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On the extraction of gas from multilayered rock

Published online by Cambridge University Press:  22 May 2007

ADRIAN FARCAS  and
ANDREW W. WOODS
ADRIAN FARCAS
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Cambridge, CB3 0EZ, UK
ANDREW W. WOODS
Affiliation:
BP Institute for Multiphase Flow, University of Cambridge, Cambridge, CB3 0EZ, UK
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Abstract

This paper presents some simple analytical and numerical models which describe the dynamics of gas flowing from a multilayered low-permeability porous rock into a fracture. The models account for the vertical flow between relatively high- and low-permeability layers. The motion of gas in a permeable rock is governed by a nonlinear diffusion equation for the gas pressure. We analyse the gas flow described by this equation in both bounded and unbounded domains. In both cases simple scalings laws are developed to determine the fluxes and the dimensions of the regions within the rock which may be depleted over a given time scale. These are compared with the results of a full numerical model.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007 , pp. 79 - 95
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Aronson, D. G. & Peletier, L. A. 1981 Large time behaviour of solutions of the porous medium equation in bounded domains. J. Diffl Equat. 39, 378–412.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.Google Scholar
Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows Through Natural Rocks. Kluwer.Google Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Boussinesq, J. 1904 Recherches theoriques sur l'ecoulement des nappes d'eau infiltrees dans le sol et sur debit de sources. C. R. H. Acad. Sci, J. Math. Pures Appl. 10, 5–78 and 363–394.Google Scholar
Dagan, G. 1989 Flow and Transport in Porous Formations. Springer.Google Scholar
King, S. E. & Woods, A. W. 2003 Dipole solutions for viscous gravity currents: theory and experiments. J. Fluid Mech. 483, 91–109.Google Scholar
Leibenzon, L. S. 1929 Gas movement in a porous medium. Neft. i Slants. Khoz. 10, 497–519 (in Russian).Google Scholar
Muskat, M. & Botset, H. G. 1931 Flow of gases through porous materials. Physics 1, 27–47.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in Fortran 77. Cambridge University Press.Google Scholar
Shestakov, V. M. 1956 Some problems of modelling. In Voprosy Filtratsionnykh Raschetov Gidrotekhnicheskikh Sooruzheniy, pp. 129–139. Gosstroyizdat, Moskow (in Russian).Google Scholar