Critical Review of Coupled Flux Formulations for Clay Membranes Based on Nonequilibrium Thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, ne, or a restrictive tortuosity factor, tr, in the formulation of Fick's first law for diffusion. Both ne and tr have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Flux and resident injection in gaseous advection experiments

The occurrence of gaseous pollutants in soils has stimulated many experimental activities, including forced ventilation in the field as well as laboratory transport experiments with gases. The dispersion coefficient in advective-dispersive gas phase transport is often dominated by molecular diffusion, which leads to a large overall dispersivity gamma. Under such conditions it is important to distinguish between flux and resident modes of solute injection and detection. The influence of the inlet type oil the macroscopic injection mode was tested in two series of column experiments with gases at different mean flow velocities nu. First we compared infinite resident and flux injections, and second, semi-infinite resident and flux injections. It is shown that the macroscopically apparent injection condition depends on the geometry of the inlet section. A reduction of the cross-sectional area of the inlet relative to that of the column is very effective in excluding the diffusive solute input, thus allowing us to use the solutions for a flux Injection also at rather low mean flow velocities nu. If the whole cross section of a column is exposed to a large reservoir like that of ambient air, a semi-infinite resident injection is established, which can be distinguished from a flux injection even at relatively high velocities nu, depending on the mechanical dispersivity of the porous medium.

Gas emissions and ROV survey tracks of the Regab pockmark (Northern Congo Fan)

Pockmarks are seafloor depressions commonly associated with fluid escape from the seabed and are believed to contribute noticeably to the transfer of methane into the ocean and ultimately into the atmosphere. They occur in many different areas and geological contexts, and vary greatly in size and shape. Nevertheless, the mechanisms of pockmark growth are still largely unclear. Still, seabed methane emissions contribute to the global carbon budget, and understanding such processes is critical to constrain future quantifications of seabed methane release at local and global scales. The giant Regab pockmark (9°42.6' E, 5°47.8' S), located at 3160 m water depth near the Congo deep-sea channel (offshore southwestern Africa), was investigated with state-of-the-art mapping devices mounted on IFREMER's (French Research Institute for Exploitation of the Sea) remotely operated vehicle (ROV) Victor 6000. ROV-borne micro-bathymetry and backscatter data of the entire structure, a high-resolution photo-mosaic covering 105,000 m2 of the most active area, sidescan mapping of gas emissions, and maps of faunal distribution as well as of carbonate crust occurrence are combined to provide an unprecedented detailed view of a giant pockmark. All data sets suggest that the pockmark is composed of two very distinctive zones in terms of seepage intensity. We postulate that these zones are the surface expression of two fluid flow regimes in the subsurface: focused flow through a fractured medium and diffuse flow through a porous medium. We conclude that the growth of giant pockmarks is controlled by self-sealing processes and lateral spreading of rising fluids. In particular, partial redirection of fluids through fractures in the sediments can drive the pockmark growth in preferential directions.

Experimental determination of barium isotope fractionation during diffusion and adsorption processes at low temperatures

Variations in barium (Ba) stable isotope abundances measured in low and high temperature environments have recently received increasing attention. The actual processes controlling Ba isotope fractionation, however, remain mostly elusive. In this study, we present the first experimental approach to quantify the contribution of diffusion and adsorption on mass- dependent Ba isotope fractionation during transport of aqueous Ba2+ ions through a porous medium. Experiments have been carried out in which a BaCl2 solution of known isotopic composition diffused through u-shaped glass tubes filled with silica hydrogel at 10 C and 25 C for up to 201 days. The diffused Ba was highly fractionated by up to -2.15‰ in d137/134Ba, despite the low relative difference in atomic mass. The time-dependent isotope fractionation can be successfully reproduced by a diffusive transport model accounting for mass-dependent differences in the effective diffusivities of the Ba isotope species (D137Ba/D134Ba = (m134/m137)^b). Values of b extracted from the transport model were in the range of 0.010–0.011. Independently conducted batch experiments revealed that adsorption of Ba onto the surface of silica hydrogel favoured the heavier Ba isotopes (a = 1.00015 ± 0.00008). The contribution of adsorption on the overall isotope fractionation in the diffusion experiments, however, was found to be small. Our results contribute to the understanding of Ba isotope fractionation pro- cesses, which is crucial for interpreting natural isotope variations and the assessment of Ba isotope ratios as geochemical proxies.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Caracterización de la cerámica para su empleo como material de enfriamiento evaporativo en la envolvente de los edificios = Ceramic characterization towards its application as evaporative cooling material in building envelopes

