Numerical Analysis of Heat Transfer Performance of In Situ Thermal Remediation of Large Polluted Soil Areas

Abstract

In recent years soil contamination has become a global problem because of industrial development. In situ thermal remediation has been proposed recently to not only lower costs, but also reduce the environmental impact compared to other soil remediation technologies such as chemical remediation. During the soil thermal remediation process, factors such as soil type and water content affecting the heat transfer pose challenges. In this study, a simple mathematical model is presented and the heat transfer performance during the soil heating process is researched via COMSOL Multiphysics 5.3 software (COMSOL Inc., Stockholm, Sweden). The temperature distribution and heating period under different operating conditions are evaluated. The simulation results show that the average soil temperature exhibits three stages during the heating process. First, soil is heated from the ambient temperature to the water boiling temperature (100 °C). Then, the soil stays at the water boiling temperature for a while before reaching the target temperature. Simultaneously, the effects of initial water content and groundwater flow on heat transfer are also studied. In addition, the results of a simulation can provide a reference for in situ heating remediation technology.

1. Introduction

Environmental problems, especially soil pollution, have already become widespread as a result of economic development, and the management of contaminated soil has become a major challenge [1,2]. Large amounts of contaminants have been released into the environment because of illegal disposals, leakage accidents, and so on [3,4]. Based on a report on the national general survey of soil contamination [5], the overall soil environment situation is not reassuring in China, with 34.9% of the 775 soil sites in the 81 industrial wastelands surveyed not meeting standards. Soil pollution has put great pressure on China’s sustainable development strategy, with increase in the types of soil contaminants and the extension of soil contaminant area. Meanwhile, soil contamination has a long-term impact on both the environment and human health, so soil remediation is an urgent task. Because of the severity of soil pollution and the difficulty of its restoration, remediation of contaminated soil has attracted unprecedented attention in the environmental field.

Numerous remediation technologies, such as physical remediation, chemical remediation, and bioremediation methods, have been developed to treat contaminated soils [6,7,8]. Among these remediation technologies, in situ thermal remediation technology stands out because of its ability to remove contaminants effectively [9]. In thermal remediation, heating and vacuum wells are applied simultaneously to treat contaminated soils [10]. The work principle of in situ thermal remediation technology is as follows: First, the heating wells release heat to the contaminated soils, and the soil temperature can be increased to, if desired, values on the order of 600 °C. Under such conditions, many contaminants would be vaporized or destroyed by a number of mechanisms in this process. Further, these gases could be released into the atmosphere after the extraction from vacuum wells and purification. Consequently, thermal remediation is mainly applied to the removal of volatile and semivolatile organic pollutants and a few volatile inorganic substances such as Hg, As, and Se [11]. In situ thermal remediation technology has many advantages. Because the thermal conductivity of soil does not change significantly (by only a factor of 4 from clay to sand), thermal remediation is effective for uniformly heating the entire contamination zone and is used in silty or clayey soils [12,13]. Compared to ex situ remediation, in situ thermal remediation entails no digging of contaminated soils, generates no dust or odors, minimizes human exposure to hazardous wastes, and is a low-noise operation [14]. Thus, in situ thermal remediation may be more ecofriendly in sensitive ecosystems because of the lack of soil disturbance.

