Linear Solution Techniques for Reservoir Simulation with Fully Coupled Geomechanics a Report Submitted to the Department of Energy Resources Engineering of Stanford University in Partial Fulfillment of the Requirements for the Degree of Master of Science

Direct modeling of geomechanics in reservoir simulation has gained a massive amount of interest in the last decade, due both to the increase in the available computing power and advances in numerical modeling, and to the importance of accurate representation of mechanical effects in many unconventional reservoirs. Both fully implicit and sequential implicit modeling approaches have been developed, with the latter being more popular due to easier coupling of existing simulation codes. Fully implicit simulation of coupled multiphase flow and poromechanics presents a challenge to the linear solver, that must be capable of handling and efficiently solving a large sparse linear system characterized by block structure resulting from discretizing and linearizing the system of governing equations of mass and momentum conservation. In this work a linear solver framework subject to the above requirements is developed, building on and extending the existing techniques, and implemented in Automatic Differentiation General Purpose Research Simulator (AD–GPRS). First, existing data structures for sparse Jacobian storage, previously specialized to flow and transport problems with wells, are extended to handle an unlimited number of physical problems, in particular, geomechanics. Second, a generalized block–partitioned preconditioning operator is implemented, to provide the baseline (though possibly inefficient) technique for handling coupled systems of equations of any kind. Finally, an efficient preconditioning operator for multiphase flow and geomechanics is presented based on a combination of Constrained Pressure Residual (CPR) approach and the Fixed–stress preconditioning operator recently developed for single–phase flow. The proposed methods are tested on several models and a clear advantage of the Fixed– stress CPR algorithm with respect to iteration count and CPU time is shown.