enhanced solvent vapour extraction processes in …
TRANSCRIPT
ENHANCED SOLVENT VAPOUR EXTRACTION PROCESSES
IN THIN HEAVY OIL RESERVOIRS
A Thesis
Submitted to the Faculty of Graduate Studies and Research
In Partial Fulfillment of the Requirements
For the Degree of
Doctor of Philosophy
in
Petroleum Systems Engineering
University of Regina
By
Xinfeng Jia
Regina, Saskatchewan
January 2014
Copyright 2014: X. Jia
UNIVERSITY OF REGINA
FACULTY OF GRADUATE STUDIES AND RESEARCH
SUPERVISORY AND EXAMINING COMMITTEE
Xinfeng Jia, candidate for the degree of Doctor of Philosophy in Petroleum Systems Engineering, has presented a thesis titled, Enhanced Solvent Vapour Extraction Processes in Thin Heavy Oil Reservoirs, in an oral examination held on December 18, 2013. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material. External Examiner: *Dr. Zhangxing Chen, University of Calgary
Co-Supervisor: Dr. Fanhua Zeng, Petroleum Systems Engineering
Co-Supervisor: **Dr. Yongan Gu, Petroleum Systems Engineering
Committee Member: **Dr. Yee-Chung Jin, Environmental Systems Engineering
Committee Member: Dr. Chun-Hua Guo, Department of Mathematics & Statistics
Committee Member: Dr. Ezeddin Shirif, Petroleum Systems Engineering
Committee Member: Dr. Farshid Torabi, Petroleum Systems Engineering
Chair of Defense: Dr. Laurie Clune, Faculty of Nursing *via teleconference **Not present at defense
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ABSTRACT
Solvent-based techniques, such as solvent vapour extraction (VAPEX) and cyclic
solvent injection (CSI), have emerged as promising processes to enhance heavy oil
recovery. However, there are still a number of technical issues with these processes, such
as the theoretical modeling and performance enhancement. This thesis aims at addressing
the following major technical topics.
Theoretical modeling of VAPEX. Heavy oil−solvent transition zone is where the
VAPEX heavy oil recovery occurs. Existing analytical VAPEX models can neither fully
characterize the transition zone nor accurately predict its growth. Numerical simulation
models use grid sizes that are much larger than the transition-zone thickness (~1 cm) and
thus cannot capture the characteristics of the transition zone. This study develops a new
two-dimensional (2D) mathematical model for the VAPEX process on the basis of its
major oil recovery mechanisms (i.e., solvent dissolution and gravity drainage) inside the
transition zone. This VAPEX model is able not only to accurately describe the distributions
of solvent concentration, oil drainage velocity, and diffusion coefficient across the
transition zone, but also to predict the evolution of the solvent chamber.
Theoretical modeling of the diffusionconvection mass transfer in CSI. CSI is a
solvent huff-n-puff process. One of the differences between CSI and VAPEX is that the
operating pressure is decreased and increased cyclically in CSI. Hence, in addition to
molecular diffusion, CSI has another mass transfer mechanism, convection, which is
attributed to the bulk motion of solvent caused by the pressure gradient between the solvent
chamber and untouched heavy oil zone. This study develops a convection−diffusion
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mass-transfer model for the heavy oil−solvent mixing process of CSI. The diffusion
coefficient and convection velocity are both considered as variables rather than constants.
Results qualitatively show that pressure gradient can greatly enhance the mixing process.
Enhancement of VAPEX and CSI. This study proposes a new process, namely foamy
oil-assisted vapour extraction (F-VAPEX) to enhance the VAPEX performance.
F-VAPEX combines merits of VAPEX (continuous production) and CSI (strong driving
force) together. It is essentially a VAPEX process during which the operating pressure is
cyclically reduced and restored. It is found that the foamy oil flow during the pressure
reduction period can effectively move the partially diluted heavy oil toward the producer.
Results show that F-VAPEX can increase both the average oil production rate and the
ultimate oil recovery of VAPEX. In comparison with CSI, F-VAPEX has a higher oil
production rate and a lower solvent−oil ratio. This thesis also proposes a new process to
enhance the performance of CSI, namely gasflooding-assisted cyclic solvent injection
(GA-CSI). GA-CSI uses dedicated solvent injector and oil producer to prevent the
‘back-and-forth movement’ of foamy oil inside the solvent chamber during the
conventional CSI process. GA-CSI applies a gasflooding slug immediately after the
pressure depletion process of CSI to produce the partially diluted foamy oil left in the
solvent chamber. It is found that the motionless foamy oil due to pressure depletion and
solvent liberation serves as a buffer zone, which effectively reduces the mobility ratio
between the displacing solvent and the displaced oil and leads to a high sweeping
efficiency. In comparison with the conventional CSI process, the GA-CSI process can
increase the oil production rate by over 3 times and in the meantime decrease the
solvent−oil ratio from ~4 to ~3 g solvent/g oil.
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ACKNOWLEDGMENTS
I want to acknowledge the following individuals or organizations:
Drs. Fanhua Zeng and Yongan Gu, my academic advisors, for their excellent
guidance, valuable advice, strong support, and continuous encouragement
throughout the course of this research work at University of Regina;
My thesis supervisory committee members: Drs. Zhangxing Chen (External
Examiner, University of Calgary), Chun-Hua Guo, Ezeddin Shirif, Farshid
Torabi, Yee-Chung Jin, and for their valuable questions and suggestions;
Natural Sciences and Engineering Research Council (NSERC) of Canada for the
Discovery Grants awarded to Drs. Fanhua Zeng and Yongan Gu;
University of Regina for financial support in the form of Graduate Scholarship
through Faculty of Graduate Studies and Research;
Petroleum Technology Research Centre (PTRC) for the Innovation Funds given
to Drs. Fanhua Zeng and Yongan Gu;
My past and present research group members, Mr. Zuojing Zhu, Ms. Lijuan Zhu,
Ms. Suxin Xu, Mr. Tao Jiang, Ms. Xiaoqi Wang, Mr. Shiyang Zhang, Mr.
Mohammad Derakhshanfar, Mr. Xiang Zhou, Mr. Zhongwei Du, and Ms.
Shanshan Yao, for their helpful technical discussions and suggestions during my
Ph.D. studies; and
My friends (Jim Jacobson, Bettie Jacobson, Graham Beke, Debra Beke, Garry
Engler, and friends from Bethany Gospel Chapel) for their care, concern, and
friendship.
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DEDICATION
To my family and friends
especially my girlfriend, Jianli Li,
and my parents, Zhizhou Jia and Xiling Xi,
for their unconditional love, understanding, and support.
v
TABLE OF CONTENTS
ABSTRACT…… ............................................................................................................ i
ACKNOWLEDGMENTS ............................................................................................. iii
DEDICATION…. ..........................................................................................................iv
TABLE OF CONTENTS ................................................................................................. v
LIST OF TABLES..........................................................................................................ix
LIST OF FIGURES ......................................................................................................... x
NOMENCLATURE ...................................................................................................... xv
CHAPTER 1 INTRODUCTION ................................................................................ 1
1.1 Heavy Oil Resources ..........................................................................................1
1.2 Heavy Oil Recovery Techniques ........................................................................1
1.3 Technical Challenges in Thin Heavy Oil Reservoirs ...........................................3
1.4 Solvent-Based EOR Techniques .........................................................................3
1.5 Problem Statement and Research Objectives ......................................................5
1.5.1 Theoretical modeling of VAPEX .................................................................5
1.5.2 Modeling of the mass transfer in CSI ...........................................................5
1.5.3 Performance improvement for VAPEX and CSI ..........................................6
1.5.4 Research objectives .....................................................................................6
1.6 Thesis Outline ....................................................................................................7
CHAPTER 2 LITERATURE REVIEW ..................................................................... 8
2.1 Vapour Extraction (VAPEX) ..............................................................................8
2.1.1 Physical modeling of VAPEX ................................................................... 10
2.1.2 Mass transfer modeling of VAPEX............................................................ 24
2.1.3 Theoretical modeling of VAPEX ............................................................... 28
2.1.4 Numerical modeling of VAPEX ................................................................ 34
2.2 Cyclic Solvent Injection (CSI) .......................................................................... 35
2.3 Chapter Summary ............................................................................................ 39
CHAPTER 3 MATHEMATICAL MODELING OF VAPEX ................................... 40
3.1 Mathematical Model and Solution .................................................................... 40
3.1.1 Heavy oil–solvent transition zone .............................................................. 40
vi
3.1.2 Mass transfer in transition zone ................................................................. 44
3.1.3 Fluid flow in transition zone ...................................................................... 47
3.1.4 Moving boundary of transition zone .......................................................... 48
3.1.5 Solution procedures ................................................................................... 50
3.1.6 Heavy oil production rate .......................................................................... 52
3.2 Results and Discussion ..................................................................................... 54
3.2.1 Solvent chamber evolution and recovery factor ......................................... 54
3.2.2 Number of transition-zone segments .......................................................... 59
3.2.3 Permeability .............................................................................................. 59
3.2.4 This study vs. analytical models ................................................................ 65
3.2.5 This study vs. numerical simulation ........................................................... 65
3.3 Chapter Summary ............................................................................................ 78
CHAPTER 4 MATHEMATICAL MODELING OF THE
CONVECTION−DIFFUSION MASS-TRANSFER PROCESS .......... 79
4.1 CSI Process ...................................................................................................... 79
4.1.1 Convection−diffusion equation .................................................................. 81
4.1.2 Diffusion coefficient and convection velocity ............................................ 81
4.2 Mathematical Models ....................................................................................... 84
4.2.1 Governing equation ................................................................................... 84
4.2.2 Boundary and initial conditions ................................................................. 84
4.3 Semi-Analytical Solutions ................................................................................ 86
4.3.1 Model 1: Convection–diffusion model with constant D and variable V ...... 86
4.3.2 Model 2: Convection–diffusion model with variable D and variable V ....... 91
4.4 Validations ....................................................................................................... 93
4.4.1 Validation with an analytical solution for a special case............................. 93
4.4.2 Validation with the numerical solution ...................................................... 95
4.5 Results and Discussion ..................................................................................... 95
4.5.1 Application of the convection–diffusion mass-transfer model .................... 95
4.5.2 Variable and constant diffusion coefficient and convection velocity .......... 97
4.5.3 Effect of convection velocity ..................................................................... 99
4.5.4 Péclet number .......................................................................................... 104
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4.5.5 Effect of gravity force in natural convection ............................................ 106
4.6 Chapter Summary .......................................................................................... 110
CHAPTER 5 FOAMY OIL-ASSISTED VAPOUR EXTRACTION (F-VAPEX)... 111
5.1 Experimental .................................................................................................. 111
5.1.1 Materials ................................................................................................. 111
5.1.2 Experimental set-up ................................................................................. 112
5.1.3 Experimental preparation ......................................................................... 116
5.1.4 Experimental procedure ........................................................................... 118
5.1.5 Other measurements ................................................................................ 120
5.2 Results and Discussion ................................................................................... 121
5.2.1 Foamy oil flow in F-VAPEX ................................................................... 121
5.2.2 F-VAPEX vs. VAPEX/CSI ..................................................................... 127
5.2.3 Effect of well configuration ..................................................................... 134
5.2.4 Residual oil saturation ............................................................................. 145
5.3 Chapter Summary .......................................................................................... 148
CHAPTER 6 GASFLOODING-ASSISTED CYCLIC SOLVENT INJECTION
(GA-CSI) .......................................................................................... 149
6.1 Experimental .................................................................................................. 149
6.1.1 Materials ................................................................................................. 149
6.1.2 Experimental set-up ................................................................................. 150
6.1.3 Experimental preparation ......................................................................... 152
6.1.4 Experimental procedure ........................................................................... 152
6.2 Results and Discussion ................................................................................... 155
6.2.1 Well configuration ................................................................................... 158
6.2.2 Operating scheme (CSI vs. GA-CSI) ....................................................... 162
6.2.3 GA-CSI ................................................................................................... 164
6.2.4 Solvent injection rate ............................................................................... 169
6.2.5 GA-CSI with cylindrical models .............................................................. 169
6.2.6 GA-CSI with rectangular model .............................................................. 172
6.2.7 Residual oil saturation ............................................................................. 172
6.3 Variations of GA-CSI..................................................................................... 177
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6.3.1 Pressure control scheme .......................................................................... 177
6.3.2 Viscous fingering .................................................................................... 180
6.3.3 Oil production ......................................................................................... 182
6.4 Chapter Summary .......................................................................................... 185
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS ............................. 186
7.1 Conclusions.................................................................................................... 186
7.2 Recommendations .......................................................................................... 189
REFERENCES…. ....................................................................................................... 190
Appendix A……. ........................................................................................................ 206
Appendix B……. ......................................................................................................... 208
Appendix C……. ......................................................................................................... 210
Appendix D……. ........................................................................................................ 211
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LIST OF TABLES
Table 2.1 VAPEX experimental studies by Butler’s group. ..................................... 15
Table 2.2 VAPEX experimental studies by Maini’s group. ..................................... 16
Table 2.2 VAPEX experimental studies by Maini’s group (Contd’). ....................... 16
Table 2.3 VAPEX experimental studies by Gu’s group. .......................................... 18
Table 2.4 VAPEX experimental studies by ARC. ................................................... 19
Table 2.5 VAPEX experimental studies by other research groups. .......................... 20
Table 2.6 Comparison of the measured diffusion coefficients of CO2, CH4, C2H6
and C3H8 in different heavy oil and bitumen samples. ............................. 26
Table 2.7 CSI experimental studies in the literature. ............................................... 38
Table 3.1 Parameters of the base case for the mathematical model. ......................... 55
Table 3.2 Parameters of the base case for the numerical simulation. ..................... 667
Table 3.3 Effect of the grid size and estimation of the numerical dispersion. ......... 722
Table 4.1 Parameters of the base case. .................................................................... 83
Table 5.1 Physical properties of the sand-packed models and experimental
conditions for VAPEX, CSI, and F-VAPEX testss ................................ 115
Table 5.2 Cumulative heavy oil production data. .................................................. 129
Table 6.1 Physical properties of the sand-packed models and experimental
conditions for CSI and GA-CSI tests. .................................................... 153
Table 6.2 Cumulative oil and solvent production data. .......................................... 156
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LIST OF FIGURES
Figure 2.1 The VAPEX heavy oil recovery process....................................................9
Figure 2.2 Solvent vapour chamber profiles at the end of (a) Rising phase; (b)
Spreading phase; and (c) Falling phase [Zhang, et al., 2006]. .................. 22
Figure 3.1 Transition zone in the VAPEX process. .................................................. 41
Figure 3.2 Approximation to the transition-zone at the (a) beginning and (b)
middle stages of the VAPEX process. ..................................................... 43
Figure 3.3 Boundary movement of a transition-zone segment. ................................. 49
Figure 3.4 Flowchart of the solution calculation for the VAPEX model. .................. 51
Figure 3.5 Discretization of the space and time domains for the numerical solution
to the mass-transfer model with a moving boundary condition. ............... 53
Figure 3.6 Evolution of the solvent vapour chamber during a VAPEX process. ....... 56
Figure 3.7 Oil recover factor of the VAPEX base case . ........................................... 57
Figure 3.8 Solvent concentration distribution at different locations along the
transition zone at different moments: (a) Solvent chamber profiles; (b)
Solvent concentration distributions at the top; (c) Solvent concentration
distributions in the middle; and (d) Solvent concentration distributions
at the bottom of the transition zone.......................................................... 58
Figure 3.9 Effect of dividing number on the average oil production rate................... 60
Figure 3.10 Effect of permeability on the solvent chamber evolution: (a) k = 25 d;
(b) k = 50 d; (c) k = 100 d; and (d) k = 200 d. .......................................... 62
Figure 3.11 Effect of permeability on the oil production rate...................................... 63
Figure 3.12 (a) Heavy oil production rate vs. Square root of diffusion coefficient;
and (b) Oil recovery factor for variable and constant diffusion
coefficients. ............................................................................................ 64
Figure 3.13 Oil production rate predicted by this study and the existing VAPEX
models. ................................................................................................... 66
Figure 3.14 (a) Numerical simulation model; (b) Relative permeability vs. liquid
saturation; and (c) Capillary pressure vs. liquid saturation. ...................... 68
xi
Figure 3.15 Effect of the timestep size on the cumulative oil production (grid size:
0.01 × 0.01 × 0.01 m3). ........................................................................... 70
Figure 3.16 Effect of the grid size on the cumulative oil production (t = 0.001 d). ... 71
Figure 3.17 Effect of the diffusion coefficient on the heavy oil production rate: (a)
Lab-scale grid size simulation results; and (b) Field-scale grid size
simulation results. ................................................................................... 74
Figure 3.18 Mole fraction of solvent in the lab-scale numerical model with different
grid-sizes at 20 h (t = 0.01 d): (a) 0.02 × 0.02 × 0.02 m3; (b) 0.01 ×
0.01 × 0.01 m3; and (c) 0.005 × 0.005 × 0.005 m3. .................................. 75
Figure 3.19 Comparison of the predicted transition-zone thicknesses of this study
and numerical simulation (grid size: 0.02×0.02×0.02 m3; t = 0.01 d). .... 77
Figure 4.1 Vapour solvent-based ‘huff-n-puff’ process (note: bold white arrows
point to the solvent diffusion direction, whereas narrow black arrows
point to convection direction). ................................................................. 80
Figure 4.2 Concentration-dependent diffusion coefficient and flow velocity: (a)
Concentration; (b) Viscosity; (c) Effective diffusion coefficient; and (d)
Convection velocity. ............................................................................... 85
Figure 4.3 Approximation to the convection velocity with a piecewise linear
profile. .................................................................................................... 90
Figure 4.4 Semi-analytical vs. Analytical cD for a convection–diffusion mass
transfer with a special convection velocity .............................................. 94
Figure 4.5 Semi-analytical vs. Numerical cD............................................................. 96
Figure 4.6 Flowchart of calculating the solvent concentration in the transition
zone (t* denotes the termination time). .................................................... 98
Figure 4.7 Comparison of cD for different cases: (a) Variable d & variable V vs.
constant D & variable V; (b) Variable D & variable V vs. variable D &
constant V; (c) Variable D & variable V vs. constant D & constant V;
and (d) Variable D & variable V and D vs. constant D & variable V vs.
variable D & constant V vs. constant D & constant V (constant d is
equal to 5.8×10−9 m2/s; constant v is equal to 1.8×10−6 m/s; t1 = 300 s; t2
= 600 s). ................................................................................................ 100
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Figure 4.8 Effect of the pressure gradient on the solvent concentration distribution.
......................................................................................................... 102
Figure 4.9 Effect of crude oil viscosity on the solvent concentration distribution.... 103
Figure 4.10 Effect of diffusion coefficient on the solvent concentration distribution.
......................................................................................................... 105
Figure 4.11 Effect of péclet number on the solvent concentration distribution. ......... 107
Figure 4.12 Effect of péclet number with different linear shape on the solvent
concentration distribution. ..................................................................... 108
Figure 4.13 Effect of gravity force on the solvent concentration distribution. ........... 109
Figure 5.1 Schematic diagram of the experimental set-up in this study. .................. 113
Figure 5.2 (a) Physical model dimensions; (b) Central well configuration; and (c)
Lateral well configuration. .................................................................... 114
Figure 5.3 Pressure-control scheme for (a) VAPEX; (b) CSI; and (c) F-VAPEX. .. 119
Figure 5.4 Injection and production pressure data during a typical F-VAPEX
cycle. .................................................................................................... 123
Figure 5.5 Foamy oil zone (a) before and (b) after foamy oil flow during a
pressure reduction period of an F-VAPEX process (Test #5.3). ............. 124
Figure 5.6 Foamy oil zone during the (a) early, (b) middle, and (c) late stages of
an F-VAPEX test (Test #5.3). ............................................................... 126
Figure 5.7 Cumulative oil production versus time data for the VAPEX, CSI and
F-VAPEX tests with the central well configuration. .............................. 130
Figure 5.8 Cumulative oil production versus time data for the CSI and F-VAPEX
tests with the lateral well configuration. ................................................ 131
Figure 5.9 Enhancement of the oil production rate of VAPEX by F-VAPEX with
different well configurations. ................................................................ 132
Figure 5.10 Enhancement of the oil production rate of CSI by F-VAPEX with
different well configurations. ................................................................ 133
Figure 5.11 Cumulative solventoil ratio versus time data for the VAPEX, CSI, and
F-VAPEX tests with the central well configuration. .............................. 135
Figure 5.12 Cumulative solventoil ratio versus time data for the VAPEX and
F-VAPEX tests with the lateral well configuration. ............................... 136
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Figure 5.13 Foamy oil zone during the (a) early, (b) middle, and (c) late stages of
an F-VAPEX test with the lateral well configuration (Test #5.7). .......... 137
Figure 5.14 Oil production data from the stable pressure period and pressure
reduction period during Test #5.3. ......................................................... 139
Figure 5.15 Oil production from the stable pressure period and pressure reduction
period during Test #5.7 ......................................................................... 140
Figure 5.16 Total oil production from the stable pressure period and pressure
reduction period during the F-VAPEX tests. ......................................... 141
Figure 5.17 Total solvent production data in the stable pressure period and the
pressure reduction period of the F-VAPEX tests. .................................. 144
Figure 5.18 Residual oil saturation at the end of (a) Test #5.1; (b) Test #5.3; and (c)
Test #5.7. .............................................................................................. 146
Figure 6.1 (a) Schematic diagram of the experimental set-up with a cylindrical
model for GA-CSI tests and a CSI test; (b) Dimensions of the
rectangular sand-packed model; and (c) Schematic diagram of the
physical model for a CSI test. ................................................................ 151
Figure 6.2 Pressure-control schemes of (a) GA-CSI and (b) CSI. ........................... 154
Figure 6.3 (a) Cumulative oil production; and (b) SOR of Tests #6.1−3. ................ 157
Figure 6.4 ‘Back-and-forth movement’ of the solvent-diluted heavy oil in a CSI
test: (a) Solvent dissolution into oil during the injection period of a
cycle; (b) Diluted oil flowing to the producer during the production
period; (c) Some diluted oil remaining in the solvent chamber at the
end of the production period; and (d) Diluted oil flowing back during
the solvent injection period of the next cycle. ........................................ 160
Figure 6.5 ‘Back-and-forth movement’ of the solvent-diluted heavy oil during a
cycle of the CSI test (Cycle #40 of Test #6): (a) Oil flowing to the
producer at the early stage of the production period; (b) Oil remaining
in the solvent chamber at the end of the production period; and (c) Oil
flowing back during the solvent injection period of the next cycle
(Cycle #41). .......................................................................................... 161
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Figure 6.6 Gasflooding process during a GA-CSI test (Test #6.7). (a) End of the
blowdown stage; (b) Early gasflooding stage; and (c) Late gasflooding
stage. .................................................................................................... 163
Figure 6.7 Injection and production pressures and the solvent injection rate during
a typical cycle (Cycle #4) of a GA-CSI test (Test #6.3). ........................ 165
Figure 6.8 Cumulative oil production, oil production rate, and solvent–oil ratio
during a typical cycle (Cycle #4) of a GA-CSI test (Test #6.3). ............. 166
Figure 6.9 (a) Heavy oil production; and (b) Solvent gas production during the
blowdown and gasflooding slugs of the production period of a GA-CSI
test (Test #6.3). ..................................................................................... 167
Figure 6.10 Cumulative oil productions of Tests #6.3 (blowdown slugs only), and
#6.1 and #6.2. ....................................................................................... 168
Figure 6.11 Solvent injection rate at early, middle, and late stages of a GA-CSI test
(Test #6.3). ........................................................................................... 170
Figure 6.12 (a) Recovery factor; and (b) Solventoil ratio of the GA-CSI tests with
cylindrical models of different lengths. ................................................. 171
figure 6.13 Oil recovery factor of GA-CSI and CSI tests with the rectangular
physical model. ..................................................................................... 173
Figure 6.14 Residual oil saturation of (a) CSI (Test #6.2); and (b) GA-CSI tests
(Test #6.3). ........................................................................................... 174
Figure 6.15 Residual oil saturation of (a) CSI (Test #6.6); and (b) GA-CSI (Test
#6.7). .................................................................................................... 176
Figure 6.16 Pressure control scheme of PP-CSI. ...................................................... 178
Figure 6.17 Injection and production pressures data during a PP-CSI test. ............... 179
Figure 6.18 Evolution of the solvent chamber throughout a PP-CSI test: (a) Cycle
#2; (b) Cycle #4; (c) Cycle #8; and (d) Cycle #12. ................................ 181
Figure 6.19 Comparison of the oil recovery factor of PP-CSI and GA-CSI tests. ...... 183
Figure 6.20 Oil production from multiple pulses in different cycles of Test #6.8 ...... 184
xv
NOMENCLATURE
Notations a slope of a linear Pe profile
'a slope of a linear dimensionless diffusion coefficient profile
A, B coefficients
b intercept of a linear Pe profile
'b intercept of a linear dimensionless diffusion coefficient profile
c solvent concentration in the solvent-diluted heavy oil, vol.%
c* solvent concentration under a operating pressure, vol.%
cD dimensionless concentration, dimensionless
cmax maximum solvent concentration in a crude oil, vol.%
cmin minimum solvent concentration in a crude oil, vol.%
C modified dimensionless concentration, dimensionless
D diffusion coefficient, m2/s
Dapp apparent diffusion coefficient in the Das−Butler model, m2/s
DD dimensionless diffusion coefficient, dimensionless
F formation electrical resistivity factor
fo, fs weighted volume fractions of crude oil and solvent in Lederer’s equation, fraction
g gravity acceleration, m/s2
H model height, m
h vertical distance between an arbitrary point and the model bottom, m
k permeability, m2
L length of the horizontal section of a horizontal well running VAPEX, m
l length of a transition-zone segment, m
M Kummer’s function
N number of grids
Ns dimensionless number in the Butler−Morkys VAPEX model
Nτ number of substeps in a time step
P pressure, kPa
xvi
Pe Péclet number, dimensionless
q oil drainage rate, m3/s
qo stabilized oil production rate in the Butler−Mokrys/Yazdani-Maini model, m3/s
qin flowrate of solvent-diluted heavy oil entering into a transition zone segment, m3/s
qout flowrate of solvent-diluted heavy oil leaving from a transition zone segment, m3/s
Q cumulative oil production, m3
Qo cumulative oil production in Moghadam et al. model, m3/s
s Laplacian operator
S oil saturation, vol.%
S’ source/sink in the convection−diffusion equation
Soi initial oil saturation, vol.%
Sor residual oil saturation, vol.%
Swr residual water saturation, vol.%
t time, s
tD dimensionless distance
U transition-zone boundary moving velocity, m/s
V convection velocity, m/s
Vp pore volume, m3
Vs sand volume, m3
Vw water volume, m3
V Darcy flow rate of solvent-diluted heavy oil in the transition zone, m/s
W model width, m
w width, m
x x coordinate, m
xD dimensionless distance
y y coordinate, m
z transformed dimensionless distance
xvii
Greek Symbols
α coefficient of viscosity
β coefficient of viscosity
specific gravity
o, s specific gravities of crude oil and liquid solvent
δ transition-zone thickness, m
θ inclination angle of transition zone, degree
λ weight factor in Shu’s equation
μ viscosity of the solvent-diluted heavy oil, mPas
μo, μs viscosities of crude heavy oil and liquid solvent, mPas
ξ distance from the boundary between the solvent chamber and transition zone to an
arbitrary point in the transition zone, m
ξ0 location of the transition-zone boundary at the beginning of a time step, m
ξmax location of the transition-zone boundary next to the solvent chamber, m.
ξmin location of the transition-zone boundary next to the untouched heavy oil zone, m.
ξmv distance of a transition-zone segment moved over a time step, m.
