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A Review on Coupled Heat and Water Vapour Transport in Unsaturated Soils
Abstract
Coupled heat and water transport has found to be relevant in unsaturated soils because of increasing interest in disposal of radioactive wastes, geothermal energy, hydrology and agricultural problems. In an unsaturated soil, heat can be either latent or sensible or both and water may take the form of either liquid or vapour or both. The impact of thermal gradient on water vapour movement in terms of both vapour and liquid flow is essential and it requires accurate experimental quantification and representation for modeling of coupled heat and water vapour flow. Although it is possible to calculate the total water vapour flux, it is difficult to distinguish experimentally between liquid and vapour fluxes in unsaturated soils. This paper focuses on providing a critical review on heat and water vapour transport in unsaturated soils.
... These coupled processes are less studied in geotechnical engineering, although more commonly seen to be of importance in soil science. 8 The classical theory for coupled diffusion of vapour and flow of liquid water in soils was set out by Philip & De Vries, 9 based on adaptions of Darcy's Law and Fick's Law. However, in some cases the theory does not give a good fit to experimental data (e.g. ...
... 15,16 Nonetheless, the complexity of fully coupling heat and mass transfer including liquid water and vapour flow means that relatively little work has been carried out on the subject within the geotechnical sphere. 8 There are also relatively few recent datasets available for testing theory, with notable recent exceptions including the laboratory scale physical models of Moradi et al. 15 and Smits et al. 12 . Experimental data at the micro scale can be particularly challenging to obtain. ...
Coupled hydrothermal flow can occur in soils, for example in applications such as ground heat storage and nuclear waste disposal. Therefore, approaches to quantitative analysis of water transfer in response to imposed thermal gradients are required, especially in unsaturated conditions. Analysis methods also require validation by laboratory and field data, which can be hard to obtain. This paper explores the possibility of using X-ray μCT techniques to observe and quantify water content changes in soils under thermal gradients. Specimens of a fine sand and a silty fine sand were prepared at degrees of saturation between 20% and 50%, before being subjected to heating from their base. Repeated scans, set up to balance image quality and scan duration, were carried out during the heating process, and Gaussian decomposition techniques were used to determine the changing soil phase proportions throughout the experiments. Based on these results and the accompanying numerical simulation of the experiments, it is shown that rapid vapour diffusion plays a more significant role than liquid flow in all cases. The rate of water content and hence degree of saturation change was more rapid in the less saturated specimens, especially for the fine sand. In practical terms, these moisture changes would result in reduction in thermal conductivity, especially in the soils of lower saturation. As well as providing insight into the dominant water transfer processes, the experiments show the feasibility of applying X-ray μCT techniques to thermal problems in soil mechanics.
The role of soil in current climate models is reviewed and discussed, with a focus on developments over the last two decades. Soil modeling may be divided into three major parts: simulation of soil hydrological dynamics, soil biogeochemistry and the soil thermal environment. Each of these three major parts is summarized with a brief description of current best practice and developments. Specific issues and modifications relevant to four extreme environments are highlighted: drylands, tropical moist and wet forests, cold regions, and peatlands and wetlands. Finally, current advances in the areas of hyperresolution and coupled model environments are discussed, which we see as the two leading edges of current soil model development.
A theoretical model is presented to predict moisture and air flow
in an unsaturated soil under non-isothermal conditions. The model takes into account the complete constitutive relations for an unsaturated soil. Two partial differential equations are derived; one for the water phase and the other for the air phase. These two equations are solved simultaneously and the solutions give the pore-air and pore-water pressures under transient flow conditions. In addition, a partial differential heat flow equation is solved and the corresponding pore-air and pore water pressures are adjusted to account for temperature changes.
