UNIVERSITY OF CALGARY. EOS Modeling and Compositional Simulation Study of Carbon Dioxide. Enhanced Oil Recovery in the Pembina Cardium Field, Alberta

Transcription

1 UNIVERSITY OF CALGARY EOS Modeling and Compositional Simulation Study of Carbon Dioxide Enhanced Oil Recovery in the Pembina Cardium Field, Alberta by Tianjie Qin A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE GRADUATE PROGRAM IN CHEMICAL AND PETROLEUM ENGINEERING CALGARY, ALBERTA JULY, 2016 c Tianjie Qin 2016

2 Abstract With thousands of multi-fractured horizontal wells completed in the Pembina Cardium field, adapting and utilizing existing wells and infrastructure for future CO 2 -EOR development is economically and environmentally attractive. Even so, drilling, completion and hydraulic fracturing design and practices can vary greatly across the field. In this thesis, an effective workflow is developed to evaluate the success of different strategies for completing Cardium horizontal wells and their suitability for conducting CO 2 injections for EOR. In addition, a method for identifying re-fracturing horizontal well candidates is developed. WAG injection is a commonly employed technique to improve sweep efficiency in gas flooding processes. A study of different WAG injection schemes is also conducted and compared to continuous CO 2 injection in this work, which includes constant WAG, SWAG, and hybrid/tapered WAG injection. The effects of various WAG parameters are investigated. The results indicate that an appropriately designed injection scheme can improve oil recovery substantially. ii

3 Acknowledgements My deepest, heartfelt gratitude to my supervisor, Dr. Zhangxing (John) Chen, for his invaluable support during my graduate studies at the University of Calgary. The tremendous opportunities, freedom, and resources he provided, are deeply appreciated. I would also like to express my gratitude to my co-supervisor, Dr. Mingzhe Dong for his immense knowledge and guidance during my study. Besides my supervisors, I would like to thank my supervisory committee members - Dr. Roberto Aguilera and Dr. Hemanta Sarma - for their time and efforts. I am also grateful to Dr. Keliu Wu for enlightening me with the first glance at this research. Special thanks go to Ms. Vicky Wang, Mr. Gary Jing and Dr. Varun Pathak, who provided insight and expertise that greatly assisted my research. My gratitude also goes to my colleagues in the Reservoir Simulation Group and my many friends who supported me in my research, sparking incentives to strive towards my goal. Last but not the least, I would like to thank my family for their unconditional support and love throughout my life. iii

4 Table of Contents Abstract ii Acknowledgements iii Table of Contents iv List of Tables vi List of Figures and Illustrations vii List of Symbols, Abbreviations and Nomenclature x 1 INTRODUCTION Location of Study Area Problem Statement Research Objectives Research Contributions Structure of the Thesis BACKGROUND The Pembina Cardium Field Geology Background of the Cardium Formation Reservoir and Fluid Characteristics Production History Key Technology Advancements for Cardium Development Horizontal Drilling Multi-stage Hydraulic Fracturing Microseismic Monitoring Carbon Dioxide Enhanced Oil Recovery Key Mechanisms Mobility Ratio Control Microscopic and Macroscopic Sweep Efficiency WAG Injection Schemes Pembina Cardium Carbon Dioxide EOR Pilot METHODOLOGIES Reservoir Fluids and EOS Modeling Reservoir Fluids Sampling and PVT Tests EOS Modeling and Tuning Components Lumping and EOS Modeling Results Reservoir Models and Reservoir Conditions Fuzzy Analytic Hierarchy Process Design of Experiments A WORKFLOW FOR EVALUATING WELL COMPLETION EF- FECTIVENESS Sensitivity Analysis Reservoir Quality Well Completion Quality Assignment of Weighting Factors Evaluation and Grading iv

5 4.3.1 Reservoir Quality Well Completion Quality Application and Validation Identifying Re-fracturing Opportunities Risk Analysis Reservoir Heterogeneity Presence of Conglomerate OPTIMIZING WAG PERFORMANCE Reservoir Model and History Matching Constant Water-Alternating-Gas Injection WAG Ratio Cycle Length Simultaneous Water-and-Gas Injection SWAG Injection Rate SWAG Ratio Hybrid/Tapered Water-Alternating-Gas Injection Hybrid WAG Tapered WAG Summary CONCLUSIONS AND RECOMMENDATIONS Conclusions Recommendations Bibliography v

6 List of Tables 3.1 Properties of Pembina Cardium fluid type I Properties of Pembina Cardium fluid type II Properties of Pembina Cardium fluid type III Summary of the pseudo-component properties of fluid type I Summary of the pseudo-component properties of fluid type II Summary of the pseudo-component properties of fluid type III Summary of fluid properties Reservoir input for the base case Properties of wells, fractures and operating conditions for the base case Fuzzy numbers used for making pairwise comparisons Random index used to compute consistency ratio (CR) Common fuzzy arithmetical operations using two TFNs Reservoir quality criteria and the associated levels for sensitivity runs Sensitivity runs and their recovery factors for the reservoir quality group Well completion quality criteria and the associated levels for sensitivity runs Sensitivity runs and their recovery factors for the well completion quality group Pairwise comparison matrix for the reservoir quality group Pairwise comparison matrix for the well completion quality group Fuzzy weight and global weight for each criterion Optimum reservoir and well completion parameters and weighting factors for evaluating well completion strategies suitable for CO 2 -EOR Fuzzy weight and global weight for each criterion Grading and ranking of candidates Geological parameters for conglomerate and sand Parameters used for history matching Parameters used for WAG performance forecasting Five injection scenarios to study the effect of WAG ratio Four injection scenarios to study the effect of WAG cycle length Five injection scenarios to study the effect of SWAG ratio Injection scheme to study the performance of tapered WAG injection vi

7 List of Figures and Illustrations 1.1 The Pembina Cardium field in western Canada (CDL, 2011) Cardium type log in the 100/ W5 well (Dashtgard et al., 2008) Historical Pembina production (Macquarie Research, 2009) Cardium annual well completions by well type (PTAC, 2014) Alberta average daily production of crude oil by well type (AER, 2015) Pembina cost/frac and average fracs/well (ARC, 2014) Pembina average well length and frac spacing (ARC, 2014) Sketch of stress regime and orientations in the WCSB (Cui et al., 2013) In situ stresses and hydraulic fracture propagation of two fracture configurations (Economides et al., 2010) Microseismic events located at a Pembina Cardium well (Duhault, 2012) Schematic of various CO 2 injection schemes (Verma, 2015) Location of horizontal and vertical injection projects (CSA Group, 2012) Pembina Cardium fluid compositions Comparison of formation volume factor and gas solubility curves of three fluid types Comparison of oil viscosity of three fluid types Pseudo-components of the Pembina Cardium fluids Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type I Comparison between the experimental and simulated oil viscosity of fluid type I Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type II Comparison between the experimental and simulated oil and gas viscosity of fluid type II Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type III Comparison between the experimental and simulated oil and gas viscosity of fluid type III Schematic plot showing SRV A close view of the base case model showing hydraulic fractures (red grid blocks), SRV (light blue grid blocks) and tight formation (dark blue grid blocks) Oil-water relative permeability Oil-gas relative permeability An eight-step method for F-AHP Hierarchical structure for evaluation of different well completion strategies for CO 2 -EOR Main effect analysis of recovery factor for the reservoir quality group Half-normal probability plot showing the significance of parameters on oil recovery factor for the reservoir quality group vii

8 4.3 Main effect analysis of recovery factor for the well completion quality group Half-normal probability plot showing the significance of parameters on oil recovery factor for the well completion quality group Recovery factor as a function of remaining oil in place Recovery factor as a function of permeability Recovery factor as a function of reservoir depth Recovery factor as a function of fluid type Recovery factor as a function of well lateral length Comparison of recovery factor among different well lateral length for a 10-year CO 2 injection period Recovery factor as a function of well spacing Comparison of cumulative CO 2 production among different well spacing for a 10-year CO 2 injection period Recovery factor as a function of fracture spacing Comparison of cumulative CO 2 production among different fracture spacing for a 10-year CO 2 injection period Recovery factor as a function of fracture half-length Comparison of cumulative CO 2 production among different fracture halflength for a 10-year CO 2 injection period Recovery factor as a function of skin factor Comparison of evaluation results and simulated recovery factor Identifying re-fracturing candidates Top view (i-j plane) and side view (i-k plane) of the model showing horizontal and vertical permeability distribution Histogram of the horizontal absolute permeability data Comparison of homogeneous and heterogeneous cases Three sets of oil-water relative permeability curves used for sand (solid), conglomerate (long dash) and fractures (dash-dot) Three sets of oil-gas relative permeability curves used for sand (solid), conglomerate (long dash) and fractures (dash-dot) Comparison of cases with and without conglomerate History matching results for well History matching results for well Relative permeability curves obtained from history matching of production data Comparison of incremental oil recovery with respect to the HCPV of injected CO 2 for injection schemes with different WAG ratios Comparison of average reservoir pressure with respect to the HCPV of injected CO 2 for injection schemes with different WAG ratios Incremental oil recovery as a function of WAG ratio Pressure distribution at the end of WAG injection scheme, top layer Interfacial tension at the end of WAG injection scheme, top layer Oil saturation at the beginning of WAG injection scheme, top layer Oil saturation at the end of WAG injection scheme, top layer viii

9 5.11 Cross-section view of oil saturation spatial distribution at the beginning of WAG injection Cross-section view of oil saturation spatial distribution at the end of WAG injection Global CO 2 mole fraction at the end of WAG injection scheme, top layer Global CO 2 mole fraction at the end of WAG injection scheme, bottom layer Water saturation at the end of WAG injection scheme, top layer Water saturation at the end of WAG injection scheme, bottom layer Cross-section view of CO 2 mole fraction spatial distribution at the end of WAG injection Cross-section view of water saturation spatial distribution at the end of WAG injection Comparison of incremental oil recovery with respect to the HCPV of injected CO 2 for injection schemes with different WAG cycle length Comparison of average reservoir pressure with respect to the HCPV of injected CO 2 for injection schemes with different WAG cycle length Comparison of oil recovery factor for different SWAG injection rates Comparison of average reservoir pressure for different SWAG injection rates Comparison of oil recovery factor for different SWAG ratios Comparison of average reservoir pressure for different SWAG ratios Comparison of incremental oil recovery for different pre-wag slug sizes Comparison of average reservoir pressure for different pre-wag slug sizes Comparison of incremental oil recovery between hybrid WAG and tapered WAG Comparison of incremental oil recovery for various CO 2 injection techniques 108 ix

10 List of Symbols, Abbreviations and Nomenclature Abbreviation BHP CI CO 2 -EOR CR DOE EOS F-AHP GOR HCPV IFT LGR MCDM MMP MW OOIP PVT RI SG SRV SWAG TFN WAG WCSB Definition Bottom-hole Pressure Consistency Index Carbon Dioxide Enhanced Oil Recovery Consistency Ratio Design of Experiments Equation-of-State Fuzzy Analytic Hierarchy Process Gas-Oil Ratio Hydrocarbon Pore Volume Interfacial Tension Local Grid Refinement Multiple Criteria Decision-Making Minimum Miscibility Pressure Molecular Weight Original Oil in Place Pressure Volume Temperature Random Index Specific Gravity Stimulated Reservoir Volume Simultaneous Water-and-Gas Triangular Fuzzy Number Water-Alternating-Gas Western Canada Sedimentary Basin x

11 Symbol B o R s P c T c ω Ω a Ω b k p b G G Definition Formation volume factor Solution gas-oil ratio Critical pressure Critical temperature Acentric factor Peng-Robinson constant Peng-Robinson constant Permeability Bubble point pressure Fuzzy global weight Global weight xi

