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A study of dispersive mixing and flow based lumping/delumping in gas injection processes

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A study of dispersive mixing and flow based lumping/delumping in gas injection processes

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A STUDY OF DISPERSIVE MIXING AND FLOW BASED LUMPING/DELUMPING
IN GAS INJECTION PROCESSES

by
Reza Rastegar Moghadam Moadab

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PETROLEUM ENGINEERING)

May 2010

Copyright 2010 Reza Rastegar Moghadam Moadab

ii

Dedication

To my mother and father, Mehri and Ali, who have always provided me with their
continuous support, endless encouragement and unconditional love.

iii

Acknowledgments
First and for most, I would like to thank my advisor, Dr. Jessen, for his invaluable
support, guidance, patience and valuable suggestions throughout my PhD work at USC.
I would like to thank Dr. Ershaghi, the director of Petroleum Engineering program at
USC, for all the support and guidance provided to me that helped in both my academic
and professional development.
Acknowledgement is extended to Dr. Brun, for serving in my thesis committee and
providing me with his valuable comments.
I would like to thank John and Kyle Mork for giving me the internship opportunity at
Energy Corporation of America that introduced me to industrial and field experiences.
I am also extremely thankful to Victor Villagran, Mike Basham, Ronald Behrens and
Brian Littlefield, my supervisors and mentor at Chevron who helped me a lot in
developing my professional skills throughout the summer internship opportunities
provided.
I also need to thank Mork Family Department, Chevron and ENI for providing
funding throughout my PhD studies at USC.
Finally, I would also like to thank my best friends at the department: Abdollah,
Mohsen, Nelia, Ehsan, Dalad, Amir, Parham, Hamid, Farnaz, Hamed, Tayeb,
Mohammad and Mahmood for providing such wonderful environment to work and
progress.

iv

Table of Contents
Dedication ........................................................................................................................... ii

Acknowledgments.............................................................................................................. iii

Table of Contents ............................................................................................................... iv

List of Tables .................................................................................................................... vii

List of Figures ......................................................................................................................x

Nomenclature .................................................................................................................. xvii

Abstract ..............................................................................................................................xx

Chapter 1: Introduction ........................................................................................................1

Chapter 2: Dispersive Mixing in EOR Processes ................................................................8

Chapter 3: Mathematical Modeling ...................................................................................13
3.1 Compositional Simulation ..............................................................................13
3.2 No Volume Change on Mixing.......................................................................16
3.3 Corey-type Relative Permeability ...................................................................17
3.4 Simulation of Dispersive Mixing in Porous Media ........................................17
3.5 Modeling of Phase Behavior ..........................................................................19
3.6 Numerical Simulation .....................................................................................20

Chapter 4: Characterization of Fluid System .....................................................................21
4.1 Fluid Properties ...............................................................................................22
4.1.1 Absolute Viscosity of the Analog Solvents ..........................................23
4.2 Gas Chromatography (GC) and Procedure .....................................................24
4.2.1 Procedure for Preparing and Analyzing GC Samples ..........................25
4.2.2 GC Calibration .....................................................................................27
4.2.3 The Water Challenge ............................................................................30

v

4.3 Characterizing the Water–Methanol–Isopropanol–Isooctane System ............31
4.3.1 Ternary System of Water – Isopropanol – Isooctane ...........................31
4.3.2 Ternary System of Water – Methanol – Isooctane ...............................33
4.3.3 Ternary System of Methanol – Isopropanol – Isooctane .....................34
4.3.4 Quaternary System of Water – Methanol – Isopropanol – Isooctane ..34
4.4 UNIQUAC Modeling of Liquid-Liquid Equilibrium .....................................35
4.5 Viscosity Modeling .........................................................................................41

Chapter 5: Design of Displacement Experiments ..............................................................46
5.1 Wettability of Selected Materials/Fluids ........................................................47
5.2 Design of Packed Column ..............................................................................51
5.3 Characterizing the Packed Column ................................................................55
5.3.1 Porosity .................................................................................................55
5.3.2 Permeability ..........................................................................................56
5.3.3 Dispersivity of the Packed Column ......................................................56
5.4 Capillary Effects .............................................................................................67
5.5 Relative Permeabilities Study .........................................................................68
5.6 IFT Measurements – Pendant Drop ................................................................71
5.6.1 IFT Modeling .......................................................................................75

Chapter 6: Displacement Experiments and Simulation .....................................................77
6.1 Selection of Oil and Gas Compositions ..........................................................77
6.2 Numerical Diffusion Vs. Physical Dispersion ................................................79
6.3 Multi-component Two-Phase Displacement Experiment ...............................86
6.3.1 Displacement Experiment A ................................................................87
6.3.2 Displacement Experiment B .................................................................95
6.4 Discussion and Conclusions .........................................................................104

Chapter 7: Flow Based Lumping/Delumping for Integrated Compositional Reservoir
Simulation ......................................................................................................105
7.1 Introduction ...................................................................................................105
7.2 A Flow-Based Lumping Scheme ..................................................................110
7.2.1 Fluid A ................................................................................................116
7.2.2 Fluid B ................................................................................................120
7.2.3 3D Compositional Simulation of CO
2
Floods ....................................125
7.3 Comparison to the Method of Newley and Merrill ......................................129
7.4 A Flow-Based Variant of Newley & Merrill’s Approach ............................133

vi

7.4.1 MCM Displacement of Fluid A by CO
2
.............................................136
7.4.2 MCM Displacement of Fluid A by Separator Gas .............................139
7.5 Delumping for Integrated Compositional Simulation ..................................141
7.5.1 Fluid A & CO
2
....................................................................................147
7.5.2 Fluid A & Separator Gas 1 .................................................................150
7.6 Discussions and Conclusions ........................................................................153

Chapter 8: Summary and Recommendations ...................................................................164
8.1 Summary .......................................................................................................164
8.2 Future Research ............................................................................................165

References ........................................................................................................................167

vii

List of Tables
Table 1: 2008 US CO
2
miscible flooding projects by companies 5

Table 2: Properties of Water, Methanol, Isopropanol (2-Propanol), Isooctane (2,2,4-
trimethylpentane) at 25
o
C and 1 atm (Loras, 1999; Batycky, 1994; Padua, 1996) 23

Table 3: Pure component viscosity of the analog solvents in centipoises (cp) 23

Table 4: Effect of applying molecular sieve to dewater Methanol, Ethanol and Isopropanol 30

Table 5: Isooctane-Isopropanol-Water equilibrium tie-line data (mole fractions) at 20
o
C 32

Table 6: Isooctane-Methanol-Water equilibrium tie-line data (mole fractions) at 20
o
C 33

Table 7: Two-phase equilibrium compositions for Methanol, Isopropanol and Isooctane
system at 20
o
C 34

Table 8: Tie-Line composition data (mole fractions) for the 4 component system of Water-
Methanol-Isopropanol-Isooctane at 20
o
C and 1 atm 35

Table 9: UNIQUAC parameters regressed and used for matching the experimental data 36

Table 10: UNIQUAC regressed binary parameters for the system of Water (1), Methanol (2),
Isopropanol (3), Isooctane (4) 36

Table 11: Regressed values of interaction coefficients and and for UNIQUAC viscosity
model 43

Table 12: Predicted viscosities for the ternary literature data published by (Soliman and
Marschall 1990) 45

Table 13: Correspondence of analog and reservoir phases by Orr (2004) 48

Table 14: Contact angels on PTFE (Teflon) and glass tubing by Orr (2004) 48

Table 15: Wettability of components on PTFE at 24
o
C and atmospheric pressure 50

Table 16: Possible scenarios for displacement: In all cases, linear density model is used for
mixture density and UNIQUAC based viscosity model is used for calculating
viscosity of the mixtures. Calculations are performed for bottom-up displacement
settings. 52

Table 17: Stability conditions for displacement 53

viii

Table 18: Calculated permeability for the column A 56

Table 19: Recorded Mass vs. Time data 59

Table 20: Experimental condition and calculated Peclet number for horizontal dispersivity test 59

Table 21: Experimental condition and calculated Peclet number for vertical dispersivity test 60

Table 22: Single phase dispersivity experiment - lab conditions 61

Table 23: Effluent concentrations in mass fractions analyzed by GC for dispersivity
experiment 62

Table 24: Different scenarios studied to avoid capillarity dominated flow 68

Table 25: Steady-state experimental result for column A 70

Table 26: Measured IFT and literature data for the system under study, phase compositions are
in mass fractions (Sets A, B and C are the experimental IFT calculation at 20
o
C) 74

Table 27: Initial and injection compositions, K-values and pure components viscosity 79

Table 28: Initial composition and injection composition 85

Table 29: Displacement experiment A: lab conditions 87

Table 30: Effluent concentrations in mass fractions analyzed by GC for experiment A 88

Table 31: Displacement experiment B: lab conditions 96

Table 32: Density and viscosity prediction for oil and gas phases 96

Table 33:Effluent concentrations in mass fractions analyzed by GC for experiment B 97

Table 34: Detailed representation of reservoir fluid A 112

Table 35: Displacement pressure, temperature and MMP 116

Table 36: Fluid A + Gas 1 lumped to 7 components 116

Table 37: Detailed representation of reservoir Fluid B 120

Table 38: Displacement pressure, temperature and MMP 121

Table 39: Fluid B + Gas 2 lumped to 7 components 121

Table 40: Data for 3D calculation examples 126

ix

Table 41 : Comparison of simulation time between lumped model and full model 129

Table 42: Comparison on lumped system using Newley & Merrill’s approach resulted with
different K-values along displacement path as shown on Figure 71 for fluid A + Gas
1 130

Table 43: Comparison on lumped systems for Fluid A + CO
2
using Newley & Merrill’s
approach with K-values from swelling tests 131

Table 44 : Lumping schemes from applying the approach of Newley & Merrill using K-values
from four different mixtures of Fluid A and CO
2
at 100 bar 135

Table 45: Lumping schemes from applying the approach of Newley & Merrill using K-values
from four different mixture of Fluid A and separator Gas at 168 bar 135

Table 46: Lumping schemes generated from different lumping methods - Fluid A & CO2 137

Table 47: Comparison of MMP & bubble point pressure (Psat) from lumped schemes and
detailed model for fluid A & CO2 138

Table 48: Lumping schemes from different lumping methods for fluid A & Separator Gas 140

Table 49: Comparison of calculated MMP & bubble point pressures with experimental
observations for Fluid A and Separator Gas 141

Table 50: Data for 3D calculation examples 146

x

List of Figures
Figure 1: Schematic of a gas injection process 2

Figure 2: Percentage of current US EOR projects by EOR methods (Data from Oil & Gas
Journal) (Koottungal 2008) 4

Figure 3: Flowchart showing the structure of the numerical simulator 20

Figure 4: Quaternary phase diagram of CO
2
, Methane, Butane, Decane at pressure of 2000 psia
and temperature of 200F constructed by using SRK EOS 21

Figure 5: Varian 3800 GC used for analyzing the samples 24

Figure 6: Retention time for Water, Methanol, Ethanol, Isopropanol and Isooctane (TCD
detector) 25

Figure 7 : Two-phase sampling vial 26

Figure 8: Temperature program for GC oven 27

Figure 9: TCD calibration for Water 28

Figure 10: TCD calibration for Isopropanol 28

Figure 11: TCD calibration for Methanol 29

Figure 12: TCD calibration for Isooctane 29

Figure 13: Ternary of Water(1)-Isopropanol(2)-Isooctane(3) at 25
o
C, compositions are in mass
fractions, The color bar shows errors introduced in calculating density based on
ideal mixing compared to the experimental data on densities [experimental density
data by Otero et al. (2000)] 32

Figure 14: Ternary of Water (C1) – Methanol (C2) – Isooctane (C3) at 20
o
C in mole fractions
(red stars show the experimental data and the blue dashed lines show the predicted
tie-lines) 37

Figure 15: Ternary of Water (C1) – Isopropanol (C2) – Isooctane (C3) at 20
o
C in mole
fractions (red stars show the experimental data and the blue dashed lines show the
predicted tie-lines) 38

Figure 16: Ternary of Methanol (C1) – Isopropanol (C2) – Isooctane (C3) at 20
o
C in mole
fractions (red stars show the experimental data and the blue dashed lines show the
predicted tie-lines) 38

xi

Figure 17: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8)
mixtures at 20
o
C in mole fractions (red stars show the experimental data and the
black dashed lines show the predicted tie-lines). 39

Figure 18: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8)
mixtures at 20
o
C in mole fractions (red stars show the experimental data and the
black dashed lines show the predicted tie-lines). 39

Figure 19: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8)
mixtures at 20
o
C in mole fractions (red stars show the experimental data and the
black dashed lines show the predicted tie-lines). 40

Figure 20: Quaternary of Water-Methanol-Isopropanol-Isooctane in mass fractions at 20
o
C 41

Figure 21: Literature viscosity data on the binaries under study at 25
o
C 42

Figure 22: Dashed lines show our predictions for the literature data previously discussed in
Figure 21. 44

Figure 23: Experimental setup for displacement experiments 46

Figure 24: Coexistence of analog liquids in the PTFE tubing (F. M. Orr 2004) 48

Figure 25: Wettability of Isopropanol (1), Isooctane (2), Methanol (3) and Water (4) on PTFE
tape at 20
o
C 50

Figure 26: Wettability of Methanol and Water mixtures on PTFE tape at 20
o
C a) 66% b) 50 %
by volume Water 50

Figure 27: Isooctane and Methanol in PTFE tube 51

Figure 28: Glass beads on left versus Teflon powders on right under microscope 51

Figure 29: Dimension of the designed column 54

Figure 30: Packed PTFE column for flow experiments 54

Figure 31: Experimental setup for vertical (bottom to top) dispersivity measurement 58

Figure 32: Effluent density changes versus time for horizontal displacement of Isooctane by
Isopropanol 59

Figure 33: Effluent density changes versus time for vertical displacement of Isooctane by
Isopropanol 60

Figure 34: Effluent concentration in mass fractions for dispersivity experiment 63

xii

Figure 35: Effluent concentration in mass fractions for dispersivity experiment and simulation
at different grid blocks using Peclet number of 305 64

Figure 36: 2D simulation of the dispersivity experiment for 20 blocks in z direction and 5
blocks in x direction is shown in which the bypassed oil is modeled by having
injector and producer cells away from the first and last rows 65

Figure 37: Effluent concentration in mass fractions for dispersivity experiment and simulation
with 2000 grid blocks in z-direction at Peclet number of 305 for the case of having
injector at 50
th
row and producer at 1950
th
row. Experimental data 8 minutes shifted
to the left 66

Figure 38: Oil and Water relative permeabilities: observations and modeling. 71

Figure 39: Pendant drop setup 72

Figure 40: Water droplet in a pendant drop cell (ds=2.49 mm and de=3.30 mm) 73

Figure 41: Natural log of interfacial tension in between phases vs. the tie-line length 76

Figure 42: Compositional paths of displacement for nine study cases 78

Figure 43: Displacement profile for nine displacement cases shown in Figure 42 78

Figure 44: The impact of dispersion on the compositional path for fixed oil and gas
compositions 80

Figure 45: Displacement profiles for different Peclet numbers 81

Figure 46: Displacement profile for Peclet number of 100 at various numbers of blocks 82

Figure 47: Displacement profile, comparing physical and numerical dispersion 83

Figure 48: Compositional path comparing no dispersion with 50 grid blocks (green), no
dispersion with 800 grid blocks (brown) and dispersion with Pe=100 with 800 grid
blocks(black) 84

Figure 49: Displacement profile, comparing cases with different levels of dispersion, 1000
grid blocks 85

Figure 50: Compositional path for different levels of dispersion 86

Figure 51: Schematic of displacement experiment 87

Figure 52: Variations in estimated liquid-liquid IFT for displacement experiment A for 1000
grid blocks simulation 89

xiii

Figure 53: Estimated capillary number based on liquid-liquid IFT for displacement experiment
A for 1000 grid blocks simulation 90

Figure 54: Compositional path for displacement experiment A 90

Figure 55: Compositional profiles for displacement experiment A. The simulations with and
without IFT models are included 91

Figure 56: Compositional paths for displacement experiment A. The simulations with and
without IFT models are included 92

Figure 57: Compositional profiles for displacement experiment A. Simulations without IFT
models compared with numerical diffusion 93

Figure 58: Compositional paths for displacement experiment A. Simulations without IFT
model showing the impact of numerical diffusion 93

Figure 59: Compositional path for displacement experiment A showing the impact of Peclet
number without IFT model 94

Figure 60: Compositional profiles for displacement experiment and simulations showing the
impact of Peclet number without IFT model. 95

Figure 61: Variations in estimated IFT for displacement experiment B 98

Figure 62: Calculated capillary number based on estimated IFT for displacement experiment B 98

Figure 63: Compositional paths for displacement experiment B 99

Figure 64: Displacement profiles for displacement experiment B 100

Figure 65: Compositional paths for displacement experiment B 100

Figure 66: Displacement profiles for displacement experiment B - comparing with numerical
diffusion 101

Figure 67: Compositional path for displacement experiment B – comparing with numerical
diffusion 102

Figure 68: Displacement profile for displacement experiment B – comparing with simulations
using different levels of physical dispersion 103

Figure 69: Compositional paths for displacement experiment B– comparing with simulations
using different levels of physical dispersion 103

xiv

Figure 70: Gas saturation vs. specific velocity for a displacement of Fluid A by Gas 1 at T =
383.15 K, P = 288 bar 113

Figure 71: K-value variations along a 1D displacement process: Fluid A + Gas 1, T = 383.15
K, P = 288 bar - Different values of K-values for the components along the
displacement path 113

Figure 72: Comparison of CME data for Fluid A and mixtures of Fluid A and Gas 1 with
predictions based on a detailed (full) and a lumped fluid description. T = 383.15K 117

Figure 73: Comparison of swelling test data (Fluid A + Gas 1) with predictions based on a
detailed (full) and a lumped fluid description. T = 383.15K 118

Figure 74: Comparison of gas saturation vs. specific velocity for a displacement of Fluid A by
Gas 1 at T = 383.15 K, P = 288 bar: lumped (Nc = 7) vs. Full (Nc = 15) fluid
description 119

Figure 75: Comparison of gas saturation vs. specific velocity for a displacement of Fluid A by
pure CO
2
at T = 383.15 K and P = 173 bar: lumped (Nc = 7) vs. Full (Nc = 15) fluid
description 119

Figure 76: Comparison of CME data for Fluid B and mixtures of Fluid B and Gas 2 with
predictions based on a detailed (full) and a lumped fluid description. T = 394.25K 122

Figure 77: Comparison of differential liberation experiment data with predictions based on a
lumped and a detailed (full) fluid description. Fluid B at T = 394.25K 123

Figure 78: Comparison of swelling test data (Fluid B + Gas 2) with predictions based on a full
and a lumped description. T = 394.25K 123

Figure 79: Comparison of gas saturation vs. specific velocity for the displacement of Fluid B
by Gas 2 at T = 394.25K and P = 352 bar as predicted by a detailed fluid description
and a lumped fluid description 124

Figure 80: Comparison of gas saturation vs. specific velocity for the displacement of Fluid B
by CO
2
at T = 394.25K and P = 179 bar as predicted by a detailed and a lumped
fluid description 125

Figure 81: Schematic of the synthetic reservoir model (derived from PUNQ3) showing the
permeability variability and the configuration of injection and production wells 127

Figure 82: Comparison of the oil production and the producing GOR as predicted by the
lumped and the original fluid model. Fluid A displaced by CO
2
at 383.15K with
well conditions given in 127

xv

Figure 83: Comparison of the oil production and the producing GOR as predicted by the
lumped and the original fluid model. Fluid B displaced by CO
2
at 394.25K with
well conditions given in Table 40 128

Figure 84: Comparison of cumulative CO
2
production as predicted by the full and lumped
descriptions of fluids A and B during the production reported in Figure 82 and
Figure 83 128

Figure 85: Comparison of the oil production and the GOR as predicted by the flow based
lumped system and Newley & Merrill’s Lumped system with the original fluid
model (Fluid A + CO
2
) 132

Figure 86: Comparison of amount of CO
2
produced comparing flow based lumped system and
Newley & Merrill’s Lumped system and Biased version of Newley & Merrill’s
with the original fluid model (Fluid A + CO
2
) 132

Figure 87: Comparison of swelling test data with predictions based on the detailed (full) and
the different lumped fluid descriptions at T = 383.15K for Fluid A and CO
2
138

Figure 88: Comparison of swelling test data with predictions based on the detailed and lumped
fluid descriptions at T = 383.15K: Fluid A and separator gas. 140

Figure 89: Errors in the concentration of the delumped stream for each component relative to a
calculation with the detailed fluid description: Fluid A displaced by pure CO
2
148

Figure 90: Errors in cumulative oil production vs. simulation time (days). Comparison of
lumped simulations with detailed simulation: Fluid A displaced by pure CO
2
149

Figure 91: Errors in Gas-Oil Ratio (std m
3
/std m
3
) as a function of time (days). Comparison of
lumped simulations with detailed simulation: Fluid A displaced by pure CO
2
149

Figure 92: Errors in cumulative CO
2
production as a function of time (days). Comparison of
lumped simulations with Detailed fluid description: Fluid A displaced by pure CO
2
150

Figure 93: Errors in the concentration of the delumped stream for each component compared
to the detailed fluid description: Fluid A displaced by separator gas 151

Figure 94: Cumulative oil production (std m
3
) plotted versus simulation time (days) for the
detailed model and the various lumped fluids: Fluid A displaced by separator gas 152

Figure 95: GOR - Gas Oil Ratio (std m
3
/std m
3
) as a function of time (days) as predicted by
the detailed model and lumped models: Fluid A displaced by separator gas 152

Figure 96: Swelling test simulation for fluid A (no BICs) and CO
2
at T=383.15K 154

Figure 97: Swelling test simulation for Fluid A (with BICs) and CO
2
at T=383.15K 155

xvi

Figure 98: Delumping errors for Fluid A and CO
2
introduced by using non-zero BICs at
different pressures 156

Figure 99: Swelling test simulation for Fluid A (no BICs) and separator Gas at T=383.15K 157

Figure 100: Swelling test simulation for Fluid A (with BICs) and separator gas at T=383.15K 157

Figure 101: Delumping errors for Fluid A and separator gas introduced by using non-zero
BICs at different pressures 158

Figure 102: Displacement at MMP for Fluid A and CO
2
with different cell numbers 159

Figure 103: Displacement at MMP for Fluid A and separator gas with different cell numbers 159

Figure 104: Errors in the concentration of the delumped stream for each component compared
to the detailed fluid description: Fluid A displaced by separator gas for no BICs
model 160

Figure 105: Cumulative oil production (std m
3
) plotted versus simulation time (days) for the
detailed model and the various lumped fluids: Fluid A displaced by separator gas
for no BICs model 160

Figure 106: Errors in cumulative oil production plotted versus simulation time (days) for the
detailed model and the various lumped fluids: Fluid A displaced by separator gas
for no BICs model 161

Figure 107: GOR - Gas Oil Ratio (std m
3
/std m
3
) as a function of time (days) as predicted by
the detailed model and lumped models: Fluid A displaced by separator gas for no
BICs model 161

Figure 108: Errors in GOR plotted versus simulation time (days) for the detailed model and the
various lumped fluids: Fluid A displaced by separator gas for no BICs model 162

xvii

Nomenclature

Aij UNIQUAC interaction parameter between component i and j
a
i
EOS parameter
b
i
EOS parameter
C Concentration
C
i
Overall volume fraction of component i
c
ij
Volume fraction of component i in phase j
D Diffusion coefficient
d Diameter
F Electrical resistivity factor
F
i
Overall volumetric fractional flow of component i
g Gravitational acceleration
H Height of the system
i Component index
J Diffusive flux
j Phase index
K
ij
Dispersion Term
k Absolute permeability
kr Relative permeability
K
i
Equilibrium constant

xviii

L Length of the system
M
o
End point water oil mobility ratio
n
c
Number of components
n
p
Number of phases
N
pe
Peclet number
N
vc
Capillary number
N
rl
Rapport and Leas number
P Pressure
Pc Capillary pressure
Q Flow rate
Q
i
Surface area of component i
Q
c
Critical flow rate
R
i
Relative Van der Waals volume of pure component i
S Saturation
T Temperature
t Time
Uc Critical velocity
v Velocity
v
D
Dimensionless velocity
v
inj
Injection velocity
Molar volume of component i

xix

Molar volume of mixture
x Direction
x
ij
Molar volume of mixture
x Direction
x
ij
Molar volume of mixture
μ
j
Viscosity of phase j
μ
ij
Chemical potential of component i in phase j
φ Porosity
Ф
i
Volume fraction of component i
α Dispersivity of the medium
τ Dimensionless time
ψ
ij
UNIQUAC viscosity interaction parameters
θ Angle
θ
i
Surface area fraction of i
ξ Dimensionless distant
λ
r1
Mobility ratio of phase 1 (displacing)
ρ Density
ρ
mj
Mass density of phase j
ρ
cj
Molar density of component i

xx

Abstract
Injection of CO
2
into an oil or gas reservoir is an approach to improve the recovery of
hydrocarbons by multi-contact miscible displacement processes.
In order to estimate the incremental oil (or gas) that can be produced by injection of
CO
2
, commercial compositional reservoir simulators are commonly used by the industry.
Successful design and implementation of CO
2
injection processes rely in part on the
accuracy by which the available simulation tools represent the physics that govern the
displacement behavior in the reservoir. In this research project, two aspects of enhanced
hydrocarbon recovery by CO
2
injection were investigated as discussed in the following.
In Part I of this research project, we investigate the accuracy of the physical models
that are used to describe dispersive mixing in compositional reservoir simulation. We
have designed a quaternary alcohol-water-hydrocarbon analog system that exhibits two-
phase liquid-liquid equilibrium behavior at room temperature and pressure. The analog
system of Water – Isooctane – Isopropanol – Methanol was chosen based on a favorable
comparison to the phase behavior of high-pressure CO
2
-hydrocarbon systems. Working
with this analog system allows us to perform displacement experiments at ambient
conditions in the lab.
A porous medium, in the form of a packed column, was designed for the experimental
component of the research project using PTFE materials (Teflon). This selection was
made to have the analog oil compositions, represented by an Isooctane-rich phase, as the
wetting phase while gas compositions represented by an aqueous phase be non-wetting to

xxi

the PTFE materials. The PTFE column was characterized in terms of porosity,
permeability and dispersivity through a series of experiments.
The interactions between the analog fluids and the porous medium were characterized
by performing steady state relative permeability experiments for the immiscible pair of
Water and Isooctane. The impact of the capillary number on the residual saturations was
included via a study the IFT for the coexisting liquid phases.
To aid the design of lab experiments, a numerical simulator that predicts the
displacement behavior in 1D was developed and tested. The simulator utilizes a
comprehensive solvents phase behavior model (UNIQUAC) that accurately predicts the
liquid-liquid equilibrium of the analog system. The phase behavior module was
successfully tested with experimental observations for two-phase ternary and quaternary
mixtures of the analog solvents. The simulator utilizes a UNIQUAC based viscosity
model that accurately predicts the viscosity of equilibrium mixtures that form during
relevant displacement processes. In addition, the simulator includes the effects of
physical dispersion and allows us to compare the accuracy of the available physical
models with experimental observations.
A set of single-phase experiments was conducted to determine the dispersivity of the
column. The effluent concentrations from the displacement experiments all exhibited a
moderate tailing behavior that is attributed to imperfect sweep in the system. A
simulation model that captures the tailing effect from the single phase experiment was
constructed by adjusting the boundary conditions to mimic mixing zones at the inlet and
outlet of the column.

