Some aspects of stochastic flow and transport in complex geologic media

This thesis has analyzed some aspects of stochastic flow and transport in geologic media with a random stationary and statistically isotropic hydraulic conductivity field. Explicit expressions for cross-covariances between velocity and head, and velocity and log conductivity as well as covariances of velocity under steady state uniform mean three-dimensional flow with an exponential log conductivity covariance are derived to first order and their structure is examined. An exact early time solution due to Batchelor for the mean concentration is compared with other existing stochastic solutions and its range of validity is determined for the case of an instantaneous point source. This early time solution is simpler and more general than any other stochastic transport solution at early time. A Monte Carlo simulation scheme is developed to study the ensemble behavior of solute particles traveling in such a field. The thesis concludes with a concentration estimation scheme conditioning on site measurements