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Asphaltene deposition during co₂ injection in enhanced oil recovery applications

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Asphaltene deposition during co₂ injection in enhanced oil recovery applications

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Content ASPHALTENE DEPOSITION DURING CO2 INJECTION IN ENHANCED OIL RECOVERY APPLICATIONS by Fahad Al-Ghanem A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirement for the Degree DOCTOR OF PHILOSOPHY (PETROLEUM ENGINEERING) August 8th, 2017 Copyright 2017 Fahad Al-Ghanem i The Messenger of Allah ( ﷺ) said, "When a man dies, his deeds come to an end except for three things: Sadaqah Jariyah (ceaseless charity); knowledge which is beneficial, or a virtuous descendant who prays for him (for the deceased)." [Muslim]. ii Dedication To my Family For their continuous love and encouragement iii Acknowledgements I would like to express my gratitude and appreciation to all who encouraged and supported me throughout my studies. I particularly want to thank my Ph.D. advisor, Professor Kristian Jessen, for his continuous reassurance, and for always exhorting me to do my best. He provided me freedom in research and guided me when I was lost or had a challenging issue. His style of questioning and curiosity tends to push the boundary of existing knowledge and to foster creativity. I have learned a lot from him, and for that, I will remain in his debt. It has been an honor to work with two distinguished gentlemen, Professor Iraj Ershaghi and Assistant Professor Felipe de Barros, my dissertation committee members. Their time, effort and comments were much appreciated and improved the quality of my dissertation. USC-KOC is a joint University of Southern California and Kuwait Oil Company Center of Excellence for Research and Academic Training, established in January 2010. I have had the privilege to study under UKC, which was founded by two visionaries -- Dr. Adel Al-Abbasi and Professor Iraj Ershaghi. They presented me with a once in a lifetime opportunity to continue my studies while enjoying the support of my family. I am sincerely grateful to the late Dr. Mohammad Osman, who fathered the program and educated us to the standard required at the USC level. I pray that the teachings and beneficial knowledge he left to us will count as good deeds that benefit him after his passing. Professor Ershaghi has been my inspiration to continue striving for more knowledge. He made my studies much easier by his involvement in the administrative details that iv ensured I received the best education possible under the UKC. And that organization would not have been the same without the ongoing support of Mrs. Idania Takimoto, who made sure that all students’ academic needs were met. I would like to extend my thanks to Kuwait Oil Company's Management for supporting the program and providing the time I needed to complete the requirements for the Ph.D. degree. I would like to thank Mr. Hamed Al-Anzi, Mr. Bader Al-Khayat and Mr. Mohammad Al-Qenae who as Manager Research & Development ensured that our needs are met. Mr. Abdulla Al-Otaibi who ensured that our logistics are handled in the best of manners and Dr. Khayria Al-Hamad who continuously enquired about our progress and ensured that our studies are progressing on track. I would like to thank the Kuwaiti Cultural Office in Los Angeles staff and the formers and current Cultural Attachés who were keen to follow up my studies. Dr. Hassan Al-Kandari and Dr. Mohammed Al-Rashidi have honored me with their presence for the graduation ceremony which I greatly appreciated given their commitment as Cultural Attaché and Cultural Counselor. I am honored to have studied with the pioneers of the UKC: Ali Al-Saffar, Hadyan Al-Ajmi, Nadia Al-Zeabot and Noha Najem. They formed the ring that enabled me to push forward. I lived for five years in the USA, where I obtained my undergraduate degree in Mechanical Engineering. I could not have achieved this highest academic mark without the love of my late mother Latifa, the encouragement of my father Abdulla, and support of my family. My deepest gratitude goes to my lovely wife, Ghazayel and my children Latifa, Ghazlan, Sherefa, Lolwa, Abdullah and Fatemah. v Abstract The need for Enhanced Oil Recovery (EOR) will become an imperative as the number of mature fields grows and the demand to recover the remaining oil increases. One of the most promising EOR methods is the CO2 injection. However, if the oil contains asphaltenes, the CO2 injection may well cause asphaltene precipitation, and introduce production related challenges. Conventional three-phase (gas/oil/water) compositional simulators are unable to predict precipitation of asphaltenes and multiphase (three or more) compositional simulation tools are required to investigate the potential impact of that behavior. The use of detailed multiphase equilibrium computations, such as pT flash calculations, is quite CPU intensive, and commercial simulation packages often opt for hybrid models that may not capture the true physics at play. Conflicting findings have been reported from experimental and theoretical studies in the context of asphaltene precipitation and related impacts. Some studies have shown that asphaltene deposition due to CO2 injection takes place near the injection well, while others have reported that the deposition occurs near the production well. In this work, we applied detailed and simplified multiphase equilibrium calculations in displacement calculations to demonstrate that both findings are possible and that many factors will affect the deposition behavior. Accordingly, we opine that a general statement such as ‘CO2 injection causes more asphaltene precipitation relative to hydrocarbon gas injection’ is not always accurate. The additional complexity of asphaltene-rich hydrocarbon systems indicates the necessity for a true multiphase compositional simulator to investigate asphaltene deposition behavior and quantify any relevant impact on EOR operations. vi Through this work, we endeavor to make real contributions towards an improved understanding of asphaltene related production challenges. Included is the implementation of a four-phase compositional simulator (gas /oil /asphaltene /water) that is subsequently used to predict the asphaltene precipitation during CO2 and hydrocarbon gas injection processes. A range of simulation models and scenarios will be presented that demonstrate the asphaltene deposition locations, quantity, and impact on displacement dynamics. Various factors that influence the deposition are also addressed. We propose, as our second contribution, a new hybrid (simplified) formulation, based upon a table look-up approach, to replace multiphase equilibrium calculations with a CPU requirement that is comparable to two-phase (gas/oil) calculations. Simulation and test results validate the new formulation, and we arrive at an excellent agreement between the hybrid model and the full multiphase method. Third, we submit our novel approach to estimate the loss of permeability due to the formation of an asphaltene-rich phase. This is based on the relationship between the asphaltene saturation, readily available during simulation and the permeability. Various situations will be forthcoming to examine the impact of the permeability reduction using a multiphase compositional simulator. The goal of this study is to offer a tool to interpret displacement performance and optimize oil recovery, to enhance reservoir characterization, and to select the most advantageous production strategies. Overall, our proposals are relatively simple to implement in commercial tools and will provide pathways to allow for more in-depth studies of asphaltene precipitation and related production challenges. vii Table of Contents Dedication .................................................................................................................................................... ii Acknowledgements ................................................................................................................................... iii Abstract ........................................................................................................................................................ v Table of Contents ..................................................................................................................................... vii List of Tables ............................................................................................................................................... x List of Figures ............................................................................................................................................ xi Chapter 1: Introduction .......................................................................................................................... 1 1.1. Background ................................................................................................................. 1 1.2. Asphaltene .................................................................................................................. 2 1.3. Motivation .................................................................................................................... 4 1.4. Research Objectives ................................................................................................. 6 1.5. Organization of the Manuscript ................................................................................ 6 Chapter 2: CO2 for Enhanced Oil Recovery ...................................................................................... 7 2.1. Overview ..................................................................................................................... 7 2.2. Kuwait Efforts ........................................................................................................... 13 Chapter 3: Literature Review.............................................................................................................. 15 3.1. Experiments .............................................................................................................. 15 3.2. Permeability Effect ................................................................................................... 19 3.3. Asphaltene Models .................................................................................................. 22 3.3.1. Cubic EOS ...................................................................................................... 22 3.3.2. Statistical Associating Fluid Theory (SAFT) .............................................. 23 3.3.3. Association Equation of State (AEOS) ....................................................... 24 3.3.4. Artificial Neural Network (ANN) Models ..................................................... 26 3.3.5. Other Models .................................................................................................. 28 3.3.6. Hybrid Models ................................................................................................. 30 3.3.7. Simulations ..................................................................................................... 33 3.4. Commercial Software Modeling of Asphaltene ................................................... 34 3.4.1. Eclipse ............................................................................................................. 35 3.4.2. CMG ................................................................................................................. 37 viii Chapter 4: Mathematical Modeling.................................................................................................... 39 4.1. Continuity .................................................................................................................. 39 4.2. Equilibrium ................................................................................................................ 40 4.3. Relative Permeability .............................................................................................. 43 4.4. Four-Phase Simulator ............................................................................................. 44 4.4.1. Identifying Asphaltene-Rich Phase ............................................................. 44 4.4.2. Saturations ...................................................................................................... 45 4.4.3. Equilibrium Calculations................................................................................ 45 4.5. New Hybrid Formulation for Asphaltene Systems .............................................. 46 4.5.1. Asphaltene Component K-values ................................................................ 46 4.5.2. Asphaltene Component K-values Sensitivity to Pressure ....................... 46 4.5.3. Asphaltene Component K-values Variation with Composition ............... 47 4.5.4. Hybrid Model Flow Chart .............................................................................. 47 Chapter 5: Fluid Characterization and Multiphase Flash Calculations ........................................ 49 5.1. Using MiPVT to Simulate Reservoir Fluid ............................................................ 49 5.2. Validating MiPVT Results ....................................................................................... 51 5.3. Fluid Selection and Properties ............................................................................... 52 5.4. Flash Calculations and K-values ........................................................................... 56 5.5. Reference Selected Fluid and Properties ............................................................ 58 Chapter 6: Permeability Reduction Modeling .................................................................................. 62 6.1. Permeability Reduction in Literature ..................................................................... 62 6.2. Permeability Reduction Calculations .................................................................... 64 Chapter 7: Gas Flood Simulations .................................................................................................... 72 7.1. Introduction ............................................................................................................... 72 7.2. 1D Model Setup ....................................................................................................... 72 7.3. 1D Displacement Calculations ............................................................................... 73 7.3.1. 1D Simulation of CO2 Injection .................................................................... 73 7.3.2. 1D Simulation of Separator Gas Injection .................................................. 77 7.4. 1D Simulation with Simplified Flash Calculations ............................................... 81 7.5. Simulation of Gas Injection into Homogeneous 2D Reservoir.......................... 89 7.5.1. CO2 Injection ................................................................................................... 90 7.5.2. Separator Gas Injection ................................................................................ 95 ix 7.6. 2D CO2 Injection in Homogeneous Reservoir with Permeability Reduction ... 99 7.7. CO2 Injection in 2D Heterogenous Reservoir – Areal Variation ..................... 106 7.8. CO2 Injection in 2D Heterogenous Reservoir - Vertical Variation .................. 110 7.9. Discussion ............................................................................................................... 112 7.10. Conclusions ............................................................................................................ 114 Chapter 8: Summary and Future Research Directions ................................................................ 115 8.1. Absolute Permeability Reduction ........................................................................ 116 8.2. Accurate Fluid Description ................................................................................... 117 Nomenclature .......................................................................................................................................... 118 References .............................................................................................................................................. 120 x List of Tables Table 1: Original Reservoir Fluid Composition .............................................................. 50 Table 2: Characterized Reservoir Fluid ......................................................................... 51 Table 3: Experimental and MiPVT Simulated Bubble Point Pressures ......................... 52 Table 4: Experimental and Simulated Flashed Gas Composition ................................. 52 Table 5: Reference Fluid Description ............................................................................ 53 Table 6: Separator Gas Used in Flood Simulation ........................................................ 53 Table 7: More Asphaltic Fluid ........................................................................................ 54 Table 8: Binary Interaction Coefficients ......................................................................... 55 Table 9: Sample Flash Calculations Using MiPVT at 147°C and 200 bars ................... 57 Table 10: SARA Compositions of Kuwaiti Oil from a Subset of Wells ........................... 59 Table 11: Rydhal 1997 Fluid Adjusted for Higher Asphaltene Contents ........................ 59 Table 12: Selected Reservoir Fluid Composition and Properties .................................. 60 Table 13: Binary Interaction Coefficients ....................................................................... 61 Table 14: Sample Calculation for Permeability Reduction ............................................. 67 Table 15: 30 mD Overall Permeability Calculations ...................................................... 69 Table 16: Sample Asphaltene Saturation Impact on Overall Permeability Calculations 70 xi List of Figures Figure 1: Classification of Oil Recovery Methods (adapted from Al-Mutairi and Kokal, 2011).............................................................................................................. 1 Figure 2: Asphaltene Modeling Tree ............................................................................... 4 Figure 3: Oil Production Profile Scenarios (from http://drmillslmu.com) .......................... 8 Figure 4: Worldwide EOR Projects by Lithology (from Enhanced Oil Recovery: An Update Review Energies 2010, 3, 1529-1575) ............................................ 12 Figure 5: Hybrid Formulation Model Flowchart .............................................................. 48 Figure 6: Phase Envelope for the Reservoir Fluid ......................................................... 56 Figure 7: K-values from Flash Calculations Using MiPVT at Different Pressures ......... 58 Figure 8: Permeability reduction regions during flow of asphaltenic oil at constant rate through a core (Kord et al., 2014) ................................................................ 63 Figure 9: Asphaltene Deposition Behavior .................................................................... 65 Figure 10: Pore and Pore Throat Model ........................................................................ 66 Figure 11: Permeability Reduction as a Function of Asphaltene Saturation Considering Pore-throat Opening Effect .......................................................................... 68 Figure 12: A Possible Pore Throats Distribution for 30 mD ........................................... 68 Figure 13 : Permeability reduction of 30 mD rock due to throats partially plugging ....... 