12 Chapter 1 INTRODUCTION Along with the growth in global demand for energy and the depletion of conventional oil resources, people s focus has been strategically shifted to the exploration and development of unconventional oil resources. As an important member of unconventional resources, tight oil plays are beginning to emerge as a reliable source of oil supply due to technological advancements in horizontal drilling coupled with multi-stage fracturing. In the development of tight oil plays, production rates decline dramatically within the first 4 to 12 months as a result of extremely low reservoir permeability and restricted flow capacity (Bybee et al., 2011). Production is confined to a fracture-surrounded space thereby leaving a significant volume of oil in place after the primary and secondary phases of production. Consequently, it is a great challenge to effectively and commercially recover oil from these tight oil plays, and employing some EOR techniques becomes necessary. In the past few decades, CO 2 -EOR has attracted significant industrial attention as a promising technique to develop mature tight oil reservoirs. Compared to other gas displacing agents, CO 2 can achieve miscibility with crude oil at a lower pressure and has a combination effect of oil swelling and viscosity reduction, which contribute to more effective displacement. In addition, CO 2 injection provides environmental benefits for reducing greenhouse gas emissions. The ultimate enhanced recovery and economic return of a CO 2 -EOR project are affected by various factors. For a successful project, reservoir quality, fluid characteristics and geological uncertainties should be taken into account. Furthermore, a careful engineering design should be conducted on well placement, hydraulic fracturing strategies and operation schemes. 1

13 1.1 Location of Study Area The area of interest in this study is the Pembina Cardium field located in central Alberta, Canada (Figure 1.1). It is one of the largest conventional oil pools in Western Canada, covering an area of over 1,000 square miles, with more than 9.4 billion barrels of original oil in place (OOIP) (Ghaderi et al., 2011; NEB, 2011). Figure 1.1: The Pembina Cardium field in western Canada (CDL, 2011) 1.2 Problem Statement Since 2008, a growing number of multi-fractured horizontal wells have been completed and planned in the tight portions of the Pembina Cardium field by different operators. Currently, over 2,500 horizontal wells have been completed in the giant Pembina Cardium field and approximately 2,000 horizontal wells in other parts of the Cardium formation (CDL, 2

14 2016). As the topic of carbon emission reduction is gaining its popularity, using existing wells and infrastructure for future CO 2 -EOR development is highly attractive, not only for the sake of the large number of horizontal wells completed in the Pembina Cardium field, but also for the environmentally-friendly aspects of the CO 2 -EOR technique. Drilling, completion, and hydraulic fracturing design and practices can vary greatly as a result of different general locations, geological conditions, operator preference, as well as technology advancements through years. In addition, the performance of CO 2 -EOR is influenced greatly by well completion qualities, including well length, well placement, fracture density, Stimulated Reservoir Volume (SRV) and a skin factor. Completion strategies, with good behavior in primary depletion, may not yield similar results in CO 2 injections for EOR. Consequently, an effective method that evaluates the success of different strategies for completing horizontal wells and their suitability for conducting CO 2 -EOR is imperative to develop. Identifying re-fracturing horizontal well candidates for future development and determining risks associated with CO 2 -EOR projects are also of great importance for hydrocarbon producers to achieve desired economic returns. 1.3 Research Objectives The focus of this thesis is to develop an effective method to evaluate the success of different strategies for completing Cardium horizontal wells and their suitability for conducting CO 2 flooding for EOR, screen horizontal well candidates for re-stimulation, identify potential risks associated with a CO 2 -EOR project in the Pembina Cardium field, and examine various gas injection schemes (continuous CO 2 injection, constant WAG injection, SWAG injection and hybrid/tapered WAG injection) for the Pembina Cardium field development. The specific objectives of this study are as follows: 1. Assess the potential to conduct CO 2 -EOR in the Pembina Cardium field through compositional simulations. To establish reservoir simulation models for this study, 3

15 two essential parts are required: fluid models and reservoir models. Build different reservoir fluid models, based on PVT analyses, to characterize the variation of the Pembina Cardium fluids. This work involves Equation-of-State (EOS) models tuned to match the experimental PVT behaviour of the Pembina Cardium fluids. Establish reservoir models that can represent the Cardium formation properties in the Pembina Field. 2. Investigate the sensitivities of various reservoir and well completion factors that may influence the CO 2 -EOR performance. 3. Evaluate the success of different Cardium well completion strategies and their suitability for conducting CO 2 injections for EOR. This work involves a combination of techniques, including compositional simulations, a Fuzzy Analytic Hierarchy Process (F-AHP) and Design of Experiments (DOE). 4. Screen re-fracturing horizontal well candidates for future development. 5. Identify potential risks that may affect a CO 2 -EOR project in the Pembina Cardium field. 6. Compare various injection schemes, including constant WAG, SWAG, and hybrid WAG to continuous CO 2 injection; optimize relevant parameters, including injection rate, CO 2 slug size, WAG ratio and cycle length, in different injection schemes. 1.4 Research Contributions The key contributions of this study include: 4

16 1. Establishment of different fine-tuned reservoir fluid models, based on extensive PVT analyses, to help understand Cardium fluid properties and characterize the variation of the Pembina Cardium fluids. 2. Evaluation of the potential for applying CO 2 injection technique for EOR from the Pembina Cardium field. 3. Development of an effective workflow to evaluate the success of different strategies for completing Cardium horizontal wells and determine if these strategies are suitable for CO 2 -EOR development. 4. Development of a method for selecting re-fracturing well candidates. 5. Identification of potential risks that may affect a CO 2 -EOR project in the Pembina Cardium field, including reservoir heterogeneity and presence of conglomerate on the top of the Cardium formation. 6. Analysis of different WAG injection schemes including constant WAG, SWAG, hybrid WAG and tapered WAG. 1.5 Structure of the Thesis This thesis contains six chapters. Chapter 1 introduces the background and the motivation of this study. It also explains the research problems, objectives, and contributions of the study. Chapter 2 presents the geological background, the key reservoir characteristics and the development history of the Pembina Cardium field. In addition, some crucial techniques applied to develop the low permeability portions of this field, including horizontal drilling, multi-stage hydraulic fracturing and microseismic monitoring, are discussed. Several key 5

17 mechanisms involved in CO 2 -EOR processes and various commonly employed WAG injection schemes are also described. Chapter 3 summarizes the methodologies applied in this study. Three different EOSbased fluid models are described. These models are then tuned to match the experimental PVT behaviour of the Pembina Cardium fluids and coupled to the reservoir models. The Fuzzy Analytic Hierarchy Process (F-AHP), as a powerful multiple criteria decision-making technique, is introduced in this study. The last part of the chapter provides an introduction to the Design of Experiments (DOE), a widely-applied statistical method for conducting sensitivity analysis, and explains how this method assists reservoir simulations and F-AHP with achieving the study s objectives. Chapter 4 provides the results of the sensitivity analysis on different reservoir and hydraulic fracturing factors, the integrated workflow to evaluate the success of different strategies for completing Cardium horizontal wells and their suitability for conducting CO 2 injections for EOR and its application, the method for screening re-fracturing candidates, and the risks that may affect a CO 2 -EOR project in the Pembina Cardium field. Chapter 5 analyzes the effectiveness of different gas injection schemes, including continuous CO 2 injection, constant WAG injection, SWAG injection, as well as hybrid/tapered WAG injection. The effects of injection rate, CO 2 slug size, WAG ratio and cycle length are also investigated. Chapter 6 provides the conclusions and recommendations for future work. 6

18 Chapter 2 BACKGROUND This chapter provides the geological background, the key reservoir characteristics and the development history of the Pembina Cardium field. Some important techniques applied to develop the low permeability portions of this field, including horizontal drilling, multistage hydraulic fracturing and microseismic monitoring, are introduced. In addition, key mechanisms involved in CO 2 -EOR processes and various commonly applied WAG injection schemes are described. 2.1 The Pembina Cardium Field Geology Background of the Cardium Formation The Cardium formation is a stratigraphic unit located in the Western Canada Sedimentary Basin (WCSB). This formation is regionally extensive, stretching across nearly 5,500 square miles in central and southern Alberta, with the structure dipping to the south-west (Bybee et al., 2011; Sennhauser et al., 2011). It has been described as a clastic wedge that accumulated during the Turonian-Coniacian time of the late Cretaceous (Bybee et al., 2011). The varying depositional environments have resulted in a wide range of reservoir rock characteristics. The greatly heterogeneous Cardium formation consists of lower, middle and upper sandstone members, which are fine to very fine-grained, with interbedded silt or shale content (Dashtgard et al., 2008; Wahl et al., 1963). The sandstone members are occasionally capped by some highly permeable conglomerate layers that have varying thickness from a few inches to approximately 20 ft. (Wahl et al., 1963). This conglomerate interval is composed of white to black chert, with a matrix of grit, sand or shaly sand (Wahl et al., 1963). Figure 2.1 provides a Cardium type log, showing the presence of conglomerate which overlies 7

19 a scoured contact with the upper Cardium sand. Hydrocarbons are produced from several stratigraphic traps formed within the Cardium formation, which is estimated to contain 10.6 billion barrels of OOIP (25% of Alberta s total discovered light oil) (Ghaderi et al., 2011). Reservoirs and pools have been found at depths ranging from 3,937 ft to 8,858 ft and typically contain light, sweet oil with varying amounts of dissolved gas (Krause et al., 1994). Figure 2.1: Cardium type log in the 100/ W5 well (Dashtgard et al., 2008) 8

20 2.1.2 Reservoir and Fluid Characteristics Among all Cardium oil play areas, the Pembina Cardium field has the most significant oil resources. As mentioned in Chapter 1, this giant field spans an area of over 1,000 square miles, with more than 9.4 billion barrels of OOIP. It is located in a stratigraphic trap without bottom water and gas cap zones (Purvis et al., 1979). As a result of its wide range of reservoir depth and rock properties, variations in fluid properties can be expected across the field. Generally, the solution gas-oil ratio (GOR) increases with depth from the northeast to the southwest of the field. Based on a total of 55 PVT analyses summarized by Wahl et al. (1963), the GOR ranges from 300 to 900 scf/stb; the formation volume factor ranges from 1.15 to 1.48 bbl/stb; and the saturation pressure ranges from 1,200 to 2,600 psi across the field. Generally, the oil is produced primarily through solution gas drive, followed closely by waterflooding Production History The Pembina Cardium field was discovered in 1953 with the Socony Seaboard Pembina No.1 Well (100/ W5). Primary production of this field began in 1953 and waterflooding practices have been ongoing since the 1960s (Dashtgard et al., 2008). The cumulative production, however, had been in a general decline for decades and was limited to about 18-20% from both primary and secondary schemes with vertical drilling. Figure 2.2 describes the historical production in this field. 9

21 Figure 2.2: Historical Pembina production (Macquarie Research, 2009) Advances in horizontal drilling and completion techniques enable the development of low permeability portions of the Pembina Cardium field, which had not been economically accessible formerly. These areas are referred to as a Halo Oil play and can provide an additional 4-8 million barrels of OOIP per section (640 acres) (Clarkson et al., 2011; Sennhauser et al., 2011). Apart from the lower permeability compared to main conventional pools, these peripheral portions have featured thinner reservoir intervals with net-pay thickness varying between 10 to 30 feet (Duhault, 2012). Since 2008, a growing number of multi-fractured horizontal wells have been completed and planned in the Pembina Cardium field by different operators. At present, over 2,500 horizontal wells have been completed in the giant Pembina Cardium field and approximately 2,000 horizontal wells in other parts of the Cardium formation (CDL, 2016). Figure 2.3 illustrates the historical Cardium well development. As can be seen from this figure, a boom in Cardium horizontal drilling occurred in Undoubtedly, the introduction of horizontal, multistage hydraulic fracturing technologies has revitalized this mature oil field. 10

