PhD Thesis - Seyed Reza (Shauheen) Etminan

UNIVERSITY OF CALGARY
Improved Experimental and Mathematical Techniques for Measurement
of Solvent Gas Diffusivity in Heavy Oils
by
Seyed Reza Etminan
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING
CALGARY, ALBERTA
JANUARY, 2014
© SEYED REZA ETMINAN 2014

ii
Abstract
Efficient recovery of heavy oil and bitumen is still very challenging and remains an issue of
ongoing research all around the world. Thermal recovery methods, which rely on heat for
viscosity reduction, are generally accepted as viable and several steam based projects have been
successful, especially in Canada. Using light hydrocarbon solvents can provide similar viscosity
reduction and is potentially more efficient in so-called challenging reservoirs where thermal
methods do not work. In comparison with thermal methods, solvent based processes are more
environmentally friendly and require no fresh water resources.
The solvent based processes rely on molecular diffusion for in situ mixing of the solvent with the
oil and generally provide much slower rates of oil production than the thermal processes. This is
so because the molecular diffusivity is often much smaller than the thermal diffusivity. However,
the published information on experimentally determined diffusivity of gaseous solvents in heavy
oil and bitumen is very scarce. Therefore, accurate measurement of molecular diffusion
coefficient is necessary for reliable design of solvent-based recovery processes in heavy oil
reservoirs.
There is no well-established and universally applicable technique for measuring molecular
diffusion coefficient. Measurements of mass transfer characteristic are often more difficult due to
difficulties in measuring point values of concentration and other issues which complicate this
transport process such as phase equilibrium, effect of convective transport and having a mixture
rather than a pure fluid. These issues make it necessary to employ several simplifying
assumptions in mathematical modeling and interpreting the experiments to determine the
diffusivity.
The focus of this thesis is on improvement of experimental and mathematical techniques for
measurement of unknown mass transfer parameters, specifically molecular diffusion coefficient,
in dissolution of gaseous solvents into bitumen in binary systems. This is accomplished through
identification of different phenomena or states occurring during the diffusion of gaseous solvents

iii
into bitumen and accordingly, development of improved experimental technique, mathematical
models and computational algorithms for different cases. Diffusion coefficient of methane,
carbon dioxide and propane were estimated as gaseous solvents diffusing into bitumen and it was
shown that the estimated parameters generally agree with those reported in the literature.
The outcome of this study is directly relevant to the in situ recovery of heavy oils and bitumen;
however, the proposed techniques could also be applied to other applications for determination
of diffusivity of gases dissolving into non-volatile liquid systems.

iv
Acknowledgements
I would like to thank the individuals who taught me something or influenced my character to
embody who I am and where I me standing this day.
There have been many people who came in assiduous guidance in completion of this thesis.
Notably, I would like to thank my supervisor Professor Brij Maini whose belief in me harnessed
all the difficulties in completion of this thesis research work. He endowed me whole freedom and
confidence to examine my ideas and whatever I was curious about and came in support by all
means through devoting his time, knowledge and resources. Dr. Maini is a real engineer with
meticulous scientific vision about physics who I always learned from and enjoyed discussing
with.
I also would like to thank Professor Zhangxin Chen, my co-supervisor for his availability and
unconditional support. I had the opportunity of being one of his very first graduate students at the
University of Calgary and wholeheartedly enjoyed being a member of his research team and
working under his professional disciplines. Professor Chen taught me how to think big, to be a
scientist and entrepreneur at the same time and act cooperatively and effectively with others.
In completion of this thesis, I have had the opportunity of learning and receiving valuable
comments from and being technically advised by my supervisory committee members. I would
like to show gratitude to Dr. Hassan Hassanzadeh for his technical advice and time devotion and
Professor Mehran Pooladi-Darvish for all instructive discussions during Advanced Reservoir
Engineering course. I am also grateful to Professor Harvey Yarranton, whom I really enjoyed
working with. His comments and different view of looking into problems has been always
challenging for me but enjoyable. I am also grateful to professor Gopal Achari and Dr. Swapan
Kumar Das for accepting to be in my examination committee.
Great appreciation goes to Bureau of Economic Geology (BEG), University of Texas in Austin
and Dr. Farzam Javadpour for hosting me as a visiting researcher through NSERC foreign study

v
financial supplement. I really enjoyed visiting BEG and working under the supervision of
Dr. Javadpour through which our proposed diffusion measurements technique was extended to
gas shale formations for the first time.
Support of Dr. Yarranton’s research lab for providing the solid extracted asphalatene and also
Dr. Abedi’s research lab for sharing experimental equipment is highly appreciated. I would like
also to thank Mike Grigg for smart development of my experimental setups digital data
acquisition system and also all the experts and machinists at the Schulich School of Engineering
Machine Shop. Permanent IT support of Andrew Sutton is highly appreciated. Andrew saved my
life twice by recovering my lost data from my crashed computers. I also would like to thank all
the staff at the Chemical and Petroleum Engineering Department graduate administration office
as well as the reservoir simulation research group. In years of studying in this department, I have
met, talked and worked with individuals whom I am delightful to be influenced by, including
Professor Jalel Azaiez and Professor Gordon Moore. I also appreciate great support of Dr. Fred
Wassmuth in completion of this thesis.
Financial supports by NSERC through Alexander Graham Bell CGS and Michael Smith awards,
Alberta Innovates Technology Futures (AITF) graduate scholarship, Chemical and Petroleum
Engineering Department at the University of Calgary and NSERC/AIEES/Foundation CMG and
AITF chairs, are highly appreciated.
In lifetime, we encounter or live with the individuals whose being, advices and acts influence our
life, shape it and in some cases perform as inflection points in our destiny. By this means, I
would like to share my soul and show my deepest gratitude to those individuals who inspired me,
taught me, had belief on me, criticized me, cared about me and loved me.
Shauheen S.R. Etminan
Autumn 2013

vi
Dedication
To the memories of my Grandma,
“Maman Bozorg”

vii
Table of Contents
Abstract............................................................................................................................... ii
Acknowledgements............................................................................................................ iv
Dedication.......................................................................................................................... vi
Table of Contents.............................................................................................................. vii
List of Tables ..................................................................................................................... xi
List of Figures and Illustrations ....................................................................................... xiii
CHAPTER ONE: INTRODUCTION..................................................................................1
1.1 Background................................................................................................................1
1.2 Solvent-Based Recovery Techniques ........................................................................5
1.3 Motivation & Problem Statement..............................................................................8
1.4 Methodology............................................................................................................10
1.5 Thesis Objective ......................................................................................................11
1.6 Thesis Structure .......................................................................................................11
1.7 Nomenclature...........................................................................................................14
1.8 References................................................................................................................15
CHAPTER TWO: MEASUREMENT OF MOLECULAR DIFFUSION COEFFICIENT IN
PETROLEUM ENGINEERING APPLICATIONS.................................................20
2.1 Introduction..............................................................................................................20
2.2 Overall Review of Molecular Diffusivity Measurement Techniques......................20
2.3 Molecular Diffusivity Measurement Techniques in Petroleum Engineering ..........22
2.4 References................................................................................................................30
CHAPTER THREE: CONSTANT-PRESSURE TECHNIQUE FOR GAS DIFFUSIVITY
AND SOLUBILITY MEASUREMENTS IN HEAVY OIL AND BITUMEN.......34
Abstract..........................................................................................................................34
3.1 Introduction..............................................................................................................34
3.2 Experimental Equipment and Measurement............................................................38
3.2.1 Experimental Setup .........................................................................................38
3.2.2 Experimental Procedure ..................................................................................40
3.2.3 Experiments and Materials..............................................................................42
3.3 Theory and Mathematical Model.............................................................................43
3.3.1 Forward Problem.............................................................................................43
3.3.2 Finite Acting Behavior ....................................................................................48
3.3.3 Infinite Acting Solution:..................................................................................48
3.3.4 Inverse problem and parameter estimation......................................................49
3.3.5 Estimation by error minimization....................................................................49
3.3.6 Graphical Method............................................................................................51
3.4 Results and Discussion ............................................................................................52
3.4.1 Estimation of Diffusivity and Ultimate Solubility Using the Minimization
Technique.........................................................................................................52
3.4.1.1 Experiments 1 and 2: .............................................................................53

viii
3.4.1.2 Experiments 3 and 4: .............................................................................57
3.4.2 Estimation of Diffusivity and Solubility using Graphical Method .................61
3.4.3 Comparison between the Two Methods..........................................................66
3.4.4 Error Analysis and Investigation of the Effect of Assumptions on the Final
Solution............................................................................................................66
3.4.4.1 Error due to Pressure Fluctuation in the Diffusion Cell ........................67
3.4.4.2 Liquid is Non-volatile and Diffusion is One Way.................................69
3.4.4.3 No Density Induced Convection Currents:............................................69
3.4.4.4 Swelling Effect: .....................................................................................70
3.5 Conclusions..............................................................................................................71
3.6 Nomenclature...........................................................................................................71
3.7 References................................................................................................................72
CHAPTER FOUR: MODELING THE INTERFACE RESISTANCE IN LOW SOLUBLE
GASEOUS SOLVENTS-HEAVY OIL SYSTEMS.........................................................
...................................................................................................................................74
Abstract..........................................................................................................................74
4.1 Introduction..............................................................................................................75
4.1.1 Pressure Decay Experiments and Interface Boundary Conditions..................76
4.2 Statement of Theory and Mathematical Model: Forward Problem .........................80
4.2.1 Diffusion model with interface resistance.......................................................80
4.3 Results and Discussion ............................................................................................84
4.3.1 Solution of the Base Case Model ....................................................................85
4.3.2 Model Verification ..........................................................................................90
4.3.3 Sensitivity Analysis on Mass Transfer Parameters .........................................92
4.3.3.1 Effect of Henry’s Law Constant (H)......................................................94
4.3.3.2 Effect of Diffusion Coefficient (D) .......................................................95
4.3.3.3 Effect of Mass Transfer Coefficient (k).................................................97
4.3.4 Comparison with an Earlier Analytical Solution.............................................99
4.3.5 Applications – Inverse Problem ....................................................................103
4.4 Conclusions............................................................................................................109
4.5 Nomenclature.........................................................................................................110
4.6 References..............................................................................................................111
4.7 Appendices.............................................................................................................113
4.7.1 General Diffusion Model and Fick’s Second Law........................................113
4.7.2 Effect of Using Constant Gas Compressibility Factor ..................................115
4.7.3 Application of Henry’s Law Constant...........................................................117
4.7.4 Interface Boundary Condition Derivation.....................................................118
4.7.5 Forward Solution of Diffusion Problem Using Laplace Transform..............119
4.7.6 Numerical Model Description .......................................................................120
CHAPTER FIVE: DETERMINATION OF MASS TRANSFER PARAMETERS IN
SOLVENT-BASED OIL RECOVERY TECHNIQUES USING A NON-
EQUILIBRIUM BOUNDARY CONDITION AT THE INTERFACE 123
Abstract........................................................................................................................123

