Publications
2020

, Jun 2020, In: Chemosphere. 249, 9 p., 126099. Abstract
Indium and gallium are used widely in modern industry, mostly for the production of semiconductors. They are considered as TechnologyCritical Elements and have therefore received growing attention in the past few years. We investigated the influence of different types of humic substances on the transport of indium and gallium in laboratoryscale, saturated column experiments, to gain understanding of their mobility in natural environments. We evaluated the effect of different humic substances on the transport of indium and gallium in quartz sand: a commercial humic acid (Aldrich Humic Acid, AHA), a fulvic acid (Suwannee River Fulvic Acid, SRFA) and an aquatic natural organic matter (Suwannee River Natural Organic Matter, SRNOM). The impact of the flow rate and the influence of different concentrations of organic matter were also investigated. Indium was shown to be more mobile than gallium in the presence of humic substances. The mobility of indium in sand was highest for SRNOM, followed by SRFA and then AHA, while for gallium the order was SRFA > SRNOM > AHA. These results can be significant in understanding the mobility of indium and gallium in soils with various compositions of organic matter.
Research output: Article 
, 16 Jan 2020, In: Journal of Endourology. 34, 1, p. 6873 6 p. Abstract
Background and Purpose: Extrinsic ureteral obstruction is caused frequently by pelvic malignancies or metastatic lymphadenopathy, necessitating renal drainage with ureteral stents to prevent renal failure and kidney damage. Understanding the nature of stent behavior under deformation and realistic external pressures may assist in evaluation of stent performance. Few published studies have investigated the flow and mechanical properties of stents within ureters, and none has considered the effects of deformation and compression on flow in realistic, in vitro, ureterstent systems. The purpose of this work was to determine whether or not stent failure is due only to stent compression and deformation in the presence of extrinsic obstruction.Methods: We developed an in vitro ureterstent experimental setup, using latex tubing to simulate a flexible ureter connecting a renal unit and a bladder side. We examined flow behavior in three stents (4.8F, 6F, 7F). The ureterstent configuration was varied, simulating four levels of deformation (0°, 20°, 40°, 60°) and then simulating different external compressive forces on a stented ureter with 40° deformation. A constant, realistic fluid flow was applied through the ureterstent configurations, and pressure fluctuations in the renal unit were monitored.Results: Deformation alone on four different levels (0°, 20°, 40°, 60°) has essentially no influence on fluid flow and renal pressure variation. Under increasing external compressive forces of 500, 1000, 2000, and up to 5000 g at 40° deformation, no effect on fluid flow and pressure within the renal unit was noted for the 6F and 7F stents. The only exception was for the 4.8F stent, which demonstrated complete failure at compressive forces near 4000 g.Conclusions: Neither realistic extrinsic ureteral compression forces nor ureteral deformation explain the high frequency of stent failure in extrinsic ureteral obstruction. Other factors such as urine composition may be a major contributor to stent failure.
Research output: Article 
, 16 Jan 2020, In: Journal of Endourology. 34, 1, p. 7575 1 p. Abstract
We thank the author of the editorial comment for his remarks on our article. In response, we fully agree that, ultimately, in vivo studies are critical and essential. However, as noted also by the editorial comment author, there are a large number of variables and intertwined responses, rendering current in vivo studies difficult and inconclusive. It is, therefore, preferable to compare, first, different stents and specific factors under wellcontrolled in vitro conditions, following the standard scientific practice of study from the bench to live models and to human exposure. [first paragraph in lieu of abstract]
Research output: Article 
, Jan 2020, In: Environmental Chemistry. 17, 2, p. 118132 15 p. Abstract
Technologycritical elements (TCEs) are now present in soil and aquifer environments, as a result not only of the geogenic origin but also of the recent anthropogenic activities and release. TCEs can interact with all components of the soil and water, which include inorganic and organic ligands (natural organic matter), clays, mineral surfaces and microorganisms. The literature regarding the transport and fate of TCEs in subsurface porous media (e.g. soil and aquifers) is limited and highly diverse. This review offers a detailed analysis of the existing literature on the transport and fate of TCEs in porous media, and emphasises what is still needed to fully understand their behaviour in the environment. Different modes of TCE transport are presented. First, the mobility of TCEs following interaction with colloids (e.g. natural organic matter, clays) is described. For these cases, an increase in the ionic strength and pH of aqueous solutions shows stronger retention or sorption of TCEs on porous matrices. The transport of nanoparticles (NPs) that contain TCEs is presented as a second mode of mobility. The ionic strength of the solution is the key parameter that controls the transport of cerium nanoparticles in porous media; natural organic matter also increases the mobility of nanoparticles. The third part of this review describes sorption and dissolution processes during transport. Finally, results from the field experiments are reported, which show that rare earth elements and indium are transported in the presence of natural organic matter. We conclude this review with suggested directions for future research.
Research output: Article
2019

, 3 Dec 2019, In: Water Resources Research. 5, 12, p. 1011910129 11 p. Abstract
We study the synergistic effects of the Peclet number and the length scale of medium heterogeneity on the evolution of bimolecular reactive transport between mobile and immobile species. We performed a suite of numerical simulations at the Darcy scale that quantify the instantaneous, irreversible bimolecular reaction A(aq)+Bs > Caq, under various transport conditions (Peclet numbers) and porous media configurations (correlation lengths). We find that the global reaction rate is sensitive to both the Peclet number and the correlation length. The total amount of product decreases with increasing Peclet number, while it increases with increasing correlation length. In addition, for all of these scenarios, the global reaction rate is shown to be time dependent and is an outcome of the anomalous transport behavior of the chemical species. The timedependent behavior of the reaction rate is amplified with increasing Peclet number and decreasing correlation length and can be well approximated by a power law relationship. We find, too, that the transport behavior of the reaction products (C) often deviates from that of the inflowing reactant species (A), because reactions occur preferentially within the flow domain. Finally, and due to the influence of the Peclet number on reactive transport, we show that temporal variations in the magnitude of the flow field (i.e, changing the Peclet number over time) shift the reaction and transport behavior into a state measurably different than that for steady flow conditions.
Research output: Article 
, 19 Nov 2019, In: Environmental Science & Technology. 53, 22, p. 1307113080 10 p. Abstract
The understanding of engineered nanoparticle (ENP) fate and transport in soilwater environments is important for the evaluation of potential risks of ENPs to the ecosystem and human health. The effects of pyrite grains and three types of oxyanions  sulfate, phosphate and arsenate  on the retention of citratecoated gold nanoparticles (citrateAuNPs) were studied in partially saturated soil column experiments. The mobility of AuNP was found to be in the order: AuNPsulfide (originating from pyrite) > AuNPsulfate > citrateAuNP > AuNParsenate > AuNPphosphate. Chemical retention mechanisms, including hydrogen bonding and calcium bridging, are proposed and discussed. The retention of AuNPs in soil columns increases with the increased ability of transformed AuNP surfaces to create strong hydrogen bonding through adsorbed oxyanions with soil surfaces. Oxyanions were also found to reduce aggregation and aggregate size of AuNPs upon interaction with Ca2+ solution. While the effects of cationic substances on ENP transport and stability have been studied frequently, the results here demonstrate that anionic substances have a substantial effect on AuNP transport and stability. Furthermore, this study highlights the importance of examining ENPs under environmentallyrelevant conditions, and the significant effect of ENP transformations on their mobility in soils.
Research output: Article 
, 10 Oct 2019, In: Hydrology and Earth System Sciences. 2019, p. 141 41 p. Abstract
While both surface water and groundwater hydrological systems exhibit structural, hydraulic and chemical heterogeneity, and signatures of selforganisation, modelling approaches between these two water world communities generally remain separate and distinct. To begin to unify these water worlds, we recognize that preferential flows, in a general sense, are a manifestation of selforganisation; they hinder perfect mixing within a system, due to a more energy efficient and hence faster throughput of water and matter. We develop this general notion by detailing the role of preferential flow for residence times and chemical transport, as well as for energy conversions and energy dissipation associated with flows of water and mass. Our principal focus is on the role of heterogeneity and preferential flow and transport of water and chemical species. We propose, essentially, that related conceptualizations and quantitative characterisations can be unified in terms of a theory that connects these two water worlds in a dynamic framework. We discuss key features of fluid flow and chemical transport dynamics in these two systems – surface water and groundwater – and then focus on chemical transport, merging treatment of many of these dynamics in a proposed quantitative framework. We then discuss aspects of a unified treatment of surface water and groundwater systems in terms of energy and mass flows, and close with a reflection on complementary manifestations of selforganisation in spatial patterns and temporal dynamic behaviour.
Research output: Article 
, 18 Sep 2019, In: Environmental Engineering Science. 36, 12, p. 14661473 8 p. Abstract
Fluorinated organic compounds (FOCs) are considered contaminants of emerging concern, and novel methods are required to achieve their degradation. 5FU is a commonly used anticancer drug that is a representative example of a FOC. Use of copperpolyethylenimine nanoparticles (nCuPEI) as a catalyst, with H2O2 as a radical source, is demonstrated for the degradation of 5fluorouracil (5FU). Optimal reaction conditions were found, and 5FU was degraded completely within 24 h, following firstorder kinetics with a reaction rate of 0.003 min(1). Stoichiometric formation of F was shown with the degradation of 5FU. Substitution of uracil with other halogen groups led to a decrease in the reaction rate. By comparison, the rate of 5Chlorouracil degradation was 0.002 min(1) and that of 5Bromouracil degradation was 0.001 min(1). Stoichiometric formation of halogens was observed. A similar trend of decreasing reaction rate was found for the degradation of uracil in the presence of halogen salts. Results presented here suggest that this catalytic method can be an effective way to degrade FOCs.
Research output: Article 
, 25 Sep 2019, In: Journal of Physics A: Mathematical and Theoretical. 52, 42, 13 p., 424005. Abstract
The nonlocalintime, integropartial differential equation (iPDE) describing the continuous time random walk (CTRW) is augmented by a nonlinear chemicalspecies term accounting for migrating bimolecular reactions in a disordered media. This augmented form of the iPDE, previously shown to be in excellent agreement with a particletracking (CTRWPT) version of reactive transport, is applied here to a reanalysis of recent experimental results to further establish its validity. The experimental setup uses an injected solution of a pH indicator (Congo red) as both an inert tracer or a reactant, depending on the pH of the solution. A refraction indexmatched, watersaturated porous medium allows tracking of the reacted concentration field, which is modeled by the solutions of the twospecies coupled iPDE, whose nonlinear form precludes the use of a Laplace Transform. The timedomain solutions are obtained with a finite element method (FEM) and a sum of exponentials representation of the kernel (memory function). The twodimensional flow field subject to the macroscopic boundary conditions is calculated by solving the Darcy equation. The CTRW is well established for nonreactive transport in disordered media. The fit for the inert tracer in this case provides a reasonable match to these particular experimental data. The comparable, agreeable fit for the reactive case further establishes the validity of the iPDE augmented with a nonlinear, secondorder reaction term.
Research output: Article 
, 1 Aug 2019, In: Advances in Water Resources. 130, p. 113128 16 p. Abstract
Mixing and reaction between chemical species during cycles of drainage and imbibition in porous media are investigated using a coupled lattice Boltzmann model (LBM). This coupled LBM is able to simulate advectiondiffusion processes with homogeneous reactions under dynamic (immiscible) multiphase flow conditions. A feature of the model is that there is no need to track the interface specifically for the transport domain, which improves the computational efficiency significantly. Transport simulations of nonreactive tracers in a natural pore domain show that some tracers can be trapped with the resident wetting fluid, with the tracers in these stagnant regions (defined here as regions where Pé < 1) being released slowly during the imbibition phase. Moreover, it is found that the relative amount of tracer diffusing from these stagnant regions increases as the system approaches steadystate flow conditions. For bimolecular reactive transport, the results demonstrate that most of the reaction product generated during mixing in stagnant regions accumulates and remains within these regions, with only some release of the product to infiltrating wetting fluid that bypasses adjacent to these regions.
Research output: Article 
, 1 May 2019, In: Groundwater. 57, 3, p. 479484 6 p. Abstract
An exposition is given of a finiteelement method (FEM) software package to calculate solutions for the continuous time random walk (CTRW) integrodifferential equation for nonFickian (and Fickian) conservative or reactive transport in disordered media. The solutions encompass onedimensional/twodimensional (1D/2D) breakthrough curves and spatial concentration profiles for general geometry and grid. The velocity field, used as input to the 2D solutions, may also be calculated by applying a compatible Darcy flow 2D solver. The software enables both "forward" modeling (1D/2D) and "inverse" (bestfit) modeling (1D) of experimental data. Various inlet and outlet boundary conditions are implemented. The CTRWFEM Package is freely downloadable and contains a User's Guide, source and executable files, and accompanying files with easytouse format, including descriptions of input/output files and pre and postprocessing. Several examples are provided to clearly demonstrate how to work with the CTRWFEM Package in many typical analyses. The CTRWFEM Package also allows users to adapt the software to specific needs, such as, for example, first and secondorder chemical reactions.
Research output: Article 
, 22 May 2019, In: Environmental Chemistry. 16, 6, p. 391400 10 p. Abstract
Unintended releases of nanoparticles (NPs) into agricultural soil have recently raised concerns regarding NP accumulation in plants. In this study, specially synthesised isotopically labelled 107AgNPs, 65CuNPs and 70ZnONPs were exposed to three representative plants (Arabidopsis thaliana, Solanum lycopersicum (tomato) and Phragmites australis (common reed)) in hydroponic cultivation and, separately, to tomato plants cultivated in soil at concentrations of 2 mg L1. Metal concentrations in all samples were analysed by inductively coupled plasma mass spectrometry following acid digestion. The use of isotopically labelled NPs confirmed that elevated levels of metals were from the NP source used for the experiments. Although the highest concentrations of NPs or metals were detected in roots in both hydroponic and soil cultivations, varied levels of translocation to shoots were observed in different plants under hydroponic cultivation. In soil cultivation, where tomato plants were grown to full maturity, low levels of 107Ag (0.38 mg kg1) with respect to controls were recorded in tomato fruits; 70Zn showed the highest level of translocation to tomato stems (2.72 mg kg1) and leaves (13.93 mg kg1). Furthermore, the amounts of NPs retained in the soil (at different depths) after harvesting tomato plants were also determined; the highest concentrations of respective isotopes (1.25 mg kg1 of 107Ag, 0.79 mg kg1 of 65Cu, 4.06 mg kg1 of 70Zn) were found in the top soil layer (∼3 cm). Analysis of NPs exposed to plants in hydroponic medium indicated that the presence of plants increases the dissolution of NPs. Scanning electron microscopy analysis enabled determination of the location of 107AgNPs in the roots of tomato plants grown in soil; these NPs were found to accumulate mainly in the cortical cells.
Research output: Article 
, Mar 2019, In: Chemosphere. 219, p. 390399 10 p. Abstract
This study reports the transport characteristics of the pharmaceutical compounds carboplatin and cisplatin, and their respective derivatives, in saturated sand and soil columns. Pharmaceuticals are recognized as emerging pollutants of soil and water resources, but studies of the transport characteristics of organometallic pharmaceuticals in soilwater environments are rare. A recent study of oxaliplatin transport in natural soil raises the question of whether or not its behavior is representative of all Ptbased pharmaceuticals behavior in soilwater systems. To address this question, transport behaviors of carboplatin and cisplatin species were studied individually in packed sand columns under unamended conditions, and in packed soil columns under unamended and acetateamended conditions. In contrast to oxaliplatin, carboplatin species exhibited very low affinity to both sand and soil surfaces: the retention of injected carboplatin was 3% and
Research output: Article 
, 7 Mar 2019, In: Physical Review. E. 99, 3, 11 p., 033108. Abstract
We investigate the effects of the Péclet number (Pe) on transport of an inert chemical tracer in heterogeneous porous media. We simulate fluid flow and transport through twodimensional porescale matrices with varying structural complexity. With increasing Pe, the anomalous nature of the transport becomes enhanced as the host domain becomes more heterogeneous, due to the increasingly dominant effects of the complex velocity field. The sensitivity of (anomalous) transport to Pe is shown to be controlled by the medium structure. We quantify the effects of Pe by interpreting the numerical simulations within the continuous time random walk method (CTRW) framework, and incorporating Pe within the underlying tracer transition time distribution. We then investigate transport behavior subjected to temporal variation in the velocity field magnitude, accounting for tracer propagation controlled by Pe. Because of the nonlinear influence of Pe on the transport behavior, we show that temporal variations in the velocity field can lead to an increase in the anomalous nature of the transport.
Research output: Article 
, 5 Feb 2019, In: Journal of Hazardous Materials. 363, p. 394400 7 p. Abstract
Transport of indium and gallium is reported in laboratory column experiments using quartz sand as a model porous medium representative of a groundwater system. With increased use of indium and gallium in recent years, mainly in the semiconductor industry, concerns arise regarding their environmental effects. The transport and retention behavior of these two metals were quantified via batch and column experiments, and numerical modeling. The effect of natural organic matter on indium and gallium mobility was studied by addition of humic acid (HA). Measured breakthrough curves from column experiments demonstrated different binding capacities between indium and gallium, stronger for indium, with the presence of HA affecting retention dynamics. For indium, the binding capacity on quartz decreases significantly in the presence of HA, leading to enhanced mobility. In contrast, gallium exhibits slightly higher retention and lower mobility in the presence of HA. In all cases, the binding capacity of gallium to quartz is much weaker than that of indium. These results are consistent with the assumption that indium and gallium form different types of complexes with organic ligands, with gallium complexes appearing more stable than indium complexes. Quantitative modeling confirmed that metal retention is controlled by complex stability.
Research output: Article
2018

, Nov 2018, In: Environmental Pollution. 242, Part B, p. 18271837 11 p. Abstract
In parallel to technological advances and everincreasing use of nanoparticles in industry, agriculture and consumer products, the potential ecotoxicity of nanoparticles and their potential accumulation in ecosystems is of increasing concern. Because scientific reports raise a concern regarding nanoparticle toxicity to plants, understanding of their bioaccumulation has become critical and demands more research. Here, the synthesis of isotopicallylabeled nanoparticles of silver, copper and zinc oxide is reported; it is demonstrated that while maintaining the basic properties of the same unlabeled ("regular") nanoparticles, labeled nanoparticles enable more sensitive tracing of nanoparticles within plants that have background elemental levels. This technique is particularly useful for working with elements that are present in high abundance in natural environments. As a benchmark, labeled and unlabeled metal nanoparticles (AgNP, CuNP, ZnONP) were synthesized and compared, and then exposed in a series of growth experiments to Arabidopsis thaliana; the NPs were traced in different parts of the plant. All of the synthesized nanoparticles were characterized by TEM, EDS, DLS, zetapotential and single particle ICPMS, which provided essential information regarding size, composition, morphology and surface charge of nanoparticles, as well as their stability in suspensions. Tracing studies with A. thaliana showed uptake/retention of nanoparticles that is more significant in roots than in shoots. Single particle ICPMS, and scanning electron micrographs and EDS of plant roots showed presence of AgNPs in particular, localized areas, whereas copper and zinc were found to be distributed over the root tissues, but not as nanoparticles. Thus, nanoparticles in any natural matrix can be replaced easily by their labeled counterparts to trace the accumulation or retention of NPs. Isotopicallylabeled nanoparticles enable acquisition of specific results, even if there are some concentrations of the same elements that originate from other (natural or anthropogenic) sources. (C) 2018 Elsevier Ltd. All rights reserved.
Research output: Article 
, Nov 2018, In: Advances in Water Resources. 121, p. 304315 12 p. Abstract
We quantify the poorlyunderstood interactions between resident and infiltrating water during drainageimbibition cycles in heterogeneous porous media, via a 2D (and 3D) lattice Boltzmann simulation method. These interactions are critical in the (partially saturated) soil layer, which is the interface from land surface to groundwater that controls the fate and transport of infiltrating water and chemicals to aquifers. The results demonstrate the sensitivity of these dynamic interactions to the contact angle, boundary flux condition, body force, and porosity. We show that the body force and contact angle have relatively small effects on interactions in the capillary flow regime, while the boundary flux and porosity alter the amount and distribution of resident and infiltrating water significantly. Moreover, airwater interfaces are shown to be dynamically concave/convex, determined by both contact angle and pore geometry. Our analysis demonstrates the coexistence of distinct pockets of resident and infiltrating water, and provides porescale, mechanistic evidence that supports field observations of soil water zones with different chemical signatures.
Research output: Article 
, Oct 2018, In: Chemosphere. 208, p. 829837 9 p. Abstract
This study reports the transport characteristics of the organometallic anticancer compound oxaliplatin and its derivatives in natural soilwater environments. Although pharmaceuticals and their derivatives have for many years been detected in water resources, and linked to toxicological impacts on ecological systems, their transport in soil and groundwater is not fully understood. Specifically, studies that describe transport of organometallic pharmaceuticals in porous media are rare, and the transport characteristics of platinum complexes have received little attention. Oxaliplatin transport was studied in sand, as a function of two added natural chelators (citrate and humic acid), and in soil, under four continuously monitored, environmentallyrelevant redox conditions: oxic, nitrate reducing, iron reducing and methanogenic. In sand, oxaliplatin species retention was about 7%, and affected only mildly by added citrate, and by humic acid under buffered pH. Transport with unbuffered humic acid was affected significantly by pH variations, and exhibited strong retention at pH <8. In soil, unexpectedly similar breakthrough patterns of oxaliplatin species were found for all redox conditions, exhibiting linear, reversible retention of 7987%. The strongest retention was observed under iron reducing conditions, whereas the weakest retention was under oxic conditions. Increased cation activity appears to promote weaker sorption. The results indicate that soil composition is the leading factor affecting oxaliplatin species mobility and fate in the soilwater environment, followed by the weaker factors of redox conditions and cation activities. (C) 2018 Elsevier Ltd. All rights reserved.
Research output: Article 
, May 2018, In: Journal of Contaminant Hydrology. 212, p. 5564 10 p. Abstract
We present a combined experimental and numerical modeling study that addresses two principal questions: (i) is any particular Eulerianbased method used to solve the classical advectiondispersion equation (ADE) clearly superior (relative to the others), in terms of yielding solutions that reproduce BTCs of the kind that are typically sampled at the outlet of a laboratory cell? and (ii) in the presence of matches of comparable quality against such BTCs, do any of these methods render different (or similar) numerical BTCs at locations within the domain? To address these questions, we obtained measurements from carefully controlled laboratory experiments, and employ them as a reference against which numerical results are benchmarked and compared. The experiments measure solute transport breakthrough curves (BTCs) through a square domain containing various configurations of coarse, medium, and fine quartz sand. The approaches to solve the ADE involve EulerianLagrangian and Eulerian (finite volume, finite elements, mixed and discontinuous finite elements) numerical methods. Model calibration is not examined; permeability and porosity of each sand were determined previously through separate, standard laboratory tests, while dispersivities are assigned values proportional to mean grain size. We find that the spatial discretization of the flow field is of critical importance, due to the nonuniformity of the domain. Although simulated BTCs at the system outlet are observed to be very similar for these various numerical methods, computed local (pointwise, inside the domain) BTCs can be very different. We find that none of the numerical methods is able to fully reproduce the measured BTCs. The impact of model parameter uncertainty on the calculated BTCs is characterized through a set of numerical Monte Carlo simulations; in cases where the impact is significant, assessment of simulation matches to the experimental data can be ambiguous.
Research output: Article 
, 2 Feb 2018, In: Physical Review Letters. 120, 5, 5 p., 054504. Abstract
We investigate the effects of high fluid velocities on flow and tracer transport in heterogeneous porous media. We simulate fluid flow and advective transport through twodimensional porescale matrices with varying structural complexity. As the Reynolds number increases, the flow regime transitions from linear to nonlinear; this behavior is controlled by the medium structure, where higher complexity amplifies inertial effects. The result is, nonintuitively, increased homogenization of the flow field, which leads in the context of conservative chemical transport to less anomalous behavior. We quantify the transport patterns via a continuous time random walk, using the spatial distribution of the kinetic energy within the fluid as a characteristic measure.
Research output: Article 
, Feb 2018, In: Environmental Science: Nano. 5, 2, p. 422435 14 p. Abstract
The need for better understanding of the environmental fate and transport of engineered nanoparticles (ENPs) is now a scientific consensus. However, the partially saturated zone, a critical region that links the earth's surface to aquifers, has to date received only minor attention in the context of ENP mobility. We investigate the transport and fate of a representative ENP, silver nanoparticles (AgNPs), in partially saturated soil Here we present a set of column experiments and modelling simulations to examine breakthrough curves (BTCs), retention profiles, and mass balances that characterize AgNP transport, and gain insights into retardation mechanisms. Unlike AgNP transport in sand columns, where the BTC pattern often resembles that of a conservative tracer, AgNP transport in soil columns shows moderate mobility and more complex BTC patterns; these results also emphasize the importance of employing realistic porous media in environmental studies. Overall, AgNP mobility decreases in the presence of Ca(NO3)(2), and increases when the solution contains humic acid, at higher water saturation levels, or at higher input concentrations of AgNPs. In addition, a different pattern was observed for AgNP aggregates, indicating nanospecific behaviour. Modelling analysis of AgNP transport in partially saturated soil suggests that a twosite kinetic model with a timedependent retention function quantifies the transport behaviour of AgNPs.
Research output: Article 
, 17 Jan 2018, In: European Physical Journal B. 91, 1, 8 p., 15. Abstract
A nonlocalintime integrodifferential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M (t), which includes the source of nonFickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is nonlinear and secondorder, relevant for a bimolecular reaction A + B → C. The interaction term ΓP
A (s, t) P
B (s, t) is symmetric in the concentrations of A and B (i.e. P
A and P
B); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M (t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRWPT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.Research output: Article 
, 1 Jan 2018, In: Science of the Total Environment. 610611, p. 10831091 9 p. Abstract
As a consequence of their growing use in electronic and industrial products, increasing amounts of technology critical elements (TCEs) are being released to the environment. Currently little is known about the fate of many of these elements. Initial research on their potential environmental impact identifies TCEs as emerging contaminants. TCE movement in the environment is often governed by water systems. Research on “natural” waters so far demonstrates that TCEs tend to be associated with suspended particulate matter (SPM), which influences TCE aqueous concentrations (here: concentration of TCEs in dissolved form and attached to SPM) and transport. However, the relative potential of different types of SPM to interact with TCEs is unknown. Here we examine the potential of various types of particulate matter, namely different nanoparticles (NPs; Al
2O
3 SiO
2, CeO
2, ZnO, montmorillonite, Ag, Au and carbon dots) and humic acid (HA), to impact TCE aqueous concentrations in aqueous solutions with soil and sand, and thus influence TCE transport in soilwater environments. We show that a combination of NPs and HA, and not NPs or HA individually, increases the aqueous concentrations of TCEs in soil solutions, for all tested NPs regardless of their type. TCEs retained on SPM, however, settle with time. In solutions with sand, HA alone is as influential as NPs + HA in keeping TCEs in the aqueous phase. Among NPs, AgNPs and AuNPs demonstrate the highest potential for TCE transport. These results suggest that in natural soilwater environments, once TCEs are retained by soil, their partitioning to the aqueous phase by throughflowing water is unlikely. However, if TCEs are introduced to soilwater environments as part of solutions rich in NPs and HA, it is likely that NP and HA combinations can increase TCE stability in the aqueous phase and prevent their retention on soil and sand, thus facilitating TCE transport.Research output: Article
2017

, Nov 2017, In: International Journal for Numerical Methods in Engineering. 112, 5, p. 459478 20 p. Abstract
A finite element method is developed to solve a class of integrodifferential equations and demonstrated for the important specific problem of nonFickian contaminant transport in disordered porous media. This transient transport equation, derived from a continuous time random walk approach, includes a memory function. An integral element is the incorporation of the wellknown sumofexponential approximation of the kernel function, which allows a simple recurrence relation rather than storage of the entire history. A twodimensional linear element is implemented, including a streamline upwind PetrovGalerkin weighting scheme. The developed solver is compared with an analytical solution in the Laplace domain, transformed numerically to the time domain, followed by a concise convergence assessment. The analysis shows the power and potential of the method developed here. Copyright (C) 2017 John Wiley & Sons, Ltd.
Research output: Article 
Copper nanoparticles for degradation of pollutants, Jun 2017. Abstract
The present invention is directed to a degradation composition, methods and kits for degrading organic pollutants comprising reduced copper based nanoparticlespolymer complex (CuNPs) and an oxidant.
Research output: Patent 
, May 2017, In: Scientific Reports. 7, 13 p., 1415. Abstract
We present the synthesis of new composite materials based on copper nanoparticles (Cu NPs) deposited onto montmorillonite (MK10) and quartz sand, for degradation of atrazine, in the context of an advanced oxidation process (AOP). The synthesis involves a first step in which polyethylenimine (PEI) capped Cu NPs (PEI_Cu NPs) are prepared, and then deposited onto, separately, MK10 and sand, through a solvent impregnation method. The resulting products are characterized in detail; the copper is found to exist as a mixture of copper (I, II) oxide. The degradation of atrazine follows a secondorder kinetic model with constant values of K2=1.7957g mg(1) min(1) for MK10_ PEI_ Cu NPs and K2= 0.8133g mg(1) min(1) for sand_ PEI_ Cu NPs. The reaction rate is linked to Cu2O and CuO redoxactive species within the layers, pores and surface of the host materials. A degradation mechanism is found with application of these composite materials in the presence of H2O2; adsorption occurs in the absence of H2O2. In contrast, the unmodified MK10 and sand exhibit adsorption in both of the above reaction conditions. Finally, the stability of the Cu NPs following degradation is evaluated, and no significant amount of copper leaching is found.
Research output: Article 
, Feb 2017, In: Clean  Soil, Air, Water. 45, 2, 11 p., 1600048. Abstract
Endocrine disrupting chemicals (EDCs) are detected in environmental matrices such as surface water, wastewater, groundwater, and drinking water in the ng/L range. For environmental sediments, values in the range of ng/g and even lower are reported. These almost omnipresent low concentrations of estrogens are of major concern, in particular as sorption parameters derived from laboratory investigations tend to imply the absence of estrogens in the natural environment. Very few studies consider the fate and transport of estrogens in column tests at environmentally relevant concentrations, including metabolite formation and sorption. Also, the effect of input concentration on hormone degradation is unclear. To close this gap, the estrogens 17aestradiol (E2), estrone (E1), and the conjugated estrogen estronesulfate (E13S) were each injected into saturated, packed soil columns as pulses with subsequent analysis of soil and aqueous samples. The transformation pathway E2 to E1 and subsequently to E13S was verified in sandy clay loam soil from Bet Dagan, Israel. Furthermore, it was shown that (i) E2 is rapidly degraded in soil and transformed in soil to E1; (ii) E1 is subject to strong retardation by sorption; and (iii) E13S behaves almost conservatively and shows the lowest sorption and transformation potential.
Research output: Article 
, Feb 2017, In: Canadian Journal of Chemical Engineering. 95, 2, p. 343352 10 p. Abstract
Many applications of copper nanoparticles (CuNPs) have been suggested in recent years, although the potential for use of CuNPs in water treatment processes has received relatively little attention. This work highlights the preparation, characterization, and application of polyethylenimine capped copper nanoparticles for use in oxidative degradation of organic pollutants in aqueous solutions; atrazine was selected as a representative pollutant. A stable aqueous CuNP suspension was prepared, with polyethylenimine (PEI) as capping agent, under ambient conditions. The Cu:PEI ratio during CuNP synthesis has a significant influence on nanoparticle properties as well as on the degradation of atrazine. The synthesized CuNPs, which comprised a mixture of Cu0 and Cu2O, induced rapid atrazine degradation (> 99 % in 1 h) and significantly superior performance over commercial nanocopper oxide powder. Mechanistic insight into the atrazine degradation, via electron spin resonance (ESR) measurements, demonstrated (i) that significant hydroxyl radicals were generated only in the presence of CuNPs, (ii) longevity of radical generation, and (iii) regeneration of hydroxide radicals. The efficiency of the CuNPs applied to oxidative degradation was further demonstrated on eight other representative organic water pollutants.
Research output: Article 
, Feb 2017, In: Ambio. 46, 1, p. 109120 12 p. Abstract
Within historically accepted, major soilforming major processes, the role of chemicals as a humaninduced factor was neglected until the middle of the last century. Over the years, however, anthropogenic chemicals have emerged and are being released on the land surface in large amounts. Irreversible changes in the matrix of soil and soil constituents may occur as a result of both intentional and accidental release of anthropogenic chemicals, as well as a byproduct of human activity. After presenting an historical evolution of the discussion on soilforming factors, we focus here on human impacts and examine the abiotic role of anthropogenic microchemical contaminant (AMCC) interactions with soils at the molecular level. Selected examples of microchemical contaminants, including heavy metals, pesticides, hydrocarbons, and engineered nanomaterials, are presented to demonstrate that AMCCseven at low concentrationmay irreversibly alter the matrix of the soil and soil constituents and lead to the formation of anthropogenic soils with different properties than those of the pristine soils.
Research output: Article 
, Jan 2017, In: Water Resources Research. 53, 5, p. 37603769 10 p. Abstract
Temporal variations in the subsurface velocity field are often (if not always) present in the real world to at least some degree. However, an accounting of their effects on chemical transport has been largely neglected. Here we demonstrate experimentally the effects of a timevarying velocity field on conservative chemical tracer transport in porous media, as compared to constant velocity conditions. We find that velocityfield fluctuations increase chemical tracer spreading and residence time, which intensify the anomalous nature of the transport. This behavior is modeled by a continuous time random walk particle tracking method formulated to account for timedependent velocity fields. The model matches the experimental results with a parsimonious and consistent set of parameters. The model is then applied to study the effects of different magnitudes in velocityfield fluctuations, as well as different degrees of porous media heterogeneity, on 1D and 2D spatiotemporal propagation of an injected, pointsource, chemical plume. Increased intensity of velocityfield fluctuations, and increased porous medium heterogeneity, each serve to increase the extent of chemical spreading and anomalous behavior.
Research output: Article
2016

, Dec 2016, In: Reviews of Geophysics. 54, 4, p. 930986 57 p. Abstract
Reactive chemical transport plays a key role in geological media across scales, from pore scale to aquifer scale. Systems can be altered by changes in solution chemistry and a wide variety of chemical transformations, including precipitation/dissolution reactions that cause feedbacks that directly affect the flow and transport regime. The combination of these processes with advectivedispersivediffusive transport in heterogeneous media leads to a rich spectrum of complex dynamics. The principal challenge in modeling reactive transport is to account for the subtle effects of fluctuations in the flow field and species concentrations; spatial or temporal averaging generally suppresses these effects. Moreover, it is critical to ground model conceptualizations and test model outputs against laboratory experiments and field measurements. This review emphasizes the integration of these aspects, considering carefully designed and controlled experiments at both laboratory and field scales, in the context of development and solution of reactive transport models based on continuumscale and particle tracking approaches. We first discuss laboratory experiments and field measurements that define the scope of the phenomena and provide data for model comparison. We continue by surveying models involving advectiondispersionreaction equation and continuous time random walk formulations. The integration of measurements and models is then examined, considering a series of case studies in different frameworks. We delineate the underlying assumptions, and strengths and weaknesses, of these analyses, and the role of probabilistic effects. We also show the key importance of quantifying the spreading and mixing of reactive species, recognizing the role of smallscale physical and chemical fluctuations that control the initiation of reactions.
Research output: Article 
, Dec 2016, In: Water Resources Research. 52, 12, p. 95659585 21 p. Abstract
Path reversibility and radial symmetry are often assumed in pushpull tracer test analysis. In reality, heterogeneous flow fields mean that both assumptions are idealizations. To understand their impact, we perform a parametric study which quantifies the scattering effects of ambient flow, localscale dispersion, and velocity field heterogeneity on pushpull breakthrough curves and compares them to the effects of mobileimmobile mass transfer (MIMT) processes including sorption and diffusion into secondary porosity. We identify specific circumstances in which MIMT overwhelmingly determines the breakthrough curve, which may then be considered uninformative about drift and localscale dispersion. Assuming path reversibility, we develop a continuoustimerandomwalkbased interpretation framework which is flowfieldagnostic and well suited to quantifying MIMT. Adopting this perspective, we show that the radial flow assumption is often harmless: to the extent that solute paths are reversible, the breakthrough curve is uninformative about velocity field heterogeneity. Our interpretation method determines a mapping function (i.e., subordinator) from travel time in the absence of MIMT to travel time in its presence. A mathematical theory allowing this function to be directly "plugged into'' an existing Laplacedomain transport model to incorporate MIMT is presented and demonstrated. Algorithms implementing the calibration are presented and applied to interpretation of data from a pushpull test performed in a heterogeneous environment. A successful fourparameter fit is obtained, of comparable fidelity to one obtained using a millionnode 3D numerical model. Finally, we demonstrate analytically and numerically how pushpull tests quantifying MIMT are sensitive to remobilization, but not immobilization, kinetics.
Research output: Article 
, Nov 2016, In: Transport in Porous Media. 115, 2, p. 209214 6 p. AbstractResearch output: Editorial

, Nov 2016, In: Catena. 146, p. 3037 8 p. Abstract
Chemical action as an anthropogenic factor in soil formation was suggested 50 years ago as a part of the metapedogenetic process. Initially, agricultural practices such as irrigation with saline water and soil liming by natural carbonated earth materials (marling) were considered as examples of chemical contamination that alter soil properties. Over the years, however, new anthropogenic substances have emerged, and their disposal on the land surface, whether intentionally or by accident, is acting as another metapedogenetic factor, leading to formation of contemporary soils with altered properties. In this context, potential transformation of natural soils may occur as a result of exposure to engineered nanomaterials (ENMs). Due to the relatively small amounts used to date, and their size and associated chemical properties, the impact of ENMs on soil may be questioned. We argue here, however, that ENMs disposed on the land surface are irreversibly retained in the soil matrix, accumulating over time and becoming a metapedogenetic factor. In support of this hypothesis, we present examples from the literature which demonstrate that deposition of carbonbased and metalbased ENMs may cause, wider specific conditions, changes to the matrix and properties of soil constituents and formation of contemporary anthropogenic soils. These examples reconfirm the hypothesis that chemicals are a factor in anthropogenicallyinduced metapedogenesis. (C) 2016 Elsevier B.V. All rights reserved.
Research output: Article 
, Nov 2016, In: Transport in Porous Media. 115, 2, p. 239263 25 p. Abstract
We study an integrodifferential equation that has important applications to problems of anomalous transport in highly disordered media. In one application, the equation is the continuum limit of a continuous time random walk used to quantify nonFickian (anomalous) contaminant transport. The finite element method is used for the spatial discretization of this equation, with an implicit scheme for its time discretization. To avoid storage of the entire history, an efficient sumofexponential approximation of the kernel function is constructed that allows a simple recurrence relation. A 1D formulation with a linear element is implemented to demonstrate this approach, by comparison with available experiments and with an exact solution in the Laplace domain, transformed numerically to the time domain. The proposed scheme convergence assessment is briefly addressed. Future extensions of this implementation are then outlined.
Research output: Article 
, Nov 2016, In: Transport in Porous Media. 115, 2, p. 291310 20 p. Abstract
We characterize the role of preferential pathways in controlling the dynamics of bimolecular reactive transport in a representative model of a heterogeneous porous medium. We examine a suite of numerical simulations that quantifies the irreversible bimolecular reaction , in a twodimensional heterogeneous domain (with logconductivity, Y), wherein solute A is injected along an inlet boundary to displace the resident solute B under uniform (in the mean) flow conditions. We explore the feedback between the reactive process and (a) the degree of system heterogeneity, as quantified by the unconditional variance of Y, , representing moderately to strongly heterogeneous media, and (b) the relative strengths of advective and diffusive mechanisms, as quantified by a grid P,clet number, . Our analysis is based on the identification of particle preferential pathways, focusing on particle residence time within cells employed to discretize the flow domain. These preferential pathways are formed mainly by high conductivity cells and generally contain an important component of (sometimes isolated and a relatively small number of) lower conductivity values. A key finding of our analysis is that while the former dominate the behavior, the latter are shown to provide a nonnegligible contribution to the global number of reactions taking place in the domain for strongly heterogeneous media, i.e., for the largest investigated values of . Reactions are detected across the complete simulation time window (of about 5.5 pore volumes) for the strongly advective case. When diffusion plays an important role, the reactive process essentially stops after the injection of a limited amount (2.5) of pore volumes.
Research output: Article 
, Jul 2016, In: Water Resources Research. 52, 7, p. 54735491 19 p. Abstract
A continuous time random walk particle tracking (CTRWPT) method was employed to model flow cell experiments that measured transport of engineered nanoparticles (ENPs) in a reactive porous medium. The experiments involved a watersaturated medium containing negatively charged, polyacrylamide beads, resembling many natural soils and aquifer materials, and having the same refraction index as water. Negatively and positively charged ENPs were injected into a uniform flow field in a 3D horizontal flow cell, and the spatial and temporal concentrations of the evolving ENP plumes were obtained via image analysis. As a benchmark, and to calibrate the model, Congo red tracer was employed in 1D column and 3D flow cell experiments, containing the same beads. Negatively charged Au and Ag ENPs demonstrated migration patterns resembling those of the tracer but were slightly more dispersive; the transport was well represented by the CTRWPT model. In contrast, positively charged AgNPs displayed an unusual behavior: establishment of an initial plume of essentially immobilized ENPs, followed by development of a secondary, freely migrating plume. The mobile plume was found to contain ENPs that, with aging, exhibited aggregation and charge inversion, becoming negatively charged and mobile. In this case, the CTRWPT model was modified to include a probabilistic law for particle immobilization, to account for the decreasing tendency (over distance and time) of the positively charged AgNPs to attach to the porous medium. The agreement between experimental results and modeling suggests that the CTRWPT framework can account for the nonFickian and surfacechargedependent transport and aging exhibited by ENPs in porous media.
Research output: Article 
, Jul 2016, In: Water Resources Research. 52, 7, p. 56345643 10 p. Abstract
Anomalous transport is ubiquitous in a wide range of disordered systems, notably in fractured porous formations. We quantitatively identify the structural controls on anomalous tracer transport in a model of a real fractured geological formation that was mapped in an outcrop. The transport, determined by a continuum scale mathematical model, is characterized by breakthrough curves (BTCs) that document anomalous (or "nonFickian") transport, which is accounted for by a power law distribution of local transition times psi(t) within the framework of a continuous time random walk (CTRW). We show that the determination of psi(t) is related to fractures aligned approximately with the macroscopic direction of flow. We establish the dominant role of fracture alignment and assess the statistics of these fractures by determining a concentrationvisitation weighted residence time histogram. We then convert the histogram to a probability density function (pdf) that coincides with the CTRW psi(t) and hence anomalous transport. We show that the permeability of the geological formation hosting the fracture network has a limited effect on the anomalous nature of the transport; rather, it is the fractures transverse to the flow direction that play the major role in forming the long BTC tail associated with anomalous transport. This is a remarkable result, given the complexity of the flow field statistics as captured by concentration transitions.
Research output: Article 
, Mar 2016, In: Journal of Hazardous Materials. 311, p. 25462 26995325. Abstract
Copyright 2016 Elsevier B.V. All rights reserved.The vadose zone is a critical region controlling fate and transport of contaminants in soils and, ultimately, groundwater. It is therefore important to understand the behavior of engineered nanoparticles (ENPs) in this zone, as a potential group of emerging contaminants. Soil is a significant sink for ENPs; however, only a few studies have considered the fate and transport of ENPs in partially saturated systems, representative of the vadose zone. Here, transport behavior of three commonly used ENPs  gold (AuNPs), silver (AgNPs) and zinc oxide (ZnONPs)  is investigated in partially saturated sand columns. High mobilities of AuNPs and AgNPs under different water saturation levels and concentrations were observed. The presence of CaCl2 reduces AgNP mobility through chemical interactions, similar to behavior reported in saturated systems. Furthermore, transformation of AgNPs in the environment may influence their mobility; aging of AgNPs following sulfidation was investigated. The silver sulfide (Ag2SNPs) remained stable in aqueous suspension, and mobile in the partially saturated sand column. In contrast, the positivelycharged ZnONPs were completely immobilized in the sand column. Significantly, though, addition of humic acid (HA) to the ZnONP suspension reverses particle surface charge and thus increases their mobility. Moreover, remobilization of entrapped ZnONPs by HA was demonstrated.
Research output: Article 
, Feb 2016, In: Chemosphere. 144, p. 71320 8 p. Abstract
The release of pharmaceuticals and personal care products (PPCPs) to the soilwater environment necessitates understanding of PPCP transport behavior under conditions that account for dynamic flow and varying redox states. This study investigates the transport of two organometallic PPCPs, GdDTPA and roxarsone (arsenic compound) and their metal salts (Gd(NO3)3, AsNaO2); GdDTPA is used widely as a contrasting agent for MRI, while roxarsone is applied extensively as a food additive in the broiler poultry industry. Here, we present column experiments using sand and Mediterranean red sandy clay soil, performed under several redox conditions. The metal salts were almost completely immobile. In contrast, transport of GdDTPA and roxarsone was affected by the soil type. Roxarsone was also affected by the different redox conditions, showing delayed breakthrough curves as the redox potential became more negative due to biological activity (chemicallystrong reducing conditions did not affect the transport). Mechanisms that include adsorptive retardation for aerobic and nitratereducing conditions, and nonadsorptive retardation for ironreducing, sulfatereducing and biologicallystrong reducing conditions, are suggested to explain the roxarsone behavior. GdDTPA is found to be a stable complex, with potential for high mobility in groundwater systems, whereas roxarsone transport through groundwater systems is affected by redox environments, demonstrating high mobility under aerobic and nitratereducing conditions and delayed transport under ironreducing, sulfatereducing and biologicallystrong reducing conditions.
Research output: Article 
Copper nanoparticles for oxidation of pollutants, Jan 2016. Abstract
The present invention is directed to a degradation composition, methods and kits for degrading organic pollutants in advanced oxidation processes (AOP) comprising reduced copper based nanoparticlespolymer complex (CuNPs) and an oxidant.
Research output: Patent
2015

, 15 Dec 2015, In: Journal of Hazardous Materials. 299, p. 513519 7 p. Abstract
We present quasi3D visualization and analysis of engineered nanoparticle (ENP) transport behavior in an experimental setup that uses a transmitted light imaging technique. A flow cell was packed with specially adapted, watertransparent, spherical polyacrylamide beads, which carry a negative surface charge representative of many natural environments. Ubiquitous, oppositelycharged ENPs  Au and Ag NPs  were synthesized and introduced into a flow cell subjected to a macroscopically uniform flow field via point source pulse injection, at three different flow rates. The negativelycharged ENPs behaved like a conservative tracer, in terms of spatiotemporal plume evolution. The positive AgNPs, however, displayed a decrease in their initially strong tendency to attach to the oppositelycharged porous medium. As a result, immobilization of the positive AgNPs was spatially and temporally limited to the vicinity of the point of injection; beyond this region, the AgNPs were mobile and effluent contained AgNPs with hydrodynamic diameters significantly larger than those of the injected AgNPs. This behavior is understood by dynamic light scattering and zeta potential measurements, which showed aggregation processes and inversion in particle surface charge to occur during transport of the positive ENPs. These findings have broad implications for ENP mobility and reactivity in the environment.
Research output: Article 
, Nov 2015, In: Environmental Pollution. 206, p. 8087 7 p. Abstract
Endocrine disrupting chemicals, such as the free estrogens 17betaestradiol (E2), estrone (E1) and the conjugated estrogen estronesulfate (E13S) are found at low concentration levels in the environment. This is somehow contradictory to the strong sorption and high degradation potentials found in laboratory experiments. In particular, the fate and transport behavior of conjugated estrogens is poorly understood, and the importance of enzymes triggering the transformation pathways has received little attention. To address these deficiencies, the present research uses packed laboratory soil columns with pulse injections of free estrogens, either E2 or E1, or E13S, to provide sound evidence of the transformation pathways. It is further shown that (i) transport of free estrogens is subject to strong retardation and degradation, (ii) the transport of conjugated estrogens is less retarded and only to a minor degree affected by degradation, and (iii) arylsulfotransferase is the enzyme triggering the transformation reaction.
Research output: Article 
, Sep 2015, In: Water Resources Research. 51, 9, p. 77027722 21 p. Abstract
Nickel migration measured in laboratoryscale, natural soil column experiments is shown to display anomalous (nonFickian) transport, nonequilibrium adsorption and desorption patterns, and precipitation/dissolution. Similar experiments using a conservative tracer also exhibit anomalous behavior. The occurrence of ion exchange of nickel, mainly with calcium (but also with other soil components), is measured in both batch and flowthrough column experiments; adsorption and desorption isotherms demonstrate hysteresis. Strong retention of nickel during transport in soil columns leads to delayed initial breakthrough (?40 pore volumes), slow increase in concentration, and extended concentration tailing at long times. We describe the mechanisms of transport and retention in terms of a continuous time random walk (CTRW) model, and use a particle tracking formulation to simulate nickel migration in the column. This approach allows us to capture the nonFickian transport and the subtle local effects of adsorption/desorption and precipitation/dissolution. Consideration also of preferential pathways accounts for the evolution of the measured breakthrough curve and measured spatial concentration profiles. The model uses nonFickian transport parameters estimated from the conservative tracer and, as a starting point, adsorption/desorption parameters based on batch experiments and a precipitation parameter based on Ksp values. The batch parameters are found to underestimate the actual amount of adsorption. We suggest that the sorption and precipitation/dissolution dynamics, and resulting breakthrough curves, are influenced strongly by preferential pathways; such pathways significantly alter the availability of sorption sites and ion availability for precipitation. Analysis of these results provides further understanding of the interaction and dynamics among transport, precipitation, and sorption mechanisms in natural soil. 2015. American Geophysical Union. All Rights Reserved
Research output: Article 
, May 2015, In: Water Resources Research. 51, 5, p. 33843402 19 p. Abstract
We consider modeling approaches to characterize solute transport in porous media, integrating them into a unique theoretical and experimental framework for model evaluation and data interpretation. To date, development of (conservative and reactive chemical) transport models and formulation of model calibration methods grounded on sensitivitybased collection of measurements have been pursued in parallel. Key questions that remain include: For a given set of measurements, which conceptual picture of the transport processes, as embodied in a mathematical model or models, is most appropriate? What are the most valuable spacetime locations for solute concentration measurements, depending on the model selected? How is model parameter uncertainty propagated to model output, and how does this propagation affect model calibration? We address these questions by merging parallel streams of researchmodel formulation, reduction, calibration, sensitivity analysis, and discriminationoffering our view on an emerging framework that guides (i) selection of an appropriate number and location of timedependent concentration measurements given a transport model and (ii) assessment (through discrimination criteria) of the relative benefit of applying any particular model from a set of several models. Our strategy is to employ metrics to quantify the relative contribution of each uncertain model parameter to the variability of the model output. We evaluate these metrics through construction of a surrogate (or "meta'') transport model that has the additional benefit of enabling sensitivity analysis and model calibration at a highly reduced computational cost. We demonstrate the applicability of this framework, focusing on transport of reactive chemicals in laboratoryscale porous media.
Research output: Article 
, May 2015, In: Physical Review E. 91, 5, 13 p., 52130. Abstract
We analyze dynamic behavior of chemically reactive species in a porous medium, subject to anomalous transport. In this context, we present transport experiments in a refractionindexmatched, threedimensional, watersaturated porous medium. A pH indicator (Congo red) was used as either a conservative or a reactive tracer, depending on the tracer solution pH relative to that of the background solution. The porous medium consisted of an acrylic polymermaterial formed as spherical beads that have pHbuffering capacity. The magnitude of reaction during transport through the porous medium was related to the color change of the Congo red, via image analysis. Here, we focused on point injection of the tracer into a macroscopically uniform flow field containing water at a pH different from that of the injected tracer. The setup yielded measurements of the temporally evolving spatial (localinspace) concentration field. Parallel experiments with the same tracer, but without reactions (no changes in pH), enabled identification of the transport itself to be anomalous (nonFickian); this was quantified by a continuous time random walk (CTRW) formulation. A CTRWparticle tracking model was then used to quantify the spatial and temporal migration of both the conservative and reactive tracer plumes. Model parameters related to the anomalous transport were determined from the conservative tracer experiments. An additional term accounting for chemical reaction was established solely from analysis of the reactant concentrations, and significantly, no other fitting parameters were required. The measurements and analysis emphasized the localized nature of reaction, caused by smallscale concentration fluctuations and preferential pathways. In addition, a threshold radius for pHcontrolled reactive transport processes was defined under buffering conditions, which delineated the region in which reactions occurred rapidly.
Research output: Article 
, Mar 2015, In: Physical Review E. 91, 3, 12 p., 32113. Abstract
We develop continuoustime random walk (CTRW) equations governing the transport of two species that annihilate when in proximity to one another. In comparison with catalytic or spontaneous transformation reactions that have been previously considered in concert with CTRW, both species have spatially variant concentrations that require consideration. We develop two distinct formulations. The first treats transport and reaction microscopically, potentially capturing behavior at sharp fronts, but at the cost of being strongly nonlinear. The second, mesoscopic, formulation relies on a separationofscales technique we develop to separate microscopicscale reaction and upscaled transport. This simplifies the governing equations and allows treatment of more general reaction dynamics, but requires stronger smoothness assumptions of the solution. The mesoscopic formulation is easily tractable using an existing solution from the literature (we also provide an alternative derivation), and the generalized master equation (GME) for particles undergoing A + B > 0 reactions is presented. We show that this GME simplifies, under appropriate circumstances, to both the GME for the unreactive CTRW and to the advectiondispersionreaction equation. An additional major contribution of this work is on the numerical side: to corroborate our development, we develop an indirect particletrackingpartialintegrodifferentialequation (PIDE) hybrid verification technique which could be applicable widely in reactive anomalous transport. Numerical simulations support the mesoscopic analysis.
Research output: Article 
, Jan 2015, In: Journal of Contaminant Hydrology. 181, p. 316 Abstract
A large number of research papers on the fate of engineered nanomaterials (ENMs) in the soilwater system have appeared in recent years, focusing on ENM transport, persistence and toxicological impact. It is clear from these publications that soil is a major sink for ENMs, and that only a small portion degrades or is mobilized further into groundwater. However, to date, very few studies have examined the impact of ENMs on the natural soilsubsurface matrix and its properties. Moreover, it is now well accepted that chemical contaminants are capable of changing soil properties either by inducing direct chemical or physical changes, or through indirect changes by, e.g., influencing biological activity that in turn modifies soil properties. Here, we review studies on the deposition, retention, and accumulation of ENMs in soil, indicative of the extent to which soil acts as a major sink of ENMs. We then examine evidence of how these retained particles lead to modification of surface properties, which are manifested by changes in the sorption capacity of soil for other (organic and inorganic) solutes, and by surface charges and composition different than the natural surfaces. Finally, we demonstrate how this results in physical and hydrological changes to soil properties, including hydraulic conductivity, swelling capacity and wettability. The overall picture revealed in this critical review sheds light on a perspective that has received little attention thus far. These aspects of soil change, due to exposure and subsequent accumulation of ENMs, may ultimately prove to be one of the most important impacts of ENM releases to the environment. (C) 2015 Elsevier B.V. All rights reserved.
Research output: Article
2014

, Dec 2014, In: Advances in Water Resources. 74, p. 5463 10 p. Abstract
The continuous time random walk (CTRW) has both an elegant mathematical theory and a successful record at modeling solute transport in the subsurface. However, there are some interpretation ambiguities relating to the relationship between the discrete CTRW transition distributions and the underlying continuous movement of solute that have not been addressed in existing literature. These include the exact definition of "transition'', and the extent to which transition probability distributions are unique/quantifiable from data. Here, we present some theoretical results which address these uncertainties in systems with an advective bias. Simultaneously, we present an alternative, reduced parameter CTRW formulation for general advective transport in heterogeneous porous media, which models early and latetime transport by use of random transition times between sparse, imaginary planes normal to flow. We show that even in the context of this reducedparameter formulation there is nonuniqueness in the definitions of both transition lengths and waiting time distributions, and that neither may be uniquely determined from experimental data. For practical use of this formulation, we suggest Pareto transition time distributions, leading to a twodegreeoffreedom modeling approach. We then demonstrate the power of this approach in fitting two sets of existing experimental data. While the primary focus is the presentation of new results, the discussion is designed to be pedagogical and to provide a good entry point into practical modeling of solute transport with the CTRW. (C) 2014 Elsevier Ltd. All rights reserved.
Research output: Article 
, Sep 2014, In: Journal of Contaminant Hydrology. 165, p. 110 10 p. Abstract
The formation of preferential flow paths in the partially saturated zone, and in naturally structured media, is well known. This study examines nonuniform flow in uniform sand columns under different pressure and infiltration/drainage conditions. Experiments were carried out in a vacuum box, with applied suction set to three different heads, and with infiltration fixed at two different flow rates. Tailing observed in some conservative tracer breakthrough curves suggests the formation of immobile resident water pockets which slowly exchange mass with the flowing water fraction. The applied suction controlled the degree of water immobilization whereas flow rate had minimal effect on the dynamic behavior. Trapping and exchange of water occurred repeatedly during successive infiltration and drainage cycles, implying a (hysteretic) memory effect of the previously formed preferential flow paths. Flow and solute transport modeling suggests that these dynamics can be described by a mobileimmobile model that corroborates measurements suggesting preferential flow path formation. These findings have implications for the natural attenuation of contaminants in the partially saturated zone, but also for the persistence of a contamination source exposed to repeated conditions of infiltration and drainage. (C) 2014 Elsevier B.V. All rights reserved.
Research output: Article 
, Jul 2014, In: Advances in Water Resources. 69, p. 146158 13 p. Abstract
Both Eulerian and Lagrangian reactive transport simulations in natural media require selection of a parameter that controls the "promiscuity'' of the reacting particles. In Eulerian models, measurement of this parameter may be difficult because its value will generally differ between natural (diffusionlimited) systems and batch experiments, even though both are modeled by reaction terms of the same form. And in Lagrangian models, there previously has been no a priori way to compute this parameter. In both cases, then, selection is typically done by calibration, or ad hoc. This paper addresses the parameter selection problem for Fickian transport by deriving, from first principles and D (the diffusion constant) the reactionratecontrolling parameters for particle tracking (PT) codes and for the diffusionreaction equation (DRE). Using continuous time random walk analysis, exact reaction probabilities are derived for pairs of potentially reactive particles based on D and their probability of reaction provided that they collocate. Simultaneously, a second PT scheme directly employing collocation probabilities is derived. Onetoone correspondence between each of D, the reaction radius specified for a PT scheme, and the DRE decay constant are then developed. These results serve to ground reactive transport simulations in their underlying thermodynamics, and are confirmed by simulations. (C) 2014 Elsevier Ltd. All rights reserved.
Research output: Article 
, Apr 2014, Second ed. Heidelberg: . 577 p. Abstract
In this updated and expanded second edition, new literature has been added on contaminant fate in the soilsubsurface environment. In particular, more data on the behavior of inorganic contaminants and on engineered nanomaterials were included, the latter comprising a group of "emerging contaminants" that may reach the soil and subsurface zones. New chapters are devoted to a new perspective of contaminant geochemistry, namely irreversible changes in pristine land and subsurface systems following chemical contamination. Two chapters were added on this topic, focusing attention on the impact of chemical contaminants on the matrix and properties of both liquid and solid phases of soil and subsurface domains. Contaminant impacts on irreversible changes occurring in groundwater are discussed and their irreversible changes on the porous medium solid phase are surveyed. In contrast to the geological time scale controlling natural changes of porous media liquid and solid phases, the time scale associated with chemical pollutant induced changes is far shorter and extends over a "human lifetime scale".
Research output: Book 
Decreasing or preventing subsurface geological matter contamination by agrochemicals, Mar 2014. Abstract
Method of exposing agricultural substrates (plant matter 10, animal matter 12) to agrochemicals (A); method of decreasing or preventing subsurface geological matter (20, 22) contamination resulting from exposing agricultural substrates to agrochemicals; composition [(A)/(T)] 30 used therein; articleofmanufacture including the composition. Includes exposing agricultural substrates to composition including combination (mixture) of an agrochemical and at least one transforming agent capable of decreasing or eliminating concentration of the agrochemical which contacts subsurface geological matter (at temporally varying times, and at spatially varying depths). Before entering subsurface geological matter, transforming agent exhibits inactivity for decreasing agrochemical concentration, and inactivity for affecting or/and interfering with agrochemical functionality with respect to agricultural substrates. Transforming agent comigrates and is codistributed with agrochemical within and throughout subsurface geological matter, and exhibits activity for decreasing or eliminating agrochemical concentration therein. Transforming agent activity is exhibited at spatially varying depths, at temporally varying times, within subsurface geological matter.
Research output: Patent 
, Feb 2014, In: Water Resources Research. 50, 2, p. 14901505 16 p. Abstract
Anomalous (or nonFickian) transport is ubiquitous in the context of tracer migration in geological formations. We quantitatively identify the origin of anomalous transport in a representative model of a heterogeneous porous medium under uniform (in the mean) flow conditions; we focus on anomalous transport which arises in the complex flow patterns of lognormally distributed hydraulic conductivity (K) fields, with several decades of K values. Transport in the domains is determined by a particle tracking technique and characterized by breakthrough curves (BTCs). The BTC averaged over multiple realizations demonstrates anomalous transport in all cases, which is accounted for entirely by a power law distribution approximate to t1 of local transition times. The latter is contained in the probability density function (t) of transition times, embedded in the framework of a continuous time random walk (CTRW). A unique feature of our analysis is the derivation of (t) as a function of parameters quantifying the heterogeneity of the domain. In this context, we first establish the dominance of preferential pathways across each domain, and characterize the statistics of these pathways by forming a particlevisitation weighted histogram, Hw(K), of the hydraulic conductivity. By converting the ln(K) dependence of Hw(K) into time, we demonstrate the equivalence of Hw(K) and (t), and delineate the region of Hw(K) that forms the power law of (t). This thus defines the origin of anomalous transport. Analysis of the preferential pathways clearly demonstrates the limitations of critical path analysis and percolation theory as a basis for determining the origin of anomalous transport. Furthermore, we derive an expression defining the power law exponent in terms of the Hw(K) parameters. The equivalence between Hw(K) and (t) is a remarkable result, particularly given the nature of the K heterogeneity, the complexity of the flow field within each realization, and the statistics of the
Research output: Article 
, Jan 2014, In: Chemosphere. 95, p. 336345 10 p. Abstract
Estrone (El), 17 betaestradiol (E2), and estronesulfate (E13S) are released into the environment in significant amounts. They are known to adversely affect the endocrine systems of aquatic organisms. Although previous studies clearly demonstrate that free hormones sorb strongly to soil and degrade quickly, significant amounts of free and the more persistent conjugated estrogens can be still detected in various environmental media. To date, E13S has been considered as a metabolite that forms either during the animal hormone cycle or as a degradation product of precursor hormones like E23S. We performed smallscale laboratory column tests to investigate two major features: transport and degradation of E2, and formation of E13S and El. To evaluate the influence of soil microbial activity, one portion of soil was autoclaved and the background solution treated with sodium azide. The results demonstrate that (i) E2 is degraded to El and E13S in nonautoclaved soil, and to El in autoclaved soil, (ii) the formation of El3S is biologically driven, and (iii) the transformation of E2 to El does not require biological interaction. An inverse modeling approach was used to quantify the transport parameters and degradation rate coefficients. (C) 2013 Elsevier Ltd. All rights reserved.
Research output: Article
2013

, Sep 2013, In: Chemosphere. 93, 1, p. 172177 6 p. Abstract
The catalytic degradation of two brominated flame retardants (BFRs), tribromoneopentyl alcohol (TBNPA) and 2,4 dibromophenol (2,4DBP) by copper oxide nanoparticles (nCuO) was investigated. The degradation kinetics, the debromination, and the formation of intermediates by nCuO catalysis were also compared to Fenton oxidation and nano zerovalent iron (nZVI) reduction methods. BFRs have been added to various products like plastic, textile, electronics and synthetic polymers at growing rates. In spite of the clear advantages of reducing fire damages, many of these BFRs may be released to the environment after their beneficial use and become contaminants. The two studied BFRs were fully degraded with sufficient time (hours to days) and oxidation agent (H2O2). Shorter reaction times showed differences in reaction pathway and kinetics. The 2,4DBP showed faster degradation than TBNPA, by nCuO catalysis. Relatively high resistance to degradation was recorded for 2,4DBP with nZVI, yielding 20% degradation after 24 h, while the TBNPA was degraded by 85% within 12 h. Electron Spin Resonance (ESR) measurements show generation of both hydroxyl and superoxide radicals. In addition, inhibition of 2,4DBP degradation in the presence of spin traps implies a radical degradation mechanism. A catalytic mechanism for radical generation and BFR degradation by nCuO is proposed. It is further suggested that H2O2 plays an essential role in the activation of the catalyst. (C) 2013 Elsevier Ltd. All rights reserved.
Research output: Article 
, Sep 2013, In: Water Resources Research. 49, 9, p. 52065220 15 p. Abstract
We apply a general strategy based on Global Sensitivity Analysis (GSA) and model discrimination criteria to (a) calibrate the parameters embedded in competing models employed to interpret laboratoryscale tracer experiments, (b) rank these models, and (c) estimate the relative degree of likelihood of each model through a posterior probability weight. We consider a conservative transport experiment in a uniform porous medium. We apply GSA to three transport models, based on: the classical advectiondispersion equation (ADE), a dualporosity (DP) formulation with mass transfer between mobile and immobile regions, and the Continuous Time Random Walk (CTRW) approach. GSA is performed through Polynomial Chaos Expansion of the governing equations, treating key model parameters as independent random variables. We show how this approach allows identification of (a) the relative importance of modeldependent parameters, and (b) the spacetime locations, where the models are most sensitive to these parameters. GSA is then employed to assist parameter estimates within a Maximum Likelihood framework. Finally, formal model identification criteria are employed to (a) rank the alternative models, and (b) associate each model with a posterior probability weight for the specific case study. The GSAbased calibration of each model returns an acceptable approximation (remarkably accurate in the case of the CTRW model) of all available concentration data, with calibration being performed using minimum sets of observations corresponding to the most sensitive (spacetime) locations.
Research output: Article 
, Jul 2013, In: Transport in Porous Media. 98, 3, p. 651682 32 p. Abstract
We present an experimental investigation and modeling analysis of tracer transport in two transparent fracture replicas. The original fractures used in this work are a Vosges sandstone sample with nominal dimensions approximately 26 cm long and 15 cm wide, and a granite sample with nominal dimensions approximately 33 cm long and 15.5 cm wide. The aperture map and physical characteristics of the fractures reveal that the aperture map of the granite fracture has a higher spatial variability than the Vosges sandstone one. A conservative methylene blue aqueous solution was injected uniformly along the fracture inlets, and exited through free outlet boundaries. A series of images was recorded at known time intervals during each experiment. Breakthrough curves were subsequently determined at the fracture outlets and at different distances, using an image processing based on the attenuation law of BeerLambert. These curves were then interpreted using a stratified medium model that incorporates a permeability distribution to account for the fracture heterogeneity, and a continuous time random walk (CTRW) model, as well as the classical advectiondispersion equation (ADE). The stratified model provides generally satisfactory matches to the data, while the CTRW model captures the full evolution of the long tailing displayed by the breakthrough curves. The transport behavior is found to be nonFickian, so that the ADE is not applicable. In both stratified and CTRW models, parameter values related to the aperture field spatial variability indicate that the granite fracture is more heterogeneous than the Vosges sandstone fracture.
Research output: Article 
, May 2013, In: Physical Review Letters. 110, 18, 5 p., 180602. Abstract
We examine distance record setting by a random walker in the presence of a measurement error delta and additive noise gamma and show that the mean number of (upper) records up to n steps still grows universally as <Rn > similar to n(1/2) for large n for all jump densities, including Levy distributions, and for all delta and gamma. In contrast, the pace of record setting, measured by the amplitude of the n(1/2) growth, depends on delta and gamma. In the absence of noise (gamma = 0), the amplitude S(delta) is evaluated explicitly for arbitrary jump distributions and it decreases monotonically with increasing delta whereas, in the case of perfect measurement (delta = 0), the corresponding amplitude T(gamma) increases with gamma. The exact results for S(delta) offer a new perspective for characterizing instrumental precision by means of record counting. Our analytical results are supported by extensive numerical simulations.
Research output: Article 
Zero valent metal composite, manufacturing, system and method using thereof, for catalytically treating contaminated water, May 2013. Abstract
Zero valent metal composite, manufacturing thereof, using thereof, and system including thereof, for (insitu or exsitu) catalytically treating contaminated water, such as subsurface water, surface water, abovesurface water, water vapor, or/and gaseous water. Composite includes powdered diatomite matrix incorporated with nanometer (11000 nm) sized particles of a zero valent (transition) metal (iron, cobalt, nickel, copper, zinc, palladium, platinum, or/and gold) and at least one electron transfer mediator (catalyst) from porphyrinogenic organometallic complexes (e.g., metalloporphyrins (chlorophylls, hemes, cytochromes) or metallocorrins (e.g., vitamin B12), and optionally, includes vermiculite. System includes composite and insitu or/and exsitu unit containing the composite, enabling exposure of contaminated water thereto. Applicable to insitu subsurface permeable reactive barriers (PRBs). Treatable water contaminants are organics (halogenated organic compounds), or/and inorganics (metal elements, metal element containing inorganic species, nonmetal elements, and nonmetal element containing inorganic species). Applicable to nonaqueous fluids (liquids, vapors, gases), for removing contaminants therefrom.
Research output: Patent 
, Apr 2013, In: Transport in Porous Media. 97, 3, p. 295315 21 p. Abstract
We study the mobility and interaction under competing conditions observed for copper () and zinc () ions in the context of laboratoryscale experiments performed in natural soil columns. The experiments focus on the analysis of solute breakthrough curves (BTCs) obtained after injection of an aqueous solution containing similar concentrations of the two metal ions into a soil column fully saturated with double deionized water. Transport of the competing ions is tested for the same soil under aerobic and anaerobic conditions. Measurements show that the species with lower affinity for the soil, , migrates occupying all available adsorption sites, and is then progressively replaced by the ion with higher affinity, . The two ions are displaced in the system with different effective retardation. The slowest species replaces the sorbed ions, resulting in observed concentrations that display a nonmonotonic behavior in time and which, for a certain period, are larger than the concentration supplied continuously at the inlet. In the absence of a complete geochemical characterization of the system, we show that the measured concentrations of both metals can be interpreted through simple models based on a set of coupled partial differential and algebraic equations, involving a small subset of aqueous and adsorbed species that are present in the system. Depending on the model considered, the relationship between aqueous and adsorbed ion concentrations is described at equilibrium by a GainesThomas (GT) formulation, a competitive SheindorfRebhunSheintuch (SRS) isotherm, or an Extended Langmuir (EL) isotherm, respectively. The GT formulation provides the best interpretation of the observed behavior among the models tested. We find that employing these simple models, which account only for the main governing reactive processes, allows reasonable estimation of the observed BTCs in experiments where only partial geochemical datasets are available.
Research output: Article 
, Mar 2013, In: Physical Review E. 87, 3, 6 p. Abstract
Mixing zone dynamics of a reaction product C during diffusion of two species (A and B) are examined, using a twodimensional particle tracking model (PT) for the reaction A + B > C, allowing for both Fickian and nonFickian transitions. The form of PT we use is equivalent to a continuous time random walk, which is a widely used model for anomalous transport and diffusion. It is shown that the basic patterns of the C dynamicsthe temporal evolution of the spatial profile and the temporal C productionare similar for both modes of diffusion. However, the distinctive time scale for the nonFickian case is very much larger even when the median transition steps are matched with the Fickian case. For immobile C, the spatial profile pattern is a broadening (Gaussian) reaction front evolving to a concentrationfluctuation dominated (Lorentzian) shape. The temporal C production is fit well by a stretched exponential for both diffusion types. In analyzing experiments, the appearance of a Gaussian C profile does not prove that the diffusion process is Fickian. DOI: 10.1103/PhysRevE.87.032812
Research output: Article 
, Jan 2013, In: Chemosphere. 90, 2, p. 640646 7 p. Abstract
In recent years the behavior and properties of nanoparticles released to the environment have been studied extensively to better assess the potential consequences of their broad use in commercial products. The fate, transport and mobility of nanoparticles in soil were shown to be strongly dependent on environmental conditions. However, little is known about the possible effects of nanoparticles on soil chemical, physical and biological properties. In this study, two types of metal oxide nanoparticles, CuO and Fe3O4 were mixed into two types of soil and the effects of the nanoparticles on various soil properties were assessed. Metal oxide nanoparticles were shown previously to catalyze the oxidation of organic pollutants in aqueous suspensions, and they were therefore expected to induce changes in the organic material in the soil, especially upon addition of an oxidant. It was found that the nanoparticles did not change the total amount of organic materials in the soil or the total organic carbon in the soil extract; however, threedimensional fluorescence spectroscopy demonstrated changes in humic substances. The nanoparticles also affected the soil bacterial community composition, based on denaturing gradient gel electrophoresis (DGGE) fingerprinting, but had little impact on the macroscopic properties of the soil. (C) 2012 Elsevier Ltd. All rights reserved.
Research output: Article 
, Jan 2013, In: PLoS One. 8, 12, 12 p. Abstract
Increased availability of nanoparticlebased products will, inevitably, expose the environment to these materials. Engineered nanoparticles (ENPs) may thus find their way into the soil environment via wastewater, dumpsters and other anthropogenic sources; metallic oxide nanoparticles comprise one group of ENPs that could potentially be hazardous for the environment. Because the soil bacterial community is a major service provider for the ecosystem and humankind, it is critical to study the effects of ENP exposure on soil bacteria. These effects were evaluated by measuring bacterial community activity, composition and size following exposure to copper oxide (CuO) and magnetite (Fe3O4) nanosized (
Research output: Article 
, Jan 2013, In: Advances in Water Resources. 51, p. 86103 18 p. Abstract
We review the analysis of the dynamics of reactive transport in disordered media, emphasizing the nature of the chemical reactions and the role of smallscale fluctuations induced by the structure of the porous medium. We are motivated by results and interpretations of laboratoryscale experiments, for which detailed characterization of the system is possible. Modeling approaches based on continuum and particle tracking (PT) schemes are examined critically, highlighting how fluctuations are incorporated. The continuum approach spans a large literature. Traditional formats of reactive transport equations, such as the advectiondispersionreaction equation (ADRE), are based on a series of assumptions related mainly to scale separation and relative magnitude of time scales involved in the reactive transport setting. These assumptions as well as further developments are assessed in depth. PT methods offer an alternative means of accounting for porescale dynamics, wherein spacetime transitions are drawn from appropriate probability distributions that have been tested to account for anomalous transport. While PT methods have been employed for many years to describe conservative transport, their application to laboratoryscale reactive transport problems in the context of both Fickian and nonFickian regimes is relatively recent. We concentrate on experimental observations of different types of reactions in disordered media: (1) the dynamics of a bimolecular reactive transport (A + B > C) in passive (nonreactive) media, and (2) a multistep chemical reaction, as exemplified in the process of dedolomitization involving both dissolution and precipitation. The fluctuations in a number of the key variables controlling the processes prove to have a dominant role; elucidation of this role forms the basis of the present study and the comparison of methods. (C) 2011 Elsevier Ltd. All rights reserved.
Research output: Article
2012

, Oct 2012. Abstract
This invention is directed to decreasing the CO2 concentration. The invention makes use of fluids and apparatuses for diminishing CO2 concentrations of fluids.
Research output: Patent 
, Aug 2012, In: Journal of Hydrology. 458, p. 4050 11 p. Abstract
This study investigates the interplay between resident ('old') water and incoming ('new') water in homogeneous, partially saturated sand undergoing infiltration, using a series of laboratory column experiments. It was hypothesized that old water pockets, defined both spatially and temporally, may be established during infiltration. This in turn, may affect the flow pattern of the infiltrating new water and/or contravene current geochemical reactions. Sands with three different particle size distributions and three initial water contents were employed. The upper end of each column was irrigated with water containing a conservative tracer, at three different flow rates, while freedrainage conditions were employed at the lower end. Analysis of the resulting 27 infiltration events was based on the Richards equation to describe fluid flow. Subsequently, the mobileimmobile model (MIM) was employed to describe the solute transport; the measurements were reproduced satisfactorily by these models. Results were further analyzed using mass balance considerations. Two regimes were identified: an initial pistonlike mechanism that displaces old water, followed by a slow mixing/entrainment of the remaining old water. The relative contributions of these regimes appear to depend on the initial water content and the average grain size. In some cases, up to onethird of the old water fraction remained in the system following five flowthrough pore volumes. Comparison between the measured fractions of old water remaining in the system at the end of each infiltration event (i.e., after five flowthrough pore volumes) and the immobile water content (optimized from the MIM) relative to the initial water content, exhibited a significant linear correlation, with values about threefold higher for the optimized immobile fraction. (c) 2012 Elsevier B.V. All rights reserved.
Research output: Article 
, Aug 2012, Heidelberg: . 366 p. Abstract
This book combines soil science, earth science, and environmental geochemistry, providing comprehensive background information for specialists interested in chemicalinduced changes in the soilsubsurface system. Readers are introduced to the chemistry of contaminants that often disturb the natural soilsubsurface equilibrium as a result of human activity. While the soilsubsurface system has in many cases been affected by human impact, the effects of chemical contaminants on the actual matrix and properties have been largely neglected. The major focus of the book is on changes to the soilsubsurface matrix and properties caused by chemical pollution. By integrating results available in the literature, we observe that chemical pollutants may lead to the irreversible formation of a new soilsubsurface regime characterized by a matrix and properties different than those of the natural regime. In contrast to the geological time scales dictating natural changes to the matrix and properties of the soilsubsurface system, the time scale associated with chemical pollutantinduced changes is far shorter and extends over a "human lifetime scale." The numerous examples presented in the book confirm that chemical contamination should be considered as an additional factor in the formation of a contemporary soilsubsurface regime that is different than that of the pristine system.
Research output: Book 
, Jul 2012, In: Chemosphere. 88, 5, p. 670675 6 p. Abstract
The effect of soil properties on the transport of silver nanoparticles (AgNPs) was studied in a set of laboratory column experiments, using different combinations of size fractions of a Mediterranean sandy clay soil. The AgNPs with average size of similar to 30 nm yielded a stable suspension in water with zeta potential of 39 mV. Early breakthrough of AgNPs in soil was observed in column transport experiments. AgNPs were found to have high mobility in soil with outlet relative concentrations ranging from 30% to 70%, depending on experimental conditions. AgNP mobility through the column decreased when the fraction of smaller soil aggregates was larger. The early breakthrough pattern was not observed for AgNPs in pure quartz columns nor for bromide tracer in soil columns, suggesting that early breakthrough is related to the nature of AgNP transport in natural soils. MicroCT and image analysis used to investigate structural features of the soil, suggest that soil aggregate size strongly affects AgNP transport in natural soil. The retention of AgNPs in the soil column was reduced when humic acid was added to the leaching solution, while a lower flow rate (Darcy velocity of 0.17 cm/min versus 0.66 cm/min) resulted in higher retention of AgNPs in the soil. When soil residual chloride was exchanged by nitrate prior to column experiments, significantly improved mobility of AgNPs was observed in the soil column. These findings point to the importance of AgNPsoil chemical interactions as a retention mechanism, and demonstrate the need to employ natural soils rather than glass beads or quartz in representative experimental investigations. (C) 2012 Elsevier Ltd. All rights reserved.
Research output: Article 
, Jul 2012, In: ACS Applied Materials and Interfaces. 4, 7, p. 34163423 8 p. Abstract
A new composite material based on deposition of nanosized zerovalent iron (nZVI) particles and cyanocobalamine (vitamin B12) on a diatomite matrix is presented, for catalytic transformation of organic contaminants in water. Cyanocobalamine is known to be an effective electron mediator, having strong synergistic effects with nZVI for reductive dehalogenation reactions. This composite material also improves the reducing capacity of nZVI by preventing agglomeration of iron nanoparticles, thus increasing their active surface area The porous structure of the diatomite matrix allows high hydraulic conductivity, which favors channeling of contaminated water to the reactive surface of the composite material resulting in faster rates of remediation. The composite material rapidly degrades or transforms completely a large spectrum of water contaminants, including halogenated solvents like TCE, PCE, and cisDCE, pesticides like alachlor, atrazine and bromacyl, and common ions like nitrate, within minutes to hours. A field experiment where contaminated groundwater containing a mixture Of industrial and agricultural persistent pollutants was conducted together with a set of laboratory experiments using individual contaminant solutions to analyze chemical transformations under controlled conditions.
Research output: Article 
, Jul 2012, In: Soil Science Society of America Journal. 76, 4, p. 12291245 17 p. Abstract
Metal sorption of single and binary (competitive) systems for several soils is analyzed to assess the ability of alternative isotherm models to interpret experimental observations. The analysis is performed within a Maximum Likelihood framework and on the basis of model identification (sometimes termed "quality" or "information") criteria. These methodologies allow the assessment of the measurement error variance in the parameter estimation process and the uncertainty arising from the use of alternative (conceptualmathematical) models. We first analyze Cu and Zn sorption in two Israeli soils, Bet Dagan and Yatir, which are slightly alkaline but with substantially different sorption capacities and perform an extensive set of batch experiments in single and binary systems. We then analyze the data set published by Liao and Selim (2009) where Ni and Cd sorption was studied in three different (one neutral and two acidic) soils. Single component data from both sets of experiments are interpreted on the basis of the Langmuir, Freundlich, and RedlichPeterson (RP) models. The family of binary systems results is analyzed in light of the SheindorfRebhunSheintuch (SRS) model, the modified RP model, and the modified and extended Langmuir models. All of the considered models are expressed in terms of initial and equilibrium concentrations, two variables that are measured independently. Maximum Likelihood and model identification criteria (such as Bayesian criteria BIC and KIC, and information theoretic criteria AIC, AICc, and HIC) are employed to (a) estimate model parameters, (b) rank alternative models, and (c) estimate the relative degree of likelihood of each model by means of a weight, or posterior probability. We show that modeling observation error variance either as a constant or as a function of concentration does not significantly affect parameter estimates for a given model. These different representations of measurement error variance impact the ranking of alt
Research output: Article 
, Jul 2012, In: Water Air And Soil Pollution. 223, 6, p. 31053115 11 p. Abstract
Copper oxide nanoparticles were immobilized on quartz sand and their catalytic activity for the degradation of an organic dye was investigated. The use of nanoparticles as catalysts for non photoinduced oxidation of water contaminants is relatively new. The CuO catalyst has shown promising results when suspended in free form in batch systems. Because heterogeneous catalysis is often the preferred mode of operation for application of catalytic technology, we studied the effect of immobilization of the nanoparticles on quartz sand in a flowthrough system and its implication for the catalytic process. The coated sand was packed in a column and its catalytic activity for the degradation of an organic dye was investigated in a series of flowthrough experiments with hydrogen peroxide as the oxidant. Control experiments with uncoated sand were also performed for comparison. The coated sand demonstrated high catalytic ability, achieving complete oxidation of the dye. During the reaction, CO2 was produced, leading to a decrease in the water saturation in the column and reduced contact surface between the nanoCuO catalysts and the dye solution. The degradation was improved by enabling a longer residence time of the dye in the column, yielding up to 85% degradation of the dye. These results suggest that CuO nanoparticlecoated sand is an efficient catalyst for complete degradation of the organic dye.
Research output: Article 
, May 2012, In: Journal of Contaminant Hydrology. 132, p. 2836 9 p. Abstract
We present experimental breakthrough curve (BTC) data and a modeling investigation of conservative and sorbing tracer transport in natural soils. By analyzing the data using the continuous time random walk (CTRW) model, we probe the traditional approach of using conservative tracer model parameters as a basis for quantifying the transport of sorbing solutes in the same domain when nonFickian transport is present. Many known contaminants in groundwater are sorbed to the host solid porous medium, to varying extents, while being transported: this enhances the long tailing of BTCs which often already occurs because of the inherent nonFickian nature of the transport. The CTRW framework has been shown to account very well for nonFickian conservative (nonsorbing) transport. Here, we examine two BTC data sets in laboratory columns packed with natural soils; the first (previously analyzed by Mao and Ren (2004)) comprises transport of (conservative) bromide and (sorbing) atrazine tracers, while the second presents new data with bromide and tribromoneopentyl alcohol (TBNPA), a key flame retardant, as a sorbing solute. TBNPA has received little attention in the past, and is shown to be sorbed onto Bet Dagan soil in a nonlinear manner. We find that the transport behavior of bromide is nonFickian in all cases, which is caused by the heterogeneity of the soil. Comparative model analysis of the nonFickian BTCs of the conservative, and sorbing tracers and examination of the fitting parameters, exemplify the coupling between transport and adsorption/desorption processes. The difference in transport parameters used to match the conservative and sorbing data sets shows that conservative tracer parameters (average velocity and dispersion coefficient) are not valid for the transport of reactive tracers. (C) 2012 Elsevier B.V. All rights reserved.
Research output: Article 
, Jan 2012, In: Chemosphere. 86, 2, p. 144149 6 p. Abstract
The activity of copper oxide, titanium carbide and silicon nitride nanoparticles for the oxidative degradation of environmentally relevant concentrations (mu g L1 range) of enrofloxacin  an important veterinary antibiotic drug  in aqueous solutions was investigated. With hydrogen peroxide as an oxidative agent, both copper oxide and titanium carbide decrease the concentration of enrofloxacin by more than 90% over 12 h. Addition of sodium halide salts strongly increases the reaction rate of copper oxide nanoparticles. The mechanism for the formation of Reactive Oxygen Species (ROS) was investigated by Electron Spin Resonance (ESR). (C) 2011 Elsevier Ltd. All rights reserved.
Research output: Article
2011

, Aug 2011, In: Geophysical Research Letters. 38, 5 p. Abstract
How often does a contaminant 'particle' migrating in a porous medium set a distance record, i.e., advance farther from the origin than at all previous time steps? This question is of fundamental importance in characterizing the nature of the leading edge of a contaminant plume as it is transported through an aquifer. It was proven theoretically by Majumdar and Ziff (2008) that, in the 1d case for pure diffusion, record setting of a random walker scales with n(1/2), where n is the number of steps, regardless of the length and time distribution of steps. Here, we use numerical simulations, benchmarked against the 1d analytical solution, to extend this result also for pure diffusion in 2d and 3d domains. We then consider transport in the presence of a drift (i.e., advectivedispersive transport), and show that the recordsetting pace of random walkers changes abruptly from alpha n(1/2) to alpha n(1). We explore the dependence of the prefactor on the distribution of step length and number of spatial dimensions. The key implication is that when, after a brief transitional period, the scaling regime commences, the maximum distance reached by the leading edge of a migrating contaminant plume scales linearly with n, regardless of the drift magnitude. Citation: Edery, Y., A. Kostinski, and B. Berkowitz (2011), Record setting during dispersive transport in porous media, Geophys. Res. Lett., 38, L16403, doi:10.1029/2011GL048558.
Research output: Article 
, Aug 2011, In: Vadose Zone Journal. 10, 3, p. 843857 15 p. Abstract
We collected and analyzed Br breakthrough curve (BTC) data to identify the parameters controlling transport from a series of soil cores and a fieldscale tracer test at the Shale Hills Critical Zone Observatory (SHCZO) in central Pennsylvania. The soil cores were retrieved from a continuous hole that extended through the soil profile to quantify also how solute transport behavior changes with depth and weathering. Additionally, we performed a fieldscale doublet tracer test to determine transport behavior in the weathered shale bedrock. Hydraulic conductivity and porosity were as low as 10(15) m s(1) and 0.035, respectively, in the shale bedrock and upward of 10(5) m s(1) and 0.45, respectively, in the shallow soils. Bromide BTCs demonstrated significant tailing in soil cores and field tracer experiments, which does not fit classical advectiondispersion processes. To quantify the behavior, numerical simulation of solute transport was performed with both a mobileimmobile (MIM) model and a continuoustime random walk (CTRW) approach. Onedimensional MIM modeling results yielded low mass transfer rates (
Research output: Article 
, May 2011, In: Vadose Zone Journal. 10, 2, p. 624633 10 p. Abstract
The interplay between resident water ("old water") and infiltrating water ("new water") in porous media was examined through experiments in an idealized, twodimensional, glass micromodel. Image analysis was used to quantify the miscible interplay between old and new water during a cycle of imbibition by new water and drainage by air in a domain that was partially saturated with old water. The dynamics of the oldnew water exchange were characterized in terms of several parameters: remaining old water, number of oldwater pockets, Volumetric fraction, and degree of mixing. In particular, it was found that some old water remained in the system at long times within stable water pockets; these pockets may remain stable even after a second cycle of infiltration.
Research output: Article 
, Mar 2011, In: Journal of Contaminant Hydrology. 12021, p. 2744 18 p. Abstract
We present an experimental and modeling study of solute transport in porous media in the presence of mixinginduced precipitation of a solid phase. Conservative and reactive transport experiments were performed in a quasitwodimensional laboratory flow cell, filled with homogeneous and heterogeneous porous media. Conservative experiments were performed by injecting solutions containing sodium chloride and calcium chloride into the domain. In reactive transport experiments, inlet solutions of calcium chloride and sodium carbonate were injected in parallel, resulting in calcium carbonate precipitation where the solutions mix. Experimental results were used as a benchmark to examine the performance of a reactive transport numerical model. Good agreement between model predictions and experimental results was obtained for the conservative transport experiments. The reactive transport experiments featured the formation of a calcium carbonate mineral phase within the mixing zone between the two solutions, which controlled the spatial evolution of calcium carbonate in the domain. Numerical simulations performed on high resolution grids for both the homogeneous and heterogeneous porous systems underestimated clogging of the system. Although qualitative agreement between model results and experimental observations was obtained, accurate model predictions of the spatial evolution of calcium concentrations at sample points within the flow cell could not be achieved. (C) 2009 Elsevier B.V. All rights reserved.
Research output: Article 
, Mar 2011, In: Journal of Contaminant Hydrology. 12021, p. 213221 9 p. Abstract
Tracer tailing in breakthrough curves in porous media with two distinct porosities is analyzed in terms of the dynamic responses of experimental fixed bed columns filled either with solid or porous beads. The flow is fast in the column interstitial space between beads (for both solid and porous beads) but slow within the porous beads that act as controlled 'traps' constituting an immobile zone. The transport is quantified using a Continuous Time Random Walk (CTRW) framework, which accounts for domains with controlled structural and flow heterogeneity associated with two distinct spatial and time spectra. We first demonstrate that breakthrough curves for a column containing solid glass beads exhibit nonFickian transport, quantifiable both in fitting and validation mode by a CTRW based on a power law transition time distribution. We then examine breakthrough curves in the porous bead case, obtaining fits with a twoscale CTRW model that accounts explicitly for the two time spectra. Because the porous beads are uniform, tracer trapping within them is described by a simple firstorder approximation trap model, with relatively weak capture and relatively faster release rates. The extent of tailing apparent in the porous bead breakthrough curves, due to the traps, can be quantitatively distinguished from the contribution to tailing due to mobile zone nonFickian transport. A parameter study of the twoscale CTRW adds further insight into the dynamics of the process, showing the interaction between the advective nonFickian transport and the mass exchange to immobile regions. (C) 2010 Elsevier B.V. All rights reserved.
Research output: Article 
, Jan 2011, In: Water Resources Research. 47, 16 p. Abstract
We simulate the processes of dedolomitization and calcium carbonate precipitation using particle tracking. The study is stimulated by the results of a laboratory experiment that examined reactive transport of injected CaCl2/HCl, into a column of sucrosic dolomite particles, with a constant flow field. The injected fluid supplies Ca2+ and H+. Dedolomitization is a protonation reaction yielding carbonic acid; a subsequent deprotonation reaction yields CO32, and reaction with the abundant Ca2+ forms the precipitate CaCO3. The dedolomitization and precipitation processes involve multistep, multispecies chemical reactions, with both irreversible and reversible stages. The particle tracking is governed by spatial and temporal distributions within a continuous time random walk framework. This accounts for the effects of disorder of heterogeneous media (leading to nonFickian transport) and includes the option of treating purely advectivedispersive (Fickian) transport. The dynamics of dedolomitization are examined for different flow conditions and reaction rates. The fluctuations in the local velocity distributions, due to porosity changes, create conditions for positive feedbacks leading to development of preferential pathways, largescale nonlinearity, and precipitation banding. These features have been observed in the laboratory experiments and are now accounted for by the simulation results at similar time frames, velocities, and pH levels.
Research output: Article 
, Jan 2011, In: Chemosphere. 82, 2, p. 244252 9 p. Abstract
The transport and fate of the pharmaceutical carbamazepine (CBZ) were investigated in the Dan Region Reclamation Project (SHAFDAN), TelAviv, Israel. Soil samples were taken from seven subsections of soil profiles (150 cm) in infiltration basins of a soil aquifer treatment (SAT) system. The transport characteristics were studied from the release dynamics of soilresident CBZ and, subsequently, from applying a pulse input of wastewater containing CBZ. In addition, a monitoring study was performed to evaluate the fate of CBZ after the SAT. Results of this study indicate adsorption, and consequently retardation, in CBZ transport through the top soil layer (05 cm) and to a lesser extent in the second layer (525 cm), but not in deeper soil layers (25150 cm). The soluble and adsorbed fractions of CBZ obtained from the two upper soil layers comprised 45% of the total CBZ content in the entire soil profile. This behavior correlated to the higher organic matter content observed in the upper soil layers (025 cm). It is therefore deduced that when accounting for the full flow path of CBZ through the vadose zone to the groundwater region, the overall transport of CBZ in the SAT system is essentially conservative. The monitoring study revealed that the average concentration of CBZ decreased from 1094 +/ 166 ng L(1) in the recharged wastewater to 560 +/ 175 ng L(1) after the SAT. This reduction is explained by dilution of the recharged wastewater with resident groundwater, which may occur as it flows to active reclamation wells. (C) 2010 Elsevier Ltd. All rights reserved.
Research output: Article
2010

, Dec 2010, In: Journal of Statistical Physics. 141, 6, p. 10931103 11 p. Abstract
The transport behavior of a migrating particle in a disordered medium is exhibited in the solution of a transport equation derived from a coupled continuous time random walk (CTRW). A core aspect of CTRW is the spectrum of transitions in displacement s and time t, psi(s,t), that characterizes the disordered system, which determine the transport. In many applications the CTRW approach has successfully accounted for the anomalous or nonFickian nature of the particle plume propagation based on a powerlaw dependence psi(t) in a decoupled p(s)psi(t) approximation to psi(s,t). For example, this powerlaw dependence in t derives from the complex Darcy flow fields in geological formations. Recently, the fully coupled CTRW was analyzed using a particle tracking approach, demonstrating that the decoupled approximation is valid only for a compact distribution of s. In this paper we solve the nonlocalintime transport equation with a psi(s,t) containing a powerlaw dependence in both s (a L,vylike distribution) and t, which necessitates the strong s,t coupling. We show enhanced transport behavior (relative to the plume propagation behavior reported in the literature) that derives from the rare large displacements in s (limited by the transition t). The interplay between the two coupled power laws is clearly shown in the changes in the breakthrough curves in the arrival times, dispersion and dependence on the velocity (v=s/t) distribution. Similar enhancements are exhibited in the particle tracking results.
Research output: Article 

, Sep 2010, In: Chemosphere. 81, 3, p. 387393 7 p. Abstract
The behavior of foul types of untreated metal oxide nanoparticles in saturated porous media was studied. The transport of Fe(3)O(4), TiO(2), CuO, and ZnO was measured in a series of column experiments Vertical columns were packed with uniform, spherical glass beads The particles were introduced as a pulse suspended in aqueous solutions and breakthrough curves at the outlet were measured using UV vis spectrometry. Different factors affecting the mobility of the nanoparticles such as ionic strength, addition of organic matter (humic acid), flow rate and pH were investigated The experiments showed that mobility varies strongly among the nanoparticles. with TiO(2) demonstrating the highest mobility The mobility is also strongly affected by the experimental conditions. Increasing the ionic strength enhances the deposition of the nanoparticles. On the other hand, addition of humic acid increases the nanoparticle mobility significantly Lower flow rates again led to reduced mobility, while changes in pH had little effect Overall, in natural systems, it is expected that the presence of humic acid in soil and aquifer materials, and the ionic strength of the resident water, will be key factors determining nanoparticle mobility. (C) 2010 Elsevier Ltd All rights reserved
Research output: Article 
, Jul 2010, In: Water Resources Research. 46, 12 p. Abstract
We use a particle tracking approach to analyze the dynamics that control bimolecular reactive transport (A + B > C) in porous media. Particle transitions are governed by spatial and temporal distributions to account for the transport within a continuous time random walk framework. Particle tracking simulations are compared to measurements from a laboratory experiment of bimolecular reactive transport in a constant flow field. The simulations capture the experimental sequence of evolving C particle profiles using a marginally Fickian temporal distribution to quantify the particle transitions. The first profile is a fit with the model parameters, and subsequent ones are predictions. The rate of production of reaction product C over time is found to follow a power law. At early times after the injection of A particles into a uniform distribution of B particles, the strong contact and reaction between A and B particles induces the formation of a spatial void between the reactants. At longer times, the production of C is nearly constant and depends on the fluctuations of velocities of reactant particles that can surmount the void. We probe the behavioral dependence of the A, B, and C spatial profiles on the spectra of velocity fluctuations of the reactants. The latter are generated by different temporal distributions, namely, a decaying exponential distribution, which is equivalent to advectivedispersive (Fickian) transport, and the truncated power law with degrees of nonFickian behavior, which is characteristic of transport in heterogeneous media. We demonstrate that the C profile exhibits subtle dynamics because of competition between the dispersion (spreading of the plumes) of A and B and the (power law) production rate.
Research output: Article 
, Jun 2010, In: Journal of Computational Physics. 229, 11, p. 43044314 11 p. Abstract
Derivations of continuum nonlocal models of nonFickian (anomalous) transport require assumptions that might limit their applicability. We present a particlebased algorithm, which obviates the need for many of these assumptions by allowing stochastic processes that represent spatial and temporal random increments to be correlated in space and time, be stationary or nonstationary, and to have arbitrary distributions. The approach treats a particle trajectory as a subordinated stochastic process that is described by a set of Langevin equations, which represent a continuous time random walk (CTRW). Convolutionbased particle tracking (CBPT) is used to increase the computational efficiency and accuracy of these particlebased simulations. The combined CTRWCBPT approach enables one to convert any particle tracking legacy code into a simulator capable of handling nonFickian transport. (C) 2010 Elsevier Inc. All rights reserved.
Research output: Article 

, Mar 2010, In: Physical Review E. 81, 3, 14 p., 31102. Abstract
The theoretical treatment of transport in a disordered system in the presence of a systemwide force field F(x) or spatially varying macroscopic velocity field v(x) is developed in the framework of continuous time random walk (CTRW). The physical basis of CTRW and related fractional derivative equations relies on a mapping of the aggregate of transition rates w(s, s'), between sites s and s', in the Master equation describing the system kinetics, onto a joint probability distribution function psi(s, t). This distribution is calculated from the ensemble average of a positiondependent functional of w(s, s'); the procedure is effective when the scale of heterogeneities is much smaller than the system size. However, statistical homogeneity does not hold in the presence of large heterogeneities, which control the macroscopic v(x), or in the case of an interaction of F(x) with the transition rates. The transport equation, incorporating largescale heterogeneity, involves the use of a local ensemble average to obtain a positiondependent psi(s, t; x); this determines a memory function, M(t; x), which is convoluted with the advectiondispersion operator. A prototype transport equation for a system with statistical inhomogeneity is developed as an integrodifferential equation. It is solved numerically for particles migrating with a steadystate Darcy velocity v(x), determined for different permeability fields and boundary conditions. The nature of the solutions as a function of key transport parameters (e.g., a characteristic time t(c)) is explored, and solutions are also compared to those of the advectiondispersion equation for v(x) and to a laboratory experiment. This transport equation is in contrast to the fractional FokkerPlanck equation, which is based on a decoupling of F(x) or v(x) with the transition rates w(s, s'). Further, an analytic expression for the effect of a variance of the ensemble average on the solution of the CTRW transport equation is derived.
Research output: Article 
, Jan 2010, In: Naturwissenschaften. 97, 1, p. 117 17 p. Abstract
To date, the field of contaminant geochemistrywhich deals with the study of chemical interactions in soil and aquifer environmentshas focused mainly on pollutant toxicity, retention, persistence, and transport and/or on remediation of contaminated sites. Alteration of subsurface physicochemical properties by anthropogenic chemicals, which reach the land surface as a result of human activity, has been essentially neglected. Contaminantinduced changes in subsurface properties are usually considered as deviations from a normal geological environment, which will disappear under natural attenuation or following remediation procedures. However, contaminants may in many cases cause irreversible changes in both structure and properties of the soilsubsurface geosystem between the land surface and groundwater. The time scales associated with these changes are on a "human time scale", far shorter than geological scales relevant for geochemical processes. In this review, we draw attention to a new perspective of contaminant geochemistry, namely, irreversible changes in the subsurface as a result of anthropogenic chemical pollution. We begin by briefly reviewing processes governing contaminantsubsurface interactions. We then survey how chemical contamination causes irreversible changes in subsurface structure and properties. The magnitude of the anthropogenic impact on the soil and subsurface is linked directly to the amounts of chemical contaminants applied and/or disposed of on the land surface. This particular aspect is of major importance when examining the effects of humans on global environmental changes. Consideration of these phenomena opens new perspectives for the field of contaminant geochemistry and for research of human impacts on the soil and subsurface regimes.
Research output: Article 
, Jan 2010, In: Physical Review E. 81, 1, 6 p., 11128. Abstract
We examine different types of heterogeneous hydraulic conductivity fields to ascertain the basic structural features that dominate the transport behavior. We contrast two approaches to the analysis, within the framework of the continuous time random walk (CTRW), considering recent simulations of particle transport in two correlated flow fields to discern these key features. These flow fields are the steadystate solutions of Darcy flow in systems with correlated distributions, P(K(x)), of hydraulic conductivity values K(x). One approach uses the organizational structure of the Lagrangian velocities determined from simulations to derive correlated spacetime distributions for particle tracking, which are used to fit simulated breakthrough curve (BTC) data. These fits emphasize the ability to account for both early arrival times and latetime long tailing. The other approach, in this paper, treats the simulated BTCs as "measurements" and uses a truncated powerlaw form of psi(t), the probability density function (pdf) of local transit times, in a partial differential equation form of CTRW. Excellent fits to both data sets are obtained with a single value of beta, the key parameter that characterizes the nature of the dispersive transport. The value of beta is derivable from the high xi behavior of the pdf histogram Phi(xi) (where xi is the inverse velocity) of the Darcy field, which determines the latetime tail within psi(t). The quality of the two fits obtained herein with a physically derived parameter set is a probe of how heterogeneous hydraulic conductivity fields with different types of correlation can affect the largerscale transport behavior. The features that give rise to a powerlaw tail of local transition times and a limit of the time range for nonFickian behavior dominate the transport. The correlation structures of the different P(K(x)) play a secondary role compared to the spectrum of less frequent events (e.g., low velocity regions) that have a l
Research output: Article
2009

, 20 Dec 2009, 1027, p. 2337 15 p. Abstract
Nanomaterials have received extensive attention recently as the next generators of scientific revolution. As such, nanomaterials are expected to be implemented in a wide range of applications. In the environmental field, nanomaterials hold promise for providing elegant solutions to numerous problems, from implementation of green chemistry processes for industrial and agrochemical uses, to production of novel materials for treatment of various contaminants. In this context the elimination of hazardous materials from the water environment is a major challenge facing environmental scientists today. In this chapter we present some results of our recent studies towards degradation of water contaminants. We exemplify both oxidative and reductive pathways for water remediation. In both cases we show the transformation of persistent contaminants through the use of nanomaterials as catalysts under ambient conditions.
Research output: Article 
, Nov 2009, In: Bulletin of the International Union Of Soil Sciences (IUSS). 115, p. 1112 2 p. Abstract
The soil and the subsurface region below it are two interrelated natural bodies that comprise the earth’s upper layer from land surface to aquifers. The ratio between these phases fluctuates as a function of environmental conditions, while the subsurface water content ranges from airdried to completely watersaturated. Because the soilsubsurface water content is controlled by rainfallirrigation, evaporation, and depth to the groundwater, a vertical water gradient always exists. The soilsubsurface zone, known also as the “critical zone” (CZ), also involves a large microbiological population, which develops under both aerobic or anaerobic conditions, and may affect the composition of the earth environment.
Research output: Article 
, May 2009, In: Water Resources Research. 45, 9 p. Abstract
The interplay between resident water already in the subsurface environment ("old water") and infiltrating water ("new water") is examined. A smoothed particle hydrodynamics technique is used to simulate the interplay between old water and new water in a porous medium over a cycle of drainage of old water and infiltration of new water. The effect of varying the average pore size is investigated via the Bond number. Four parameters (maximal mixing amount, minimal average size of old water pockets, mixing value for which the number of old water pockets decreases, and amount of old water remaining in the system for long times) are found to be independent of the average pore size. However, the rate of change is always higher for larger pores. In particular, some old water remains in the system within stable water pockets even after infiltrating new water reaches steady state.
Research output: Article 
, May 2009, In: Advances in Water Resources. 32, 5, p. 756766 11 p. Abstract
We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically quantify salient features of complex mixingdriven multicomponent reactive transport problems in porous media. Flow cells are commonly used to examine processes affecting reactive transport through porous media, under controlled conditions. An advantage of flow cells is their suitability for relatively fast and reliable experiments, although measuring spatial distributions of a state variable within the cell is often difficult. In general, fluid is sampled only at the flow cell outlet, and concentration measurements are usually interpreted in terms of integrated reaction rates. In reactive transport problems, however, the spatial distribution of the reaction rates within the cell might be more important than the bulk integrated value. Recent advances in theoretical and numerical modeling of complex reactive transport problems [De Simoni M, Carrera J, SanchezVila X, Guadagnini A. A procedure for the solution of multicomponent reactive transport problems. Water Resour Res 2005;41:W11410. doi: 10.1029/2005WR004056 De Simoni M, SanchezVila X, Carrera J, Saaltink MW. A mixing ratiosbased formulation for multicomponent reactive transport. Water Resour Res 2007;43:W07419. doi: 10.1029/2006WR005256] result in a methodology conducive to a simple exact expression for the spacetime distribution of reaction rates in the presence of homogeneous or heterogeneous reactions in chemical equilibrium. The key points of the methodology are that a general reactive transport problem, involving a relatively high number of chemical species, can be formulated in terms of a set of decoupled partial differential equations, and the amount of reactants evolving into products depends on the rate at which solutions mix. The main objective of the current study is to show how this methodology can be used in conjunction w
Research output: Article 
, May 2009, In: Advances in Water Resources. 32, 5, p. 750755 6 p. Abstract
Observations of nonFickian transport in sandbox experiments [Levy M, Berkowitz B. Measurement and analysis of nonFickian dispersion in heterogeneous porous media. J Contam Hydrol 2003;64:20326] were analyzed previously using a power law tail psi(t) similar to t(1beta) with 0 <beta <2 for the spectrum of transition times comprising a tracer plume migration. For each sandbox medium a choice of beta resulted in an excellent fit to the breakthrough curve (BTC) data, and the value of beta decreased slowly with increasing flow velocity. Here, the data are reanalyzed with the full spectrum of psi(t) gleaned from analytical calculations [Cortis A, Chen Y, Scher H, Berkowitz B. Quantitative characterization of porescale disorder effects on transport in "homogeneous" granular media. Phys Rev E 2004:10(70):041108. doi:10.1103/PhysRevE.70.0411081, numerical simulations [Bijeljic B, Blunt MJ. Porescale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 2006;42:W01202. doi: 10.1029/2005WR004578] and permeability fields IN Donato G, Obi EO, Blunt MJ. Anomalous transport in heterogeneous media demonstrated by streamlinebased simulation. Geophys Res Lett 2003;30:160812s. doi: 10.1029/2003GL017196]. We represent the main features of the full spectrum of transition times with a truncated power law (TPL), psi(t) similar to (t(1) + t)(1beta) exp(t/t(2)), where t(1) and t(2) are the limits of the power law spectrum. An excellent fit to the entire BTC data set, including the changes in flow velocity, for each sandbox medium is obtained with a single set of values of t(1), beta, t(2). The influence of the cutoff time t(2) is apparent even in the regime t <t(2). Significantly, we demonstrate that the previous apparent velocity dependence of beta is a result of choosing a pure power law tail for psi(t). The key is the change in the loglog slope of the TPL form of psi(t) with a shifting observational time window caused by the
Research output: Article 
, Mar 2009, In: Chemosphere. 75, 1, p. 4855 8 p. Abstract
Atrazine(2chloro4(ethylamine)6(isopropylamine)striazine) is a widely used herbicide which is considered a persistent groundwater contaminant. Its selective transformation mediated by cobalt or nickel porphyrins was studied in aqueous solutions at room temperature and ambient pressure. Several metalloporphyrins were examined as catalysts for the reaction and all yielded the same reaction, transforming atrazine solely to the seldomly reported form 2,4bis(ethylamine)6methylstriazine. The reaction involves dechlorination and migration of a methyl group to yield a symmetric product. Nickel 5,10,15,20tetrakis(1methyl4pyridinio)porphyrin tetra(ptoluenesulfonate) (TMPyP) was activated by nanosized zerovalent iron (nZVI) while cobalt porphyrins (TMPyP, 5,10,15,20tetrakis(4hydroxyphenyl)21H,23Hporphine(TP(OH)P) and 4,4',4 '',4"'(porphine5,10,15,20tetrayl)tetrakis (benzenesulfonic acid)(TBSP)) were activated by titanium(III) citrate as the electron donor. The effect of pH on atrazine transformation was demonstrated for the catalytic system of TP(OH)PCo/Ti(III) citrate. Finally, a comparison of the reactivities of cobalt TMPyP and TP(OH)P was given and the differences discussed. (C) 2008 Elsevier Ltd. All rights reserved.
Research output: Article 
, Feb 2009, In: Water Resources Research. 45, 6 p. Abstract
We present experimental evidence of asymmetrical dispersive transport of a conservative tracer across interfaces between different porous materials. Breakthrough curves are measured for tracer pulses that migrate in a steady state flow field through a column that contains adjacent segments of coarse and fine porous media. The breakthrough curves show significant differences in behavior, with tracers migrating from fine medium to coarse medium arriving significantly faster than those from coarse medium to fine medium. As the flow rate increases, the differences between the breakthrough curves diminish. We argue that this behavior indicates the occurrence of significant, timedependent tracer accumulation in the resident concentration profile across the heterogeneity interface. Conventional modeling using the advectiondispersion equation is demonstrated to be unable to capture this asymmetric behavior. However, tracer accumulation at the interface has been observed in particletracking simulations, which may be related to the asymmetry in the observed breakthrough curves.
Research output: Article 
, Jan 2009, In: Applied Catalysis BEnvironmental. 85, 34, p. 207211 5 p. Abstract
The catalytic activity of copperoxide nanoparticles was investigated for the removal of organic pollutants in aqueous solutions, using hydrogen peroxide as an oxidant. Complete degradation of both alachlor and phenanthrene was achieved after 20 min. The kinetics of the reaction was found to be pseudofirstorder with respect to the pollutant. The influence on the reaction kinetics of different catalyst samples, consisting of the same material but of different origin and different particle properties, was examined. The effects of several factors such as irradiation, oxidant concentration, ionic strength and pH on the reaction were also investigated. The catalysis is not photoinduced and can be performed without UVvis irradiation. In particular. an optimal oxidant concentration was determined for the studied system. The presence of salts was found to inhibit the alachlor degradation rate. The addition of high concentrations of oxidant or salt results in pseudozeroorder kinetics. However, NaCl at very high concentrations (>1 M) was found to cause a dramatic increase in reaction rate. The catalysis is efficient over a wide range of pH values. (C) 2008 Elsevier B.V. All rights reserved.
Research output: Article 
, Jan 2009, In: Geophysical Research Letters. 36, 5 p. Abstract
We quantitatively account for the measured concentration profile from a laboratory experiment of bimolecular (A + B > C) reactive transport in a porous medium with a particle tracking (PT) model. The PT results are in contrast to the analytical solution of the continuum scale advectiondispersionreaction equation, which results in an excess quantity of reaction product (C). The approaches differ in the treatment of the mixing zone, the fluctuations due to the low reactant concentrations, and the localized nature of the reaction. The PT can accommodate a range of transport modes with different temporal distributions. An exponential temporal distribution is equivalent to Fickian transport, which we use for the comparison to the laboratory data; a truncated powerlaw (TPL) temporal distribution yields a nonFickian transport characteristic of heterogeneous media. We study the influence of disorder on the mixing zone and the product concentration profiles via these contrasting transport modes. Citation: Edery, Y., H. Scher, and B. Berkowitz (2009), Modeling bimolecular reactions and transport in porous media, Geophys. Res. Lett., 36, L02407, doi: 10.1029/2008GL036381.
Research output: Article
2008

, Dec 2008, First ed. Heidelberg: . 412 p. Abstract
This book combines earth science, subsurface hydrology and environmental geochemistry, providing a comprehensive background for specialists interested in the protection and sustainable management of the subsurface environment. The reader is introduced to the chemistry of contaminants, which usually disturb the natural equilibrium in the subsurface as a result of human activity. The major focus of the book is on contaminant reactions in soil solutions, groundwater and porous media solid phases, accounting for their persistence and transformation in the subsurface, as they are transported from the land surface into groundwater. Discussions on selected case studies are provided.
Research output: Book 
, Oct 2008, In: Physical Review E. 78, 4, 9 p. Abstract
The origin of anomalous or nonFickian transport in disordered media is the broad spectrum of transition rates intrinsic to these systems. A system that contains within it heterogeneities over multiple length scales is geological formations. The continuous time random walk (CTRW) framework, which has been demonstrated to be an effective means to model nonFickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density psi(s,t) of random space time displacements (s,t). Transport in a random fracture network (RFN) has been calculated with a coupled psi(s,t) and has subsequently been shown to be approximated well by a decoupled form psi(s,t)=F(s)psi(t). The latter form has been used extensively to model nonFickian transport in conjunction with a velocity distribution Phi(xi),xi equivalent to 1/v, where v is the velocity magnitude. The powerlaw behavior of psi(t)proportional to t(1beta), which determines nonFickian transport, derives from the large xi dependence of Phi(xi). In this study we use numerical CTRW simulations to explore the expanded transport phenomena derived from a coupled psi(s,t). Specifically, we introduce the features of a powerlaw dependence in the s distribution with different Phi(xi) distributions (including a constant v) coupled by t=s xi. Unlike Levy flights in this coupled scenario the spatial moments of the plumes are well defined. The shapes of the plumes depend on the entire Phi(xi) distribution, i.e., both small and large xi dependence; there is a competition between long displacements (which depend on the small xi dependence) and large time events (which depend on a power law for large xi). These features give rise to an enhanced range of transport behavior with a broader scope of applications, e.g., to correlated migrations in a RFN and in heterogeneous permeability fields. The approximation to the decoupled case is investigated as a functi
Research output: Article 
, Apr 2008, In: Chemosphere. 71, 8, p. 14091421 13 p. Abstract
Most studies on contaminant interactions with the subsurface environment focus on contaminant transport, retention and persistence, and on potential remediation of polluted soils, vadose zones and aquifers. Changes in the soilvadoseaquifer zone (SVAZ) matrix and properties, caused by human activities, are thus usually considered to be deviations from a normal geochemical environment, which will disappear by natural processes or by specific remediation procedures. However, contaminants may also cause, under specific conditions, irreversible changes in SVAZ properties. In this critical overview, we discuss a different aspect of contaminantSVAZ interactions: irreversible changes in natural SVAZ properties as a result of anthropogenicallyinduced chemical contamination. We survey selected research results that illustrate various aspects of such phenomena, in soils, aquifers and the vadose zone. Grouping contaminants according to major and trace elements, we observe that major elements can irreversibly affect water transmission and other physical and chemical properties of the SVAZ, mainly in the liquid phase, while trace elements affect mostly the solid phase matrix. (C) 2007 Elsevier Ltd. All rights reserved.
Research output: Article 
, Mar 2008, In: Physical Review E. 77, 3, 6 p. Abstract
Diffusion on lattices with random mixed bonds in two and three dimensions is reconsidered using a random walk (RW ) algorithm, which is equivalent to the master equation. In this numerical study the main focus is on the simple case of two different transition rates W(1), W(2) along bonds between sites. Although analysis of diffusion and transport on this type of disordered medium, especially for the case of one bond pure percolation (i. e., W(1)= 0 ), comprises a sizable subliterature, we exhibit additional basic results for the two bond case: When the probability p of W2 replacing W1 in a lattice of W1 bonds is below the percolation threshold pc, the mean square displacement <r(2) > is a nonlinear function of time t. A best fit to the ln <r(2)> vs ln t plot is a straight line with the value of the slope varying with p, Delta, d, where Delta equivalent to W(2) /W(1) and d is the dimension, i. e., <r(2)> proportional to t(1+eta)(p,Delta,d) with eta>0 for Delta>1. In other terms, all the diffusion (D equivalent to <r(2)> /2t proportional to t(eta)) is anomalous superdiffusion for p <pc and Delta > 1 for d= 2,3. Previous work in the literature for d= 2 with a different RW algorithm established an effective diffusion constant D(eff), which was shown to scale as (p(c) p )(1/2). However, the anomalous nature (time dependence ) of D (t ) becomes manifest with an expanded regime of t, increased range of Delta, and the use of our algorithm. The nature of the superdiffusion is related to the percolation cluster geometry and Levy walks.
Research output: Article 
, Mar 2008, In: Water Resources Research. 44, 3, 16 p. Abstract
NonFickian behavior is due to a broad spectrum of rates limiting the solute transport. There are two generic mechanisms that can generate these spectra: the complex flow field of a highly heterogeneous medium and the mass exchange between a mobile phase and a distribution of immobile states. We have developed a physical model that incorporates both of these mechanisms into the continuous time random walk (CTRW) framework. We study their interacting dynamics as a function of the spectra of advectivediffusive transition times and exchange times and the relative separation of their respective time domains. Examples of interacting transport in a dispersive medium with immobile states include tracer migration in a random fracture network with matrix diffusion and transport in a porous medium with adsorption/desorption sites. To date, nonFickian transport has been quantified effectively using the CTRW in a wide variety of porous and fractured geological formations. The basis of the CTRW framework is the portrayal of transport as a sequence of transition rates (e. g., between pore spaces, fracture intersections) and the incorporation of the full spectrum of these rates into the transport equations. The emphasis herein is on systems in which the time domains of the two different types of spectra are distinguishable, so that a more complete characterization of the transport can be obtained (i.e., rather than lumping all the rates together). Experimental data are analyzed from two of these systems: (1) tracer transport in a fractured shear zone and (2) sorbing species transported through a heterogeneous porous domain. The CTRW framework is found to produce excellent fits to and predictions from the experimental data.
Research output: Article
2007

Decontaminating fluids and methods of use thereof, Dec 2007. Abstract
The present invention is directed to materials for the decontamination of fluids and methods of use thereof. The material and methods find applications in the decontamination of intermediates, chemical contaminants, a biological contaminants, wastewater, industrial effluents, municipal or domestic effluents, agrochemicals, herbicides and/or pharmaceuticals.
Research output: Patent 
, Nov 2007, In: Chemosphere. 69, 10, p. 15931601 9 p. Abstract
The behavior of several hydrophobic organic compounds (HOCs) in water at concentrations close to and above their maximum solubility values was studied. For this purpose, solutions of benzene, toluene, xylene, trichloroethylene (TCE) and a mixture of them were prepared in excess in freshwater and in saltwater, and solution stability was examined. High organic concentrations were found to remain stable in both freshwater and saltwater. In saltwater, for example, toluene and xylene concentrations remained as high as 14 and 26 times their solubilities, respectively, over a period of 6 days, while in freshwater, their concentrations remained 8 and 30 times their solubilities over the same period. This phenomenon is attributed to the presence of stable organic droplets, which were observed using optical microscopy. In addition, the transport of HOC droplets through sand is demonstrated, using an experimental system consisting of a saltwater source reservoir connected by a porous inactive sand layer to a freshwater collector reservoir. (c) 2007 Elsevier Ltd. All rights reserved.
Research output: Article 
, Nov 2007, In: Advances in Water Resources. 30, 11, p. 23732386 14 p. Abstract
Twophase imbibition behavior of immiscible fluids was studied in dry and prewetted porous media using a laserinduced fluorescence technique. Imbibition was first investigated in twodimensional (2D) systems under conditions comparable to those for a study of drainage [Ovdat H, Berkowitz B. Porescale study of drainage displacement under combined capillary and gravity effects in indexmatched porous media. Water Resources Research 2006;42:W06411. doi: 10.1029/2005WROO4553] in the capillarydominated regime. The effect of initial wetting saturation (IWS) was then explored in 2D and 3D porous media under the combined effect of gravity, capillary and viscous forces, within and outside the capillarydominated regime. Parameters that describe maximum vertical advance, Volumetric fraction, total surface area and specific surface area of the invading fluid were used to quantify the behavior. Comparison of 2D drainage and imbibition patterns demonstrates significant qualitative differences under analogous viscosity ratio, buoyancy number, and capillary number values. However, quantitative analyses show strong porescale similarities between these patterns. Invasion structures in 3D, prewetted (IWS approximate to 8% of the pore volume) porous media are ramified, with lateral branching and regions containing trapped residual fluid. These structures are qualitatively and quantitatively different from the compact, branchless structures that develop in dry (IWS = 0) porous media. (C) 2007 Elsevier Ltd. All rights reserved.
Research output: Article 
, Jun 2007, In: Chemosphere. 68, 2, p. 210217 8 p. Abstract
The hydrogenation of polycyclic aromatic hydrocarbons (PAHs) (naphthalene, anthracene, and phenanthrene) catalyzed by metalloporphyrins based on cobalt, nickel or iron was studied in aqueous solutions at room temperature and ambient pressure. Nickel porphyrin (PI) activated by nanosized zerovalent iron (nanoZVI) and cobalt porphyrins (P2) and (P4) activated by titanium(III) citrate as the electron donor were demonstrated to be promising catalysts for the reductive hydrogenation of PAHs. In particular, partially saturated di, tetra, and octahydrogenated products were obtained for anthracene or phenanthrene using a nickel porphyrin activated by nanoZVI, while naphthalene was transformed to tetralin. Systems containing cobalt porphyrins activated by titanium(III) citrate exhibited a high selectivity and activity toward hydrogenation of anthracene, producing 9, 10dihydroanthracene. However, no formation of hydrogenated hydrocarbons was observed from naphthalene or phenanthrene using cobalt porphyrins. (C) 2007 Elsevier Ltd. All rights reserved.
Research output: Article 
, Jun 2007, In: Geochimica et Cosmochimica Acta. 71, 11, p. 26572671 15 p. Abstract
The O18/O16 ratio of CO2 is a potentially powerful tracer of carbon dioxide fluxes from the soil to the atmosphere, which is influenced by complex interactions involving both biotic and abiotic soil processes. We use a simplified experimental approach and numerical simulations to examine in isolation the O18 exchange between CO2 and soil water associated with the abiotic invasion of atmospheric CO2 into soil. This allowed us to verify, in particular, whether the O18 of the retrodiffusion flux of CO2 from the soil reflects O18 equilibration with water at the soil surface, or at some depth. Sterile soil samples with known water isotopic composition were placed in a closed box attached to a specially designed flow chamber and the changes in delta O18 of CO2 between the chamber inlet and outlet, due only to invasion effects, were determined. Numerical simulations constrained by the laboratory gas exchange measurements indicated that between the two commonly used diffusion models [Penman, H.L. (1940). Gas and vapor movements in soil, l: the diffusion of vapors through porous solids. Int. J. Agric. Sci. 30, 437462; Moldrup, P., Olesen, T., Yamaguchi, T., Schjonning, P., Rolston, D.E. (1999). Modeling diffusion and reaction in soils, IX, the BackinghamBurdineCampbell equation for gas diffusivity in undisturbed soil. Soil Sci. 164, 542551], only the former provided good agreement with the measurements over a wide range of soil water contents. Based on the model calculations constrained by experimental data, and on comparison of characteristic diffusion/reaction times, we conclude that the depth required for full CO2water O18 equilibration ranges between 2 and 8.5 cm. The depth depends, in order of importance, on (1) soil moisture content; (2) temperature, which dominates the rate of hydration isotopic exchange; (3) CO2 residence time, which is determined by the time of replacement of the column air above the soil; and (4) soil structure, including porosity,
Research output: Article 
, May 2007, In: Journal Of Geophysical ResearchSolid Earth. 112, B5, 10 p. Abstract
[1] We examine experimentally the effect of phase separation of a binary fluid on convection and heat transfer in porous domains with heterogeneous permeability fields. In midocean ridge hydrothermal systems, a dense brine phase and a coexisting vapor phase form during the phase separation of seawater at supercritical conditions; this process strongly influences the chemistry of vents and the convective transfer of heat. Furthermore, convection and phase separation are likely to occur in oceanic crust that is highly heterogeneous in nature. Because of high temperatures and pressures required for phase separation in saline systems, a binary fluid [H2O2butoxyethanol], with a lower consolute point of 48.5 degrees C, was used as a proxy for seawater. A saturated pseudotwodimensional porous domain containing high permeability [k] zones embedded in a lower permeability matrix was heated from below and cooled from above. As with homogeneous systems, chemical stratification develops in heterogeneous domains, with dense fluid accumulating in lowvelocity regions at the bottom of the porous matrix. Furthermore, in both types of porous media, the efficiency of thermal transport is reduced relative to singlephase systems. Heterogeneities in the permeability field, however, can act to amplify these effects; in systems with vertical highk zones, the thickness of the densephase layer increases in the lowk regions, and thermal transport is suppressed even more. Also, the experiments show that regions of both high and low permeabilities can act as a store for brines and facilitate the formation of much thicker brine layers than are otherwise predicted by models based on homogeneous oceanic crust.
Research output: Article 
Catalytically treating water contaminated with halogenated organic compounds, May 2007. Abstract
Catalytically treating groundwater (10), surface water, or above surface water, contaminated (12) with halogenated organic compounds being members of chlorotriazine, chloroacetanilide, or halogenated aliphatic, herbicide groups, and, halogen containing analogs and derivatives thereof. Method: exposing contaminated water to catalytic amount of electron transfer mediator (18) under reducing conditions, to decrease concentrations of halogenated organic compounds. System: at least one electron transfer mediator (18) contained in at least one (insitu or/and exsitu) unit (20), for exposing to contaminated water under reducing conditions. Exemplary electron transfer mediators are porphyrinogenic organometallic complexes, being metalloporphyrins, metallocorrins, or metallochlorins. Exemplary metalloporphyrins are a [TMPyP], [TP(OH)P], [TPP], or [TBSP], free base porphyrin complexed to a transition metal (cobalt, nickel, iron, zinc, or copper). Implemented according to homogeneous or/and heterogeneous catalysis, via batch or flow mode. Reducing conditions naturally exist, or/and are anthropogenically produced, in the contaminated water. Applicable to insitu groundwater permeable reactive barriers (PRBs) (22).
Research output: Patent 
, Apr 2007, In: Transport in Porous Media. 67, 3, p. 413430 18 p. Abstract
An approach to describe heat transfer in porous media is presented on the basis of the continuous time random walk (CTRW) framework. CTRW is capable of quantifying both local equilibrium and nonequilibrium heat transfer in heterogeneous domains, and is shown here to match published experimental data of nonequilibrium thermal breakthrough. It is argued that CTRW will be particularly applicable to the quantification of heat transfer in naturally heterogeneous geological systems, such as soils and geothermal reservoirs.
Research output: Article 
, Mar 2007, In: Geophysical Research Letters. 34, 6, 5 p. Abstract
Poresize controlled solubility (PCS) is incorporated into continuum equations for fluid transport and porosity evolution. The physical properties of a porous domain, in particular poresize, can modify the effective solubility of minerals, allowing highly supersaturated fluids to exist within submicronscale pores of rocks; when fluid flows from small pores into larger ones, or vice versa, precipitation or dissolution may occur. Using numerical simulations, we demonstrate that the PCS mechanism can account for the filling of large pore spaces during transport though a heterogeneous rock matrix. Furthermore, depending on flow and initial conditions, the steady state porosity patterns that develop may be heterogeneous. The mechanism is expected to be of significance during diagenesis and fracture mineralization.
Research output: Article 
Method for extracting and upgrading of heavy and semiheavy oils and bitumens, Mar 2007. Abstract
Improvements in the selective extraction of relatively low molecular weight oils from coal, coal liquids, oil shales, shale oils, oil sands, heavy and semiheavy oils, bitumens, and the like are provided by a continuous process involving contacting the material to be treated with supercritical water in a continuous operation at pressures of from 500 psi to 3000 psi, temperatures of 250 DEG C. to 450 DEG C., and inreactor dwell times generally in excess of 25 seconds and up to 10 minutes.
Research output: Patent
2006

, Sep 2006, In: Journal Of Geophysical ResearchSolid Earth. 111, B9, 12 p. Abstract
Experiments were conducted to explore the behavior of convection and heat transfer during phase separation in porous media. Phase separation is considered to be an important process in many midocean ridge hydrothermal systems in which a dense brine separates from a lighter, less saline vapor phase at supercritical temperatures. As this process occurs at high temperatures and pressures in seawater systems, a binary fluid (H2O2butoxyethanol) with a lower consolute point of 48.5 degrees C, was used as a proxy for the hydrothermal fluid. In the experiments, a cell containing glass beads saturated with the binary fluid was heated from below and cooled from above. It was demonstrated that chemically differentiated regions can exist as part of a steady state convective regime, with the denser fluid phase separating and accumulating in a stagnant bottom layer. Furthermore, in upwelling regions phase separating fluids can become entrained. Phase separation was also found to lower the efficiency of convective thermal transfer, indicated by the deviation from the calculated singlephase RayleighNusselt curve. It is proposed that the reduction of convective heat transfer at supercritical conditions may be a crucial factor in controlling heat transfer through the oceanic crust.
Research output: Article 
, Jun 2006, In: Water Resources Research. 42, 6, 14 p. Abstract
[ 1] Fluid displacement patterns were observed in two and threedimensional ( 2 and 3D), gravitydriven drainage experiments. A nonintrusive, laserinduced fluorescence technique, using refractive index matching between solid and fluid phases and subsequent imaging processing, enabled measurement of the flow patterns in porous media. The methodology allows visualization of 3D porescale flow dynamics of two immiscible fluid phases in porous media at a low capillary number (Ca approximate to 10(4)). Qualitative analyses indicate considerable diversity in the 2 D and 3D displacement patterns of the invading fluid within and among the experimental systems. Quantitative analyses of these patterns, however, provide unique functional forms that characterize the invasion behavior of the nonwetting fluids, with clear differences in behavior between 2 D and 3D systems. In particular, scaling relations are defined which describe the maximum vertical advance, Volumetric fraction, total surface area ( or, equivalently, the ratio of total surface area to volume), and specific surface area of the invading fluid. These findings are in excellent agreement with predictions from dynamic invasion percolation growth models, which were developed originally without consideration of buoyancy effects.
Research output: Article 
, Mar 2006, In: Earth and Planetary Science Letters. 243, 34, p. 657668 12 p. Abstract
The effect of serpentinization on hydrothermal convection is explored using a dynamic 2D numerical model. Serpentinization is a highly exothermic mineral hydration process that consumes large quantities of water. The reaction is ubiquitous in the oceanic lithosphere and is generally associated with hydrothermal activity. Here, the thermal and hydration effects are incorporated into conservation equations describing fluid flow and heat transfer in hydrothermal systems. Models representing two different geological scenarios are explored. The "permeabilityinitiated" case simulates rapid uplift of ultramafic basement rock accompanied by rock fracturing, while the "temperatureinitiated" scenario simulates the uplift of an ultramafic complex followed by a magmatic event at depth. In both models, simulations of convection with and without serpentinization demonstrate that mineral alteration can have an important effect on hydrothermal flow patterns and vent temperatures. Two parameters determine the impact of serpentinization on the system: (1) the basal temperature (Tb), and (2) the dimensionless Rayleigh number (Ra). At Ra <50 and Tb <170, peak temperatures were only slightly affected by serpentinization and convection was initially suppressed due to the downward flow of water induced by the hydration reaction. At higher Rayleigh numbers and basal temperatures, serpentinization effectively stimulated the onset of convection and significantly affected transient vent temperatures; differences in peak vent temperatures between the standard convective case and that with serpentinization were found to be as high as 170 degrees C. Thus, together with the geothermal heat flux, serpentinization could act to control temperatures at seafloor hydrothermal sites. (c) 2006 Elsevier B.V. All rights reserved.
Research output: Article 
, Jan 2006, In: Reviews of Geophysics. 44, 2, 49 p. Abstract
[ 1] NonFickian ( or anomalous) transport of contaminants has been observed at field and laboratory scales in a wide variety of porous and fractured geological formations. Over many years a basic challenge to the hydrology community has been to develop a theoretical framework that quantitatively accounts for this widespread phenomenon. Recently, continuous time random walk (CTRW) formulations have been demonstrated to provide general and effective means to quantify nonFickian transport. We introduce and develop the CTRW framework from its conceptual picture of transport through its mathematical development to applications relevant to laboratory and fieldscale systems. The CTRW approach contrasts with ones used extensively on the basis of the advectiondispersion equation and use of upscaling, Volume averaging, and homogenization. We examine the underlying assumptions, scope, and differences of these approaches, as well as stochastic formulations, relative to CTRW. We argue why these methods have not been successful in fitting actual measurements. The CTRW has now been developed within the framework of partial differential equations and has been generalized to apply to nonstationary domains and interactions with immobile states ( matrix effects). We survey models based on multirate mass transfer ( mobileimmobile) and fractional derivatives and show their connection as subsets within the CTRW framework.
Research output: Article
2005

, Nov 2005, In: Ground Water. 43, 6, p. 947950 4 p. Abstract
We describe the continuous time random walk (CTRW) MATLAB toolbox, a collection of MATLAB scripts and functions that compute breakthrough curves (BTCs) and onedimensional/twodimensional (1D/2D) resident concentration profiles for passive tracer dispersion. The transport model is based on the CTRW theory. CTRW includes as special cases the classical Fickian dispersion based advectiondispersion equation, multirate and mobileimmobile models, and the fractionalintime derivative transport equation. Several models for treating the memory effects responsible for the anomalous character of dispersion have been implemented in the CTRW toolbox. In the current version of the toolbox, it is possible to solve explicitly for the forward problem (concentration prediction) in 1D and 2D and for the inverse problem (parameter identification from experimental BTC data) in ID. Future extensions will include explicit treatment of sorbing tracers, simple subroutines for treating radial flow from wells, introduction of arbitrary initial conditions, treatment of heterogeneous domains by use of the FokkerPlanck with Memory equation, and treatment of transport in multidimensional systems.
Research output: Article 
, Oct 2005, In: Physical Review E. 72, 4, 10 p. Abstract
Current models of morphogeninduced patterning assume that morphogens undergo normal, or Fickian, diffusion, although the validity of this assumption has never been examined. Here we argue that the interaction of morphogens with the complex extracellular surrounding may lead to anomalous diffusion. We present a phenomenological model that captures this interaction, and derive the properties of the morphogen profile under conditions of anomalous (nonFickian) diffusion. In this context we consider the continuous time random walk formalism and extend its application to account for degradation of morphogen particles. We show that within the anomalous diffusion model, morphogen profiles are fundamentally distinct from the corresponding Fickian profiles. Differences were found in several key aspects, including the role of degradation in determining the profile, the rate by which it spreads in time and its longterm behavior. We analyze the effect of an abrupt change in the extracellular environment on the concentration profiles. Furthermore, we discuss the robustness of the morphogen distribution to fluctuations in morphogen production rate, and describe a feedback mechanism that can buffer such fluctuations. Our study also provides rigorous criteria to distinguish experimentally between Fickian and anomalous modes of morphogen transport.
Research output: Article 
, Sep 2005, In: Physical Review E. 72, 3, 12 p., 031110. Abstract
We study effective transport under linear equilibrium adsorption characterized by a spatially random retardation factor. In a stochastic framework, we present a methodology to quantify explicitly the impact of spatial disorder on effective transport dynamics. We derive an exact effective transport equation, which is equivalent to transport under linear kinetic adsorption characterized by a spectrum of adsorption times. The distribution of adsorption times is given explicitly in terms of the spatial disorder distribution. Furthermore, we find that effective transport is formally equivalent to a decoupled continuous time random walk. This observation and the explicit nature of the presented results allow for a mapping of the static disorder distribution on the transition time distribution.
Research output: Article 
, Sep 2005, In: Environmental Science & Technology. 39, 18, p. 72087216 9 p. Abstract
Measurements of particle deposition and mobilization in watersaturated porous columns were performed using nuclear magnetic resonance imaging (MRI). The use of MRI enabled the acquisition of detailed, noninvasive measurements that quantify spatial and temporal evolution of particle transport patterns and porosity changes due to particle deposition. Measurements indicate that for the considered particle sizes and flow conditions significant particle deposition occurs at some distance into the column. Because identification of unique parametrizations for processes of particle straining, deposition, and detachment is complex and nonunique, a simple phenomenological model of particle deposition and porosity reduction is suggested. This model captures the essential features of the experimental measurements on spatial and temporal flow and deposition patterns.
Research output: Article 
, May 2005, In: Advances in Water Resources. 28, 5, p. 507521 15 p. Abstract
A series of laboratory experiments is presented which investigates the influence of fractures on the evolution of hydraulic conductivity and porosity caused by flow, dissolution and precipitationand the interplay among themin carbonate rocks. We inject input solutions of HCl and H2SO4, at different flow rates, into carbonate rock samples containing different configurations of fractures. As a consequence, host rock dissolves and gypsum subsequently precipitates. These experiments allowed us to determine effects of fracture orientation, fracture wall roughness, fluid flow rate and chemistry, and coupled dissolution/precipitation reaction mechanisms on overall patterns of hydraulic conductivity and porosity evolution. To separate the relative effects of these parameters, flow experiments used quasitwodimensional (2D) rock fractures, threedimensional (3D) intact rock cores, and 3D rock cores containing different fracture configurations. Changes in pressure gradient along the sample, recorded at specific time intervals during the experiments, were used to calculate the overall evolution of hydraulic conductivity. The effluent acid was analyzed for Ca2+ and SO42=2 concentrations to estimate corresponding porosity changes. After each experiment, the rock sample was retrieved and sectioned in order to study the pore space geometry, micromorphology, and distribution of precipitated and dissolved minerals. We find that fracture sample geometry and chemical composition of the reacting fluid are the two main factors most strongly influencing precipitation and dissolution patterns within a fracture. The interplay of these factors is controlled largely by the flow rate of the injected fluid. In 3D systems, we find that fracture orientation controls whether precipitation or dissolution is the dominant process: a throughflow fracture led to a dissolutiondominated system, in contrast to an isolated fracture which led to a precipitationdominated system under the same expe
Research output: Article 
, Apr 2005, In: Advances in Water Resources. 28, 4, p. 337344 8 p. Abstract
The dynamics of porosity evolution are explored during mineral precipitation that is induced by the mixing of two fluids of different compositions. During mineral precipitation in geological formations, the physical parameters that characterize the porous matrix, such as porosity and specific surface area, can change significantly. A series of coupled equations that determine the changes in porosity is outlined and solved for a 2D model domain using a finite element scheme. Using model parameters equivalent to those for calcite precipitation in a saline system, the evolution of porosity is examined for two types of porous media: (1) an initially homogeneous system and (2) a heterogeneous system containing high porosity regions that serve initially as preferential flow paths. In addition, the influence of two different expressions that relate specific surface area to porosity is explored. The simulations in both domains indicated that porosity was reduced primarily in the regions in which significant degrees of mixing occurred. Although an effective barrier was created in these regions, the fluids bypassed the clogged areas allowing precipitation to continue farther "downstream". Furthermore, mixinginduced precipitation can account for systems in which some high porosity regions are filled while others remain almost unchanged. Thus, mixinginduced precipitation represents a viable mechanism for the infilling of pores in fractured and porous rocks. The simulations also demonstrate that the choice of functional form for specific surface area plays an important role in controlling porosity patterns by influencing both the kinetics of precipitation and the permeability of the porous medium. As specific surface area is currently one of the least constrained parameters in models of porosity evolution, this result highlights the need for future experimental studies in this field of research. (c) 2004 Elsevier Ltd. All rights reserved.
Research output: Article 
, Mar 2005, In: Environmental Science & Technology. 39, 5, p. 12831290 8 p. Abstract
A new method to transform anthropogenic, chloroorganic compounds (COC) by use of nanosized molecular catalysts immobilized in solgel matrixes is presented. COC represent a serious threat to soil and groundwater quality. Metalloporphyrinogens are nanometer sized molecules that are known to catalyze degradation of COC by reduction reactions. In the current study, metalloporphyrinogens were immobilized in solgel matrixes with pore throat diameters of nanometers. The catalytic activity of the matrix arrays for anaerobic reduction of tetra chloroethylene (PCE), trichlorciethylene (TCE), and carbon tetrachloride (CT) was examined. Experiments were performed under conditions pertinent to groundwater systems, with titanium I and zerovalent iron as electron donors. All chloroorganic compounds were reduced in the presence of several solgelmetalloporphyrinogen hybrids (heterogeneous catalysts). For example, cobalt5,10,15,20(4hydroxyphenyl)21 H,23Hporphine (TF(0H)PCo) and cyanocobalamin (vitamin 1312) reduced CT concentrations to less than 5% of their initial values in a matter of hours. Cyanocobalamin was found to reduce PCE to trace amounts in less than 48 h and TCE to less than 25% of its initial concentration in 144 h. The reactions were compared to their homogeneous (without solgel matrix) analogues. The reduction activity of COC for the homogeneous and heterogeneous systems ranged between similar reactivity in some cases to lower reduction rates for the heterogeneous system. These lower rates are, however, compensated by the ability to encapsulate and reuse the catalyst. Experiments with cyanocobalamin showed that the catalyst could be reused over at least 12 successive cycles of 24 h each.
Research output: Article 
, Jan 2005, Dynamics of fluids and transport in fractured rock. Faybishenko B., Gale J. & Witherspoon P. A.(eds.). Washington, D. C.: Vol. 162. p. 2331 9 p. (Geophysical Monograph Series). Abstract
NonFickian (or anomalous) transport of contaminants arises naturally, at both laboratory and field scales, for a wide range of fractured and heterogeneous geological formations. Over many years, the advectiondispersion equation (ADE) and a range of ensembleaverage or homogenization variants have been considered, developed, and applied to modeling of transport in such systems. In general, however, these methods are intrinsically and fundamentally not suited to account for anomalous transport features, and fits to actual measurements are often inadequate. We examine how continuoustime randomwalk (CTRW) formulations represent a general and effective means by which to quantify nonFickian transport. The CTRW approach thoroughly accounts for observations, and is based on a physical picture of contaminant motion that is consistent with the geometric and hydraulic characterization of the fractured formation. We examine the conceptual picture and mathematical development of the CTRW framework and consider specific. applications to fractured systems.
Research output: Chapter 
2004

, Dec 2004, In: Geophysical Research Letters. 31, 24, 4 p. Abstract
An experimental study was carried out to examine the evolution of flow patterns in both time and space under different flow regimes, caused by incongruent dissolution of fractured dolomite. Analysis of oscillatory behavior of the overall hydraulic conductivity was based on the fluid residence time, which influences strongly aragonite and calcite precipitation in fractured dolomite rocks. The results are in accordance with field observations.
Research output: Article 
, Oct 2004, In: Physical Review E. 70, 4, 8 p. Abstract
Breakthrough curves (BTC) of a passive tracer in macroscopically homogeneous granular materials (wellsorted, unconsolidated sands or glass beads) were measured in a series of column experiments. The early and late arrival times are observed to differ systematically from theoretical predictions based on solution of the advectivedispersion equation for uniform porous media. We propose that subtle and residual porescale disorder effects in the porous media can account for these observations. We determine an ensembleaveraged distribution of particle transfer rates (based on a master equation for the local fluxaveraged concentration which incorporates these effects, and utilize it to calculate BTC that are in excellent agreement with the entire series of observations. Theoretical prediction of the dependence of the effective macroscopic parameters on measurable quantities is also in excellent agreement with the observations.
Research output: Article 
, Sep 2004, In: Water Resources Research. 40, 9, 22 p. Abstract
[1] The effects of air injection on flow through porous media were explored in a series of 1m and 2m laboratory flow cells. Our motivation was to examine air barriers as an alternative to hydraulic barriers to inhibit saline intrusion in coastal areas. Steady flow conditions were created in homogeneous and heterogeneous unconsolidated sand systems. Dry air was injected at progressively higher flow rates through a well in the center of each flow cell. Discharge and NaCl  tracer breakthrough data were measured at the outflow reservoir of each cell. In addition, a dye tracer was used to visualize the flow patterns. In all cases, air injection was found to produce stable, lowconductivity barriers that reduced discharge by an order of magnitude or more. Effective hydraulic conductivity values determined from discharge and hydraulic head data showed exponential declines with increased airinjection rates in all cases. Numerical simulation was used to quantify hydraulic conductivity and effective porosity values in the saturated and aerated regions created by air injection, and to study advective flow behavior. Porefilling cement formed in the airinjection region and was analyzed to determine its composition, mass, and volume. Approximately 60% of the cement consisted of soluble minerals, and 40% was less soluble carbonates. Evaporation and increase in solution pH due to stripping of CO2 by the injected air were responsible for creating the cement. The cement occupied <10% of the pore space in the sandcement aggregate. Both the air and mineral porefillings dissolved when air injection ceased, indicating that both barriers are temporary. These results serve as a preliminary proof of concept that airinjection barriers might effectively inhibit undesired subsurface flow, such as saline intrusion or contaminated groundwater.
Research output: Article 
, Sep 2004, In: Soil Science Society of America Journal. 68, 5, p. 15391548 10 p. Abstract
We reexamine  in light of recent theoretical developments  classical experiments on dispersion of a passive tracer in fully and partially saturated porous columns. We rind that the dispersion breakthrough curves (BTCs) exhibit anomalous (nonFickian) early arrival times and late time tailing, which can be explained by the Continuous Time Random Walk (CTRW) theory. The CTRW framework includes as a special case the classical advectiondispersion equation (ADE) for Fickian transport. We argue that existing measurements and interpretations of dispersion should be carefully reconsidered in the framework of these advances in conceptual understanding and quantification.
Research output: Article 
, Jul 2004, In: Chemical Physics. 302, 13, p. 2130 10 p. Abstract
This work examines diffusion in ternary nonideal systems and derives coupled nonlinear equations based on a nonequilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (Maa, Mab, Mba, and Mbb), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two nonideality parameters (chi(ac) and chi(bc)) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and chi parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested. (C) 2004 Elsevier B.V. All rights reserved.
Research output: Article 
, May 2004, In: Vadose Zone Journal. 3, 2, p. 534548 15 p. Abstract
We critically examine historical and recent studies of flow and transport at the local scale within the capillary fringe (CF). The characterization of subsurface pathways traveled by water  and the impact of these pathways on the movement of chemicals and the viability of subsurface microbial populations  has been the subject of intensive investigation in the last 50 yr in the fields of soil science and hydrology. However, consideration of the complexity of local pathways within the CF has been largely ignored. Recent studies, as well as some historical ones, have reported observations of fluid flow and chemical transport within the CF, emphasizing the impact of physical heterogesuchneity and exchange of water and chemicals between the CF and the region below the water table. These observations lead to the conclusion that the CF may affect, at the local scale, the natural geochemical and microbial conditions present in the region of transition from unsaturated to saturated groundwater flow far more significantly than usually assumed. Here, we examine underlying physical factors that local flow and transport behaviors in and across the CF and these factors through examination of images collected in the laboratory. We also provide a brief survey of the literature on the CF. It is argued that existing definitions of the CF are inadequate to describe flow and transport behavior in the vicinity of the water table. We suggest replacing the concept of the CF with the concept of a partially saturated fringe, which involves multiphase transport in the immediate vicinity of ( both above and below) the water table.
Research output: Article 
, Apr 2004, In: Water Resources Research. 40, 4, 16 p. Abstract
We develop a numerical method to model contaminant transport in heterogeneous geological formations. The method is based on a unified framework that takes into account the different levels of uncertainty often associated with characterizing heterogeneities at different spatial scales. It treats the unresolved, smallscale heterogeneities (residues) probabilistically using a continuous time random walk (CTRW) formalism and the largescale heterogeneity variations (trends) deterministically. This formulation leads to a FokkerPlanck equation with a memory term (FPME) and a generalized concentration flux term. The former term captures the nonFickian behavior arising from the residues, and the latter term accounts for the trends, which are included with explicit treatment at the heterogeneity interfaces. The memory term allows a transition between nonFickian and Fickian transport, while the coupling of these dynamics with the trends quantifies the unique nature of the transport over a broad range of temporal and spatial scales. The advectiondispersion equation (ADE) is shown to be a special case of our unified framework. The solution of the ADE is used as a reference for the FPME solutions for the same formation structure. Numerical treatment of the equations involves solution for the Laplace transformed concentration by means of classical finite element methods, and subsequent inversion in the time domain. We use the numerical method to quantify transport in a twodimensional domain for different expressions for the memory term. The parameters defining these expressions are measurable quantities. The calculations demonstrate long tailing arising (principally) from the memory term and the effects on arrival times that are controlled largely by the generalized concentration flux term.
Research output: Article 
, Apr 2004, In: Water Resources Research. 40, 4, 13 p. Abstract
[1] We have conducted laboratory experiments to examine CaCO3 dissolution and precipitation in saltwaterfreshwater mixing zones, with a view to understanding and predicting porosity changes in coastal environments. Mixing of seawater or saline subsurface water with fresh water can be of major importance in the chemical diagenesis of carbonate rocks and sediments. We used artificial seawater and NaCl solutions of different concentrations under different CO2 partial pressures and with different mixing ratios. Twodimensional flow cells filled with glass beads and crushed calcium carbonate rock were used to measure calcium carbonate precipitation and dissolution, respectively. An important feature of these experiments is that the results are shown to agree well with a relatively simple transport theory describing mineral precipitation/dissolution that results from the nonlinear dependence of CaCO3 saturation upon electrolyte concentration. The theory demonstrates that the rate of dissolution or precipitation depends on the curvature ( and sign) of the solubility as a function of salinity, the square of the salinity gradient, and the macroscopic dispersion coefficient. The theory is largely scale independent and depends upon field parameters that can be determined. Analysis of data from three field sites (Yucatan peninsula, Bermuda, and Mallorca) demonstrates excellent agreement between field observations and theory.
Research output: Article 
, Mar 2004, In: Physica AStatistical Mechanics And Its Applications. 334, 12, p. 4666 21 p. Abstract
We investigate continuous time random walk (CTRW) theory, which often assumes an algebraic decay for the single transition time probability density function (pdf) psi(t)similar tot(1beta) for large times t. In this form, beta is a constant (0 <beta <2) defining the functional behavior of the transport. The use of algebraically decaying single transition time/distance distributions has been ubiquitous in the development of different transport models, as well as in construction of fractional derivative equations, which are a subset of the more general CTRW. We prove the need for and develop modified solutions for the first passage time distributions (FPTDs) and spatial concentration distributions for 0.5 <beta <1. Good agreement is found between our CTRW solutions and simulated distributions with an underlying lognormal single transition time pdf (that does not possess a constant beta). Moreover, simulated FPTD distributions are observed to approximate closely different Levy stable distributions with growing beta as travel distance increases. The modifications of CTRW distributions also point to the limitations of fractional derivative equation (FDE) approaches appearing in the literature. We propose an alternative form of a FDE, corresponding to our CTRW distributions in the biased 1d case for all 0 <beta <2, beta not equal 1. (C) 2003 Elsevier B.V. All rights reserved.
Research output: Article 
, Jan 2004, In: Advances in Water Resources. 27, 2, p. 155173 19 p. Abstract
We study the time behavior of solute transport in a heterogeneous medium. We consider a spatially biased continuous time random walk (CTRW) governed by psi(s, t), the joint probability density for an eventdisplacement s with an eventtime t. In this effective transport framework the concentration distribution of a solute is given by a generalized master equation (GME). We present results detailing the time dependence for the resident and flux concentrations, the center of mass velocity and the macroscopic dispersion coefficients of the solute plume. The Laplace transform of the GME is converted to a spatial differential equation resembling the advection dispersion equation (ADE), with Laplace space dependent coefficients though, and can then be solved explicitly in Laplace space. The transport behavior of the solute is then determined by accurate numerical inverse Laplace transforms. The confirmation of the accuracy of our methods is demonstrated by the excellent agreement with efficient random walk simulations based on the same psi(s, t). The psi(s, t) is given by the product of a Gaussian distribution for s and a truncated powerlaw distribution for t. This particular choice allows for a systematic study of the time regimes of anomalous and normal transport behavior and the transition from normal to anomalous behavior. The presented results show new aspects for the modeling of solute transport in heterogeneous media, in particular the effect of the system "memory" on plume patterns at asymptotically long times. In a specific application we solve for the contaminant flux entering a stream from a point injection of tracer in a catchment. The results are discussed as an independent test of a model of fractal stream chemistry in catchments. (C) 2004 Elsevier Ltd. All rights reserved.
Research output: Article
2003

, Nov 2003, In: Chemical Physics. 295, 1, p. 7180 10 p. Abstract
We address the question of how to relate between macroscopic transport behaviors of passive and sorbing (reactive) tracers in heterogeneous media. We use continuous time random walk (CTRW) and multirate mass transfer (MRMT) approaches for this purpose. In the framework of CTRW, we formulate the sorption process using a 'sticking' rate and a 'sticking' time distribution and derive a relation between the distributions of the sorbing and nonsorbing tracer in terms of these quantities. In the MRMT approach. the medium is divided into mobile and immobile regions with diffusive mass transfer between them. The mobile and immobile zones are characterized by different sorption properties. The relations between sorbing and passive tracer distributions derived within the two modeling frameworks turn out to be equivalent. Thus, both approaches show different aspects of the same transport behavior of a sorbing tracer and so lead to a deeper understanding of the underlying processes and the governing transport equations. (C) 2003 Elsevier B.V. All rights reserved.
Research output: Article 

, Jun 2003, In: Water Resources Research. 39, 6, 13 p. Abstract
[1] The evolution of hydraulic conductivity and porosity during the process of dedolomitization was examined in a series of laboratory experiments by analyzing the effects of concurrent dolomite dissolution and calcium carbonate precipitation. Linear flow experiments were performed in columns of crushed sucrosic dolomite by injecting different concentrations of HCl at various flow rates. Temporal changes in head gradient were used to calculate overall hydraulic conductivities of each column, while chemical analyses of the effluent acid enabled estimation of porosity changes during the experiments. After each experiment, the rock samples were retrieved and sectioned in order to study the pore space geometry, micromorphology, and mineral concentrations. A range of injected HCl concentrations and flow rates was identified which leads to oscillations in the effective hydraulic conductivity and porosity of the evolving rock samples; in all cases, however, the porous medium ultimately clogged. Shortterm experiments were also used to study the formation of dissolution and precipitation bands along the columns. Under the experimental conditions, dolomite dissolution is a reaction rate controlled process; experiments indicated that, as such, the flow rate and the pH of the injected fluid affect dissolution only during the initial stages, when calcium carbonate is dissolved. On the other hand, both the flow rate and the pH of the injected fluid strongly influence the precipitation process throughout the duration of the experiments because higher flow rates retard nucleation. These findings are in qualitative accordance with field observations of dolomite formations.
Research output: Article 
, May 2003, In: Water Resources Research. 39, 5, 20 p. Abstract
[1] We consider the transport behavior of a passive solute in a heterogeneous medium, modeled by continuous time random walks (CTRW) and linear multirate mass transfer (MRMT). Within the CTRW framework, we formulate a transport model which is formally equivalent to MRMT. In both approaches the total concentration is divided into mobile and immobile parts. The immobile concentration is given by the convolution in time of the mobile concentration and a memory function. The memory function is a functional of the distribution of transition and trapping times for the CTRW and the MRMT approach, respectively, and determines the transport behavior of the solute. Based on different expressions for the memory function in the two frameworks, we derive conditions for which both approaches describe the same transport behavior. We focus on anomalous transport behavior that can arise if the transition and trapping time distributions behave algebraically in a given time regime. Using an expansion of the Laplace transform of the memory function, we develop explicit expressions for the time behavior of the flux concentration as well as for the center of mass velocity and the (macro) dispersion coefficients of the solute distribution. We observe (anomalous) power law as well as (normal) Fickian transport behavior, depending on the exponents that dominate the trapping and transition time distributions, respectively. The results show that the character of the anomalous transport does not depend on the details of the transport model but only on the exponents dominating the transition or trapping time distributions. The unified transport framework presented here comprising CTRW and MRMT shows new aspects and opens new perspectives for the modeling of transport in heterogeneous media.
Research output: Article 

, Mar 2003, In: Geophysical Research Letters. 30, 5, 4 p. Abstract
We perform a novel set of laboratory experiments that depict CaCO3 precipitation upon mixing between saturated fresh and salt water solutions, thus simulating mixing diagenesis in a coastal aquifer. The experimental results are shown to agree with the result predicted from a relatively simple mathematical model, thus suggesting that the model may be extrapolated to natural environments. Application of the model to the coastal aquifer of Mallorca, Spain indicates calcite precipitation is reducing porosity at a rate of similar to 13% per 10,000 years. Consideration of precipitation processes can thus explain contradictory interpretations of natural evolution in carbonate formations.
Research output: Article 
, Jan 2003, In: Water Resources Research. 39, 1, 14 p. Abstract
[1] The evolution of hydraulic conductivity and flow patterns, controlled by simultaneous precipitation and dissolution in porous rocks, was examined in a series of laboratory experiments. Linear flow experiments were performed in columns of crushed calcareous sandstone by injecting different concentrations of HCl/H2SO4 mixtures at various flow rates. The effect of simultaneous calcium carbonate dissolution and gypsum precipitation was analyzed. Changes in head gradient, recorded at specific time intervals during the experiments, were used to calculate overall hydraulic conductivity of each column. The effluent acid was analyzed for Ca2+ and SO42 concentrations in order to calculate porosity changes during the experiments. After each experiment, the rock sample was retrieved and sectioned in order to study the pore space geometry, micromorphology, and mineral concentrations. A range of injected H+/SO42+ ratios and flow rates was identified which leads to oscillations in the effective hydraulic conductivity of the evolving carbonate rock samples. Because the dissolution of calcium carbonate is a mass transfer limited process, higher flow rates cause a more rapid dissolution of the porous medium; in such cases, with dissolution dominating, highly conductive flow wormholes were observed to develop. At slower flow rates, no wormhole formation was observed, but the porosity varied in different parts of the columns. Analysis of the sectioned parts of the column, after each experiment, showed that total porosity increased significantly by dissolution of carbonate mineral near the inlet of the column and decreased along the interior length of the column by gypsum precipitation. These findings are in qualitative accordance with conceptual understanding of such phenomena.
Research output: Article 
, Jan 2003, In: Separation Science and Technology. 38, 1, p. 149163 15 p. Abstract
The impregnation of 8hydroxyquinoline5sulfonic acid (HQS) onto an anionic strong base resin Lewatit MP 600 is described. The procedure was carried out by mixing HQS with Lewatit MP 600 in water, instead of in organic solvents generally used in solvent impregnated resins (SIRs). The maximum impregnation is 0.95 mmol of HQS/g of Lewatit MP 600. The HQSimpregnated resin was used in a flow injection system incorporating a minicolumn for cadmium chelation. Measured cadmium breakthrough curves were used to study the influence of various impregnated HQS, the influent concentration of cadmium, and the packed HQSLewatit MP 600, on cadmium binding. By increasing the impregnated HQS from 0.098 to 0.830 mmol/g of Lewatit NIP 600, column capacity increased from 11.29 to 52.57 mmol Cd/L of HQSLewatit MP 600. Increasing the influent concentration of Cd reduced the column capacity due to a concurrent increase of competing anion (004). This in turn reduced the stability of cadmium complex in the resin phase. Varying the amounts of HQSLewatit MP 600 packed in a minicolumn caused variations in Cd binding. A 450 mg quantity of 0.95 mmol HQS/g of Lewatit MP 600 can remove cadmium from an initial value of I ppm to 30 ppb (detection limit of our instrument). Cadmium and partially impregnated HQS can be eluted by 2 mol/L HNO3 and the resin can be regenerated to impregnate HQS for further cadmium complexation.
Research output: Article 
, Jan 2003, In: Water Resources Research. 39, 8, 9 p. Abstract
Flow and transport patterns in threedimensional fracture intersections are investigated, with emphasis on the occurrence and effects of local flows around each intersection. Flow and transport simulations indicate that local flow circulations (referred to as "local flow cells") arise because of an interplay between intersection geometry and corresponding boundary conditions for flow along the fracture boundaries. Local flow cells are thus unique features in threedimensional fracture networks. The analysis here suggests that local flow cells have little effect on the overall fluid flow in a fracture network but may constitute an effective mechanism which contributes to the long breakthrough tailing and retardation often observed in transport through discrete fracture networks.
Research output: Article 
, Jan 2003, In: Journal of Contaminant Hydrology. 64, 34, p. 203226 24 p. Abstract
Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advectiondispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to nonFickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two midscale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a "homogeneous" packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the "homogeneous" one, subtle yet measurable differences between Fickian and nonFickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE. (C) 2003 Elsevier Science B.V. All rights reserved.
Research output: Article
2002

, Nov 2002, In: Chemical Physics. 284, 12, p. 349359 11 p. Abstract
We develop a unified framework to model the anomalous transport of tracers in highly heterogeneous media. While the framework is general, our working media in this study are geological formations. The basis of our approach takes into account the different levels of uncertainty, often associated with spatial scale, in characterizing these formations. The effects on the transport of smaller spatial scale heterogeneities are treated probabilistically with a model based on a continuous time random walk (CTRW), while the larger scale variations are included deterministically. The CTRW formulation derives from the ensemble average of a disordered system, in which the transport in each realization is described by a Master Equation. A generic example of such a system  a 3D discrete fracture network (DFN)  is treated in detail with the CTRW formalism. The key step in our approach is the derivation of a physically based psi(s,t), the joint probability density for a displacement s with an eventtime t. We relate the 0(s, t) to the velocity spectrum Phi(xi) (\xi\ = 1/v, (ξ) over cap= (v) over cap) of the steady flowfield in a fluidsaturated DFN. Heterogeneous porous media are often characterized by a lognormal permeability distribution; the P() we use in this case is an analytic form approximating the velocity spectrum derived from this distribution. The common approximation of psi(s, t) similar to p(s)(t1beta) with a constant beta, is evaluated in these cases. For the former case it is necessary to include s  t coupling while the latter case points,to the presence of an effective tdependent beta. The full range of these features can be included in the CTRW solution but, as is shown, not in the fractionaltime derivative equation (FDE) formulation of CTRW. Finally, the methods used for the unified framework are critically examined. (C) 2002 Elsevier Science B.V. All rights reserved.
Research output: Article 
, Oct 2002, In: Water Resources Research. 38, 10, 12 p. Abstract
The basic conceptual picture and theoretical basis for development of transport equations in porous media are examined. The general form of the governing equations is derived for conservative chemical transport in heterogeneous geological formations for single realizations and for ensemble averages of the domain. The application of these transport equations is focused on accounting for the appearance of nonFickian (anomalous) transport behavior. The general ensembleaveraged transport equation is shown to be equivalent to a continuous time random walk (CTRW) and reduces to the conventional forms of the advectiondispersion equation (ADE) under highly restrictive conditions. Fractional derivative formulations of the transport equations, both temporal and spatial, emerge as special cases of the CTRW. In particular, the use in this context of Levy flights is critically examined. In order to determine chemical transport in fieldscale situations, the CTRW approach is generalized to nonstationary systems. We outline a practical numerical scheme, similar to those used with extended geological models, to account for the often important effects of unresolved heterogeneities.
Research output: Article 
, Jun 2002, In: Water Resources Research. 38, 6, 11 p. Abstract
[1] A combined experimental and numerical analysis is used to examine the movement and interaction of saltwater and freshwater in unconfined porous media. Particular emphasis is placed on flow phenomena in the partially saturated region above the water table and along the interface between the saturated and partially saturated regions. While some numerical models are apparently capable of simulating these phenomena, there is still a significant lack of experimental data with which to verify the models. Here a series of laboratoryscale experiments is considered to evaluate densitydependent, saltwaterfreshwater flow patterns in both the saturated and partially saturated zones. The laboratory experiments demonstrate clearly that significant lateral flows and coupled densitydriven flow effects may take place in the partially saturated region above the water table and at the interface between the saturated and partially saturated zones. In parallel, a finite element numerical model is developed. The model reproduces effectively the observed flow behaviors; the quality of the results suggests that the numerical model has the capacity to provide realistic predictions.
Research output: Article 
, Apr 2002, In: Environmental Science & Technology. 36, 8, p. 18511855 5 p. Abstract
Laboratory studies were conducted to investigate the feasibility of using ionexchange resins in permeable reactive barriers (PRBs) for the remediation of groundwater contaminated by heavy and transition metals. Ionexchange resins represent an essentially neglected class of materials which may, in addition to iron, activated carbon, and zeolites, prove effective for use in PRBs. Four resins were considered: two commercially available resins, Duolite GT73 (Rohm and Haas) and Amberlite IRC748 (Rohm and Haas), and two solventimpregnated resins (SIRs). The SIRs were prepared from Amberlite IRA96 (Rohm and Haas) and two different thiophosphoric extractants. All four resins are able to reduce cadmium, lead, and copper concentrations from 1000 mug/L (typical for contaminated groundwaters) to below 5 mug/L. Significantly, all of the resins are effective for the capture of cadmium, copper, and lead, even in the presence of CaCl2 and clay. Because of their high hydraulic conductivity, the use of these resins in clusters of wells, as an alternative to continuous walls, is considered in the design of effective PRBs. Numerical solution of the groundwater flow equations shows Thai depending on the well configuration, most (or all) of the contaminated groundwater can pass through the resins. These results demonstrate the possibility of using selective ionexchange resins as an effective, active material in PRBs for in situ groundwater remediation.
Research output: Article 
, Mar 2002, In: Physical Review E. 65, 3, 11 p. Abstract
We present a general derivation of onedimensional spatial concentration distributions for anomalous transport regimes. Such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution. This general theory includes a FokkerPlanck equation as a particular limiting case. All of the concentration profiles, as well as the associated temporal first passage time distributions, can be written in terms of a single special function (that belongs to the class of Fox functions). In addition, we consider the first two moments of the spatial concentration distributions, and determine not only their scaling behavior with time but also the coefficients and correction terms.
Research output: Article 
, Mar 2002, In: Geophysical Research Letters. 29, 5, 4 p. Abstract
We present a physical model to explain the behavior of longterm, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments [Kirchner et al., Nature, 403( 524), 2000]. A spectral analysis of the data shows the chloride concentrations in rainfall to have a white noise spectrum, while in streamflow, the spectrum exhibits a fractal 1/f scaling. The empirically derived distribution of tracer travel times h(t) follows a powerlaw, indicating lowlevel contaminant delivery to streams for a very long time. Our transport model is based on a continuous time random walk (CTRW) with an event time distribution governed by psi(t) similar to A(beta)t(1beta). The CTRW using this powerlaw psi(t) (with 0 <β <1) is interchangeable with the timefractional advectiondispersion equation (FADE) and has accounted for the universal phenomenon of anomalous transport in a broad range of disordered and complex systems. In the current application, the events can be realized as transit times on portions of the catchment network. The travel time distribution is the first passage time distribution F( t; l) at a distance l from a pulse input (at t = 0) at the origin. We show that the empirical h( t) is the catchment areal composite of F( t; l) and that the fractal 1/f spectral response found in many catchments is an example of the larger class of transport phenomena cited above. The physical basis of psi(t), which determines F( t; l), is the origin of the extremely long chemical retention times in catchments.
Research output: Article 
, Feb 2002, In: Water Resources Research. 38, 2, 12 p. Abstract
Nuclear magnetic resonance imaging (NMRI) is applied to noninvasively measure flow and dissolution patterns in natural, roughwalled, watersaturated halite fractures. Threedimensional images of water density and flow velocity acquired with NMRI allow quantification of the developing fracture morphology and flow patterns. The flow patterns are correlated strongly to the local apertures and the largescale wall toughness. The correlations of the dissolution patterns to the fracture morphology, flow patterns, and mineralogical composition of the rock matrix are a function of the overall dimensionless Damkohler number. At high Damkohler numbers the dissolution patterns are dominated by the flow structure. In addition, at high Damkohler numbers buoyancy (stratified flow) becomes important. In such cases the dissolution patterns also depend on the orientation and elevation of the fracture walls, resulting in preferential upward dissolution. At low Damkohler numbers the dissolution patterns depend mainly on the mineralogical composition of the rock matrix. These findings suggest that coupled flow and dissolution processes are much more complex and unpredictable than commonly assumed, even under simplified conditions.
Research output: Article 
, Jan 2002, In: Advances in Water Resources. 25, 812, p. 861884 24 p. Abstract
We analyze measurements, conceptual pictures, and mathematical models of flow and transport phenomena in fractured rock systems. Fractures and fracture networks are key conduits for migration of hydrothermal fluids, water and contaminants in groundwater systems, and oil and gas in petroleum reservoirs. Fractures are also the principal pathways, through otherwise impermeable or low permeability rocks, for radioactive and toxic industrial wastes which may escape from underground storage repositories. We consider issues relating to (i) geometrical characterization of fractures and fracture networks, (ii) water flow, (iii) transport of conservative and reactive solutes, and (iv) twophase flow and transport. We examine the underlying physical factors that control flow and transport behaviors, and discuss the currently inadequate integration of conceptual pictures, models and data. We also emphasize the intrinsic uncertainty associated with measurements, which are often interpreted nonuniquely by models. Throughout the review, we point out key, unresolved problems, and formalize them as open questions for future research. (C) 2002 Elsevier Science Ltd. All rights reserved.
Research output: Article 
, Jan 2002, In: Ground Water. 40, 1, p. 7684 9 p. Abstract
Laboratory experiments involving both homogeneous and heterogeneous porous media are used to demonstrate that fluid flow and solute transport will occur regularly in the capillary fringe (CF), including both vertical (upward as well as downward) and horizontal flow velocities. Horizontal flow above the water table appears to be limited primarily to the region of high water saturation (i.e., the CF), an observation supported by numerical modeling and consistent with the literature. Beyond observations presented in prior literature, it was observed that exchange of water within the CF with water below the water table is active, with flux both from the CF downward across the water table and from the region below the water table, upward into the CF. This flux is enhanced by the presence of physical heterogeneity. These findings strongly contrast the common conceptualization of predominantly downward vertical fluid flow through the unsaturated zone, with transition to fully threedimensional flow only below the water table. Based on these observations, it is suggested that the CF may affect, far more significantly than is usually assumed, the natural geochemical and microbial conditions present in the region of transition from unsaturated to saturated ground water flow.
Research output: Article
2001

, Nov 2001, In: Physical Review E. 64, 5, 4 p., 056305. Abstract
We show that, in the case of advective transport on the percolation backbone, the relevant structure below the correlation length is an ensemble of tortuous paths, rather than the classical linksnodesblobs system. These paths are embedded in the few largest blobs that dominate the structure of the backbone. We find numerically that the mean particle displacement differs from the prediction given by classical finitesize scaling arguments. We also show that because of the complex velocity distribution between the paths, the mean firstpassage time of the particles cannot be inferred directly from the mean particle displacement.
Research output: Article 
, Aug 2001, In: Reviews of Geophysics. 39, 3, p. 347383 37 p. Abstract
Scaling in fracture systems has become an active field of research in the last 25 years motivated by practical applications in hazardous waste disposal, hydrocarbon reservoir management, and earthquake hazard assessment. Relevant publications are therefore spread widely through the literature. Although it is recognized that some fracture systems are best described by scalelimited laws (lognormal, exponential), it is now recognized that power laws and fractal geometry provide widely applicable descriptive tools for fracture system characterization. A key argument for power law and fractal scaling is the absence of characteristic length scales in the fracture growth process. All power law and fractal characteristics in nature must have upper and lower bounds. This topic has been largely neglected, but recent studies emphasize the importance of layering on all scales in limiting the scaling characteristics of natural fracture systems. The determination of power law exponents and fractal dimensions from observations, although outwardly simple, is problematic, and uncritical use of analysis techniques has resulted in inaccurate and even meaningless exponents. We review these techniques and suggest guidelines for the accurate and objective estimation of exponents and fractal dimensions. Syntheses of length, displacement, aperture power law exponents, and fractal dimensions are found, after critical appraisal of published studies, to show a wide variation, frequently spanning the theoretically possible range. Extrapolations from one dimension to two and from two dimensions to three are found to be nontrivial, and simple laws must be used with caution. Directions for future research include improved techniques for gathering data sets over great scale ranges and more rigorous application of existing analysis methods. More data are needed on joints and veins to illuminate the differences between different fracture modes. The physical causes of power law scaling and variat
Research output: Article 
, Jul 2001, In: Ground Water. 39, 4, p. 593604 12 p. Abstract
We examine a set of analytical solutions based on the continuous time random walk (CTRW) approach, which can be evaluated numerically and used to analyze breakthrough data from tracer tests. Practical application of these solutions, with discussion of the physical meaning of the relevant model parameters, is emphasized. The CTRW theory accounts for the often observed nonFickian (or scaledependent) dispersion behavior that cannot be properly quantified by using the advectiondispersion equation. The solutions given here, valid for a wide range of dispersive behaviors of conservative tracers, and useful for both characterization and prediction, have been integrated into a library of external functions for use with the GRACE graphical display acid analysis package, Example applications of these solutions are presented. The library and graphics software are freely accessible from a Web site.
Research output: Article 
, Feb 2001, In: Advances in Water Resources. 24, 34, p. 309323 15 p. Abstract
Stochastic models that account for a wide range of porescale effects are discussed in the context of twophase, immiscible displacement problems in natural porous media. We focus on migration of dense, nonaqueous phase liquids (DNAPLs) through watersaturated geological materials. DNAPL movement is governed by buoyancy, capillary, and viscous forces, as well as by the details of the porous medium. We examine key issues relevant to development of stochastic growth models. We then present a particular stochastic growth model, based on a generalization of invasion percolation and Eden growth approaches, which realistically simulates twophase flows in a computationally efficient manner. Fingering patterns are shown to depend critically on the competing buoyancy, capillary, and viscous forces between the DNAPL and the water, and their interactions with the porous medium at the local scale. We conclude with recommendations for future research.
Research output: Article 
, Jan 2001, In: Transport in Porous Media. 42, 12, p. 241263 23 p. Abstract
A physical picture of contaminant transport in highly heterogeneous porous media is presented. In any specific formation the associated governing transport equation is valid at any time and space scale. Furthermore, the advective and dispersive contributions are inextricably combined. The ensemble average of the basic transport equation is equivalent to a continuous time random walk (CTRW). The connection between the CTRW transport equation, in a limiting case and the familiar advectiondispersion equation (ADE) is derived. The CTRW theory is applied to the results of laboratory experiments, field observations, and simulations of random fracture networks. All of these results manifest dominant nonGaussian features in the transport, over different scales, which are accounted for quantitatively by the theory. The key parameter beta controlling the entire shape of the contaminant plume evolution and breakthrough curves is advanced as a more useful characterization of the transport than the dispersion tensor, which is based on moments of the plume. The role of probabilistic approaches, such as CTRW, is appraised in the context of the interplay of spatial scales and levels of uncertainty. We then discuss a hybrid approach, which uses knowledge of nonstationary aspects of a field site on a larger spatial scale (trends) with a probabilistic treatment of unresolved structure on a smaller scale (residues).
Research output: Article 
, Jan 2001, In: Journal of Contaminant Hydrology. 47, 1, p. 2951 23 p. Abstract
We analyze a set of observations from a recently published, fieldscale tracer test in a fractured till. These observations demonstrate a dominant, underlying nonFickian behavior, which cannot be quantified using traditional modeling approaches. We use a continuous time random walk (CTRW) approach which thoroughly accounts for the measurements, and which is based on a physical picture of contaminant motion that is consistent with the geometric and hydraulic characterization of the fractured formation. We also incorporate convolution techniques in the CTRW theory, to consider transport between different regions containing distinct heterogeneity patterns. These results enhance the possibility that limitations in predicting nonFickian modes of contaminant migration can be overcome. (C) 2001 Elsevier Science B.V. All rights: reserved.
Research output: Article 

, Jan 2001, In: Water Resources Research. 37, 4, p. 909923 15 p. Abstract
The influence of fracture junction, solute transfer characteristics on transport patterns in discrete fracture networks is analyzed. Regular fracture networks with either constant or variable aperture distributions are considered in conjunction with particle tracking methods. Solute transfer probabilities at fracture junctions are determined from analytical considerations. The second spatial moment and the dilution index are used as measures of the spreading and the degree of channelized transport, respectively; these measures also account for varying mixing ratios at fracture junctions under different flow conditions. For fracture networks with variable aperture distributions, mixing conditions at fracture junctions, determined by the local flow conditions and by the junction geometry, are always dominated by complete mixing and streamline routing "endmember" cases. Moreover, the frequency distribution of the lowvelocity regime that arises from variable aperture distributions strongly affects channelized transport and local flow conditions in fracture networks. Simulations suggest that simplified particle tracking models of solute transport in discrete fracture networks will best represent largescale transport by assuming streamline routing, rather than complete mixing, at fracture junctions. Finally, analysis of both the constant and variable aperture distributions indicates that solute spreading may typically be underestimated in forced hydraulic gradient tracer tests owing to changes in local flow conditions at fracture junctions.
Research output: Article 
, Jan 2001, In: Transport in Porous Media. 45, 2, p. 303319 17 p. Abstract
The distribution of water and air phases in small blocks of porous sandstone is examined by using a simulated annealing technique that finds the minimum interfacial energy distributions at different saturations. Simulations are based on existing sandstone microstructures that were determined by Xray microtomography. At low saturations, some of the water is distributed in films along the walls of larger pore spaces, and connects to pendular structures in the crevices and smaller pores. As the amount of water in the pores increases the water films become thicker and pores fill from the pendular structures. The distribution of water voxels in the pore space is examined by calculating interfacial areas, by classifying water voxels as to whether they lie within films or clusters, and by determining the size and distribution of these film clusters. An exponential relationship is found between the fraction of water voxels in the films and the degree of saturation. In addition, the dependency of smallsample electrical conductivity on saturation is examined by using a random walk method.
Research output: Article 
, Jan 2001, In: Water Resources Research. 37, 10, p. 24932501 9 p. Abstract
The importance of fracture intersection mixing rules, complete mixing and streamline routing, on simulated solute migration patterns in random fracture networks is assessed, For this purpose, aad based on geological evidence, twodimensional model networks having power law fracture length distributions and lognormal fracture permeability distributions are considered. Different fracture network structures are accounted for by the power law length distribution, ranging from networks composed of infinite length fractures to percolation networks, with constant length fractures. Comparison of solute particle statistics shows that there is no significant difference between the bulk transport properties calculated with the two mixing rules. In fact, it is found that the choice of. Mixing assumptions has a significant influence in less than 5% of the total number of fracture intersections in most fracture networks. This result can be attributed to the small mean effective coordination number, defined as the number of branches connected to an intersection with nonzero flux. It is concluded that solute transport in fracture networks is strongly influenced by variability and uncertainty in parameters defining the geometrical structure of networks and that, by comparison, the choice of mixing rules at fracture intersections is of little importance.
Research output: Article 
, Jan 2001, Flow and Transport through Unsaturated Fractured Rock. Evans D. D., Rasmussen T. C. & Nicholson T. J.(eds.). Second ed. Washington, D.C.: Vol. 42. p. 183196 14 p. (Geophysical Monograph Series). Abstract
The nature of flow and transport through fractures crossing an unsaturated chalk formation were investigated in the northern Negev desert, Israel. An experimental setup was developed to allow controlled infiltration experiments through discrete, in situ fractures. Percolation experiments showed significant spatial and temporal flow variability through the fractures. Steady state flow was not reached for the duration of the experiments, either through individual small regions or across the entire flow domain, although the boundary conditions were kept relatively constant. Moreover, flow trajectories within the fracture plane, defined by tracer tests, varied over time. Over 70% of the fluid flux was transmitted through less than 20% of the studied fracture openings. Water flow through the fracture was focused into dissolution channels, which were typically associated with fracture intersections. The flow through these channels was governed primarily by the mineralogical composition of the filling material and the inner structure of the fracture voids. In particular, salt dissolution, solidparticle migration and clay swelling were found to be the main processes controlling flow through these dissolution paths; these processes account for the observed unstable flow regime.Our results suggest that models for simulating water percolation through fractures in the vadose zone, at least in chalk formations, should consider the mapping of fracture intersections, in addition to the more common mapping of fractures. Moreover, detailed characterization of these fracture geometries is not the sole key parameter determining fracture flow patterns  flow is also strongly controlled by physical variations in the filling materials during wetting and drying cycles.
Research output: Chapter 
, Jan 2001, Conceptual Models of Flow and Transport in the Fractured Vadose Zone. National Research Council(eds.). Wahington, DC: p. 115147 33 p. Abstract
Patterns of fluid flow and chemical transport in heterogeneous porous and fractured media tend to be highly complex. Models of flow and transport processes in these systems must account for the inherent heterogeneity and scaling properties of porous rocks, as well as the typically sparse and uncertain field data that can be obtained to characterize a geological formation. Recent introduction of advanced theoretical and experimental techniques is providing new insight into our understanding of these highly nonuniform patterns. Statistical network models can be used to characterize the structure of pore and fracture systems, and to define power laws that quantify flow and transport processes within them. In a similar spirit, a random walk formalism can quantify anomalous (nonGaussian) patterns of chemical transport that are frequently observed in laboratory and field experiments. Analyses of transport of reactive chemicals, including effects of precipitation and dissolution, as well as changes in fracture morphology, also demonstrate highly nonuniform behavior. In the context of these results, we discuss some conceptual and quantitative models of fluid flow and chemical transport in the fractured vadose zone, and the laboratory and field data that are required to evaluate them.
Research output: Chapter
2000

, Nov 2000, In: Geology. 28, 11, p. 10511054 4 p. Abstract
The structures of geological formations, as well as flow and chemical transport patterns within them, are profoundly affected by chemical dissolution and precipitation processes (i,e,, the interactions among flow, chemical transport, buoyancy, and dissolution and precipitation reactions). These processes are intrinsically hard to measure, and therefore are not well understood. Nuclear magnetic resonance imaging is applied to study the dynamic behavior of coupled flow and dissolution in natural rock fractures. Our findings reveal that flow and transport in evolving fractures are far more unpredictable than commonly assumed, due to complex interactions among fracture morphology, flow, dissolution, and buoyancy. This can explain physical processes causing catastrophic collapse and subsurface structural instabilities, such as sinkholes and land subsidence.
Research output: Article 
, 14 Sep 2000, In: Journal Of Physical Chemistry B. 104, 36, p. 87628762 1 p. Abstract
Following are two corrections to the paper. The analysis, results, and conclusions remain unchanged.
Research output: Article 
, Aug 2000, In: Transport in Porous Media. 40, 2, p. 145151 7 p. Abstract
Calculations of effective conductivities of generalized random bond lattices representing porous media are compared to approximations using effective medium theory (EMT). We use numerical simulations of flow through 2D and 3D random lattice models, which allow for variable lattice densities and a lognormal distribution of local conductivities, to compare effective conductivities to effective medium approximations. We find that the analytical expressions provide good agreement to the simulations in 2D systems, but are in significant error in 3D systems when the standard deviation of the local conductivities is large.
Research output: Article 
, Jul 2000, In: Mathematical Geology. 32, 5, p. 543560 18 p. Abstract
Monte Carlo simulation was used to examine the error (statistical bias) introduced in estimating a sample semivariogram through application of oriented sample pattern to variables which are correlated with fracture orientation. Sample semivariograms of the directional components of the water velocity were used to illustrate that oriented sampling schemes can provide biased data sets which result in error in the estimation of the semivariogram, particularly in the estimation of the sill (or variance). Three sampling patterns were used to analyze directional semivariograms of the components of the fluid velocity: sampling along lines parallel to the mean regional hydraulic gradient, sampling among lines perpendicular to the mean regional hydraulic gradient, and sampling along fracture segments. The first two sampling patterns were shown to introduce substantial error in the sills of the velocity variograms. it is argued that this error is due to the combination of unequal sampling of fractures with different orientations (i.e., sampling bias) and the systematic variation in the magnitude of the velocity components with orientation of the fracture. As a consequences, it is suggested that correction factors developed to correct fracture frequency statistics need to be extended to improve estimation of spatial moments of variables which are correlated with fracture orientation.
Research output: Article 
, Jul 2000, In: Geophysical Research Letters. 27, 14, p. 20612064 4 p. Abstract
A new method to quantify fracture network connectivity is developed and applied to analyze two classical examples of fault and joint networks in natural geological formations. The connectivity measure accounts for the scaling properties of fracture networks, which are controlled by the power law length distribution exponent a, the fractal dimension D and the fracture density. The connectivity behavior of fracture patterns depends on the scale of measurement, for a <D + 1, but is independent of scale for a > D + 1. Analysis of the San Andreas fault system shows that a <D + 1 and that the connectivity threshold is reached only at a critical length scale. In contrast, for a typical sandstone joint pattern, a approximate to D + 1, which is on the cusp where the connectivity threshold is highly sensitive to the minimum fracture length in the system.
Research output: Article 
, May 2000, In: Ground Water. 38, 3, p. 444451 8 p. Abstract
The mechanisms controlling fluid flow through fractures intersecting chalk in the vadose zone were studied through mater percolation experiments in natural discrete fractures and by close examination of the inner structure of fracture voids. The percolation experiments showed that the flow is focused in dissolution channels along the fracture plane, and that fluxes and Row trajectories within that net vary in both time and space. The locations of the dissolution channels, the main potential flowpaths within the fracture plane, were generally associated with fracture intersections, The flow through. these channels was governed primarily by the mineralogical composition of the filling material and the inner structure of the fracture voids. Salt dissolution, solidparticle migration, and clay smelling were found to be the predominant processes controlling flow through the dissolution channels, These physical changes in the structure of the filling material in the dissolution channels accounted for the observed unstable flow behavior. Our results suggest that models aimed at simulating water percolation through fractures in unsaturated chalk should consider the mapping of fracture intersections in addition to the commonly used mapping of fracture lineaments, Moreover, the detailed characterization of fracture apertures may not he the key parameter determining fracture Row, because in such formations the flow. is controlled primarily. by filling material. These materials undergo significant physical variations during wetting and drying cycles.
Research output: Article 
, Apr 2000, In: Journal Of Physical Chemistry B. 104, 16, p. 39423947 6 p. Abstract
The behavior of chemical species as they migrate through heterogeneous porous media is considered. The socalled "anomalous'' transport patterns frequently measured in these materials are quantified in the framework of a continuous time random walk (CTRW) formalism. The physical basis for application of the CTRW is discussed, and new solutions for the first passage time distribution are presented to covet the entire range of transport behaviors. Application of these solutions to analysis of experimental data is also discussed.
Research output: Article 
, Jan 2000, In: Water Resources Research. 36, 1, p. 149158 10 p. Abstract
We analyze measured breakthrough curves in a laboratory model which consists of a uniformly heterogeneous porous medium; these curves were previously shown to be indicative of scaledependent transport and therefore inconsistent with the (macroscopic) advectiondispersion equation [Silliman and Simpson, 1987]. Our analysis is based on an analytical expression for the firstpassage time distribution (FPTD) of migrating contaminants in random media, developed with the use of a continuous time random walk (CTRW) formalism. The general CTRW has been shown to be effective in quantifying anomalous transport patterns frequently observed in fractured and strongly heterogeneous porous media [Berkowitz and Scher, 1997, 1998]. We calculate a family of FPTD curves, usually referred to as "breakthrough curves," which are a function of an exponent beta; this exponent is related to the lowvelocity tail of the velocity distribution. The FPTD curves fit well the measured data, with a single value of the beta exponent over the spatial/temporal scale of the experiment. This is in contrast to previous analyses using solutions of the Gaussianbased advectiondispersion equation with timeindependent parameters in a uniform flow held. We conclude that the CTRW may allow analysis of transport in porous media subject to complex heterogeneities at large scale, which may not be amenable to analysis using classical advectiondispersion theory. Hence the CTRW represents a potentially valuable tool in the assessment of dispersive processes in heterogeneous porous media.
Research output: Article
1999

, Dec 1999, In: Water Resources Research. 35, 12, p. 39553959 5 p. Abstract
Nuclear magnetic resonance imaging is applied to measure flow patterns in natural, watersaturated, roughwalled rock fractures. From threedimensional water density and velocity vector images the fracture morphology and flow patterns are determined. The parabolic nature and asymmetry of the velocity;profiles, and thus the accuracy of local cubic law flow rate predictions, Vary greatly. This depends on the degree of wall roughness. Particularly complex flow patterns are found in one sample which contains a sharp fracture wall discontinuity. A power law for the flow rate versus aperture for the lowflow region was found without considering the hydraulic gradients.
Research output: Article 
, Nov 1999, In: Water Resources Research. 35, 11, p. 33153326 12 p. Abstract
Flow through a natural fracture crossing unsaturated chalk in an arid region was investigated in a field experiment using a speciality designed experimental setup. The setup allowed complete control of the flow domain inlet and outlet. Water flux into and out of the fracture was measured in small segments of the fracture openings, and flow trajectories were identified using seven fluorobenzoic acid tracers. A 5 day percolation experiment on a 5.3 m long fracture showed significant spatial and temporal variability of the flow regime. Flow through fracture openings did not reach a steady state either in individual segments or across the entire flow domain, although the boundary conditions were kept relatively steady for the entire duration of the experiment. Flow trajectories within the fracture plane varied over time; however, most of the flow was confined to small sections of the fracture. Over 70% of the flux was transmitted through
Research output: Article 
, Feb 1999, In: Icarus. 137, 2, p. 348354 7 p. Abstract
We describe a Monte Carlo model that simulates dust migration in a porous cometary nucleus. We present computations for media in which the poresize distributions are either random or normal; additional computations indicate that media with powerlaw size distributions behave very similarly to random distributions. We show how the average time to cross the medium varies as a function of porosity and how the structure of the medium varies with time. Implications for the structure of the cometary nucleus are discussed. (C) 1999 Academic Press.
Research output: Article 
, Jan 1999, In: Geophysical Research Letters. 26, 12, p. 17651768 4 p. Abstract
We use numerical simulations to examine the variability of flow patterns in representative fracture intersection geometries. In contrast to existing studies of perfectly orthogonal intersections, we demonstrate that more realistic geometries lead to a rich spectrum of flow patterns. Moreover, numerical solutions of the NavierStokes equations in these fracture intersections indicate that nonlinear inertial effects become important for Reynolds numbers as tow as 1100. Such Reynolds numbers often exist in naturally fractured formations, particularly in karst systems and in the vicinity of wells during pump tests.
Research output: Article 
, Jan 1999, In: Water Resources Research. 35, 2, p. 347360 14 p. Abstract
The application of nuclear magnetic resonance imaging (NMRI) to the direct threedimensional measurement of flow in roughwalled watersaturated rock fractures is presented for the first time. The study demonstrates the abilities of NMRI to noninvasively measure rockwater interfaces and water flow velocities in these fractures and investigates the effects of wall morphology on flow patterns inside a typical rock fracture. Two and threedimensional flowencoded spinecho pulse sequences were applied. The stability and reproducibility of the water flow patterns were confirmed by analyzing twodimensional velocity images. A variety of geometrical and hydraulic features were determined from threedimensional velocity images, including the rockwater interfaces, the fracture aperture distribution, and the critical aperture path; velocity profiles and volumetric flow rates; flow and stagnant regions; and the critical velocity path. In particular, the effects of a sharp step discontinuity of the fracture walls and the applicability of the cubic law were examined. As a result of the complex threedimensional geometry, velocity profiles are generally parabolic but often highly asymmetric, with respect to the fracture walls. These asymmetric velocity profiles are clustered together, with significant correlations; they are not just local random phenomena. However, theoretical considerations indicate that the effects of the measured asymmetry on volumetric flow rates and hydraulic conductivities are insignificant, in that the overall flow inside rough fractures still obeys the cubic law. The features discussed in this study emphasize the strong heterogeneity and the highly threedimensional nature of the flow patterns in natural rock fractures and consequently the need for threedimensional flow analysis.
Research output: Article
1998

, Nov 1998, In: Water Resources Research. 34, 11, p. 28112825 15 p. Abstract
We investigate the validity of applying the "local cubic law" (LCL) to flow in a fracture bounded by impermeable rock surfaces. A twodimensional orderofmagnitude analysis of the NavierStokes equations yields three conditions for the applicability of LCL flow, as a leadingorder approximation in a local fracture segment with parallel or nonparallel walls. These conditions demonstrate that the "cubic law" aperture should not be measured on a pointbypoint basis but rather as an average over a certain length. Extending to the third dimension, in addition to defining apertures over segment lengths, we find that the geometry of the contact regions influences flow paths more significantly than might be expected from consideration of only the nominal area fraction of these contacts. Moreover, this latter effect is enhanced by the presence of nonLCL regions around these contacts. While contact ratios of 0.10.2 are usually assumed to have a negligible effect, our calculations suggest that contact ratios as low as 0.030.05 can be significant. Analysis of computergenerated fractures with selfaffine walls demonstrates a nonlinear increase in contact area and a fasterthancubic decrease in the overall hydraulic conductivity, with decreasing fracture aperture; these results are in accordance with existing experimental data on flow in fractures. Finally, our analysis of fractures with selfaffine walls indicates that the aperture distribution is not lognormal or gamma as is frequently assumed but rather truncatednormal initially and increasingly skewed with fracture closure.
Research output: Article 
, Sep 1998, In: Water Resources Research. 34, 9, p. 21032121 19 p. Abstract
We present a threedimensional (3D) model of fractures that within the same framework, allows a systematic study of the interplay and relative importance of the two key factors determining the character of flow in the system. The two factors of complexity are (1) the geometry of fracture plane structure and interconnections and (2) the aperture variability within these planes. Previous models have concentrated on each separately. We introduce anisotropic percolation to model a wide range of fracture structures and networks. The conclusion is that either of these elements, fracture geometry and aperture variability, can give rise to channeled flow and that the interplay between them is especially important for this type of flow. Significant outcomes of our study are (1) a functional relationship that quantifies the dependence of the effective hydraulic conductivity on aperture variability and on the network structure and fracture element density, (2) a relation between aperture variability and the Peclet number, and (3) a basis for a new explanation for the fieldlength dependence of permeability observed in fractured and heterogeneous porous formations.
Research output: Article 
, Aug 1998, In: Geology. 26, 8, p. 755758 4 p. Abstract
The level of the Dead Sea (the lowest surface on Earth) is currently declining at a rate of 0.8 m/yr, and has dropped about 20 m since the beginning of the twentieth century; it reached 410 m in 1997, We address the question of whether the level of the Dead Sea will continue to decline. A numerical model, developed in this study to determine the water balance, accounts for the increase in salinity and the concomitant decrease in the rate of evaporation that accompanies reduction in the activity of the water. Simulations based on ranges of water withdrawal scenarios suggest that the Dead Sea will not "die"; rather, a new equilibrium is likely to be reached in about 400 yr after a waterlevel decrease of 100 to 150 m.
Research output: Article 
, Jul 1998, In: Journal of Geophysical ResearchSolid Earth. 103, B7, p. 1533915360 22 p. Abstract
Relationships between threedimensional fracture networks consisting of polydisperse disks and the corresponding twodimensional trace maps are systematically analyzed. Bulk densities of disks and disk intersections are related to surface densities of traces and trace intersections; this results in a new relation for the average length of disk intersections. The probability densities of trace lengths and disk intersections are studied for several disk diameter distributions. The inverse problem of deriving the disk distribution from the trace distribution is then solved, assuming only that the disks have uniformly random locations and orientations. These results are applied to a variety of synthetically generated data, as well as to several sets of field data. Analysis of the field data suggests that fracture diameter distributions follow a power law, in agreement with previous conclusions based on trace length histograms, with exponents varying from 1.3 to 2.1.
Research output: Article 
, May 1998, In: Ground Water. 36, 3, p. 444449 6 p. Abstract
A new methodology was developed for the in situ investigation of flow and transport processes through undisturbed, discrete fractures in the vadose zone. The experimental setup and technical means were designed for a scale of several meters, larger than any conceivable laboratory experiment. The setup consists of four components: (1) a 25 cm diameter horizontal borehole is coredrilled along a vertical, discrete fracture plane, exposing the fracture at the borehole ceiling; (2) compartmental ponds are installed along the traced fracture on the horizontal part of the outcrop, Each compartment (25 cm long) is connected to a separate feeding source, which can be tagged by a different tracer, and the water head is electronically controlled. Thus, each segment of the exposed fracture could be subjected to a different flux with a specific tracer under a constant hydraulic head; (3) a compartmental sampler, divided into 20 cm long cells, is installed beneath the compartmental ponds in the horizontal borehole, The effluent draining from a particular fracture segment is collected by individual cells of the sampler; (4) the percolating fluids accumulating in the various sampler cells are frequently drained by a collection system into individual sampling vessels. This experimental setup was fieldtested with untagged water in preliminary experiments in fractured chalk. It can provide unique and important information about flowpath distributions along a natural fracture, and about the chemical evolution of the solutions percolating through the fractures.
Research output: Article 
, Apr 1998, In: Water Resources Research. 34, 4, p. 611622 12 p. Abstract
Modeling the migration of spilled nonaqueous phase liquids (NAPLs) is currently difficult because the physics governing their movement is complex and knowledge of the local geology is always incomplete. NAPL movement is subject to buoyancy, capillary, and viscous forces in addition to being directed by the particular structural and hydraulic properties of the porous medium. Consideration of buoyancy forces suggests that the flow regime diagram of Lenormand et al. [1988] can be expanded to a third dimension. We develop a generalized growth model, based on invasion percolation, that captures the essential physics of initial NAPL migration but is simple enough computationally that simulations can be conducted much faster than by using continuum simulation models that attempt to capture all details of the physics. In comparison with available experimental data, our model realistically simulates movement of a NAPL for a wide range of values of Bond and capillary numbers, in any kind of porous medium. Because this approach allows much faster and simpler simulation than other approaches, a higher spatial resolution and/or the use of Monte Carlo methods to reduce the effect of geological uncertainty becomes a realistic possibility.
Research output: Article 
, Mar 1998, In: Water Resources Research. 34, 3, p. 457470 14 p. Abstract
The precipitation and dissolution of reactive solutes, transported under the action of fully developed laminar flow in saturated fractures, is analyzed assuming an irreversible firstorder kinetic surface reaction for one component. Equations describing solute transport, precipitation and dissolution, and the evolution of fracture aperture were approximated and solved using combined analytical and numerical techniques; dimensionless transport parameters incorporated into the solutions were estimated from data available in the literature. Fractures with initially flat, linearly constricted, and sinusoidal apertures were investigated. The initial fracture geometry and the solute saturation content of the inflowing fluid have a profound effect on the reaction processes. The results show that the evolution of the solute transport and fracture geometry can be adequately described by the Damkohler and Peclet numbers. Two extreme transport regimes were identified: relatively uniform evolution of fracture apertures and nonuniform evolution of fracture apertures restricted to the inlet region of fractures. In the case of precipitation with halflife times of the order of seconds to years and with fluid residence times of the order of minutes to days, the time for a fracture to close completely is of the order of days to millions of years. This is consistent with the order of magnitude of hydrogeological timescales. In the model the process of dissolution is the inverse of precipitation, although the combined solute transport and reaction processes are irreversible. These results and the applied dimensionless analysis can be used as a basis for the development of more complex models of reactive solute transport, precipitation, and dissolution in saturated fractured media.
Research output: Article 
, Jan 1998, In: Surveys in Geophysics. 19, 1, p. 2372 50 p. Abstract
The application of percolation theory to porous media is closely tied to network models. A network model is a detailed model of a porous medium, generally incorporating porescale descriptions of the medium and the physics of porescale events. Network models and percolation theory are complementary: while network models have yielded insight into behavior at the pore scale, percolation theory has shed light, at the larger scale, on the nature and effects of randomness in porous media. This review discusses some basic aspects of percolation theory and its applications, and explores work that explicitly links percolation theory to porous media using network models. We then examine assumptions behind percolation theory and discuss how network models can be adapted to capture the physics of water, air and solute movement in soils. Finally, we look at some current work relating percolation theory and network models to soils.
Research output: Article 
, Jan 1998, In: Physical Review E. 57, 5, p. 58585869 12 p. Abstract
We show that dominant aspects of chemical (particle) transport in fracture networksnonGaussian propagationresult from subtle features of the steady howheld distribution through the network. This is an outcome of a theory, based on a continuous time random walk formalism, structured to retain the key spacetime correlations of particles as they are advected across each fracture segment. The approach is designed to treat the complex geometries of a large variety of fracture networks and multiscale interactions. Monte Carlo simulations of steady flow in these networks are used to determine the distribution of velocities in individual fractures as a function of their orientation. The geometry and velocity distributions are used, in conjunction with particle mixing rules, to map the particle movement between fracture intersections onto a joint probability density psi(r,t). The chemical concentration plume and breakthrough curves can then be calculated analytically. Particle tracking simulations on these networks exhibit the same nonGaussian profiles, demonstrating quantitative agreement with the theory. The analytic plume shapes display the same basic behavior as extensive field observations at the Columbus Air Force Base, Mississippi. The quantitative correlation between the time dependence of the mean and standard deviation of the field plumes, and their shape, is predicted by the theory.
Research output: Article
1997

