Use of dynamically adapted basis functions to accelerate multiscale simulation of complex geomodels

Abstract

A number of different multiscale methods have been developed as a robust alternative to upscaling and as a means for accelerated reservoir simulation of high-resolution geomodels. In their basic setup, multiscale methods use a restriction operator to construct a reduced system of flow equations on a coarser grid, and a prolongation operator to map pressure unknowns from the coarse grid back to the original simulation grid. The prolongation operator consists of basis functions computed numerically by solving localized flow problems. The resulting multiscale solver can both be used as a CPR-preconditioner in fully implicit simulators or as an efficient approximate iterative linear solver in a sequential setting; successful implementation of the latter approach in a commercial simulator was reported at ECMOR XV. Recently, it has been shown that significantly faster convergence is observed if one instead of using a single pair of prolongation-restriction operators, applies a sequence of such operators, where some of the operators are adapted to faults, fractures, facies, or other geobodies. Herein, we present how the convergence can be accelerated even further, if we also include additional basis functions that capture local changes in the pressure.