ix
5.1 Introduction............................................................................................................124
5.2 Theory and Mathematical Model...........................................................................128
5.2.1 Direct Problem...............................................................................................128
5.3 Inverse Problem and Numerical Optimization ......................................................131
5.4 Experimental Study and Measurements ................................................................135
5.4.1 Pressure Decay Experimental Setup..............................................................135
5.4.2 Materials........................................................................................................136
5.4.3 Experimental Scenarios.................................................................................137
5.5 Data Interpretations and Parameter Estimations....................................................141
5.5.1 CO2 in Bitumen System: ...............................................................................141
5.5.2 CH4 in Bitumen System: ...............................................................................148
5.5.3 Methane in Heptane – Toluene – Asphaltene System:..................................152
5.6 Concluding Remarks..............................................................................................160
5.7 Nomenclature.........................................................................................................161
5.8 References..............................................................................................................162
5.9 Appendix................................................................................................................165
5.9.1 Jacobian Matrix and Normalized/Relative Sensitivity Coefficients .............165
CHAPTER SIX: MODELING THE DIFFUSION CONTROLLED SWELLING AND
DETERMINATION OF MOLECULAR DIFFUSION COEFFICIENT IN
PROPANE-BITUMEN SYSTEM USING A FRONT TRACKING MOVING
BOUNDARY TECHNIQUE..................................................................................167
Abstract........................................................................................................................167
6.1 Introduction............................................................................................................168
6.2 Mathematical Model..............................................................................................172
6.2.1 Direct Problem: Front Tracking Technique using Variable Space Grids......174
6.2.1.1 Solution Algorithm ..............................................................................175
6.2.2 Inverse Problem: Levenberg-Marquardt Technique to Locate Diffusion
Coefficient and Saturation Concentration......................................................182
6.3 Experimental Studies.............................................................................................184
6.3.1 Molecular Diffusion Measurement................................................................184
6.3.2 Experimental Procedure ................................................................................186
6.3.3 Solubility Measurement.................................................................................187
6.3.4 Experimental Procedure ................................................................................188
6.3.5 Materials........................................................................................................190
6.4 Results and Discussion ..........................................................................................190
6.4.1 Solubility Data for Numerical Model............................................................190
6.4.2 Verification of Solution at No-Swelling Condition and Direct Model Results193
6.4.3 Diffusion Experiments Conducted and Parameter Estimation......................196
6.4.4 Comparisons of the Results...........................................................................201
6.5 Concluding Remarks..............................................................................................202
6.6 Nomenclature.........................................................................................................203
6.7 References..............................................................................................................204
6.8 Appendix................................................................................................................206

x
CHAPTER SEVEN: MEASUREMENT OF GAS STORAGE PROCESSES IN SHALE
AND OF THE MOLECULAR DIFFUSION COEFFICIENT IN KEROGEN .....209
Abstract........................................................................................................................209
7.1 Introduction............................................................................................................210
7.2 Theory and Background.........................................................................................213
7.3 Experimental Study................................................................................................215
7.3.1 Experimental setup and procedure ................................................................216
7.3.2 Sample preparation and properties ................................................................218
7.4 Mathematics of Gas Storage Processes .................................................................219
7.4.1 Gas Expansion in Pores.................................................................................220
7.4.2 Gas Adsorption on Inner Pore Surfaces in Kerogen .....................................221
7.4.3 Gas Molecular Diffusion into Kerogen .........................................................224
7.4.3.1 Direct Model........................................................................................224
7.4.3.2 Inverse Model and Parameter Estimation............................................226
7.5 Results and Discussion ..........................................................................................227
7.5.1 Evaluation of Results – Gas Expansion Region............................................227
7.5.2 Evaluation of Results – Gas Adsorption Region...........................................228
7.5.3 Evaluation of Results – Gas Diffusion into the Kerogen Region..................230
7.6 Conclusions............................................................................................................233
7.7 Nomenclature.........................................................................................................234
7.8 References..............................................................................................................235
CHAPTER EIGHT: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ..237
8.1 Summary................................................................................................................237
8.2 Overall Conclusions...............................................................................................240
8.3 Recommendations for Future Work ......................................................................242
8.4 References..............................................................................................................243

xi
List of Tables
Table ‎2.1: Review of related literature for measurement of molecular diffusion coefficient
using PVT cell....................................................................................................................... 28
Table ‎3.1: Summary of the conducted experiments...................................................................... 42
Table ‎3.2: Comparison of experiments 1 & 2 with Jamialahmadi et al.’s (2006) results............. 55
Table ‎3.3: Comparison of experiments 1 & 2 solubility results ................................................... 56
Table ‎3.4: Comparison of experiments 3 and 4 with three other results –Solubility and
diffusivity comparison .......................................................................................................... 58
Table ‎3.5: Timing of each three sections in all 4 experiments from graphical method................ 62
Table ‎3.6: Results of graphical method and its comparison with minimization approach
results .................................................................................................................................... 63
Table ‎3.7: Average value of pressure fluctuation in diffusion cell in each experiment ............... 69
Table ‎3.8: Density change and investigation of density induced convection possibility in
experiments 1 and 2 .............................................................................................................. 69
Table ‎3.9: Investigation of swelling factor magnitude ................................................................. 70
Table ‎4.1: Classification of Gas-Oil Interface Boundary Conditions........................................... 80
Table ‎4.2: Specifications of pressure decay experiment used in our study .................................. 84
Table ‎4.3: Literature reported and Base Case parameters ............................................................ 84
Table ‎4.4: Sensitivity cases and values of each case .................................................................... 93
Table ‎4.5: Experiments’ properties and estimated parameters ................................................... 107
Table ‎4.6: Effect of using constant compressibility factor on estimated mass transfer
parameters........................................................................................................................... 117
Table ‎5.1: Properties of conducted experiments using bitumen................................................. 136
Table ‎5.2: Properties of Heptane-Toluene-Asphaltene experiments in different concentrations
adjacent to the onset of asphaltene precipitation ................................................................ 137
Table ‎5.3: Estimated parameters for CO2-Bitumen experiment and their comparison with
other works.......................................................................................................................... 142

xii
Table ‎5.4: Estimated parameters for CH4-Bitumen experiment and their comparison with
other works.......................................................................................................................... 150
Table ‎5.5: Estimated parameters for all experiments in diffusion of methane in C7-Toluene-
Asphaltene mixture ............................................................................................................. 154
Table ‎5.6: Liquid mixture swelling data and changes in gas compressibility factor in certain
gas dissolution amounts ...................................................................................................... 156
Table ‎6.1: Properties of diffusion experiments conducted ......................................................... 196
Table ‎6.2: Diffusion coefficient and saturation concentrations determined from history
matching, direct measurement and literature data. ............................................................. 198
Table ‎7.1: Dimension, mass, mineralogy, porosity, TOC, Vitrinite reflectance, grain density,
average pore and distribution, and bulk density data of the samples.................................. 218
Table ‎7.2: Data from Langmuir adsorption tests, mass of gas adsorbed and calculated area. ... 219
Table ‎7.3: Different mechanisms contributing into the gas uptake into the plugs ..................... 228
Table ‎7.4: Estimated values of diffusion coefficients................................................................. 231

xiii
List of Figures and Illustrations
Figure ‎1.1: Canadian Oil Sands & Conventional Production, Millions of bbl/d............................ 1
Figure ‎1.2: Oil Sands Regions in Alberta (Courtesy of CAPP Report June 2013) ........................ 2
Figure ‎1.3: VAPEX Solvent Vapour Chamber (Etminan 2006)..................................................... 6
Figure ‎2.1: Measuring concentration gradient along the medium a) by direct sampling from
different points along the model (Islas-Juarez et al. 2004) 2) by relating measured CT
number to density of solution through CT scanning of a vessel containing CO2 and
heavy oil (Song et al. 2010) .................................................................................................. 23
Figure ‎2.2: Pressure Decay Technique (Upreti and Mehrotra 2000)........................................... 25
Figure ‎2.3: Dynamic Pendant Drop Shape Analysis (DPDSA) Technique (Yang and Gu
2006) ..................................................................................................................................... 25
Figure ‎2.4: Rapid Microfluidics-Based Technique....................................................................... 26
Figure ‎2.5: Tracking Volume Change in Capillary Tubes (James et al. 2012)............................ 26
Figure ‎3.1: Experimental setup schematic.................................................................................... 39
Figure ‎3.2: Schematic of diffusion cell and our model coordinates ............................................. 44
Figure ‎3.3: Cumulative mass of CH4 withdrawn from the supply cell vs. infinite acting
analytical-model plot for D=4.8610-5
cm2
/sec and 01103.0
gC g/cm3
- System of CH4
and dodecane at P=3460.2 kPa and T=65° C........................................................................ 53
Figure ‎3.4: Cumulative mass of CH4 withdrawn from the supply cell vs. finite acting model
plot for D=4.8610-5
cm2
/sec and 01103.0
gC g/cm3
- System of CH4 & dodecane at
P=3460.2 kPa and T=65° C. ................................................................................................. 56
Figure ‎3.5: Cumulative mass of CH4 withdrawn from the supply cell vs. finite acting model
cm2
/sec and 01168.0
gC g/cm3
- System of CH4 & dodecane at
P=3446.4 kPa and T=45° C. ................................................................................................. 57
Figure ‎3.6: Cumulative mass of CO2 withdrawn from the supply cell vs. finite acting model
cm2
/sec and Cg*=0.03414 g/cm3
- System of CO2 & Bitumen at
P=3239.6 kPa and T=75°C. .................................................................................................. 60
Figure ‎3.7: Cumulative mass of CO2 withdrawn from the supply cell vs. infinite acting model
cm2
P=3239.6 kPa and T=75°C ................................................................................................... 60

