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In an accompanying paper, we presented an overview of a wide variety of modeling concepts, varying in complexity, used to describe evaporation from soil. Using theoretical analyses, we explained the simplifications and parameterizations in the different approaches. In this paper, we numerically evaluate the consequences of these simplifications and parameterizations. Two sets of simulations were performed. The first set investigates lateral variations in vertical fluxes, which emerge from both homogeneous and heterogeneous porous media, and their importance to capturing evaporation behavior. When evaporation decreases from parts of the heterogeneous soil surface, lateral flow and transport processes in the free flow and in the porous medium generate feedbacks that enhance evaporation from wet surface areas. In the second set of simulations, we assume that the vertical fluxes do not vary considerably in the simulation domain and represent the system using one-dimensional models which also consider dynamic forcing of the evaporation process, for example, due to diurnal variations in net radiation. Simulated evaporation fluxes subjected to dynamic forcing differed considerably between model concepts depending on how vapor transport in the air phase and the interaction at the interface between the free flow and porous medium were represented or parameterized. However, simulated cumulative evaporation losses from initially wet soil profiles were very similar between model concepts and mainly controlled by the desorptivity, Sevap, of the porous medium, which depends mainly on the liquid flow properties of the porous medium.

Evaporation is an important component of the soil water balance. It is composed of water flow and transport processes in a porous medium that are coupled with heat fluxes and free air flow. This work provides a comprehensive review of model concepts used in different research fields to describe evaporation. Concepts range from nonisothermal two-phase flow, two-component transport in the porous medium that is coupled with one-phase flow, two-component transport in the free air flow to isothermal liquid water flow in the porous medium with upper boundary conditions defined by a potential evaporation flux when available energy and transfer to the free airflow are limiting or by a critical threshold water pressure when soil water availability is limiting. The latter approach corresponds with the classical Richards equation with mixed boundary conditions. We compare the different approaches on a theoretical level by identifying the underlying simplifications that are made for the different compartments of the system: porous medium, free flow and their interface, and by discussing how processes not explicitly considered are parameterized. Simplifications can be grouped into three sets depending on whether lateral variations in vertical fluxes are considered, whether flow and transport in the air phase in the porous medium are considered, and depending on how the interaction at the interface between the free flow and the porous medium is represented. The consequences of the simplifications are illustrated by numerical simulations in an accompanying paper.

© 2016 Elsevier Ltd A major concern resulting from the increased use and production of natural gas has been how to mitigate fugitive greenhouse gas emissions (predominantly methane) from natural gas infrastructure (e.g., leaky shallow pipelines). Subsurface migration and atmospheric loading of methane from pipeline leakage is controlled by source configurations and subsurface soil conditions (e.g., soil heterogeneity and soil moisture) and are further affected by atmospheric conditions (e.g., wind and temperature). However, the transport and attenuation of methane under varying subsurface and atmospheric conditions are poorly understood, making it difficult to estimate leakage fluxes from methane concentration measurements at and above the soil surface. Based on a series of controlled bench-scale experiments using a large porous media tank interfaced with an open-return wind tunnel, this study investigated multiphase processes controlling migration of methane from a point source representing a buried pipeline leaking at fixed flow rate (kg/s) under various saturation and soil-texture conditions. In addition, potential effects of atmospheric boundary controls, wind (0.5 and 2.0 m s−1) and temperature (22 and 35 °C), were also examined. Results showed the distinct effects of soil heterogeneity and, to a varying degree, of soil moisture on surface methane concentrations. In addition, results also showed the pronounced effects of wind and, to a lesser degree, of temperature on surface methane concentrations in the presence of varying soil and moisture conditions. The observed subsurface methane profiles were simulated using the multiphase transport simulator TOUGH2-EOS7CA. Observed agreement between measured and simulated data demonstrates that for the conditions studied, multiphase migration of a multicomponent gas mixture (including methane) under density-dependent flow can be adequately represented with a Fickian advection-diffusion (or dispersion) model (ADM) framework. The dominant effect of saturation over the soil texture, could also be inferred from numerical characterization.

