Ahatract
-A solution for one-dimensional diffusion of a contaminant in a semi-infinite, porous slab is presented. The diffusion coefficient is constant, but sorption between the fluid and solid phase is nonlinear. Freundlicb-and Langmuir-type isotherms are considered. The solution is based on a pieoewise-linear approximation to the sorption isotherm. During transport, regions develop where analytical solutions corresponding to the linear segments of the isotherm can be used. The movement of the interfaces between these regions with time is tracked. 2-, 3-, 5. and IO-region models were tested. The accuracy of the results was tested by comparing to a collocation solution using an Lz error analysis. L2 errors in all the cases were less than 3.1%. Accuracy generally improves as the number of regions used in the model is increased. In general, a 5-region qlodel produces results with L2 error values less than 1%. The most important feature of the method, however, is that results are produced at a fraction of the computing cost. Central processing unit (CPU) times on a VAX 8650 computer for a Wegion, piecewise-linear model are, in general, five times smaller than the corresponding CPU time for the collocation technique. More importantly, the CPU time for the pieazwise-linear solution is independent of the simulation time. The CPU time for the collocation solution increases with the total problem time because solutions are required at intermediate time steps. The piezewise-linear solution is strictly a function of the time and distance of interest.