ENHANCED SOLVENT VAPOUR EXTRACTION PROCESSES IN THIN HEAVY OIL RESERVOIRS. A Thesis. In Partial Fulfillment of the Requirements.

Transcription

1 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

2 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, 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: Co-Supervisor: Co-Supervisor: Committee Member: Committee Member: Committee Member: Committee Member: *Dr. Zhangxing Chen, University of Calgary Dr. Fanhua Zeng, Petroleum Systems Engineering **Dr. Yongan Gu, Petroleum Systems Engineering **Dr. Yee-Chung Jin, Environmental Systems Engineering Dr. Chun-Hua Guo, Department of Mathematics & Statistics Dr. Ezeddin Shirif, Petroleum Systems Engineering Dr. Farshid Torabi, Petroleum Systems Engineering Chair of Defense: Dr. Laurie Clune, Faculty of Nursing *via teleconference **Not present at defense

3 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 i

4 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. ii

5 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. iii

6 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. iv

7 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 Heavy Oil Resources Heavy Oil Recovery Techniques Technical Challenges in Thin Heavy Oil Reservoirs Solvent-Based EOR Techniques Problem Statement and Research Objectives Theoretical modeling of VAPEX Modeling of the mass transfer in CSI Performance improvement for VAPEX and CSI Research objectives Thesis Outline...7 CHAPTER 2 LITERATURE REVIEW Vapour Extraction (VAPEX) Physical modeling of VAPEX Mass transfer modeling of VAPEX Theoretical modeling of VAPEX Numerical modeling of VAPEX Cyclic Solvent Injection (CSI) Chapter Summary CHAPTER 3 MATHEMATICAL MODELING OF VAPEX Mathematical Model and Solution Heavy oil solvent transition zone v

8 3.1.2 Mass transfer in transition zone Fluid flow in transition zone Moving boundary of transition zone Solution procedures Heavy oil production rate Results and Discussion Solvent chamber evolution and recovery factor Number of transition-zone segments Permeability This study vs. analytical models This study vs. numerical simulation Chapter Summary CHAPTER 4 MATHEMATICAL MODELING OF THE CONVECTION DIFFUSION MASS-TRANSFER PROCESS CSI Process Convection diffusion equation Diffusion coefficient and convection velocity Mathematical Models Governing equation Boundary and initial conditions Semi-Analytical Solutions Model 1: Convection diffusion model with constant D and variable V Model 2: Convection diffusion model with variable D and variable V Validations Validation with an analytical solution for a special case Validation with the numerical solution Results and Discussion Application of the convection diffusion mass-transfer model Variable and constant diffusion coefficient and convection velocity Effect of convection velocity Péclet number vi

9 4.5.5 Effect of gravity force in natural convection Chapter Summary CHAPTER 5 FOAMY OIL-ASSISTED VAPOUR EXTRACTION (F-VAPEX) Experimental Materials Experimental set-up Experimental preparation Experimental procedure Other measurements Results and Discussion Foamy oil flow in F-VAPEX F-VAPEX vs. VAPEX/CSI Effect of well configuration Residual oil saturation Chapter Summary CHAPTER 6 GASFLOODING-ASSISTED CYCLIC SOLVENT INJECTION (GA-CSI) Experimental Materials Experimental set-up Experimental preparation Experimental procedure Results and Discussion Well configuration Operating scheme (CSI vs. GA-CSI) GA-CSI Solvent injection rate GA-CSI with cylindrical models GA-CSI with rectangular model Residual oil saturation Variations of GA-CSI vii

10 6.3.1 Pressure control scheme Viscous fingering Oil production Chapter Summary CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations REFERENCES Appendix A Appendix B Appendix C Appendix D viii

11 LIST OF TABLES Table 2.1 VAPEX experimental studies by Butler s group Table 2.2 VAPEX experimental studies by Maini s group Table 2.2 VAPEX experimental studies by Maini s group (Contd ) Table 2.3 VAPEX experimental studies by Gu s group Table 2.4 VAPEX experimental studies by ARC Table 2.5 VAPEX experimental studies by other research groups Table 2.6 Comparison of the measured diffusion coefficients of CO 2, CH 4, C 2 H 6 and C 3 H 8 in different heavy oil and bitumen samples Table 2.7 CSI experimental studies in the literature Table 3.1 Parameters of the base case for the mathematical model Table 3.2 Parameters of the base case for the numerical simulation Table 3.3 Effect of the grid size and estimation of the numerical dispersion Table 4.1 Parameters of the base case Table 5.1 Physical properties of the sand-packed models and experimental conditions for VAPEX, CSI, and F-VAPEX testss Table 5.2 Cumulative heavy oil production data Table 6.1 Physical properties of the sand-packed models and experimental conditions for CSI and GA-CSI tests Table 6.2 Cumulative oil and solvent production data ix

12 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] Figure 3.1 Transition zone in the VAPEX process Figure 3.2 Approximation to the transition-zone at the (a) beginning and (b) middle stages of the VAPEX process Figure 3.3 Boundary movement of a transition-zone segment Figure 3.4 Flowchart of the solution calculation for the VAPEX model Figure 3.5 Discretization of the space and time domains for the numerical solution to the mass-transfer model with a moving boundary condition Figure 3.6 Evolution of the solvent vapour chamber during a VAPEX process Figure 3.7 Oil recover factor of the VAPEX base case 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 Figure 3.9 Effect of dividing number on the average oil production rate 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 Figure 3.11 Effect of permeability on the oil production rate 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 Figure 3.13 Oil production rate predicted by this study and the existing VAPEX models Figure 3.14 (a) Numerical simulation model; (b) Relative permeability vs. liquid saturation; and (c) Capillary pressure vs. liquid saturation x

13 Figure 3.15 Effect of the timestep size on the cumulative oil production (grid size: m 3 ) Figure 3.16 Effect of the grid size on the cumulative oil production (t = d) 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 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) m 3 ; (b) m 3 ; and (c) m Figure 3.19 Comparison of the predicted transition-zone thicknesses of this study and numerical simulation (grid size: m 3 ; t = 0.01 d) 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) Figure 4.2 Concentration-dependent diffusion coefficient and flow velocity: (a) Concentration; (b) Viscosity; (c) Effective diffusion coefficient; and (d) Convection velocity Figure 4.3 Approximation to the convection velocity with a piecewise linear profile Figure 4.4 Semi-analytical vs. Analytical c D for a convection diffusion mass transfer with a special convection velocity Figure 4.5 Semi-analytical vs. Numerical c D Figure 4.6 Flowchart of calculating the solvent concentration in the transition zone (t* denotes the termination time) Figure 4.7 Comparison of c D 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 m 2 /s; constant v is equal to m/s; t 1 = 300 s; t 2 = 600 s) xi

14 Figure 4.8 Effect of the pressure gradient on the solvent concentration distribution Figure 4.9 Effect of crude oil viscosity on the solvent concentration distribution Figure 4.10 Effect of diffusion coefficient on the solvent concentration distribution Figure 4.11 Effect of péclet number on the solvent concentration distribution Figure 4.12 Effect of péclet number with different linear shape on the solvent concentration distribution Figure 4.13 Effect of gravity force on the solvent concentration distribution Figure 5.1 Schematic diagram of the experimental set-up in this study Figure 5.2 (a) Physical model dimensions; (b) Central well configuration; and (c) Lateral well configuration Figure 5.3 Pressure-control scheme for (a) VAPEX; (b) CSI; and (c) F-VAPEX Figure 5.4 Injection and production pressure data during a typical F-VAPEX cycle 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) Figure 5.6 Foamy oil zone during the (a) early, (b) middle, and (c) late stages of an F-VAPEX test (Test #5.3) Figure 5.7 Cumulative oil production versus time data for the VAPEX, CSI and F-VAPEX tests with the central well configuration Figure 5.8 Cumulative oil production versus time data for the CSI and F-VAPEX tests with the lateral well configuration Figure 5.9 Enhancement of the oil production rate of VAPEX by F-VAPEX with different well configurations Figure 5.10 Enhancement of the oil production rate of CSI by F-VAPEX with different well configurations Figure 5.11 Cumulative solventoil ratio versus time data for the VAPEX, CSI, and F-VAPEX tests with the central well configuration Figure 5.12 Cumulative solventoil ratio versus time data for the VAPEX and F-VAPEX tests with the lateral well configuration xii

