Thermodynamic Analysis of Phase Behavior at High Capillary Pressure
- Mohsen Rezaveisi (University of Texas at Austin) | Kamy Sepehrnoori (University of Texas at Austin) | Gary A. Pope (University of Texas at Austin) | Russell T. Johns (Pennsylvania State University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2018
- Document Type
- Journal Paper
- 1,977 - 1,990
- 2018.Society of Petroleum Engineers
- capillary condensation, phase behavior in nanopores, shale gas and tight oil reservoirs, capillary equilibrium, stability analysis
- 43 in the last 30 days
- 173 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs because of the small pores in the rock, so understanding the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale-gas and tight-oil reservoirs. As the main finding of this paper, first we show that the tangent-plane-distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis of the problem of phase stability with capillary pressure. Second, we demonstrate that there is a maximum capillary pressure (Pcmax) where calculation of capillary equilibrium using bulk-phase thermodynamics is possible and derive the necessary equations to obtain this maximum capillary pressure. We also briefly discuss the implementation of the capillary equilibrium in a general-purpose compositional reservoir simulator. Two simulation case studies for synthetic gas condensate reservoirs were performed to illustrate the influence of capillary pressure on production behavior for the fluids studied.
|File Size||1 MB||Number of Pages||14|
Al-Rub, F. A. A. and Datta, R. 1998. Theoretical Study of Vapor Pressure of Pure Liquids in Porous Media. Fluid Phase Equilibr. 147 (1–2): 65–83. https://doi.org/10.1016/S0378-3812(98)00223-4.
Al-Rub, F. A. A. and Datta, R. 1999. Theoretical Study of Vapor–Liquid Equilibrium Inside Capillary Porous Plates. Fluid Phase Equilibr. 162 (1–2): 83–96. https://doi.org/10.1016/S0378-3812(99)00197-1.
Beegle, B. L., Modell, M., and Reid, R. C. 1974. Legendre Transforms and Their Application in Thermodynamics. AIChE J. 20 (6): 1194–1200. https://doi.org/10.1002/aic.690200620.
Brusilovsky, A. I. 1992. Mathematical Simulation of Phase Behavior of Natural Multicomponent Systems at High Pressures With an Equation of State. SPE Res Eng 7 (1): 117–117. SPE-20180-PA. https://doi.org/10.2118/20180-PA.
Bui, K. and Akkutlu, I. Y. 2017. Hydrocarbons Recovery From Model-Kerogen Nanopores. SPE J. 22 (3): 854–862. SPE-185162-PA. https://doi.org/10.2118/185162-PA.
Chang, Y. B. 1990. Development and Application of an Equation of State Compositional Simulator. PhD dissertation, University of Texas at Austin, Austin, Texas.
Clarkson, C. R., Wood, J., Burgis, S. et al. 2012. Nanopore-Structure Analysis and Permeability Predictions for a Tight Gas Siltstone Reservoir By Use of Low-Pressure Adsorption and Mercury-Intrusion Techniques. SPE Res Eval & Eng 15 (6): 648–661. SPE-155537-PA. https://doi.org/10.2118/155537-PA.
Corey, A. T. 1986. Mathematics of Immiscible Fluids in Porous Media. Highlands Ranch, Colorado: Water Resources Publications.
Devegowda, D., Sapmanee, K., Civan, F. et al. 2012. Phase Behavior of Gas Condensates in Shales Due to Pore Proximity Effects: Implications for Transport, Reserves and Well Productivity. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-160099-MS. https://doi.org/10.2118/160099-MS.
Fevang, Ø. and Whitson, C. H. 1996. Modeling Gas-Condensate Well Deliverability. SPE Res Eval & Eng 11 (4): 221–230. SPE-30714-PA. https://doi.org/10.2118/30714-PA.
Firoozabadi, A. 1999. Thermodynamic of Hydrocarbon Reservoirs. New York City: McGraw-Hill.
Frooqnia, A. 2014. Numerical Simulation and Interpretation of Borehole Fluid-Production Measurements. PhD dissertation, University of Texas at Austin, Austin, Texas.
Frooqnia, A., Torres-Verdi´n, C., Sepehrnoori, K. et al. 2017a. Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs. SPE J. 22 (1): 389–406. SPE-183628-PA. https://doi.org/10.2118/183628-PA.
