A Semi-Analytical Analysis of Gas Slippage Effect in Pressure Transient Behavior of Non-Condensate Gas Reservoirs with the Different Boundary Condition

Document Type : Research Article

Author

Skolkovo Institute of Science and Technology, Moscow, RUSSIA

Abstract

The conventional models utilized to study flow behavior in a Non-Condensate gas reservoir did not consider the effects of gas slippage and different outer boundary conditions. For gas wells with a constant production flow rate in a bounded oil or gas reservoir, commonly, the outer boundary conditions are infinite boundary conditions or zero flux. In this study, the dimensionless pseudo pressure and dimensionless derivative of pseudo pressure in the presence of 4 different outer boundary conditions (infinite reservoir, constant pressure, exponential, and power-law) besides effects of gas slippage, wellbore storage, and skin factor are analyzed. To do this, the dimensionless pseudo pressure partial differential equation of radial flow was derived from the combination of continuity equation with Darcy’s law, the equation of state, compressibility equation, and dimensionless parameters. Then the derived partial differential equation is solved analytically in the Laplace domain. The obtained results of this work have important significance to understand the effects of different conditions on the transient pressure behavior of Non-Condensate gas reservoirs.

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[1] Pascal H., Pascal F., Flow of Non-Newtonian Fluid Through Porous Media, International Journal of Engineering Science, 23(5): 571-585 (1985).
[2] Dabiri Atashbeyk M., Shahbazi K., Fattahi M., Pressure Profile Estimation through CFD in UBD Operation Considering with Influx to Wellbore, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 37(6): 271-283 (2018).
[3] Barzegar F., Azadi Tabar M., Masihi M., New Method of Generating and Clustering Pore Network Model, Oil Geomechanic, 3(2): 1-17 (2019).
[4] Ahmed T., "Reservoir Engineering Handbook", 3rd ed., Houton, Texas (2006).
[5] Azadi Tabar M., Barzegar F., Ghazanfari M.H., Mohammadi M., On the Applicability Range of Cassie–Baxter and Wenzel Equation: a Numerical Study, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10): 399- 399 (2019).
[6] Aziz K., Settari A., "Petroleum Reservoir Simulation", Chapman & Hall (1979).
[7] Azadi Tabar M., Ghazanfari M.H., Experimental Study of Surfapore Nanofluid Effect on Surface Free Energy of Calcite Rock, (in eng), Modares Mechanical Engineering, 19(3): 709-718 (2019).
[8] Azadi Tabar M., Ghazanfari M.H., Monfared A.D., On the Size-Dependent Behavior of Drop Contact Angle in Wettability Alteration of Reservoir Rocks to Preferentially Gas Wetting Using Nanofluid, Journal of Petroleum Science and Engineering, 178: 1143-1154 (2019).
[9] Zhao Y.-l., Zhang L.-h., Zhao J.-z., Luo J.-x., Zhang B.-n., Triple porosity Modeling of Transient Well Test and Rate Decline Analysis for Multi-Fractured Horizontal Well in Shale Gas Reservoirs, Journal of Petroleum Science and Engineering, 110: 253-262 (2013).
[10] Bahrami H., Siavoshi J., Interpretation of Reservoir Flow Regimes and Analysis of Well Test Data in Hydraulically Fractured Unconventional Oil and Gas Reservoirs, in: "SPE Unconventional Gas Conference and Exhibition", Society of Petroleum Engineers (2013).
[11] Spivey J.P., Lee W.J., "Applied Well Test Interpretation", Society of Petroleum Engineers Richardson, TX (2013).
[12] Xu S., Lee W.J., Two-Phase Well Test Analysis of Gas Condensate Reservoirs, in: "SPE Annual Technical Conference and Exhibition", Society of Petroleum Engineers (1999).
[13] Earlougher R.C., "Advances in Well Test Analysis", Henry L. Doherty Memorial Fund of AIME New York, (1977).
