The influence of adsorption layer thickness and pore geometry on gas production from tight compressible shales

Abstract

In tight shales, gas is stored in both free and adsorbed form. A one-dimensional model is derived for shale gas production by pressure depletion where the adsorbed layer thickness is of similar magnitude as the pore radius and can affect flow performance. The adsorbed layer thickness is a function of pressure. Different pore geometries are assumed varying continuously between spherical pores to more fracture shaped pores. The shale is assumed compressible and its porosity and pore radius reduce with pressure depletion. The effective pore radius (pore radius minus adsorption layer thickness) controls intrinsic and apparent permeability. The impact of the adsorption layer, compressibility and geometry are investigated. A given adsorbed layer thickness fills more of the pores when they are more spherical and concentrates more of the volumetric flow to the effective pore boundaries giving lower permeability for a given effective radius. Increasing the adsorbed thickness increases the adsorbed fraction initial gas in place. A high volume fraction adsorbed gas reduces apparent permeability and delays production. Pressure depletion causes both pore radius and adsorbed layer to be reduced. The change in adsorbed layer thickness is low at high pressure and greater at low pressure, while pore radius changes more linearly and more with higher compressibility. The free gas saturation and slip increases with pressure depletion for low compressible cases, but if matrix compression dominates there can be a net reduced permeability. Recovery was linear with the square root of time for all cases. Adsorbed gas is less effectively produced by pressure depletion than free gas and higher adsorbed content by more spherical pores or higher layer thickness reduces end recovery. Higher compressibility reduces permeability and delays recovery but increases end recovery. Higher compressibility reduces permeability and delays recovery but increases end recovery.

Cited as: Abolghasemi, E., Andersen, P.Ø. The influence of adsorption layer thickness and pore geometry on gas production from tight compressible shales. Advances in Geo-Energy Research, 2022, 6(1): 4-22. https://doi.org/10.46690/ager.2022.01.02

References

Ambrose, R. J., Hartman, R. C., Diaz-Campos, M., et al. Shale gas-in-place calculations part I: New pore-scale considerations. SPE Journal, 2012, 17(1): 219-229.

Andersen, P. Ø. A semi-analytical solution for shale gas production from compressible matrix including scaling of gas recovery. Journal of Natural Gas Science and Engineering, 2021a, 95: 104227.

Andersen, P. Ø. Steady state gas flow from tight shale matrix subject to water blocking. SPE Journal, 2021b, (in Press). Batchelor, C. K., Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge, UK, Cambridge University Press, 2000.

Berawala, D. S., Andersen, P. Ø. Evaluation of multicomponent adsorption kinetics for carbon dioxide enhanced gas recovery from tight shales. SPE Reservoir Evaluation & Engineering, 2020a, 23(3): 1060-1076.

Berawala, D. S., Andersen, P. Ø. Numerical investigation of non-Darcy flow regime transitions in shale gas production. Journal of Petroleum Science and Engineering, 2020b, 190: 107114.

Berawala, D. S., Andersen, P. Ø., Ursin, J. R. Controlling parameters during continuum flow in shale-gas production: A fracture/matrix-modeling approach. SPE Journal, 2019, 24(3): 1-378.

Beskok, A., Karniadakis, G. E. Report: A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophysical Engineering, 1999, 3(1): 43-77.

Bird, G. A., Brady, J. M. Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Vol. 5). Oxford, UK, Clarendon Press, 1994.

Bruggeman, V. D. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizit ätskonstanten und Leitf ¨ahigkeiten der Mischkörper aus isotropen Substanzen. Annalen Der Physik, 1935, 416(7): 636-664.

Cao, P., Liu, J., Leong, Y. K. Combined impact of flow regimes and effective stress on the evolution of shale apparent permeability. Journal of Unconventional Oil and Gas Resources, 2016, 14: 32-43.

Carman, P. C. Flow of Gases Through Porous Media. New York, USA, Academic Press, 1956.

Chen, F., Lu, S., Ding, X., et al. Evaluation of the density and thickness of adsorbed methane in differently sized pores contributed by various components in a shale gas reservoir: A case study of the Longmaxi Shale in Southeast Chongqing, China. Chemical Engineering Journal, 2019, 367: 123-138.

Civan, F. Reservoir Formation Damage-Fundamentals, Modeling, Assessment, and Mitigation. Gulf Professional Publishing, Amsterdam, the Netherlands, 2007.

Civan, F. Effective correlation of apparent gas permeability in tight porous media. Transport in Porous Media, 2010, 82(2): 375-384.

Civan, F., Rai, C. S., Sondergeld, C. H. Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Transport in Porous Media, 2011, 86(3): 925-944.

Clarkson, C. R., Nobakht, M., Kaviani, D., et al. Production analysis of tight-gas and shale-gas reservoirs using the dynamic-slippage concept. SPE Journal, 2012, 17(1): 230-242.

Curtis, J. B. Fractured shale-gas systems. AAPG Bulletin, 2002, 86(11): 1921-1938.

Darabi, H., Ettehad, A., Javadpour, F., et al. Gas flow in ultra-tight shale strata. Journal of Fluid Mechanics, 2012, 710: 641-658.

Dong, J. J., Hsu, J. Y., Wu, W. J., et al. Stress-dependence of the permeability and porosity of sandstone and shale from TCDP Hole-A. International Journal of Rock Mechanics and Mining Sciences, 2010, 47(7): 1141-1157.

Evans, H. P. Volume of an n-dimensional sphere. The American Mathematical Monthly, 1947, 54(10): 592-594.

GeoQuest, S. EcLipse 100 (Black Oil): Reference Manual and Technical Description. Houston, 2014.

Gou, Q., Xu, S. Quantitative evaluation of free gas and adsorbed gas content of Wufeng-Longmaxi shales in the Jiaoshiba area, Sichuan Basin, China. Advances in Geo-Energy Research, 2019, 3(3): 258-267.

Higashi, K., Ito, H., Oishi, J. Surface diffusion phenomena in gaseous diffusion. I. Surface diffusion of pure gas. Nippon Genshiryoku Gakkaishi (Japan), 1963, 5: 4129274.

Hornyak, G. L., Dutta, J., Tibbals, H. F., et al. Introduction to Nanoscience and Nanotechnology. Boca Raton, USA, CRC Press, 2008.

Javadpour, F. Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). Journal of Canadian Petroleum Technology, 2009, 48(8): 16-21.

Javadpour, F., Fisher, D., Unsworth, M. Nanoscale gas flow in shale gas sediments. Journal of Canadian Petroleum Technology, 2007, 46(10): 55-61.

Jiang, J., Yang, J. Coupled fluid flow and geomechanics modeling of stress-sensitive production behavior in fractured shale gas reservoirs. International Journal of Rock Mechanics and Mining Sciences, 2018, 101: 1-12.

Karniadakis, G., Beskok, A., Aluru, N. Microflows and Nanoflows: Fundamentals and Simulation. Berlin, Germany, Springer Science & Business Media, 2006.

Klewiah, I., Berawala, D. S., Walker, H. C. A., et al. Review of experimental sorption studies of CO2 and CH4 in shales. Journal of Natural Gas Science and Engineering, 2020, 73: 103045.

Langmuir, I. The constitution and fundamental properties of solids and liquids. Part I. Solids. Journal of the American Chemical Society, 1916, 38(11): 2221-2295.

Lee, A. L., Starling, K. E., Dolan, J. P., et al. Viscosity correlation for light hydrocarbon systems. AIChE Journal, 1964, 10(5): 694-697.

Li, M., Tang, Y. B., Bernab ´e, Y., et al. Percolation connectivity, pore size, and gas apparent permeability: Network simulations and comparison to experimental data. Journal of Geophysical Research: Solid Earth, 2017, 122(7): 4918-4930.

Li, Z. Z., Min, T., Kang, Q., et al. Investigation of methane adsorption and its effect on gas transport in shale matrix through microscale and mesoscale simulations. International Journal of Heat and Mass Transfer, 2016, 98: 675-686.

Loeb, L. B. The Kinetic Theory of Gases. North Chelmsford, USA, Courier Corporation, 2004.

Memon, A., Li, A., Jacqueline, N., et al. Study of gas sorption, stress effects and analysis of effective porosity and permeability for shale gas reservoirs. Journal of Petroleum Science and Engineering, 2020, 193: 107370.

Mengal, S. A., Wattenbarger, R. A. Accounting for adsorbed gas in shale gas reservoirs. Paper SPE 141085 Presented at SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 25-28 September, 2011.

Montgomery, S. L., Jarvie, D. M., Bowker, K. A., et al. Mississippian Barnett Shale, Fort Worth basin, north-central Texas: Gas-shale play with multi–trillion cubic foot potential. AAPG Bulletin, 2005, 89(2): 155-175.