15 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) Figure 5.14 Oil production data from the stable pressure period and pressure reduction period during Test # Figure 5.15 Oil production from the stable pressure period and pressure reduction period during Test # Figure 5.16 Total oil production from the stable pressure period and pressure reduction period during the F-VAPEX tests Figure 5.17 Total solvent production data in the stable pressure period and the pressure reduction period of the F-VAPEX tests Figure 5.18 Residual oil saturation at the end of (a) Test #5.1; (b) Test #5.3; and (c) Test # 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 Figure 6.2 Pressure-control schemes of (a) GA-CSI and (b) CSI Figure 6.3 (a) Cumulative oil production; and (b) SOR of Tests # 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 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) xiii

16 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 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) 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) 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) Figure 6.10 Cumulative oil productions of Tests #6.3 (blowdown slugs only), and #6.1 and # Figure 6.11 Solvent injection rate at early, middle, and late stages of a GA-CSI test (Test #6.3) Figure 6.12 (a) Recovery factor; and (b) Solventoil ratio of the GA-CSI tests with cylindrical models of different lengths figure 6.13 Oil recovery factor of GA-CSI and CSI tests with the rectangular physical model Figure 6.14 Residual oil saturation of (a) CSI (Test #6.2); and (b) GA-CSI tests (Test #6.3) Figure 6.15 Residual oil saturation of (a) CSI (Test #6.6); and (b) GA-CSI (Test #6.7) Figure 6.16 Pressure control scheme of PP-CSI Figure 6.17 Injection and production pressures data during a PP-CSI test 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 # Figure 6.19 Comparison of the oil recovery factor of PP-CSI and GA-CSI tests Figure 6.20 Oil production from multiple pulses in different cycles of Test # xiv

17 NOMENCLATURE Notations a a ' slope of a linear Pe profile slope of a linear dimensionless diffusion coefficient profile A, B coefficients b b ' c c * c D c max c min C intercept of a linear Pe profile intercept of a linear dimensionless diffusion coefficient profile solvent concentration in the solvent-diluted heavy oil, vol.% solvent concentration under a operating pressure, vol.% dimensionless concentration, dimensionless maximum solvent concentration in a crude oil, vol.% minimum solvent concentration in a crude oil, vol.% modified dimensionless concentration, dimensionless D diffusion coefficient, m 2 /s D app apparent diffusion coefficient in the Das Butler model, m 2 /s D D F f o, f s dimensionless diffusion coefficient, dimensionless formation electrical resistivity factor weighted volume fractions of crude oil and solvent in Lederer s equation, fraction g gravity acceleration, m/s 2 H h model height, m vertical distance between an arbitrary point and the model bottom, m k permeability, m 2 L l M N N s N τ P length of the horizontal section of a horizontal well running VAPEX, m length of a transition-zone segment, m Kummer s function number of grids dimensionless number in the Butler Morkys VAPEX model number of substeps in a time step pressure, kpa xv

18 Pe Péclet number, dimensionless q oil drainage rate, m 3 /s q o stabilized oil production rate in the Butler Mokrys/Yazdani-Maini model, m 3 /s q in flowrate of solvent-diluted heavy oil entering into a transition zone segment, m 3 /s q out flowrate of solvent-diluted heavy oil leaving from a transition zone segment, m 3 /s Q cumulative oil production, m 3 Q o cumulative oil production in Moghadam et al. model, m 3 /s s Laplacian operator S oil saturation, vol.% S source/sink in the convection diffusion equation S oi S or S wr t t D U V initial oil saturation, vol.% residual oil saturation, vol.% residual water saturation, vol.% time, s dimensionless distance transition-zone boundary moving velocity, m/s convection velocity, m/s V p pore volume, m 3 V s sand volume, m 3 V w water volume, m 3 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 x D y z dimensionless distance y coordinate, m transformed dimensionless distance xvi

19 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 μ o, μ s 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 ξ 0 location of the transition-zone boundary at the beginning of a time step, m ξ max location of the transition-zone boundary next to the solvent chamber, m. ξ min location of the transition-zone boundary next to the untouched heavy oil zone, m. ξ mv distance of a transition-zone segment moved over a time step, m. ρ density of solvent-diluted heavy oil, kg/m 3 ρ o, ρ s densities of crude oil and liquid solvent, kg/m 3 τ time, s ψ arbitrary constant porosity, vol.% cementation factor, dimensionless xvii

20 Subscripts app D dew o oi or out i in max min mv p s τ apparent dimensionless dew point oil initial oil Residual oil outflow i th time interval inflow maximum minimum movement pore solvent time Abbreviations ARC CHOPS CMG CPCSI CSI CSS CT DPDVA EOR F-VAPEX GA-CSI GEM Alberta Research Council Cold Heavy Oil Production with Sands Computer Modelling Group Cyclic Production with Continuous Solvent Inejction Cyclic Solvent Injection Cyclic Steam Stimulation Computer Tomography Dynamic Pendant Drop Volume Analysis Enhanced Oil Recovery Foamy Oil-Assisted Vapour Extraction Gasflooding-Assisted Cyclic Solvent Injection Generalized Equation of State Model Reservoir Simulator xviii

21 ISC OOIP RF SAGD SAS SOR SRC STARS VAPEX In-Situ Combustion Original-Oil-In-Place Recovery Factor Steam-Assisted Gravity Drainage Steam Alternating Solvent Solvent Oil Ratio Saskatchewan Research Council Steam, Thermal and Advanced Reservoir Simulator Vapour Extraction Units API C bbl cc cm D dm g h kg kpa m m 2 /s m/s 2 min ml MPa mpas s American Petroleum Institute gravity Celsius barrel cubic centimeter centimeter Darcy decimeter gram hour kilogram kilopascal meter square meter per second meter per square second minute mililiter megapascal milipascal-second second xix

22 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 1

23 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 2

24 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 m 3 of proven and 3.7 billion m 3 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 3

25 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 4

26 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 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 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 2 nd 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. 5

27 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 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; 6

28 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. 7

29 CHAPTER 2 LITERATURE REVIEW 2.1 Vapour Extraction (VAPEX) VAPEX was first studied as a solvent-analogy of SAGD by Butler and Mokrys in 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. 8

30 [ Figure 2.1 The VAPEX heavy oil recovery process. 9

31 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 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 10

32 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 CO 2 -based VAPEX process for tar sand reservoirs. It was found from their experimental results that CO 2 propane mixture shows better performance in comparison with the methane propane mixture at a high operating pressure. The use of CO 2 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 11

33 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 CO 2 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 12

34 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 13

35 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. 14

36 Table 2.1 VAPEX experimental studies by Butler s group. No. Author Name Heavy Oil Model Injection Production ρ o μ o Size ϕ k T P q s t q o RF Type Shape Sand Solvent kg/m 3 / C mpas/ C cmcmcm % D C kpa cc/h h g/h % 1 Tangleflags 979/ /20 Hele Shaw square C 3 +hot H 2 O Tangleflags 979/ /20 Hele Shaw square C 3 +hot H 2 O Tangleflags 979/ /20 Hele Shaw square C 3 +hot H 2 O Butler Tangleflags 979/ /20 Hele Shaw square C 3 +hot H 2 O and Tangleflags 979/ /20 Hele Shaw square C 3 +hot H 2 O Mokrys 6 [1991, Tangleflags 979/ /20 sandpack rectangle Hele-Shaw C ] Tangleflags 979/ /20 sandpack rectangle Hele-Shaw C Tangleflags 979/ /20 sandpack rectangle Hele-Shaw C Tangleflags 979/ /20 sandpack rectangle Hele-Shaw C Tangleflags 979/ /21 sandpack rectangle glass beads C 3 +steam Peace River /20 sandpack rectangle sand C 4 +N Lloydminster 9350/20 sandpack rectangle sand C 4 +N Das Lloydminster 9350/20 sandpack rectangle sand C 4 +N and Lloydminster 9350/20 sandpack rectangle sand C 4 +N Butler Cold Lake 65000/20 sandpack rectangle sand C 4 +N [1995] Lloydminster 9350/20 sandpack rectangle sand C 4 +N Lloydminster 9350/20 sandpack rectangle sand C 4 +N Lloydminster 9350/20 sandpack rectangle sand C 4 +N Atlee Buffalo /27 sandpack rectangle sand n-c Atlee Buffalo /27 sandpack rectangle sand n-c Butler Atlee Buffalo /27 sandpack rectangle sand n-c and Atlee Buffalo /27 sandpack rectangle sand n-c Jiang Lloydminster /20 sandpack rectangle sand n-c [1996] Lloydminster /20 sandpack rectangle sand n-c Peace river /20 sandpack rectangle sand n-c Peace river /20 sandpack rectangle sand n-c

37 Table 2.2 VAPEX experimental studies by Maini s group. No. Author Heavy Oil Model Injection Production ρ o μ o Size ϕ k Name Type Shape Sand Solvent T P q s t q o RF kg/m 3 /C mpas/ C cmcmcm % D C kpa cc/h h g/h % 1 Dover /20 bulk rectangle Hele-Shaw C Dover /20 bulk rectangle Hele-Shaw C Boustani Dover /20 bulk rectangle Hele-Shaw C and Panny 970 bulk rectangle Hele-Shaw C Maini Panny 970 bulk rectangle Hele-Shaw C [2001] 51767/10 6 Panny 970 bulk rectangle Hele-Shaw C 8971/ Panny 970 bulk rectangle Hele-Shaw C Panny 970 bulk rectangle Hele-Shaw C Talbi /24 sandpack annular glass beads C 3 +CO and /25 sandpack annular glass beads C 3 +CH Maini /26 sandpack annular glass beads C [2003] 3 +CH /27 sandpack annular (30.73, 27.2) glass beads C 3 +CO sandpackrectangle US mesh C / / /7 9000/20 sandpackrectangle US mesh C sandpackrectangle US mesh C / /20 sandpackrectangle US mesh C / sandpackrectangle US mesh C / Karmaker 40000/ sandpackrectangle US mesh C and 9000/ / Maini sandpackrectangle US mesh C / [2003] /15 sandpackrectangle glass beads n-c /15 sandpackrectangle sands n-c /15 sandpackrectangle sands n-c /15 sandpackrectangle glass beads n-c /15 sandpackrectangle sands n-c /15 sandpackrectangle sands n-c

38 Table 2.2 VAPEX experimental studies by Maini s group (Contd ) No. Author Name Heavy Oil Model Injection Production ρ o μ o Size ϕ k T P q s t q o RF Type Shape Sand Solvent kg/m 3 / C mpas/ C cmcmcm % D C kpa cc/h h g/h % 1 Dina /9 sandpack rectangle beads C Yazdani Dina /9 sandpack rectangle beads C and Dina /9 sandpack rectangle geads C Maini 4 [2004, Dina /9 sandpack cylindrical30(42.3, 36.3) 1216 beads C ] Dina /9 sandpack cylindrical30(42.3, 36.3) 1620 beads C Dina /9 sandpack cylindrical30(42.3, 36.3) 2030 beads C Athabasca 1007/ /20 sandpack annular Zedah 1214 beads C 3 +CO and Athabasca 1007/ /20 sandpack annular 1214 beads C 3 +CO Maini Athabasca 1007/ /20 sandpack annular 1214 beads C 3 +CO (30.73, 27.2) 4 [2008] Athabasca 1007/ /20 sandpack annular 1214 beads C 3 +CO Frog lake 987.5/ /22.5 sandpack rectangle sand n-c Etminan Frog lake 987.5/ /22.5 sandpack rectangle sand n-c [2007] Frog lake 987.5/ /22.5 sandpack rectangle sand n-c Frog lake 987.5/ /22.5 sandpack rectangle sand n-c Ekl Point 987.5/ /22 cylindrical rectangle sand C Ekl Point 987.5/ /23 cylindrical rectangle sand C Haghighat Ekl Point 987.5/ /24 cylindrical rectangle sand C 3 +toluene and Maini 4 [2010] Ekl Point 987.5/ /25 cylindrical rectangle (30.73, 27.20) sand C 3 +toluene 20 variable Ekl Point 987.5/ /26 cylindrical rectangle sand C Ekl Point 987.5/ /27 cylindrical rectangle sand C

39 Table 2.3 VAPEX experimental studies by Gu s group. No. Author Name Heavy Oil Model Injection Production ρ o μ o Size ϕ k T P q s t q o RF Type Shape Sand Solvent kg/m3/ C mpas/ C cmcmcm % D C kpa cc/h h g/h % 1 Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Zhang Lloydminster /20 sandpackrectangle Ottwa C et al. 7 [2007] Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle v50 Ottwa C MoghadamLloydminster /20 sandpackrectangle Ottwa C et al. Lloydminster /20 sandpackrectangle Ottwa C [2008] Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C Lloydminster /20 sandpackrectangle Ottwa C 3 +C

40 Table 2.4 VAPEX experimental studies by ARC. No. Author Name Heavy Oil Model Injection Production ρ o μ o Size ϕ k T P q s t q o RF Type Shape Sand Solvent kg/m 3 / C mpas/ C cmcmcm % D C kpa cc/h PV g/h % 1 Lloydminster 5500/25 sandpackrectangle silica 90 toluene Cuthiell Lloydminster 5500/25 sandpackrectangle silica 90 toluene et al. Lloydminster 5500/25 blend rectangle /5070 blend 88 toluene [2003] Lloydminster 5500/25 field rectangle Rash lake sand 8 toluene Lloydminster 5500/25 sandpackrectangle silica 90 toluene Lloydminster 23000/20 sandpackrectangle C 1 +C 2 +C Lloydminster 23000/20 sandpackrectangle C Lloydminster 39000/20 sandpackrectangle C Frauenfeld Kerrobert 994.1/ /20 sandpackrectangle n-c et al. 5 [2006, 2007] Kerrobert 994.1/ /21 sandpackrectangle n-c Kerrobert 994.1/ /22 sandpackrectangle /90 n-c Kerrobert 994.1/ /23 sandpackrectangle /90 n-c Kerrobert 994.1/ /24 sandpackrectangle n-c Zhao 1 Northern et al sandpackrectangle Ottwa C Alberta 3 +steam [2005]

