The Development of a Coupled Geomechanics and Reservoir Simulator Using a Staggered Grid Finite Difference Approach

Abstract

Abstract For a stress-sensitive reservoir, the constant rock compressibility term used in a conventional reservoir simulator (CRS), does not account for change of porosity and permeability. This paper develops a coupled geomechanics and reservoir simulator (CGRS) which accounts for changes in porosity and permeability related to deformation. The simulator in this paper adopts a staggered grid finite difference method for fluid flow and displacements. Displacements and pore pressures are placed at centers of faces and grid blocks, which increases numerical accuracy. Four types of nonlinear, coupled equations (porosity, permeability, displacements, and pressure equations) have been derived for use in CGRS. The Newton-Raphson method requires solving all the unknowns simultaneously, a computationally intensive procedure. An alternative is to use the Macro Gauss-Seidel method, which divides a huge nonlinear matrix into several smaller matrices, thus speeding up computations. Solutions from CGRS have been validated using two analytical solutions: a one dimensional consolidated reservoir and an idealized reservoir. This validated simulator is used to simulate a 3D reservoir with multiple vertical and horizontal wells. The comparison between CRS and CGRS shows that pressure depletes faster in CRS as compared to CGRS. CGRS results in higher bottom-hole pressure for a constant rate well. Constant rate wells yield a result of 1 to 1.26 times higher bottom-hole pressure than CRS. This shows that neglecting geomechanics effects in CRS can lead to an under prediction of reservoir/bottom hole pressures and production rates. Another powerful function of CGRS is the output of 3D displacements, which cannot be predicted by CRS. After producing for 1000 days, the maximum vertical displacement reaches 0.34 ft. (0.085% of reservoir thickness). Maximum displacements in the x and y directions (lateral displacements) are 4 × 10-4 ft. and 0.015 ft., both of which are smaller than vertical displacement because of fixed lateral boundary conditions. Unlike traditional iterative coupled (IC) methods, fluid flow and geomechanics share the same mesh, which solves the problem of numerical instability in two discretization methods used in traditional IC. Also, the change of volumetric strain with respect to time (usually neglected in traditional IC) has been included in the fluid flow equation to better characterize the effects of solids movement on fluid flow. The Macro Gauss-Seidel method was adopted to increase computation efficiency of the simulations. The simulator introduced in this paper has its own data structure for geomechanics analysis which can be incorporated in single-phase, two-phase, three-phase or compositional reservoir simulators.