70 Figure 14: Permeability reduction of 300 mD rock due to throats partially plugging ...... 71 Figure 15: One-Dimension Simulation Model ................................................................ 72 Figure 16: Asphaltene saturations and the corresponding K-values for CO2 injection in 1D ................................................................................................................ 74 Figure 17: Pressure profiles and gas saturation profiles for injection of CO2 ................ 74 Figure 18: Asphaltene Component K-value Versus CO2 Mole Fraction in the Simulation Cell............................................................................................................... 75 Figure 19: Asphaltene Component K-value Versus CO2 Mole Fraction in the Simulation Cell (Semi-Log base10 Scale) ..................................................................... 76 Figure 20: Calculated and correlated K-values Versus Mole fraction of CO2 ................ 76 Figure 21: Asphaltene Saturations and the Corresponding K-values for Separator Gas Injection ....................................................................................................... 77 Figure 22: Asphaltene Component K-value Versus Methane(C1) in the Simulation Cell ..................................................................................................................... 78 Figure 23: Asphaltene Component K-values Correlated with CO2 in the Simulation Cell ..................................................................................................................... 78 Figure 24: Asphaltene Component K-values Correlated with C7-C25 in the Feed ........ 79 Figure 25: Fitted K-values and Multiphase Simulated Versus Mole Fraction of C7-C25 80 Figure 26: Asphaltene and Gas Saturations During CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid Multiphase) ............................................................................ 81 Figure 27: Asphaltene and Gas Saturations During CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid w/o asphaltene Multiphase) ................................................... 82 xii Figure 28: Asphaltene Saturations During CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid Multiphase) ....................................................................................... 84 Figure 29: Oil Density and Gas Saturations Along the 1D Length at PVI=0.08 & 0.33 (Full & Hybrid Multiphase) ............................................................................ 84 Figure 30: Oil Density and Asphaltene Saturations Along the 1D Length at PVI=0.08 & 0.33 (Full & Hybrid Multiphase) .................................................................... 85 Figure 31: First, 1/4th of the length and midpoint cell saturations (1.68% wt Asphaltene Crude) during CO2 injection ........................................................................ 86 Figure 32: First, 1/4th of the length and middle Cell Saturations (3.86 % wt Asphaltene Crude) during CO2 injection ........................................................................ 87 Figure 33: First, 1/4th of the Way and Middle Cells Saturations (1.68% wt Asphaltene Crude) Flooded by C1.................................................................................. 87 Figure 34: First, 1/4th of the Way and Middle Cells Saturations (3.86% wt Asphaltene Crude) Flooded by C1.................................................................................. 88 Figure 35: Asphaltene and Gas Saturations During Separator Gas Injection at PVI=0.08, 0.25 & 0.33 (Full & Hybrid Multiphase) ........................................................ 88 Figure 36: 2D Homogeneous Reservoir Model ............................................................. 90 Figure 37: Asphaltene Saturations During CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase) .......................................................................................... 91 Figure 38: Gas Saturations During CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase) .................................................................................................. 92 Figure 39: Asphaltene Saturations During CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values) ................................................................................... 93 Figure 40: Gas Saturations During CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values) ................................................................................... 94 Figure 41: Asphaltene Saturations During Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase) ....................................................................... 95 Figure 42: Gas Saturations During Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase) .................................................................................. 96 Figure 43: Asphaltene Saturations During Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values) ............................................................... 97 Figure 44: Gas Saturations During Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values) ........................................................................... 98 Figure 45: Asphaltene Saturations Difference for the Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI's for 3.86% wt Asphaltene Crude ........................................................................................ 99 Figure 46: Pressure Difference for the Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI's for 3.86% wt Asphaltene Crude ......................................................................................................... 100 Figure 47: Permeability Multiplier for 3.86% wt Asphaltene Crude .............................. 101 xiii Figure 48: Total Mobility for 3.86% wt Asphaltene Crude (Viscosity in Pa-s) .............. 101 Figure 49: Asphaltene Saturations Difference for the Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI’s For Original Rydhal Crude ............................................................................................. 102 Figure 50: Pressure Difference for The Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI's for Rydhal Original Crude ................................................................................................................... 103 Figure 51: Permeability Multiplier for Rydhal Original Crude ....................................... 103 Figure 52: Total Mobility for Rydhal Original Crude (Viscosity in Pa-s) ....................... 104 Figure 53: Average Reservoir Pressure for Original & 3.86% wt Asphaltene Fluids ... 104 Figure 54: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Homogenous Reservoir Using 3.86% wt. Asphaltene Crude ..................... 105 Figure 55: Natural log Permeability Distribution of Heterogenous Reservoir in Ln(mD) ................................................................................................................... 106 Figure 56: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Heterogenous Reservoir Using 3.86% wt. Asphaltene Crude .................... 107 Figure 57: Asphaltene Saturations Difference for the Simulation With/Without Perm Reduction Factor ....................................................................................... 108 Figure 58: Gas Saturation for Heterogenous Reservoir with and without Permeability Impairment ................................................................................................. 109 Figure 59: Natural log Permeability Distribution in Vertical Direction of Heterogenous Reservoir in Ln(mD) ................................................................................... 110 Figure 60: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Heterogenous Reservoir (Vertical Variation) Using 3.86% wt. Asphaltene Crude ......................................................................................................... 110 Figure 61: Gas Saturation for Heterogenous Reservoir (Vertical Variation) with and without Permeability Impairment ................................................................ 111 Figure 62: Asphaltene Saturations Difference for the Simulations With/Without Perm Reduction Factor (Vertical Variation) ......................................................... 112 Figure 63: Different Permeability Reduction Ratios due to Asphaltene as reported by Kord et al. (2014) ....................................................................................... 116 1 Chapter 1: Introduction 1.1. Background Al-Mutairi and Kokal (2011) indicated that only between 10 and 20% of oil in a reservoir, Original Oil in Place (OOIP), is usually recovered by primary recovery operations. Secondary recovery methods, such as water flooding, can achieve a recovery of about 15-25% of the OOIP. By using EOR techniques, that number can be further increased by at least 10-15%. A total recovery above 60% is very rare, although Shell did predict a recovery of 64% for one of their fields, using miscible gas injection such as CO2. Figure 1 shows the classification of oil recovery methods: Figure 1: Classification of Oil Recovery Methods (adapted from Al-Mutairi and Kokal, 2011). 2 The potential benefits of Enhanced Oil Recovery (EOR) may encourage CO2 capture from industries and its sequestration, depending upon several factors, including: the cost of the CO2 chain from source to the well, the expected incremental oil recovery, estimates of future oil prices, and receiving credits for a reduction in CO2 emissions. Additionally, an EOR operation is a strategic decision that provides a path to cut CO2 emissions, extend the life of a reservoir by an additional twenty to thirty years, retain the employment level, and avoid decommissioning facilities, which also involves a cost. 1.2. Asphaltene Asphaltene is a set of components that can precipitate, depending on their percentage, molar weight in the solution. The percentage limit is defined by the user as a function of pressure, temperature or molar fraction. The default is pressure. It can also be a function of either of the parameters. Flocculation is a procedure whereby fine particles obtained from the precipitation process aggregate to form bigger particles, referred to as flocs. That method is modeled by a set of two kinetic reactions to allow reversibility, partial or total, between the aggregation of the fines into flocs, and dissociation of the flocs into fines. Deposition is the means by which the flocs are exchanged between the oil phase and the rock surface. Flocs can either adsorb onto the rock surface, be trapped within the porous media because of their size, or be entrained and returned to the oil phase due to high local velocity (shear). The three states of asphaltene: i. Asphaltene dissolved in oil 3 ii. Fine particles -- can form larger particles iii. Large particles -- can also change into fine particles Changes caused by asphaltene deposition: ➢ Reduced pore volume ➢ Decreased absolute permeability ➢ Changes in oil viscosity increased due to precipitation Asphaltene precipitation is a phenomenon experienced primarily in light crude oil systems, and shows a marked increase with the addition of solvents. Temperature plays a role, as there tends to be more asphaltene deposition at lower temperatures than at those above the bubble point. Other factors, such as the type of gas injected, affects the asphaltene behavior and can impel the deposition towards either dissolution or precipitation, which adds to the challenge of understanding the prevailing mechanism that affects deposition in any given setting. A variety of model types have been used to predict asphaltene precipitation; however, the accuracy of predicting the onset has remained static. Most scientists, understandably, prefer their own model to those who came before. The reality is that although each is different, all models can match a given set of experimental data, which suggests that most are heuristic in nature, and do not address the fundamental physics and mechanisms. No predictive model is currently available; data fitting is required, resulting in semi-empirical models. An example of that observation concerns the broad range of values stated for asphaltene molecular weight; Forte and Taylor (2014) reported the numbers in the literature vary between hundreds and millions. Figure 2 denotes the most oft-used methods for the modeling of asphaltene. This will be discussed in detail in Chapter 3.3. 4 Figure 2: Asphaltene Modeling Tree. Given the need to increase oil production and recovery, engineers have moved towards EOR operations; one favored technique is the CO2 miscible flood. Unfortunately, the injected CO2 acts as a solvent to the crude oil and may result in asphaltene precipitation. As there are multiple factors involved, it is not always straightforward to detect the onset of asphaltene precipitation during core flooding or actual reservoir operations. Arciniegas and Babadagli (2014) found that when asphaltene was precipitating, the remaining oil properties were enhanced, and counter-balanced the negative effects of that precipitation. 1.3. Motivation Prioritizing is a good first step to any successful EOR project. First, ascertain which EOR method best suits the reservoir at hand, next is simulation at various scales to estimate 5 the expected incremental recovery, and finally, one must assess the financial viability. If the project seems feasible, the next phase would be the actual testing and piloting. To obtain an estimate of the hydrocarbon recovery during a gas injection process, compositional reservoir simulation must be used. The results of which provide some of the information needed to establish the practicality of the project. Moreover, compositional simulators indicate issues and challenges that need to be addressed before or during field trials and pilots. Accordingly, the success of an EOR project depends, in part, on the accuracy of the simulation model. Kuwait and the Middle East, in general, have concerns stemming from asphaltene deposition. Philp and Gilbert (2015) concluded that asphaltene is a transition stage from kerogen to crude oil. Due to the nature of the source rock and the thermal maturity critical window, where the hydrocarbons were formed, Kuwait has crude oil containing asphaltene. Hence, any EOR project in Kuwait must address that matter. During the past half century, many authors have attempted to explain asphaltene-rich systems and have proposed different models to predict its behavior. Nevertheless, the fact that we still classify asphaltene-based on progressively exposing the crude oil to multiple solvents, and claim that what is left is asphaltene, demonstrates the limits of our knowledge. This classification of asphaltene (e.g. SARA fractionation by IP-143) shows our lack of understanding the detailed nature of asphaltenes. We are motivated to investigate the accuracy of the models that are frequently used in the compositional simulation of asphaltene deposition processes to enhance the simulation tools, and promote the fit-for-purpose design of EOR operations in asphaltene-rich reservoirs. 6 1.4. Research Objectives The objective of this research is to investigate the effect of CO2 injection on asphaltene deposition in Kuwait reservoirs via simulation of four-phase flow. Most conventional methods of multiphase flow simulation in porous media include up to three phases (gas/oil/water). However, experimental and theoretical studies have shown that when an asphaltene-rich phase forms, the impact cannot be ignored. In the simulation of enhanced oil recovery methods, it is common to regard the asphaltene as a solid phase, as per the commercial simulation software (Eclipse & CMG). We will demonstrate that the separation of the asphaltene into a distinct phase does take place, and thus influences the flow of the other fluids during CO2 injection in EOR operations. Herein, we further investigate the impact of integrating the effect of asphaltene deposition regarding fluid mobility and permeability reductions. 1.5. Organization of the Manuscript The remainder of this manuscript is organized as follows: Chapter 2 provides a brief literature review of compositional simulation and asphaltene deposition. Chapter 3 discusses the significance of considering asphaltene deposition in CO2 gas floods. Chapter 4 describes the mathematical modeling used in our simulator. Chapter 5 considers crude oil characterization and the specific fluids used in this work. Chapter 6 offers our approach to modeling of the permeability reduction due to asphaltene deposition. Chapter 7 presents a series of simulations results and our observations. Finally, Chapter 8 concludes the thesis by presenting our proposed future directions of research in this area. 7 Chapter 2: CO2 for Enhanced Oil Recovery 2.1. Overview Gas injection is currently the most common EOR approach, although other techniques such as chemical injection, microbial injection and thermal methods are also in use. Injection gases include CO2, natural gas or nitrogen, with varying effectiveness. Oil displacement by CO2 relies on the unique properties of super critical CO2 by developing complete miscibility with the oil under certain conditions. That leads to a homogenous phase with no boundary between gas and oil, thereby lowering or nullifying the surface tension of the fluid, and viscosity reduction by dissolving in the oil and by oil swelling. CO2 transports inside the reservoir due to the lower partial pressure and can contact the oil in rock pores, which a water flood during secondary recovery cannot contact. The oil production rates from a given asset will decline eventually (see Figure 3) and EOR is needed to sustain practical production rates. Verma (2015) divided the CO2 injection into two categories: miscible CO2 floods and immiscible CO2 floods, depending upon the reservoir conditions, including temperature, pressure and oil API. Incremental oil recovery is higher in miscible CO2 flooding. Rubin et al. (2008) estimated the average fresh CO2 requirement to be 6-7 MCF/STB (Stock Tank Barrel) of incremental oil, whereas in the immiscible case that value was reported to be 5-12 MCF/STB. 8 Figure 3: Oil Production Profile Scenarios (from http://drmillslmu.com). Worldwide CO2 EOR projects as presented by Taber et al. (1997) are usually operated as miscible floods, which is achievable at an API Gravity of more than 22 and depth at more than 3000 ft. The depth limit allows for a sufficient injection pressure that is greater than the Minimum Miscibility Pressure (MMP), as determined by slim tube experiments. The Koottungal (2014) survey showed that the only large EOR project that utilizes the immiscible process is in Turkey. Taber et al. (1997) screening criteria indicated that an immiscible process is applied when both the reservoir pressure and oil gravity are too low (API 13 to 22). Below 13 API, CO2 EOR has not been applied successfully. 9 Duda (2010) discussed the optimum conditions for an EOR project. Sandstone and Carbonate reservoirs are considered good candidates for CO2 EOR. There is also an industry consensus that the areas with the best water flooding performance will also do well under CO2 flooding. That thinking is in opposition to the initial perceptions of engineers, who believed reservoirs with low recovery during water flooding would perform better during EOR operations, given the amount of oil left behind. Typically CO2 is injected in an alternating water and gas (WAG) process. Slugs of CO2 followed by water is commonly understood to provide better sweep efficiency, while the CO2 provides high local displacement efficiency. The frequency of alternating water and gas, as reported by Awan et al. (2008), can vary from days to months depending upon reservoir conditions. Overall, an EOR based on CO2 injection is a complicated process where one must consider a range of technical and economic aspects including but not limited to: 1. High EOR production costs due to the substantial initial investment, operations in the field, the expense of CO2 delivered, and the variance of oil prices. 