El presente trabajo de investigación determina las características de la cerámica que más eficientemente se comporta a evaporación y a enfriamiento. Con el objeto de ser empleado como material integrado en la envolvente de los edificios para reducir su carga de refrigeración. La cerámica es un buen material para ser empleado para la refrigeración por evaporación. Es un sólido poroso inerte que, tras ser sometido a cocción a temperaturas por encima de los 900ºC, resulta uno de los materiales que mejor se comportan como contenedor de agua en su red capilar para, posteriormente, ir liberándola por evaporación al mismo tiempo que se enfría su superficie. La metodología general de investigación, se divide en tres etapas: Búsqueda y análisis del estado de la técnica y de la investigación. Estudio teórico de la eficacia del enfriamiento evaporativo como estrategia de enfriamiento pasivo en la arquitectura. Etapa experimental, desarrollada en tres fases: una primera de definición de los parámetros determinantes del Enfriamiento Evaporativo en piezas cerámicas, una segunda de selección cerámica y diseño de ensayos experimentales y una tercera de caracterización de la cerámica bajo criterios de evaporación y de enfriamiento. El recorrido por el estado de la cuestión ha identificado las aplicaciones tecnológicas y las investigaciones científicas que emplean el Enfriamiento Evaporativo con piezas cerámicas como técnica de enfriamiento. Como resultado se ha obtenido una tabla de clasificación de sistemas de enfriamiento evaporativo y se ha constatado que el conjunto de las aplicaciones están centradas en el diseño de piezas o sistemas pero que, sin embargo, no existe una definición de las características de la cerámica para su empleo como material de enfriamiento por evaporación. El estudio teórico de la eficacia del empleo del enfriamiento evaporativo como estrategia de enfriamiento pasivo en la arquitectura se ha realizado mediante cálculos de porcentaje de ampliación de horas en confort con empleo de técnicas de enfriamiento evaporativo directo e indirecto (EED y EEI). Como resultado se obtienen unos mapas para el ámbito español de potencial de aplicación del EED y EEI. Los resultados permiten afirmar que mediante EE se puede llegar a confort en prácticamente la totalidad de las horas de los días más cálidos del año en muchas localidades. La metodología experimental se ha desarrollado en tres fases. En la fase inicial, se han definido los parámetros determinantes del enfriamiento evaporativo en un medio cerámico mediante ensayos experimentales de capacidad de evaporación y de caracterización. Se realizaron un total de 12 ensayos. Se determinó que el material cerámico tiene una gran influencia en la capacidad de evaporación y enfriamiento en las piezas cerámicas, apoyando la hipótesis inicial y la necesidad de caracterizar el material. La primera fase empírica se centró en la selección cerámica y el diseño de los ensayos experimentales de comportamiento hídrico. Se seleccionaron muestras de 5 tipos de cerámica. Se realizaron 4 tipos de ensayos de caracterización y 6 tipos de ensayos experimentales de comportamiento hídrico (total 123 muestras ensayadas). Los resultados obtenidos son de dos tipos, por un lado, se determinó cuál es el tipo de cerámica que más eficientemente se comporta a EE y, por otro, se rediseñaron los ensayos de la última fase experimental. Para la segunda fase experimental se seleccionaron cerámicas de fabricación manual abarcando el mayor número de localidades del ámbito español. Se realizaron ensayos de caracterización de 7 tipos y ensayos de comportamiento hídrico de 5 tipos (total 197 muestras ensayadas). Los resultados de caracterización han permitido aportar unos rangos de las características de la cerámica que más eficientemente se comporta en los ensayos de comportamiento hídrico. Al final de la