xxii

Two 4-component displacement experiments were designed and performed. In these
experiments, the effluent compositions were analyzed by gas chromatography (GC). The
results of the experiments were in agreement with existing theory of gas injection
processes and represented both condensing and vaporizing segments along the
displacement paths.
The displacement behavior observed in the lab was analyzed through numerical
calculations and we demonstrate that the use of numerical diffusion to replace physical
dispersion introduce additional artifacts to the displacement profile that are difficult to
control. However, the degree of heterogeneity in the PTFE column prevented us from
providing a detailed analysis and conclusions related to the dispersion phenomena in
these complex multicomponent two-phase systems.
In Part II of this research project, the use of pseudo-components (lumping) for
compositional simulation of a gas injection process and the related effects on accuracy
and simulation time has been investigated.
Two novel flow-based lumping methods have been proposed that both integrate the
displacement characteristics into the selection of component groups. The two new
methods have been tested for a realistic reservoir fluid where fluid description were
reduced from 15 to 7 components. The lumped fluid descriptions are demonstrated to
maintaining accuracy in the prediction of displacement characteristics as well as in the
prediction of available PVT experiments. The flow-based methods provide a unique
answer to the problem of what components to lump depending on the relevant oil and
injection gas composition.

xxiii

The impact of the selected lumping scheme on the accuracy of delumped streams
from 3D displacement calculations was investigated through a detailed comparison of the
delumped streams from the proposed lumping schemes with other lumping methods that
commonly used in the industry. Both flow based methods were demonstrated to introduce
less error in the associated delumped streams.
Additional analysis of the delumping process demonstrates that the industry standard
has a flaw that is particularly pronounced when used in the modeling of multi-contact
miscible CO
2
injection processes.

1

Chapter 1: Introduction
Given the increase in the demand for crude oil and the limited reserve available,
Enhanced Oil Recovery (EOR) methods with the purpose of increasing recovery from
existing reserves will play an important role in petroleum production over the next
decades.
In the early stage of the production life of an oil reservoir, oil is typically produced to
the surface by natural flow (energy of the reservoir) and is referred to as primary
production/recovery. As a consequence of the oil production, the reservoir pressure is
gradually reduced and reaches a point where oil can no longer flow to the surface by the
energy stored in the reservoir. In order to overcome this pressure decline issue, the
reservoir pressure is typically maintained by injecting gas into the gas cap of the reservoir
or by injecting water into the associated aquifer. Dependent on reservoir parameters and
geological settings, pressure maintenance can provide for incremental oil recovery but
will not exploit the full potential of a given reservoir. Therefore, to increase the ultimate
recovery of oil, water is usually injected into the reservoir to sweep oil that is left behind
after the primary production. This mode of oil production where water is injected to
extend the life of the reservoir is usually referred to as secondary recovery. Because of
the impact of capillary forces and unswept areas in the reservoir, secondary methods
often recover only as little as 15 to 40 % of the original oil in place. The next stage in the
production life of a reservoir often utilizes Enhanced Oil Recovery (EOR) or tertiary
recovery methods which are generally speaking all the methods that can help in

2

extracting the remained portion of oil and improve the overall recovery for the reservoir.
Steam flooding, in-situ combustion, surfactant-polymer injection, miscible hydrocarbon
displacements and CO
2
injection are some examples of the EOR processes (Van Poollen
1980).
Injection of CO
2
into an oil or gas reservoir at miscible or immiscible conditions is
one of the rapidly growing approaches to improve the recovery of hydrocarbons from
maturing as well as new reservoirs. In addition, this approach can also serve as a method
of sequestering CO
2
in the ongoing efforts to reduce the emission of greenhouse gases
into the atmosphere. Figure 1 shows a schematic of how gas can be injected into an oil
reservoir to assist in enhancing the recovery by displacing the oil swelling the unswept
oil.

Figure 1: Schematic of a gas injection process

3

Miscible injection of CO
2
into oil reservoirs is the main focus of this research project
and has the following advantages over the other available EOR methods (Van Poollen,
1980 ; Wijaya, 2006):
It causes oil to swell and reduces the oil viscosity
CO
2
forms a liquid-like dense phase at high pressure with the advantage of
having low viscosity compared to oil and high density compared to other gases.
In general, a low viscosity of the displacing fluid does not provide for a good
sweep efficiency. In the case of CO
2
,however, where the oil viscosity is reduced
and the oil molar volume is increased (swelling)increases in the overall recovery
are commonly achieved: (Wijaya, 2006 ; Stalkup, 1983 ; Jarrel, et al., 2002)
The minimum miscibility pressure (MMP) of oil/CO
2
systems is relatively low in
most reservoirs
The importance of CO
2
miscible flooding is clear from the survey of US EOR
methods published by “Oil and Gas Journal”, reporting that more than 50% of the current
EOR projects under operation are miscible CO
2
floods. Figure 2 shows the percentage of
the US EOR projects by the different EOR methods and Table 1 reports the number of
current miscible CO
2
projects by the companies in US (Koottungal 2008).
There are several factors that can cause CO
2
flooding to fail including reservoir
heterogeneity, low permeability, high water cuts, channeling through natural fractures
and gravity segregation (Nelms and Burke 2004).

4

Figure 2: Percentage of current US EOR projects by EOR methods (Data from Oil & Gas Journal)
(Koottungal 2008)

Choosing the best EOR method that can yield the maximum additional recovery is
always vital for the life of a reservoir. For this purpose, the potential incremental increase
in oil production from each candidate EOR method is usually estimated before a decision
is made. In order to estimate the incremental recovery for a CO
2
injection project and
forecast the future production for decision making and optimization, commercial
compositional reservoir simulators are commonly used by the industry. Therefore, to
guarantee a successful planning and implementation of CO
2
injection processes, the
accuracy of the available simulation tools is instrumental.
33.33%
53.76%
2.69%
6.45%
0.54% 0.54%
1.61%1.08% Thermal Methods
CO2 Miscible
CO2 Immiscible
HydroCarbon Miscible
HydroCarbon
Immiscible
Nitrogen Miscible
Nitrogen Immiscible
Chemical, Polymer,
surfactant

5

Table 1: 2008 US CO
2
miscible flooding projects by companies
(Data from Oil & Gas Journal) (Koottungal 2008)

One area that deserves some attention is the interaction of fluids and the associated
components exchange between the phases that occur during a multicontact miscible flood
as well as the effect of the heterogeneity and dispersion on the degree of mixing that
occurs during a displacement process. Even a moderate amount of mixing in the reservoir
can affect the efficiency of CO
2
injection and increase the pressure required to obtain
high local displacement efficiencies (Wijaya 2006). Accurate modeling and simulation of
Company Name Number of Projects
Anadarko 4
Apache 2
Chaparral Energy 3
Chevron 4
ConocoPhillips 2
Core Energy 8
Denbury Resources 13
Energen Resources 1
ExxonMobil 2
Fasken 2
Great Western Drilling 1
George R. Brown 1
Hess 6
Kinder Morgan 1
Merit Energy 7
Murfin Drilling 1
Orla Petco 1
Occidental 29
Pure Resources 3
Resolute Natural Resources 1
Stanberry Oil 1
Whiting Petroleum 3
XTO Energy Inc. 4

6

physical dispersion is vital in successful design of a miscible flood (Ewing 1983).
Numerical diffusion/dispersion is a common problem in simulation of a miscible
injection process and special care is required to reduce the associated artifacts (Ewing
1983). This problem is introduced by the numerical approximations that are introduced
using e.g. finite difference approximations where the accuracy is highly dependent on the
grid sizing used in the reservoir simulation model.
Development of miscibility in multi-contact miscibility gas injection processes can be
caused by any combination of two simultaneous displacement mechanisms: a condensing
gas drive and a vaporizing gas drive. Condensing gas drive is a mechanism in which rich
gas displaces oil with a relatively low amount of intermediate components whereas in a
vaporizing gas drive, lean gas vaporizes the intermediate components of richer oil. It has
been shown that in most realistic multi-contact miscible displacement processes, a
combination of these two mechanisms is responsible for high local displacement
efficiency of the oil (Zick, 1986 ; Stalkup, 1987).
In this research project, we investigate the accuracy of the physical models that are
used in describing dispersive mixing in compositional reservoir simulation and challenge
the industrial practice of using numerical artifacts to represent the mixing that occurs in
the reservoir. In most of the cases, the effects of dispersion and diffusion are neglected in
the simulation of EOR processes and can introduce significant errors.
This is mainly because of the fact that dispersion and diffusion terms are poorly
understood at field scale and can increase the CPU requirement of a given simulation. In
addition, available single phase representations of the dispersion in porous media is a

7

coarse approximation for actual field modeling and simulation purposes.
To investigate the effect of dispersion on miscible flooding in more details, we
combine experimental and numerical efforts. In our approach, the high pressure injection
of CO
2
into a typical oil reservoir is mimicked at standard conditions by using analog
solvents that exhibit a similar phase behavior to that of high-pressure Oil/CO
2
systems
.

A quaternary alcohol-water-hydrocarbon analog system that exhibits two-phase
liquid-liquid equilibrium (LLE) behavior at room temperature and pressure was selected
for this study. Among the candidate solvents that were examined, the analog system of
Water – Isooctane – Isopropanol – Methanol was chosen based of a favorable comparison
to the phase behavior of high-pressure CO
2
-hydrocarbon systems. A numerical simulator
for multi-component two-phase displacements in a porous media was developed to help
us in designing and interpreting our experimental program. This simulator utilizes the
UNIQUAC activity coefficients model for predicting the LLE behavior of the analog
system accurately. The effects of dispersion and diffusion are represented explicitly by
the simulator. This allows us to compare the result of applying available physical models
with our experimental observations.

8

Chapter 2: Dispersive Mixing in EOR Processes
The incremental recovery from an oil reservoir using miscible gas flooding is
contingent on the amount of mixing that occurs between the reservoir oil and injected gas
in a given reservoir (Walsh, et al., 1990 ; Johns, et al., 1993 ; Solano, et al., 2001 ; Johns,
et al., 2002 ; Jessen, et al., 2004; Garmeh, et al., 2007).
Among the mixing mechanisms, diffusion and dispersion are two of the main
phenomena during a displacement in a porous media. Diffusion occurs when two
miscible fluids are placed in contact. The resultant concentration gradient among the
fluids will cause the components of each fluid to transport towards a homogeneous phase
at equilibrium. In addition to the mixing that is caused by diffusion, mixing is also
introduced by local variations in the flow velocity of the fluids in the porous media. This
velocity induced mixing is generally referred to as dispersion (Perkins and Johnston,
1963).
Various classifications of dispersion exist in the literature. Dispersion is typically
discussed per direction: one is dispersion along the main flow direction which is called
longitudinal dispersion and the other is transverse dispersion that acts in the direction
perpendicular to the main direction of the flow. Dispersion is in general a combination of
two transport phenomna “convection” and “molecular diffusion”. This type of dispersion
is also referred to as mechanical dispersion or convective diffusion (Bear 1972).
Diffusion caused by random molecular motion can be represented by Fick’s Equation as
follow (Russell and Wheeler 1983):

9

2-1
where J represents the diffisive flux (mol/m
2
.s), x is the direction (m), C is the
concentration (mol/m
3
) and D is the diffusion coefficient ( m
2
/s ) in the absence of porous
media. In a porous media, the right hand side of the equation should be multiplied by
F
1
, where F is the electrical resistivity factor of the formation and is the porosity
(Perkins and Johnston, 1963; Russell, 1983).
Perkins and Johnston (1963) presented an extensive review of all the efforts and
research on diffusion and dispersion in porous media. In a porous medium with high
velocity fluids, diffusion does not play a significant role because of the inadequate
amount of time for it to eliminate the concentration gradients within the porous media. In
this case, the rate of growth of transition zones due to longitudinal dispersion will be
faster than the fluid velocity in the porous media and vice versa at low velocity pores,
transverse diffusion dominates.
There are several parameters that affects dispersion in a porous media of which the
most important ones are: flow rate, viscosity differences, density differences, turbulence,
effect of immobile phases and porous media characteristics like heterogenity, particle size
distribution, particle shape and gravity forces (Perkins and Johnston, 1963 ; Wijaya,
2006).
Deans (1963) introduced a mathematical model for longitudinal dispersion in a
porous media to predict accurately the dispersion of fluids over a wide range of Reynolds
number. He stated that dispersion is also dependent on the flow conditions. He modified

10

the mixing cell model of Aris and Amundson (1957) to consider diffusion and mass
transport into stagnant volumes (Coats, et al., 1964).
Peaceman (1965) presented an improved version of the representation of dispersion
for numerical calculation of multidimensional miscible displacements. In his paper he
generalized the dispersion term to consider dispersion in other directions rather than
having it along the horizontal direction only.
Lake and Hirasaki (1981) extended Taylor’s Diffusion for stratified porous media.
Their work was based on the observation that in a case of two adjacent layers with large
transverse mixing, the two layers can be considered as one single layer with averaged
properties.
In 1988, Arya et al. investigated how dispersion may vary with aspect ratio,
heterogeneity and diffusion coefficients. For most of their calculation, they used
megascopic dispersivity which is given by the dispersion coefficient divided by velocity.
They dealt with two types of dispersion: megascopic and macroscopic. Macroscopic
dispersion is the mixing at small scale (hundreds of grain size diameter) which controls
the local displacement efficiency. Megascopic dispersion is essential in field scales
simulation and modeling of miscible process due to the fact that it controls volumetric
sweep efficiency within each grid block (unresolved heterogeneity). Based on the
simulations, they observed that for the systems with h/L (ratio of layer to system length)
between 0.02 and 1.0, with mobility of 1 and having variable layer lengths produce
dispersion in the system (Arya, et al. 1988).
In 1989, Kossack, investigated the dispersive effect at variable lengths for miscible

11

displacements in layered heterogeneous porous media. He used Monte Carlo simulation
to investigate the effects of small and intermediate scale heterogeneity in miscible
displacement (Kossack 1989).
Peters et al. (1995) presented a method for measuring longitudinal dispersion
coefficients in porous media through computed tomography imaging.
Schulze-Makuch (2005) reviewed 109 dispersion related studies and listed the value
of dispersivity for different types of formations as a database.
Bijeljic and Blunt (2006), proposed a new function which is a measure of the transit
times for particles when moving between neighboring pores. This function was based on
the observation that the conventional time independent coefficient for dispersion is
unable to reproduce experimental observations at small scale.
Garmeh et al. (2007) used pore scale simulation of dispersion in porous media. The
results of their simulations agree with the classical work of Perkins and Johnston that
dictates a relationship between the Peclet number and the observed longitudinal
dispersion.
In the context of multi-phase dispersion, despite its wide industrial applicability, less
effort has been presented to understand and develop models for the mixing that occurs in
two- and multi-phase displacements. Sahimi et al. (1982) reported their results on
investigating the dispersion in two- phase system based on Monte Carlo simulation. In
their study, the statistical distribution of phases within pores was determined by
percolation theory. They concluded that dispersivities are dependent on the phases, in
addition to the saturation and saturation history.

12

Delshad et al. (1985) performed an extensive set of multi-phase experiments on
sandpacks and Brea sandstone to measure relative permeabilities and dispersion of the
phases. They generalized the dispersion theory of single phase system and applied it to
interpret their multi-phase dispersion experiments. The dispersivities obtained differed
from the single phase dispersivities for the medium.
After reviewing the relevant works on dispersion, a gap in modeling dispersion for
different phases is observed. Current representations of dispersion for multi-phase
systems are linear extensions of the formula of single phase systems and may not be a
good representation of mixing especially in multi-contact miscible flooding process.
Transverse and longitudinal dispersion models are basically derived for an isotropic
system and applying them for an anisotropic system may not be representative.
Therefore, throughout this work, we focuses on a) experimental investigation of
dispersive mixing in two-phase compositional flows within a porous media and b)
modeling of experimental observations of dispersion using existing models.

13

Chapter 3: Mathematical Modeling
3.1 Compositional Simulation
To investigate the effect of dispersion and diffusion on multi-contact miscible
displacement processes, the fundamental principles of flow and transport in porous media
must be addressed in detail. Among the most important physical mechanisms influencing
the performance of a given oil/gas displacement process, the followings should be
mentioned:
1. Convection: components movement as result of phase flow (pressure gradients)
2. Diffusion: components movement due to concentration gradients
3. Dispersion: components movement as a result of small scale fluctuation in flow
velocity which causes smearing of the front (Orr, 2007).
4. Gravity segregation: low density gas is likely to override the oil in a given
formation, resulting in low sweep efficiency.
To derive a model that represents the displacement of oil by gas in porous media, the
material balance is usually written for a given component over a control volume. In the
absence of chemical reactions, the rate of accumulation of a given component i in control
volume V(t) will be equal to the rate of flow of component i due to convection into the
control volume plus the rate of inflow due to dispersion. This can be written as:

14

3-1
where j represents the phase number, is the total number of phases, is the mole
fraction of component i in phase j, φ is the porosity, is the saturation of phase j, is
the molar density of phase j, is the velocity of phase j and represents the combined
impact of dispersion and diffusion. This term will be discussed in more details
subsequently. is the normal to the surface of the differential volume element.
By applying the Reynolds transport theorem and the Divergence theorem, for multi-
component multi-phase flow, the general form of the continuity equation can be written
as: (Orr, 2007 ; Lake, 1989):
3-2
Initially, the effect of dispersion is investigated in one dimension only. Phase
velocities are calculated from Darcy’s law which relates the velocity to the pressure
gradient across the flow path. Darcy’s law for multi-phase flow can be written as follow:
3-3
where is the relative permeability of phase j, is the viscosity of phase j, is the
mass density of phase j, is the pressure of phase j and k represents the absolute

15

permeability, and H is the height. Darcy’s formula gives us the superficial velocity and
represents the flow velocity inside the pore space (the interstitial velocity).
To solve the flow problem, the number of unknowns and equations must be equal.
The number of unknowns for the material balance equations is . Besides the
material balance equations that can be written for components, we must include phase
equilibrium relations, the capillary pressure, Darcy’s law and constraints on phase
saturations and mole fractions simultaneously to solve for the unknowns. These
additional equations are explained more in details below.
At thermodynamic equilibrium, the chemical potential of a given component i must
be equal in all phases:
3-4
where is the chemical potential of component i in phase j and the chemical potentials
can be calculated from an equation of state.
In a displacement process in a porous media, phases are moving at different velocities
and are subject to different pressures due to interfacial phenomena. The difference
between the pressures of any two-phases is referred to as the capillary pressure,

3-5
For each phases, the mole fractions of components must sum to one

3-6
Also, the summation of the volume fractions of the phases must equal unity.

16

3-7
Equation 3-2 can be written in 1D as
3-8
3.2 No Volume Change on Mixing
Volume change of mixing is a result of non-ideal phase behavior of mixtures where
the partial molar volume of a component is different from the pure component molar
volume. By assuming no volume on mixing, the volume occupied by component i in any
phase will be constant. Luo et al. (2007) concluded that for most of the fluids (e.g. oil-gas
displacement with high solubility of gas in the oil phase), the effect of volume changes
during mixing on the diffusion coefficient determination is not negligible. For the initial
steps of this work, the assumption of no volume change of mixing has been used for
numerical simulation of the system. By ignoring volume change on mixing, mole
fractions can be replaced by volume fractions
3-9
where is the volume fraction of component i in phase j and is the pure component
molar density of component i.

17

3.3 Corey-type Relative Permeability
In our initial modeling efforts, Corey type correlations have been used to represent
relative permeabilities in the system as shown below.

3-10

3-11
where and are the relative permeability of non-wetting phase and wetting
phase, is the residual non-wetting phase saturation, is the residual wetting phase
saturation S
nw
is the saturation of non-wetting phase, S
w
is the saturation of wetting phase,
m and n are the exponents of the Corey’s relative permeabilities correlation . In addition,
we start by a applying a simple linear viscosity model in the design phase.
3-12
where is the viscosity of phase j and is the mole fraction of component i in phase j
and is the viscosity of pure component i. A more sophisticated model is introduced
later.
3.4 Simulation of Dispersive Mixing in Porous Media
Dispersive mixing is typically not included explicitly in compositional reservoir
simulation at field scale. Instead, it has become a tradition to assume that numerical
diffusion that arises from using a coarse discretization of the computational domain

18

behaves similarly. In this work, we investigate the impact of including dispersive mixing
explicitly on the predicted displacement behavior of multi-contact miscible gas

injection
processes. With the assumption of no volume change of mixing, the conservation
equations are written as:
0 ) (
1
x
c
K S
v
F
x
v C
t
ij
ij
n
j
j i i
p
3-13
for i=1,n
c
-1where is the overall volume fraction and is the overall
volumetric fractional flow of component i given by:

3-14

3-15
It can also be written in dimensionless form as:
0
1 1
p p
n
j
ij
j ij
j
j ij D
n
j
j ij
c
S K
Lv
f c v S c 3-16
where
L
t v
inj
3-17
L
x

3-18
inj
D
v
v
v
3-19
and v
inj
is the injection velocity which is as a constant for our simulation purposes to
exclude any pressure terms from the equation.

19

Dispersion terms are commonly represented in terms of the linear directions of the
local displacement velocity. Typical formulations for calculation of dispersion in the
longitudinal and transverse directions are as follows (Bear 1972):

It should be noted that a convection-dispersion type equation is not valid for
heterogeneous reservoirs as the dispersion coefficient is implausible to reach an
asymptotic value for realistic heterogeneous media (Bijeljic and Blunt 2006).
3.5 Modeling of Phase Behavior
In an initial attempt to model the phase behavior of the analog system, we used the
Cubic Plus Association (CPA) equation of state(EOS) that is used widely to predict the
liquid-liquid equilibrium properties beside the VLE of mixtures containing polar
components. This EOS was proposed by Kontogeorgis et al. (1999) and combines the
Soave-Redlich-Kwong (SRK) EOS with the association term proposed by the Wertheim
Theory. To test the application of CPA for our analog system, the phase diagram for the
Methanol-Isopropanol-Isooctane ternary was constructed using experimental data at lab
condition and compared to predicted results using both the CPA EOS and the SRK EOS.
Although the CPA EOS was good in predicting the two-phase locus, the slopes of the
3-20
3-21

20

predicted tie-lines were in great error relative to the experimental data.
As an alternative, the Universal Quasi Chemical (UNIQUAC) activity coefficient
model was used in this study to predict the phase behavior of the quaternary system under
investigations. In the UNIQUAC model, the activity coefficient of a mixture component
is related to the excess Gibbs energy per mole of the mixture (Abrams and Prausnitz
1975). Intermolecular forces are related to the surface areas
i
and the relative Van der
Waals volumes
i
of pure components.

The UNIQUAC model includes two adjustable
binary interaction coefficients for each pair of components in a given system. We discuss
the application of the UNIQUAC model in more detail in Section 4.
3.6 Numerical Simulation
To aid the design of lab scale displacement experiments, a numerical simulator that
predicts the displacement behavior in 1D has been developed and tested. The simulator
utilizes a comprehensive solvents phase behavior model that accurately predicts the
liquid-liquid equilibrium of the analog system. In addition, the simulator includes the
effects of dispersion and diffusion and allows us to compare the accuracy of the available
physical models with experimental observations. Figure 3 shows a flowchart of this
simulator.