ρ density of solvent-diluted heavy oil, kg/m3
ρo, ρs densities of crude oil and liquid solvent, kg/m3
τ time, s
ψ arbitrary constant
porosity, vol.%
cementation factor, dimensionless
xviii
Subscripts
Abbreviations
app apparent
D dimensionless
dew dew point
o oil
oi initial oil
or Residual oil
out outflow
i ith time interval
in inflow
max maximum
min minimum
mv movement
p pore
s solvent
τ time
ARC Alberta Research Council
CHOPS Cold Heavy Oil Production with Sands
CMG Computer Modelling Group
CPCSI Cyclic Production with Continuous Solvent Inejction
CSI Cyclic Solvent Injection
CSS Cyclic Steam Stimulation
CT Computer Tomography
DPDVA Dynamic Pendant Drop Volume Analysis
EOR Enhanced Oil Recovery
F-VAPEX Foamy Oil-Assisted Vapour Extraction
GA-CSI Gasflooding-Assisted Cyclic Solvent Injection
GEM Generalized Equation of State Model Reservoir Simulator
xix
Units
ISC In-Situ Combustion
OOIP Original-Oil-In-Place
RF Recovery Factor
SAGD Steam-Assisted Gravity Drainage
SAS Steam Alternating Solvent
SOR Solvent−Oil Ratio
SRC Saskatchewan Research Council
STARS Steam, Thermal and Advanced Reservoir Simulator
VAPEX Vapour Extraction
API American Petroleum Institute gravity
C Celsius
bbl barrel
cc cubic centimeter
cm centimeter
D Darcy
dm decimeter
g gram
h hour
kg kilogram
kPa kilopascal
m meter
m2/s square meter per second
m/s2 meter per square second
min minute
ml mililiter
MPa megapascal
mPas milipascal-second
s second
1
CHAPTER 1 INTRODUCTION
1.1 Heavy Oil Resources
Effective and economical recovery of unconventional heavy oil and bitumen
resources has become a key technical challenge due to the depletion of conventional
petroleum resources and the increase of hydrocarbon fuel demands. In comparison with
conventional crude oil, heavy oil and bitumen are much more viscous and heavier, and they
are characterized by high viscosities (i.e., higher than 100 mPas for heavy oil and 10,000
mPas for bitumen) and low API (American Petroleum Institute) gravities (i.e., lower than
20.0API for heavy oil and 10.0API for bitumen) [Speight, 1991].
In the world, the total crude oil resources are approximately 9−11 trillion bbls,
among which more than 2/3 are unconventional heavy oil and bitumen [Dusseault, 2001].
Out of the total eight trillion bbls of heavy oil and bitumen reserve, Canada and Venezuela
each possesses 2–3 trillion barrels. In Canada, heavy oil and bitumen resources are found in
Western Canada, mainly in Alberta and Saskatchewan with an estimated
original-oil-in-place (OOIP) of 2.5 trillion barrels [Petroleum Communication Foundation,
2000; Dusseault, 2001; Farouq Ali, 2003]. Most of western Canadian heavy oil and
bitumen deposits are located in the three major basins in northern Alberta: Athabasca, Cold
Lake, and Peace River.
1.2 Heavy Oil Recovery Techniques
In general, there are two kinds of heavy oil and bitumen recovery methods: open-pit
mining and in-situ methods [Butler and Yee, 2002]. Open-pit mining methods are used to
2
recover minable bitumen deposits that are less than 100 m deep [Petroleum
Communication Foundation, 2000]. It relies on massive earth-moving equipment and
processing facilities, and has limited future capacity since 80 percent of the oil sand
resources lie deep underground and are not accessible by open-pit mining. The latter
extraction methods include three categories: primary production techniques, thermal-based
techniques, and non-thermal-based techniques. These in-situ heavy oil recovery methods
currently rely on the injection of energy-intensive steam and large volumes of natural gas.
In most cases, only 5–10% of the original-oil-in-place (OOIP) can be recovered from
western Canadian reservoirs after primary and secondary oil recovery processes, such as
cold heavy oil production with sand (CHOPS) and waterflooding. Afterward, these
techniques become uneconomical due to reservoir pressure depletion and/or water
encroachment to the production well [Ivory et al., 2010]. Therefore, the latter two
enhanced oil recovery (EOR) techniques are resorted to produce the heavy oil and bitumen
reserves.
Thermal-based methods, such as steam-assisted gravity drainage (SAGD), cyclic
steam stimulation (CSS), and in-situ combustion (ISC) [Butler et al., 1981; Vittoratos et al.,
1990; Moore et al., 1995] can drastically reduce the crude oil viscosity by means of thermal
energy. Specifically, SAGD and CSS have achieved great success in heavy oil reservoirs
with a thickness larger than 10 m. However, many Canadian heavy oil reservoirs have thin
pay zones, for which the thermal-based methods become uneconomical due to large heat
losses to the overburden and underburden.
Solvent-based methods, such as solvent vapour extraction (VAPEX) [Butler and
Mokrys, 1991; Das, 1998], is not an apparent option because of its inefficient gravity
3
drainage and extremely low oil production rate. As another type of solvent-based
techniques, cyclic solvent injection (CSI) [Lim et al., 1995, 1996; Ivory et al., 2010; Firouz
et al., 2012] has emerged as a promising follow-up process of CHOPS in recent years.
1.3 Technical Challenges in Thin Heavy Oil Reservoirs
A large number of Canadian heavy oil reserves are located in thin reservoirs,
especially in Saskatchewan. Saskatchewan accounts for almost 62% of Canada’s total
heavy oil resources, including 1.7 billion m3 of proven and 3.7 billion m3 of probable
reserves. According to Reservoir Annual [Saskatchewan Energy and Mines, 2000] of the
province's proven initial heavy oil-in-place, 97% is contained in reservoirs with less than
10 m pay zones, and 55% is in reservoirs less than 5 m thick. Primary and secondary
methods combined recover less than 10% of the OOIP, on average. Hence, there is a strong
incentive for the development of appropriate oil recovery techniques, which will maximize
the recovery potential of these thin heavy oil reservoirs [Dong et al., 2006].
The heavy oil and bitumen recovery from these reservoirs with displacement or
thermal recovery processes is neither economically viable nor environmentally friendly
because of the accompanying losses of displacement fluid or energy to the overburden and
underburden. Besides, these methods require huge amounts of water and solvent gas and
vast surface facilities, and are inefficient in the frequently-encountered thin heavy oil
reservoirs. Therefore, it is necessary to develop proper recovery methods to maximize the
recovery potential of the profitability from these thin heavy oil reservoirs.
1.4 Solvent-Based EOR Techniques
In the literature, extensive studies have been conducted to explore the potential of
4
solvent-based EOR methods, including VAPEX and CSI. VAPEX is a direct experimental
and theoretical analog of SAGD. In the VAPEX process, gaseous condensable solvents,
such as propane and butane [Butler et al., 1995] in conjunction with non-condensable
carrier gases, such as methane and carbon dioxide [Talbi and Maini, 2003], are used to
extract heavy oil and bitumen from reservoir formations. The major oil recovery
mechanisms in this process consist of viscosity reduction through solvent dissolution and
possible asphaltene precipitation and gravity drainage of the solvent-diluted heavy oil. CSI
is basically a solvent huff-n-puff process. It is considered as a solvent-analog of CSS.
The potential advantages of solvent-based EOR methods over thermal-based EOR
methods are: (1) Cost-effectiveness. Solvent-based techniques do not involve large surface
facilities. Therefore, it saves the cost for steam generation equipment and the consequent
costs for operation and treatment of the produced wastewater. For example, VAPEX
requires only approximately 3% of the energy needed for SAGD for the same production
rate [Singhal, et al, 1997]. (2) Environmental friendliness. Solvent-based techniques
produce much less water than thermal-based techniques. Thereby, they would less possibly
cause the environment pollution by the produced wastewater. Moreover, greenhouse gas
emission would be greatly reduced since over 80% of the produced solvent can be captured
and reused in a solvent-based EOR process [Butler and Mokrys, 1991]. (3) Oil in-situ
upgrading. The heavier component of crude oil might be precipitated in the reservoir in the
process of solvent dissolution into heavy oil, which makes the heavy oil become lighter.
This is beneficial for the subsequent oil transportation and processing.
The major disadvantage of solvent-based EOR methods is its low oil production rate,
especially in some thin heavy oil reservoirs. For VAPEX, it is because of the slow mass
5
transfer and inadequate gravity drainage. For CSI, it might be due to the unproductive, long
injection and soaking periods and the relatively short production period.
1.5 Problem Statement and Research Objectives
1.5.1 Theoretical modeling of VAPEX
Theoretical modeling of VAPEX has not achieved as much progress as the physical
modeling in the past two decades. Existing analytical models are established on the basis of
some major assumptions for the heavy oilsolvent transition zone, such as constant
boundary moving velocity and steady-state mass transfer. They are unable to describe the
solvent chamber evolution. Numerical simulation models use grid sizes much larger than
the transition zone thickness (~1 cm), which makes it difficult for these models to capture
the heavy oil and solvent properties inside the transition zone.
1.5.2 Modeling of the mass transfer in CSI
CSI is a solvent huff-n-puff process. One of the differences between VAPEX and
CSI is that the operating pressure is cyclically decreased and increased in CSI, whereas it is
maintained at a constant value in VAPEX. Hence, in addition to molecular diffusion, the
heavy oil−solvent mixing process in CSI is influenced also by another mechanism,
convection. Convection describes the mass transfer through a bulk motion of the solvent
due to the pressure gradient in the CSI process. So far, few studies have been done to
describe the mass transfer process in CSI. Existing mass-transfer models for VAPEX are
based on Fick’s 2nd law and do not consider the effect of pressure gradient across the
transition zone. In addition, the diffusion coefficient or the dispersion coefficient in
existing models is usually assumed to be a constant, which is not true in the actual cases.
6
1.5.3 Performance improvement of VAPEX and CSI
The major limitation of the VAPEX process is its extremely low oil production rate,
especially in thin heavy oil reservoirs. This is caused by: (1) The small diffusion
coefficient; (2) Limited contact area between solvent and heavy oil; (3) ‘Concentration
shock’ [Ninniger and Dunn, 2008]; and (4) Inefficient gravity drainage. The first three are
inherent properties of the VAPEX process, resulting in a low mass transfer rate between
the solvent and crude heavy oil. In particular, the concentration shock makes it difficult for
the solvent to pass through the transition zone to dilute the fresh heavy oil. The inefficient
gravity drainage is due to the small inclination angle, especially in thin reservoirs.
Although CSI has stronger driving forces (solution-gas drive and foamy oil flow) for
heavy oil recovery, its technical limitations are as follows: (1) The solvent injection and
soaking periods are unproductive and long, whereas the oil production period is relatively
short. This leads to a low average oil production rate over the entire process. (2) The oil
production rate declines fast and most of the oil production occurs during the early stage of
the production period. This is because the solvent disengages from the oil due to pressure
depletion during the production period, which leads the oil to regain its high viscosity and
eventually lose its mobility. Hence, a considerable amount of solvent-diluted heavy oil
becomes motionless and remains in the reservoir at the end of the production period.
1.5.4 Research objectives
Aiming at the aforementioned technical issues with VAPEX and CSI, this thesis
wants to achieve the following objectives:
1. To develop a new 2D mathematical model to describe the solvent-chamber
evolution during the VAPEX process;
7
2. To develop a new mass-transfer model to study the effects of the pressure
gradient on the heavy oil−solvent mixing process during the CSI process;
3. To design new operating schemes to enhance the oil production rate of the
conventional VAPEX process; and
4. To design new operating schemes to enhance the performance of the
conventional CSI process.
1.6 Thesis Outline
This thesis is composed of seven chapters. Specifically, Chapter 1 gives an
introduction to the thesis research topic together with the purpose and scope of this study.
Chapter 2 provides an up-to-date literature review on the solvent-based EOR techniques,
such as VAPEX and CSI. Chapter 3 describes a new 2D mathematical model for the
solvent-chamber evolution during the VAPEX process. The mathematical model,
semi-analytical solution, and data analysis are presented in this chapter. Chapter 4 develops
a new convection−diffusion mass-transfer model to investigate the effect of the pressure
gradient on the heavy oil−solvent mixing process during the CSI process. Chapter 5
proposes a new modified VAPEX technique, namely foamy oil-assisted vapour extraction
(F-VAPEX). The experimental set-up, operating scheme, and data analysis of the
F-VAPEX process are presented in this chapter. Chapter 6 presents another a novel
technique, namely gasflooding-assisted cyclic solvent injection (GA-CSI). The special
operating scheme of GA-CSI and its experimental results are described and discussed.
Chapter 7 summarizes the major scientific findings of this thesis study and provides some
technical recommendations for future studies.
8
CHAPTER 2 LITERATURE REVIEW
2.1 Vapour Extraction (VAPEX)
VAPEX was first studied as a solvent-analogy of SAGD by Butler and Mokrys in
1989. In a typical VAPEX process, a gaseous solvent (typically a lighter hydrocarbon gas)
is injected into a reservoir formation through an upper horizontal injection well. The heavy
oil is diluted by the solvent in the transition zone, drained downward by gravity, and
produced from a lower horizontal well (Figure 2.1). Three zones are formed during this
process: a solvent chamber, an untouched heavy oil zone, and a transition zone in between.
The VAPEX process occurs in the following way: (1) Dissolution of solvent into oil at the
transition zone; (2) Diffusion of solvent molecules in the bulk heavy oil; (3) Reduction of
heavy oil viscosity as the solvent concentration increases; (4) Above a critical
concentration, asphaltene precipitation takes place, further reducing the oil viscosity; and
(5) Due to the effects of Steps #34 and the difference in density between the liquid oil and
gaseous solvent, solvent-diluted heavy oil drains downward along the transition zone to the
production well by gravity and capillary imbibitions.
9
[http://www.japex.co.jp]
Figure 2.1 The VAPEX heavy oil recovery process.
10
2.1.1 Physical modeling of VAPEX
A summary of VAPEX laboratory experiments conducted by several research
groups in the past two decades is presented in Table 2.1–5. It includes several major
research groups in VAPEX in Canada, such as Bulter’s group, Maini’s group, and Gu’s
group. The research topics are mainly the traditional VAPEX process. This section first
introduces the previous research work on VAPEX group by group and then summarizes
some major technical aspects of VAPEX that are of interest in this thesis.
Table 2.1 shows the experimental results achieved by Dr. Butler’s group. Butler and
Mokrys [1989, 1991, 1993] used toluene to extract Athabasca and Suncor bitumen samples
in a Hele−Shaw cell. They found that at low permeabilities, oil rate is a linear function of
the square root of the permeability. At high permeabilities, the drainage rate is nonlinear
and approaches asymptotically a constant value that is independent of the permeability.
Das and Butler [1995] conducted VAPEX tests to examine the effect of bottom water on
the VAPEX performance. It was observed that the water injection in a small quantity along
with the solvent and non-condensable gas enhances the extraction rate at the initial stage.
The solvent-diluted heavy oil is efficiently displaced by the injected water which was the
wetting fluid in most oil reservoirs. Major parameters affecting VAPEX performance were
thoroughly studied by Butler and Jiang [1996, 1997] in order to develop optimum
operating conditions for high oil production rates with economical solvent requirements.
The parameters investigated were temperature, pressure, solvent injection rates, pure
solvent type, mixed solvent, well spacing, and well configurations etc. It was found that
propane works better than butane and a mixture of propane and butane works as well as
propane alone. A wider lateral well spacing allows a higher oil production rates and makes
11
the process more economical. A high start-up solvent-injection rate followed by a reduced
rate performs better than a constant solvent-injection rate.
Table 2.2 shows the VAPEX experimental results of Maini’s group. Boustani and
Maini [2001] undertook a number of experiments with a Hele−Shaw cell to identify the
main process that governs the interfacial mass transfer of solvent into bitumen. The
apparent diffusion coefficient [Das and Butler, 1995] is based on the correlations
developed by Hayduk et al. [1976] as well as the experimental data. It was found that Das
and Butler’s correlations tend to overestimate the diffusion coefficient and underestimate
the overall mass-transfer dispersion coefficient in porous media. Talbi and Maini [2003]
studied a CO2-based VAPEX process for tar sand reservoirs. It was found from their
experimental results that CO2−propane mixture shows better performance in comparison
with the methane−propane mixture at a high operating pressure. The use of CO2 instead of
methane at lower operating pressures is thus justified.
Karmaker and Maini [2003] evaluated the VAPEX process for a reservoir with a
small gas cap. They found that a small gas cap is helpful for the application of VAPEX for
heavy oil recovery. A 1C increase in temperature could increase oil production by 2%.
The oil production rate almost doubled when the original oil viscosity is lowered by 15
times. A long delay in the start of oil production occurs for the increased lateral distance
between the injector and producer. They reinvestigated the oil drainage rate and examined
the scale-up methods for the VAPEX process with three physical models of different sizes.
It is found the grain size distribution does not make a difference on the oil drainage rate,
whereas the model height significantly increases the convective dispersion and the
consequent oil rate. Also they believed that higher oil rates than predicted were possible on
12
the basis of the results from Hele−Shaw cell experiments and the available scale-up
method. Yazdani and Maini [2004, 2005] designed a new cylindrical model to overcome
the limitation of the rectangular models at higher pressures. The annular space between
two cylindrical pipes constructs the slice-type sand-packed models. It was found that the
stabilized oil drainage rates from their new cylindrical models agree perfectly with those
from the rectangular ones. The new models could also save laboratory space and
construction costs in comparison with flat models. Etminan and Maini [2007] evaluated the
effect of connate water on the VAPEX performance. They found the presence of connate
water causes faster spreading of the solvent vapour chamber in the lateral direction and
tends to increase the thickness of the mixing zone, which seems to be driven by capillary
fingering. In addition, the mobile water increases the oil production rate in the initial stage
and decreases it in the late stage of VAPEX. Moreover, oil deasphalting was found to be
more significant in the presence of connate water.
Zadeh et al. [2008] used a fixed CO2−propane mixture to produce the Athabasca
bitumen. They found it important to control the composition of the injected gas mixture to
avoid a multiple liquid-phase formation. They mapped experimentally and theoretically the
compositional change by using an EOS model during the VAPEX test. Haghighat and
Maini [2010] studied the effect of asphaltene precipitation on VAPEX performance to
determine whether the beneficial effects of asphaltene precipitation would outweigh the
detrimental ones. They found that at higher pressures, the produced oil was substantially
deasphalted but the viscosity was not drastically reduced as expected, i.e., in-situ
deasphalting did not lead to a higher production rate. In addition, the formation damage
caused by asphaltene precipitation and deposition seems irreparable through the huff and
13
puff injection of toluene. However, a solvent mixture of propane and toluene was found to
be successful in increasing the oil production rate and upgrading the oil quality.
Table 2.3 shows the experimental results obtained by Dr. Gu’s group. Zhang et al.
[2007] carried out a series of VAPEX experiments with a visual rectangular sand-packed
high-pressure physical model, which can be used to visualize the entire VAPEX process,
throughout the vapour chamber rising, spreading, and falling phases. They predicted the oil
production rate by using the modified Butler−Mokrys analytical model and found a good
match with the experimental data. Moghadam et al. [2008] established a new theoretical
model on the basis of the incline angle of the transition zone, to predict the cumulative oil
production rate. The transition zone was assumed to have two straight-line boundaries with
a constant thickness during the VAPEX process. The adjustable transition-zone thickness
keeps almost constant during each VAPEX test and in general, it increases with the
decrease in the permeability of the VAPEX physical model. Furthermore, their results
showed that the horizontal spreading velocity of the solvent chamber is reduced with time
during the spreading phase, thus the heavy oil production rate during this phase declines
with time as the VAPEX process proceeds. Finally, the theoretical predictions showed that
the falling velocity of the solvent chamber is extremely low during its falling phase and
decreases with time as well.
Table 2.4 shows the experimental results obtained by ARC. Cuthiell et al. [2003]
implemented a series of top-down solvent injection experiments under varying conditions,
and the fluid movement was monitored by a CT scanner. They observed that oil production
rate becomes unstable before solvent breakthrough (BT), after which the displacement
remains steady. They also conducted numerical simulation to predict the oil production
14
rate, the simulated BT time, post-BT oil production rate, and the general character of the
fingering. They found that the experimental data was matched after a certain amount of
physical dispersion is introduced. Frauenfeld et al. [2006] conducted a series of VAPEX
experiments with bottom water. The experimental oil production rates were negatively
impacted by the continuous low permeability layers and initial gas content. The small
diffusivity requires that the surface area exposed to solvents be increased in order to
achieve a commercial oil recovery rate. The bottom water offers a large oilwater contact
area between the wells provides the contact for solvent. Frauenfeld et al. [2007] studied
thermal VAPEX with live heavy oil. They run three experiments to evaluate the VAPEX
process in which the oil had significant initial methane saturation. After solvent injection,
steam was injected into the production well to reflux the solvent. Test results indicate that
the live oil inhibits solvent absorption and hence oil production rates. However, a properly
designed solvent system could produce oil at a reasonable rate. It was also observed that
solvent can be recycled more easily by heating the production well with either electrical or
steam heat. A fairly local heated zone around the wellbore was formed through direct
wellbore heating. Asphaltene precipitation was not significant in these experiments. Zhao
et al. [2005] attempted to combine the advantages of SAGD and VAPEX together to
minimize the energy input in heavy oil and bitumen recovery. They conducted
steam-alternating-solvent (SAS) experiments and the corresponding numerical simulation.
Their results showed that the energy input in the SAS process was 47% lower than that of
the SAGD process for recovering the same amount of oil. In addition, the post-run analysis
revealed that asphaltene precipitation occurred in the porous media. Table 2.5 shows the
VAPEX test results achieved by various researchers who are not mentioned above.
15
Table 2.1 VAPEX experimental studies by Butler’s group.
No. AuthorHeavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RFkg/m3/°C mPas/°C cmcmcm % D °C kPa cc/h h g/h %
1
Butler and
Mokrys[1991, 1993]
Tangleflags 979/15.6 10000/20 Hele−Shaw square 770.068 — 100 1356 C3+hot H2O 36 1034 1034 — 41 97 2 Tangleflags 979/15.6 10000/20 Hele−Shaw square 770.068 — 100 1356 C3+hot H2O 44 1379 1379 — 49 86 3 Tangleflags 979/15.6 10000/20 Hele−Shaw square 770.068 — 100 1356 C3+hot H2O 45 1241 1241 — 60 89 4 Tangleflags 979/15.6 10000/20 Hele−Shaw square 770.068 — 100 1356 C3+hot H2O 47 1379 1379 — 62.5 90 5 Tangleflags 979/15.6 10000/20 Hele−Shaw square 770.068 — 100 1356 C3+hot H2O 55 1724 1724 — 63 84 6 Tangleflags 979/15.6 10000/20 sandpack rectangle 70223.5 Hele-Shaw 100 81030 C3 20 621 621 9 61.11 — 7 Tangleflags 979/15.6 10000/20 sandpack rectangle 70223.5 Hele-Shaw 100 81030 C3 22.8 689 689 9 82.20 — 8 Tangleflags 979/15.6 10000/20 sandpack rectangle 70223.5 Hele-Shaw 100 81030 C3 23-30 827 827 9 101.11 — 9 Tangleflags 979/15.6 10000/20 sandpack rectangle 70223.5 Hele-Shaw 100 81030 C3 20 896 896 9 64.44 — 10 Tangleflags 979/15.7 10000/21 sandpack rectangle 70223.5 glass beads 30.9 830 C3+steam 31 1108 1108 8.5 33.7 — 1
Das and
Butler [1995]
Peace River — 138300/20 sandpack rectangle70.620.53.23050 sand 31 43.5 C4+N2 21.5 814 25.5+1.2 13.3+8.0 — 2 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 31 194.4 C4+N2 22 779 19.4+1.6 21 46.9+36 68 3 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 35 191.5 C4+N2 21.7 779 12.5+3 22 28.2 57 4 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 33 191.1 C4+N2 21.2 779 11.4+3.4 33 28+18 5 Cold Lake — 65000/20 sandpack rectangle70.620.53.22030 sand 33 186.8 C4+N2 21.6 779 12+3.7 27 9.5 44 6 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 32 192.4 C4+N2 21.6 434 24.8+2.3 21 40.5 — 7 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 37 195.8 C4+N2 21.8 779 9.5+1.5 35 22.4 — 8 Lloydminster — 9350/20 sandpack rectangle70.620.53.22030 sand 33 194 C4+N2 21.5 959 15+1 29.5 50+25 — 1
Butler and
Jiang [1996]
Atlee Buffalo 969 1140/27 sandpack rectangle 13410.23.8 2030 sand3335 217 n-C4 21 204 10 — 19.4 70 2 Atlee Buffalo 969 1140/27 sandpack rectangle 13410.23.8 2030 sand3335 217 n-C4 27 204 10 — 34 80 3 Atlee Buffalo 969 1140/27 sandpack rectangle 13410.23.8 2030 sand3335 217 n-C4 27 204 5 — 31.4 80 4 Atlee Buffalo 969 1140/27 sandpack rectangle 13410.23.8 2030 sand3335 217 n-C4 27 204 10 — 25.4 80 5 Lloydminster 978 7000/20 sandpack rectangle 35.622.933 2030 sand3537 217 n-C4 20-21 124 — 17.5 33.1 — 6 Lloydminster 978 7000/20 sandpack rectangle 35.622.933 2030 sand3537 217 n-C4 20-21 124 — 15 23.8 — 7 Peace river — 930000/20 sandpack rectangle 35.622.933 2030 sand3537 43.5 n-C4 20-21 124 8.71 14 10.73 — 8 Peace river — 930000/20 sandpack rectangle 35.622.933 2030 sand3537 43.5 n-C4 20-21 124 — 27 — —
16
Table 2.2 VAPEX experimental studies by Maini’s group.
No. Author Heavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RF kg/m3/C mPas/°C cmcmcm % D °C kPa cc/h h g/h %
1
Boustani and
Maini [2001]
Dover 1027 543800/20 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 20.5 875 — 20.43 — 51.682 Dover 1027 543800/20 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 20.5 875 — 20.79 — 48.893 Dover 1027 543800/20 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 20.5 875 — 18.66 — 40.934 Panny 970
51767/10 8971/20
bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 10.5 875 — — — — 5 Panny 970 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 10.5 875 — 7.36 — 40.356 Panny 970 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 10.5 875 — 8.78 — 43.797 Panny 970 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 23 875 — 7.09 — 48.728 Panny 970 bulk rectangle7.47.60.254 Hele-Shaw 100 5376 C3 19.5 875 — 7.66 — 47.691 Talbi
and Maini [2003]
— 982.6 3300/24 sandpack annular 30.48
(30.73, 27.2)
12-16 glass beads 35 640 C3+CO2 24 1723 20 9 58.5248.542 — 983.6 3300/25 sandpack annular 12-16 glass beads 35 640 C3+CH4 24 1723 20 9 61.1651.213 — 984.6 3300/26 sandpack annular 12-16 glass beads 35 640 C3+CH4 24 1723 20 9 57.1432.454 — 985.6 3300/27 sandpack annular 12-16 glass beads 35 640 C3+CO2 23 17230.04 9 92.0243.451
Karmakerand
Maini [2003]
— 998 40000/10 9000/20
sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 104840/110/7
8 16.11 — 2 — 998 sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 19 1048 8 19.08 — 3 — 998 sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 930 50/1
10/78 16.04 —
4 — 998 600/20 sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 1048 8 37.76 — 5 — 998
40000/10 9000/20
sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 104810/8 8 10.29 — 6 — 998 sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 104840/1 8 15.71 — 7 — 998 sandpackrectangle15.367.33.2 16-20 US mesh 38 330 C3 10 104845/8 8 9.82 — 8 — 980 18500/15 sandpackrectangle 7.511.32.5 12-16 glass beads 40 640 n-C4 15 69 — 8 7.91 74.679 — 980 18500/15 sandpackrectangle 7.511.32.5 16-20 sands 39 330 n-C4 15 69 — 8 6.91 65.2310 — 980 18500/15 sandpackrectangle 7.511.32.5 20-30 sands 37 220 n-C4 15 69 — 8 4.14 39.0811 — 980 18500/15 sandpackrectangle 1522.52.5 12-16 glass beads 40 640 n-C4 15 69 — 8 27.1564.0712 — 980 18500/15 sandpackrectangle 1522.52.5 16-20 sands 39 330 n-C4 15 69 — 8 18.7044.1313 — 980 18500/15 sandpackrectangle 1522.52.5 20-30 sands 37 220 n-C4 15 69 — 8 16.4538.82
17
Table 2.2 VAPEX experimental studies by Maini’s group (Contd’)
No. Author Heavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RF kg/m3/°C mPas/°C cmcmcm % D °C kPa cc/h h g/h %
1 Yazdani
and Maini [2004, 2005]
Dina 982.6 18650/9 sandpack rectangle 30452.5 1216 beads 37 640 C4 9 68 0.11 8 16.55 35 2 Dina 982.6 18650/9 sandpack rectangle 30452.5 1620 beads 36 330 C4 9 68 0.10 8 12.26 24 3 Dina 982.6 18650/9 sandpack rectangle 30452.5 2030 geads 35 220 C4 9 68 0.11 8 9.69 18 4 Dina 982.6 18650/9 sandpack cylindrical30(42.3, 36.3) 1216 beads 37 640 C4 9 40 0.10 8 17.17 43 5 Dina 982.6 18650/9 sandpack cylindrical30(42.3, 36.3) 1620 beads 36 330 C4 9 40 0.11 8 12.03 33 6 Dina 982.6 18650/9 sandpack cylindrical30(42.3, 36.3) 2030 beads 35 220 C4 9 40 0.11 8 9.43 23 1 Zedah
and Maini [2008]
Athabasca 1007/20 148000/20 sandpack annular 30.48
(30.73, 27.2)
1214 beads 35.7 640 C3+CO2 21.1 1974 2.05121.55 0.005 37.3 2 Athabasca 1007/20 148000/20 sandpack annular 1214 beads 35.7 640 C3+CO2 20.8 2015 — 122.42 0.005 38.7 3 Athabasca 1007/20 148000/20 sandpack annular 1214 beads 35.7 640 C3+CO2 20.7 3406 2.56 157 0.006 53.6 4 Athabasca 1007/20 148000/20 sandpack annular 1214 beads 35.7 640 C3+CO2 20.8 784 6.36 48.24 0.017 43.5 1
Etminan [2007]
Frog lake 987.5/22.518600/22.5 sandpack rectangle 67.515.23.1 120140 sand35.18 10 n-C4 30 100 — 100 15.55 48 2 Frog lake 987.5/22.518600/22.5 sandpack rectangle 67.515.23.1 120140 sand33.29 10 n-C4 42 100 — 100 13 41 3 Frog lake 987.5/22.518600/22.5 sandpack rectangle 67.515.23.1 120140 sand32.78 10 n-C4 61 100 — 100 10.13 32 4 Frog lake 987.5/22.518600/22.5 sandpack rectangle 67.515.23.1 120140 sand32.79 10 n-C4 60 100 — 100 12.55 38 1
Haghighatand Maini
[2010]
Ekl Point 987.5/22 27500/22 cylindrical rectangle
30.48
(30.73, 27.20)
140200 sand36.42 2.7 C3 20 814 — 380 1.23 — 2 Ekl Point 987.5/23 27500/23 cylindrical rectangle 140200 sand34.24 2.7 C3 20 850 — 380 1.09 — 3 Ekl Point 987.5/24 27500/24 cylindrical rectangle 140200 sand34.71 2.7 C3+toluene 20 850 — 370 — — 4 Ekl Point 987.5/25 27500/25 cylindrical rectangle 140200 sand36.44 2.7 C3+toluene 20 variable — 390 — — 5 Ekl Point 987.5/26 27500/26 cylindrical rectangle 140200 sand 37.7 2.7 C3 20 750 — 380 1.07 — 6 Ekl Point 987.5/27 27500/27 cylindrical rectangle 140200 sand39.93 2.7 C4 20 200 — 400 1.38 —
18
Table 2.3 VAPEX experimental studies by Gu’s group.
