The Development and Application of EOS-based VT Phase Behavior Calculation Algorithms in Petroleum Industry
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Published
Nov 30, 2022
Abstract
The use of equation of state (EOS)-based phase behavior calculations is widespread in the petroleum industry, including the calculation of oil and gas reserves, production forecasting, and optimization of enhanced oil recovery (EOR) plans, surface separator design, and pipe flow calculation. The most commonly used method for providing phase behavior information is PT phase-equilibrium-calculation algorithms, which have been extensively studied for decades. However, simulation and engineering design of these processes using VT phase-equilibrium- calculation algorithms is sometimes more convenient than using conventional PT algorithms and has distinct advantages. The VT algorithm has been continuously improved over the last decade to ensure calculation accuracy, robustness, and efficiency, and it has been gradually applied in the petroleum industry. This article provides an overview of research findings in the field of EOS-based VT phase behavior calculation algorithms and their applications in oil and gas engineering. The Helmholtz-free-energy minimization approach, the Gibbs-free-energy minimization approach, and the nested approach based on the PT algorithm are three typical VT algorithm approaches discussed. The petroleum industry’s main applications of phase equilibrium calculation using the VT algorithm are described. Furthermore, some existing problems are identified, and several prospects for the application of the VT algorithm in the petroleum engineering field are presented. A critical review of the current state of the VT algorithm process, we believe, will fill the gap by shedding light on the process’s flaws and limitations, future development areas, and new research topics.
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Keywords
Phase Behavior Calculation, Phase Equilibrium Calculation, VT Algorithm, Petroleum Industry
References
1. Pan H, Chen Y, Sheffield J, Cheng Y, Zhou D. Phase-behavior modeling and flow simulation for low-temperature CO2 injection. SPE Res Eval Eng 2015; 18(2): 250-263. SPE-170903-PA. DOI: https://doi.org/10.2118/170903-PA
2. Pasqualette MD, Carneiro J, Johansen ST, Løvfall BT, Fonseca, Jr R, Ciambelli J. A numerical assessment of carbon-dioxide-rich two-phase flows with dense phases in offshore production pipelines. SPE J 2020; 25(2):712-731. SPE-199876-PA. DOI: https://doi.org/10.2118/199876-PA
3. Gao J, Okuno R, Li H. An Experimental study of mul- tiphase behavior for n-butane/bitumen/water mixtures. SPE J 2017; 22(3):783-798. SPE-180736-PA. DOI: https://doi.org/10.2118/180736-PA
4. Petitfrere M, Nichita DV, Voskov D, Zaydullin R, Bogdanov I. Full-EoS based thermal multiphase compositional simulation of CO2 and steam injection processes. J Pet Sci Eng 2020; 192(6):107241. DOI: http://dx.doi.org/10.1016/j.petrol.2020.107241
5. Katz DL, Kobayashi P, Vary E. Handbook of Natural Gas Engineering. New York: McGraw-Hill Book Co. Inc. 1959.
6. Sage BH, Lacey WN. Some Properties of the Lighter Hydrocarbons, Hydrogen Sulfide, and Carbon Diox- ide, Monograph on API Research Project 37. New York: API. 1955.
7. Eilerts CK. Phase Relations of Gas Condensate Flu- ids, Monograph 10, USBM. New York: American Gas Assn. 1957.
8. Standing MB and Katz DL. Vapor/liquid equilibria of natural gas/crude oil systems. Transact AIME 1944; 155(1):232-245. DOI: https://doi.org/10.2118/944232-G
9. Standing MB. A Pressure-Volume-Temperature Cor- relation for Mixtures of California Oils and Gases. In Drilling and Production Practice. OnePetro, 1947.