Figure 3: Flowchart showing the structure of the numerical simulator
Displacement
simulation
Compositional path
for displacement
Displacement profile
for each component

Viscosity Model
Flash calculation
(UNIQUAC)
Initial composition
Injection Composition
Absolute viscosities
Number of grid blocks
Dispersivity
Temperature &Pressure

21

Chapter 4: Characterization of Fluid System
In order to select an analog system for studying dispersive mixing in two-phase 4
component displacement processes, the quaternary system of CO
2
, Methane, Butane and
Decane at high pressure was initially examined. Figure 4 shows the quaternary phase
diagram for this system at 2000 psi and 200
o
F.

Figure 4: Quaternary phase diagram of CO
2
, Methane, Butane, Decane at pressure of 2000 psia and
temperature of 200F constructed by using SRK EOS

CO
2
represents the injection gas composition and a representative oil composition
consisting of Methane, Butane and Decane is shown in the base ternary of the figure. At
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
nC
4
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
CO
2
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
nC
10
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
Oil Composition

22

these given conditions, the displacement of oil by CO
2
is multi-contact miscible (Orr,
2007).
This quaternary diagram is constructed from four ternary diagrams. In order to
generate an equivalent phase diagram in the laboratory at standard condition, a search for
appropriate constituents that would mimic the high pressure CO
2
/hydrocarbon phase
diagram was performed. After looking into various ternary phase diagrams of available
solvents, the system of Water, Isopropanol (IPA), Isooctane (IC8) and Methanol (MeOH)
was selected due to similarities with the high pressure CO
2
/hydrocarbon phase diagram.
Analog solvents provide the advantage of working at ambient conditions and have
accordingly been used widely in the study of displacement processes. Examples of such
application include Batycky (1994) who used mixtures of Water, n-Propanol, Isopropanol
and Isooctane to verify analytical solutions to gas injection processes which were based
on displacement experiments with three and four components. Al-Wahaibi et al. (2007)
used the mixture of Water-Isopropanol and Cyclohexane in the study of multi-contact
miscible displacements in homogeneous and crossbedded medium.
In this section, we present available experimental and simulated data of the desired
analog solvents phase system.
4.1 Fluid Properties
This section reports the properties of the analog solvent and summarizes the available
experimental data for these fluids. Isooctane (99.93 % from OmniSolv), Isopropanol
(99.9% from Burdick and Jackson), Methanol (dried from VWR) and Ethanol (200 proof

23

from Pharmco-Aaper) were used in this study. Table 2 reports the properties of these
solvents:
Table 2: Properties of Water, Methanol, Isopropanol (2-Propanol), Isooctane (2,2,4-
trimethylpentane) at 25
o
C and 1 atm (Loras, 1999; Batycky, 1994; Padua, 1996)
IUPAC
Name
Molar
Weight
(g/mol)
Density
(g/cm
3
)

Viscosity
(cP)
Boiling
Point
(
o
C)
T
c
(K)
P
c

(atm)
ω
Water 18.01 0.997 0.89 99.97 647.13 217.66 0.345
Methanol 32.04 0.787 0.544 64.7 512.64 79.911 0.564
2-Propanol 60.10 0.781 1.96 82.3 508.29 47.017 0.668
2,2,4-trimethyl
pentane
114.23 0.687 0.473 99.3 543.96 25.364 0.266

4.1.1 Absolute Viscosity of the Analog Solvents
In order to obtain a better understanding of the displacement behavior of our fluid
system, the viscosity of the phases must be represented accurately by the simulator as the
mobility of the system is highly dependent on the viscosity of the phases. Table 3 reports
experimental data (Lide, 81th edition ; H. Padua, 1996) for the pure component
viscosities at various temperatures.
Table 3: Pure component viscosity of the analog solvents in centipoises (cp)
(Lide, 81th edition ; H. Padua 1996)
Temperature (
o
C) -25 0 25 50 75 100
Water -- 1.793 0.89 0.547 0.378 0.282
Methanol (MeOH) 1.258 0.793 0.544 -- -- --
Isopropanol (IPA) -- 4.619 2.038 1.028 0.576 --
Isooctane (IC8) 0.939 0.65 0.473 0.365 0.289 --

24

4.2 Gas Chromatography (GC) and Procedure
In order to identify the compositions of the samples taken in the course of the planned
displacement experiments and to construct the phase diagram of the fluid system, a Gas
Chromatography (GC) was used. The GC separates the components while flowing them
through a column, much like a porous media, and detects their residence time and
quantities by different techniques. We have used a Varian 3800 GC (see Figure 5)
equipped with a Capillary Column (WCOT Fused Silica 50MX 0.53 MM ID Coating CP-
SIL 5CB).

Figure 5: Varian 3800 GC used for analyzing the samples

This GC is equipped with two detectors: FID (Flame Ionization Detector) and TCD
(Thermal Conductivity Detector). The FID detects the components by measuring the
generated electrical current from burning the components in the sample while the TCD

25

uses the thermal conductivity of the components to detect and quantify them.

Figure 6: Retention time for Water, Methanol, Ethanol, Isopropanol and Isooctane (TCD detector)

Ethanol was used as the solvent for diluting the mixture samples in the initial phase of
our experimental work. The retention time for the four base components and the solvent
is shown in Figure 6. Each peak represents a component that is detected by the GC. For
the selected column, the separation of components is appropriate with Water moving
faster than Methanol, Ethanol, Isopropanol and Isooctane with increasing order of
retention time.
4.2.1 Procedure for Preparing and Analyzing GC Samples
All the samples used in this study were created at atmospheric pressure and room
temperature (T=20
o
C). In order to have an accurate two-phase samplings from two-phase
IC8
Water
MeOH
Ethanol
IPA
Time (min)
Amplitude (μV)

26

systems, two GC glass vials were connected at the bottom to create a two-phase container
with double sided caps. This structure allows us to take samples with a syringe from each
phase without interrupting the other phase and avoids contamination of the needle of the
syringe. The maximum volume of these vials is 4mL. Figure 7 shows the two-phase
sampling vial created for this study.

Figure 7 : Two-phase sampling vial

The GC was programmed and calibrated for the solvents to achieve separate timely
peaks with enough accuracy as discussed in the next section (R-square for all the
calibration curves were greater than 0.999).
As an example of sample preparation, the mixtures of Water – Isopropanol -
Isooctane, starting from binary mixtures of Isooctane and Water were prepared by adding
Isopropanol to the initial mixture of 1mL Isooctane and 1mL Water in the two-phase
sampling vials. The samples were then shaken for couple of minutes and left to reach
equilibrium for 24hrs. By using a 500μL syringe, samples from the equilibrated phases
were taken and diluted with 1mL Ethanol in separate GC vials (Ethanol served as the
solvent to all of the samples for GC analysis). The samples taken from the two-phase
equilibrium cell were then analyzed using the GC with the thermal conductivity detector
(TCD).

27

Helium was used as carrier gas for TCD with flow rate set to 5mL/min. 1μL of the
samples were taken by an automatic sampler and injected through a split/splitless injector
with a split ratio of 10. The injector’s temperature was set at 220
o
C. The column’s
temperature was programmed to initiate at 60
o
C and maintain at constant temperature for
6 minutes followed by a gradually increase to 150
o
C with the rate of 20
o
C/min. Figure 8
shows the temperature variation of the GC oven. With this temperature profile, Water,
Ethanol, Isopropanol and Isooctane are separated in peaks without any overlap.

Figure 8: Temperature program for GC oven
4.2.2 GC Calibration
External standardization where calibration samples are prepared and analyzed at the
same concentration range as the unknown samples was used in the GC calibration. This
method provides additional flexibility for analyzing multiple components in one sample
(Grob 1995).
For the TCD calibration that most of the presented characterization works was based
on, different concentrations of each component with the solvent were analyzed. The plots
of mass fractions versus the observed area under the peak in ( μV.m in) are reported as
follow for each component:

28

Figure 9: TCD calibration for Water

Figure 10: TCD calibration for Isopropanol
R² = 0.9997
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Mass Fraction
Area under Peak
Water
R² = 0.9997
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 5000 10000 15000 20000 25000
Mass Fraction
Area under Peak
IPA

29

Figure 11: TCD calibration for Methanol

Figure 12: TCD calibration for Isooctane
R² = 0.9999
0.00
0.05
0.10
0.15
0.20
0.25
0 2000 4000 6000 8000 10000
Mass Fraction
Area under Peak
MeOH
R² = 0.9994
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 1000 2000 3000 4000 5000 6000 7000 8000
Mass Fraction
Area under Peak
IC8

30

4.2.3 The Water Challenge
For samples with a small fraction of water, it was observed that the result of the GC
analysis was in significant error with respect to the water mass fraction. The major source
of this error was due to the hydrophilic characteristic of the Ethanol (solvent) that causes
absorption of moisture from the air into the samples. A first step to correct this problem
was to replace the solvent used in the GC analysis with n-Propanol that has less affinity
to water. However, we still observed the error for samples with small amounts of water.
The next step to overcome this issue was to dry the Ethanol. Molecular Sieves (bought
from EMD Chemicals) of size 3A
o
was used to remove molecules of the water from the
pure components and solvent. The effect of using molecular sieve on the alcohols was
analyzed by taking samples of the alcohols 60 hours after exposure to molecular sieve
and comparing it to the same samples before applying molecular sieve as is shown in
following table:

Table 4: Effect of applying molecular sieve to dewater Methanol, Ethanol and Isopropanol

Alcohols
Area under the peak from GC TCD analysis by applying
molecular sieve in ( μ V . m i n)
Before After 60 hours
Methanol
29.4 19
Isopropanol
35.1 16.1
Ethanol
29.3 17.9

The reduction of the water content was sufficient to allow for more accurate GC
analysis of the samples.

31

4.3 Characterizing the Water–Methanol–Isopropanol–
Isooctane System
The main purpose of this section is to characterize the quaternary system of Water-
Methanol-Isopropanol-Isooctane system at ambient conditions and to provide data for
estimating the interaction coefficients that are needed for the LLE predictions by the
UNIQUAC model. Any combination of Water-Methanol-Isopropanol mixture is always
fully miscible and forms a single phase at ambient conditions. Experimental assessment
of the mentioned ternary system confirmed the above statement. Consequently, the 4
component system was initially considered as three individual two-phase ternary systems
as follow:
4.3.1 Ternary System of Water – Isopropanol – Isooctane
The ternary of Water-Isopropanol-Isooctane is of high importance due to the fact that
the analog oil composition in this study is designed to be on this ternary close to the
Isooctane–rich binodal curve. Although two-phase equilibrium data for this ternary were
available in the literature(Arda et al. (1992) at 20
o
C and Otero et al (2000) at 25
o
C), two-
phase samples were created (20
o
C and atmospheric pressure) and the compositions
defining the tie-lines were analyzed by GC to validate the published experimental data.
Table 5 reports our experimental data for this ternary.

32

Table 5: Isooctane-Isopropanol-Water equilibrium tie-line data (mole fractions) at 20
o
C
Hydrocarbon-rich phase Aqueous-rich phase
Water IPA IC
8
Water IPA IC
8
0.000 0.000 1.000 1.000 0.000 0.000
0.000 0.001 0.999 0.992 0.008 0.000
0.000 0.003 0.997 0.983 0.018 0.000
0.000 0.018 0.982 0.940 0.060 0.000
0.014 0.055 0.930 0.910 0.091 0.000
0.014 0.073 0.913 0.896 0.104 0.000
0.025 0.101 0.874 0.873 0.127 0.000

Based on the data by Otero et al. (2000) for the density of mixture compositions of
Water – Isopropanol – Isooctane at ambient temperature and pressure, the error
introduced by assuming ideal mixing was examined. By assuming ideal mixing (no
volume change on mixing), the ideal phase densities of the mixtures were calculated and
compared with the measured densities. Figure 13 shows the error introduced for different
mixtures of Water-Isopropanol-Isooctane. On this figure, the red color fades into yellow
as the error on the calculated density increases.

Figure 13: Ternary of Water(1)-Isopropanol(2)-Isooctane(3) at 25
o
C, compositions are in mass
fractions, The color bar shows errors introduced in calculating density based on ideal mixing
compared to the experimental data on densities [experimental density data by Otero et al. (2000)]
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2

C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1
C
1

C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
C
3
0
0.5
1
1.5
2
2.5
3
Density Error %

33

The maximum deviation (error) in estimating the measured density by assuming ideal
mixing is observed to be around 3.3 % and appears in the aqueous part of the ternary.
Accordingly, the assumption of ideal mixing seems reasonable relative to other sources
of error in the experimental program.

4.3.2 Ternary System of Water – Methanol – Isooctane
The two-phase liquid-liquid region for the ternary system of Water-Methanol-
Isooctane occupies the majority of the compositional space for this ternary. To validate
the experimental data for this system by other authors (Waksmundzki and Soczewinski
1959), samples in two-phase region were created starting from the binary of Isooctane-
Water and a fixed amount of Methanol was added to the original two-phase samples.
After equilibrium was reached for the phases within the vials, samples were taken from
each phase and analyzed by GC. The equilibrium phase compositions are reported in the
following table:
Table 6: Isooctane-Methanol-Water equilibrium tie-line data (mole fractions) at 20
o
C
Hydrocarbon-rich phase Aqueous phase
Water MeOH IC
8
Water MeOH IC
8
0.000 0.000 1.000 1.000 0.000 0.000
0.000 0.000 1.000 0.987 0.013 0.000
0.000 0.000 1.000 0.834 0.166 0.000
0.000 0.000 1.000 0.758 0.242 0.000
0.000 0.000 1.000 0.564 0.436 0.000
0.000 0.018 0.982 0.387 0.612 0.002
0.000 0.039 0.961 0.224 0.767 0.009
0.000 0.058 0.942 0.144 0.838 0.019
0.000 0.214 0.786 0.000 0.911 0.089

34

4.3.3 Ternary System of Methanol – Isopropanol – Isooctane
The ternary system of Methanol-Isopropanol-Isooctane exhibits a small liquid-liquid
equilibrium region at ambient conditions which involves a portion of Methanol-Isooctane
binary. No consistent set of experimental data on this ternary exists at ambient conditions
in the literature. A set of measurements were consequently performed. Three samples
starting from the binary of Isooctane-Methanol with increasing amount of Isopropanol
were prepared (two-phase mixtures). After sample preparation, the vials were allowed to
equilibrate for 24 hours. Samples were then taken from the top and bottom phases of each
vial and analyzed with the GC to determine the equilibrium phase compositions. The
TCD detector was used for analyzing the mixture compositions. The equilibrium phase
compositions are reported in Table 7.
Table 7: Two-phase equilibrium compositions for Methanol, Isopropanol and Isooctane system at
20
o
C
Hydrocarbon-rich phase Aqueous phase
MeOH IPA IC
8
MeOH IPA IC
8
0.177 0 0.823 0.926 0 0.074
0.217 0.009 0.774 0.874 0.023 0.103
0.283 0.0245 0.692 0.819 0.046 0.135

4.3.4 Quaternary System of Water – Methanol – Isopropanol –
Isooctane
In addition to the LLE data for the above mentioned ternaries, 15 two-phase samples
containing all four components were created to provide a better understanding of the two-
phase regions within the quaternary phase diagram. The compositions for each of the

35

phases were analyzed by the GC and equilibrium compositions were reported in
Table 8. The first 4 samples were created by increasing the amount of water to a given
initial composition. Next, 5 samples of increasing Methanol concentration were created
and finally 6 samples of increasing Isopropanol concentration were created. The
experimental observations are reported in
Table 8.

Table 8: Tie-Line composition data (mole fractions) for the 4 component system of Water-Methanol-
Isopropanol-Isooctane at 20
o
C and 1 atm
Hydrocarbon-rich phase Aqueous phase
Water MeOH IPA IC
8
Water MeOH IPA IC
8
0.0018 0.0193 0.0036 0.9753 0.3641 0.6058 0.0286 0.0015
0.0041 0.0130 0.0028 0.9801 0.5098 0.4689 0.0211 0.0003
0.0071 0.0103 0.0026 0.9800 0.6123 0.3706 0.0170 0.0001
0.0066 0.0072 0.0019 0.9843 0.6543 0.3307 0.0149 0.0001
0.0165 0.0000 0.0544 0.9291 0.9124 0.0000 0.0875 0.0001
0.0141 0.0033 0.0468 0.9358 0.8802 0.0340 0.0854 0.0004
0.0062 0.0060 0.0453 0.9425 0.8487 0.0671 0.0840 0.0002
0.0166 0.0069 0.0353 0.9412 0.8080 0.1040 0.0880 0.0001
0.0102 0.0087 0.0338 0.9472 0.7956 0.1270 0.0773 0.0001
0.0085 0.0031 0.0000 0.9884 0.8940 0.1060 0.0000 0.0001
0.0126 0.0035 0.0069 0.9769 0.8719 0.0888 0.0393 0.0000
0.0131 0.0049 0.0224 0.9596 0.8331 0.0904 0.0764 0.0001
0.0149 0.0074 0.0504 0.9272 0.8234 0.0804 0.0962 0.0001
0.0141 0.0094 0.0789 0.8977 0.7925 0.0789 0.1282 0.0004
0.0170 0.0097 0.0900 0.8833 0.7630 0.0740 0.1622 0.0009

4.4 UNIQUAC Modeling of Liquid-Liquid Equilibrium
The Universal Quasi Chemical (UNIQUAC) activity coefficient model was used in

36

this study to predict the phase behavior of the quaternary system under investigation. In
the UNIQUAC model, activity coefficient of a mixture component is related to the excess
Gibbs energy per mole of the mixture (Abrams and Prausnitz 1975). Intermolecular
forces are related to the surface areas
i
and the relative Van der Waals volumes
i
of
pure components. For the analog system, these values have been calculated from the type
of molecular bonds and reported in Table 9:
Table 9: UNIQUAC parameters regressed and used for matching the experimental data
Parameters Water Methanol Isopropanol Isooctane
i
1.4000 2.0480 2.5080 5.0080
i
0.9200 1.9011 2.7792 5.8463

The UNIQUAC model includes two adjustable interaction coefficients for each pair
of components in a given system. Table 10 reports the binary interaction coefficients used
with this model for UNIQUAC LLE predictions.

Table 10: UNIQUAC regressed binary parameters for the system of Water (1), Methanol (2),
Isopropanol (3), Isooctane (4)
i-j A
ij
/K A
ji
/K
1-2 -743.30 3244.40
1-3 348.16 -271.99
1-4 392.09 974.03
2-3 353.54 -203.98
2-4 10.669 609.60
3-4 -74.242 233.33

For modeling the 4 components system, the UNIQUAC parameters were tuned using
the measured liquid-liquid equilibrium data. The following objective function was used
and minimized to get the best match between the experimental observations and

37

UNIQUAC model predictions (Englezos and Kalogerakis 2001).
4-1
where is the experimental and are the calculation mole fractions , m is the number
of components and N is the total number of experimental samples. In finding the best
binary interaction coefficients, it was initially attempted to match all three ternaries with
the UNIQUAC model and then include the 4 components equilibrium data into the
regression and find the optimum values for the binary coefficients. Table 11 reports the
regressed values of the interaction parameters. Figure 14 to Figure 16 show and compare
observations and predictions for the three ternaries.

Figure 14: Ternary of Water (C1) – Methanol (C2) – Isooctane (C3) at 20
o
C in mole fractions (red
stars show the experimental data and the blue dashed lines show the predicted tie-lines)

38

Figure 15: Ternary of Water (C1) – Isopropanol (C2) – Isooctane (C3) at 20
o
C in mole fractions (red
stars show the experimental data and the blue dashed lines show the predicted tie-lines)

Figure 16: Ternary of Methanol (C1) – Isopropanol (C2) – Isooctane (C3) at 20
o
C in mole fractions
(red stars show the experimental data and the blue dashed lines show the predicted tie-lines)

Figure 17 to Figure 19 report the predictions of the UNIQUAC model for the 15 4-
components liquid-liquid equilibrium samples.

39

Figure 17: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8) mixtures
at 20
o
C in mole fractions (red stars show the experimental data and the black dashed lines show the
predicted tie-lines).

Figure 18: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8) mixtures
at 20
o
C in mole fractions (red stars show the experimental data and the black dashed lines show the
predicted tie-lines).

40

Figure 19: Quaternary of Water – Methanol (MeOH) – Isopropanol (IPA) – Isooctane (IC8) mixtures
at 20
o
C in mole fractions (red stars show the experimental data and the black dashed lines show the
predicted tie-lines).

The system of Water-Methanol-Isopropanol-Isooctane was accordingly successfully
characterized experimentally and modeled with UNIQUAC model. The previous sections
demonstrate that the UNIQUAC model can accurately predict the phase diagram of the
quaternary system of Methanol-Isopropanol-Water-Isooctane at ambient conditions. As it
is shown in Figure 20, the quaternary system of Water-Methanol-Isopropanol-Isooctane
embodies 3 two-phase regions which are very close in shape to the high pressure CO
2

injection quaternary system as shown in Figure 4.

41

Figure 20: Quaternary of Water-Methanol-Isopropanol-Isooctane in mass fractions at 20
o
C

4.5 Viscosity Modeling
The viscosity of the Water-Methanol-Isopropanol-Isooctane system is expected to
deviate strongly from any linear mixing rule due to hydrogen bonding between alcohols
and water. The available literature data for the viscosities of the binary mixtures for the
above system confirm this argument. The available literature data for the binaries of
Methanol-Water (Tanaka, et al. 1987), Water-Isopropanol (Tanaka, et al. 1987),
Isopropanol-Isooctane (Ku 2008), Methanol-Isopropanol (Soliman and Marschall 1990),
are shown in Figure 21 versus the mole fraction of the components. A linear model, on
the one hand, would underpredict the viscosity of Water-Methanol and Water-
IPA
IC8
MEOH
WATER

42

Isopropanol mixtures while on the other hand would overpredict the viscosity for
Isopropanol-Methanol and Isopropanol-Isooctane mixtures.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00 0.20 0.40 0.60 0.80 1.00
Viscosity (cP)
Xi (mole fraction of a)
Methanol(a)-Water by Tanaka et al. (1986)
Isopropanol(a)-Water by Tanaka et al. (1986)
Isopropanol(a)-Isooctane by Ku et al. (2008)
Isopropanol(a)-Methanol by Soliman et al. (1990)

Figure 21: Literature viscosity data on the binaries under study at 25
o
C

Therefore, for the purpose of modeling and simulation of displacement processes
where the displacement path are highly dependent on the viscosities of displaced and
displacing fluids, a generalized model that can predict the viscosities for the relevant 4-
components mixtures is needed. Here we apply the approach of Martin et al., (2001)
which is an analogy of the UNIQUAC activity coefficient model used in phase
equilibrium calculations. This viscosity model is given by written as:

43

4-2
where, is the calculated viscosity, is the viscosity of component i, is the number
of components, is the mole fraction of component i in the mixture, is the molar
volume of component i, is the molar volume of the mixture, is the coordination
number, is the surface area parameter and is the UNIQUAC interaction
coefficients between components k and i. is the volume faction of component i and
is the surface area fraction given by:

4-3
4-4
For the system under study, the above mentioned UNIQUAC viscosity model has
been implemented and the binary interaction coefficients were tuned based on available
literature data for binary mixtures. The result of tuning for the binary interaction
coefficients in addition to the values of and are reported in Table 11.
Table 11: Regressed values of interaction coefficients and and for UNIQUAC viscosity model
Components Water Methanol Isopropanol Isooctane
Water 0 -276.03 -536.44 0 0.9945 0.28486
Methanol 423.54 0 398.3 0 1.4320 1.4311
Isopropanol 999.08 -210.98 0 -155.96 2.2571 3.3915
Isooctane 0 0 -8.3179 0 5.0080 5.8463

44

Using the above model and parameters, the experimental data of Figure 21 is
predicted with reasonable accuracy as shown in Figure 22.

Figure 22: Dashed lines show our predictions for the literature data previously discussed in Figure
21.

The resultant viscosity model was tested with the viscosity data on Methanol-
Isopropanol-Water mixtures published by (Soliman and Marschall 1990). Table 12
reports the comparisons of the model estimation to the ternary mixtures viscosity data
and a maximum error for the prediction at less than 7 percent is observed.
The tuned model was used as the basis of the viscosity modeling in subsequent
displacement calculations.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2
2.5
3
3.5
Xa (mole fraction of a)
Predicted
Viscosities(cP)

Water-Isopropanol prediction
Water-Isopropanol experiment
Water-Methanol prediction
Water-Methanol experiment
Isooctane-Isopropanol prediction
Isooctane-Isopropanol experiment
Isopropanol-Methanol prediction
Isopropanol-Methanol experiment

45

Table 12: Predicted viscosities for the ternary literature data published by (Soliman and Marschall
1990)
Mole fractions Viscosity(cp) Error
Data Water Methanol Isopropanol measured predicted (%)
1 0.8 0.1 0.1 2.5149 2.3663
-5.9
2 0.5 0.3 0.2 1.9080 1.8540 -2.8
3 0.3 0.3 0.4 1.6030 1.5637 -2.4
4 0.15 0.05 0.8 1.9119 1.9324 1.1
5 0.4 0.5 0.1 1.3487 1.3455 -0.2
6 0.1 0.7 0.2 0.8250 0.8783 6.5
7 0.3 0.4 0.3 1.4274 1.3981 -2.0
8 0.4 0.1 0.5 2.2218 2.1431 -3.5
9 0.4 0.2 0.4 1.9866 1.9154 -3.6
10 0.1 0.4 0.5 1.2101 1.2677 4.76

46

Chapter 5: Design of Displacement Experiments
A porous media was built and used for our experimental investigation of the multi-
contact miscible displacements. The porous media was constructed from a 1 foot long
Teflon column packed with beads. The selection of the porous material was vital to this
study and was mainly dictated by the wettability to the fluids to ensure that the
hydrocarbon-rich phase was the wetting phase. A schematic of the experimental setup is
shown in Figure 23.