No. Author Heavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RFkg/m3/°C mPas/°C cmcmcm % D °C kPa cc/h h g/h %
1
Zhang et al.
[2007]
Lloydminster 988 24137/20 sandpackrectangle 40102 2030 Ottwa 36.8 441 C4 21 240 — 49.5 3.89 75 2 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 37.5 132 C3 21 240 — 98 1.77 67 3 Lloydminster 988 24137/20 sandpackrectangle 40102 2030 Ottwa 36.2 438 C3 22.5 500 — 101 1.26 46 4 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 36.8 158 C3 23.3 500 — 179.5 0.87 61 5 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 37.4 418 C3 23.4 600 — 54 2.84 56 6 Lloydminster 988 24137/20 sandpackrectangle 40102 2030 Ottwa 35.4 417 C3 23.5 800 — 25 4.76 64 7 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 35.4 122 C3 23.2 800 — 59 2.85 63 8 Lloydminster 988 24137/20 sandpackrectangle 40102 2030 Ottwa 35.8 424 C3 23 900 — 58.75 3.54 73 9 Lloydminster 988 24137/20 sandpackrectangle 40102 2030 Ottwa 35.3 410 C3 23 900 — 78.5 2.1 62 10 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 36.7 143 C3 23.6 918 — 21.33 8.7 76 11 Lloydminster 988 24137/20 sandpackrectangle 40102 3050 Ottwa 36.1 118 C3 23.41050 — 54.5 1.94 — 12 Lloydminster 988 120000/20 sandpackrectangle 40102 5070 Ottwa 30.15 7 C3 20 300 — 72 0.11 — 13
Moghadamet al.
[2008]
Lloydminster 978 11900/20 sandpackrectangle 40102 2030 Ottwa 32.5 310 C3 20.8 854 — 13.5 16.96 — 14 Lloydminster 978 11900/20 sandpackrectangle 40102 3050 Ottwa 32.9 310 C3 20.8 854 — 14 4.08 — 15 Lloydminster 978 11900/20 sandpackrectangle 40102 30v50 Ottwa 33.1 103 C3 20.8 854 — 53 — — 16 Lloydminster 978 11900/20 sandpackrectangle 40102 4060 Ottwa 35.4 96 C3 20.8 854 — 103 3.31 — 17 Lloydminster 978 11900/20 sandpackrectangle 40102 6080 Ottwa 35.7 49 C3 20.8 854 — 55.5 1.62 — 18 Lloydminster 978 11900/20 sandpackrectangle 40102 80100 Ottwa 36.3 25 C3 20.8 854 — 35.5 1.12 — 19 Lloydminster 978 11900/20 sandpackrectangle 40102 80100 Ottwa 36.2 16 C3 20.8 854 — 52 — — 20 Lloydminster 978 11900/20 sandpackrectangle 40102 80100 Ottwa 35.2 15 C3 20.8 854 — 63 0.56 — 21 Lloydminster 978 11900/20 sandpackrectangle 40102 80100 Ottwa 35.2 4.5 C3+C1 24 307 20 70 0.96 —
19
Table 2.4 VAPEX experimental studies by ARC.
No. Author Heavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RF kg/m3/°C mPas/°C cmcmcm % D °C kPa cc/h PV g/h %
1 Cuthiell
et al. [2003]
Lloydminster — 5500/25 sandpackrectangle 25302.8 2040 silica — 90 toluene 25 — 40 0.54 18.3 — 2 Lloydminster — 5500/25 sandpackrectangle 25302.8 2040 silica — 90 toluene 26 — 10 0.58 4.46 — 3 Lloydminster — 5500/25 blend rectangle 25302.8 2040/5070 blend — 88 toluene 27 — 10 0.98 3.46 — 4 Lloydminster — 5500/25 field rectangle 25302.8 Rash lake sand — 8 toluene 28 — 10 1.08 1.3 — 5 Lloydminster — 5500/25 sandpackrectangle 25302.8 2040 silica — 90 toluene 29 — 100 1.44 17.7 — 1
Frauenfeld et al.
[2006, 2007]
Lloydminster — 23000/20 sandpackrectangle 902010 — 33.8 250 C1+C2+C3 15180 3400 20 26.00 32.2 1 2 Lloydminster — 23000/20 sandpackrectangle 902010 — 33.8 250 C2 15180 3400 36 13.40 148 31.73 Lloydminster — 39000/20 sandpackrectangle 902010 — 33.8 250 C2 20240 3600 30 15.00 150 36.94 Kerrobert 994.1/20 50000/20 sandpackrectangle 303010 — 35 400 n-C4 20 100 174 13.12 26 61.65 Kerrobert 994.1/21 50000/21 sandpackrectangle 303010 — 35 4 n-C4 20 100 560.3 189.0 1.18 47.46 Kerrobert 994.1/22 50000/22 sandpackrectangle 303010 — 35 400/90 n-C4 20 100 157.6 21.30 9.31 37 7 Kerrobert 994.1/23 50000/23 sandpackrectangle 303010 — 35 400/90 n-C4 20 100 87.53 13.50 25.4 62 8 Kerrobert 994.1/24 50000/24 sandpackrectangle 303010 — 35 400 n-C4 20 100 318.9 13.50 16.65 40
1 Zhao et al.
[2005]
Northern Alberta — 10000 sandpackrectangle 248010 Ottwa 33 115 C3+steam 218 2200
1 +
129.4 12 288 58.7
20
Table 2.5 VAPEX experimental studies by other research groups.
No. Author Heavy Oil Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Solvent
T P qs t qo RF kg/m3/°C mPas/°C cmcmcm % D °C kPa cc/h h g/h %
1 Lim et al.
[1995]
Cold lake — 100000/25 sandpack rectangle 474227 — 32.8 80 C3 45 830-1000 — 9 912.94 47 2 Cold lake — 100000/26 sandpack rectangle 474227 — 35 20 C2 20 2800-4000 — 100 115.66 62 3 Cold lake — 100000/27 sandpack rectangle 474227 — 35 110 C2 20 3000-3900 — 75 119.39 48 1
Hadil [2009]
Athabasca 1001/22 225000/22 sandpack cylinder 25 (45, 35) 3040 38 204 C3 70 690 — 3 39.00 — 2 Athabasca 1001/22 225000/22 sandpack cylinder 25 (45, 35) 4050 38 102 C3 70 690 — 3 31.00 — 3 Athabasca 1001/22 225000/22 sandpack cylinder 25 (45, 35) 5070 38 51 C3 70 690 — 3 21.00 — 1
Rezaei [2011]
— 960/25 9231/25 sandpack circular 295
glass beads
40 500 C4 70 1030 — 4 — 55.6 2 — 960/25 9231/25 sandpack circular 295 40 500 C4 80 1030 — 4 — 52.6 3 — 960/25 9231/25 sandpack circular 185 30 500 C4 98 1400 — 6 — 94.5 4 — 960/25 9231/25 sandpack circular 265 30 500 C4 98 1500 — 12 — 72.1 5 — 960/25 9231/25 sandpack circular 105 30 500 C4 98 1600 — 8 — 62.3 6 — 960/25 9231/25 sandpack circular 175 30 500 C4 112 1500 — 7 — 45 7 — 960/25 9231/25 sandpack circular 175 30 500 C4 108 1600 — 8 — 64.5 8 — 960/25 9231/25 sandpack circular 295 40 500 C3 90 1500 — 4 — 55.3 9 — 960/25 9231/25 sandpack circular 155 30 500 C3 85 1500 — 4 — 53.7
10 — 960/25 9231/25 sandpack circular 175 30 500 C3 67 1500 — 4 — 47.8 14 — 960/25 9231/25 sandpack circular 275 30 500 C3 53 1500 — 10 — 60.3 15 — 960/25 9231/25 sandpack circular 205 30 500 C3 52 1500 — 10 — 65.5 16 — 960/25 9231/25 sandpack circular 175 30 500 C3 54 1650 — 6 — 43.3 17 — 960/25 9231/25 sandpack circular 185 30 500 C3 53 1450 — 8 — 74.6 18 — 960/25 9231/25 sandpack circular 195 30 2400 C3 52 1450 — 8 — 56.9 19 — 960/25 9231/25 sandpack circular 155 30 2400 C3 54 1650 — 7 — 40.4 20 — 960/25 9231/25 sandpack circular 155 Berea
core
23 350 C3 53 1500 — 48 — 27.5 21 — 960/25 9231/25 sandpack circular 155 21 350 C4 98 1350 — 28 — 44.4 22 — 960/25 9231/25 sandpack circular 305 21 350 C3 53 1600 — 360 — 41.2
21
Solvent chamber evolution
Zhang et al. [2007] conducted a series of laboratory-scale VAPEX tests to study the
solvent chamber evolution under different operating conditions. The evolution of the
solvent vapour chamber was roughly divided into four stages: the initial solvent chamber
formation period and the solvent chamber rising, spreading, and falling phases. Butane and
propane were used as two respective solvents to recover a Lloydminster heavy oil sample
at a room temperature and different pressures. Their physical model was packed with
Ottawa sands of different mesh sizes of 20−30 and 30−50. Some representative digital
images were taken at the end of the three phases. First, the initial solvent chamber was
formed around the injector after the solvent was dissolved into the heavy oil and some
diluted heavy oil was produced. Then the solvent chamber rising phase started from the
initially formed solvent chamber until it reached the top of the physical model. As can be
seen in Figure 2.2a, in the spreading phase, the solvent chamber spreads laterally and
finally reaches the upper left-hand and right-hand corners of the physical model, as shown
in Figure 2.2b. Afterward, the solvent chamber kept falling down until the oil production
rate became extremely low. Figure 2.2c shows the solvent chamber profile at the end of its
falling phase. In terms of time and oil production, the spreading and falling phases take the
longest periods and contribute more than 80% of the oil production. Therefore, the solvent
chamber spreading and falling phases are the focus of the mathematical modeling in the
next chapter.
22
(a)
(b)
(c)
Figure 2.2 Solvent vapour chamber profiles at the end of (a) Rising phase; (b)
Spreading phase; and (c) Falling phase [Zhang, et al., 2006].
23
Operating pressure
The operating pressure is a crucial factor that affects the heavy oil production rate in
the VAPEX process because the solvent solubility is strongly dependent on the operating
pressure. As one of the major factors for inducing asphaltene precipitation, the operating
pressure influences oil production rate significantly. It was reported that the optimum
operating pressure was set close to but lower than the solvent vapour/dew point pressure to
obtain a higher oil production rate [Butler and Mokrys, 1991; Das and Butler, 1998; Butler
and Jiang, 2000; Boustani and Maini, 2001].
Das and Butler [1995] investigated the effect of the operating pressure on the heavy
oil production rate in the VAPEX process. They tested two different pressures of Pinj = 779
and 434 kPa by using butane as an extracting solvent and nitrogen as a carrier gas to
increase the operating pressure. It was found the operating pressure does not have a
significant effect on the oil production rate if a gas mixture is used to extract heavy oil.
Butler and Jiang [2000] tested Pinj = 30, 185, and 300 psig at a temperature of 27C
with butane, propane, and the mixture thereof as the extracting solvents, respectively. It
was observed that for the first four hours, the two experiments gave almost the same oil
production rate, which was due to the initial communication between the injector and the
producer. During the solvent chamber spreading phase, the experiment at a lower operating
pressure gave a higher oil production rate than that at a higher operating pressure. The
average oil production rate over the entire experiment was reduced by approximately 8% at
an increased operating pressure. This is probably because the exacting solvent became less
gaseous at the increased operating pressure.
24
Well configuration
The well configuration represents the spatial placement of the injector and producer
placement during the VAPEX heavy oil production process. Butler and Jiang [2000]
conducted an experimental study to investigate the effect of a well configuration on the oil
production rate. Two well configurations were attempted: (1) The injector is closely
located right above the producer; (2) The injector is located horizontally apart from and
above the producer. It is found that the cumulative oil production in the latter case is higher
than that in the former case, even though the oil production rate for the latter case at the
very beginning of the VAPEX test was lower. It was concluded that a wider well spacing is
more beneficial to enhancing the contact area between the solvent vapour and oil so as to
increase the oil production rate. Field-scale well spacing of the order of 100−200 m is
feasible for the situation considered.
2.1.2 Mass transfer modeling of VAPEX
Diffusion equation
The most important mechanism of VAPEX is the significant oil viscosity reduction
through sufficient solvent dissolution, which is actually a mass-transfer process between
the solvent and heavy oil. Fick’s 2nd Law [Fick, 1955] is applied to describe the dissolution
of solvent into a crude heavy oil:
c cDt x x
, (1.1)
where, c is the solvent concentration in heavy oil, vol.%; D is the diffusion coefficient, m2/s;
x is the space variable, m; t is the time variable, s.
25
Diffusion coefficient
Diffusion coefficient is a transport property that is required to calculate the
mass-transfer rate between the solvent and heavy oil due to molecular diffusion. There are
two categories of diffusion coefficients in the literature: constant value and variable value.
A diffusion coefficient can be assumed to be a constant value when the solubility of the
solvent in heavy oil is not high under the test conditions. Based on this assumption,
diffusion coefficients of gaseous solvents such as methane, propane, and carbon dioxide
were measured by using the so-called pressure decay method [Schmidt, 1985; Upreti and
Mehrotra, 2000, 2002; Tharanivasan et al., 2006], the dynamic pendant drop volume
analysis (DPDVA) method [Yang and Gu, 2006], as well as the modified pressure decay
method [Etminan et al., 2010]. Their measured values are shown in Table 2.6.
Hayduk and Cheng [1971] conducted extensive experimental studies on the
diffusion coefficients of ethane in normal hexane, heptanes, octane, dodecane, and
hexadecane at 25C, and of carbon dioxide in hexadecane at 25 and 50C. They found that
the diffusion coefficient of a solvent depended on the mixture viscosity, which could be
commonly expressed as:
D , (1.2)
where, α and β are constants depending on the crude oil and solvent properties as well as
the operating conditions; is the viscosity of oil−solvent mixture, mPas. β is less than
unity.
26
Table 2.6 Comparison of the measured diffusion coefficients of CO2, CH4, C2H6 and
C3H8 in different heavy oil and bitumen samples.
Solvent Crude oil Pressure (MPa)
Temperature (C)
Viscosity (mPas)
Diffusivity (10−9 m2/s)
CO2 Athabasca1 5.0 20 361,700 at 20C 0.28 Athabasca2 3.1−4.1 25 767 at 80C 0.16−0.22 Athabasca3 4.0 25 821,000 at 25C 0.12−0.20 Llyodminster4 3.5−4.2 23.9 20,267 at 23.9C 0.46−0.55 Llyodminster5 2.0−6.0 23.9 23,000 at 23.9C 0.22−0.55 Athabasca6 3.2 75 100,000 at 23.9C 0.5 CH4 Athabasca3 4.0 25 224,500 at 25C 0.08−0.11 Athabasca3 4.0−8.0 25 821,000 at 25C 0.06−0.08 Llyodminster4 4.9−5.0 23.9 20,267 at 23.9C 0.21−0.22 Llyodminster5 6.0−14.0 23.9 23,000 at 23.9C 0.12−0.19 Dodecane6 3.5 45, 65 1.34 at 15.6C 4.22−5.28 C2H6 Athabasca3 4.0 25 821,000 at 25C 0.21−0.38 Llyodminster1 1.5−3.5 23.9 23,000 at 23.9C 0.13−0.77 C3H8 Llyodminster5 0.4−0.8 23.9 20,267 at 23.9C 0.49−0.79 Llyodminster5 0.4−0.9 23.9 23,000 at 23.9C 0.09−0.68
Note: 1— Schmidt [1989] 2— Upreti and Mehrotra [2000] 3— Upreti and Mehrotra [2002] 4— Tharanivasan [2004] 5— Yang and Gu [2006] 6— Etminan et al. [2010]
27
The diffusion coefficients of propane in hexane, heptanes, octane, hexadecane,
n-butanol, and chorobenzene at P = 100 kPa and T = 25C and in n-butanol and
chlorobenzene at 0 and 50C were measured by using the steady-state capillary cell method
[Hayduk et al., 1973], and their results showed the following correlation:
10 0.5450.591 10D (for propane). (1.3)
Das and Butler [1996] applied the general correlation proposed by Hayduk and
Cheng [1971] to determine the values of α and β in Eq. (1.2). Based on their ten VAPEX
experimental tests conducted in the ranges of P = 820−1,160 kPa and T = 21−35C, the
correlations for propane and butane in Peace River bitumen with a viscosity of 126,500
mPas were back-calculated as:
10 0.4613.06 10D (for propane), (1.4)
10 0.464.13 10D (for butane). (1.5)
It is worthwhile to note that in the actual VAPEX process, the solvent-diluted heavy
oil drains down along the transition zone and thus the upward-moving solvent keeps
contacting the fresh heavy oil. In this case, both the molecular diffusion and convective
dispersion of the solvent in the heavy oil contribute to the mass transfer between a heavy
oil and solvent. The back-calculated effective diffusion coefficient by Das and Butler
contained both of the effects [Boustani and Maini, 2001].
Heavy oil viscosity
After the solvent dissolves into the heavy oil, the high viscosity of the crude heavy oil
decreases dramatically. In the literature, the correlation between the viscosity of the
solvent-diluted heavy oil and the solvent concentration was commonly modeled by using
the Lederer equation [Lederer, 1933]:
28
ss o
of f , (1.6)
s 1cfc c
, 1o sf f . (1.7)
where, o, s, and are viscosities of the crude oil, liquid solvent, and mixture of the two,
respectively, mPas; fo and fs are the weighted volume fractions, vol.%; λ is a weight factor.
Shu [1984] formulated the following correlation to determine the above-mentioned
weight factor for a heavy oilsolvent mixture:
0.5237 3.2745 1.631617.04ln
o s o s
o s
, (1.8)
where o and s are specific gravities of the crude heavy oil and liquid solvent, respectively.
Heavy oil density
The density of solvent-diluted heavy oil can be determined by using the mixture rule
for an ideal solution [McCain, 1990]:
1
1 o sc c
. (1.9)
where, o and s are the densities of the heavy oil and liquid solvent, respectively, kg/m3;
The above equation is applicable only if the volume change due to the solvent dissolution
into the heavy oil is negligible. In addition, the solvent is assumed to be a liquid once it
dissolves into the heavy oil.
2.1.3 Theoretical modeling of VAPEX
Butler−Mokrys model
Butler and Mokrys [1989] carried out the first VAPEX experiments in a Hele−Shaw
cell as a solvent-analog of the SAGD process. They used liquid toluene as the solvent to
29
recover two bitumen samples. In addition, they developed an analytical mathematical
model on the basis of the following assumptions:
1. Mass transfer of solvent into the bitumen bulk is under pseudo-steady state
condition: 0ct
;
2. Solute−solvent interface moves at a constant unspecified velocity: constU ;
3. Oil flows along the interface in a thin diffusion boundary layer;
4. Drainage of the undiluted bitumen was considered negligible;
5. Effect of surface tension is ignored because it is not crucial;
6. Change in velocity gradient in the direction normal to the flow surface is
negligible: 2
2 constv
;
7. Viscosity, density, and diffusivity, are all concentration dependent and assumed
to be uniform along the boundary and across the cell thickness but changing
across the transition zone: c , c , and D D c .
Two correlations are applied:
1. Concentration is a function of the distance from an arbitrary point to the
boundary between solvent chamber and transition zone: c c ;
2. Geometric relation between the normal velocity U and horizontal velocity xt
:
sin Uxt
.
30
Three governing equations constitute the foundation of the theoretical model:
1. Fick’s 1st law: dcD Ucd
;
2. Darcy’s Law: sinkv g
;
3. Mass balance equation: o0
t H
y
qdt S xdy .
where, is the distance from the boundary between the solvent chamber and transition
zone to an arbitrary point in the transition zone, m; θ is the inclination angle of the
transition zone, degree; v is heavy oil drainage velocity, m/s; k is the permeability, D; g is
the gravitational acceleration, m/s2; is the porosity, fraction; ∆So = Soi−Sor is the oil
saturation change in the solvent chamber; Soi is the initial oil saturation and Sor is the
residual oil saturation; x and y are the distances in the horizontal and vertical directions,
respectively.
On the basis of the above assumptions, correlations, and governing equations, Butler
and Mokrys derived the famous analytical model for predicting the heavy oil drainage
volume flow rate, qo, during the solvent spreading phase:
o o s2 2q L kg S N H , (1.10)
where, L is the length of a horizontal production well; H is the height of the sand-packed
physical model; and sN is the dimensionless number:
max
min
s
1c
c
c DN dc
c
. (1.11)
31
In the integrand, ∆ρ is the density difference of the solvent-diluted heavy oil and the liquid
solvent, kg/m3.
Das−Butler model
Das [1995] investigated the VAPEX performance in a sandpack. It was observed that
the oil extraction rate in porous media was 3 to 5 times higher than that predicted by the
Butler−Mokrys analytical model. He attributed the higher production rate in porous media
to the increased bitumen–solvent contact area, increased solvent solubility, and surface
renewal. Since the previous theoretical model was developed on the basis of bulk flow and
could no longer properly predict the oil production rate, Das modified it to make the
prediction better match the measurements:
1o s2 2 ( )q L kg S N h y . (1.12)
where, is the cementation factor, dimensionless. Cementation factor measures the
consolidation of the matrix due to asphaltene precipitation onto the surface of the reservoir
rock. In the meantime, Das replaced the earlier intrinsic molecular diffusion coefficient D
with an apparent diffusion coefficient Dapp:
DDapp . (1.13)
Earlier study [Perkins and Johnston, 1963] indicated this relationship is rather as follows:
appDDF
. (1.14)
F is the formation electrical resistivity factor. Archie [1942] suggested F is related to the
porosity, , and a constant ‘Λ’ by the following equation:
F
(1.15)
32
The experimentally measurement of is between 1.3 and 2.2, and it changes with the
rock lithology. The more consolidated the reservoir rock, the smaller would be.
Moghadam et al. model
Moghadam et al. [2008] conducted a number of VAPEX experiments with a visual
rectangular sand-packed high-pressure physical model, to examine the effects of the
solvent chamber evolution, the transition-zone thickness, and the inclination angle on the
VAPEX process. Propane was used as the extracting solvent to recover a Lloydminster
heavy oil sample at a pressure slightly lower than the saturation pressure of the solvent.
They found that the ‘inclination angle’ of the spreading phase and the falling phase was
closely related to the oil production rate during the two phases, respectively. A theoretical
VAPEX model was developed on the basis of two assumptions:
1. Two boundaries of the transition zone between the solvent chamber and the
untouched heavy oil zone are assumed to be straight lines with a constant
transition-zone thickness;
2. Downward oil drainage velocity in the transition zone is assumed to be a linear
function of the transverse distance between the solvent chamber and the
untouched heavy oil zone.
The principal governing equations in their model are:
1. Darcy’s Law: sinkv c gc
.
2. Geometric relations: sin HW
; x
sin ; cot x
H .
where, W is the width of the sand-packed physical model, m; δ is the thickness of the
transition zone, m. Cumulative oil production rates during the solvent chamber spreading
33
and falling phases were derived as:
2o o cotQ H S (for the spreading phase), (1.16)
o o s2 cot tanQ HW S (for the falling phase). (1.17)
where, Qo is the cumulative oil production rates, m2; s is the inclination angle of the
transition zone at the end of the solvent chamber spreading phase.
This is the first attempt to analytically describe the evolution of the solvent vapour
chamber during the VAPEX process. However, its application is quite limited since this
model did not include the solvent diffusion coefficient of the solvent.
Yazdani−Maini model
Yazdani and Maini [2007] examined the effects of the drainage height and grain size
on the stabilized oil drainage rates. On the basis of several sandpack tests in two
rectangular and cylindrical models with three different heights and three sand sizes, they
generated two empirical scale-up correlations for the VAPEX process:
1.26o 0.0174q H k , (1.18)
1.13o 0.0288q H k . (1.19)
They found that the stabilized heavy oil production rate was a function of the
drainage height to the power of 1.1–1.3 rather than 0.5 as predicted in the previous models.
The constant coefficient in the above equation, 0.0174 in Eq. (1.18) and 0.0288 in Eq. (1.19)
represented the combined effect of the gravity drainage, mass transfer, residual oil
saturation, and original oil viscosity. Therefore, these empirical coefficients need to be
determined for specific solvent−oil−reservoir systems. In addition, it is still uncertain for
whether these empirical models can be applied in other cases.
34
2.1.4 Numerical modeling of VAPEX
Numerical simulators, such as Steam, Thermal and Advanced Reservoir Simulator
(STARS) of Computer Modelling Group (CMG), have been attempted to model the
VAPEX process by different authors [Yazdani, 2007; Qi and Polikar, 2005]. Cuthiell et al.
[2003] used a semi-compositional model (STARS) to model the VAPEX process and
concluded that the simulation could match the solvent breakthrough time, oil production
rate, and the general character of the viscous fingering phenomenon. Das used a fully
compositional model, Generalized Equation of State Model Reservoir Simulator (GEM),
to simulate laboratory VAPEX tests. They applied a high diffusion coefficient and a thick
transition zone in their simulation model to match the experimental data. Wu et al. [2005]
simulated the asphaltene precipitation during the VAPEX process with STARS and
investigated the effect of operation parameters on the VAPEX performance. Rehnema et al.
[2007] conducted a screening study for practical application of VAPEX by using the GEM
module. Zeng et al. [2008] evaluated the VAPEX performance with a Tee well pattern by
using STARS. They concluded that the Tee well pattern shortened the breakthrough time
and increased oil production rate by 28 times. Cuthiell [2012] simulated a laboratory
VAPEX experiment by using a semi-compositional simulator, Tetrad, which was able to
incorporate the diffusion/dispersion physics with the VAPEX process. It was concluded
that most of the gravity drainage occurred in the capillary transition zone.
