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Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, Issue 7(118), Pages 75–84 (Mi vsgu429)  

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics

Method of sequential changing of stationary states for one-dimensional filtration problem with limiting gradient of pressure

O. V. Belovaa, V. Sh. Shagapovb

a Birsk branch of Bashkir State University, Birsk, 452453, Russian Federation
b Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa, 450025, Russian Federation

Abstract: Taking into account nonlinear effects observed in experiments with low-permeability layers, at low pressure gradients (e.g., about $10^5$ Pa/m), refinement of Darcy law is proposed. On the basis of this model, by means of method of sequential change of stationary states and the problem of one-dimensional filtering is numerically solved. It is established that approximate solutions received by the method of sequential change of stationary states, for the description of distribution of pressure in layer and a well production, will be agreed with the numerical solution of the equation of a filtration in full statement. The analysis of influence of pressure gradient $q$ and limiting exponent defining the rate of yield of the nonlinear filtration law to the linear Darcy's law with increasing pressure gradient $\gamma$, on the features of hydrodynamic fields and well production is carried out.

Keywords: filtration, ultra-low permeability, limiting pressure gradient, method of sequential change of stationary states.

Full text: PDF file (217 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file
UDC: 532.546
Received: 11.04.2014
Accepted:11.04.2014

Citation: O. V. Belova, V. Sh. Shagapov, “Method of sequential changing of stationary states for one-dimensional filtration problem with limiting gradient of pressure”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 7(118), 75–84

Citation in format AMSBIB
\Bibitem{BelSha14}
\by O.~V.~Belova, V.~Sh.~Shagapov
\paper Method of sequential changing of stationary states for one-dimensional filtration problem with limiting gradient of pressure
\jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya
\yr 2014
\issue 7(118)
\pages 75--84
\mathnet{http://mi.mathnet.ru/vsgu429}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Sh. Shagapov, O. V. Dudareva, “Proyavlenie nelineinykh effektov filtratsii v nizkopronitsaemykh kollektorakh pri peremennykh rezhimakh funktsionirovaniya skvazhiny”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 1(39), 102–114  mathnet  crossref  elib
  • Вестник Самарского государственного университета. Естественнонаучная серия
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