Publications

Molecular diffusion of chemical species in subsurface environments─rock formations, soil sediments, marine, river, and lake sediments─plays a critical role in a variety of dynamic processes, many of which affect water chemistry. We investigate and demonstrate the occurrence of anomalous (non-Fickian) diffusion behavior, distinct from classically assumed Fickian diffusion. We measured molecular diffusion through a series of five chalk and dolomite rock samples over a period of about two months. We demonstrate that in all cases, diffusion behavior is significantly different than Fickian. We then analyze the results using a continuous time random walk framework that can describe anomalous diffusion in heterogeneous porous materials such as rock. This methodology shows extreme long-time tailing of tracer advance as compared to conventional Fickian diffusion processes. The finding that distinct anomalous diffusion occurs ubiquitously implies that diffusion-driven processes in subsurface zones should be analyzed using tools that account for non-Fickian diffusion.

Groundwater input in natural systems can vary over a wide range of time scales due to different natural phenomena and anthropogenic activities. These variations give rise to time-dependent velocity fields, which in turn may influence the dynamics of a migrating chemical plume relative to migration in a constant-velocity domain. Anomalous transport, which is ubiquitous in many groundwater systems and generally yields longer (non-Fickian) tails of migrating chemical plumes relative to those subject to Fickian dispersive processes, is of particular interest in this context. Herein, transport of conservative chemical species in macroscopically 1D columns and 2D flow cells was analyzed via laboratory experiments and corresponding numerical simulations. Different time-dependent velocity field magnitude conditions were compared to study how the transient water input affects the resulting tracer breakthrough curves. A stochastic-based numerical model was employed to interpret the results and simulate conditions that extend beyond the laboratory scale. The laboratory measurements show that different time-dependent velocity magnitude conditions, which preserve the average discharge of a comparable constant-velocity system, yield similar, long-tailed breakthrough curves compared to those of the constant-velocity case. The breakthrough curves are then shown to be quantified with the continuous time random walk (CTRW) framework. Appropriate choice of particle transition times and distances at the moment of velocity change enables matching of the CTRW results to the experimental results obtained in the experiments. The negligible impact of time-dependent velocity field magnitudes is shown to be consistent for 1D and 2D flow fields, homogeneous and heterogeneous media, and different flow scenarios.

We investigate the occurrence of anomalous (non-Fickian) transport in an hydrological catchment system at kilometer scales and over a 36-year period. Using spectral analysis, we examine the fluctuation scaling of long-term time series measurements of a natural passive tracer (chloride), for rainfall and runoff. The scaling behavior can be described by a continuous time random walk (CTRW) based on a power-law distribution of transition times, which indicates two distinct power-law regimes in the distribution of overall travel times in the catchment. The CTRW provides a framework for assessing anomalous transport in catchments and its implications for water quality fluctuations.

Objective, To quantify the relative volumetric flows in stent and ureter lumina, as a function of stent size and configuration, in both unobstructed and externally obstructed stented ureters. Methods, Magnetic resonance imaging was used to measure flow in stented ureters using a phantom kidney model. Volumetric flow in the stent and ureter lumina were determined along the stented ureters, for each of four single stent sizes (4.8F, 6F, 7F, and 8F), and for tandem (6F and 7F) configurations. Measurements were made in the presence of a fully encircling extrinsic ureteral obstruction as well as in benchmark cases with no extrinsic ureteral obstruction. Results, Under no obstruction, the relative contribution of urine flow in single stents is 110%, while the relative contributions to flow are ~6 and ~28% for tandem 6F and 7F, respectively. In the presence of an extrinsic ureteral obstruction and single stents, all urine passes within the stent lumen near the extrinsic ureteral obstruction. For tandem 6F and 7F stents under extrinsic ureteral obstruction, relative volumetric flows in the two stent lumina are ~73% and ~81%, respectively, with the remainder passing through the ureter lumen. Conclusions, Magnetic resonance imaging demonstrates that with no extrinsic ureteral obstruction, minimal urine flow occurs within a stent. Stent lumen flow is significant in the presence of extrinsic ureteral obstruction, in the vicinity of the extrinsic ureteral obstruction. For tandem stents subjected to extrinsic ureteral obstruction, urine flow also occurs in the ureter lumen between the stents, which can reduce the likelihood of kidney failure even in the case of both stent lumina being occluded.

Purpose: The purpose of our study was to evaluate the ability of ureteral stents with different diameters to drain pus that accumulates in an obstructed kidney using an in vitro model. Methods: We developed an in vitro model of an obstructed kidney filled with pus. The model included a silicon kidney unit based on computed tomography (CT) data, a 3D printed ureteral stone based on a real extracted ureteral stone, a latex ureter model, a bladder vessel, and a fluid with qualities resembling pus. Identical printed stones were inserted into four ureter models containing stents with varying diameters (4.8F, 6F, 7F, 8F), each of which was connected to the kidney unit and the bladder vessel. The kidney unit was filled with artificial pus to pressures of 30 cmH2O to simulate an infected and obstructed kidney. The obstruction was relieved with stents in place, while artificial urine was pumped into the kidney; pressure in the kidney and remaining pus were measured continuously. Results: The rate of pressure drop and the final pressure measured in the kidney were unaffected by the diameter of the stent. For all stent diameters, the pressure reached non-obstructed levels within 30 s, final pressure was reached within 90120 s, and minimal amounts of pus remained in the kidney after 120 min. Conclusions: In vitro experiments demonstrate that all stent diameters drain pus-filled, obstructed kidneys with the same efficacy. The common perception that larger diameter tubes are more effective under such circumstances should be re-examined.

