Self-similarity in fate and transport of contaminants in groundwater

Abstract

Similarity within non-linear geophysical processes under different space and time has been investigated in literature to understand and model the sophisticated nature of these processes. This study deals with the self-similarity of the governing processes of fate and transport of contaminants in groundwater, which include advection, dispersion, sorption, and degradation, either by chemical reaction or microbiological interaction. As such, self-similarity conditions of three-dimensional advective-dispersive-reactive transport (ADR) equation with various initial and boundary conditions are obtained by employing one-parameter Lie group of point scaling transformations. The strength of the proposed scaling approach lies in its ability to handle initial and boundary conditions of the process together with the governing equation. Then, utilizing reported conditions in Borden Field experiment domain, numerical simulations are performed to demonstrate examples of self-similarity when first-order degradation rate constant is zero and nonzero under three sorption conditions. The results of the numerical examples showed the effectiveness of the derived self-similarity conditions and the strength of the proposed approach in handling initial and boundary conditions of the governing transport process. It is possible to obtain both smaller and larger size self-similar (scaled-up or scaled-down) domains, which result in faster and slower transport processes, respectively. The obtained self-similarity criteria can offer further understanding of ADR transport phenomena and can provide spatial, temporal, and economical flexibility in constructing scaled models of field conditions governed by three-dimensional ADR transport process.