Decomposition method for solving multi-species reactive transport problems coupled with first-order kinetics applicable to a chain with identical reaction rates

A new method for decomposing of multiple solute transport equations, coupled by first-order reactions, is developed. The approach is based on the semigroup theory and reduces the multi-species problem to single-species equations with various initial and boundary conditions. Analytical formulas are derived for all reactants. This new method overcomes some of the limitations that were implicit in previously published algorithms. More exactly, the derivation of closed formulas for a reaction chain with identical reaction rates is possible. The proposed approach is flexible for solving one-, two- or three-dimensional advection-dispersion systems. The methodology is demonstrated on the reductive biodegradation of chlorinated solvents, such as tetrachloroethene (PCE) and trichloroethene (TCE).