Vapor movement is often an important part in the total water flux in the vadose zone of arid or semiarid regions because the soil moisture is relatively low. The two major objectives of this study were to develop a numerical model in the HYDRUS-1D code that (i) solves the coupled equations governing liquid water, water vapor, and heat transport, together with the surface water and energy balance, and (ii) provides flexibility in accommodating various types of meteorological information to solve the surface energy balance. The code considers the movement of liquid water and water vapor in the subsurface to be driven by both pressure head and temperature gradients. The heat transport module considers movement of soil heat by conduction, convection of sensible heat by liquid water flow, transfer of latent heat by diffusion of water vapor, and transfer of sensible heat by diffusion of water vapor. The modifications allow a very flexible way of using various types of meteorological information at the soil-atmosphere interface for evaluating the surface water and energy balance. The coupled model was evaluated using field soil temperature and water content data collected at a field site. We demonstrate the use of standard daily meteorological variables in generating diurnal changes in these variables and their subsequent use for calculating continuous changes in water contents and temperatures in the soil profile. Simulated temperatures and water contents were in good agreement with measured values. Analyses of the distributions of the liquid and vapor fluxes vs. depth showed that soil water dynamics are strongly associated with the soil temperature regime.
Coupled heat and water transport in soils has enjoyed extensive focus in soil physics and hydrology and yet, until recently, there has never been a satisfactory comparison of water vapor fluxes measured in the field with theory. At least two factors have led to this, first, most of the experimental work has been laboratory oriented with steady state boundary conditions imposed and second, there have been relatively few field experiments to test the existing theory. In this paper we review a new theoretical development which explains field observations of water vapor movement. The diurnal warming at the land surface leads to an expansion and contraction of the soil air as it warms and cools resulting in a convective (or “advective”) transport of water vapor. This mechanism has important consequences for the transport of any vapor in the soil air near the land-atmosphere interface.
The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on regional and global scales, in particular in relation to mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation is still rarely considered in most models or practical applications. Moreover, questions remain about the correct computation of key factors such as the soil surface resistance or the soil surface temperature. This study was conducted to: (a) implement a fully coupled numerical model to solve the governing equations for liquid water, water vapor, and heat transport in bare soils, (b) test the numerical model with detailed measurements of soil temperature, heat flux, water content, and evaporation from the surface, and (c) test different formulations for the soil surface resistance parameter and test their effect on soil evaporation. The code implements a non-isothermal solution of the vapor flux equation that accounts for the thermally driven water vapor transport and phase changes. Simulated soil temperature, heat flux, and water content were in good agreement with measured values. The model showed that vapor transport plays a key role in soil mass and energy transfer and that vapor flow may induce sinusoidal variations in soil water content near the surface. Different results were obtained for evaporation calculations, depending on the choice of the soil surface resistance equation, which was shown to be a fundamental term in the soil–atmosphere interactions. The results also demonstrated that soil water dynamics are strongly linked to temperature variations and that it is important to consider coupled transport of heat, vapor and liquid water when assessing energy dynamics in soils.
Compacted bentonite blocks have been heated and hydrated in a stainless steel cell in order to simulate, in the laboratory, the conditions of the clay barrier in a high-level radioactive waste repository. Temperature distributions at different times, rate of hydration, final water content and dry density have been measured. Some chemical parameters, as electrical conductivity in an aqueous extractable amorphous silica, have also been obtained. For the periods of time considered (up to 2500 h), the hydration process is not affected by the thermal gradient, the high suction of the bentonite being the critical factor in the initial water uptake of the clay barrier. A remarkable saline environment has been detected near the heater, due to salt migration towards dried areas. This phenomenon should be taken into account in further investigations of the mechanical and geochemical behaviour of the clay barrier.
