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Analytical analysis of gas diffusion into non-circular pores of shale organic matter

Published online by Cambridge University Press:  27 April 2017

Mehran Mehrabi ,
Farzam Javadpour Open the ORCID record for Farzam Javadpour [Opens in a new window]  and
Kamy Sepehrnoori
Mehran Mehrabi
Affiliation:
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, University Station, Austin, TX 78712, USA
Farzam Javadpour*
Affiliation:
Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X, Austin, TX 78713, USA
Kamy Sepehrnoori
Affiliation:
Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, University Station, Austin, TX 78712, USA
*
†Email address for correspondence: farzam.javadpour@beg.utexas.edu
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Abstract

The total of the gas in shale gas reservoirs is sourced from a combination of free, adsorbed and dissolved/diffused gas. The mechanisms of production of free and adsorbed gas have been studied by numerous researchers. In contrast, the evolution of the dissolved gas and its contribution to the total gas production is not well understood. In this study we model the effect of pore micro-structure in organic matter (OM) on the rate of gas production in shale reservoirs. In this regard, first, we solve the gas-in-solid diffusion equation over a general doubly connected spatial domain with external Neumann and internal Dirichlet boundary conditions. The obtained solution is applied systematically to multi-pore porous OM domains and then the effect of pore morphology on the rate of gas production is studied. Our model results show that pore geometry has a slight effect on the gas diffusion process, while total organic carbon, and OM porosity, pore size distribution and specific surface area, are dominant parameters. An abundance of very small pores in OM tremendously increases the diffuse gas contribution in the total gas reserve and production.

JFM classification

Mathematical Foundations: Computational methods Geophysical and Geological Flows: Geophysical and Geological Flows Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 656 - 677
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Copyright
© 2017 Cambridge University Press 