2. Shell has been successful in marketing CO2 EOR by relating the CO2 price to oil prices in exchange for part of the oil production. 3. Air (N2 and O2). N2 is not a good injectant because it will be immiscible with the oil and O2 cannot be used because the oil will catch fire. Therefore, CO2 must be separated from flue gas which usually contains 5% oxygen, due to excess air used for combustion, in addition to other impurities. 10 4. 50-66% of the injected CO2 returns with the oil and is usually re-injected into the reservoir. Consequently, the Recycle/Fresh CO2 ratio ranges from 1 to 2. 5. EOR typically produce large quantities of brine, which may contain toxic metals and radioactive substances, and might also lead to groundwater contamination. 6. A rather lengthy response time of one to two years is possible before there is a noticeable increase in production. 7. The net climate benefit of CO2 EOR is considered marginal because CO2 needs to be compressed to around 2500 psig for injection. The CO2 recovery from flue gas and compression requires a huge amount of energy – an 8 to 12% drop in a power plant output due to the increase in internal consumption to retrofit a CO2 removal system. That leads to additional electricity demands, causing considerable additional CO2 emissions. 8. CO2 is heavier than air. Uncontrolled release of CO2 as in a well blow-out or pipeline leak can accumulate in low-lying areas. Parfomak and Folger (2007) elaborated on the associated risks. Above 25% concentration, it poses a significant hazard to health. An event occurred in 1986 in Cameroon where the release of a CO2 cloud killed 1800 people in the nearby villages (asphyxiation risk). HSE aspects should be tightly controlled. The first application of CO2 EOR in the United States took place in 1972; currently, the process is operating in more than 13,00 wells in 74 fields, injecting 2.14 BCFD CO2 and producing oil at about 245,000 BOPD. The U.S. high-pressure CO2 pipeline network is over 3,500 miles and used for injecting more than 600 million tons of CO2. On average, 11 the above operations are achieving about 2.2 BBLs/Ton of CO2 injected, which translates into 8.6 MCF/Barrel. The operational integrity can be considered equal to that of conventional wells. It is notable there are no indications of risk related to the geologic integrity of the formation after long-term exposure to CO2. No major technology breakthrough is required, other than access to low-cost CO2, and CO2 EOR production is expected to provide 25% (1.5 MM BOPD) of the U.S. oil production (6 MMBOPD) by 2030. The pressure required to inject CO2 is a function of reservoir permeability, zone thickness, and bottom-hole pressure. CO2 is usually delivered by pipelines at 1400 psig and <75°F. It is then boosted to about 2400 psig before injection. As water is denser and more viscous than CO2, during water injection, back pressure from the reservoir is moderate, about 1800 psig. However, when switching from CO2 to water, the water pressure must exceed the in-situ CO2 pressure. Therefore, water header pressure is kept higher than CO2 header pressure. Injected CO2 is a mixture of both fresh and recycled CO2. The fresh is typically 97% pure; therefore, the injected CO2 is 92 to 97% pure, depending upon the quality of the recycled gas. There are more than 1,500 EOR projects worldwide. Figure 4, below, shows the break- down by lithology. 12 Figure 4: Worldwide EOR Projects by Lithology (from Enhanced Oil Recovery: An Update Review Energies 2010, 3, 1529-1575). Apart from the USA, Canada, Hungary, Trinidad and Turkey have all implemented CO2 EOR projects. The North Sea is progressing apace. Several NOCs in the Arab side of the Gulf region have announced ambitious CO2 EOR pilot programs to improve recovery and to sequester significant CO2 volumes. Abdulla (2012) presented an overview of an ADNOC EOR pilot program using 60 tons/day CO2 (about 1.1 MM SCFD) in the Rumaitha field, and that ADNOC has identified larger areas of the field to inject 1750 TPD CO2. 13 2.2. Kuwait Efforts Kuwait would prefer to sustain its oil production through CO2 flooding. However, some of the reservoirs planned for the EOR method are already encountering serious asphaltene related issues. Asphaltene deposits in wellbores have been observed in Marrat Jurassic reservoirs in South East Kuwait (SEK), West Kuwait (WK) and North Kuwait (NK). That setback has caused some reduction in production and shutting-in of the wells, which has had an extremely detrimental effect on the economics of the oil recovery. In West Kuwait Marrat reservoir, 50% of the wells have a history of asphaltene clean- outs. Those wells contribute approximately 7% to the total oil production in WK. The reservoir pressure for that reservoir is around 9500 psig, which is significantly above the Asphaltene Onset Pressure (AOP), estimated to be around 4000 psig. It seemed as if there was no likelihood of asphaltene deposition in the reservoir in the near future. During production, however, as the pressure of the produced fluid went below the AOP, asphaltene started to flocculate, deposits gradually appeared in the tubing, reducing its diameter and, in the process, causing production rates to decline and eventually the well to stop flowing entirely. Consequently, the well tubing must be cleaned out to restore production, which takes about one month, during which time the well is completely shut off. The production loss is estimated to be 50,000 barrels each day. In SEK, the Marrat reservoir had an initial reservoir pressure of 9600 psig, while the current reservoir pressure is about 8400 psig and AOP estimates range from 5700 to 6700 psig. Any further reduction in reservoir pressure below the AOP could cause asphaltene deposition within. Hence, all Marrat wells in SEK have been shut since 1998 14 to avoid further pressure drops and entering the asphaltene dropout region. Lately, the Kuwait Oil Company has decided to restore production from this reservoir following the implementation of a comprehensive development plan, which includes pressure maintenance through water injection. 15 Chapter 3: Literature Review This chapter provides a review of the literature related to asphaltene precipitation with an emphasis on experiments, modeling, simulation and commercial software. Mansoori (1997) postulated a holistic view of deposition mechanisms including asphaltenes. He explained that when the economic implications of formation damage are massive and if predictive models based on different theories can be used to establish the phase behavior of multicomponent mixtures, then it is also possible to devise plans to either solve the problems or avoid them altogether. He suggested that thermodynamic models fail because they cannot explain the irreversibility of asphaltene precipitation, i.e. when conditions are reversed, the asphaltene will not re-dissolve. In our work, we assume that asphaltene will re-dissolve. 3.1. Experiments Huang (1992) performed core flooding experiments and demonstrated that the MMP, obtained from slim tube experiments, could not be replicated via the core flood. The recovery was observed to be far less, and resembled an immiscible flood even though it was carried out at 2500 psig, which is higher than MMP established 2150 psig through the slim tube, likely a consequence of heterogeneity of the core. The results also indicated that oil recovery efficiency decreases if the C5 to the C19 fraction in the oil decreases, or the asphaltene content increases. Srivastava et al. (1999) conducted experiments to investigate dynamic and static precipitation of asphaltene mixed with CO2 in a PVT cell, and also during core flooding 16 followed by a CAT scan for three different oil samples. In the PVT cell, the asphaltene deposition was proportional to the increase in the CO2 concentration and the initial asphaltene content of the oil. In the core flood experiment, significantly more asphaltene deposition was observed, probably due to the formation of different compositions during displacement, as compared to the PVT cell, with constant overall composition. Asphaltene deposited locally along the core length, with an additional significant deposition occurring near the inlet of the core. The core flood was performed with dead oil. Yin and Yen (2000) reported on inhibitor injection at the wellhead to avoid asphaltene precipitation in a CO2 flood operation in Texas. They found that WAG operations not only helped mobility control but also reduced the asphaltene problem. When the WAG operation was stopped, and only CO2 was injected, then blockage was observed. Idem and Ibrahim (2002) evaluated the kinetics of CO2 -induced asphaltene precipitation for three Canadian dead crude oils at isothermal and isobaric conditions. They used a molar CO2 programmed titration technique and observed that the oil asphaltene content and the CO2 content controlled the rate of asphaltene precipitation. They established the reaction orders for both asphaltene and CO2, for the same oil at different temperatures, which indicated that the CO2 -induced asphaltene precipitation was temperature dependent. Moreover, the values of the CO2 reaction order for all the oils, at all temperatures, were much larger than the corresponding values for the reaction order for asphaltene. That again indicated that CO2 content has a greater influence on the asphaltene precipitation than the asphaltene content has in the oil itself. They demonstrated for a light oil, at two different temperatures and constant pressure, that a 17 higher CO2 content was required to induce asphaltene precipitation, which supported the general belief that an increase in temperature enhances the stability of asphaltene. A study of a Kuwaiti reservoir by Gholum et al. (2003) found that as the temperature decreased, the AOP increased for a live oil. However, when CO2 is added to STO, they found that, as the temperature increased, so did the AOP. Escrochi et al. (2008) reported that the effect of temperature on asphaltene precipitation is, in general, weak, but at higher temperatures, as observed in Thermal EOR, the temperature did have an impact. Fisher et al. (2003) used a PVT cell with specialized optic equipment. They developed a model to describe the process of asphaltene precipitation / flocculation / deposition under typical reservoir conditions. Unfortunately, no useful data was shared; their work has not been replicated. Hu et al. (2004) studied reservoir oil samples with no reported asphaltene precipitation issues, which was verified through a pressure depletion experiment. However, during CO2 injection the asphaltene was seen to precipitate. No asphaltene precipitation was observed when the operating pressure was below the minimum miscibility pressure (MMP). But appreciable asphaltene precipitation was detected when the operating pressure approached or exceeded the MMP, and the amount of that precipitation increased with the concentration of injected CO2. They proposed corresponding states principle theory for prediction of asphaltene precipitation, which complements the scaling equation for same. 18 Okwen (2006) attempted to establish why the presence of water reduces the amount of asphaltene precipitation during CO2 injection in oil reservoirs. The experiment was performed at low pressure with moderate evidence as to the impact of water. Broad et al. (2007) conducted an experimental PVT analysis and cautioned that the gas chromatograph does not provide any data on molecular weights (PVT labs commonly use published data from Katz and Firoozabadi 1978). They recommended that the gas chromatograph data be calibrated with TBP distillation data. It was suggested that the MMP is sometimes achieved by changing the oil composition and dropping asphaltene to make the oil composition more compatible with CO2. They did not predict the asphaltene volume, just AOP, and surmised that without proper laboratory experiments, one could not conclusively state that the precipitate is pure asphaltene, but might include paraffin as well. Zekri et al. (2009) shared their experimental work that the deposition of sulfur and asphaltene during CO2 flooding occurs near the miscible slug. Hayashi and Okabe (2010) conducted PVT experiments with the solid detection system (SDS) and core flooding for sandstone and carbonate. They noticed that during injection of CO2, asphaltene deposited near the inlet of the core, but when HC gas was injected, the asphaltene distributed throughout the core. They reported that when the temperature increased, the AOP increased. That is not in accord with findings reported in other papers, possibly because they used a different method to detect the AOP - not SDS. The asphaltene deposition was found to exceed 60% around the saturation pressure at any given temperature. Another contradictory finding was that as temperature decreased, Asphaltene deposition decreased at constant pressure. 19 Oskui et al. (2011) proposed a systematic approach to examine asphaltene difficulties in reservoirs. AOP tests for a sample at different temperatures showed that as temperature decreased, the AOP increased. Abdulla (2012) reported on PVT experiments with CO2. No detailed crude analysis was forthcoming, only SARA and AOP data. The field experience showed no evidence of asphaltene precipitation near the CO2 injector, but rather at the producer. Soroush et al. (2014) used mixtures of toluene and asphaltene, with a constant mass fraction of 0.0034, as a model oil to study the effect of CO2 on asphaltene precipitation. The pressure and temperature at which phases changed were observed and reported; the study confirmed that the bubble point curve is not very sensitive to the presence of asphaltene. They suggested that, in general, CO2 acts as a co-solvent when present at low concentrations, while at high concentrations it becomes anti-solvent. Therefore, upon reduction of pressure, part of the dissolved CO2 migrated to the vapor phase, which in turn resulted in lower CO2 content in the liquid phase, and caused the asphaltene to re- dissolve and the solid phase to vanish. It is worth noting that the behavior is similar, even for live crude containing asphaltene; as the oil drops below the bubble point, it crosses the low AOP and all asphaltene vanishes. 3.2. Permeability Effect Wang et al. (2013) conducted CO2 core flood experiments under immiscible conditions. Via X-ray CT scanning, they established the distribution of crude oil and brine in the cores through the comparison of two CT images, before and after, the recovery process. The 20 cores used were artificially consolidated sandstone produced by cementing silica sand with an epoxy resin adhesive. Permeability reduction of the sandstone cores was noticed, due to asphaltene deposition after immiscible CO2 flooding. Their observation diverges from other findings -- that under immiscible conditions, asphaltene does not precipitate. Kord et al. (2014) proposed that surface deposition of asphaltene is the main mechanism of permeability reduction in porous media. Their core flooding experiments confirmed that pore throat plugging causes a linear reduction of permeability down to a certain value when another mechanism starts -- the pore throat opening, which restores the core permeability and flattens the reduction rate of permeability due to the dynamic effects. They identified four different flow regions during the core flooding with asphaltenic oil, according to the different mechanisms that cause permeability reduction: first -- the mechanisms of surface deposition and entrainment resulted in most of the permeability reduction; second -- the mechanisms in the first region counter-balance each other, and permeability reduction reached a steady state; third -- the pore throat plugging mechanism came into effect and caused a linear decline in permeability versus the pore volume injected; and fourth -- a new mechanism called pore throat opening began where the deposition stopped, due to the displacement of previously clogged pore throats. The experimental apparatus used in their work was a pipe-shaped reactor where all surfaces were available for deposition. It was designed and constructed by Soulgani et al. (2011) to measure the mass of deposited asphaltene versus time. Utilizing the mechanisms named above, specifically surface deposition and pore throat opening, a model was built, and, when checked against experimental results, a very good match was observed. 21 Behbahani et al. (2014) conducted core flood experiments on sandstone cores to study the asphaltene adsorption during miscible CO2 injection. Elemental and SEM analyses of sandstone core samples were also performed. The work indicated that the asphaltene was adsorbed as a multilayer, with the formation of large clusters of asphaltene on the surface. They observed that by increasing the flow rate of injected CO2, the permeability and porosity reduction increased significantly, due to an increase of asphaltene deposited in the material within the core. Moreover, they noted that asphaltene deposited more at the inlet of the core than at the outlet section, and found a decreasing trend along the length of the core. They proposed a model based on a multilayer adsorption theory rather than the more common monolayer (Langmuir type) adsorption based model. They suggested that their model described asphaltene adsorption more accurately, and concluded that the asphaltene adsorption does follow a multilayer behavior. Arciniegas and Babadagli (2014), conducted PVT cell experiments and concluded that the asphaltene deposition surface roughness is fundamental in explaining the plugging of a reservoir. They stated that the effect of temperature is far less than the effects of pressure and composition in high-pressure conditions. A strong solvent would result in thick asphaltene layers and thereby increase the possibility of pore plugging. However, the solvent will cause the oil viscosity to drop and mobility to increase, which could mask the initial pore plugging effect. As more asphaltene drops out, the oil production cannot be maintained. In other words, higher asphaltene precipitation improves oil properties but creates a greater possibility of pores plugging and permeability reduction. 22 3.3. Asphaltene Models A sizeable number of models have been suggested to model asphaltene. The subsections below provide an overview of those models and their associated uses. 3.3.1. Cubic EOS Ying et al. (2006) used Nghiem multiphase equilibrium model, which models asphaltene as a solid phase. They checked the validity of the equilibrium model against the results of static mixing experiments, which was agreeable. They ran numerous multiphase equilibrium calculations under different pressures and remarked about the asphaltene behavior against the molecular percent of CO2 injected, and that asphaltene dropout is greatest near the bubble point. They developed a simulation which included solving a non-Newtonian term. Li and Firoozabadi (2012) suggested a general strategy for two and three-phase split calculation for liquid/liquid and vapor/liquid/liquid equilibrium calculations. The two approaches used for phase split calculation follow: 1. Perform the flash; if it results in unrealistic numbers, increase the number of phases and repeat. 2. The stability test is performed before the phase split calculation, to determine whether it is necessary to increase the number of phases. They developed Michelsen’s (1984) suggestion to use pure substances as the trial phase for stability testing. They proposed that the initial composition of the components is 90 mol% and the others equally share 10 mol% in the phase. 