This paper focuses on characterization of the heat-transfer and water-fl ow processes in physical models of borehole heat exchanger arrays in unsaturated soil layers. The overall goal is to develop a data set that can be used to validate the coupled thermo-hydraulic fl ow models needed to simulate the effi ciency of heat transfer in soil-borehole thermal energy storage systems. Two bench-scale physical models consisting of a triangular array of vertical heat exchangers within a layer of unsaturated silt were constructed in insulated cylindrical tanks to evaluate the impact of different boundary conditions on the heat-transfer and water-fl ow processes in the silt during heat injection into the array. In one model, the heat exchangers were placed at a radial location at 26% of the tank radius, while in the other model, the heat exchangers were placed on the inside of the tank wall. During circulation of heated fl uid through the heat exchangers, the changes in soil temperature and volumetric water content along the centerline of the array at different depths were measured using dielectric sensors. The thermal conductivity and specifi c heat capacity of the silt were also monitored using a thermal probe at the center of the silt layer at midheight. Permanent drying was observed for the soil within the array with the smaller spacing, while an increase in water content was observed in the array with a spacing equal to the container diameter. An increase in thermal conductivity of the soil was observed within the array in the case of larger spacing, while the opposite was observed in the case of smaller spacing. The results indicate the possible formation of a convective cell within the larger array as water was driven inward from the heat exchangers. These results highlight the importance of coupled heat transfer and water fl ow in soil-borehole thermal energy storage systems in the vadose zone.
A theory of moisture movement in porous, materials under temperature gradients is developed which explains apparently discordant experimental information, including (a) the large value of the apparent vapor transfer, (b) effect of moisture content on net moisture transfer, and (c) the transfer of latent heat by distillation.
The previous simple theory of water vapor diffusion in porous media under temperature gradients neglected the interaction of vapor, liquid and solid phases, and the difference between average temperature gradient in the air‐filled pores and in the soil as a whole. With these factors taken into account, an (admittedly approximate) analysis is developed which predicts orders of magnitude and general behavior in satisfactory agreement with the experimental facts.
An important implication of the present approach is that experimental methods used to distinguish between liquid and vapor transfer have not done so, since what has been supposed to be vapor transfer has actually been series‐parallel flow through liquid ‘islands’ located in a vapor continuum.
Equations describing moisture and heat transfer in porous materials under combined moisture and temperature gradients are developed. Four moisture‐dependent diffusivities arising in this connection are discussed briefly.
Heat and mass transfer between capillary-porous bodies and surrounding incompressible liquid accompanied by a change of phase is not only of theoretical interest but also of great practical importance for some technological processes. Heat and mass transfer inside a porous body (internal heat and mass transfer) also has its unique character. Even now the mechanism of heat and mass transfer in evaporation processes is scantily investigated, and analytical investigations do not, therefore, lead to reliable results. This chapter presents an experimental study of heat and mass transfer in evaporation processes. To elucidate peculiarities of heat transfer with simultaneous mass transfer, a dry body (pure heat transfer) and a moist body (heat transfer in the presence of mass transfer) are investigated. Such a comparison makes it possible to establish relations for interconnected heat and mass transfer processes. In order to describe quantitative relations it is necessary to have a method of analysis which makes it possible to consider the interaction of the heat and mass transfer processes. One such method is the thermodynamics of irreversible processes. The experimental data presented well confirm the mathematical theory of thermodynamics of irreversible transfer processes.
Results of an experimental and theoretical investigation of heat and moisture movement in unsaturated MX-80 bentonite are presented. A thermo-hydraulic cell that allows measurement of transient temperatures and facilitates the determination of pseudo-transients of moisture content, dry density and chemical composition has been used to perform thermal gradient tests. Results of a number of tests are presented, and observation of the accumulation of chloride ions near the hot end clearly indicates that there is a cycle of vapour and liquid moisture movement, with vapour moving from hotter to cooler regions, condensing, and then moving as liquid towards the hotter regions. An empirical method is applied to calculate approximate vapour fluxes using measured variations in chloride ion concentration and moisture content with time. The vapour fluxes calculated empirically are found to be lower than those determined by some existing vapour flow theories. Subsequently, an existing vapour flow model is modified to represent the observed vapour fluxes more closely.