Many scholars have conducted research on soil remediation including thermal desorption technology, microwave heating technology, and steam injection technology. Araruna et al. [15] researched the influence of thermal desorption on oil spill debris clean up. Their results showed that oil causes a slight increase in grain size and uniformity, and oiled debris exhibited a smaller void ratio but a larger unit weight. However, the oil and grease content from oiled debris decreased with rising temperature and prolonged exposure. Navarro et al. [16] studied the application of solar thermal desorption to remediate mercury-contaminated soils. Their experiment showed that when soil and mine waste samples were heated to 400–500 °C, mercury elimination is significant (41.3%–87%). Electrical resistive heating (ERH) has been proposed as a low-environmental-impact thermal recovery method for heavy oil reservoirs [17]. Conductive heat transfer during in situ electrical heating of oil sands was studied by Hassanzadeh et al. [18]. In this work, a simple analytical model was presented that allowed estimation of the rate of makeup water or other fluid required for efficient heat delivery to the bitumen-bearing formations. The effects of formation porosity, rock type, and fluid saturation on heat transfer were also evaluated. Merino et al. [19] studied the effect of temperature on the release of hexadecane from soil by thermal treatment. Their results indicated that good removal efficiencies (>99.9%) were achievable at 300 °C, with higher temperatures not being necessary to significantly improve the degree of contamination removal. Steam as a sweep gas in low-temperature thermal desorption processes used for contaminated soil cleanup was investigated by Averett et al. [20]. Falciglia et al. [21] studied energy and economic considerations for full-scale in situ remediation of low-dielectric hydrocarbon-polluted soils using a microwave heating technique. Their results showed very short remediation times, and the modest energy costs demonstrated the usefulness of in situ microwave heating as a deliverable alternative to conventional thermal desorption or physical–chemical techniques.

In situ thermal remediation technology is widely used in soil treatment. From 2002 to 2005, the soil of an old wood mill in California was polluted by PAHs (Polycyclic Aromatic Hydrocarbons) and dioxins. The amount of soil to be treated was 12,600 m³. The average heating depth was 6.1 m and the target heating temperature was 335 °C. After the restoration, the concentration of PAHs was successfully reduced from 30.6 mg kg⁻¹ to 5 ug kg⁻¹ and dioxins from 18 μg kg⁻¹ to 0.1 μg kg⁻¹, after acceptance by the national toxic substances monitoring center of the United States, said that the restored land can be put into use unconditionally [22]. From 2003 to 2007, a site polluted by chlorinated solvents was successfully repaired by in situ thermal technology in Washington State, USA, the removal rate of trichloroethylene in the site was more than 90% [23]. Heron et al. have carried out experimental research on the organic pollution site by using in situ thermal remediation technology, and analyzed the repair cycle and the comprehensive repair cost in detail. Normally the experiment is divided into two categories: (a) practical projects experiments and (b) laboratory tests. But both of these experimental methods are defective, the diffusion of moisture and vapor cannot be detected during the practical projects experiments and laboratory test can’t truly reflect water seepage. So the numerical simulation method is used to study the influence of the moisture migration on remediation process. Despite the progress made in past works, there are still issues that have not been analyzed. The above study did not discuss in detail the influencing factors such as the distance between heating wells and extraction wells, the arrangement mode and the influence of groundwater seepage and so on. In fact, very few studies have been conducted for investigating the temperature distribution and heat transfer performance during the in situ thermal heating process. In actual remediation processes, factors such as moisture seepage, initial water content, soil properties, and operational conditions can significantly affect the soil temperature distribution and remediation period.

Temperature has a great influence on contaminant removal in terms of thermal temperature technology. The main objective of this work is to research the heat transfer performance during in situ thermal remediation process. In this study, mass and thermal models are proposed for in situ soil thermal remediation. Analysis of the temperature rise under different operations is conducted. Variations of the soil temperature distribution and heating period of this engineering technology are studied. Simultaneously, the influence of groundwater seepage, initial water content, and site thermal design on the remediation period are researched by simulation. The results of this study can provide a reference for in situ thermal remediation under different operating conditions.

2. Concept and Mathematical Model of In Situ Thermal Remediation Technology

2.1. Fundamental Idea and Issues

Figure 1a shows the flow diagram of the in situ thermal remediation system. First, electricity is transported to the electric power control unit from the electric power network. Electric power from the electric power control unit is then converted into thermal power. The polluted soil is heated to a high temperature by heating wells to destroy the contaminants in soil and the parameters of each system are monitored by a monitoring unit. The gaseous product is extracted to a gas treatment unit by a vacuum well under the effect of the extraction unit. This gaseous product is then purified through washing, chemical reaction, and so on in the gas treatment unit. Finally, the treated gas is discharged into the atmosphere.