23 3.3.2. Statistical Associating Fluid Theory (SAFT) Panuganti et al. (2012) developed a detailed procedure to characterize crude oil and to evaluate the asphaltene phase envelope, using the Perturbed Chain form of the Statistical Associating Fluid Theory (PC-SAFT). They claimed that, through the proposed characterization method, an excellent match with the experimental data points was achieved for both the bubble point and asphaltene precipitation onset curves. They proposed a characterization based on a split of the crude oil as primarily saturates (paraffin) and non-saturates. Both gas and liquid phases were characterized using a different number of components, then re-combined accordingly to represent the live oil. The characterized gas phase comprised seven components: N2, CO2, H2S, methane, ethane, propane, and a heavy gas pseudo component. The light gas components were maintained because of their significant effect on the bubble pressure and the AOP. The characterized oil phase had three components 1. Saturates pseudo-component (aromatics+resins); 2. pseudo-component - defined as regarding the degree of aromaticity; and 3. asphaltene utilizing the STO SARA analysis. Punnapala and Vargas (2013) enhanced the PC-SAFT characterization methodology described above by Panuganti et al. (2012). The new procedure reduced the number of adjustable parameters for asphaltene from three to two and sometimes just one. The Panuganti et al. (2012) method tuned the three PC-SAFT parameters for the asphaltene fraction to match the experimental AOP, whereas here the molecular weight (MW) and aromaticity were used. 24 Although it is well known that asphaltenes are a polydisperse distribution with a wide range of molecular weight aggregates, the addition of more asphaltene fractions would substantially increase the number of simulation parameters; the current simulation methods assume that asphaltenes are mono-dispersed with one single molecular weight. Punnapala and Vargas (2013) opined that their work enabled the investigation of the effect of polydispersity on asphaltene phase behavior, without increasing the number of simulation parameters, by assuming a constant aromaticity. Forte and Taylor (2014) claimed that earlier experimental studies confirmed the colloidal behavior of asphaltene; many models were built on that concept. They reviewed the advances in modeling asphaltene phase behavior using the SAFT. They declared that asphaltene solution and interfacial behavior, including their aggregation and precipitation tendencies, were not yet thoroughly understood and further research was required because we continue to have limited knowledge concerning characterization. 3.3.3. Association Equation of State (AEOS) Vafaie-Sefti et al. (2003) assumed that the asphaltene deposit was a mass of pure hydrocarbon components that contained mutually immiscible precipitating elements. They incorporated an association term in an Equation of State (EOS) and claimed that their model was able to predict the effects of pressure and composition changes due to CO2 injection on the asphaltene deposition. Their calculation results were in reasonable agreement with experimental data but did not follow established trends. Vafaie-Sefti and Mousavi-Dehghani (2006) modified their previous attempt at association modeling of asphaltene deposition, with the use of applied thermodynamic principles, resulting in a simplified model applicable for prediction of asphaltene deposition due to 25 pressure and miscible gas injection. The association term incorporated in the EOS was obtained from molecular weight distribution and average asphaltene molecular weight. They claimed that their model could predict the amount of asphaltene deposition from pressure and CO2 gas injection variations. Their conclusion that the results of the proposed model were in accord with experimental data was not supported by other results and figures. Shirani et al. (2012) developed an Association Equation of State (AEOS) model for predicting asphaltene precipitation in crude oil, which considered both a physical and a chemical term. In their proposed model, the association behavior of the fluid molecules was reflected in the form of a compressibility factor equation. The compressibility factor in their model was based on a physical part, either PR or SRK, and a chemical part which is precipitation of two association components: asphaltene and resin. They also disagreed with the theory which states that asphaltene is sterically stabilized by resins. They quoted many researchers who refute that theory; some of whom have shown that the theory conflicts with experimental observations and there is no physical evidence that resins lie preferentially at the surface of the asphaltene aggregates. Based on earlier research, and because asphaltene and resins do not exist in the vapor phase, the precipitated asphaltenes are more like liquids than solids. Therefore, they modeled the solid in this work as the liquid; the liquid–liquid equilibrium (LLE) calculation was utilized between the precipitated phase and solvent or oil phase. They observed that the amount of asphaltene deposition increased with increasing CO2 composition; they claimed the reason for that phenomenon was that by increasing the CO2 content, the pH of crude oil decreased and therefore asphaltene precipitation increased. 26 Buriro and Shuker (2012) performed PVT experiments with a solid detection system (SDS) and core flooding with CO2. They modeled the asphaltene using the Cubic Plus Association (CPA) EOS combined with Multiflash (infochem). Asphaltene was split into two parts: Easy to Dissolve Asphaltene (EDA) and Difficult to Dissolve Asphaltene (DDA). However, no data or comparison to other data was provided. Shirani et al. (2012) used the CPA Equation of State to model asphaltene precipitation. CPA EOS is composed of a physical part using PR or SRK EOS, and an association part. The values of binary interaction coefficients, association volume, and association energy were adjusted to fit the experimental data. The results showed that the CPA EOS could predict asphaltene precipitation with good accuracy. Furthermore, they demonstrated that using the SRK EOS in the CPA model resulted in the better prediction of the asphaltene phase behavior than when the PR EOS was used. Nasrabadi et al. (2013) used the CPA EOS to model asphaltene precipitation in compositional modeling. They proposed to split the heavy end into a heavy component that contained the heavy alkanes, the heavy aromatics, and the resins, then model the asphaltene as a separate component. They modeled the fluid as gas, hydrocarbon-rich liquid, and asphaltene-rich liquid, and proposed to study primary depletion and CO2 injection in upcoming work. 3.3.4. Artificial Neural Network (ANN) Models Ahmadi and Golshadi (2012) modeled asphaltene precipitation due to natural depletion using a feed-forward ANN, optimized by a hybrid genetic algorithm and particle swarm optimization (HGAPSO). 27 Their results, at a relatively low temperature, were in line with the known behavior of asphaltene systems – which is that maximum precipitation occurs around the bubble point. However, based on the figures presented, it was shown that at a high temperature of more than 220 °F, the asphaltene precipitate even at zero pressure, which contradicts other works, wherein an increase in temperature enhanced the stability of asphaltene. Hemmati-Sarapardeh et al. (2013) proposed the Least Squares Support Vector Machine (LSSVM) for their predictive model. They asserted that this was a reliable method based on 157 experimental datasets for 32 different Iranian crude oils. Such models do not, however, offer any additional theoretical insight, but might be used to understand the magnitude of the effect of each parameter on the asphaltene precipitation in its domain of applicability. Zendehboudi et al. (2014) conducted static and dynamic experiments to examine the effects of temperature, pressure, pressure drop, dilution ratio, and mixture compositions on asphaltene precipitation and deposition. Because both the precipitation and deposition phenomenon are strongly non-linear, the use of thermodynamic tools, which tend to linearize, is valid within specific process conditions. The authors duly promoted the use of ANNs in conjunction with techniques to approximate asphaltene precipitation and deposition during CO2 injection. Their study showed that the effect of temperature on the AOP (using NIR) leads to the reduction of onset pressure with an increase in temperature. However, it also caused a larger amount of asphaltene flocculated and deposited during the depressurization process. Moreover, during natural depletion, an increase in temperature leads to an 28 increase of asphaltene precipitated in a light oil sample, but a decrease of asphaltene precipitated in a heavy oil. That might be attributed to the solubility of asphaltene in the oil as a function of temperature and pressure. The temperature impact appears to vary depending upon whether the corresponding pressure is higher or lower than the bubble point of the mixture. From the data presented, it seems that dynamic testing resulted in lower precipitation when compared to static testing. The authors claimed that the effect of pressure drop was predominant compared to the flowing pressure throughout the asphaltene deposition process. They observed that all models used showed less accuracy in forecasting the dynamic asphaltene deposition case than in the static one, as more variables were involved in the dynamic scenario, which added to the uncertainties of the predictive models. They observed that pressure and temperature were the most important parameters effecting the asphaltene precipitation during static experiments. However, pressure drop and temperature both played important roles during asphaltene deposition onto the surface of the porous medium during the dynamic experiments. 3.3.5. Other Models Hirschberg et al. (1984) concluded that light crude oils could be described with a thermodynamic molecular model to verify the influence of temperature, pressure and gas dissolution on asphaltene precipitation. While they could describe a relationship between pressure and asphaltene solubility, they were unable to capture the temperature effect. They suggested that it could not be delineated, because thermal expansion and the 29 reduction of asphaltene/resin interactions may counter the effect of the increase in solubility due to the increase in temperature. Nikookar et al. (2008) concluded that asphaltene precipitation could be modeled as the thermodynamic system or by using a scaling approach. There was no direct temperature dependence in the scaling approach. Pan and Firoozabadi (1998) modeled the asphaltene micelles and precipitation as a solid phase and predicted the micellar size in dilute systems at room temperature. They also predicted the amount of asphaltene and resin precipitate and the micellar growth. The authors proposed a reversible micelle-formation process and modeled it accordingly; they minimized the Gibbs free energy by applying the mean-field theory to simplify such a calculation. Nourbakhsh et al. (2011) presented a model based on the Flory–Huggins theory, wherein a new correlation that considered the solvent ration and the molecular weight was used to express interaction parameters that play an important role in modeling the asphaltene precipitation. A dead oil was used for establishing the interaction parameter. Behbahani et al. (2011) used a solid model to describe asphaltene precipitation. The deposition and re-entrainment were considered at the same time, but usually one would be more dominant than the other for a given pressure, temperature and composition. They applied their model to published data and observed plugging of pore throats and a reduction in porosity. 30 Choiri and Hamouda (2011) developed their model to determine the asphaltene stability region under changing pressure, temperature, and composition. The model was based on polymer-solution theory. Shirdel et al. (2012) suggested using models from different disciplines for describing particle deposition in flow streams, such as iron particles in the gas stream, to model asphaltene particle deposition within the wellbore. Silva et al. (2013) analyzed the variables that affect asphaltene deposition during natural depletion. They then enhanced and simplified the model of Hirschberg et al. (1984) by proposing modifications to the oil characterization and to calculate the oil/asphaltene solubility parameter. They showed that for a pressure depletion process, the prediction could be significantly improved by utilizing the minimum amount of experimental data. However, they did caution that the prediction was highly sensitive to C7+ fraction density. They submitted that splitting the C7+ into more components would enhance the prediction of the model. Also, the fraction of the C7+ that was attributed to the asphaltene did impact the prediction capability. 3.3.6. Hybrid Models Pan and Firoozabadi (2000) used a thermodynamic micellization model combined with the Peng-Robinson EOS description of all monomers to model asphaltene deposition as liquid-liquid equilibrium. The composition and amount of each phase were then calculated. The effect of pressure, temperature, and composition on precipitation was properly represented by the model. Asphaltene precipitation is considered as solid at room temperature, but as a liquid at a higher (reservoir) temperature. The model 31 predictions for asphaltene phase volume percentage of the overall oil volume did not match the data accurately, with some data far removed from the calculated curves. The resin and asphaltene precipitation showed different behaviors, with a sharp increase in precipitation at bubble point only demonstrated for resin. Higher CO2 concentrations appeared to cause more asphaltene than resin precipitation. Takahashi et al. (2003) reported PVT and core flood experiments with injection above the MMP using a fluid recombined from separator oil and synthetic gas. They measured the AOP through a light scattering technique, and the asphaltene quantity was measured by taking a control sample from the PVT cell through 0.5 mm filter and doing mass balance to check the content of asphaltene precipitation. In all flooding procedures, dead oil was used to bring the core to Swirr; live oil was not subsequently employed. They modeled the asphaltene with a solid model and the gas-liquid equilibrium using the PR EOS with eight pseudo-components, while the precipitated asphaltene was assumed to obey Langmuir isothermal equation. They reported a larger asphaltene deposition in their carbonate rock sample than in that of the sandstone and attributed the difference to the more heterogeneous nature of the carbonate core. Moghadasi et al. (2006) performed PVT cell experiments and core flood experiment. They found that asphaltene dropout reached a maximum around the bubble point. For the core flood experiment, they observed a linear reduction in the permeability and most asphaltene precipitate at the inlet of the core. Correra et al. (2010) developed a tool for predicting the asphaltene dropout under CO2 injection for EOR purposes. The targeted field contained heavy asphaltene-rich oil; to 32 validate the tool, they performed PVT cell analysis and concluded that under EOR conditions for the field, no asphaltene dropout was expected. Adyani et al. (2011) proposed a systematic approach to evaluating the CO2 miscibility and the potential of asphaltene precipitation for a field in the South China Sea. They measured the MMP and asphaltene precipitation during CO2 injection and developed a thermodynamic model based on bottom-hole and recombined samples. There was a difference between the two oils regarding the C20+ which was not fully explained. They used Oil phase-DBR PVTPro for the simulation using PR EOS and Oil phase-DBR dbrSolids to model asphaltene behavior (asphaltene association model). The authors adjusted the BIC to tune the asphaltene model using BIC's between CO2 /C1 and asphaltene. During the core displacement test, a significant increase in the pressure was noticed which is indicative of a blockage taking place; however, as more CO2 was injected, the pressure decreased. Zadeh et al. (2011) performed PVT experiments with C1 and N2 and used published data to generate a model for asphaltene. They used an EOS and scaling equations and provided a good review of the history of existing models. Their proposed model was simple but appeared to work well for their data and in experiments from other authors. Darabi et al. (2014) modeled the asphaltene phase behavior and the flow from the injector to the producer. Their simulator represented varying pressure, temperature and composition via a solid model for asphaltene, and the PR EOS for gas/liquid. They coupled a reservoir simulator to a wellbore simulator. No experimental data was presented to support the dynamic process; however, they used an AOP that is supported by experimental data from the literature. 33 Silva et al. (2014) proposed a model that would help to detect the conditions at which the onset of asphaltene deposition starts. The model utilized the difference between the asphaltene solubility parameter and that of the solvent containing the non-asphaltene liquid (hydrocarbon) and CO2. Using two parameters: the binary interaction parameters between the lightest and the heaviest components, and the density of C7+ fraction, they tuned the model to match the saturation pressure. Only three pieces of information were required for the model: the oil composition including C7+ characteristics, the bubble point pressure at the reservoir temperature, and the SARA analysis. Their model did not predict the amount of asphaltene that precipitated but did show that the difference in the solubility remained constant for an increase in the CO2 concentration, which is in accord with other observations that there is no further appreciable increase in the asphaltene precipitation once a maximum limit has been crossed. 3.3.7. Simulations Pedersen et al. (2012) used a 1D model, combined with the SRK EOS, to study asphaltene precipitation. They demonstrated that deposition would not take place at a single location because the transition zone is moving forward. It was their contention that if a blockage takes place, then CO2, at higher mobility, will manage to bypass that blockage. In their simulations, they used the tie-line technique (Jessen 1998) to determine the phase compositions in each zone of the displacement and to ascertain the MMP. They demonstrated that the tie-line method failed due to the asphaltene phase (more than two 34 phases present). They then removed the asphaltene from the oil, re-performed the simulation, and found it to be in agreement with reported slim tube experiments. Ju et al. (2013) developed a 3D multiphase mathematical model describing CO2 transport in oil reservoirs and asphaltene precipitation. The model was used for predicting CO2 flooding performances for EOR. The mechanism of asphaltene flocculation during CO2 flooding in oil formations was analyzed, and a relation was established, which was included in the flow governing equations for the flocculated asphaltene transported in porous media. They validated the model using 1D experimental core flooding and demonstrated reasonable agreement. The permeability drops to about 40% after one pore volume of CO2 injection and remains unchanged after that. In their 3D model, the permeability of the block that contained the sink was reduced to about 70%, while the cells in between the injector and producer drop to ~ 58%. Khurshid and Choes (2014) suggested that if CO2 is injected above the minimum miscibility, any asphaltene that precipitates will re-dissolve. They used the ASPHALTE keyword in Eclipse-300 for simulating a 1D model (see additional information below). They checked whether the asphaltene behavior was due to pressure or a change in composition (water injection and CO2 injection), and concluded that it was a result of the change in composition. 