Modified Piezoconductivity Equation for Modeling Unsteady Filtration Processes in a Cavernous Medium

Abstract

The numeric investigation of non-stationary filtration slightly-compressible viscous fluid in porous media with high-permeable vugs was carried out. Obtained evidence that dynamic of pressure distribution in such media could not be described by solution of classical piezoconductivity equation (analogue of the heat equation). Using multipole expansion for describing pressure field perturbation was taken into account. This approach   allowed to  describe the  change of  the  liquid density in porous phase near vugs during filtration and, as a result, modified piezoconductivity equation was obtained. Comparison of numeric solution of modified piezoconductivity equation with results of direct numeric simulation of filtration in heterogeneous media shows that new equation could better describe this process.