Nonlinear Behavior and Characterization of Flow through Preferential Seepage Channels

Abstract

The Darcy linear equation has been widely used to describe the fluid flow in porous media. It is inaccurately used to describe the flow through preferential flowing paths which exert important influence on the performance of waterflooding reservoir. In this paper, the following two problems have been studied: (1) flow law in preferential flowing paths generated by water flooding; (2) sound nonlinear mathematical model considering special internal and external boundary conditions. The greater the permeability in porous medium becomes, the easier fluid can flow. Meanwhile the flow mechanism would change correspondingly as well. Exact solution of the nonlinear model is obtained analytically by integration. It is shown that in preferential flowing channels the flow velocity and the pressure gradient are a nonlinear relationship which is different from the traditional Darcy theory described as a straight line. Finally, the seepage characteristics of nonlinear flow and its influence are determined by analyzing the pressure gradient curve and velocity distribution between the observation point and the target well. Keywords: Preferential flowing paths; Non-linear model; Forchheimer equation; Integration method; Pressure gradient.