In this study, we numerically and experimentally evaluated heat transfer in soils under unsaturated conditions in the context of simulating a laboratory-scale, three-dimensional soil-borehole thermal energy storage (SBTES) system. Most previous studies assumed that soil thermal and hydraulic properties are constant and that heat transfer in soil occurs only in the form of conduction, neglecting convective and latent heat transfer. In addition, there is a lack of data from controlled experiments to validate multiphase numerical models that can be used to better study SBTES systems installed in the vadose zone. The goal of this study was to evaluate the significance and impact of variable soil thermal and hydraulic properties, as well as different heat transfer mechanisms, in unsaturated soils. Four laboratory experiments were performed using a three-dimensional laboratory-scale SBTES system, incorporating sensors to collect soil temperature and moisture data at high spatial and temporal resolutions. Experimental data were then used to validate a numerical model that solves for water and vapor flow and considers nonequilibrium phase change. Results revealed that for the test conditions studied, convective heat transfer was higher than conductive heat transfer in the middle of the borehole array. Moreover, for the experiments on unsaturated sand, about 10% of the total heat transfer was in the form of latent heat. Simulation results demonstrated the importance of including both convection and latent heat in SBTES system modeling. Results also revealed a need for using saturation-dependent effective thermal conductivity in modeling SBTES systems in unsaturated soils rather than using constant values such as those obtained from system thermal response tests.

This paper presents a novel method to couple an environmental bioremediation system with a subsurface renewable energy storage system. This method involves treating unsaturated contaminated soil using in-situ thermally enhanced bioremediation, the thermal system is powered by renewable energy. After remediation goals are achieved, the thermal system can then be used to store renewable energy in the form of heat in the subsurface for later use. This method can be used for enhanced treatment of environmental pollutants for which temperature is considered a limiting factor. For instance, this system can be used at a wide variety of petroleum-related sites that are likely contaminated with hydrocarbons such as oil refineries and facilities with above- and underground storage tanks. In this paper, a case-study example was analyzed using a previously developed numerical model of heat transfer in unsaturated soil. Results demonstrate that coupling energy storage and thermally-enhanced bioremediation systems offer an efficient and sustainable way to achieve desired temperature&ndash, moisture distribution in soil that will ultimately enhance the microbial activity.

Implementation of injection-extraction treatment well pairs for in situ, in-well, or on-site remediation may be facilitated by development and application of modeling tools to aid in hydraulic design and remediation technology selection. In this study, complex potential theory was employed to derive a simple one-step design equation and related type curves that permit the calculation of the extraction well capture zone and the hydraulic recirculation between an injection and extraction well pair oriented perpendicular to regional flow. This equation may be used to aid in the design of traditional fully screened injection-extraction wells as well as innovative tandem recirculating wells when an adequate geologic barrier to vertical ground water flow exists. Simplified models describing in situ bioremediation, in-well vapor stripping, and in-well metal reactor treatment efficiency were adapted from the literature and coupled with the hydraulic design equation presented here. Equations and type curves that combine the remediation treatment efficiency with the hydraulic design equation are presented to simulate overall system treatment efficiency under various conditions. The combined model is applied to predict performance of in situ bioremediation and in-well palladium reactor designs that were previously described in the literature. This model is expected to aid practitioners in treatment system screening and evaluation.

Detailed characterization of partially saturated porous media is important for understanding and predicting vadose zone transport processes. While basic properties (e.g., particle- and pore-size distributions and soil-water retention) are, in general, essential prerequisites for characterizing most porous media transport properties, key transport parameters such as thermal conductivity and gas diffusivity are particularly important to describe temperature-induced heat transport and diffusion-controlled gas transport processes, respectively. Despite many experimental and numerical studies focusing on a specific porous media characteristic, a single study presenting a wide range of important characteristics, together with the best-performing functional relationships, can seldom be found. This study characterized five differently textured sand grades (Accusand no. 12/20, 20/30, 30/40, 40/50, and 50/70) in relation to physical properties, water retention, hydraulic conductivity, thermal conductivity, and gas diffusivity. We used measured basic properties and transport data to accurately parameterize the characteristic functions (particle- and pore-size distributions and water retention) and descriptive transport models (thermal conductivity, saturated hydraulic conductivity, and gas diffusivity). An existing thermal conductivity model was improved to describe the distinct three-region behavior in observed thermal conductivity–water saturation relations. Applying widely used parametric models for saturated hydraulic conductivity and soil-gas diffusivity, we characterized porous media tortuosity in relation to grain size. Strong relations among average particle diameter, characteristic pore diameter from soil-water retention measurements, and saturated hydraulic conductivity were found. Thus, the results of this work are useful toward better describing, linking, and predicting mass transfer and pore network properties in variably saturated porous media. © Soil Science Society of America.

