Uncertainty quantification in modeling flow and transport in porous media

Abstract

This special issue of Stochastic Environmental Research and Risk Assessment in honor of Shlomo P. Neuman presents recent developments in uncertainty quantification in predictions of flow and transport in heterogeneous porous media. It covers subjects as diverse as stochastic hydrogeology, aquifer characterization, effective (average) descriptions of subsurface processes, inverse modeling, and scaling theory, all of which benefited from the insightful contributions of Shlomo P. Neuman. We hope that this volume will become a reference point for students learning these subject, scientists pursuing innovative research, and professionals and water resources planners looking to quantify predicting uncertainty arising from the intrinsic complexity of the subsurface environment. S. P. Neuman is one of the pioneers in the use of stochastic modeling as a means of dealing with uncertainty in hydraulic and transport parameters of heterogeneous subsurface environments. This special issue contains a number of contributions in this field. Riva et al. introduce a stochastic approach to interpret field-scale tracer tests conducted in heterogeneous aquifers. By using Monte Carlo simulations, the authors demonstrate that directly linking porosity and permeability distribution to the spatial variability of soil particle sizes renders the best prediction of the observed heavy tailing of measured breakthrough curves. Zhang et al. compare the performance of Monte Carlo and stochastic collocation methods to evaluate the probability of the concentration of a conservative solute attaining a given threshold. Their analysis shows that Latin Hypercube sampling and Quasi Monte Carlo outperform standard Monte Carlo simulations, and that a sparse-grid collocation and a probabilistic collocation method provide an accurate and efficient alternative to Monte Carlo simulations. Broyda et al. develop partial differential equations satisfied by the probability density function (PDF) of the concentration of solutes undergoing heterogeneous reactions in porous media with uncertain chemical properties. The authors obtain a semi-analytical solution for the concentration PDF and demonstrate that its shape and evolution are significantly affected by both spatial variability of advective velocity and the Damkohler number. Tartakovsky presents a novel Lagrangian particle model based on smoothed particle hydrodynamics (SPH). His analysis reveals the advantages of Lagrangian methods for the stochastic analysis of miscible density-driven fluid flows in the presence of RayleighTaylor instability. When used in the context of Monte Carlo simulations, the method can provide reliable estimated of the probability of occurrence of rare events. Two papers are concerned with the estimation of hydrogeological parameters governing groundwater flow. Liu et al. present an approach to efficient and accurate parameter estimation for nonlinear flow and transport problems in porous media. They discuss the relative merits and weaknesses of different schemes, including Maximum a posteriori (MAP) and Monte Carlo based methods, used to parameterize a DNAPL dissolution/transport model. Methods to diagnose Markov Chain Monte Carlo (MCMC) samples are introduced, compared and discussed in the context of computationally demanding parameter estimation A. Guadagnini (&) Dipartimento di Ingeneria Idraulca, Ambientale, Infrastrutture Viarie e Rilevamento, Politecnico di Milano, Piazza L. Da Vinci, 32, 20133 Milan, Italy e-mail: alberto.guadagnini@polimi.it