In general, VAPEX simulations fall into two categories: one is to study the effects of
the reservoir/fluid properties and operating parameters and the other one is to simulate and
validate the laboratory tests. The limitations with the numerical simulation models are: (1)
Simulation models are unable to apply very fine grids to accurately capture the transition
35
zone which is estimated to be just 2.8–11.2 mm wide [Das and Butler, 1995; Moghadam et
al., 2008; Yazdani and Maini, 2009]; (2) Numerical simulation wastes a great deal of
computational time on the solvent chamber and the untouched heavy oil zone, both of
which occupy a larger area but contributes less oil production in comparison with the
transition zone; (3) Numerical simulation results are not sensitive to the diffusion
coefficient [Qi and Polikar, 2005], which is probably due to the fact that the numerical
dispersion may affect the simulation result to a larger extent than the physical
diffusion/dispersion.
2.2 Cyclic Solvent Injection (CSI)
Solvent-based process with cyclic pressure increase and decrease was investigated
long before the VAPEX process. Shelton and Morris [1973] applied a rich gas to produce
oil in a huff-n-puff mode, where a single well was used alternately as the solvent injector
and oil producer. Allen [1974] patented a huff-n-puff type process in which propane or
butane was injected in cycles to extract oil from a cell packed with Athabasca tar sands. A
typical cyclic solvent injection (CSI) cycle consists of three periods: solvent injection,
soaking, and oil production periods. Unlike VAPEX which is a constant-pressure process,
the pressure of CSI is cyclically built up during solvent injection period and drawn down
during the oil production period.
Lim et al. [1995, 1996] conducted some CSI tests to enhance the oil production of the
VAPEX process. Ethane was applied to produce Cold Lake bitumen at the supercritical
and sub-critical conditions. They found that supercritical ethane performs better than the
sub-critical ethane in terms of either bitumen production rate or the eventual recovery
factor. It was found that the molecular diffusion is not the major mechanism of a
36
higher-than-expected production rate. Solvent dispersion or viscous fingering might play a
larger role. It was also found that the full utilization of the horizontal well was not achieved
in the model through the residual oil saturation measurement. They observed that the oil
production during the production period comes from two distinct mechanisms: wellbore
inflow and gravity drainage. The production profile exhibited a declining rate in the early
cycles, which suggested the near wellbore inflow mechanism is more significant before the
solvent chamber is fully developed. Afterward, the oil production rate starts to increase,
which is attributed to a growing solvent chamber size as well as the gravity drainage.
Ivory et al. [2010] investigated the CSI process with a real-scale 3 m long stepped
cone model run at field-scale times. A mixture solvent (28 vol.% propane + 72 vol.%
methane) was cyclically injected into the physical model at a pressure of around 3 MPa.
After nearly 6 cycles and 2 years of test, they achieved an oil recovery factor of 6.8% for
the primary production and 50.4% for the entire test, which showed that CSI has potential
to be a good follow-up process of cold production processes.
Dong et al. [2006] designed a methane pressure-cycling (MPC) process to recover
the residual oil after the termination of either primary or waterflood production in some
heavy oil reservoirs. The essence of this method is to restore the solution-gas drive
mechanism for a ‘primary’ production. They found that the mobile-water saturation greatly
affects the performance of the MPC process.
Jamaloei et al. [2012] studied an enhanced cyclic solvent process (ECSP) by using
two solvent gases: one was more soluble (propane) and the other was more volatile
(methane). They found that by using the two-slug injection strategy, the oil recovery factor
could be as high as 34.4% compared with an oil recovery factor of 4.27% by using the
37
one-slug pure methane. It was concluded that methane CSI can be greatly enhanced by
introducing a propane slug during the injection period. In the ECSP process, methane
provides expansion and some propane stays in the oil to keep the oil viscosity low during
the pressure reduction process. This indicates that the major mechanisms of ECSP are
viscosity reduction and solvent-gas-drive during the early stage of the production.
Jiang et al. [2013] proposed another process, cyclic production with continuous
injection (CPCSI), to enhance heavy oil recovery. In this process, vapour solvent is
continuously injected into the model to maintain the pressure and also supply an extra gas
drive force to flood the solvent-diluted heavy oil out. They found that the oil recovery
factor could be increased to 85% with the CPCSI method.
Studies on the CSI heavy oil recovery process, especial those for post-CHOPS, are
quite limited in the literature. Table 2.7 lists the up-to-date efforts on physical modeling
and numerical simulations of the CSI processes.
38
Table 2.7 CSI experimental studies in the literature.
No. Author Heavy Oil/bitumen Model Injection Production
Name ρo μo Type Shape
Size Sand
ϕ k Config. Solvent
T P t RF kg/m3/°C mPas/°C cmcmcm % D °C MPa h %
1 Lim
et al., [1996]
Cold lake — 100,000/25 sandpack rectangle 474227 Quartz
0.330.350.35
80 20 110
line source
C3 C2
25 1 4.2
1−3 h 3/13/15 c 4050
2 Dong et al., [2006]
Senlac Cactus Lake
North Plover Lake
— 1,700−5,400sandpack — 30.55 Quartz
35.532.8
6.589.70 lateral C1 —
4.5 drop to
0.5
5−17 h 8 c
23.3 28.8
3 Ivory et al., [2010]
Rush Lake — 39,320/20 sandpack circular cone
300 (H) (9.7, 1)
(Dtop, Dbtm)
Quartz 38 4.5 point 28% C3+
72% CO2 —
2.23.4drop to 0.51
inj: 63−80 d prd: 17−26 d
6 c
52
4 Firouz et al., [2012]
Saskatchewan heavy oil — 1,420/22 sandpack cylinder
30.84
5.08
Quartz 24 1.8 lateral
C1 C3 C4
CO2
20.51.76.8drop to 0.276
soak: 24 h 7−10 c
58−73
5 Jamaloei
et al., [2012]
South Britnell — 1,080/22 sandpack cylinder
101.3
(4.9, 3.2)
Quartz 38 41.8 point C1
C3 — 0.823
0.1
soak: 22 h prod: 0.5 h
6 cycles 34.3
6 Huerta et al., [2012]
Lloydminster — 35,000/20 sandpack — — Quartz
— — lateral 90% CO2+10% H2S —
3.0 drop to
0.5 Soak: 24 h —
7 Jiang et al., [2013]
Lloydminster — 5,875/20 sandpack rectangular 40102 Glass beads 36 4.7 lateral propane 20.2 0.8 soak: 55 min
prod: 5 min 60
39
2.3 Chapter Summary
From the literature review in this chapter, it can be seen that extensive laboratory
experiments have been conducted to evaluate the VAPEX process, and both analytical
methods and numerical simulation have been attempted to predict the VAPEX
performance. However, the analytical models are only able to roughly estimate the oil
production rate but unable to describe the solvent chamber evolution. Simulation models
can match the production rate but cannot reasonably describe the oil properties inside the
transition zone. On the other hand, the low oil production rate still exists and affects the
applicability of VAPEX. The CSI process is considered as a promising process for
post-CHOPS. Nevertheless, both theoretical and experimental studies of CSI are rather
limited in the literature. A variety of factors, such as the well configuration and operating
scheme, need to be examined to optimize the productivity of the CSI process.
40
CHAPTER 3 MATHEMATICAL MODELING OF VAPEX
In this chapter, a new mathematical model is developed to describe the solvent
chamber evolution during the VAPEX heavy oil recovery process. This new model is
based on two physical processes: mass transfer and gravity drainage. The mass transfer
process is modelled as a transient process with a variable diffusion coefficient. The heavy
oil−solvent transition zone in which most of the mass transfer occurs is modelled as a
piecewise linear zone that is updated step by step temporally. The boundary of the
transition zone is considered moving with time and calculated on the basis of the material
balance equation. This VAPEX model is able not only to describe the distributions of
solvent concentration, oil drainage velocity, and diffusion coefficient across the transition
zone, but also to predict the solvent chamber evolution and the heavy oil production rate.
3.1 Mathematical Model and Solution
3.1.1 Heavy oil–solvent transition zone
As shown in Figure 3.1, there are three zones during a typical VAPEX process: a
solvent vapour chamber, an untouched heavy oil zone, and a transition zone in between.
Properties of the heavy oil and solvent in the solvent vapour chamber and untouched heavy
oil zone are unchanged: the solvent chamber is filled with the residual oil and solvent
vapour and the untouched heavy oil zone is full of the original untouched heavy oil. The
solvent chamber has three phases during a VAPEX process: rising, spreading, and falling
phases. Due to the complexity and its relatively minor contribution to the oil production,
the solvent chamber rising phase is disregarded and the spreading and falling
41
Figure 3.1 Transition zone in the VAPEX process.
Solvent chamber
Transition zone
Injector
Heavy oil
Producer
cmin
cmax
Concentration
Distance
Diluted oil
Solvent
Heavy oil
Diluted oil
42
phases of the solvent chamber are examined in this study. The solvent-chamber evolution
is caused by the oil drainage from the transition zone. Therefore, modeling of the transition
zone is the key to model the entire VAPEX process.
The heavy oil−solvent transition zone is defined on the basis of the solvent
concentration in the solvent-diluted heavy oil. As shown on the left-hand side of Figure 3.1,
the first boundary of the transition zone (Boundary 1) is at the edge of the solvent chamber
and located at c = cmax, and the second one (Boundary 2) neighbors the untouched heavy oil
zone at c = cmin ≈ 0.01 [Butler and Mokrys, 1989]. cmax is the saturation concentration under
the operating pressure and temperature and cmin is the minimum concentration at which the
solvent-diluted heavy oil starts to flow. The position of Boundary 2 depends on the solvent
concentration profile as well as the position of Boundary 1. This study simplifies the
curved boundary (Boundary 1) as a piecewise linear profile. Figure 3.2 schematically
shows the simplified transition zone at the early and middle stages of the VAPEX process.
It is worthwhile to note that Boundary 1 is defined at the very beginning of VAPEX.
Afterward, its position is calculated automatically by the VAPEX model, which is going to
be formulated in this chapter.
The VAPEX model in Figure 3.2 is a simplified model, in which the solvent is
injected from a line source, and the heavy oil is produced from the left bottom corner of the
model. Followings are the assumptions of the new mathematical model:
1. The porosity and permeability are spatially uniform;
2. The drainage of the solvent-diluted heavy oil in the transition zone, which is
assumed to be in liquid phase and caused only by gravity;
3. The heavy oil–solvent mass transfer along the transition zone is negligible;
43
(a) (b)
Figure 3.2 Approximation to the transition-zone at the (a) beginning and (b) middle
stages of the VAPEX process.
Solvent chamber
Producer
Transition zone
Heavy oil
Solvent Solvent chamber
Transition zone
Heavy oil
44
4. The diffusion coefficient takes account of both molecular diffusion and
convective dispersion [Das and Bulter, 1995].
Two spatial coordinate systems are used: a two-dimensional (2D) coordinate system
(x, y) with x in the horizontal direction and y in the vertical direction for the solvent
chamber evolution, and a one-dimensional (1D) coordinate system (ξ) for the mass transfer
in the transition-zone segments. The ξ coordinate starts from and is normal to Boundary 1
of each transition-zone segment. The 2D coordinate system is linked to the 1D coordinate
system through the inclination angle of each transition-zone segment.
A new mathematical model is developed on the basis of the major mechanisms of
VAPEX, such as solvent dissolution and gravity drainage. The new model consists of three
sub-models: a mass transfer model, a fluid flow model, and a boundary movement model,
which will be described one by another in the following sections.
3.1.2 Mass transfer in transition zone
As mentioned above, the mass transfer between solvent and heavy oil is the most
important mechanism of VAPEX. Previous studies assumed it as a steady-state diffusion
process, and used Fick’s 1st law to describe it [Butler and Mokrys, 1989]. However, this
assumption is invalid for the actual cases: solvent chamber grows fast at the top and
spreads slowly at the bottom, which indicates that the heavy oil–solvent mass transfer in
the transition zone changes with both time and space. Therefore, this study considers the
heavy oil–solvent mass transfer as a more realistic transient diffusion process, and Fick’s
2nd law is applied to calculate the solvent concentration distribution in each transition-zone
segment:
45
c cD
, (3.1)
where, τ is the time, s; ξ is the position normal to the Boundary 1 of a transition-zone
segment, m; D is the diffusion coefficient, m2/s.
For a heavy oil−hydrocarbon solvent system, the diffusion coefficient of solvent into
heavy oil is a function of the viscosity of a heavy oil–solvent mixture, which follows a
general formula [Heyduk and Cheng, 1971]:
D , (3.2)
where, is the viscosity of the solvent-diluted heavy oil, mPas; α and β are both constants
depending on the properties of the heavy oil and solvent as well as the operating conditions.
In this study, the Das and Butler’s correlations [1996] are adopted to calculate the diffusion
coefficient:
10 0.4613.06 10D (for propane), (3.3)
10 0.464.13 10D (for butane). (3.4)
In this study, is computed by using the one-parameter Lederer equation [1933]:
ss o
of f , (3.5)
s 1cfc c
, 1o sf f , (3.6)
where, o and s are viscosities of the crude heavy oil and the liquid solvent, respectively,
mPas; fs and fo are the weighted volume fractions, vol.%; the weight factor is obtained by
using the Shu’s correlation [1984]:
0.5237 3.2745 1.6316o s o s
s
17.04ln o
, (3.7)
46
where, γo and γs are specific gravities of the crude heavy oil and the liquid solvent,
respectively. The density of the heavy oil–solvent mixture is calculated by using:
1
1 o sc c
. (3.8)
At the left boundary (Boundary 1) of the transition-zone segment, the solvent
concentration is assumed to be the saturation concentration under the operating pressure
and temperature:
max0,c c . (3.9)
The right boundary of the transition zone is treated as a closed boundary:
, 0c L
, (3.10)
Initially, there is no solvent in the oil:
, 0 0c . (3.11)
It is worthwhile to note that the transition zone is updated step by step temporally. In
the first time step, the left boundary condition (BC) and the initial condition (IC) are Eqs.
(3.9) and (3.11), respectively. During the following steps, however, the left boundary is
always moves toward the untouched heavy oil zone and the left boundary condition
becomes a free boundary problem:
max,c s c , (3.12)
where, s is the location of Boundary 1 during a time step, m. Suppose that Boundary 1 of
one transition-zone segment is at ξ0 in the beginning of a time step and it moves at a
velocity of U during that step. Then the location of Boundary 1 during the step becomes:
0s U . (3.13)
47
Boundary moving velocity U can be determined by using the mass balance equation, which
will be specified in the later section. The IC for the second and the following time steps is
actually the solvent concentration distribution at the end of their previous time steps:
1 , 0t tc c . (3.14)
3.1.3 Fluid flow in transition zone
Given a known concentration profile, the viscosity and density of the solvent-diluted
heavy oil can be calculated by using Eqs. (3.5) and (3.8), respectively. Hence, the gravity
drainage velocity across the transition zone can be determined by using the Darcy’s law:
sinskv c gc
, (3.15)
where, v is the drainage velocity, m/s; k is the permeability, D; ρ(c) and ρs are densities of
the solvent-diluted heavy oil and the liquid solvent, kg/m3; g is the gravitational
acceleration, m/s2; θ is the inclination angle, degree.
The drainage velocity gradually decreases from the maximum value at Boundary 1 to
the minimum value at Boundary 2 of the transition zone. The total amount of the
solvent-diluted heavy oil that drains from one segment into another can be calculated by
integrating Eq. (3.15) across the transition zone:
max
min
dq v
, (3.16)
where, q is the oil drainage flux of one segment, m2/s; max and min are the locations of
Boundary 1 and Boundary 2 of the transition zone, respectively, m.
48
3.1.4 Moving boundary of transition zone
As shown in Figure 3.3, the solvent-diluted heavy oil flows into and drains out of a
transition-zone segment at fluxes of qin and qout, respectively. Over a short period of time,
τ, Boundary 1 moves by ξ due to the depletion of the oil. Assume the length change of
the outer segment boundary during τ is trivial and the oil saturation change is uniform in
the depleted area, Then ξ can be determined by using the mass balance equation:
out in oi orq q l S S , (3.17)
where, l is the length of the transition-zone segment boundary, m; Soi and Sor are the initial
and residual oil saturations, respectively, vol.%. qin and qout can be obtained from Eq. (3.16).
If the timestep size is small enough, the boundary moving velocity can be approximated as:
out ind q qUd l S
. (3.18)
Eq. (3.18) is substituted into Eq. (3.13) for the concentration calculation.
With a known timestep size ∆t and the boundary moving velocity U, the moving
distance over the time step can be obtained:
mv U t . (3.19)
The movement of the transition-zone segment in the horizontal direction is:
sinmvx
. (3.20)
Similarly, the movement of the transition-zone segment in the vertical direction is:
cosmvy
. (3.21)
Eq. (3.20) is used to estimate the solvent chamber evolution during its spreading phase and
Eq. (3.21) is used to estimate the solvent chamber evolution during its falling phase.
49
Figure 3.3 Boundary movement of a transition-zone segment.
vin Heavy oil
h
Solvent chamber Transition zone
ξ at t ξ+dξ at t+dt
vout
ξ
50
3.1.5 Solution procedures
Due to the complexity of the correlation between D and c, it is difficult to analytically
solve the nonlinear governing equation. Therefore, an approximate solution method is
applied: (1) the solvent concentration is calculated step by step; (2) for the first step, D is
considered as a constant since the model is solvent free in the beginning; (3) for the
following steps, D is a function of c at the end of the previous step; thus, D is a known
variable during one step. In this way, the governing equation can be reduced to a linear
partial differential equation (PDE). Specifically, the calculation procedures are described
as below (Figure 3.4):
1. Applying BCs and IC of Eqs. (3.9−3.11) to the governing equation of Eq. (3.1)
for the first time step to obtain a solvent concentration profile for each
transition-zone segment;
2. Computing ρ(c), μ(c), D(c), v(c), q, and U of the solvent-diluted heavy oil by
using Eqs. (3.12, 3.9−3.11, 3.7 or 3.8, 3.19, 3.20, and 3.22), respectively;
3. Calculating the left-boundary movement of each transition-zone segment in the
horizontal or vertical direction by using Eq. (3.24) or (3.25), and then updating
the solvent-chamber profile at the end of the present time step;
4. Entering the next step and updating the solvent diffusion coefficient, left BC, and
IC with those obtained at the end of the previous time step;
5. Calculating a new solvent concentration profile for each transition-zone segment;
and
6. Repeating Steps #2−5 till the end of the process.
51
Figure 3.4 Flowchart of the solution calculation for the VAPEX mathematical model.
ρ
v
D
U
Governing Eq.
Finish
IC BCs
c
Yes No Terminate
52
It is worthwhile to emphasize that the mass-transfer model is solved with the finite
difference method (FDM). The key to solving the diffusion equation with a moving
boundary is to discretize of the time and space domains. Figure 3.5 shows the discretization
of ξ and τ axes for a transition-zone segment during a time step. Suppose that there are Nξ
grids with a grid size of ∆ξ across the transition zone, the time needed for the boundary to
pass by ∆ξ at a moving velocity of U is:
U
. (3.22)
Then the number of sub-step during a step ∆t can be estimated as:
tN
. (3.23)
If Nτ < 1, it can be treated as a fixed boundary problem. Otherwise, it will be solved as a
moving boundary problem. The detailed solution to the mathematical model with the
Crank−Nicolson FDM is presented in Appendix A.
3.1.6 Heavy oil production rate
The cumulative heavy oil production can be found by integrating the area of the
solvent vapour chamber in the (x, y) coordinate system:
0
W
Q S H y x dx , (3.24)
where, Q is the cumulative heavy oil production, m3; H is the model height, m; W is the
model width, m. The heavy oil production rate can be obtained by taking the derivative of
Q with respect to t.
53
Figure 3.5 Discretization of the space and time domains for the numerical solution to
the mass-transfer model with a moving boundary condition.
s = ξ/U
t2=∆ξ/U
t1=0
t3=2∆ξ/U
t4=3∆ξ/U
t5=4∆ξ/U
ξN = L ξ3=2∆ξ ξ2=∆ξ ξ1=0 ξ4=3∆ξ ξ5=4∆ξ
54
3.2 Results and Discussion
Table 3.1 lists the parameters of a base case. The other cases are discussed below and
their parameters that are different from those in Table 3.1 will be specified.
3.2.1 Solvent chamber evolution and recovery factor
Figure 3.6 shows the solvent chamber evolution with time for the base case. Solvent
chamber grows faster at the top than at the other parts. That is because nothing flows into
the first segment but the solvent-diluted heavy oil keeps draining out, which is different
from the other segments. After around 14 h, the solvent chamber reaches to the right-hand
side of the model, indicating the solvent chamber is near the end of its spreading phase and
starts the falling phase at that moment. Figure 3.7 presents the heavy oil recovery factor
(RF) curve. The RF curve is quite flat in the first a few hours and then increases linearly
during the solvent chamber rising phase, indicating a stabilized oil production rate. This is
consistent with observations in the previous studies. In the last 10 h, the RF curve decreases
slightly as the solvent chamber keeps falling. This is caused by the reduced inclination
angle and the diminishing gravity drainage.
The solvent concentration is quite small due to its fast movement during the first 15 h.
It becomes slightly higher during the solvent chamber falling phase due to the decreased
drainage and accumulation of solvent-diluted heavy oil. For the middle segment, its
thickness is quite stable throughout the VAPEX process, indicating a balance between the
mass transfer and fluid flow. For the bottom segment, because of the smaller gravity effect
and solvent accumulation, the transition zone grows steadily from several millimeters in
the beginning to several centimeters at the end of the VAPEX process. Hence, it can be
seen that transition zone is a dynamic zone and it always changes with time and location.
55
Table 3.1 Physical properties and operating conditions of the base case for the
VAPEX mathematical model.
Parameters Value Model dimensions, m2 0.1 × 0.1 Porosity, % 35 Permeability, D 50 Relative oil permeability, fraction 1 Solvent type C3H8 Solvent solubility, g solvent/100 oil 26.5 Heavy crude oil viscosity @ 23°C and 800 kPa, mPas 12,000 Heavy crude oil density @ 23°C and 800 kPa, kg/m3 975 Solvent viscosity (liquid) @ 23°C and 800 kPa, mPas 0.106 Solvent density (liquid) @ 23°C and 800 kPa, kg/m3 517 Diffusion coefficient, m2/s 1.306×10-9-0.46 Operating pressure, kPa 800 Operating temperature, C 23 Connate water saturation, % 5 Residual oil saturation, % 15 Number of transition-zone segments 12
56
Horizontal distance, m
0.00 0.02 0.04 0.06 0.08 0.10
Ver
tical
dis
tanc
e (m
)
0.00
0.02
0.04
0.06
0.08
0.10
Figure 3.6 Evolution of the solvent vapour chamber during a VAPEX process.
2 h
30 h
57
Time (h)
0 5 10 15 20 25 30
Oil
reco
very
fact
or (%
)
0
20
40
60
Figure 3.7 Oil recover factor of the VAPEX base case.
Spreading phase Falling phase
58
x (m)
0.00 0.02 0.04 0.06 0.08 0.10
y (m
)
0.00
0.02
0.04
0.06
0.08
0.10
t=0.1 ht=5.0 ht=10.0 ht=15.0 ht=20.0 h
(m)
0.00 0.01 0.02 0.03 0.04 0.05
c/c m
ax
0.0
0.2
0.4
0.6
0.8
1.0t=0.1 ht=5.0 ht=10.0 ht=15.0 ht=20.0 h
(m)0.00 0.01 0.02 0.03 0.04 0.05
c/c m
ax
0.0
0.2
0.4
0.6
0.8
1.0t=0.1 ht=5.0 ht=10.0 ht=15.0 ht=20.0 h
(m)0.00 0.01 0.02 0.03 0.04 0.05
c/c m
ax
0.0
0.2
0.4
0.6
0.8
1.0t=0.1 ht=5.0 ht=10.0 ht=15.0 ht=20.0 h
Figure 3.8 Solvent concentration distribution at different locations along the transition
zone at different moments: (a) Solvent chamber profiles; (b) Solvent concentration
distributions at the top; (c) Solvent concentration distributions in the middle; and (d)
Solvent concentration distributions at the bottom of the transition zone.
(a) (b)
(c) (d)
59
3.2.2 Dividing number of the transition zone
Figure 3.9 shows the effect of the dividing number of transition-zone segments on
the solvent chamber profile. The transition zone is respectively divided into 5, 10, 15, 20,
and 25 segments and the corresponding average oil production rates are shown in Figure
3.9. It can be seen that the more segments, the higher the average oil production rate.
However, the production rate incremental decreases with the increase of total segment
numbers. In addition, more segments involve much longer computation time due to the
numerical solution method applied to the mass transfer model. Therefore, it is important to
divide the transition zone with a reasonable number of segments. This study applies 10
segments to the transition zone in the following calculations.
3.2.3 Permeability
Permeability is one of the most important model properties. The previous studies
concluded that the stabilized heavy oil production rate is proportional to the square root of
the permeability. This study analyzed four different permeability values: 5, 50, 100, and
200 D. These values are chosen to be consistent with the experimental permeability ranges
in the literature. Figure 3.10 demonstrates the solvent chamber profiles from the very
beginning to 2, 4, 6, 8, and 10 h for the four permeability cases. As expected, a higher
permeability will lead to faster oil recovery. Figure 3.11 compares the stabilized heavy oil
production rate against the square root of the permeability, and a good linear trend was
regressed with R2 = 0.9696, which agrees well with the conclusions in the previous studies.
60
Dividing number
0 5 10 15 20 25 30
Oil
prod
uctio
n ra
te (c
c/h)
0.10
0.11
0.12
0.13
0.14
Figure 3.9 Effect of dividing number on the average oil production rate.
61
The new VAPEX model is able to deal with both constant and variable diffusion
coefficients. Figure 3.12a shows a good linear dependence of the stabilized heavy oil
production rate on the square root of the constant diffusion coefficient, which is consistent
with the Butler−Mokrys model. This study further analyzes the effect of variable diffusion
coefficients. Figure 3.12b displays the recovery factor curve for three variable diffusion
coefficients, which adopts the correlations in Eqs. (3.3−3.4) with the same exponent of
−0.46 but different coefficients of α = 1.5, 1.0, and 0.5×10−9. As expected, a larger
diffusion coefficient will make the solvent chamber grow faster than a smaller diffusion
coefficient. Figure 3.12b also compares a constant diffusion coefficient (D = 2.29×10−9
m2/s) with an equivalent variable diffusion coefficient (D = 0.5×10−9μ−0.46). It is found that
the RF curve for the former case is much smaller than that for the latter case. This implies
that the constant diffusion might underestimate the oil production rate of a VAPEX process
because the concentration-dependent variable diffusion coefficient becomes larger and
larger with time, whereas the constant diffusion coefficient does not. Therefore, the
constant diffusion coefficient may be acceptable for a short time but unacceptable for a
longer time of simulation.
62
x (m)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
0.00
0.02
0.04
0.06
0.08
0.10
t=0 ht=2 ht=4 ht=6 ht=8 ht=10 h
x (m)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
0.00
0.02
0.04
0.06
0.08
0.10
t=0 ht=2 ht=4 ht=6 ht=8 ht=10 h
x (m)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
y (m
)
0.00
0.02
0.04
0.06
0.08
0.10
t=0 ht=2 ht=4 ht=6 ht=8 ht=10 h
x (m)0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
0.00
0.02
0.04
0.06
0.08
0.10
t=0 ht=2 ht=4 ht=6 ht=8 ht=10 h
k = 5 Darcy k = 50 Darcy
k = 100 Darcy k = 200 Darcy
y (m
)
y (m
)y
(m)
Figure 3.10 Effect of permeability on the solvent chamber evolution: (a) k = 25 D; (b)
k = 50 D; (c) k = 100 D; and (d) k = 200 D.
(a) (b)
(c) (d)
63
0 2 4 6 8 10 12 14 16
q o (cc
/h)
0
1
2
3
4
5
(Darcy0.5)
Figure 3.11 Effect of permeability on the oil production rate.
20.3394 , 0.9696q K R
K
64
(m2/s)1/2
0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012
q o (cc
/h)
0.0
0.5
1.0
1.5
2.0
2.5
(a)
Time (h)
0 2 4 6 8 10 12 14 16
Oil
reco
very
fact
or (%
)
0
2
4
6
8
10
12
14
16
18
20
D=2.25e-9
D=0.5e-9m-0.46
D=1.0e-9m-0.46
D=1.5e-9m-0.46
(b)
Figure 3.12 (a) Heavy oil production rate vs. square root of diffusion coefficient; and
(b) Oil recovery factor for variable and constant diffusion coefficients.
