An experimental study of coupled heat and moisture transfer in soils at high temperature conditions for a medium coarse soil

https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.131Get rights and content

Highlights

  • Characteristics of heat and moisture transfer at different temperature levels.

  • Characteristics of heat and moisture transfer at various temperature differences.

  • For dry soil at steady-state conditions highest temperature deviation is 18.6%.

  • For dry soil at steady-state conditions highest heat flux difference is 34%.

  • For wet soil at steady-state conditions highest temperature deviation is 7.7%.

  • For wet soil at steady-state conditions highest heat flux difference is 4.2%.

  • Maximum moisture flux of 0.003 kg·s–1·m–2 is obtained after 30 minutes into the test.

  • Maximum moisture flux is obtained at the temperature gradient of 560 °C· m–1.

Abstract

A study of one-dimensional heat and moisture transfer within a vertical soil column was conducted experimentally. An experimental soil cell made of stainless-steel tube was exposed to differential heating by sandwiching it between two differentially-heated plates for studying heat and moisture transfer in the soil column at different temperature levels and temperature differences. The main objective of the experimental study was to investigate heat and moisture transfer characteristics in a medium coarse soil at temperatures greater than 40 °C up to 90 °C. In this paper, the results are divided into two parts. In the first part, the results of heat transfer in dry soil are presented and discussed. The purpose was to investigate temperature distributions and heat gains/losses at the steady-state conditions along the soil cell at the various temperature levels. In the second part, the results of heat and moisture transfer in wet soil are presented and discussed. In this part, the transient temperatures, moisture contents and thermal properties along the soil column were obtained using the heat pulse technique. A loamy sand with a porosity and an initial water content of 0.40 and 0.26 m3/m3 (or saturation degree of 65%), respectively, was used in the study. The results of the case with the largest temperature difference of 65 °C (or overall temperature gradient of 440 °C/m) and the mean temperature of 55 °C are presented in detail. The highest temperature gradient of 1450 °C/m was recorded at the top of the soil column during the test, driving downward a moisture flux as high as 3 g/s·m2 when the soil was at temperature of 51 °C and saturation degree of 40%. Under these conditions, the thermal vapor diffusion is the main mechanism for the moisture flux.

Introduction

Soil is considered, in a strict sense, a non-homogeneous and non-isotropic porous material. The term soil, as used by engineers, refers to a complicated material consisting of solid particles of various compositions (mineral and organic) and various shapes and sizes that are randomly arranged with pore spaces between them. These pores contain air and usually water in its various phases as vapor, liquid or ice. The composition of naturally occurring soil varies continuously because of changes in the amount and phase of water at various locations. These changes result mainly from the continuously varying temperature field to which the soil is subject. The daily temperature fluctuations are superimposed on the seasonal cycle, and there is a geothermal heat flux resulting from the flow of heat upwards from the hot interior of the ground. These changing temperature gradients alter the soil composition, particularly with regard to changes in the amount, phase and condition of water. This leads to variations in the thermal properties of the soil [5]. The study of moisture and heat distribution in soil is useful in various applications, such as: agriculture, earth-contact structure, underground power cable and so on. Thermal gradients induce moisture transfer and so this transport will affect heat flow. Indeed moisture and temperature fields are more or less coupled. The thermal gradients produced by these temperature fields cause soil moisture to be transferred from warmer to cooler areas in both the vapor and the liquid phases. The thermally induced moisture flow may significantly affect the net transfer of the soil water and nutrients by changing the moisture content gradients and the capillary conductivity, in addition to the direct effects of mass transfer. Thermal moisture transport may be thought of as the moisture flux through soil which arises solely due to a temperature gradient. Thermal gradients and the associated moisture transfer cause changes in moisture contents and pressures. These effects need to be taken into consideration in analysis of net moisture flow through the soil. Moisture flows in the form of liquid and vapor where the flow of the vapor phase is mainly considered as a molecular diffusion process. In unsaturated soils, thermally induced flow increases rapidly as the moisture content decreases. Indeed, the decrease in moisture content is accompanied by a decrease in the thermal liquid moisture flow and an increase in the thermal vapor moisture flow [2]. The process of heat and moisture transfer in soil is basically driven by the thermal gradients. This process forms the temperature and moisture content distribution in the soil as a porous medium. The conveyance of the latent heat by vapor migration through the soil and within the boundary of the soil/atmosphere is a main process which controls the coupling between the heat and the moisture transfer. Precise modeling of coupled heat and moisture transfer in a high-temperature ground thermal storage is yet wanting and so requires further studies.

