Nonideal transport of reactive solutes in heterogeneous porous media: 1. Numerical model development and moments analysis

The transport of reactive solutes at the field scale is characteristically nonideal, and this nonideality is often caused by more than one factor. In these cases, mathematical models that explicitly account for multiple factors are necessary for proper simulation of transport and for accurate analysis of causative factors. The purpose of this paper is to present a mathematical model for simulating the transport of reactive solute in heterogeneous porous media. We have taken a multi-scale, multi-factor approach that explicitly accounts for such factors as hydraulic-conductivity variability, structured porous media, rate-limited diffusive mass transfer, and nonlinear, rate-limited, spatially variable sorption. The influence of these factors on the displacement and spreading of solute plumes and on mass flux is illustrated with a series of two-dimensional (vertical) simulations. It is shown that rate-limited sorption/mass transfer and nonlinear sorption can significantly influence the first, second, and third spatial moments, whereas hydraulic-conductivity variability significantly influences only the second spatial moment. Plume skewness is especially sensitive to the specific factor controlling nonideal transport. For example, both rate-limited sorption/mass transfer and nonlinear sorption can create negatively skewed plumes during early stages of transport. However, the plume influenced by rate-limited sorption/mass transfer tends toward symmetry as global residence time increases. Conversely, the plume influenced by nonlinear sorption tends toward a constant degree of asymmetry as the spreading forces balance the concentration-dependent retardation behavior associated with nonlinear sorption. Furthermore, the results illustrate that unique behavior can result from the coupling of multiple processes. For example, when influenced by coupled heterogeneity and nonlinear sorption, the shape of a plume may change from positive to negative skewness during the course of transport.