An Efficient Finite-Difference Method for Simulating Phase Segregation in the Matrix Blocks in Double-Porosity Reservoirs

Abstract

Summary An efficient finite-difference method is presented for simulating unsteady-state multi phase flow in the matrix blocks (primary porosity) of naturally fractured systems or other reservoirs that have two different porosities. The scheme obtains pressure and saturation distributions in the matrix blocks (rather than average values) by dividing the matrix into subdomains. The method is an extension of the double-porosity concept in which fractures are the continuum for fluid flow and the matrix rock is the primary storage medium that acts as a source term to the fractures. Examples show that this subdivision results in different recoveries from the conventional double-porosity models when phase segregation in the matrix blocks is important to the recovery mechanism. In this formulation, the fracture medium is the major flow path to the wellbore with the matrix subdomains as source terms. The matrix subdomains can be connected to each other or to the fractures in any way desired to conform to the physics of the reservoir. This approach lends itself to an efficient scheme for reducing the system of flow equations to the same structure as conventional single-porosity simulators. The method is presented for a fully implicit, one-dimensional (1D), two-phase (oil/water) simulator.