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References

Akkutlu, I. Y. & Fathi, E. 2012 Multiscale gas transport in shales with local kerogen heterogeneities. SPE J. 17 (04), 1–002.Google Scholar
Bai, B., Elgmati, M., Zhang, H. & Wei, M. 2013 Rock characterization of Fayetteville shale gas plays. Fuel. 105, 645–652.Google Scholar
Cao, T., Song, Z., Wang, S. & Xia, J. 2015 A comparative study of the specific surface area and pore structure of different shales and their kerogens. Sci. China. Earth. Sci. 58 (4), 510–522.Google Scholar
Carlson, E. S. & Mercer, J. C. 1991 Devonian shale gas production: mechanisms and simple models. J. Petrol. Tech. 43 (04), 476–482.Google Scholar
Civan, F. 2010 Effective correlation of apparent gas permeability in tight porous media. Trans. Porous Med. 82 (2), 375–384.Google Scholar
Civan, F., Rai, C. S. & Sondergeld, C. H. 2011 Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Trans. Porous Med. 86 (3), 925–944.Google Scholar
Cueto-Felgueroso, L. & Juanes, R. 2013 Forecasting long-term gas production from shale. Proc. Natl Acad. Sci. USA 110 (49), 19660–19661.Google Scholar
Cui, X., Bustin, A. M. M. & Bustin, R. M. 2009 Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications. Geofluids 9 (3), 208–223.CrossRefGoogle Scholar
Curtis, M. E., Sondergeld, C. H., Ambrose, R. J. & Rai, C. S. 2012 Microstructural investigation of gas shales in two and three dimensions using nanometer-scale resolution imaging. AAPG Bull. 96 (4), 665–677.Google Scholar
Darabi, H., Ettehad, A., Javadpour, F. & Sepehrnoori, K. 2012 Gas flow in ultra-tight shale strata. J. Fluid. Mech. 710, 641–658.Google Scholar
Delillo, T. K. & Pfaltzgraff, J. A. 1998 Numerical conformal mapping methods for simply and doubly connected regions. SIAM J. Sci. Comput. 19 (1), 155–171.Google Scholar
Etminan, S. R., Javadpour, F., Maini, B. B. & Chen, Z. 2014 Measurement of gas storage processes in shale and of the molecular diffusion coefficient in kerogen. Intl J. Coal. Geol. 123, 10–19.Google Scholar
Fornberg, B. 1984 A numerical method for conformal mapping of doubly connected regions. SIAM J. Sci. Stat. Comput. 5 (4), 771–783.Google Scholar
Gu, X., Cole, D. R., Rother, G., Mildner, D. F. R. & Brantley, S. L. 2015 Pores in marcellus shale: a neutron scattering and fib-sem study. Energ. Fuel. 29 (3), 1295–1308.CrossRefGoogle Scholar
Henrici, P. 1979 Fast fourier methods in computational complex analysis. SIAM Rev. 21 (4), 481–527.Google Scholar
Henrici, P. 1993 Applied and Computational Complex Analysis, Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions, vol. 3. Wiley.Google Scholar
Ibarra, D. R. O.2016 A new material balance methodology for quintuple porosity shale gas and shale condensate reservoirs. PhD thesis, University of Calgary.Google Scholar
Ibarra, D. R. O. & Aguilera, R. 2015 A material balance equation for stress-sensitive shale gas condensate reservoirs. In SPE Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers.Google Scholar
Ibarra, D. R. O. & Aguilera, R. 2017 A material-balance equation for stress-sensitive shale-gas-condensate reservoirs. SPE. Reserv. Eval. Eng 20 (1), 177260.Google Scholar
Javadpour, F. 2009 Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Petrol. Technol. 48 (08), 16–21.Google Scholar
Javadpour, F., Fisher, D. & Unsworth, M. 2007 Nanoscale gas flow in shale gas sediments. J. Can. Petrol. Technol. 46 (10).Google Scholar
Ji, L., Zhang, T., Milliken, K. L., Qu, J. & Zhang, X. 2012 Experimental investigation of main controls to methane adsorption in clay-rich rocks. Appl. Geochem. 27 (12), 2533–2545.Google Scholar
Kucuk, F., Alam, J. & Streib, D. L.1978 Reservoir engineering aspects and resource-assessment methodology of eastern devonian gas shales. Tech. Rep. Science Applications, Inc., Morgantown, WV (USA).Google Scholar
Laura, P. A. 1965 Conformal Mapping of a Class of Doubly Connected Regions. Catholic University of America.Google Scholar
Laura, P. A. & Ercoli, R. 1972 A solution of the unsteady diffusion equation in an arbitrary, doubly connected region. Nucl. Engng Des. 23 (1), 1–9.Google Scholar
Laura, P. A. & Susemihl, E. A. 1973 Determination of heat flow shape factors for hollow, regular polygonal prisms. Nucl. Engng Des. 25 (3), 409–412.Google Scholar
