One-way versus two-way coupling in reservoir-geomechanical models

Procedures to couple reservoir and geomechanical models are reviewed. The focus is on immiscible, compressible, non-compositional reservoir - geomechanical models. Such models require the solution to: coupled stress, pressure, saturation and temperature equations. Although the couplings between saturation and temperature with stress and fluid pressure are «weak» and can be adequately captured thru staggered (fixed point) iterations, the coupling between stress and pressure equations are «strong» and require special procedures for accurate integration. Issues related to both simultaneous integration and sequential integration of pressure and stress equations are investigated. It is shown that simultaneous integration can be achieved by computing the contribution to the coupled Jacobian matrix through finite differencing of the residual equations. Forming the Jacobian matrix can also be avoided thru a partitioned CG iterative solution procedure of the Schur complement matrix. Iterative sequential integration (fixed point iterations) of pressure and stress equations are then discussed, and detailed algorithms are provided. Assessment of the accuracy of such iterative procedures is made through comparison with available exact analytical solutions for the half-space consolidation (McName and Gibson [1960]). The iterative sequential procedure (one-way coupling iteration) is shown to require an unreasonably large number of iterations (>50) to capture accurately coupling effects. Finally, the coupling effects in a field case are investigated: CO2 injection at In Salah, Algeria where CO2 is injected at a temperature (50 dgC) below the resident brine reservoir (90 dgC) temperature. Surface uplift displacements and induced tensile stresses in the caprock computed with both a fully two-way coupled scheme versus a one-way scheme are compared.