Advances in calculation of minimum miscibility pressure

I would like to express my deepest gratitude to my supervisor, Professor Russell T. Johns, who contributed immensely to my education and research throughout my studies at UT Austin. It was my privilege to be his student and to complete my studies under his supervision. I would like to thank my research committee, Drs. Bryant, DiCarlo, Dindoruk, and Sepehrnoori, who have further enriched this dissertation with their suggestions and comments. I am also grateful for the feedback I received from Kristian Mogensen at Maersk regarding PennPVT calculations. His feedback led to new perspectives related to the subject of this dissertation and formed the basis of Chapter 4. The funding of this research was provided by Gas Flooding JIP. I sincerely thank Gas Flooding JIP and its industry affiliates for their financial support, and for investing on fundamental research in the field of Petroleum Engineering

Copyright by Kaveh Ahmadi Rahmatabadi 2011 The Dissertation Committee for Kaveh Ahmadi Rahmatabadi Certifies that this is the approved version of the following dissertation: Advances in Calculation of Minimum Miscibility Pressure Committee: Russell T Johns, Supervisor Steven L Bryant David DiCarlo Birol Dindoruk Kamy Sepehrnoori Advances in Calculation of Minimum Miscibility Pressure by Kaveh Ahmadi Rahmatabadi, B.Sc.; M.Sc Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy The University of Texas at Austin May 2011 “Until you attain the truth, you will not be able to amend it But if you not amend it, will not attain it Meanwhile, not resign yourself.” from The Book Exhortations* * Jose Saramago, the History of the Siege of Lisbon Acknowledgements I would like to express my deepest gratitude to my supervisor, Professor Russell T Johns, who contributed immensely to my education and research throughout my studies at UT Austin It was my privilege to be his student and to complete my studies under his supervision I would like to thank my research committee, Drs Bryant, DiCarlo, Dindoruk, and Sepehrnoori, who have further enriched this dissertation with their suggestions and comments I am also grateful for the feedback I received from Kristian Mogensen at Maersk regarding PennPVT calculations His feedback led to new perspectives related to the subject of this dissertation and formed the basis of Chapter The funding of this research was provided by Gas Flooding JIP I sincerely thank Gas Flooding JIP and its industry affiliates for their financial support, and for investing on fundamental research in the field of Petroleum Engineering The outstanding staff of the Petroleum and GeoSystem Engineering department greatly enhanced my research experience at UT They are too many to name; however, I wish to single out Roger Terzian, Nina Schecnk, Glen Baum, and Dori Coy for their constant support v Advances in Calculation of Minimum Miscibility Pressure Publication No. _ Kaveh Ahmadi Rahmatabadi, Ph.D The University of Texas at Austin, 2011 Supervisor: Russell T Johns Minimum miscibility pressure (MMP) is a key parameter in the design of gas flooding There are experimental and computational methods to determine MMP Computational methods are fast and convenient alternatives to otherwise slow and expensive experimental procedures This research focuses on the computational aspects of MMP estimation It investigates the shortcomings of the current computational models and offers ways to improve the robustness of MMP estimation