Figure 23: Experimental setup for displacement experiments
A series of experiments is needed to characterize the porous media, the fluid system
and the solid/fluid interaction. These experiments include:
Wettability behavior
Relative permeability measurements

47

Single phase flow experiment to measure the dispersivity of the porous media
Multi-contact miscible displacement experiments to observe the effects of
dispersive mixing
In the following sections, we discuss the different elements of our experimental program
in more details:
5.1 Wettability of Selected Materials/Fluids
A proper selection of the porous material is very essential to our study. For the
alcohol-hydrocarbon system under investigation, alcohol-water mixtures serves as the
injection gas (gas phase) and a hydrocarbon-rich phase serves as the initial oil phase.
Therefore, it is essential to construct the porous medium that it is wet by hydrocarbon-
rich phases and non-wet by water/alcohol mixtures. For this purpose, different materials
were tested with our fluid system. Polytetraflouroethylene (PTFE) was selected based on
availability and characteristics (wetting to hydrocarbons and non-wetting to water). In the
following, we provide a brief summary of previous studies related to the wettability of
this material.
Morrow and McCaffery (1978) used PTFE materials to study immiscible
displacement covering a range of contact angles and as the result of their study, they
concluded that displacement behavior is highly related to the contact angle. (Morrow and
McCaffery, 1978 ; Tang, et al., 1997 ; Morrow, et al., 1988 ; Taber, 1980)
From the DOE report by Orr (2004), PTFE was used to mimic a water wet porous
media. Solid-liquid interface images and capillary rise measurements were used to decide

48

the wetting behavior of the phases. The following tables and figure summarize the results
of their investigation:
Table 13: Correspondence of analog and reservoir phases by Orr (2004)
Analog Liquids
Water-wet Reservoir
System
(Teflon beads packing)
Oil-wet Reservoir System
(Glass beads packing)
C
16
-rich phase Water Water
NBA-rich phase Oil Gas
H
2
O-rich phase Gas Oil

Table 14: Contact angels on PTFE (Teflon) and glass tubing by Orr (2004)
Composition
Phase in which contact
angle measured
Contact angle, degrees
Glass capillary Teflon capillary
C
16
-rich / NBA-rich C
16
-rich
143 (NBA-rich
wets)
38 (C
16
-rich wets)
C
16
-rich / H
2
O -rich C
16
-rich
108 (H
2
O-rich
wets)
45 (C
16
-rich wets)
NBA-rich / H
2
O-rich H
2
O-rich
76 (H
2
O-rich
wets)
138 (NBA-rich
wets)

Figure 24: Coexistence of analog liquids in the PTFE tubing (F. M. Orr 2004)

49

In the work by Sompalli et al. (2002) on “Methods of Preparing Membrane Electrode
Assemblies”, the following observations were reported:
Preferred wetting phase with PTFE is mentioned as isopropyl alcohol and
alcohol solution with isopropyl alcohol. The preferred non-wetting solvent is
water. In the case of porous PTFE, methanol is in-between non-wetting and
wetting. It is relatively less wetting than Isopropanol alcohol.

In the paper by Yang and Liang (2005) on “A Self Contained Direct Methanol Fuel
Cell with Surface Tension Fuel Delivery”, it is stated that:
Teflon PTFE as a common organic liquid filter material is found to be wet
spontaneously by an organic liquid when this organic liquid’s surface tension
is lower than 27mN/m. For methanol, the critical surface tension is 23.7mN/m
at 20
o
C while that of water is 72.8mN/m at 20
o
C. On the contrary, the liquid
will wet the surface easily if material’s surface tension is greater than that of
liquid. In our case of methanol and water, their surface tensions are very
different. Therefore, a solid material with a critical surface tension value
between those of methanol and water will be expected to show the different
wetting characteristics to them according to above theory.”

While considering the above mentioned efforts using PTFE, there was a concern
regarding Methanol as it wets PTFE and the fact that Methanol should be non-wetting to
the porous materials for our studies. Therefore, designing an injection mixture of Water
and Methanol which would be non-wetting to the PTFE is recommended. In order to
verify the non-wetting characteristics of Methanol/Water mixtures with PTFE, series of
experiments using PTFE sealing tape were performed at T=20
o
C. Observations from
those experiments are summarized in following figures and table:

50

Figure 25: Wettability of Isopropanol (1), Isooctane (2), Methanol (3) and Water (4) on PTFE tape at
20
o
C

Figure 26: Wettability of Methanol and Water mixtures on PTFE tape at 20
o
C a) 66% b) 50 % by
volume Water

Table 15: Wettability of components on PTFE at 24
o
C and atmospheric pressure
Mixtures by Mass Wettability to PTFE at 20
o
C
53% MeOH - 47% Water Non-wet
64% MeOH - 36 % water Non-wet
58% IC8 - 42 % IPA Wet
36% IC8 - 64% IPA Wet
Water Non-wet
Methanol Wet
Isopropanol Wet
Isooctane Wet

The interaction of Isooctane and Methanol in the PTFE porous media is of significant
importance. In order to see this interaction from a wettability point of view, mixtures of
Isooctane and Methanol were introduced into a PTFE capillary tube as shown in Figure
27 where the Isooctane is preferably wetting PTFE when Methanol is also present.
Therefore, PTFE is a suitable candidate material for our experiments.
(1) (2) (3) (4)
(a) (b)

51

Figure 27: Isooctane and Methanol in PTFE tube
PTFE 100 micron powder (from Sigma-Aldrich) was used to construct the porous
material in this project. As shown in Figure 28, the PTFE powder particles are more
irregular in shape and size than equivalently sized glass beads suggesting that the packing
should be expected to differ from that of equaled sized spheres.

Figure 28: Glass beads on left versus Teflon powders on right under microscope
5.2 Design of Packed Column
In order to maintain a stable displacement front in the system, the velocity of the flow
should be maintained below the critical rate. This critical rate as discussed in more details
by Lake (1989) can be expressed as:
Isooctane
Methanol

52

5-1
where is the maximum limit for the velocity to maintain stable flow without fingering.
is the mobility of displacing phase, is the end-point water oil mobility ratio and
is the inclination angle.
For the system of Methanol, Water, Isooctane and Isopropanol, the displacing phase
(Water/alcohol mixtures) is denser than the displaced phase (hydrocarbon-rich), and thus
the mobility ratio of the displacement is greater than 1. Consequently, the only condition
that will provide stability in a displacement and avoid fingering is to have the system
setup in vertical mode and to inject the denser phase into the bottom of the system. The
critical flow rates using the equation 5-1 are calculated for a number of scenarios and
summarized in Table 16.

Table 16: Possible scenarios for displacement: In all cases, linear density model is used for mixture
density and UNIQUAC based viscosity model is used for calculating viscosity of the mixtures.
Calculations are performed for bottom-up displacement settings.
Scenario
Displacing Phase
(% by mass)
Displaced Phase
(% by mass)
μ
o

(cP)
μ
w

(cP)
Q
c

(mL/min)
1 100 % Water 100 % IC8 0.48 0.89 -0.011
2 75% MeOH + 25 % Water 75% IC8 + 25% IPA 0.57 1.12 -0.004
3 25% MeOH + 75 % Water 75% IC8 + 25% IPA 0.57 1.47 -0.004
4 25% MeOH + 75 % Water 25% IC8 + 75% IPA 1.27 1.47 -0.012
5 75% MeOH + 25 % Water 25% IC8 + 75% IPA 1.27 1.12 0.014

From these scenarios, the first four with a negative value of the critical rate indicate
that the displacing phase is denser and more viscous than the oil phase, and as the result
these displacements are always stable. For the fifth scenario the rate should be kept less

53

than 0.014mL/min to have stable displacement.
Lake (1989) categorized the stability conditions for displacement into four classes as
shown in the following table:
Table 17: Stability conditions for displacement
Mobility Ratio Gravity Term Stability
M<1 >0 Always Stable
M>1 >0 Conditionally Stable
M<1 <0 Conditionally Stable
M>1 <0 Unstable

For the case under investigation, the mobility ratio is greater than one. So the only
option would be to have gravity term greater than zero to achieve a conditionally stable
displacement. The density of the constituents is an important parameter to consider in
designing the porous material (column) and selecting the correct flow direction to avoid
viscous fingering. This means that we should inject from the bottom of the column in
vertical direction. Figure 29 shows the dimension of the PTFE tube and the end structures
that were used in building the PTFE packed column. Manifolds were constructed for both
ends of packed column to evenly distribute the flow and a 300 mesh screen applied to
prevent the PTFE powder from entering the manifolds. A column diameter of
approximately 100 times greater than the grain diameter was selected to avoid wall
effects.
Figure 30 shows the PTFE packed column that was built and used in our
displacement experiments. The various PTFE parts were bonded together using a special
PTFE cement.

54

Figure 29: Dimension of the designed column

Figure 30: Packed PTFE column for flow experiments

55

5.3 Characterizing the Packed Column
After constructing the packed column, the next step was to determine the porosity,
permeability and dispersivity of the column through a set of single phase experiments. In
following subsections, the methods used for characterizing each parameter are discussed
in more details.
5.3.1 Porosity
Porosity is a measure of void space of the packed column that can store the fluids.
Generally it is calculated from the ratio of pore volume to bulk volume of the packed
column. There are many methods to measure the pore volume and grain volume of the
packed column. In this work, two methods were used to estimate the porosity: a
gravimetrical approach and an approach based on Boyle’s law. In the gravimetrical
approach, the packed column is weighted before and after being saturated with a wetting
fluid. By knowing the density of the fluid, the pore volume can then be calculated. The
other method uses Boyle’s law where a reference cell with known volume is pressurized
and opened to the packed column and the equilibrium pressure is recorded. The pore
volume is then calculated from the following equation.
P
r
V
r
= P
2
( V
r
+ V
p
+ V
T
) 5-2
where P
r
is the reference pressure, V
r
is the reference cell volume, P
2
is the equilibrium
pressure after connecting the reference cell to the packed column, V
T
is the connecting
tubes volume and V
p
is the pore volume of the packed column. With this method the

56

porosity of the system is measured as 53%.
Also for validation purpose, the porosity of the medium is calculated as 47% with
gravitational method. However, the latter approach was deemed more accurate resulting
in an estimate of the porosity of 47%.
5.3.2 Permeability
The permeability of the packed column was calculated from Darcy’s law. The
pressure drop across the column was measured while the wetting phase was injected into
the column and the pressure drop was stabilized at the given rate. The permeability
obtained for the packed column is reported in Table 18.
Table 18: Calculated permeability for the column A
Q(mL/min) ∆P(psia) K
a
(mD)
0.20 2.58 385

5.3.3 Dispersivity of the Packed Column
Dispersivity is a property of the porous medium which is an indication of the amount
of dispersive mixing that occurs within a medium. Accordingly, dispersivity is
considered a good indication of small-scale heterogeneity of a packed column.
To measure the dispersivity, the miscible displacement experiment (or a tracer
experiment) is usually carried out in which the amount of smearing observed in the
effluent concentrations is proportional to the dispersivity of the medium.
Using effluent data, the dispersivity of the medium is calculated by: (Bear 1972)
(Sternberg 2004)

57

5-3
in which is the dispersivity of medium (m), L is the displacement length, ,
and are the time during the displacement at which fluids with 30, 50 and 70 percents
of the injected composition is observed at the effluent respectively. This equation is
mostly used for tracer experiment with no change of viscosity throughout displacement.
The Peclet number is commonly used to quantity the dispersivity in porous medium.
It is defined as the ratio of convection to dispersion-based transport: (L. W. Lake 1989)
5-4
To measure the dispersivity for the system under study the following steps was taken:
1. Evacuate the column
2. Inject 3 pore volumes of wetting phase (100 % Isooctane) into the system
3. Capture the changes in mass rate by diverting the effluent into a container sited on
top of a balance
4. Inject Isopropanol into the system to displace Isooctane.
Due to the density differences between Isooctane and Isopropanol, the cumulative
mass of effluent, if plotted versus time, will form two connected lines with different
slopes. The transition between these two rates is used to calculate the Peclet number for
this system.

The experimental setup for the dispersivity measurements is shown in Figure 31. As it is

58

shown, the sources of Isooctane and Isopropanol are connected through pumps to a three
way valve which is connected to the inlet of the column. The effluent of the column is
also diverted through tubing to a container sited on top of the balance. The rate of
changes in the mass of the container is recorded.

Figure 31: Experimental setup for vertical (bottom to top) dispersivity measurement

The results of the dispersivity experiments and the calculation of Peclet numbers are
reported as follows:
5.3.3.1 Dispersivity from Horizontal Displacement
Table 19 reports the measured mass of effluent for this dispersivity experiment. The
conditions at which the experiment was carried out in addition to the calculated Peclet
number are reported in Table 20. The observed smearing of the effluent is shown in
Figure 32.

59

Table 19: Recorded Mass vs. Time data
Time(min) Mass(g) Time(min) Mass(g)
136.98 4.49 257.13 8.68
152.00 5.00 272.15 9.24
167.02 5.52 287.17 9.82
182.03 6.03 302.18 10.41
197.05 6.55 317.20 10.99
212.07 7.06 332.22 11.58
227.08 7.58 347.25 12.17
242.12 8.12 362.27 12.75

Table 20: Experimental condition and calculated Peclet number for horizontal dispersivity test
Column A
Orientation Horizontal
Injection Rate(mL/min) 0.05
Temperature (K) 298
Calculated Peclet Number 315

Figure 32: Effluent density changes versus time for horizontal displacement of Isooctane by
Isopropanol

The Convection-Diffusion (CD) equation was used to simulate the effluent for the
dispersivity measurement. As it is shown in Figure 32, the run with the Peclet number of
500 has the closest match to the experimental data. However, the tailing behavior at the
end part of the smearing is observed which could be associated with the non ideality and
100 150 200 250 300 350 400
0.03
0.031
0.032
0.033
0.034
0.035
0.036
0.037
0.038
0.039
0.04
Time (min)
Mass rate (g/min)

Pe 100
Pe 500
Pe 1000
exp data

60

heterogeneities within the medium that would trap a portion of initial oil inside the
medium. This trend can also be attributed to the lack of evenly distribution of the fluids at
the inlet and outlet of the column, although manifolds were created at the ends to avoid
this phenomenon.
5.3.3.2 Dispersivity from Vertical Displacement
A second experiment where Isopropanol was injected from the bottom of the column
in a vertical displacement was performed. The results in terms of profile and Peclet
number are given below.
Table 21: Experimental condition and calculated Peclet number for vertical dispersivity test
Column A
Orientation Vertical
Injection Rate(mL/min) 0.05
Temperature (K) 298
Calculated Peclet Number 350

Figure 33: Effluent density changes versus time for vertical displacement of Isooctane by Isopropanol

The same tailing effect is observed in the vertical dispersivity measurement although
0 50 100 150 200 250 300 350 400
0.03
0.031
0.032
0.033
0.034
0.035
0.036
0.037
0.038
0.039
0.04
Time (min)
Mass rate (g/min)

Pe 100
Pe 500
Pe 1000
exp data

61

the effect is less pronounced in vertical flow compared to the horizontal flow. As it is
seen with the simulation using Peclet number of 500 a good match is observed with
experimental data.
Also in this experiment, the experimental data on the tailing part of the effluent is off
at a point and the resolution is very low to have an accurate decision on the dispersivity
of the medium. As an alternative to this experiment and with the purpose of better
resolution, this experiment is repeated and effluent analyzed using GC as discussed in the
next section.
5.3.3.3 Dispersivity Experiment Analyzed using GC
In order to validate the dispersivity experiments using the mass rates and to have
better resolution on the tailing effects occurred at the end portion of the effluent, a single
phase dispersivity experiment was conducted in which samples from effluent were taken
and analyzed by GC. In this experiment, Isopropanol was injected to displace Isooctane
in the packed column. Samples were taken from the effluent and diluted with 0.8 mL of
Ethanol and analyzed by GC. and the GC results from this experiment are reported in
Table 23.
Table 22 reports the lab conditions in which the dispersivity experiment was
performed and the GC results from this experiment are reported in Table 23.
Table 22: Single phase dispersivity experiment - lab conditions
Initial composition 100 % Isooctane
Injection composition 100 % Isopropanol
Injection rate ( mL/min) 0.05
Temperature(C) 25
Duration(min) 300

62

Table 23: Effluent concentrations in mass fractions analyzed by GC for dispersivity experiment
Adjusted
Time (min)
Isopropanol Isooctane
0 0.003 0.997
101 0.004 0.996
179 0.005 0.995
186 0.005 0.995
192 0.010 0.990
196 0.030 0.969
199 0.067 0.932
202 0.254 0.746
206 0.484 0.515
210 0.651 0.349
213 0.745 0.255
216 0.789 0.211
219 0.830 0.170
222 0.857 0.143
225 0.878 0.122
228 0.896 0.104
231 0.911 0.089
234 0.917 0.083
237 0.929 0.071
241 0.938 0.061
246 0.943 0.057
273 0.970 0.030

Figure 34 shows the effluent data for Isopropanol and Isooctane. The simulation of
the dispersivity experiment with different Peclet numbers of 100, 500 and 1000 are also
shown for comparison in the same figure. The simulation results for the Peclet numbers
of 500 and 1000 could capture the early result of the dispersivity experiment but the
experimental data show a pronounced tailing effect at the end portion of the effluent
which originates from heterogeneity within the system and cannot be easily simulated.
Also it should be noted that the timing of the effluent for this experiment is different
from the ones observed before which is caused by having different experimental setup. In

63

the recent experiment, samples were collected from the effluent just off the outlet of the
medium and then analyzed with GC. However, for the previous two dispersivity
experiments the output of the column diverted through tubing to a container sited on top
of the balance which caused later timings.

Figure 34: Effluent concentration in mass fractions for dispersivity experiment

5.3.3.4 Discussion of Dispersivity Experiments
In order to have a good measure of the dispersivity within the medium, it is
recommended to find the dispersivity for which the simulation would match the first
portion (leading edge) of the effluent which embodies less impact of other heterogeneous
170 180 190 200 210 220 230 240 250
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time(min)
Concentration
Isopropanol
170 180 190 200 210 220 230 240 250
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time(min)
Concentration
Isooctane

Pe 100
Pe 500
Pe 1000
Experimental Data

64

different values of the Pe number were conducted and we found that with Pe = 305
(dispersivity of 0.001 m), the leading edge of the effluent was matched with simulation.
Figure 35 shows the result of these simulations at which for 2000 gird blocks where Pe =
305 provides the best match of the leading edge of the effluent. This figure also shows
the impact of numerical diffusion on the simulation results. Simulations with a Peclet
number of 305 and grid blocks ranging from 100 to 2000 are shown in the figure.

Figure 35: Effluent concentration in mass fractions for dispersivity experiment and simulation at
different grid blocks using Peclet number of 305

We observed from dispersivity experiments, that the trailing portion of the effluent
does not follow the solution of the CD equation. Two plausible mechanisms can cause
100 120 140 160 180 200 220 240 260 280 300
0
0.2
0.4
0.6
0.8
1
Time(min)
Concentration
Isopropanol
100 120 140 160 180 200 220 240 260 280 300
0
0.2
0.4
0.6
0.8
1
Time(min)
Concentration
Isooctane

GB 2000 Pe inf
GB 2000 Pe 305
GB 1000 Pe 305
GB 500 Pe 305
GB 100 Pe 305
Experimental Data

65

this behavior: a) Heterogeneity in the column or b) poor distribution at the inlet and
outlet. Below, we look at these mechanisms in more detail.
It is very likely that the effluent tail is caused by some bypassed oil that gradually will
reach the outlet of the column. To investigate this, simulations in 2D were conducted
where the injector and producer wells are located at some distance from the first and last
blocks. Figure 36 shows a schematic of this type of simulation for a system with 5*20
grid blocks.

Figure 36: 2D simulation of the dispersivity experiment for 20 blocks in z direction and 5 blocks in x
direction is shown in which the bypassed oil is modeled by having injector and producer cells away
from the first and last rows

For our simulation purposes, a 2D 5×2000 blocks system was used in which the
injector well placed at the 50
th
row and the producer well placed at the 1950
th
row of the
blocks in z-direction. The result of this simulation is plotted in Figure 37 for a Peclet
number of 305. As the result of this simulation, the simulated profile can match the
experimental profile closely but the effluent from the simulation arrives 8 minutes earlier

66

(corresponding ~ 4% of a pore volume). The simulated effluent is shifted b minutes in the
figure to verify the shape.

Figure 37: Effluent concentration in mass fractions for dispersivity experiment and simulation with
2000 grid blocks in z-direction at Peclet number of 305 for the case of having injector at 50
th
row and
producer at 1950
th
row. Experimental data 8 minutes shifted to the left

In all the simulations so far, the medium is considered as homogeneous medium.
However, irregular shape of Teflon beads and imperfect packing due to elasticity of
Teflon can lead to having heterogeneous medium. To study this, 2D simulations with
layers differing in the values of porosity and permeability conducted and as the result of
100 120 140 160 180 200 220 240 260 280 300
0
0.2
0.4
0.6
0.8
1
Time(min)
Concentration
Isopropanol
100 120 140 160 180 200 220 240 260 280 300
0
0.2
0.4
0.6
0.8
1
Time(min)
Concentration
Isooctane

I:50 P:1950 Pe 305
Experimental Data

67

the can be concluded:
Dependent on the degree of heterogeneity introduced through layers of different
porosity and permeability, the shape of effluent in the simulations, can be off in
the leading edge or trailing edge or at both ends
Although in some cases, the shape of the dispersivity experiment’s effluent could
be produced by simulation, the timing of the breakthrough changes significantly

5.4 Capillary Effects
Capillary forces can impact the displacement characteristics in multi-phase flows and
cause trapping of fluids within the pores of a porous media. The displacement
experiments should be designed in a way to avoid capillary pressure affecting them. The
capillary number which is defined as the ratio of viscous to capillary forces is an
indicator of extent of the capillary effects in the system.

5-5
where, is the velocity, is the viscosity of displacing phase, is the IFT and is the
contact angle between the displaced and displacing phases. Rapport and Leas (1953)
dimensionless number is also used as a criterion for estimating the significance of
capillarity effects in displacements: (L. W. Lake 1989)
5-6

68

where is the porosity, is the absolute permeability and is the length of the system.
Viscous dominated flow is observed for greater than 3. Table 24 reports for a
range of conditions relevance to our experimental investigation.
Table 24: Different scenarios studied to avoid capillarity dominated flow
Case
Rate
(mL/min)
μ
d

(cP)
IFT
(dynes/cm)
Comments
1 0.20 0.89 39.0 30 1.2E-06 0.44
High IFT steady state
relative permeability
experiment
2 0.05 0.89 39.0 30 3.1E-07 0.11
High IFT unsteady state
experiments carried out
3 0.05 2.00 39.0 30 6.9E-07 0.25
Viscosity of displacing
phase increased to 2 cP
4 0.20 2.00 39.0 30 2.8E-06 0.99
Rate changed from 0.05
to 0.2 mL/min
5 0.20 2.00 7.5 30 1.4E-05 5.16
IFT decreased from 39
to 7.55
6 0.05 2.00 7.5 30 3.6E-06 1.29
Rate decreased to 0.05
mL/min
7 0.05 2.00 3.2 30 8.4E-06 3.03
IFT decreased to 3.2
dynes/cm
8 0.05 0.89 1.4 30 8.4E-06 3.01
IFT decreased to 3.2
dynes/cm and viscosity
decreased from 2 to
0.89 cP

From Table 24, we observe that a range of conditions will result in viscous dominated
displacements (scenario 5, 7 and 8). We return to this analysis later as part of the analysis
of the two-phase four component displacement experiments.
5.5 Relative Permeabilities Study
For single phase flow, the permeability of the medium is only a function of rock
properties. However, in multi-phase flow, the permeability of each phase flowing in

69

contact with the other phases is a function of both the porous media and the other phases
flowing within the pore space. Accordingly, it is important to obtain a solid
understanding of the effective permeability of the wetting and the non-wetting phases for
our system. In general, there are two methods for determining the phase relative
permeabilities; one is a static or steady state method and the other one is a dynamic or
unsteady state method (Abaci and Edwards 1992). In the first method, a fixed ratio of
phases is driven with constant flow rate through the porous media simultaneously,
whereas, in the dynamic method, the in-situ phase is displaced by injecting the other
phase into the porous media (Abaci and Edwards 1992). This dynamic method has the
advantage of requiring fewer experiments to map the saturation region and the main
limitation is that it is unable to determine relative permeabilities for the regions with
saturation shock fronts (Grader and O'Meara Jr. 1986). In this work, we determine the
relative permeability by a steady state experiment.
In the steady state experiment, the column is initially saturated with wetting phase
and the saturated column is displaced in steps of increasing ratios of non-wetting to
wetting fluid. The changes in the mass of the column are captured in addition to the
pressure drop across the column. At the steady state conditions, the fixed values of the
pressure difference and mass difference are used for the calculation of the relative
permeabilities for each phase at the specified saturation. The saturation of wetting phase
at each step is calculated using the mass balance on the system as follows:
5-7

70

where, is the saturation of non-wet phase at the ith step, is the observed
increment in mass, is the pore volume of the system, and are the densities of
the wetting and non-wetting phases respectively. By using Darcy’s law, at each step the
effective permeability of each phase is calculated and is divided by the absolute
permeability of the medium to determine the relative permeability of each phase.
A steady state relative permeability experiment was carried out for the immiscible
pair Isooctane - Water where Isooctane serves as the wetting phase and Water is the non-
wetting phase. The experiment is carried out in 5 steps in which stabilization time for the
steps varied from 12 to 24 hours. Table 25 shows the stabilized mass and pressure after
each step for varying fractional flows.
Table 25: Steady-state experimental result for column A

Vo(m/s) Vw(m/s) Mass (g) P (Psia) Sw Kro Krw
Step 1 4.68E-05 0 0.000 2.58 0 1 0
Step 2 3.51E-05 1.17E-05 1.368 6.30 0.39 0.31 0.19
Step 3 2.34E-05 2.34E-05 1.618 7.29 0.46 0.18 0.33
Step 4 1.17E-05 3.51E-05 2.113 6.73 0.60 0.10 0.53
Step 5 0 4.68E-05 2.503 4.96 0.71 0 0.96

Figure 38 shows the relative permeabilities of the medium to water and oil phases
versus Water saturation. Both curves show a concave behavior. From the experiments,
we observe a residual saturation of the wetting phase as 29%. We note that the residual
saturation is a function of the IFT and the flow rate, commonly expressed through the
capillary number.

