
 Differential and Flash Data
 Separator flash, Bo, Rs, Conversion of DL to New Flash
Conditions
 PVTi Export Module: Black Oil and Compositional
COMB
COMB
 Compositional Material Balance
 Checks consistency of CVD experiment
Experiments in PVTi
Experiments in PVTi
 What are the experiments?
 How are they done?
 Recognizing and Correcting Errors
Which Data Set to Use
 Do the data appear to



contradict each other?
Would you expect them to
be different?
Have you got a
measurement quality
problem
Which data are reliably
representative of the bulk of
the reservoir?
Incorrect Sampling
 Reservoir, pres ~ 4700 psia
 Saturation Pressure, Psat ~ 4460 psia
 where zc1 = 53.47, zC7+ = 16.92
 Sampling p ~ 300 psia  liquid dropout in reservoir  produced fluid
deficient in heavy ends
 say zC1 = 58.47, zC7+ = 11.92
 Then Psat = 4810 psia > pres !!
 Correction?
 Add (synthetic) dew point oil until psat < pres ?
 Fix this
Sample Composition Checks
 Mole percentages sum to 100?
 Nitrogen content - possible air contamination?
 H2S concentration
 were any values reported at the well site
 are the lab measured values comparable
 Hoffman, Crump, Hocott Plot
Constant Composition Expansion
Schematic Diagram of
Constant Composition Expansion
for Gas Condensate
Vapor
Vapor
Cell
Volume at
Dew Point
Vapor
Vapor
p>pdew
pdew
Liquid
Liquid
p<pdew
p<<pdew
Constant Volume Depletion
Schematic Diagram of
Constant Volume Depletion
for Gas Condensate
Withdrawn
Gas
Withdrawn
Gas
Vapor
Vapor
Cell
Volume at
Dew Point
Vapor
Vapor
p>pdew
pdew
Liquid
Liquid
p<pdew
p<<pdew
Compositional Material Balance
Compositional Material Balance
Compositional Material Balance
 Take 100 moles of reservoir fluid at p = psat = p1 and
composition {zi,1}
 At pressures pj < p1 measure
 Sl, j liquid saturation in cell
 Zv ,j Z-factor of removed gas
 np, j moles of removed gas
 yi, j composition of removed gas
 MN+ plus fraction mole weight
 N+ plus fraction Spec. Grav.
 xi, N final stage liquid comp.
Material Balance
 Conservation of moles
t , j  l , j  v , j
t , j zi , j  l , j xi , j  v , j yi , j
 Where
j
t , j  t ,1    p ,k
k 2
j
t , j zij  t ,1 zi ,1    p ,k yi ,k
k 2
 p ,k   p ,k   p ,k 1
Liquid, Vapour Volumes
 Condensate cell volume
 Volatile oil cell volume
Vcell 
Vcell
p1
nt ,1Z1 RT
t ,1M w,1

