Transport in Porous Media 37: 327–346, 1999. c  1999 Kluwer Academic Publishers. Printed in the Netherlands. 327 A Decomposition Method for Solving Coupled Multi-Species Reactive Transport Problems YUNWEI SUN and T. PRABHAKAR CLEMENT Pacific Northwest National Laboratory, Richland, WA 99352, U.S.A. (Received: 6 July 1998) Abstract. Concerns over the problems associated with mixed waste groundwater contamination have created a need for more complex models that can represent reactive contaminant fate and transport in the subsurface. In the literature, partial differential equations describing solute transport in porous media are solved either for a single reactive species in one, two or three dimensions, or for a limited number of reactive species in one dimension. Those solutions are constrained by many simplifying assumptions. Often, it is desirable to simulate transport in two or three dimensions for a more practical system that might have multiple reactive species. This paper presents a decomposition method to solve the partial differential equations of multi-dimensional, multi-species transport problems that are coupled by linear reactions. A matrix method is suggested as a tool for describing the reaction network. In this way, the level of complexity required to solve the multi-species reactive transport problem is significantly reduced. Key words: analytical solution, partial differential equation, reactive transport, multi-species, decomposition. 1. Introduction Analytical models are powerful tools for expressing enormous amounts of infor- mation within a compact mathematical framework. However, analytical solutions to several transport problems of practical interest may not be feasible because of the complexities associated with nonlinear boundary conditions and inhomogeneous aquifer properties. Ogata (1958) and Bear (1960) were the first to derive analytical solutions to contaminant transport equations for one-dimensional problems. Van Genuchten and Alves (1982) and Toride et al. (1995) compiled various analytical solutions available for solving one-dimensional solute transport equations. Beljin (1991) reviewed analytical solute transport models for three-dimensional ground- water systems. However, in all of the above references the fundamental partial differential equations represent the transport of either a nonreactive species or a single reactive species. In recent years, increased interest in the fate and transport of reactive contam- inants in the subsurface environment has created a need for mathematical tools to solve multi-species transport problems. For example, chlorinated solvent contam- inants such as PCE (tetrachloroethylene) and TCE (trichloroethylene) are known