71

Figure 38: Oil and Water relative permeabilities: observations and modeling.

In order to model the observed relative permeability data, Core-type relative
permeability functions were used with exponents for wetting and non-wetting phases
equal to 1.5 and 3 respectively.
5.6 IFT Measurements – Pendant Drop
Among the available methods for measuring surface tension between equilibrium
phases, the pendant drop approach was selected for this work. The required setup for
pendant drop analysis was constructed in the lab and consisted of a microscope (Dino-
Lite) with the capability of taking digital images, a light source and a visual cell as shown
in Figure 39. The inner space of the cell has the diameter of 2.5 inch and a width of 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8
Kr
Sw
Kro
Krw
Kro-Corey
Krw-Corey

72

inch resulting in a volume of approximately 80 mL.

Figure 39: Pendant drop setup
The theory behind this method is the relationship between the shape of a suspended
droplet which forms in the other phase to the amount of the interfacial tension between
the two-phases. The suspended droplet is in an equilibrium state which is a result of the
balance between gravity and surface forces. The following equation is used to calculate
the interfacial tension based on the dimensions of the droplet (d
s
& d
e
) and density
differences between the phases ( ).

5-8
In this equation, d
e
is the maximum equatorial diameter of the drop and and 1/H is the
function of the ratio of d
s
over d
e
which is usually given in a tabular format in which ds is
the diameter of the droplet in plane with d
e
distance away from the apex of the droplet
(Misak 1968). In this work the equations proposed by Misak (1968) was used and
programmed to find the value of 1/H and as a result the interfacial tension between the
phases.

73

To test the pendant drop setup, Water – Air interfacial tension was measured at
ambient conditions with above mentioned method and the value of 70 dynes/cm was
calculated from the observations using the above equation. The measured value was in
good agreement with 72 dynes/cm experimental data reported by Vazquez et al (1995).
The dimension of the water droplet is shown in Figure 40 as shown below:

Figure 40: Water droplet in a pendant drop cell (ds=2.49 mm and de=3.30 mm)

After testing our pendent drop cell with water/air, the IFT was measured for three
mixture compositions on the Isooctane-Isopropanol-Water ternary. The results in addition
to available literature data are summarized in the Table 26:

74

Table 26: Measured IFT and literature data for the system under study, phase compositions are in
mass fractions (Sets A, B and C is the experimental IFT calculation at 20
o
C)

Aqueous rich phase
Hydrocarbon rich
phase
IFT (dynes/cm)
Shape of pendent drop
Sets
Water
Methanol
Isopropanol
Isooctane
Water
Methanol
Isopropanol
Isooctane
A 1 0 0 0 0 0 0 1 39.3

B 0.92 0 0.08 0 0.00 0 0.01 0.99 8.66

C 0.45 0 0.53 0.02 0.00 0 0.08 0.92 1.68

D 0.44 0.56 0 0 0.01 0.09 0 0.90 7.55
by Garcia-Flores et al.
(2007)
E 0.52 0 0.37 0.11 0.09 0 0.34 0.57 0.024 by Orr (2004)

75

5.6.1 IFT Modeling
By reviewing the available applicable IFT models, no single model was found that
can predict the IFT in between multi-phase multi-component liquid-liquid system with a
good degree of accuracy. The model presented by Bahramian and Danesh (2004) is one
of the only extensive methods proposed for this type of systems. However, this model
produced a significant amount of errors when applied to ternary systems in which over
45% deviations from the mixture IFT reported for the systems studied.. To overcome the
IFT modeling issue for the system under study, a simple correlation was developed based
on the data from Morrow et al. (1988) for the system of Brine-Isopropanol-Isooctane.
In this correlation, the logarithmic value of IFT was directly related to the tie-line
length in the mass fractions of the phases on the ternary plot. Figure 41 shows this
correlation and reports the R-squared of this correlation which is greater than 0.99. To
validate the result of this correlation on the two-phase liquid-liquid system of the other
ternaries, the result of the prediction of the model for experimental data reported by
Garcia-Flores et al. (2007) on the ternary of Water-Methanol-Isooctane is compared and
shown on the same figure. A very good agreement between the prediction and the
experiment is observed. This correlation is used later in our simulator as the IFT model
for predicting tensions in between liquid-liquid phases.
Also on the same figure, experimental IFT data are plotted with triangles and as it is
seen, these data are aligned with the correlation but the values are slightly off. This can
be due to the nature of Morrow et al. (1988) IFT data that brine is used instead of Water.

76

Figure 41: Natural log of interfacial tension in between phases vs. the tie-line length

y = 7.9386x - 7.7545
R² = 0.9946
-3
-2
-1
0
1
2
3
4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
ln (IFT)
Tie-line length (mass fraction)
Water-IPA-IC8
Water-MeOH-IC8
Exp. (Water-IPA-IC8)
Linear (Water-IPA-IC8)

77

Chapter 6: Displacement Experiments and
Simulation
6.1 Selection of Oil and Gas Compositions
In this study of dispersive mixing in multi-component displacement process, it is
desired to design the displacement experiment that develops multi-contact miscibility
during the displacement of the initial oil by the injected gas. Per our earlier discussion on
the compositions of the oil and gas in our analog system, the initial oil compositions will
be mixtures of Water – Isopropanol – Isooctane and the injection gas composition should
be a mixture of Water, Methanol and Isopropanol.
In a first step, the total of nine cases with different initial and injection compositions
were selected in which different oil binary mixtures of Isopropanol- Isooctane containing
25%, 50% and 75% Isooctane by mole are displaced with three gases with composition
of 25%, 50% and 75% Methanol by mole. The displacements for these nine combinations
of oil and gas mixtures were simulated using the developed simulator and the
composition path and component displacement profile are reported in following figures:
It should be noted that in all the simulation, the UNIQUAC activity coefficient model
was used as the engine for phase behavior calculations; the UNIQUAC based viscosity
model is also used for estimating viscosities. In this initial scoping of displacement
calculations, no diffusion or dispersion was included in the simulations.

78

Figure 42: Compositional paths of displacement for nine study cases

Figure 43: Displacement profile for nine displacement cases shown in Figure 42

IPA IPA IPA IPA IPA IPA IPA IPA IPA
MEOH MEOH MEOH MEOH MEOH MEOH MEOH MEOH MEOH
WATER WATER WATER WATER WATER WATER WATER WATER WATER
IC8 IC8 IC8 IC8 IC8 IC8 IC8 IC8 IC8

Case1: 0.5W 0.5M 0.25P 0.75C8
Case2: 0.5W 0.5M 0.5P 0.5C8
Case3: 0.5W 0.5M 0.75P 0.25C8
Case4: 0.25W 0.75M 0.25P 0.75C8
Case5: 0.25W 0.75M 0.5P 0.5C8
Case6: 0.25W 0.75M 0.75P 0.25C8
Case7: 0.75W 0.25M 0.25P 0.75C8
Case8: 0.75W 0.25M 0.5P 0.5C8
Case9: 0.75W 0.25M 0.75P 0.25C8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
Concentration
Water
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
Concentration
Methanol
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
Concentration
Isopropanol
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
Concentration
Isooctane

79

Figure 42 shows the compositional paths of the displacement for all the 9 cases.
Figure 43 shows the displacement profiles for the 4 components involved in the
displacement. Cases 3, 6 and 9 which held 75 % by mole of Isopropanol as initial oil
would create a viscosity of approximately 1 cP which is likely to cause instabilities in an
equivalent displacement experiments. The low oil viscosity was in favor for scenarios 1,
4 and 7 in which viscosity of oil was estimated to be 0.52 cP for these cases. Among
these three cases, case number 4 was selected for an initial displacement experiment. This
case has the highest Methanol percentage in the injection composition and more closely
mimics a real CO
2
injection process.
6.2 Numerical Diffusion Vs. Physical Dispersion
One of the questions that we seek to address in this work is if the influence of
numerical diffusion in compositional simulation of gas injection process is similar to
influence of actual physical dispersion. To investigate this, we first consider the injection
of CO
2
into an oil reservoir and describe the phase behavior by constant equilibrium
ratios. The injection compositions in addition to equilibrium K-values are tabulated in
Table 27.
Table 27: Initial and injection compositions, K-values and pure components viscosity
Components C
1
CO
2
C
4
C
10

Initial composition 0 0 0.4918 0.5082
Injection composition 0.625 0.375 0 0
Constant K-values 2.5 1.5 0.5 0.05
Viscosity (cp) 0.013 0.015 0.0091 0.005

80

In this system, the injection composition is a mixture of CO
2
and Methane, and the
Mixture of C
4
and C
10
represents the oil. To illustrate the impact of dispersive mixing,
four scenarios with different levels of dispersivity are considered. The Peclet number for
the porous media ranges from Peclet number of 50 to infinity representing very
dispersive to very convective displacements. The result of this initial study is shown in
Figure 44 and Figure 45. These figures show the effect of dispersion and its importance
on the compositional path that any particular displacement takes. We observe that cases
with the high Peclet numbers (500+) are similar to the purely convective displacement.
The compositional path shown as a solid black line represents the lowest Peclet number
(50) which means the largest amount of dispersive mixing.

Figure 44: The impact of dispersion on the compositional path for fixed oil and gas compositions
C
4
C
3
C
2
C
1
C
4

C
10
CO
2

C
1

81

Figure 44 and Figure 45 report the overall concentration for the individual
components along with the gas saturation. From the composition and saturation profiles,
we clearly see the effect of different levels of dispersion.

Figure 45: Displacement profiles for different Peclet numbers
0 0.2 0.4 0.6 0.8 1
0
0.5
1
C1
0 0.2 0.4 0.6 0.8 1
0
0.5
CO2
0 0.2 0.4 0.6 0.8 1
0
0.5
C4
0 0.2 0.4 0.6 0.8 1
0
0.5
C10
0 0.2 0.4 0.6 0.8 1
0
0.5
1
Sg

82

Figure 46: Displacement profile for Peclet number of 100 at various numbers of blocks
In order to demonstrate the effect of the number of grid blocks used in a simulation
on the mixing and whether the numerical dispersion, arising from truncation error of
finite difference approximation as well as flash calculation averaging over the grid block
distance, can really represents the physical dispersion, a set of simulations was designed
where a mixture of CO
2
and Methane was injected into an oil represented by mixture a of
C
4
and C
10
.
First, by assigning a fixed amount of physical dispersion to the displacement process
(Pe = 100), the effect of grid refinement on the convergence of the simulation results was
0.2 0.3 0.4 0.5 0.6 0.7 0.8
-0.2
0
0.2
0.4
0.6
C
1
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
0
0.2
0.4
CO
2
0.2 0.3 0.4 0.5 0.6 0.7
0.1
0.2
0.3
0.4
0.5
C
4
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.2
0.4
0.6
C
10
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0.2
0.4
0.6
0.8
Sg
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
C
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
CO
2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
C
4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
C
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
Sg

N=400
N=200
N=100
N=800

83

investigated. Figure 47 shows the displacement profiles for this set of simulations where
the numerical errors were gradually minimized by refining the simulation grid blocks (n
= 100, 200, 400, 800). The simulation result of 400 and 800 grid blocks (black line and
blue line) are converging, so the simulation with 800 blocks is selected to study the effect
of grid block coarsening in the case of no dispersion to see if this approach can be used
instead of real physical dispersion. Figure 47 compares the simulations result with no
physical dispersion included for different numbers of grid blocks with the case where
dispersion is included explicitly as discussed above.

Figure 47: Displacement profile, comparing physical and numerical dispersion
As it is observed from this figure, the behavior of physical dispersion and numerical
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.2
0.4
0.6
C
1

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
0
0.2
0.4
CO
2
0.2 0.3 0.4 0.5 0.6 0.7
0
0.2
0.4
0.6
C
4
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.2
0.4
C
10
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.2
0.4
0.6
0.8
Sg
No Dispersion N=50
No Dispersion N=100
No Dispersion N=200
No Dispersion N=400
Pe =100 N=800
No Dispersion N=800
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.2
0.4
0.6
C
1

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
0
0.2
0.4
CO
2
0.2 0.3 0.4 0.5 0.6 0.7
0
0.2
0.4
0.6
C
4
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.2
0.4
C
10
0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.2
0.4
0.6
0.8
Sg
No Dispersion N=50
No Dispersion N=100
No Dispersion N=200
No Dispersion N=400
Pe =100 N=800
No Dispersion N=800

84

dispersion is different and numerical diffusion is not a good approximation of real
dispersion (black solid line shows the displacement with physical dispersion). Figure 48
shows the compositional path of the simulation by comparing the case of no dispersion
using 50 and 800 blocks with the converged case where dispersion is included explicitly
(Pe = 100).

Figure 48: Compositional path comparing no dispersion with 50 grid blocks (green), no dispersion
with 800 grid blocks (brown) and dispersion with Pe=100 with 800 grid blocks(black)

A similar analysis has been performed for the analog solvents and the comparison
between physical and numerical dispersion is reported below. Figure 49 shows the
displacement profiles from the simulations using analog solvents and Table 28 lists the
composition of the initial fluid in place as well as of the injected fluid.

C
10
C
4
CO
2

C
1 C
10
C
1
CO
2

85

Table 28: Initial composition and injection composition
Components Water Methanol Isopropanol Isooctane
Initial composition 0 0 0.25 0.75
Injection composition 0.25 0.75 0 0

In this case, Methanol represents the CO
2
as the injected gas and Isooctane represents
the major constituent of original oil in place. In order to compare the physical dispersion
with numerical diffusion, cases with 1000 grid blocks with different level of dispersions
are simulated.

Figure 49: Displacement profile, comparing cases with different levels of dispersion, 1000 grid
blocks

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
Concentration
Water
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
1
Concentration
Methanol
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
Concentration
Isopropanol
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
1
Concentration
Isooctane

Pe 100
Pe 500
Pe 1000
Pe inf

86

Figure 50: Compositional path for different levels of dispersion

Therefore, as it is implied from the simulations a thorough modeling of dispersion is
needed to accurately predict the performance of miscible CO
2
injection and the proposed
experimental work on multi-phase dispersion will assist us in selecting an accurate
representation of dispersion.

6.3 Multi-component Two-Phase Displacement Experiment
Two multi-contact miscible displacements were conducted at the lab conditions to
observe dispersive mixing. For both experiments the experimental setup is depicted in
Figure 51. Samples from the effluent off the column are taken and analyzed by GC. The
results of two displacement experiments are discussed as follows:

IPA IPA IPA IPA IPA
MEOH MEOH MEOH MEOH MEOH
IC8 IC8 IC8 IC8 IC8
WATER WATER WATER WATER WATER
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
Concentration
Water
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
1
Concentration
Methanol
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
Concentration
Isopropanol
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0
0.5
1
Concentration
Isooctane

Pe 100
Pe 500
Pe 1000
Pe inf

87

Figure 51: Schematic of displacement experiment

6.3.1 Displacement Experiment A
The first experiment with the compositions obtained from the earlier study on the
initial and injection compositions was conducted under the following conditions shown in
Table 29:
Table 29: Displacement experiment A: lab conditions
Initial composition 25 % Isopropanol , 75 % Isooctane by mole
Injection composition 24.7 % Water, 75.3 % Methanol
Injection rate (mL/min) 0.05
Temperature(
o
C) 19
Duration(min) 300

This displacement was carried out for 300 minutes with the sampling rate of as low as
every 5 minutes. All samples were taken from the effluent for a minute and then diluted
with 0.8 mL of Ethanol. These samples were then analyzed by GC and the observed
effluent concentrations are reported in Table 30:

88

Table 30: Effluent concentrations in mass fractions analyzed by GC for experiment A
Adjusted
Time (min)
Water Methanol Isopropanol Isooctane
37.5 0.003 0.005 0.135 0.857
53.5 0.003 0.004 0.139 0.855
61.5 0.002 0.003 0.133 0.862
72.5 0.001 0.004 0.135 0.860
81.5 0.004 0.003 0.135 0.858
88.5 0.003 0.004 0.136 0.857
98.5 0.005 0.003 0.138 0.854
110.5 0.004 0.002 0.137 0.858
116.5 0.008 0.003 0.143 0.845
125 0.005 0.002 0.140 0.853
132.5 0.005 0.003 0.140 0.853
137.5 0.005 0.003 0.141 0.851
141.5 0.006 0.003 0.141 0.850
146.5 0.025 0.030 0.240 0.705
151.5 0.084 0.316 0.391 0.208
161.5 0.097 0.748 0.121 0.033
171.5 0.144 0.783 0.045 0.028
186.5 0.148 0.805 0.018 0.029
201.5 0.126 0.842 0.009 0.022
221.5 0.126 0.848 0.005 0.021
241.5 0.128 0.847 0.004 0.021
261.5 0.130 0.848 0.004 0.018
291.5 0.130 0.850 0.003 0.018

In this experiment, the viscosity of displacing phase is estimated to be 0.90 cP. As
previously discussed in section 5.4, should be greater than 3 to have a viscous
dominated displacement. is directly proportional to and the value of is
inversely proportional to the IFT of the system. To have an understanding of the IFT
throughout this displacement, the tie-line extending through the initial composition on the
Water-Isopropanol –Isooctane ternary was compared to the IFT experimental data of
Morrow et al. (1988). This tie-line is estimated to have an IFT of less than 1 dynes/cm in

89

between the equilibrium phases. Using the IFT correlation discussed earlier in chapter 5,
the plot of IFT variation over the length of displacement is shown in Figure 52. A
maximum IFT of 9.31 dynes/cm is estimated for this displacement.

Figure 52: Variations in estimated liquid-liquid IFT for displacement experiment A for 1000 grid
blocks simulation

For this IFT, the maximum estimated capillary number is ranging from 10
-6
to 10
-3
as
it is shown in Figure 53 which it suggests that a residual wetting saturation would exist
inside the system. Lake (1989) based on capillary desaturation curves for wetting phase,
suggests that in displacements with capillary numbers greater than approximately 10
-3
,
the residual wetting saturation starts to decrease.
100 150 200 250 300 350 400 450
0
1
2
3
4
5
6
7
8
9
10
Grid Block Number
Estimated IFT (dynes/cm)

90

Figure 53: Estimated capillary number based on liquid-liquid IFT for displacement experiment A for
1000 grid blocks simulation

The compositional path and component profiles from the displacement experiment
are plotted and shown in Figure 54 and Figure 55.

Figure 54: Compositional path for displacement experiment A
100 150 200 250 300 350 400 450
10
-6
10
-5
10
-4
10
-3
Grid Block Number
Nvc Capillary Number
IPA IPA
MEOH MEOH
IC8 IC8
WATER WATER

91

Figure 55 shows the displacement profile for the four components involved in
displacement experiment A. Two approaches were applied to model this displacement
experiment: First, including the IFT model that goes to zero for the compositions near a
critical point and second, by assuming constant relative permeability curves for the
system. By the first approach, three simulations at different degrees of dispersion are
compared. Figure 56 shows these simulations in the quaternary compositional space in
which in both cases the simulations are very close to the experimental observation.

Figure 55: Compositional profiles for displacement experiment A. The simulations with and without
IFT models are included
50 100 150 200 250
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
Simulation with no IFT
Simulation with IFT Model Pe =inf
Simulation with IFT Model Pe =500
Simulation with IFT Model Pe =100

92

Figure 56: Compositional paths for displacement experiment A. The simulations with and without
IFT models are included

The influence of numerical coarsening on the result of the simulations is also
investigated excluding the IFT model with grid blocks ranging from 50 to 1000, as it is
clear that none of these simulations can capture the shape of the smearing observed in the
experiment. In terms of the arrival timing the simulation with 250 grid blocks captures
the arrival for Water and Methanol but it is off in the arrival time for Isopropanol and
Isooctane as it is shown in Figure 57. Figure 58 shows the compositional path of all the
simulations which are very close with each other and still away from the observed
experimental data.

93

Figure 57: Compositional profiles for displacement experiment A. Simulations without IFT models
compared with numerical diffusion

Figure 58: Compositional paths for displacement experiment A. Simulations without IFT model
showing the impact of numerical diffusion
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
1000 GB
500 GB
250 GB
100 GB
50 GB

94

In terms of physical dispersion, simulations were performed using 1000 grid blocks to
minimize any numerical diffusion that could affect the result. Dispersivities ranging from
100 to infinity in terms of the Peclet number were investigated excluding the IFT model.
The result of this study is shown in Figure 59 and Figure 60. All cases display close
variations in terms of the profile and path of displacement.
It should be noted that the lack of a very accurate IFT model that can predict the
tension between the liquid-liquid phases created throughout displacement would make it
almost impossible to present a solid model to analyze the dispersion behavior of this
displacement. Additionally, the non-idealism in the medium as was observed in the
profiles of dispersivity test as discussed in the previous chapter would have a definite
impact on the shape of the profiles observed from the displacement experiment.

Figure 59: Compositional path for displacement experiment A showing the impact of Peclet number
without IFT model

95

Figure 60: Compositional profiles for displacement experiment and simulations showing the impact
of Peclet number without IFT model.

6.3.2 Displacement Experiment B
In the second displacement experiment, small amount of water was added to the oil
composition to place the oil composition on the Water – Isopropanol –Isooctane ternary.
In order to minimize the impact of capillarity, the initial composition is richer in
Isooctane compared to experiment A.
The lab conditions of the second displacement experiment (experiment B) are
reported in Table 31. Also the linear densities and estimated value of viscosities based on
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
Pe=inf
Pe=1000
Pe=500
Pe=250
Pe=100

96

UNIQUAC viscosity model for the oil and gas phases are calculated and reported in
Table 31. The critical flow rate for this set up is calculated as 0.052 mL/min.

Table 31: Displacement experiment B: lab conditions
Initial Composition 13% Water, 33% Isopropanol and 54% Isooctane by mole
Injection composition 4% water, 94% Methanol and 2% Isopropanol by mole
Injection rate (mL/min) 0.05
Temperature(C) 21
Duration(min) 1000

Table 32: Density and viscosity prediction for oil and gas phases
Properties Oil Phase Gas Phase
Linear density (g/cm
3
) 0.700 0.790
Estimated viscosity (cP) 0.656 0.605

Similar to experiment A, samples of the effluent were diluted with 0.8 mL of Ethanol
before GC analysis. Unlike, experiment A, for better resolution on the changes
throughout the displacement, the sampling frequency was reduced from 5 to 3 minutes to
capture the important segments of the displacement process. The observed effluent
concentrations are reported in Table 33.
For this experiment, the base ternary IFT for the tie-line extended through the oil
composition would be less than 0.446 dynes/cm comparing to Morrow et al. (1988) IFT
data. The estimated IFT variation for this experiment is shown in Figure 61.
The maximum IFT for this displacement would be approximately 4 dynes/cm which
is equivalent to the capillary number of 1.8x10
-6
which still there would be some residual
trapping occurred within the system. Figure 62 shows the range of capillary number for

97

this displacement which is within the range of 10
-6
to 10
-4
which suggests that there
would be a residual saturation sitting within the column.
Table 33: Effluent concentrations in mass fractions analyzed by GC for experiment B
Adjusted
Time (min)
Water Methanol Isopropanol Isooctane
0 0.016 0.000 0.188 0.796
41 0.016 0.002 0.185 0.797
61 0.014 0.002 0.185 0.799
89 0.015 0.002 0.184 0.799
106 0.015 0.002 0.185 0.798
126 0.015 0.002 0.185 0.798
146 0.014 0.002 0.186 0.798
151 0.061 0.248 0.374 0.317
156 0.063 0.354 0.369 0.215
161 0.061 0.482 0.277 0.181
166 0.055 0.498 0.238 0.209
171 0.055 0.578 0.205 0.162
176 0.052 0.609 0.182 0.156
181 0.048 0.626 0.164 0.162
186 0.049 0.675 0.126 0.150
191 0.043 0.713 0.095 0.149
196 0.041 0.750 0.069 0.140
201 0.041 0.742 0.069 0.147
221 0.038 0.768 0.048 0.146
236 0.038 0.773 0.044 0.145
251 0.041 0.777 0.042 0.140
281 0.039 0.777 0.039 0.145
316 0.040 0.779 0.039 0.142
366 0.037 0.781 0.037 0.144
391 0.042 0.905 0.042 0.011
1001 0.056 0.901 0.043 0.001

98

Figure 61: Variations in estimated IFT for displacement experiment B

Figure 62: Calculated capillary number based on estimated IFT for displacement experiment B
280 300 320 340 360 380 400 420 440 460
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Grid Block Number
Estimated IFT (dynes/cm)
280 300 320 340 360 380 400 420 440 460
10
-6
10
-5
10
-4
10
-3
Grid Block Number
Nvc Capillary Number

99

The displacement path and composition profiles for displacement experiment B are
shown in Figure 63 and Figure 64. Also Figure 64 and Figure 65 show the displacement
path and profile of the simulated experiment with models both including and ignoring the
IFT changes for the system. For the model with IFT, simulations with no dispersion,
Peclet of 500 and 100 are compared. All cases follow the same trend with small
variations. Also for the purpose of comparison, the simulation with No IFT model
assuming zero dispersion is generated.