First, we develop a new mixing cell method of estimating MMP that, unlike previous “mixing cell” methods, uses a variable number of cells and is independent of gas-oil ratio, volume of the cells, excess oil volumes, and the amount of gas injected The new method relies entirely on robust P-T flash calculations using any cubic equationof-state (EOS) We show that mixing cell MMPs are comparable with those of other analytical and experimental methods, and that our mixing cell method finds all the key tie lines predicted by MOC; however, the method proved to be more robust and reliable than current analytical methods vi Second, we identify a number of problems with analytical methods of MMP estimation, and demonstrate them using real oil characterization examples We show that the current MOC results, which assume that shocks exist from one key tie line to the next may not be reliable and may lead to large errors in MMP estimation In such cases, the key tie lines determined using the MOC method not control miscibility, likely as a result of the onset of L1-L2-V behavior We explain the problem with a simplified pseudo-ternary model and offer a procedure for determining when an error exists and for improving the results Finally, we present a simple mathematical model for predicting the MMP of contaminated gas Injection-gas compositions often vary during the life of a gasflood because of reinjection and mixing of fluids in situ Determining the MMP by slim-tube or other methods for each possible variation in the gas-mixture composition is impractical Our method gives an easy and accurate way to determine impure CO2 MMPs for variable field solvent compositions on the basis of just a few MMPs Alternatively, the approach could be used to estimate the enrichment level required to lower the MMP to a desired pressure vii Table of Contents Table of Contents viii List of Tables xi List of Figures xiii List of Figures xiii CHAPTER 1: INTRODUCTION 1.1 Description of the Problem .1 1.2 Research Objectives 1.3 Structure of the dissertaion .5 CHAPTER 2: BACKGROUND .7 2.1 MMP and Development of Miscibility in Gas Injection 2.2 Methods of Estimating MMP 2.2.1 Experimental methods for estimating MMP 2.2.1.a Slim-tube experiments 10 2.2.1.b Multiple-contact experiment (mixing cell experiment) 11 2.2.1.c Rising bubble /falling drop experiment 12 2.2.1.d Vanishing interfacial tension (VIT) experiment .14 2.2.1.e Summary 15 2.2.2 Computational method of estimating MMP .16 2.2.2.a Slim-tube simulation .16 2.2.2.b Method of Characteristics (MOC) 18 2.2.2.b.1 Development of the analytical solution for oil and gas displacement 18 2.2.2.c Mixing cell (cell-to-cell) methods 32 2.2.2.c.1 MMP calculation with a single cell 32 2.2.2.c.2 MMP calculation with multiple cells (cell-to-cell) 34 2.3 Summary 39 viii CHAPTER 3: A NEW MULTIPLE MIXING-CELL METHOD OF ESTIMATING MMP41 3.1 A New Multiple Mixing -Cell Model .41 3.2 Examples of MMP Calculations .46 Example 1: Four-Component Condensing/Vaporizing (CV) Displacement 46 Example 2: CO2 Displacement of Ten-Component Oil 48 Example 3: Rich Gas Displacement of Eight-Component Oil .50 3.3 Fast MMP Approximation with New Mixing Cell Method 51 3.4 Discussion .53 3.4.1 The new mixing-cell method does not find the compositional path 53 3.4.2 Mixing-cell method predicted MMP improves with more contacts .54 3.4.3 Impacts of the parameters α and m .55 3.4.4 Key differences from other mixing-cell methods 56 3.4.5 Key advantages of our new mixing-cell method