22 Figure 2.3: Cardium annual well completions by well type (PTAC, 2014) 2.2 Key Technology Advancements for Cardium Development Horizontal Drilling The advent of horizontal drilling and completion technologies has opened up the development of tight hydrocarbon resources worldwide. With horizontal drilling, tight resource plays, which were considered uneconomic to produce when drilled vertically, become accessible. Compared to traditional vertical drilling, horizontal drilling has significantly increased wellbore length exposed to the pay zone. One horizontal well is capable of accessing and draining resources that would require several vertical wells. Typically, multiple horizontal wells are drilled from the same surface location (multi-well pads) which minimize the cost and environmental footprint. The drilling landscape has changed significantly in WCSB by use of horizontal drilling. 11

23 Since 2013, an estimated 80% of oil wells completed on production in Alberta applied horizontal drilling techniques. Development of Halo areas in the Pembina Cardium field benefits from horizontal drilling as well. The low permeability and thin net pay of these areas are only economically accessible through horizontal drilling. According to a recent report provided by the Alberta Energy Regulator (AER), a fast growing trend of oil production from horizontal drilling has been projected for the next 10 years, as suggested by Figure 2.4. It is believed that there continues to be a great potential for reserves growth from new horizontal drilling in the Cardium formation at Pembina, as well as in other fields. Figure 2.4: Alberta average daily production of crude oil by well type (AER, 2015) Multi-stage Hydraulic Fracturing To successfully develop tight hydrocarbon resources, the application of well-established techniques of horizontal drilling is usually combined with multi-stage hydraulic fracturing, as horizontal drilling alone could not achieve profitable production profiles. A multi-stage fracturing treatment involves placement of hydraulic fractures at multiple intervals along the 12

24 horizontal wellbore. This is realized by pumping fracturing fluids into a formation to create pathways to allow fluids to flow through the low-permeability rock to a wellbore. These fractures are kept open by proppants contained in fracturing fluids. Multi-fractured horizontal wells have been widely used to access various types of formations in North America. Since 2009, almost all wells completed in the Cardium formation have been horizontal wells. Even so, the drilling, completion and hydraulic fracturing design and practices can vary greatly as a result of different in-situ geological conditions, reservoir characteristics, operator preference and technology advancements through years. In recent years, the Cardium producers have attempted a variety of completion strategies with different impacts and results. Therefore, it can be anticipated that each operator has been gone through a learning curve to determine the optimal strategy for completing Cardium horizontal wells in different areas. Figures 2.5 and 2.6 describe a learning process of a multistage hydraulic fracturing design from a major Pembina Cardium operator. As suggested by these two figures, from 2012 to 2015, they have benefited from the extended reach of horizontals with increased fracture density. In addition, with a continuously improving technology, the average completion cost for each stage has been reduced by around 40% during this period. 13

25 Figure 2.5: Pembina cost/frac and average fracs/well (ARC, 2014) Figure 2.6: Pembina average well length and frac spacing (ARC, 2014) 14

26 In general, size and orientation of a fracture are determined largely by the in-situ stress field of a formation. The stress field can be represented by three compressive principal stress components, which are oriented perpendicular to each other, namely the minimum horizontal stress σh, the maximum horizontal stress σh and the vertical stress, σv. Magnitudes and orientations of these three principal stresses are dictated by the regional tectonic regime and by formation depth, pore pressure and rock properties. A sketch of the stress regime and orientations in the WCSB is given in Figure 2.7, with symbol A approximately representing the location of the Pembina Cardium field. In a hydraulic fracturing process, the orientation and propagation direction of hydraulic fractures are controlled by in-situ stresses. Hydraulic fractures tend to open in the direction of the least principal stress and propagate in the plane of the greatest and intermediate stresses. Typically, horizontal wells are drilled either along the minimum horizontal stress, which would result in transverse fractures; or drilled along the maximum horizontal stress, which would result in longitudinal fractures (Economides et al., 2010). The in-situ stresses and hydraulic fracture propagation of these two scenarios are described in Figure 2.8. In oil reservoirs with low permeability, transverse fractures are usually preferred (Sennhauser et al., 2011). Figure 2.7: Sketch of stress regime and orientations in the WCSB (Cui et al., 2013) 15

27 Figure 2.8: In situ stresses and hydraulic fracture propagation of two fracture configurations (Economides et al., 2010) Microseismic Monitoring Microseismic monitoring is a state-of-the-art technique which enables real time measurements of fracture propagation during fracture stimulation. Microseismic events are very weak earthquakes, which result from local geomechanical changes induced by hydraulic fracturing treatments in reservoirs (Van Der Baan et al., 2013). These microseismic events can be recorded from both surface and downhole geophones. Visualization of the microseismic cloud delineates the spatial extent of hydraulic fracturing at first glance. Advanced interpretations of microseismic measurements provide detailed information to determine the effectiveness of stimulations. A Stimulated Reservoir Volume (SRV) is one of the key parameters extracted from microseismic data sets (Yousefzadeh et al., 2015). Within the stimulated rock volume, large fracture networks could be present after stimulation, resulting in enhanced rock permeability. Cipolla et al. (2008) initiated to use fracture complex index to characterize the complexity of a large fracture network. This index is defined as the ratio of width to length of the fracture network, whose values are obtained from the microseismic event cloud mappings. Figure 2.9 shows the areal extent of the microseismic events located at a Pembina 16

28 Cardium horizontal well. Figure 2.9: Microseismic events located at a Pembina Cardium well (Duhault, 2012) 2.3 Carbon Dioxide Enhanced Oil Recovery In the past few decades, CO 2 -EOR has attracted significant industry attention, considered as a promising and environmentally-friendly technique to develop mature tight oil reservoirs (Arshad et al., 2009). Most CO 2 used for EOR comes from naturally occurring sources. More recently, the Weyburn CO 2 -EOR project in Canada has demonstrated the successful use of anthropogenic CO 2, which is a meaningful step in climate change mitigation (Gozalpour et al., 2005). Compared to other gas displacing agents, CO 2 has been considered more favorable due to its higher miscibility with oil. Field projects suggest that CO 2 injection into mature oil reservoirs could yield an additional 4-12% OOIP oil production (Gozalpour et al., 2005). 17

29 2.3.1 Key Mechanisms While the operating conditions and injection schemes vary from project to project, the main mechanisms involved in CO 2 -EOR processes are similar, which include oil swelling, viscosity and interfacial tension (IFT) reduction, solution gas drive and light components extraction (Ghedan, 2009). Oil swelling: Carbon dioxide is highly soluble in crude oil systems. Dissolved CO 2 is capable of swelling an oil volume (Rahman et al., 2010). A large number of laboratory and field tests results show that sufficient CO 2 dissolution in crude oil can bring about a 10% to 30% oil volume expansion (Rahman et al., 2010). This expansion will not only increase the kinetic energy of crude oil, but also reduce the capillary forces and flow resistance for oil flow in porous media. In addition, some disconnected oil blobs join together as the oil swells and displace water out of the pore space, resulting in enhanced oil phase relative permeability (Song, 2013). As a consequence, the mobility of crude oil is significantly improved. Viscosity reduction: As crude oil swells when CO 2 is dissolved into the system, oil density and viscosity decrease markedly. The oil is then able to mobilize more easily, thus improving the ultimate recovery (Ghedan, 2009). IFT reduction: The displacement of oil by CO 2 injection can be grouped into two broad categories - immiscible and miscible - depending on reservoir conditions, oil characteristics, as well as the purity of CO 2 injectants. Miscible CO 2 flooding is the most common application and accounts for the majority of CO 2 -EOR projects. Near-miscible or immiscible flooding is sometimes implemented as a result of technical or economic restrictions. Immiscible gas floods are found less effective in comparison to miscible floods due to relative permeability and capillary pressure effects. At constant temperature, the lowest pressure at which liquids achieve miscibility is defined as the Minimum Miscibility Pressure (MMP). In miscible CO 2 flooding, the injected CO 2 is able to be completely miscible with crude oil to form a single homogeneous phase. The IFT between them tends to be zero, eliminating the capillary forces 18

30 and resulting in a lowered residual oil saturation (Ghedan, 2009). Solution gas drive: A certain fraction of pore space is occupied when CO 2 is injected into the reservoir, which elevates the formation pressure initially and improves production. As the reservoir pressure continuously declines during the production process, or after termination of the injection phase, dissolved CO 2 is liberated and served for solution gas drive. As a result, a driving force is generated, thereby improving oil displacement efficiency (Song, 2013). Components extraction: In addition to CO 2 dissolution into oil phase, light and intermediate crude oil components may be vaporized into injected CO 2 under favorable conditions. After multiple contacts between the oil and CO 2, a bank of light hydrocarbons and CO 2 is formed. This mixture will further promote miscibility between CO 2 and the remaining reservoir crude (Pasala, 2010) Mobility Ratio Control The mobility of a fluid is defined as the effective permeability of this fluid divided by its viscosity and it is a measure of how easily a fluid moves through porous media. A fluid with low viscosity, such as CO 2, usually has high mobility. The mobility ratio is generally defined as the mobility of the displacing phase (in the gas/oil case, gas) divided by the mobility of the displaced phase (oil): where: M = k rg/µ g k ro /µ o (2.1) M: mobility ratio, dimensionless µ g : gas viscosity, cp µ o : oil viscosity, cp k rg : relative permeability to gas, dimensionless k ro : relative permeability to oil, dimensionless 19

31 In continuous CO 2 injection, as the viscosity of CO 2 is relatively low, mobility ratio between gas phase and oil phase becomes unfavorable (M > 1). Displacements that take place at very unfavorable mobility ratios are unstable, leading to viscous fingering of the gas phase through the oil phase, early gas breakthrough and poor sweep efficiency. In fact, this is the situation for essentially all gas/oil displacements. To ease these problems, CO 2 is often injected in a WAG mode, in which water and gas are injected intermittently, in which the injection of water can help control the mobility ratio and stabilize the displacement front. Adequate mobility control can contribute to a greater reservoir pore volume being contacted, and thus more favorable sweep efficiency Microscopic and Macroscopic Sweep Efficiency The overall recovery efficiency of a fluid displacement process is determined by the macroscopic, or volumetric displacement efficiency E v, and microscopic displacement efficiency E d : E = E v E d (2.2) The macroscopic displacement efficiency describes how well the reservoir hydrocarbon pore volume is being contacted with the displacing fluid, while the microscopic displacement efficiency describes how effective the displacing agent mobilizes the residual oil when it comes in contact with oil (Terry, 2001). The macroscopic displacement efficiency consists of two components, the areal efficiency E i, and the vertical efficiency, E i : E v = E s E i (2.3) Previous studies have revealed that the rock wettability strongly affects the oil phase trapping during CO 2 -WAG flooding processes, and thus plays a critical role in microscopic displacement efficiency (Huang et al., 1988). In addition, the microscopic sweep efficiency is affected by interfacial tension forces, capillary pressure and relative permeability (Terry, 2001). 20

32 In regard to macroscopic sweep efficiency, studies have shown that it is affected by the mobility ratio, formation heterogeneity and anisotropy, the well pattern configuration, as well as the type of rock matrix in which the oil exists. (Terry, 2001) WAG Injection Schemes Depending on geology conditions, rock and fluid properties, timing of the switch from primary or waterflooding and the development pattern (well placement and completion strategies), the CO 2 injection for EOR may use one of the several injection schemes described as follows (Verma, 2015). Continuous CO 2 injection: This process involves continuous injection of a predetermined volume of CO 2 slug with no other fluid. Continuous CO 2 injection followed with water: This process is similar to the continuous CO 2 injection process, apart from the chase water injection that follows the total injected CO 2 slug volume. Constant WAG followed with water: In this process, a predetermined volume of CO 2 is injected in cycles alternating with varying volumes of water, which are determined by design parameters, including a WAG ratio and cycle length. The water alternating with CO 2 injection provides better mobility control and prevents gas channeling and premature gas breakthrough, thereby improving overall CO 2 sweep efficiency. Hybrid/Tapered WAG: This technique is a combination of both a single slug injection and WAG injection. In this process, a predetermined volume of CO 2 slug is injected continuously, followed by the injection using the WAG technique at either a constant or gradually elevated WAG ratio (Nasir and Chong, 2009). With an objective to improve overall CO 2 use, this injection scheme is widely applied today to improve flood efficiency and prevent early CO 2 breakthrough (Verma, 2015). Constant WAG followed with gas: This process is a constant WAG process followed by a chase of cheaper gas (for example, nitrogen) after the injection of a pre-determined CO 2 21

