An Adaptive Algebraic Dynamic Multilevel (A-ADM) and Multiscale Method with Enriched Basis Functions for the Simulation of Two- Phase Flows in Highly Heterogeneous Petroleum Reservoirs

Resumo

Classical Multiscale Finite Volume (MsFV) methods can produce highly oscillatory pressure solutions
(i.e. non-monotonic) for high permeability contrasts. This can be a serious problem as it can produce spurious gas
throughout the reservoir when the pressure erroneously falls below the bubble point pressure and it can
substantially increase the computational cost to solve the problem due to the necessity of extensive use of iterative
procedures in order to obtain a low-recirculation velocity field. In this paper, we propose an adaptive flow based
agglomeration strategy for correcting the non-physical terms present in the coarse transmissibility matrix by means
of a preprocessing local step. This is done by using a local recalculation of the basis functions in a patch defined
by a judicious grouping of dual coarse volumes that eliminates the spurious oscillations. Classical multilevel and
multiscale methods define a uniform level at each coarse control volume, i.e., the same mesh level is used at each
coarse control volume. As a result, it generates, in multiphase transport problems, the necessity of the inclusion of
volumes that do not contain the saturation front in the high-resolution level. In this context, we present a framework
to deal with non-uniform levels at each coarse control volume, which allows the use of fine-scale control volumes
only where it is strictly needed, in order to produce smaller coarse scale matrices than those from classical
multilevel multiscale methods.