225669 , 0.9275q D R
9
9 0.46
9 0.46
9 0.46
2.25 10
0.5 101.0 101.5 10
DDDD
D
65
3.2.4 This study vs. analytical models
Existing analytical models including the Bulter−Mokrys model, the Das−Butler
model, and the Yazdani−Maini model [Yazdani and Maini, 2005], and the model in this
thesis are all applied to calculate the heavy oil production rate for the base case. Four
permeability values are considered: k = 25, 50, 100, and 200 D. Figure 3.13 shows the
calculation results. The new model’s prediction is close to that of the Yazdani–Maini
model and much higher than those of the other two models. The reason may be that the first
two models were developed on the basis of the steady-state mass transfer and constant
diffusion coefficients. The coefficients in the Yazdani–Maini model incorporated the
effects of all system variables, such as porous media, grain size, and convective dispersion.
However, these empirical coefficients are regressed for specific laboratory tests only and
their applicability for a general VAPEX process remains questionable.
3.2.5 This study vs. numerical simulation
A numerical simulation model is developed by using the CMG STARS module
[Version 2011, Computer Modelling Group Limited, Canada] in this section to compare
with the new mathematical model in this research. Properties of the simulation model are
listed in Table 3.2 and Figure 3.14.
66
k (Darcy)
0 20 40 60 80 100 120 140 160 180 200 220
q o (cc
/h)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40This studyYazdani-Maini (2005)Yazdani-Maini, (2005)Das-Butler (1995)Butler-Mokrys, (1989)
Figure 3.13 Oil production rate predicted by this study and the existing VAPEX
models.
67
Table 3.2 Physical parameters and operation conditions for the base case of the
numerical simulation.
Parameters Value Model dimensions (lab-scale), m3 0.4 × 0.02 × 0.1 Model grid (lab-scale) 40 × 2 × 10 Run time (lab-scale), d 3 Model dimensions (field-scale), m3 1 × 1 × 1 Model grid (field-scale) 100 × 100 × 10 Run time (field-scale), d 3,000 Porosity, vol.% 35 Permeability, D 50 KV1 (k value correlation), kPa 2.31106 KV2 (k value correlation), 1/kPa 0 KV3 (k value correlation) 0 KV4 (k value correlation), C −2,725.4 KV5 (k value correlation), C −273.15 Dispersion coefficients, m2/d 0.000864 Injection pressure, kPa 800 Production pressure, kPa 799 Gas/liquid relative permeability curve Figure 3.14
68
(a)
(b) (c)
Figure 3.14 (a) Numerical simulation model; (b) Relative permeability vs. liquid
saturation curve; and (c) Capillary pressure vs. liquid saturation curve.
69
Numerical dispersion
Numerical dispersion is always a major concern in a numerical simulation, since it is
inherent in the finite difference simulation method and arises from time and space
discretization [Smith, 1985; Fanchi, 2006; Chen, 2007]. Numerical dispersion depends on
gridblock size x, timestep size t, as well as numerical formulation [Fanchi, 2006]. Fig.
13(a) displays the effect of the timestep size on the cumulative heavy oil production. Four
timestep sizes (t = 0.1, 0.01, 0.001, and 0.0001 d) are run and it can be seen that the
cumulative heavy oil production for t = 0.001 d behaves strangely near the end of
production. This shows the instability of simulation results caused by the timestep size.
Figure 3.16 presents four scenarios of grid sizes. Comparing Scenarios #2 and #4, it is
found that the heavy oil production rate is quite sensitive to the grid size as well as to the
geometric ratio. In contrast, although the mass-transfer model in this study is numerically
solved, it suffers less numerical dispersion because of the small grid size (ξ ≈ 0.0001 m)
applied to the transition-zone segment discretization. Therefore, the diffusion coefficient
of this study is used to roughly estimate the numerical dispersion in the simulation results.
First, the stabilized heavy oil production rate is calculated for the scenarios in Figure 3.16.
Then the coefficient α in Eq. (3.2) is adjusted to make the heavy oil production rate for each
case equal to that of the numerical simulation. Finally, the equivalent numerical dispersion
is estimated by subtracting the results for the original diffusion coefficient from those
adjusted one. Table 3.3 listed the results, suggesting that the error caused by gridding could
be as high as 60% and a smaller grid size can lead to more reliable stable simulation results.
70
Time (d)
0 1 2 3
Cum
ulat
ive
oil p
rodu
ctio
n (c
c)
0
20
40
60
80
100
120
140
160
180
200
t = 0.0001 d t = 0.001 d t = 0.01 d t = 0.1 d
Figure 3.15 Effect of the timestep size on the cumulative oil production (grid size: 0.01
× 0.01 × 0.01 m3).
71
Time (d)
0 1 2 3
Cum
ulat
ive
oil p
rodu
ctio
n (c
c)
0
20
40
60
80
100
120
140
160
180
Scenario #1Scenario #2Scenario #3Scenario #4
Figure 3.16 Effect of the grid size on the cumulative oil production (t = 0.001 d).
72
Table 3.3 Effect of the grid size and estimation of the numerical dispersion.
Parameters Scenario #1 Scenario #2 Scenario #3 Scenario #4 This study ΔX, m 0.005 0.01 0.01 0.02 ― ΔY, m 0.01 0.02 0.005 0.01 ― ΔX:ΔY 1:2 1:2 2:1 2:1 ― Oil production rate, cc/h 1.729 1.685 1.511 1.589 1.463
Effective diffusion coefficient, m2/s 0.000778 0.000778 0.000778 0.000778 ―
Original α (αor) ― ― ― ― 1.306×10−9 Adjusted α (αad) 2.13×10−9 1.97×10−9 1.42×10−9 1.65×10−9 ― Relative error, % 63.093 50.842 8.729 26.341 ―
Note: The original α is equivalent to the constant diffusion coefficient. The adjusted α
matches the predicted production rates by using this study’s model with the numerical
simulation result. Relative error = (αad−αor)/αor×100%.
73
Diffusion coefficient
One of the most important mechanisms of VAPEX is the solvent−heavy oil mass
transfer, which is characterized by the diffusion coefficient. This section further analyzes
the sensitivity of variable and constant diffusion coefficients to the modeling results of this
study and the numerical simulation, respectively. Five variable diffusion coefficients (D =
5, 1, 0.5, 0.1, and 0.05 × 10−9μ−0.46 m2/s) and five equivalent constant diffusion coefficients
in oil phase (D = 22.9, 4.58, 2.29, 0.458, and 0.229 × 10−9 m2/s) are applied for one
lab-scale and one field-scale models. Figure 3.17 demonstrates the results. It is found that
for the lab-scale cases, the oil production rates are quite sensitive to diffusion coefficient
for both this study and the numerical simulation. However, for the field-scale cases, the
new model’s results keep the similar trend to that in the lab-scale cases, whereas the
simulation results become insensitive to the diffusion coefficients. For D = 2.29×10−10 to
4.58×10−9 m2/s in the numerical simulation, though the latter diffusion coefficient is 20
times of the former one. Its corresponding heavy oil production rate (7.04 m3/d) is just 1.14
times of that of the former one (6.15 m3/d). This insensitivity is probably caused by the
larger grid size, resulting larger numerical dispersion in the field-scale simulations.
Transition-zone thickness
Transition zone is the most important area for the VAPEX heavy oil recovery process,
since it contributes to the most of the heavy oil production. In order to locate the transition
zone and capture the mass transport phenomena inside it, Yazdani and Maini [2007] stated
that the grid size of simulation model should be smaller than the transition-zone thickness,
which was estimated to be approximately 1 cm in the literature [Das et al., 1995;
Moghadam et al., 2008; Yazdani and Maini, 2009a]. Finer grids enable a more detailed
74
D (m2/s)
0.0 5.0e-9 1.0e-8 1.5e-8 2.0e-8 2.5e-8
q o (cc
/h)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Numerical simulationThis study
(a)
D (m2/s)
0.0 5.0e-9 1.0e-8 1.5e-8 2.0e-8 2.5e-8
q o (m
3 /d)
0
2
4
6
8
10
Numerical simulationThis study
(b)
Figure 3.17 Effect of the diffusion coefficient on the heavy oil production rate: (a)
Lab-scale grid size simulation results; and (b) Field-scale grid size simulation results.
75
(a)
(b)
(c)
Figure 3.18 Mole fraction of solvent in the lab-scale numerical model with different
grid-sizes at 20 h (t = 0.01 d): (a) 0.02 × 0.02 × 0.02 m3; (b) 0.01 × 0.01 × 0.01 m3; and
(c) 0.005 × 0.005 × 0.005 m3.
76
description of the component exchanges in the transition zone, yet the small grid size
and the accompanied minor time step will be limited by the computational time. Figure
3.18 shows the mole fraction distribution of solvent in the lab-scale numerical simulation
results with different grid sizes. For a grid size of 0.02 × 0.02 × 0.02 m3, the transition zone
has approximately one grid at the top, two grids in the middle, and more than three grids at
the bottom, corresponding to a thickness of ~2 cm at the top, ~4 cm in the middle, and over
6 cm at the bottom. This happens similarly to the cases of 0.01 × 0.01 × 0.01 m3 and 0.005
× 0.005 × 0.005 m3. Obviously, this estimate is much larger than the experimentally
measured and mathematically calculated ranges (between 0.3 and 1.5 cm) in the literature
[Samane et al., 2008]. In contrast, the assessment on the transition-zone thickness made in
this study (~1 cm at the top and middle and ~2 cm at the bottom) is relatively closer to the
previous conclusion, as clearly displayed in Figure 3.19.
In summary, in comparison with the numerical simulation model, this study’s model
demonstrated more sensitivity to diffusion coefficient. In addition, it is able to more
accurately describe the properties of the heavy oil and solvent inside the transition zone.
77
Figure 3. 19 Comparison of the predicted transition-zone thickness of this study and the
numerical simulation (grid size: 0.02×0.02×0.02 m3; t = 0.01 d) at 20 h.
78
3.3 Chapter Summary
This chapter formulates a new mathematical model to predict the VAPEX process.
The following conclusions can be drawn:
1. The new VAPEX mathematical model is developed on the basis of its major
mechanisms, such as mass transfer and gravity drainage;
2. The new model is able to describe the solvent concentration, oil viscosity and
density, diffusion coefficient, and drainage velocity inside the transition zone;
3. The evolution of the solvent chamber during its spreading and falling phases, as
well as the heavy oil production rate can be predicted by using the new model;
4. This new model confirms the linear correlations of qo vs. k and qo vs. D
for a permeability range of 5−200 Darcy and 50−0.5 × 10−10μ0.46, respectively.
5. It is found that the constant diffusion coefficient applied in the existing analytical
models may underestimate the oil production rate because it disregards the
growth of the diffusion coefficient during the VAPEX process; and
6. In comparison with the numerical simulation, the new model presented in this
chapter demonstrates more sensitivity to the diffusion coefficient and has much
less numerical dispersion.
79
CHAPTER 4 MATHEMATICAL MODELING OF THE
CONVECTION−DIFFUSION MASS-TRANSFER PROCESS
Due to the inherent slow oil production rate of VAPEX, another solvent-based
method, CSI, is studied in this chapter. A convection−diffusion mathematical model is
developed for the mass-transfer process in the CSI process. Convection velocity represents
the effect of pressure gradient between the solvent chamber and untouched heavy oil zone.
In this model, variable diffusion coefficient and convection velocity are considered and a
special approximation method for them is applied to obtain the semi-analytical solution.
Results qualitatively show that the mass-transfer process between solvent and heavy oil
can be significantly enhanced by the bulk motion of the solvent due to the pressure gradient
during the solvent injection period of the CSI process, especially at the early stage.
4.1 CSI Process
As a solvent-based EOR method, CSI showed promising potential to recover heavy
oil and bitumen in thin heavy oil reservoirs. CSI is basically a solvent huff-n-puff process.
Typically, each cycle consists of three periods, as schematically shown in Figure 4.1. First,
a vapour solvent is injected into the reservoir at a high pressure for some time (injection
period). Then the well is shut in for a period of time to let the solvent soak into the crude oil
(soaking period). Finally, the well is opened and its pressure is reduced so that the
solvent-diluted crude oil can be produced from the reservoir (production period). After one
cycle, the well would be converted into an injector again and the entire process will be
repeated for another cycle, until the oil production rate reaches an economic limit.
80
(a) Injection (b) Soaking (c) Production (d) Flow velocity
Figure 4.1 Vapour solvent-based ‘huff-n-puff’ process (Note: bold white arrows point
to the solvent diffusion direction, whereas narrow black arrows point to convection
direction).
x
V Injector/ producer Solvent
Transition zone
Dead oil
Solvent Transition
zone
Dead oil
Solvent Transition
zone
Dead oil
High Low
81
This chapter focuses on the mass-transfer process during the solvent injection period,
during which the pressure of the injected solvent is higher than that of the untouched heavy
oil. This causes a pressure gradient between the solvent chamber and the untouched crude
oil. Under the effect of the pressure gradient, solvent would have a bulk motion that could
accelerate the mixing process between solvent and crude oil. This chapter analyzes the
contribution from the pressure gradient to the mass-transfer process.
4.1.1 Convection−diffusion equation
One foremost feature of all solvent-based EOR techniques is oil viscosity reduction
due to the mass transfer between crude oil and solvent: solvent molecules mix with the bulk
heavy oil through Brownian motion (concentration gradient) and/or bulk motion (pressure
gradient). Without the latter bulk motion, the mass transfer between solvent and crude oil is
a diffusion process that can be modelled by using the Fick’s law. With the bulk motion, the
mass-transfer process is modelled by using the convection−diffusion equation:
'c cD cV St x x
, (4.1)
where, V is the convection velocity, m/s; S’ is the source/sink term. Diffusion coefficient
describes the effect of random walk of the diffusing particles, whereas the convection
velocity represents the effect of the bulk motion between the solvent and the crude oil.
4.1.2 Diffusion coefficient and convection velocity
Viscosity
The viscosity of the solvent-diluted heavy oil is calculated by using the Lederer−Shu
correlations [Lederer, 1933; Shu, 1984], as specified in Eqs. (3.5−7).
82
Diffusion coefficient
The diffusion coefficient of a hydrocarbon solvent into crude oil is determined by
using the Das and Butler correlations which are back-calculated on the basis of their
VAPEX experiments, as specified in Eqs. (3.3−4).
Convection velocity
Convection velocity in a porous medium can be described by using the Darcy’s law
[1933]. Under the effect of a pressure gradient and gravity force, it is
k dPV gdx
. (4.2)
where, dPdx
is the pressure gradient, kPa/m; Δρ is density difference between the
solvent-diluted crude oil and the liquid solvent, kg/m3; The density of solvent-diluted oil
can be determined by using the mixture rule for an ideal solution, as shown in Eq. (1.9).
Convection velocity is commonly treated as a constant mean value [Scott and Jirka,
2002] in various previous studies. This simplification is acceptable for the cases where
fluid is incompressible and the flow velocity is quite uniform, such as tracer flow [Sposito
and Weeks, 1998]. However, in solvent-based EOR processes, this simplification may be
unreasonable. More specifically, the diffusion coefficient and convection velocity are both
functions of viscosity and viscosity is a function of concentration, which is further a
function of time and location, as shown by Eqs. (3.3−5, 4.2). Thereby, at a certain time,
diffusion coefficient and convection velocity are both functions of location inside the
transition zone: V = V[c(x)] and D = D[c(x)].
Using the parameters of a base case in Table 4.1, a concentration profile is calculated
and shown in Figure 4.2a, based on which a viscosity curve is calculated by using Eq. (3.6)
83
Table 4.1 Physical properties and operating conditions of the base case.
Property Value Length, m 0.01 Permeability, D 10 Oil gravity 0.975 Solvent gravity (liquid) 0.517 Oil viscosity, mPas 6000 Solvent viscosity (liquid), mPas 0.1 Pressure gradient, kPa/m 5 Diffusion coefficient, m2/s 1.306×10−9μ−0.46 Time, s 600 Solubility, g solvent/g oil 0.26 Inlet solvent concentration, fraction 0.329 Inlet diffusion coefficient, m2/s 1.21×10−8
84
and plotted in Figure 4.2b. The associated diffusion coefficient and convection velocity
curves are computed by using Eqs. (3.4) and (4.1) and plotted in Figures 4.2c–d,
respectively. Calculations in the following sections are all based on the parameters of the
base case. For some special cases, their particular parameters will be noted.
4.2 Mathematical Models
4.2.1 Governing equation
Considering the effects of the concentration gradient and pressure gradient on the
mass transfer process between two materials, one dissolving into another (i.e., crude oil
and solvent), and disregarding the source/sink term, the governing equation would be:
c cD cVt x x
, (4.3)
4.2.2 Boundary and initial conditions
One boundary of the modeling object, transition zone, is assumedly saturated with
solvent at all times, which means a Dirichlet boundary condition (BC). The other boundary
of the transition zone is regarded as a Neumann BC. Initially, the entire model is free of
solvent. The BCs and initial condition (IC) are described by:
*( 0, ) , 0x tc c t
, (4.4)
( , )
0, 0x t
c tx
, (4.5)
( , 0) 0, 0x tc x
, (4.6)
85
x (m)0.000 0.002 0.004 0.006 0.008 0.010
c
0.0
0.1
0.2
0.3
0.4
x (m)0.000 0.002 0.004 0.006 0.008 0.010
D (m
2 /s)
0.0
2.0e-9
4.0e-9
6.0e-9
8.0e-9
1.0e-8
1.2e-8
1.4e-8
x (m)0.000 0.002 0.004 0.006 0.008 0.010
V (m
/s)
0
1e-6
2e-6
3e-6
4e-6
5e-6
6e-6
7e-6
x (m)0.000 0.002 0.004 0.006 0.008 0.010
c
P
0
1000
2000
3000
4000
5000
6000
7000
Figure 4.2 Concentration-dependent diffusion coefficient and flow velocity: (a)
Concentration; (b) Viscosity; (c) Effective diffusion coefficient; and (d) Convection
velocity.
(a) (b)
(c) (d)
86
where, c* is maximum concentration under the operating conditions, fraction; is
transition zone thickness, m. It is worthwhile to note that in fact, the boundaries of the
transition zone are moving and the solvent chamber is expanding all the time, which makes
the mass transfer model become a free boundary problem. This study does not consider the
whole mass transfer process, but focuses on a mass-transfer process in a short time interval
and thus uses fixed-boundary conditions to simplify the problem.
4.3 Semi-Analytical Solutions
4.3.1 Model #1: Convection–diffusion model with constant D and variable V
This model considers a convection–diffusion equation with a constant D and a
variable V. With the definitions of following dimensionless variables and number:
Dinlet
ccc
, 2Dt Dt
, Dxx
, VPeD
, (4.7)
where, cinlet is the inlet concentration at x = 0, which is equal to c* under the operating
conditions, fraction; Pe is Péclet number, dimensionless. The governing equation, BCs,
and IC of Model 1 can be normalized as:
2
2
( 0, )
( 1, )
( , 0)
1 0
0 0
0 0 1
D D
D D
D D
D D DD
D D D D
D Dx t
DD
D x t
D Dx t
c c c PePe ct x x x
c t
c tx
c x
. (4.8)
Pe measures the relative importance of convection to diffusion during a mass-transfer
process. It is worthwhile to state that in this thesis, Pe is a variable rather than constant
dimensionless number, and it actually represents the convection velocity.
87
Solution to Model #1with a constant D and a linear V
In order to derive the solution to a convection–diffusion model with a general Pe
profile, a simple convection–diffusion model with a simple linear Pe profile is studied as
the first step:
DPe ax b , (4.9)
where, a and b are the slope and x-intercept of a linear Pe profile. a and b should meet a<0,
b>0, and |b|>|a| for a positive flow velocity (direction of V is consistent with that of D), and
a>0, b<0, and |b|>|a| for a negative flow velocity (direction of V is opposite to that of D).
Substituting Eq. (4.8) for Pe in Eq. (4.8):
2
2D D D
D DD D D
c c cax b act x x
. (4.10)
Performing the Laplace transformation and integrating IC, Eq. (4.10) can be transformed
into an ordinary difference equation (ODE):
22
21 04
d C z J Cdz
, (4.11)
where
2
4 2D Da bx x
DC c e
, (4.12a)
, 0Dax bz aa
or , 0Dax bz aa
, (4.12b)
1 , 02
sJ aa
or 1 , 02
sJ aa
, (4.12c)
where, C and z are transformed cD and x in the Laplacian domain, respectively; s is the
Laplacian operator. Eq. (4.11) is the canonical form of the parabolic cylindrical function
[Abramowitz and Stegun, 1970], to which the general solution is in the following form:
88
1 2C AC BC . (4.13)
Here, C1 and C2 are two independent solutions to Eq. (4.11):
21 2
41
1 1, ( , , )2 4 2 2
z J zC J z e M
, (4.14)
21 2
42
3 3, ( , , )2 4 2 2
z J zC J z ze M
, (4.15)
where, M is the Kummer’s function; A and B are two constant coefficients and can be
obtained by applying the two BCs. Appendix A presents the detailed derivation of the
solution to Model #1 with a constant D and a linear V.
Solution to Model #1 with a constant D and a variable V
On the basis of the above foundation, a more general variable Pe profile is studied
here. As shown in Figure 4.3, a special approximation method is applied to solve a
convection–diffusion model with an arbitrary monotonous smoothly curved Pe profile: the
curved V profile is approximated with a piecewise linear (n segments) profile. Since the
governing equation and IC for each segment are the same as those in Model #1 with a
constant D and a linear V, the transformed dimensionless concentration in Laplacian
domain for each segment should have the same form as Eq. (4.13):
1, 2, 1i i i i iC AC B C i n , (4.16)
where, Ai and Bi can be obtained by applying the BCs of the ith segment: D,i
Di
D x
c qx
for
the left boundary and , 1
1
D i
Di
D x
c qx
for the right one (qi and qi+1 denote the mass-transfer
rates at the left and right boundaries of the ith segment, respectively). It is worthwhile to
89
note the left BC for the first segment is 01
DD x
c , and that the right BC for the last
segment is 1
0D
D
D x
cx
.
Back replacing the determined Ai and Bi into the Eq. (4.16), C is obtained over the
entire spatial domain as functions of qi:
* *1 1 1 2,C J z A B q , (4.17a)
* *1, 1 < <i i i i iC J z A q B q i n , (4.17b)
* *,n n n nC J z A q B . (4.17c)
Considering the continuity condition for the solvent concentration at the interior common
boundaries between any neighboring two segments:
1D,i D,i
D,i D,ix xc c , (4.18)
and in the Laplacian domain, this is
2 21 1
, ,
4 2 4 21
i i i i
D i D i
a b a bx x x x
i ix x
C e C e
. (4.19)
Applying Eq. (4.19) to Eqs. (4.17a−c), n−1 equations can be obtained:
* * * *2 2 1 2 2 2 3 1A B q B q A , (4.20a)
* * * *1 1 1 1 0 2 < <i i i i i i i i iA q A B q B q i n , (4.20b)
* * * *1 1 1n n n n n n n nA q B A q B , (4.20c)
where
21 1
4 2i i i ia a b bx x
i e
. (4.21)
90
Figure 4.3 Approximation to the convection velocity with a piecewise linear profile.
max( 0, )x tc c
( , )
0x L t
cx
( , 0) 0x tc
( , ) ?x tc
x1 i ii ix x
c c
Pe
91
Eqs. (4.20a−c) can be coupled altogether to form a linear system:
1 1 1 1n n n n M q F , (4.22)
where, the coefficient matrix [M](n-1)×(n-1) is a tridiagonal matrix; {q}n-1 is the
to-be-determined unknown column matrix; the column matrix {F}n-1 and the coefficient
matrix [M](n-1)×(n-1) can be constructed given a piecewise linear Pe profile. {q}n-1 can be
solved by using the Thomas algorithm [Muller, 2001]. Back replacing it into Eqs.
(4.17a−c), C over the entire space can be obtained. Finally, solvent concentration in
physical domain can be obtained by using the Stehfest Laplace inverse transform [Stehfest,
1970] (loop number in this study is set as 8).
4.3.2 Model #2: Convection–diffusion model with variable D and variable V
This model considers both diffusion coefficient and convection velocity as variables:
D=D(x) and V=V(x). With the definitions of following dimensionless variables and
number:
Dinlet
ccc
, Dinlet
DDD
, Dxx
, 2inlet
Dt Dt
, inlet
VPeD
, (4.23)
where Dinlet is the diffusion coefficient at the left/inlet boundary under the operating
conditions, m2/s. The governing equation, BCs, and IC of Model #2 can be normalized as:
2
2
( 0, )
( 1, )
( , 0)
1 0
0 0
0 0 1
D D
D D
D D
D D D DD D
D D D D D
D Dx t
DD
D x t
D Dx t
c c D c PeD Pe ct x x x x
c t
c tx
c x
. (4.24)
92
Similar to Model #1, a simple case for Model #2 with a linear DD and a linear Pe is first
studied as a first step for a more general case:
DPe ax b , ' 'D DD a x b . (4.25)
where 'a and 'b are the slope and x-intercept of the linear DD profile. Substituting Eq.
(4.25) for DD and Pe in the governing equation of Model #2:
2
2' ' 'D D DD D D
D D D
c c ca x b a ax b act x x
. (4.26)
Eq. (4.26) can be analytically solved in the same way as that for Model #1 with a constant
D and a linear V. The general solution is:
1, ; 1, 2 ;C AM B M , (4.27)
here, definitions of ϛ, ξ, and ε are provided in Appendix B; coefficients A and B can be
determined by applying the BCs. The solvent concentration in the physical domain can be
obtained by conducting the Stehfest Laplace inverse transformation (loop number in this
study is chosen as 8).
For a more general case where DD and Pe profiles are arbitrary monotonous smooth
curves, DD and Pe can be respectively approximated to have a piecewise linear profile.
Then the model can be semi-analytically solved by using the same approach as described in
the previous section. It is worthwhile to note that DD and Pe profiles must be divided into
the same segments on the x axis when the approximations of them are made.
The above-derived solutions are for the IC of cD(xD,0) = 0. In the case of tD > 0, the
transformed governing equation in the Laplacian domain would be a non-homogeneous
equation whose general solution can be obtained:
1 2 1 2' 'C AC BC A C B C . (4.28)
93
Here, A and B are the coefficients for the corresponding homogeneous equation and have
the same values as those in Eq. (4.16); A’ and B’ can be determined by using the BCs and
the method of undetermined coefficients [Zill, 2001].
4.4 Validations
4.4.1 Validation with an analytical solution for a special case
Considering a special case of Model #1 where D is a constant and Pe is a hyperbolic
function of xD:
2D
D
Pe xx
, (4.29)
where, ψ is an arbitrary constant. The analytical solution to Eq. (4.29) can be obtained in
the Laplacian domain (the detailed derivations are given in Appendix C) as:
(2 )
2( )
(1 )
D Dsx s x
s
e eC ss e
, (4.30)
where
(1 ) 1(1 ) 1
ss
. (4.31)
Then the hyperbolic Pe profile is approximated with a piecewise linear profile, and the
model is semi-analytically solved by using the aforementioned approach. Figure 4.4
compares the analytical and semi-analytical solutions, suggesting that the semi-analytical
solution is not reliable when the Pe profile is roughly approximated with five segments but
rather accurate with twenty-five segments. The accuracy of the semi-analytical solution
depends on the approximation to the Pe profile—The better approximation is, the more
accurate the semi-analytical result would be. However, too many segments would greatly
94
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6Semianalytical, N=5Semianalytical, N=15Semianalytical, N=25Analytical
xD0.0 0.2 0.4 0.6 0.8 1.0
Pe
0
2
4
6
8
10
Figure 4.4 Semi-analytical vs. analytical cD for a convection–diffusion mass transfer
with a special convection velocity
20.25D
Pex
95
increase the computational time but trivially enhance the incremental accuracy. Therefore,
the segment number for obtaining a reliable and precise solution varies with the linearities
of the D and V profiles. It is worthy of stating that in order to improve the proximity of a
piecewise linear profile, the segment-division can be densified where Pe changes
drastically and sparsed where it varies slowly, rather than evenly distributed.
4.4.2 Validation with the numerical solution
The Crank−Nicolson finite difference method (FDM) with a truncation error of
O(∆x4) is applied to acquire the numerical solution to the aforementioned
convection–diffusion model. Two spatial grid sizes (0.00005 and 0.0001 m) and two time
steps (10 and 20 s) are used for the numerical solution. Figure 4.5 compares the
semi-analytical and numerical solutions, showing the numerical solution with a grid size of
0.00005 m and a time step of 10 s gives the best match with the semi-analytical solution.