, Nov 1997, In: Physical Review Letters. 79, 20, p. 40384041 4 p. Abstract
We show that dominant aspects of contaminant (particle) transport in random fracture networksnonGaussian propagationresult from subtle features of the steady flowfield distribution through the network. This is an outcome of a new theory, based on a continuous time random walk formalism, structured to retain the key spacetime correlations of contaminants as they are advected across each fracture segment. Particle tracking simulations on these networks exhibit the same nonGaussian profiles, demonstrating quantitative agreement with the theory.
Research output: Article 
, Aug 1997, In: Physical Review E. 56, 2, p. 13791395 17 p. Abstract
We use a mapping between the continuum percolation model and the Potts fluid (a system of interacting sstate spins which are free to move in the continuum) to derive the lowdensity expansion of the pair connectedness and the mean cluster size. We prove that given an adequate identification of functions, the result is equivalent to the density expansion derived from a completely different point of view by Coniglio, DeAngelis, and Forlani [J. Phys. A 10, 1123 (1977)] to describe physical clustering in a gas. We then apply our expansion to a system of hypercubes with a hard core interaction. The calculated critical density is within approximately 5% of the results of simulations, and is thus much more precise than previous theoretical results which were based on integral equations. We suggest that this is because integral equations smooth out overly the partition function (i.e., they describe predominantly its analytical part), while our method targets instead the part which describes the phase transition (i.e., the singular part).
Research output: Article 
, Jun 1997, In: Journal of Geophysical ResearchSolid Earth. 102, B6, p. 1220512218 14 p. Abstract
We have analyzed the fractal and multifractal nature of a series of 17 natural fracture trace maps, representing a wide variety of scales, geological settings, and lithologies, as well as a number of typical synthetic fracture networks in which fracture locations, orientations, and lengths are drawn from various probability distribution functions. Recent studies have shown that multifractal methods can be used to investigate fracture networks at greater depth, since the fractal dimension represents only part of the scaling spectrum characterizing each network. We find that the real and synthetic fracture maps display fractal and multifractal properties. Moreover, the properties of the synthetic networks are very similar to those of the real networks, with nontrivial fractal dimensions and multifractal spectra. We suggest that different fracturing mechanisms can lead to two or more distinct subranges over which a fractal dimension can be defined, while the heterogeneity of the rock, and the nature of the fracturing mechanisms, lead to multifractal properties. We also find that the fractal dimension of a synthetic fracture network is relatively insensitive to parameters such as fracture length and orientation but can be controlled by appropriate choice of the relative fracture density.
Research output: Article
1996

, May 1996, In: Geophysical Research Letters. 23, 9, p. 925928 4 p. Abstract
Crystalline rock formations are prime candidates for siting of repositories for radioactive and toxic wastes. Even the possibility of tenuous proximity of these sites to the biosphere requires realistic means of predicting subtle features of contaminant migration, such as very lowlevel seepage. We generate percolation clusters to reproduce the often observed ramified embedded fracture structures in these formations. Diffusion paths through these clusters and the shortest spans of rock between them can so significantly decrease contaminant breakthrough times that previous estimates can be in error by up to an order of magnitude. Our analysis suggests that current methods for determining the suitability of geological formations as natural barriers to contamination are inadequate, and may result in dangerously misleading conclusions.
Research output: Article 
, Apr 1996, In: Water Resources Research. 32, 4, p. 901913 13 p. Abstract
The transport of reactive and nonreactive solutes under the action of fully developed laminar flow in a parallel plate fracture has been analyzed. Three types of surface reactions are examined: (1) irreversible firstorder kinetic, (2) instantaneous reversible, and (3) reversible firstorder kinetic. Approximate analytical models for the dispersion of nonreactive and reactive solutes with an irreversible firstorder reaction are developed, and numerical ''exact'' solutions for the three surface reaction types are obtained. The conditions under which the approximate solutions hold are determined by comparison with the numerical solutions. The solute migration patterns and the extent of retardation due to surface reactions are then analyzed and compared with the nonreactive case. Dimensionless reaction coefficients incorporated into the solutions are estimated from data available in the literature. It is found that the approximate solutions are consistent with the numerical solutions; that the criterion for applicability of a local equilibrium assumption is based on the values of dimensionless time and a dimensionless number representing the ratio of the rate at which the surface reaction reaches equilibrium to the rate of the molecular diffusion in the transverse direction; and that the effect of surface reaction can be described by a retardation factor R(f) = 1 + Kd* for the case in which the reaction can be assumed at equilibrium, with small Peclet number, small dimensionless distribution coefficient Kd*, and large dimensionless time. Conditions are also found under which reactive solute transport can be well approximated by nonreactive solute transport and reversible reactions can be treated as irreversible. These results and the dimensionless analysis method employed herein may serve as a basis for development of more complex models of reactive solute transport in saturated fractured media.
Research output: Article
1995

, Oct 1995, In: Physical Review E. 52, 4, p. 44824494 13 p. Abstract
We compute the percolation threshold of systems of interacting particles by a tandemadding algorithm with a rejection criterion based on the density distribution of the particles. The results are very close to those obtained in our previous work based on a simple Boltzmann centralparticle approximation. The results are also essentially the same as those obtained by the Metropolis method, even though our algorithm is conceptually different and does not generate a true equilibrium, configuration. This finding suggests that connectivity, in comparison with other system properties, is more ''general'' and is not sensitive to the particulars of the equilibrium state. Thus, our findings offer an efficient method for obtaining percolation thresholds in systems of interacting particles. This method is computationally simpler and faster than the well known Metropolis method.
Research output: Article 
, Oct 1995, In: Geophysical Research Letters. 22, 20, p. 27612764 4 p. Abstract
We report here, for the first time, the finding of a 24 to 31 m deep, 10,000 y old, watersaturated and highly hydraulically conductive salt layer composed of idiomorphic halite crystals in the coastal area of the Dead Sea. The high hydraulic conductivity of the layer was evidenced by laboratory and field tests and by the rapid fluctuations of the water table, in a well penetrating the layer, following variations in the water level of the Dead Sea. Such layers may lead to intensive and rapid flow of water and nonpolar liquids.
Research output: Article 
, Sep 1995, In: Journal of Statistical Physics. 80, 56, p. 14151423 9 p. Abstract
Conductivity behavior of continuum percolation in restricted twodimensional domains is simulated by considering systems of randomly distributed disks. The domain is restricted in that conducting objects are permitted to lie in only a portion of the domain. Such a restricted domain might better approximate some natural systems. Simulations of twodimensional systems, based on three distributions of local conductances, are examined and found to demonstrate a powerlaw behavior with conductivity exponents smaller than those arising in regular lattice and continuum percolation.
Research output: Article 
, Jun 1995, In: Water Resources Research. 31, 6, p. 14611466 6 p. Abstract
A key characterization of dispersion inaquifers and other porous media has been to map the effects of inhomogeneous velocity fields onto a Fickian dispersion term (D) within the context of the conventional advectiondispersion equation (ADE), Recent compilations of data have revealed, however, that the effective D coefficient is not constant but varies systematically with the length or timescale over which transport occurs. A natural strategy to encompass this ''anomalous'' behavior into the context of the conventional ADE is to make D time dependent. This approach, to use D(t) to handle the same anomalous dispersion phenomena, has also been common in the field of electronic transport in disordered materials. In this paper we discuss the intrinsic inadequacy of considering a timedependent dispersivity in the conventional ADE context, and show that the D = D(t) generalization leads to quantifiably incorrect solutions. In the course of proving this result we discuss the nature of anomalous dispersion and provide physical insight into this important Problem in hydrogeology via analysis of a class of kinetic approaches. Particular emphasis is placed on the effects of a distribution of solute ''delay times'' with a diverging mean time, which we relate to configurations of preferential pathways in heterogeneous media.
Research output: Article 
, May 1995, In: Mathematical Geology. 27, 4, p. 467483 17 p. Abstract
Connectivity aspects of fracture networks are analyzed in terms of percolation theory. These aspects are of fundamental importance in characterization, exploitation, and management of fractured formations. General connectivity and power law relationships are determined that characterize the density of fractures and average number of intersections per fracture necessary to ensure network connectivity, the likelihood of a fractured formation being hydraulically connected, and the probability that any specific fracture is connected to the conducting portion of the network. Monte Carlo experiments with a twodimensional fracture network model confirm the percolation theory predictions. These relationships may prove useful in formulating theoretically tractable approximations of fracture networks that capture the essential system properties.
Research output: Article 
, May 1995, In: Aquaculture. 133, 1, p. 920 12 p. Abstract
Removal of organic matter and nitrate was studied in a laboratoryscale treatment system consisting of a digestion basin and a fluidized bed reactor. Fish feed was anaerobically degraded in the digestion basin and supernatant from the digestion basin, rich in dissolved organic degradation products, was used to fuel nitrate removal by denitrifying organisms in the fluidized bed reactor. Anaerobic digestion of the feed was determined insitu using nylonmesh bags. Feed degradation was described by considering the feed to consist of two fractions: a labile, rapidly degradable fraction and a recalcitrant, slowly degradable fraction. By using firstorder kinetics, the degradation rate constants of each of these fractions were obtained allowing a quantitative prediction of sludge accumulation in the digestion basin. It was predicted that degradation rates and accumulation rates of sludge reached equilibrium after approximately 400 days of operation. The amount of sludge at equilibrium was approximately 23 times the weight of the feed which was added daily. The release of volatile fatty acids during fermentation of fish feed and sludge was determined as it is these organic compounds that mediate the denitrifying activity in the fluidized bed reactor. Predicted values for sludge accumulation and volatile fatty acid release were in agreement with measured values.
Research output: Article 
, Apr 1995, In: Water Resources Research. 31, 4, p. 893902 10 p. Abstract
The water level of the Dead Sea, a terminal hypersaline lake (total dissolved solids, approximately 340 g/L) has decreased at an average rate of 0.5 m/yr since 1960 and by 0.8 m/yr between 1981 and 1989. The dramatic longterm water level variation of the Dead Sea and the seasonal shortterm fluctuations are accompanied by parallel variations of groundwater levels in an adjacent aquifer. A general methodology based on a simplified yet reliable onedimensional flow model, together with continuous measurements of groundwater levels in observation wells, enables analysis of aquifer structural and hydraulic properties. Furthermore, this analysis enables prediction of future groundwater levels in unconfined and confined aquifers due to future changes in lake levels.
Research output: Article
1994

Modelling flow and contaminant transport in fractured media, Jan 1994, Advances in Porous Media. Corapcioglu Y.(eds.). Amsterdam: Vol. 2. p. 395449 55 p. AbstractResearch output: Chapter

, Jan 1994, In: Water Resources Research. 30, 6, p. 17651773 9 p. Abstract
Models of solute transport in fractured geologic media that are based on the discrete network approach require that a method be adopted for transferring mass through each fracture intersection. The two usual models for mass partitioning between the outflow branches of crossing fractures assume either stream tube routing or complete mixing. A mathematical analysis of twodimensional, laminar flow through the intersection of two orthogonal fractures with smooth walls is carried out to examine the mixing process. Mixing ratios are expressed in terms of a local Peclet number (Pe = vr/D), where v is an average fluid velocity within the fracture intersection, r is the radius of the fracture intersection, and D is the diffusion coefficient. As a general observation the concept of complete mixing within a fracture intersection does not properly represent the mass transfer process at any value of the Peclet number. A mixing ratio equivalent to complete mixing may be observed, but only for particular flow geometries and in a limited range of the Peclet number. Stream tube routing models provide a good approximation for Peclet numbers greater than 1; and in some cases this limit may be as low as 10(2). The actual value of the lower limit depends upon the geometry of the bounding streamline that separates the flow into the two outflow fractures, in relation to the fracture through which solute enters the intersection. There is a range in the Peclet number, of roughly 3 orders of magnitude, where the extent of mixing is dependent upon the value of Pe within the intersection.
Research output: Article 
An analysis of two automatic historymatching procedures for estimation of subsurface reservoir properties, 1 Jan 1994, In: Israel Journal of Earth Sciences. 43, 34, p. 239247 9 p. Abstract
An intuitive, trialanderror approach to historymatching (parameter identification) can be costly and timeconsuming. In an attempt to reduce these factors, considerable efforts have been made, primarily in the petroleum engineering literature, to automate historymatching procedures for implementation on highspeed computers; and several methods based on ex post facto techniques have been developed for this purpose. This study examines two frequently used automatic historymatching algorithms and demonstrates their fundamental weaknesses. Authors
Research output: Article 
, 1 Jan 1994, In: Physical Review E. 49, 2, Abstract
A generalization of the randomadding procedure for the determination of percolation parameters in interacting systems is demonstrated. This method which simply utilizes the Boltzmann distribution function is shown to reproduce quite accurately results which were obtained previously by the much less efficient and much less direct method of the Metropolis algorithm. The success of the present method is attributed to the fact that, for typical objects considered in such systems, the effect of the squarewell attractive interaction compensates for the effect of the (hardcore) repulsive interaction on the spatial distribution of the objects around a given object.
Research output: Article 
, 1 Jan 1994, In: Journal of Geophysical Research. 99, B3, p. 44954503 9 p. Abstract
Geysers are systems that exhibit hydrothermal eruptive behavior at irregular and, occasionally, relatively regular intervals. Because geyser dynamics are governed by strongly nonlinear differential equations, it is reasonable to expect that these systems are capable of displaying chaotic behavior. Geyser dynamics are shown to be analogous to a simple conceptual model known to exhibit chaotic behavior. State space reconstructions of eruption interval data then show that the geyser Old Faithful erupts at chaotic intervals. Establishing the system as chaotic explains the inability to predict longterm eruptive behavior of Old Faithful. Authors
Research output: Article
1993

, Dec 1993, In: Water Resources Research. 29, 12, p. 41754175 1 p. AbstractResearch output: Article

, 15 Mar 1993, In: Journal of Hydrology. 143, 34, p. 169190 22 p. Abstract
In the Beer Sheva region of the Negev desert, the only significant fresh groundwater is contained within the Judea Group carbonate aquifer. It is found that this aquifer holds two distinctly different old water bodies. One such groundwater body has evolved in equilibrium with the carbonate aquifer rocks after being recharged during the Holocene in the Hebron Mountains north of the study area. At present, modern recharge, as denoted by the tritium and radiocarbon contents, is very minor. A subtle 'piston effect' generated by contemporary replenishment is discussed in representative hydrographs in Beer Sheva wells. Another groundwater body identified in the Judea Group aquifer derives from the underlying Kurnub Group aquifer. The regional artesian Kurnub Group aquifer (Nubian Sandstone) contains an older and brackish groundwater body which has been recharged in Sinai during Pleistocene pluvials. Faulting in the Beer Sheva region facilitated hydrologic contact between the two aquifers. Exploitation of the Judea Group has released confining pressures and resulted in the intrusion of Kurnub Group water into the overlying Judea Group carbonate aquifer. This process is most significant in those wells drilled close to major faults where salinity increases with pumping. The intruding water originating from the Kurnub Group sandstone aquifer has not yet equilibrated chemically with the carbonate host. The low pH and high temperatures that have been encountered indicate continuing and very recent intrusion. In the Beer Sheva area, in the absence of direct significant modern recharge (as determined from tritium and 14C values), all waters should be considered as paleowaters that are being mined. A complete revision of the hydrologic concept by which the multiple aquifer system can be exploited is required, to take into account the fact that the fresh Judea Group groundwater is actually an old (Holocene) water body intruded by brackish and older (Pleistocene) water along fault zones.
Research output: Article 
, 1 Jan 1993, In: Water Resources Research. 29, 4, p. 775794 20 p. Abstract
The theory of percolation, originally proposed over 30 years ago to describe flow phenomena in porous media, has undergone enormous development in recent years, primarily in the field of physics. The principal advantage of percolation theory is that it provides universal laws which determine the geometrical and physical properties of the system. This survey discusses developments and results in percolation theory to date, and identifies aspects relevant to problems in groundwater hydrology. The methods of percolation theory are discussed, previous applications of the theory to hydrological problems are reviewed, and future directions for study are suggested.
Research output: Article 
, Jan 1993, In: Ground Water. 31, 1, p. 3340 8 p. Abstract
Groundwater management decisions are usually taken under uncertainty, since they depend on unknown parameters of the aquifer such as hydraulic conductivity and specific discharge. This study applies a number of analytical techniques to a case study in order to demonstrate the potential effect of vertical heterogeneity in the horizontal component of specific discharge on evaluating contaminant travel time in an aquifer. The modified point dilution technique developed by Ronen et al. (1986) is applied to study the vertical variability of the horizontal component of specific discharge in a deep unconfined sandy aquifer. This technique, used under natural flow conditions, employs multilayer sampler, a tracer, and a mathematical diffusion model. Also analyzed are data from a very large unplanned trac er test where the ''tracer,'' sewage effluent with a high chloride content, was infiltrated into the aquifer for about 30 years, To date, based on available sedimentological evidence and pumping tests, the aquifer has been regarded as homogeneous. However, information from analysis of the tracer test data by two different flow models, and findings obtained by the modified point dilution technique, indicate the existence of zones of high hydraulic conductivity with specific discharges one order of magnitude higher than expected. As a consequence, chloride breakthrough in a pumping well downstream of effluent infiltration was detected after 110 years, at least 70 years earlier than could have been estimated from previously available data. The results demonstrate that consideration must be given to vertical heterogeneity when evaluating contaminant transport and show that detailed sitespecific field studies are needed in order to prevent or control aquifer contamination.
Research output: Article
1992

, 1 Nov 1992, In: Transport in Porous Media. 9, 3, p. 275286 12 p. Abstract
While percolation theory has been studied extensively in the field of physics, and the literature devoted to the subject is vast, little use of its results has been made to date in the field of hydrology. In the present study, we carry out Monte Carlo computer simulations on a percolating model representative of a porous medium. The model considers intersecting conducting permeable spheres (or circles, in two dimensions), which are randomly distributed in space. Three cases are considered: (1) All intersections have the same hydraulic conductivity, (2) The individual hydraulic conductivities are drawn from a lognormal distribution, and (3) The hydraulic conductivities are determined by the degree of overlap of the intersecting spheres. It is found that the critical behaviour of the hydraulic conductivity of the system, K, follows a powerlaw dependence defined by K ∞ (N/Nc1)x, where N is the total number of spheres in the domain, Nc is the critical number of spheres for the onset of percolation, and x is an exponent which depends on the dimensionality and the case. All three cases yield a value of x≈1.2±0.1 in the twodimensional system, while x≈1.9±0.1 is found in the threedimensional system for only the first two cases. In the third case, x≈2.3±0.1. These results are in agreement with the most recent predictions of the theory of percolation in the continuum. We can thus see, that percolation theory provides useful predictions as to the structural parameters which determine hydrological transport processes.
Research output: Article 
, 1 Jan 1992, In: Journal of Hydrology. 135, 14, p. 133142 10 p. Abstract
Procedures for analysis of data from a hydrologic network usually assume that a collection schedule is fully followed. In practice, however, data are frequently missing (or simply unknown, in regions where measurements were not planned), and must be estimated on the basis of other available observations and information. During the 1980s a simple method to estimate missing data (e.g. on water levels) by use of a spatial approach was developed. Spatial and temporal variations of a measurable state variable (such as hydraulic head) were assumed to be described by a deterministic function, with randomness introduced by the choice of location and timing of observations. The function describes a spatial surface, and allows only for fluctuation parallel to itself along the time axis. Missing (or unknown) data can then be estimated from predicted surfaces. The constraint of parallel fluctuations has now been removed. The proposed method, which is more general, is based on integration of two sources of information: prior estimates and online estimates. It allows for continuous updating of the function as additional information becomes available, and as a consequence, missing (or unknown) data can be more accurately estimated.
Research output: Article 
, 1 Jan 1992, In: Journal of Hydrology. 132, 14, p. 107135 29 p. Abstract
The Cl content of ground water in the central and northern Negev ranges between 250 mg 11 in the Beer Sheva area and 1600 mg 11 near the Egyptian border, where the water is also thermal with high concentrations of sulphates and iron. During the last few years, groundwater resources in the heavily populated Beer Sheva area have become endangered by a continuing process of salinization. In the course of the present work, it was found that, in the study area, ground water flows through a multiple aquifer system including the JurassicLower Cretaceous Kurnub Group and the Upper Cretaceous Judea Group aquifers. Because of the absence of impermeable beds at the boundary between the two groups, brackish ground water flows from the Kurnub Group into the overlying Judea Group aquifer. Moreover, numerous faults discovered in the subsurface facilitate lateral inflow of Kurnub ground water into the Judea aquifer. By interpreting new lithostratigraphic data from the Kurnub Group and seismic surveys made in the study area, it is shown that the Kurnub aquifer extends far beyond the hitherto known boundaries and contains an additional estimated volume of 51 × 109 m3 of paleowater. The limiting factors of its exploitability are groundwater depth and salinity. The rational exploitation of the Kurnub paleowater may prevent salinization of the overlying Judea Group aquifer.
Research output: Article 
, Jan 1992, In: Water Resources Research. 28, 1, p. 199207 9 p. Abstract
A new methodology is proposed to estimate the actual direction of water flow in a fractured aquitard. According to the conceptual model, the flow direction in a fractured aquitard is dictated by the azimuth of the fractures, since almost no flow occurs within the rock matrix, which possesses very low hydraulic conductivity. Thus, while groundwater in reality continues to flow along the fractures, calculations based on water level data may incorrectly indicate changes in hydraulic gradients and azimuth of flow. The present methodology is based on simultaneous analysis of hydraulic gradients and flow direction, as calculated from equipotential surfaces. The approach was tested in a fractured chalky aquitard, and the calculated direction of principal fractures was found to be in good agreement with subsurface fracture data obtained from a tunnel excavated in the vicinity of the study area.
Research output: Article
1991

, Dec 1991, In: Water Resources Research. 27, 12, p. 31593164 6 p. Abstract
A law for dispersion in fracture networks below the representative elementary volume (REV) is established by analyzing random walks in twodimensional fracture networks in conjunction with percolation theory. Irregular fracture networks near the percolation threshold were obtained by removing some of the fractures of a regular orthogonal network, consisting of fractures of equal length and different apertures, drawn randomly from a lognormal distribution. The random walk was directed by an exact solution of flow through the network, and Monte Carlo simulations were performed to track particles through the fracture system. The percolation theory analysis indicates a proportionality between the mean square displacement and time raised to the power 1.27, in excellent agreement with the simulations in the fracture networks, which indicate a proportionality with time raised to the power 1.3.
Research output: Article 
, 10 Jun 1991, In: Journal of Geophysical Research. 96, B6, p. 1001510021 7 p. Abstract
The "backbone" (i.e., conducting part of the network) of a computergenerated twodimensional percolation model of fractured formations is examined. The lengths of the conducting elements (line segments) are found to follow a power law distribution defined by N1 proportional 1(1.9), where 1 is the length of the line segment sections, and N1 is the number of elements of length 1 in the backbone. The measured electrical resistivity of the model is found to yield a power law behavior defined by R proportional (N/N(c)  1)1.3, where R is the overall resistance of the network, N(c) is the threshold for the onset of electrical conduction, and N is the number of line segments in the system. Both the threshold and the electrical resistivity exponent are in agreement with the theoretical values expected for percolation systems in the continuum. Examination of available geological data supports these results, although additional field data are required. The model presented here provides a useful reference for comparison and suggests the nature of geologicalgeophysical data that should be obtained in future field studies. An analysis of the effect of a distribution of fracture apertures in the network on its transport properties is also presented. Based on the limited data available, it is suggested that the socalled universal behavior predicted by percolation theory is in general to be expected for both the fluid hydraulic conductivity and the electrical conductivity in common systems of fractures.
Research output: Article 
, 1 Jun 1991, In: Phys. Rev. E. 43, p. 66046612 9 p. Abstract
We present a systematic derivation of the percolation thresholds in anisotropic systems composed of permeable elongated boxes. The analytic calculation is based on an orderbyorder diagrammatic expansion of the pairconnectedness function. A comparison of the results with those of Monte Carlo simulations shows excellent quantitative agreement. We conclude that, of the analytic methods suggested thus far, the present approach is the most suitable one for quantitative derivation of system properties in continuum percolation.
Research output: Article 
, Feb 1991, In: Geophysical Research Letters. 18, 2, p. 227230 4 p. Abstract
Many studies of flow and solute transport in fractured rocks are based on a conceptual model whereby flow occurs between parallel plates which approximate the fracture walls. Recently, it has been observed that this representation is not consistent with actual fractures. Real fractures are actually composed of a complex system of void spaces of varying aperture, and contact areas which are closed to flow. In such fractures, flow takes place through a network of channels and deadend regions. The present investigation analyzes and compares the behavior of solute breakthrough curves in these channels and parallel plate representations. Numerical experiments show that breakthrough curves obtained with channel models are characterized by a long tail and jumps in the solute concentration, consistent with those observed experimentally. It is concluded that the considered channel models provide a sound explanation for the behavior of real breakthrough curves, which cannot be reproduced by parallel plate models.
Research output: Article 
, Jan 1991, In: Computers and Geosciences. 17, 4, p. 489503 15 p. Abstract
A general model for generating statistically optimal estimates is presented, together with an accompanying Pascal program developed for solution on a microcomputer. The model, based on the theory of objective analysis, is a powerful tool to estimate mapped data fields based on scattered point observations. The special feature of the method is its ability to quantify the accuracy of the estimates, allowing determination of an associated error field. The Pascal code for the model and sample input and output are provided. The code is implemented easily and modified.
Research output: Article
1990


, Sep 1990, In: SIAM Journal on Scientific and Statistical Computing. 11, 5, p. 975989 15 p. Abstract
The paper derives column relaxation schemes for calculating the $\ell _p $ solution of an inconsistent system of linear equations. The need for such methods arises when the system to be solved is large, sparse, and unstructured. Special attention is given to each of the cases $p = 1$, $1 < p < 2$, $2 < p < \infty $, and $p = \infty $. Numerical experiments illustrate the ability of the proposed schemes to handle large $\ell _1 $ and $\ell _\infty $ problems.
Research output: Article
1989

, Aug 1989, In: Water Resources Research. 25, 8, p. 19191922 4 p. AbstractResearch output: Article

, Jun 1989, In: Transport in Porous Media. 4, 3, p. 295306 12 p. Abstract
In a phreatic aquifer, bubbles may result from the entrapment of air during groundwater recharge and/or bacterial metabolism. The calculated critical depth of about 1 m at which bubbles are most likely to be found in a granular aquifer, coincides with the depth of 0.60 m of an almost stagnant water layer (specific discharge 1 × 106 cm sec1) found at the water table region under natural flow conditions. Bubbles clog pores and therefore reduce the hydraulic conductivity without significantly reducing the volumetric water content. Stagnation at the water table region results since prevailing pressures (in the order of 101 atmospheres) are not sufficiently large to move bubbles through porous media in a water environment.
Research output: Article
1988

, 1 Apr 1988, In: Transport in Porous Media. 3, 2, p. 199205 7 p. Abstract
The governing equation describing solute transport in porous media is reformulated using standard volume averaging techniques. The alternative formulation is based on a modified definition of the deviation, which allows for variation of macroscopic velocity across the REV. The new equation contains additional scaledependent terms which are functions of the size of the averaging volume (REV). This result indicates that the scaledependent nature of the dispersion phenomenon is inherent even at the scale of the REV.
Research output: Article 
, 1 Mar 1988, In: Water Resources Management. 2, 1, p. 1120 10 p. Abstract
This paper deals with the frequently encountered problem of preposterior data evaluation, i.e., assessment of the value of data before they become available. The role of data is to reduced the risk associated with decisions taken under conditions of uncertainty. However, while the inclusion of relevant data reduces risk, data acquisition involves cost, and there is thus an optimal level beyond which any addition of data has a negative net benefit. The Bayesian approach is applied to construct a method for updating decisions and evaluating the anticipated reduction in risk following consideration of additional data. The methodology is demonstrated on a problem of management of an aquifer under threat of contamination.
Research output: Article 
, 1 Jan 1988, In: Water Resources Research. 24, 8, p. 12251236 12 p., 7W4877. Abstract
This work examines some conditions under which contaminant transport in fractured porous rocks can be described by an equivalent porous medium (single continuum) model. For this purpose, a two‐dimensional mathematical and numerical model for flow and contaminant transport was developed. The model allows for contaminant transport by advection, diffusion, and dispersion in both fractures and porous blocks. Concentration distributions were calculated for different flow conditions and medium properties. The resulting S‐shaped breakthrough curves, characteristic of ordinary porous media, indicated the possibility of regarding the fractured porous medium as a single (equivalent) continuum. The results were compared to an existing analytical solution for contaminant movement in ordinary porous media. Analysis showed that within the range of considered parameter values, and except for the region close to the source, a single continuum model is sufficient for modelling the movement of contaminants. In such cases, application of the equivalent porous medium model is an actual field situation requires knowledge of the “equivalent” porosity and the equivalent coefficient of dispersion appearing in the governing transport equation. In practice, these coefficients must be determined by analysis of breakthrough curves obtained from field tests.
Research output: Article
1987

Groundwater flow and pollution in fractured rock aquifers, Sep 1987, Developments in Hydraulic Engineering. Novak P.(eds.). New York: Vol. 4. p. 175238 64 p. AbstractResearch output: Chapter
1985

, Jan 1985, In: Water Resources Research. 21, 8, p. 12931293 1 p. Abstract
The criticisms of Bayeye and Sposito [1984] concerning assumptions associated with application of the REV (representative elementary volume) concept to models of transport phenomena in porous media are most welcome, and generally, quite wellfounded. We agree, in particular, with discussions on the lack of proof of existence of a plateau, and on difficulties associated with relating sample volumes measured by various instruments to the volume of a REV.... [first paragraph in lieu of abstract]
Research output: Article