There is growing concern that rare earth elements (REEs) will become emerging soil-water contaminants because of their increased use in new technologies and products, which may lead to unavoidable release to the environment. To better understand the environmental behavior of REEs, a comprehensive set of adsorption and column transport experiments was conducted in quartz sand media. The retention and mobility of three representative REEs (La, Gd, and Er) were studied in the presence and absence of humic acid (HA; 5, 20, and 50 mg L^-1) and under a range of pH conditions (5-8). Results show that REE mobility and retention are controlled by the amount of REE-HA complexes formed in a solution, which increases with increasing HA concentrations and solution pH. Gadolinium is the most mobile among the representative REEs, followed by Er and La, corresponding to the amount of (calculated) REE-HA complexes. Increasing HA concentrations in the REE solution inhibits REE retention in both the batch adsorption and column experiments. The same retardation trend was observed for lower HA concentrations (Gd > Er > La). In a fixed HA concentration, HA and REE adsorption decrease simultaneously as the solution pH increases, indicating the co-adsorption of REEs and HA on the sand. Scanning electron microscopy detection of elongated regions attached to the sand, where high REE and carbon (HA) concentrations were measured, further suggests the co-adsorption of REE-HA complexes. Modeling the column experiments shows that the time-dependent attachment is dominant at high HA concentrations, while at lower HA concentrations, both the time-dependent and spontaneous attachments play equal roles. These results provide a quantitative characterization of REE retention and mobility in sand media.

Background: Ureteral stents are employed regularly to facilitate urine drainage and ureteral healing in a wide variety of endourological procedures, associated mainly with ureteral stone obstruction. However, stent use frequently impairs patient quality of life, which is generally attributed to the presence of anchoring stent curls in the bladder and/or kidney. The purpose of this study was to examine the potential effectiveness and safety of a newly designed, fully intraureteral stent, in an initial proof-of-concept in vivo evaluation. Methods: \u201cYoticurl\u201d stents were synthesized from copolymeric, commercially-available ureteral stents. A first test to confirm the intended expansion of the spiral curls in a ureter was performed on a pig cadaver. Subsequently, a preliminary in vivo evaluation in a single pig model was completed to test stent viability, over a period of 25 days. Two stents were inserted to fully intraureteral positions into the two ureters, by standard human endourological procedure. Daily observational checks of the pig, and regular radiographic analyses were performed; the animal was then euthanized and examined by explorative laparotomy, followed by histological analysis of kidney, ureter and bladder tissue samples. Results: The pig displayed normal activity, appetite and sleep patterns, and radiography indicated free flow of urine, and no significant stent migration nor anatomical abnormalities. Subsequent histology found only mild inflammation in the ureter. Conclusions: The innovative stent design tested here, if ultimately proven safe and effective for human use, may offer an alternative to currently available stents for multiple indications.

A recent experiment of Bowers et al. (2020) revealed that diffusive mixing of water isotopes (δ2H and δ18O) over a fully saturated soil sample of a few centimetres in length required several days to equilibrate completely. In this study, we present an approach to simulate such time-delayed diffusive mixing processes, on the pore scale, beyond instantaneously and perfectly mixed conditions. The diffusive pore mixing (DIPMI) approach is based on a Lagrangian perspective on water particles moving by diffusion over the pore space of a soil volume and carrying concentrations of solutes or isotopes. The idea of DIPMI is to account for the self-diffusion of water particles across a characteristic length scale of the pore space using pore-size-dependent diffusion coefficients. The model parameters can be derived from the soil-specific water retention curve, and no further calibration is needed. We test our DIPMI approach by simulating diffusive mixing of water isotopes over the pore space of a saturated soil volume using the experimental data of Bowers et al. (2020). Simulation results show the feasibility of the DIPMI approach for reproducing the measured mixing times and concentrations of isotopes at different tensions over the pore space. This result corroborates the finding that diffusive mixing in soils depends on the pore size distribution and the specific soil water retention properties. Additionally, we perform a virtual experiment with the DIPMI approach by simulating mixing and leaching processes of a solute in a vertical, saturated soil column and compare the results against simulations with the common perfect mixing assumption. The results of this virtual experiment reveal that the frequently observed steep rise and long tailing of breakthrough curves, which are typically associated with non-uniform transport in heterogeneous soils, may also occur in homogeneous media as a result of imperfect subscale mixing in a macroscopically homogeneous soil matrix.

The capillary pressure-saturation relation is one of the key constitutive equations used for modeling multiphase (or partially saturated) flow in porous materials. It is known that this empirical relation depends strongly on dynamic conditions, but the impact of a heterogeneity interface on this relationship has been studied less. The present study employed optical imaging to visualize two-phase drainage under different injection rates and two flow directions, in a heterogeneous micromodel. By analyzing the curvatures of the fluid-fluid interfaces, the averaged capillary pressures for the coarse and fine sections of the micromodel, and the entire micromodel were estimated. Results show that the capillary pressure-saturation relation in the vicinity of a heterogeneity interface does not follow the conventional models proposed in the literature. The averaged capillary pressure over the entire micromodel for the fine-to-coarse (FtC) direction shows decreasing capillary pressure with decreasing wetting phase saturation. However, in the coarse-to-fine direction, a non-monotonic trend was observed. These initial findings highlight the gaps in the knowledge of upscaling capillary pressure in heterogeneous porous materials. Moreover, discontinuity in saturation was clearly more pronounced for the FtC direction, as a result of lower entry capillary resistance against the flow in the coarse section.