This suggests that the numerical solution is accurate enough as long as the grid size and
time step are sufficiently small.
4.5 Results and Discussion
4.5.1 Application of the convection–diffusion mass-transfer model
The convection−diffusion mass transfer model is applied to a CSI process (Figure
4.1). The solvent concentration distribution inside the transition zone is calculated by using
the semi-analytical solutions to the above models. Eqs. (3.3−5, 4.2) show that D and V are
both functions of and is a function of c, which make the governing equation a
non-linear partial differential equation (PDE). In this study, this non-linear PDE is solved
in a special way. First, the time domain is divided into a number of steps. Second, at one
96
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2Numerical-1Numerical-2Numerical-3Semianalytical
Figure 4.5 Semi-analytical vs. numerical cD.
97
time step, D and V are treated as functions of the solvent concentration at the end of the
previous time step; Therefore, D and V can be explicitly plotted so that the governing
equation becomes a linear PDE that is semi-analytically solved by using the method
provided in this study. Then the solvent concentration can be calculated and its value at the
end of that step will be used as the initial condition for the next time step. Figure 4.6
schematically demonstrates the flow chart for calculating the solvent concentration in the
transition zone. First, a solvent concentration profile can be computed with the governing
equation, BCs, and IC at a certain time point. Then, based on the solvent concentration, μ
and of solvent-diluted crude oil can be calculated by using Eqs. (1.6−8) and Eq. (1.9),
respectively; then D and V can be respectively obtained by using Eqs. (3.5−6) and (4.2).
Finally, the IC can be updated by the present solvent concentration profile; D and V in the
governing equation should also be updated for the calculation in the next time point. Table
4.1 lists the parameters of a base case, and most calculations in the following part are for
the base case. For comparison cases, their particular parameters will be specified.
4.5.2 Variable and constant diffusion coefficient and convection velocity
The effects of constant and variable diffusion coefficient/flow velocity on the solvent
concentration distribution across the transition zone are analyzed in this section. Four cases
are considered:
Case #1: a variable D and a variable V
Case #2: a constant D and a variable V
Case #3: a variable D and a constant V
Case #4: a constant D and a constant V
98
Figure 4.6 Flowchart of calculating the solvent concentration in the transition zone (t*
denotes the termination time).
Equations 1. Semi-analytical solutions 2. Mixture rule of ideal solution, Eq. 1.9 3. Lederer–Shu correlation, Eq. 1.6−8 4. Das–Butler correlation, Eq. 3.5−6 5. Darcy’s law, Eq. 4.2
Governing Eq. IC BCs
c
ρ
V
D Finish
Yes t > t*
1
2 3
4
5
99
For comparison purposes, the constant D in Cases #2 and #4 is equivalent to the mean
value of the variable D over a range of [Dinlet, 0.01Dinlet], and the constant V in Case #3 and
#4 is equivalent to the mean value of the variable V over a range of [Vinlet, 0.01Vinlet]. Two
times (300 and 600 s) are calculated. Figure 4.7 compares the results of the four cases.
By Analyzing of the results for the four cases, several conclusions can be made: (1)
compared with Cases #2−4, cD for Case 1 (variable D and variable V) is underestimated
near the left boundary but overestimated at the other locations. (2) The deviation between
Case #1 and the rest cases are smaller at a shorter time t1 but larger at a longer time t2.
Because the constant D and V are equivalent to the variable D and V at the initial time and
are unchanged as time increases; however, the variable D and V become larger and larger
with time. Therefore, the constant D and V would be less than the mean values of the
variable D and V at a later time. (3) Although the integral area of cD curves for the four
cases are closer to each other, their solvent concentration profiles have quite distinct shapes.
This is most evident in Figure 4.7c. The shape of the cD curve is mainly determined by D
and V in the governing equation. (4) The effect of constant V on the cD profile is much
larger than that of D, as can be seen in Figures 4.7a and 4.7b. This implies that the pressure
gradient may play a larger role than the concentration gradient and that the crude
oilsolvent mass transfer can be strengthened by a pressure difference.
4.5.3 Effect of convection velocity
Pressure gradient
During the majority of huff-n-puff process, the pressure over the entire reservoir is
unbalanced: the pressure in the solvent chamber is higher (positive) than that in the
untouched crude oil zone during the huff period whereas lower (negative) than that in the
100
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2t1: var. D & var. Vt2: var. D & var. Vt1: const. D & var. Vt2: const. D & var. V
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2t1: var. D & var. Vt2: var. D & var. Vt1: var. D & const. Vt2: var. D & const. V
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2t1: var. D & var. Vt2: var. D & var. Vt1: const. D & const. Vt2: const. D & const. V
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2t2: var. D & var. Vt2: const. D & var. Vt2: var. D & const. Vt2: const. D & const. V
Figure 4.7 Comparison of cD for different cases: (a) Variable D & variable V vs.
constant D & variable V; (b) Variable D & variable V vs. variable D & constant V; (c)
Variable D & variable V vs. constant D & constant V; and (d) Variable D & variable V
and D vs. constant D & variable V vs. variable D & constant V vs. constant D & constant
V (Constant D is equal to 5.8×10−9 m2/s; constant V is equal to 1.8×10−6 m/s; t1 = 300 s; t2
= 600 s).
(a) (b)
(c) (d)
101
untouched crude oil zone during the puff period. This part analyzes the effect of the
pressure gradient on the solvent concentration distribution across the transition zone. It is
worthwhile to mention that in fact, the pressure gradient becomes smaller and smaller with
time. Here, a constant pressure gradient is used to simplify the calculation and qualitatively
illustrate the problem.
Figure 4.8 shows the cD profiles under the effect of positive, zero, and negative
pressure gradients. Compared with the pure diffusion process where the pressure gradient
equals zero, the cD profile is greatly improved by a positive pressure gradient of 5 kPa/m:
the integral area of the cD profile for 5 kPa/m is almost twice of that for 0 kPa/m. In contrast,
the cD profile is slightly shrunk by a negative pressure gradient of −5 kPa/m: the integral
area of the cD profile for −5 kPa/m is ~80% of that for 0 kPa/m. It is found that the positive
pressure gradient could prompt the solvent dissolution into the crude oil while the negative
pressure gradient would hinder the solvent dissolution into the crude oil, implying that the
transition zone expands during the huff period while shrinks during the puff period. This
also demonstrates one of the advantages of the cyclic solvent process (such as CSI) over
the continuous solvent process (such as VAPEX): the crude oilsolvent mixing process can
be more effective in CSI than in VAPEX.
Crude oil viscosity
Figure 4.9 presents the effect of the crude oil viscosity on the cD profile. Four
viscosities are chosen: 600, 6,000, 60,000, and 600,000 mPas. The results are quite
straightforward: (1) The solvent can dissolve further into the crude oil with a lower oil
viscosity, which means that less viscous crude oil can be more easily diluted by the solvent;
102
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2grad_P=5.0 kPa/mgrad_P=2.5 kPa/mgrad_P=0 kPa/mgrad_P=-2.5 kPa/mgrad_P=-5.0 kPa/m
Figure 4.8 Effect of the pressure gradient on the solvent concentration distribution.
103
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2mPa.smPa.smPa.smPa.s
Figure 4.9 Effect of crude oil viscosity on the solvent concentration distribution.
104
(2) The transition-zone thickness increase is not linear: the dimensionless transition-zone
thickness is increased by 0.04 for a viscosity change from 600,000 to 60,000 mPas, by
0.12 of the unit dimensionless distance for a viscosity change from 60,000 to 6,000 mPas,
and by 0.24 for a viscosity change from 6,000 to 600 mPas. This indicates that the
solvent-based CSI process can be more effective for a relatively less viscous crude oil.
Note that the transition-zone thickness covers a distance from xD (cD = 1) to xD (cD = 0.01).
Diffusion coefficient
Figure 4.10 displays the effect of the diffusion coefficient on the solvent
concentration distribution. The diffusion coefficient correlation of propane and Peace
River bitumen [Das and Butler, 1996], Eqs. (3.5−6), is used as a basic formula. Parameter β
is kept constant as −0.46 since it is around −0.5 in most cases as cited in the literature; α
varies from 1.0×10−9 to 3.0×10−9. The results show that the cD profile with a smaller D
would have a sharper front yet a shorter diffusing distance while the cD profile with a larger
D would have a gentler front but a longer diffusing distance. This is because a smaller D
would make solvent molecules aggregate near the inlet, leading to a higher concentration
but sharper decline near the inlet since very little solvent can dissolve into the crude oil.
4.5.4 Péclet number
All the above-mentioned factors (i.e., pressure gradient, viscosity and diffusion
coefficient) can be integrated into a dimensionless number, Péclet number. The above
analyses indicate a general trend: an increased V can accelerate the crude oilsolvent
mixing. In practice, the permeability is easy to measure but the pressure gradient and
diffusion coefficient across the transition zone are difficult to determine. Therefore, some
simple Pe profiles are assumed to qualitatively analyze its effect on the cD distribution.
105
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2=1.0e-9=1.5e-9=2.0e-9=2.5e-9=3.0e-9
Figure 4.10 Effect of diffusion coefficient on the solvent concentration distribution.
0.46D
106
Concave, linear, and convex Pe profiles
Figure 4.11 displays the cD profiles for Pe curves of three different shapes: concave,
linear, and convex with the same starting and ending points and mean values. Comparing
the results, it is found that a declining Pe profile tends to make the solvent accumulate at
the inlet boundary, which is the bumping (cD > 1) portion in the cD profile. The sharper the
decline is, the more easily the solvent would aggregate—the amplitude of cD profile for the
concave Pe is the largest among the three scenarios.
Linear Pe profile with different slopes
Figure 4.12 shows the cD profiles for different linear Pe profiles with the same
x-incept but different slopes. It can be seen that a smaller Pe slope would lead to a lower cD
profile, indicating a less efficient crude oilsolvent mixing. In addition, Figure 4.12
demonstrates a proof to the conclusion generated in Figure 4.11: a larger decrease of Pe
could lead to a more notable bumping of the cD profile.
4.5.5 Effect of gravity force in natural convection
Effect of natural convection on the solvent concentration is studied. In some
solvent-based EOR processes, such as the rising phase of VAPEX and upwards leaching,
solvent diffuses upwards into the crude oil that is diluted and drained downward. In this
case, the flow direction is against the diffusing direction and the flow velocity in the
governing equation is negative. Figure 4.13 shows the concentration distributions of
propane and butane for a diffusion process with and without natural convection, suggesting
that butane with gravity force is the least efficient while propane without gravity force is
the most effective one. This means that the natural convection caused by density difference
may hinder the solvent from mixing with the crude oil.
107
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2
ConvexLinearConcave
xD
0.0 0.2 0.4 0.6 0.8 1.0
Pe
0
2
4
6
8
Figure 4.11 Effect of Péclet number on the solvent concentration distribution.
108
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2Pe=-8xD+8Pe=-6xD+6Pe=-4xD+4Pe=-2xD+2
xD0.0 0.2 0.4 0.6 0.8 1.0
c D
0
2
4
6
8
Figure 4.12 Effect of Péclet number with different linear shape on the solvent
concentration distribution.
109
xD
0.0 0.2 0.4 0.6 0.8 1.0
c D
0.0
0.2
0.4
0.6
0.8
1.0
1.2Propane, without gravityPropane, with gravity Butane, without gravityButane, with gravity
Figure 4.13 Effect of gravity force on the solvent concentration distribution.
Solvent
Heavy oil
With gravity force Without gravity force
Solvent
Heavy oil
110
4.6 Chapter Summary
This chapter develops two 1D convection–diffusion mass transfer models for the CSI
process: one model considers a constant diffusion coefficient and a variable flow velocity
and the other considers both parameters as variables. Semi-analytical solutions are
obtained and applied to analyze the mass transfer process between crude oil and solvent.
The following conclusions can be made:
1. The accuracy of the semi-analytical solution largely depends on the
approximation of the diffusion coefficient and convection velocity profiles—a
better approximation can lead to a more accurate solution.
2. The approximation of the actual variable diffusion coefficient with a constant
value can be inaccurate, since the latter does not consider the change of
diffusion coefficient throughout a CSI process. This is true for the convection
velocity.
3. The convection velocity can play a larger role than the diffusion coefficient in the
crude oilsolvent mixing process during a CSI process.
4. An increased convection velocity can accelerate the dissolution of solvent into
the crude oil during the solvent injection period of CSI.
5. Gravity force may reduce the mass transfer between crude oil and solvent due to
the natural convection.
111
CHAPTER 5 FOAMY OIL-ASSISTED VAPOUR EXTRACTION
(F-VAPEX)
CSI benefits from a stronger mass transfer (Chapter 4) and a higher oil production
rate during the pressure reduction period but suffers from the unproductive and long
injection and soaking periods and the consequent low average oil production rate. This
chapter proposes a new process, namely foamy oil-assisted vapour extraction (F-VAPEX).
F-VAPEX combines VAPEX and CSI together to take advantage of the continuous
production of VAPEX and the stronger mass transfer and oil production mechanisms of
CSI. It is essentially a VAPEX process during which the operating pressure is cyclically
decreased and increased. Technical details, experimental results, and comparative analyses
of the new technique are presented in this chapter.
5.1 Experimental
5.1.1 Materials
The heavy oil sample was collected from a western Canadian heavy oil reservoir,
with a density of o = 976 kg/m3 and a viscosity of μo = 5,875 cP, both of which were
measured at the atmospheric pressure and a room temperature of 20.2C. The asphaltene
content of the original heavy oil sample was measured by using the standard ASTM D2700
method [2003] with filter papers (No. 5, Whatman, England) with a pore size of 2.5 μm and
found to be 17.69 wt.% (n-pentane insoluble). Propane with a stated purity of 99.5 mol.%
(Praxair, Canada) was used as the extracting solvent. Glass beads with an average size of
90−150 μm were used to pack the cylindrical and rectangular physical models.
112
5.1.2 Experimental set-up
Figure 5.1 shows the schematic diagram of the experimental set-up, which is
comprised of four major operation units: a solvent injection unit, a physical model, a fluids
production unit, and a data acquisition system. The solvent injection unit consists of a
propane cylinder (Praxair, Canada), a two-stage gas regulator (KCY Series, Swagelok,
USA) installed on the propane cylinder, a solvent injection valve, and an injector.
The major component of the experimental set-up is a visual rectangular sand-packed
high-pressure physical model. This physical model has a rectangular cavity (40 10 2
cm3) grooved in a steel plate to be packed with sand. The front of the model is covered with
an acrylic as a visual window, through which the test process can be visualized and
photographed. A digital camera (Rebel T3, Canon, Japan), in conjunction with a florescent
light sources (Catalina Lighting, USA), is used to take digital images of the solvent
chamber during each VAPEX test. The technical details regarding the rectangular physical
model can be found elsewhere [Moghadam et al., 2008].
Two types of well configurations are adopted for the VAPEX and F-VAPEX tests
(Figure 5.2): (1) Central well configuration. The producer is set at the center bottom part of
the model, whereas the injector is placed 3 cm above the producer; (2) Lateral well
configuration. The injector and producer are positioned at the top right and bottom left
corners of the physical model, respectively. The lateral well configuration is applied to
simulate a pair of horizontal injector and producer with proper vertical and horizontal
separation distances. The well configuration for each test is specified in Table 5.1. It is
worthwhile to mention that one CSI test (Test #5.2) used a single well alternately as the
injector and producer to simulate a conventional solvent huff-n-puff process.
113
Figure 5.1 Schematic diagram of the experimental set-up in this study.
Injection unit Physical model
Propane Camera
Data acquisition unit Production unit
Back-pressure regulator Digital pressure gauge
Pressure transducer
Notebook computer
Steel tubing Plastic flexible hose Data ware
Sand pack Injector Producer
Scale Surge flask Flow meter
Oil collector
114
(a)
(b)
(c)
Figure 5.2 (a) Physical model dimensions; (b) Central well configuration; and (c)
Lateral well configuration.
20 cm 7 cm
Height = 10 cm
Width = 40 cm Thickness = 2 cm
115
Table 5.1 Physical properties of the sand-packed model and experimental conditions
for the VAPEX, CSI and F-VAPEX tests.
Test No. Well Configuration Operating Scheme Cycle Length (h)
PV (cc)
Soi (%)
k (D)
(%)
5.1 VAPEX, Fig. 5.3a — 284.8 92.7 4.9 35.6
5.2 CSI, Fig. 5.3b 1 284.5 92.1 4.7 36.2
5.3 F-VAPEX, Fig. 5.3c 1 286.6 93.5 5.4 35.7
5.4 F-VAPEX, Fig. 5.3c 2 286.1 92.4 5.1 36.7
5.5 F-VAPEX, Fig. 5.3c 4 285.8 93.2 5.8 35.9
5.6 VAPEX, Fig. 5.3a — 287.1 94.5 4.9 35.8
5.7 F-VAPEX, Fig. 5.3c 1 283.2 93.8 4.7 35.9
5.8 F-VAPEX, Fig. 5.3c 2 288.8 94.1 5.2 36.3
Injector/ producer
116
The production unit is comprised of a production valve, a high-sensitivity
back-pressure regulator (BPR) (LBS4 Series, Swagelok, USA), a produced oil collector, an
electronic scale (ML302E, Mettler Toledo, Switzerland), and a precision drum-type gas
flowmeter (TG05, Ritter, Germany). The produced oil was collected in a flask and weighed
by using the electronic scale to determine the cumulative oil production for all the tests.
The produced gas volume was recorded by using the precision drum-type gas flowmeter.
The data acquisition system includes a high-precision digital pressure transducer
(PPM-2, Heise, USA) and a notebook personal computer (PC) (Hewlett Packard, USA).
The injection pressure and production pressure are recorded in the notebook PC
automatically and continuously. The cumulative oil production and solvent production are
recorded into the notebook PC manually at a fixed time interval of 1 h during each test.
5.1.3 Experimental preparation
Sand-packing
Prior to the sand-packing, a leakage test was carried out by using water at a pressure
of 1,200 kPa. After the water leakage test, the glass beads with a grain size of 90−150 μm
(diameter) were used to pack the physical model. Once the cavity of the physical model
was fully packed with glass beads, it was covered with the polycarbonate plate, acrylic
plate and metal frame in sequence. Then the physical model was positioned vertically or
horizontally, and the sands were dried by using the pressurized air for at least 48 h. The
physical model was shaken with an air-actuated vibrator (BV, Vibco, USA) for at least two
hours. Some void space might be formed at the top of the cavity after the dry sands were
shaken and settled downward. Therefore, the physical model needed to be repacked 2 to 3
times in the same way until no void space was formed at the top of the physical model.
117
Porosity measurement
The imbibition method was used to measure the porosity of the sand-packed physical
model. More specifically, the physical model was vacuumed and then saturated with water
by imbibitions. With the measured volume of the imbibed water and the known volume of
the cavity of the physical model, its porosity can be calculated. The measured porosity for
the experiments was found to be in a range of 34.5% to 37.5%.
Permeability measurement
During the permeability measurement, a digital pressure transducer was used to
record the pressure difference. Distilled water with the density of 1,000 kg/m3 was used as
the working medium. The permeability of the sandpack is determined by using the Darcy’s
law for a steady-state one-phase flow prior to each test. The pressure drop of the distilled
water at the two ends of the physical model was measured and recorded by using a digital
pressure transducer. The permeability measurements were conducted for three times, and
the average permeability of the sand-packed physical model was found to be k = 4.6−6.9
Darcy.
Initial oil saturation
After the permeability measurement, the wet glass beads were dried by using the
pressurized air for at least 48 hours. The heavy oil was injected into the physical model at a
volume flow rate of 0.1−0.25 cm3/h until it was completely saturated with the heavy oil
sample. The initial oil saturation was measured as the ratio of the injected oil volume to the
pore volume of the physical model, which was found to be in the range of Soi =
90.2−94.5%.
118
5.1.4 Experimental procedure
In this study, eight laboratory tests were performed with three operating schemes
(VAPEX, CSI, and F-VAPEX). The VAPEX and CSI tests served as base tests for the
F-VAPEX tests. The first five tests were conducted with the central well configuration to
evaluate the F-VAPEX process and the last three tests were undertaken with the lateral well
configuration to validate and further assess the F-VAPEX process. Pressure-control
schemes for the VAPEX, CSI, and F-VAPEX tests are shown in Figure 5.3 and described
in the following sub-sections.
VAPEX
The extracting solvent (propane) is continuously injected into the physical model at
Pinj = 800 kPa (Figure 5.3a) and T = 20.2C, which is close to the propane’s saturation
pressure Pdew = 841 kPa at T = 20.2C. Meanwhile, the BPR is properly controlled so that
the pressure inside the physical model is maintained at P = 800 kPa and no oil is
accumulated above the producer.
CSI
Each CSI cycle lasts for 1 h and consists of two periods: (1) Injection period. Propane
is continuously injected into the sand-packed physical model at Pinj = 800 kPa and T =
20.2C for 55 min; (2) Production period. The production pressure Pprod is reduced from
800 to 200 kPa within 5 min (Figure 5.3b).
F-VAPEX.
F-VAPEX is a cyclic process and each cycle continues over 1 h that comprises two
periods:
119
Time (hh:mm)
00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10
Pres
sure
(kPa
)
0
200
400
600
800
1000
(a)
Time (hh:mm) 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10
Pres
sure
(kPa
)
0
200
400
600
800
1000
One cycle
Injection Production
(b)
Time (hh:mm) 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10
Pre
ssur
e (k
Pa)
0
200
400
600
800
1000
One cycle
Stable pressure period
Pressure reduction period
(c)
Figure 5.3 Pressure-control scheme for (a) VAPEX; (b) CSI; and (c) F-VAPEX.
120
1. Stable pressure period. This period lasts for 55 min, during which the injection
and production pressures are operated in the VAPEX mode: the model pressure is
maintained at Pinj = 800 kPa and the oil is produced continuously.
2. Pressure reduction period. This period lasts for 5 min, during which the solvent
injector is closed and both the BPR and the producer are quickly opened to
induce a sharp blowdown.
Some F-VAPEX tests with longer cycle lengths (2 and 4 h) prolong the stable
pressure period and pressure reduction period proportionally. For instance, Test #5.4 (cycle
length = 2 h) has a 110 min of stable pressure period and a 10 min of pressure reduction
period in each cycle. It is worthwhile to mention that prior to the formal process of the
VAPEX and F-VAPEX tests, the initial communication between the injector and the
producer was established by keeping the injection pressure at a pre-set pressure (800 kPa)
and the production pressure at the atmospheric pressure until a column of continuous gas
bubbles were observed at the producer. In this study, the communication took 30–45 min to
establish and led to an oil production of 1.1–2.3 g for the tests with the central well
configuration and 2.3–3.5 h to result in an oil production of 2.1–3.6 g for the tests with the
lateral well configuration.
5.1.5 Other measurements
Residual water and oil saturations
The residual water and oil saturations at different representative locations inside the
sand-packed physical models were measured after each test. First, the physical model was
opened and sand samples saturated with the residual water and oil were taken and placed
into beakers of 25 ml. Second, the beakers were placed in an oven and heated at 70C for
121
24 h so that the residual water in the sand sample can be evaporated. The weight difference
before and after the heating was noted as Ww. Finally, the water-free sand sample was
rinsed with toluene to remove the residual oil, and then heated inside the oven to vaporize
the toluene from the sand sample. The weight change before and after the rinsing and
heating was noted as Wo. The final weight of the dried and cleaned sand samples were
noted as Ws. The volumes of the residual oil, residual water, and sand were computed by
dividing Ww, Wo, and Ws by their respective densities w, o, and s. The pore volume of the
initial sand sample, Vp, was calculated by using the volume of the final dried and cleaned
sand sample and the measured porosity. The pore volume, residual water saturation, and
residual oil saturation were determined by using the following equations:
p s 1V V
, (5.1)
wwr
p
VSV
, (5.2)
oor
p
VSV
. (5.3)
5.2 Results and Discussion
5.2.1 Foamy oil flow in F-VAPEX
Foamy oil zone
Figure 5.4 shows the measured injection and production pressure versus time data for
an F-VAPEX test (Test #5.3). A special phenomenon, namely ‘foamy oil flow’, was
observed during the pressure reduction period of Test #5.3, as shown in Figure 5.5a. Three
zones can be identified in Figure 5.5a: a solvent chamber, an untouched heavy oil zone, and
122
a ‘foamy oil zone’ in between. The boundary of foamy oil zone on the right-hand side of
the model is roughly marked with the white dash lines. It is found that the foamy oil zone
grew throughout the F-VAPEX test, especially during the pressure reduction period.
During the early stage of a pressure reduction period, the foamy oil zone shrank slightly
due to the production of the solvent-diluted heavy oil from it. Afterward, when the pressure
was decreased to a certain level (i.e., bubble-point pressure), a flow front suddenly
emerged from the boundary between the foamy oil zone and untouched heavy oil zone and
moved quickly toward the solvent chamber and the producer. This speculated foamy oil
flow lasted for a short period of time (typically 5–20 s) and resulted in an expanded foamy
oil zone. Figure 5.5b shows the model only 10 s later than that in Figure 5.5a. It can be seen
that the foamy oil zone became much larger on both sides of the model after the expansion.
In addition, the foamy oil zone became darker near the solvent chamber and lighter near the
untouched heavy oil zone, and its boundaries also became clearer in Figure 5.5b. This is
because the foamy oil flow moved solvent-diluted heavy oil closer to the producer and
redistributed the oil saturation inside the foamy oil zone.
123
Time (hh:mm)
00:00 00:20 00:40 01:00 01:20 01:40
Pre
ssur
e (k
Pa)
0
200
400
600
800
1000Pinj
Pprod
00:30 00:40 00:50 01:00770
780
790
800
810
Figure 5.4 Injection and production pressure data during a typical F-VAPEX cycle.
124
(a)
(b)
Figure 5.5 Foamy oil zone (a) before and (b) after foamy oil flow during a pressure
reduction period of an F-VAPEX process (Test #5.3).
Solvent chamber
Foamy oil zone
Untouched heavy oil zone
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125
Evolution of foamy oil zone
Figure 5.6 shows the foamy oil zone during the early, intermediate, and late stages of
an F-VAPEX process (Test #5.3). It is found that the foamy oil zone was rather small at
the early stage of Test #5.3 (Figure 5.6a). It grew larger and larger with time (Figure 5.6b)
and occupied almost half of the model at the late stage (Figure 5.6c). Moreover, it can be
seen that the solvent chamber had a funnel shape and the foamy oil zone on each side of
the model had irregular shapes, wider at the bottom and thinner at the top. This is because
the solvent-diluted heavy oil was drained downward to the bottom of the foamy oil zone
by gravity, which led to a stronger foamy oil flow and more significant expansion at the
bottom than at the top of the foamy oil zone during the pressure reduction period.
Effects of foamy oil zone
The foamy oil flow during the pressure reduction period of an F-VAPEX test has two
major effects:
1. Mass transfer enhancement. The foamy oil flow redistributed the solvent-diluted
heavy oil inside the model and greatly alleviated the ‘concentration shock’,
giving the solvent more chance to touch the heavy crude oil. In addition, since the
foamy oil zone was a two-phase zone that had a large solvent−oil contact area, the
partially diluted heavy oil could be more easily and completely diluted by solvent
during the stable pressure period.
2. Production enhancement. In addition to the gravity drainage and pressure
gradient [Knorr and Imran, 2012] in conventional VAPEX, F-VAPEX
introduced two more production mechanisms, i.e., solution-gas drive and foamy
oil flow, to enhance the heavy oil recovery.
126
(a)
(b)
(c)
Figure 5.6 Foamy oil zone during the (a) early, (b) middle, and (c) late stages of an
F-VAPEX test (Test #5.3).
127
It is worthwhile to mention that the foamy oil flow also helped to estimate the size of
the foamy oil zone. Because the foamy oil zone boundary, especially the boundary near the
untouched heavy oil zone, became distinguishable after the foamy oil flow (Figure 5.6b).
Therefore, the size of the foamy oil zone can be estimated to optimize the operating
conditions of F-VAPEX.
Oil production mechanisms
Similar to VAPEX, F-VAPEX had oil production throughout the process. During the
stable pressure period, the solvent-diluted heavy oil was continuously drained downward
by gravity and intermittently produced by a small pressure gradient around the producer, as
shown by the close-up of the injection and production pressure profiles in the insert of
Figure 5.4. The small pressure gradients can suck out the solvent-diluted heavy oil around
the producer without causing a serious solvent breakthrough. During the pressure reduction
period, the solvent-diluted heavy oil was produced through the pressure gradient,
solution-gas drive, and foamy oil flow that are similar to the puff period of the
conventional CSI process.
