A locally conservative finite element framework for the simulation of coupled flow and reservoir geomechanics

Abstract

In this paper, we present a computational framework for the simulation of coupled flow and reservoir geomechanics. The physical model is restricted to Biot's theory of single-phase flow and linear poroelasticity, but is sufficiently general to be extended to multiphase flow problems and inelastic behavior. The distinctive technical aspects of our approach are: (1) the space discretization of the equations. The unknown variables are the pressure, the fluid velocity, and the rock displacements. We recognize that these variables are of very different nature, and need to be discretized differently. We propose a mixed finite element space discretization, which is stable, convergent, locally mass conservative, and employs a single computational grid. To ensure stability and robustness, we perform an implicit time integration of the fluid flow equations. (2) The strategies for the solution of the coupled system. We compare different solution strategies, including the fully coupled approach, the usual (conditionally stable) iteratively coupled approach, and a less common unconditionally stable sequential scheme. We show that the latter scheme corresponds to a modified block Jacobi method, which also enjoys improved convergence properties. This computational model has been implemented in an objectoriented reservoir simulator, whose modular design allows for further extensions and enhancements. We show several representative numerical simulations that illustrate the effectiveness of the approach.

Stress and pore pressure histories in complex tectonic settings predicted with coupled geomechanical-fluid flow models

“…The geomechanical and flow fields are fully coupled in a stag- gered solution strategy using either sequential or iterative approaches (Lewis and Sukirman, 1993;Settari and Mourits, 1998;Settari and Walters, 2001;Mainguy and Longuemare, 2002;Dean et al, 2003;Thomas et al, 2002;Tran et al, 2004;Jha and Juanes, 2007).…”

Gas Flow Tightly Coupled to Elastoplastic Geomechanics for Tight- and Shale-Gas Reservoirs: Material Failure and Enhanced Permeability

“…This mixed-space discretization can provide advantages such as local mass conservation and better numerical stability in space, compared with the finite element method for both flow and geomechanics (Jha and Juanes 2007;Kim et al 2011a,b).…”

Numerical Studies on Two-Way Coupled Fluid Flow and Geomechanics in Hydrate Deposits

“…Two representative approaches can be used to simulate the 2W coupling of fluid flow and geomechanics: the fully coupled (monolithic) method or the sequential method (Zienkiewicz et al, 1988;Armero and Simo, 1992;Settari and Mourits, 1998;Wan, 2002;Dean et al, 2006;Jha and Juanes, 2007;Jean et al, 2007). The fully coupled method can provide a stable and convergent solution, but it requires a unified flow-mechanics simulator, and a unified grid that can provide sufficient definition of both the flow and geomechanical processes.…”

“…The space discretization implemented in the code provides local mass conservation at the element level and stable pressure fields due to piecewise constant interpolation (Phillips and Wheeler, 2007a,b;Jha and Juanes, 2007). This approach has distinct advantages compared to the piecewise continuous interpolation used in finite element schemes, which may result in early-time spurious pressure oscillations in consolidation problems (Vermeer and Verruijt, 1981;Loula, 1992, 1994;Wan, 2002;White and Borja, 2008).…”