Some Comments on Nonlocal Transport Models

Nonlocal models have been developed in a variety of contexts for applications to transport in heterogeneous porous media, and can often represent more complex phenomena than can local models. However, this additional capability comes with some cost. Nonlocal models also demand more information, and thus require more effort to use both from the theoretical or applied perspective. In this work, a fully nonlocal development of the macroscale (nonreactive) transport equation for a heterogeneous porous media is presented in the context of volume averaging by upscaling from the microscale. In the most general case, the nonlocal model has nearly as much information content as the original microscale representation. It is not until certain simplifying assumptions are made that the nonlocal model shows a reduction in the number of degrees of freedom over that seen for the microscale model. Implications for nonlocal models, and models that are derivable from the nonlocal formulation, will be discussed.