Contaminant transport forecasting in the subsurface using a Bayesian framework

In monitoring subsurface aquifer contamination, we want to predict quantities—fractional flow curves of pollutant concentration—using subsurface fluid flow models with expertise and limited data. A Bayesian approach is considered here and the complexity associated with the simulation study presents an ongoing practical challenge. We use a Karhunen–Loève expansion for the permeability field in conjunction with GPU computing within a two–stage Markov Chain Monte Carlo (MCMC) method. Further reduction in computing costs is addressed by running several MCMC chains. We compare convergence criteria to quantify the uncertainty of predictions. Our contributions are two-fold: we first propose a fitting procedure for the Multivariate Potential Scale Reduction Factor (MPSRF) data that allows us to estimate the number of iterations for convergence. Then we present a careful analysis of ensembles of fractional flow curves suggesting that, for the problem at hand, the number of iterations required for convergence through the MPSRF analysis is excessive. Thus, for practical applications, our results provide an indication that an analysis of the posterior distributions of quantities of interest provides a reliable criterion to terminate MCMC simulations for quantifying uncertainty.