To predict heat transfer in soil under the conditions of steady and unsteady heat flow requires knowledge of the basic thermal properties of soil [23]. While the flow of heat by conduction is the predominating mechanism, all possible mechanisms are involved for the flow of heat from warmer to cooler regions. The soil composition, temperature, moisture content and structure affect the heat transfer. Generally convection and radiation have negligible effects [16]. The heat transfer process may be affected by water phase changes in the soil. In unsaturated soils the process of evaporation along with the vapor diffusion results in condensation and subsequently heat transfer. Freezing of water or melting of ice within soils may also result in considerable latent heat effects. In many situations the transfer of moisture and heat occurs simultaneously [4]. Heat conduction occurs in all the soil constituents. In soil the amount of heat transferred by conduction increases as the soil dry bulk density increases and as its degree of saturation (Sr) increases. Heat being conducted through soil will take all available paths. Paths through contacting solids generally provide the major part of conductive heat transfer but thermal contact resistance may exist. There is a thermal contact resistance that gives a sudden discontinuity in the soil temperature at the contacts between solid particles with an interstitial fluid such as a gas or liquid in the gap around contacts [3]. Similar effects may be expected to occur in the pore spaces of the soil. The physics concerning the process of heat and mass transfer in soils has been a subject of importance for researchers in the past decades. The mathematical analysis of the response of soil to atmospheric conditions is problematical since the temperature and moisture variations in the unsaturated soil rely on the parameters in the transport equations, which in turn depend on the temperature and moisture content [9]. The pioneers in modeling coupled heat and mass transfer in porous media are Philip and de Vries [25] and Luikov [14]. Philip and de Vries [25] came up with theoretical expressions for the thermal moisture and isothermal moisture diffusivities which occur in their governing partial differential equations of combined heat and moisture transfer in which they are dependent on soil hydraulic conductivity, temperature gradients, moisture potential and soil volumetric water content. They also presented an equation of heat conduction that incorporated latent heat transfer by water vapor diffusion. Later de Vries [4] generalized these equations by considering moisture and latent heat storage in the vapor phase and sensible heat transfer by liquid migration in the soil. Hence recent mathematical models mainly engage in modifications of Philip, de Vries and Luikov’s approaches [34] which have been studied by Moukalled and Saleh [17].

In 1982, Milly [15] revised Philip and de Vries [25] and de Vries [4] formulation of moisture and heat transport in partially saturated soil accounting for the coupling between the fields of matric potential and temperature, instead of moisture content and temperature, as dependent variables. In the revised model, the effects of heat of wetting on transport processes were considered. They showed that thermodynamic equilibrium assumptions at pore scale are acceptable for most conditions. To account for the effects of hysteresis for nonisothermal conditions, they proposed a generalization of isothermal hysteresis models according to capillary hypothesis. Indeed, the revised model facilitated an important generalization of the theory to accommodate the complications of hysteresis and inhomogeneity.

Based on their previous work, i.e. Nassar and Horton [18], [20], Nassar and Horton [22] presented a detailed theory to describe the simultaneous heat, water, and solute transfer in unsaturated nonisothermal, salty porous media. Their theory includes three fully-coupled partial differential equations. Heat, water, and solute move in the presence of temperature, matric pressure head, solution osmotic pressure head and solute concentration gradients. Their theory includes a number of transport coefficients for heat, water, and solute. As the second objective, they showed values of the coefficients and evaluated their dependency on temperature, water content and solute concentration. Their study showed that all the coefficients are affected by water content and temperature. Some of the coefficients decrease their values as the solute concentration increases. They concluded that thermal vapor transfer is a main mechanism for flow of vapor in unsaturated porous media. In order to test their theory, Nassar and Horton [19] conducted experimental observations of steady-state distributions of temperature, water content, and solute concentration within horizontal closed soil columns (polyvinyl chloride (PVC) tubes of 0.14-m-long and 0.04-m-diameter) containing either moist salinized or moist solute-free soils. However, they only tested on a silt loam soil at a temperature difference of about 10 °C and a mean temperature of about 14 °C. They found that the presence of solute clearly affected the observed soil water redistributions in the soil columns. Basing the experimental results, Nassar and Horton [18] calculated the transport coefficients and magnitudes of water fluxes for the steady-state soil columns. In 1992, Nassar et al. [21] conducted experimental and numerical studies to compare the measured and simulated soil temperature, water content, and solute concentrations in soil columns (0.10-m-long and 0.04-m-diameter) at 60 and 156 h. Stainless-steel and PVC tubes were used to contain a sandy loam soil and a silt loam soil in their experiments at horizontal and vertical positions with temperature differences of about 10 °C and 6 °C and mean temperatures of about 27 °C and 12 °C, respectively. These experimental studies are very limited and at low temperature levels and differences. In addition, there were no uncertainty analyses to indicate the accuracy of the results and also no discussion about the extent of heat loss/gain from/to the soil columns.

In the early 1980s, a team of researchers at the Lawrence Berkeley National Laboratory (LBNL) in Berkeley, California, USA developed a computer code for geothermal reservoir simulation. It was first released as TOUGH (TOUGH is an acronym for Transport of Unsaturated Groundwater and Heat) in 1987 [26]. In 2004, Pruess [28] discussed about the TOUGH suite of codes which have the capability to model multiphase flows with phase change in porous or fractured media. Pruess summarized history and goals in the development of the TOUGH codes, and presented the governing equations for multiphase, multicomponent fluid flows and heat flow; but special emphasis was given to space discretization using integral finite differences. TOUGH2 was released in 1991 as a general-purpose numerical simulation program for nonisothermal flows of multiphase, multicomponent fluids in porous media [27]. In early 2008, Finsterle et al. [6] discussed fundamental and computational challenges in simulating vadose zone processes and demonstrated some capabilities of the TOUGH suite of codes using illustrative examples. They demonstrated that the TOUGH simulators are well suited to perform advanced vadose zone studies.

Later in 2008, as the preface for a special issue of the Vadose Zone Journal, which contained revised and expanded versions of a selected set of papers presented at the TOUGH Symposium 2006,1 Liu et al. [13] underlined that simulation results from any numerical model are advantages only when the model is precisely validated with data collected at suitable scales, and only when the model can apprehend the key physical mechanisms for the flow and transport processes under consideration. So far, the uses of TOUGH family of codes are mainly in vadose zone hydrology, environmental engineering, hydrocarbon and gas hydrate recovery, carbon sequestration, nuclear waste isolation, mining engineering, and geothermal reservoir engineering. Therefore, its use in the simulations of ground source heat pump (GSHP) and ground thermal energy storage (GTES), especially for high-temperature applications up to 90 °C, has yet to be validated and confirmed.

Ricerca sul Sistema Energetico [30] in Milano, Italy has developed an integrated Geo-Modeling Analysis System (GeoSIAM) modeling suite, containing Tough2RdS simulator which was developed starting from the TOUGH2 code, to characterize a geological reservoir for low, medium and high enthalpy gas or CO2 or geothermal storage, studying its behavior from a fluid dynamics, geomechanical and geochemical point of view. In 2016, Perego et al. [24] used the GeoSIAM to evaluate a borehole thermal energy storage (BTES) with 15 vertical boreholes in Alessandria (Italy). The objective of their study was to implement sustainability assessment of a medium to large scale GSHP system located in heating-dominated region which was characterized by a heterogeneous subsurface. They found that heterogeneous, stratigraphic subsurface with some poor thermal-property layers can cause thermal imbalance issues especially in heating dominated regions. It was concluded that the developed 3D-model of the BTES, considering geological, energetic and engineering parameters of GSHP systems, is proved to be very valuable in assessing sustainability of the systems. Although the use of GeoSIAM and TOUGH in GSHP and GTES is still very limited, they have great potential for future studies of such applications.

