Pore to continuum upscaling of permeability in heterogeneous porous media using mortars

Pore-scale modelling has become an accepted method for estimating macroscopic properties (such as permeability) that describe flow and transport in porous media. In many cases extracted macroscopic properties compare favourably to experimental measurements. However, computational and imaging restrictions generally limit the network size to the order of 1.0 mm3 and these models often ignore effects of surrounding flow behaviour. In this work permeability is upscaled in large (~106 pores), heterogeneous pore-scale network models using an efficient domain decomposition method. The large pore network is decomposed into 100 smaller networks (sub-domains) and then coupled with the surrounding models to determine accurate boundary conditions. Finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the network boundaries. The results compare favourably to the more computationally intensive (and impractical) approach of upscaling the medium as a single model. Additionally, the results are more accurate than straightforward hierarchical upscaling methods.