Rare earth elements (REEs) are an emerging pollutant whose increasing use in various technological applications causes increasing risk of environmental contamination. Electronic waste (E-waste) could be one major source of REE pollution, as E-waste typically contains elevated REE concentrations and is often handled in unsafe and environmentally hazardous ways. Here, a series of leaching assays revealed that

Solute transport under single-phase flow conditions in porous micromodels was studied using high-resolution optical imaging. Experiments examined loading (injection of ink-water solution into a clear water-filled micromodel) and unloading (injection of clear water into an ink-water filled micromodel). Statistically homogeneous and fine-coarse porous micromodels patterns were used. It is shown that the transport time scale during unloading is larger than that under loading, even in a micromodel with a homogeneous structure, so that larger values of the dispersion coefficient were obtained for transport during unloading. The difference between the dispersion values for unloading and loading cases decreased with an increase in the flow rate. This implies that diffusion is the key factor controlling the degree of difference between loading and unloading transport time scales, in the cases considered here. Moreover, the patterned heterogeneity micromodel, containing distinct sections of fine and coarse porous media, increased the difference between the transport time scales during loading and unloading processes. These results raise the question of whether this discrepancy in transport time scales for the same hydrodynamic conditions is observable at larger length and time scales.

Thus, the key to advancing our science, and medical (and ultimately clinical) understanding, is to treat these three approachesin vivo, in vitro, in silicoas fully complementary tools, each with strengths and limitations, that taken together will lead to extensive advances in the study of urological pathologies and treatments. [last paragraph in lieu of abstract]

Purpose To quantify the occurrence of stent failure and the dynamic behavior of urine flow in ureter-stent systems, including the relative flow in the ureter and stent lumina, subject to various degrees of ureter and stent blockage. Methods Numerical simulations based on computational fluid dynamics (CFD) were used to quantify urine flow behavior in stented ureters, in the presence of extrinsic ureteral obstruction (EUO) and stent occlusions. Two stented ureter configurations were considered, one with circumferential occlusion of the ureter and the second with pressure on one side of the ureter wall. The pressure within the renal unit for different degrees of ureter closure and stent lumen occlusion was determined systematically. Onset of stent failure and the distribution of urine flow between stent and ureter lumina were determined. Results In the case of EUO completely encircling the ureter, causing 100% obstruction of the ureter lumen, pressure in the renal unit is essentially unaffected until the stent lumen reaches~90% occlusion, and fails only with>95% occlusion. Occlusions of 50% in stent side holes in the vicinity of the EUO only alter local flow patterns but have no significant influence on renal unit pressure. For EUO deforming and compressing the ureter from one side, with~50% reduction in ureter lumen, urine drainage proceeds with negligible increase in renal pressure even with 100% occlusion in the stent lumen. Conclusion CFD simulations show that stent failure under EUO tends to occur suddenly, only when both ureter and stent lumina become almost fully blocked.

We present an approach to simulate reactive solute transport within the Lagrangian Soil Water and Solute Transport Model framework (LAST). The LAST-Model is based on a Lagrangian perspective describing the (1-D) movement of discrete water particles, which travel at different velocities and carry solutes through a heterogeneous, partially saturated soil that is separated into a soil matrix and structural macropore domain. In this study, we implement an approach to represent non-linear sorption and first-order degradation processes of reactive solutes under well-mixed and preferential flow conditions in the critical zone. The intensity of the two reactive transport processes may vary with the soil depth, to account for topsoil that facilitates enhanced microbial activity (and hence sorption) as well as chemical turnover rates. This expanded LAST-Model is evaluated with simulations of conservative tracer transport and reactive transport of the herbicide Isoproturon, at different flow conditions, and compared to data from field experiments. Additionally, the model is compared to simulations from the commonly used HYDRUS 1-D model. Both models show equal performance at a matrix flow dominated site, but LAST better matches indicators of preferential flow at a macropore flow dominated site. These results demonstrate the feasibility of the approach to simulate reactive transport in the LAST-Model framework, and highlight the advantage of the structural macropore domain to cope with preferential bypassing of topsoil and subsequent re-infiltration into the subsoil matrix.

We study pore-scale dynamics of reactive transport in heterogeneous, dual-porosity media, wherein a reactant in the invading fluid interacts chemically with the surface of the permeable grains, leading to the irreversible reaction Aaq + Bs → Caq. A microfluidic porous medium was synthesized, consisting of a single layer of hydrogel pillars (grains), chemically modified to contain immobilized enzymes on the grain surfaces. Fluorescence microscopy was used to monitor the spatiotemporal evolution of the reaction product Caq at different flow rates (Péclet values) and to characterize the impact on its transport. The experimental setup enables delineation of three key features of the temporal evolution of the reaction product within the domain: (i) the characteristic time until the rate of Caq production reaches steady state, (ii) the magnitude of the reaction rate at steady state, and (iii) the rate at which Caq is flushed from the system. These features, individually, are found to be sensitive to the value of the Péclet number, because of the relative impact of diffusion (vs advection) on the production and spatiotemporal evolution of Caq within the system. As the Péclet number increases, the production of Caq is reduced and the transport becomes more localized within the vicinity of the grains. The dual-porosity feature causes the residence time of the transported species to increase, by forming stagnant zones and diffusive-dominant regions within the flow field, thus enhancing the reaction potential of the system. Using complementary numerical simulations, we explore these effects for a wider range of Péclet and Damköhler numbers and propose nonlinear scaling laws for the key features of the temporal evolution of Caq.