investigación se ha caracterizado el material cerámico aportando características acerca de su porosidad, capacidad de absorción, color, rugosidad y mineralogía. Así como datos de referencia de su comportamiento hídrico. Además se ha desarrollado una metodología de ensayo específica que permite evaluar la capacidad de enfriamiento eficiente de una pieza cerámica. ABSTRACT The purpose of this research is to determine the characteristics of ceramic materials having the most efficient performance in terms of evaporation and cooling, so that they can be integrated in building envelopes to reduce cooling loads. Ceramics are suitable materials for cooling through passive evaporation. After being fired at temperatures over 900 °C (1,652 °F), the capillary network of this inert porous medium turns to be excellent to retain water, which is progressively liberated by evaporation while the material surface gets colder. Research methodology has involved the following steps: Search and analysis on the state of the art in technology and research. Theoretical study on the efficiency of evaporation as passive cooling strategies in buildings. Experimental stage developed in three phases, namely: definition of parameters determining evaporative cooling in ceramic elements; ceramic selection and design of experimental tests; characterization of ceramic materials under evaporation and cooling criteria. Search and analysis on the state of the art in this field have been useful to identify technology applications and scientific research where ceramics are employed for evaporative cooling. The resulting table shows that applications are wholly focused on the design of pieces and systems. Nonetheless, there is lack of definition of material characteristics in this scope. The theoretical study on efficiency of the passive strategy applied to buildings has been realized by calculation of the percentage increase in comfort hours through direct/indirect evaporative cooling techniques (DEC/IEC). The mapping of their potential application in Spain clearly shows that comfort conditions can be reached in almost all the hours of the hottest days in many towns. In the initial phase of the experimental stage, parameters determining evaporative cooling in ceramic media have been defined. For this purpose, characterization tests and evaporation and cooling rates experiments have been carried out; the number of samples tested amounted to 12. It has been concluded that material characteristics have great influence on these rates, which supports the initial hypothesis and the need for their characterization. The first empirical phase has focused on ceramic selection and design of water behaviour experimental methods. The samples covered five different kinds of ceramic materials. Four different characterization tests and six different water behaviour experiments were carried out; the number of samples tested amounted to 123. The experimental testing procedures served to determine the most efficient types of ceramic materials in terms of evaporative cooling efficiency and, at the same time, made it necessary to change the original designed experimental test for the last phase. In the second phase, a number of varied hand-made ceramic tiles have been selected. Seven different characterization tests and five different water behaviour tests were carried out; the number of samples amounted to 197. The results of characterization served to establish a range of features in ceramic materials according to their efficiency in water behaviour experiments. Finally, ceramic materials have been characterized according to porosity, water absorption, colour, surface roughness and mineralogy. Also, reference data regarding water behaviour have been included. Moreover, an innovative and specific experimental test to evaluate cooling efficiency of ceramic tiles has been developed.

