Modelling solute transport in porous media with spatially variable multiple reaction processes.

In this dissertation, a new numerical method is developed for the simulation of nonideal solute transport in porous media, and a first order semi-analytical solution is derived for solute transport in porous media with spatially variable multiple reaction processes. The Laplace transform is used to eliminate the time dependency and the transformed transport equations are solved both numerically and analytically. The transport solution is ultimately recovered by an efficient quotient-difference inversion algorithm. By introducing complex-valued artificial dispersion in the weighting functions, characteristics of transport solutions have been successfully addressed. The optimum of the complex-valued artificial dispersion has been derived for one dimensional problems. In multidimensional cases, the streamline upwind scheme is modified by adding complex-valued artificial dispersion along the streamline. Within this numerical scheme, the grid orientation problems have been successfully treated. The limitations on the cell Peclet number and on the Courant number were greatly relaxed. Both one dimensional and two dimensional numerical examples are used to illustrate applications of this technique. The analysis has been made for solute transport in systems with spatially variable multiple reaction processes. Specific reaction processes include reversible sorption and irreversible transformations (such as radioactive decay, hydrolysis reactions with fixed pH, and biodegradation). With the assumptions of solute transport in a system with constant hydraulic conductivity and hydrodynamic dispersion and spatially variable multiple reaction processes, a first-order semi-analytical solution is derived for an arbitrary autocovariance function, which characterizes the spatial variation of the multiple reaction processes. Results indicate that spatial variation of the transformation constants for the solution phase and the sorbed phase decreases the global rate of mass loss and enhances solute transport. If the transformation constant for the sorbed phase is spatially uniform but not zero, a similar effect is observed when there is spatial variation of the equilibrium sorption coefficient. The global rate of mass loss and apparent retardation are decreased when the spatial variability of the sorbed-phase transformation constant is positively correlated with the spatial variability of the equilibrium sorption coefficient, and increased for a negative correlation. Spatial variation of the sorption rate coefficient had minimal effect on transport