A Comparison of Techniques for Coupling Porous Flow and Geomechanics

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis paper compares three techniques for coupling multiphase porous flow and geomechanics. Sample simulations are presented to highlight the similarities and differences in the techniques. One technique uses an explicit algorithm to couple porous flow and displacements where flow calculations are performed every time step and displacements are calculated only during selected time steps. A second technique uses an iteratively coupled algorithm where flow calculations and displacement calculations are performed sequentially for nonlinear iterations during time steps. The third technique uses a fully coupled approach where the program's linear solver must solve simultaneously for fluid flow variables and displacement variables. The techniques for coupling porous flow with displacements are described, and comparison problems are presented for single-phase and three-phase flow problems involving poroelastic deformations. All problems in this paper are described in detail so the results presented here may be used for comparison with other geomechanical/porous flow simulators.

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

“…For example, reservoir geomechanics plays a critical role in compaction drive oil recovery, surface subsidence, stress dependent permeability of the matrix and fractures, wellbore stability, and production of tar-sand and heavy oil [12][13][14][15]. However, conventional reservoir simulation has oversimplified the mechanical effects using the rock compressibility, taken as a constant coefficient or a simple function of porosity, which cannot quantify the deformation and stress fields accurately.…”

“…In contrast to solving the mechanical problem first, other sequential methods have been investigated in reservoir engineering, where the flow problem is solved first [10,12,16,27,28]. The fluid flow produces a parabolic partial differential equation (PDE), whereas quasi-static mechanics produces an elliptic PDE.…”

“…The partitioning allows for the use of existing robust simulators for the sub-problems, producing smaller systems of equations to be solved than the fully coupled methods [26]. loosely coupled methods [3,12] or hybrid schemes of the fully coupled and sequential methods [25]. For all the strategies, stability and convergence are required for an accurate solution.…”

“…We partition the coupled problem and solve sub-problems sequentially. Each sub-problem can take a different implicit time-stepping algorithm [1,12,25]. The partitioning allows for the use of existing robust simulators for the sub-problems, producing smaller systems of equations to be solved than the fully coupled methods [26].…”

A comparison of adaptive time stepping methods for coupled flow and deformation modeling

“…An attractive alternative to full coupling is to hook together two independent codes (flow and deformation) through an interface (loose coupling) [5]. Settari and Mourits [12] and Dean et al [13] discuss iterative schemes which attempt to ensure the loosely-coupled solution converges to the fully-coupled (''true'') solution.…”