5.2.2 F-VAPEX vs. VAPEX/CSI
Oil production
Table 5.2 summarizes the measured test durations t, cumulative oil production data
Qo, and cumulative solvent production data Qg, and the calculated average oil production
rates qo, oil recovery factors (RFs), and solvent−oil ratios (SOR) for the VAPEX, CSI, and
F-VAPEX tests in this study. Figure 5.7 shows the cumulative oil production versus time
data for the VAPEX, CSI, and F-VAPEX tests with the central well configuration. It can be
seen that the F-VAPEX tests (Tests #5.3−4) had higher average oil production rates and the
128
ultimate oil recovery factors than the VAPEX (Test #5.1) and CSI (Test #5.2) tests. In
addition, Test #5.3 achieved the best performance among all the three F-VAPEX tests
(Tests #5.3−5.5). Figure 5.8 shows the cumulative oil production versus time data for the
VAPEX and F-VAPEX tests with the lateral well configuration. It verifies the superiority
of the F-VAPEX process over the conventional VAPEX and CSI processes in terms of the
average oil production rate. The average oil production rate of VAPEX was enhanced by
F-VAPEX by approximately 50% with the central well configuration and about 115% with
the lateral well configuration, as shown in Figure 5.9. In addition, the average oil
production rate of CSI was slightly enhanced by F-VAPEX with the central well
configuration and significantly improved (over 100%) by F-VAPEX with the lateral well
configuration (Figure 5.10).
129
Table 5.2 Cumulative heavy oil and solvent production data.
Test no. t (h)
Qo (g)
Qs (dm3)
qo (g/h)
Oil RF (% OOIP)
SOR (g solvent/g oil)
5.1 60 114.8 38.421 1.91 44.6 0.61 5.2 57 153.6 393.13 2.69 60.1 4.70 5.3 60 179.3 345.52 2.99 68.6 3.54 5.4 60 171.5 312.06 2.86 66.5 3.34 5.5 60 156.1 299.23 2.60 60.1 3.52 5.6 60 137.6 51.075 2.29 52.0 0.68 5.7 28 143 311.38 5.11 55.2 4.00 5.8 28 135.2 252.11 4.83 51.0 3.43
130
Time (h)
0 10 20 30 40 50 60 70
Cum
ulat
ive
oil p
rodu
ctio
n (g
)
0
20
40
60
80
100
120
140
160
180
200VPAEXCSIF-VAPEX, cycle length = 1 hF-VAPEX, cycle length = 2 hF-VAPEX, cycle length = 4 h
Figure 5.7 Cumulative oil production versus time data for the VAPEX, CSI and
F-VAPEX tests with the central well configuration.
CSI Injector/ producer
VAPEX & F-VAPEX
131
Time (h)
0 10 20 30 40 50 60 70
Cum
ulat
ive
oil p
rodu
ctio
n (g
)
0
20
40
60
80
100
120
140
160
180
200VPAEXF-VAPEX, cycle length = 1 hF-VAPEX, cycle length = 2 h
Figure 5.8 Cumulative oil production versus time data for the CSI and F-VAPEX tests
with the lateral well configuration.
VAPEX & F-VAPEX
132
Test No.
3 4 5 6 7 8
Oil
prod
uctio
n ra
te e
nhan
emen
t (%
)
0
20
40
60
80
100
120
140
160
180
Figure 5.9 Enhancement of the oil production rate of VAPEX by F-VAPEX with
different well configurations.
VAPEX / F-VAPEX
VAPEX / F-VAPEX
100%F VAPEX VAPEX
VAPEX
q qenhancementq
133
Test No.
3 4 5 6 7 8
Oil
prod
uctio
n ra
te e
nhan
emen
t (%
)
0
50
100
150
Figure 5.10 Enhancement of the oil production rate of CSI by F-VAPEX with different
well configurations.
F-VAPEX
F-VAPEX
CSI Injector/ producer
100%F VAPEX CSI
CSI
q qenhancementq
134
Solvent−oil ratio
Figure 5.11 shows the cumulative solvent−oil ratio versus time data for the VAPEX,
CSI, and F-VAPEX tests with the central well configuration. It can be seen that F-VAPEX
with a cycle length of 2 h had a SOR higher than that of VAPEX but lower than that of CSI.
Figure 5.12 shows the cumulative solvent−oil ratio versus time data for the VAPEX and
F-VAPEX tests with the lateral well configuration. It is found that F-VAPEX also had a
higher SOR, which is consistent with the observation in Figure 5.11. Although F-VAPEX
requires much more solvent than VAPEX for the oil production, most of the injected
solvent can be recovered and reused [McMillen, 1985; Butler and Mokrys, 1991; Singhal
et al., 1997]. Nevertheless, the solvent usage is still a major issue for the solvent-based
methods, and the oil production rate and SOR should be optimized in an F-VAPEX
process.
5.2.3 Effect of well configuration
Foamy oil zone
Figures 5.13 shows the foamy oil zone during the early, intermediate, and late stages
of an F-VAPEX test with the lateral well configuration (Test #5.7). The foamy oil zone
above the untouched heavy oil zone in Test #5.7 had a different shape from that in Test
#5.3 (Figure 5.5). It grew mainly in the vertical direction in Test #5.7 and in the horizontal
direction in Test #5.3. Although with different shapes, the foamy oil zones were both
caused by the foamy oil flow during the pressure reduction period.
135
Time (h)
0 10 20 30 40 50 60 70
Cum
ulat
ive
solv
ent-o
il ra
tio (g
sol
vent
/g o
il)
0
1
2
3
4
5
6VPAEXCSIF-VAPEX, cycle length = 1 hF-VAPEX, cycle length = 2 hF-VAPEX, cycle length = 4 h
Figure 5.11 Cumulative solvent−oil ratio versus time data for the VAPEX, CSI, and
F-VAPEX tests with the central well configuration.
136
Time (h)
0 10 20 30 40 50 60 70
Cum
ulat
ive
solv
ent-o
il ra
tio (g
sol
vent
/g o
il)
0
1
2
3
4
5
6VPAEXF-VAPEX, cycle length = 1 hF-VAPEX, cycle length = 2 h
Figure 5.12 Cumulative solvent−oil ratio versus time data for the VAPEX and
F-VAPEX tests with the lateral well configuration.
137
(a)
(b)
(c)
Figure 5.13 Foamy oil zone during the (a) early, (b) middle, and (c) late stages of an
F-VAPEX test with the lateral well configuration (Test #5.7).
Solvent chamber Foamy oil zone
Untouched heavy oil zone
138
Oil production
Figure 5.14 shows the oil production from the stable pressure period and pressure
reduction period of the even numbered cycles of Test #5.3 (odd numbered cycles are
hidden for the sake of a clear illustration). Apparently, the stable pressure period produced
much more oil than the pressure reduction period in most cycles of Test #5.3. In total, the
former recovered 121.4 g of oil and the latter produced only 58.9 g. This trend agreed with
the oil production data from Test #5.7 (Figure 5.15) as well as the other F-VAPEX tests
(Tests #5.4−5, and #5.8) (Figure 5.16). The smaller contribution from the pressure
reduction period is caused by the solvent dissociation and the resulting oil viscosity
re-increase and mobility loss due to pressure reduction. However, without the pressure
reduction period, F-VAPEX would become a conventional VAPEX and its oil production
rate would be much lower (Table 5.2). Therefore, the pressure reduction period is an
indispensable part of the F-VAPEX process. Because the foamy oil flow during the
pressure reduction period moved the solvent-diluted heavy oil closer to the producer,
which facilitated the oil production during the subsequent stable pressure period.
139
Cycle number
0 10 20 30 40 50 60
Oil
prod
uctio
n (g
)
0
1
2
3
4
5
6Stable pressure periodPressure reduction period
Figure 5.14 Oil production from the stable pressure period and pressure reduction
period during Test #5.3.
F-VAPEX
140
Cycle number
0 5 10 15 20 25
Oil
prod
uctio
n (g
)
0
2
4
6
8
10
12
14Stable pressure periodPressure reduction period
Figure 5.15 Oil production from the stable pressure period and pressure reduction
period during Test #5.7.
F-VAPEX
141
Test No.
3 4 5 6 7 8
Oil
prod
uctio
n (g
)
0
20
40
60
80
100
120
140
160
180Stable pressure periodPressure reduction period
Test no. Cycle length (h) 3 1 4 2 5 4 7 1 8 2
Figure 5.16 Total oil production from the stable pressure period and pressure reduction
period during the F-VAPEX tests.
142
Comparison of Tests #5.3 (Figures 5.14) and #5.7 (Figures 5.15) suggests: (1) Test
#5.7 has a higher oil production rate than Test #5.3 in their early stages; (2) The oil
production rate declines with time in both Tests #5.3 and #5.7 and the decrease in Test #5.7
is much faster than that in Test #5.3; (3) Test #5.7 has a lower oil production rate than Test
#5.3 in their late stages. In Test #5.7, oil was produced mainly by pressure gradients during
the stable pressure period rather than gravity drainage due to the small inclination angle. In
the early stage, Test #5.7 had a larger solvent−oil contact area and more solvent-diluted
heavy oil than Test #5.3. Therefore, the oil could be more effectively produced in Test #5.7
than in Test #5.3. In the middle and late stages, the foamy oil zone could not reach to the
upper portion of the model and a high gas saturation band (solvent chamber) formed above
it in Test #5.7. Consequently, the solvent easily broke through from the solvent chamber
during the stable pressure period, which suppressed the oil production. During the pressure
reduction period, the foamy oil mainly flows vertically upward rather than horizontally
toward the producer, which also hindered the oil production. In contrast, Test #5.3 always
had a considerable inclination angle and the foamy oil flow constantly moved the oil
toward the producer, which led to a more stable oil production throughout the test.
Cycle length
Figure 5.17 shows the total solvent production data of the F-VAPEX tests with
different cycle lengths. Obviously, more solvent was required in the pressure reduction
period than that in the stable pressure period in the F-VAPEX tests with a cycle length of 1
h (Tests #5.3 and #5.7), which is contrary to the F-VAPEX tests with longer cycle lengths
(Tests #5.4−5, and #5.8). This suggests that a longer cycle length required a less amount of
solvent meanwhile had a similar oil production rate (Table 5.2). However, this does not
143
mean a longer cycle length would necessarily lead to a higher oil production rate, as shown
by the results of Tests #5.4 (cycle length: 2 h) and #5.5 (cycle length: 2 h). Test #5.5 saved
4.17% of the total solvent usage but lost 9.10% of the total oil production in comparison
with Test #5.4. Because the increase of cycle length decreased the cycle number, which
further affected the foamy oil flow to mobilize the oil toward the producer. Therefore,
during the stable pressure period, solvent broke through easily once the oil around the
producer was produced, which increased the solvent production. This interpreted why Test
#5.5 used more solvent than Test #5.4 during their stable pressure periods (Figure 5.17) but
produced less oil than Test #5.4 (Table 5.2).
144
Test No.
3 4 5 6 7 8
Solv
ent p
rodu
ctio
n (d
m3 )
0
50
100
150
200
250
300Stable pressure periodPressure reduction period
Test no. Cycle length (h) 3 1 4 2 5 4 7 1 8 2
Figure 5.17 Total solvent production data in the stable pressure period and the pressure
reduction period of the F-VAPEX tests.
145
5.2.4 Residual oil saturation
The residual oil and water saturation distributions inside the model were measured at
the end of each test. The residual water saturation was found to be in the range of Swr =
2.3−5.4%. Figure 5.16 shows the sandpack models at the end of Tests #5.1, #5.3, and #5.7.
The rough front surface of the sandpack models was formed because the viscous heavy oil
in the untouched heavy oil zone stuck to the cover plate. Figures 5.18a and 5.18b compare
the residual oil saturation distributions at several representative locations in the models of
Tests #5.1 and #5.3. It can be seen that the residual oil saturation at Location #1 (solvent
chamber) of both tests are about 10%. The residual oil saturation at Location #3 (untouched
heavy oil zone) of both tests are about 90%, which are close to their respective initial oil
saturations (92.7% for Test #5.1 and 93.5% for Test #5.3). The residual oil saturations at
Locations #2 and #4−5 (foamy oil zone) of Test #5.3 was found to be Sor = 37.6−49.9%,
which are much lower than those (Sor = 78.5−85.5%) at the same locations of Test #5.1. In
addition, the residual oil saturation in the foamy oil zone of Test #5.7 is found to be Sor =
51.2% and 31.3%, which is consistent with the measured residual oil saturation in the
foamy oil zone of Test #5.3.
Figure 5.19 shows the cross-sectional views of the Test #5.4 and #5.6, respectively. It
can be seen that oil saturation distributions are quite uniform in the thickness direction.
The asphaltene precipitation is observed in Test #5.6, which is shown as the multiple rigid
dark strips mingled with soft brown strips in Figure 5.19b. This is consistent with the
previous study [Das 1998]. The asphaltene precipitation in other F-VAPEX tests are not as
pronounced as that in Test #5.6.
146
(a)
(b)
(c)
Figure 5.18 Residual oil saturation at the end of (a) Test #5.1; (b) Test #5.3; and (c)
Test #5.7.
38.5%
23.1%
11.4%
78.5%
85.5% 91.2%
85.4%
63.3%
16.1%
12.5%
47.3%
3.6% 40.6%
48.9% 91.1%
77.7%
5.7%
12.2%
67.1%
78.8% 89.2% 41.2%
17.3%
5
4
49.9% 5
37.6% 4
2
1
3
86.4% 3
2 47.3%
16.3% 1
1 51.2% 2 37.3%
Injector
Producer
Injector
Producer
Injector
Producer
147
(a)
(b)
Figure 5.19 Cross-sectional views of the post-test sandpack of (a) Test #5.4 and (b)
Test #5.6.
148
5.3 Chapter Summary
This chapter presents a new solvent-based process, F-VAPEX, to enhance heavy oil
recovery of conventional VAPEX/CSI. F-VAPEX benefits the technical advantages of
both VAPEX and CSI, such as continuous production and strong driving force.
In comparison with VAPEX, F-VAPEX introduces more production mechanisms,
including gravity drainage and intermittent sucking during the stable pressure period and
the solution-gas drive and foamy oil flow during the pressure reduction period. Foamy oil
flow moves the solvent-diluted heavy oil closer to the producer, which not only enhances
the oil production during the pressure reduction period but also facilitates the oil recovery
during the subsequent stable pressure period. The average oil production rate of VAPEX is
increased by 1.15 times with F-VAPEX. In comparison with CSI, F-VAPEX has a higher
average oil production rate and a lower solvent−oil ratio. The oil saturation inside the
foamy oil zone is measured to be in the range of 35−50%.
F-VAPEX with the lateral well configuration produces oil faster in the early stage but
slower in the late stage than that with the central well configuration. A longer cycle length
can lower the solvent gas usage but reduce the oil production. The cycle length has to be
optimized for an F-VAPEX process.
149
CHAPTER 6 GASFLOODING-ASSISTED CYCLIC SOLVENT INJECTION (GA-CSI)
The CSI process takes advantage of solution-gas drive and foamy oil flow (as shown
in Chapter 5) for the oil production. However, CSI process suffers from the solvent
liberation during its production period. This leads the partially diluted heavy oil to regain
its high viscosity and eventually lose its mobility. How to recover the partially diluted
heavy oil becomes a key challenge for a CSI process. This chapter first experimentally
analyzes the conventional CSI process with different well configurations. It is found that
the ‘back-and-forth movement’ of some partially diluted heavy oil in the solvent chamber
limits the oil productivity of the conventional CSI process. On the basis of this observation,
a new process, namely gasflooding-assisted cyclic solvent injection (GA-CSI), is proposed
to enhance the performance of the CSI process. In the GA-CSI process, two wells are used
respectively as the solvent injector and oil producer, and a gasflooding slug is applied after
the pressure reduction process to produce the partially diluted foamy oil left in the solvent
chamber. The experimental results show that GA-CSI can significantly enhance the CSI
performance in terms of both the average oil production rate and the ultimate oil recovery
factor.
6.1 Experimental
6.1.1 Materials
Heavy oil sample and solvent (propane) material are the same as those specified in
the previous chapter: Crude heavy oil has a viscosity of 5,875 mPas and a density of 975
kg/m3. Propane with a purity of 99.5 mol.% is used as the extracting solvent.
150
6.1.2 Experimental set-up
Figure 6.1a shows a schematic diagram of the experimental set-up, which was
comprised of four major operation units: a solvent injection unit, a physical model, a fluids
production unit, and a data acquisition system. The solvent injection unit, fluids production
unit, and data acquisition system are quite similar to those specified in Chapter #5. The
only difference is that a digital gas flowmeter (XFM17, Aalborg, USA) was installed in the
solvent injection unit to record the solvent injection rate and the cumulative solvent
injection during the tests, especially during the solvent injection period.
The major characteristic of the experimental set-up in this chapter is that two types of
physical models were used in this chapter to evaluate the performance of the GA-CSI
process: three cylindrical models and a 2D rectangular model. The cylindrical models were
steel pipes with the constant inner diameter (ID) of 3.8 cm and different lengths of 34, 63,
and 93 cm, respectively. The injector and producer were installed in the center of the caps
at two ends. The 2D rectangular model was the same as described in the previous chapter.
It is worthwhile to note that in this chapter, the rectangular physical model was placed
horizontally rather than vertically. The first five tests were conducted with the cylindrical
physical models and the last two tests were undertaken with the rectangular physical model.
Two types of well configurations were adopted during the tests: (1) A single well is
alternately used as the injector or producer (one-well configuration, see Figure 6.1c) and (2)
The injector is horizontally apart from the producer (two-well configuration, see Figure
6.1a). In the experiments, two CSI tests were carried out with the one-well configuration,
while one CSI test and four GA-CSI tests were performed with the two-well configuration.
151
(a)
(b)
(c)
Figure 6.1 (a) Schematic diagram of the experimental set-up with a cylindrical model
for GA-CSI tests and a CSI test; (b) Dimensions of the rectangular sand-packed model;
and (c) Schematic diagram of the physical model for a CSI test.
Physical model Injector/ Producer
To Solvent injector
To Production unit
Sand pack
P P
H = 2 cm L = 40 cm
W = 10 cm
Solvent injection unit
Data acquisition unit
Physical model
Fluids production unit
Pressure transducer Computer
Producer Injector Sand pack
Gas regulator
Propane cylinder
Gas flow meter
Scale Surge flask Flow meter
Back-pressure regulator Digital pressure gauge
Oil collector
Steel tubing Plastic flexible hose Data ware
152
6.1.3 Experimental preparation
Experimental preparations, such as sand packing, porosity, permeability, and initial
oil saturation measurements, are the same as those described in Chapter 5. Table 6.1
summarizes the detailed physical properties of the sand-packed physical models.
6.1.4 Experimental procedure
In this chapter, seven laboratory tests were performed with two operating schemes
(CSI and GA-CSI). The first five tests were conducted with the cylindrical physical models
to analyze the CSI and GA-CSI processes. The last two tests were undertaken with the
rectangular physical model to verify the effectiveness of the GA-CSI process. The
pressure-control processes for the CSI and GA-CSI tests are schematically shown in Figure
6.2 and described in the following section.
CSI
Each CSI cycle lasted for 1 h and consisted of two periods (Figure 2a): (1) Injection
period. Propane is continuously injected into the sand-packed physical model at Pinj = 800
kPa and T = 20.2C for 50 min; (2) Production period. The production pressure Pprod is
reduced from 800 to 200 kPa within 10 min.
GA-CSI
Similar to CSI, each GA-CSI cycle lasted for 1 h and also consisted of two periods: a
44−48 min of constant-pressure injection period (Pinj = 800 kPa) and a 12−16 min of
production period that has three stages:
1. Blowdown: The solvent injection valve was closed and the oil production valve
was opened so as to decrease the Pprod from 800 to approximately 200 kPa within
3−5 min;
153
Table 6.1 Physical properties of the sand-packed physical model and experimental
conditions for CSI and GA-CSI tests.
Test No. Well Configuration Production
Scheme PV (cc)
Soi (%)
k (D)
(%)
6.1 CSI, Fig. 6.2a 140 94.2 5.8 36.5 6.2 CSI, Fig. 6.2a 138 94.9 4.9 35.9 6.3 GA-CSI, Fig. 6.2b 139 94.2 5.3 36.2 6.4 GA-CSI, Fig. 6.2b 271 96.3 4.8 36.4 6.5 GA-CSI, Fig. 6.2b 393 96.1 4.6 35.7 6.6 CSI, Fig. 6.2a 281 93.9 4.8 35.1 6.7 GA-CSI, Fig. 6.2b 284 93.3 5.1 35.5 6.8 PP-CSI, Fig. 6.16 283 93.6 5.2 35.9
L = 34 cm, D = 3.8 cm
L = 34 cm, D = 3.8 cm
L = 93 cm, D = 3.8 cm
L = 34 cm, D = 3.8 cm L = 63 cm, D = 3.8 cm
40 10 2 cm3
40 10 2 cm3
40 10 2 cm3
154
Time (hh:mm)
00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20
Pres
sure
(kPa
)
0
200
400
600
800
1000
Pprod
Injection Production
ONE CYCLE
(a)
Time (hh:mm)
00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20
Pres
sure
(kPa
)
0
200
400
600
800
1000Pinj
Pprod
Injection Production
ONE CYCLE
(b)
Figure 6.2 Pressure-control scheme of (a) GA-CSI and (b) CSI.
155
2. Reinjection: The injection valve is opened and the production valve is closed.
Propane is re-injected into the physical model to restore the model pressure to the
previous level; and
3. Gasflooding: The producer is reopened and the production pressure is carefully
adjusted to maintain a proper pressure difference between the injector and the
producer. The flooding stage continues over 6, 8, and 10 min for the 34, 63, and
93 cm cylindrical models, respectively. For rectangular model, it lasts for 8 min.
It is worthwhile to mention that prior to the cyclic process of the CSI and GA-CSI
tests with the two-well configuration, an initial communication between the injector and
the producer was established by keeping the injection pressure at a pre-set pressure (800
kPa) and the production pressure at the atmospheric pressure until a column of continuous
gas bubbles were observed at the producer.
6.2 Results and Discussion
Table 6.2 summarizes the measured test durations t, cumulative oil production data
Qo, and cumulative solvent production data Qg, and the calculated average oil production
rates qo, oil recovery factors (RFs), and solvent−oil ratios (SOR) for the CSI and GA-CSI
tests in this study. Figure 6.3 shows the cumulative oil production and solvent−oil ratio
versus time data for two CSI tests and one GA-CSI with the same cylindrical physical
model but different well configurations. It can be seen from this figure that the
performance of the two-well CSI test (Test #6.2) is much better than that of the one-well
CSI test (Test #6.1), whereas the GA-CSI test (Test #6.3) performs the best among the
three tests. Apparently, the performance of a cyclic solvent process is affected more by the
operating scheme than by the well configuration. The enhancement of oil production rate
156
Table 6.2 Cumulative oil and solvent production data of eight CSI and GA-CSI tests.
Test No. t (h)
Qo (g)
Qs (dm3)
qo (g/h)
Oil RF (% OOIP)
SOR (g solvent/g oil)
6.1 29 64.4 150.7 2.2 48.8 4.3 6.2 22 75.5 154.2 3.4 57.6 3.8 6.3 12 96.9 158.6 8.1 74.0 3.0 6.4 14 176.3 276.7 12.6 67.5 2.9 6.5 16 258.4 362 16.2 68.4 2.6 6.6 47 126.1 283.1 2.7 47.8 4.1 6.7 15 169.9 325.1 11.2 63.6 3.5 6.8 13 178.2 359.2 13.5 67.2 3.6
157
Time (h)
0 5 10 15 20 25 30
Oil
reco
very
fact
or (%
)
0
20
40
60
80
(a)
Time (h)
0 5 10 15 20 25 30
Cum
lativ
e so
lven
t-oil
ratio
(g s
olve
nt/g
oil)
0
1
2
3
4
5
(b)
Figure 6.3 (a) Cumulative oil production; and (b) SOR of Tests #6.1−3.
Test #6.3
Test #6.2 (CSI)
Test #6.3
Test #6.2 (CSI)
Test #6.1
Test #6.1
158
due to the operating-scheme change from Test #6.2 to Test #6.3 (qo = 4.7 g/h) is much
larger than that due to the well-configuration change from Test #6.1 to Test #6.2 (qo = 1.2
g/h). The detailed effects of these factors on the performance of a cyclic solvent process
will be analyzed in the following sections.
6.2.1 Well configuration
Tests #6.1−2 have similar physical model properties and pressure-control schemes,
except for the well configuration. Test #6.1 used a single well alternately and cyclically as
the injector or producer, whereas Test #6.2 used two wells as the injector and the producer,
respectively. The well placements resulted in a significant difference on their performance.
Test #6.1 achieved an average oil production rate of 2.2 g/h and Test #6.2 obtained 3.4 g/h.
The reason for the lower average oil production rate in Test #6.1 is the ‘back-and-forth
movement’ of the solvent-diluted heavy oil in the solvent chamber, which is schematically
illustrated in Figure 6.4 and explained below.
Similar to VAPEX, a sand-packed model during a cyclic solvent process also has
three zones: a solvent chamber, an untouched heavy oil zone, and a foamy oil zone in
between. During the solvent injection period, propane is injected into the model and
dissolved into the partially diluted heavy oil inside the foamy oil zone and the dead oil at
the boundary between the foamy oil zone and the untouched heavy oil zone, as shown in
Figure 6.4a. During the production period, solvent in the solvent chamber is first released
and the solvent-diluted heavy oil starts to flow to the producer. Meanwhile, the solvent
dissolved into the heavy oil begins to nucleate into extremely small bubbles due to pressure
reduction [Smith, 1988] and most of these bubbles will keep entrained in the oil and move
toward the producer, causing the so-called foamy oil flow [Sarma and Maini, 1992] (Figure
159
6.4b). Afterward, the gas bubbles grow larger and larger and finally disengage from the oil
phase to form a continuous gas phase when the pressure is below the ‘pseudo-bubble-point
pressure’ [Kraus et al., 1993]. As a result, the solution gas is quickly released and the
partially diluted heavy oil regains a high viscosity and gradually loses its mobility, and
some foamy oil remains in the model at the end of the production period, as shown in
Figure 6.4c. During the solvent injection period of the subsequent cycle, the injected
solvent re-dissolves into the partially diluted heavy oil in the foamy oil zone and pushes the
oil back to the untouched heavy oil zone (Figure 6.4d). This ‘back-and-forth movement’ of
the foamy oil during the oil production period of one cycle and the solvent injection period
of the next cycle would hinders the oil production, and its influence is expected to become
more and more serious as the solvent chamber grows longer and longer.
This ‘back-and-forth movement’ hypothesis was validated by the digital photographs
of Test #6.6 with the rectangular model. Figure 6.5a shows a clear flowing front in the early
stage of the oil production period of a cycle of Test #6.6. Several foamy oil flowing fronts
can be seen in Figure 6.5b and they became almost immobile at the end of the production
period when Pprod ≈ 200 kPa. During the solvent injection period of the subsequent cycle,
the partially diluted heavy oil in the foamy oil zone was re-diluted and pushed backward by
the injected solvent, and a thick backward flow band of the oil moving away from the
injector was observed (Figure 6.5c).
In contrast, with the two-well lateral well configuration in Tests #6.2−5 and #6.7, the
‘back-and-forth movement’ of the foamy oil did not exist since the oil always flew in one
direction from the injector to the producer.
160
(a) (b)
(a)
(c) (d)
Figure 6.4 ‘Back-and-forth movement’ of the solvent-diluted heavy oil in a CSI test:
(a) Solvent dissolution into oil during the injection period of a cycle; (b) Diluted oil
flowing to the producer during the production period; (c) Some diluted oil remaining in
the solvent chamber at the end of the production period; and (d) Diluted oil flowing back
during the solvent injection period of the next cycle.
Injector Producer
Injector Producer
Solvent chamber
Untouched heavy oil Diluted oil
161
(a)
(b)
(c)
Figure 6.5 ‘Back-and-forth movement’ of the solvent-diluted heavy oil during a cycle
of the CSI test (Cycle #40 of Test #6): (a) Oil flowing to the producer at the early stage of
the production period; (b) Oil remaining in the solvent chamber at the end of the
production period; and (c) Oil flowing back during the solvent injection period of the
next cycle (Cycle #41).
