A THEORY FOR THE TRANSPORT OF KINETICALLY SORBING SOLUTES IN HETEROGENEOUS SEDIMENTS WITH MULTIMODAL CONDUCTIVITY AND HIERARCHICAL ORGANIZATION ACROSS SCALES

Solute transport in subsurface environments is controlled by geologic heterogeneity over many scales. In reactive transport characterized by low Damkohler numbers, it is also controlled by the rate of kinetic mass transfer. A theory for the influence of sedimentary texture on the transport of kinetically sorbing solutes in heterogeneous porous formations is derived using the Lagrangian-based stochastic methodology. The resulting model represents the hierarchical organization of sedimentary textures and associated modes of log conductivity (K) for reactive hydrofacies through a hierarchical Markov Chain. The model characterizes kinetic sorption using a spatially uniform linear reversible rate expression. Our main interest is to investigate the relative effects of sorption kinetics and dispersion. Our analysis is focused on model parameters defined at each hierarchical level (scale) including the integral scales of K spatial correlation, the anisotropy ratios (ratio of the vertical conductivity integral scales to the horizontal counterpart), the indicator correlation scales, and the contrast in mean K between facies defined at different scales. Anisotropy ratios have negligible effect upon the longitudinal dispersion of sorbing solutes. Dispersion depends mostly on indicator correlation scales, integral scales, and the contrast of the mean conductivity between units at different scales. It is most sensitive to the contrast in mean K.