Moridis, G. J., Blasingame, T. A., Freeman, C. M. Analysis of mechanisms of flow in fractured tight-gas and shale-gas reservoirs. Paper SPE 139250 Presented at SPE Latin American and Caribbean Petroleum Engineering Conference, Lima, Peru, 1-3 December, 2010.

Pang, Y., Soliman, M. Y., Deng, H., et al. Analysis of effective porosity and effective permeability in shale-gas reservoirs with consideration of gas adsorption and stress effects. SPE Journal, 2017, 22(6): 1739-1759.

Patzek, T., Male, F., Marder, M. A simple model of gas production from hydrofractured horizontal wells in shales. AAPG Bulletin, 2014, 98(12): 2507-2529.

Peng, D. Y., Robinson, D. B. A new two-constant equation of state. Industrial and Engineering Chemistry Fundamentals, 1976, 15(1): 59-64.

Perez, F., Devegowda, D. Estimation of adsorbed-phase density of methane in realistic overmature kerogen models using molecular simulations for accurate gas in place calculations. Journal of Natural Gas Science and Engineering, 2017, 46: 865-872.

Ren, W., Li, G., Tian, S., et al. Adsorption and surface diffusion of supercritical methane in shale. Industrial and Engineering Chemistry Research, 2017, 56(12): 3446-3455.

Shen, L., Chen, Z. Critical review of the impact of tortuosity on diffusion. Chemical Engineering Science, 2007, 62(14): 3748-3755.

Sheng, G., Javadpour, F., Su, Y. Effect of microscale compressibility on apparent porosity and permeability in shale gas reservoirs. International Journal of Heat and Mass Transfer, 2018, 120: 56-65.

Sheng, G., Su, Y., Zhao, H., et al. A unified apparent porosity/permeability model of organic porous media: Coupling complex pore structure and multi-migration mechanism. Advances in Geo-Energy Research, 2020, 4(2): 115-125.

Starling, K. E., Ellington, R. T. Viscosity correlations for nonpolar dense fluids. AIChE Journal, 1964, 10(1): 11-15.

Strapoc, D., Mastalerz, M., Schimmelmann, A., et al. Geo-chemical constraints on the origin and volume of gas in the New Albany Shale (Devonian–Mississippian), eastern Illinois Basin. AAPG Bulletin, 2010, 94(11): 1713-1740.

Valk ´o, P. P., Lee, W. J. A better way to forecast production from unconventional gas wells. Paper SPE 134231 Presented at SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September, 2010.

Wang, J., Luo, H., Liu, H., et al. An integrative model to simulate gas transport and production coupled with gas adsorption, non-Darcy flow, surface diffusion, and stress dependence in organic-shale reservoirs. SPE Journal, 2017, 22(1): 244-264.

Wu, Y. S., Li, J., Ding, D., et al. A generalized framework model for the simulation of gas production in unconventional gas reservoirs. SPE Journal, 2014, 19(5): 845-857.

Xiong, X., Devegowda, D., Michel, G. G., et al. A fully-coupled free and adsorptive phase transport model for shale gas reservoirs including non-Darcy flow effects. Paper SPE 159758 Presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8-10 October, 2012.

Yang, B., Kang, Y., You, L., et al. Measurement of the surface diffusion coefficient for adsorbed gas in the fine meso-pores and micropores of shale organic matter. Fuel, 2016, 181: 793-804.

Yin, Y., Qu, Z. G., Zhang, J. F. An analytical model for shale gas transport in kerogen nanopores coupled with real gas effect and surface diffusion. Fuel, 2017, 210: 569-577.

Yu, W., Sepehrnoori, K. Simulation of gas desorption and geomechanics effects for unconventional gas reservoirs. Fuel, 2014, 116: 455-464.

Zarragoicoechea, G. J., Kuz, V. A. Critical shift of a confined fluid in a nanopore. Fluid Phase Equilibria, 2004, 220(1): 7-9.

Zhao, K., Du, P. Performance of horizontal wells in composite tight gas reservoirs considering stress sensitivity. Advances in Geo-Energy Research, 2019, 3(3): 287-303.

Zimmerman, R. W., Bodvarsson, G. S. Hydraulic conductivity of rock fractures. Transport in Porous Media, 1996, 23(1): 1-30.