Analytical solutions for multiple species reactive transport in multiple dimensions

Many numerical computer codes used to simulate multi-species reactive trans port and biodegradation have been developed in recent years. Such numerical codes must be validated by comparison of the numerical solutions with an a nalytical solution. In this paper, a method for deriving analytical solutio ns of the partial differential equations describing multiple species multi- dimensional transport with first-order sequential reactions is presented. A lthough others have developed specific solutions of multi-species transport equations, here a more general analytical approach, capable of describing any number of reactive species in multiple dimensions is derived. A substit ution method is used to transform the multi-species reactive transport prob lem to one that can be solved using previously published single-species sol utions for various initial and boundary conditions. One- and three-dimensio nal examples are presented to illustrate the steps involved in extending si ngle-species solutions to a four-species system with sequential first-order reactions. (C) 1999 Elsevier Science B.V. All rights reserved.