10. Nemeth LK, Kennedy HT. A Correlation of dewpoint pressure with fluid composition and temperature. SPE J 1967; 7(2):99-104. SPE-1477-PA. DOI: https://doi.org/10.2118/1477-PA
11. Redlich O, Kwong J.N.S. On the thermodynamics of solutions. V: an equation of state. Fugacit Gas Solut Chem Rev 1949; 44(1), 233-244. DOI: https://pubs.acs.org/doi/pdf/10.1021/cr60137a013
12. Soave G. Equilibrium constants from a modified Redlich-Kwong EOS. Chem Eng Sci 1972; 27(6):1197-1203. DOI: http://dx.doi.org/10.1016/0009-2509(72)80096-4
13. PengDY,RobinsonDB.Anewtwo-constantequation of state. Ind Eng Chem Fund 1976; 15(1):59-64. DOI: https://doi.org/10.1021/i160057a011
14. CoatsKH.Anequationofstatecompositionalmodel. SPE J 1980; 20(5):363-376; Trans AIME, 269. DOI: https://doi.org/10.2118/8284-PA
15. Young LC, Stephenson RE. A generalized composi- tional approach for reservoir simulation. SPE J 1983; 23(5):727-742. SPE-10516-PA. DOI: https://doi.org/10.2118/10516-PA
16. Michelsen ML. The Isothermal flash problem. Part I. stability test. Fluid Phase Equilib 1982; 9(1):1-19. DOI: https://doi.org/10.1016/0378-3812(82)85001-2
17. Michelsen M L. The isothermal flash problem. Part II. Phase-split calculation. Fluid Phase Equilib 1982;9(1):21-40. DOI: https://doi.org/10.1016/0378-3812(82)85002-4
18. MichelsenML,MollerupJM.ThermodynamicModels: Fundamentals and Computational Aspects. Holte, Denmark: Tie-Line Publications. 2004. DOI: https://doi.org/10.1016/J.FLUID.2005.11.032
19. FiroozabadiA.ThermodynamicsandApplicationsof Hydrocarbon Energy Production. New York: McGraw-Hill Education. 2015. https://www.accessengineeringlibrary.com/content/bo ok/9780071843256
20. MehraRK,HeidemannRA,AzizK.Anaccelerated successive substitution algorithm. Can J Chem Eng 1983; 61(4):590-596. DOI: https://doi.org/10.1002/cjce.5450610414
21. Ammar MN, Renon H. The isothermal flash problem: new methods for phase split calculations. AIChE J 1987; 33(6):926-939. DOI: https://doi.org/10.1002/aic.690330606
22. Perschke DR. Equation of State Phase Behavior Modeling for Compositional Simulation. PhD disser- tation, University of Texas at Austin, Austin, Texas, USA. 1988. DOI: http://dx.doi.org/10.26153/tsw/7567
23. Pan H, Firoozabadi A. Fast and robust algorithm for compositional modeling: Part II—Two-phase flash computations. SPE J 2003; 8(4):380-391. SPE-71603-PA. DOI: https://doi.org/10.2118/87335-PA
24. NghiemLX,AzizK,LiYK.Arobustiterativemethod for flash calculations using the Soave-Redlich-Kwong or the Peng-Robinson Equation of state. SPE J 1983; 23(3):521-530. SPE-8285-PA. DOI: https://doi.org/10.2118/8285-PA
25. Petitfrere M, Nichita DV. Robust and efficient trust-region based stability analysis and multiphase flash calculations. Fluid Phase Equilib 2014; 362(25 January): 51-68. DOI: https://dx.doi.org/10.1016/j.fluid.2013.08.039
26. Pan H, Connolly M, Tchelepi H. Multiphase equilib- rium calculation framework for compositional simula- tion of CO2 injection in low temperature reservoirs. Ind Eng Chem Res 2019; 58(5):2052-2070. DOI: https://doi.org/10.1021/acs.iecr.8b05229
27. Nagarajan NR, Cullick AS, Griewank A. New strategy for phase equilibrium and critical point calculations by thermodynamic energy analysis. Part I. Stability analysis and flash. Fluid Phase Equilib 1991; 62(3):191-210. DOI: https://doi.org/10.1016/0378-3812(91)80010-S