Previous experiments have demonstrated “enhanced” water vapor fluxes from partially saturated porous media relative to fluxes predicted based on Fick's law. This led to various mechanistic and phenomenological enhancement factors to reconcile discrepancies between experiments and predictions. In the present study, analyses of abrupt transitions from liquid- to diffusion-controlled mass transport during evaporation from porous media is used to offer new insights regarding key assumptions and adequacy of experimental setups used to develop vapor transport enhancement factors. We reevaluate these concepts considering the role of capillary-induced liquid flow through the unsaturated zone in supplying the total fluxes. The extent and existence of hydraulic connections through the unsaturated zone has been predicted theoretically and demonstrated experimentally using high-resolution X-ray tomography of sand columns during evaporation. Extending these results to the late stages of evaporation from porous media shows simultaneous capillary induced liquid flow and vapor diffusion supplying the total vapor fluxes as validated by laboratory evaporation experiments. Additionally, analysis of evaporation from porous media provides well defined conditions for testing vapor transport based solely on Fick's law. New insights regarding transport mechanisms controlling evaporation rates from porous media emphasize the extended role of capillary flows beyond previously assumed models and may reconcile observations with prediction without invoking unobservable local thermal gradients and similar enhancement factors. We illustrate that considering the coupling between capillary flow and vapor diffusion predicted by Fick's law of diffusion without any enhancement factors is the essential key to estimate the total vapor flux.
Redistribution of soil water within insulated, uniformly packed, horizontal samples of unsaturated Columbia fine sandy loam at several soil‐water contents was studied in response to imposed temperature gradients ranging from 0.5 to 1.0C/cm. Soil bulk density and initial, transient, and final soil‐water‐content distributions were determined each 0.5‐cm along the column by gamma‐radiation attenuation. Initial, transient, and final soil temperature distributions were monitored by glass‐encased thermistors at 2‐cm intervals—both at the center and 0.3 cm from the column wall. Apparent thermal and isothermal soil‐water diffusivity values were calculated using transient water content data. The observed net water flux was found to increase with decreasing water content throughout the 0.077–0.274 cm ³ /cm ³ range. For Columbia soil at 0.077 cm ³ /cm ³ the observed mean net water flux across 1‐cm sections of the soil showed acceptable agreement with that predicted by the theory of Philip and deVries; Fick's law and the modified Taylor‐Cary irreversible thermodynamic equation both underpredicted the observed fluxes.
Using an air gap technique, it has been shown that the flow of moisture in the soil from warm to cool regions might occur largely in the vapor phase. This is accompanied by a return flow of liquid water in response to an induced flow potential gradient. The use of wire screens to make air gaps interferes with this process.
The measured diffusion coefficient for vapor flow was higher than had been expected from diffusion data, but was substantially in agreement with that of other workers. The reasons for this high diffusion coefficient might be that the diffusion of moisture and heat is coupled in soils; the phenomena of surface migration and molecular hopping of adsorbed water might also cause this increase.
The factors having greatest effect on the moisture distribution in continuous soil columns in a closed system are: (1) the diffusion and the convection of vapor or some related processes; (2) the evaporation and condensation occurring in the two end regions of the cylinders; (3) the hydraulic conductivity of the soil.
The thickness of the air gap in broken columns influences the amount of water that will be transferred in the vapor phase and must be considered whenever an air gap is used to prevent fluid flow.
The existence of two distinct drying and wetting moisture characteristic curves has been verified, and they play an important part in determining the liquid flow of moisture in the soil. The influence of this factor as well as the reason for the large vapor transfer need further study in relation to the transfer of soil moisture.
Many parts of the Great Basin have thick zones of unsaturated alluvium
which might be suitable for disposing of high-level radioactive wastes.
A mathematical model accounting for the coupled transport of energy,
water (vapor and liquid), and dry air was used to analyze
one-dimensional, vertical transport above and below an areally extensive
repository. Numerical simulations were conducted for a hypothetical
repository containing spent nuclear fuel and located 100 m below land
surface. Initial steady state downward water fluxes of zero
(hydrostatic) and 0.0003 m yr-1 were considered in an attempt
to bracket the likely range in natural water flux. Predicted
temperatures within the repository peaked after approximately 50 years
and declined slowly thereafter in response to the decreasing intensity
of the radioactive heat source. The alluvium near the repository
experienced a cycle of drying and rewetting in both cases. The extent of
the dry zone was strongly controlled by the mobility of liquid water
near the repository under natural conditions. In the case of initial
hydrostatic conditions, the dry zone extended approximately 10 m above
and 15 m below the repository. For the case of a natural flux of 0.0003
m yr-1 the relative permeability of water near the repository
was initially more than 30 times the value under hydrostatic conditions,
consequently the dry zone extended only about 2 m above and 5 m below
the repository. In both cases a significant perturbation in liquid
saturation levels persisted for several hundred years. This analysis
illustrates the extreme sensitivity of model predictions to initial
conditions and parameters, such as relative permeability and moisture
characteristic curves, that are often poorly known.