Copper oxide nanoparticles (CuO-NPs) have been suggested as effective catalysts to degrade many persistent organic contaminants. In parallel, CuO-NPs are considered toxic to soil microorganisms, plants and human cells, possibly because they induce oxidative stress and generation of reactive oxygen species (ROS). However, the mechanism of the catalytic process and the generated ROS are poorly understood. Here we discuss the reaction mechanism of CuO-NPs during the catalytic degradation of enrofloxacin - an antibiotic pharmaceutical used in this study as a representative persistent organic compound. The degradation of an aqueous solution of the enrofloxacin exposed to CuO-NPs and hydrogen peroxide was studied showing fast removal of the enrofloxacin at ambient conditionsns. ROS production was identified by electron spin resonance and a spin trapping technique. The distribution of the free radical species indicated production of a high percentage of superoxide (O2-.) radicals as well as hydroxyl radicals; this production is similar to the "radical production" activity of the superoxide dismutase (SOD) enzyme in the presence of hydrogen peroxide. This activity was also tested in the opposite direction, to examine if CuO-NPs show reactivity that potentially mimics the classical SOD enzymatic activity. The CuO-NPs were found to catalyze the dismutation of superoxide to hydrogen peroxide and oxygen in a set of laboratory experiments.

We present a hybrid approach to groundwater transport modeling, \u201cCTRWonastreamline,\u201d that allows continuoustime random walk (CTRW) particle tracking on largescale, explicitly delineated heterogeneous groundwater velocity fields. The combination of a nonFickian transport model (in this case, the CTRW) with general heterogeneous velocity fields represents an advance of the current state of the art, in which nonFickian transport models or heterogeneous velocity fields are employed but generally not both. We present a general method for doing this particle tracking that fully separates the model parameters characterizing macroscopic flow, subscale advective heterogeneity, and mobileimmobile mass transfer, such that each can be directly specified a priori from available data. The method is formalized and connections to classic CTRW and subordination approaches are made. Numerical corroboration is presented.

Karst aquifers are important drinking water resources, but highly vulnerable to contamination. Contaminants can be transported rapidly through a network of fractures and conduits, with only limited sorption or degradation, which usually leads to a fast and strong response at karst springs. During migration, contaminants can also enter less mobile zones, such as pools or water in intra-karstic sediments, or advance from conduits into the adjacent fractured rock matrix. As contaminant concentrations in the main flow path(s) decrease, contaminants may migrate back into the main flow path and reach the karst springs at low (but significant) concentrations over a long time span. This is the conventional interpretation for the oft-observed steep rising limb and the long-tailed falling limb of tracer breakthrough curves in karst systems. Here, field measurements are examined from an alpine karst system in Austria where a series of distinctive, long-tailed breakthrough curves (BTCs) of conservative tracers were observed over distances up to 7400\u202fm. Recognizing that the conventional advection-dispersion equation (ADE) cannot usually quantify such behavior, two other modeling approaches are considered, namely the two-region non-equilibrium (2RNE) model, which explicitly includes mobile and immobile zones, and a continuous time random walk (CTRW) model, which is based on a physically-based, probabilistic approach that describes anomalous (or non-Fickian) transport behavior characteristic of heterogeneous systems such as karst. In most cases, the ADE and 2RNE models do not quantify the low concentrations at longer travel times. The CTRW, in contrast, accounts for the long-tailed breakthrough behavior found in this karst system.

While both surface water and groundwater hydrological systems exhibit structural, hydraulic, and chemical heterogeneity and signatures of self-organization, 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 self-organization; 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 characterizations 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 self-organization in spatial patterns and temporal dynamic behaviour.

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, ureter-stent 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 ureter-stent 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 ureter-stent 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 ureter-stent 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 5000g 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 4000g.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.

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)+B-s -> C-aq, 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 time-dependent 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.

The nonlocal-in-time, integro-partial differential equation (iPDE) describing the continuous time random walk (CTRW) is augmented by a nonlinear chemical-species 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 particle-tracking (CTRW-PT) version of reactive transport, is applied here to a reanalysis of recent experimental results to further establish its validity. The experimental set-up 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 index-matched, water-saturated porous medium allows tracking of the reacted concentration field, which is modeled by the solutions of the two-species coupled iPDE, whose nonlinear form precludes the use of a Laplace Transform. The time-domain solutions are obtained with a finite element method (FEM) and a sum of exponentials representation of the kernel (memory function). The two-dimensional 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, second-order reaction term.

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 advection-diffusion 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 non-reactive 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

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 two-dimensional pore-scale 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.

We quantify the poorly-understood interactions between resident and infiltrating water during drainage-imbibition cycles in heterogeneous porous media, via a 2-D (and 3-D) lattice Boltzmann simulation method. These interactions are critical in the (partially saturated) soil layer, which is the interface from land surface to ground-water 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, air-water 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 pore-scale, mechanistic evidence that supports field observations of soil water zones with different chemical signatures.

We present a combined experimental and numerical modeling study that addresses two principal questions: (i) is any particular Eulerian-based method used to solve the classical advection-dispersion 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 Eulerian-Lagrangian 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 non-uniformity of the domain. Although simulated BTCs at the system outlet are observed to be very similar for these various numerical methods, computed local (point-wise, 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.

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 two-dimensional pore-scale 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.

The present invention is directed to a degradation composition, methods and kits for degrading organic pollutants comprising reduced copper based nanoparticles-polymer complex (Cu-NPs) and an oxidant.

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 time-varying velocity field on conservative chemical tracer transport in porous media, as compared to constant velocity conditions. We find that velocity-field 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 time-dependent 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 velocity-field fluctuations, as well as different degrees of porous media heterogeneity, on 1-D and 2-D spatiotemporal propagation of an injected, point-source, chemical plume. Increased intensity of velocity-field fluctuations, and increased porous medium heterogeneity, each serve to increase the extent of chemical spreading and anomalous behavior.