28. Michelsen ML. State Function based flash specifica- tions. Fluid Phase Equilibria 1999; 158:617-626. DOI: https://doi.org/10.1016/S0378-3812(99)00092-8
29. CismondiM.Phaseenvelopesforreservoirfluidswith asphaltene onset lines: An integral computation strategy for complex combinations of two- and three-phase behaviors. Energ Fuel 2018; 32(3):2742-2748. DOI: https://doi.org/10.1021/acs.energyfuels.7b02790
30. Polıvka O, Mikyska J. Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification. J Comput Phys 2014; 272(4):149-169. DOI: http://dx.doi.org/10.1016/j.jcp.2014.04.029
31. Sandoval DR, Michelsen ML, Yan W, Stenby EH. VT-based phase envelope and flash calculations in the presence of capillary pressure. Ind Eng Chem Res 2019; 58(13):5291-5300. DOI: https://doi.org/10.1021/acs.iecr.8b05976
32. Achour SH, Okuno R. Phase stability analysis for tight porous media by minimization of the Helmholtz free energy. Fluid Phase Equilib 2020; 520: 112648. DOI: http://dx.doi.org/10.26153/tsw/8298
33. Achour SH, Okuno R. Two-phase flash for tight po- rous media by minimization of the Helmholtz free energy. Fluid Phase Equilib 2021; 534:112960. Available at: https://www.x-mol.com/paperRedirect/126647712249 6536576
34. Fontalba F, Richon D, and Renon H. Simultaneous
determination of vapor-liquid equilibria and saturated densities up to 45 MPa and 433 K. Rev Sci Instrum 1984; 55(6):944-951. DOI: https://doi.org/10.1063/1.1137870
35. Kikani J, Ratulowski J. Consistency check and rec- onciliation of PVT data from samples obtained with formation testers using EOS models. SPE Res Eval Eng 1998; 1(4):348-353. SPE-50979-PA. DOI: https://doi.org/10.2118/50979-PA
36. Roedder E, Bodnar RJ. Geologic pressure determi- nations from fluid inclusion studies. Ann Rev Earth Planet Sci 1980; 8(1):263-301. DOI: https://doi.org/10.1146/annurev.ea.08.050180.00140 3
37. Liu DH, Xiao XM, Mi JK, Li XQ, Shen JK, Song ZG, Peng PA. Determination of trapping pressure and temperature of petroleum inclusions using pvt simu- lation software—A case study of lower ordovician carbonates from the Lunnan low uplift, Tarim Basin. Marin Petrol Geol 2003; 20(1):29-43. DOI: https://doi.org/10.1016/S0264-8172(03)00047-3
38. Esposito RO, Castier M, Tavares FW. Calculations of thermodynamic equilibrium in systems subject to gravitational fields. Chem Eng Sci 2000; 55(17):3495-3504. DOI: https://doi.org/10.1016/S0009-2509(00)00010-5
39. CabralVF,CastierM,TavaresFW.Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases. Chem Eng Sci 2005; 60(6):1773-1782. DOI: http://dx.doi.org/10.1016%2Fj.ces.2004.11.007
40. Castier M, Tavares FW. Centrifugation equilibrium of natural gas. Chem Eng Sci 2005; 60(11):2927-2935. DOI: https://doi.org/10.1016/j.ces.2004.12.027
41. Velez A, Pereda S, Brignole EA. Isochoric lines and determination of phase transitions in supercritical reactors. J Supercrit Fluids 2010; 55(2):643-647. DOI: https://doi.org/10.1016/j.supflu.2010.09.033
42. Mikyska J, Firoozabadi A. A new thermodynamic function for phase-splitting at constant temperature, moles, and volume. AIChE J 2011; 57(7):1897-1904. DOI: https://doi.org/10.1002/aic.12387
43. Jindrova T, Mikyska J. Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles. Fluid Phase Equilib 2013; 353(7):101-114. DOI: http://dx.doi.org/10.1016/j.fluid.2013.05.036
44. Jindrova T, Mikyska, J. General algorithm for multi- phase equilibria calculation at given volume, temper- ature, and moles. Fluid Phase Equilib 2015; 393:7-25. DOI: http://dx.doi.org/10.1016/j.fluid.2015.02.013