3.4. Commercial Software Modeling of Asphaltene There are different ways to model asphaltene, as shown in Figure 2. The commercial software models asphaltene either as solid or liquid. In the following subsections, we will elaborate further on that topic. 35 3.4.1. Eclipse Kuwait Oil Company (KOC) sponsored the development of the Eclipse Asphaltene Model in 2007/2008, which has been included in all subsequent versions of E300. The KOC, furthermore, engaged Schlumberger to conduct a specific asphaltene study, the objectives of which are below: 1. Determine the asphaltene onset pressure for live fluid from Marrat formation and model asphaltene precipitation phase envelope. 2. Investigate the kinetics of asphaltene flocculation and model that process. 3. Explore the deposition tendency of asphaltene on the reservoir rock, and variation in the permeability of the core sample. The E300 includes a Multiphase Flash tool for situations when there are more than two hydrocarbon phases, and detects all the phases present in given pressure, temperature, and composition. Typically, multiphase systems form when wax or asphaltene are present in the oil, or when there is a high CO2 concentration at low temperatures. At the end of each time-step, a multiphase flash is performed to determine if a stable asphaltene phase exists, by first recognizing if one or more liquid phases are stable, then identifying a liquid phase as an asphaltene phase if the following two conditions apply: ✓ The heaviest hydrocarbon is an aromatic ✓ The heaviest hydrocarbon represents more than one-third of the phase by weight For example, suppose the flash outputs four stable phases and provides the component splits for each phase. Light components identify gas, while heavy components identify oil. 36 If a lot of paraffin is present, the phase is a wax; if there is a significant amount of heavy aromatic, the phase is asphaltene. The saturation, density, and molar density of the asphaltene phase are stored in the simulator as solid properties. The E300 predicts when asphaltene precipitation first occurs. Currently, with this option, the asphaltene phase is ignored in flow calculations, so this model should only be used as an indicator of whether or not asphaltene precipitation occurs in the reservoir. Asphaltene prediction is carried out in the compositional simulator using an EOS, if the keyword SOLID is used, and if the heaviest hydrocarbon is aromatic. E300 models the asphaltene as a kinetic for flow through the reservoir provided that certain input is provided by the user. E300 can also model the appearance of asphaltene using a multi flash algorithm, but it is not used in modeling the flow inside the reservoir. If asphaltene is present, the user must change the model and make precise inputs to model the asphaltene as a kinetic flow. In Eclipse, the asphaltene precipitate depending upon the percentage of molar weight in the solution. The percentage limit is defined by the user as a function of pressure. Moreover, in Eclipse Multiphase Flash, the asphaltene phase is ignored in flow calculations, so that model should only be used as an indicator of whether or not asphaltene precipitation occurs in the reservoir. Difficulties can arise when three hydrocarbon phases are present, as that situation is not modeled by E300. Eclipse suggests the use of permeability multipliers to model for the effect of asphaltene adsorbed into the formation, but details have not been shared. 37 3.4.2. CMG CMG WinProp uses a multiphase flash calculation where the fluid phases are simulated using an EOS, and the solid (asphaltene phase) is described using a solid model. The solid phase can consist of one or more components, but once precipitated, the phase is represented as an ideal mixture of solid components. The fugacity of precipitating components in the solid phase under isothermal prediction is: ln 𝑓 𝑠 = ln 𝑓 𝑠 ∗ + 𝑣 𝑠 ( 𝑝 − 𝑝 ∗ ) 𝑅𝑇 ⁄ (3.1) where 𝑓 𝑠 is the fugacity at pressure 𝑝 and temperature 𝑇 , 𝑓 𝑠 ∗ is the fugacity at pressure 𝑝 ∗ and temperature 𝑇 ∗ , 𝑣 𝑠 is the solid phase molar volume of the component, and 𝑅 is the universal gas constant. It was found that by splitting the heaviest components into two parts, a non-precipitating, and a precipitating fraction, a good quantitative match with experimental data was obtained. That has been independently verified for both wax and asphaltene precipitation problems. Resistance to flow due to solid deposition is generalized so that a power law or Kozeny- Carman relations with adjustable exponents can be used for permeability reduction calculations caused by asphaltene deposition. CMG-GEM models solid adsorption in the reservoir using an adsorption model, which simplifies to the following: 𝑤 𝑖 = 𝑤 𝑖 ,𝑚𝑎𝑥 𝐶 𝑖 𝑐 𝑖𝑜 1 + 𝐶 𝑖 𝑐 𝑖𝑜 (3.2) 38 Once the solid phase has adsorbed onto the reservoir rock, partial plugging of the formation is expected. The resistance is simply modeled as: 𝑅 𝑓 = 1 + ( 𝑅 𝑓 ,𝑚𝑎𝑥 − 1) 𝑤 𝑖 𝑤 𝑖 ,𝑚𝑎𝑥 ⁄ (3.3) This factor is divided into each of the gas/oil/aqueous phase mobilities, thereby reducing the volumetric flow rates for all the flowing phases. Permeability varies with saturation due to its changes from solid deposition and/or mineral precipitation or dissolution: 𝑘 = 𝑘 0 𝑅 𝑓 (3.4) 39 Chapter 4: Mathematical Modeling In this chapter, the governing equations for flow and mass transfer in porous media is introduced, with an emphasis on how best to extend an existing simulator to include asphaltene precipitation and dissolution. 4.1. Continuity Because mass is conserved, the continuity equation for multicomponent, multiphase flow in a porous medium is written as: 𝜕 𝜕𝑡 𝜙 ∑ 𝑥 𝑖𝑗 𝜌 𝑗 𝑆 𝑗 𝑛𝑝 𝑗 =1 + 𝛻 . ∑ 𝑥 𝑖𝑗 𝜌 𝑗 𝑣 ⃗ 𝑗 𝑛𝑝 𝑗 =1 = 0, 𝑖 = 1, … , 𝑛𝑐 (4.1) where 𝜙 is the porosity, 𝑥 𝑖𝑗 is the mole fraction of component 𝑖 in phase 𝑗 , 𝑆 𝑗 is the saturation of phase 𝑗 , 𝜌 𝑗 is the molar density of phase 𝑗 , 𝑣 𝑗 is the velocity of phase 𝑗 , 𝑡 represents time, 𝑛𝑝 represents the number of phases, and 𝑛𝑐 is the number of components. The phase velocities in Equation (4.1) are evaluated from the pressure field, which is obtained by solving the following volume-balance equation: 1 V t 𝑑 𝑉 𝑡 = 𝑐 𝑡 𝜕𝑝 𝜕𝑡 + ∑ 𝜕 𝑉 𝑡 𝜕 𝑛 𝑖 𝑛𝑐 𝑗 =1 (𝛻 . ∑ 𝑥 𝑖𝑗 𝜌 𝑗 𝑣 ⃗ 𝑗 𝑛𝑝 𝑗 =1 ) , ( V t + dV t )− 𝑉 𝑐𝑒𝑙𝑙 = 0, (4.2) 40 where 𝑐 𝑡 is the total fluid compressibility; 𝑝 is the pressure; 𝑉 𝑡 is the total fluid volume; 𝑉 𝑐𝑒𝑙𝑙 is the pore volume; and 𝑛 𝑖 is the number of moles of component 𝑖 . Capillarity is neglected because it is not significant. The second part of Equation (4.1) is related to the momentum balance, and Darcy equation is used to calculate the velocities: 𝒗 𝒋 = − 𝑘 𝑘 𝑟𝑗 𝜇 𝑗 ( 𝛻 𝑃 𝑗 + 𝜌 𝑚𝑗 𝑔 ℎ) (4.3) Here 𝑘 is the absolute permeability, 𝑘 𝑟𝑗 is the relative permeability of phase 𝑗 , 𝜇 𝑗 is the viscosity of phase 𝑗 , 𝜌 𝑚𝑗 is the mass density of phase 𝑗 , 𝑃 𝑗 is the pressure of phase 𝑗 , 𝜌 𝑚𝑗 𝑔 ℎ is the flow potential due to gravity. 4.2. Equilibrium Thermodynamic equilibrium among all phases are assumed at each time-step. If we select phase 𝐹 as the reference phase, the equilibrium equations become: 𝑥 𝑖𝑗 𝜑 𝑖𝑗 = 𝑥 𝑖𝐹 𝜑 𝑖𝐹 , 𝑖 = 1,2, … , 𝑛𝑐 , 𝑗 = 1,2, … , 𝐹 − 1 (4.4) where 𝜑 𝑖𝑗 is the fugacity coefficient of component 𝑖 in phase 𝑗 . Shojaei (2014) detailed the calculations of the fugacity for the fluids using an Equation of State. The equilibrium factors (𝐾 𝑖𝑗 ) are defined as: 41 𝐾 𝑖𝑗 = 𝑥 𝑖𝑗 𝑥 𝑖𝐹 = 𝜑 𝑖𝐹 𝜑 𝑖𝑗 𝑖 = 1,2, … , 𝑛𝑐 , 𝑗 = 1,2, … , 𝐹 − 1 (4.5) For multiphase flash calculations, Michelsen (2004) has shown that 𝐹 − 1 equations in the 𝐹 − 1unknown, 𝛽 𝑙 can be written as: ∑ 𝑧 𝑖 𝐾 𝑖𝑗 − 1 1 + ∑ 𝛽 𝑙 ( 𝐾 𝑖𝑙 − 1) 𝐹 −1 𝑙 = 0 𝑛𝑐 𝑖 =1 𝑖 = 1,2, … , 𝑛𝑐 , 𝑗 = 1,2, … , 𝐹 − 1 (4.6) Equation (4.6) looks simple enough to be solved by Newton’s method, but it is anything but simple. The complexity arises from the fact that an incorrect initial estimate of the phase fractions (𝛽 𝑙 ) will drive the calculation out of control and convergence will not be achieved. Hence, in our approach, we utilized the phase fractions obtained from the two- phase flash calculations, and assumed a small fraction of the asphaltene phase to ensure that the calculation does indeed converge. Once the phase fractions (𝛽 𝑙 ) have been determined, each phase compositions can be calculated from the equations below: 𝑥 𝑖𝐹 = 𝑧 𝑖 1 + ∑ 𝛽 𝑙 ( 𝐾 𝑖𝑙 − 1) 𝐹 −1 𝑙 (4.7a) 𝑥 𝑖𝑗 = 𝑧 𝑖 𝐾 𝑖𝑗 1 + ∑ 𝛽 𝑙 ( 𝐾 𝑖𝑙 − 1) 𝐹 −1 𝑙 (4.7b) The phase fractions, saturations and mole fractions in each phase must sum to one. 42 ∑ 𝛽 𝑗 𝑛𝑝 𝑗 =1 = 1 (4.8) ∑ 𝑆 𝑗 𝑛𝑝 𝑗 =1 = 1 (4.9) ∑ 𝑥 𝑖𝑗 𝑛𝑐 𝑖 =1 = 1 , 𝑗 = 1, … , 𝑛𝑝 (4.10) The above is all the needed information to solve the flow and transport equations (see Equation 4.1). Jessen et al. (2008) developed a 3-Phase simulator which was able to manage oil/gas/water systems. The simulator used a finite volume IMPES (implicit pressure explicit saturation/composition) formulation with a Cartesian grid. That means at each new time level, Equation (4.2) is solved with coefficients fixed at the old time level. The discrepancy between cell volume and fluid volume is minimized by carrying errors forward in time. Once the pressure field is obtained at the new time level using Equation (4.2), phase velocities at the grid block interfaces are achieved using Darcy’s law Equation (4.3) The total number of moles of each component in a grid block l is then updated using: 43 𝑁 𝑖 ,𝑙 𝑛 +1 = 𝑁 𝑖 ,𝑙 𝑛 − ∆𝑡 {∑ 𝐴 𝑙𝑚 𝑚 (∑ 𝑥 𝑖𝑗 𝜌 𝑗 𝑣 ⃗ 𝑗 𝑛𝑝 𝑗 =1 ) 𝑖 ,𝑙𝑚 𝑛 } (4.11) where 𝐴 𝑙𝑚 denotes the area connecting grid blocks 𝑖 and 𝑚 ; the term in the bracket is the total molar flux of component 𝑖 out of gridblock 𝑙 at the interface 𝑙𝑚 . The phase-equilibrium calculations are performed using Soave-Redlich-Kwong (SRK) EOS. The advective flux is calculated using the standard single point upwind (SPU) scheme. Refer to the work of Jessen et al. (2008) for more details. 4.3. Relative Permeability In water /oil /gas /asphaltene systems, up to four phases may form. Accordingly, we need a system of relative permeability suitable for those phases. Here, we use a three-phase permeability model for the system above, and consider that asphaltene has a zero mobility. Sherafati et al. (2014) have shown the three phases of relative permeability curves generated from the two-phase system using Corey’s equations and the modified Stone 1 model. In a water-wet system, the gas relative permeability is the same as that of the gas in the gas-oil two-phase system (calculated by Corey’s equation). The water relative permeability is the same as that of water in an oil-water two phase system. The modified Stone 1 model equations are presented below: 44 𝑘 𝑟𝑜 = 𝑘 𝑟𝑜𝑤𝑚𝑎𝑥 𝑆 𝑜𝑛𝑜𝑟 ( 𝑘 𝑟𝑜𝑤 𝑘 𝑟𝑜𝑤𝑚𝑎𝑥 ( 1 − 𝑆 𝑤𝑛𝑜𝑟 ) ) ( 𝑘 𝑟𝑜𝑔 𝑘 𝑟𝑜𝑤𝑚𝑎𝑥 ( 1 − 𝑆 𝑔𝑛𝑜𝑟 ) ) (4.12) 𝑆 𝑜𝑛𝑜𝑟 = 𝑆 𝑜 − 𝑆 𝑜𝑚 1 − 𝑆 𝑤𝑐 − 𝑆 𝑜𝑚 (4.13) 𝑆 𝑤𝑛𝑜𝑟 = 𝑆 𝑤 − 𝑆 𝑤𝑐 1 − 𝑆 𝑤𝑐 − 𝑆 𝑜𝑚 (4.14) 𝑆 𝑔𝑛𝑜𝑟 = 𝑆 𝑔 1 − 𝑆 𝑤𝑐 − 𝑆 𝑜𝑚 (4.15) Here, 𝑘 𝑟𝑜𝑤𝑚𝑎𝑥 is the maximum oil relative permeability in a two-phase oil-water system. 𝑆 𝑜𝑚 is the three-phase residual oil saturation, 𝑆 𝑤𝑐 is the connate water saturation, 𝑘 𝑟𝑜𝑔 is the oil relative permeability in the two-phase gas-oil system, and 𝑘 𝑟𝑜𝑤 is the oil relative permeability in the two-phase oil-water system. 4.4. Four-Phase Simulator An in-house simulator discussed by Jessen et al. (2008) can calculate a three-phase flow in a reservoir. The challenge was to extend the simulator code to four phases. The governing equations did not change; the code had to be modified to account for the new fourth phase, asphaltene. 4.4.1. Identifying Asphaltene-Rich Phase The first issue was identifying the phases; a multiphase flash calculation output the phases present at equilibrium, but without explicitly identifying them. Because we know 45 that gas is lighter than oil and that oil is lighter than asphaltene, we had to rank the phase density in ascending order, assign the lightest as gas and the heaviest as asphaltene, in case the multiphase equilibrium calculations split three phases. The next challenge was identifying the phases when there are only two. We adopted the following approach: Ascertain the lighter density of the phases, if it is within the gas values limit, the phase is identified as gas and the second phase, by default, will be oil. If the lighter phase density is too high to be considered gas, then it was assigned as oil and the second phase, by default, would be asphaltene. The case of only asphaltene and gas being present could not exist, and therefore was not considered. 4.4.2. Saturations The presence of asphaltene will change the saturations and subsequently all other properties calculated based upon the saturation. Because Equation 4.9 still holds, the saturations of the other existing hydrocarbon phases had to be adjusted. Water saturation was used to make sure that all phases add up to one. 4.4.3. Equilibrium Calculations We considered that the asphaltene phase can re-dissolve; therefore, at each time-step, the total cell composition was flashed at the newly updated pressure. This ensured that the asphaltene phase remained active and contributed to the equilibrium calculations. 46 Further, we considered the asphaltene phase to have zero permeability; hence, that phase remained in the cell for the next time calculation, when it would change its composition and could also change to another phase, based upon the multiphase equilibrium calculations. The asphaltene phase we show in Chapter 7 contains a significant volume of light components, which aid in containing the gas phase. MiPVT, a multiphase software, was also used to check the accuracy of multiphase flash module used in the new four-phase simulator. 4.5. New Hybrid Formulation for Asphaltene Systems The newly introduced multiphase flash equilibrium calculations require a high percentage of CPU usage and time. Thus, we started to look for approaches to reduce that cost. 4.5.1. Asphaltene Component K-values Under a simulation, the properties that influence the multiphase calculations are pressure, temperature, and composition. The reservoir temperature is usually held constant; so we are left with just pressure and composition. 4.5.2. Asphaltene Component K-values Sensitivity to Pressure Using the MiPVT software, we performed some multiphase flash calculations for a selected fluid under different pressures. We observed that the K-values for the asphaltene components were not significantly influenced by pressure, as seen in Figure 7 under Section 5.4. This provided reassurance that fixed K-values can be used for a given pressure range. 47 4.5.3. Asphaltene Component K-values Variation with Composition To monitor how the asphaltene component K-values change with the changing composition, we ran the new four-phase simulator in a 1D model and established a correlation for the K-values, verified it, used it for a 2D model, and checked the results against the full multiphase simulator. This will be covered in more detail starting in Section 7.2. 4.5.4. Hybrid Model Flow Chart In our proposed hybrid formulation, we extract the K-values from the two-phase module, look up the K-values for the asphaltene component, and then perform the equilibrium calculations. The outcome could be a positive, zero or negative beta for the asphaltene phase. Negative beta values indicate that the given phase does not exist; the relevant phase is removed and the calculations are repeated until convergence. A flow chart of the hybrid model is depicted in Figure 5. 48 Figure 5: Hybrid Formulation Model Flowchart. yes no yes (set asphaltene phase to zero) no Start with cell's composition, p and T Is it single phase? Is the phase gas? yes Perform 2-phase calculations no Is the asphaltene fraction negative? End the multiphase calculations set oil and asphaltene phases to zeros set the gas phase to zero Lookup the corrsponding composition, pressure and temperature asphaltene phase K-values and calculate the asphaltene fraction Using the gas/oil and asphaltene/oil k-values calculate the gas/oil/asphaltene phases fractions Calculate the gas/oil k-values that emerged from the 2-phase flash 49 Chapter 5: Fluid Characterization and Multiphase Flash Calculations An in-house simulator discussed by Jessen et al. (2008) was used to evaluate the effect of gas injection on the recovery. Our idea is to build on the simulation program to add the capability for predicting reservoir simulation when CO2 is used for EOR and modeling the asphaltene impact. 5.1. Using MiPVT to Simulate Reservoir Fluid The Kuwait Oil Company is working on piloting a CO2 Enhanced Oil Recovery project in one of its fields. A typical reservoir fluid composition for the targeted field, which is known to have asphaltene drop out issues, is shown in Table 1. Initially, we characterized the reservoir fluid by using Pedersen (1989). The characterization at that stage did not include an asphaltene component of C50+. The calculated bubble pressure was close to the experimentally established pressure, 3000 psia versus 3400 psia. The Pedersen (1989) correlation in MiPVT software was updated, and results have improved. Another issue of some concern was that the density of the C29 was about 1.08 g/cc as pre-defined in MiPVT, whereas the C30+ density was 1.01 g/cc. Therefore, the density and MW of the components from C7 to C29 was multiplied by a factor of 0.9 to establish a continuity of increasing density from C7 to C30+. 50 Table 1: Original Reservoir Fluid Composition Component MW Flashed Gas Flashed Oil Monophasic (g/mol) wt. % mole % wt. % mole % wt. % mole % N2 28.01 0.35 0.34 0 0 0.08 0.23 CO2 44.01 2.34 1.45 0 0 0.52 0.97 H2S 34.08 0.06 0.05 0 0 0.01 0.03 C1 16.04 36.29 61.47 0 0 8.13 41.08 C2 30.07 17.24 15.58 0 0 3.86 10.41 C3 44.1 16.51 10.17 0.16 0.71 3.83 7.03 i-C4 58.12 2.81 1.32 0.08 0.25 0.69 0.96 n-C4 58.12 9.67 4.52 0.45 1.46 2.52 3.51 i-C5 72.15 3.28 1.24 0.46 1.21 1.09 1.23 n-C5 72.15 4.97 1.87 1.02 2.69 1.91 2.14 C6 84 3.94 1.28 2.89 6.51 3.12 3.53 C7 96 1.27 0.36 3.51 6.92 3.01 3.3 C8 107 0.3 0.08 4.02 7.13 3.19 3.04 C9 121 0.13 0.03 4.26 6.67 3.33 2.23 C10 134 0.04 0.01 5.49 7.77 4.27 2.58 C11 147 0.01 0 5.04 6.5 3.92 2.16 C12 161 0 0 4.56 5.36 3.54 1.78 C13 175 0 0 4.31 4.67 3.35 1.55 C14 190 0 0 3.76 3.75 2.92 1.24 C15 206 0 0 3.95 3.64 3.07 1.21 C16 222 0 0 3.49 2.98 2.71 0.99 C17 237 0 0 3.26 2.61 2.53 0.87 C18 251 0 0 3.02 2.28 2.35 0.76 C19 263 0 0 3.04 2.19 2.36 0.73 C20 275 0 0 2.82 1.95 2.19 0.65 C21 291 0 0 2.75 1.79 2.13 0.59 C22 300 0 0 2.52 1.59 1.96 0.53 C23 312 0 0 2.22 1.35 1.72 0.45 C24 324 0 0 2.15 1.26 1.67 0.42 C25 337 0 0 1.92 1.08 1.49 0.36 C26 349 0 0 1.89 1.02 1.46 0.34 C27 360 0 0 1.77 0.93 1.37 0.31 C28 372 0 0 1.82 0.93 1.41 0.31 C29 382 0 0 1.67 0.83 1.3 0.28 C30+ 535.8 0 0 19.03 6.73 14.77 2.23 51 Table 2: Characterized Reservoir Fluid Component mole % MW density (g/cc) Tc (K) Pc (atm)   N2 0.23 126.2 33.6 CO2 0.97 304.2 72.9 H2S 0.03 373.2 88.20133 C1 41.08 190.6 45.4 C2 10.41 305.4 48.2 C3 7.03 369.8 41.9 i-C4 0.96 408.1 36 n-C4 3.51 425.2 37.5 i-C5 1.23 460.4 33.4 n-C5 2.14 469.6 33.3 C6 3.53 507.4 39.3 C7-C10 10.80 112.96 0.71 561.1 25.8 0.416 C11-C14 6.77 168.96 0.80 638.9 21.2 0.654 C15-C19 5.02 230.75 0.87 712.1 17.7 0.902 C20-C26 3.53 311.53 0.94 796.1 15.1 1.186 C27-C49 2.60 463.41 1.04 941.1 12.7 1.449 C50-C200 PN 0.19 808.89 1.17 1122.3 9.2 0.388 C50-C200 A 0.19 808.89 1.17 1398.5 14.8 1.274 The reservoir fluid was characterized using Pedersen (1989) as shown in Table 2. C50+ was split into asphaltene and non-asphaltene components; the bubble pressure remained unchanged, 3000 psia, similar to the characterization step without splitting the asphaltene component. The calculated GOR using a single flash stage was calculated to be 1125 SCF/STB, which is in good accord with the experimental value of 1179 SCF/STB. 5.2. Validating MiPVT Results The Table below reports the experimental and calculated saturation pressures at different temperatures; the reservoir temperature is 116 °C: 52 Table 3: Experimental and MiPVT Simulated Bubble Point Pressures Temperature (°C) Experimental Pb Pressure (psig) MiPVT Calculated Pb Pressure (psig) 69 2730 2655 90 2946 2883 111.5 3081 3081 As another step of validation, the reported gas composition from a single stage flashed was compared with the gas composition calculated by MiPVT. Because only components up to C6 (light ends) were reported, the comparison was carried out up to C6. The results matched favorably with the actually measured gas composition, as indicated in Table 4. Table 4: Experimental and Simulated Flashed Gas Composition Component Mole Percent Reported Mole Percent by MiPVT N2 0.34 0.35 CO2 1.45 1.48 H2S 0.05 0.04 C1 61.47 63.01 C2 15.58 15.71 C3 10.17 10.06 i-C4 1.32 1.24 n-C4 4.52 4.18 i-C5 1.24 1.06 n-C5 1.87 1.57 C6 1.28 1.12 The calculated GOR was 1120 SCF/STB while the reported value was 1179 SCF/STB. Unfortunately, the reported fluid did not have other PVT experiments, such as differential liberation, to tune the properties of the characterized fluids. 