over MOC-based algorithms 57 3.5 Summary 57 CHAPTER 4: LIMITATIONS OF MOC APPROACHES TO CALCULATING MMP 72 4.1 An Improved MOC-based algorithm for Estimating MMP 72 4.2 Limitations of MOC-Based Methods 76 4.2.1 MMP Calculation Discrepancies 76 4.2.2 Bifurcation problem 78 4.2.3 Correction of Component K-Value Ordering Using MOC .86 4.2.4 Other Potential Problems with MOC Approaches .88 4.2.4.a Existence of multiple tie lines 88 4.2.4.b Existence of two roots in constant K-flash 89 4.3 Summary 91 CHAPTER 5: MMP PREDICTION FOR CONTAMINATED CO2 MIXTURES 106 5.1 MMP Contamination Model 106 Example 1: Oil A Displacements .108 ix Example 2: Oil B Displacements .111 5.2 Results and Conclusions .113 CHAPTER 6: SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH 123 6.1 Summary and Conclusions 123 6.2 Recommendations for Future Research 126 Appendices 128 Appendix A: Enhancement to Li-Johns Constant-K Window of Search 128 A.1 Li-Johns Formulation 128 A.2 Examples .131 Appendix B: PennPVT Toolkit 140 Glossary .239 References 242 Vita …………………………………………………………………………….249 x PennPVT Spread sheet and Functions 92 SPE Journal, March 1996, 39-49, SPE 30798 [8]- Y Wang and F M Orr, “Analytical calculation of minimum miscibility pressure”, Fluid Phase Equilibria 139 (1997), 101-124 [9]- K Jessen, M L Michelsen and E H Stenby, “Global approach for calculation of minimum miscibility pressure”, Fluid Phase Equilibria 153 (1998), 251-263 [10]- H Yuan and R T Johns, “Simplified Method for Calculation of Minimum Miscibility Pressure or Enrichment”, SPE Journal, December 2005, 416-424 [11]- K Ahmadi and R T Johns, “Multiple Mixing-Cell Method for MMP Calculations”, SPE 116823-MS (in press - SPE Journal) [12]- K Ahmadi, R T Johns, K Mogensen, R Noman, “Limitations of Current MOC (Method of Characteristic) Methods to Predict MMPs for Complex Gas/Oil Displacements”, 2010 SPE Improved Oil Recovery Symposium, SPE 129709-MS 235 PennPVT Spread sheet and Functions 93 APPENDIX - EQUATION OF STATE PennPVT uses the general form EOS: P= RT a − v (v + δ1b)(v + δ b) From this general form the various form EOS could be found (Table A1) Table A1 EOS δ1 δ2 RK SRK PR + √2 - √2 PR78 + √2 - √2 The program uses a dimensionless form of the above equation that is obtained by following definitions A= aP R 2T B= bP RT Z= Pv RT 236 PennPVT Spread sheet and Functions 94 PennPVT uses van der Waals mixing rule to calculate A and B of a mixture For a mixture with Nc components Nc B = ∑ xi Bi i =1 Nc Nc A = ∑∑ xi x j Aij i =1 j =1 Aij = Aji = Ai Aj (1 − kij ) kij are binary interaction parameter Ai = Ω Pri [1 + m(ωi )(1 − Tri )]2 Tri Bi = Ωbi Pri Tri Ωa and Ωb and m(ωi) are defined in Table A2 for each EOS 237 PennPVT Spread sheet and Functions 95 Table A2 Ωa Ωb m (ω) RK 0.42748 0.08664 SRK 0.42748 0.08661 0.48 + 1.574 ωi - 0.176 ωi2 PR 0.45724 0.0778 0.37464 + 1.54226 ωi - 0.269922 ωi2 EOS PR78 0.45724 0.0778 0.37464 ωi + 1.54226 ωi - 0.269922 ωi3 if ωi < 0.4 else 0.379642 + 1.48503 ωi - 0.164423 ωi2 + 0.016667ωi3 The implicit form of above cubic EOS would be Z − [(δ1 + δ − 1) B − 1]Z + [ A + δ1δ B − (δ1 + δ ) B ( B + 1)]Z − [ AB + δ1δ B ( B + 1)] = And the fugacity coefficient is calculated by B A ⎛ ψ i Bi ⎞ ⎛ Z + δ1 B ⎞ ln φˆi = ( Z − 1) i − ln( Z − B) − − ln ⎜ ⎟ B (δ1 − δ ) B ⎜⎝ A B ⎟⎠ ⎝ Z + δ B ⎠ Nc ψ i = ∑ x j Aij j =1 238 Glossary Roman symbols Ci Overall volume fraction and cij Volume fraction of species i in phase j Fi Overall fractional volumetric flow of component i fj Fractional flow of phase j