[14] Gringarten A.C., Ramey Jr H.J., Raghavan R., Unsteady-State Pressure Distributions Created by a Well with a Single Infinite-Conductivity Vertical Fracture, Society of Petroleum Engineers Journal, 14(04): 347-360 (1974).
[15] Ertekin T., Abou-Kassen J.H., King G.R., "Basic Applied Reservoir Simulations", Society of Petroleum Engineers (2001).
[16] von Rosenberg D.U., Local Mesh Refinement for Finite Difference Methods, in: "SPE Annual Technical Conference and Exhibition", Society of Petroleum Engineers (1982).
[17] Zhao Y.-L., Zhang L.-H., Liu Y.-h., Hu S.-Y., Liu Q.-G., Transient Pressure Analysis of Fractured Well in Bi-Zonal Gas Reservoirs, Journal of Hydrology, 524: 89-99 (2015).
[18] Azadi Tabar M., Mohammadi M., Jamshidi S., Hydraulically Fractured Bi-zonal Gas Reservoir Well Testing Using Dimensionless Numerical Simulation, Journal of Petroleum Research, 27(96-6): 32-45 (2018).
[19] Acosta L., Ambastha A., Thermal Well Test Analysis Using an Analytical Multi-Region Composite Reservoir Model, in: "SPE Annual Technical Conference and Exhibition": Society of Petroleum Engineers (1994).
[20] Earlougher Jr R.C., Kersch K., Kunzman W., Some Characteristics of Pressure Buildup Behavior in Bounded Multiple-Layered Reservoirs without Crossflow, Journal of Petroleum Technology, 26(10):  1178-1186 (1974).
[21] Corbett P.W., Hamdi H., Gurav H., Layered Fluvial Reservoirs with Internal Fluid Cross Flow: A Well-Connected Family of Well Test Pressure Transient Responses, Petroleum Geoscience, 18(2): 219-229 (2012).
[23] Veyskarami M., Hassani A.H., Ghazanfari M.H., "A New Insight Into Onset of Inertial Flow in Porous Media Using Network Modeling with Converging/Diverging Pores," Computational Geosciences, pp. 1-18, (2017).
[24] Freeman C., Moridis G., Blasingame T., A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems, Transport in Porous Media, 90(1): 253-  (2011).
[25] Holditch S.A., Tight Gas Sands, Journal of Petroleum Technology, 58(06): 86-93 (2006).
[26] Nelson P.H., Pore-Throat Sizes in Sandstones, Tight Sandstones, and Shales, AAPG Bulletin, 93(3): 329-340 (2009).
[27] Falk K., Coasne B., Pellenq R., Ulm F.-J., Bocquet L., Subcontinuum Mass Transport of Condensed Hydrocarbons in Nanoporous Media, Nature Communications, 6: 1-7 (2015).
[28] Clarkson C.R., Solano N., Bustin R. M., Bustin A.M.M., Chalmers G.R.L., He L., Melnichenko Y.B., Radliński A.P., Blach T.P., Pore Structure Characterization of North American Shale Gas Reservoirs Using USANS/SANS, Gas Adsorption, and Mercury Intrusion, Fuel, 103: 606-616 (2013).
[29] Wang L., Zhang Ronglei, Wang Cong, Xiong Yi, Zheng Xishen, Li Shangru, Jin Kai, Rui Zhenhua, Review of Multi-Scale and Multi-Physical Simulation Technologies for Shale and Tight Gas Reservoirs, Journal of Natural Gas Science and Engineering, 37: 560-578 (2017).
[30] Javadpour F., Fisher D., Unsworth M., Nanoscale Gas Flow in Shale Gas Sediments, Journal of Canadian Petroleum Technology, 46(10): 55-61 (2007).
[31] Ziarani A.S., Aguilera R., Knudsen’s Permeability Correction for Tight Porous Media, Transport in Porous Media, 91(1): 239-260 (2012).
[32] Civan F., Effective Correlation of Apparent Gas Permeability in Tight Porous Media, Transport in Porous Media, 82(2): 375-384 (2010).
[33] Veyskarami M., Hassani A.H., Ghazanfari M.H., Modeling of Non-Darcy Flow Through Anisotropic Porous Media: Role of Pore Space Profiles, Chemical Engineering Science,151: 93-104 (2016).
[34] Gerald C.F., Wheatley P.O., "Applied Mumerical Analysis", Addison-Wesley Reading, MA, (1984).
[35] Abramowitz M., Stegun I.A., "Handbook of Mathematical Functions: with Formulas", Graphs, and Mathematical Tables, Courier Corporation (1964).
[36] H. Cinco-Ley, Well-Test Analysis for Naturally Fractured Reservoirs, Journal of Petroleum Technology, 48(01): 51-54 (1996).
[38] Da Prat G., "Well Test Analysis for Fractured Reservoir Evaluation", Elsevier (1990).
[39] Lee J., "Well Testing, Society of Petroleum Engineers" (1982).