An Efficient Implementation of the Method of Lines for Multicomponent Reactive Transport Equations

Modeling reactive transport with chemical equilibrium reactions requires solution of coupled partial differential and algebraic equations. In this work, two formulations are developed to combine the method of lines (MOL) with the global implicit approach. The first formulation has a non-conservative form and leads to a nonlinear system of ordinary differential equations with a reduced number of unknowns. The second formulation presents better conservation properties but leads to a nonlinear system of differential algebraic equations with a large number of unknowns. In both formulations, the resulting systems are integrated in time using the DLSODIS time solver which adapts both the order of the time integration and the time step size to provide the necessary accuracy. Numerical experiments show that higher-order time integration is effective for solving the non-conservative formulation and point out the high benefit of the MOL for solving reactive transport problems.