Figure 63: Compositional paths for displacement experiment B
IPA IPA
MEOH MEOH
IC8 IC8
WATER WATER

100

Figure 64: Displacement profiles for displacement experiment B

Figure 65: Compositional paths for displacement experiment B
50 100 150 200 250
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
Simulation with no IFT
Simulation with IFT Model Pe =inf
Simulation with IFT Model Pe =500
Simulation with IFT Model Pe =100

101

The result of this experiment is also compared with simulations using no IFT models
with varying the number of grid blocks used for simulation. Figure 66 and Figure 67
show the displacement profile and path for the simulations in which grid block numbers
are ranging from 50 to 1000. Simulation with 250 grid blocks introduces a level of
smearing on the profile that matches the timing of the events happened throughout
displacement. But, if we look thoroughly at it, still the shapes of the bumps and smearing
seen are different and cannot be matched by numerical diffusion through coarsening the
grid blocks. Also the displacement paths for all the simulations are off and the 50 grid
blocks simulation with maximum numerical diffusion has the closest path to the real
experiment.

Figure 66: Displacement profiles for displacement experiment B - comparing with numerical
diffusion
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
1000 GB
500 GB
250 GB
100 GB
50 GB

102

Figure 67: Compositional path for displacement experiment B – comparing with numerical diffusion

In addition to numerical diffusion, it was tried to simulate the experiment using 1000
grid blocks with different level of physical dispersion to see the impact on the shape of
the profiles and path of displacement. Figure 68 and Figure 69 show the results of these
simulations. The effect of physical dispersion is more pronounced compared to
experiment A. for a very low Peclet number of 100, the simulation agrees very well with
the profile observed for the concentration of Isopropanol. However, it still cannot capture
the observed bumps on the profile of Isooctane and Water. In terms of the displacement
path, the case with Peclet number of 100 which has the maximum amount of dispersivity
still has the closest path to the real experimental observations.

103

Figure 68: Displacement profile for displacement experiment B – comparing with simulations using
different levels of physical dispersion

Figure 69: Compositional paths for displacement experiment B– comparing with simulations using
different levels of physical dispersion
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Water
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Methanol
50 100 150 200 250 300
0
0.1
0.2
0.3
0.4
Time(min)
Concentration
Isopropanol
50 100 150 200 250 300
0
0.5
1
Time(min)
Concentration
Isooctane

Experimental Date
Pe=inf
Pe=1000
Pe=500
Pe=250
Pe=100

104

6.4 Discussion and Conclusions
In conclusion, two sets of 4-component two-phase displacement experiments were
designed and carried out at lab conditions. For both cases, multi-contact miscibility was
observed in between the initial oil (on the ternary of Water-Isopropanol-Isooctane) and
injection gas (binary of Water and Methanol).
The GC analyzed results of these experiments were compared with the simulation
results on the cases with and without IFT model implemented. Also simulation with
different degrees of dispersivity were conducted and compared with the effect of
numerical diffusion with no physical dispersion.
It should be noted that due to the heterogeneity (involved within the system) as it was
seen throughout the dispersivity experiment, it is almost impossible to have an accurate
models for these types of displacement with assuming homogeneous medium.
It is recommended that the system under study should be modeled with a random
field of permeability and porosity in which the end result of that would match the
experimental observation on dispersivity experiment. Then this model can be used to
simulate our observations on two-phase multi-components displacement experiments.
Although, we have tried to match the experimental behavior with the dispersion
introduced through numerical diffusion and physical dispersion, but not having a very
accurate IFT model within the simulator which limits us in terms of conclusion on the
dispersive observations.

105

Chapter 7: Flow Based Lumping/Delumping for
Integrated Compositional Reservoir Simulation
7.1 Introduction
For the purpose of compositional reservoir simulation and EOR evaluation, working
with a large number of components is computationally expensive and the demand for
computer storage can become very large. In order to resolve this issue, it has been
suggested to group/lump the components of a detailed EOS model into a reduced set of
pseudo-components. The success of such lumping strategies rely on the accuracy of the
reduced model relative to the detailed EOS model in capturing the phase behavior of the
composition mixtures that form during a displacement process. Several procedures have
been proposed in literature for lumping crude oil fractions and for calculation of group
properties. In this section, we present a brief review of these contributions.
Lee et al. (1981) proposed a simple approach for grouping crude oil components
based on the physio-chemical properties of the components. In their work, they plotted
the properties such as specific gravity, molecular weight, viscosity etc. versus a weight-
averaged boiling point that serves as independent variable. Then they computed the
weighted sum of the slopes of these curves and grouped the fractions with similar values.
This procedure requires extensive laboratory data that may not be available due to the
cost of detailed compositional analysis and associated PVT measurements (Lee, et al.,
1981; Hong, 1982 ; Mehra, et al., 1982).

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Hong (1982) extended the work of Lee et al. (1981) by reducing the number of
interrelated properties and considered the fact that the properties of hydrocarbon
fractions, in general, correlate well with the molecular weight. Based on his approach,
C
7+
fractions were lumped into one component and in addition C
2
-C
6
were lumped to one
component unless the P-z diagram of the lumped components did not satisfactory
reproduce the observed experimental data. Mixing rules were selected for each lumped
fraction based on the agreement between observed and predicted dew-point and bubble-
point pressures when variable amounts of separator gas were added to the original oil.
Mehra et al. (1982) presented a statistical approach for lumping components. Their
approach was based on the fact that phase saturations play an important role in mobility
and displacement calculations. In their approach, errors in predicted phase saturations of
a lumped model were minimized relative to the saturations predicted by the original EOS
model.
Montel and Gouel (1984) proposed an iterative clustering algorithm that is applicable
to any number of components and any EOS model. This method utilizes the molecular
weight (M
w
) and EOS parameters as input to define groups by minimizing a distance
function that relates the properties of a given component to a predetermined number of
clusters. The optimal clustering then defines the lumped components and the properties
of the lumped components can be calculated.
Schlijper (1986) proposed an approach that is referred to as the pseudo-potential
method. The pseudo-components are formally associated with mixture-like characters
that are not treated similarly to pure components. For EOS related calculations Schlijper

107

suggested that the chemical potential should be replaced by the pseudo-potential which
represents the lumped components as a mixture rather than a single component. The
pseudo-components were selected based on minimizing the differences in Gibbs free
energy between the lumped fluid description and the original fluid description (Schlijper,
1986 ; Joergensen, et al., 1995).
Wu and Batycky (1988) pointed out the need to check the accuracy of the EOS model
based on the selected pseudo-components and their properties, not only for the oil but
also for the mixtures of oil and solvent. In their approach they used P
c
, T
c
, the critical
volume (V
c
), acentric factor ( ω), M
w
and the binary interaction coefficients (BIC) as the
input parameters and applied a combination of molar and weight based mixing rules. In
this approach, components were lumped based on the ability of the resultant model to
match the observed solvent-oil phase behavior. They concluded that lumping may have a
greater impact on the predicted solvent-oil phase behavior than on the predicted gas-oil
ratio (GOR) and demonstrated that the latter may not be affected significantly by the
selected lumping scheme or the mixing rules used for calculating the pseudo-component
properties.
Newley and Merrill (1991) proposed the use of empirical mixing rules that employ
information from co-existing phases near saturation pressures of the original fluid to
condition the EOS model. This aims at improving the phase behavior representation near
saturation points of the lumped fluid description. The grouping scheme proposed in their
work was based on minimizing the K-value differences between the pure components and
pseudo-components.

108

Danesh et al. (1992) proposed a lumping scheme based on concentrations and
molecular weights of the original fluid description. In their approach, the components are
initially sorted by ascending boiling points. The components are subsequently lumped
into groups by balancing the summation of the component mole fractions times the
natural logarithm of the molecular weight of the components for each group. Based on
the selected groups, a new set of mixing rules was suggested to calculate the properties of
the pseudo-components. In their study, vapor-liquid equilibrium (VLE) experiments were
also designed to mimic the conditions at the leading and trailing edges of a gas-oil
displacement process.
Hustad and Dalen (1993) used a statistical approach based on principal component
analysis (PCA) to lump components. In this PCA approach, an eigenvalue problem was
formulated that provides eigenvectors and eigenvalues for a multivariate set. In the
context of lumping, eigenvectors account for the importance of the components in the
compositional space and eigenvalues account for the significance of a given direction.
Based on this analysis, they proposed to lump components with similar contributions to
the delineation of the compositional space.
Leibovici et al. (1993) proposed a new method for calculating the physical properties
of the lumped components regardless of lumping schemes. They proposed a set of
equations in which P
c
and T
c
of the pseudo-components were treated as unknowns.
Dependent on the type of EOS used, they introduced the temperature dependency into the
set of equations and minimized the differences between the full and lumped descriptions.
Joergensen and Stenby (1995) studied and tested twelve different available lumping

109

schemes. The results of their study demonstrated that none of these methods may
function considerably better than others. They also recommended using the temperature
dependent mixing rules for estimating the pseudo-components physical properties as
proposed by Leibovici et al. (1993). Based on their analysis, they suggested using 6 to 8
pseudo-components to provide for optimal predictive capabilities.
Liu (2001) proposed an algorithm which is referred to as the “best lumping scheme”
that promises to find an optimal lumped fluid description based on the accuracy of the
predicted phase behavior of the fluid system and proposes an automatic regression
procedure to improve the predictive capabilities of the resultant EOS model. This work
included experimental observation from standard PVT experiments.
Egwuenu et al. (2008) extended the approach of Newley and Merrill (1981) by
generating K-values for a linear combination of the reservoir fluid and the injection gas in
the study of combined condensing and vaporizing displacement processes. They
demonstrated that the number of components used in the fluid description can be reduced
significantly as long as the lumped model is re-tuned to the experimental observations.
In general, the above lumping approaches do not include a significant amount of
information regarding the mixture compositions that will form during a gas injection
process. The mixture composition that forms during a gas injection process differs
significantly from those investigated by standard PVT and swelling experiments (Jessen,
et al., 2007 ; Orr, 2007).
Accordingly, valuable information from the dynamics of gas injection processes in
the selection of pseudo-component has so far not been included in any proposed

110

grouping/lumping scheme. In the following section, we propose a lumping scheme that
includes such information to define the pseudo-components of a reduced fluid description
and in addition to that, a modified version of the scheme of Newley and Merrill is also
proposed. Each of the proposed methods considers the variation in K-values of the
components that is observed in a given gas injection process. One of the proposed
methods is the modified version of the Newley and Merrill lumping scheme.
7.2 A Flow-Based Lumping Scheme
Jessen and Stenby (2007) and Egwuenu et al. (2008) demonstrated the need for
including compositional information beyond the standard PVT experiments (constant
mass expansion and/or differential liberation experiments) and swelling test data to
ensure an accurate prediction of the development of miscibility in terms of the minimum
miscibility pressure (MMP). This observation is due to the nature of gas/oil displacement
processes where mixture compositions that differ significantly from those that can be
constructed by linear combinations of the reservoir oil and the injected gas are formed as
a result of the interplay of flow and phase behavior (Orr and Jessen 2007).
In this work we investigate the potential benefits of including such additional
information from displacement dynamics in the selection of component groups to form
EOS models with a reduced number of components suitable for compositional reservoir
simulation. To do this, we use analytical solutions for one-dimensional (1D) gas/oil
displacement processes (F. M. Orr 2007) to define an optimal lumping/grouping strategy
based on the observed displacement characteristics. We then use the approach of

111

Leibivici et al. (1993) to calculate the properties of the selected groups (pseudo-
components).
The variation in equilibrium K-values that are observed along the compositional path
that defines a near-miscible gas injection process can differ significantly from the K-
values that are observed for the original reservoir fluid at the saturation pressure and also
from the K-values that are observed for two-phase mixtures of oil and injection gas (Orr
and Jessen 2007). The variations in K-values that are observed during a gas/oil
displacement process are dictated by the coupling between the phase behavior and flow
of equilibrated phases (Orr, 2007). Accordingly, we wish to investigate the benefit of
defining a grouping scheme that is based on the observed relative proximity of the K-
values during a displacement process. The key idea behind this approach is that
components that exhibit a similar K-value behavior (magnitude and variation) throughout
a displacement process must be good candidates for lumping.
To demonstrate this idea, we consider initially the reservoir fluid #6 presented by
Jaubert et al. (2002). In our analysis, we refer to this fluid system as Fluid A. This fluid
system was analyzed in detail by Jessen and Stenby (2007) that generated a 15
component fluid description by the approach of Pedersen et al. (1989) for use with the
SRK EOS (Soave 1972). The EOS model was subsequently tuned to all available
experimental observations from standard PVT experiments, swelling test and slim-tube
displacement experiments (MMP) to condition the detailed fluid description. The EOS
inputs for Fluid A are reported in Table 34. Table 34 also reports an injection gas
composition (Gas 1) that was used in measuring the slim-tube MMP as reported by

112

Jaubert et al. (2002).
Table 34: Detailed representation of reservoir fluid A
C
Tc
(K)
Pc
(bar)
ω
Mw
(g/mole)
Z
c
Shift BIC N
2
BIC CO
2
Feed Gas 1
N 2 126.20 34.04 0.040 28.01 0.2857 -0.00790 0 0.00015484 0.0001 0.0045
CO 2 304.27 73.88 0.227 43.99 0.2850 0.08330 0.00015 0 0.00775 0.0219
C 1 190.60 46.00 0.008 16.04 0.2850 0.02340 0.02 0.11995 0.36203 0.7665
C 2 305.40 48.83 0.098 30.06 0.2817 0.06050 0.06 0.1499 0.09736 0.1202
C 3 369.80 42.45 0.152 44.09 0.2779 0.08250 0.08 0.1499 0.06745 0.0526
iC 4 408.10 36.47 0.176 58.12 0.2742 0.08300 0.08 0.14988 0.01287 0.0074
nC 4 425.20 37.99 0.193 58.12 0.2742 0.09750 0.08 0.14988 0.03672 0.0149
iC 5 460.40 33.84 0.227 72.15 0.2707 0.10220 0.08 0.14988 0.01557 0.0033
nC 5 469.60 33.74 0.251 72.15 0.2702 0.12090 0.08 0.14988 0.02337 0.0041
C 6 507.40 29.68 0.296 86.17 0.2658 0.14670 0.08 0.14987 0.03290 0.0026
C 7-11 612.12 29.43 0.204 117.54 0.2596 0.14490 0.08 0.14985 0.15586 0.0020
C 12-16 642.55 23.35 0.452 183.10 0.2506 0.01740 0.08 0.14985 0.07826 0
C 17-23 688.51 19.43 0.751 268.11 0.2409 -0.09040 0.08 0.14985 0.05032 0
C 24-35 758.82 16.97 1.113 396.24 0.2303 -0.23770 0.08 0.14985 0.03651 0
C 36-80 898.89 15.41 1.119 653.78 0.2165 -0.48450 0.08 0.14985 0.02304 0

The experimental MMP for the displacement of Fluid A by Gas 1 is 309 bar,
whereas the predicted MMP is 300 bar; well within the accuracy of slim-tube
displacement experiments. The variation of K-values along the displacement direction
was generated by 1D semi-analytical calculations based on the method of characteristics
(Orr, 2007). Figure 70 and Figure 71 report the gas saturation profiles and the
components K-values as a function of the specific velocity for a near-miscible
displacement of Fluid A by Gas 1 at 383.15K and 288 bar respectively.

113

Figure 70: Gas saturation vs. specific velocity for a displacement of Fluid A by Gas 1 at T = 383.15 K,
P = 288 bar

Figure 71: K-value variations along a 1D displacement process: Fluid A + Gas 1, T = 383.15 K, P =
288 bar - Different values of K-values for the components along the displacement path

This displacement process is a combined condensing and vaporizing drive as can be

114

seen from the hour-glass shape of the K-value profiles at the downstream portion. From
this initial displacement calculation, we find that the K-values of nC
5
and iC
5
follow each
other closely along the entire composition path that connects the injection composition to
the initial oil composition. Accordingly, these components are initially grouped and the
properties of the lumped components are calculated by the approach of Leibovici et al.
(1993). The quality of the new (and reduced) fluid description can readily be checked
against experimental observations (PVT, swelling and MMP) in an automated manner
before repeating the grouping process. By continuing this approach, the number of
components can gradually be reduced in a sequential manner while ensuring that an
appropriate accuracy of the reduced EOS model is maintained. We note that the semi-
analytical calculations can be replaced by a 1D numerical simulator. However, the
efficiency of the semi-analytical calculations combined with well-defined segments (K-
value variations) along the displacement path makes the semi-analytical calculations our
preferred approach. The algorithm for our proposed sequential flow-based lumping
scheme is summarized below:
a) Generate a detailed and accurate fluid description.
b) Perform a 1D displacement calculation by semi-analytical calculations or by
numerical calculations.
c) Group two components (i, j) that minimize the integral

7-1
where L denotes the length along the 1D displacement path.
d) Evaluate the properties of the lumped component.

115

e) Check accuracy of the new EOS model relative to the available experimental
observations
f) Repeat from b) until the desired number of components in the lumped description
is reached while still maintaining the desired accuracy.
The above algorithm does not include a regression step. The regression step can
easily be included between stages e) and f) and be activated automatically if the error
between predictions and experimental data exceed a preset tolerance. However, in this
work, we have omitted this stage to investigate the predictive capabilities of the proposed
lumping scheme. Below, we test the proposed lumping algorithm for two reservoir fluids
and a total of 4 injection gas compositions.
The performance of the proposed lumping approach has been tested for two reservoir
fluids; fluid #6 and fluid #5 from the database of Jaubert et al. (2002), and thus we refer
in the following to these fluids as Fluid A and B.
Experimental observations from constant mass expansion experiments (CME),
swelling test experiments and slim-tube displacement experiments (MMP) are available
for both reservoir fluids. Additional differential liberation (DLE) data are available for
Fluid B. The detailed fluid descriptions were generated by the characterization approach
of Pedersen et al. (1989) followed by regression to all experimental data. Additional
details regarding characterization and regression strategy can be found in Jessen and
Stenby (2007). A total of 15 components are used in the detailed fluid descriptions. Table
34 reports the properties of the detailed fluid descriptions. We use the SRK EOS
throughout this work.

116

7.2.1 Fluid A
Initially, we apply the proposed lumping approach to Fluid A and target a reduced
model with 7 components. At 383.15K, the experimental MMP for Fluid A and
associated separator gas (Table 34) is 296 bar (see Table 35) and the MMP predicted by
the detailed fluid description is 300 bar (-3% error).
Table 35: Displacement pressure, temperature and MMP
Fluid A +CO
2
Fluid A + Gas 1
Temperature (K) 383.15 383.15
Oil saturation pressure (bar) 172.9
*

Displacement pressure (bar) 173 288
MMP (bar) – calculated (detailed) 185 300
MMP (bar) – calculated (lumped) 196 307
MMP (bar) - experimental n/a 309
*
*) Reported by Jaubert et al. 2002
We used a displacement pressure of 288 bar in the semi-analytical calculations to
create a near-miscible displacement process. The K-values from this displacement
calculation are then used as input to the lumping algorithm to arrive at a reduced model
with 7 components. The lumped fluid description is reported in Table 36.
Table 36: Fluid A + Gas 1 lumped to 7 components
C
Tc
(K)
Pc
(bar)
ω
Mw
(g/mole)
Z
c
Shift BIC N
2
BIC
CO
2

Oil A Gas 1
N
2
/C
1
190.5 45.99 0.0080 16.04 0.2850 0.02338 0 0.11991 0.36213 0.7710
CO
2
304.2 73.88 0.2278 43.99 0.2850 0.08330 0.11991 0 0.007749 0.0219
C
2
305.4 48.83 0.0980 30.07 0.2817 0.06050 0 0.1499 0.097359 0.1202
C
3-4
392.0 40.16 0.1676 50.03 0.2761 0.08803 0 0.14989 0.11704 0.0749
C
5-6
485.5 31.72 0.2669 78.57 0.2681 0.13014 0 0.1499 0.071839 0.0100
C
7-16
623.0 27.04 0.2920 139.45 0.2556 0.08894 0 0.14987 0.23412 0.0020
C
17+
764.0 17.64 0.9525 391.56 0.2288 -0.27791 0 0.14983 0.10987 0

117

The MMP predicted by the lumped fluid description is 307 bar (-1% error), as slight
improvement over the full description. Both predictions are, however, within the
accuracy of experimental MMP data obtained from slim-tube experiments (+/- 5%).
Figure 72 compares the experimental observations of a CME experiment with the original
oil along with CME experiments for mixtures of the original oil and the injected gas
relative to the predictions of the detailed and the lumped fluid description. The accuracy
of the lumped fluid description is found to be in good agreement with the experimental
CME observations.

Figure 72: Comparison of CME data for Fluid A and mixtures of Fluid A and Gas 1 with predictions
based on a detailed (full) and a lumped fluid description. T = 383.15K

Xgas = 0
Xgas = 0.375
Xgas = 0.286
Xgas = 0.167
Xgas = 0.444
Xgas = 0.5

118

Figure 73 compares the available swelling test data in terms of saturation pressures
and saturated liquid densities with the detailed and lumped fluid descriptions. Again, we
see a good agreement between the lumped fluid description and the experimental
observations with a moderate deviation in the saturation pressure at the maximum solvent
fraction.

Figure 73: Comparison of swelling test data (Fluid A + Gas 1) with predictions based on a detailed
(full) and a lumped fluid description. T = 383.15K

Figure 74 reports the gas saturation profiles from semi-analytical calculations using
the detailed and the lumped fluid description. The two fluid descriptions are in excellent
agreement with respect to the specific velocity of the leading edge of the displacement.
In addition to the MMP for the separator gas, we generated an artificial MMP data point
(185 bar at 383.15K) for the injection of CO
2
based on the detailed fluid descriptions and
predicted the MMP based on the lumped fluid description to be 196 bar at 383.15K. The

119

observed difference in the predicted MMP (6% error) is very reasonable considering that
no CO
2
/oil data are available for conditioning the detailed EOS model.

Figure 74: Comparison of gas saturation vs. specific velocity for a displacement of Fluid A by Gas 1
at T = 383.15 K, P = 288 bar: lumped (Nc = 7) vs. Full (Nc = 15) fluid description

Figure 75: Comparison of gas saturation vs. specific velocity for a displacement of Fluid A by pure
CO
2
at T = 383.15 K and P = 173 bar: lumped (Nc = 7) vs. Full (Nc = 15) fluid description

120

Figure 75 compares the predicted displacement behavior of a near-miscible CO
2
flood
(173 bar and 383.15K) and shows that the lumped and the detailed fluid descriptions are
in good agreement. Table 35 shows a summary of displacement pressures, saturation
pressures and miscibility pressures for Fluid A and associated gases.