xiv
Figure ‎3.8: Cumulative mass of CO2 withdrawn from the supply cell vs. finite acting model
cm2
P=3804.8 kPa and T=50 °C. ................................................................................................. 61
Figure ‎3.9: Determination of diffusivity and saturation concentration from graphical method
for experiment 1- Experimental results are divided into three regions based on this
evaluation.............................................................................................................................. 63
Figure ‎3.10: Linear regression of 2nd
region - Experiment 1........................................................ 64
Figure ‎3.11: Linear regression of 2nd region - Experiment 2....................................................... 64
Figure ‎3.12: Linear regression of 2nd region - Experiment 3....................................................... 65
Figure ‎3.13: Linear regression of 2nd regions - Experiment 4..................................................... 65
Figure ‎3.14: Effect of correcting for P fluctuation error in the gas cap on predicted diffusivity
value...................................................................................................................................... 68
Figure ‎3.15: Effect of correcting for P fluctuation error in the gas cap on predicted saturation
concentration......................................................................................................................... 68
Figure ‎4.1: Schematic of pressure decay cell and Interface concentrations in presence of film
resistance............................................................................................................................... 76
Figure ‎4.2: Concentration profile in the bitumen column showing the interface concentrations
at t = 12.225 hr...................................................................................................................... 86
Figure ‎4.3: Behavior of concentrations above and below the interface at k=1.5 × 10-6
m/sec .... 87
Figure (‎4.4): Behavior of concentrations above and below the interface at k=1.5 × 10-4
m/sec
– Comparison with Sheikha et al.’s solution ........................................................................ 88
Figure ‎4.5: Behavior of concentrations above and below the interface at k=1.5 × 10-7
m/sec .... 89
Figure ‎4.6: Comparison of flux term at the interface for various k’s ........................................... 89
Figure ‎4.7: Estimated pressure at the gas cap for the Base Case.................................................. 90
Figure ‎4.8: Comparison of analytical and numerical solution for prediction of concentration
below the interface................................................................................................................ 92
Figure ‎4.9: Comparison of analytical and numerical solution for prediction of gas cap
pressure – Effect of using constant gas compressibility factor, Z versus Z from PR EOS... 93
Figure ‎4.10: Effect of Henry’s law constant on the concentration below the interface,
Cg(z=0,t)................................................................................................................................ 94

xv
Figure ‎4.11: Effect of Henry’s law constant on predicted gas cap pressure and the amount of
gas dissolved ......................................................................................................................... 95
Figure ‎4.12: Effect of diffusivity coefficient on the concentration below the interface,
Cg(z=0,t)................................................................................................................................ 96
Figure ‎4.13: Effect of diffusivity coefficient on predicted gas cap pressure and the amount of
gas dissolved ......................................................................................................................... 96
Figure ‎4.14: Effect of mass transfer coefficient on the concentration below the interface,
Cg(z=0,t)................................................................................................................................ 98
Figure ‎4.15: Effect of mass transfer coefficient on the predicted gas cap pressure and the
mass of gas dissolved............................................................................................................ 98
Figure ‎4.16: Comparison between the predicted interface concentrations through our solution
and Civan and Rasmussen’s solution – Base Case parameters........................................... 100
Figure ‎4.17: Comparison between the predicted amounts of gas dissolved in bitumen through
our solution and Civan and Rasmussen’s solution – Base Case parameters ...................... 101
Figure ‎4.18: Comparison between the predicted interface concentrations through our solution
and Civan and Rasmussen’s solution – Case of k=0.5 x 10-7
m/sec................................... 102
Figure ‎4.19: Comparison between the predicted amounts of gas dissolved in bitumen through
our solution and Civan and Rasmussen’s solution – Case of k=0.5 x 10-7
m/sec............... 102
Figure ‎4.20: History matching of calculated pressures using Riazi experimental data, this
work’s model and Sheikha et al.’s (equilibrium) model – Methane in pentane at
T=37.85°C........................................................................................................................... 105
Figure ‎4.21: History matching of calculated pressures using Zhang et al. (2000) experimental
data, this work’s model and Sheikha et al.’s (equilibrium) model – CO2 in Venezuelan
Heavy Oil at 21°C............................................................................................................... 106
Figure ‎4.22: History matching of calculated pressures using Upreti et al. experimental data,
this work’s model and Sheikha et al.’s (equilibrium) model – CO2 in Athabasca Bitumen
at 75°C ................................................................................................................................ 108
Figure ‎4.23: History matching of calculated pressures using Tharanivasan et al. experimental
data, this work’s model and Sheikha et al.’s (equilibrium) model – CO2 in Heavy Oil at
23.9°C ................................................................................................................................. 109
Figure ‎4.24: Change of gas compressibility factor with pressure using Peng-Robinson EOS in
Upreti et al.’s experiment for CO2 and bitumen in 75 degree C......................................... 116
Figure ‎4.25: Numerical model discretization.............................................................................. 122

xvi
Figure ‎5.1: Schematic of pressure decay cell and interface concentrations in presence of film
resistance............................................................................................................................. 128
Figure ‎5.2: Pressure decay experimental setup used to measure unknown mass transfer
parameters........................................................................................................................... 136
Figure ‎5.3: Fractional precipitation of asphaltene from solution of n-heptane and toluene....... 139
Figure ‎5.4: Change of density of Heptane-Toluene-Asphaltene mixtures with concentration
change ................................................................................................................................. 140
Figure ‎5.5: Preparation and states of heptane-toluene-asphaltene solution in different volume
fractions............................................................................................................................... 141
Figure ‎5.6: Experimental pressure decay vs. calculated pressure from the model, case of CO2
– Bitumen............................................................................................................................ 143
Figure ‎5.7: Normalized/relative sensitivity of the calculated pressure to each of three
unknown parameters, case of CO2/ Bitumen ...................................................................... 144
Figure ‎5.8: Comparison of equilibrium and non-equilibrium solutions ..................................... 146
Figure ‎5.9: Surface plot of objective function in H-D domain (Kmin =0.254x10-6
m/sec) -
CO2/Bitumen case............................................................................................................... 147
Figure ‎5.10: Surface plot of objective function in H-K domain (Dmin =1.34x10-10
m2
/sec) -
CO2/Bitumen case............................................................................................................... 148
Figure ‎5.11: Experimental pressure decay vs. calculated pressure from the model and
Comparison of equilibrium and non-equilibrium solutions – Case of CH4/Bitumen......... 149
unknown parameters, case of CH4/Bitumen ....................................................................... 149
Figure ‎5.13: Estimation of Henry’s Law constant through solubility and saturation pressure
measurement ....................................................................................................................... 151
Figure ‎5.14: Experimental pressure decay vs. calculated pressure from the model, case of
37.5 vol. % C7 – 62.5 vol. % Toluene................................................................................ 152
unknown parameters, case of 37.5 vol. % Heptane – 62.5 vol. % Toluene........................ 153
Figure ‎5.16: Normalized/relative sensitivity of the calculated pressure to k, all cases .............. 154
Figure ‎5.17: Normalized/relative sensitivity of the calculated pressure to D and H, all cases... 155

xvii
Figure ‎5.18: Error bars for the changes of estimated diffusion coefficients with uncertainties
in height and gas compressibility factor (Z) ....................................................................... 156
Figure ‎5.19: Error bars for the changes of mass transfer coefficients with uncertainties in
height and gas compressibility factor (Z) ........................................................................... 158
Figure ‎5.20: Interface resistance (1/k) determined from our model vs. fractions of asphaltene
precipitated by Alboudwarej et al. (2003) .......................................................................... 158
Figure ‎5.21: Error bars for the changes of Henry’s law constant with uncertainties in height
and Z (gas compressibility)................................................................................................. 159
Figure ‎5.22: Weight % of asphaltene added/dissolved into C7-Toluene mixture in each case.. 160
Figure ‎6.1: Schematic of Constant Pressure Technique Diffusion Cell and Interface
Movement as a Result of Dissolution ................................................................................. 172
Figure ‎6.2: Schematic of grid size change algorithm a) Uniform grids will be used and the
equation will be solved for finding concentrations by lagging dz to an old time step and
linearizing the PDE. b) The grid sizes will be changed based on the amount of
dissolution of gas in each grid. Through iteration, the grid sizes will be calculated in
n+1. c) Re-gridding the domain to equal-spaced grids while preserving the concentration
gradient. .............................................................................................................................. 181
Figure ‎6.3: The algorithm proposed for solving the diffusion problem with significant
volume change. ................................................................................................................... 182
Figure ‎6.4: Schematic of diffusion measurement setup.............................................................. 186
Figure ‎6.5: Schematic of solubility measurement setup............................................................. 189
Figure ‎6.6: Propane-MacKay River bitumen solution saturation pressure versus concentration
at 24°C ................................................................................................................................ 191
Figure ‎6.7: Propane-MacKay River bitumen solution density versus solution concentration ... 192
Figure ‎6.8: Density of liquid propane in solution versus solution concentration ....................... 193
Figure ‎6.9: Validation of numerical solution with analytical solution at no swelling condition 194
Figure ‎6.10: Calculated concentration profile along the solution body and the interface
boundary movement in dissolution of propane in bitumen ................................................ 195
Figure ‎6.11: Mass of propane dissolved and location of propane-bitumen solution interface.. 195
Figure ‎6.12: Pressure fluctuations in diffusion cell for two tests in set point pressures of
413.7 and 827.4 kPa............................................................................................................ 197

