Explicit and implicit coupling during solute transport through clay membrane barriers

Simulations of salt (KCl) flux through a 1-m-thick clay membrane barrier (CMB) based on coupled solute transport theory are compared to simulated fluxes based on traditional advective-dispersive transport theory. The simulations are based on measured values for the effective salt-diffusion coefficient (Ds*) and chemico-osmotic efficiency coefficient (omega) for a bentonite-based barrier material subjected to KCl solutions. The results indicate that the exit salt flux is reduced due to both explicit coupling (hyperfiltration and chemico-osmotic counter-advection) and an implicit coupling effect resulting from the decrease in Ds* due to a decrease in the apparent tortuosity factor, tau a, with an increase in omega. Implicit coupling is shown to be more significant than explicit coupling for reducing and retarding salt flux through a CMB under diffusion-dominated conditions. Failure to account for the implicit coupling effect may result in unrealistic results, such as the existence of salt flux through a perfect (ideal) clay membrane (i.e., omega=1).     

Operator-splitting errors in coupled reactive transport codes for transient variably saturated flow and contaminant transport in layered soil profiles

One possible way of integrating subsurface flow and transport processes with (bio)geochemical reactions is to couple by means of an operator-splitting approach two completely separate codes, one for variably-saturated flow and solute transport and one for equilibrium and kinetic biogeochemical reactions. This paper evaluates the accuracy of the operator-splitting approach for multicomponent systems for typical soil environmental problems involving transient atmospheric boundary conditions (precipitation, evapotranspiration) and layered soil profiles. The recently developed HP1 code was used to solve the coupled transport and chemical equations. For steady-state flow conditions, the accuracy was found to be mainly a function of the adopted spatial discretization and to a lesser extent of the temporal discretization. For transient flow situations, the accuracy depended in a complex manner on grid discretization, time stepping and the main flow conditions (infiltration versus evaporation). Whereas a finer grid size reduced the numerical errors during steady-state flow or the main infiltration periods, the errors sometimes slightly increased (generally less than 50%) when a finer grid size was used during periods with a high evapotranspiration demand (leading to high pressure head gradients near the soil surface). This indicates that operator-splitting errors are most significant during periods with high evaporative boundary conditions. The operator-splitting errors could be decreased by constraining the time step using the performance index (the product of the grid Peclet and Courant numbers) during infiltration, or the maximum time step during evapotranspiration. Several test problems were used to provide guidance for optimal spatial and temporal discretization.