Comparison of split-operator methods for solving coupled chemical non-equilibrium reaction/groundwater transport models

Numerical models of reactive solute transport in groundwater are often solved using an approximate two-step approach that separates the transport and reaction processes. Even though the transport and reaction steps are split, using a novel formulation it is possible to pose the reaction step in general form as a system of ordinary differential equations (ODEs) such that the original, fully coupled model is solved exactly. The reaction step in the ‘standard’ two-step method is shown to be a special case of this general form. In this paper, these two approaches are compared in terms of accuracy and efficiency. The general and the standard ODEs representing the reaction steps are solved using the public domain ODE solver, LSODI. The ODEs representing the standard reaction step are also solved by the fourth-order Runge–Kutta (RK) method. Both the RK method and LSODI are capable of solving the system of ODEs in the standard two-step method. The RK method is found to be the most efficient even though it requires comparatively smaller time steps to yield accurate solutions. The LSODI solution of the general ODEs representing the reaction step was found to be extremely time consuming without any significant gain in accuracy.