41 Table 2.5 VAPEX experimental studies by other research groups. No. Author Name Heavy Oil Model Injection Production ρ o μ o Size ϕ k Type Shape Sand Solvent T P q s t q o RF kg/m 3 / C mpas/ C cmcmcm % D C kpa cc/h h g/h % 1 Lim Cold lake /25 sandpack rectangle C et al. Cold lake /26 sandpack rectangle C [1995] Cold lake /27 sandpack rectangle C Athabasca 1001/ /22 sandpack cylinder 25 (45, 35) C Hadil 2 Athabasca 1001/ /22 sandpack cylinder 25 (45, 35) C [2009] Athabasca 1001/ /22 sandpack cylinder 25 (45, 35) C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C glass 960/ /25 sandpack circular C beads 9 960/ /25 sandpack circular C Rezaei / /25 sandpack circular C [2011] / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular C / /25 sandpack circular 155 Berea C / /25 sandpack circular 155 core C / /25 sandpack circular C

42 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 and 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. 21

43 (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]. 22

44 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 P inj = 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 P inj = 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. 23

45 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 m is feasible for the situation considered 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 2 nd Law [Fick, 1955] is applied to describe the dissolution of solvent into a crude heavy oil: c c D t x x, (1.1) where, c is the solvent concentration in heavy oil, vol.%; D is the diffusion coefficient, m 2 /s; x is the space variable, m; t is the time variable, s. 24

46 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. 25

47 Table 2.6 Comparison of the measured diffusion coefficients of CO 2, CH 4, C 2 H 6 and C 3 H 8 in different heavy oil and bitumen samples. Solvent Crude oil Pressure (MPa) Temperature (C) Viscosity (mpas) Diffusivity (10 9 m 2 /s) CO 2 Athabasca ,700 at 20C 0.28 Athabasca at 80C Athabasca ,000 at 25C Llyodminster ,267 at 23.9C Llyodminster ,000 at 23.9C Athabasca ,000 at 23.9C 0.5 CH 4 Athabasca ,500 at 25C Athabasca ,000 at 25C Llyodminster ,267 at 23.9C Llyodminster ,000 at 23.9C Dodecane , at 15.6C C 2 H 6 Athabasca ,000 at 25C Llyodminster ,000 at 23.9C C 3 H 8 Llyodminster ,267 at 23.9C Llyodminster ,000 at 23.9C 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] 26

48 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: D (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: D (for propane), (1.4) D (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]: 27

49 , (1.6) fs s f o o f s c 1 c c, f 1 o fs. (1.7) where, o, s, and are viscosities of the crude oil, liquid solvent, and mixture of the two, respectively, mpas; f o and f s 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: o s o s 17.04, (1.8) ln 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]: o s 1 1 c o c s. (1.9) where, o and s are the densities of the heavy oil and liquid solvent, respectively, kg/m 3 ; 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 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 28

50 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 c condition: 0 ; t 2. Solute solvent interface moves at a constant unspecified velocity: U const ; 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 v const ; 2 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 Dc. 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 x t : U sin x. t 29

51 Three governing equations constitute the foundation of the theoretical model: 1. Fick s 1 st law: dc D Uc ; d k 2. Darcy s Law: v g sin ; 3. Mass balance equation: qdt S oxdy t 0 H. y 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/s 2 ; is the porosity, fraction; S o = S oi S or is the oil saturation change in the solvent chamber; S oi is the initial oil saturation and S or 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, q o, during the solvent spreading phase: q 2L 2kg S N H, (1.10) o o s where, L is the length of a horizontal production well; H is the height of the sand-packed physical model; and N s is the dimensionless number: cmax cmin 1 c D Ns dc. (1.11) c 30

52 In the integrand, ρ is the density difference of the solvent-diluted heavy oil and the liquid solvent, kg/m 3. 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: q L kg S N h y. (1.12) o s( ) 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 D app : D app D. (1.13) Earlier study [Perkins and Johnston, 1963] indicated this relationship is rather as follows: D app D. (1.14) F 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) 31

53 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: k v c g sin. c H 2. Geometric relations: sin ; W sin x x ; cot. 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 32

54 and falling phases were derived as: Q H 2 S o cot o (for the spreading phase), (1.16) o o s Q HWS 2 cot tan (for the falling phase). (1.17) where, Q o is the cumulative oil production rates, m 2 ; 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: 1.26 q H k o , (1.18) 1.13 q H k o (1.19) They found that the stabilized heavy oil production rate was a function of the drainage height to the power of rather than 0.5 as predicted in the previous models. The constant coefficient in the above equation, in Eq. (1.18) and 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. 33

55 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 34

56 zone which is estimated to be just 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 35

57 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 36

58 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. 37

59 Table 2.7 CSI experimental studies in the literature. No. Author Lim et al., [1996] Dong et al., [2006] Ivory et al., [2010] Heavy Oil/bitumen Model Injection Production ρ o μ o Size ϕ k T P t RF Name Type Shape Sand Config. Solvent kg/m 3 / C mpas/ C cmcmcm % D C MPa h % Cold lake 100,000/25 sandpack rectangle Quartz Senlac Cactus Lake North Plover Lake 1,700 5,400sandpack Rush Lake 39,320/20 sandpack circular cone line source C 3 C 2 25 Quartz lateral C drop to h 3/13/15 c 5 17 h 8 c inj: d 300 (H) Quartz 28% C (9.7, 1) point % CO prd: d drop to (D top, D btm ) 2 6 c Firouz et al., [2012] Jamaloei et al., [2012] Huerta et al., [2012] Jiang et al., [2013] Saskatchewan heavy oil South Britnell Lloydminster 1,420/22 sandpack cylinder 1,080/22 sandpack cylinder (4.9, 3.2) 35,000/20 sandpack Lloydminster 5,875/20 sandpack rectangular Quartz lateral C 1 C 3 C 4 CO 2 Quartz point C 1 C 3 Quartz lateral 90% CO % H 2 S Glass beads drop to lateral propane drop to 0.5 soak: 24 h 7 10 c soak: 22 h prod: 0.5 h 6 cycles Soak: 24 h soak: 55 min prod: 5 min 60 38

60 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. 39

61 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 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 40

62 Concentration Solvent chamber Solven c max Diluted oil Heavy oil Diluted oil c min Distance Transition zone Injector Producer Heavy oil Figure 3.1 Transition zone in the VAPEX process. 41

63 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 = c max, and the second one (Boundary 2) neighbors the untouched heavy oil zone at c = c min 0.01 [Butler and Mokrys, 1989]. c max is the saturation concentration under the operating pressure and temperature and c min 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; 42

64 Solvent chamber Solvent Transition zone Heavy oil Solvent chamber Transition zone Heavy oil Producer (a) (b) Figure 3.2 Approximation to the transition-zone at the (a) beginning and (b) middle stages of the VAPEX process. 43

65 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 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 1 st 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 2 nd law is applied to calculate the solvent concentration distribution in each transition-zone segment: 44

66 c c D, (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, m 2 /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: D (for propane), (3.3) D (for butane). (3.4) In this study, is computed by using the one-parameter Lederer equation [1933]:, (3.5) fs s f o o f s c 1 c c, f 1 o f, (3.6) s where, o and s are viscosities of the crude heavy oil and the liquid solvent, respectively, mpas; f s and f o are the weighted volume fractions, vol.%; the weight factor is obtained by using the Shu s correlation [1984]: o s o s 17.04, (3.7) ln o s 45

67 where, γ o and γ s 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 c o c s. (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: c 0, cmax. (3.9) The right boundary of the transition zone is treated as a closed boundary: c Initially, there is no solvent in the oil: L, 0, (3.10) c, 0 0. (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:, cmax c s, (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 ξ 0 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: s 0 U. (3.13) 46

68 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: c t1 t, 0 c. (3.14) 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: k v c s g sin, (3.15) c where, v is the drainage velocity, m/s; k is the permeability, D; ρ(c) and ρ s are densities of the solvent-diluted heavy oil and the liquid solvent, kg/m 3 ; g is the gravitational acceleration, m/s 2 ; 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 q vd, (3.16) min where, q is the oil drainage flux of one segment, m 2 /s; max and min are the locations of Boundary 1 and Boundary 2 of the transition zone, respectively, m. 47

