Analysis of split operator methods applied to reactive transport with Monod kinetics

Split operator approaches are commonly used to solve coupled nonlinear reactive transport problems. The benefits of split operator algorithms come with the cost of an O(Δt) truncation error. This error has two components: (i) an error strictly associated with the boundary, and (ii) an error occurring within the domain. Previous analyses of split operator methods for Monod reactions are incomplete and conflicting. First, previous analyses have focused only on the boundary error while ignoring the internal error. This is problematic as the boundary error is irrelevant in many practical applications. Second, conflicting results regarding the accuracy of alternating split operator methods have been reported. This new work exactly characterizes the net splitting error for an arbitrary system of nonequilibrium reactive transport equations showing that both the boundary and internal error can always be removed with alternating methods for sufficiently small Δt. Numerical results are presented for reactive transport governed by single and multiple species with Monod kinetics.