Generalized solution to multi-dimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors

This paper presents a general method for solving coupled multi-dimensional, multi-species reactive transport equations. The new method can be used for solving multi-species transport problems involving first-order kinetic interactions and distinct retardation factors. The solution process employs Laplace transformation and linear transformation steps to uncouple the governing set of coupled partial differential equations. The uncoupled equations are solved using an elementary solution. The details of the solution algorithm are illustrated by deriving an explicit analytical solution to a two-species reactive transport problem. In addition, three one-dimensional problems and two three-dimensional problems are solved to illustrate the use of the method. The proposed solution scheme is a robust procedure for solving a variety of multi-dimensional, multi-species transport problems that are coupled with a first-order reaction network.