A theoretical, experimental and numerical investigation of combined heat and mass transfer in unsaturated sand is described. The theoretical formulation adopted is that of Philip & de Vries but slightly different forms of the vapor transfer diffusivities are developed. Experimental work is reported on the determination, for a medium sand, of the full set of material parameters incorporated in the formulation, using both methods developed by the authors and standard techniques. Explicit equations are given for the capillary potential, unsaturated hydraulic conductivity and thermal conductivity as functions of moisture content and temperature. Laboratory experimental results are presented for the steady temperature distribution within an unsaturated sample of the sand in which a rod is buried and heated.
The transient heat and mass transfer in a moist porous medium adjacent to a cylindrical heat source is analyzed in order to characterize the thermal stability of the medium. Thermal instability occurs in a moist porous medium as a result of significant drying due to excessive thermally induced moisture movement. A dry zone is created which propagates into the medium and thereby inhibits dissipation of heat from the source. The drying of the porous medium adjacent to the heat source is predicted to occur in two stages. The value of the critical moisture content is found to be essentially independent of the strength of the heat source. The parameters which most significantly influence the transport processes are identified and correlated on the basis of numerical solutions of the governing equations. The critical moisture content and critical heat flux are defined and used to quantify thermal stability limits.
In this paper, moisture migration in loess considering temperature effect is studied by tests on unsaturated loess samples with different densities and initial moisture contents. Test results reveal that obvious changes in moisture content distribution in a loess sample can be observed after temperature difference is exerted on the two ends of the sample. Moisture content at the cold end increases and that at the hot end decreases. Under the effect of temperature difference, moisture content difference at the two ends of a soil sample is related to the initial moisture content, soil density, and magnitude of the temperature difference. Generally speaking, larger temperature differences and smaller soil densities result in more obvious moisture migration and larger moisture content differences at the two ends of the soil sample. When the initial moisture content is large, the moisture content difference caused by a temperature difference is small; when the initial moisture content is small, the moisture content difference caused by a temperature difference is also small; when the initial moisture content is moderate, the moisture content difference caused by a temperature difference is large. After the analysis of test results, taking the soil density and moisture content into account, a formula is obtained to determine the moisture content gradient resulting from the temperature gradient. Reliability of the formula is verified by comparing the measured and calculated data. Because of the reverse migration of liquid water and water vapor at the end of the experiment, it is difficult to determine the thermal potential and matrix potential. Based on the experimental data, this paper probes into the water potential equation that can be used for stability analysis. The equation considers the comprehensive impact of soil density, temperature gradient, moisture content, and moisture content gradient on water potential. It only applies to analyze stable distributions of temperature and does not apply to unstable temperature distributions.
Some transfer processes in soil are considered with respect to recent developments in the theory of thermodynamics of irreversible processes. The theory provides a general and systematic guide for setting up interrelated equations describing the transport of one or more components through soil. Darcy's law and the “diffusion equation” are shown to be components of this general development. Particular attention is given to the non‐isothermal flow of moisture and energy through soil. A general relation between the fluxes induced by the combined gradients of moisture content, temperature, and solutes is also suggested.
