Upscaling permeability to unstructured grids using the multipoint flux approximation

Abstract

Grids used for flow simulation are often at a much coarser scale than that of grids for geological modelling due to computational demand. Unstructured grids offer increased flexibility for the flow grid design; however, solving the flow equations and upscaling from high resolution geological grids to the coarse flow grid is more complex than using coarse regular grids. The multipoint flux approximation (MPFA) is one technique applied to discretize the flow equations on unstructured grids. This paper develops an upscaling technique that uses the MPFA method to solve the flow equations on the fine- and coarse-scale grids. Unlike most cases where the fine-scale grid is regular or structured, this work utilizes a high resolution triangular grid that conforms to the coarse-scale grid. The triangular grid is generated using the coarse-scale interaction regions as constraints. Upscaling leads to transmissibility matrices of the coarse-scale interaction regions. Two different types of local boundary conditions for the MPFA upscaling approach are developed, including linear varying pressures and pressures computed by solving the flow equations around the element boundary. The method is tested using flow simulation on several cases. Results are comparable with flow using a high resolution regular grid.