Analytical Solutions for Coupled Reactive Transport Equations

by V. Srinivasan,
T. P. Clement,

Document Type: Proceeding Paper

Part of: World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat


Modeling the transport of reactive contaminants is one of the key challenges faced by groundwater engineers worldwide. Specifically, problems involving the transport of sequentially decaying contaminants occur frequently in soil and groundwater systems. Several models both analytical and numerical have been formulated to solve these equential decay transport problems. Although numerical models are capable of solving complex and heterogeneous problems, analytical solutions provide computationally efficient modeling tools to predict the fate and transport of contaminants. In addition they are also useful for verification and testing of complex numerical models. Furthermore, analytical models have the potential to be used as screening level tools in contaminated sites. Several analytical solutions have been presented for various initial and boundary conditions for sequentially coupled multi-species transport. However, one major limitation of these solutions is that they can model multi-species problems involving small chain lengths only. The solutions that can model relatively larger chain lengths are non-closed from solutions which involve numerical methods to evaluate the final solution. This work presents a general solution for a sequentially coupled multispecies reactive transport problem involving arbitrary number of species. This new solution is an explicit closed form solution and can model both Dirichlet and Newman boundaries. The advantage of this solution is that it enables one to directly obtain the particular solution for any 'ith' (I less then =n) species in an 'n' species reaction network without evaluating the predecessor species. This is helpful in focusing our resources only in the species of concern (a feature unavailable in numerical models) making it a highly efficient screening tool.

Subject Headings: Numerical models | Contaminant transport | Decision support systems | Numerical analysis | Coupling | Transportation engineering | Numerical methods

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