Temporal Fractionation Models for Depicting Mass Transfer Limiting Conditions of Multispecies Transport in Porous Media

Abstract

Numerical modeling is widely recognized as the most flexible and reliable method for predicting the flow and transport of contaminants in the sub-surface under highly heterogenous and complex environment. Many times, the classical advection-dispersion model needs to be customarily modified and solved in order to address these complexities in porous media at least in Darcy-scale domain. This is particularly crucial when different mass transfer processes happen at different rates and temporal scales. In an attempt to depict the limiting conditions of multispecies mass transfer within the temporal scales, the present study simulates the fractional mass transfer phenomena in porous media by considering different levels of time fractionation by solving a set of partial differential equations using finite difference method. The incorporation of the time fractionation provides new insights to the solute transport behavior in complex systems, highlighting the changes in the temporal concentration profiles and tailing phenomena. Further, the sensitivity of the flow and transport parameters such as flow velocity, dispersion coefficient, retardation coefficient and contaminant reaction rates are found to be enhanced within the flow domain. Based on the direct proportion observed between the time fractionation scale and the contaminant propagation level (in terms of peak and skewness), the present study postulates the significance of design and adjustment of suitable temporal fractionation for accurately profiling multi-species transport in different types of porous domains.