Numerical stochastic analysis of groundwater contaminant transport and plume containment

First- and second-order reliability methods (FORM and SORM) are applied as alternatives to the Monte Carlo simulation method in the probabilistic analysis of groundwater contaminant transport and remediation. A two-dimensional finite-element model is interfaced with a reliability analysis program to account for uncertainty in aquifer media. Hydraulic conductivity is modeled as a spatial random field with prescribed marginal probability distribution and correlation structure. FORM and SORM provide the probability that a contaminant exceeds a target level at a well, termed the probability of failure. Sensitivity of the probability of failure to basic uncertainty in grid block conductivities is also obtained, at no additional computational effort. Component reliability is used to analyze failure in a single well. Results indicate that, at the most likely failure scenario, grid block conductivities attain their maximum value near the source, the receptor well, and along the stream tubes connecting the two. System reliability is used to analyze the joint probability of failure at several wells in the aquifer. Results indicate that system failure probability is greater than the largest component failure probability. Correlation between component failure events is greater when the individual wells are closer. Sensitivity of the upper bound on system probability with respect to grid block conductivities is highest along the path the contaminant follows to reach the receptor wells. Furthermore, the probability of failure to contain a plume from escaping site boundaries is analyzed, along with the corresponding sensitivity information. Probability of failure to contain the plume decreases as the well pumping rate increases. The presence of regions of lower conductivity dramatically increases the probability of remediation failure. A careful analysis of aquifer material uncertainty and heterogeneity is vital to the success of groundwater remediation systems.