Figure 1b presents a schematic of heated soil. Heat is dissipated from the heating wells to the surrounding soil, and the steam moves to the middle under the effect of the vacuum wells. In general, insulation covers the soil surface to prevent heat loss. Meanwhile, surrounding water would flow into the heated soil during the remediation process.

Figure 1c reveals the soil temperature change in typical thermal remediation. The soil temperature mainly goes through three stages. During the heat-up stage, the soil minerals and fluids are heated to T₁ (the boiling point of water) from T₀. The evaporation of liquid water and liquid migration from unheated zones are negligible in this period. During the boiling stage, the main mechanism is the evaporation of water. The soil maintains a temperature of T₁ until the pore water has been boiled off. The duration of this stage is decided by the amount of water to be boiled. When the pore water has been vaporized, the soil enters the superheated stage. At this stage, the soil can be heated to the target temperature and the water from surrounding unheated soils would be evaporated quickly because of the high temperature. Contaminants could be decomposed with increasing soil temperature to achieve the goal of remediating the contaminated soil.

Heating soil is a complicated process and there are many uncertain factors including weather conditions and soil geological conditions. The process of soil remediation is affected by the initial water content, surrounding water seepage, and other factors. Consequently, it is meaningful to study the influence of these factors on heat transfer performance during the remediation process.

2.2. Mathematical Models

2.2.1. Governing Equation

Heat transfer during soil remediation includes conduction, convection, phase change, and radiation. The conduction behavior occurs in the soil phase. The convection behavior during the soil phase and liquid phase occur when the water content is high. The liquid water evaporates because of high temperature and radiation can be ignored. The following assumptions are made:

(1)

Soil is homogeneous and its type does not change along the thermal wells, whereas in a real situation, soil is a nonhomogeneous, non-isotropic porous material. The effect of this assumption on heat conduction can be negligible because the thermal conductivities of different dry soils exhibit limited variation.

(2)

There is no chemical interaction, and the gas is assumed to be ideal.

(3)

The convection of fluid in porous media satisfies Darcy’s law.

(4)

The gas phase in soils includes non-condensable gases (such as air) and water vapor. The influence of dry air on heat and moisture migration is neglected.

(5)

Solid, liquid, and gas phases are continuous in unsaturated soil, separately.

(6)

The migrations of liquid and gas do not affect each other.

(7)

The compressive work and viscous dissipation effects of the liquid are negligible.

(8)

The effects of contaminants are ignored.

(a) Liquid flow model

For mass conservation, the variable quantity of liquid water per unit volume is equal to the difference between the amount of migration from the surrounding units and the amount of inside evaporation. The liquid balance can be expressed as:

$${\rho }_w\frac{\partial {\theta }_w}{\partial \tau }=-\nabla J_w-\dot{E}$$

(1)

where ${\rho }_W$ ($\mathrm{kg}{\mathrm{m}}^{-3}$) is the density of liquid water, ${\theta }_w$ (${\mathsf{\theta }}^3{\mathsf{\theta }}^{-3}$) is the volumetric liquid water content, $J_w$ (${\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$) is the liquid water flux, and $\dot{E}$ (${\mathrm{kg}\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$) is the evaporation rate of liquid water.

