A New Solution Procedure for a Fully Coupled Geomechanics and Compositional Reservoir Simulator

Abstract

Traditional reservoir simulators cannot capture the complicated interactions between fluid production and reservoir rock deformation during hydrocarbon recovery. In particular, in a recovery process when both phase behavior and deformation of reservoir rock play critical roles, a coupled geomechanics and compositional reservoir model can rigorously capture the above physical relations between solid and fluids and thereby perform more precise history matchings and predictions for better well planning and reservoir management decisions. This paper considers a fully coupled geomechanics and compositional modeling process. A novel solution procedure for the associated fully coupled Jacobian system is presented using the Schur complement technique. The proposed approach has the following features:(1) it has similar convergence properties as the fully implicit method,(2) combined with Krylov subspace iterative solvers, it can deal with symmetric and unsymmetric problems, and(3) it can be easily parallelized to solve large-scale reservoir simulation problems. In this work, a parallel, fully implicit, equation of state compositional reservoir simulator was fully coupled with a geomechanics FEM module. For each Newton iteration, an original two by two block Jacobian system is converted to a Schur complement system, and then the associated Schur complement system is solved using a BiCGstab(l) iterative method; subsequently all the unknowns for the reservoir simulator and the geomechanics module are obtained at the same time. The above partition solution procedure is equivalent to a block Gaussian elimination; hence its convergence is similar to a fully implicit coupled procedure. The proposed approach is implemented to solve two- and three-dimensional compositional reservoir simulation case studies considering geomechanics effects. We also compare the results between the fully coupled and the iteratively coupled approaches. It is shown that this approach presents a viable alternative in solution methods for solving general coupled physical problems. Introduction It has been more than twenty years since researchers realized the importance of geomechanics for hydrocarbon production in stress-sensitive or stress-dependent reservoirs. The field problems caused by geomechanics impacts include reservoir subsidence, field producibility, well casing deformation, solid production, etc. Two elements, fluid (water, oil, and gas) and solid (porous rock), reside in the same reservoir. The porous medium serving as a skeleton may contain oil, gas, and water in its pores. The interactions between pore fluids and porous reservoir rock are complex and affect hydrocarbon recovery. In general, a traditional reservoir simulator cannot adequately or fully represent the ongoing coupled fluid-solid interactions during production, while a fully coupled geomechanics and fluid-flow model can capture these relations between fluid and solid and thereby present more precise history matchings and predictions for better field development and reservoir management decisions. Thus, a fully coupled geomechanics and reservoir simulator is a very useful tool for evaluating and analyzing oil and gas production in stress-sensitive fields. There are two types of solution procedures for solving a fully coupled multicomponent, multiphase flow and geomechanics model: iteratively coupled solution procedures (Settari and Mourits 1994; Chin et al. 2002; Pan, Sepehrnoori, and Chin 2007) and simultaneous solution procedures(Gutierrez and Lewis 1998; Chin, Raghavan, and Thomas 2000; Stone et al. 2000). Generally an iteratively coupled solution procedure is much more computationally efficient but less robust in solution convergence than a simultaneous solution procedure.

Iteratively Coupled Fluid Flow & Geomechanics Simulation using Estimated Equivalent Permeability and Porosity by Fractal and Statistical Methods

“…For the geomechanics model, the elasto-plastic model using Mohr-Coulomb failure criterion is employed. The basic governing equations for the geomechanics consist of equilibrium equation, strain-displacement relationship and constitutive equation (Chin, Raghavan, andThomas 1998, Pan, Sepehrnoori, andChin 2009). …”

“…For fluid flow analysis in FDM, the bulk volume of a reservoir domain is regarded to be constant during the simulation (Settari and Mourits 1998), whereas bulk volume and pore volume in the geomechanics FEM model are changed during the simulation. Therefore, the true porosity calculated from the geomechanics model cannot be directly used in the fluid flow model and it must be converted to reservoir porosity based on the constant bulk volume for the corresponding grid (Settari and Mourits 1998, Chin, Raghavan, and Thomas 2000, Chin et al 2002, Thomas et al 2003, Tran, Settari, and Nghiem 2004, Pan, Sepehrnoori, and Chin 2009.…”

“…Based on Terzaghi's theory, Biot (1941) developed a generalized 3D formulation of consolidation using a linear stress-strain relationship and single phase fluid flow. Following their work, many researchers have studied coupling between fluid flow and geomechanics (Geertsma 1957, Settari and Mourits 1998, Chin et al 2002, Thomas et al 2003, Tran, Settari, and Nghiem 2004, Jalali and Dusseault 2008, Pan, Sepehrnoori, and Chin 2009.…”

Evaluation of the impact of strain-dependent permeability on reservoir productivity using iterative coupled reservoir geomechanical modeling

“…In the full coupled scheme, the governing equations of reservoir and rock deformation are solved simultaneously at every time step. This method is unconditionally stable but it is computationally expensive (Gutierrez & Lewis, 2002;Pan et al, 2009). In the iterative coupled scheme, there exit different types depending on which variables are kept constant.…”

Numerical Modeling and Field Monitoring of Overburden Response during Geologic Sequestration

“…Also, these values were consistent and similar to results obtained from geophysical studies performed and suggested at the site (Wilson, 2009). (Biot, 1955;Biot, 1956a;Biot, 1956b;Biot and Wills, 1957;Geerstma, 1973;Geerstma, 1974;Hassanizadeh, 1986 b ;Settari and Mourits, 1998;Tran et al, 2002;Cook et al, 2004;Nghiem et al, 2004;Du and Wong, 2005;Settari et al, 2005;Chen et al, 2006;Nordbotten and Celia, 2006;Tran et al, 2008;Pan and Sepehrnoori, 2009). However, the mathematical details of coupled flow-deformation finite element analyses using ABAQUS is present in this study.…”