A Novel Dual-Domain Analytical Model for Multispecies Contaminant Transport Subject to Nonequilibrium Sorption in a Permeable Reactive Barrier-Aquifer System

Transport behaviors of contaminants through a permeable reactive barrier (PRB)-aquifer system are complicated because of the different physical and chemical properties of the PRB and the aquifer. Dual-domain contaminant transport models are efficient tools for better understanding the various processes and mechanisms of reactive transport through a PRB–aquifer system. Multispecies transport models should have the ability to account for mass accumulation from parent species while simultaneously considering the distinct transport and reactive properties of both the parent and daughter species during the transport of degradable contaminants. For mathematical simplicity, the current multispecies dual-domain transport analytical models are derived assuming equilibrium-controlled sorption. However experimental and theoretical research results indicate that nonequlibrium sorption could have a profound effect upon solute transport in the subsurface environment. The making of the instantaneous equilibrium sorption assumption precludes consideration or examination of the potentially significant impact of the nonequilibriun sorption process. This study is thus designed to develop a novel dual-domain multispecies transport analytical model for the reactive transport of degradable contaminants through a PRB–aquifer system. The first-order reversible kinetic sorption reaction equation system is incorporated into two sets of simultaneous advection-dispersion equations coupled by sequential first-order decay reactions that describe the multispecies nonequlibrium transport in both the PRB and the aquifer. The analytical solutions to the complicated governing equation system can be obtained by using the Laplace transform and the generalized integral transform technique. The correctness of the derived analytical model and its corresponding computer code will be evaluated by comparison of the computational results against those obtained with the equilibrium-controlled sorption analytical model and a numerical model where the same governing equations are solved using the advanced Laplace transform finite difference method. Ultimately, the derived analytical model will be used to investigate how the sorption reaction rate influences the performance of a PRB-aquifer system.