Exact analytical solutions with great computational efficiency to three-dimensional multispecies advection-dispersion equations coupled with a sequential first-order reaction network

Abstract

This study presents novel exact analytical solutions to a set of simultaneous three-dimensional advection-dispersion equations coupled with a sequential first-order degradation reaction network involving distinct retardation factor values among individual species. The analytical solutions to the coupled partial differential equation system subject to both the first - and third -type inlet source boundary conditions are derived by consecutive application of the three integral transformations in combination with sequential substitutions. The correctness of the developed analytical solutions is confirmed through numerical comparisons of three verification examples between our derived exact analytical solutions and a three-dimensional single-species analytical model in a semi-infinite domain, a two-dimensional multispecies exact analytical model in a finite domain and a three-dimensional multispecies semi-analytical model in a semi-infinite domain of the previous studies, respectively. The advantage of the derived analytical solutions is that its computational efficiency is 104 times the computational efficiency of two-dimensional multispecies analytical solutions for a finite domain when two solutions are simultaneously used to solve a two-dimensional multispecies transport problem. The developed analytical solutions are then used to evaluate the performance of the public domain BIOCHLOR model that simulates aquifer remediation by natural attenuation of dissolved multispecies at a chlorinated-solvent contaminated site provided by the Center for Subsurface Modeling Support (CSMoS) of USEPA. Results show that the BIOCHLOR model that was developed based on three-dimensional analytical model assuming a single retardation factor value for all dissolved species would not be suitable for simulating most multispecies plume migration at contaminated sites where each contaminant has its own retardation factor value. The effects of the inlet source boundary conditions on the multispecies plume migration are also investigated. The high computational efficiency of the developed analytical model in this current study renders it a very efficient tool for executing a probabilistic health risk assessment involving a large number of simulations required for problems of multispecies transport of dissolved chlorinated solvent in groundwater at a contaminated site with uncertainties in many different variables.