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 17a-estradiol (E2), estrone (E1), and the conjugated estrogen estrone-sulfate (E1-3S) 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 E1-3S 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) E1-3S behaves almost conservatively and shows the lowest sorption and transformation potential.

Path reversibility and radial symmetry are often assumed in push-pull 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, local-scale dispersion, and velocity field heterogeneity on push-pull breakthrough curves and compares them to the effects of mobile-immobile 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 local-scale dispersion. Assuming path reversibility, we develop a continuous-time-random-walk-based interpretation framework which is flow-field-agnostic 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 \u201cplugged into\u201d an existing Laplace-domain transport model to incorporate MIMT is presented and demonstrated. Algorithms implementing the calibration are presented and applied to interpretation of data from a push-pull test performed in a heterogeneous environment. A successful four-parameter fit is obtained, of comparable fidelity to one obtained using a million-node 3-D numerical model. Finally, we demonstrate analytically and numerically how push-pull tests quantifying MIMT are sensitive to remobilization, but not immobilization, kinetics.

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 carbon-based and metal-based ENMs may cause, under 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 anthropogenically-induced metapedogenesis.

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 two-dimensional heterogeneous domain (with log-conductivity, 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 non-negligible 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.

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 (Au-NPs), silver (Ag-NPs) and zinc oxide (ZnO-NPs) - is investigated in partially saturated sand columns. High mobilities of Au-NPs and Ag-NPs under different water saturation levels and concentrations were observed. The presence of CaCl2 reduces Ag-NP mobility through chemical interactions, similar to behavior reported in saturated systems. Furthermore, transformation of Ag-NPs in the environment may influence their mobility; aging of Ag-NPs following sulfidation was investigated. The silver sulfide (Ag2S-NPs) remained stable in aqueous suspension, and mobile in the partially saturated sand column. In contrast, the positively-charged ZnO-NPs were completely immobilized in the sand column. Significantly, though, addition of humic acid (HA) to the ZnO-NP suspension reverses particle surface charge and thus increases their mobility. Moreover, remobilization of entrapped ZnO-NPs by HA was demonstrated.

The release of pharmaceuticals and personal care products (PPCPs) to the soil-water 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, Gd-DTPA and roxarsone (arsenic compound) and their metal salts (Gd(NO₃)₃, AsNaO₂); Gd-DTPA 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 Gd-DTPA 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 (chemically-strong reducing conditions did not affect the transport). Mechanisms that include adsorptive retardation for aerobic and nitrate-reducing conditions, and non-adsorptive retardation for iron-reducing, sulfate-reducing and biologically-strong reducing conditions, are suggested to explain the roxarsone behavior. Gd-DTPA 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 nitrate-reducing conditions and delayed transport under iron-reducing, sulfate-reducing and biologically-strong reducing conditions.

Endocrine disrupting chemicals, such as the free estrogens 17β-estradiol (E2), estrone (E1) and the conjugated estrogen estrone-sulfate (E1-3S) 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 E1-3S, 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.

Nickel migration measured in laboratory-scale, natural soil column experiments is shown to display anomalous (non-Fickian) 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 flow-through 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 non-Fickian 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 non-Fickian 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 K_sp 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.

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 sensitivity-based 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 space-time 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 research - model formulation, reduction, calibration, sensitivity analysis, and discrimination - offering our view on an emerging framework that guides (i) selection of an appropriate number and location of time-dependent 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 laboratory-scale porous media.

The formation of preferential flow paths in the partially saturated zone, and in naturally structured media, is well known. This study examines non-uniform 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 mobile-immobile 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.

In this updated and expanded second edition, new literature has been added on contaminant fate in the soil-subsurface 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".

Anomalous (or "non-Fickian") 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 ∼t-1-β of local transition times. The latter is contained in the probability density function ψ(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 ψ(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 particle-visitation 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 ψ(t), and delineate the region of Hw(K) that forms the power law of ψ(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 β in terms of the Hw(K) parameters. The equivalence between Hw(K) and ψ(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 particle transitions. Key Points Quantitative connection between CTRW parameters and conductivities is determined Dynamic controls are critical factors to determine key transport features Transport is not explained only by structural knowledge of the disordered medium

The catalytic degradation of two brominated flame retardants (BFRs), tribromoneopentyl alcohol (TBNPA) and 2,4 dibromophenol (2,4-DBP) 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 zero-valent 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 2,4-DBP showed faster degradation than TBNPA, by nCuO catalysis. Relatively high resistance to degradation was recorded for 2,4-DBP with nZVI, yielding 20% degradation after 24h, while the TBNPA was degraded by 85% within 12h. Electron Spin Resonance (ESR) measurements show generation of both hydroxyl and superoxide radicals. In addition, inhibition of 2,4-DBP 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.

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 Beer-Lambert. 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 advection-dispersion 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 non-Fickian, 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.

We examine distance record setting by a random walker in the presence of a measurement error δ and additive noise γ and show that the mean number of (upper) records up to n steps still grows universally as âŸ̈R_nâŸ

Non-Fickian (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 advection-dispersion equation (ADE) and a range of ensemble-average 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 continuous-time random-walk (CTRW) formulations represent a general and effective means by which to quantify non-Fickian 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.

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, three-dimensional 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.

This book combines soil science, earth science, and environmental geochemistry, providing comprehensive background information for specialists interested in chemical-induced changes in the soil-subsurface system. Readers are introduced to the chemistry of contaminants that often disturb the natural soil-subsurface equilibrium as a result of human activity. While the soil-subsurface 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 soil-subsurface 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 soil-subsurface 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 soil-subsurface system, the time scale associated with chemical pollutant-induced 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 soil-subsurface regime that is different than that of the pristine system.

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 photo-induced 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 flow-through 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 flow-through 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, CO ₂ was produced, leading to a decrease in the water saturation in the column and reduced contact surface between the nano-CuO 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 nanoparticle-coated sand is an efficient catalyst for complete degradation of the organic dye.

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 ∼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. Micro-CT 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 AgNP-soil chemical interactions as a retention mechanism, and demonstrate the need to employ natural soils rather than glass beads or quartz in representative experimental investigations.

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 non-Fickian 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 non-Fickian nature of the transport. The CTRW framework has been shown to account very well for non-Fickian 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 non-Fickian in all cases, which is caused by the heterogeneity of the soil. Comparative model analysis of the non-Fickian 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.

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 CaCl ₂/HCl, into a column of sucrosic dolomite particles, with a constant flow field. The injected fluid supplies Ca ²⁺ and H ⁺. Dedolomitization is a protonation reaction yielding carbonic acid; a subsequent deprotonation reaction yields CO ₃^2-, and reaction with the abundant Ca ²⁺ forms the precipitate CaCO ₃. 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 non-Fickian transport) and includes the option of treating purely advective-dispersive (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, large-scale 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.

The interplay between resident water ("old water") and infiltrating water ("new water") in porous media was examined through experiments in an idealized, two dimensional, 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 old-new water exchange were characterized in terms of several parameters: remaining old water, number of old-water 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.

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 non-Fickian 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 two-scale 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 first-order 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 non-Fickian transport. A parameter study of the two-scale CTRW adds further insight into the dynamics of the process, showing the interaction between the advective non-Fickian transport and the mass exchange to immobile regions.

Derivations of continuum nonlocal models of non-Fickian (anomalous) transport require assumptions that might limit their applicability. We present a particle-based 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 non-stationary, 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). Convolution-based particle tracking (CBPT) is used to increase the computational efficiency and accuracy of these particle-based simulations. The combined CTRW-CBPT approach enables one to convert any particle tracking legacy code into a simulator capable of handling non-Fickian transport.

The theoretical treatment of transport in a disordered system in the presence of a system-wide 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 ψ (s,t). This distribution is calculated from the ensemble average of a position-dependent 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 large-scale heterogeneity, involves the use of a local ensemble average to obtain a position-dependent ψ (s,t;x); this determines a memory function, M (t;x), which is convoluted with the advection-dispersion 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 steady-state 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 tc) is explored, and solutions are also compared to those of the advection-dispersion equation for v (x) and to a laboratory experiment. This transport equation is in contrast to the fractional Fokker-Planck 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.

To date, the field of contaminant geochemistry-which deals with the study of chemical interactions in soil and aquifer environments-has 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. Contaminant-induced 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 soil-subsurface 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 contaminant-subsurface 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.

The soil and the subsurface region below it are two interrelated natural bodies that comprise the earths 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 air-dried to completely watersaturated. Because the soil-subsurface water content is controlled by rainfall-irrigation, evaporation, and depth to the groundwater, a vertical water gradient always exists. The soil-subsurface zone, known also as the \u201ccritical zone\u201d (CZ), also involves a large microbiological population, which develops under both aerobic or anaerobic conditions, and may affect the composition of the earth environment.

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 mixing-driven 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, Sanchez-Vila 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, Sanchez-Vila X, Carrera J, Saaltink MW. A mixing ratios-based 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 space-time 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 with laboratory experiments to properly describe the key processes that occur in a complex, geochemically-active system under chemical equilibrium conditions. We model three CaCO₃ dissolution experiments reported in Singurindy et al. [Singurindy O, Berkowitz B, Lowell RP. Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration. Water Resour Res 2004;40:W04401. doi: 10.1029/2003WR002651, Singurindy O, Berkowitz B, Lowell RP. Correction to Carbonate dissolution and precipitation in coastal environments: laboratory analysis and theoretical consideration. Water Resour Res 2005;41:W11701. doi: 10.1029/2005WR004433], in which saltwater and freshwater were mixed in different proportions. The integrated reaction rate within the cell estimated from the experiments are modeled independently by means of (a) a state-of-the-art reactive transport code, and (b) the uncoupled methodology of [12, 13], both of which use dispersivity as a single, adjustable parameter. The good agreement between the results from both methodologies demonstrates the feasibility of using simple solutions to design and analyze laboratory experiments involving complex geochemical problems.

Atrazine(2-chloro-4-(ethylamine)-6-(isopropylamine)-s-triazine) 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 2,4-bis(ethylamine)-6-methyl-s-triazine. The reaction involves dechlorination and migration of a methyl group to yield a symmetric product. Nickel 5,10,15,20-tetrakis(1-methyl-4-pyridinio)porphyrin tetra(p-toluenesulfonate) (TMPyP) was activated by nanosized zero-valent iron (nZVI) while cobalt porphyrins (TMPyP, 5,10,15,20-tetrakis(4-hydroxyphenyl)-21H,23H-porphine-(TP(OH)P) and 4,4',4 '',4"'-(porphine-5,10,15,20-tetrayl)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)P-Co/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.

[1] 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 advectiondispersion- reaction 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 power-law (TPL) temporal distribution yields a non-Fickian 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.