© 2015 Elsevier Ltd. A promising energy storage option is to inject and store heat generated from renewable energy sources in geothermal borehole arrays to form soil-borehole thermal energy storage (SBTES) systems. Although it is widely recognized that the movement of water in liquid and vapor forms through unsaturated soils is closely coupled to heat transfer, these coupled processes have not been considered in modeling of SBTES systems located in the vadose zone. Instead, previous analyses have assumed that the soil is a purely conductive medium with constant hydraulic and thermal properties. Numerical modeling tools that are available to consider these coupled processes have not been applied to SBTES systems partly due to the scarcity of field or laboratory data needed for validation. The goal of this work is to test different conceptual and mathematical formulations that are used in heat and mass transfer theories and determine their importance in modeling SBTES systems. First, a non-isothermal numerical model that simulates coupled heat, water vapor and liquid water flux through soil and considers non-equilibrium liquid/gas phase change was adopted to simulate SBTES systems. Next, this model was used to investigate different coupled heat transfer and water flow using nonisothermal hydraulic and thermal constitutive models. Data collected from laboratory-scale tank tests involving heating of an unsaturated sand layer were used to validate the numerical simulations. Results demonstrate the need to include thermally induced water flow in modeling efforts as well as convective heat transfer, especially when modeling unsaturated flow systems. For the boundary conditions and soil types considered, convective heat flux arising from thermally induced water flow was greater than heat transfer due to conductive heat flux alone. Although this analysis needs to be applied to the geometry and site conditions for SBTES systems in the vadose zone, this observation indicates that thermally induced water flow can have significant effects on the efficiency of heat injection and extraction.

Evaporation is directly influenced by the interactions between the atmosphere, land surface and soil subsurface. This work aims to experimentally study evaporation under various surface boundary conditions to improve our current understanding and characterization of this multiphase phenomenon as well as to validate numerical heat and mass transfer theories that couple Navier-Stokes flow in the atmosphere and Darcian flow in the porous media. Experimental data were collected using a unique soil tank apparatus interfaced with a small climate controlled wind tunnel. The experimental apparatus was instrumented with a suite of state of the art sensor technologies for the continuous and autonomous collection of soil moisture, soil thermal properties, soil and air temperature, relative humidity, and wind speed. This experimental apparatus can be used to generate data under well controlled boundary conditions, allowing for better control and gathering of accurate data at scales of interest not feasible in the field. Induced airflow at several distinct wind speeds over the soil surface resulted in unique behavior of heat and mass transfer during the different evaporative stages.

International audience; In an effort to develop methods based on integrating the subsurface to the atmospheric boundary layer to estimate evaporation, we developed a model based on the coupling of Navier-Stokes free flow and Darcy flow in porous medium. The model was tested using experimental data to study the effect of wind speed on evaporation. The model consists of the coupled equations of mass conservation for two-phase flow in porous medium with single-phase flow in the free-flow domain under nonisothermal, nonequilibrium phase change conditions. In this model, the evaporation rate and soil surface temperature and relative humidity at the interface come directly from the integrated model output. To experimentally validate numerical results, we developed a unique test system consisting of a wind tunnel interfaced with a soil tank instrumented with a network of sensors to measure soil-water variables. Results demonstrated that, by using this coupling approach, it is possible to predict the different stages of the drying process with good accuracy. Increasing the wind speed increases the first stage evaporation rate and decreases the transition time between two evaporative stages (soil water flow to vapor diffusion controlled) at low velocity values; then, at high wind speeds the evaporation rate becomes less dependent on the wind speed. On the contrary, the impact of wind speed on second stage evaporation (diffusion-dominant stage) is not significant. We found that the thermal and solute dispersion in free-flow systems has a significant influence on drying processes from porous media and should be taken into account.

[1] Bare soil evaporation is a key process for water exchange between the land and the atmosphere and an important component of the water balance. However, there is no agreement on the best modeling methodology to determine evaporation under different atmospheric boundary conditions. Also, there is a lack of directly measured soil evaporation data for model validation to compare these methods to establish the validity of their mathematical formulations. Thus, a need exists to systematically compare evaporation estimates using existing methods to experimental observations. The goal of this work is to test different conceptual and mathematical formulations that are used to estimate evaporation from bare soils to critically investigate various formulations and surface boundary conditions. Such a comparison required the development of a numerical model that has the ability to incorporate these boundary conditions. For this model, we modified a previously developed theory that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion to better account for dry soil conditions. Precision data under well-controlled transient heat and wind boundary conditions were generated, and results from numerical simulations were compared with experimental data. Results demonstrate that the approaches based on different boundary conditions varied in their ability to capture different stages of evaporation. All approaches have benefits and limitations, and no one approach can be deemed most appropriate for every scenario. Comparisons of different formulations of the surface boundary condition validate the need for further research on heat and vapor transport processes in soil for better modeling accuracy.