In order to better utilize the heat from industrial waste heat or the solar energy, it is beneficial to store it in a high-temperature GTES; so the stored heat can be retrieved directly without the need of using a GSHP. This would improve the efficiency of such systems. The Drake Landing Solar Community2 is a community in Okotoks, Alberta, Canada, equipped with a central solar heating system and other energy efficient technology. It is a first-in-the-world example of successful application of seasonal high-temperature GTES system with over 90% of residential space heating needs being met by solar thermal energy which is collected and stored in the ground at high temperatures up to 80 °C over the summer season. In this project, the GTES contains mainly clay which has relatively low moisture diffusivity and so it can retain its moisture content and be able to store the heat. This type of soil cannot be found in most places; therefore to improve the design of such systems, a fundamental study in high-temperature heat and moisture transfer in other types of soils is essential. From the literature only few studies about high-temperature heat and moisture transfer with experimental or field comparisons were found. For example the existing work, e.g. Reuss et al. [29], showed numerical simulations and compared numerical results with experimental data of 60 °C and below. Therefore, the objective of this study is to precisely measure transient variations of temperature, water content and thermal properties along a vertical closed soil column, which contains a medium coarse soil, exposing to a wide range of thermal conditions (10 < T < 90 °C) and present the experimental results, especially at high-temperature conditions, which can be used in the future as a benchmark to validate any numerical simulation model or code of coupled heat and moisture transfer in soils. The results of other soil types and soil-column orientations will also be published in the future. If a numerical simulation model or code, e.g. GeoSIAM, functions well on the benchmark problem, it should also function well on simulating high-temperature GTES.

Section snippets

Materials and methods

In this study, a specially-designed experimental apparatus for studying one-dimensional heat and moisture transfer in a soil column has been considered. The intended study is focused on high-temperature conditions (up to 90 °C), so that the phenomenon of high-temperature coupled heat and moisture transfer in various soils can be studied more precisely. In this paper, a medium coarse soil (Matilda soil) was studied. Matilda soil is from Ontario, Canada with an identification code of ON-3 which

Heat transfer in dry soil

The study of dry soil is beneficial because the capability of the apparatus to have one-dimensional heat transfer can be examined in the most critical condition. The critical condition is expected for dry soil because of its low thermal conductivity; therefore, the highest temperature and heat transfer deviations are expected to occur within the soil. Several tests were carried out to investigate the heat transfer in dry soil. For the series of tests, dry Matilda soil was evenly packed in the

Experimental uncertainties

In this study, the analysis was carried out to estimate the uncertainties of the experimentally-determined quantities using root-sum-square (RSS) technique according to the classic work of Kline and McClintock [10]. The analysis was consisted of four main parts: 1- Uncertainty analysis of heat pulse technique, 2- Uncertainty analysis of soil sample preparation, 3- Uncertainty analysis of temperature measurement via T-TDR Probe and 4- Uncertainty analysis of volumetric moisture content.

Conclusion

One-dimensional heat and moisture transfer characteristics of a loamy sand (Matilda soil) was experimentally studied within a vertical soil column at high temperatures. The results were presented for both dry and wet soils. For the case of dry soil, temperature distributions and heat gains/losses at the steady-state conditions along the soil cell at the various temperature levels were investigated.

The highest temperature deviation from the LTP was found to be 18.6% at the temperature level of

Conflict of interest

The authors declared that there is no conflict of interest.

Acknowledgements

Financial support through a Discovery Grant provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. Also the support from the Faculty of Engineering and Architectural Science of Ryerson University through a Dean’s Research Fund-Undergraduate Research Experience (DRF-URE) award for Shekinah Shilesh is much appreciated.

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