5.3. Fluid Selection and Properties Due to a lack of experimental data to verify the reservoir fluid, we selected a published fluid with readily available data and one characterized by the procedure of Pedersen (1989). Table 5 below denotes the characterized reservoir fluid, along with its properties: 53 Table 5: Reference Fluid Description z (frac) Tc [C] Pc [bar] Omega MW Nitrogen 0.00490 -146.9500 33.9996 0.0400 28.0140 CO2 0.11369 31.0600 73.8305 0.2250 44.0100 H2S 0.03220 100.3800 89.6291 0.1000 34.0820 Methane 0.27357 -82.5900 45.9904 0.0080 16.0430 Ethane 0.09409 32.1700 48.7201 0.0995 30.0700 Propane 0.06699 96.6800 42.4795 0.1523 44.0960 i-Butane 0.00810 134.9900 36.4801 0.1808 58.1230 n-Butane 0.03170 151.9700 37.9604 0.2002 58.1230 i-Pentane 0.01220 187.2800 33.8101 0.2275 72.1500 n-Pentane 0.01980 196.5500 33.6997 0.2515 72.1500 n-Hexane 0.02490 234.4500 30.2496 0.3013 86.1770 C7-25 0.25278 393.1000 20.3900 0.7560 176.6000 C26-49 0.05524 620.8000 14.1900 1.2620 473.1000 C50-64_PN 0.00545 683.8000 13.7200 1.3130 774.8000 C50-64_A 0.00192 1013.6000 18.1100 1.2740 774.8000 C65-80_PN 0.00183 845.3000 14.1000 0.8760 989.2000 C65-80_A 0.00064 1013.6000 18.1100 1.2740 989.2000 The gas used for the flood simulations were separator gas and 100% CO2 gas. The composition of the separator gas is shown below: Table 6: Separator Gas Used in Flood Simulation Separator Gas Nitrogen 0.0100 CO2 0.0041 H2S 0.0088 Methane 0.7533 Ethane 0.1333 Propane 0.0905 To investigate the impact of the asphaltene content, 1% of the heavy end, containing an equal proportion of C50-C80 to that of the fluid shown in Table 5, was added to the reference fluid. The heavier, more asphaltic fluid is reported below in Table 7: 54 Table 7: More Asphaltic Fluid z (frac) Nitrogen 0.004851 CO2 0.112553 H2S 0.031878 Methane 0.270834 Ethane 0.093149 Propane 0.06632 i-Butane 0.008019 n-Butane 0.031383 i-Pentane 0.012078 n-Pentane 0.019602 n-Hexane 0.024651 C7-25 0.250252 C26-49 0.054688 C50-64_PN 0.007896 C50-64_A 0.004401 C56-80_PN 0.004312 C56-80_A 0.003134 In this work, we used the binary interaction coefficients (BIC) shown in Table 8, as assigned by the characterization procedure proposed by Pedersen (2007) for asphaltene calculations. 55 Table 8: Binary Interaction Coefficients N2 CO2 H2S Methane Ethane Propane i_Butane n_Butane i_Pentane n_Pentane Hexane C7_C25 C26_C49 C50_C64_P N C50_C64_A C65_C80_P N C65_C80_A N2 0 -0.032 0.17 0.028 0.041 0.076 0.094 0.07 0.087 0.088 0.08 0.08 0.08 0.08 0.08 0.08 0.08 CO2 -0.032 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 H2S 0.17 0.099 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Methane 0.028 0.12 0.08 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ethane 0.041 0.12 0.085 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Propane 0.076 0.12 0.089 0 0 0 0 0 0 0 0 0 0 0 0 0 0 i_Butane 0.094 0.12 0.051 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n_Butane 0.07 0.12 0.06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 i_Pentane 0.087 0.12 0.06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 n_Pentane 0.088 0.12 0.069 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Hexane 0.08 0.12 0.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C7_C25 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C26_C49 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C50_C64_PN 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C50_C64_A 0.08 0.1 0 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0 0 0 0 0 0 C65_C80_PN 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C65_C80_A 0.08 0.1 0 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0 0 0 0 0 0 56 5.4. Flash Calculations and K-values In the simulation, the flash routine will calculate the K-values and update them in the loop for each cell at each time-step. That is both very costly and time-consuming. To eliminate the need to update the K-values at each step, we used MiPVT software and flashed the reservoir fluid at different pressures at the reservoir temperature of 147°C. That enabled us to evaluate how K-values varied over the range of our pressures of interest. Figure 6 below shows the phase envelope for reservoir fluid, and the path the fluid takes as pressure decreases entering the two-phase region and crossing asphaltene onset pressures. Figure 6: Phase Envelope for the Reservoir Fluid. 57 To establish the K-values range and behavior under different pressures, we carried out several multiphase flash calculations; a sample of which is shown in Table 9. Table 9: Sample Flash Calculations Using MiPVT at 147°C and 200 bars Component zfeed Gas phase Asph. phase Oil phase Kog Koa Nitrogen 0.0049 0.0144 0.0012 0.0043 3.3613 0.2727 CO2 0.1139 0.1738 0.0550 0.1101 1.5786 0.4998 H2S 0.0322 0.0289 0.0267 0.0324 0.8928 0.8249 Methane 0.2737 0.5445 0.0946 0.2565 2.1228 0.3687 Ethane 0.0940 0.1159 0.0397 0.0926 1.2513 0.4288 Propane 0.0669 0.0597 0.0277 0.0674 0.8856 0.4110 i-Butane 0.0081 0.0059 0.0029 0.0082 0.7128 0.3513 n-Butane 0.0317 0.0204 0.0126 0.0324 0.6289 0.3893 i-Pentane 0.0122 0.0063 0.0043 0.0126 0.4992 0.3397 n-Pentane 0.0198 0.0095 0.0071 0.0204 0.4628 0.3468 n-Hexane 0.0249 0.0090 0.0078 0.0259 0.3467 0.2997 C7_C25 0.2528 0.0118 0.0749 0.2681 0.0438 0.2792 C26_C49 0.0552 0.0000 0.0288 0.0587 0.0003 0.4913 C50_C64_PN 0.0054 0.0000 0.0045 0.0058 0.0000 0.7852 C50_C64_A 0.0019 0.0000 0.4587 0.0020 0.0000 228.09 C65_C80_PN 0.0018 0.0000 0.0007 0.0019 0.0000 0.3537 C65_C80_A 0.0006 0.0000 0.1529 0.0007 0.0000 228.14 After performing multiple flash calculations, one observed that for the pressures of our interest the change in the K-values was small, within 5%, as shown by the error bars. We envisage an opportunity to use constant K-values for the asphaltene flash calculation. Figure 7 below reports those values for each component as obtained from multiphase pT calculations at different pressures. We perceived relatively small changes to the values. Please note that the K-values for the asphaltene components is reported as k*1000, so as to maintain the same scale as the other K-values. 58 Figure 7: K-values from Flash Calculations Using MiPVT at Different Pressures 5.5. Reference Selected Fluid and Properties Once we established that the asphaltene K-value changes are insignificant at a constant composition and within a pressure range of interest, we used a fluid with only 15 components to reduce the number of equations and realize a more speedy result from the simulations. We used a model fluid from Rydhal 1997 which was characterized by the Pederson method. The fluid included 1.29% wt. of asphaltene, while the Kuwaiti crude oil of interest contained more than that amount. Table 10 below reports a subset of wells in the target Kuwaiti reservoir showing the asphaltene content by weight % for the dead oil. 59 Table 10: SARA Compositions of Kuwaiti Oil from a Subset of Wells Well Saturates (wt.%) Aromatics (wt.%) Resins (wt.%) Asphaltenes (wt.%) A 40.53 48.79 8.26 2.42 B 39.83 48.98 7.32 3.86 C 40.56 47.57 6.36 5.52 D 39.71 50.47 8.13 1.68 We modified the asphaltene component of the Rydhal 1997 fluid to match the target Kuwaiti crude and arrived at a more realistic fluid for the purpose of this study. That was accomplished by adjusting the weight % of the asphaltene component in the C7+ fraction to match Table 10, above. It is a good approximation because the dead oil will have minimal light ends (up to C6) and their contribution to the oil weight is also negligible. Table 11 reports the resultant fluids. Table 11: Rydhal 1997 Fluid Adjusted for Higher Asphaltene Contents Component Rydhal Original Fluid 1.68 wt.% Reservoir Fluid 2.42 wt.% Reservoir Fluid 3.86 wt.% Reservoir Fluid 5.52 wt.% Reservoir Fluid Nitrogen 0.01497 0.01497 0.01497 0.01497 0.01497 CO2 0.00220 0.00220 0.00220 0.00220 0.00220 Methane 0.23066 0.23066 0.23066 0.23066 0.23066 Ethane 0.06907 0.06907 0.06907 0.06907 0.06907 Propane 0.08614 0.08614 0.08614 0.08614 0.08614 i-Butane 0.01298 0.01298 0.01298 0.01298 0.01298 n-Butane 0.05290 0.05290 0.05290 0.05290 0.05290 i-Pentane 0.01777 0.01777 0.01777 0.01777 0.01777 n-Pentane 0.02705 0.02705 0.02705 0.02705 0.02705 n-Hexane 0.03633 0.03633 0.03633 0.03633 0.03633 C7 0.00000 0.00000 0.00000 0.00000 0.00000 C7-25 0.38340 0.38340 0.38340 0.38340 0.38340 C26-49 0.05972 0.05972 0.05972 0.05972 0.05972 C50-80_PN 0.00528 0.00480 0.00391 0.00218 0.00017 C50-80_A 0.00155 0.00203 0.00292 0.00465 0.00666 The reservoir properties of the fluid and injection gas are shown in Table 12, while Table 13 reports the relevant binary interaction coefficients (BIC). 60 Table 12: Selected Reservoir Fluid Composition and Properties Component 3.86% wt. Asphaltene Reservoir Fluid Separator Gas Tc (°C) Pc (bar)   MW (g/mol) Z crit Nitrogen 0.01497 0.01880 -147 33.94 0.04 28 0.2916 CO 2 0.00220 0.00410 31.1 73.76 0.225 44 0.2742 Methane 0.23066 0.70690 -82.6 46 0.008 16 0.286 Ethane 0.06907 0.13330 32.3 48.84 0.098 30.1 0.279 Propane 0.08614 0.09050 96.7 42.46 0.152 44.1 0.276 i-Butane 0.01298 0.01080 135 36.48 0.176 58.1 0.282 n-Butane 0.05290 0.02330 152.1 38 0.193 58.1 0.274 i-Pentane 0.01777 0.00450 187.3 33.84 0.227 72.2 0.27 n-Pentane 0.02705 0.00580 196.5 33.74 0.251 72.2 0.27 n-Hexane 0.03633 0.00130 234.3 29.69 0.296 86.2 0.266 C7 0.00000 0.00070 253.9 31.78 0.458 92.8 0.25037 C7-25 0.38340 386 20.87 0.741 169.4 0.22554 C26-49 0.05972 611.9 13.81 1.252 463.3 0.1807 C50-80_PN 0.00218 714.8 12.8 1.216 814.2 0.18386 C50-80_A 0.00465 1184.1 15.67 1.274 814.2 0.17877 61 Table 13: Binary Interaction Coefficients Nitrogen CO 2 Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane C7 C7-C25 C26-C49 C50-C80_PN C50-C80_A Nitrogen 0 -0.032 0.028 0.041 0.076 0.094 0.07 0.087 0.088 0.08 0.08 0.08 0.08 0.08 0.08 CO2 -0.032 0 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.1 0.1 0.1 0.1 0.1 Methane 0.028 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 Ethane 0.041 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 Propane 0.076 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 i-Butane 0.094 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 n-Butane 0.07 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 i-Pentane 0.087 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 n-Pentane 0.088 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 n-Hexane 0.08 0.12 0 0 0 0 0 0 0 0 0 0 0 0 0.017 C7 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 C7-C25 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 C26-C49 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 C50-C80_PN 0.08 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 C50-C80_A 0.08 0.1 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0 0 0 0 0 62 Chapter 6: Permeability Reduction Modeling In this chapter, we review and analyze the potential impact of asphaltene precipitation on the permeability. Our intent is to formulate a permeability reduction model that can be integrated into the compositional simulator and applied to reservoir engineering studies. 6.1. Permeability Reduction in Literature Permeability reductions due to asphaltene precipitation is considered to happen by three different mechanisms (Wang and Civan-2001): 1. Surface Deposition 2. Pore Throat Plugging 3. Entrainment of Asphaltene Deposits The surface deposition occurs when the asphaltenes are exchanged between the oil phase and the rock surface. Pore throat plugging happens when the asphaltene deposits into the pore throats and entrainment takes place when the velocity is high enough to carry some of the deposited asphaltenes. Kord et al. (2014) illustrated, experimentally, that pore throat plugging, due to asphaltene precipitation, caused a linear reduction in permeability until the pore throat mechanism began and the permeability reached a steady value. However, before the above two mechanisms become active, pore throat surface deposition is, arguably, the cause of much of the observed permeability loss. See Figure 8. 63 Figure 8: Permeability Reduction Regions during Flow of Asphaltenic Oil at Constant Rate Through a Core (Kord et al., 2014). Nghiem et al. (2000) modeled the permeability reduction due to asphaltene deposition via a reduction factor 𝑅 𝑓 that is given by: 𝑅 𝑓 = { 1 + ( 𝑅 𝑓 ,𝑚𝑎𝑥 − 1) 𝑤 𝑠𝑑 𝑤 𝑠𝑑 ,𝑚𝑎𝑥 , 𝑤 𝑠𝑑 ≤ 𝑤 𝑠𝑑 ,𝑚𝑎𝑥 𝑅 𝑓 ,max , 𝑊 𝑠𝑑 >𝑊 𝑠𝑑 ,𝑚𝑎𝑥 (6.1) where 𝑤 𝑠𝑑 is the weight percent of solid deposited through adsorption and mechanical entrapment and 𝑅 𝑓 ,𝑚𝑎𝑥 is the permeability reduction factor at 𝑤 𝑠𝑑 ,𝑚𝑎 𝑥 , the maximum deposition. 64 That equation corresponds to a linear relationship between 𝑅 𝑓 and 𝑤 𝑠𝑑 with a plateau at 𝑅 𝑓 ,𝑚𝑎𝑥 , the maximum permeability reduction factor. From the above it is clear that complete plugging of cores should not take place: permeability reduction happens up to a certain limit. Kord et al. (2014) referred to that limit the as “pore throat opening mechanism” while Nghiem et al. (2000) called it a “Plateau at 𝑅 𝑓 ,𝑚𝑎𝑥 ”. 6.2. Permeability Reduction Calculations Anovitz & Cole (2015) characterized and analyzed porosity and pore structures. They determined that the pore throat accounts for about 1% or less of the total pore volume. Also, they found in a typical example that the pore-to-pore-throat ratio is in the order of 100. Here, we utilize the theory from the capillary tube model and the Kozeny equation to calculate an average pore throat radius, given the permeability and porosity of porous media. The tortuosity factor (𝜏 ) is assumed to be ~1/porosity: 𝑘 = 𝜑 𝑟 2 8 𝜏 2 (6.2) Solving for the radius of the pore throat we get: 𝑟 = √ 8 𝑘 𝜏 2 𝜑 (6.3) Now, if we assume that the asphaltene deposits upon formation, and that it forms a layer of asphaltene of equal thickness throughout the pore volume, including the throats, then 65 we can calculate a new pore throat radius (based on that layer) and apply Equation (6.2) to calculate the new permeability. A schematic of the assumed asphaltene deposition process is shown in Figure 9. Original state Asphaltene build up in pore and pore throat Maximum thickness reached at pore throat Further increase in the asphaltene only takes place in pore Figure 9: Asphaltene Deposition Behavior. This, of course, is just the starting point. We need to correlate the permeability reduction to the overall asphaltene saturation rather than the throat saturation. To do that, we assume that the throat accounts for 1% of the overall porosity and that the pore throat radius is 1/100 of the pore radius. Figure 10 below illustrates the assumed configuration: 66 Figure 10: Pore and Pore Throat Model. However, as per the literature, we need to set a limit where permeability does not reduce further. Behbahani et al. (2014) experiments results suggested that the plateau be about 20% of the initial permeability. If we use their boundary, we can calculate the permeability reduction as a function of the asphaltene saturation. We used Equation (6.3) and the permeability of 30 mD to calculate the pore throat radius as follows: 𝑟 = √ 8( 30𝑥 9.869𝑥 10 −9 ) 2 2 0.20 = 2.176𝑥 10 −4 𝑐𝑚 Applying the assumption of the pore throat to the pore radius relation, i.e. that the pore is 100 times bigger than the radius above, we get: 𝑅 = 100 𝑟 = 2.176𝑥 10 −2 𝑐𝑚 R=100 r r 67 Because we assumed that the pore throat accounts for 1% of the overall porosity and assuming capillary tubes, we can calculate the lengths of the pore throat and the pore. To satisfy that supposition, the relation between the length of the pore throat and the length of the pore must be: 𝐿 𝑅 = 1 100 𝐿 𝑟 Now we can use those relationships and simple volume relationships to build a table. Starting from an assumed asphaltene layer thickness, we calculated the asphaltene saturation as well as the resultant permeability due to the reduction of the pore throat radius up to the maximum limit. Table 14 below shows the sample calculations. Table 14: Sample Calculation for Permeability Reduction r (cm) from wall SatAsph k (md) 0 0.00% 30.00 2.176E-05 0.39% 24.30 4.353E-05 0.76% 19.20 6.529E-05 1.11% 14.70 8.706E-05 1.44% 10.80 1.088E-04 1.75% 7.50 1.203E-04 1.91% 6.00 1.524E-04 2.20% 6.00 1.741E-04 2.40% 6.00 1.959E-04 2.60% 6.00 2.176E-04 2.81% 6.00 2.394E-04 3.01% 6.00 Figure 11 below reflects the resulting permeability reduction and limited to 20% of the initial value. 68 Figure 11: Permeability Reduction as a Function of Asphaltene Saturation Considering Pore Throat Opening Effect. The above calculation example assumes a single pore throat radius. To relax that assumption, we continued by assuming a pore throat distribution, a normal distribution with an overall permeability of 30 mD as shown in Figure 12 below: Figure 12: A Possible Pore Throats Distribution for 30 mD. 69 To calculate the resulting permeability, we used the average permeability for a linear flow, where each pore throat radius represents a permeability in the linear flow: 𝐾 ̅ = 𝐿 𝑡 ∑ 𝐿 𝑗 𝐾 𝑗 𝑛 𝑗 =1 (6.4) The calculations are presented below for the distribution shown in Figure 12: Table 15: 30 mD Overall Permeability Calculations ri (cm) Length ki (md) L/K 0.00007 1 12.41 0.08 0.00008 1 16.21 0.06 0.00009 3 20.52 0.15 0.0001 25 25.33 0.99 0.00011 43 30.65 1.40 0.00012 23 36.48 0.63 0.00013 3 42.81 0.07 0.00014 1 49.65 0.02 0.00015 1 57.00 0.02 0.00016 1 64.85 0.02 0.013 1 428,108 2.34E-06 103.00 Sum L/K 3.43 K_total 30.0 Now if we assume that the pore throats clog because of asphaltene deposition, then we will have a total blockage, which is not in line with the literature. However, if that blockage can be partial, up to a limit of half of the smallest pore in the pore distribution, then we can calculate the resulting permeability as a function of the asphaltene saturation, as shown in the sample below for a layer of 0.00001 cm thick. 70 Table 16: Sample Asphaltene Saturation Impact on Overall Permeability Calculations Film Thickness Asphaltene Saturation 0.00001 0.55% Length ki (md) L/K Volume 0.00005 1 6.33 0.16 7.85398E-09 0.00006 1 9.12 0.11 1.13097E-08 0.00007 3 12.41 0.24 4.61814E-08 0.00008 25 16.21 1.54 5.02655E-07 0.00009 43 20.52 2.10 1.09422E-06 0.0001 23 25.33 0.91 7.22566E-07 0.00011 3 30.65 0.10 1.1404E-07 0.00012 1 36.48 0.03 4.52389E-08 0.00013 1 42.81 0.02 5.30929E-08 0.00014 1 49.65 0.02 6.15752E-08 0.01298 1 426,792 0.00 0.000529297 103.00 Sum L/K 5.22 0.000531956 K_total 19.72 If the same calculations are repeated for different thicknesses of the asphaltene layer, we can represent the permeability reduction factor as a function of the asphaltene saturation as depicted in Figure 13. Figure 13 : Permeability Reduction of 30 mD Rock due to Throats Partially Plugging. 71 And if we again repeat the calculations for a different rock of higher permeability, we expected the same behavior. The calculations were repeated for a 300 mD rock, the permeability reduction factor as a function of the asphaltene saturation as depicted below in Figure 14 for 300 mD and 30 mD rocks: Figure 14: Permeability Reduction of 300 mD Rock due to Throats Partially Plugging. 