Mortar Methods for Pore-to-Continuum Modeling of Flow and Transport in Porous Media

Abstract:

Pore-scale network modeling has become an effective method for accurate prediction and upscaling of macroscopic properties in porous media. Computational and imaging restrictions generally limit the network size to the order of 1.0 mm³ (few thousand pores). For extremely heterogeneous media these models are not large enough to capture the petrophysical properties of the entire medium and inaccurate results can be obtained when upscaling to the continuum scale. Moreover, the boundary conditions imposed are artificial; a pressure gradient is imposed in one dimension so the influence of flow behavior in the surrounding media is not included. Here we model flow and transport at the pore scale but develop hybrid multiscale techniques to bridge the pore and macro-scales. Novel domain decomposition methods are used for upscaling; finite element mortars are used as a mathematical tool to ensure interfacial pressures and fluxes are matched at the interfaces of the networks boundaries. The results compare favorably to the more computationally intensive (and impractical) approach of upscaling the media as a single model. Moreover, the results are much more accurate than traditional hierarchal upscaling methods. This upscaling technique has important implications for using pore-scale models directly in reservoir simulators in a multiscale setting.