Prediction of Solute Concentration in the Presence of Uncertainty: beyond Moments

Abstract:

Subsurface flow and transport models are affected by parametric uncertainty because of the inaccessibility and the multi-scale nature of the environments. We consider an advection-diffusion model with uncertain flow velocity field and initial and boundary conditions. We derive a deterministic equation that governs the evolution of cumulative distribution function (CDF) of solute concentration. Although requiring closures, this CDF equation is subject to uniquely defined boundary and initial conditions and can be solved with classic techniques. The effective coefficients are given in terms of the mean and variance of concentration, which need to be provided. We analyze the accuracy and robustness of the proposed closed equations by comparison with Monte Carlo simulations for different correlation structures and parameters.