A reduced complexity model for probabilistic risk assessment of groundwater contamination

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.

Additionally, we derive an asymptotic value for the probability of contamination that is equivalent to the so-called rare event approximation. 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. Finally, we apply the model to a simple example to illustrate the method and its potential.