33 slug volume. SWAG: This injection scheme involves injecting both CO 2 and water simultaneously into the reservoir. A schematic of the above mentioned injection schemes appears in Figure Figure 2.10: Schematic of various CO 2 injection schemes (Verma, 2015) 2.4 Pembina Cardium Carbon Dioxide EOR Pilot To test the technical and economic viability of injecting CO 2 as a miscible solvent for oil recovery, one of the major Pembina Cardium producers initiated a vertical well CO 2 -EOR pilot in 2005 in the Pembina Cardium pool. The pilot consisted of two 20 acre, back-toback 5-spot patterns, centered in sections 11 and W5M, as illustrated by Figure Good vertical sweep efficiency was obtained and an incremental oil recovery of 0.95% OOIP 22

34 was observed. Nevertheless, the production profile was not desirable, which gave rise to the need for more efficient completion practices. As a follow-up, in 2007, the pilot was expanded to include two newly drilled horizontal wells to determine if improved economics could be achieved through horizontal drilling (Gunter et al., 2013). Figure 2.11: Location of horizontal and vertical injection projects (CSA Group, 2012) Although CO 2 injection for EOR is anticipated to be capable of increasing oil recovery, the development of more economically attractive Halo areas using multi-stage fractured horizontal drilling, coupled with a shortage of CO 2 sources in this region, diverted producer s efforts from further CO 2 -EOR development. The limited recovery achieved from primary and secondary schemes, the growing number of multi-fractured horizontal wells completed and planned in the Pembina Cardium field, however, along with the absolute necessity to reduce greenhouse gas emissions, has brought new opportunities for scientific and industrial endeavor to develop mature oil fields by CO 2 - EOR. 23

35 Chapter 3 METHODOLOGIES To account for the phase equilibrium between the injected CO 2 agent and in-situ reservoir fluids, a fully compositional simulator is essential to simulate the CO 2 injection processes (Ghaderi et al., 2012b). To perform compositional simulations, Equation-of-State (EOS) based fluid models should first be established and tuned to characterize reservoir fluids. In this chapter, three different EOS-based fluid models are described. These models are then tuned to match the experimental PVT behavior of the Pembina Cardium fluids and coupled to the reservoir models. Next, the Fuzzy Analytic Hierarchy Process (F-AHP), as a powerful multiple criteria decision-making technique, is introduced. The last section of this chapter speaks to the Design of Experiments (DOE), which is a widely-applied statistical method for conducting sensitivity analysis, and how this method assists reservoir simulations and F-AHP with achieving the study s objectives. 3.1 Reservoir Fluids and EOS Modeling Reservoir Fluids Sampling and PVT Tests Significant variations in fluid properties were found across the Pembina Cardium field. Properties, such as the solution gas-oil ratio, bubble point, viscosity and oil gravity, varied markedly in both the geographical and vertical (different producing sandstone zones) sense in the Cardium pool (Kerr et al., 1980; Wahl et al., 1963). Based on fluid composition and PVT test data collected (Bouck et al., 1975; Ghaderi et al., 2011; PTAC, 2014; Wahl et al., 1963), three types of Pembina Cardium fluids were defined and the corresponding fluid models were established to study the impacts of fluid characteristics on CO 2 injection performance. Figure 3.1 provides the compositions of these three different types of fluids 24

36 in mole fractions. The PVT data, namely the oil formation volume factor, solution gas-oil ratio and fluid viscosity, are listed in Tables 3.1, 3.2 and 3.3 for fluid type I, II and III, respectively. A more intuitive comparison on the PVT data of these three types of fluids appears in Figures 3.2 and 3.3. These PVT data are the major inputs for the following EOS modeling and tuning. Figure 3.1: Pembina Cardium fluid compositions 25

37 Table 3.1: Properties of Pembina Cardium fluid type I Pressure Oil Formation Volume Factor Solution GOR Oil Viscosity (psi) (rb/stb) (scf/stb) (cp)

38 Table 3.2: Properties of Pembina Cardium fluid type II Pressure Oil Formation Volume Factor Solution GOR Oil Viscosity Gas Viscosity (psi) (rb/stb) (scf/stb) (cp) (cp)

39 Table 3.3: Properties of Pembina Cardium fluid type III Pressure Oil Formation Volume Factor Solution GOR Oil Viscosity Gas Viscosity (psi) (rb/stb) (scf/stb) (cp) (cp)

40 Figure 3.2: Comparison of formation volume factor and gas solubility curves of three fluid types 29

41 Figure 3.3: Comparison of oil viscosity of three fluid types 30

42 3.1.2 EOS Modeling and Tuning In this study, the Peng-Robinson EOS (PR EOS) was selected for predicting phase behavior and the Jossi-Stiel-Thodos correlation was employed to match oil and gas viscosity. The mathematical expression of Peng-Robinson cubic EOS appears in Equation 3.1 (Peng and Robinson, 1976). where: p = RT v b a(t ) v(v + b) + b(v b) (3.1) p: pressure, psi R: gas constant, T : temperature, R v: specific volume ft 3 psia R lb.mol a: attraction parameter b: repulsion parameter The parameter a is a measure of intermolecular attraction forces and b is related to the size of the molecules. The a and b parameters can be obtained by applying Equation 3.1 at the critical point where the first and second derivatives of pressure with respect to volume are equal to zero. Expressions for a and b at the critical point in terms of the critical properties are given in Equations 3.2 and 3.3. a(t c ) = Ω a R 2 (T c ) 2 b(t c ) = Ω b RT c P c P c = R2 (T c ) 2 P c (3.2) = RT c P c (3.3) At temperatures other than the critical, a and b can be calculated from Equations 3.4, 31

43 3.5 and 3.6. a(t ) = a(t c ) α(t r, ω) (3.4) b(t ) = b(t c ) (3.5) α(t r, ω) = 1 + [ ( ω ω 2 )(1 T 0.5 r ) ] 2 (3.6) The acentric factor ω in Equation 3.6 measures the non-sphericity of a molecule, and is defined for each pure component (Chen, 2007). For a mixture, parameters a and b become composition dependent, and require mixing rules. The mixing rules for mixtures are illustrated in Equations 3.7, 3.8 and 3.9. b = j (y j b j ) (3.7) a(t ) = i [y i y j a(t ) ij ] (3.8) j a(t ) ij = (1 δ ij )[a(t ) i a(t ) j ] 0.5 (3.9) where: δ ij : binary interaction coefficients The binary interaction coefficients in Equation 3.9 are assumed to be independent of pressure and temperature. In order to accurately describe reservoir fluid properties and phase behavior in the Pembina Cardium field, a proper tuning of the EOS model is necessary, which can be achieved by adjusting EOS model parameters to match with the experimental PVT data. In this study, p c, T c, and molecular weights of the plus fraction and volume shift parameters were selected as primary tuning parameters. Ω a and Ω b will be further adjusted to match with experimental PVT data if tuning results are not desirable. It is worth mentioning that there are no clear-cut procedures for selecting tuning parameters and performing EOS tuning. This process requires expertise and the solution is not unique. 32

44 3.1.3 Components Lumping and EOS Modeling Results Compositional simulation can be computationally expensive due to a large number of fluid components. To reduce computing time, pseudo-components are commonly used instead. In this study, fluid components were lumped into six pseudo-components. Their mole fractions are displayed in Figure 3.4 for three types of the Pembina Cardium fluids. Carbon dioxide was grouped as a single component since the focus of this study is on miscible CO 2 injection. Figure 3.4: Pseudo-components of the Pembina Cardium fluids By continuously adjusting tuning parameters and performing regressions, a good match was obtained between the experimental and simulated PVT behavior in terms of the solution GOR, formation volume factor and fluid viscosity, as illustrated in Figures It is worth mentioning that the effect of temperature was not considered in this study and relevant properties were calculated at a fixed reservoir temperature of 150 F. The summaries of pseudo-component properties for each fluid type are tabulated in Tables 3.4, 3.5 and 3.6, respectively. 33

45 !! Figure 3.5: Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type I!"#$ % &' (% Figure 3.6: Comparison between the experimental and simulated oil viscosity of fluid type I 34

46 Figure 3.7: Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type II!"# $ %& '$ %& '$ Figure 3.8: Comparison between the experimental and simulated oil and gas viscosity of fluid type II 35

47 !! Figure 3.9: Comparison between the experimental and simulated solution GOR and oil formation volume factor of fluid type III!" # $% &# $% &# Figure 3.10: Comparison between the experimental and simulated oil and gas viscosity of fluid type III 36

48 Table 3.4: Summary of the pseudo-component properties of fluid type I Component P c (atm) T c (K) ω MW Vol. Shift Ω A Ω B SG CO N 2 -CH C 2 -C C 4 -C C C Table 3.5: Summary of the pseudo-component properties of fluid type II Component P c (atm) T c (K) ω MW Vol. Shift Ω A Ω B SG CO N 2 -CH C 2 -C C 4 -C C C Table 3.6: Summary of the pseudo-component properties of fluid type III Component P c (atm) T c (K) ω MW Vol. Shift Ω A Ω B SG CO N 2 -CH C 2 -C C 4 -C C C

49 It can be observed that these three types of fluids possess varying properties. Fluid type I contains more plus fraction with an API gravity of 33 and is featured in the lower solution gas-oil ratio and oil formation volume factor. The bubble point pressure is around 1,300 psi. Fluid type II has intermediate properties with an API of 38. Fluid type III is higher in the C 1 component and lower in the C 7 + component. Therefore, this fluid type is characterized by a higher solution GOR and saturation pressure with an API gravity of 44. These properties are summarized in Table 3.7. The CO 2 minimum miscibility pressure (MMP) was calculated to be 2,050, 1,960 and 1,800 psi for fluid type I, II and III, respectively. Table 3.7: Summary of fluid properties Properties Fluid I Fluid II Fluid III Solution gas-oil ratio, scf/stb Saturation Pressure, psi Formation volume saturation pressure, rb/stb Crude saturation pressure, cp Crude gravity, API Reservoir Models and Reservoir Conditions The base case model established in this study was one section (640 acres) of the Pembina Cardium field with a uniform reservoir thickness of 30 ft. The input parameters for the reservoir model are tabulated in Table 3.8. It is assumed that the whole field is well maintained with good pressure support. Therefore, the initial reservoir pressure is a function of depth and is calculated as the product of the reservoir depth and a pressure gradient of the Pembina Cardium field (0.58 psi/ft) (IHS, 2016). To investigate the effect of different parameters on CO 2 -EOR performance, a 10-year CO 2 injection scheme, using three hydraulic fractured horizontal wells, was carried out, with one CO 2 injector straddled by two oil producers. The horizontal wells are completed in equal lateral lengths with multiple fractures stimulated in 38

50 the transverse direction along the wells and vertically extended from the top to the bottom of the target formation. To effectively simulate the flow behavior from a low-permeability matrix to high-permeability fractures in the model, a local grid refinement (LGR) strategy is applied to the fracture blocks (Gu et al., 2015). Typically, a stimulated reservoir volume (SRV) is estimated from microseismic event cloud mappings. For simplicity, the SRV in this model is represented by a permeability enhanced area around the wellbore, as illustrated in Figure 3.11, and defined as the product of the fracture length, well lateral length and formation thickness. Other than permeability, properties within and outside of SRV are assumed to be the same. The permeability multiplier is assumed to be two in this study. Table 3.9 summarizes the properties of the wells and hydraulic fractures, along with operation conditions for the base case. A close view of LGR applied to one of the fractures and the 3D base case model are depicted in Figure Table 3.8: Reservoir input for the base case a Parameter Value Length, ft 5,250 Width, ft 5,250 Thickness, ft 30 Depth at the top of formation, ft 6,000 b Initial reservoir pressure, psi 3,480 Initial water saturation, fraction 0.25 Initial oil saturation, fraction 0.75 Reservoir temperature, F 150 Avg. porosity, % 10 Avg. horizontal permeability, md 0.1 Vertical to horizontal permeability ratio 0.1 Reference pressure, psia 1,000 Rock P ref, psi Number of grids (N x N y N z ) Minimum grid size (D x D y D z ) a Parameters may be varied for sensitivity analysis b This parameter is a function of formation depth 39

51 Figure 3.11: Schematic plot showing SRV Table 3.9: Properties of wells, fractures and operating conditions for the base case a Parameter Value Well length, ft 3,500 Well spacing, ft 1,000 Fracture spacing, ft 300 Fracture half-length, ft 300 Fracture height, ft 30 Fracture conductivity, md ft 150 Skin factor 0 k SRV multiplier 2 Duration of CO 2 injection, year 10 Minimum well production BHP, psi p b Maximum oil production rate per well, stb/d 1,000 b Maximum well injection BHP, psi 5,460 Maximum gas injection rate, mscf/d 2,000 Formation fracturing pressure gradient, psi/ft 0.9 a Parameters may be varied for sensitivity analysis b This parameter is a function of formation depth 40

52 Figure 3.12: A close view of the base case model showing hydraulic fractures (red grid blocks), SRV (light blue grid blocks) and tight formation (dark blue grid blocks) As suggested by Figure 3.12, the reservoir volume is divided by three different components. The hydraulic fractures are the main fluid flow path, and are characterized by the highest permeability, marked in red. Due to the existence of secondary fractures, the permeability of rock volumes between the long bi-wing fractures is enhanced, which is represented by light blue. The low-permeability matrix is depicted by dark blue in this figure. In addition to the above mentioned properties, the water, oil, and gas relative permeability data were obtained from a previous Pembina Cardium simulation study (Ghaderi et al., 2012a); the relative permeability curves are shown in Figures 3.13 and For hydraulic fractures, the straight relative permeability lines were used. 41

53 Figure 3.13: Oil-water relative permeability Figure 3.14: Oil-gas relative permeability 42

54 3.3 Fuzzy Analytic Hierarchy Process To successfully evaluate different strategies for completing horizontal wells and determine if these strategies are suitable for conducting CO 2 -EOR, a variety of factors need to be considered, which requires a sophisticated multi-criteria decision-making (MCDM) approach. MCDM techniques manage a decision-making process in which alternatives are predefined and available alternatives are ranked through the process (Tesfamariam and Sadiq, 2006). Among MCDM methods, the analytic hierarchy process (AHP) is one of the most commonly used methods to convert complex multiple criteria problems into readily manageable hierarchical structures for arithmetic operations (Hamidi et al., 2008). This method involves conducting pairwise comparisons between criteria, thereby introducing vagueness type uncertainty (Tesfamariam and Sadiq, 2006). Essentially, the traditional AHP is modified to a Fuzzy-AHP, in which a fuzzy-based technique is used to handle uncertainty introduced by human subjectivity. In the petroleum industry, Denney et al. (2002) described the use of this method in strategic reservoir planning. Tesfamariam and Sadiq (2006) used this method to select a drilling fluid for offshore oil and gas operations. Chang et al. (2006) employed F-AHP to identify risks associated with oil and gas investment activities. Hamidi et al. (2008) applied this technique for the selection of a rock tunnel boring machine. As mentioned, uncertainty is an inevitable component of any decision-making process. To cope with uncertainty, a fuzzy number is introduced in F-AHP, which describes a relationship between an uncertain quantity x and a membership function µ x and ranges from 0 to 1 (Tesfamariam and Sadiq, 2006). In this study, triangular fuzzy numbers (TFNs) are used, among other shapes of fuzzy numbers, to simplify the implementation. TFN is represented by three points (a, b, c) within the domain where the criterion is defined, indicating the minimum, most likely, and maximum values, respectively (Tesfamariam and Sadiq, 2006). In this study, an eight-step procedure for F-AHP is proposed to guide decision-making towards the evaluation of different well completion strategies suitable for CO 2 -EOR, as il- 43

55 lustrated in Figure A step-by-step description of the methodology, based on the study conducted by Tesfamariam and Sadiq (2006), is presented as follows. Figure 3.15: An eight-step method for F-AHP Step 1 Formulation of a hierarchic tree Establishing a hierarchical model involves the dis-assembly of a complex decision-making problem into smaller manageable elements at different hierarchical levels (Tesfamariam and Sadiq, 2006). The performance of CO 2 -EOR is affected by reservoir quality, fluid charac- 44

56 teristics, as well as the horizontal well completion quality. In this study, two groups of parameters (i.e., two general criteria) are used to evaluate the effectiveness of different well completion strategies and their suitability for performing CO 2 -EOR. The first group, which is defined as the reservoir quality group, consists of criteria in terms of reservoir and fluid properties, including remaining oil in place, permeability, reservoir depth (reservoir pressure) and a fluid type. The second group is defined as the well completion quality group. This group incorporates criteria of well length, well spacing, fracture spacing, SRV and a skin factor. The complete hierarchical structure is shown in Figure As can be seen, the first level represents the goal of the decision-making process, and the last level corresponds to the evaluation alternatives; the intermediate levels stand for criteria and sub-criteria. Figure 3.16: Hierarchical structure for evaluation of different well completion strategies for CO 2 -EOR 45

57 Step 2 Creation of fuzzy pairwise comparison matrices At intermediate levels, criteria and sub-criteria are compared pairwise to generate fuzzy judgment matrices. The fuzzified scale of 1-9 (Table 3.10), which is capable of capturing vagueness in perception, is used to assign relative importance to the pairwise comparison (Hamidi et al., 2008). For an n number of comparison items, the fuzzy judgement matrix J is expressed as: j 11 j 12 j 1n. j J = 21.. j 2n..... j n1 j n2 j nn (3.10) For diagonal entries, all elements are equal to 1, which means that the criteria are of equal importance when compared to themselves. Upper triangular entries are fuzzy pairwise comparison indices that need to be defined by a decision maker, whereas lower triangular entries are obtained by taking reciprocals of their symmetry elements. In order to have a better understanding of the relative importance of criteria selected within each group, the Design of Experiments (DOE) approach is employed to determine the sensitivity of each criterion to the recovery factor of CO 2 -EOR for both the reservoir and well completion groups. This is explained in the following section. 46

58 Table 3.10: Fuzzy numbers used for making pairwise comparisons Relative importance a,b Fuzzy scale Definition 1 (1, 1, 1) Equal importance 3 (3, 3, 3 + ) Weak importance 5 (5, 5, 5 + ) Essential or strong importance 7 (7, 7, 7 + ) Demonstrated importance 9 (8, 9, 9) Extreme importance 2, 4, 6, 8 (x, x, x + ) Intermediate importance between two adjacent judgements 1/ x (1/(x+ ), 1/x, 1/(x )) - 1/ 9 (1/9, 1/9, 1/8) - a is a fuzzification factor and assumed to be 1 in this study b In (a, b, c), a, b and c are the minimum, most likely and maximum values, respectively. Step 3 Check for consistency The fuzzy pairwise comparison matrix obtained in the previous step is prone to inconsistency as a result of human subjectivity and preference. To ensure consistency in pairwise comparisons, a consistency index (CI) is introduced and defined as follows: CI = (λ max n)/(n 1) (3.11) where λ max is the maximum eigenvalue of the judgement matrix and n is the dimension of the matrix. The final determinant of consistency in the pairwise comparison is the consistency ratio (CR): CR = CI/RI (3.12) where RI is the random index, whose values are tabulated in Table To ensure consistency, CR is not supposed to exceed the threshold value of

59 Table 3.11: Random index used to compute consistency ratio (CR) No. of criteria Random index (RI) Step 4 Calculation of fuzzy weights For the purpose of grading and ranking candidate well pads with different completion strategies, weighting factors need to be assigned to each criterion based on process performance. In this step, fuzzy weights are calculated for each criterion. This can be realized by various methods, including eigenvectors, arithmetic means and geometric means, which provide insignificant differences (Hamidi et al., 2008). In this study, the geometric mean method is adopted. To apply this method, one needs to manipulate fuzzy arithmetic operations over fuzzy pairwise comparison matrices. The details of fuzzy arithmetic operations are described in Table Given J from Equation 3.10, the geometric mean is calculated for each row J i and the corresponding fuzzy weights are obtained as: J i = ( J i1 J in ) 1/n (3.13) w i = J i ( J 1 J n ) 1 (3.14) where w i (i = 1, 2,..., n) is the fuzzy weight for each criterion. Next, the local weights at each level are aggregated to obtain the global weight of each criterion. The fuzzy global weights are computed as: G k = w k G k 1 (3.15) G 1 = w 1 ; G 2 = w 2 G 1 (3.16) 48

60 Table 3.12: Common fuzzy arithmetical operations using two TFNs Operators a Formulae Results Summation A + B (a 1 + b 1, a 2 + b 2, a 3 + b 3 ) Subtraction A B (a 1 b 3, a 2 b 2, a 3 b 1 ) Multiplication A B (a 1 b 1, a 2 b 2, a 3 b 3 ) Division A/B (a 1 /b 3, a 2 /b 2, a 3 /b 1 ) Scalar product Q B (Q b 1, Q b 2, Q b 3 ) a A = (a 1, a 2, a 3 ); B = (b 1, b 2, b 3 ) Step 5 Defuzzification In this step, the fuzzy weights are converted to crisp numbers, which is called defuzzification. Meixner (2009) employed the centroid method for this purpose, which is defined as: w i = a i + (b i a i ) + (c i a i ) 3 (3.17) where the fuzzy weight w i = (a i, b i, c i ). Step 6 Evaluation of alternatives Once defuzzified global weights are obtained for each criterion, the final grade for each alternative or, for instance, a well pad, is calculated. Rivas et al. (1994) developed a parametric optimization method to rank reservoirs suitable for CO 2 flooding based on intrinsic reservoir and oil characteristics (Shaw et al., 2002). This method is introduced in this study. Considering the different physical meanings, units and value ranges of reservoir, fluid and well completion parameters, these parameters are transformed into new normalized variables that vary linearly between 0 and 1. For each property (j) of the well pad (i) being ranked (P i,j ), this normalized parameter X i,j is defined as: Pi,j P o,j X i,j = P w,j P o,j (3.18) where P o,j is the value of property j in the fictitious optimum well pad that gives the best response to CO 2 flooding and P w,j is the magnitude of property j in the fictitious worst well pad that is not suitable for CO 2 flooding. The fictitious optimum well pad is obtained 49

61 by performing numerical simulations on a base case to search for an optimal set of reservoir and well completion parameters that provides the best CO 2 -EOR performance. The worst value of each reservoir and/or well completion parameter is selected from the candidate well pads to be ranked. The value farthest away from the optimum value is determined as the worst value. Compared to a linear function, an exponential function is more adequate for comparing different elements within a set. Therefore, the normalized parameter X i,j is transformed into an exponential varying parameter A i,j, given as: A i.j = 100e 4.6X2 i,j (3.19) To account for the relative weight of each criterion on CO 2 -EOR performance, the weighted grading matrix is used: W i,j = A i.j w j (3.20) where w j is the weight of each reservoir and well completion parameter obtained in the last step. The final ranking characteristic parameter R i is defined as: R i = [ j ] P 2 i,j [ j 1 P 1,j ] 1 2 (3.21) where P i,j is the product of W i,j and its transpose W j,i and P 1,j represents the values corresponding to the fictitious optimum well pad. By applying this equation, well pads are ranked not only based on the added contribution of each criterion but also the comparison among themselves. The final grades obtained using this method vary between 1 and 100, with 100 representing the best suitable and 1 the non-recommended well pad for CO 2 -EOR, for a given set of weighting factors. 50

