1887

Abstract

Summary

Gas flow in shale is a complex phenomenon and is currently being investigated using a variety of modelling and experimental approaches. A range of flow mechanisms need to be taken into account when describing gas flow in shale including continuum, slip, transitional flow and Knudsen diffusion. A finite volume method (FVM) is presented to mathematically model these flow mechanisms. The approach incorporates the Knudsen number as well as the gas adsorption isotherm, allowing different flow mechanisms to be taken into account as well as methane sorption on organic matter. The approach is applicable to non-linear diffusion problems, in which the permeability and fluid density both depend on the scalar variable, the pressure. The FVM is fully conservative, as it obeys exact conservation laws in a discrete sense integrated over finite volumes. The method is validated first on unsteady-state problems for which analytical or numerical solutions are available. The approach is then applied for solving pressure-pulse decay tests and a comparison with an alternative finite element numerical solution is made. Results for practical laboratory pressure-pulse decay tests of samples with very low permeability are also presented.

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2014-09-08
2019-12-06
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References

  1. Al-Dhahir, A.A. and Tan, S.B.
    [1968] A Note on One-Dimensional Constant-Head Permeability Tests. Géotechnique, 18(4), 499–505.
    [Google Scholar]
  2. Beskok, A. and Karniadakis, G.E.
    [1999] A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales. Microscale. Thermophy. Eng., 3(1), 43–77.
    [Google Scholar]
  3. Civan, F., Rai, C.S. and Sondergeld, C.H.
    [2011a] Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms. Transport in Porous Media, 86(3), 925–944.
    [Google Scholar]
  4. [2011b] Shale Permeability Determined by Simultaneous Analysis of Multiple Pressure-Pulse Measurements Obtained under Different Conditions. Paper 144253-MS, Society of Petroleum Engineers. North American Unconventional Gas Conference and Exhibition, 14–16 June, The Woodlands, Texas, USA.
    [Google Scholar]
  5. Crook, T.
    [2013] Personal communication.
    [Google Scholar]
  6. Esaki, T., Zhang, M., Takeshita, A. and Mitani, Y.
    [1996] Rigorous Theoretical-Analysis of a Flow Pump Permeability Test. ASTM Geotechnical Testing Journal, 19(3), 241–246.
    [Google Scholar]
  7. Freeman, C.M., Moridis, G.J. and Blasingame, T.A.
    [2011] A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems. Transport in Porous Media, 90, 268–.
    [Google Scholar]
  8. Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D. and Silliman, S.E.
    [1981] A Transient Laboratory Method for Determining the Hydraulic Properties of ‘Tight’ Rocks-I. Theory. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 18(3), 245–252.
    [Google Scholar]
  9. Javadpour, F.
    [2009] Nanopores and Apparent Permeability of Gas Flow in Mudrocks (shales and siltstone). J. Can. Pet. Technol., 48(8), 16–21.
    [Google Scholar]
  10. Klinkenberg, L.J.
    [1941] The permeability of porous media to liquids and gases. Drilling and Production Practice. American Petroleum Inst., 200–213.
    [Google Scholar]
  11. Lesnic, D., Elliott, L., Ingham, D.B., Clennell, B. and Knipe, R.J.
    [1997] A Mathematical Model and Numerical Investigation for Determining the Hydraulic Conductivity of Rocks. International Journal of Rock Mechanics and Mining Sciences, 34(5), 741–759.
    [Google Scholar]
  12. Lin, W.
    [1977] Compressible Fluid Flow Through Rocks of Variable Permeability. Rep. UCRL - 52304, 15 Lawrence Livermore Lab., Livermore, California.
    [Google Scholar]
  13. Lorinczi, P., Burns, A.D., Lesnic, D., Fisher, Q.J., Crook, A.J., Grattoni, C., Rybalcenko, K.
    [2014] Direct and Inverse Methods for Determining Gas Flow Properties of Shale. Paper SPE 167750, Society of Petroleum Engineers. SPE/EAGE European Unconventional Resources Conference and Exhibition, 25–27 February2014, Vienna, Austria.
    [Google Scholar]
  14. Neuzil, C.E., Cooley, C., Silliman, S.E., Bredehoeft, J.D. and Hsieh, P.A.
    [1981] A Transient Laboratory Method for Determining the Hydraulic Properties of ‘Tight’ Rocks-II. Application. Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 18(3), 253–258.
    [Google Scholar]
  15. Oden, J.T.
    [1991] Finite Elements: An Introduction. In Handbook of Numerical Analysis, vol. 2, North-Holland, Amsterdam, 3–15.
    [Google Scholar]
  16. Patankar, S.V.
    [1980] Numerical Heat Transfer and Fluid Flow. Minkowycz and Sparrow (Eds) Series in Computational Methods in Mechanics and Thermal Sciences. Mc Graw Hill.
    [Google Scholar]
  17. Pong, K.C., Ho, C.M., Liu, J.Q. and Tai, Y.C.
    [1994] Non-Linear Pressure Distribution in Uniform Micro Channels. Applications of microfabrication to fluid mechanics. In: ASMEFED, 197, 56–.
    [Google Scholar]
  18. Roy, S., Raju, R., Chuang, H.F., Cruden, B.A. and Meyyappan, M.
    [2003] Modeling Gas Flow Through Microchannels and Nanopores. J. Appl. Phys., 93(8), 4870–4879.
    [Google Scholar]
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