45. Lu C, Jin Z, Li H. A Two-phase flash algorithm with the consideration of capillary pressure at specified mole numbers, volume and temperature. Fluid Phase Equilib 2019; 485:67-82. DOI: https://doi.org/10.1016/j.fluid.2018.12.002
46. Nichita DV. New unconstrained minimization methods for robust flash calculations at temperature, volume and moles specifications. Fluid Phase Equilib 2018; 466:31-47. DOI: https://doi.org/10.1016/j.fluid.2018.03.012
47. Cismondi M, Ndiaye PM, Tavares FW. A new simple and efficient flash algorithm for T-v specifications. Fluid Phase Equilib 2018; 464:32-39. DOI: http://dx.doi.org/10.1016/j.fluid.2018.02.019
48. Lu C, Jin Z, Li H, Xu L. Simple and robust algorithm for multiphase equilibrium computations at tempera- ture and volume specifications. SPE J 2021; 26(4):2397-2416. https://www.x-mol.com/paperRedirect/142556247354 5318400
49. Mikyska J, Firoozabadi A. Investigation of mixture stability at given volume, temperature, and number of moles. Fluid Phase Equilib 2012; 321:1-9. DOI: https://doi.org/10.1016/j.fluid.2012.01.026
50. Agarwal, RK, Li, YK, Nghiem, LX, Coombe DA. Mul- tiphase multi- component isenthalpic flash calcula- tions. J Can Pet Technol 1991; 30(3):69-75. PETSOC-91-03-07. DOI: https://doi.org/10.2118/91-03-07
51. Rezaveisi M, Sepehrnoori K, Pope GA, Johns RT. Thermodynamic analysis of phase behavior at high capillary pressure. SPE J. 2018; 23(6):1438-1451.
DOI: https://doi.org/10.2118/175135-PA
52. NeshatSS,OkunoR,PopeGA.Arigoroussolutionto the problem of phase behavior in unconventional formations with high capillary pressure, SPE J. 2018; 23(4):1438-1451. DOI: https://doi.org/10.2118/187260-PA
53. Neshat SS, Okuno R, Pope GA. Thermodynamic Stability Analysis of MultiComponent Mixtures with Capillary Pressure. SPE Reservoir Simulation Con- ference, Galveston, Texas, 10-11 April 2019. DOI: https://doi.org/10.2118/193888-MS
54. ShapiroAA,StenbyEH.Thermodynamicsofthe multicomponent vapor liquid equilibrium under capil- lary pressure difference. Fluid Phase Equilib 2001; 178(1-2): 17-32. DOI: https://doi.org/10.1016/S0378-3812(00)00403-9
55. Ertas D, Kelemen SR, Halsey TC. Petroleum expul- sion part 1. Theory of Kerogen Swelling in Multi- component solvents. Energ Fuel 2006; 20(1): 295-300. DOI: https://doi.org/10.1021/ef058024k
2. Pasqualette MD, Carneiro J, Johansen ST, Løvfall BT, Fonseca, Jr R, Ciambelli J. A numerical assessment of carbon-dioxide-rich two-phase flows with dense phases in offshore production pipelines. SPE J 2020; 25(2):712-731. SPE-199876-PA. DOI: https://doi.org/10.2118/199876-PA
3. Gao J, Okuno R, Li H. An Experimental study of mul- tiphase behavior for n-butane/bitumen/water mixtures. SPE J 2017; 22(3):783-798. SPE-180736-PA. DOI: https://doi.org/10.2118/180736-PA
4. Petitfrere M, Nichita DV, Voskov D, Zaydullin R, Bogdanov I. Full-EoS based thermal multiphase compositional simulation of CO2 and steam injection processes. J Pet Sci Eng 2020; 192(6):107241. DOI: http://dx.doi.org/10.1016/j.petrol.2020.107241
5. Katz DL, Kobayashi P, Vary E. Handbook of Natural Gas Engineering. New York: McGraw-Hill Book Co. Inc. 1959.
6. Sage BH, Lacey WN. Some Properties of the Lighter Hydrocarbons, Hydrogen Sulfide, and Carbon Diox- ide, Monograph on API Research Project 37. New York: API. 1955.
