MACROSCOPIC PRESSURE FILTRATION FIELD IN A MEDIUM WITH DOUBLE POROSITY

This article presents a mathematical model of the pressure fi ltration fi eld in a porous medium with a skeleton formed by two solid phases of identical elemental composition but differing by porosity and permeability, in which the pore space of solid phases is fi lled by a homogeneous fi ltering liquid. Based on the continuity equations for each of the phases, equations have been found for the pressure fi eld, and it was shown that the macroscopic averaged fi eld is described by a nonlinear equation which in the case of a weakly compressible moving phase is reduced to the equation of piezoconductivity with an effective compressibility parameter. Based on the asymptotic method, expressions have been constructed for the zero and fi rst coeffi cients of expansion of a nonlinear problem on macroscopic pressure fi ltration fi eld in the case of one-dimensional axisymmetric radial fi ltration in an oil-bearing gassy bed. An approach is suggested establishing the correspondence between the pressure fi elds for the linear and radial fl ows. Results of calculations by the obtained analytical dependences and fi nite-difference algorithms are presented, and the ideas about the dynamics of the pressure fi ltration fi elds are refi ned
   
Author:  A. I. Filippov, A. A. Koval′skii, O. V. Akhmetova, M. A. Zelenova, and M. R. Gubaidullin
Keywords:  fi ltration, double porosity, asymptotic expansion, fi nite-difference algorithm, nonlinear piezoconductivity equation
Page:  837