liq
1
 Volume of cell occupied by liquid and vapor after gas removal
Vv , j  Vcell (1  Sl , j )
Vl , j  Vcell Sl , j
Liquid Compositions, K-Values
Moles of vapor remaining in the cell from real gas law
nv , j 
p jVv j
Z j RT
Thus liquid composition and hence K-values
Ki, j 
yi , j
xi , j
Data Quality
 80 gas-condensate samples analyzed by CVD experiment
(Drohm, et al.)
 71 gave calculated negative liquid compositions
 45 gave abnormally high liquid densities (liq > 950 kg/m3)
 Liquid density should increase with decreasing pressure
 Liquid saturation curve should NOT be concave near dew
point
Cleaning-Up CVD?
 Negative Liquid Mole Fractions
 Decreases Moles Removed
 Change Wellstream Composition
 Abnormal Liquid Densities
 Increase Liquid Saturations
 Some analyses may not yield to remedial action  discard
report (and change your laboratory?)
Oil and Gas Sample Recombination
Oil and Gas Sample Recombination -1
 Having obtained and validated the compositional analyses of
separator gas and separator oil, reservoir fluid composition
can be calculated, given separator GOR
 Prior to this the field reported gas flow rate measurements
need correcting, as they are based on calculations which need
values for Z factor and gas gravity.
Oil and Gas Sample Recombination - 2
 Gravity is measured in the field, but not to the kind of
accuracy that it can be recalculated knowing the composition.
 The field Z-factors are based on correlations from the gas
gravity.
 The correction therefore is the recalculation of the gas flow
rate based on composition derived gas gravity and Z factor,
and hence recalculation of separator GOR.
Oil and Gas Sample Recombination - 3
 The recombination itself consists of calculating the number of
moles of each component in each phase at the quoted GOR,
adding them together to get the number of moles in the
reservoir fluid, and then renormalizing back to 100%.
Oil and Gas Sample Recombination - 4
 GOR as given by the field often has to be corrected
 Since the determination of the separator gas gravity is
frequently NOT correct
 Gas rate measurement in field performed with an orifice meter
 Gas gravity enters the calculation of the flow rate
Oil and Gas Sample Recombination - 5
 Correction to be applied
g1
Correct GOR 
 Field GOR
g2
 g1 = specific gravity of separator gas determined in the field
 g2 = specific gravity of separator gas determined in the
laboratory
Constant Volume Depletion
Schematic Diagram of
Constant Volume Depletion
for Gas Condensate
Withdrawn
Gas
Withdrawn
Gas
Vapor
Vapor
Cell
Volume at
Dew Point
Vapor
Vapor
p>pdew
pdew
Liquid
Liquid
p<pdew
p<<pdew
Details of CVD Experiment -1
 It should be performed on all Condensates and volatile oils as
these are the fluids which are going to undergo the greatest
compositional changes if the reservoir pressure is allowed to
drop below the saturation pressure.
 As the pressure drops below the bubble point/dew point
pressure, the following calculations and procedures are taken:
Details of CVD Experiment -2
 The volume occupied by 1 mole of the sample fluid at psat is
given by
Vcell  Vsat  V ( psat )
Details of CVD Experiment -3
 The total volume of the liquid and vapour phases is calculated
and then compared with the control volume, Vsat, (previous
slide)
 The excess of the new total volume compared with the control
volume, Vdel=Vtot-Vsat, is then removed from the gas volume:
aft
gas
V
V
 oil volume is left unchanged
bef
gas
 Vdel
Details of CVD Experiment -4
 The gas and oil saturations are calculated using the new
volume
S gas 
V
aft
gas
Vsat
since the new total volume is the control volume
Details of CVD Experiment -5
 The total mole composition which will be the feed-stream for
the next pressure depletion must be calculated
aft
gas
i
i
f
i f
bef
tot
z  x (1  v )  y v
V
V
 where xi and yi are the liquid and vapour mole
compositions from the flash prior to the gas removal
 vf is the vapour fraction from the flash = total fluid volume
before the gas removal
 This procedure continues down to the lowest specified
pressure
CVD Data Consistency
 CVD - have liquid and vapor samples at each pressure
 Analysis of composition gives K-Values
 Initial plots of vapour composition versus pressure
 Experimental Problems manifest themselves as material
balance errors, causing negative mole fractions in the
calculated liquid composition
 COMB: Compositional Material Balance in PVTi
CVD Data Consistency
 Having determined the K-values, two tests of consistency
 Plot the log(Ki) versus pressure for each component
 Generate a Hoffman-Crump-Hocott plot.
CVD Data Consistency
 Components log(Ki)’s plot against pressure:
 All lines must be monotonic and smooth
 Lines must not cross except at some extrapolated



