A simplified model for probabilistic assessment of the risk of groundwater contamination

We present a model of reduced complexity for assessing the risk of groundwater pollution from a point-source that is an extension of our earlier work on simplified models of contaminant transport. The progress of contamination is represented as a sequence of transitions among coarsely resolved states corresponding to simple statements like "a spill has occurred". Transitions between states are modeled as a Markov jump process, and a general expression for the probability of aquifer contamination is obtained from two basic assumptions: that the sequence of transitions leading to contamination is Markovian and that the time when a given transition occurs is independent of its end state. First we develop the model for sites in statistically homogeneous natural porous media, and then we extend it to highly heterogeneous media composed of multiple materials. Then we apply the model to a simple example to illustrate the method and fix ideas. Additionally, we derive an asymptotic value for the probability of contamination that is equivalent to the so-called rare event approximation. Our original model depended only on probabilities of state transitions and did not take contaminant concentration per se into account. The new model accommodates concentration by making state transitions depend on concentration. We conclude by comparing and contrasting the performance of each model on a simple test case.