Advances in imaging technologies and high-performance computing are making it possible to perform Direct Numerical Simulation (DNS) of flow processes at the pore scale; nevertheless, the restrictions on the physical size of the sample (porous rock) that can be fully resolved using Navier-Stokes-based DNS are quite severe. For samples on the order of a cm 3 , the complexity of the spatial heterogeneity of the pore space precludes Navier-Stokes-based DNS. Even for smaller sizes, some microstructures are below the instrument resolution and are not resolved in the image. To deal with this challenge of having a wide range of length scales -even for ’small’ systems, we describe a micro-continuum formalism, based on the Darcy-Brinkman-Stokes (DBS) equation where flow and transport phenomena are governed by Navier-Stokes equations in the resolved regions (voxels containing fluids only) and by Darcy in the unresolved (solid-fluid aggregates) regions . This hybrid-scale modeling framework has been used successfully to compute the flow in a digital sandstone imaged with X-ray microtomography including sub-voxel porosity . The micro-continuum DBS approach has also been used to simulate dissolution phenomena at the pore-scale under single-phase conditions .
In this work, the micro-continuum formulation is extended to multiphase flow where two-immiscible fluids share the pore-space involving surface tension force and moving contact lines at the mineral surfaces. The multiphase micro-continuum model is used to investigate multiphase system with reactive transport and is compared with microfluidic experiments.
 C. Soulaine and H.A. Tchelepi. Micro-continuum approach for pore-scale simulation of subsurface processes. Transport
in Porous Media, 113, 431–456, (2016).
 C. Soulaine, F. Gjetvaj, C. Garing, S. Roman, A. Russian, P. Gouze and H.A. Tchelepi. The impact of sub-resolution
porosity of X-ray microtomography images on the permeability. Transport in Porous Media, 113, 227-243, (2016).
 C. Soulaine, S. Roman, A. Kovscek and H.A. Tchelepi. Mineral dissolution and wormholing from a pore-scale per-
spective. Journal of Fluid Mechanics, 827, 457–483, (2017).
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