7.2.2 Fluid B
Next, we consider Fluid B (see Table 37) which is slightly heavier oil than Fluid A.
Again we target a lumped fluid description with 7 components.
Table 37: Detailed representation of reservoir Fluid B
C
Tc
(K)
Pc
(bar)
ω
Mw
(g/mole)
Z
c
Shift BIC N
2
BIC CO
2
Oil B
Gas
2
N 2 126.20 34.04 0.0400 28.01 0.2857 -0.00790 0 0.0187 0.00450 0
CO 2 312.88 75.84 0.2094 42.45 0.2850 0.07760 0.0187 0 0.02453 0
C 1 190.60 46.00 0.0080 16.04 0.2850 0.02340 0.02 0.1137 0.26576 0.880
C 2 305.40 48.83 0.0980 30.06 0.2817 0.06050 0.06 0.1375 0.07894 0.070
C 3 369.80 42.45 0.1520 44.09 0.2779 0.08250 0.08 0.1375 0.06730 0.030
iC 4 408.10 36.47 0.1760 58.12 0.2742 0.08300 0.08 0.1359 0.01485 0.005
nC 4 425.20 37.99 0.1930 58.12 0.2742 0.09750 0.08 0.1359 0.03899 0.005
iC 5 460.40 33.84 0.2270 72.15 0.2707 0.10220 0.08 0.1359 0.01937 0.005
nC 5 469.60 33.74 0.2510 72.15 0.2702 0.12090 0.08 0.1359 0.02505 0.005
C 6 507.40 29.68 0.2960 86.17 0.2658 0.14670 0.08 0.1343 0.03351 0
C 7-12 639.28 28.85 0.2539 122.56 0.2589 0.14050 0.08 0.1312 0.18448 0
C 13-18 683.17 22.23 0.6002 207.39 0.2481 -0.01180 0.08 0.1312 0.10498 0
C 19-26 738.30 18.60 0.9882 307.10 0.2378 -0.13500 0.08 0.1312 0.06079 0
C 27-39 815.53 16.71 1.3577 443.82 0.2281 -0.28980 0.08 0.1312 0.04822 0
C 40-80 962.74 15.61 1.1778 710.03 0.2157 -0.54310 0.08 0.1312 0.02871 0

121

For this fluid, the experimental MMP for injection of the associated separator gas as
reported in Table 38 is 366 bar at 394.25K. The detailed fluid description predicts an
MMP of 364 bar (1% error). We set the displacement pressure used in the semi-analytical
calculations to 352 bar, again, to generate a near-miscible displacement process.
The MMP predicted by the lumped fluid description is 396 bar (7.5% error), a less
accurate prediction than what we observed for Fluid A; however, still within a reasonable
agreement of the experimental MMP.
Table 38: Displacement pressure, temperature and MMP
Fluid B +CO
2
Fluid B +Gas 2
Temperature (K) 394.25 394.25
Oil saturation pressure (bar) 145.8
*

Displacement pressure (bar) 179 352
MMP (bar) – calculated (detailed) 195 364
MMP (bar) – calculated (lumped) 210 396
MMP (bar) - experimental n/a 366
*
*) Reported by Jaubert et al. 2002
The number of components was then reduced from 15 to 7 in the proposed sequential
manner, resulting in the lumped fluid description reported in Table 39.
Table 39: Fluid B + Gas 2 lumped to 7 components
C Tc
(K)
Pc
(bar)
ω
Mw
(g/mole)
Z
c
Shift BIC N
2
BIC
CO
2

Fluid B
Gas
2
N
2
/C
1
189.38 45.78 0.0084 16.24 0.2850 0.02250 0 0.11248 0.27026 0.88
CO
2
312.88 75.84 0.2094 42.45 0.2850 0.07760 0.11248 0 0.02453 0
C
2
305.40 48.83 0.0980 30.06 0.2817 0.06050 0.00044 0.13751 0.07894 0.07
C
3-5
413.86 38.04 0.1884 56.18 0.2740 0.09662 0.00063 0.13645 0.16556 0.05
C
6
507.40 29.68 0.2959 86.17 0.2658 0.14670 0.00062 0.13437 0.03351 0
C
7-18
657.18 26.01 0.3869 153.33 0.2536 0.06579 0.00050 0.13123 0.28946 0
C
19+
817.53 17.22 1.1546 438.97 0.2269 -0.32741 0.00054 0.13128 0.13774 0

Figure 76 compares the experimental CME behavior of the original oil with the

122

behavior predicted by the lumped and detailed fluid descriptions. In addition, Figure 76
also shows a comparison of the experimental CME behavior during a swelling test with
the behavior predicted by the two EOS models. For all the available CME data, the two
fluid descriptions are found to be in excellent agreement.

Figure 76: Comparison of CME data for Fluid B and mixtures of Fluid B and Gas 2 with predictions
based on a detailed (full) and a lumped fluid description. T = 394.25K

Figure 77 reports the observed liquid densities from a DLE and compares the
experimental data with predictions from the two fluid descriptions. Moderate deviations
are observed between the experimental values and the predicted values. However, the
predicted values are in good agreement.
Additional experimental swelling test data are shown in Figure 78 and compared
favorably with the predictions of the lumped and detailed EOS models. As it is shown for
the different fractions of oil and gas, the saturation pressure and saturated liquid densities
Xgas = 0
Xgas = 0.394
Xgas = 0.333
Xgas = 0.231
Xgas = 0.429
Xgas = 0.460

123

were calculated and compared with experimental data. As the result very good match
observed for the lumped system compared with the detailed model and experiments.

Figure 77: Comparison of differential liberation experiment data with predictions based on a lumped
and a detailed (full) fluid description. Fluid B at T = 394.25K

Figure 78: Comparison of swelling test data (Fluid B + Gas 2) with predictions based on a full and a
lumped description. T = 394.25K

124

Figure 79 shows a comparison of the gas saturation profiles from semi-analytical
displacement calculations based on the two EOS models at 352 bar. From Figure 79, we
see that the gas saturation profiles predicted by two EOS models differ slightly at the
leading edge of the displacement. This should be expected given the difference in the
predicted MMP (7.5% error for the lumped model) and suggests that we are approaching
the limit in terms of accuracy in lumping without including the additional regression step
as discussed above. As for Fluid A, the MMP based on a displacement of Fluid B by pure
CO
2
was generated from the detailed fluid description and compared to the MMP
predicted by the lumped fluid description. The calculated values of the MMP were 195
bar and 210 bar respectively. The observed difference (7%) is again reasonable
considering that the detailed model is developed without any CO
2
/oil data.

Figure 79: Comparison of gas saturation vs. specific velocity for the displacement of Fluid B by Gas 2
at T = 394.25K and P = 352 bar as predicted by a detailed fluid description and a lumped fluid
description

125

Figure 80 compares the gas saturation profiles predicted by the two fluid descriptions
for a near-miscible CO
2
flood at 179 bar and 394.25K. The two displacement calculations
are seen to be in better agreement than for the separator gas (Figure 79).

Figure 80: Comparison of gas saturation vs. specific velocity for the displacement of Fluid B by CO
2

at T = 394.25K and P = 179 bar as predicted by a detailed and a lumped fluid description

7.2.3 3D Compositional Simulation of CO
2
Floods
In order to test the performance of the proposed lumping approach in more realistic
settings, a synthetic anticline reservoir model derived from the PUNQ3 comparative
study was prepared with four production wells and one injection well arranged in a top-
down injection scheme. Two scenarios were constructed based on the two reservoir
fluids: a) Fluid A displaced by CO
2
at 383.14K and b) Fluid B displaced by CO
2
at

126

394.25K. In both cases, the injection well and the production wells were operated at
constant bottom-hole pressure.
For each of the two scenarios, we simulated the injection of CO
2
for 4000 days based
on the detailed and the lumped fluid descriptions. The results in terms of cumulative oil
production and producing gas/oil ratio are reported in Figure 82 and Figure 83 for Fluid
A and B respectively. An additional comparison of the cumulative production of CO
2
for
the two scenarios is reported in Figure 84.

Table 40: Data for 3D calculation examples
Parameters Fluid A + CO
2
Fluid B + CO
2
Producing well pressure (bar) 123 134
Injector well pressure (bar) 223 234
Initial reservoir pressure (bar) 173 184
Reservoir temperature (K) 383.15 394.25
Injection gas CO
2
CO
2

Simulation time (days) 4000 4000
Corey-type relative permeability:
(Sor = 0.10, Sgc = 0.05, ng = 2, no = 2)

For both scenarios, we see that the oil production, the GOR and the cumulative CO
2

production are in good agreement between the lumped and the detailed fluid descriptions.
These results suggest that the proposed lumping scheme provides a reasonably good
accuracy for large scale simulations even if moderate differences are observed in the 1D
semi-analytical and dispersion-free displacement calculations.

127

Figure 81: Schematic of the synthetic reservoir model (derived from PUNQ3) showing the
permeability variability and the configuration of injection and production wells

Figure 82: Comparison of the oil production and the producing GOR as predicted by the lumped and
the original fluid model. Fluid A displaced by CO
2
at 383.15K with well conditions given in Table 40

128

Figure 83: Comparison of the oil production and the producing GOR as predicted by the lumped and
the original fluid model. Fluid B displaced by CO
2
at 394.25K with well conditions given in Table 40

Figure 84: Comparison of cumulative CO
2
production as predicted by the full and lumped
descriptions of fluids A and B during the production reported in Figure 82 and Figure 83

129

Table 41 shows the computation time of simulation, comparing the simulation time
for the 7 component model with the one for full model and as the result, the lumped
model simulation is 3 times faster than full model simulation for both fluids A & B.
Table 41 : Comparison of simulation time between lumped model and full model
Fluid
Simulation Time Elapsed (second)
Full Model Lumped Model
A 444 154
B 376 131

7.3 Comparison to the Method of Newley and Merrill
In this section, the accuracy of the lumped fluid description derived from the
proposed flow-based lumping approach is compared with fluid description obtained from
the lumping approach of Newley and Merrill. The approach of Newley and Merrill
(1991) aims at selecting a grouping scheme that minimizes the difference between
equilibrium K-values of the detailed fluid description and the resulting set of apparent K-
values obtained from the lumped fluid description.
7-2
It is clear from the above equation that the selected K-values used in obtaining the
optimum lumping scheme is of great importance. In the original work, they used
equilibrium K-values from a saturation point of the reservoir fluid. For simulation of gas
injection processes; however, it is imperative to include information from mixtures of oil
and injected gas into the selection of pseudo-components. We discuss this in more details
below.

130

The approach of Newley and Merril was applied for Fluid A using components K-
values obtained from mixture of the oil and injected gas that form along the displacement
path of a 1D near-miscible displacement as shown in Figure 71. Four different lumping
schemes were obtained depending on the sections of the displacement calculation that
were used to define the K-values. In addition, we generated a lumped fluid description
following the approach of Egwuenu et al. (2008) by using K-values that are observed
from the simulation of a swelling test. The obtained lumping schemes are summarized in
Table 42.

Table 42: Comparison on lumped system using Newley & Merrill’s approach resulted with different
K-values along displacement path as shown on Figure 71 for fluid A + Gas 1
Newley and Merrill’s Method, K-values from Flow Based
section A section B section C section D
swelling
test
Proposed
approach
N
2
C
1
N
2
C
1
N
2
C
1
N
2
C
1
N
2
C
1
N
2
C
1

CO
2
C
2-3
CO
2
C
2
CO
2
C
2
CO
2
C
2
CO
2
C
2
C
3
CO
2

C
4-6
C
3
C
3-4
C
3
C
4-6
C
2

C
7-16
iC
4
nC
4
iC
5
nC
5
C
6
iC
4
nC
4
C
7-11
C
12-16
C
3
iC
4
nC
4

C
17-23
iC
5
nC
5
C
6
C
7-11
C
12-16
C
17-23
iC
5
nC
5
C
6
C
17-23
iC
5
nC
5
C
6

C
24-35
C
7-11
C
12-16
C
17-23
C
24-35
C
7-11
C
12-16
C
24-35
C
7-11
C
12-16

C
36-80
C
24-35
C
36-80
C
36-80
C
17-23
C
24-35
C
36-80
C
36-80
C
17-23
C
24-35
C
36-80

From these results, it is clear that the approach of Newley and Merrill does not
provide a unique answer to the question of how to lump a reservoir fluid for simulation of
gas injection processes. Depending on our selection of K-values, we obtain 4 different
lumping schemes and additional work is required to identify the best possible lumping
scheme.
To focus on the injection of CO
2
for EOR and storage purposes, we have generated
the equivalent lumping schemes for Fluid A displaced by pure CO
2
. Table 43 reports the
lumping scheme for this oil/gas system. We introduce a biased lumping scheme for the

131

approach of Newley and Merrill to keep CO
2
as a single component in the reduced fluid
description.
Table 43: Comparison on lumped systems for Fluid A + CO
2
using Newley & Merrill’s approach
with K-values from swelling tests
Newley Newley Biased Flow Based
N
2
N
2
C
1
C
2
N
2
/C
1

CO
2
C
1
C
2
CO
2
CO
2

C
3-6
C
3-6
C
2

C
7-16
C
7-16
C
3-4

C
17-23
C
17-23
C
5-6

C
24-35
C
24-35
C
7-16

C
36-80
C
36-80
C
17+

Next, we compare the predictions of the lumped fluid descriptions to that of the
detailed fluid description for the 3D reservoir model discussed previously. We compare
the performance in terms of cumulative oil production, producing gas-oil ratio and in
terms of the total amounts of CO
2
produced.
Figure 85 and Figure 86 present the results of the 3D numerical simulations and we
observe that the flow-based lumping scheme is more accurate in predicting the gas-oil
ratio and the amount of total produced oil. In addition, it is observed that the lumped fluid
description derived from approach of Newley and Merrill tends to present the heavy
fractions of the original fluid as single pseudo-component. This is, in part, due to the
significant differences in K-values between the heavy fractions and the lighter fractions
of the crude oil; any attempt to group the heavy ends will increase the value of the
objective function.

132

Figure 85: Comparison of the oil production and the GOR as predicted by the flow based lumped
system and Newley & Merrill’s Lumped system with the original fluid model (Fluid A + CO
2
)

Figure 86: Comparison of amount of CO
2
produced comparing flow based lumped system and
Newley & Merrill’s Lumped system and Biased version of Newley & Merrill’s with the original fluid
model (Fluid A + CO
2
)
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
0.0E+00
2.0E+06
4.0E+06
6.0E+06
8.0E+06
1.0E+07
1.2E+07
1.4E+07
1.6E+07
0 1000 2000 3000 4000 5000
GOR (sm
3
/sm
3
)
Total Oil Production ( sm
3
)
Days of Injection
Flow Based Lumped Original components
Newley Lumped Biased Newley Lumped
0.00E+00
5.00E+08
1.00E+09
1.50E+09
2.00E+09
2.50E+09
3.00E+09
0 1000 2000 3000 4000
Total Amount of CO2 Produced
(Kg Mole)
Days of Injection
Original Model
Flow Based Lumped
Newley Lumped
Biased Newley Lumped
Fluid A

133

7.4 A Flow-Based Variant of Newley & Merrill’s Approach
As discussed above, the approach of Newley and Merrill (1991) determines a
grouping scheme for a detailed fluid description to define a lumped fluid description
based on the equilibrium K-values and phase compositions of the detailed description.
The main objective of this approach is to minimize the difference between the apparent
K-values of the lumped components and the K-values of the detailed components. The
grouping scheme (and lumped components) generated by this approach is highly
dependent on the K-values are used in the process. In the original work of Newley and
Merrill (1991), equilibrium K-values from a saturation point of the original reservoir
fluid were used to define the lumping scheme. The approach was subsequently extended
to K-values from mixtures of oil and solvent for gas injection processes by Egwuenu et
al. (2008). However, as K-values depend both on composition and pressure (at a constant
temperature), there is no clear way to select an optimal mixture of oil and gas unless the
approach of Newley and Merrill provides for a unique solution. We demonstrate
previously that this is not the case. In addition, the composition path of oil/gas
displacement processes are well known to form mixtures that differs significantly from
any linear combination of initial oil and injection gas compositions.
In order to overcome the ambiguity in selecting the right mixture of initial oil and
injection gas for the approach of Newley and Merrill, we investigate the following
modified version of Newley and Merrill in which the effect of K-values variations along
a displacement process is included in a new objective function. The proposed objective

134

function can be written as

7-3

where is the index for detailed component, is the index for the lumped components,
is the index for the number of different K-values observed in a displacement process
(sample points in numerical solutions or segments in analytical solutions), is the K-
value for the detailed components, is an apparent K-value of the pseudo-component.
The apparent K-value for a given pseudo-component is calculated from
7-4
where and are liquid and vapor phase compositions of the detailed fluid description.
In this work, we utilize an exhaustive search to locate the minimum of the objective
function. This is feasible due to the low cost of evaluating Eq. 7-3 combined with the
manageable number N of lumping schemes that can be used to lump Q components into
R pseudo-components:

7-5
In the following section, we apply the above methods and compare the accuracy of
the flow-based lumping schemes in terms of the accuracy in predicting swelling test
observations and slim-tube MMP experiments. The two proposed flow-based methods
are compared with the original approach of Newley and Merrill.
We start by demonstrating the non-unique behavior of the traditional approach of

135

Newley and Merrill using K-values from mixtures of reservoir fluid and injection gas in
more detail. Tables 44 and 45 report the lumping schemes that are obtained from
minimizing Eq. 7-3 with K-values from mixtures of reservoir fluid and CO
2
or separator
gas at 100bar and 168 bar respectively. To apply Eq. 3 in this setting, we set l equal to
one to recover the original objective function of Newley and Merrill.
Table 44 : Lumping schemes from applying the approach of Newley & Merrill using K-values from
four different mixtures of Fluid A and CO
2
at 100 bar
20 % CO
2
40% CO
2
60 % CO
2
80 % CO
2

CO
2
CO
2

N
2
C
1
C
2
C
3
N
2
C
1
C
2

iC
4
nC
4
iC
5
nC
5
C
6
C
3
iC
4
nC
4
iC
5
nC
5
C
6

C
7-11
C
12-16
C
7-11
C
12-16

C
17-23
C
17-23

C
24-35
C
24-35

C
36-80
C
36-80

Table 45: Lumping schemes from applying the approach of Newley & Merrill using K-values from
four different mixture of Fluid A and separator Gas at 168 bar
20% Gas 40% Gas 60 % Gas 80 % Gas
N
2
C
1
CO
2
N
2
C
1
C
2
CO
2

C
2
C
3
C
3
iC
4
nC
4

iC
4
nC
4
iC
5
nC
5
C
6
iC
5
nC
5
C
6

C
7-11
C
12-16
C
7-11
C
12-16

C
17-23
C
17-23

C
24-35
C
24-35

C
36-80
C
36-80

We observe that two different lumping schemes are obtained for each combination of
reservoir fluid and injection gas (CO
2
or separator gas): One lumping scheme is obtained
for mixture compositions with 20% and 40% gas and another scheme is obtained for
mixture compositions with 60% or 80% gas. This ambiguity complicates the choice of

136

what lumping scheme to select and additional work is required to identify the better
scheme. We note that when pure CO
2
is used as injection gas, we bias the minimization
of the objective function by keeping CO
2
as a separate component.
Next, we compare the performance of the three lumping strategies:
1. Newley and Merrill’s approach with K-Values from oil/gas mixtures.
2. The flow-based lumping scheme by Rastegar and Jessen (2009) as discussed.
3. A flow-based variant of Newley and Merrill’s approach as proposed above
We compare the lumping schemes in terms of a) prediction of relevant PVT data and b)
the accuracy of the delumped production composition from 3D displacement calculations
relative to that of the detailed calculations.
7.4.1 MCM Displacement of Fluid A by CO
2

For this displacement process, the detailed fluid description was lumped into 7
components according to the three different lumping schemes. In this work, we use semi-
analytical solutions to 1D near-miscible displacement to generate input to the flow-based
lumping schemes. However, numerical calculations can also be used. The resulting
lumping schemes from the different approaches are reported in Table 46.
One of the two schemes generated by the approach of Newley and Merrill with K-
values from different solvent/oil mixtures is identical to the scheme generated by the
proposed flow-based version of Newley and Merrill’s approach. We refer to these
schemes as the Newley scheme. The second lumping scheme that is obtained from the
approach of Newley and Merrill is named the Alternate Newley scheme in this study. It is

137

clear from Table 46 that the major difference in the lumping scheme of Newley and
Merrill compared to the flow-based approach is the grouping of the heavy ends. In the
approach of Newley and Merrill, most of the heavy components are kept as individual
components whereas in the flow-based approach the light components are kept as
individual components. We keep CO
2
as a separate component to maintain a good
resolution of the injected gas and hence bias the original approach of Newley and Merrill.
In an initial comparison of the lumped fluid descriptions with the detailed fluid
description we report the predicted saturation pressures and the saturated liquid densities
from a swelling test relative to available experimental observations in Figure 87. The
flow-based approach is found to be in better agreement with the experimental
observations (and the detailed model). In contrast, the Newley scheme is in error by
approximately 10 % in predicting saturation pressures and the alternate Newley scheme is
in error of more than 20 % in predicting the saturation pressures.

Table 46: Lumping schemes generated from different lumping methods - Fluid A & CO2
Newley & Merrill
Alternate
Newley & Merrill
Original
Flow-Based
Flow-Based
Newley & Merrill
CO
2
CO
2
N
2
C
1
CO
2

N
2
C
1
C
2
N
2
C
1
C
2
C
3
CO
2
N
2
C
1
C
2

C
3
iC
4
nC
4
iC
5
nC
5
C
6
iC
4
nC
4
iC
5
nC
5
C
6
C
2
C
3
iC
4
nC
4
iC
5
nC
5
C
6

C
7-11
C
12-16
C
7-11
C
12-16
C
3
iC
4
nC
4
C
7-11
C
12-16

C
17-23
C
17-23
iC
5
nC
5
C
6
C
17-23

C
24-35
C
24-35
C
7-11
C
12-16
C
24-35

C
36-80
C
36-80
C
17-23
C
24-35
C
36-80
C
36-80

138

Figure 87: Comparison of swelling test data with predictions based on the detailed (full) and the
different lumped fluid descriptions at T = 383.15K for Fluid A and CO
2

In addition to the swelling test data, the bubble point pressure of the oil and the
minimum miscibility pressure of fluid A displaced by CO
2
were calculated for the four
lumping scheme. The results of the lumping schemes are compared to the result of the
detailed fluid description and experimental observations presented in Table 47.

Table 47: Comparison of MMP & bubble point pressure (Psat) from lumped schemes and detailed
model for fluid A & CO2
Lumping Method MMP
[bar]
P
sat
[bar]
Newley 205 154
Alternate Newley 230 143
Flow Based Newley 205 154
Original Flow Based 196 167
Detailed Stream 185 168
Experiment -- 173

Solvent fraction

139

The MMP predicted by the flow-based approach is in better agreement with the full
model. A similar behavior is seen for predictions of the saturation pressure of the
reservoir fluids. In contrast, the alternate scheme of Newley and Merrill is in significant
error for both the MMP and the saturation pressure relative to the other schemes.
We note that the performance of the lumping fluid descriptions can be improved by
additional regression. However, we have refrained from additional regression to focus on
the default predictive capabilities of a given lumping scheme.
7.4.2 MCM Displacement of Fluid A by Separator Gas
Next, we apply a similar workflow for an EOR process where fluid A is displaced by
the separator gas 1 as defined in Table 34. The detailed fluid description was lumped into
7 pseudo-components by the three approaches, resulting in 4 different lumped fluids (2
Newley and Merrill schemes and 2 flow-based schemes). The lumping schemes
generated by the different approaches are reported in Table 48. As we observed for the
previous example with CO
2
as an injection gas, the major difference in the lumping
schemes of Newley and Merrill and the original flow based approach is in the
representation of light and heavy ends where the schemes of Newley and Merrill provides
a higher resolution for the heavy ends at the cost of lower resolution in the light ends.
One of the schemes from the approach of Newley and Merrill is again identical to the
proposed flow-based Newley approach. Consequently, we are looking at 3 different
lumping schemes in following sections.

140

Table 48: Lumping schemes from different lumping methods for fluid A & Separator Gas
Newley &
Merrill
Alternate
Newley &
Merrill
Flow-Based
Newley &
Merrill
Original
Flow –Based
Scheme
N
2
C
1
CO
2
N
2
C
1
C
2
CO
2
N
2
C
1
CO
2
N
2
C
1

C
2
C
3
C
3
iC
4
nC
4
C
2
C
3
CO
2

iC
4
nC
4
iC
5
nC
5
C
6
iC
5
nC
5
C
6
iC
4
nC
4
iC
5
nC
5
C
6
C
2

C
7-11
C
12-16
C
7-11
C
12-16
C
7-11
C
12-16
C
3
iC
4
nC
4

C
17-23
C
17-23
C
17-23
iC
5
nC
5
C
6

C
24-35
C
24-35
C
24-35
C
7-11
C
12-16

C
36-80
C
36-80
C
36-80
C
17-23
C
24-35
C
36-80

Figure 88 compares the prediction of a swelling test based on the different lumping
schemes with the experimental observations and the prediction from the detailed fluid
description. In this example, all lumping schemes except for the alternate Newley scheme
predict the saturation pressures from the swelling test and the saturated liquid densities
with a reasonable accuracy.

Figure 88: Comparison of swelling test data with predictions based on the detailed and lumped fluid
descriptions at T = 383.15K: Fluid A and separator gas.

141

Table 49 reports the calculated MMP for each of the tested lumping schemes in
addition to the experimental observations and the predictions from the detailed fluid
description. As observed for the swelling test, all lumping schemes except the alternate
Newley and Merrill scheme predict the MMP with reasonable accuracy. The original
flow based approach provides a slightly better accuracy in predicting the MMP.

Table 49: Comparison of calculated MMP & bubble point pressures with experimental observations
for Fluid A and Separator Gas
Lumping approach MMP [bar] Saturation Pressure [bar]
Newley / Flow-based
Newley
291 165
Original Flow-based 307 167
Alternate Newley 268 157
Detailed fluid 300 168
Experimental observation 309 173

Based on the presented examples and analysis, we conclude that the flow-based
lumping scheme performs better than the other lumping schemes for the investigated
reservoir fluids.
7.5 Delumping for Integrated Compositional Simulation
In the previous section, various strategies for generating a lumped fluid description
were investigated and compared in terms of PVT data and 3D displacement calculations.
In this section, we investigate the accuracy of the presented lumping strategies in terms of
the accuracy in delumping (deconvoluting) production streams back into a detailed fluid
description.