Frooqnia, A., Torres-Verdín, C., Sepehrnoori, K. et al. 2017b. Inference of Near-Borehole Permeability and Water Saturation From Time-Lapse Oil-Water Production Logs. J. Pet. Sci. Eng. 152 (April): 116–135. https://doi.org/10.1016/j.petrol.2017.03.005.
Ganjdanesh, R., Rezaveisi, M., Pope, G. A. et al. 2015. Treatment of Condensate and Water Blocks in Hydraulic Fractured Shale Gas-Condensate Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. SPE-175145-MS. https://doi.org/10.2118/175145-MS.
Hamada, Y., Koga, K., and Tanaka, H. 2007. Phase Equilibria and Interfacial Tension of Fluids Confined in Narrow Pores. J. Chem. Phys. 127 (8): 084908. https://doi.org/10.1063/1.2759926.
Helland, J. O. and Skjæveland, S. M. 2004. Three-Phase Capillary Pressure Correlation for Mixed-Wet Reservoirs. Presented at the SPE International Petroleum Conference in Mexico, Puebla City, Mexico, 7-9 November. SPE-92057-MS. https://doi.org/10.2118/92057-MS.
Javadpour, F. 2009. Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone). J Can Pet Technol 48 (8): 16–21. PETSOC-09-08-16-DA. https://doi.org/10.2118/09-08-16-DA.
Javadpour, F., Fisher, D., and Uusworth, M. 2007. Nanoscale Gas Flow in Shale Gas Sediments. J Can Pet Technol 46 (10): 55–61. PETSOC-07-10-06. https://doi.org/10.2118/07-10-06.
Jones, J. E. 1924. On the Determination of Molecular Fields.—II. From the Equation of State of a Gas. Proc. R. Soc. Lond. A. 106 (738): 463–477. https://doi.org/10.1098/rspa.1924.0082.
Katsube, T. J. 2000. Shale Permeability and Pore-Structure Evolution Characteristics. Report 2000-15, Geological Survey of Canada, Ontario, Canada.
Korrani, A. K. N. 2014. Mechanistic Modeling of Low Salinity Water Injection. PhD dissertation, the University of Texas at Austin, Austin, Texas.
Leverett, M. C. 1941. Capillary Behavior in Porous Solids. Society of Petroleum Engineers. Trans. AIME 142 (1): 152–169. SPE-941152-G. https://doi.org/10.2118/941152-G.
Li, Z., Jin, Z., and Firoozabadi, A. 2014. Phase Behavior and Adsorption of Pure Substances and Mixtures and Characterization in Nanopore Structures by Density Functional Theory. SPE J. 19 (1): 1096–1109. SPE-169819-PA. https://doi.org/10.2118/169819-PA.
Ma, Y. and Jamili, A. 2014. Modeling the Effects of Porous Media in Dry Gas and Liquid Rich Shale on Phase Behavior. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 12–16 April. SPE-169128-MS. https://doi.org/10.2118/169128-MS.
Michelsen, M. L. 1982. The Isothermal Flash Problem: Part I Stability Analysis. Fluid Phase Equilibr. 9 (1): 1–19. https://doi.org/10.1016/0378-3812(82)85001-2.
Morishige, K., Fujii, H., Uga, M. et al. 1997. Capillary Critical Point of Argon, Nitrogen, Oxygen, Ethylene, and Carbon Dioxide in MCM-41. Langmuir 13 (13): 3494–3498. https://doi.org/10.1021/la970079u.
Nojabaei, B., Johns, R. T., and Chu, L. 2013. Effect of Capillary Pressure on Phase Behavior in Tight Rocks and Shales. SPE Res Eval & Eng 16 (3): 281–289. SPE-159258-PA. https://doi.org/10.2118/159258-PA.
Nojabaei, B., Siripatrachai, N., Johns, R. T. et al. 2014. Effect of Saturation Dependent Capillary Pressure on Production in Tight Rocks and Shales: A Compositionally-Extended Black Oil Formulation. Presented at the SPE Eastern Regional Meeting, Charleston, West Virginia, 21–23 October. SPE-171028-MS. https://doi.org/10.2118/171028-MS.
Ortiz, V., López-Álvarez, Y. M., and López, G. E. 2005. Phase Diagrams and Capillarity Condensation of Methane Confined in Single- and Multi-Layer Nanotubes. Mol. Phys. 103 (19): 2587–2592. https://doi.org/10.1080/00268970500201869.
