Generalized solution to multispecies transport equations coupled with a first-order reaction network

A generalized solution methodology is presented for deriving analytical solutions to multispecies transport equations coupled with multiparent, serial, parallel, converging, diverging, and/or reversible first-order reactions. The method is flexible for solving one-, two-, or three-dimensional advection-dispersion equations that are coupled with a set of first-order reactions. However, a major limitation is that the method cannot be used for solving multispecies transport equations with different retardation factors. Mathematical steps are provided to illustrate how the general solution method can be derived using linear transformation principles and to show why the method would fail when the retardation factors are different. Derivations are also presented to demonstrate how the Sun et al. [1999b] method for solving sequential reactive transport problems, which was previously presented without any fundamental analysis, can be deduced from the general solution. The results of the presented solution scheme for a test problem compare well with the numerical solution computed using the RT3D code. The proposed methodology is useful for developing simple analytical models that can be used to perform screening simulations and can be used to test complex multispecies transport codes.