A study on solving the nonlinear seepage flow model of three-region composite reservoir

Abstract

This paper builds a seepage model of three-region composite reservoir, in which quadratic-gradient effect, well-bore storage, effective radius and three kinds of outer boundary conditions (constant pressure boundary, closed boundary and infinity boundary) are considered. With Laplace transformation, the seepage flow model is transformed into a boundary value problem of three-region composite zero-order modified Bessel equation by the substitution of variables and introduction of dimensionless variables. Based on the similar structure of the solution of the boundary value problem of differential equation, this paper obtains solutions of dimensionless reservoir pressure and dimensionless bottom-hole pressure of three-region composite reservoir in Laplace space. This research not only contributes to further analyse the inherent law of the solution and compile corresponding well test analysis software, but also solves corresponding mathematical model of reservoir and supplements the study on composite reservoir. Keywords-composite reservoir; non-linear seepage; quadratic-gradient term; well-bore storage; effective radius; similar structure of solution; similar kernel function