Streamline-based simulation in highly heterogeneous and anisotropic petroleum reservoirs using a non-orthodox MPFA method and an adaptive timestep strategy with unstructured meshes

Abstract

In this paper, an adaptive timestep size selection algorithm applied in streamline-based simulation for highly heterogeneous and anisotropic reservoirs is presented. To handle an arbitrarily, anisotropic, and discontinuous permeability tensor, we use a non-orthodox Multipoint Flux Approximation Method with a Diamond stencil (MPFA-D) discretize the pressure equation. For the solution of the transport equation, a classical time of flight discretization approach is used. To improve computational efficiency we use an adaption of the Modified IMPES (MIMPES), initially devised by Hurtado et al. (2006) and da Silva et al. (2016). To demonstrate and validate the efficiency and usefulness of our approach, we present various numerical simulations, including two-phase flows of oil and water in highly heterogeneous and anisotropic petroleum reservoirs and flows with high mobility ratios that present a challenge to streamline simulation. Our results are encouraging in comparison with other results found in the literature, achieving a better balance between accuracy and performance with minor grid orientation effects.