Probabilistic sensitivity analysis for one‐dimensional reactive transport in porous media

Abstract

A reliability approach for probabilistic modeling of reactive transport in porous media provides two important quantitative results: (1) an estimate of the probability that dimensionless concentration equals or exceeds some specified level and (2) a probabilistic sensitivity measure which quantifies the relative importance of each uncertain variable with respect to the probabilistic outcome. The approach is potentially attractive because it can provide both a probability estimate and probabilistic sensitivity measures; this is especially important for relatively low probability events where Monte Carlo simulation may require hundreds of thousands of realizations for reasonable results. The reliability method can incorporate marginal probability distribution functions (PDF) and correlation between uncertain variables, and the general method can be used with existing analytical or numerical solutions. However, a first‐order reliability approach provides only an approximate probability measure; the accuracy is a function of performance criterion and statistical characteristics of the uncertain variables. The methodology and results here focus on probabilistic sensitivity measures which indicate the importance of any uncertain variable to the probabilistic outcome. In this work, one‐dimensional reactive transport is investigated with the following uncertain variables: groundwater flow velocity, diffusion coefficient, dispersivity, distribution coefficient, porosity, and bulk density. We examine how probabilistic outcome and sensitivity are influenced by choice of marginal PDF, correlation, and magnitude of uncertainty for the variables. We also compare the probabilistic sensitivity results to typical deterministic sensitivity measures. Results indicate that the probabilistic outcome is most sensitive to likely changes in flow velocity and the reaction terms. Diffusion coefficient can also be an important uncertain variable but only when it has significantly higher uncertainty (coefficient of variation) than any other variable. For some cases shown in this paper, dispersivity and diffusion coefficient can be treated as deterministic variables with little impact on the probabilistic outcome.