Date of Award

Spring 1-1-2013

Document Type


Degree Name

Master of Science (MS)


Applied Mathematics

First Advisor

Harihar Rajaram

Second Advisor

Anne Dougherty

Third Advisor

Jem N. Corcoran


In this paper, we study solute transport in an individual fracture and the surrounding porous rock. Specifically, we consider a parallel-plate model of a single fracture that allows for the diffusion of solute within the matrix and the adsorption of solute to the fracture walls. We developed two stochastic particle-tracking methods to numerically solve for the concentration of the fracture model. The first is the hi-res method which captures the solute dynamics at a micro-scale. The second algorithm we develop, the upscaled method, captures the large-scale dynamics of the system at vastly reduced computational cost. We verified the accuracy of these methods by comparing their results to numerical results from the literature. We also compared the efficiency of the developed particle tracking methods to an existing particle tracking method from the literature in the case of no interface absorption.