Heterogeneity is the single most salient feature of hydrogeology. An enormous amount work has been devoted during last 30 years to addressing this issue. Our objective synthesize and offer a critical appraisal results related problem finding representative hydraulic conductivities. By conductivity we mean parameter controlling average behavior groundwater flow within an aquifer at given scale. Three concepts are defined: effective conductivity, which relates ensemble averages flux head...

Abstract Global Sensitivity Analysis (GSA) is key to assisting appraisal of the behavior hydrological systems through model diagnosis considering multiple sources uncertainty. Uncertainty typically comprise incomplete knowledge in (a) conceptual and mathematical formulation models (b) parameters embedded models. In this context, there need for detailed investigations aimed at a robust quantification importance parameter uncertainties rigorous multi‐model context. This study aims evaluating...

Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate pollutants and geochemical processes occurring in aquifers, rivers, estuaries, oceans. Geochemical involving multiple species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited development analytical solutions multicomponent heterogeneous reactions such as precipitation/dissolution. We present procedure to solve groundwater case homogeneous...

Numerical Monte Carlo simulation is considered to be one of the main tools used in groundwater hydrology (1) quantify uncertainty flow predictions due imperfect knowledge aquifer architecture, hydraulic parameters, and forcing terms or (2) assess reliability approximated moment‐based equations for and/or transport. While framework conceptually straightforward very flexible, it recognized as lacking well‐established convergence criteria. Here we propose a methodology analysis simulations...

Anomalous (or "non-Fickian") transport is ubiquitous in the context of tracer migration geological formations. We quantitatively identify origin anomalous a representative model heterogeneous porous medium under uniform (in mean) flow conditions; we focus on which arises complex patterns lognormally distributed hydraulic conductivity (K) fields, with several decades K values. Transport domains determined by particle tracking technique and characterized breakthrough curves (BTCs). The BTC...

Multiphase flow in porous media is strongly influenced by the wettability of system, which affects arrangement interfaces different phases residing pores. We present a method for estimating effective contact angle, quantifies and controls local capillary pressure within complex pore space natural rock samples, based on physical constraint constant curvature interface between two fluids. This algorithm able to extract large number measurements from single core, resulting characteristic...

Abstract We document results of a set laboratory experiments aimed at exploring impacts injection rate and bacterial density on biomineralization across water‐saturated porous media. The study relies Low‐Field Nuclear Magnetic Resonance technology the ensuing transverse spin‐spin relaxation time distributions. latter is documented to provide robust quantification temporal histories pore size distributions during biomineralization. As such, our work explores quantifies pore‐size dependent...

We consider the effect of measuring randomly varying hydraulic conductivities K ( x ) on one's ability to predict numerically, without resorting either Monte Carlo simulation or upscaling, steady state flow in bounded domains driven by random source and boundary terms. Our aim is allow optimum unbiased prediction heads h fluxes q(x means their ensemble moments, 〈 )〉 c , respectively, conditioned measurements ). These predictors have been shown Neuman Orr [1993a] satisfy exactly an...

In this work, we show how the use of global sensitivity analysis (GSA) in conjunction with polynomial chaos expansion (PCE) methodology can provide relevant information for interpretation transport experiments laboratory‐scale heterogeneous porous media. We perform GSA by calculating Sobol indices, which a variance‐based importance measure effects uncertain parameters on output chosen interpretive model. The choice PCE has following two benefits: (1) it provides indices straightforward...

We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The involves advection‐dominated transport in porous media three dissolved species, i.e., two reactants undergoing fast irreversible reaction and resulting product. authors found that their observations could not be properly fitted with model based on an advection‐dispersion‐reaction equation (ADRE) assuming was instantaneous, actual measured total product being lower than predictions for...

Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact uncertain parameters on main features probability density function, pdf, a target model output, y. These include expected value y, spread around mean degree symmetry tailedness pdf Since reliable assessment higher-order statistical moments can be computationally demanding, we couple our GSA with surrogate model, approximating full response...

We perform a set of detailed numerical simulations single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (\ensuremath{\phi}) and degrees connectivity, analyze the probability density functions (PDFs) sizes, $S$, vertical velocity components, $w$, which are aligned mean direction. Both PDFs markedly skewed pronounced positive tails. This feature PDF is dictated by structure determines shortest travel times, one key transport...

In paper 1 [ Guadagnini and Neuman , this issue] of two‐part series we presented exact nonlocal equations for first second conditional ensemble moments hydraulic head flux under steady state groundwater flow in bounded, randomly nonuniform domains the presence uncertain source boundary terms. We derived recursive approximations these based on expansion powers a small parameter σ Y which represents standard estimation error log conductivity; developed two‐dimensional finite element scheme...

The properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty. It may, however, possible to describe the spatial variability these terms geostatistical parameters such as mean, integral (spatial correlation) scale, and variance. Neuman et al. (2004) proposed graphical method estimate (natural) log transmissivity on basis quasi–steady state head data when randomly confined aquifer is pumped at constant rate from fully penetrating well. They...