Pedersen, K. S., Christensen, P. L., and Shaikh, J. A. 2014. Phase Behavior of Petroleum Reservoir Fluids. Boca Raton, Florida: CRC Press.
Peng, D.-Y. and Robinson D. B. 1976. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundamen. 15 (1): 59–64. https://doi.org/10.1021/i160057a011.
Pope, G. A., Wu, W., Narayanaswamy, G. et al. 2000. Modeling Relative Permeability Effects in Gas-Condensate Reservoirs With a New Trapping Model. SPE Res Eval & Eng 3 (2): 171–178. SPE-62497-PA. https://doi.org/10.2118/62497-PA.
Rachford Jr., H. H. and Rice, J. D. 1952. Procedure for Use of Electronic Digital Computers in Calculating Flash Vaporization Hydrocarbon Equilibrium, Technical Note 136. J Pet Technol 4 (10): 327–328. SPE-952327-G. https://doi.org/10.2118/952327-G.
Rai, R. R. 2003. Parametric Study of Relative Permeability Effects on Gas-Condensate Core Floods and Wells. Master’s thesis, University of Texas at Austin, Austin, Texas.
Rezaveisi, M. 2015. Improvements in Phase Behavior Modeling for Compositional Simulation. PhD dissertation, University of Texas at Austin, Austin, Texas.
Sapmanee, K. 2011. Effects of Pore Proximity on Behavior and Production Prediction of Gas/Condensate. Master’s thesis, University of Oklahoma, Tulsa, Oklahoma.
Shapiro, A. A. and Stenby, E. H. 1999. High Pressure Multicomponent Adsorption in Porous Media. Fluid Phase Equilibr. 158–160 (June): 565–573. https://doi.org/10.1016/S0378-3812(99)00144-2.
Shapiro, A. A. and Stenby, E. H. 2001. Thermodynamics of the Multicomponent Vapor–Liquid Equilibrium Under Capillary Pressure Difference. Fluid Phase Equilibr. 178 (1–2): 17–32. https://doi.org/10.1016/S0378-3812(00)00403-9.
Sigmund, P. M., Dranchuk, P. M., Morrow, N. R. et al. 1973. Retrograde Condensation in Porous Media. SPE J. 13 (2): 93–104. SPE-3476-PA. https://doi.org/10.2118/3476-PA.
Singh, S. K., Sinha, A., Deo, G. et al. 2009. Vapor–Liquid Phase Coexistence, Critical Properties, and Surface Tension of Confined Alkanes. J. Phys. Chem. C 113 (17): 7170–7180. https://doi.org/10.1021/jp8073915.
Siripatrachai, N., Ertekin, T., and Johns, R. T. 2017. Compositional Simulation of Hydraulically Fractured Tight Formation Considering the Effect of Capillary Pressure on Phase Behavior. SPE J. 22 (4): 1046–1063. SPE-179660-PA. https://doi.org/10.2118/179660-PA.
Skjaeveland, S. M., Siqveland, L. M., Kjosavik, A. et al. 2000. Capillary Pressure Correlation for Mixed-Wet Reservoirs. SPE Res Eval & Eng 3 (1): 60–67. SPE-60900-PA. https://doi.org/10.2118/60900-PA.
Teklu, T. W., Alharthy, N., Kazemi, H. et al. 2014. Phase Behavior and Minimum Miscibility Pressure in Nanopores. SPE Res Eval & Eng 17 (3): 396–403. SPE-168865-PA. https://doi.org/10.2118/168865-PA.
Tester, J. W. and Modell, M. 1996. Thermodynamics and Its Applications. Upper Saddle River, New Jersey: Prentice Hall.
Trebin, F. A. and Zadora, G. I. 1968. Experimental Study of the Effect of a Porous Media on Phase Changes in Gas Condensate Systems. Neft i Gaz 8: 37–40.
Wang, Y., Yan, B., and Killough, J. 2013. Compositional Modeling of Tight Oil Using Dynamic Nanopore Properties. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166267-MS. https://doi.org/10.2118/166267-MS.
Zarragoicoechea, G. J. and Kuz, V. A. 2004. Critical Shift of a Confined Fluid in a Nanopore. Fluid Phase Equilibr. 220 (1): 7–9. https://doi.org/10.1016/j.fluid.2004.02.014.