A Coupled Markov Chain Model for Quantification of Uncertainty in Transport in Heterogeneous Formations

Abstract

Field tracer tests show that aquifer heterogeneity leads to irregularly shaped contaminant plumes. Our inability to characterize this heterogeneity deterministically suggests that predictions of plume sizes must be expressed in probabilistic terms. In this paper the uncertainty in predicting solute transport is addressed. Different kinds of uncertainty are distinguished: geological, parameter and a combination of both. Geological uncertainty is handled with coupled Markov chains, while parameter uncertainty is treated in the classical Gaussian way. Calculations have been performed for 100 realizations. It is demonstrated that the coupled Markov chains model is successful in quantifying geological uncertainty in systems with discrete features. A fixed geological structure (a single realization) gives a significantly different dispersion behavior from the ensemble mean. It has been found that the contaminated area can be indicated with some certainty, but the local concentration at a given point is highly uncertain. Outside the envelope of all possible plumes the concentration is practically zero, with certainty. Deterministic information about the geological structure reduces the uncertainty in the local concentration.

on leave from Faculty of Engineering, Mansoura University, Egypt