Model reduction for coupled near-well and reservoir models using multiple space-time discretizations

Abstract

In reservoir simulations, fine fully-resolved grids deliver accurate model representations, but lead to large systems of nonlinear equations to solve every time step. Numerous techniques are applied in porous media flow simulations to reduce the computational effort associated with solving the underlying coupled nonlinear partial differential equations. Many models treat the reservoir as a whole. In other cases, the near-well accuracy is important as it controls the production rate. Near-well modeling requires finer space and time resolution compared with the remaining of the reservoir domain. To address these needs, we combine Model Order Reduction (MOR) with local grid refinement and local time stepping for reservoir simulations in highly heterogeneous porous media. We present a domain decomposition algorithm for a gas flow model in porous media coupling near-well regions, which are locally well-resolved in space and time with a coarser reservoir discretization. We use a full resolution for the near-well regions and apply MOR in the remainder of the domain. We illustrate our findings with numerical results on a gas flow model through porous media in a heterogeneous reservoir.