Regressed Models for Multirate Mass Transfer in Heterogeneous Media

Abstract

AbstractSeveral applications to flow and transport in sorptive porous media are fundamentally dependent on the heterogeneous medium properties. This poses a challenge for direct numerical simulations, as fine grids are needed. One alternative approach is the application of the multirate mass transfer (MRMT) method. In this approach, rather than explicitly modeling immobile regions, such as clay layers, the solute concentration in these regions is treated by explicit state variables, and the transport between mobile and immobile regions is modeled by first‐order exchange terms. In the implementation of this approach, fine‐scale simulations on subdomains are often necessary to develop appropriate parameters, since regressed models for the estimation of these parameters, based on a priori data, are unavailable. To facilitate applications of MRMT to three‐dimensional heterogeneous media at the field scale, in this work, upscaled parameters needed for a two‐rate MRMT model are fit to several hundred three‐dimensional fine‐scale simulations by employing a two‐step fitting procedure. The fitted parameters are then regressed with respect to geostatistical, sorptive, and flow parameters. Upscaled simulations using the fitted and the regressed parameters produce breakthrough curves that are very similar to fine‐scale curves. The data used to regress the parameters span a range of heterogeneous properties and flow conditions, and the model is demonstrated to be robust to untested parameter values and initial and boundary conditions. These developed regressions can be employed to efficiently account for back‐diffusion and desorption in future modeling of transport in heterogeneous media without the need to perform fine‐scale simulations.