A formulation for decoupling components in reactive transport problems

Reactive transport equations may become cumbersome to solve when a large number of species are coupled through fast ( equilibrium) and slow ( kinetic) reactions. Solution is further encumbered when both mobile ( solutes) and immobile ( minerals) species are involved. In these cases, sequential iteration approaches (SIA) may become extremely slow to converge. Direct substitution approaches (DSA), which solve all transport equations together, may become extremely large. Here we propose a formulation for optimally decoupling the reactive transport equations. The procedure is described sequentially using a paradigm system. We start by a tank paradigm in which all species are mobile and undergo equilibrium reactions. In this case, all components are fully decoupled. If some of the reactions are kinetic (canal paradigm), then we can still decouple components corresponding to equilibrium reactions. The same can be said regarding a system in which immobile species only react kinetically ( river). The number of components can be reduced in the case that both types of reactions and species are present ( aquifer). In short, the number of coupled equations that need to be solved simultaneously is, at most, equal to the number of kinetic reactions. This benefits both SIA and DSA solution methods. SIA should improve convergence because most components are linear and effectively decoupled, thus reducing nonlinearity to kinetic terms only in transport equations for kinetic components. DSA systems become reduced as the number of components that need to be solved together is, at most, equal to the number of independent kinetic reactions.