7. Eilerts CK. Phase Relations of Gas Condensate Flu- ids, Monograph 10, USBM. New York: American Gas Assn. 1957.
8. Standing MB and Katz DL. Vapor/liquid equilibria of natural gas/crude oil systems. Transact AIME 1944; 155(1):232-245. DOI: https://doi.org/10.2118/944232-G
9. Standing MB. A Pressure-Volume-Temperature Cor- relation for Mixtures of California Oils and Gases. In Drilling and Production Practice. OnePetro, 1947.
10. Nemeth LK, Kennedy HT. A Correlation of dewpoint pressure with fluid composition and temperature. SPE J 1967; 7(2):99-104. SPE-1477-PA. DOI: https://doi.org/10.2118/1477-PA
11. Redlich O, Kwong J.N.S. On the thermodynamics of solutions. V: an equation of state. Fugacit Gas Solut Chem Rev 1949; 44(1), 233-244. DOI: https://pubs.acs.org/doi/pdf/10.1021/cr60137a013
12. Soave G. Equilibrium constants from a modified Redlich-Kwong EOS. Chem Eng Sci 1972; 27(6):1197-1203. DOI: http://dx.doi.org/10.1016/0009-2509(72)80096-4
13. PengDY,RobinsonDB.Anewtwo-constantequation of state. Ind Eng Chem Fund 1976; 15(1):59-64. DOI: https://doi.org/10.1021/i160057a011
14. CoatsKH.Anequationofstatecompositionalmodel. SPE J 1980; 20(5):363-376; Trans AIME, 269. DOI: https://doi.org/10.2118/8284-PA
15. Young LC, Stephenson RE. A generalized composi- tional approach for reservoir simulation. SPE J 1983; 23(5):727-742. SPE-10516-PA. DOI: https://doi.org/10.2118/10516-PA
16. Michelsen ML. The Isothermal flash problem. Part I. stability test. Fluid Phase Equilib 1982; 9(1):1-19. DOI: https://doi.org/10.1016/0378-3812(82)85001-2
17. Michelsen M L. The isothermal flash problem. Part II. Phase-split calculation. Fluid Phase Equilib 1982;9(1):21-40. DOI: https://doi.org/10.1016/0378-3812(82)85002-4
18. MichelsenML,MollerupJM.ThermodynamicModels: Fundamentals and Computational Aspects. Holte, Denmark: Tie-Line Publications. 2004. DOI: https://doi.org/10.1016/J.FLUID.2005.11.032
19. FiroozabadiA.ThermodynamicsandApplicationsof Hydrocarbon Energy Production. New York: McGraw-Hill Education. 2015. https://www.accessengineeringlibrary.com/content/bo ok/9780071843256
20. MehraRK,HeidemannRA,AzizK.Anaccelerated successive substitution algorithm. Can J Chem Eng 1983; 61(4):590-596. DOI: https://doi.org/10.1002/cjce.5450610414
21. Ammar MN, Renon H. The isothermal flash problem: new methods for phase split calculations. AIChE J 1987; 33(6):926-939. DOI: https://doi.org/10.1002/aic.690330606
22. Perschke DR. Equation of State Phase Behavior Modeling for Compositional Simulation. PhD disser- tation, University of Texas at Austin, Austin, Texas, USA. 1988. DOI: http://dx.doi.org/10.26153/tsw/7567
23. Pan H, Firoozabadi A. Fast and robust algorithm for compositional modeling: Part II—Two-phase flash computations. SPE J 2003; 8(4):380-391. SPE-71603-PA. DOI: https://doi.org/10.2118/87335-PA
24. NghiemLX,AzizK,LiYK.Arobustiterativemethod for flash calculations using the Soave-Redlich-Kwong or the Peng-Robinson Equation of state. SPE J 1983; 23(3):521-530. SPE-8285-PA. DOI: https://doi.org/10.2118/8285-PA
25. Petitfrere M, Nichita DV. Robust and efficient trust-region based stability analysis and multiphase flash calculations. Fluid Phase Equilib 2014; 362(25 January): 51-68. DOI: https://dx.doi.org/10.1016/j.fluid.2013.08.039