xviii
Figure ‎6.13: Liquid solution interface height from dissolution of propane in Mac Kay River
bitumen results vs. the numerical model prediction for D=2.55×10-7
cm2
/sec and
Cg*=0.045 g/ cm3
at 24°C and diffusion cell pressure of 413.7 kPa.................................. 199
Figure ‎6.14: Cumulative mass of gas dissolved from dissolution of propane in Mac Kay
River bitumen results vs. the numerical model prediction for D=2.55×10-7
cm2
/sec and
Cg*=0.045 g/ cm3
Figure ‎6.15: Liquid solution interface height from dissolution of propane in Mac Kay River
bitumen results vs. the numerical model prediction for D=4.17×10-6
cm2
/sec and
Cg*=0.159 g/ cm3
Figure ‎6.16: Cumulative mass of gas dissolved from dissolution of propane in Mac Kay
River bitumen results vs. the numerical model prediction for D=4.17×10-6
cm2
/sec and
Cg*=0.159 g/ cm3
at 24°C and diffusion cell pressure of 827.4 kPa. ................................. 201
Figure ‎7.1: (a) An exemplary SEM image revealing organic material (slightly darker spots)
and existence of in some of the kerogenic materials. (b) A carton of the zoomed-in pore
inside kerogenic material. Gas molecules (yellow dots) can be stored by different gas
storage processes. Gas stores as compressed gas in pores, as adsorbed gas to the inner
surface area of the pores in kerogen, and as dissolved gas in the body of kerogenic
material. (c) Schematic of the diffusion domain, z=0 is located at the inner surface of a
pore and z= h is the kerogen-rock no-flow boundary. The concentration profile in the
body of the kerogen is shown. ............................................................................................ 213
Figure ‎7.2: (a) Shale core plug, (b) Top view of the high pressure diffusion cell including the
shale plug sample................................................................................................................ 215
Figure ‎7.3: Schematic diagram of the experimental setup.......................................................... 216
Figure ‎7.4: Semi-log pressure decay data – Experiment at 50°C. .............................................. 220
Figure ‎7.5: Semi-log plot of determined mass corresponding to the pressure decay data -
Experiment at 50°C............................................................................................................. 221
Figure ‎7.6: Langmuir isotherm data for the pressure range in the experiments - Experiment at
50°C. ................................................................................................................................... 222
Figure ‎7.7: (a) Schematic diagram of a model for two sizes of pores in kerogenic material. .... 224
Figure ‎7.8: Mass of methane diffused into the kerogen body at 50°C vs. infinite acting
diffusion model confirming that region 4 has diffusive nature........................................... 231
Figure ‎7.9: Graphical method of estimating the value of the diffusion coefficient of methane
in kerogenic material........................................................................................................... 232

xix
Figure ‎7.10: Selected data (Region 4) of Fig. 5 to fit the diffusion model (Eq. 12) to
determine gas molecular diffusion in kerogenic material................................................... 233
Figure ‎8.1: Deasphalting and formation of new phases close to dew point pressure of gaseous
solvents ............................................................................................................................... 243

xx
Epigraph
Action is the foundational key to all success.
Pablo Picasso

1
Chapter One: Introduction
1.1 Background
Fossil fuels have been at the centre of growth and trade since industrialisation re-organised
economies for the purpose of manufacturing goods (O'Sullivan et al. 2006). Global demand for
energy and scarcity of conventional oil reserves has drawn attention toward unconventional
fossil fuel resources over the last 25 years. The development of advanced drilling and recovery
techniques has made heavy oil/oil sands as well as shale oil/gas the promising energy resource
components for future. Venezuela and Canada possess the world’s two largest deposits of heavy
and extra heavy oil (Dusseault 2001). Heavy oil and bitumen reserves promoted these two
countries to sit on second and third place of the countries with the largest oil reserves, with
respectively 211 and 173.6 billion barrels . In 2012, total Canadian production increased from
2011 levels by 223,000 bbl/d to over 3.2 million bbl/d and it continues to grow. Over half of it,
around 1.8 million bbl/d, was from the oil sands (CAPP Report June 2013). The rest of the oil
has been produced from conventional resources in the broader Western Canadian Sedimentary
Basin (WCSB) and offshore oil fields in the Atlantic with 1.2 and 0.2 million bbl/d, respectively
(CAPP Report June 2013).
Figure 1.1: Canadian Oil Sands & Conventional Production, Millions of bbl/d
(Courtesy of CAPP Report June 2013)

2
Figure 1.1 is produced by Canadian Association of Petroleum Producers (CAPP) and displays
the forecast for total Canadian petroleum production. Conventional production from Western
Canada is expected to remain fairly constant at around 1.4 million bbl/d throughout the outlook
period in their forecast. Production from the oil sands is expected to grow from 1.8 million bbl/d
to 5.2 million bbl/d at the end of the forecast period. Growth from oil sands production drives the
overall increase in current production levels from 3.2 million bbl/d to 6.7 million bbl/d in 2030.
In northern Alberta, there are three designated oil sands areas; Athabasca, Cold Lake and Peace
River (Figure 1.2) that, at the year-end 2012, were estimated by Alberta Energy Resources
Conservation Board (ERCB) to contain remaining established reserves of 168 billion barrels.
Depth of the deposit specifies if open pit mining or in situ recovery techniques could be used for
oil exploitation. The API gravity of natural bitumen resources in these areas are usually less than
10° and their viscosity are greater than 10,000 cp at reservoir condition (Meyer and Freeman
2007). Therefore, bitumen is usually immobile in reservoir and its viscosity must be reduced to
make the oil producible.
Figure 1.2: Oil Sands Regions in Alberta (Courtesy of CAPP Report June 2013)

3
The success of in situ methods depends on the resolution of two major issues: 1) reducing the
viscosity of bitumen so that it can flow, and 2) recovering the bitumen in situ and producing it to
the surface. Heating reduces the viscosity of the bitumen drastically so that it can be pumped to
the surface. In situ methods are expensive compared to mining; nonetheless, production of
bitumen from in situ projects is already substantial such that 80% of the remaining established
bitumen reserves in Alberta can be recovered using these in situ techniques. Amongst different
thermal techniques Cyclic Steam Stimulation (CSS) and Steam Assisted Gravity Drainage
(SAGD) are the major active techniques for bitumen recovery.
In Cyclic Steam Stimulation (CSS), high-pressure, high temperature (300°C) steam is injected
into a vertical wellbore in the oil sands deposit, which is fractured by the steam pressure. As the
steam soaks through the oil sands, the bitumen melts and flows to a producing well, and then is
pumped to the surface. Each cycle of this process can take from four months to two years, and
several cycles can be completed in a formation (Farouq Ali 1994, Donnelly 1999).
Steam Assisted Gravity Drainage (SAGD) is currently the most commonly used in situ recovery
method. This method involves the drilling of two horizontal wells through the oil sands deposit.
High quality steam is injected into the upper well, where the build-up of pressure and heat melts
the bitumen and makes it to flow downward to the second horizontal well, from which it is
pumped to the surface. Water or non-condensable gases might be injected into the deposit to
maintain stability after the bitumen has been removed (Mokrys and Butler 1993, Butler 1994,
Butler 1998).
Despite the success of thermal methods in the recovery of natural bitumen resources,
consumption of large quantities of water and natural gas are major problems with these
techniques. Gas must be burnt for producing steam leading to significant greenhouse gas (GHG)
emissions. Large amount of fresh and brackish water and large water recycling facilities are
required in order to create the steam for SAGD process. Both of these could raise environmental
concerns which lead to the continuing search for more efficient methods.

4
An alternative to thermal recovery techniques is reducing the viscosity of immobile bitumen
through dilution with solvents. Instead of heat transfer mechanisms, mass transfer plays the
major role in transporting the molecules of lighter injected components into the bitumen body to
reduce its viscosity. Limited GHG emission is involved in this technique and no water is
required. In addition to dilution, solvent can culminate in in situ upgrading of bitumen. The latter
happens through de-asphaltening of the bitumen such that bitumen’s heavier components are
precipitated from the oil, adsorb on the sand grains and are not produced to the surface. Vapor
Extraction (VAPEX) process is the solvent analogue of the SAGD process and uses essentially
the same well configuration. Luhning et al. (2003) provide more details on the advantages of
VAPEX production mechanisms over SAGD.
Das and Butler (1994, 1998) defined the principle of VAPEX as the process in which a pure
hydrocarbon vapour or a vaporized hydrocarbon mixture sometimes containing non-condensable
gases, as solvent is allowed to dissolve and diffuse in heavy oil/bitumen to reduce its viscosity.
As suggested by Butler (1993), a solvent such as propane, is injected at or near its dew point and
solvent forms a vapour chamber within the reservoir. The solvent vapour dissolves in the oil
around the chamber and dilutes the viscous oil which drains due to gravity, to a horizontal
production well placed lower in the formation.
Despite the higher energy efficiency and environmental benefits of VAPEX process compared to
SAGD, molecular diffusion dominates the whole process making it too slow to be competitive.
Therefore, over the more than 20 years that have elapsed since the process was introduced
(Butler and Mokrys 1991), only a handful of field trials have been attempted. A recent paper by
Pourabdollah et al. (2012) reviews the research on this process.
The enhancement to both thermal and mass transfer based techniques, like SAGD and VAPEX,
has been pursued through combining these two techniques. The hybrid thermal-solvent
techniques sound more promising since that can potentially take advantage of both methods of
reducing the oil viscosity. Combining technologies in the form of hybrid steam-solvent processes

5
offer the potential of higher oil rates and recoveries, but at less energy and water consumption
than processes such as SAGD (Nasr and Ayodele 2006).
1.2 Solvent-Based Recovery Techniques
Overcoming the inefficiencies involved with thermal methods was the major motivation in
development of solvent assisted techniques. VAPEX process as a concept of a solvent-based
analogue of SAGD was first used to describe a process that combined heated water and propane
injection (Butler 1989, Cuthiell et al. 2006). Later, the term VAPEX was associated with use of
only gaseous solvents in the process and hybrid processes that combine solvent and heat effects
were considered separately. Low rates were the major economic barrier in VAPEX as a
commercial process and that was why it was not well received by the industry producers. Factors
controlling the drainage rate for an established chamber were viscosity of oil within and around
the vapour chamber, chamber dimension and height, reservoir heterogeneity, interfacial tension
within the vapour chamber and molecular diffusion and dispersion coefficients (Singhal et al.
1996). Almost all of these parameters have been studied individually by different researchers
over these years (Jiang and Butler 1996, Das 1998, Boustani and Maini 2001, Das 2005, Yang
and Gu 2005, Yazdani and Maini 2005, Frauenfeld et al. 2006, Yazdani and Maini 2006,
Badamchi-Zadeh et al. 2009, Badamchi-Zadeh et al. 2009, Okazawa 2009, Leung and Shi 2013).
The two main mechanisms involved in VAPEX are molecular diffusion of solvent into immobile
bitumen and active gravity drainage due to the large difference between the density of the
gaseous solvent and diluted oil. Solvent is injected close to its dew point pressure where ultimate
dissolution amount (solubility) and swelling (positive volume change) are maximum. Higher
solubility culminates in more dramatic viscosity reduction which has a direct contribution into
Darcy flow. The dissolved asphaltene part of the bitumen could be precipitated at larger solvent
solubilities (Das and Butler 1994, Haghighat and Maini 2010). The advantage of in situ
deasphalting is upgrading of the oil and its drawback could be impairing the drainage through
pore plugging by precipitated asphaltenes (Das and Butler 1994). Figure 1.3 illustrates a cross
section of horizontal and vertical wells as well as the vapour chamber and diffusion zone. The
diffusion and drainage mechanisms are coupled with each other such that the time scale of flow