142

In simulations of downstream processes, more detailed fluid descriptions are required
to design and optimize separation processes. To connect up- and down-stream processes,
delumping approaches have been proposed that de-convolute a production stream from a
reservoir simulator into a more detailed fluid description. We propose that the accuracy
of delumping stream is closely tied to the lumping approach that is used to generate
equation of state input for the reservoir simulator. To this end, we have introduced a
flow-based lumping scheme that includes information from the dynamics of a given
displacement process into the grouping of detailed components. In this section, we
present and compare the results of delumping the production stream from various gas
injection processes. We investigate the benefit of applying the flow-based lumping
scheme in the selection of pseudo-components for compositional reservoir simulation and
find a significant improvement in terms of accuracy of the composition of the delumped
well streams. We start by a brief review of previous work on delumping.
Inverse lumping (Delumping) for the purpose of retrieving the original components
from the lumped components with reasonable accuracy was first investigated by Schlijper
et al. (1988). In their approach, they used the K-value of the lumped components as an
approximate value for the K-values of the original components. Split parameters were
then defined to link the lumped components to the original components based on the feed
composition. The split parameters can be estimated from a range of feed compositions
that reflects the changes that can take place during a displacement process. Based on the
K-values of the lumped components and the split parameters, the mole fraction and phase
fraction of each detailed component can be determined.

143

Danesh et al. (1992) applied a modified version of Wilson’s equation for describing
K-value variations. At constant pressure and temperature, the logarithmic form of K-
value of a component has a linear correlation with the acentric factor and reduced
temperature of that component as:
7-6
They determined and with least square method based on the lumped components
mixture data and then applied the equation to calculate the K-values of the original
components to retrieve the detailed compositions of the relevant phases using a material
balance.
Leibovici et al. (1996) developed a thermodynamically consistent delumping
procedure to calculate phase equilibrium compositions at specified pressure and
temperature. Their method was based on the linear relation of logarithm of K-value with
equation of state parameters when all binary interaction coefficients are equal to zero. For
the Redlich-Kwong family of EOS this relation can be expressed as follow:

7-7
where are constants and and are equation of state parameters. When all binary
interaction coefficients are equal to zero, the constants of this equation can be calculated
analytically. When non-zero interactions are included, the equation is an approximation
and the constants must be determined by regression. In their algorithm, referred to as
LSK algorithm, the delumping procedure starts by flashing the lumped system at relevant
conditions to evaluate the K-values for the lumped components. ’s are then calculated
using either the analytical formula in the case of no interaction coefficients or by a least

144

square fit in the case of non-zero binary interaction coefficients. Based on these
constants, the K-values of the original components can be determined and used in the
Rachford-Rice equation to calculate phase fractions and phase mole fractions.
Stenby et al. (1996) successfully applied the LSK procedure as a post processing tool
for compositional reservoir simulation and they demonstrated that a detailed production
stream could be obtained for a constant volume depletion (CVD) process.
Faissat and Duzan (1996) proposed a method to minimize the loss of compositional
information that they observed in between delumped stream and detailed stream when
delumping is performed on the basis of initial fractions of the components in each
pseudo-components. In their approach, a single cell simulator was used for depletion
processes (dual cell simulator for gas injection scenarios) with two set of simulations of
lumped and detailed fluid description in which the bottom-hole gas and oil production
rates and reservoir average pressure at each time step came from the full reservoir
simulator. The observed proportions of the components from the single and dual cell
simulators were then used to delump the output stream of a compositional reservoir
simulator and reduced the amount of compositional discrepancies observed in between
delumped and detailed stream.
Leibovici et al. (1999) applied the LSK algorithm to compositional reservoir
simulation. They addressed the problem of tracking the overall composition of the
detailed fluid, as needed in the delumping procedure) during compositional simulation.
They proposed to use the LSK algorithm in each time step to determine the detailed
phase compositions in each grid block. Using the transport equations, the overall

145

composition of the detailed fluid is computed based on the phase velocities of the lumped
fluid. Accordingly, the approach treats the detailed components within a given lumped
component as tracers. This approach was subsequently applied and successfully tested to
the reservoir simulation of a real field.
In addition to delumping studies on compositional simulation, there has been some
efforts on delumping the result of black oil simulation into detailed components. In this
technique, tables of composition versus grid cell pressure were used to find the delumped
stream (Weisenborn and Schulte 2000). Ghorayeb and Holmes (2005) delumping method
was based on tables of liquid and vapor compositions versus saturation pressure
generated from a depletion process.
Nichita and Leibovici (2006) modified the LSK algorithm by introducing an
analytical solution when an equation of state with non-zero binary interaction coefficients
is used. They applied the reduction method and reformulated the EOS parameters to
reduce the number of independent variables. Resulting their work, they formulate the
fugacity coefficients in terms of a new set of variables and parameters (reduction
parameters). At a given temperature and pressure they then applied the LSK algorithm
with the new formulation to find the detailed delumped stream. An excellent agreement
was reported between the properties of delumped stream and original detailed fluid.
Vignati et al. (2008) applied the LSK algorithm to an Integrated Asset Management
(IAM) problem that couples the reservoir model with a detailed surface model. Their
proposed workflow for coupling surface and reservoir was tested successfully on two
field cases where gas is injected into a volatile oil and a condensate reservoir.

146

In the next sections, using a commercial reservoir simulator (E300), the delumped
composition of the produced streams are compared to detailed displacement calculations
for three different lumping schemes and a range of different reservoir fluids. We use the
tracer tracking option of E300 (Numerical Simulator) to convert the lumped result of the
numerical simulator into the full fluid description for fluids A combined with injection of
CO
2
and separator gases. In each example, the delumped stream is compared to the
original model output (detailed fluid) for each component and the level of error for each
lumping method is depicted versus the time of production for each of the 15 components.
A 3D reservoir model used in our comparison was derived from the PUNQ3 model
(single anticline) with top-down injection of gas in one well and production from 4 wells
arranged in an approximate 5-spot pattern [see e.g. Rastegar and Jessen, (2009)]. Table
50 summarizes the parameters of the 3D displacement calculations.

Table 50: Data for 3D calculation examples
Parameters Fluid A & CO
2
Fluid A & Separator Gas

Producing well pressures (bar) 123 238
Injection well pressure (bar) 223 338
Initial reservoir pressure (bar) 173 288
Reservoir temperature (K) 383.15 383.15
Injection gas CO
2
Separator gas
Simulation time (days) 4000 4000
Corey-type relative permeability:
S
or
= 0.10, S
gc
= 0.05, n
g
= 2, n
o
= 2

147

In each example, the delumped stream is compared to the detailed model output and
the level of error for each lumping approach is reported versus time for each of the
original 15 components. We note that after lumping the detailed components, the values
of the critical compressibility factor of the heavy ends were adjusted to ensure that the
lumped models match the viscosity of the original detailed model. No additional tuning
was performed.
The result of this comparison is shown for different combinations of the fluids and
injection gases:
7.5.1 Fluid A & CO
2

We investigate the accuracy of the delumped fluid streams from a 3D displacement
calculation relative to the detailed simulation. Figure 89 compares the error of the
delumped production stream obtained from numerical calculations with the lumped fluid
descriptions relative to a simulation with the detailed fluid description. The original flow-
based method is found to provide a better accuracy in predicting the concentrations of the
lighter components (up to C
6
) as would be expected given the lumping scheme (see Table
46). In addition, a reasonable accuracy is observed for the original flow based approach
in representing the lightest and heaviest of the pseudo-components that describe the C
7+

fraction.

148

Figure 89: Errors in the concentration of the delumped stream for each component relative to a
calculation with the detailed fluid description: Fluid A displaced by pure CO
2

In terms of errors in the cumulative production (volumes) as shown in Figure 90, all
schemes are in reasonable agreement with the detailed model prediction with maximum
deviation of 3% for the alternate Newley scheme. The original flow based approach
performs slightly better compared to the other schemes. Figure 91 reports the predicted
gas-oil ratio for the various fluid descriptions and we observe little difference between
the different approaches.
For CO
2
injection processes, it is important to model the amount of CO
2
that is
produced accurately to allow for accurate design of separation and recycle facilities.
Figure 92, compares the errors in cumulative production of CO
2
as predicted by the
different lumping schemes and we observe that the original flow-based lumping scheme
is in slightly better agreement with the detailed calculations than the other lumping
0 1000 2000 3000 4000
0
2
4
6
8
N
2
Time, days
Error (%)

Original Flow Based
Newley 20-40% CO
2
(Alternate)
Newley(Flow Based Newley)
0 1000 2000 3000 4000
0
5
10
15
CO
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
C
1
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
C
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
C
3
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
iC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
nC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
iC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
nC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
C
6
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
HE1
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
HE2
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
HE3
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
20
25
HE4
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
20
HE5
Time, days
Error (%)

149

schemes with less than 5% error relative to the prediction of the detailed model.

Figure 90: Errors in cumulative oil production vs. simulation time (days). Comparison of lumped
simulations with detailed simulation: Fluid A displaced by pure CO
2

Figure 91: Errors in Gas-Oil Ratio (std m
3
/std m
3
) as a function of time (days). Comparison of
lumped simulations with detailed simulation: Fluid A displaced by pure CO
2

0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
1.5
2
2.5
3
Time, days
Errors in Cumulative Oil (%)

Original Flow Based
Alternate Newley
Modified Newley
0 500 1000 1500 2000 2500 3000 3500 4000
0
2
4
6
8
10
Time, days
Errors in Gas-Oil Ratio (%)

Original Flow Based
Alternate Newley
Modified Newley

150

Figure 92: Errors in cumulative CO
2
production as a function of time (days). Comparison of lumped
simulations with Detailed fluid description: Fluid A displaced by pure CO
2

7.5.2 Fluid A & Separator Gas 1

Next, we compare the results from delumping the 3D reservoir simulation for each of
these lumping schemes when separator gas is injected to displace Fluid A. The errors in
the predicted production stream are reported for the individual detailed components in
Figure 93. Again, the flow based approach display a better overall performance in
predicting the detailed production with better resolution in the light ends and less
accuracy only for the heaviest component.
For the heavy ends, the magnitude of errors for all investigated schemes is
significantly higher than in previous example. This is in part attributed to the trace
0 500 1000 1500 2000 2500 3000 3500 4000
0
5
10
15
20
25
Time, days
Errors in comulative CO
2
production (%)

Original Flow Based
Alternate Newley
Modified Newley

151

concentrations of heavy ends (in the range of 10
-4
) that are produced at later times. In
addition the approximation errors that are introduced by the assumptions of the
delumping approach may also play a role.

Figure 93: Errors in the concentration of the delumped stream for each component compared to the
detailed fluid description: Fluid A displaced by separator gas

However, in terms of prediction of the cumulative oil production and the producing
gas oil ratio are shown in Figure 94 and Figure 95 for 4000 days of production. As it is
clear, the flow-based Newley and Merrill approach performs slightly better than the flow-
based method.
0 1000 2000 3000 4000
0
20
40
60
80
100
N
2
Time, days
Error (%)

Original Flow Based Alternate Newley Newley
0 1000 2000 3000 4000
0
10
20
30
40
CO
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
20
25
C
1
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
C
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
C
3
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
iC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
nC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
iC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
nC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
50
100
150
200
C
6
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
HE1
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
HE2
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
HE3
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
HE4
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
80
HE5
Time, days
Error (%)

152

Figure 94: Cumulative oil production (std m
3
) plotted versus simulation time (days) for the detailed
model and the various lumped fluids: Fluid A displaced by separator gas

Figure 95: GOR - Gas Oil Ratio (std m
3
/std m
3
) as a function of time (days) as predicted by the
detailed model and lumped models: Fluid A displaced by separator gas

0 500 1000 1500 2000 2500 3000 3500 4000
0
2
4
6
8
10
12
14
16
18
x 10
6
Total Oil Production
Time, days
Cumulative Oil (std m
3
)

Detailed
Original Flow Based
Alternate Newley
Modified Newley
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
1.5
2
2.5
x 10
4
Gas Oil Ratio
Time, days
Gas Oil Ratio (std m
3
/ std m
3
)

Detailed
Original Flow Based
Alternate Newley
Modified Newley

153

7.6 Discussions and Conclusions
A majority of oil fields currently under production as well as new developments are
candidates for EOR processes such as miscible gas floods. The approach presented here
are directly applicable to the study and design of such EOR processes and offers an
improved workflow for integration of up- and down-stream processes.
In the previous sections we have applied two different flow-based lumping strategies
that allows for automation of integrated compositional modeling. The impact of the
lumping strategy on the accuracy of the delumped production streams was investigated
for the flow-based approaches and an alternate version of the Newley and Merrill scheme
are compared to the production stream obtained with the detailed fluid description. The
presented examples demonstrate the uniqueness and strength of the proposed flow-based
approach and the flow-based Newley and Merrill in deconvoluting the lumped system
more accurately compared to the other method. In particular when CO
2
is injected, the
benefit of using the flow-based approach is evident. Therefore, it is concluded that the
proposed lumping/delumping strategy provides for additional control of the predictive
quality over currently available lumping/delumping approaches.
Both the original flow-based approach and the proposed modification of the approach
of Newley and Merrill include the variation in K-values over the displacement and
provide unique lumping schemes. This is a clear advantage over the extended Newley
and Merrill approach (Egwuenu et al., 2008) where the lumping scheme is non-unique
and strongly dependent on the selection of mixture compositions of oil and gas that are

154

used to generate K-values.
The huge observed errors in all delumped streams, can be attributed in part, to the
assumptions of the LSK delumping method using equation7-7. In this equation, when the
components BICs in the fluid models are taken different from zero, this correlation will
produce approximation on the calculated K-values for the components rather than the
exact solution. This was verified using a set of swelling test simulations for fluid A using
both CO
2
and separator gas with the models having BICs as zero and the ones with non
zero BICs.
Starting with CO
2
as the injection gas, at first, the fluid model regenerated using zero
BICs and then at constant temperature of 383.15K, using different mixture ratios of oil
and CO
2
, the saturation pressure was estimated. At the critical pressure of 222 atm the
solvent fraction of 0.71 was calculated as it is shown in Figure 96.

Figure 96: Swelling test simulation for fluid A (no BICs) and CO
2
at T=383.15K
150
170
190
210
230
250
270
0 0.2 0.4 0.6 0.8 1
Psat (atm)
Fraction of gas

155

The solvent fraction at the critical mixture was then used at various pressures starting
from 10 to 222 atm with step of 2 atm, using flash calculation on the detailed
compositions the phase fraction calculated and compared with the one estimated using
the K-values calculated by equation 7-7. As the result, the same phase fraction with no
difference obtained.
Now, the same procedure was used with CO
2
and oil model having BICs different
from zero. As it is shown in Figure 97, the saturation pressure is calculated at different
solvent fractions and at the critical pressure of 341 atm the gas fraction is 0.59.

Figure 97: Swelling test simulation for Fluid A (with BICs) and CO
2
at T=383.15K

Again, comparing the phase fraction of the detailed fluid with and without estimation
by equation 7-7 was studied and in this case, huge amount of errors observed in the
delumping procedure and the errors increased as the pressure of the displacement merges
150
250
350
450
550
650
750
850
950
0 0.2 0.4 0.6 0.8 1
Psat (atm)
Fraction of gas

156

to the critical pressure. The trend of the errors is shown in Figure 98.

Figure 98: Delumping errors for Fluid A and CO
2
introduced by using non-zero BICs at different
pressures

The same practice was conducted on the fluid A and separator gas and the result of
the swelling tests for non-BICs and BICs models are shown in Figure 99 and Figure 100.
Similar to the case of CO
2
as the injection gas, for the zero BICs, the delumping errors
were calculated as zero. However, still for the cases of non-zero BICs, errors develop
throughout delumping model assumption which increases as the pressure goes toward the
critical pressure of the fluid. The delumping error for the case of fluid A and separator
gas is plotted in Figure 101.
-120
-100
-80
-60
-40
-20
0
0 100 200 300 400
Delumping error(%)
Pressure (atm)

157

Figure 99: Swelling test simulation for Fluid A (no BICs) and separator Gas at T=383.15K

Figure 100: Swelling test simulation for Fluid A (with BICs) and separator gas at T=383.15K

100
150
200
250
300
350
400
450
500
550
0 0.2 0.4 0.6 0.8 1
Psat (atm)
Fraction of gas
100
150
200
250
300
350
400
450
500
550
0 0.2 0.4 0.6 0.8 1
Psat (atm)
Fraction of gas

158

Figure 101: Delumping errors for Fluid A and separator gas introduced by using non-zero BICs at
different pressures

Figure 102 and Figure 103 show the result of the displacement simulation at MMP for
both CO
2
and separator gas, comparing the logarithm of K-values variation with cell
number. As it is clear, having the nonzero BICs errors are more pronounced for the case
of CO
2
injection compared to separator gas.
A further step would be to regenerate the result on delumped stream of different
lumping schemes with no BICs fluid model and observe the improvement on the
delumped stream errors. Fluid A and separator gas are used for this exercise.
Figure 104 shows the error in the concentration of delumping revived components
compared to the detailed stream as the output of a 3D numerical simulator. Comparing
this figure to the Figure 93, huge improvements observed by assuming BICs as zero on
the delumping introduced errors.
0
10
20
30
40
50
60
70
0 100 200 300 400 500
Delumping error(%)
Pressure (atm)

159

Figure 102: Displacement at MMP for Fluid A and CO
2
with different cell numbers

Figure 103: Displacement at MMP for Fluid A and separator gas with different cell numbers

-12
-10
-8
-6
-4
-2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
LnK
Fraction of vapor
Cell number
frac est
lnK(nc)
frac sim
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100
LnK
Fraction of vapor
Cell number
frac sim
frac delump
lnK(nc)

160

Figure 104: Errors in the concentration of the delumped stream for each component compared to
the detailed fluid description: Fluid A displaced by separator gas for no BICs model

Figure 105 shows the cumulative production for zero BICs model and the errors
comparing with the detail models for all lumping schemes are shown in Figure 106.

Figure 105: Cumulative oil production (std m
3
) plotted versus simulation time (days) for the detailed
model and the various lumped fluids: Fluid A displaced by separator gas for no BICs model
0 1000 2000 3000 4000
0
20
40
60
80
100
N
2
Time, days
Error (%)

Original Flow Based
Alternate Newley
Flow Based Newley
0 1000 2000 3000 4000
0
10
20
30
40
CO
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
12
C
1
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
60
C
2
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
C
3
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
iC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
50
nC
4
Time, days
Error (%)
0 1000 2000 3000 4000
0
5
10
15
20
25
30
iC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
10
20
30
40
nC
5
Time, days
Error (%)
0 1000 2000 3000 4000
0
20
40
60
80
100
120
C
6
Time, days
Error (%)
0 1000 2000 3000 4000
0
1
2
3
4
5
6
HE1
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
HE2
Time, days
Error (%)
0 1000 2000 3000 4000
0
1
2
3
4
5
6
HE3
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
10
HE4
Time, days
Error (%)
0 1000 2000 3000 4000
0
2
4
6
8
HE5
Time, days
Error (%)
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
7
Total Oil Production
Time, days
Cumulative Oil (std m
3
)

Detailed
Original Flow Based
Alternate Newley
Modified Newley

161

Figure 107 shows the gas oil ratio for this displacement with no BIC fluid model. Also
the errors using different lumping schemes on GOR are depicted in Figure 108.

Figure 106: Errors in cumulative oil production plotted versus simulation time (days) for the detailed
model and the various lumped fluids: Fluid A displaced by separator gas for no BICs model

Figure 107: GOR - Gas Oil Ratio (std m
3
/std m
3
) as a function of time (days) as predicted by the
detailed model and lumped models: Fluid A displaced by separator gas for no BICs model
0 500 1000 1500 2000 2500 3000 3500 4000
0
1
2
3
4
5
6
7
Errors in Total Oil Production
Time, days
Errors in Cumulative Oil (%)

Original Flow Based
Alternate Newley
Flow Based Newley
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
1.5
2
2.5
3
3.5
x 10
4
Gas Oil Ratio
Time, days
Gas Oil Ratio (std m
3
/ std m
3
)

Detailed
Original Flow Based
Alternate Newley
Modified Newley

162

Figure 108: Errors in GOR plotted versus simulation time (days) for the detailed model and the
various lumped fluids: Fluid A displaced by separator gas for no BICs model

Hence, for comparing the lumping schemes, it is highly recommended that the BICs
of zero for all the components should be used to avoid additional errors introduced in the
delumping schemes.
Additionally, there are additional assumptions in the delumping model such as phase
densities and viscosities are assumed to be identical for the delumped and detailed fluid
descriptions and it is recommended that the quality of these assumptions should be
investigated in more details to understand the impact on the accuracy of the delumping
process. However, the level of delumping errors that can be tolerated in integrated
compositional modeling efforts must be evaluated on the basis of the specific
downstream processes as well.
We note that the results presented in this work were generated without additional
tuning of the lumped EOS model (except for the fluid viscosity via z
c
). A retuning of the
0 500 1000 1500 2000 2500 3000 3500 4000
0
5
10
15
20
25
30
35
Errors in Gas Oil Ratio
Time, days
Errors in Gas Oil Ratio (%)

Original Flow Based
Alternate Newley
Flow Based Newley

163

EOS models for these lumping schemes may improve the accuracy of the delumped fluid
systems.
Throughout this work, we have used K-values from analytical solutions to near-
miscible displacement calculations as input to the flow-based lumping schemes.
Numerical calculations can equally well be used to mimic the level of mixing that occurs
during a field scale displacement processes. This approach was tested for the cases
presented in this paper and agreement was observed between the analytical and numerical
calculations when more than 10 grid blocks was used in the numerical calculations.
In closing, we note that compositional information will invariable be lost in a
lumping/delumping process. However, a good starting point in terms of the lumped fluid
description is instrumental in minimizing the loss of compositional information.

164

Chapter 8: Summary and Recommendations
8.1 Summary
In summary, to understand the dispersion in multiphase systems, displacements with
analog solvents (Water - Methanol - Isopropanol – Isooctane) at lab conditions were
designed to mimic high pressure gas injection into an oil reservoir.
The fluid system was characterized for each ternary by making sets of two-phase
mixtures and analyzing those with GC. Then, the phase behavior of the fluid system was
modeled using the UNIQUAC activity coefficient model, with excellent accuracy, to
predict the liquid-liquid equilibrium at standard conditions. The nonlinear observation of
the viscosity for the binary systems was modeled with good degree of accuracy using a
UNIQUAC based viscosity model that subsequently tested well with literature data for
ternaries mixtures. The IFT between liquid-liquid phases for the system under study was
correlated using both measured and literature data.
A porous medium was designed to behave wetting with the initial compositions of
analog solvents and non-wetting to a representative injection gas based on the analog
solvents. The porous media was then characterized by measurements of porosity and
permeability. The dispersivity of the medium to single phase displacements was also
determined.
The interaction between fluid and medium was determined by measuring the Relative
permeabilities of the system for the binary of Isooctane and Water. This was conducted

165

through steady state experiment and the end points correlated with the base IFT for the
binary.
A numerical compositional simulator was designed and implemented with suitable
phase behavior, viscosity and IFT models to design the displacement experiments
needed.
In a last step, two sets of four component displacement experiments were designed
and conducted in which multi-contact miscibility was observed for selected oil and gas
compositions. The two displacement experiments were subsequently modeled.
In a second part of the research project, two flow-based methods were proposed
which both have the advantage of using the flow information in addition to the phase
behavior information to decide on the proper components to be lumped together.
8.2 Future Research
The tailing behavior of the tracer experiments made the interpretation of two-phase
displacement very difficult.
A future direction of this work would be to model the multi-phase experiments by a
set of randomly generated porosity and permeability fields to match simulation and the
available dispersivity experiment for single phase flow. Then the two-phase displacement
can be modeled based on the selected permeability/porosity model. It should be noted
that the errors from both IFT and viscosity models can contribute to the quality of the end
result and make an investigation of dispersion difficult. For IFT predictions of this type
of system, no model is available which can predict the experimental observations with

166

less than 50 % deviation in the quaternary systems. Also it would be beneficial to
observe the performance of the viscosity model in predicting the 4 component mixtures
compared to the experimental data on that system.
For the lumping and delumping section of this work, it is highly recommended to
perform a thorough study of the assumptions that are made to delump pseudo-
components and the amount of error each assumption introduces in the delumped
streams.

167

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Abstract (if available)

Abstract Injection of CO2 into an oil or gas reservoir is an approach to improve the recovery of hydrocarbons by multi-contact miscible displacement processes. In order to estimate the incremental oil (or gas) that can be produced by injection of CO2, commercial compositional reservoir simulators are commonly used by the industry. Successful design and implementation of CO2 injection processes rely in part on the accuracy by which the available simulation tools represent the physics that govern the displacement behavior in the reservoir. In this research project, two aspects of enhanced hydrocarbon recovery by CO2 injection were investigated as discussed in the following.

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Creator Rastegar Moghadam Moadab, Reza (author)

Core Title A study of dispersive mixing and flow based lumping/delumping in gas injection processes

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Petroleum Engineering

Publication Date 05/04/2010

Defense Date 03/26/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag analog solvents,capillary,Carbon,CO₂,component,compositional simulation,condensing,delumping,diffusion,dispersion,dispersive,dispersivity,effluent,EOR,Experimental and Molecular Pathology,flow based,flowbased,gas,hydrocarbon,IFT,injection,isooctane,isopropanol,lumping,methanol,miscible displacement,mixing,mixture,Modeling,multicontant,OAI-PMH Harvest,oil,phase,pseudocomponent,PTFE,relative permeability,reservoir,saturation,sequestration,sweep,UNIQUAC,vaporizing,viscosity,Water

Language English

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Advisor Jessen, Kristian (committee chair), Brun, Todd A. (committee member), Ershaghi, Iraj (committee member)

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