69 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 q in and q out, 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: q q l S S, (3.17) out in oi or where, l is the length of the transition-zone segment boundary, m; S oi and S or are the initial and residual oil saturations, respectively, vol.%. q in and q out can be obtained from Eq. (3.16). If the timestep size is small enough, the boundary moving velocity can be approximated as: d q q U out in d 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: mv x. (3.20) sin Similarly, the movement of the transition-zone segment in the vertical direction is: mv y. (3.21) cos 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. 48

70 Solvent chamber Transition zone v in Heavy oil ξ at t ξ+dξ at t+dt h ξ v out Figure 3.3 Boundary movement of a transition-zone segment. 49

71 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. ( ) 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, , 3.7 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. 50

72 BCs Governing Eq. IC c Yes No Terminate Finish ρ v U D Figure 3.4 Flowchart of the solution calculation for the VAPEX mathematical model. 51

73 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 N ξ 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:. (3.22) U Then the number of sub-step during a step t can be estimated as: N t. (3.23) If N τ < 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 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: W 0 Q S H y x dx, (3.24) where, Q is the cumulative heavy oil production, m 3 ; 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. 52

74 s = ξ/u t 5 =4 ξ/u t 4 =3 ξ/u t 3 =2 ξ/u t 2 = ξ/u t 1 =0 ξ 1 =0 ξ 2 = ξ ξ 3 =2 ξ ξ 4 =3 ξ ξ 5 =4 ξ ξ N = L 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

75 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 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. 54

76 Table 3.1 Physical properties and operating conditions of the base case for the VAPEX mathematical model. Parameters Value Model dimensions, m Porosity, % 35 Permeability, D 50 Relative oil permeability, fraction 1 Solvent type C 3 H 8 Solvent solubility, g solvent/100 oil 26.5 Heavy crude oil 23 C and 800 kpa, mpas 12,000 Heavy crude oil 23 C and 800 kpa, kg/m Solvent viscosity 23 C and 800 kpa, mpas Solvent density 23 C and 800 kpa, kg/m Diffusion coefficient, m 2 /s Operating pressure, kpa 800 Operating temperature, C 23 Connate water saturation, % 5 Residual oil saturation, % 15 Number of transition-zone segments 12 55

77 h 0.08 Vertical distance (m) h Horizontal distance, m Figure 3.6 Evolution of the solvent vapour chamber during a VAPEX process. 56

78 60 Spreading phase Falling phase Oil recovery factor (%) Time (h) Figure 3.7 Oil recover factor of the VAPEX base case. 57

79 y (m) x (m) (a) t=0.1 h t=5.0 h t=10.0 h t=15.0 h t=20.0 h c/c max (m) (b) t=0.1 h t=5.0 h t=10.0 h t=15.0 h t=20.0 h c/c max t=0.1 h t=5.0 h t=10.0 h t=15.0 h t=20.0 h c/c max t=0.1 h t=5.0 h t=10.0 h t=15.0 h t=20.0 h (m) (c) (m) (d) 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

80 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 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 R 2 = , which agrees well with the conclusions in the previous studies. 59

81 0.14 Oil production rate (cc/h) Dividing number Figure 3.9 Effect of dividing number on the average oil production rate. 60

82 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. ( ) with the same exponent of 0.46 but different coefficients of α = 1.5, 1.0, and 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 = m 2 /s) with an equivalent variable diffusion coefficient (D = μ 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. 61

83 k = 5 Darcy 0.08 k = 50 Darcy y (m) t=0 h t=2 h t=4 h t=6 h t=8 h t=10 h x (m) 0.10 (a) y (m) t=0 h t=2 h t=4 h t=6 h t=8 h t=10 h x (m) 0.10 (b) 0.08 k = 100 Darcy 0.08 k = 200 Darcy y (m) t=0 h t=2 h t=4 h t=6 h t=8 h t=10 h x (m) (c) y (m) t=0 h t=2 h t=4 h t=6 h t=8 h t=10 h x (m) (d) 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

84 5 4 q o (cc/h) 3 2 q K, R K (Darcy 0.5 ) Figure 3.11 Effect of permeability on the oil production rate. 63

85 q o (cc/h) q D, R D (m 2 /s) 1/2 (a) Oil recovery factor (%) D D=2.25e D=0.5e-9m D 10 9 D=1.0e-9m D 10 9 D=1.5e-9m D Time (h) (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. 64

86 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 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

87 This study Yazdani-Maini (2005) Yazdani-Maini, (2005) Das-Butler (1995) Butler-Mokrys, (1989) 0.25 q o (cc/h) k (Darcy) Figure 3.13 Oil production rate predicted by this study and the existing VAPEX models. 66

88 Table 3.2 Physical parameters and operation conditions for the base case of the numerical simulation. Parameters Value Model dimensions (lab-scale), m Model grid (lab-scale) Run time (lab-scale), d 3 Model dimensions (field-scale), m Model grid (field-scale) Run time (field-scale), d 3,000 Porosity, vol.% 35 Permeability, D 50 KV1 (k value correlation), kpa 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 Dispersion coefficients, m 2 /d Injection pressure, kpa 800 Production pressure, kpa 799 Gas/liquid relative permeability curve Figure

89 (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. 68

90 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 d) are run and it can be seen that the cumulative heavy oil production for t = 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 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 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. 69

91 Cumulative oil production (cc) t = d t = d t = 0.01 d t = 0.1 d Time (d) Figure 3.15 Effect of the timestep size on the cumulative oil production (grid size: m 3 ). 70

92 Cumulative oil production (cc) Scenario #1 Scenario #2 Scenario #3 Scenario # Time (d) Figure 3.16 Effect of the grid size on the cumulative oil production (t = d). 71

93 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 ΔY, m ΔX:ΔY 1:2 1:2 2:1 2:1 Oil production rate, cc/h Effective diffusion coefficient, m 2 /s Original α (α or ) Adjusted α (α ad ) Relative error, % 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 = (α ad α or )/α or 100%. 72

94 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 μ 0.46 m 2 /s) and five equivalent constant diffusion coefficients in oil phase (D = 22.9, 4.58, 2.29, 0.458, and m 2 /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 = to m 2 /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 m 3 /d) is just 1.14 times of that of the former one (6.15 m 3 /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 73

95 q o (cc/h) e-9 1.0e-8 1.5e-8 2.0e-8 2.5e-8 D (m 2 /s) (a) Numerical simulation This study 10 8 q o (m 3 /d) e-9 1.0e-8 1.5e-8 2.0e-8 2.5e-8 D (m 2 /s) (b) Numerical simulation This study 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

96 (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) m 3 ; (b) m 3 ; and (c) m 3. 75

97 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 m 3, 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 m 3 and m 3. 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 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. 76

98 Figure Comparison of the predicted transition-zone thickness of this study and the numerical simulation (grid size: m 3 ; t = 0.01 d) at 20 h. 77

99 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 q o vs. k and q o vs. D for a permeability range of Darcy and μ 0.46, 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. 78

100 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. 79

101 Injector/ producer Solvent Transition zone Solvent Transition zone Solvent Transition zone V High x Low Dead oil Dead oil Dead oil (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). 80

102 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 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 c D cv S ', (4.1) t x x 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 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). 81

103 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 V k dp g dx. (4.2) where, dp dx is the pressure gradient, kpa/m; Δρ is density difference between the solvent-diluted crude oil and the liquid solvent, kg/m 3 ; 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) 82

104 Table 4.1 Physical properties and operating conditions of the base case. Property Value Length, m 0.01 Permeability, D 10 Oil gravity Solvent gravity (liquid) Oil viscosity, mpas 6000 Solvent viscosity (liquid), mpas 0.1 Pressure gradient, kpa/m 5 Diffusion coefficient, m 2 /s μ 0.46 Time, s 600 Solubility, g solvent/g oil 0.26 Inlet solvent concentration, fraction Inlet diffusion coefficient, m 2 /s

105 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 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 c D cv t x x, (4.3) 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: c * c, t 0, (4.4) ( x0, t ) c x ( x, t ) 0, t 0, (4.5) c 0, 0 x, (4.6) ( x, t 0) 84

106 c D (m 2 /s) x (m) 1.4e-8 1.2e-8 1.0e-8 8.0e-9 6.0e-9 4.0e-9 2.0e-9 (a) V (m/s) x (m) (c) cp e-6 6e-6 5e-6 4e-6 3e-6 2e-6 1e x (m) (b) x (m) (d) Figure 4.2 Concentration-dependent diffusion coefficient and flow velocity: (a) Concentration; (b) Viscosity; (c) Effective diffusion coefficient; and (d) Convection velocity. 85

107 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 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: c D c t D x, td, x 2 D, c inlet V Pe, (4.7) D where, c inlet 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 cd cd cd Pe Pe c 2 D td xd xd xd cd 1t 0 ( xd 0, td ) D. (4.8) cd 0 td 0 xd ( xd 1, td ) cd 0 0 x 1 ( xd, td 0) D 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. 86

108 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: Pe axd 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): c c c ax b ac t x x D 2 D 2 D D D D D D. (4.10) Performing the Laplace transformation and integrating IC, Eq. (4.10) can be transformed into an ordinary difference equation (ODE): where 2 d C 2 dz z J C 0, (4.11) D a 2 b xd xd 4 2 C c e, (4.12a) J axd b z, a 0 a 1 s, a 0 2 a ax b, (4.12b) a D or z, a 0 1 s, (4.12c) 2 a or J, a 0 where, C and z are transformed c D 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: 87

109 Here, C 1 and C 2 are two independent solutions to Eq. (4.11): C AC1 BC2. (4.13) z J 1 1 z 4 C1 J, z e M (,, ), (4.14) z J 3 3 z 4 C2 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): i i 1, i i 2, i 1 C AC B C i n, (4.16) where, A i and B i can be obtained by applying the BCs of the i th segment: c x D D x D,i q i for the left boundary and c x D D xd, i1 q i1 for the right one (q i and q i+1 denote the mass-transfer rates at the left and right boundaries of the i th segment, respectively). It is worthwhile to 88

110 note the left BC for the first segment is c D xd 1, and that the right BC for the last 0 segment is c x D D xd 1 0. Back replacing the determined A i and B i into the Eq. (4.16), C is obtained over the entire spatial domain as functions of q i : * *, C J z A B q, (4.17a) , * * 1 < < C J z A q B q i n, (4.17b) i i i i i1 * *, C J z A q B. (4.17c) n n n n Considering the continuity condition for the solvent concentration at the interior common boundaries between any neighboring two segments: c c, (4.18) D,i 1 x D,i D,i x D,i and in the Laplacian domain, this is ai1 2 bi 1 ai 2 bi x x x x i 1 i C e C e. (4.19) x D, i D, i x Applying Eq. (4.19) to Eqs. (4.17a c), n 1 equations can be obtained: where A B q B q A, (4.20a) * * * * * * * * Ai 1qi 1 Ai i Bi 1 qi Bi iqi < i < n, (4.20b) * * * * n1 n1 n1 n n n n n A q B A q B, (4.20c) a a b b x 4 2 i i 1 2 i i 1 x i e. (4.21) 89

111 c ( x0, t) c max Pe c 0 ( x, t 0) c? ( x, t ) c x ( x L, t ) 0 c c i1 x i i x i x Figure 4.3 Approximation to the convection velocity with a piecewise linear profile. 90

112 Eqs. (4.20a c) can be coupled altogether to form a linear system: M q F, (4.22) n1 n1 n1 n1 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) 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: c D c, DD c inlet D x t D, xd, td D 2 inlet inlet, Pe V, (4.23) D inlet where D inlet is the diffusion coefficient at the left/inlet boundary under the operating conditions, m 2 /s. The governing equation, BCs, and IC of Model #2 can be normalized as: 2 cd c D D D cd Pe DD 2 Pe cd td xd xd xd xd cd 1t 0 ( xd 0, td ) D. (4.24) cd 0 td 0 xd ( xd 1, td ) cd 0 0 x 1 ( xd, td 0) D 91

113 Similar to Model #1, a simple case for Model #2 with a linear D D and a linear Pe is first studied as a first step for a more general case: Pe axd b, DD a ' xd b'. (4.25) where a ' and b ' are the slope and x-intercept of the linear D D profile. Substituting Eq. (4.25) for D D and Pe in the governing equation of Model #2: c c c t x x 2 D D D a' xd b' 2 a' axd b acd D D D. (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 D D and Pe profiles are arbitrary monotonous smooth curves, D D 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 D D 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 c D (x D,0) = 0. In the case of t D > 0, the transformed governing equation in the Laplacian domain would be a non-homogeneous equation whose general solution can be obtained: C AC BC A' C B' C. (4.28)

114 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 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 x D : Pe x D x D 2, (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: D e e C( s) s sx s (2 x ) 2 s (1 e ) D, (4.30) where (1 ) s 1 (1 ) s 1. (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 93

115 Semianalytical, N=5 Semianalytical, N=15 Semianalytical, N=25 Analytical 10 c D Pe Pe x D x D x D Figure 4.4 Semi-analytical vs. analytical c D for a convection diffusion mass transfer with a special convection velocity 94

116 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 Validation with the numerical solution The Crank Nicolson finite difference method (FDM) with a truncation error of O( x 4 ) is applied to acquire the numerical solution to the aforementioned convection diffusion model. Two spatial grid sizes ( and 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 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 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 95

117 Numerical-1 Numerical-2 Numerical-3 Semianalytical 0.8 c D x D Figure 4.5 Semi-analytical vs. numerical c D. 96

118 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 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 97

119 BCs Governing Eq. 1 c IC Finish Yes t > t* ρ V 4 D Equations 1. Semi-analytical solutions 2. Mixture rule of ideal solution, Eq Lederer Shu correlation, Eq Das Butler correlation, Eq Darcy s law, Eq. 4.2 Figure 4.6 Flowchart of calculating the solvent concentration in the transition zone (t* denotes the termination time). 98

120 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 [D inlet, 0.01D inlet ], and the constant V in Case #3 and #4 is equivalent to the mean value of the variable V over a range of [V inlet, 0.01V inlet ]. 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, c D 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 t 1 but larger at a longer time t 2. 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 c D 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 c D curve is mainly determined by D and V in the governing equation. (4) The effect of constant V on the c D 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 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 99

121 t1: var. D & var. V t2: var. D & var. V t1: const. D & var. V t2: const. D & var. V t1: var. D & var. V t2: var. D & var. V t1: var. D & const. V t2: var. D & const. V c D 0.6 c D x D (a) x D (b) t1: var. D & var. V t2: var. D & var. V t1: const. D & const. V t2: const. D & const. V t2: var. D & var. V t2: const. D & var. V t2: var. D & const. V t2: const. D & const. V c D 0.6 c D x D (c) x D (d) Figure 4.7 Comparison of c D 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 m 2 /s; constant V is equal to m/s; t 1 = 300 s; t 2 = 600 s). 100

122 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 c D profiles under the effect of positive, zero, and negative pressure gradients. Compared with the pure diffusion process where the pressure gradient equals zero, the c D profile is greatly improved by a positive pressure gradient of 5 kpa/m: the integral area of the c D profile for 5 kpa/m is almost twice of that for 0 kpa/m. In contrast, the c D profile is slightly shrunk by a negative pressure gradient of 5 kpa/m: the integral area of the c D 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 c D 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; 101

123 grad_p=5.0 kpa/m grad_p=2.5 kpa/m grad_p=0 kpa/m grad_p=-2.5 kpa/m grad_p=-5.0 kpa/m c D x D Figure 4.8 Effect of the pressure gradient on the solvent concentration distribution. 102

124 mpa.s mpa.s mpa.s mpa.s 0.8 c D x D Figure 4.9 Effect of crude oil viscosity on the solvent concentration distribution. 103

125 (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 x D (c D = 1) to x D (c D = 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 to The results show that the c D profile with a smaller D would have a sharper front yet a shorter diffusing distance while the c D 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 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 c D distribution. 104

126 =1.0e-9 =1.5e-9 =2.0e-9 =2.5e-9 =3.0e-9 c D 0.6 D x D Figure 4.10 Effect of diffusion coefficient on the solvent concentration distribution. 105

127 Concave, linear, and convex Pe profiles Figure 4.11 displays the c D 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 (c D > 1) portion in the c D profile. The sharper the decline is, the more easily the solvent would aggregate the amplitude of c D profile for the concave Pe is the largest among the three scenarios. Linear Pe profile with different slopes Figure 4.12 shows the c D 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 c D 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 c D profile 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. 106

128 Convex Linear Concave c D 0.6 Pe x D x D Figure 4.11 Effect of Péclet number on the solvent concentration distribution. 107

129 Pe=-8x D +8 Pe=-6x D +6 Pe=-4x D +4 Pe=-2x D c D c D x D x D Figure 4.12 Effect of Péclet number with different linear shape on the solvent concentration distribution. 108

130 Propane, without gravity Propane, with gravity Butane, without gravity Butane, with gravity 0.8 Heavy oil c D 0.6 Solvent Solvent Heavy oil 0.4 With gravity force Without gravity force x D Figure 4.13 Effect of gravity force on the solvent concentration distribution. 109

131 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. 110

132 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 Materials The heavy oil sample was collected from a western Canadian heavy oil reservoir, with a density of o = 976 kg/m 3 and a viscosity of μ o = 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 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 μm were used to pack the cylindrical and rectangular physical models. 111

133 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 ( cm 3 ) 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. 112

134 Physical model Injection unit Sand pack Injector Producer Camera Production unit Propane Data acquisition unit Digital pressure gauge Back-pressure regulator Oil collector Pressure transducer Scale Surge flask Flow meter Notebook computer Steel tubing Plastic flexible hose Data ware Figure 5.1 Schematic diagram of the experimental set-up in this study. 113

135 Height = 10 cm Width = 40 cm (a) Thickness = 2 cm 20 cm 7 cm (b) (c) Figure 5.2 (a) Physical model dimensions; (b) Central well configuration; and (c) Lateral well configuration. 114

136 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) S oi (%) k (D) (%) 5.1 VAPEX, Fig. 5.3a Injector/ 5.2 CSI, Fig. 5.3b producer 5.3 F-VAPEX, Fig. 5.3c F-VAPEX, Fig. 5.3c F-VAPEX, Fig. 5.3c VAPEX, Fig. 5.3a F-VAPEX, Fig. 5.3c F-VAPEX, Fig. 5.3c

137 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 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 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. 116

138 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/m 3 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 = 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 cm 3 /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 S oi = %. 117

139 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 P inj = 800 kpa (Figure 5.3a) and T = 20.2C, which is close to the propane s saturation pressure P dew = 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 P inj = 800 kpa and T = 20.2C for 55 min; (2) Production period. The production pressure P prod 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: 118

140 1000 Pressure (kpa) :00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 Time (hh:mm) (a) 1000 Pressure (kpa) Injection Production One cycle 0 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 Time (hh:mm) (b) 1000 Pressure (kpa) Figure Stable pressure period 200 Pressure reduction period One cycle 0 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 Time (hh:mm) (c) Pressure-control scheme for (a) VAPEX; (b) CSI; and (c) F-VAPEX. 119

141 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 P inj = 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 min to establish and led to an oil production of g for the tests with the central well configuration and h to result in an oil production of g for the tests with the lateral well configuration 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 120

142 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 W w. 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 W o. The final weight of the dried and cleaned sand samples were noted as W s. The volumes of the residual oil, residual water, and sand were computed by dividing W w, W o, and W s by their respective densities w, o, and s. The pore volume of the initial sand sample, V p, 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: Vp V s 1, (5.1) S wr V V w, (5.2) p S or V V o. (5.3) p 5.2 Results and Discussion 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 121

143 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. 122

144 1000 P inj P prod 800 Pressure (kpa) :30 00:40 00:50 01: :00 00:20 00:40 01:00 01:20 01:40 Time (hh:mm) Figure 5.4 Injection and production pressure data during a typical F-VAPEX cycle. 123

145 02/11/ :58:04 Solvent chamber Foamy oil zone (a) Untouched heavy oil zone 02/11/ :58:14 (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). 124

146 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. 125

147 (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). 126

148 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 F-VAPEX vs. VAPEX/CSI Oil production Table 5.2 summarizes the measured test durations t, cumulative oil production data Q o, and cumulative solvent production data Q g, and the calculated average oil production rates q o, 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 127

149 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 # ). 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). 128

150 Table 5.2 Cumulative heavy oil and solvent production data. t Q Test no. o Q s q o Oil RF SOR (h) (g) (dm 3 ) (g/h) (% OOIP) (g solvent/g oil)

151 Cumulative oil production (g) VPAEX CSI F-VAPEX, cycle length = 1 h F-VAPEX, cycle length = 2 h F-VAPEX, cycle length = 4 h Time (h) VAPEX & F-VAPEX CSI Injector/ producer Figure 5.7 Cumulative oil production versus time data for the VAPEX, CSI and F-VAPEX tests with the central well configuration. 130

152 Cumulative oil production (g) VPAEX F-VAPEX, cycle length = 1 h F-VAPEX, cycle length = 2 h VAPEX & F-VAPEX Time (h) Figure 5.8 Cumulative oil production versus time data for the CSI and F-VAPEX tests with the lateral well configuration. 131

153 Oil production rate enhanement (%) q enhancement F VAPEX q q VAPEX VAPEX / F-VAPEX VAPEX 100% VAPEX / F-VAPEX Test No. Figure 5.9 Enhancement of the oil production rate of VAPEX by F-VAPEX with different well configurations. 132

154 Oil production rate enhanement (%) q enhancement F VAPEX CSI q Injector/ producer F-VAPEX CSI q CSI 100% F-VAPEX Test No. Figure 5.10 Enhancement of the oil production rate of CSI by F-VAPEX with different well configurations. 133

155 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 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 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. 134

156 Cumulative solvent-oil ratio (g solvent/g oil) VPAEX CSI F-VAPEX, cycle length = 1 h F-VAPEX, cycle length = 2 h F-VAPEX, cycle length = 4 h Time (h) Figure 5.11 Cumulative solvent oil ratio versus time data for the VAPEX, CSI, and F-VAPEX tests with the central well configuration. 135

157 Cumulative solvent-oil ratio (g solvent/g oil) VPAEX F-VAPEX, cycle length = 1 h F-VAPEX, cycle length = 2 h Time (h) Figure 5.12 Cumulative solvent oil ratio versus time data for the VAPEX and F-VAPEX tests with the lateral well configuration. 136

158 Solvent chamber Foamy oil zone Untouched heavy oil zone (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). 137

159 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 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. 138

160 6 5 Stable pressure period Pressure reduction period F-VAPEX Oil production (g) Cycle number Figure 5.14 Oil production from the stable pressure period and pressure reduction period during Test #