6
by gravity drainage is much smaller than the time scale of diffusion process (Etminan 2006).
This combination results in a surface renewal type of recovery at the edge of the chamber.
VAPEX is not a miscible process but dissolution of solvent into bitumen reduces their interfacial
tension significantly (Das 1998). Butler’s analytical model (Butler et al. 1981) for prediction of
heavy oil recovery in SAGD was adapted to model the recovery rates in VAPEX (Mokrys 1989,
Mokrys and Butler 1993).
Figure 1.3: VAPEX Solvent Vapour Chamber (Etminan 2006)
Their mathematical model was primarily developed by combining Fick’s first law of diffusion
and Darcy equation into the mass and momentum balance of their model, respectively. After
incorporation of other initial and boundary conditions, Butler and Mokrys (Butler R.M. 1989,
Cuthiell et al. 2006) derived a relationship for estimation of recovery rates as follows:

7
hNSkgLQ So 
22
(1.1)




max
min
)1(
)(
)(int
C
C
S
S
S
C
CS
dC
C
CD
Ns
S
S

 (1.2)
In their equations, Q, the stabilized drainage rate is proportional to the square root of h, drainage
height and k, permeability, and Ns, is a dimensionless parameter depending on thermo-physical
properties of solvent-oil system. The calculation of Ns parameter requires knowledge of
molecular diffusion coefficient, viscosity of diluted oil and density difference between diluted oil
and vapour solvent, which are all function of solvent volume faction, Cs. These data can be
obtained experimentally or predicted from correlations. For the diffusivity term, Butler and
Mokrys (1991) recommended to use the so-called intrinsic diffusivity of the solvent in bitumen.
The intrinsic diffusivity of solvent in bitumen is the molecular diffusion coefficient of solvent in
bitumen in a very dilute mode. Das and Butler (1995, 1998) modified the original mathematical
model of Butler and Mokrys (1996) by introducing an apparent diffusion coefficient in porous
media. They related the apparent diffusion coefficient to the intrinsic diffusivity of solvent in
bitumen Dint, system porosity , and cementation factor Ω.

 intDDa
(1.3)
Original mechanistic studies of VAPEX were conducted in Hele-Shaw cells and in absence of
porous medium (Das and Butler 1998). Early VAPEX experiments in porous media had oil rates
that were significantly higher than expected from Hele-Shaw experiments (Cuthiell and
Edmunds 2013). Boustani and Maini (2001) suggested that one explanation for the faster
drainage is the presence of mechanical dispersion in addition to molecular diffusion. Mechanical
dispersion in porous media is created by chaotic passage of fluids through pores and throats and
is therefore not present in the simplified Hele-Shaw experiment (Cuthiell and Edmunds 2013).
Yazdani and Maini (2009) and Etminan et al. (2011) have studied how the diffusion and
dispersion coefficient could be different.

8
Many derivatives of VAPEX process have been developed so far in which different solvents,
combination of solvents, combined solvent and steam, alternating solvents and steam have been
tested. Solvent Assisted Process (SAP) (Gupta and Gittins 2005), Expanding Solvent-SAGD
(ES-SAGD) (Nasr et al. 2003), Cyclic Solvent Injection (CSI) or Cyclic Solvent Process (CSP)
(Islip and Shu 1985, Lim et al. 2004) Steam Butane Hybrid (SBH) (Frauenfeld et al. 2012),
N-Solv (Nenniger and Nenniger 2008), SAVEX (Gutek, Harschnitz et al. 2003), LASER (Leaute
2002) are the names of some of these techniques. The primary attraction of the VAPEX process
and its various hybrids has always been the opportunity to reduce energy and water inputs
required for SAGD (Cuthiell and Edmunds 2013).
1.3 Motivation & Problem Statement
Amongst the parameters that have direct influence on VAPEX and other solvent-based processes
production rates, molecular diffusion coefficient of solvents into bitumen is essential. Molecular
diffusion coefficient or diffusivity controls the rate at which gas dissolves in oil. The other
important key parameter is solubility, which specifies the ultimate amount of gas dissolution in
oil in a specific temperature and pressure. The economy is paramount in applying any new
technology in the field and this applies to solvent-based processes too. The hydrocarbon solvents
can be expensive and transportation cost to the well location may be significant and therefore,
both the rate at which it dilutes the oil and also the amount of the solvent consumed play key
roles in economic viability of the process.
The amount of solvent used to dilute the oil has direct relation with solubility. It can be
controlled by solvent recycling schemes at the surface and re-injecting it into the reservoir
(Butler et al. 1995, Luhning et al. 2003). Improving the rate of dissolution is the foremost
dilemma and the reason why VAPEX was not commercially very successful. Molecular
diffusion coefficients are on average three to five orders of magnitude smaller than thermal
conductivity coefficients. One way to increase molecular diffusion coefficients is through
increasing temperature. However, temperature increase has adverse effect on solubility and could
reduce it substantially. One of the reasons for popularity of hybrid steam-solvent techniques is

9
the potential for benefiting from faster heat transfer to reduce the bitumen viscosity and at the
same time improving the rate of mass transfer due to larger molecular diffusion coefficient of
solvents into bitumen at higher temperatures.
In any of these cases, having an accurate estimation of mass transfer parameters, specifically
molecular diffusivity, is essential for pilot designs and modeling/simulation of solvent-assisted
recovery techniques. Mass transport phenomena have been extensively studied in modeling the
diffusion of ideal gases into each other. The kinetic theory of gases has been used to define the
diffusion coefficient based on the mean free path of gas molecules and their average velocity.
For liquids, the Stokes-Einstein equation, which relates the diffusion coefficient to viscosity of
the medium, size of the particle and temperature is often used. Their equation was modified to be
used for particles of the same size and represent self-diffusion (Engel 2007). However, diffusion
coefficients in most of the engineering and scientific applications are determined experimentally
using the inverse solution of Fick’s law and the conservation of mass equations.
Unlike viscosity and thermal conductivity, for which standardized techniques are available for
their measurements, there is no universally-established technique for the measurement of
molecular diffusion coefficients (Etminan et al. 2010) and researchers with different
backgrounds have suggested various experimental procedures as well as modeling algorithms to
estimate this key parameter (Pomeroy et al. 1933, Scott et al. 1951, Schmidt 1989, Das and
Butler 1996, Riazi 1996, Sachs 1998, Upreti and Mehrotra 2000, Zhang et al. 2000, Civan and
Rasmussen 2001, Civan and Rasmussen 2002, Upreti and Mehrotra 2002, Tharanivasan et al.
2004, Creux et al. 2005, Sheikha et al. 2005, Wen et al. 2005, Yang and Gu 2005, Yang and Gu
2005, Civan and Rasmussen 2006, Jamialahmadi et al. 2006, Sheikha et al. 2006, Tharanivasan
et al. 2006, Yang and Gu 2006, Farajzadeh et al. 2007, Guerrero-Aconcha et al. 2008, Civan
and Rasmussen 2009, Etminan et al. 2009, Farajzadeh et al. 2009, Guerrero Aconcha and
Kantzas 2009, Haugen and Firoozabadi 2009, Okazawa 2009, Etminan 2010, Song et al. 2010,
Song et al. 2010, Etminan et al. 2011, Fadaei et al. 2011, Nasirahmadi et al. 2011, Rongy et al.
2011, Etminan et al. 2012, Ewing et al. 2012, Frauenfeld et al. 2012, James et al. 2012, Fadaei
et al. 2013, Potsch et al. 2013). The motivation behind this thesis work was the development of

10
improved experimental and mathematical techniques for measurement of solvent molecular gas
diffusivity in heavy oil and bitumen systems. Several physical mechanisms are involved in the
diffusion of gaseous solvents into bitumen including: change of volume/density of bitumen
solution due to dissolution (swelling), interface resistance and dependency of diffusion
coefficient on concentration. At the same time there is no consensus on how the gas-oil interface
should be modeled. This latter could change the whole modeling results required for estimation
of diffusivity and it is very important to capture it correctly from the experiment and model
accordingly. Determination of other mass transport parameters, such as solubility and mass
transfer coefficient, through an integrated efficient estimation technique from results of only one
set of diffusion experiment could reduce the expense and time involved in obtaining these
parameters. Accounting for above-mentioned physical phenomena and mathematical
considerations in estimation of diffusion coefficient requires extra efforts on enhancement of
experimental techniques/measurements as well as mathematical models which are pursued in this
thesis.
1.4 Methodology
In this work, the focus is on measurement of mass transfer coefficients involved in dissolution of
vaporized solvents into bitumen using a PVT cell technique, where two non-equilibrium phases
are allowed to interact inside a cell at constant temperature. With appropriate description of
dissolution and evaporation processes, diffusion coefficients can be inferred from changes in
bulk properties such as total mass, pressure and phase volumes. Unidirectional diffusion of
gaseous solvents into bitumen was considered and the dissolution process was studied. In the
proposed experimental approach, the cell volume is fixed and pressure is kept constant by
injecting gas at the top of the cell. The diffusion coefficient and solubility are obtained from the
amount of injected gas as a function of time. In another approach used, known as pressure decay
technique (Riazi 1996, Sachs 1998), a closed cell with fixed mass is used. The total mass of
solvent gas and bitumen in the system remains constant and the diffusion coefficient is inferred
from recorded changes in pressure. Analytical and numerical techniques have been applied to
develop and solve the one-dimensional partial differential equation constructed based on Fick’s

