Micro-continuum Formulation for Modelling Dissolution in Natural Porous Media
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. Even for samples on the order of a cm3, the complexity of the spatial heterogeneity of the pore space precludes Navier-Stokes-based DNS. To deal with this challenge of having a wide range of length scales – even for `small’ systems, we describe a micro-continuum formalism, whereby locally averaged equations and associated coefficients can be used to model the effects of scales that are below instrument resolution and/or DNS capability. A hybrid modeling framework based on the Darcy-Brinkman-Stokes (DBS) equation is employed. In this approach, a single equation is applicable for flow in `channels’ (so-called `free flow') and in porous media (solid-fluid aggregates). A unified simulation framework for multi-physics problems of mass and heat transport in natural porous media based on a hybrid Darcy-Brinkman-Stokes approach is described. We discuss two specific applications: minerals dissolution in CO2-brine systems, and dissolution instabilities (worm-holing phenomena) associated with the acidizing treatment of carbonate formations.