in the flow, and K ij Dispersion tensor of component i in phase j K K-values L Length N Number of contacts in (in mixing cell) Nc Number of components Np Number of phases qj Volumetric flow rate of phase j RF1.2∞ Extrapolated recovery to infinite cells when 1.2 pore volume is injected Sj Saturation of phase j t Time TL Tie-line length TL∞ Minimum tie line length at infinite number of contacts (in mixing cell) v Total flow velocity 239 vj Darcy velocity of phase j vinj Injection velocity x Composition of liquid phase xi Mole fraction of component i in liquid phase xij Mole fraction of component i in phase j y Composition of gas phase yi Mole fraction component i in gas phase z Overall composition of mixture zi Mole fraction of component i in mixture Greek letters ρi Density of pure component i ρj Density of phase j φ Porosity α Mixing-ratio parameter (in mixing cell) λ Eigenvalues Superscript G Gas O Oil m Linearizing exponent used in 1/Nm (mixing cell) 240 Abbreviations MOC Method of Characteristics MMP Minimum miscibility pressure MMP* Extrapolated minimum miscibility pressure (Chapter 5) MME Minimum miscibility enrichment BIP Binary interaction parameters 241 References Ahmadi, K and Johns, R., 2008 Multiple Mixing-Cell Method for MMP Calculations In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/116823-MS Ayirala, S and Rao, D., 2006 Comparative Evaluation of a New MMP Determination Technique In Proceedings of SPE/DOE Symposium on Improved Oil Recovery SPE/DOE Symposium on Improved Oil Recovery doi: 10.2118/99606-MS Bryant, D.W and Monger, T.G., 1988 Multiple-Contact Phase Behavior Measurement and Application with Mixtures Of CO2 and Highly Asphaltic Crude SPE Reservoir Engineering, 3(2) doi: 10.2118/14438-PA Buckley, S.E and Leverett, M.C., 1942 Mechanism of Fluid Displacement in Sands American Institute of Mining and Metallurgical Engineers - Transactions Petroleum Development and Technology Division, 146, pp.107-116 Christiansen, R.L., 1986 United States Patent: 4610160 - Method of Determining the Minimum Level of Enrichment for a Miscible Gas Flood Christiansen, R.L and Haines, H., 1987 Rapid Measurement of Minimum Miscibility Pressure with the Rising-Bubble Apparatus SPE Reservoir Engineering, 2(4) doi: 10.2118/13114-PA Cook, A., Walker, C.J and Spencer, G., 1969 Realistic K Values of C7+ Hydrocarbons for Calculating Oil Vaporization During Gas Cycling at High Pressures Journal of Petroleum Technology, 21(7) doi: 10.2118/2276-PA Creek, J.L and Sheffield, J.M., 1993 Phase Behavior, Fluid Properties, and Displacement Characteristics of Permian Basin Reservoir Fluid/CO2 Systems SPE Reservoir Engineering, 8(1) doi: 10.2118/20188-PA Danesh, A., 1998 PVT and Phase Behaviour of Petroleum Reservoir Fluids, New York: Elsevier ISBN: 9780444821966 De Nevers, N., 1964 A Calculation Method for Carbonated Water Flooding SPE Journal, 4(1), pp.9 - 20 Dindoruk, B., 1992 Analytical Theory of Multiphase, Multicomponent Displacement in Porous Media PhD Dissertation Stanford University Dindoruk, B., Orr, F.M and Johns, R., 1997 Theory of Multicontact Miscible Displacement with Nitrogen SPE Journal, 2(3) doi: 10.2118/30771-PA Dumore, J.M., Hagoort, J and Risseeuw, A.S., 1984 An Analytical Model for OneDimensional, Three-Component Condensing and Vaporizing Gas Drives Society of Petroleum Engineers journal, 24(2), pp.169-179 Elsharkawy, A.M., Poettmann, F.H and Christiansen, R.L., 1992 Measuring Minimum 242 Miscibility Pressure: Slim-Tube or Rising-Bubble Method? In