Lopez, B. & Aguilera, R. 2013 Evaluation of quintuple porosity in shale petroleum reservoirs. In SPE Eastern Regional Meeting. Society of Petroleum Engineers.Google Scholar
Ma, Y., Zhong, N., Cheng, L., Pan, Z., Dai, N., Zhang, Y. & Yang, L. 2016 Pore structure of the graptolite-derived OM in the Longmaxi shale, southeastern upper Yangtze region, China. Mar. Petrol. Geol. 72, 1–11.Google Scholar
Mehmani, A., Prodanović, M. & Javadpour, F. 2013 Multiscale, multiphysics network modeling of shale matrix gas flows. Trans. Porous Med. 99 (2), 377–390.Google Scholar
Naraghi, M. E. & Javadpour, F. 2015 A stochastic permeability model for the shale-gas systems. Intl J. Coal. Geol. 140, 111–124.Google Scholar
Patzek, T. W., Male, F. & Marder, M. 2013 Gas production in the Barnett shale obeys a simple scaling theory. Proc. Natl Acad. Sci. USA 110 (49), 19731–19736.Google Scholar
Ross, D. J. K. & Bustin, R. M. 2009 The importance of shale composition and pore structure upon gas storage potential of shale gas reservoirs. Mar. Petrol. Geol. 26 (6), 916–927.Google Scholar
Sang, Q., Li, Y., Yang, Z., Zhu, C., Yao, J. & Dong, M. 2016a Experimental investigation of gas production processes in shale. Intl J. Coal. Geol. 159, 30–47.Google Scholar
Sang, Q., Li, Y., Zhu, C., Zhang, S. & Dong, M. 2016b Experimental investigation of shale gas production with different pressure depletion schemes. Fuel 186, 293–304.Google Scholar
Schinzinger, R. & Laura, P. A. 1991 Conformal Mapping: Methods and Applications. Elsevier.Google Scholar
Singh, H., Javadpour, F., Ettehadtavakkol, A. & Darabi, H. 2014 Nonempirical apparent permeability of shale. SPE. Reserv. Eval. Engng 17 (03), 414–424.Google Scholar
Sparrow, E. M. & Ortiz, M. C. 1982 Heat transfer coefficients for the upstream face of a perforated plate positioned normal to an oncoming flow. Intl J. Heat Mass Transfer 25 (1), 127–135.CrossRefGoogle Scholar
Suleimenova, A., Bake, K. D., Ozkan, A., Valenza, J. J., Kleinberg, R. L., Burnham, A. K., Ferralis, N. & Pomerantz, A. E. 2014 Acid demineralization with critical point drying: a method for kerogen isolation that preserves microstructure. Fuel 135, 492–497.Google Scholar
Swami, V. & Settari, A. 2012 A pore scale gas flow model for shale gas reservoir. In SPE Americas Unconventional Resources Conference. Society of Petroleum Engineers.Google Scholar
Swami, V., Settari, A. & Javadpour, F. 2013 A numerical model for multi-mechanism flow in shale gas reservoirs with application to laboratory scale testing. In 75th EAGE Conference & Exhibition incorporating SPE EUROPEC, Society of Petroleum Engineers.Google Scholar
Tahmasebi, P., Javadpour, F. & Sahimi, M. 2015 Multiscale and multiresolution modeling of shales and their flow and morphological properties. Sci. Rep. 5.CrossRefGoogle ScholarPubMed
Tahmasebi, P., Javadpour, F., Sahimi, M. & Piri, M. 2016 Multiscale study for stochastic characterization of shale samples. Adv. Water. Resour. 89, 91–103.Google Scholar
Wang, Y., Zhu, Y., Liu, S. & Zhang, R. 2016 Methane adsorption measurements and modeling for organic-rich marine shale samples. Fuel 172, 301–309.Google Scholar
Wu, T. & Zhang, D. 2016 Impact of adsorption on gas transport in nanopores. Sci. Rep. 6.Google ScholarPubMed
Yan, B., Wang, Y. & Killough, J. E. 2016 Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs. Comput. Geosci. 20 (1), 69–91.Google Scholar
Yang, Z., Wang, W., Dong, M., Wang, J., Li, Y., Gong, H. & Sang, Q. 2016 A model of dynamic adsorption–diffusion for modeling gas transport and storage in shale. Fuel 173, 115–128.Google Scholar
Yu, W., Sepehrnoori, K. & Patzek, T. W. 2016 Modeling gas adsorption in marcellus shale with langmuir and bet isotherms. SPE J. 21 (2), 170801.Google Scholar
Zhang, P., Hu, L., Meegoda, J. N. & Gao, S. 2015 Micro/nano-pore network analysis of gas flow in shale matrix. Sci. Rep. 5.Google Scholar
Zhang, T., Ellis, G. S., Ruppel, S. C., Milliken, K. & Yang, R. 2012 Effect of organic-matter type and thermal maturity on methane adsorption in shale-gas systems. Org. Geochem. 47, 120–131.Google Scholar
Zhou, S., Yan, G., Xue, H., Guo, W. & Li, X. 2016 2d and 3d nanopore characterization of gas shale in Longmaxi formation based on FIB-SEM. Mar. Petrol. Geol. 73, 174–180.Google Scholar