Application of a lumped-process mathematical model to dissolution of non-uniformly distributed immiscible liquid in heterogeneous porous media

The use of a lumped-process mathematical model to simulate the complete dissolution of immiscible liquid non-uniformly distributed in physically heterogeneous porous-media systems was investigated. The study focused specifically on systems wherein immiscible liquid was poorly accessible to flowing water. Two representative, idealized scenarios were examined, one wherein immiscible liquid at residual saturation exists within a lower-permeability unit residing in a higher-permeability matrix, and one wherein immiscible liquid at higher saturation (a pool) exists within a higher-permeability unit adjacent to a lower-permeability unit. As expected, effluent concentrations were significantly less than aqueous solubility due to dilution and by-pass flow effects. The measured data were simulated with two mathematical models, one based on a simple description of the system and one based on a more complex description. The permeability field and the distribution of the immiscible-liquid zones were represented explicitly in the more complex, distributed-process model. The dissolution rate coefficient in this case represents only the impact of local-scale (and smaller) processes on dissolution, and the parameter values were accordingly obtained from the results of experiments conducted with one-dimensional, homogeneously-packed columns. In contrast, the system was conceptualized as a pseudo-homogeneous medium with immiscible liquid uniformly distributed throughout the system for the simpler, lumped-process model. With this approach, all factors that influence immiscible-liquid dissolution are incorporated into the calibrated dissolution rate coefficient, which in such cases serves as a composite or lumped term. The calibrated dissolution rate coefficients obtained from the simulations conducted with the lumped-process model were approximately two to three orders-of-magnitude smaller than the independently-determined values used for the simulations conducted with the distributed-process model. This disparity reflects the difference in implicit versus explicit consideration of the larger-scale factors influencing immiscible-liquid dissolution in the systems.