Water reduction in waste-activated sludge by resettling and filtration in batch. Phase (1): pilot-scale experiments to optimize performance

This article describes an effective procedure for reducing the water content of excess sludge production from a wastewater treatment plant by increasing its concentration and, as a consequence, minimizing the volume of sludge to be managed. It consists of a pre-dewatering sludge process, which is used as a preliminary step or alternative to the thickening. It is made up of two discontinuous sequential stages: the first is resettling and the second, filtration through a porous medium. The process is strictly physical, without any chemical additives or electromechanical equipment intervening. The experiment was carried out in a pilot-scale system, consisting of a column of sedimentation that incorporates a filter medium. Different sludge heights were tested over the filter to verify the influence of hydrostatic pressure on the various final concentrations of each stage. The results show that the initial sludge concentration may increase by more than 570% by the end of the process with the final volume of sludge being reduced in similar proportions and hydrostatic pressure having a limited effect on this final concentration. Moreover, the value of the hydrostatic pressure at which critical specific cake resistance is reached is established.

A unique behavior of sub-critical hydrocarbon permeability in activated carbon at low pressures

In our study on sub-critical hydrocarbon permeation in activated carbon, a minimum in the total permeability (B-T) at low pressure has been observed for only long-chain hydrocarbons such as n-hexane and n-heptane. Such an observation suggests that the minimum appearance depends on the properties of permeating vapors as well as the porous medium. In this paper a permeation model is presented to explain the minimum behavior with the allowance of the collision-reflection factor in the Knudsen diffusivity to be a function of surface loading. Surface diffusion was found to be very significant compared to other transport mechanisms such as Knudsen diffusion and gaseous viscous flow at low pressures. Since the gaseous viscous flow contributes negligibly to the B, at low pressures, the minimum appearance in the B, is mainly attributed to the interplay between Knudsen diffusion and surface diffusion. Also, the molecular structure of adsorbates plays an important role in the minimum appearance.

Numerical investigation of seawater intrusion at Gooburrum, Bundaberg, Queensland, Australia

Seawater intrusion in coastal agricultural areas due to groundwater abstraction is a major environmental problem along the northeastern coast of Australia. Management options are being explored using numerical modelling, however, questions remain concerning the appropriate level of sophistication in models, choice of seaward boundary conditions, and how to accommodate heterogeneity and data uncertainty. The choice of seaward boundary condition is important since it affects the amount of salt transported into the aquifers and forms the focus of the present study. The impact of this boundary condition is illustrated for the seawater-intrusion problem in the Gooburrum aquifers, which occur within Tertiary sedimentary strata. A two-dimensional variable-density groundwater and solute-transport model was constructed using the computer code 2DFEMFAT (Cheng et al. 1998). The code was tested against an experiment for a steady-state freshwater-saltwater interface and against the Elder (Elder 1967) free-convection problem. Numerical simulations show that the imposition of the commonly-used equivalent hydrostatic freshwater heads, combined with a constant salt concentration at the seaward boundary, results in overestimated seawater intrusion in the lower Gooburrum aquifer. Since the imposition of this boundary condition allows water flow across the boundary, which subsequently takes salt into the aquifer, a careful check is essential to estimate whether too much mass of salt is introduced.

Thermal strain in the mushy zone related to hot tearing

A volume-averaged two-phase model addressing the main transport phenomena associated with hot tearing in an isotropic mushy zone during solidification of metallic alloys has recently been presented elsewhere along with a new hot tearing criterion addressing both inadequate melt feeding and excessive deformation at relatively high solid fractions. The viscoplastic deformation in the mushy zone is addressed by a model in which the coherent mush is considered as a porous medium saturated with liquid. The thermal straining of the mush is accounted for by a recently developed model taking into account that there is no thermal strain in the mushy zone at low solid fractions because the dendrites then are free to move in the liquid, and that the thermal strain in the mushy zone tends toward the thermal strain in the fully solidified material when the solid fraction tends toward one. In the present work, the authors determined how variations in the parameters of the constitutive equation for thermal strain influence the hot tearing susceptibility calculated by the criterion. It turns out that varying the parameters in this equation has a significant effect on both liquid pressure drop and viscoplastic strain, which are key parameters in the hot tearing criterion. However, changing the parameters in this constitutive equation will result in changes in the viscoplastic strain and the liquid pressure drop that have opposite effects on the hot tearing susceptibility. The net effect on the hot tearing susceptibility is thus small.

Entropy generation for microscale forced convection: effects of different thermal boundary conditions, velocity slip, temperature jump, viscous dissipation, and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001

Theory and application of inverse problems in groundwater: numerical, laboratory and field studies.

Aquifers are a vital water resource whose quality characteristics must be safeguarded or, if damaged, restored. The extent and complexity of aquifer contamination is related to characteristics of the porous medium, the influence of boundary conditions, and the biological, chemical and physical processes. After the nineties, the efforts of the scientists have been increased exponentially in order to find an efficient way for estimating the hydraulic parameters of the aquifers, and thus, recover the contaminant source position and its release history. To simplify and understand the influence of these various factors on aquifer phenomena, it is common for researchers to use numerical and controlled experiments. This work presents some of these methods, applying and comparing them on data collected during laboratory, field and numerical tests. The work is structured in four parts which present the results and the conclusions of the specific objectives.

