Mixing cell models for nonlinear nonequilibrium single species adsorption and transport
The oft-used “standard” mixing cell model describing reactive solute transport is extended to cater for nonequilibrium reactions. For tracer transport, the standard model is second-order accurate in the space and time discretization used. However, an error analysis of the standard model reveals that its accuracy is degraded when reactions are included. An “improved” model which maintains second-order accuracy is developed. The improved mixing cell model is demonstrated to be more accurate than the standard model. The solution obtained from the improved model is found to agree very well with the results of a numerical Crank-Nicolson solution for various isotherms. The improved mixing cell predictions are also shown to agree very well with the exact solution for the two-site adsorption model, where a linear isotherm is considered. Application of the improved model was illustrated by simulating the experimental data from a laboratory Ca-K exchange experiment in which a solution containing Ca was passed through a column filled with K- saturated soil. The model was used in conjunction with the experimentally determined nonlinear adsorption isotherm to predict the experimental breakthrough data. By changing the value of kinetic coefficient, it was demonstrated that the predictions varied markedly. However, the simulations suggest that the equilibrium model is more appropriate than the assumption of nonequilibrium.