Proceedings of SPE/DOE Enhanced Oil Recovery Symposium SPE/DOE Enhanced Oil Recovery Symposium doi: 10.2118/24114-MS Fong, W.S., Sheffield, J.M., Ehrlich, R and Emanuel, A.S., 1992 Phase Behavior Modeling Techniques for Low-Temperature CO2 Applied to McElroy and North Ward Estes Projects In Proceedings of SPE/DOE Enhanced Oil Recovery Symposium SPE/DOE Enhanced Oil Recovery Symposium doi: 10.2118/24184MS Glaso, O., 1990 Miscible Displacement: Recovery Tests with Nitrogen SPE Reservoir Engineering, 5(1) doi: 10.2118/17378-PA Hagoort, J and Dumore, J.M., 1985 Determination of Minimum Miscibility Pressures with an Equation of State Program In European Meeting Improved Oil Recovery Rome, pp 61-66 Harten, A., 1997 High Resolution Schemes for Hyperbolic Conservation Laws, Journal of Computational Physics, 135(2), pp.260-278 doi: 10.1006/jcph.1997.5713 Helfferich, F., 1981 Theory of Multicomponent, Multiphase Displacement in Porous Media Society of Petroleum Engineers Journal, 21(1) doi: 10.2118/8372-PA Hirasaki, G.J., 1981 Application of the Theory of Multicomponent, Multiphase Displacement to Three-Component, Two-Phase Surfactant Flooding Society of Petroleum Engineers journal, 21(2), pp.191-204 Holm, L.W and Josendal, V.A., 1974 Mechanisms of Oil Displacement By Carbon Dioxide Journal of Petroleum Technology, 26(12) doi: 10.2118/4736-PA Hudgins, D., Llave, F and Chung, F., 1990 Nitrogen Miscible Displacement of Light Crude Oil: A Laboratory Study SPE Reservoir Engineering, 5(1) doi: 10.2118/17372-PA Hutchinson, J and Braun, P.H., 1961 Phase Relations of Miscible Displacement in Oil Recovery A.I.Ch.E Journal, 7(1), pp.64-72 Jacobson, H., 1972 Acid Gases and Their Contribution to Miscibility Journal of Canadian Petroleum Technology doi: 10.2118/72-02-03 Jaubert, J.N., Arras, L., Neau, E and Avaullee, L., 1998a Properly Defining the Classical Vaporizing and Condensing Mechanisms When a Gas Is Injected into a Crude Oil Industrial & Engineering Chemistry Research, 37(12), pp.4860-4869 doi: 10.1021/ie9803016 Jaubert, J.N., Wolff, L., Neau, E and Avaullee, L., 1998b A Very Simple Multiple Mixing Cell Calculation to Compute the Minimum Miscibility Pressure Whatever the Displacement Mechanism Industrial & Engineering Chemistry Research, 37(12), pp.4854-4859 doi: 10.1021/ie980348r 243 Jensen, F and Michelsen, M.L., 1990 Calculation of First Contact and Multiple Contact Minimum Miscibility Pressures In Situ, 14(1), pp.1-17 Jessen, K., Michelsen, M.L and Stenby, E., 1998 Global Approach for Calculation of Minimum Miscibility Pressure Fluid Phase Equilibria, 153(2), pp.251-263 doi: 10.1016/S0378-3812(98)00414-2 Jessen, K and Orr, F., 2008 On Interfacial-Tension Measurements to Estimate Minimum Miscibility Pressures SPE Reservoir Evaluation & Engineering, 11(5) doi: 10.2118/110725-PA Jessen, K., Stenby, E and Orr, F., 2004 Interplay of Phase Behavior and Numerical Dispersion in Finite-Difference Compositional Simulation SPE Journal, 9(2) doi: 10.2118/88362-PA Johns, R.T., Dindoruk, B and Orr, F.M.J., 1993 Analytical Theory of Combined Condensing/Vaporizing Gas Drives SPE Advanced Technology Series, 1(2), pp.7 - 16 doi: 10.2118/24112-PA Johns, R.T and Orr, J., 1996 Miscible Gas Displacement of Multicomponent Oils SPE Journal, 1(1) doi: 10.2118/30798-PA Johns, R.T., Sah, P and Solano, R., 2002 Effect of Dispersion on Local Displacement Efficiency for Multicomponent Enriched-Gas Floods Above the Minimum Miscibility Enrichment SPE Reservoir Evaluation & Engineering, 5(1) doi: 