Applying a Duchon Spline Based on a Gauss-Newton Optimizer for Coupled Flow and Geomechanics for CO2 Sequestration

Abstract We utilize a superposition principle and an inversion approach to compute a consistent stress field that honors the available measurements and equilibrium. We address the compatibility problem by minimizing an objective function, which allows us to tune the degrees of freedom (DOF) we represent by piecewise linears as a depth function, i.e., like well-logs. As an extension, we propose an object-oriented software architecture that relies on an abstract "evaluator," injecting the variation of the underlined properties into existing finite element codes with minimal modifications. We explain the architecture, its testing, and applications to synthetic but realistic reservoir models for CO2 capture and sequestration applications (CCS). We present comprehensive numerical results encompassing the whole 3-D synthetic field heterogeneous poroelastic cases, one-way coupled with our in-house reservoir simulator, emphasizing CCS. We also tackle a gigantic synthetic Middle Eastern reservoir to show the approach's scalability on cluster computers. We present tabular information, such as the number of iterations, objective function values, and flops, to assess the optimization process performance. The results dictate that our optimization-based approach and evaluator's architecture can handle realistic stress fields that match the predefined measurements with a minimal computational cost regarding iterations and simulation jobs.