Application of nonstationary stochastic theory to solute transport in fractured porous media

Many practical requirements have lead to quantitatively studying groundwater flow and solute transport in fractured media. These requirements include seeking and evaluating water resources, and other resources such as geothermal and petroleum, in reservoirs contained in fractured rocks.; In this dissertation, stochastic theories were applied to develop a series of analytical and numerical stochastic solutions for chemical transport in structured porous media. Firstly, an Eulerian analytical solution to solute transport in a fractured medium was developed. Although the analytical method is based on the stationary stochastic theories, which limit its practical application, it can be used as a simple solution to check the accuracy of other stochastic methods before they are applied to more complicated studies.; To relax many assumptions adopted in stationary stochastic theories, nonstationary transport theories were developed. Based on a Lagrangian framework, a numerical moment method (NMM) for reactive solute transport in a nonstationary fractured prous medium was developed. A time retention function related to physical and chemical sorption in the dual-porosity medium was developed and coupled with solute advection along random trajectories. The mean and variance of total solute flux were expressed in terms of the probability density function of the parcel travel time and transverse displacement. However, that method neglected the local dispersion in the advection region. To overcome the limitation of NMM, a numerical Eulerian method of moment (NEMM) was developed. The NEMM was compared with the stationary transport theory with a dual-porosity and a dual-permeablity model to check the accuracy. The comparisons indicated that the two methods matched very well in predicting first and second spatial moments. NEMM solutions were also compared with Monte Carlo simulations for solute transport in stationary fractured media. The results from the two methods match well in predicting mean concentration and slightly differ in predicting the standard devation of concentration. The theory was then used to study effects of various parameters and nonstationarity of the medium on flow and transport processes. Results indicated that medium nonstationarity would significantly influence the solute transport process. The nonstationary transport theories pave the way for applying stochastic methods to real environmental projects.