10.2118/75806-PA Johns, R.T., 1992 Analytical Theory of Multicomponent Gas Drives with Two-phase Mass transfer PhD Dissertation Stanford University Juanes, R., 2008 A Robust Negative Flash Based on a Parameterization of the Tie-line Field Fluid Phase Equilibria, 267(1), pp.6-17 doi: 10.1016/j.fluid.2008.02.009 Jutila, H.A., Logmo-Ngog, A.B., Sarkar, R., Killough, J.E and Ross, F.C., 2001 Use of Parallel Compositional Simulation to Investigate Productivity Improvement Options for a Retrograde-Gas-Condensate Field: A Case Study In Proceedings of SPE Reservoir Simulation Symposium SPE Reservoir Simulation Symposium doi: 10.2118/66397-MS Kuo, S.S., 1985 Prediction of Miscibility for the Enriched-Gas Drive Process In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/14152-MS LaForce, T and Johns, R., 2005 Composition Routes for Three-Phase Partially Miscible Flow in Ternary Systems SPE Journal, 10(2) doi: 10.2118/89438-PA Lantz, R.B., 1971 Quantitative Evaluation of Numerical Diffusion (Truncation Error) Society of Petroleum Engineers Journal, 11(3) doi: 10.2118/2811-PA Larson, L.L., Silva, M.K., Taylor, M.A and Jr., F.M., 1989 Temperature Dependence of 244 L1/L2/V Behavior in CO2/Hydrocarbon Systems SPE Reservoir Engineering, 4(1) doi: 10.2118/15399-PA Larson, R.G and Hirasaki, G.J., 1978 Analysis of the Physical Mechanisms in Surfactant Flooding , 18(1) Larson, R.G., 1979 The Influence of Phase Behavior on Surfactant Flooding , 19(6), pp.411-422 Li, Y., 2007 Fast and Robust Phase Behavior Modeling for Compositional Reservoir Simulation PhD Dissertation The University of Texas at Austin Li, Y and Johns, R., 2007 A Rapid and Robust Method to Replace Rachford-Rice in Flash Calculations In Proceedings of SPE Reservoir Simulation Symposium SPE Reservoir Simulation Symposium doi: 10.2118/106080-MS Luks, K.D., Turek, E.A and Baker, L.E., 1987 Calculation of Minimum Miscibility Pressure SPE Reservoir Engineering, 2(4) Menzie, D.E and Nielsen, R.F., 1963 A Study of the Vaporization of Crude Oil by Carbon Dioxide Repressuring Journal of Petroleum Technology, 15(11) doi: 10.2118/568-PA Metcalfe, R.S., Fussell, D.D and Shelton, J.L., 1973 A Multicell Equilibrium Separation Model for the Study of Multiple Contact Miscibility in Rich-Gas Drives Society of Petroleum Engineers Journal, 13(3) doi: 10.2118/3995-PA MMPz Manual, 2001 Zick Technologies Mogensen, K., Hood, P., Lindeloff, N., Frank, S and Noman, R., 2009 Minimum Miscibility Pressure Investigations for a Gas-Injection EOR Project in Al Shaheen Field, Offshore Qatar In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/124109-MS Monroe, W., Silva, M., Larson, L.L and Orr Jr., F., 1990 Composition Paths in FourComponent Systems: Effect of Dissolved Methane on 1D CO2 Flood Performance SPE Reservoir Engineering, 5(3) doi: 10.2118/16712-PA Neau, E., 1996 A New Algorithm for Enhanced Oil Recovery Calculations Fluid Phase Equilibria, 117(1-2), pp.265-272 doi: 10.1016/0378-3812(95)02962-1 Okuno, R., 2009 Modeling of Multiphase Behavior for Gas Flooding Simulation PhD Dissertation University of Texas at Austin Okuno, R., Johns, R and Sepehrnoori, K., 2011 Mechanisms for High Displacement Efficiency of Low-Temperature CO2 Floods SPE Journal (in print) Orr, F.M., 2007 Theory of Gas Injection Processes, Holte, Denmark: Tie-Line Publications Orr, F.M and Jensen, C.M., 1984 Interpretation of Pressure-Composition Phase 245 Diagrams for CO2/Crude-Oil Systems Society of Petroleum Engineers Journal, 24(5) doi: 10.2118/11125-PA