62 Step 7 Risk analysis A risk analysis is conducted in this study to identify potential issues associated with a CO 2 - EOR project. This process is described in the following chapter. Candidates identified with potential risk will either lose marks or be further evaluated. Step 8 Final ranking and decision making Moving on to this step, an effective workflow that evaluates the success of different strategies for completing horizontal wells and their suitability for CO 2 -EOR development has been established. This method is applicable to rank a large number of horizontal well pads with various completion strategies for CO 2 flooding. In addition, it provides guidance for Pembina Cardium producers on optimum completion strategies. An example will be given to demonstrate the application of this method in Chapter Design of Experiments To ensure a better understanding of the relative importance of criteria selected within the reservoir and completion quality groups, the Design of Experiments (DOE) approach is employed to determine the sensitivity of each criterion to the recovery factor of a CO 2 injection EOR process. DOE is a widely applied technique to determine the relationship between factors affecting a process and the output of that process. A variety of methods to perform a successful experiment design study exist, including full and fractional factorial designs, and some optimal designs such as A, D, and I. In this work, D-Optimal is selected. This design method greatly reduces the number of experiments compared to a full factorial design, and also allows for non-orthogonal design matrices (Ghaderi et al., 2012b). 51

63 Chapter 4 A WORKFLOW FOR EVALUATING WELL COMPLETION EFFECTIVENESS This chapter describes the results of sensitivity analysis on different reservoir and hydraulic fracturing factors, an integrated workflow to evaluate the success of different strategies for completing Cardium horizontal wells and their suitability for CO 2 -EOR development, a method for screening re-fracturing candidates, and the risks that may affect a CO 2 -EOR project in the Pembina Cardium field. 4.1 Sensitivity Analysis To quantify the relative importance of criteria selected to evaluate well completion strategies within the reservoir and well completion quality groups and to construct fuzzy pairwise comparison matrices, the Design of Experiments (DOE) approach was employed to determine the sensitivity of each criterion to the recovery factor of CO 2 -EOR processes Reservoir Quality Table 4.1 provides a summary of all criteria considered in the reservoir quality group and the levels associated with each. The D-optimal design was applied to generate simulation runs. A total of 20 runs were required for this group. By using the aforementioned reservoir model in Section 3.2, recovery factors were obtained through compositional simulations of a 10-year CO 2 injection. The generated simulation runs and the corresponding recovery factor for each run are tabulated in Table

64 Table 4.1: Reservoir quality criteria and the associated levels for sensitivity runs Factor Low Medium High A: Remaining oil in place, fraction B: Permeability, md C: Depth, ft 5,000-8,000 D: Fluid, type I II III Table 4.2: Sensitivity runs and their recovery factors for the reservoir quality group Run Remaining oil Permeability, Fluid, Recovery Depth, ft in place md type factor ,000 I ,000 II ,000 II ,000 I ,000 I ,000 III ,000 II ,000 III ,000 I ,000 III ,000 I ,000 I ,000 III ,000 III ,000 II ,000 III ,000 II ,000 II ,000 III ,000 I

65 The ultimate recovery factors were statistically evaluated upon the completion of all simulation runs. Figure 4.1 gives the results of a main effect analysis. As can be seen from this plot, permeability plays a significant role in the oil recovery of a CO 2 injection EOR process. In addition, as these compositional simulation runs are based on the three different types of Pembina Cardium fluid models established in Chapter 3, it can be readily observed that fluid type II offers the best oil recovery performance. On the contrary, residual oil saturation and reservoir depth have a minor effect on oil production compared to the other two factors. This observation can be further supported by the half-normal probability plot displayed in Figure 4.2. The distance of each point to the straight line, representing no effect, indicates its significance of the effect on oil recovery. According to this plot, all these four factors have important effects, with permeability being the most decisive factor, followed by the fluid type, remaining oil in place and reservoir depth. The rest of the points, standing along the straight line, reveal that the interactions among these factors are insignificant, probably due to chance. The efficiency of a CO 2 flood can be described using a CO 2 utilization factor, which is defined as the total volume of gas injected to produce one barrel of oil. A lower number signifies a more efficient flood. Typically, utilization factors range from 8 to 17 Mscf/bbl for most reservoirs flooded with CO 2 (Barnhart et al., 1999). Although the statistical analysis in this study is not based upon the CO 2 utilization factor, it is an useful economic indicator for CO 2 flood projects. In this study, the utilization factors of sensitivity runs for the reservoir quality group range from 5 to 16 Mscf/bbl. 54

66 Figure 4.1: Main effect analysis of recovery factor for the reservoir quality group 55

67 Figure 4.2: Half-normal probability plot showing the significance of parameters on oil recovery factor for the reservoir quality group Well Completion Quality A summary of all criteria considered in the well completion quality group and the levels associated with each is given in Table 4.3. Similar to the reservoir quality group, 16 runs were generated by the D-optimal design to investigate the relative importance among these factors. The design for each simulation run and the recovery factors obtained from these runs are tabulated in Table 4.4. The main effect and half-normal probability plots are presented in Figures 4.3 and 4.4. As suggested by the main effect plot, the well lateral length has a profound impact on oil recovery as an extended reach of a horizontal wellbore allows for much more exposure to the pay zone. Beyond that, well placement and SRV also make a difference in oil production. Fracture spacing and the skin factor have a minor effect in comparison to the other factors. A more intuitive comparison on the relative importance of these parameters is illustrated by the half-normal probability plot. As can be observed, the well lateral length is the most dominant factor in oil recovery, followed by well distance and 56

68 SRV. It is worth mentioning that an interaction effect can be observed from this plot. This is because a tighter well spacing or infill drilling will increase the chance of SRV overlapping. When the stage and/or cluster placement is in an aligned pattern between neighboring wells, fractures may intersect and a reduction in individual well recovery can be expected. In this analysis, a staggered fracture pattern is applied when the well distance is equal to or less than the fracture length. In addition, a greater impact upon CO 2 injection for EOR from SRV would be expected if a greater value of k multiplier were adopted. The statistical interpretation is a useful input for construction of pairwise comparison matrices for F-AHP, which is explained in the following section. Table 4.3: Well completion quality criteria and the associated levels for sensitivity runs Factor Low High A: Well length, ft 2,500 5,000 B: Well spacing, ft 800 1,500 C: Fracture spacing, ft D: Fracture half-length (SRV), ft (ft 3 ) E: Skin factor

69 Table 4.4: Sensitivity runs and their recovery factors for the well completion quality group Run Well length, Well spacing, Fracture Fracture Recovery Skin factor ft ft spacing, ft half-length, ft factor 1 5,000 1, , ,000 1, ,000 1, , , , ,500 1, , ,000 1, ,500 1, ,500 1, , , ,500 1, ,

70 Figure 4.3: Main effect analysis of recovery factor for the well completion quality group 59

71 Figure 4.4: Half-normal probability plot showing the significance of parameters on oil recovery factor for the well completion quality group 4.2 Assignment of Weighting Factors Based upon the statistical interpretation on the D-optimal design for both reservoir and well completion quality groups, the fuzzy judgement matrices can be constructed by performing fuzzy pairwise comparisons, which correspond to step 2 described in the F-AHP method. For the reservoir quality group, the fuzzy judgement matrix J 1 is constructed as: Table 4.5: Pairwise comparison matrix for the reservoir quality group Criterion X1,1 3 X2,1 3 X3,1 3 X4,1 3 X1,1 3 (1,1,1) (1/7,1/6,1/5) (2,3,4) (1/6,1/5,1/4) X2,1 3 (5,6,7) (1,1,1) (8,9,9) (1,2,3) X3,1 3 (1/4,1/3,1/2) (1/9,1/9,1/8) (1,1,1) (1/9,1/8,1/7) X4,1 3 (4,5,6) (1/3,1/2,1) (7,8,9) (1,1,1) 60

72 Similarly, the fuzzy pairwise comparison matrix constructed for the well completion quality group J 2 is given as: Table 4.6: Pairwise comparison matrix for the well completion quality group Criterion X1,2 3 X2,2 3 X3,2 3 X4,2 3 X5,2 3 X1,2 3 (1,1,1) (4,5,6) (7,8,9) (5,6,7) (8,9,9) X2,2 3 (1/6,1/5,1/4) (1,1,1) (3,4,5) (2,3,4) (4,5,6) X3,2 3 (1/9,1/8,1/7) (1/5,1/4,1/3) (1,1,1) (1/4,1/3,1/2) (1,2,3) X4,2 3 (1/7,1/6,1/5) (1/4,1/3,1/2) (2,3,4) (1,1,1) (2,3,4) X5,2 3 (1/9,1/9,1/8) (1/6,1/5,1/4) (1/3,1/2,1) (1/4,1/3,1/2) (1,1,1) In addition, compared to the well completion quality, the reservoir quality has a more significant impact on production (Sinha et al., 2011). A fuzzy number of 3, therefore, was assigned to the pairwise comparison between reservoir quality and well completion quality. Using Equations 3.11 and 3.12, the consistency ratios of J1 and J 2 were computed to be and 0.054, respectively, which are below the threshold value of 0.1 and, hence, are acceptable. Next, by using Equations , the corresponding local and global fuzzy weights were computed and then defuzzified by Equation 3.17 from fuzzy numbers to crisp numbers. The results are summarized in Table 4.7. As can be seen from this table, compared to other criteria, permeability, a fluid type and well length received greater global weights. 61

73 Table 4.7: Fuzzy weight and global weight for each criterion Level 2 w 1 Level 3 w 2 G 2 G 2 Reservoir quality, X1,1 2 (0.52,0.75,1.04) Remaining oil in place, X1,1 3 (0.06,0.09,0.13) (0.03,0.07,0.14) 0.07 Permeability, X2,1 3 (0.34,0.52,0.75) (0.18,0.39,0.78) 0.38 Depth/Pressure, X3,1 3 (0.03,0.04,0.06) (0.02,0.03,0.06) 0.03 Fluid type, X4,1 3 (0.24,0.34,0.56) (0.16,0.26,0.57) 0.27 Well completion quality, X2,1 2 (0.18,0.25,0.37) Well length, X1,2 3 (0.44,0.58,0.76) (0.08,0.15,0.28) 0.14 Well spacing, X2,2 3 (0.14,0.21,0.29) (0.03,0.05,0.11) 0.05 Fracture spacing, X3,2 3 (0.04,0.06,0.09) (0.007,0.015,0.033) 0.02 SRV(x f ), X4,2 3 (0.01,0.11,0.16) (0.01,0.03,0.06) 0.03 Skin factor, X5,2 3 (0.03,0.04,0.06) (0.006,0.010,0.024)

74 4.3 Evaluation and Grading For the purpose of grading and ranking candidate well pads with different completion strategies, an optimal set of reservoir and well completion parameters that provides for the best CO 2 -EOR performance needs to be searched. This is achieved by applying numerical simulations of 10-year continuous CO 2 injections on the base case (see Tables 3.8 and 3.9). Nearly a hundred simulation runs were carried out, with the results demonstrated in this section Reservoir Quality The optimum set of parameters for the reservoir quality group are obtained by performing simulation runs of 10-year CO 2 injections, in which variables of interest are changed one at a time within a reasonable range and other variables are fixed to their baseline values. Results of the simulation runs are described in Figures Figure 4.5: Recovery factor as a function of remaining oil in place 63