[1] In the shallow subsurface immediately below the land-atmosphere interface, it is widely recognized that the movement of water vapor is closely coupled to thermal processes. However, their mutual interactions are rarely considered in most soil water modeling efforts or in practical applications where it becomes necessary to understand the spatial and temporal distribution of soil moisture. The validation of numerical models that are designed to capture these processes is difficult due to the scarcity of field or laboratory data with accurately known hydraulic and thermal parameters of soils, limiting the testing and refinement of heat and water transfer theories. The goal of this paper is to perform controlled experiments under transient conditions of soil moisture and temperature and use this data to test existing theories and develop appropriate numerical models. Water vapor flow under varying temperature gradients was implemented on the basis of a concept that allows nonequilibrium liquid/gas phase change with gas phase vapor diffusion. To validate this new approach, we developed a long column apparatus equipped with a network of sensors and generated data under well-controlled thermal boundary conditions at the soil surface. The nonequilibrium approach yielded good agreement with the experimental results, validating the hypothesis that transport in the gas phase is better suited to be modeled with nonequilibrium liquid/gas phase change for highly transient field conditions where the thermal conditions at the land-atmosphere interface are constantly changing.

[1] Recently improved ECH2O soil moisture sensors have received significant attention in many field and laboratory applications. Focusing on the EC-5 sensor, a simple and robust calibration method is proposed. The sensor-to-sensor variability in the readings (analog-to-digital converter (ADC) counts) among 30 EC-5 sensors was relatively small but not negligible. A large number of ADC counts were taken under various volumetric water contents (θ) using four test sands. The proposed two-point α-mixing model, as well as linear and quadratic models, was fitted to the ADC – θ data. Unlike for conventional TDR measurements, the effect of sensor characteristics is lumped into the empirical parameter α in the two-point α-mixing model. The value of α was fitted to be 2.5, yielding a nearly identical calibration curve to the quadratic model. Errors in θ associated with the sensor-to-sensor variability for the two-point α-mixing model were ±0.005 cm3 cm−3 for dry sand and ±0.028 cm3 cm−3 for saturated sand. In the validation experiments, the highest accuracy in water content estimation was achieved when sensor-specific ADCdry and ADCsat were used in the two-point α-mixing model. Assuming that α = 2.5 is valid for most mineral soils, the two-point α-mixing model only requires the measurement of two extreme ADC counts in dry and saturated soils. Sensor-specific ADCdry and ADCsat counts are readily measured in most cases. Therefore, the two-point α-mixing model (with α = 2.5) can be considered as a quick, easy, and robust method for calibrating the ECH2O EC-5 sensor. Although further investigation is needed, the two-point α-mixing model may also be applied to calibrating other sensors.

Thermal conductivity of unsaturated soil depends on soil water content and soil type. A transient water release and imbibition method (TRIM) is modified to include measurement of the thermal conductivity function (TCF) in conjunction with concurrent measurement of the soil water retention curve (SWRC) and hydraulic conductivity function (HCF). Two pairs of dielectric and thermal needle sensors are embedded in the soil specimen to monitor spatial and temporal variation of water content, thermal conductivity, and thermal diffusivity during drying and wetting processes. Three different soils, including pure sand, silt, and clayey sand are used to examine the effectiveness and validity of the new technique. The thermal conductivity data from the modified TRIM technique accords well with other independent measurements. The results show that the modified TRIM technique provides a fast and accurate way of obtaining thermal properties of different types of soils under both drying and wetting states. The typical testing time for a soil going through a full saturation variation is less than 3 weeks. We observe that the hysteresis in thermal conductivity during a wetting and drying cycle is much less pronounced than that of the hydraulic hysteresis.

Due to the dynamic nature of the shallow subsurface, knowledge of soil thermal properties across a wide range of soil moisture and temperature conditions is necessary to accurately describe heat transport in many settings. Soil thermal properties are difficult to measure at high temperatures, however, due to the lack of suitable measurement devices and the potential for measurement-induced changes. Therefore, thermal property data are often scarce and incomplete and very often limited to specific soils. Due to this scarcity of accurate experimental data, empirical relationships often do not accurately predict the thermal properties of soils as a function of both soil moisture and temperature. In this study, thermal conductivity and diffusivity were measured for silica sands under loose and tight packing conditions and a field sand under varied water saturation and temperature. Several recent sensor-based technologies were integrated into a small cell modified to have a network of sampling ports, continuously monitoring water saturation, temperature, and soil thermal properties. For the test sands studied, data showed that the thermal conductivity and diffusivity increased noticeably for sample temperatures >50°C. At sample temperatures between 30 and 50°C, any change in thermal properties with temperature was small. Thermal conductivities measured in this study were compared with independent estimates made using empirical models from the literature. In general, good agreement was observed for most thermal conductivity data when proper fitting parameters were established, except at intermediate saturation values.