Abstract
The coverage of a medium by percolation and the effective permeability of a medium with stagnant zones are determined. It is shown that effective permeability is a function of external conditions, particularly the average pressure gradient. Three-, two-, and one-dimensional flows are discussed. The theory of overshoots of random functions and fields beyond a prescribed level [1, 2] is used for the investigation. Overshoots of elements of the percolation field in media with random inhomogeneities are studied. Overshoots of energy being dissipated in a volume are discussed in particular; this permits an approximate determination of the coverage of an inhomogeneous porous medium by migration during percolation with a limiting gradient, i.e., in the case of formation of stagnant zones chaotically disseminated in the flow region.
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Literature cited
A. A. Sveshnikov, Applied Methods of Random Functions [in Russian], Nauka, Moscow, 2nd edition (1968).
H. Cramer and M. Leadbetter, Stationary and Related Stochastic Processes, Wiley (1970).
M. M. Mendel'son and M. I. Shvidler, “Dispersion percolation effects in media with random inhomogeneities,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 6 (1967).
M. I. Shvidler, “Solution of the type of source in the problem of unsteady percolation of a fluid in a medium with random inhomogeneity,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1966).
B. I. Sultanov, “Percolation of viscoelastic fluids in a porous medium,” Izv. Akad. Nauk Azerb. SSR, Ser. Fiz.-Mat. i Tekhn. Nauk. No. 5 (1960).
Development of Investigations in Percolation Theory in the USSR (1917–1967) [in Russian], Nauka, Moscow (1969).
A. Kh. Mirzadzhanzade, A. M. Khasaev, R. S. Gurbanov, and Z. M. Akhmedov, “Gas-hydrodynamic characteristics of the exploitation of deposits of non-Newtonian oils,” Neft. Khoz., No. 8 (1968).
V. M. Entov, “Two-dimensional and unsteady one-dimensional problems of migration of non-Newtonian fluids in porous media,” Neft. Khoz., No. 10 (1968).
V. V. Devlikamov and Z. A. Khabibullin, “Structural-mechanical properties of oils of certain deposits of Bashkiria,” Neft. Khoz., No. 10 (1968).
M. G. Akishaev, G. G. Vakhitov, I. F. Glumov, and I. E. Fomenko, “Percolation of Devonian stratal oil at low temperatures,” in: Theory and Practice of Petroleum Production, Yearbook [in Russian], Nedra, Moscow (1966).
M. G. Alishaev, “Steady percolation with an initial gradient,” in: Theory and Practice of Petroleum Production, Yearbook [in Russian], Nedra, Moscow (1968).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 159–165, September–October, 1970.
The authors thank V. M. Entov for discussing the article and useful comments.
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Mendel'son, M.M., Shvidler, M.I. Percolation with a limiting gradient in a medium with random inhomogeneities. Fluid Dyn 5, 851–856 (1970). https://doi.org/10.1007/BF01017307
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DOI: https://doi.org/10.1007/BF01017307