Abstract
Multiscale methods have been shown to offer an order-of-magnitude increase in the speed of reservoir simulators. This may enable users to model complex fluid flow and geology with greater speed and flexibility than is available with the current computational technologies. Contemporary multiscale methods typically use a restriction operator to construct a reduced system of flow equations and a prolongation operator to map pressure unknowns from the reduced flow equations back to the original simulation grid. When combined with a local smoother, this gives an iterative solver that can efficiently compute approximate pressures to within a prescribed accuracy and still provide mass-conservative fluxes. We present an adaptive and flexible framework for combining multiple sets of such multiscale approximations. Each multiscale approximation can target a certain scale; geological features like faults, fractures, facies, or other geobodies; or a particular computational challenge like propagating displacement and chemical fronts, wells being turned on or off, etc. Multiscale methods that fit the framework are characterized by three features. First, the prolongation and restriction operators are constructed using a non-overlapping partition of the fine grid. Second, the prolongation operator is composed of a set of basis functions, each of which has compact support within a support region that contains a coarse grid block. Finally, the basis functions form a partition of unity.
Through a series of numerical examples that include idealized geology and flow physics as well as geological models of real assets, we demonstrate that the new framework increases the accuracy and efficiency of multiscale technology. In particular, we show how it is possible to combine multiscale approximations with different resolution as well as multiscale approximations targeting, among others, high-contrast fluvial sands; fractured carbonate reservoirs; challenging grids including faults, pinchouts and inactive cells; and complex wells.
Through a series of numerical examples that include idealized geology and flow physics as well as geological models of real assets, we demonstrate that the new framework increases the accuracy and efficiency of multiscale technology. In particular, we show how it is possible to combine multiscale approximations with different resolution as well as multiscale approximations targeting, among others, high-contrast fluvial sands; fractured carbonate reservoirs; challenging grids including faults, pinchouts and inactive cells; and complex wells.
