Modeling Chemical and Physical Sources of Non-Fickian Contaminant Transport on Arbitrary Groundwater Velocity Fields.

In the subsurface, there are two reasons why contaminant transport behavior may not be properly captured by a discretized advection-dispersion equation (ADE) model, and instead require a non-Fickian treatment. These are: (i) velocity fluctuations smaller than the model support scale, and (ii) mobile-immobile mass transfer (MIMT) processes such as kinetic sorption and diffusion into secondary porosity. Non-Fickian phenomena have been much studied in the literature, are reasonably well understood, and can be modeled using a variety of techniques, such as the continuous-time random walk (CTRW), fractional ADE, and subordination approaches. When these more sophisticated approaches to contaminant transport are used in the academic literature, it is commonly with spatially uniform, quasi-1D velocity fields. In professional practice, the situation is essentially the converse: elaborate, large-scale numerical models of flow are the norm, but transport modeling is generally limited to use of the ADE. Naturally, it would be beneficial to both camps to combine sophisticated flow models with sophisticated transport models. To do so, it is natural to use particle tracking, as this allows for spatially non-uniform advection. However, the primary question is how to define the stochastic behavior of the particles in a way that directly corresponds to underlying physics, is advection-independent, and can be used for prediction rather than for post-hoc fitting, which is essentially the state of the art. We will answer this question, presenting a new conceptual approach that may be thought of as CTRW-on-a-streamline, in which the travel-time probability distribution is constructed by successive subordination using two distributions that (i) have direct physical interpretations, (ii) can be predicted a priori, and (iii) are independent of the underlying velocity field. Open-source software using the new approach to model the two key sources of non-Fickian contaminant transport on any arbitrary spatially heterogeneous, transient velocity field that can be generated with MODFLOW is in late-stage development. The software will be briefly described and an illustrative simulation of a push-pull tracer test, subject to kinetic sorption and drift in a heterogeneous aquifer, will be presented.