72 Chapter 7: Gas Flood Simulations 7.1. Introduction To streamline the multiphase simulator, we replicated multiple 1D models under different pressure conditions in order to determine the range of the asphaltene component K- values at different pressures. Once established, the K-values were arranged in a table format, or correlated to both pressure and CO2 or any selected component(s) from the injected gas composition. The range of the K-values is narrow, which helps in establishing a lookup arrangement or a correlation specific to the reservoir fluid and injected gas combination. 7.2. 1D Model Setup Using the full multiphase flash algorithm, a 1D reservoir simulation was performed to establish the variation in the asphaltene component K-values. The model is shown in Figure 15: Figure 15: One-Dimension Simulation Model. First, the model was created as one dimension. The gas injector on the left side was set to sustain a certain injection flow rate; the producer, on the right side, was set to maintain a fixed pressure. The porosity was constant at a value of 20%, and a constant 1 2 3 ………………………… ………………………… ………………………… ………………………… 158 159 160 0.1875 m 3 m wide and 3 m deep 73 permeability of 30 mD was used. The connate water saturation was fixed at 0.20 (irreducible water saturation). The relative permeability of Sherafati et al. (2014) was adopted in this work. The injected gas, along with the reservoir fluid under consideration, as detailed in Table 12, was used to initialize the simulator, while the back pressure on the producing well was held at 117.5 bar, and the injector well was injecting at 2.25 reservoir cubic meters per day. Subsequent to the 1D displacement calculation, the resulting K-values were correlated to a key component of the injected gas (e.g. CO2). One pore volume of gas/CO2 was injected over an 8-day period. 7.3. 1D Displacement Calculations One dimensional simulations were performed using CO2 and separator gas to investigate the behavior of the asphaltene component (K-values) along the displacement length, and to identify a good indicator for predicting the K-values via correlations. 7.3.1. 1D Simulation of CO2 Injection First, we considered the injection of CO2 at a rate of 2.25 Rm 3 /day (reservoir cubic meter per day) and a back pressure of 117.5 bar. The results of the CO2 displacement calculation were compiled to identify indicators to correlate the asphaltene K-values. Figure 16 illustrates the asphaltene saturation and the asphaltene component K-values from the 1D displacement calculation at different times (0.04, 0.21 and 0.29 PVI) during the flood. Figure 17 shows the pressure and the gas saturation profile along the length of the 1D domain. 74 Figure 16: Asphaltene Saturations and the Corresponding K-values for CO2 Injection in 1D. Figure 17: Pressure Profiles and Gas Saturation Profiles for Injection of CO2. 75 Next, we selected a component to correlate the K-values. The obvious choice, in this case, was the CO2 concentration in the cell. Figure 18 shows the correlation of the K- values versus CO2 concentration. Figure 18: Asphaltene Component K-value Versus CO2 Mole Fraction in the Simulation Cell. Figure 19 shows the same asphaltene K-values plotted on a log (base 10) scale which also produces a smooth curve. There are multiple curves from which to choose; however, if the intent is to reach the upper bound of the simulation one would use the high values curve. Correlations based on the curves above provide an envelope of boundaries of the asphaltene phase. In this work, we used the more conservative approach to show upper limits of that phase. The correlated K-values from PVI=0.33 along with the equation are shown in Figure 20, which displays a good match to full multiphase simulation. 76 Figure 19: Asphaltene Component K-values Versus CO2 Mole Fraction in the Simulation Cell (Semi-Log base 10 Scale). Figure 20: Calculated and Correlated K-values Versus Mole Fraction of CO2. 77 7.3.2. 1D Simulation of Separator Gas Injection In a second case, separator gas was injected to displace the oil in the 1D model. The results were, again, compiled to identify indicators to correlate the asphaltene K-values. Figure 21 conveys the asphaltene saturation and the asphaltene component K-values from separator gas flood in the 1D model at different times (0.04 ,0.21 and 0.29 PVI) during displacement calculation. Figure 21: Asphaltene Saturations and the Corresponding K-values for Separator Gas Injection. Next, we needed to select a component to correlate the K-values. There was not an obvious choice in this case, but methane or CO2 were potential candidates. Figure 22 below shows the K-values of the asphaltene as a function of the overall C1 concentration, while Figure 23 reports the K-values as a function of the CO2 concentration. 78 Figure 22: Asphaltene Component K-value Versus Methane (C1) in the Simulation Cell. Figure 23: Asphaltene Component K-values Correlated with CO2 in the Simulation Cell. 79 These Figures demonstrate that the K-values of the asphaltene do not correlate well with the methane and CO2 concentrations, as the mapping between concentration and K- values is non-unique. To arrive at better a correlation of the asphaltene K-values for the separator gas displacement calculations, several other components, and their combinations, were investigated. Figure 24 denotes the K-values as a function of the C7-C25 group of components in the feed. Figure 24: Asphaltene Component K-values Correlated with C7-C25 in the Feed. The relationship is relatively smooth but has a discontinuity around a mole fraction of 0.225 at later times. To overcome that issue, we chose a curve at an earlier time and avoided the discontinuity. However, that will result in an underestimation of the 80 asphaltene saturation at later times. It is still unclear how to arrive at a better correlation of the asphaltene K-values for the separator gas injection; additional work towards that end is warranted. The fitted K-values were compared to the calculated K-values at PVI = 0.33 in Figure 25, below. The fit was made over four different ranges of the total C7-C25 mole (x) fraction as follows: Range Fit 0.09729 ≤ C7-C25 ≤ 0.15590 K= 715+(965-715)/(0.15590-0.09729)*(x-0.09729) 0.15590 <C7-C25 ≤ 0.16885 K=965 0.16885 < C7-C25 ≤ 0.24000 K=965-(965-540)/(0.24-0.16885)*(x-0.16885) 0.24000 < C7-C25 ≤ 0. 27772 K= 540-(540-432)/(0.25841-0.24)*(x-0.24) 0. 27772 < C7-C25 ≤ 0.38000 K= 432 Any other value K=415 Figure 25: Fitted K-values and Multiphase Simulated Versus Mole Fraction of C7-C25. 81 7.4. 1D Simulation with Simplified Flash Calculations To validate the use of the simplified equilibrium calculations, based on correlated K- values for the asphaltene component, we compared the accuracy and efficiency of the proposed hybrid formulation in a 1D model before investigating the behavior in 2D. We limited our focus to the CO2 injection process. Figure 26 below shows the asphaltene and gas saturations along the displacement length of the 1D domain as calculated by the full multiphase flash module and the proposed hybrid formulation. . Figure 26: Asphaltene and Gas Saturations during CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid Multiphase). The streamlined simulation reproduced, with relatively good accuracy, both the saturation of the gas and the saturation of the asphaltene. However, that simplified approach overestimated the asphaltene saturations slightly, at early times, due to the selected 82 correlation (K-values at a later time). Figure 26 also illustrates that the correlated K-value simulation overestimated the gas saturations towards the leading edge of the flood, irrespective of the K-value correlation used. That is because the flash algorithm based on the two-phase flash used in the correlated K-value simulation will always overestimate the saturation as it does not account for the asphaltene phase separation in the equilibrium calculations. To correct that behavior, we repeated the displacement calculation and removed the asphaltene component from the feed before the two-phase equilibrium calculations were performed, and arrived at the results shown in Figure 27, following. Figure 27: Asphaltene and Gas Saturations during CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid w/o Asphaltene Multiphase). This time, the saturation profile with the simplified simulation shows a delayed start of the position of the gas saturation profile. The simplified approach underestimated the 83 asphaltene saturations. The Figure also demonstrates that the correlated K-value simulation underestimated the gas saturations throughout the length regardless of the K- value correlation used. That is primarily because the flash algorithm based on two-phase flash without asphaltene used in the correlated K-value simulation will always underestimate the saturation, as the asphaltene phase will contain some light end components as well. Consequently, we reverted to the earlier formulation where asphaltene is kept in the two-phase flash calculation. Figure 28 allows a more focused view of Figure 27; it shows the envelope of the asphaltene saturations based on the different correlated K-vales. Figure 29 examines the variation of the oil density and the gas saturation along the length of the domain. There is a link, but not as obvious as that shown in Figure 30, which indicates oil density and asphaltene saturation. 84 Figure 28: Asphaltene Saturations during CO2 Injection at PVI=0.08 & 0.33 (Full & Hybrid Multiphase). Figure 29: Oil Density and Gas Saturations along the 1D Length at PVI=0.08 & 0.33 (Full & Hybrid Multiphase). 85 Figure 30 illustrates that the oil density is high where the asphaltene separates from it. That is consistent with observations reported in the literature, where it was noticed that as light paraffin was extracted from the oil by the injected CO2, the oil became denser and the asphaltene started to drop out of solution. Figure 30: Oil Density and Asphaltene Saturations along the 1D Length at PVI=0.08 & 0.33 (Full & Hybrid Multiphase). To further investigate the dynamics of the displacement process and the location of the precipitated asphaltene, we selected three cells along the displacement length. Displacement calculation with 1.68% wt. and 3.86% wt. asphaltene were considered. The selected cells included the first cell (injection point), a cell located at 25% of the length, 86 and another at 50% of the length. Figures 31 and 32 show the gas, oil and asphaltene saturations versus pore volumes injected for the three cells. The expected behavior is that asphaltene saturation will show before gas saturation because the upper AOP is crossed first. Figures 31 and 32 affirm that assumption. Earlier simulations have shown that when hydrocarbon gas is injected, the gas breakthrough takes place sooner than in the case of CO2 injection. We have changed the gas from CO2 to pure methane (C1); Figures 31 and 32 are reproduced as Figures 33 and 34 using the newly injected gas simulations. For methane, the gas saturation starts at a PVI value less than that of the CO2 injection. Figure 31: First, 1/4 th of the Length and Midpoint Cell Saturations (1.68% wt. Asphaltene Crude) during CO2 Injection. 87 Figure 32: First, 1/4 th of the Length and Midpoint Cell Saturations (3.86 % wt. Asphaltene Crude) during CO2 Injection. Figure 33: First, 1/4 th of the Length and Midpoint Cell Saturations (1.68% wt. Asphaltene Crude) Flooded by C1. 88 Figure 34: First, 1/4th of the Length and Midpoint Cell Saturations (3.86% wt. Asphaltene Crude) Flooded by C1. Figure 35: Asphaltene and Gas Saturations during Separator Gas Injection at PVI=0.08, 0.25 & 0.33 (Full & Hybrid Multiphase). 89 In the case of the separator gas flood displacement, the same remarks and checks hold true. Figure 35 denotes the asphaltene and gas saturations for the displacement using the full multiphase and the newly proposed hybrid formulation simulations. About accuracy, the simplified simulation shows the position of the saturation profile. The simplified approach does overestimate the asphaltene saturations, which is understandable because the upper limit was chosen for correlating the K-values, in addition to a correlation chosen based upon an earlier time from the 1D displacement. The modified method for 1D takes 2.8 minutes to complete the simulation, which is less than the full multiphase simulation, which requires 7 minutes to complete. That translates into a time saving of over 60%. 7.5. Simulation of Gas Injection into Homogeneous 2D Reservoir We employed a two-dimensional homogeneous reservoir model that helped us to establish the effectiveness of the new hybrid formulation. We used ¼ of an inverted 5- Spot CO2 injection pattern. It is 50 by 50 cells, as seen in Figure 36, and the grid and cell block dimensions are displayed. The permeability is 30 mD and porosity is 20%. 90 Figure 36: 2D Homogeneous Reservoir Model. The reservoir temperature was 363.15 K and the initial reservoir pressure 11.8 MPa; the producer was maintained at 11.75 MPa. The CO2 injector was held at the constant rate of 11.25 Rm3/day. We used an IMPEC finite difference compositional approach to simulate the reservoir flow dynamics. To evaluate the effectiveness of the proposed hybrid formulation, we checked the accuracy of our new method, compared it to the full simulation displacement, and considered the time required to perform the simulation for the same reservoir model. 7.5.1. CO2 Injection Figures 37 and 38 below show the asphaltene saturation during the displacement, followed by the gas saturation for the full multiphase simulation displacement. 91 High Asphaltene Saturation Low Figure 37: Asphaltene Saturations during CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase). The maximum asphaltene saturation is aligned with gas flow, the zone of CO2 mixing with the fresh oil deposited the maximum asphaltene. As the high asphaltene saturation ring expands, the intensity of the asphaltene saturation is reduced. The front continues to grow in size. Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 92 High Gas Saturation Low Figure 38: Gas Saturations during CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase). The above simulation was performed on a laptop running Intel Core i7-5500U CPU @ 2.40 GHz. Figures 39 and 40, following, illustrate the asphaltene saturation during the displacement, then followed by the gas saturation using our proposed hybrid formulation. Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 93 High Asphaltene Saturation Low Figure 39: Asphaltene Saturations during CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values). The simulation using the same laptop was faster; there was more than 82% saving in time. The streamlined simulation shows the accurate position of the saturation profile. The method does overestimate the asphaltene saturations, but as those saturations are low, the overestimate is visible. Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 94 High Gas Saturation Low Figure 40: Gas Saturations during CO2 Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values). At the end of 320 days, the average asphaltene saturation throughout the modeled reservoir was 1.12% in the full multiphase displacement simulation. The recovery showed at 41.5%, while the GOR began at 75 and reached 190 by the end of the process. Our simplified approach averaged asphaltene saturation at 1.15%, the recovery was 41%, and the GOR started at 75 and reached 99 at the end of the simulation. Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 95 7.5.2. Separator Gas Injection Figures 41 and 42 display the asphaltene saturation during the displacement, followed by the gas saturation for the full multiphase simulation. High Asphaltene Saturation Low Figure 41: Asphaltene Saturations during Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase). We observed the same pattern as before, wherein the asphaltene saturation was aligned with gas flow, the zone of separator gas mixing with the fresh oil deposited less asphaltene than the trailing end of the front, where the asphaltene deposition was the highest. As the high asphaltene saturation ring expands, the intensity of the asphaltene saturation front does not change but continues to grow in size. Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 96 High Gas Saturation Low Figure 42: Gas Saturations during Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Full Multiphase). The above simulation was performed on a laptop running Intel Core i7-5500U CPU @ 2.40 GHz. Figures 43 and 44 show asphaltene saturation during the displacement, followed by the gas saturation using the newly proposed hybrid formulation. Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 97 High Asphaltene Saturation Low Figure 43: Asphaltene Saturations during Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-values). The simulation using the same laptop was faster; there was more than 78% saving in the simulation time and shows the position of the saturation profile. Our simplified approach does underestimate the asphaltene saturations, but the saturations are low, and therefore clearly visible. This is due to choosing a correlation based on an earlier time from the 1D displacement. Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 Asphaltene Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation up to 2% 2 4 6 8 10 0.5 1 1.5 0 0.005 0.01 0.015 0.02 98 High Gas Saturation Low Figure 44: Gas Saturations during Separator Gas Injection at PVI=0.09, 0.18, 0.27 & 0.36 (Correlated K-Values). After 320 days, the average asphaltene saturation throughout the modeled reservoir was 1.12% in the full multiphase displacement simulation, the recovery was 41.5%, while the GOR started at 75 and reached 190 at the end. Our streamlined approach averaged 1.12%, the recovery was 41.7%, and the GOR began at 75 and was 200 at the end of the simulation. Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Gas Saturation up to 80% 2 4 6 8 10 0.5 1 1.5 0 0.2 0.4 0.6 0.8 99 7.6. 2D CO2 Injection in Homogeneous Reservoir with Permeability Reduction At this juncture, we utilized two different crudes, one more asphaltic than the other, and gauged the impact of the permeability reduction on the simulation. Using the more asphaltic crude at 3.86% wt., which starts with the asphaltene phase, and is then flooded by CO2. The asphaltene saturations and pressure differences are shown in Figures 45 and 46, respectively. Asphaltene Saturation Change Increase No Change Decrease Figure 45: Asphaltene Saturation Differences for the Simulation Using Perm Reduction Factor and One Without Perm Reduction at Different PVI's for 3.86% wt. Asphaltene Crude. Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 100 Pressure Increase (bar) High Increase No Change Figure 46: Pressure Difference for the Simulation Using Perm Reduction Factor and One Without Perm Reduction at Different PVI's for 3.86% wt. Asphaltene Crude. The pressure is increasing following the asphaltene phase, therefore the pressure increases at the injector, the asphaltene phase is lessened in the permeability reduction formulation due to the increase in pressure and thus a reduced asphaltene phase. The corresponding permeability multipliers in the case of 3.86% wt. asphaltene displacement is shown in Figure 47, whereas the total mobility is seen in Figure 48. Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map 0 to +7 bar 2 4 6 8 10 0.5 1 1.5 0 1 2 3 4 5 6 7 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map 0 to +7 bar 2 4 6 8 10 0.5 1 1.5 0 1 2 3 4 5 6 7 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map 0 to +7 bar 2 4 6 8 10 0.5 1 1.5 0 1 2 3 4 5 6 7 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map 0 to +7 bar 2 4 6 8 10 0.5 1 1.5 0 1 2 3 4 5 6 7 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map 0 to +7 bar 2 4 6 8 10 0.5 1 1.5 0 1 2 3 4 5 6 7 101 Permeability Multiplier No/Low Reduction in Perm. Maximum Reduction Figure 47: Permeability Multiplier for 3.86% wt. Asphaltene Crude. Total Mobility (Viscosity in Pa-s) High Mobility Low Mobility Figure 48: Total Mobility for 3.86% wt. Asphaltene Crude (Viscosity in Pa-s). Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 5000 2 4 6 8 10 0.5 1 1.5 0 5000 10000 15000 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 5000 2 4 6 8 10 0.5 1 1.5 0 5000 10000 15000 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 5000 2 4 6 8 10 0.5 1 1.5 0 5000 10000 15000 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 5000 2 4 6 8 10 0.5 1 1.5 0 5000 10000 15000 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 5000 2 4 6 8 10 0.5 1 1.5 0 5000 10000 15000 102 When one uses the original Rydhal crude, which starts without an asphaltene phase and is flooded by CO2, the absolute permeability changes significantly. Those asphaltene saturations and pressure differences are demonstrated in Figures 49 and 50, respectively. The corresponding permeability multipliers for the Rydhal original crude displacement are indicated in Figure 51, and the total mobility is seen in Figure 52. Asphaltene Saturation Change Increase No Change Decrease Figure 49: Asphaltene Saturation Difference for the Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI’s For Original Rydhal Crude. Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -3 -2 -1 0 1 2 3 x 10 -3 103 Pressure Change (bar) Increase No Change Decrease Figure 50: Pressure Difference for the Simulation Using Perm Reduction Factor and the One Without Perm Reduction at Different PVI's for Rydhal Original Crude. Permeability Multiplier No/Low Reduction in Perm. Maximum Reduction Figure 51: Permeability Multiplier for Rydhal Original Crude. Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map -0.2 to +0.2 bar 2 4 6 8 10 0.5 1 1.5 -0.2 -0.1 0 0.1 0.2 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map -0.2 to +0.2 bar 2 4 6 8 10 0.5 1 1.5 -0.2 -0.1 0 0.1 0.2 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map -0.2 to +0.2 bar 2 4 6 8 10 0.5 1 1.5 -0.2 -0.1 0 0.1 0.2 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map -0.2 to +0.2 bar 2 4 6 8 10 0.5 1 1.5 -0.2 -0.1 0 0.1 0.2 Pressure Difference Map at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Pressure Difference Map -0.2 to +0.2 bar 2 4 6 8 10 0.5 1 1.5 -0.2 -0.1 0 0.1 0.2 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 Permeability Multiplier at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Permeability Multiplier 0.2 to 1 2 4 6 8 10 0.5 1 1.5 0.2 0.4 0.6 0.8 1 104 Total Mobility (Viscosity in Pa-s) High Mobility Low Mobility Figure 52: Total Mobility for Rydhal Original Crude (Viscosity in Pa-s). Figure 53: Average Reservoir Pressure for Original & 3.86% wt. Asphaltene Fluids. Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 31000 2 4 6 8 10 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 x 10 4 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 31000 2 4 6 8 10 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 x 10 4 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 31000 2 4 6 8 10 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 x 10 4 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 31000 2 4 6 8 10 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 x 10 4 Total Mobility at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.18 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Total Mobility at PVI=0.36 10 20 30 40 50 10 20 30 40 50 Total Mobility 0 to 31000 2 4 6 8 10 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 x 10 4 105 The average reservoir pressures for the displacement calculations above are indicated in Figure 53. Upon a closer examination of the case with more asphaltic crude (3.86% wt. asphaltene), one can see that the recovery is somewhat higher in the case with permeability reduction, at 70.36% after injecting one pore volume, as opposed to the recovery without permeability impairment, which is 68.23%, The permeability impairment also delays the gas breakthrough by about 3% pore volume. The average pressure of the reservoir drops more quickly without the permeability impairment. Figure 54 depicts the average pressure and recovery in the case of a 2D homogenous reservoir simulation. Figure 54: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Homogenous Reservoir Using 3.86% wt. Asphaltene Crude. 106 7.7. CO2 Injection in 2D Heterogenous Reservoir – Areal Variation The 2D simulation was repeated but this time in a heterogenous reservoir using the crude oil with 3.86% wt. asphaltene. The natural log permeability distribution is seen in Figure 55; the distribution is adopted from (Sherafati and Jessen, 2015). Figure 56 portrays the average pressure and recovery for the 2D heterogenous reservoir simulation. Permeability Distribution in Ln(mD) High Perm Low Perm Figure 55: Natural log Permeability Distribution of Heterogenous Reservoir in Ln (mD). 10 20 30 40 50 5 10 15 20 25 30 35 40 45 50 2 3 4 5 6 7 8 107 Figure 56: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Heterogenous Reservoir Using 3.86% wt. Asphaltene Crude. As seen above, the recovery is higher with permeability impairment, at 64.81% after injecting one pore volume, as opposed to the case without permeability impairment, at 59.88%. The recovery is less than that of the homogenous reservoir, but the difference between the recoveries is greater. The permeability impairment case recovery is about 2% higher than that without permeability impairment in the homogenous simulation. However, in the heterogenous simulation, the difference is about 5% more in favor of the permeability impairment, which also delayed the gas breakthrough by about 9% pore volume. And the average pressure of the reservoir drops sooner in the scenario without the permeability impairment in contrast to the case with the impairment. 108 Figure 57 indicates the difference in asphaltene saturation at the same PVI's; permeability impairment leads to a higher pressure which in turns means less asphaltene. The gas saturation for this displacement is shown in Figure 58 below. It confirms the contribution of the permeability impairment of holding back the gas. Asphaltene Saturation Change Increase No Change Decrease Figure 57: Asphaltene Saturation Difference for the Simulation With/Without Perm Reduction Factor. Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 109 Gas Sat at PVI=0.09, 0.27, 0.45 and 1 Gas Sat at same PVI but w/ perm. Red. High Gas Saturation Low Figure 58: Gas Saturation for Heterogenous Reservoir with and without Permeability Impairment. Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=1 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=1 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=1 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Gas Saturation at PVI=1 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 Permeability Impairment 10 20 30 40 50 10 20 30 40 50 110 7.8. CO2 Injection in 2D Heterogenous Reservoir - Vertical Variation A new 2D simulation was completed in a heterogenous reservoir with a vertical variation using crude oil with 3.86% wt. asphaltene. The natural log permeability distribution is shown in Figure 59; the distribution is adopted from (Sherafati and Jessen, 2015). Figure 60 illustrates the average pressure and recovery in the case of the 2D heterogenous reservoir with vertical variation simulation. Figure 59: Natural Log Permeability Distribution in Vertical Direction of Heterogenous Reservoir in Ln (mD). Figure 60: Average Reservoir Pressure, Recovery and Gas Breakthrough for 2D Heterogenous Reservoir (Vertical Variation) Using 3.86% wt. Asphaltene Crude. 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 3 4 5 6 7 111 Unlike the earlier simulation, the recovery is higher without the permeability impairment, at 72.29%, in contrast to the case with permeability impairment, which is 63.74% after injecting one pore volume. The average pressure of the reservoir is almost the same for both cases. The permeability impairment case speeded up the gas breakthrough by about 9% pore volume, but the recovery was about 9% less than in the case without permeability impairment. The gas saturation for this displacement is shown below in Figure 61. It indicates the contribution of the permeability impairment in steering the gas towards the high permeability region, and the production well. Figure 62 shows the difference in Asphaltene saturation at the same PVI's; as the pressures are not significantly higher, the permeability impairment leads to higher contact with oil, which in turns means more asphaltene. Gas Sat at PVI=0.09, 0.27, 0.45 and 1 Gas Sat at same PVI but w/ perm. Red. High Gas Saturation Low Figure 61: Gas Saturation for Heterogenous Reservoir (Vertical Variation) with and without Permeability Impairment. Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 5 10 15 20 25 30 35 40 45 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.09 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.27 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=0.45 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 Gas Saturation at PVI=1 with Permeability Impairment 5 10 15 20 25 30 35 40 45 50 2 4 6 8 10 112 Asphaltene Saturation Change Increase No Change Decrease Figure 62: Asphaltene Saturation Difference for the Simulations With/Without Perm Reduction Factor (Vertical Variation). 7.9. Discussion The above results show that the newly proposed hybrid formulation was more accurate in the case of a CO2 flooding than in the separator gas flood. That is mainly due to the weak link when attempting to correlate C1 for the separator gas for the asphaltene component K-values; we used C7-C25 component instead. Whereas, with the CO2 flooding there was a strong link between CO2 in the feed gas and the asphaltene component K-values. Nevertheless, the correlated separator gas simulation showed the general asphaltene area, which tallies with the full simulation model. Another interesting finding was that the CO2 flooding showed a narrower asphaltene dropout region as compared to the separator gas; however, the average asphaltene saturation for the reservoir was the same for both the separator gas and the CO2 flood Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 2 4 6 8 10 Asphaltene Sat. Diff. -0.1% to +0.1% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 2 4 6 8 10 Asphaltene Sat. Diff. -0.1% to +0.1% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 10 20 30 40 50 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 10 20 30 40 50 Asphaltene Sat. Diff. -0.3% to +0.3% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 2 4 6 8 10 Asphaltene Sat. Diff. -0.1% to +0.1% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.09 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.27 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=0.45 10 20 30 40 50 2 4 6 8 10 Asphaltene Saturation Difference due to Perm. Red. at PVI=1 10 20 30 40 50 2 4 6 8 10 Asphaltene Sat. Diff. -0.1% to +0.1% 2 4 6 8 10 0.5 1 1.5 -0.01 -0.005 0 0.005 0.01 113 displacements. That is in conflict with many researchers, who claim that CO2 will drop more asphaltene than hydrocarbon gas. The asphaltene saturation profile for a CO2 injection case seems to move, while for the separator gas the asphaltene profile seems to build up. In both the CO2 and separator gas floods, the asphaltene region was becoming wider as the flood progressed, the difference being that with the separator gas the region was growing considerably faster than the CO2 flood. Also, the highest asphaltene saturation was in the middle of the asphaltene region for the CO2, while for the separator gas the highest asphaltene saturation was at the trailing end. Another interesting finding was that gas breakthrough occurs more quickly when the flooding gas is separator gas, not CO2. The hybrid simulation showed the position of the saturation profile with relatively good accuracy; the correlated K-value simulation overestimated the gas saturation towards the leading edge of the flood irrespective of the K-value correlation that was used. The permeability impairment from asphaltene causes the pressure to increase after the asphaltene phase, and consequently, the pressure also increases at the injector; therefore, the asphaltene phase is lessened, which contributes to a delayed gas breakthrough and a higher recovery. The same holds true for homogenous and heterogenous 2D reservoirs. In the heterogenous reservoir with vertical variations, the permeability impairment resulted in diverting the gas towards the higher permeability side of the reservoir, as such for the permeability distribution considered, the gas broke through sooner, and the overall recovery was less. 114 7.10. Conclusions Based on the simulation and analysis presented, we arrived at the following significant conclusions: 1. It is possible to simplify the multiphase flash calculation and retain good accuracy when the gas used is predominantly CO2. 2. The simplified multiphase calculation can reduce the simulation time by more than 50%. 3. The asphaltene saturation is more intense with the CO2 than the hydrocarbon gas. 4. Separator gas is likely to cause the same, if not more, asphaltene precipitation as compared to CO2, but spread over the entire length of the reservoir. 5. A gas breakthrough occurred faster when the flood simulation was carried using separator gas. 6. The simplified approach overestimated the asphaltene saturation, but the saturation was very low. 7. Asphaltene saturation is dependent upon the asphaltene content in the crude oil; the higher the asphaltene content, the higher the permeability impairment. 8. The heterogeneity of the reservoir leads to less recovery when compared with the homogenous reservoir. 9. The permeability impairment could help to recover more in a heterogeneous reservoir based on the permeability distribution. 10. One should consider an increase in the injection pressure as asphaltene drops out, and permeability starts to reduce. 115 Chapter 8: Summary and Future Research Directions We have launched a novel approach to estimate the loss of permeability due to the formation of an asphaltene-rich phase. That loss can easily be linked to the asphaltene saturation and calculated, in conjunction with other properties, before the simulator solves the flow equations. It will become an important refinement of existing simulation tools when the forward simulation that does not account for the permeability loss starts to depart from actual field production observations. An innovative hybrid formulation was introduced to replace the full multiphase calculations at a CPU requirement that is comparable to two-phase equilibrium calculations. Our fresh formulation was tested and validated against the full multiphase compositional simulator, and arrived at an excellent agreement. We developed a detailed four-phase compositional simulator (gas /oil /asphaltene /water) to predict the asphaltene precipitation during CO2 and hydrocarbon gas injection processes. We have quantified the asphaltene phase saturation and identified the deposition locations for a range of displacement scenarios. As part of the meticulous analysis, several factors influencing the asphaltene deposition dynamics were addressed. The proposed approaches are straightforward and can be implemented in existing simulation tools without delay. We show the pathway to allow for more thorough studies of asphaltene precipitation and related production challenges. 116 8.1. Absolute Permeability Reduction Research has confirmed that asphaltene causes permeability loss. However, as suggested by Nghiem et al. (2000) and Kord et al. (2014), the reduction in absolute permeability occurs up to certain limits. There remains a need to conduct studies and experiments to establish the minimum permeability for a given displacement process. Figure 63 shows limits ranging from below 0.002 to about 0.1 permeability ratios: Figure 63: Different Permeability Reduction Ratios due to Asphaltene as Reported by Kord et al. (2014). Core flooding experiments usually involve two or three phases, which could mask the effect of the permeability loss attributed solely to asphaltene deposition. Therefore, we must design a proper experiment to investigate the absolute permeability reduction. The 117 experiment should be conducted on a single-phase fluid containing asphaltene circulated through the core. That trial should be performed at different back pressures, ranging from above the upper asphaltene onset pressure (AOP) to a value just above the bubble point pressure. The experiment would provide a direct link between the pressure drop across the core and the asphaltene deposition. The reservoir fluid sample would undergo static PVT testing to establish the AOP, and other properties, as deemed needed for an accurate interpretation of the displacement experiment(s). 8.2. Accurate Fluid Description Crude oil analysis regarding asphaltene, as reported by many laboratories, does not provide all the required parameters for input to a simulator. Accordingly, many authors suggest ways in which to characterize the fluids to be used in subsequent displacement calculations. That classification, coupled with the normal PVT tests, will help to condition the fluid description and the simulator to reproduce the PVT tests. Unfortunately, there is no asphaltene PVT test that can be used to tune the asphaltene component to reproduce the asphaltene PVT experiment. Frequently, asphaltene is reported as a weight percent with no specific PVT properties. For example, in the literature, one finds a wide array of properties for critical parameters and even molecular weight (MW). MW can range from a few thousand up to millions. There is a clear need to develop new PVT tests to promote accurate characterization of asphaltene. 118 Nomenclature 𝑔 ⃗ Gravitational vector 𝑘 𝑟𝑔 Gas relative permeability 𝑘 𝑟𝑜𝑔 Oil relative permeability in an oil-gas system 𝑘 𝑟𝑜 Oil relative permeability 𝑘 𝑟𝑜𝑤 Oil relative permeability in an oil-water system 𝑘 𝑟𝑜𝑤𝑚𝑎𝑥 Oil maximum relative permeability in an oil-water system 𝑘 𝑟𝑤 Water relative permeability 𝑛 Number of moles 𝑛𝑝 Number of phases 𝑝 Pressure 𝑅 Universal gas constant 𝑆 Saturation 𝑆 𝑔𝑛𝑜𝑟 Normalized gas saturation 𝑆 𝑔𝑟 Residual gas saturation 𝑆 𝑜𝑚 Residual oil saturation in an oil-water-gas system 𝑆 𝑜𝑛𝑜𝑟 Normalized oil saturation 119 𝑆 𝑤𝑐 Connate water saturation 𝑆 𝑤𝑛𝑜𝑟 Normalized water saturation 𝑡 Time 𝑇 Temperature 𝑣 Velocity 𝑥 𝑖𝑗 Mole fraction of component i in phase j 𝑧 Feed Composition 𝛽 Phase fraction 𝜇 Viscosity 𝜌 Density 𝜑 Fugacity 𝜙 Porosity (%) 120 References A. R. Awan, R. Teigland and J. 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Creator Al-Ghanem, Fahad Abdulla (author)

Core Title Asphaltene deposition during co₂ injection in enhanced oil recovery applications

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Petroleum Engineering

Publication Date 07/18/2017

Defense Date 03/22/2017

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

Tag asphaltene,CO₂,EOR,four-phase compositional simulator,hybrid simulator,injection,loss of permeability,multiphase compositional simulation,OAI-PMH Harvest,precipitation,simplified multiphase equilibrium calculations

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Jessen, Kristian (committee chair), de Barros, Felipe (committee member), Ershaghi, Iraj (committee member)

Creator Email alghanem@usc.edu,fghanem@kockw.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-401718

Unique identifier UC11263293

Identifier etd-AlGhanemFa-5534.pdf (filename),usctheses-c40-401718 (legacy record id)

Legacy Identifier etd-AlGhanemFa-5534.pdf

Dmrecord 401718

Document Type Dissertation

Rights Al-Ghanem, Fahad Abdulla

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA