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## Publications

Publications (82)

Uniform mean flow takes place in a 3D heterogeneous formation of normal hydraulic logconductivity Y = ln K. The aim of the study is to derive the dependence of the horizontal Kefh and vertical Kefv effective conductivities on the structural parameters of hydraulic conductivity and investigate the impact of departure from multi-Gaussianity on Kef, b...

Natural gradient steady flow of mean velocity U takes place in heterogeneous aquifers of random logconductivity Y=lnK, characterized by the normal univariate PDF f(Y) and autocorrelation ρY, of variance σY² and horizontal integral scale I. Solute transport is quantified by the Breakthrough Curve (BTC) M at planes at distance x from the injection pl...

Natural gradient steady flow of mean velocity U takes place in heterogeneous aquifers of random logconductivity characterized by the univariate PDF f(Y) and autocorrelation ρY. Solute transport is analyzed through the Breakthrough Curve (BTC) at planes at distance x from the injection plane. The study examines the impact of permeability structures...

We examine the prediction capability of two approximate models (Multi-Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non-Fickian transport, by comparison with accurate 2-D and 3-D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advec...

Coupled impacts of slow advection, diffusion and sorption were investigated using two heterogeneity models that differ in structure and in the mathematical framework that was used to simulate flow and transport and to quantify contaminant tailing. Both models were built using data from a highly heterogeneous exposure of the Borden Aquifer at a site...

Accurate characterization of internal structures and geometries of aquifers is critical for evaluation of plume migration and dispersion of contaminants. For this reason, high-resolution transport study field sites, such as the Waterloo Groundwater Research Site at the Canadian Forces Base Borden, Ontario, Canada, have been established. However, ge...

This work investigated the impacts of permeability and sorption heterogeneity on contaminant transport in groundwater using simulation experiments designed to elucidate the causes of tailing. The effects of advection, diffusion and sorption mechanisms and plume history were explored. A simple conceptual model consisting of a single inclusion (heter...

The effective retardation factor of highly heterogeneous porous formations is investigated using an analytical derivation and numerical simulations based on the self-consistent approximation and the multi-indicator conductivity model, used in the past for the effective hydraulic conductivity estimation. Both positive and negative correlation betwee...

Water flow and solute transport take place in formations of spatially variable conductivity K. The logconductivity Y = ln K is modeled as a random stationary space function, of normal univariate pdf (of mean In K
G and variance \({\sigma_{Y}^{2}}\)) and of axisymmetric autocorrelation of integral scales I
h,I
v (anisotropy ratio f = I
v/I
h < 1). T...

[1] The transport experiment at the MADE site (a highly heterogeneous aquifer) was investigated extensively in the last 25 years. The longitudinal mass distribution m(x,t) of the observed solute plume differed from the Gaussian shape and displayed strong asymmetry. This is in variance with the prediction of stochastic models of flow and transport i...

We consider three-dimensional uniform flow in heterogeneous porous media characterized by a spatially variable hydraulic conductivity K(x); the latter is considered as a stationary random function of lognormal distribution (mean ln K-G and variance sigma(2)(Y) of Y = ln K) and of finite integral scale I-Y. We investigate the effective conductivity...

This paper analyzes the emergence of channeling and preferential flow in heterogeneous porous media. Connectivity is studied through the statistical characterization of the length L of connected, high velocity patterns in both two-dimensional and three-dimensional media. A simple, physically based, fully analytic expression for the probability of L...

Effects of three key transport mechanisms (advection, diffusion and
sorption) on transport and contaminant tailing of chlorinated solvents
have been investigated using a numerical model. Thousands of model
simulations have been conducted for various combinations of transport
parameters that govern three key mechanisms in order to quantify tailing
a...

Determining the velocity field V(x) by accurate numerical solutions of flow through heterogeneous formations of three-dimensional random structures requires a fine-scale discretization by a dense grid. With l(m) the maximal cell size needed to ensure an accurate solution and I(Y) the logconductivity integral scale, l(m)/I(Y) = 1/5 is commonly adopt...

The paper deals with the effective conductivity tensor K(ef) of anisotropic random media subject to mean uniform flux. The hydraulic conductivity K field is modeled as a collection of spheroidal disjoint inclusions of different, isotropic and independent Y = ln K; the latter is a random variable with given distribution of variance sigma(2)(Y). Incl...

Large-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quanti...

This paper introduces a new method for simulating large-scale subsurface contaminant transport that combines an Analytic Element Method (AEM) groundwater flow solution with a split-operator Streamline Method for modeling reactive transport. The key feature of the method is the manner in which the vertically integrated AEM flow solution is used to c...

In advective transport through weakly heterogeneous aquifers of random stationary and isotropic three-dimensional permeability distribution, transverse macrodispersivity alpha T is found to be zero. This was determined in the past by solving the transport equation at first order in the log conductivity variance sigma Y 2. However, field findings in...

Flow and transport are solved for a heterogeneous medium modeled as an ensemble of spherical inclusions of uniform radius R and of conductivities K, drawn from a pdf f(K) (Fig. 1). This can be regarded as a particular discretization scheme, allowing for accurate numerical and semi-analytical solutions, for any given univariate and integral scale IY...

Quantification of solute transport in heterogeneous aquifers is usually carried out by the spatial or temporal moments of the local concentration C. The heterogeneous medium is characterized by a spatially variable logpermeability Y (x)=ln K(x), which is often modeled as a space random function where Y is characterized by the mean =lnKG, variance s...

The effective conductivity K ef of porous formations of spatially variable permeability K is determined for media of random two-dimensional and isotropic structures. The medium is modeled as an ensemble of multiphase circular inclusions of different Y=lnK, characterized by a pdf f(Y), and of different radii R (polydisperse medium), of pdf f(R|Y), w...

Subject collections (60 articles) mathematical modelling (27 articles) analysis Articles on similar topics can be found in the following collections A general framework for analytic evaluation of singular integral equations with a Cauchy kernel is developed for higher order line elements of curvilinear geometry. This extends existing theory which r...

A contaminant plume of mass Mo is inserted at time t = 0 at an injection plane at × = 0 in an aquifer of spatially variable conductivity K. The log-conductivity Y = InK is modelled as stationary and isotropic, of univariate distribution f(Y), and of finite integral scale I. The flow of water is uniform in the mean (natural gradient) and the plume i...

We analyse the mass arrival (breakthrough curve) at control planes at × of a plume of conservative solute injected at time t = 0 in the plane × = 0. The formation is of random three-dimensional stationary and isotropic conductivity K, characterized by the univariate normal distribution f(Y), Y = lnK, and the integral scale I. The flow is uniform in...

The Analytic Element Method (AEM) formulation for steady 2D groundwater flow is combined with deterministic Streamline Method (SM) to model large-scale transport of reactive contaminants. AEM is an alternative to the Finite Element (FEM) and Finite Difference Methods (FDM) for solving subsurface flow problems on large scales. The domain is discreti...

Three-dimensional simulations of flow in highly heterogeneous anisotropic porous formations are conducted to estimate horizontal and vertical effective conductivities of aquifer formations. Multi-Indicator conductivity model, developed by Dagan et al (2003), was employed to test validity of the classical self-consistent solution (Dagan 1989) and th...

The Analytic Element Method (AEM) was originally developed (e.g. Strack,
1989) for solving steady-state groundwater flow problems in
two-dimensional (2D) and three-dimensional (3D) isotropic domains. In
the present study the AEM approach is extended to solve for head and
specific discharge due to inhomogeneities (inclusions) of isotropic
conductivi...

Three-dimensional advective transport of passive solutes through isotropic porous formations of stationary non-Gaussian log conductivity distributions is investigated by using an approximate semianalytical model, which is compared with accurate numerical simulations. The study is a continuation of our previous works in which formation heterogeneity...

This work introduces a new iterative Analytic Element Method (AEM) algorithm for solving 2D steady-state groundwater flow models containing large numbers of head-specified elements (e.g., rivers and lakes). The new algorithm improves convergence of models containing head-specified elements by explicitly computing fluxes of all such features at the...

The analytic-element method (AEM) is an appealing technique for modeling steady-state groundwater flow at the supraregional scale (defined here as > 10,000 km(2)) because the computational demand is determined primarily by the number of modeled hydrologic features and not constrained by the size of the domain. In this paper, we introduce AEM to pra...

A new approach is introduced to use the Analytic Element Method (AEM) for contaminant transport modeling. AEM is an alternative to the Finite Element (FEM) and Finite Difference Methods (FDM) for solving subsurface flow problems on large scales. The domain is discretized along the hydrogeologic elements (e.g. surface water features, zones where con...

Flow and contaminant transport in groundwater aquifers are influenced by hydraulic conductivity, a property that is characterized by erratic spatial variations. A stochastic framework has been established over the last three decades to incorporate the resulting uncertainty systematically and study the problem in terms of respresentative statistical...

Flow and transport take place in a heterogeneous medium of lognormal distribution of the conductivity K. Flow is uniform in the mean, and the system is defined by U (mean velocity), sigmaY2 (log conductivity variance), and integral scale I. Transport is analyzed in terms of the breakthrough curve of the solute, identical to the traveltime distribut...

Uniform flow of mean velocity U takes place in a highly heterogeneous, isotropic, aquifer of lognormal conductivity distribution (variance sigmaY2, integral scale I). A conservative solute is injected instantaneously over an area A0 at x = 0, normal to the mean flow, in a flux-proportional mode. Longitudinal spreading is caused by advection by the...

Determination of hydraulic head, H, as a function of spatial coordinates and time, in ground water flow is the basis for aquifer management and for prediction of contaminant transport. Several computer codes are available for this purpose. Spatial distribution of the transmissivity, T(x,y), is a required input to these codes. In most aquifers, T va...

A new approach is presented for improving the computational efficiency of regional-scale ground water models based on the analytic element method (AEM). The algorithm is an extension of the existing "superblock" algorithm, which combines the effects of multiple analytic elements into Laurent series and Taylor series (superblock expansions). With th...

The solution of the advective transport problem is difficult because of its intrinsic nonlinearity. The aim of this work is to present a few new results concerning nonlinear transport of passive solutes valid for large conductivity variance. The impact of high heterogeneity is twofold: (i) highly conductive zones may create preferential paths leadi...

Transport of a nonreactive solute takes place in a three-dimensional, highly heterogeneous porous formation. The heterogeneous structure is modeled as a random collection of inclusions of hydraulic conductivity K; the latter is a random variable characterized by a probability density function (pdf) f(K). With t the travel time of a solute particle...

The Analytic Element Method (AEM) is an alternative to Finite Element and Finite Difference Methods for solving subsurface flow and transport problems on large scales. Each hydrogeologic element (e.g. surface water feature, inhomogeneity in hydraulic conductivity, well, etc.) in the domain of interest is represented by an analytic function. In orde...

Three-dimensional flow and advective transport of inert solutes in highly heterogeneous isotropic formations are simulated in a numerically laboratory. The medium is made of a homogenous background and inclusions of varying conductivity. The mean, variance and correlation structure of hydraulic conductivity in the model can be adjusted by varying c...

Determining the effective conductivity of heterogeneous media is a central problem in different fields of physics. The medium considered here contains cylinders (inclusions) of random conductivities that are distributed at random in an embedding matrix. For random systems, widely encountered in applications, we derive an approximative analytical so...

Groundwater modelers have embraced the use of automated calibration tools based on classical nonlinear regression techniques. While clearly an improvement over trial-and-error calibration, it is not clear to what extent these popular inverse modeling tools yield accurate parameter sets for groundwater flow models. The impact of model configuration...

One of the main assumptions that renders the stochastic theories applicable to real aquifers is the ergodic hypothesis, i.e. the possibility to exchange ensemble and spatial averages of a variable of interest. The principal aim of this paper is to elucidate the conditions that allow for an exchange between ensemble and spatially averaged second mom...

Flow and transport in natural aquifers depend on the spatially variable transmissivity T, usually modeled as a space random function. As a consequence, all the derived quantites, like piezometric head H, are random functions, and their statistical moments depend on those of T. The present work introduces a methodology for identification of logtrans...

Large-scale numerical simulations were conducted to investigate the stationarity and ergodicity requirements for modeling flow and transport in highly heterogeneous formations. The size of the flow domain was in the excess of 1200 integral scales of log-conductivity in 2. D and 200 in 3. D. Results show that the velocity field is nonstationary only...

The Analytic Element Method (AEM) is an alternative to Finite Element and Finite Difference Methods for solving subsurface flow and transport problems in highly heterogeneous domains. Each hydrogeologic element (e.g. a zone where conductivity differs from the surrounding conductivity, a well, a river, etc.) in the domain of interest is represented...

The effective conductivity of isotropic formations is investigated using a combination of the effective medium approximation and accurate numerical simulations. The 2D isotropic heterogeneous medium contains circular inclusions of uniform radii and of two different conductivities, K1 and K2. The inclusions are submerged into a homogeneous matrix. T...

Spatially variable transmissivity T of aquifers is modeled as random. Analysis of field data [Water Resour. Res. 21 (1985) 563] indicate that the logtransmissivity is normal and its covariance can be characterized by three parameters: the variance σYc2 and the integral scale IY of correlated residuals and a nugget σYn2, representing variability of...

A new analytic element solution has been derived for steady two-dimensional groundwater flow through an aquifer that contains an arbitrary number of elliptical inhomogeneities. The hydraulic conductivity of each inhomogeneity is homogeneous and differs from the conductivity of the homogeneous background. In addition to elliptical inhomogeneities, o...

In the present part the results of numerical simulations of flow and transport in media made up from circular inclusions of conductivity K that are submerged in a matrix of conductivity K
0, subjected to uniform mean velocity, are presented. This is achieved for a few values of =K/K
0 (0.01, 0.1 and 10) and of the volume fraction n (0.05, 0.1 and 0...

Flow and transport take place in a heterogeneous medium made up from inclusions of conductivity K submerged in a matrix of conductivity K
0. We consider two-dimensional isotropic media, with circular inclusions of uniform radii, that are placed at random and without overlap in the matrix. The system is completely characterized by the conductivity c...

The basic principle of the Analytic Element Method (AEM) is the superposition: complex regional-scale flows are simulated by adding the influences of individual analytic elements. Each analytic element contains geographic information and mathematical functions that describe its influence on regional groundwater flow. The main AEM advantage, relevan...

Flow of uniform mean velocity U takes place in a formation of spatially variable, random conductivity K(x). Advective transport of a plume of an inert solute is investigated by the Lagrangean approach. The aim of the study is to determine the spatial moments of the plume, i.e., of fluid particle trajectories, for highly heterogeneous aquifers, for...

Flow and transport of nonreactive solutes in heterogeneous porous media is studied by adopting a multi-indicator model of permeability structure. The porous formation is modeled as a collection of blocks of uniform permeability K implanted at random in a matrix of constant conductivity K0. The multi-indicator model leads to simple semianalytical so...

The study aims at deriving the effective conductivity K ef of a three-dimensional heterogeneous medium whose local conductivity K(x) is a stationary and isotropic random space function of lognormal distribution and finite integral scale I Y . We adopt a model of spherical inclusions of different K, of lognormal pdf, that we coin as a multi-indicato...

This chapter presents contaminant spreading (dispersion) in groundwater caused by heterogeneity in the hydraulic conductivity of aquifer formations. It investigates the transport phenomena using accurate numerical simulations that are based on the Analytic Element Method, and evaluates the performance of two stochastic dispersion models: the compos...

The Analytic Element Method (AEM) models groundwater flow via the superposition of analytic functions ("elements") which represent hydrologic features. Conventionally, the method has utilized explicit methods for solving for unknown coefficients. Purely explicit methods are traditionally characterized by fully populated matrices, strict adherence t...

Flow and transport in porous formations are analyzed using numerical simulations. Hydraulic conductivity is treated as a spatial random function characterized by a probability density function and a two-point covariance function. Simulations are performed for a multi-indicator conductivity structure developed by Gedeon Dagan (personal communication...

High-resolution numerical simulations of flow and transport in porous media were performed to examine the performance of the first-order dispersion model and newly introduced "self-consistent" model (Dagan, 2003; Fiori, 2003). Simulations were performed using the Analytic Element Method that allows for large contrasts in hydraulic conductivity betw...

Stream surfaces are used to examine the arrangement of neighboring streamlines in steady, divergence-free axisymmetric flow. Expressions are obtained that relate the angle of intersection between stream surfaces with general orientations to the Stokes stream function and to the specific discharge vector. These expressions are used to quantify defor...

This paper presents a new Analytic Element formulation for high-order line elements in modeling two-dimensional groundwater flow. These elements are line-doublets, line-dipoles and line-sinks. The jump functions for line elements are expressed as Chebyshev series. The unknown coefficients are computed by applying the principle of overspecification...

An implicit analytic solution is presented for three-dimensional (3D) groundwater flow through a large number of non-intersecting spheroidal inhomogeneities in the hydraulic conductivity. The locations, dimensions, and conductivity of the inhomogeneities may be arbitrarily selected. The specific discharge potential due to each inhomogeneity is expa...

It is shown that the approach presented by Strack (Strack, O.D.L., 1989. Groundwater Mechanics. Prentice Hall, New Jersey) for determining the discharge potential for an area-sink leads to a function that is unique except for an arbitrary constant. The approach is applied to a special area-sink, namely one with an extraction rate that varies inside...

An implicit analytic solution is presented for two-dimensional groundwater flow through a large number of non-intersecting circular inhomogeneities in the hydraulic conductivity. The locations, sizes and conductivity of the inhomogeneities may be arbitrarily selected. The influence of each inhomogeneity is expanded in a series that satisfies the La...

An approach, the superblock approach, is presented for increasing computational efficiency of analytic element models. The approach is based on computing the combined effect of functions using both asymptotic expansions and Taylor Series expansions. The superblocks are used to reduce both the computational effort required to determine the coefficie...

Thesis (Ph. D.)--University of Minnesota, 1997. Includes bibliographical references (leaves 128-130).

A numerical experiment of flow in variably saturated porous media was performed in order to evaluate the spatial and temporal distribution of the groundwater recharge at the phreatic surface for a shallow aquifer as a function of the input rainfall process and soil heterogeneity. The study focused on the groundwater recharge which resulted from the...

The analytic element method is used to model local three-dimensional flow in the vicinity of partially penetrating wells. The flow domain is bounded by an impermeable horizontal base, a phreatic surface with recharge and a cylindrical lateral boundary. The analytic element solution for this problem contains (1) a fictitious source technique to sati...

The Analytic Element Method (AEM) models groundwater flow via the superposition of analytic functions ("elements"). A large library of functions exists to account for linear and non-linear conditions prescribed along internal features and external boundaries with analytic precision. AEM is a grid-independent method that eliminates the need for cons...

1] In parts 1 [Dagan et al., 2003] and 2 [Fiori et al., 2003] a multi-indicator model of heterogeneous formations is devised in order to solve flow and transport in highly heterogeneous formations. The isotropic medium is made up from circular (2-D) or spherical (3-D) inclusions of different conductivities K, submerged in a matrix of effective cond...