Abstract: 
We propose a new paradigm for modeling flow and transport when the porescale 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 adhoc algebraic relationships such as CarmanKozeny for Darcy conductivities $K(\phi)$. Based on our experience with real porescale imaging data, we propose a new reduced order hybrid dynamic methodology for $K(u)$. We do not require transient simulations at porescale, but rather we rely on a set of values computed offline based on a) a stochastic parametrization of the modified poregeometries, b) porescale 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 porescale. Next, (ii) given the character of $u$ (e.g., porefilling, or porecoating), 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 porenetwork. The latter step prevents the prohibitive complexity of local porescale transport computations. 