Orr, F.M., Johns, R.T and Dindoruk, B., 1993 Development of Miscibility in FourComponent CO2 Floods SPE Reservoir Engineering, 8(2) doi: 10.2118/22637PA Orr, F.M., Silva, M.K., Lien, C.L and Pelletier, M.T., 1982 Laboratory Experiments to Evaluate Field Prospects for CO2 Flooding Journal of Petroleum Technology, 34(4) doi: 10.2118/9534-PA Orr, F.M and Jessen, K., 2007 An Analysis of the Vanishing Interfacial Tension Technique for Determination of Minimum Miscibility Pressure Fluid Phase Equilibria, 255(2), pp.99-109 doi: 10.1016/j.fluid.2007.04.002 Pedersen, K.S and Christensen, P.L., 2006 Phase behavior of petroleum reservoir fluids, CRC Press ISBN: 9780824706944 Pederson, K.S., Fjellerup, J., Thomassen, P and Fredenslund, A., 1986 Studies of Gas Injection Into Oil Reservoirs by a Cell-to-Cell Simulation Model In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/15599-MS Peng, D.-Y and Robinson, D.B., 1976 A New Two-Constant Equation of State Industrial & Engineering Chemistry Fundamentals, 15(1), pp.59-64 doi: 10.1021/i160057a011 PennPVT, 2011 Version 3.9, Gas Flooding Project PVTsim, 2009 Version 19.0.0, Calsep A/S Rachford, J and Rice, J.D., 1952 Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization Hydrocarbon Equilibrium American Institute of Mining and Metallurgical Engineers Journal of Petroleum Technology, 4(10, Sec 2), p.3 Rao, D.N., 1997 A New Technique of Vanishing Interfacial Tension for Miscibility Determination Fluid Phase Equilibria, 139(1-2), pp.311-324 doi: 10.1016/S0378-3812(97)00180-5 Rao, D.N and Lee, J.I., 2002 Application of the New Vanishing Interfacial Tension Technique to Evaluate Miscibility Conditions for the Terra Nova Offshore Project Journal of Petroleum Science and Engineering, 35(3-4), pp.247-262 doi: 10.1016/S0920-4105(02)00246-2 Robinson, D.B and Peng, D.Y., 1978 Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs, Gas Processors Association, GPA Sandler, S.I., 2006 Chemical, Biochemical, and Engineering Thermodynamics 4th ed., 246 Wiley ISBN: 0471661740 Seto, C.J and Orr, F.M., 2008 Analytical Solutions for Multicomponent, Two-Phase Flow in Porous Media with Double Contact Discontinuities Transport in Porous Media, 78(2), pp.161-183 doi: 10.1007/s11242-008-9292-y Stalkup, F.I., 1987 Displacement Behavior of the Condensing/Vaporizing Gas Drive Process In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/16715-MS Stalkup, F.I., Lo, L.L and Dean, R.H., 1990 Sensitivity to Gridding of Miscible Flood Predictions Made with Upstream Differenced Simulators In Proceedings of SPE/DOE Enhanced Oil Recovery Symposium SPE/DOE Enhanced Oil Recovery Symposium doi: 10.2118/20178-MS Stalkup, F.I., 1990 Effect of Gas Enrichment and Numerical Dispersion on EnrichedGas-Drive Predictions SPE Reservoir Engineering, 5(4) doi: 10.2118/18060-PA Turek, E., Metcalfe, R and Fishback, R., 1988 Phase Behavior of Several CO2/ West Texas-Reservoir-Oil Systems SPE Reservoir Engineering, 3(2) doi: 10.2118/13117-PA Uleberg, K and Høier, L., 2002 Miscible Gas Injection in Fractured Reservoirs In Proceedings of SPE/DOE Improved Oil Recovery Symposium SPE/DOE Improved Oil Recovery Symposium doi: 10.2118/75136-MS Wachmann, C., 1964 A Mathematical Theory for the Displacement of Oil and Water by Alcohol Society of Petroleum Engineers Journal, 4(3) doi: 10.2118/879-PA Walsh, B.W and Orr Jr., F.M., 1990 Prediction of Miscible Flood Performance The Effect of Dispersion on Composition Paths in Ternary Systems In Situ, 14(1), pp.19-47 Wang, Y and