Skip to main content
SpringerLink
Log in

Bridging between macroscopic behavior of shale gas reservoirs and confined fluids in nanopores

  • ORIGINAL PAPER
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

The macroscopic behavior of gas flow in multi-porosity shale gas reservoirs is rigorously derived within the framework of the reiterated homogenization procedure in conjunction with the Thermodynamics of Inhomogeneous Gases in nanopores. At the nanoscale, the Density Functional Theory is applied to reconstruct general adsorption isotherms and local density profiles of pure methane in the intraparticle porosity of the gas-wet organic matter. The description of adsorption incorporates both repulsive hard sphere effects and Lennard–Jones attractive intermolecular interactions between fluid-fluid supplemented by a fluid-solid exterior potential. Such local description reproduces the monolayer surface adsorption ruled by the Langmuir isotherm in the asymptotic regime of large pore size distributions. The nanoscopic model is upscaled to the microscale where kerogen particles and nanopores are viewed as overlaying continua forming the organic aggregates with adsorbed gas at local thermodynamic equilibrium with the free gas in the water partially saturated interparticle pores. The reaction/diffusion equation for pure gas movement in the kerogen aggregates is coupled with the Fickian diffusion of dissolved gas in the water phase and free gas Darcy flow in the adjacent interparticle pores which also lye in the vicinity of the inorganic solid phase (clay, quartz, calcite) assumed impermeable. By postulating continuity of fugacity between free and dissolved gas in the interparticle pores and neglecting the water movement, we upscale the microscopic problem to the mesoscale, where organic and inorganic matters along with interparticle pores are viewed as overlaying continua. The upscaling gives rise to a new nonlinear pressure equation for gas hydrodynamics in the interparticle pores including a new storativity coefficient dependent on water saturation, total organic carbon content (TOC), and intra- and interparticle porosities. When coupled with the nonlinear single phase gas flow in the hydraulic fractures, the homogenization of the mesoscopic model leads to a new microstructural model of triple porosity type with distributed mass transfer function between the different levels of porosity. Computational simulations illustrate the potential of the multiscale approach proposed herein in providing accurate numerical simulations of methane flow in shale gas reservoirs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Akkutlu, I.Y., Fathi, E.: Multiscale gas transport in shales with local kerogen heterogeneities. Soc. Pet. Eng. 17(04), 1002–1011 (2012)

    Google Scholar 

  2. Arbogast, T., Douglas, J., Hornung, U.: Modeling of naturally fractured reservoirs by formal homogenization techniques. In: Dautray, R (ed.) Frontiers in Pure and Applied Mathematics, pp 1–19. Elsevier, Amsterdam (1991)

  3. Auriault, J.L.: Heterogeneous media: Is an equivalent homogeneous description always possible? Int. J. Eng. Sci. 29, 785–795 (1991)

    Article  Google Scholar 

  4. Auriault, J.L., Boutin, C., Geindreau, C.: Homogenization of coupled phenomena in heterogenous media. Wiley (2009)

  5. Barenblatt, G.I., Zhelton, I.P., Kochina, I.N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. 24, 1286–1303 (1960)

    Article  Google Scholar 

  6. Bhatia, S.K., Nguyen, T.X., Tran, K., Nicholson, D.: The structure of high-pressure adsorbed fluids in slit-pores. Stud. Surf. Sci. Catal. 160, 503–509 (2007)

    Article  Google Scholar 

  7. Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media, vol. 3. Hydrological Papers (Colorado State University) (1964)

  8. Collin, M., Rasmuson, A.: A comparison of gas diffusivity models for unsaturated porous media. Soil Sci. Soc. Am. J. 52, 1559–1565 (1988)

    Article  Google Scholar 

  9. Daniel, J., Bohm, B., Layne, M.: Hydraulic fracturing considerations for natural gas wells of the marcellus shale. In: The Groundwater Protection Council 2008 Annual Forum, vol. 21-24, Cincinnati, OH (2008)

  10. Darabi, H., Ettehad, A., Javadpour, F., Sepehrnoori, K.: Gas flow in ultra-tight shale strata. J. Fluid Mech. 710, 641–658 (2012)

    Article  Google Scholar 

  11. Douglas, J., Arbogast, T.: Dual porosity models for flow in naturally fractured reservoirs. In: Cushman, J. H (ed.) Dynamics of Fluid in Hierarchical Porous Media, pp 177–222. Academic, New York (1990)

  12. Gonzalez, A., White, J.A., Roman, F.L., Velasco, S.: Density functional theory of fluids in nanopores: analysis of the fundamental measures theory in extreme dimensional-crossover situations. J. Chem. Phys. 125, 64703 (2006)

