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Pre‐Darcy Flow in Porous Media
Author(s) -
Dejam Morteza,
Hassanzadeh Hassan,
Chen Zhangxin
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2017wr021257
Subject(s) - darcy's law , porous medium , mechanics , pressure gradient , permeability (electromagnetism) , fluid dynamics , flow (mathematics) , geotechnical engineering , materials science , geology , porosity , physics , chemistry , biochemistry , membrane
Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre‐Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre‐Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre‐Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low‐permeability media such as shale and tight formations, where pre‐Darcy is the dominant flow regime.