11
first law and conservation of mass equations on the bitumen liquid solution control volume.
Graphical/analytical as well as numerical iteration-based inverse techniques (
2000) have been developed and applied to estimate the values of unknown mass transfer
parameters in dissolution of solvents into bitumen. The uniqueness and stability of the estimated
parameters are discussed and examined.
1.5 Thesis Objective
Values of diffusion or mass transfer coefficients are determined indirectly from measurements of
mass, pressure or volume change in PVT based diffusion measurement techniques. Mathematical
methods are required to estimate the unknown parameters from measured values. To determine
these parameters accurately, it is crucial to have very close agreement between the prevailing
physics in the diffusion experiments and the developed model. In this thesis, the aim was to
develop techniques for accurate measurement of mass transfer parameters through:
 Introducing novel experimental and mathematical techniques that closely match each
other specifically at the condition at the gas-oil interface.
 Including related physical phenomena occurring during diffusion of solvents into bitumen
and developing proper mathematical models with the least number of simplifying
assumptions to allow for more accurate estimation of unknown mass transfer parameters.
 Proposing inverse techniques and models to estimate solubility and interface resistance in
addition to molecular diffusivity using data through one set of diffusion experiments for
each solvent and bitumen system and applying strategies to evaluate the sensitivity of the
measurements with respect to each of the predicted unknowns.
 Applying the proposed methodology for the other related applications.
1.6 Thesis Structure
This thesis comprises eight chapters, four of which are copies of the peer-reviewed publications
in Energy & Fuel (2010), Fuel (2012, 2013) and International Journal of Coal Geology (2013).
A brief summary of each chapter is presented in the following:

12
Chapter Two: This chapter is a concise overview of the techniques used in measurement of
molecular diffusion coefficient in petroleum engineering applications. Details of other related
techniques through using a PVT diffusion cell have been reviewed in detail in the introduction
section of chapter three, five and six and therefore, this chapter presents a detailed survey of
techniques used for measurement of molecular diffusion coefficient.
Chapter Three: A constant pressure experimental technique is introduced for measurement of
diffusion coefficient of gaseous solvents into bitumen. The experimental setup is designed such
that the pressure is kept constant inside the diffusion cell during the course of the experiment.
This leads into having a constant equilibrium concentration as the interface boundary condition.
Through the graphical as well as non-linear least squares proposed inverse techniques, both
constant diffusion coefficient and equilibrium concentration (solubility) were determined
through running one diffusion experiment. Diffusion of carbon dioxide in bitumen and methane
in dodecane were estimated and the validity of obtained results from our method were compared
with the other available results.
Chapter Four: In this chapter a review of different interface boundary conditions is presented.
An analytical solution is proposed for the most general form of the boundary condition which
models the interface. This model takes into account all mass transfer key parameters including
gas solubility, diffusion coefficient, and a possible interfacial resistance. A detailed sensitivity
analysis of each parameter is conducted and, specifically in the case of interface resistance, it
was determined that values can be reported for interfacial resistance while it does not hinder the
diffusion process physically. Through using this proposed non-equilibrium time dependant
boundary condition at the interface in pressure decay technique, it was shown that some of the
previous works on the modeling of interface resistance are subject to underestimation of the rate
of gas dissolution which leads to erroneous estimation of unknown parameters.
Chapter Five: The analytical model developed in Chapter Four is used in conjunction with an
inverse technique to obtain the three unknown parameters using a single pressure decay dataset.
Sensitivity coefficient analysis is applied as an additional practical evaluation tool to examine the

13
sensitivity of the measured pressure to each of the unknown parameters. The existence of an
interface resistance in dissolution of methane and carbon dioxide in bitumen is investigated.
Chapter Six: In this chapter a rigorous numerical model is developed to model the diffusivity of
propane in bitumen. The proposed model accounts for bitumen solution density change as a
result of dilution through applying a front-tracking moving boundary algorithm and numerical
procedure. The constant-pressure diffusion technique proposed in Chapter Three was used to
record the mass of gas dissolved into bitumen as well as the solution height change. Molecular
diffusion coefficient as well as solubility of propane in bitumen was measured to pressures close
to dew point pressure of propane at 24°C.
Chapter Seven: This chapter was completed through a collaboration research study with the
Bureau of Economic Geology at the University of Texas in Austin. In this chapter, we applied
our developed measurement technique for determination of gas molecular diffusion in a totally
different application. A technique was developed to measure the gas capacity in shale gas
reservoirs. The gas existing as compressed in micro and nano pores, adsorpbed on the surface of
pores in kerogen and dissolved molecules in kerogen. Assuming that gas molecules diffuse into
the walls of the pores in kerogen, Fickian diffusion model and a graphical parameter-estimation
technique was used to estimate the gas molecular diffusion in kerogen through pressure decay
technique.
Chapter Eight: This chapter presents a brief summary of the outcome of the research
documented in this thesis and lists overall conclusions and recommendation for future works.
Each chapter has its own separate nomenclature, appendices and cited references listed at the end
of the chapter.

14
1.7 Nomenclature
C = Solvent concentration, Volume fraction
D = Diffusion coefficient, m2
/sec
g = gravitational acceleration, m/sec2
h = Drainage height, m
k = Sand pack absolute permeability, m2
L = Length of horizontal well, m
N = VAPEX dimensionless number
Q = Dead oil production rate, m3
/sec
S = saturation
Greek letters
 = Cementation factor
 = viscosity, cp (mPa.sec)
 = density, g/cc or kg/m3
 = weight fraction
 = difference
V = Valve
Subscripts
app = apparent
g = gas
i = ith
component
max = maximum
min = minimum
mix = mixture
n = arbitrary integer number
o = oil
s = solvent
Abbreviations
VAPEX = Vapour Extraction
SAP = Solvent Assisted Process
SAGD = Steam Assisted Gravity Drainage
ES-SAGD Expanding Solvent - Steam Assisted Gravity Drainage
CSI = Cyclic Solvent Injection
CSP = Cyclic Solvent Process
SBH = Steam Butane Hybrid
SAVEX = Solvent and Vapour Extraction Process
LASER = Liquid Addition to Steam for Enhanced Recovery (LASER)

15
1.8 References
"U.S. Energy Information Administration http://www.eia.gov/”, 2013.
Badamchi-Zadeh, A., H. Yarranton, B. Maini and M. Satyro (2009). "Phase behaviour and physical property
measurements for VAPEX solvents: part II. propane, carbon dioxide and Athabasca bitumen." Journal of Canadian
Petroleum Technology 48(3): 57-65.
Badamchi-Zadeh, A., H. Yarranton, W. Svrcek and B. Maini (2009). "Phase behaviour and physical property
measurements for VAPEX solvents: Part I. Propane and Athabasca bitumen." Journal of Canadian Petroleum
Technology 48(1): 54-61.
Boustani, A. and B. Maini (2001). "The role of diffusion and convective dispersion in vapour extraction process."
Journal of Canadian Petroleum Technology 40(4).
Butler, R. (1994). "Steam-assisted gravity drainage: concept, development, performance and future." Journal of
Canadian Petroleum Technology 33(2).
Butler, R. (1998). "SAGD comes of age!" Journal of Canadian Petroleum Technology 37(7).
Butler, R., G. McNab and H. Lo (1981). "Theoretical studies on the gravity drainage of heavy oil during in‐situ
steam heating." The Canadian journal of chemical engineering 59(4): 455-460.
Butler, R. and I. J. Mokrys (1991). "A new process (VAPEX) for recovering heavy oils using hot water and
hydrocarbon vapour." Journal of Canadian Petroleum Technology 30(1).
Butler, R., I. J. Mokrys and S. Das (1995). The solvent requirements for Vapex recovery. SPE International Heavy
Oil Symposium.
Butler R.M., I. J. Mokrys (1989). "Solvent Analog Model of Steam-Assisted Gravity Drainage." AOSTRA Journal
of Research, 5: 17-32.
Butler R.M., I. J. Mokrys (1993). "Recovery of heavy oils using vaporized hydrocarbon solvents: Further
development of the Vapex process." Journal of Canadian Petroleum Technology 32(6): 56-62.
Civan, F. and M. Rasmussen (2006). "Determination of gas diffusion and interface-mass transfer coefficients for
quiescent reservoir liquids." SPE Journal 11(1): 71-79.
Civan, F. and M. L. Rasmussen (2001). "Accurate measurement of gas diffusivity in oil and brine under reservoir
conditions." paper SPE 67319.
Civan, F. and M. L. Rasmussen (2002). "Improved measurement of gas diffusivity for miscible gas flooding under
nonequilibrium vs. equilibrium conditions." paper SPE 75135.
Civan, F. and M. L. Rasmussen (2009). "Rapid simultaneous evaluation of four parameters of single-component
gases in nonvolatile liquids from a single data set." Chemical engineering science 64(23): 5084-5092.
Creux, P., V. Meyer, P. Cordelier, F. Franco and F. Montel (2005). "Diffusivity in heavy oils" paper SPE 97798.
Cuthiell, D. and N. Edmunds (2013). "Thoughts on Simulating the VAPEX Process." Journal of Canadian
Cuthiell, D., C. McCarthy, G. Kissel and S. Cameron (2006). "The role of capillarity in VAPEX". Canadian
International Petroleum Conference. Paper 2006-073.
Das, S. (2005). "Diffusion and Dispersion in the Simulation of VAPEX Process." paper SPE 97924.