Flow
fron
t Fl
ow fr
ont
Bac
kflo
w
Producer
Producer
Injector
Flow
fron
t
Flow
fron
t
162
6.2.2 Operating scheme (CSI vs. GA-CSI)
The only difference in the pressure-control scheme between Tests #6.2 and #6.3 is
that Test #6.3 has reinjection and flooding processes after the pressure reduction process
during the oil production period of each cycle. However, this small change in the operating
scheme made a large difference in their performance. The average production rate of Test
#6.3 is 2.38 times of that of Test #6.2. This is because although the oil viscosity was
re-increased to some extent at the end of the oil production period, there was still a large
amount of solvent dissolved into the oil. In addition, the oil was relatively uniformly
distributed in the foamy oil zone. Therefore, during the reinjection and flooding processes,
the partially diluted oil in the foamy oil zone near the injector can be quickly diluted by the
solvent and pushed toward the producer to form a flooding front, which was served as a
‘buffer zone’ to greatly control the mobility ratio between the displacing solvent and the
displaced oil.
Figure 6.6 presents a solvent flooding process during a GA-CSI test (Test #6.7). The
brown area in Figure 6.6a shows the foamy oil zone at the end of a blowdown stage. The
white area in Figure 6.6b indicates the swept zone with low residual oil saturation.
Moreover, the advancing front was rather uniform, which was probably attributed to the
‘buffer zone’. At the end of the flooding stage, the advancing front was separated into
several large fingers that resulted in a reduced sweeping efficiency as well as a decreased
oil production rate (Figure 6.6c).
163
(a)
(b)
(c)
Figure 6.6 Gasflooding process during a GA-CSI test (Test #6.7). (a) End of the
blowdown stage; (b) Early gasflooding stage; and (c) Late gasflooding stage.
Producer Injector
Producer Injector
Producer Injector
164
6.2.3 GA-CSI
Figure 6.7 shows the injection pressure, production pressure, and solvent injection
rate during a typical cycle of Test #6.3. It is worthwhile to mention that during the oil
production period, the BPR was adjusted to the minimum level so as to induce a larger
pressure gradient and a higher pressure reduction rate, which would result in more bubbles
and greater foamy oil stability [Handy, 1958; Maini et al., 1996; Sheng, 1997]. Figure 6.8
depicts the cumulative oil production, oil production rate, and the corresponding SOR
during the blowdown, reinjection, and flooding stages of the oil production period of a
representative cycle of Test #6.3.
It is found that during the blowdown stage, the oil production rate decreased sharply,
while the SOR increased quickly. During the flooding stage, the cumulative oil production
curve had an ‘S’ shape while the SOR fluctuated around 1.9 g solvent/g oil. Figure 6.8 also
shows that the oil production during the flooding stage was significantly higher than that
during the blowdown stage, which was a general trend in Test #6.3 and the other GA-CSI
tests. Figure 6.9a confirms this trend and also shows that the oil production from the
flooding stage of each cycle first increased and then gradually decreased, while the oil
production from the blowdown stage was 3 g/cycle. The total oil production from the
flooding stages of Test #6.3 was 61.1 g, which was 1.71 times higher than that from the
blowdown stages (35.8 g). Figure 6.9b shows that the solvent gas production during the
blowdown and flooding stages increased steadily with the cycle number throughout Test
#6.3. Figure 6.10 compares the cumulative oil production data due to pressure reduction
in Tests #6.1−3, indicating that the oil production trend due to pressure reduction in the
GA-CSI test was similar to those in the CSI tests.
165
Time (hh:mm)
00:00 00:20 00:40 01:00 01:20
Pres
sure
(kPa
)
0
200
400
600
800
1000
Solv
ent i
njec
tion
rate
(cc/
min
)
0
200
400
600
800
1000
1200
1400
Pinj
Pprod
qs,inj
Injection
ONE CYCLE
1 2 3
1: Blowdown2: Reinjection3: Gasflooding
Figure 6.7 Injection and production pressures and the solvent injection rate during a
typical cycle (Cycle #4) of a GA-CSI test (Test #6.3).
166
Time (min)
0 1 2 3 4 5 6 7 8 9 10 11 12
Cum
lativ
e oi
l pro
duct
ion
(g)
0
2
4
6
8
10
12
14
Oil
prod
uctio
n ra
te (g
/min
)
0
1
2
3
4
5
6
Solv
ent-o
il ra
tio (g
sol
vent
/g o
il)
0.0
0.5
1.0
1.5
2.0
2.5
Blowdown Reinjection Gasflooding
Figure 6.8 Cumulative oil production, oil production rate, and solvent–oil ratio during
a typical cycle (Cycle #4) of a GA-CSI test (Test #6.3).
167
Time (h)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Oil
prod
uctio
n (g
)
0
2
4
6
8
10
BlowdownGasflooding
(a)
Time (h)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Solv
ent p
rodu
ctio
n (s
c,L)
0
2
4
6
8
10
12
14 BlowdownGasflooding
(b)
Figure 6.9 (a) Heavy oil production; and (b) Solvent gas production during the
blowdown and gasflooding slugs of the production period of a GA-CSI test (Test #6.3).
168
Time (h)
0 5 10 15 20 25 30
Cum
lativ
e oi
l pro
duct
ion
(g)
0
20
40
60
80
Figure 6.10 Cumulative oil productions of Tests #6.3 (blowdown slugs only), and #6.1
and #6.2.
Test #6.3
Test #6.2 (CSI)
Test #6.1
169
6.2.4 Solvent injection rate
Figure 6.11 shows the solvent injection rate during the early (Cycle #2), middle
(Cycle #6), and late (Cycle #11) stages of Test #6.3. All the three curves declined and
reached to a small value within 45 min, indicating that the dissolution of propane into the
heavy oil became rather slow after 45 min of constant pressure injection. This justifies the
selection of one hour as the full cycle length for the CSI and GA-CSI tests in this study. In
addition, it can be seen that less solvent was injected and dissolved into the heavy oil
during the early and late stages than during the middle stage. The lower solvent injection
rate was due to the small solvent chamber size and limited contact area at the early stage
and the high solvent saturation in the heavy oil at the late stage. The higher solvent
injection rate at the middle stage was probably because of the more developed solvent
chamber and the relatively lower solvent saturation. Assuming that the injection period of
each cycle ends when the solvent injection rate is below certain value, the cycle length
must be a function of time and change with the solvent chamber size and solvent saturation
throughout a test. Variable cycle lengths for CSI/GA-CSI need to be studied in future.
6.2.5 GA-CSI with cylindrical models
Figure 6.12 shows the oil RFs and SORs of three GA-CSI tests with three cylindrical
physical models of different lengths. It is found that the three oil RF curves all have an ‘S’
shape and their final values are close to each other and decrease slightly with the increase
of the model length (Figure 6.12a). In addition, longer cylindrical models result in lower
ultimate SOR values in comparison with shorter models (Figure 6.12b). This is because
longer models had smaller pressure gradients for the solvent gas displacement during the
flooding stage. On one hand, a smaller driving force would lead to a lower oil production
170
Time (min)
00 10 20 30 40
Sol
vent
inje
ctio
n ra
te (s
cm3 /m
in)
0
100
200
300
400
500
600
Figure 6.11 Solvent injection rate at early, middle, and late stages of a GA-CSI test
(Test #6.3).
Test #6.3
171
Time (h)
0 5 10 15 20
Oil
reco
very
fact
or (%
)
0
20
40
60
80
100
(a)
Time (h)
0 5 10 15 20
Cum
ulat
ive
solv
ent-o
il ra
tio (g
sol
vent
/g o
il)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
(b)
Figure 6.12 (a) Recovery factor; and (b) Solvent−oil ratio of the GA-CSI tests with
cylindrical models of different lengths.
Test #6.5
Test #6.4
Test #6.3
Test #6.5
Test #6.4 Test #6.3
172
for longer cylindrical models. On the other hand, a smaller driving force may result in
neither an earlier gas breakthrough nor a larger solvent usage. In short, the pressure
gradient is an important factor for the solvent flooding process and further study is needed
to determine its optimum value for a GA-CSI process.
6.2.6 GA-CSI with rectangular model
Figure 6.13 shows the oil recovery curves for a CSI test and a GA-CSI test with the
rectangular model. It is obvious that Test #6.7 performed much better than Test #6.6. The
average oil production rate of Test #6.7 was 4.48 times of that of Test #6.6, which validated
the superiority and effectiveness of the GA-CSI process over the conventional one-well
CSI process. Comparison of Figure 6.3a and Figure 6.13 shows that the enhancement on
the average oil production rate of the conventional one-well CSI process by the GA-CSI
process with the short cylindrical model (Test #6.3 vs. Test #6.1) is consistent with that
with the rectangular model (Test #6.7 vs. Test #6.6).
Comparison of Tests #6.4 and #6.7 shows that with the same operating scheme and
similar permeabilities and PVs, both tests achieved similar oil production rates (12.6 g/h
for Test #6.4 and 12.1 g/h for Test #6.7) and ultimate oil RF values (67.5% of the OOIP for
Test #6.4 and 64.1% of the OOIP for Test #6.7).
6.2.7 Residual oil saturation
In this study, the residual water and oil saturations at different representative
locations were measured by analyzing the sand samples taken at the end of the CSI and
GA-CSI tests. The residual water saturation was found to be in the range of 26% for all
the measurements and this study focuses on the distributions of the residual oil saturation.
Figure 6.14 shows the digital photographs of the cross sections of the short cylindrical
173
Time (h)
0 10 20 30 40 50
Oil
reco
very
fact
or (%
)
0
10
20
30
40
50
60
70
Figure 6.13 Oil recovery factor of GA-CSI and CSI tests with the rectangular physical
model.
Test #6.7
Test #6.6
174
(a)
(b)
Figure 6.14 Residual oil saturation of (a) CSI (Test #6.2); and (b) GA-CSI tests (Test
#6.3).
29.8%
l = 1 cm (Injection/production side)
l = 8 cm
54.1%
l = 24 cm
65.2%
l = 32 cm
72.2%
l = 1 cm (Injection side)
4.1%
14.8%
l = 8 cm
6.9%
l = 32 cm (Production side)
37.3%
l = 24 cm
50.3%
9.8%
175
sand-packed physical model (L = 34 cm) at the end of Tests #6.1 and #6.3, respectively.
The measured residual oil saturations were in an excellent agreement with the sand
samples’ colours. The whiter the sand samples, the lower the corresponding residual oil
saturation would be. It is found that the colour of the cross sections of Test #6.1 was quite
uniform (Figure 6.14a), which is because: (1) The foamy oil flow uniformly redistributed
the oil during the production period of the CSI process; (2) The effect of gravity force
was negligible. In contrast, it is found that the residual oil saturation in the upper part of
the model of Test #6.3 was much lower than that in the lower part (Figure 6.14b). This is
due to the gravity overriding, which made the solvent-diluted heavy oil move downward
during the test so that the obtained sand sample was lighter in the upper part and darker in
the lower part.
Figure 6.15 shows the front of the rectangular sand-packed physical model after
sampling at the ends of Tests #6.6 and #6.7. Obviously, the model color of Test #6.6 was
much darker than that of Test #6.7, which was consistent with fact that the oil RF of Test
#6.6 was much lower than that of Test #6.7. It is worthwhile to emphasize that the residual
oil saturation was lower at the two ends but higher in the middle part of Test #6.6 (Figure
6.15a), which is due to the aforementioned ‘forth-and-back movement’ of the foamy oil.
The residual oil saturation of Test #6.7 declined from the left-hand side to the right-hand
side (Figure 6.15b). Precipitated asphaltenes were observed as the gray patches on the
right-hand side of the model for Test #6.7. However, It seems that asphaltene precipitation
did neither affect the solvent injection nor the oil production throughout the test.
176
(a)
(b)
Figure 6.15 Residual oil saturation of (a) CSI (Test #6.6); and (b) GA-CSI (Test #6.7).
45.7%
34.7%
54.1%
43.4%
60.1%
55.7%
46.7%
60.4%
52.3%
54.2%
54.2%
51.9%
63.9%
26.4%
32.6%
34.6%
23.1%
36.3%
39.7%
18.8%
27.8%
25.0%
16.1%
3.1%
16.4%
20.8%
Injector/Producer
Injector Producer
Sampling hole
177
6.3 Variations of GA-CSI
In the GA-CSI process, foamy oil flow and gasflooding are coupled together to
provide a strong driving force for the heavy oil production. This section presents an
extension of the GA-CSI process, pressure-pulsing cyclic solvent injection (PP-CSI).
6.3.1 Pressure control scheme
PP-CSI is a special form of GA-CSI. The physical properties of a PP-CSI test are
listed in Table 6.1 and its operating scheme is showed in Figure 6.16 and described as
follows.
The pressure control scheme of PP-CSI is similar to that of GA-CSI. Solvent
injector and oil producer are placed horizontally apart. Its pressure is cyclically operated
and each cycle has two periods:
Injection period. Propane is continually injected into the sand-packed physical model
at 800 kPa and 20.2C for ~40 min.
Production period. The production period contains several pressure pulses and each
pulse is a three-step process: blowdown, reinjection, and gasflooding. More specially, in
each pulse, first, decrease the model pressure to induce foamy oil flow; Then, build up the
pressure by injecting solvent for a few minutes; Finally, maintain a certain pressure
difference between injector and producer for a period of gasflooding. Afterward, the
pressure pulse is repeated for another pulse until the oil production rate drops below an
economical limit.
Figure 6.17 shows the typical injection and production pressure measured during the
PP-CSI test (Test #6.8). It is worthwhile to mention that the pulse can be applied as many
times as necessary.
178
Time (hh:mm)
00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20
Pres
sure
(kPa
)
0
200
400
600
800
1000
Ping
Pprod
Injection Production
ONE CYCLE
1 2 3
Pulse
1: blowdown2: re-injection3: flooding
Figure 6.16 Pressure control scheme of PP-CSI.
179
Time (hh:mm)
00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20 01:30
Pre
ssur
e, k
Pa
300
400
500
600
700
800
900
Pinj
Pprod
Injection Production
Figure 6.17 Injection and production pressures data during a PP-CSI test.
180
6.3.2 Viscous fingering
Figure 6.18 displays the solvent chamber evolution throughout the PP-CSI test (Test
#6.8). In the early stage (Cycle #2 and #4), it can be seen that viscous fingers are formed
near the injector. The formation of the solvent fingers is due to the high mobility ratio
between the solvent and heavy oil during the flooding process. Viscous fingering reduces
the sweeping efficiency and caused early solvent breakthrough during the immiscible
flooding processes, such as water flooding, chemical flooding. However, in the PP-CSI
process, viscous fingers play a good role in the following ways: first, the finger growth in
the length was not as fast as anticipated due to the foamy oil flow. Meanwhile, its growth in
the width is much better than expected. Second, solvent fingers greatly increased the
solvent–oil contact area, which significantly enhanced the mass-transfer rate.
Figure 6.18c−d shows the solvent chamber at the middle and late stage of the PP-CSI
process. It can be seen that the solvent fingers at the early stage mingle together to form a
big one, and it did not breakthrough at Cycle #8 when 54.6% of the OOIP was recovered.
From the colour of the model, it can be seen that a sweeping efficiency was achieved in the
PP-CSI test. A noticeable solvent chamber connection to the producer occurred in Cycle
#12 when 61.1% of the OOIP was recovered.
181
(a)
(b)
(c)
(d)
Figure 6.18 Evolution of the solvent chamber throughout a PP-CSI test: (a) Cycle #2;
(b) Cycle #4; (c) Cycle #8; and (d) Cycle #12.
Injector Producer
Injector Producer
Injector Producer
Injector Producer
182
6.3.3 Oil production
Figure 6.19 compares the cumulative oil production versus time data for the GA-CSI
and PP-CSI tests (Tests #6.7−8). Obviously, the oil was recovered faster in the PP-CSI test
(Test #6.8) than in the GA-CSI test (Test #6.7). The average oil production rate of the
PP-CSI test was qo = 13.5 g/h, which was 20.1% higher than that of the GA-CSI test (qo =
11.2) g/h. Furthermore, the final recovery factor of the PP-CSI test was 3.6% higher than
that of the GA-CSI test.
Figure 6.20 shows the oil production of multiple pulses (Cycles #2, #7, #11, and #12)
in different cycles of the PP-CSI test. It can be seen that the oil production during the
second and third pulses are similar to that in the first one. In addition, the pulse number was
increased from 2 to 3 in the early stage since the oil production increased with the cycle.
However, in the late stage, the pulse number was reduced (from 3 in Cycle #11 to 2 in
Cycle #12), which is because the oil production decreased with the pulse number and the
decline rate increased in the late stage of the test. It is worthwhile to note that in Test #6.8,
the length of each cycle was set as 1 h and the pulse was set as ~8 min for comparison. In
fact, the operational parameters of the PP-CSI process, such as cycle length, pulse number,
and pulse length, need to be optimized.
183
Time (h)
0 5 10 15 20
Oil
reco
very
fact
or (%
)
0
20
40
60
80
PP-CSI (Test #6.8)GA-CSI (Test #6.7)
Figure 6.19 Comparison of the oil recovery factor of PP-CSI and GA-CSI tests.
Tests #6.76.8
184
Cycle number
1 2 3 4
Oil
prod
uctio
n (g
)
0
2
4
6
8
10
12Pressure pulse #1Pressure pulse #2Pressure pulse #3
4 7 11 12
Figure 6.20 Oil production from multiple pulses in different cycles of Test #6.8
185
6.4 Chapter Summary
In this chapter, a new operating scheme, GA-CSI, is designed and evaluated through
a series of laboratory tests. The following conclusions can be drawn:
1. The performance of conventional one-well CSI is hampered by the
‘back-and-forth movement’ of the foamy oil in the solvent chamber.
2. The major difference between conventional CSI and GA-CSI is the
pressure-control scheme. GA-CSI applies a gasflooding slug between the ‘puff’
and ‘huff’ periods of a conventional CSI process.
3. Aside from solution-gas drive, foamy oil flow, and gravity drainage, GA-CSI
introduces a new and stronger production mechanism, gasflooding, into oil
recovery.
4. The gasflooding slug of the GA-CSI process can effectively produce the partially
diluted heavy oil remained in solvent chamber due to solvent liberation and
mobility loss at the end of the pressure reduction process. A good sweeping
efficiency of gasflooding was observed because of the ‘buffer zone’, which
reduces the mobility ratio between the displacing solvent and the displaced oil.
5. GA-CSI can greatly enhance the performance of conventional CSI in terms of
both the average oil production rate and the ultimate recovery factor. The average
oil production rate enhancement of CSI by GA-CSI is 3.64 times with the
cylindrical model and 4.52 times with the rectangular model.
6. As a variation of GA-CSI, PP-CSI produces oil faster but uses more solvent than
GA-CSI. More research work is needed to further explore and optimize the
variations of GA-CSI.
186
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusions
This thesis conducts some theoretical modeling of the traditional solvent-based EOR
techniques (VAPEX and CSI) and proposes several new solvent-based EOR processes to
improve their performances. The major conclusions are summarized as follows:
Modeling of VAPEX
1. A new mathematical model of VAPEX is established to predict the evolution of
the solvent vapour chamber during its rising and falling phases. This new model
is developed on the basis of the major mechanisms of VAPEX, such as viscosity
reduction and gravity drainage. The transient heavy oil−solvent mass transfer and
the moving boundary condition are considered in this new model.
2. The new VAPEX mathematical model is able to not only estimate the growth of
the solvent chamber, but also to describe the solvent concentration, oil viscosity
and density, diffusion coefficient, and drainage velocity inside the transition zone.
It is found that the upper-part of the transition zone is thinner and moves faster
than the lower part. It is also found that the constant diffusion coefficient is
acceptable only for a short period of time. It underestimates the oil production
rate for a longer time period since it ignores the increase of the diffusion
coefficient during the VAPEX process.
3. In comparison with the numerical simulation, the new theoretical model
demonstrates more sensitivity to the diffusion coefficient and has less numerical
dispersion.
187
Modeling of the mass transfer in CSI
4. A 1D convection–diffusion mass-transfer model is developed to describe the
heavy oil−solvent mixing process in CSI. It estimates the effect of pressure
gradient on the mass transfer process. Solvent diffusion coefficient and
convection velocity are both considered as functions of solvent concentration in
this new model.
5. Semi-analytical solutions are obtained through a special approximation of the
variable diffusion coefficient and convection velocity.
6. Modeling results qualitatively suggest that a pressure gradient between the
solvent chamber and untouched heavy oil zone provides a pushing force for the
solvent to mix with heavy oil during the solvent injection period of CSI. The
convection plays a larger role than the diffusion during the CSI process,
especially in the early stage of the solvent injection period.
Enhanced VAPEX (F-VAPEX)
7. F-VAPEX is a combined process of VAPEX and CSI. It is essentially a VAPEX
process during which the operating pressure is cyclically reduced and restored.
8. F-VAPEX is superior to the VAPEX in terms of both the average oil production
rate and the ultimate oil recovery factor. F-VAPEX has a higher oil production
rate and a lower solvent−oil ratio in comparison with CSI.
9. Production mechanisms of the F-VAPEX process include the intermittent
sucking and gravity drainage during the stable pressure period and the
solution-gas drive and foamy oil flow during the pressure reduction period.
188
10. The foamy oil flow during the pressure reduction period moves the
solvent-diluted heavy oil toward the producer to facilitate the oil production in
the subsequent stable pressure period. As a result, the stable pressure period of
F-VAPEX contributes more oil production than the pressure reduction period.
11. F-VAPEX with the lateral well configuration produces oil faster in the early
stage but slower in the late stage than that with the central well configuration.
12. A longer cycle length for F-VAPEX saves gas usage but may reduce the oil
production.
13. The oil saturation inside the foamy oil zone is measured to be in the range of
35−50%.
Enhanced CSI (GA-CSI)
14. The oil productivity of conventional one-well CSI process is largely limited by
the ‘back-and-forth movement’ of the partially diluted foamy oil in the solvent
chamber. In the GA-CSI process, the solvent injector and oil producer are placed
laterally apart, which effectively eliminates the ‘back-and-forth’ movement of
conventional CSI.
15. GA-CSI applies a gasflooding slug between the ‘puff’ and ‘huff’ periods of the
conventional CSI process. Therefore, in addition to solution-gas drive, foamy oil
flow, and gravity drainage, GA-CSI introduces a stronger production mechanism,
gasflooding. The average oil production rate of CSI is enhanced by GA-CSI by
3.64 times with a cylindrical model and 4.52 times with a rectangular model.
16. Gasflooding slug in GA-CSI results in a good sweeping efficiency due to the
189
‘buffer zone’. The ‘Buffer zone’ is actually a foamy oil band at the flooding front
that effectively controls the mobility ratio between the displacing solvent and the
displaced oil.
7.2 Recommendations
The following recommendations for future work are made on the basis of the
research in this study.
Modeling of the mass transfer process in CSI
In the present convection–diffusion model, the pressure gradient is assumed as a
constant, which is not reasonable for a practical case. Therefore, variable and dynamic
pressure gradients need to be considered in the future mass-transfer model.
Characterization of the foamy oil flow
Foamy oil flow and the resulting foamy oil zone are observed in this study. The
foamy oil flow and the foamy oil zone in the F-VAPEX and CSI needs to be further
characterized. In addition, the mass transfer of solvent into foamy oil also needs to be
investigated.
Parametric study of F-VAPEX and GA-CSI
More laboratory experiments and numerical simulation need to be conducted to
analyze and optimize these new processes in order to maximize their productivities.
Solvent recovery
Solvent retention is a major concern in the solvent-based EOR processes. Without
high solvent recovery, these processes would be economically unviable. How to
effectively recover the retained solvent needs more research efforts.
190
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APPENDIX A
Numerical solution to the diffusion equation with a moving boundary
The solvent–heavy oil mass transfer model is composed of the governing equation,
boundary conditions with a moving velocity, and initial conditions:
c cD
, (A1)
1 , 0t tc c , (A2)
max,c s c , (A3)
, 0c L
, (A4)
0s U . (A5)
Discretize the space and time domains, and rewrite the governing equation by using
Crank–Nicolson FDM:
1 1 1 1 11 1 1 1
1 11
2i i i i i i i i i i
i i i ic c c c c c c c c cD D D D
. (A6)
Let
22
, (A7)
then
1 1 1 1 11 1 1 1 1 1
ti i i i i i i i i i i i i ic c D c c D c c D c c D c c
. (A8)
Rearrange Eq. (A8)
1 1 11 1 1 1 1 1 1 1i i i i i i i i i i i i i iD c D D c D c D c D D c D c . (A9)
207
Apply the FDM to the BCs:
1 maxc c , (A10)
1 0N Nc c . (A11)
For the second step, left boundary point moves to x2; therefore, apply left BC to x2:
12 maxc c . (A12)
For points x3~xN-1:
1 1 11 1 1 1 1 1 1 1i i i i i i i i i i i i i iD c D D c D c D c D D c D c . (A13)
Apply the right BC to the last point xN
1 0N Nc c . (A14)
Hence, a matrix function can be formed as:
n-1 n-1 n-1 n-1c F
M , (A15)
where, the coefficient matrix [M] is a tri-diagonal matrix, {c}n-1 is the to-be-determined
unknown concentration matrix. The column matrix {F}n-1 and the coefficient matrix
[M](n-1)×(n-1) can be constructed given a velocity profile. Eq. (A15) can be solved by using
Thomas method to get the solvent concentration profile in the solvent-diluted heavy oil.
208
APPENDIX B
Semi-analytical solution to an convection-diffusion equation with a constant d and a
variable v.
Mathematical model in dimensionless form is:
2
2D D D
DD D D D
c c c PePe ct x x x
,
(B1)
( 0, ) 1 0D DD Dx tc t
, (B2)
( 1, )
0 0D D
DD
D x t
c tx
, (B3)
( , 0) 0 0 1D DD Dx tc x
. (B4)
Set cD as 2
* 4 2D Da bx x
Dc c e
, and assume a linear Pe as DPe ax b , then Eq. (B1)
becomes:
* 2 *2 *
2
1( )4 2D
D D
c c aax b ct x
. (B5)
Performing the Laplace transformation and considering IC:
2 *2 *
2
1 ( ) 04 2D
D
c aax b s cx
. (B6)
Allow 1 ( )Dz ax ba
, and substitute xD with z in Eq. (B6) yields:
22
2
1 04
C z J Cz
, (B7)
209
where, )21( a
sJ . Eq. (B7) is the canonical form of hyperbolic cylindrical equation,
whose general solution is:
1 2C AC BC , (B8)
where, C1 and C2 are the independent odd and even solutions. Coefficients A and B can
be obtained by applying the BCs:
21 24
11 1( , ) ( , , )
2 4 2 2z J zC J z e M
,
21 24
23 3( , ) ( , , )
2 4 2 2z J zC J z ze M
. (B9)
Applying BCs, Eqs. (B2−B3), A and B can be obtained as:
0 01 2
1 1As C C
, 0 01 2
1Bs C C
, (B10)
where,
1111
1122
2
2
C a ba Cz
C a ba Cz
; subscripts ‘1’ and ‘2’ of C stand for the two
independent solutions; superscripts ‘0’ and ‘1’ denote the left and the right boundaries,
respectively; M denotes the Kummer’s function. The concentration in real domain can be
obtained by applying the Stehfest Laplace inverse transformation:
2
4 2
1
ln 2 ( )D Da b nx x
D jjD
c e V C st
, (B11)
where,
min2 2+
2
12
(2 )!( 1)( )!( )!( 1)!( )!(2 )!2
n n, jn j
jjk
k kV n k k k j k k j
, ln 2
D
s jt
. (B12)
210
APPENDIX C
Definitions of the dimensionless terms
The dimensionless terms in Eq. (4.27) are defined as:
a sa
, (C1)
2
' ''
a a s b aa
, (C2)
2' ( ' )
'Da ax a a b
a . (C3)
211
APPENDIX D
Analytical solution to an convection-diffusion equation with a special hyperbolic
convection velocity profile.
For a hyperbolic Pe profile, Eq. (4.29), set ( )
D
D
cCx
and substitute it in Eq.
(4.3):
2
2D D
C Ct x
. (D1)
Applying the Laplace transformation and considering the IC, Eq. (D1) becomes:
2
2D
CsCx
. (D2)
Its solution is:
D Ds x sxC Ae Be . (D3)
Coefficients A and B can be obtained by applying the BCs in the Laplacian domain:
D D( 0, )
1x t
Cs
, (D4)
( 1, )
(1 ) 0D D
D x t
C Cx
. (D5)
Back replace A and B into Eq. (D3), the analytical solution becomes:
(2 )
2( )
(1 )
D Dsx s x
D s
e eC xs e
, (D6)
212
where, (1 ) 1(1 ) 1
ss
. The concentration in real domain can be acquired by applying
the Stehfest Laplace inverse transformation.