pressure, pconv > psat
Lines must plot in a given order, preceding from top (high
K-value) to bottom (low K-value) as:
N2, C1, CO2, C2, C3, iC4, iC5, nC5, C6,...., CN+
H2S can be found anywhere between C1 and C3.
CVD Data Consistency
Validation of Oil/Gas Samples to
Separator Conditions
 Having obtained the compositional analyses of the separator
samples - possible to check that the calculated “K” values are
compatible with the reported separator conditions.
 Technique - graphical method of examining compositional
data from two equilibrium phases - verify the compositional
measurements against correlations using the reported
equilibrium conditions.
Hoffman Crump Hocott Analysis - 1
 If the log of the product Kp (where p is the separator pressure)
is plotted (for each component) versus the function b(1/Tb-1/T)
(also referred to as the “F” factor), the resulting plot should
show all the points lying on a straight line for each
component.
Hoffman Crump Hocott Analysis - 2
 Significant departures from the straight line relationship point
to potential problems for either the samples or the analysis.
 Minor deviations can be corrected by moving stray points
back to the line.
Hoffman Crump Hocott Analysis - 3
 The Hoffman-Crump-Hocott plot consists of plotting the
product logarithm of the product of the calculated K-values
and pressure log(Ki,jpj) against the Hoffman characterisation
factor, F, where:
 1 1
F  bi 
 
 Tb ,i T 
 where T is the CVD experiment temperature, Tb,i is the normal
boiling point temperature of the ith component
Hoffman Crump Hocott Analysis - 4
 bi is the Hoffman b-factor, given by:
log( pc ,i )  log( pref )
bi 
1
1

Tb ,i Tc ,i
where Tc,i and pc,i are the critical temperature and pressure of
the ith component and pref is the reference pressure, say 14.7
psia.
Hoffman Crump Hocott Analysis
COMB plots
Differential Liberation
 In principle, could do the same material balance checks for

Differential Liberation.
Not currently available in PVTi
Understanding an oil PVT Lab Report
 Form of data presented in the report developed from use in

material balance calculation
Report should cover all past, present and future situations
with may require calculations
 To do this with a complete set of table and curves
 To do this with a minimum of table and curves
 Data normalized to a reference state
 Petroleum engineer must then “work back” from the
reference state to his particular situation
Understanding an Oil PVT Lab Report
 Laboratory test are carried out on the basis that two difference

thermodynamic processes are underway at the same time
 Flash equilibrium separation of gas and oil in the surface
traps (separator chain) during production
 differential equilibrium separation of gas and oil the the
reservoir during pressure decline
PVT report gives both “flash” and “differential” data
 Engineer must be able to shift between the two sets of data
Understanding an Oil PVT Lab Report
 Keep in mind that the PVT report gives data on the particular



sample obtained
This may not be the proper “average” of all the fluid in the
reservoir
Later it may be necessary to adjust the data slightly
Sufficient detail of the sampling process and conditions so the
adjustment are possible
Differential and Flash Data
 Separator Test - Flash conditions as the whole fluid system

enters the trap (separators) immediately - i.e., reservoir fluid
comes to the surface and is immediately separated into gas
and oil
Differential Liberation - referred to as “differential data” - gas
solubility and phase volume data taken so as to model what
some people believe happens to oil phase in the reservoir
during pressure decline
Differential Data
 Reservoir pressure changes slowly compared to separator 
subsurface changes are more gradual - considered to be a
series of infinitesimal changes
Because of mobility considerations (relative permeability and
viscosity) the gas phase moves toward the well faster rate
than the liquid phase OR because of gravity moves up to a gas
cap.
Differential Data
 Thus, the overall composition of the entire reservoir system

changes
In DL experiment can not perform a true differential procedure
- usually use 10-12 steps
Differential and Flash Data
 Differential liberation - final volume of liquid phase remaining