A computer code TRUCHAM developed to model the coupled heat and moisture flow through a porous medium is used to assess the thermohydraulic performance of the clay-based engineered barrier encapsulating nuclear waste containers in a deep geological disposal vault in the borehole emplacement concept. This paper contains an overview of the development of the numerical model and its application to the buffer–container experiment at the Underground Research Laboratory of Atomic Energy of Canada Limited Research. The thermohydraulic transport parameters required for the analysis were determined by specially designed laboratory experiments. The needs for further development of the model and the material properties are identified. Key words : buffer, clay barrier, coupled heat and moisture, heater experiment, numerical model, nuclear waste disposal, thermal diffusivity, unsaturated soil.
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
Non isothermal moisture movement in unsaturated kaolin is investigated in a series of experiments. Vapour transfer is then empirically quantified, and its theoretical representation considered. A thermo-hydraulic cell is used to apply thermal and hydraulic gradients to confined specimens in a number of thermal gradient, thermal-hydraulic gradient, and isothermal-hydraulic tests. Transient measurements of the thermal regime are made, and end of test measurement of moisture content, porosity, and chemical composition from a number of identical tests run for different durations allow pseudo transient variations of these parameters to be established. In each of the tests, where a thermal gradient is applied, the accumulation of chloride ions in the hottest regions indicates a cyclic movement of vapour and liquid moisture. Estimated vapour fluxes are determined by consideration of overall moisture and conservative ion movements in the sealed thermal gradient tests. These vapour fluxes are then compared to those predicted by an established vapour flow theory, and a modification to this theory is proposed based on a variable enhancement factor. © 2011 ASTM Int'l (all rights reserved).
To determine moisture movement and heat transfer through an unsaturated soil under temperature and volumetric water content gradients, it is necessary to have knowledge of phenomenological coefficients of the soil. However, in unsaturated flow, i.e. flow through unsaturated soil, these phenomenological coefficients are not constants, but vary with volumetric water content as well as temperature. In this paper, an identification technique is proposed for evaluation of the phenomenological coefficients. The phenomeno-logical coefficients are first assumed to be certain kinds of functions of volumetric water content and temperature. The choice of the functional forms is based on an understanding of the physical situation, and previous knowledge of water flow in the isothermal case. The constant parameters associated with the functional forms are evaluated through the use of the identification technique. Once these phenomenological coefficients are obtained as certain functions of the volumetric water content and the temperature for a specified soil, analysis of coupled moisture flow and heat transfer in the unsaturated soil can proceed.
A theoretical model is presented to predict simultaneous transient coupled heat and moisture transfer in partly saturated soils. The formulation is in terms of volumetric moisture content, is two dimensional, includes gravitational flow and takes into account latent heat of vaporization effects. The numerical solution of the problem is accomplished by means of a finite element solution algorithm. Predictions from the numerical model are used to investigate the importance of gravitational flow, for the case of a soil stratum subjected to evaporation losses at the surface. The results achieved show good qualitative agreement with expected behaviour.
An analysis of coupled heat and moisture movement in unsaturated soil in terms of the fundamental potentials for flow is examined. The approach adopted is based on the assumption that the total potential for liquid flow consists of two components, the elevation and the capillary potential. The fundamental potentials employed in the work are, therefore, temperature and capillary potential.
The full theoretical formulation of the problem is presented, together with full details of the solution algorithm employed. Spatial discretization is achieved via the use of the finite element method, with the time-varying behaviour described by a finite difference technique. Soil parameter variations as functions of both temperature and moisture content are included in a one-dimensional approach.
The work is applied to a practical engineering problem, namely heat and mass transfer in the upper layers of a soil stratum. This problem is of importance to the utilities, since many services are buried in this zone. Material parameters obtained from an associated programme of experimental work are employed. Moisture content and temperature profiles indicating the extent and rate of penetration of drying and heating fronts are produced.
This study was done to evaluate a phenomenological approach for determining the coupled heat and water diffusion parameters. This technique requires the use of both theory and experimental data. The transport equation was solved analytically using nondimensional analysis.
The calculated diffusion parameters of a compacted sand–bentonite-based material are presented. The agreement between the back calculated values and the experimental volumetric water content profiles was good. Practical application of the technique is also discussed.
