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 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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