    Article  Google Scholar 

  13. Javadpour, F.: Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Petrol. Technol. 48(8), 16–21 (2009)

    Article  Google Scholar 

  14. Kierlik, E., Rosinberg, M.L.: Density-functional theory for inhomogeneous fluids: adsorption of binary mixtures. Phys. Rev. A 44, 5025–5037 (1991)

    Article  Google Scholar 

  15. Knudsen, M.: The laws of molecular and viscous flow of gases through tubes. Ann. Phys. 28, 75–177 (1909)

    Article  Google Scholar 

  16. Langmuir, I.: The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 40, 1403–1461 (1918)

    Article  Google Scholar 

  17. Mason, E.A., Malinauskas, A.P.: Gas transport in porous media: the dusty-gas model. Elsevier Science (1983)

  18. Mehmani, A., Prodanovic, M., Javadpour, F.: Multiscale, multiphysics network modeling of shale matrix gas flows. Trans. Porous Media 99, 377–390 (2013)

    Article  Google Scholar 

  19. Nguyen, T.X., Suresh, K.B., Nicholson, D.: Prediction of high-pressure adsorption equilibrium of supercritical gases using density functional theory. Langmuir 2005 21, 3187–3197 (2005)

    Google Scholar 

  20. Prausnitz, J.M., Lichtenthaler, R.N., Azevedo, D., Edmundo, G.: Molecular thermodynamics of fluid-phase equilibria. Prentice Hall (1998)

  21. Ranjbar, E., Hassanzadeh, H.: Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv. Water Resour. 34, 627–639 (2011)

    Article  Google Scholar 

  22. Robert, G.L., Robert, M.R., Stephen, C.R., Daniel, M.J.: Morphology, genesis, and distribution of nanometer-scale pores in siliceous mudstones of the mississippian barnett shale. J. Sed. Res. 79, 848–861 (2009)

    Article  Google Scholar 

  23. Rosenfeld, Y.: Free-energy model for the inhomogeneous hard-sphere fluid mixture and density functional theory of freezing. Phys. Rev. Lett. 63(09), 980–983 (1989)

    Article  Google Scholar 

  24. Roth, R.: Fundamental measure theory for hard-sphere mixtures: a review. J. Phys.: Condens. Matter 22, 063102 (2010)

    Google Scholar 

  25. Sakhaee-Pour, A., Bryant, S.: Gas permeability of shale. Soc. Pet. Eng. 15(04), 401–409 (2012)

    Google Scholar 

  26. Segura, C.J., Vakarin, E.V., Chapman, W.G., Holovko, M.F.: A comparison of density functional and integral equation theories vs Monte Carlo simulations for hard sphere associating fluids near a hard wall. J. Chem. Phys. 108, 4837 (1998)

    Article  Google Scholar 

  27. Sondergeld, C.H., Newsham, K.E., Rice, M.C., Rai, C.S.: Petrophysical considerations in evaluating and producing shale gas resources. Society of Petroleum Engineers, SPE Unconventional Gas Conference, Pennsylvania, USA (2010)

    Google Scholar 

  28. Steele, W.A.: The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci. 36(01), 317–352 (1973)

    Article  Google Scholar 

  29. Warren, J.E., Root, P.J: The behavior of naturally fractured reservoirs. Soc. Pet. Eng. 3, 245–255 (1963)

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Witherspoon, P.A., Saraf, D.N.: Diffusion of methane, ethane, propane, and n-butane in water from 25 to 43 °. J. Phys. Chem. 69(11), 3752–3755 (1965)

    Article  Google Scholar 

  32. Yan, B., Wang, Y., Killough, J.E.: Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs. Society of Petroleum Engineers, SPE Reservoir Simulation Symposium (2013)

  33. Ziarani, A., Aguilera, R.: Knudsen’s permeability correction for tight porous media. Trans. Porous Media 91, 239–260 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratório Nacional de Computação Científica LNCC/MCT, Av Getúlio Vargas 333, 25651–070, Petrópolis, RJ, Brazil

    Tien Dung Le, Marcio A. Murad & Patricia A. Pereira

  2. Ecole Nationale des Travaux Publics de l’Etat - ENTPE, Département Génie Civil et Bâtiment, Rue Maurice Audin, 69518, Vaulx-en-Velin Cedex, France

    Claude Boutin

Authors
  1. Tien Dung Le
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcio A. Murad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Patricia A. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Claude Boutin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcio A. Murad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Le, T.D., Murad, M.A., Pereira, P.A. et al. Bridging between macroscopic behavior of shale gas reservoirs and confined fluids in nanopores. Comput Geosci 20, 751–771 (2016). https://doi.org/10.1007/s10596-015-9511-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-015-9511-x

Keywords

Search

Navigation