The origin of anomalous or non-Fickian 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 non-Fickian transport features in these systems and to have predictive capacities, has at its core this full spectrum represented as a joint probability density ψ (s,t) of random space time displacements (s,t). Transport in a random fracture network (RFN) has been calculated with a coupled ψ (s,t) and has subsequently been shown to be approximated well by a decoupled form ψ (s,t) =F (s) ψ (t). The latter form has been used extensively to model non-Fickian transport in conjunction with a velocity distribution Φ (ξ), ξdistributions (including a constant v, where v is the velocity magnitude. The power-law behavior of ψ (t) t-1-β, which determines non-Fickian transport, derives from the large ξ dependence of Φ (ξ). In this study we use numerical CTRW simulations to explore the expanded transport phenomena derived from a coupled ψ (s,t). Specifically, we introduce the features of a power-law dependence in the s distribution with different Φ (ξ) distributions (including a constant v) coupled by t=sξ. Unlike Lévy flights in this coupled scenario the spatial moments of the plumes are well defined. The shapes of the plumes depend on the entire Φ (ξ) distribution, i.e., both small and large ξ dependence; there is a competition between long displacements (which depend on the small ξ dependence) and large time events (which depend on a power law for large ξ). 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 function of the nature of the s distribution.

Non-Fickian 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 advective-diffusive 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, non-Fickian 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.

Two-phase imbibition behavior of immiscible fluids was studied in dry and prewetted porous media using a laser-induced fluorescence technique. Imbibition was first investigated in two-dimensional (2-D) systems under conditions comparable to those for a study of drainage [Ovdat H, Berkowitz B. Pore-scale study of drainage displacement under combined capillary and gravity effects in index-matched porous media. Water Resources Research 2006;42:W06411. doi: 10.1029/2005WROO4553] in the capillary-dominated regime. The effect of initial wetting saturation (IWS) was then explored in 2-D and 3-D porous media under the combined effect of gravity, capillary and viscous forces, within and outside the capillary-dominated 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 2-D drainage and imbibition patterns demonstrates significant qualitative differences under analogous viscosity ratio, buoyancy number, and capillary number values. However, quantitative analyses show strong pore-scale similarities between these patterns. Invasion structures in 3-D, 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.

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 (P1) activated by nanosized zero-valent iron (nano-ZVI) 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 nano-ZVI, 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 9,10-dihydroanthracene. However, no formation of hydrogenated hydrocarbons was observed from naphthalene or phenanthrene using cobalt porphyrins.

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 mid-ocean 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 [H₂o-2-butoxyethanol], with a lower consolute point of 48.5°C, was used as a proxy for seawater. A saturated pseudo-two-dimensional 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 low-velocity regions at the bottom of the porous matrix. Furthermore, in both types of porous media, the efficiency of thermal transport is reduced relative to single-phase systems. Heterogeneities in the permeability field, however, can act to amplify these effects; in systems with vertical high-k zones, the thickness of the dense-phase layer increases in the low-k 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.

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 non-equilibrium heat transfer in heterogeneous domains, and is shown here to match published experimental data of non-equilibrium 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.

Fluid displacement patterns were observed in two- and three-dimensional (2- and 3-D), gravity-driven drainage experiments. A nonintrusive, laser-induced 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 3-D pore-scale flow dynamics of two immiscible fluid phases in porous media at a low capillary number (Ca ≈ 10^-4). Qualitative analyses indicate considerable diversity in the 2-D and 3-D 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 3-D 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.

We describe the continuous time random walk (CTRW) MATLAB toolbox, a collection of MATLAB scripts and functions that compute breakthrough curves (BTCs) and one-dimensional/two-dimensional (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 advection-dispersion equation, multirate and mobile-immobile models, and the fractional-in-time 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 1D. 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 Fokker-Planck with Memory equation, and treatment of transport in multidimensional systems.

Measurements of particle deposition and mobilization in water-saturated 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.

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 precipitation - And the interplay among them - In 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 quasi-two-dimensional (2D) rock fractures, three-dimensional (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 SO₄^2- 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 through-flow fracture led to a dissolution-dominated system, in contrast to an isolated fracture which led to a precipitation-dominated system under the same experimental conditions. Moreover, comparison of the hydraulic conductivity and porosity evolution among the intact core, the isolated fracture and (multiple) fracture system experiments demonstrates that, under the same flow conditions, cores containing isolated fractures clog more rapidly than intact cores, while cores with multiple fractures clog even more rapidly than the isolated fracture systems. Finally, in spite of the complex coupling of flow and reaction processes between intact rock and fractures, good agreement was obtained between time-varying estimates and experimentally obtained values of system hydraulic conductivity for a core sample containing a through-flow fracture.

A new method to transform anthropogenic, chloro-organic compounds (COC) by use of nanosized molecular catalysts immobilized in sol-gel 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 sol-gel matrixes with pore throat diameters of nanometers. The catalytic activity of the matrix arrays for anaerobic reduction of tetrachloroethylene (PCE), trichloroethylene (TCE), and carbon tetrachloride (CT) was examined. Experiments were performed under conditions pertinent to groundwater systems, with titanium citrate and zero-valent iron as electron donors. All chloro-organic compounds were reduced in the presence of several sol-gel-metalloporphyrinogen hybrids (heterogeneous catalysts). For example, cobalt-5,10,15,20-(4-hydroxyphenyl)-21H,23H-porphine (TP(OH)P-Co) and cyanocobalamin (vitamin B₁₂) 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 sol-gel 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.

Breakthrough curves (BTC) of a passive tracer in macroscopically homogeneous granular materials were measured in a series of column experiments. The early and late arrival times were observed to differ systematically from theoretical predictions. An ensemble-averaged distribution of particle transfer rates were found to be in excellent agreement with the entire series of observations. It was proposed that the subtle and residual pore-scale disorder effects in the porous media can account for these observations.

This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium 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 (M_aa, M_ab, M_ba, and M_bb), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ_ac and χ_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 χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested.