Orr, J., 1997 Analytical Calculation of Minimum Miscibility Pressure Fluid Phase Equilibria, 139(1-2), pp.101-124 doi: 10.1016/S03783812(97)00179-9 Welge, H.J., E.F Johnson, E.F., Ewing Jr., S.P and Brinkman, F.H., 1961 The Linear Displacement of Oil from Porous Media by Enriched Gas Journal of Petroleum Technology, 13(8) doi: 10.2118/1525-G Whitson, C.H and Michelsen, M.L., 1989 The Negative Flash Fluid Phase Equilibria, 53, pp.51-71 doi: 10.1016/0378-3812(89)80072-X Winzinger, R et al., 1991 Design of a Major CO2 Flood, North Ward Estes Field, Ward County, Texas SPE Reservoir Engineering, 6(1) doi: 10.2118/19654-PA Yellig, W.F and Metcalfe, R.S., 1980 Determination and Prediction of CO2 Minimum Miscibility Pressures (includes associated paper 8876 ) Journal of Petroleum Technology, 32(1) doi: 10.2118/7477-PA 247 Yuan, H., 2003 Application of Miscibility Calculations to Gas Floods PhD Dissertation University of Texas at Austin Yuan, H and Johns, R., 2005 Simplified Method for Calculation of Minimum Miscibility Pressure or Enrichment SPE Journal, 10(4) doi: 10.2118/77381-PA Yuan, H., Johns, R., Egwuenu, A and Dindoruk, B., 2005 Improved MMP Correlations for CO2 Floods Using Analytical Gasflooding Theory SPE Reservoir Evaluation & Engineering, 8(5) doi: 10.2118/89359-PA Zhao, G., Adidharma, H., Towler, B and Radosz, M., 2006a Minimum Miscibility Pressure Prediction Using Statistical Associating Fluid Theory: Two- and ThreePhase Systems In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/102501-MS Zhao, G.-B., Adidharma, H., Towler, B and Radosz, M., 2006c Using a MultipleMixing-Cell Model to Study Minimum Miscibility Pressure Controlled by Thermodynamic Equilibrium Tie Lines Industrial and Engineering Chemistry Research, 45(23), pp.7913-7923 doi: 10.1021/ie0606237 Zhou, D and Orr, F.M.J., 1998 An Analysis of Rising Bubble Experiments to Determine Minimum Miscibility Pressures SPE Journal, 3(1) doi: 10.2118/30786-PA Zick, A.A., 1986 A Combined Condensing/Vaporizing Mechanism in the Displacement of Oil by Enriched Gases In Proceedings of SPE Annual Technical Conference and Exhibition SPE Annual Technical Conference and Exhibition doi: 10.2118/15493-MS 248 Vita Kaveh Ahmadi was born in 1979 in Tehran, Iran, the son of Hossein Ahamadi Rahmatabadi and Parivash Masoudi Moughari After graduating in Math and Physics from Amooyan High School in 1998, he entered Petroleum University of Technology, Abadan, Iran He graduated with Bachelors of Science in Petroleum Engineering in 2002 In the following year, he entered the Petroleum Engineering program at the University of Kansas where he received the degree of Master of Science in Petroleum Engineering in December of 2005 He then moved to Austin where he started doctoral studies at Department of Petroleum and Geosystem Engineering, University of Texas at Austin in January of 2007 Permanent email: kaveh.ahmadi@utexas.edu This dissertation was typed by Kaveh Ahmadi 249 ... v Advances in Calculation of Minimum Miscibility Pressure Publication No. _ Kaveh Ahmadi Rahmatabadi, Ph.D The University of Texas at Austin, 2011 Supervisor: Russell T Johns Minimum miscibility. .. Advances in Calculation of Minimum Miscibility Pressure by Kaveh Ahmadi Rahmatabadi, B.Sc.; M.Sc Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in. .. version of the following dissertation: Advances in Calculation of Minimum Miscibility Pressure Committee: Russell T Johns, Supervisor Steven L Bryant David DiCarlo Birol Dindoruk Kamy Sepehrnoori Advances