Osmotic dehydration in plant tissues

The primary aim of the thesis is to provide a comprehensive investigation of the osmotic dehydration processes in plant tissue. Effort has been concentrated on the modelling for simulating the processes. Two mathematical models for simulating the mass transfer during osmotic dehydration processes in plant tissues are developed and verified using existing experimental data. Both models are based on the mechanism of diffusion and convection of any mobile material that can transport in plant tissues. The mass balance equation for the transport of each constituent is established separately for intracellular and extra-cellular volumes with taking into account the mass transfer across the cell membrane the intracellular and extra-cellular volumes and the shrinkage of the whole tissue. The contribution from turgor pressure is considered in both models. Model two uses Darcy’s law to build the relation between shrinkage velocity and hydrostatic pressure in each volume because the plant tissue can be considered as the porous medium. Moreover, it has been extended to solve the multi-dimensional problems. A lot of efforts have been made to the parameter study and the sensitivity analyses. The parameters investigated including the concentration of the osmotic solution, diffusion coefficient, permeability of the cell membrane, elastic modulus of the cell wall, critical cell volume etc. The models allow us to quantitatively simulate the time evolution of intracellular and extra-cellular volumes as well as the time evolution of concentrations in each cross-section.

Preparation and characterization of gas-filled liposomes:Can they improve oil recovery?

Although well known for delivering various pharmaceutical agents, liposomes can be prepared to entrap gas rather than aqueous media and have the potential to be used as pressure probes in magnetic resonance imaging (MRI). Using these gas-filled liposomes (GFL) as tracers, MRI imaging of pressure regions of a fluid flowing through a porous medium could be established. This knowledge can be exploited to enhance recovery of oil from the porous rock regions within oil fields. In the preliminary studies, we have optimized the lipid composition of GFL prepared using a simple homogenization technique and investigated key physico-chemical characteristics (size and the physical stability) and their efficacy as pressure probes. In contrast to the liposomes possessing an aqueous core which are prepared at temperatures above their phase transition temperature (Tc), homogenization of the phospholipids such as 1,2-dipalmitoyl-sn-glycero-3- phosphocholine (DPPC) or 1,2-distearoyl-sn-glycero-3-phosphocoline (DSPC) in aqueous medium below their Tc was found to be crucial in formation of stable GFL. DSPC based preparations yielded a GFL volume of more than five times compared to their DPPC counter part. Although the initial vesicle sizes of both DSPC and DPPC based GFL were about 10 μm, after 7 days storage at 25°C, the vesicle sizes of both formulations significantly (p < 0.05) increased to 28.3 ± 0.3 μm and 12.3 ± 1.0 μm, respectively. When the DPPC preparation was supplemented with cholesterol at a 1:0.5 or 1:1 molar ratio, significantly (p < 0.05) larger vesicles were formed (12-13 μm), however, compared to DPPC only vesicles, both cholesterol supplemented formulations displayed enhanced stability on storage indicating a stabilizing effect of cholesterol on these gas-filled vesicles. In order to induce surface charge on the GFL, DPPC and cholesterol (1: 0.5 molar ratio) liposomes were supplemented with a cationic surfactant, stearylamine, at a molar ratio of 0.25 or 0.125. Interestingly, the ζ potential values remained around neutrality at both stearylamine ratios suggesting the cationic surfactant was not incorporated within the bilayers of the GFL. Microscopic analysis of GFL confirmed the presence of spherical structures with a size distribution between 1-8 μm. This study has identified that DSPC based GFL in aqueous medium dispersed in 2% w/v methyl cellulose although yielded higher vesicle sizes over time were most stable under high pressures exerted in MRI. Copyright © Informa Healthcare USA, Inc.