16
Das, S. and R. Butler (1994). "Effect of asphaltene deposition on the Vapex process: A preliminary investigation
using a Hele-Shaw cell." Journal of Canadian Petroleum Technology 33(6).
Das, S. and R. Butler (1995). Extraction of heavy oil and bitumen using solvents at reservoir pressure. Technical
Meeting/Petroleum Conference of The South Saskatchewan Section.
Das, S. K. (1998). "VAPEX: an efficient process for the recovery of heavy oil and bitumen." SPE journal 3(3): 232-
237.
Das, S. K. and R. M. Butler (1996). "Diffusion coefficients of propane and butane in Peace River bitumen." The
Canadian Journal of Chemical Engineering 74(6): 985-992.
Das, S. K. and R. M. Butler (1998). "Mechanism of the vapor extraction process for heavy oil and bitumen." Journal
of Petroleum Science and Engineering 21(1): 43-59.
Donnelly, J. (1999). The Best Process for Cold Lake CSS Verses SAGD. Annual Technical Meeting.
Dusseault, M. (2001). Comparing Venezuelan and Canadian heavy oil and tar sands. Canadian International
Petroleum Conference.
Engel, T. (2007). Thermodynamics: Statistical Thermodynamics And Kinetics, Pearson Education India.
Etminan, S. R. (2006). The Role of Connate Water Saturation in Vapour Extraction Process. MSc, Petroleum
University of Technology.
Etminan, S. R., P. Haghighat, B. Maini and Z. J. Chen (2011). "Molecular Diffusion and Dispersion Coefficient in a
Propane-Bitumen System: Case of Vapour Extraction (VAPEX)" Process. Paper SPE 143633
Etminan, S. R., B. Maini, H. Hassanzadeh and Z. J. Chen (2009). Determination of concentration dependent
diffusivity coefficient in solvent gas heavy oil systems. SPE Annual Technical Conference and Exhibition.
Etminan, S. R., Maini, B.B., Chen, Z., Hassanzadeh, H. (2010). "Constant-Pressure Technique for Gas Diffusivity
and Solubility Measurements in Heavy Oil and Bitumen." Energy & Fuels 24(1): 533-549.
Etminan, S. R., Pooladi-Darvish,M., Maini,B.B., Chen,Z. (2012). "Modeling the Interface Resistance in Low
Soluble Gaseous Solvents-Bitumen Systems " Fuel 105: 672-687.
Ewing, R. P., C. Liu and Q. Hu (2012). "Modeling intragranular diffusion in low‐connectivity granular media."
Water Resources Research 48(3).
Fadaei, H., B. Scarff and D. Sinton (2011). "Rapid Microfluidics-Based Measurement of CO2 Diffusivity in
Bitumen." Energy & Fuels 25(10): 4829-4835.
Fadaei, H., J. M. Shaw and D. Sinton (2013). "Bitumen–Toluene Mutual Diffusion Coefficients Using
Microfluidics." Energy & Fuels 27(4): 2042-2048.
Farajzadeh, R., A. Barati, H. A. Delil, J. Bruining and P. L. J. Zitha (2007). "Mass transfer of CO2 into water and
surfactant solutions." Petroleum Science and Technology 25(12): 1493-1511.
Farajzadeh, R., P. L. J. Zitha and J. Bruining (2009). "Enhanced mass transfer of CO2 into water: experiment and
modeling." Industrial & engineering chemistry research 48(13): 6423-6431.
Farouq Ali, S. (1994). "CSS-Canada's Super Strategy For Oil Sands." Journal of Canadian Petroleum Technology
33(9).
Frauenfeld, T., C. Jossy, E. Jossy, B. Wasylyk and B. Meza Diaz (2012). "Experimental Evaluation of Dispersion
and Diffusion in UTF Bitumen/n-Butane System". Paper SPE 157904.

17
Frauenfeld, T., C. Jossy and K. Rispler (2006). "Evaluation of the bottom water reservoir VAPEX process." Journal
of Canadian Petroleum Technology 45(9).
Guerrero-Aconcha, U., D. Salama and A. Kantzas (2008). "Diffusion Coefficient of n Alkanes in Heavy Oil" paper
SPE 115346.
Guerrero Aconcha, U. and A. Kantzas (2009). "Diffusion of hydrocarbon gases in heavy oil and bitumen" paper SPE
122783.
Gupta, S. and S. Gittins (2005). Christina Lake solvent aided process pilot. Canadian International Petroleum
Conference.
Gutek, A. H., B. Harschnitz, R. D. Myers and T. Okazawa (2003). Combined steam and vapor extraction process
(SAVEX) for in situ bitumen and heavy oil production, Patent US6662872.
Haghighat, P. and B. Maini (2010). "Role of asphaltene precipitation in Vapex process." Journal of Canadian
Haugen, K. B. and A. Firoozabadi (2009). "Mixing of two binary nonequilibrium phases in one dimension." AIChE
journal 55(8): 1930-1936.
Islip, P. N. and W. R. Shu (1985). Cyclic solvent assisted steam injection process for recovery of viscous oil, Patent
US4513819.
James, L. A., M. A. Ioannidis and I. Chatzis (2012). "Experimentally Validated Model for the Determination of
Concentration-Dependent Diffusion of a Light Hydrocarbon in Bitumen." Energy & Fuels 26(10): 6200-6209.
Jamialahmadi, M., M. Emadi and H. Muller-Steinhagen (2006). "Diffusion coefficients of methane in liquid
hydrocarbons at high pressure and temperature." Journal of Petroleum Science and Engineering 53(1-2): 47-60.
Jiang, Q. and R. Butler (1996). "Experimental studies on effects of reservoir heterogeneity on the Vapex process."
Journal of Canadian petroleum technology 35(10).
Leaute, R. (2002). "Liquid addition to steam for enhancing recovery (LASER) of bitumen with CSS: Evolution of
technology from research concept to a field pilot at Cold Lake." Paper SPE 79011.
Leung, J. and J. Shi (2013). "Physics-Based Proxy for Vapex Process Modeling in Heterogeneous Reservoirs."
paper SPE 165558.
Lim, G. B., P. R. Kry, J. P. Lebel and M. Y. Kwan (2004). Cyclic solvent process for in-situ bitumen and heavy oil
production, Patent CA2349234.
Luhning, R., S. Das, L. Fisher, J. Bakker, J. Grabowski, J. Engleman, S. Wong, L. Sullivan and H. Boyle (2003).
"Full Scale VAPEX Process-Climate Change Advantage and Economic Consequences" Journal of Canadian
Petroleum Technology 42(2).
Meyer R.F., A. E. D., Freeman Ph.A. (2007). Heavy Oil and Natural Bitumen Resources in Geological Basins of the
World. U.S. Geological Survey, Reston, Virginia, U.S. Department of the Interior U.S. Geological Survey. 2007-
1084: 42.
Mokrys, I. and R. Butler (1993). "The rise of interfering solvent chambers: solvent analog model of steam-assisted
gravity drainage." Journal of Canadian Petroleum Technology 32(3).
Mokrys, I. J. (1989). The rise of interfering solvent chambers: solvent analog model of SAGD, Chemical and
Petroleum Engineering, University of Calgary.

18
Nasirahmadi, E., R. Kharrat, M. Ghazanfari and D. Rashtchian (2011). "Experimental Investigation of Constant and
Concentration-dependent Diffusivity of a Hydrocarbon Solvents-Heavy Oil System: A Comparative Study." Energy
Sources, Part A: Recovery, Utilization, and Environmental Effects 34(3): 235-245.
Nasr, T. and O. Ayodele (2006). "New hybrid steam-solvent processes for the recovery of heavy oil and bitumen."
paper SPE 101717.
Nasr, T., G. Beaulieu, H. Golbeck and G. Heck (2003). "Novel Expanding Solvent-SAGD Process- ES-SAGD".
Journal of Canadian Petroleum Technology 42(1).
Nenniger, J. and E. Nenniger (2008). Method and apparatus for stimulating heavy oil production, Patent
CA2567399C.
O'Sullivan, A., S. M. Sheffrin and S. J. Perez (2006). Economics: principles, applications, and tools, Pearson
Education.
Okazawa, T. (2009). "Impact of concentration-dependence of diffusion coefficient on VAPEX drainage rates."
Journal of Canadian Petroleum Technology 48(2): 47-53.
isik, M. . and H. R. B. Orlande (2000). Inverse heat transfer: fundamentals and applications, Taylor & Francis.
Pomeroy, R. D., W. N. Lacey, N. F. Scudder and F. P. Stapp (1933). "Rate of solution of methane in quiescent
liquid hydrocarbons." Industrial & Engineering Chemistry 25(9): 1014-1019.
Potsch, K., P. Toplack and T. Gumpenberger (2013). "A New Interpretation of CO2 Diffusion Experiments" paper
SPE 164933.
Pourabdollah, K., B. Mokhtari and R. Kharrat (2012). "The VAPEX process, from beginning up to date." Fuel 107
1-33.
Canadian Association of Petroleum Producers (CAPP Jun 2013). Crude Oil Forecast, Markets & Transportation: 48.
Riazi, M. R. (1996). "A new method for experimental measurement of diffusion coefficients in reservoir fluids."
Journal of Petroleum Science and Engineering 14(3-4): 235-250.
Rongy, L., K. Haugen and A. Firoozabadi (2011). "Mixing from Fickian diffusion and natural convection in binary
non‐equilibrium fluid phases." AIChE 58(5): 1336-1345.
Sachs, W. (1998). "The diffusional transport of methane in liquid water: method and result of experimental
investigation at elevated pressure." Journal of Petroleum Science and Engineering 21(3-4): 153-164.
Schmidt, T. (1989). "Mass transfer by diffusion." AOSTRA Technical Handbook on Oil Sands, Bitumens and
Heavy Oils.
Scott, E., L. Tung and H. Drickamer (1951). "Diffusion through an interface." The Journal of Chemical Physics 19:
1075.
Sheikha, H., A. K. Mehrotra and M. Pooladi-Darvish (2006). "An inverse solution methodology for estimating the
diffusion coefficient of gases in Athabasca bitumen from pressure-decay data." Journal of Petroleum Science and
Engineering 53(3-4): 189-202.
Sheikha, H., M. Pooladi-Darvish and A. K. Mehrotra (2005). "Development of graphical methods for estimating the
diffusivity coefficient of gases in bitumen from pressure-decay data." Energy & Fuels 19(5): 2041-2049.
Singhal, A., S. Das, S. Leggitt, M. Kasraie and Y. Ito (1996). "Screening of reservoirs for exploitation by application
of steam assisted gravity drainage/VAPEX processes." Paper SPE 37144.

