An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media

Reservoir Simulator Runtime Enhancement Based ona PosterioriError Estimation Techniques

“…In [10,11] we derive fully computable a posteriori error estimates of the dual norm of the residual augmented by a nonconformity evaluation term for the thermal multiphase compositional general model. Moreover, in [8] the authors bound an energy-type norm of immiscible incompressible two-phase flow.…”

“…In [10,11] a posteriori error estimates are driven for the thermal multiphase compositional general model. However, in this work we focus on the two-phase flow since it is the model of our chosen study case (SPE10 case, see Sect.…”

“…First rigorous approachs can be found in [2][3][4] suitable for unsteady nonlinear models, and [5][6][7] for degenerated problems. Recently, abstract frameworks for a posteriori estimates appeared, for two-phase flow [8,9], multiphase compositional model [10], and the thermal multiphase compositional global model [11]. In these frameworks the dual norm of the residual augmented by a nonconformity evaluation term is controlled by fully computable estimators decomposed into space, time, linearization, and algebraic error components.…”

“…In this paper we propose an engineering approach of the a posteriori error estimates, provided by recent works [10,11], in order to establish an efficient computation of the estimators in such a way that we can ensure important computational savings for realistic complex models. Our approach is based on providing a low-cost evaluation formula by avoiding flux reconstructions.…”

“…Our approach is based on providing a low-cost evaluation formula by avoiding flux reconstructions. As mentioned before we rely here on the general ideas of [10,11], we apply a posteriori error estimators allowing to distinguish the different components of the global error, and we use them to formulate stopping criteria for the iterative algebraic and nonlinear solvers together with refinement/coarsening criteria for both the time step and the space mesh. The present work brings two major novelties: first, we propose a well-implemented evaluation of the estimators using a practical simplified formula making them usable in engineering practices; second, we apply the stopping criteria for the iterative algebraic solver in the context of a three-dimensional realistic reservoir simulation study.…”