Rapoport -Leas Model for Two-phase Flow in Anisotropic Porous Media

As real hydrocarbon collectors have anisotropic properties the problem of generalization of classical theory describing two-phase flow in porous media for is very actual now. In classical Rapoport -Leas model [1] it used concept determination of absolute and phase permeability. For anisotropic media the tensor model for anisotropic porous media was created [2-3]. The tensor connection between speed of filtration and pressure gradient was established. Tensors phase and relative phase permeability are written out and examined and also laboratory method of determination of absolute permeability tensor has been developed . However problem of description two-phase flow in anisotropic layer had been solved only as generalization of the theory of Bakli-Leverett in which it is necessary that pressure in both phases was equal. In model pressure in various phases is different. Therefore for generalization of the Rapoport -Leas theory for anisotropic media it is necessary to take into consideration anisotropy for definition of the capillary pressure which equal to a difference of pressure in phases. In this report generalization of the mathematical model of Rapoport -Leas for anisotropic porous media is given. The formula for definition of the capillary pressure, setting communication between pressure in phases, is represented by scalar function from vector argument. For definition that scalar function the tensor of capillary pressure and a inverse tensor of characteristic linear dimension are introduced. It is shown that the Leverett function of saturation entered for isotropic porous media ( can be generalized by the fourth rank tensor. For generic the common theory of Rapoport -Leas for anisotropic media case new function (type of Leverett function ) and new relative phase permeability functions were created.