19
Song, L., A. Kantzas and J. Bryan (2010). "Experimental Measurement of Diffusion Coefficient of CO2 in Heavy
Oil Using X-Ray Computed-Assisted Tomography Under Reservoir Conditions." paper SPE 137545.
Song, L., A. Kantzas and J. Bryan (2010). "Investigation of CO2 Diffusivity in Heavy Oil Using X-Ray Computer-
Assisted Tomography Under Reservoir Conditions" paper SPE 138205.
Tharanivasan, A. K., C. Yang and Y. Gu (2004). "Comparison of three different interface mass transfer models used
in the experimental measurement of solvent diffusivity in heavy oil." Journal of Petroleum Science and Engineering
44(3-4): 269-282.
Tharanivasan, A. K., C. Yang and Y. Gu (2006). "Measurements of molecular diffusion coefficients of carbon
dioxide, methane, and propane in heavy oil under reservoir conditions." Energy & Fuels 20(6): 2509-2517.
Upreti, S. R. and A. K. Mehrotra (2000). "Experimental measurement of gas diffusivity in bitumen: results for
carbon dioxide." Industrial & engineering chemistry research 39(4): 1080-1087.
Upreti, S. R. and A. K. Mehrotra (2002). "Diffusivity of CO2, CH4, C2H6 and N2 in Athabasca bitumen." The
Canadian Journal of Chemical Engineering 80(1): 116-125.
Wen, Y., J. Bryan and A. Kantzas (2005). "Estimation of diffusion coefficients in bitumen solvent mixtures as
derived from low field NMR spectra." Journal of Canadian Petroleum Technology 44(4).
Yang, C. and Y. Gu (2005). Effects of Heavy Oil-Solvent Interfacial Tension on Gravity Drainage in the vapor
extraction (VAPEX) Process. paper SPE 97906.
Yang, C. and Y. Gu (2005). "New experimental method for measuring gas diffusivity in heavy oil by the dynamic
pendant drop volume analysis (DPDVA)." Industrial & engineering chemistry research 44(12): 4474-4483.
Yang, C. and Y. Gu (2006). "A new method for measuring solvent diffusivity in heavy oil by dynamic pendant drop
shape analysis (DPDSA)." SPE Journal 11(1): 48-57.
Yazdani, A. and B. Maini (2005). "Effect of Height and Grain Size on the Production Rates in the Vapex Process:
Experimental Study." SPE Reservoir Evaluation & Engineering 8(3): 205-213.
Yazdani, A. and B. Maini (2006). "Further Investigation of Drainage Height Effect on Oil Production Rate in
Vapex." paper SPE 101684.
Yazdani, A. and B. Maini (2009). "The Effective Diffusion/Dispersion Coefficient in Vapor Extraction of Heavy
Oil." Petroleum Science and Technology 27(8): 817-835.
Zhang, Y., C. Hyndman and B. Maini (2000). "Measurement of gas diffusivity in heavy oils." Journal of Petroleum
Science and Engineering 25(1-2): 37-47.

20
Chapter Two: Measurement of Molecular Diffusion Coefficient in
Petroleum Engineering Applications
2.1 Introduction
There are numerous reservoir and drilling engineering applications in which mass transfer plays
a significant role. Gas diffusion coefficient is the main parameter which controls the rate of
dissolution of the injected gas in oil during secondary and tertiary recovery of a reservoir (Hill
and Lacey 1934, Aronofsky and Heller 1957, Van der 1962, Verlaan et al. 1999, Salama and
Kantzas 2005, Sim et al. 2009). It also controls the rate of dissolution of the carbon dioxide into
the reservoir aquifers during sequestration (Hassanzadeh et al. 2005, Farajzadeh et al. 2009). In
drilling, the rate of dissolution of the produced gases into the drilling mud or completion fluids is
controlled by diffusion coefficient (O'Bryan et al. 1988, O'Bryan and Bourgoyne 1990, Bradley
et al. 2002).
The diffusion mechanisms time scale is usually very long in comparison with the other transport
phenomena. Therefore, in recovery processes in which multiple physical mechanisms are
involved, although molecular diffusion is active in the background, its effect might be
overlooked in comparison with convective mass transfer.
There is no well-established and universally applicable technique for measuring the molecular
diffusion coefficient. Estimation of the diffusion coefficient is often more difficult because phase
equilibrium, effect of convective transport and having a mixture rather than a pure component
are involved in mass transport (Etminan et al. 2010). Besides, mapping the solution
concentration field and gradients in a non-destructive way is costly and labor intensive.
2.2 Overall Review of Molecular Diffusivity Measurement Techniques
The measurement of diffusion coefficients in fluids has been, until recently, a time-consuming
and error-prone activity. In view of the importance of diffusion in both naturally occurring and

21
industrial processes the lack of reliable diffusion coefficients is regrettable. With the
advancement of technology, new methods have been developed for the measurement of the
diffusion coefficients in various types of systems.
Surveying the literature on measurement of molecular diffusion discloses that this area has been
long studied. The earliest works on study of molecular diffusion coefficient belongs to Thomas
Graham (1829). Graham’s first experiment was the diffusion of different gases into atmospheric
air and he was measuring the time of diffusion. His method is known as “capillary diffusion”
method and was a very simple test tube. The vessel was filled in succession with various pure
gases. Then the gas was allowed to diffuse into air for a certain length of time and then the
quantity of air that had entered and the amount of gas that remained were determined. The seven
gases he tested were hydrogen, methane, ammonia, ethylene, carbon dioxide, sulfur dioxide and
chlorine. For instance, he found that as much hydrogen left the container in two hours as did
carbon dioxide in ten hours (Graham 1833, Ruckstuhl 1951). This work belongs to years before
Adolf Fick’s article (1855) was published.
Methods of measurement of diffusion coefficients of fluids were reviewed by IUPAC in its
Experimental Thermodynamic Series (Wakeham et al. 1991), by Dunlop et al. (1992) as well as
by Marrero and Mason (1972). The main categories of measurements techniques based on these
references are:
1. NMR (Nuclear Magnetic Resonance) Spin Echo
2. Optical (Interferometry, Light scattering)
3. Capillary Diffusion (Closed tube, Two-bulb, Evaporation (Stefan Cell))
4. Chromatography (Gas chromatography, Taylor dispersion, Arrested/Reversed
flow)
5. Diffusion in Diaphragm Cells and through a Porous Barrier
6. Steady State (Diffusion bridge, Back diffusion, Point source)
7. Gas Adsorption (Laminar liquid jet, Bubble collapse/solution)

22
Some of these methods have been applied in oil and gas industry to measure the diffusion
coefficient of gases and liquids into each other. The PVT diffusion cell technique pursued in this
thesis is widely used in petroleum and chemical engineering application and falls under the
category of Capillary Diffusion methods although it has nothing to do with capillary tubes. NMR
and CT (Computed Tomography) scanning techniques (Freedman et al. 2001, Freedman and
Heaton 2004, Wen et al. 2005, Chen and Chen 2008, Song et al. 2010, Song et al. 2010), the
Taylor dispersion method (Boustani and Maini 2001, Ghanavati 2013), light scattering (Oballa
and Butler 1989) and image processing techniques (Nasirahmadi et al. 2011) have also been
broadly used in the recent years for the determination of diffusion coefficient of hydrocarbon
gases and liquids.
2.3 Molecular Diffusivity Measurement Techniques in Petroleum Engineering
Based on the technical literature reviewed for this study, diffusion coefficient measurement
methods can be divided into two major categories. In the first category, the concentration
gradient/profile of the diffusing solute1
in solution is measured directly and its change with time
is used to determine the diffusion coefficient. The gradient could be measured through sampling
of the fluid along the diffusion direction to determine solvent concentration at various times
(Islas-Juarez et al. 2004). This method is system-intrusive and disturbs the concentration
profiles. However, the mathematical solutions are usually straight forward as integration over
spatial coordinate of Fick’s second law gives the value of the diffusion coefficient (Sarafianos
1986). To overcome intrusion related issues, NMR and CT scanning techniques have been used
to measure the concentration profiles without disturbing the diffusion experiment (Song et al.
2010). Figure 2.1 depicts the two approaches described above. In Figure 2.1a, Islas-Juarez et al.
(2004) have introduced nitrogen into a porous matrix saturated with hexane. They collect
samples of 0.3 cc from Valves 1 to 4 over the course of diffusion experiment and analyse them to
find the hexane-nitrogen concentration. Figure 2.1b displays a glass vessel used by (Song et al.
2010) to measure the diffusion coefficient of carbon dioxide in heavy oil. The red color
represents the glass container and its cap. The purple color shows the carbon dioxide and the
1
In Petroleum Eng. solvent has been used frequently and interchangeably instead of solute in Chem. Eng.

23
blue color is bitumen. These colors are assigned to different CT numbers calibrated with
different densities (concentration) of carbon dioxide and bitumen solution. The concentration
profiles could be determined from the CT numbers without disturbing the diffusion process. CT
scanning or NMR measurement equipment are usually costly and need skilled labour and
substantial data post processing costs involved.
a b
Figure 2.1: Measuring concentration gradient along the medium a) by direct sampling from different points along
the model (Islas-Juarez et al. 2004) 2) by relating measured CT number to density of solution through CT scanning
of a vessel containing CO2 and heavy oil (Song et al. 2010)
Besides direct measurement and NMR/CT scanning techniques, optical techniques have also
been used in petroleum-related applications to measure concentration gradients directly for
estimation of molecular diffusion coefficient. Oballa and Butler (1989) used a pulsed infrared
laser as the light source with a silicon semi-conductor diode detector to measure the
concentration distributions in dissolution of toluene in bitumen. Lambert-Beer’s law (Jiménez et
al. 2006) was applied to relate the light intensity to concentration. Nasirahmadi et al. (2011) used
an image processing technique to evaluate the concentration profiles. In both of these techniques,
since bitumen is opaque, either a very powerful light source must be used in the visible region
for the beam to pass through thickness of bitumen (Oballa and Butler 1989) or like Nasirahmadi

PhD Thesis - Seyed Reza (Shauheen) Etminan

PhD Thesis - Seyed Reza (Shauheen) Etminan

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (11)

Similar to PhD Thesis - Seyed Reza (Shauheen) Etminan

Similar to PhD Thesis - Seyed Reza (Shauheen) Etminan (20)

Recently uploaded

Recently uploaded (20)

PhD Thesis - Seyed Reza (Shauheen) Etminan