75 Figure 4.6: Recovery factor as a function of permeability Figure 4.7: Recovery factor as a function of reservoir depth 64

76 Figure 4.8: Recovery factor as a function of fluid type According to Figure 4.5, the recovery factor peaked around the remaining oil in place of 0.75, and hence, this value is selected as the optimum. As for permeability, it is found that the oil recovery factor climbs rapidly from 0.01 md to 0.5 md, yet hardly increases at a higher permeability as a result of limited injectivity. Since the area of interest in this study is the tight portions of the Pembina Cardium field, with permeability usually under 1 md, the optimum permeability is consequently determined to be 1 md. The growing trend of a recovery factor with reservoir depth is relatively gradual, as can be seen from Figure 4.7, because the reservoir pressure is assumed to be well maintained and is greater than MMP in this study. In terms of fluid type, Figure 4.8 makes apparent that type II fluid gives the best performance, because it features a high percentage of light to intermediate hydrocarbons in the oil compositions, along with the minimum oil viscosity among the three types of oil at reservoir conditions, which can be beneficial in making the overall recovery process more efficient. 65

77 4.3.2 Well Completion Quality Similarly, an optimum set of parameters for the completion quality group is obtained. The results of simulation runs are demonstrated as follows. Figure 4.9: Recovery factor as a function of well lateral length 66

78 Figure 4.10: Comparison of recovery factor among different well lateral length for a 10-year CO 2 injection period Figure 4.11: Recovery factor as a function of well spacing 67

79 Figure 4.12: Comparison of cumulative CO 2 production among different well spacing for a 10-year CO 2 injection period Figure 4.13: Recovery factor as a function of fracture spacing 68

80 Figure 4.14: Comparison of cumulative CO 2 production among different fracture spacing for a 10-year CO 2 injection period Figure 4.15: Recovery factor as a function of fracture half-length 69

81 Figure 4.16: Comparison of cumulative CO 2 production among different fracture half-length for a 10-year CO 2 injection period Figure 4.17: Recovery factor as a function of skin factor 70

82 As can be concluded from Figures 4.9 and 4.10, the extended reach of wellbore horizontals contributes to higher oil recovery. This advantage, however, becomes less obvious as well lateral length continues to increase. In this study, the optimum well lateral length is determined based on candidate profiles (i.e., the longest well length from all candidates). With regard to well placement, the oil recovery factor initially increases, and then decreases with incremental well spacing, as seen from Figure This can be explained by the interaction effect between the well spacing and fracture half-length, which is fixed at 350 ft in this case. When well spacing is far greater than the fracture length, one can take advantages from tighter well spacing. As the CO 2 injector and oil producer get closer, the distance between the fractures tips of neighboring wells is reduced. At some point, fractures may intersect. Consequently, the highly mobile CO 2 will travel through these more permeable paths with least resistance instead of flowing uniformly. This adverse effect outweighs the benefit of tighter well spacing, and an earlier breakthrough coupled with poor sweep efficiency can be expected. Figure 4.12 illustrates the CO 2 breakthrough time for different cases. The CO 2 breakthrough time is significantly shortened as well distance is reduced from 1,400 ft to 600 ft. The results of sensitivity runs in fracture spacing are displayed in Figures 4.13 and As shown by Figure 4.13, the impact of fracture spacing on oil recovery is relatively moderate compared to well length and well spacing. According to Figure 4.14, the breakthrough of CO 2 occurs at roughly the same time. This is because the breakthrough time is determined largely by the distance required for the CO 2 traveling from one fracture tip to another, which are the joint effects of well placement and fracture half-length. It is observed from this plot, however, that cumulative CO 2 production increased with decreased fracture spacing. Although an increased fracture density provides an improved fluid flow capacity, this will, in turn, hamper the efficiency of CO 2 use. This is because once the connection between the injector and producers is established, the injected CO 2 travels along these pathways of 71

83 least resistance, repetitively, for the entire process. A higher fracture density permits more pathways for the CO 2 to flow and thus, turns out a higher cumulative gas production and lower CO 2 utilization efficiency. In order to investigate a wider range of fracture half-length, the well distance is set as 1,500 ft instead of 1,000 ft. Figure 4.15 depicts the relationship between the recovery factor and fracture half-length. The recovery factor keeps an upward tendency first with fracture half-length, and then reaches a peak at the fracture half-length of 400 ft. After that, there is a decline towards an increased fracture half-length. Again, this is a joint effect of well placement and fracture half-length. Long transverse fractures give rise to short gaps between fractures tips along the injector and producers. This will accelerate the CO 2 breakthrough and impair the overall sweep efficiency. As described by Figure 4.16, the CO 2 breakthrough occurs earlier with longer fractures. As a commonly used measure of formation damage in a well, a large positive skin factor indicates much greater damage, and hence, a lower recovery factor. The relationship between the recovery factor and skin factor is depicted in Figure Table 4.8 presents the results for the parameters which optimized CO 2 injection EOR performance as given by the simulation runs discussed above. Once the optimum value and weighting factor for each parameter are determined, they are used for grading and evaluating the effectiveness of well completion strategies and ascertaining if they are suitable for performing CO 2 injections for EOR. 72

84 Table 4.8: Optimum reservoir and well completion parameters and weighting factors for evaluating well completion strategies suitable for CO 2 -EOR Parameter Optimum Value Parametric Weight Remaining oil in place (Fraction) Permeability (md) Reservoir depth (ft) 7, Fluid (type) II 0.27 Well length (ft) a Max 0.14 Well spacing (ft) 1, Fracture spacing (ft) Fracture half-length (ft) Skin factor b Min 0.01 a The longest well lateral length of candidate well pads to be ranked b The smallest skin factor of candidate well pads to be ranked 4.4 Application and Validation Six candidate well pads with various completion strategies are evaluated and ranked using the workflow developed in this study as an example. It is assumed that all horizontal wells placed in their belonging well pad are of equal completion quality. The reservoir and well completion variables of these candidates are summarized in Table 4.9. The final grades of each well pad were calculated by Equations Apart from the global grade, two individual grades for the reservoir quality and well completion quality of each candidate were computed as well, as summarized by Table 15. To verify the final ranking results, six reservoir models were established based on the corresponding properties of candidate well pads and their belonging reservoirs. A 10-year CO 2 injection scheme was compositionally simulated using three consecutive horizontal wells of each well pad. A great agreement was obtained in the ranks in order between the calculated global grade and simulated oil recovery factor for each candidate, as illustrated by Figure

85 Recovery Factor, % Global grade Simulated recovery factor Candidate Figure 4.18: Comparison of evaluation results and simulated recovery factor In this way, a workflow has been developed for the rapid evaluation, grading and ranking of a large number of horizontal well pads with varying completion strategies suited for CO 2 -EOR. This workflow involves a Fuzzy Analytic Hierarchy Process (F-AHP), Design of Experiments (DOE) as well as compositional simulation studies of the CO 2 injection processes. Two groups of parameters were defined as criteria to evaluate different suitable well completion strategies for performing CO 2 -EOR, namely, a reservoir quality group (remaining oil in place, permeability, reservoir depth/pressure and a fluid type) and a well completion quality group (well length, well spacing, fracture spacing, SRV and a skin factor). It has been well validated against reservoir simulation results. In this example, well pads 2 and 3 rank the top amongst all candidates and their completion strategies are suitable to perform CO 2 injections. 74

86 Table 4.9: Fuzzy weight and global weight for each criterion Candidate S o k, md D, ft Fluid Well length, ft Well spacing, ft Frac spacing, ft Frac half-length, ft Skin ,265 I 4,850 1, ,250 II 5,150 1, ,258 II 2, ,310 I 4,520 1, ,840 III 3, ,820 I 2,550 1, Table 4.10: Grading and ranking of candidates Reservoir quality grade Completion quality grade Global grade Ranking

87 4.5 Identifying Re-fracturing Opportunities According to Sinha et al. (2011), a cross plot of the reservoir quality indicator and well completion indicator - namely the two individual grades calculated for reservoir and completion quality of each candidate - was introduced in this study to screen potential re-fracturing candidates. Using the relevant dataset from Table 4.10, a cross plot was obtained in Figure 4.19.!"!"!" #!" Figure 4.19: Identifying re-fracturing candidates As can be seen from this cross plot, the whole area is divided into four quadrants based on the average grade of the reservoir and well completion quality of all candidates. Specifically, candidates 3 and 5 fall into quadrant I, which represents an area of below-average completion quality, but relatively good reservoir quality. These two candidates, therefore, are recommended to perform re-stimulation to enlarge the contact area to the target formation. 76

88 4.6 Risk Analysis Reservoir Heterogeneity As mentioned in Subsection 2.1.1, the Cardium formation is extremely heterogeneous in permeability, which may play a significant role in CO 2 -EOR performance. To investigate the effect of permeability heterogeneity, the Gaussian Geostatistical Simulation was applied to introduce permeability heterogeneity to the simulation model. Figure 4.20 displays the horizontal and vertical permeability distribution generated by the Gaussian Geostatistical Simulation in a cross-section view. The mean value of horizontal permeability is 0.1 md, and the standard deviation is 0.5 md (calculations did not include blocks enclosing fractures). Figure 4.21 provides a histogram of the statistical analysis of the permeability distribution. The permeability was set as 0.1 md for the homogeneous case. Figure 4.20: Top view (i-j plane) and side view (i-k plane) of the model showing horizontal and vertical permeability distribution 77

89 $!"# Figure 4.21: Histogram of the horizontal absolute permeability data Figure 4.22 displays the comparison of the ultimate oil recovery factor between the homogeneous case and the heterogeneous case for the 10 years CO 2 injection. It can be seen that permeability heterogeneity has a great impact on CO 2 -EOR performance. A recovery discrepancy of 5.6% is observed between these two cases. This is because preferential flow paths are dictated by reservoir heterogeneity. The highly mobile CO 2 seeks out more permeable paths with least resistance instead of flowing uniformly. In this way, it travels the same path for the entire process, leaving a large amount of oil untouched and thereby leading to extremely unfavorable sweep efficiency. 78

90 Figure 4.22: Comparison of homogeneous and heterogeneous cases Presence of Conglomerate The sandstone members of the Cardium formation are occasionally capped by some highly permeable conglomerate layers that have varying thickness from a few inches to approximately 20 ft. A conglomerate member can act as a thief zone for the injected CO 2 agent as a result of its high permeability (Dashtgard et al., 2008). To investigate the effects of a highly permeable conglomerate member on CO 2 injection, permeability and porosity of the top layer were modified in the base model. Their values are listed in Table In addition, a new set of relative permeability curves were generated for the conglomerate member, as plotted in Figures 4.23 and Table 4.11: Geological parameters for conglomerate and sand Thickness, ft Porosity, fraction Permeability, md Conglomerate Sand

91 The comparison of the ultimate oil recovery factor for the two cases is illustrated in Figure As can be observed from this plot, the presence of conglomerate has a pronounced effect on CO 2 -EOR performance. Although the initial production rate is much higher with the conglomerate present, it declines much more quickly and, finally, results in a much lower oil recovery factor compared to the case without conglomerate. The primary cause of the lowered recovery is that the conglomerate on the top of the Cardium formation leads to CO 2 upward moving. Consequently, the majority of the fluid flow is contained in the thief zone. The overriding CO 2 stands a less chance of contacting and displacing oil contained in the lower sand. In practical, the performance of CO 2 injection into reservoirs with conglomerate present can be affected by the placement of a horizontal wellbore and pay thickness. Moreover, the vertically extended hydraulic fractures may complicate the process, reducing the effectiveness of the CO 2 injection. Consequently, mechanisms should be considered to minimize migration of the CO 2 slug into the conglomerate layer. Figure 4.23: Three sets of oil-water relative permeability curves used for sand (solid), conglomerate (long dash) and fractures (dash-dot) 80