According to the Philip and De Vries model [24], the liquid migration equation in unsaturated soils is:

$$J_w=-{\rho }_w{K}_w\nabla \psi =-{\rho }_w(D_{wT}\nabla T+D_{w\theta }\nabla \theta )$$

(2)

where $D_{wT}=K_w\frac{\partial \psi }{\partial T}$ (${\mathrm{m}}^2{\mathrm{s}}^{-1}{\mathrm{K}}^{-1}$) and $D_{w\theta }=K_w\frac{\partial \psi }{\partial \theta }$ (${\mathrm{m}}^2{\mathrm{s}}^{-1}$) are the transport coefficient for liquid flow owing to the temperature gradient and the volumetric water content gradient, respectively. The $D_{wT}$ and $D_{w\theta }$ contain the influence of the capillary force. The relationship between soil water potential ψ and water content and temperature T can be obtained by Gardner and De Vries [24] as $\psi =a{\left(\frac{{\theta }_w}{\epsilon }\right)}^{-b}\exp \left(\gamma \cdot \left(T-273.15\right)\right)$, where $a$, $b$, and $\gamma$ are characteristic soil parameters and $\epsilon$ indicates the porosity of the soil.

The evaporation rate of liquid water can be given as:

$$\dot{E}=k_{vap}{\rho }_w\left(p^{*}-p_G\right)/p_G$$

(3)

where $k_{vap}$ (${\mathrm{s}}^{-1}$) is a rate constant and $p_G$ ($\mathrm{Pa}$) is the actual vacuum pressure. Here, ${\mathrm{p}}^{*}$ can be evaluated from the Antoine equation:

$${\log }_{10}{p}^{*}=A-\frac{B}{C+T}$$

(4)

where $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{C}$ are the Antoine constants of water, respectively

(b) Vapor flow model

Similarly, for mass conservation, the variable quantity of vapor in a certain unit volume is equal to the sum of the amount of migration from surrounding units and the amount of internal evaporation. Therefore, the mass balance equation of vapor is [25]:

$$\frac{\partial \left({\rho }_v{\theta }_v\right)}{\partial \tau }=-\nabla J_v+\dot{E}$$

(5)

where ${\rho }_v$ (${\mathrm{kg}\mathrm{m}}^{-3}$) is the density of vapor water, ${\theta }_v$ (${\mathrm{m}}^3{\mathrm{m}}^{-3}$) is the volumetric water vapor content, and $J_v$ (${\mathrm{kg}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$) is the vapor water flux. Moreover, ${\theta }_w+{\theta }_v=\epsilon$.

The mechanism of vapor migration in soil is mainly diffusion, which is a transitional form of Fick and Knudsen diffusion. The vapor migration equation is:

$$J_v=-D_e\nabla {\rho }_v$$

(6)

where $D_e$ (${\mathrm{m}}^2{\mathrm{s}}^{-1}$) is the vapor equivalent diffusivity. Moreover, $\frac{1}{D_e}=\frac{1}{D_{atm}}+\frac{1}{D_{kn}}$, where $D_{atm}$ and $D_{kn}$ are the molecular diffusivity and Knudsen diffusivity, respectively.

According to continuum fluid dynamics theory, the flow velocity of gases, under the extraction of vacuum wells, can be described in the form of a modified Darcy’s law:

$$J=-\frac{k_{rg}k}{{\mu }_{gv}}\left(\nabla p-{\rho }_{v}g\right)$$

(7)

where $k$ is the intrinsic permeability of the soil, ${\mu }_{gv}$ and $p$ are the viscosity and pressure of the gas phase, respectively, and $k_{rg}$ is the relative permeability of the gas phase. $k_{rg}$ can be obtained through the Van Genuchten–Parker empirical formula [25], $k_{rg}\left(S_{gv}\right)=S_{gv}^{1/2}{\left[1-{\left(1-S_{gv}\right)}^{1/m}\right]}^{2m}$, where $S_{gv}$ is the saturation of the gas phase and $m$ is an empirical parameter. Here ${\rho }_v$ satisfies:

$${\rho }_v=\frac{p_v}{R_{v}T}$$

(8)

where $R_v$ (${\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$) is the specific gas constant for vapor. Equation (6) can be rewritten as:

$$J_v=\frac{-D_e}{R_{v}T}\left(\nabla p_v-\frac{p_v}{T}\nabla T\right)$$

(9)