in the cell at STC is called RESIDUAL OIL
Flash Experiment - measure quantity of surface gases and
stock tank oil that results when one m3 or barrel of bubble
point oil is flashed through certain surface trap sequences
(separator chain) - This give STOCK TANK OIL.
Differential and Flash Data
 RESIDUAL OIL and STOCK TANK OIL are not the same - both
are product of the original oil in the system by are developed
by different pressure-temperature routes.
 multiple series of flashes at the elevated reservoir
temperature
 a one or two-stage flash at low pressure and temperature
Differential and Flash Data Differences
 Quantity of gas released will be different
 In Oil PVT Report
 Rs flash = 232.38 sm3 / sm3
 Rs diff = 235.94 sm3 / sm3
 Quantity of final liquid will be different
 Bo flash = 2.0441 m3/sm3
 Bo diff = 2.0810 m3/sm3
Separator Test
Separator Separator
Pressure Temperature
o
Barsa
C
Gas/Oil Ratio
50
91.46
50
Formation
Volume
Factor
Molar fraction
to Liquid
Stream
Density Density
of Liquid of Vapor
Fraction Fraction
0.642
697.41 44.614
to
1.0132 30
105.78
2.0441
0.344
787.22 1.623
Cumulative for
Separator Train
232.38
2.0441
0.344
795.25 1.260
1.0132 15.5556
240.81
2.0925
0.336
797.48 1.280
25
133.89
0.583
731.70 22.646
25
to
1.0132 5
53.23
1.8629
0.418
783.37 1.612
Cumulative for
Separator Train
187.86
1.8629
0.418
777.25 1.064
Conversion of DL Data for the Specific
Separator Conditions
 For Rs - wish to determine the amount of gas at the surface
when a unit of saturated reservoir oil at a pressure less than
the bubble point pressure is flashed through the separator
chain
 For Bo - wish to shift the differential Bo curve for the special
separator conditions present in the field.
Bo from Separator Flash and DL
DIFFERENTIAL
@ 150OC
Bodb
2.0810=Vb/VR
Bo diff
V / Vr
Bob
Volume Factor
Bo m3/s m3
Bo shift
TWO STAGE
SURFACE FLASH
Pressure (barsa)
Bo
2.0441=Bob
184.067
barsa
Conversion of DL to New Flash
Conditions
flash
B
2.0441
(Bo ) shift  (Bo ) diff  ob
 (Bo ) diff 
2.0810
 Vb 
 
 VR  diff
 Bob 
Bob  Bo   Bodb  Bod   
 Bodb 
 Bob 

Bo  Bod  
 Bodb 
Rs from Separator Flash and DL
Rs DIFFERENTIAL
@150 oC
235.94(diff)
Rsdb
Rsb
scf/bbl
residual oil
Rs diff
Rs shift
Rs
sm3 / sm3
232.38(flash)
scf/bbl
bubble pt. oil
184.067 barsa
Rs from TWO STAGE
SURFACE FLASH
Pressure (barsa)
Conversion of DL to New Flash
Conditions
flash
B
2.0441
(Rs ) shift  (Rs ) diff  ob
 (Rs ) diff 
2.0810
 Vb 
 
 VR  diff
 Bob 
Rsb  Rs   Rsdb  Rsd   
 Bodb 
 Bob 

Rs  Rsb  Rsdb  Rsd  
 Bodb 
Tutorials: Exercise 5
 Data Analysis and Quality Control
 Reading Systems
 Reading COMB
 Material Balance Plots
 Hoffman-Crump-Hocott
Tutorials: Exercise 5
Exporting to Eclipse
PVT Data for Simulation
 One objective of PVT Analysis
 Produce data for simulation
 Type of model to use
 Blackoil Model
 Pseudo-Compositional
 Compositional
 All assume that EOS has been tuned to reliable measured data
Black-Oil or Compositional?
 When can you use a Black-Oil model ?
 When should you use a Compositional Model ?
Black-Oil or Compositional ?
 Typical uses of Black-Oil and Compositional
 Black-Oil: Pressure Depletion,
Heavy to medium oils
 Compositional: Gas injection, Miscibility,
Near-critical fluids, Condensates
Eclipse E100
 Extended Blackoil Model
 Consider Rs, Rv, Bo, Bg as functions of p, psat
 Also, mliq, mvap
 Perform depletion experiment to define properties in the

reservoir
 Below psat defines reservoir liquid and vapour
Flash reservoir liquid and vapour through separator network
to define Blackoil quantities
Blackoil Properties
 Reservoir compositions xi, yi from depletion experiment, i.e.,
CVD or DL
 Whitson and Torp: flash liquid and vapour through separators
 Blackoil properties ratio of reservoir/separator volumes,
etc.
 Coats: vapour as Whitson and Torp
 Liquid volumes by mass conservation
 Satisfies reservoir oil density
Tutorials: Exercise 4
 Exporting Eclipse 100 PVT tables
 Changing the unit system
 Generating Eclipse 100 PVT tables