26. Pan H, Connolly M, Tchelepi H. Multiphase equilib- rium calculation framework for compositional simula- tion of CO2 injection in low temperature reservoirs. Ind Eng Chem Res 2019; 58(5):2052-2070. DOI: https://doi.org/10.1021/acs.iecr.8b05229
27. Nagarajan NR, Cullick AS, Griewank A. New strategy for phase equilibrium and critical point calculations by thermodynamic energy analysis. Part I. Stability analysis and flash. Fluid Phase Equilib 1991; 62(3):191-210. DOI: https://doi.org/10.1016/0378-3812(91)80010-S
28. Michelsen ML. State Function based flash specifica- tions. Fluid Phase Equilibria 1999; 158:617-626. DOI: https://doi.org/10.1016/S0378-3812(99)00092-8
29. CismondiM.Phaseenvelopesforreservoirfluidswith asphaltene onset lines: An integral computation strategy for complex combinations of two- and three-phase behaviors. Energ Fuel 2018; 32(3):2742-2748. DOI: https://doi.org/10.1021/acs.energyfuels.7b02790
30. Polıvka O, Mikyska J. Compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification. J Comput Phys 2014; 272(4):149-169. DOI: http://dx.doi.org/10.1016/j.jcp.2014.04.029
31. Sandoval DR, Michelsen ML, Yan W, Stenby EH. VT-based phase envelope and flash calculations in the presence of capillary pressure. Ind Eng Chem Res 2019; 58(13):5291-5300. DOI: https://doi.org/10.1021/acs.iecr.8b05976
32. Achour SH, Okuno R. Phase stability analysis for tight porous media by minimization of the Helmholtz free energy. Fluid Phase Equilib 2020; 520: 112648. DOI: http://dx.doi.org/10.26153/tsw/8298
33. Achour SH, Okuno R. Two-phase flash for tight po- rous media by minimization of the Helmholtz free energy. Fluid Phase Equilib 2021; 534:112960. Available at: https://www.x-mol.com/paperRedirect/126647712249 6536576
34. Fontalba F, Richon D, and Renon H. Simultaneous
determination of vapor-liquid equilibria and saturated densities up to 45 MPa and 433 K. Rev Sci Instrum 1984; 55(6):944-951. DOI: https://doi.org/10.1063/1.1137870
35. Kikani J, Ratulowski J. Consistency check and rec- onciliation of PVT data from samples obtained with formation testers using EOS models. SPE Res Eval Eng 1998; 1(4):348-353. SPE-50979-PA. DOI: https://doi.org/10.2118/50979-PA
36. Roedder E, Bodnar RJ. Geologic pressure determi- nations from fluid inclusion studies. Ann Rev Earth Planet Sci 1980; 8(1):263-301. DOI: https://doi.org/10.1146/annurev.ea.08.050180.00140 3
37. Liu DH, Xiao XM, Mi JK, Li XQ, Shen JK, Song ZG, Peng PA. Determination of trapping pressure and temperature of petroleum inclusions using pvt simu- lation software—A case study of lower ordovician carbonates from the Lunnan low uplift, Tarim Basin. Marin Petrol Geol 2003; 20(1):29-43. DOI: https://doi.org/10.1016/S0264-8172(03)00047-3
38. Esposito RO, Castier M, Tavares FW. Calculations of thermodynamic equilibrium in systems subject to gravitational fields. Chem Eng Sci 2000; 55(17):3495-3504. DOI: https://doi.org/10.1016/S0009-2509(00)00010-5
39. CabralVF,CastierM,TavaresFW.Thermodynamic equilibrium in systems with multiple adsorbed and bulk phases. Chem Eng Sci 2005; 60(6):1773-1782. DOI: http://dx.doi.org/10.1016%2Fj.ces.2004.11.007
40. Castier M, Tavares FW. Centrifugation equilibrium of natural gas. Chem Eng Sci 2005; 60(11):2927-2935. DOI: https://doi.org/10.1016/j.ces.2004.12.027