161 14 12 Stable pressure period Pressure reduction period Oil production (g) F-VAPEX Cycle number Figure 5.15 Oil production from the stable pressure period and pressure reduction period during Test #

162 Stable pressure period Pressure reduction period Test no. Cycle length (h) Oil production (g) Test No. Figure 5.16 Total oil production from the stable pressure period and pressure reduction period during the F-VAPEX tests. 141

163 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 142

164 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). 143

165 Solvent production (dm 3 ) Stable pressure period Pressure reduction period Test no. Cycle length (h) Test No. Figure 5.17 Total solvent production data in the stable pressure period and the pressure reduction period of the F-VAPEX tests. 144

166 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 S wr = %. 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 S or = %, which are much lower than those (S or = %) 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 S or = 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 #

167 11.4% 16.1% % 23.1% 78.5% % Injector 38.5% 85.5% % Producer (a) % 12.5% 16.3% % 40.6% 3.6% Injector 37.6% % % 48.9% 47.3% Producer (b) 49.9% % % 12.2% Injector % 51.2% 67.1% % Producer 78.8% 89.2% (c) Figure 5.18 Residual oil saturation at the end of (a) Test #5.1; (b) Test #5.3; and (c) Test #

168 (a) (b) Figure 5.19 Cross-sectional views of the post-test sandpack of (a) Test #5.4 and (b) Test #

169 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. 148

170 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 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/m 3. Propane with a purity of 99.5 mol.% is used as the extracting solvent. 149

171 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. 150

172 Producer Physical model Sand pack Injector Gas flow meter Solvent injection unit Gas regulator Propane cylinder Fluids production unit Data acquisition unit Digital pressure gauge Back-pressure regulator Oil collector Scale Surge flask Flow meter Pressure transducer (a) Computer Steel tubing Plastic flexible hose Data ware H = 2 cm L = 40 cm (b) W = 10 cm P Physical model Injector/ Producer Sand pack P To Solvent injector To Production unit (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. 151

173 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 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 P inj = 800 kpa and T = 20.2C for 50 min; (2) Production period. The production pressure P prod 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 min of constant-pressure injection period (P inj = 800 kpa) and a 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 P prod from 800 to approximately 200 kpa within 3 5 min; 152

174 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) S oi (%) k (D) (%) 6.1 L = 34 cm, D = 3.8 cm CSI, Fig. 6.2a L = 34 cm, D = 3.8 cm CSI, Fig. 6.2a L = 34 cm, D = 3.8 cm GA-CSI, Fig. 6.2b L = 63 cm, D = 3.8 cm 6.4 GA-CSI, Fig. 6.2b L = 93 cm, D = 3.8 cm 6.5 GA-CSI, Fig. 6.2b CSI, Fig. 6.2a cm GA-CSI, Fig. 6.2b cm PP-CSI, Fig cm 3 153

175 1000 P prod 800 Pressure (kpa) Injection ONE CYCLE Production 0 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20 Time (hh:mm) (a) P inj P prod Pressure (kpa) Injection ONE CYCLE Production 0 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20 Time (hh:mm) (b) Figure 6.2 Pressure-control scheme of (a) GA-CSI and (b) CSI. 154

176 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 Q o, and cumulative solvent production data Q g, and the calculated average oil production rates q o, 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 155

177 Table 6.2 Cumulative oil and solvent production data of eight CSI and GA-CSI tests. t Q Test No. o Q s q o Oil RF SOR (h) (g) (dm 3 ) (g/h) (% OOIP) (g solvent/g oil)

178 80 Test #6.3 Oil recovery factor (%) Test #6.2 Test # Time (h) (a) 5 Cumlative solvent-oil ratio (g solvent/g oil) Test #6.3 Test #6.2 Test #6.1 0 Figure Time (h) (b) (a) Cumulative oil production; and (b) SOR of Tests #

179 due to the operating-scheme change from Test #6.2 to Test #6.3 (q o = 4.7 g/h) is much larger than that due to the well-configuration change from Test #6.1 to Test #6.2 (q o = 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 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 158

180 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 P prod 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. 159

181 Solvent chamber Injector Diluted oil Untouched heavy oil Producer (a) (b) (a) Producer (c) Injector (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. 160

182 Producer Flow front (a) Producer Flow front Flow front Flow front (b) Injector Backflow (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). 161

183 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). 162

184 Producer Injector (a) Producer Injector (b) Producer Injector (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. 163

185 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. 164

186 1000 ONE CYCLE 1400 Pressure (kpa) P inj P prod q s,inj Injection 1: Blowdown 2: Reinjection 3: Gasflooding Solvent injection rate (cc/min) :00 00:20 00:40 01:00 01:20 Time (hh:mm) 0 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

187 Cumlative oil production (g) Blowdown Reinjection Gasflooding Oil production rate (g/min) Solvent-oil ratio (g solvent/g oil) Time (min) 0.0 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

188 10 8 Blowdown Gasflooding Oil production (g) Time (h) (a) 14 Blowdown Gasflooding 12 Solvent production (sc,l) Time (h) (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). 167

189 80 Test #6.3 Test #6.2 Cumlative oil production (g) Test # Time (h) Figure 6.10 Cumulative oil productions of Tests #6.3 (blowdown slugs only), and #6.1 and #

190 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 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 169

191 600 Solvent injection rate (scm 3 /min) Test # Time (min) Figure 6.11 Solvent injection rate at early, middle, and late stages of a GA-CSI test (Test #6.3). 170

192 100 Oil recovery factor (%) Test #6.3 Test #6.4 Test # Time (h) (a) Cumulative solvent-oil ratio (g solvent/g oil) Test #6.3 Test #6.4 Test # Time (h) (b) Figure 6.12 (a) Recovery factor; and (b) Solvent oil ratio of the GA-CSI tests with cylindrical models of different lengths. 171

193 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 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) 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 172

194 70 Test # Oil recovery factor (%) Test # Time (h) Figure 6.13 Oil recovery factor of GA-CSI and CSI tests with the rectangular physical model. 173

195 l = 1 cm (Injection/production side) l = 8 cm 29.8% 54.1% l = 24 cm l = 32 cm 65.2% 72.2% l = 1 cm (Injection side) (a) l = 8 cm 14.8% 4.1% 6.9% l = 24 cm 9.8% l = 32 cm (Production side) 37.3% 50.3% (b) Figure 6.14 Residual oil saturation of (a) CSI (Test #6.2); and (b) GA-CSI tests (Test #6.3). 174

196 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. 175

197 45.7% Injector/P roducer 34.7% 43.4% 60.1% Sampling hole 63.9% 46.7% 60.4% 54.2% 54.2% 54.1% 55.7% 52.3% 51.9% (a) 26.4% 23.1% 18.8% 16.1% Producer 32.6% 36.3% 20.8% 27.8% Injector 3.1% 34.6% 39.7% 25.0% 16.4% (b) Figure 6.15 Residual oil saturation of (a) CSI (Test #6.6); and (b) GA-CSI (Test #6.7). 176

198 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) 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. 177

199 1000 Injection Production Pulse Pressure (kpa) : blowdown 2: re-injection 3: flooding ONE CYCLE P ing P prod 0 00:00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20 Time (hh:mm) Figure 6.16 Pressure control scheme of PP-CSI. 178

200 900 Injection Production 800 Pressure, kpa P inj P prod :00 00:10 00:20 00:30 00:40 00:50 01:00 01:10 01:20 01:30 Time (hh:mm) Figure 6.17 Injection and production pressures data during a PP-CSI test. 179

201 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. 180

202 Producer Injector (a) Producer Injector (b) Producer Injector (c) Producer Injector (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 #