This paper considers a particular heat and water vapor transfer problem in a nonisothermal steady state system. The results are applicable to a condition that may develop during the normal drying of porous materials. The rate equations are based on the theory of irreversible thermodynamics and the validity of Onsager's reciprocity relation is demonstrated with a macroscopic analysis of this particular model. The results of an experiment are presented which show the effects of temperature, pressure, and salt concentration on the evaporation and heat transfer from a porous plate. These data combined with the thermodynamic flux equations provide a means of calculating the effective concentration of dissolved salts at the air-water interface and the approximate depth of this increased concentration. The analysis also provides a method for determining the rate-limiting process in the experiment.
A discussion of water phase change in unsaturated soils that develop capillary effects is first carried out in the paper. A distinction between the GR (geothermal reservoir) and the NUS (nonisothermal unsaturated soil) approaches is performed. Several aspects concerning advective and nonadvective fluxes of vapour are described secondly and some relationships concerning the case of mass motion in a closed system subjected to temperature gradients derived. Since the structure of unsaturated clays changes with moisture content, in order to correctly simulate the coupled phenomena induced by temperature gradients a model for intrinsic permeability as a function of humidity is required. A preliminary version of the model is presented and applied to interpret a laboratory test by means of a numerical simulation using CODE_BRIGHT
Several series of one-dimensional heat and moisture flow tests were performed to examine the moisture and temperature distributions in the buffer material compacted to a dry density of 1.67 Mg m−3 and water content of 17.7%. In all tests, water was allowed to infiltrate into a horizontal soil column from one end under a constant hydrostatic head of 276 kPa. Also the specimens were heated from the other end by the heater to a constant temperature.It is experimentally demonstrated that the moisture moves from both ends toward the mid part of the soil column due to both thermal gradient from one end and hydraulic gradient from the other end. It was observed that, in spite of no overall volume change, local volume change occurs in the system. The measured temperatures along the length of the specimen indicate that temperature distributions stabilize within a short period of time. The time required for the temperature to stabilize decreases as the heater skin temperature increases.The diffusivity parameters are calculated using the measured moisture and temperature profiles combined with the finite difference method. Powell's optimization algorithm was used to determine the material parameters. Good agreements between experimentally measured and calibrated volumetric water content shows that the diffusion parameters can be expressed in a linear function of the volumetric water content and temperature.
The heat induced moisture movement in buffer materials to be used for the geologic disposal of high-level radioactive waste is investigated by a series of experiments and numerical simulations. Highly compacted blocks of Japanese Na bentonite are used in the experiments as the buffer materials. Mechanistic models including those proposed by Philip et al. and Ewen et al. are formulated to the finite-element program which are applied to interpret the experimental results. The applicability of the mechanistic models to the compacted bentonite is examined. The numerical results agree well with the experimental results qualitatively, though a few quantitative discrepancies are found. Those discrepancies demand better descriptions for material properties on compacted bentonite and introducing an effect of volume change associated with change in water content.
The paper presents a general methodology to perform backanalysis of laboratory tests involving thermohydraulic behaviour of bentonite in a systematic manner. The procedure is based on a maximum likelihood approach that defines a probabilistic framework in which error measurements and the reliability of the parameters identified can be estimated. The method is applied to the identification of some thermal and hydraulic properties of a bentonite specimen, using temperature and water content measurements as input data. Three basic cases have been considered: (a) thermal case, identifying the global thermal conductivity, λe, and the global specific heat, ce; (b) hydraulic case, identifying the tortuosity factor, τ, and the exponent of the unsaturated permeability law, n; and (c) thermohydraulic case, in which τ, n, and the saturated thermal conductivity, λsat, have been estimated. A numerical code that solves the coupled thermohydraulic equations has been used as main computational tool. A detailed description of the experimental device and a discussion on the tests results and on the parameters identified are also included. The values obtained are within the normal range of these parameters, but the method provides a systematic and consistent procedure to find the best parameters that reproduce the measurements for the selected models. Also the method gives an insight into the model structure, and allows detecting dependence and coupling between parameters.
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