92 Figure 4.24: Three sets of oil-gas relative permeability curves used for sand (solid), conglomerate (long dash) and fractures (dash-dot) Figure 4.25: Comparison of cases with and without conglomerate 81

93 While the presence of permeability heterogeneity and conglomerate has a pronounced effect and may pose risks to the success of a CO 2 -EOR project, they are unavoidable factors in the development of the Pembina Cardium field. A detailed simulation study on a specific well pad and area is required after an initial evaluating process. To ease the issues associated with heterogeneity and conglomerate, water-alternating-gas (WAG) injection is one solution to maintain a pressure level, enhance sweep efficiency and, thus, improve ultimate recovery. Other than this, a proper configuration of hydraulic fractures, such as staggered fractures, can be designed before stimulation or re-stimulation to minimize the risk associated with CO 2 -EOR performance. 82

94 Chapter 5 OPTIMIZING WAG PERFORMANCE Water-alternating-gas (WAG) injection is a commonly employed technique to reduce gas viscous fingering and improve volumetric sweep efficiency in gas flooding processes. In this chapter, a study of different CO 2 injection schemes is conducted and compared to continuous CO 2 injection, which includes constant WAG injection, simultaneous water-and-gas injection (SWAG), and hybrid/tapered WAG injection. The effects of the injection rate, CO 2 slug size, WAG ratio and cycle length are investigated. The results indicate that an appropriately designed and optimized injection scheme can improve oil recovery substantially. 5.1 Reservoir Model and History Matching It is of great importance to validate a reservoir model with field production data to ensure the reliability of simulation results. In this study, two Pembina Cardium horizontal wells ( W5 and W5), with a shared surface pad, and completion strategies similar to the optimum strategy obtained in chapter 4, were selected to perform history matching and production forecasting. These two horizontal wells are of equal lateral length of 4,250 ft and stimulated with seventeen hydraulic fracturing stages. An area of 343 acres was simulated by setting a basic 3D reservoir model with dimensions of 5,250 ft 2,850 ft 20 ft, which corresponds to length, width and thickness, respectively. The reservoir is assumed to be homogeneous and the fractures are evenly spaced along the well. Primary production has been conducted from October, 2011 to December, According to the field data, a relatively high producing gas-oil ratio was noticed, and fluid type III defined in Chapter 3 was used in this model to predict PVT behavior. Oil rates were used as input and relative permeability curves, together with hydraulic fracturing parameters, were tuned to 83

95 perform history matching. Water production was negligible as there was no sign of a bottom water zone. The history matching results for cumulative gas production are displayed in Figures 5.1 and 5.2. The detailed reservoir and fracture properties of the two horizontal wells are summarized in Table 5.1. It should be noted that the solution of history matching is not unique and the match obtained in this study is only one possible solution. Figure 5.1: History matching results for well 1 Figure 5.2: History matching results for well 2 84

96 Table 5.1: Parameters used for history matching Parameter Value The model dimensions, ft 5,250 2, Depth at the top of formation, ft 6,040 Initial reservoir pressure, psi 3,135 Initial water saturation, fraction 0.3 Initial oil saturation, fraction 0.7 Reservoir temperature, F 150 Avg. porosity, % 10 Avg. horizontal permeability, md 0.1 Horizontal well length, ft 4,250 Well spacing, ft 1,350 Number of stages 17 Fracture half-length, ft 350 Fracture height, ft 20 Fracture conductivity, md ft 150 Production time, year 4.2 Figure 5.3: Relative permeability curves obtained from history matching of production data 85

97 To perform the WAG injection, the history-matched model is modified to include an additional horizontal well with multi-stage hydraulic fractures. One inner well is placed at the center and two side wells are located at the boundaries, with an even well spacing of 1,350 ft. A combination of initial primary recovery, with three producers, and subsequent WAG processes, with the middle well converted to an injector, is simulated in this study. In addition, to maximize the the distance between the fracture tips of the injector and producers and delay the CO 2 breakthrough, a staggered fracture configuration is applied in this model. Table 5.2 summarizes the properties of this model for WAG performance forecasting. Table 5.2: Parameters used for WAG performance forecasting Parameter Value The model dimensions, ft 5,250 2, Depth at the top of formation, ft 6,040 Initial reservoir pressure, psi 3,135 Initial water saturation, fraction 0.3 Initial oil saturation, fraction 0.7 Reservoir temperature, F 150 Avg. porosity, % 10 Avg. horizontal permeability, md 0.1 Rock compressibility, psi Horizontal well length, ft 4,250 Well spacing, ft 1,350 BHP of producers, psi 1,500 Injection rate, rb/d 350 Duration of primary recovery, year 5 Number of stages along producers 17 Number of stages along injector 16 Stage spacing, ft 250 Fracture half-length, ft 350 Fracture height, ft 20 Fracture conductivity, md ft

98 5.2 Constant Water-Alternating-Gas Injection Some limitations exist in continuous CO 2 flooding. Technically, as a result of the low viscosity of injected gas and, hence, an unfavorable mobility ratio between the CO 2 and displaced oil bank, viscous fingering and gas override usually occur, leading to an early CO 2 breakthrough and reduced sweep efficiency. Economically, a continuous CO 2 injection requires a significantly large amount of CO 2 sources, accompanied by the high capital and operating costs associated with CO 2 acquisition, delivery, storage, compression, and recycling (Han and Gu, 2014). In addition, permeability heterogeneity and the presence of the conglomerate layer on the top of the Cardium formation can add complexity to the whole process. To overcome these problems, CO 2 is often injected in a WAG mode, in which water and gas are injected intermittently to improve the volumetric sweep efficiency and reduce CO 2 consumption. This technique helps increase and maintain reservoir pressure, which is necessary for miscibility development between the CO 2 and oil. It also provides the mobility control with the injection of water and extends the CO 2 project life. Owing to the density contrast, the aqueous phase is in charge of sweeping in the lower portion while the gas phase usually migrates upward and primarily sweeps the upper reservoir WAG Ratio In constant water-alternating-gas injection, a predetermined volume of CO 2 is injected in cycles alternating with varying volumes of water, which are determined by design parameters including a WAG ratio and cycle length. In this study, the effect of these two parameters on oil recovery are investigated. The WAG ratio is defined as the ratio of the volume of an injected water slug to that of gas in each WAG cycle at reservoir conditions. A WAG ratio of 1:1, for instance, indicates that the pore volume of injected water slugs equals the pore volume of injected gas slugs. It plays a significant role in WAG processes. Even so, the optimal value for this parameter varies 87

99 from reservoir to reservoir, as the overall performance of a WAG injection can be affected by permeability distribution, fluid characteristics as well as the well pattern configuration and hydraulic fracturing design. To investigate the effect of the WAG ratio on oil recovery for this specific reservoir model, five cases with a WAG ratio of 0 (continuous CO 2 injection), 1:3, 1:2, 1:1 and 2:1 were considered. Each injection scenario is continued until a 0.25 PV of CO 2 slug is injected. The cycle length was fixed at 12 months and the injection rate of fluids was set at 350 rb/day. Table 5.3: Five injection scenarios to study the effect of WAG ratio Case WAG ratio WAG cycle length CO 2 inj. length Water inj. length (months) (months) (months) 1 0 Continuous CO 2 injection 2 1: : : : Figures 5.4 and Figure 5.5 depict the incremental oil recovery and average reservoir pressure for the five different scenarios listed in Table 5.3 with respect to the HCPV of injected CO 2. According to the first plot, the WAG injection gives a better performance compared to the continuous CO 2 injection. Among all WAG injection scenarios, the oil recovery factor increased with the overall WAG ratio; the WAG ratio of 2:1 provides the optimal oil recovery. This is because at a higher WAG ratio, the amount of water injected into the reservoir is increased while the CO 2 injected remains constant. The injected water helps with mobility ratio management, reservoir pressure maintenance and, consequently, sweep efficiency improvement. Furthermore, as a result of its higher density, the injected water slug tends to sweep lower portions of the reservoir, where CO 2 stands a less chance of contact and displacement. 88

100 !!" #$%&#$%'() #$%&#$%'() #$%&#$%'() #$%&#$%'() Figure 5.4: Comparison of incremental oil recovery with respect to the HCPV of injected CO 2 for injection schemes with different WAG ratios &!"!#$%!"!#$%!"!#$%!"!#$% Figure 5.5: Comparison of average reservoir pressure with respect to the HCPV of injected CO 2 for injection schemes with different WAG ratios 89

101 ! " #$%& " #$& " #$& " #$& Figure 5.6: Incremental oil recovery as a function of WAG ratio Figure 5.6 describes the relationship between the incremental oil recovery and WAG ratio. According to the trend given in this plot, although the oil recovery increases with the WAG ratio, the rate of increase drops gradually. The reason is that injecting more water into the reservoir leads to an insufficient contact of CO 2 and oil and a rapid increase in the water cut. In the extreme case of a near infinite WAG ratio (waterflooding), the oil recovery factor can be unfavorable compared to the continuous CO 2 and WAG injection. With regard to the average reservoir pressure for the continuous injection scenario, it can be observed that the continuous CO 2 injection gives a good performance in pressure maintenance. As a result of the proper well placement and hydraulic fracture design, CO 2 did not experience breakthrough until around 0.22 PV of CO 2 was injected. A rapid pressure decline, however, can occur if CO 2 is continuously injected into the reservoir. In comparison to the continuous injection, pressure increased more rapidly and is maintained better with the WAG injection. Pressure distribution and IFT at the end of WAG injection appear in Figures 5.7 and 5.8 (WAG ratio=2, cycle length=12 months, and HCPV injection=0.25). It can be seen from these two plots that miscibility has been achieved in this case. The comparison between the 90

102 residual oil saturation for the top layer at the beginning and the end of the WAG injection is displayed in Figures 5.9 and The comparison clearly reveals a superior areal sweep efficiency of WAG displacement. In addition, the cross-sectional views of the oil saturation distribution at the beginning and the end of WAG injection are described in Figures 5.11 and It can be observed that a good vertical sweep efficiency is obtained through the WAG injection as well. Figures 5.13 and 5.14 provide a comparison for the CO 2 mole fraction distribution between the top and bottom layers. As expected, the buoyancy effect plays a significant role. Due to the density contrast, CO 2 tends to move upward, accumulating and displacing oil remaining in the upper portions of the reservoir. Conversely, one can barely see any CO 2 accumulation in the bottom layer. The water saturation distribution in the top and bottom layers is given in Figures 5.15 and Contrary to observations in the CO 2 distribution, water stays predominantly in the bottom layer. Figures 5.17 and 5.18 provide the cross-sectional views of the phase distribution. The conical shape of the vertical distribution of both CO 2 and water further demonstrate the gravity effect during the WAG injection, in which CO 2 and water collaborate with each other and displace different portions of the reservoir. 91

103 Figure 5.7: Pressure distribution at the end of WAG injection scheme, top layer Figure 5.8: Interfacial tension at the end of WAG injection scheme, top layer 92

104 Figure 5.9: Oil saturation at the beginning of WAG injection scheme, top layer Figure 5.10: Oil saturation at the end of WAG injection scheme, top layer 93

105 Figure 5.11: Cross-section view of oil saturation spatial distribution at the beginning of WAG injection Figure 5.12: Cross-section view of oil saturation spatial distribution at the end of WAG injection 94

106 Figure 5.13: Global CO 2 mole fraction at the end of WAG injection scheme, top layer Figure 5.14: Global CO 2 mole fraction at the end of WAG injection scheme, bottom layer 95

107 Figure 5.15: Water saturation at the end of WAG injection scheme, top layer Figure 5.16: Water saturation at the end of WAG injection scheme, bottom layer 96

108 Figure 5.17: Cross-section view of CO 2 mole fraction spatial distribution at the end of WAG injection Figure 5.18: Cross-section view of water saturation spatial distribution at the end of WAG injection 97