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, small-scale heterogeneities (residues) probabilistically using a continuous time random walk (CTRW) formalism and the large-scale heterogeneity variations (trends) deterministically. This formulation leads to a Fokker-Planck equation with a memory term (FPME) and a generalized concentration flux term. The former term captures the non-Fickian 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 non-Fickian 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 advection-dispersion 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 two-dimensional 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.

We investigate continuous time random walk (CTRW) theory, which often assumes an algebraic decay for the single transition time probability density function (pdf) ψ(t)∼t^-1-β for large times t. In this form, β is a constant (0

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection-dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale 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 non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.

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.

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 non-Fickian (anomalous) transport behavior. The general ensemble-averaged transport equation is shown to be equivalent to a continuous time random walk (CTRW) and reduces to the conventional forms of the advection-dispersion 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 Lévy flights is critically examined. In order to determine chemical transport in field-scale 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.

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 laboratory-scale experiments is considered to evaluate density-dependent, saltwater-freshwater flow patterns in both the saturated and partially saturated zones. The laboratory experiments demonstrate clearly that significant lateral flows and coupled density-driven 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.

We present a physical model to explain the behavior of long-term, 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 power-law, indicating low-level 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(-1-beta). The CTRW using this power-law psi(t) (with 0

Nuclear magnetic resonance imaging (NMRI) is applied to noninvasively measure flow and dissolution patterns in natural, rough-walled, water-saturated halite fractures. Three-dimensional 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 large-scale wall roughness. 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 Damköhler number. At high Damköhler numbers the dissolution patterns are dominated by the flow structure. In addition, at high Damköhler 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 Damköhler 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.

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 X-ray 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 small-sample electrical conductivity on saturation is examined by using a random walk method.

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 advection-dispersion 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 non-Gaussian features in the transport, over different scales, which are accounted for quantitatively by the theory. The key parameter β 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 non-stationary aspects of a field site on a larger spatial scale (trends) with a probabilistic treatment of unresolved structure on a smaller scale (residues).

Stochastic models that account for a wide range of pore-scale effects are discussed in the context of two-phase, immiscible displacement problems in natural porous media. We focus on migration of dense, nonaqueous phase liquids (DNAPLs) through water-saturated 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 two-phase 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.

In spite of many years of intensive study, our current abilities to actually quantify and predict contaminant migration in natural geological formations remain severely limited. While transport theories that treat homogeneous porous media are mathematically convenient, such homogeneity rarely, if ever, exists in the field. The heterogeneity of natural geological formations at a wide range of scales necessitates consideration of more sophisticated transport theories. [first paragraph]

We analyze a set of observations from a recently published, field-scale tracer test in a fractured till. These observations demonstrate a dominant, underlying non-Fickian 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 non-Fickian modes of contaminant migration can be overcome. (C) 2001 Elsevier Science B.V.

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, and based on geological evidence, two-dimensional 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.

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.

We analyze measured breakthrough curves in laboratory model which consists of a uniformly heterogeneous porous medium; these curves were previously shown to be indicative of scale-dependent transport and therefore inconsistent with the (macroscopic) advection-dispersion equation [Silliman and Simpson, 1987]. Our analysis is based on an analytical expression for the first-passage 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 β; this exponent is related to the low-velocity tail of the velocity distribution. The FPTD curves fit well the measured data, with a single value of the β exponent over the spatial/temporal scale of the experiment. This is in contrast to previous analyses using solutions of the Gaussian-based advection-dispersion equation with time-independent parameters in a uniform flow field. 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 advection-dispersion theory. Hence the CTRW represents a potentially valuable tool in the assessment of dispersive processes in heterogeneous porous media.

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.

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 Navier-Stokes equations in these fracture intersections indicate that non-linear inertial effects become important for Reynolds numbers as tow as 1-100. Such Reynolds numbers often exist in naturally fractured formations, particularly in karst systems and in the vicinity of wells during pump tests.

Flow through a natural fracture crossing unsaturated chalk in an arid region was investigated in a field experiment using a specially 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 segment 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

We present a three-dimensional (3-D) 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 field-length dependence of permeability observed in fractured and heterogeneous porous formations.

Relationships between three-dimensional fracture networks consisting of polydisperse disks and the corresponding two-dimensional 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.

The precipitation and dissolution of reactive solutes, transported under the action of fully developed laminar flow in saturated fractures, is analyzed assuming an irreversible first-order 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 fiat, 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 half-life 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.

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 pore-scale descriptions of the medium and the physics of pore-scale 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.

We use a mapping between the continuum percolation model and the Potts fluid (a system of interacting [Formula Presented]-state spins which are free to move in the continuum) to derive the low-density 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).

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.

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 advection-dispersion 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 time-dependent 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.

Removal of organic matter and nitrate was studied in a laboratory-scale 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 in-situ using nylon-mesh 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 first-order 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.

An intuitive, trial-and-error approach to history-matching (parameter identification) can be costly and time-consuming. In an attempt to reduce these factors, considerable efforts have been made, primarily in the petroleum engineering literature, to automate history-matching procedures for implementation on high-speed computers; and several methods based on ex post facto techniques have been developed for this purpose. This study examines two frequently used automatic history-matching algorithms and demonstrates their fundamental weaknesses. -Authors

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 long-term eruptive behavior of Old Faithful. -Authors

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.

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.

We present a systematic derivation of the percolation thresholds in anisotropic systems composed of permeable elongated boxes. The analytic calculation is based on an order-by-order diagrammatic expansion of the pair-connectedness 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.

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 dead-end 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.

This paper deals with the frequently encountered problem of pre-posterior 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.