41. Velez A, Pereda S, Brignole EA. Isochoric lines and determination of phase transitions in supercritical reactors. J Supercrit Fluids 2010; 55(2):643-647. DOI: https://doi.org/10.1016/j.supflu.2010.09.033
42. Mikyska J, Firoozabadi A. A new thermodynamic function for phase-splitting at constant temperature, moles, and volume. AIChE J 2011; 57(7):1897-1904. DOI: https://doi.org/10.1002/aic.12387
43. Jindrova T, Mikyska J. Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles. Fluid Phase Equilib 2013; 353(7):101-114. DOI: http://dx.doi.org/10.1016/j.fluid.2013.05.036
44. Jindrova T, Mikyska, J. General algorithm for multi- phase equilibria calculation at given volume, temper- ature, and moles. Fluid Phase Equilib 2015; 393:7-25. DOI: http://dx.doi.org/10.1016/j.fluid.2015.02.013
45. Lu C, Jin Z, Li H. A Two-phase flash algorithm with the consideration of capillary pressure at specified mole numbers, volume and temperature. Fluid Phase Equilib 2019; 485:67-82. DOI: https://doi.org/10.1016/j.fluid.2018.12.002
46. Nichita DV. New unconstrained minimization methods for robust flash calculations at temperature, volume and moles specifications. Fluid Phase Equilib 2018; 466:31-47. DOI: https://doi.org/10.1016/j.fluid.2018.03.012
47. Cismondi M, Ndiaye PM, Tavares FW. A new simple and efficient flash algorithm for T-v specifications. Fluid Phase Equilib 2018; 464:32-39. DOI: http://dx.doi.org/10.1016/j.fluid.2018.02.019
48. Lu C, Jin Z, Li H, Xu L. Simple and robust algorithm for multiphase equilibrium computations at tempera- ture and volume specifications. SPE J 2021; 26(4):2397-2416. https://www.x-mol.com/paperRedirect/142556247354 5318400
49. Mikyska J, Firoozabadi A. Investigation of mixture stability at given volume, temperature, and number of moles. Fluid Phase Equilib 2012; 321:1-9. DOI: https://doi.org/10.1016/j.fluid.2012.01.026
50. Agarwal, RK, Li, YK, Nghiem, LX, Coombe DA. Mul- tiphase multi- component isenthalpic flash calcula- tions. J Can Pet Technol 1991; 30(3):69-75. PETSOC-91-03-07. DOI: https://doi.org/10.2118/91-03-07
51. Rezaveisi M, Sepehrnoori K, Pope GA, Johns RT. Thermodynamic analysis of phase behavior at high capillary pressure. SPE J. 2018; 23(6):1438-1451.
DOI: https://doi.org/10.2118/175135-PA
52. NeshatSS,OkunoR,PopeGA.Arigoroussolutionto the problem of phase behavior in unconventional formations with high capillary pressure, SPE J. 2018; 23(4):1438-1451. DOI: https://doi.org/10.2118/187260-PA
53. Neshat SS, Okuno R, Pope GA. Thermodynamic Stability Analysis of MultiComponent Mixtures with Capillary Pressure. SPE Reservoir Simulation Con- ference, Galveston, Texas, 10-11 April 2019. DOI: https://doi.org/10.2118/193888-MS
54. ShapiroAA,StenbyEH.Thermodynamicsofthe multicomponent vapor liquid equilibrium under capil- lary pressure difference. Fluid Phase Equilib 2001; 178(1-2): 17-32. DOI: https://doi.org/10.1016/S0378-3812(00)00403-9
55. Ertas D, Kelemen SR, Halsey TC. Petroleum expul- sion part 1. Theory of Kerogen Swelling in Multi- component solvents. Energ Fuel 2006; 20(1): 295-300. DOI: https://doi.org/10.1021/ef058024k
How to Cite
Lu, C., Wang, C., & Lin, R. (2022). The Development and Application of EOS-based VT Phase Behavior Calculation Algorithms in Petroleum Industry. Science Insights, 41(6), 697–712. https://doi.org/10.15354/si.22.or028
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