Statistical continuum modeling of mass transport through fractured media, in two and three dimensions

The Statistical Continuum Method (SCM) provides a technique to model aqueous phase transport through a fractured rock mass at the field scale, while explicitly including the effects on transport of fracturing that are observed on the scale of a borehole or outcrop. The SCM approach models mass transport in two stages: (1) particles are first "educated" in a subdomain consisting of multiple discrete networks in order to capture the range of motion possible within a fracture system; and (2) particles are then moved in a random-walk through a larger continuum, obeying the range of motion "learned" within the subdomain. The use of discrete networks allows particle movements in the SCM continuum to honor the particle motion that occurs in the discrete subdomain, without the fundamental changes in the nature of the transport process necessary in most continuum approximations. The use of the continuum permits these movements to be extended into domains significantly larger or more complex than those that can be modeled by conventional discrete network simulations. The key element in the SCM method is the determination of the most appropriate methods for translating the motion of particles in the discrete subdomain into a set of statistical distributions that are then sampled in the continuum. To evaluate the effectiveness of the SCM approach the evolution of spatial moments through time for SCM models are compared with the evolution of moments for equivalent discrete network models. The SCM method is capable of reproducing mass transport in two and three-dimensional discrete fracture networks, as evidenced by the match between the trends in spatial moments through time for the discrete network and the spatial moments for the SCM model. A number of SCM modeling approaches produce moment values within one standard deviation of the average of the network realizations, although no one model works best for all fracture systems.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat