TWO-LEVEL MODEL OF TIME-DEPENDENT FILTRATION IN SEAMY-POROUS MEDIA

V.M. Konyukhov, A.N. Chekalin
VANT. Ser.: Mat. Mod. Fiz. Proc 2001. Вып.3. С. 37-48.

The authors have developed a two-level mathematical model of timedependent processes of oil recovery under water drive in a seamy-porous pool, formed with blocks, surrounded by cracks. The processes in the cracks (outer level) are described by the equations of two-phase filtration with regard to elasticity capacity of cracks and fluids with linear saturation dependence of phase permeabilities. Mass sources, included into these equations, are integral characteristics of the problem solution for blocks (inner level). The process of two-phase filtration is considered in each individual block. The blocks have their own coordinate system; coordinates of an outer problem act as parameters of an inner problem. The equations of two-phase filtration with regard to elasticity capacity of porous medium and phases with cubic saturation dependence of relative phase permeabilities are used for describing processes in blocks. In these equations source terms are absent, as mass transfer between a crack and a block goes on through the block boundary.
    A difference scheme for solving these interrelated problems is presented; numerical methods and algorithms are described. The results of computational experiments on studying oil recovery mechanism and iterative effect on seamy-porous pool are given.