Special Session 108: New Developments in porous media

Reduced order hybrid modeling from pore-scale to core-scale

Malgorzata Peszynska
Oregon State University
Co-Author(s):    Tim Costa, Anna Trykozko
We propose a new paradigm for modeling flow and transport when the pore-scale geometry is changing due to, e.g., reactive transport, phase transitions, bioclogging, proppant, and/or matrix swelling; (denoted by the proxy $u$). Such changes are sometimes accounted for with ad-hoc algebraic relationships such as Carman-Kozeny for Darcy conductivities $K(\phi)$. Based on our experience with real pore-scale imaging data, we propose a new reduced order hybrid dynamic methodology for $K(u)$. We do not require transient simulations at pore-scale, but rather we rely on a set of values computed offline based on a) a stochastic parametrization of the modified pore-geometries, b) pore-scale flow solver with an Immersed Boundary, c) and a reduced order model which approximates $K(u)$. We (i) use a probability distribution $K(\phi,\omega)$ instead of $K(\phi)$ to accurately account for the evolving pore-scale. Next, (ii) given the character of $u$ (e.g., pore-filling, or pore-coating), we sample efficiently from the corresponding distribution of $K(\phi,\omega)$. In addition, (iii) we account for the local in time and space changes in $K(u)$ by introducing the intermediate third scale of pore-network. The latter step prevents the prohibitive complexity of local pore-scale transport computations.