Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media

04/2019

Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media

Monday 4th February 2019

Delpopolo Carciopolo, L.; Formaggia, L.; Scotti, A.; Hajibeygi, H.

Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The time-dependent saturation profile, on the other hand, has local sharp gradients (fronts) where the accuracy of the solution demands for tight time-step sizes. Therefore, accurate flow solvers need to resolve the spatial multiscale challenge, while advanced transport solvers need to also resolve the challenge related to time-step size. In this work, we develop the first integrated multirate multiscale method which implements a space-time conservative multiscale framework for sequentially coupled flow and transport equations. The method solves the pressure equation with a multiscale finite volume method at the spatial coarse scale, the transport equation is solved by taking different time-step sizes at different locations of the domain. At each time step, a coarse time step is taken, and then based on an adaptive recursive strategy, the front region is sharpened through a local-fine-scale time stepping strategy. The accuracy and efficiency of the method is investigated for a wide range of heterogeneous test cases. The results demonstrate that the proposed method provides a promising strategy to minimise the accuracy-efficiency tradeoff by developing an integrated space-time multiscale simulation strategy.

This report, or a modified version of it, has been also submitted to, or published on
Updated version 2019/11/26. Submitted to Elsevier