Abstract
The key idea with multiscale methods for reservoir simulation is to construct a set of prolongation operators that interpolate solutions from a coarse spatial resolution to the grid resolution. Efficient multiscale methods need prolongation operators that accurately represent flow at the grid resolution. For high-contrast models, it is especially important that this flow interpolation is confined within high-contrast boundaries. In this paper, we present an improved algorithm to construct multiscale prolongation operators that better capture strong contrasts in geological properties. Specifically, to construct effective prolongation operators, the improved algorithm first finds dominant flow directions by comparing the values of connection transmissibility in a neighborhood, then emphasizes the interpolation along these dominant directions and ignores the interpolation in transverse direction if connection transmissibility is weak.
The new algorithm is implemented in a commercial reservoir simulator that also provides a commercial implementation of a state-of-the-art multiscale method. The advantage of the new algorithm is demonstrated using synthetic and real reservoir models with high-contrast features. We also analyze the interpolation errors of poorly constructed prolongation operators for such models to identify the root cause of the slow linear solver convergence rate. With the new algorithm, we obtain better linear and nonlinear convergence rates in the pressure solver and shorter simulation time than with a previously published state-of-the-art multiscale method.
For completeness, we also benchmark our multiscale pressure solver performance against a standard algebraic multigrid (AMG) fine-scale pressure solver, and we highlight differences in linear solver convergence and computational efficiency. Finally, we demonstrate that the new algorithm is beneficial for a real high-contrast heterogeneous field model.
