Solute flux approach to transport through spatially nonstationary flow in porous media

A theoretical framework for solute flux through spatially nonstationary flo ws in porous media is presented. The flow nonstationarity may stem from med ium nonstationarity (e.g., the presence of distinct geological layers, zone s, or facies), finite domain boundaries, and/or fluid pumping and injecting . This work provides an approach for studying solute transport in multiscal e media, where random heterogeneities exist at some small scale while deter ministic geological structures and patterns can be prescribed at some large r scale. In such a flow field the solute flux depends on solute travel time and transverse displacement at a fixed control plane. The solute flux stat istics (mean and variance) are derived using the Lagrangian framework and a re expressed in terms of the probability density functions (PDFs) of the pa rticle travel time and transverse displacement. These PDFs are given with t he statistical moments derived based on nonstationary Eulerian velocity mom ents. The general approach is illustrated with some examples of conservativ e and reactive solute transport in stationary and nonstationary flow fields . It is found based on these examples that medium nonstationarities (or mul tiscale structures and heterogeneities) have a strong impact on predicting solute flux across a control plane and on the corresponding prediction unce rtainty. In particular, the behavior of solute flux moments strongly depend s on the configuration of nonstationary medium features and the source dime nsion and location. The developed nonstationary approach may result in non- Gaussian (multiple modal) yet realistic behaviors for solute flux moments i n the presence of flow nonstationarities, while these non-Gaussian behavior s may not be reproduced with a traditional stationary approach.