Analysis of multiphase flow in porous media for slightly compressible flow and rock

Abstract

Multiphase flow in porous media is a matter of different complexities with a long, rich history in the field of fluid mechanics. This is a subject with important technical applications, most notably in oil recovery from petroleum reservoirs and so on. The single-phase fluid flow through a porous medium is well characterized by Darcy’s law. In the petroleum industry and in other technical applications, transport is modeled by postulating a multiphase generalization of the Darcy’s law. In this; distinct pressures are defined for each constituent phase with the difference known as capillary pressure, determined by the interfacial tension, micro pore geometry and surface chemistry of the solid medium. For flow rates, relative permeability is defined that relates the volume flow rate of each fluid to its pressure gradient. In the present paper, there is an analysis about the mathematical laws and equations for the slightly compressible flow and rock and some important results have been founded. The results show that the velocity of the fluid at any phase varies inversely with the viscosity of the fluid. The capillary pressure of the capillary tube varies inversely with the radius of tube, and increases with increase in the surface tension of the fluid. It also varies inversely with the radii of curvature of the interface of the fluid. The pressure exerted by the fluid varies directly with its velocity and varies inversely with the absolute permeability of the porous medium.