2.2.2. Energy Equation

During the soil heating process, the heat transfer mechanism comprises three parts: (1) Conductive heat transfer is the contribution from the soil solid, and conduction is the main mechanism for heat transport in soil. (2) Convective heat in the soil is conveyed by liquid flux and vapor flux. (3) The latent heat of vaporization is released by the evaporation of liquid water. Accordingly, the thermal balance may be written as follows:

(a)

For conduction in the soil solid:

$$q_{\lambda }=-\lambda \nabla T$$

(10)

where $q_{\lambda }$ (${\mathrm{W}\mathrm{m}}^{-2}$) is the conduction flux and $\lambda$ (${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$) is the effective thermal conductivity.

(b)

For convection by the liquid water flux and water vapor flux:

$$q_w=J_w{h}_w$$

(11)

$$q_v=J_v{h}_v$$

(12)

where $q_w$ (${\mathrm{W}\mathrm{m}}^{-2}$) and $q_v$ (${\mathrm{W}\mathrm{m}}^{-2}$) are the convection fluxes resulting from the liquid flux and the vapor flux, respectively, and $h_w$ (${\mathrm{J}\mathrm{kg}}^{-1}$) and $h_v$ (${\mathrm{J}\mathrm{kg}}^{-1}$) are the enthalpies of the liquid water and water vapor, respectively.

In practice, in addition to the simple conduction and convection mechanisms discussed above, the actual temperature rise is also affected by latent enthalpy changes by the evaporation of liquid water.

(c)

The latent heat of vaporization is released by the evaporation of liquid water:

$$Q_w=\dot{E}{H}_r$$

(13)

where $H_r$ (${\mathrm{J}\mathrm{kg}}^{-1}$) is the latent heat of vaporization.

The conservation equation for energy transfer is given as

$$\frac{\partial \left({\rho }_s{\theta }_s+{\rho }_w{\theta }_w+{\rho }_v{\theta }_v\right)}{\partial \tau }=-\nabla \left(-\lambda \nabla T+J_w{h}_w+J_v{h}_v\right)+\dot{E}{H}_r$$

(14)

$$h_w=C_{w}T$$

(15)

$$h_v=C_{v}T+H_v$$

(16)

where ${\rho }_s$ (${\mathrm{kg}\mathrm{m}}^{-3}$) is the density of the soil and $C_w$ (${\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$) and $C_v$ (${\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$) are the specific heat capacities of liquid water and water vapor, respectively.

2.2.3. Physical Model

The sites remediated by in situ heating technology generally take up a large area. Based on one remediation project, a typical soil unit was used to research heat transfer under different operating conditions during the remediation process in this study. Many heating wells releasing heat to soil and vacuum wells, which can transfer vapor in the soil to the surface, are placed in actual projects.

The physical model for the simulation is shown in Figure 2. It contains four parts: Soil, insulation, heating wells, and vacuum wells. The simulation soil is 4 m in length, 4 m in width, and 5 m in height. There is a layer of insulation, having a 0.5 m thickness and covering the soil to prevent heat from escaping. The heating wells are of cylindrical shape and release heat to raise the soil temperature; they have a 0.07 m radius and a height of 5 m. The vacuum wells have the same dimensions as the heating wells. The heating wells are placed in a square pattern and the heating well spacing is 2 m. The vacuum well is located in the center of the soil. Generally, a negative pressure environment (3000 Pa) is needed in the vacuum well to extract the vapor water from the soil. The insulation maintains a constant soil temperature to a large extent and prevents the ground surface from overheating as well as provides a certain vacuum effect (3000 Pa). Only conduction in the insulation and convection between the environment and the insulation surface are considered.

2.3. Definition and Simulation Cases

2.3.1. Characteristics of Parameters

The simulation was performed using COMSOL Multiphysics 5.3. Based on the finite element method, COMSOL Multiphysics is used to solve the equations for the real physical phenomena by solving partial differential equations (for single and multiple fields).

During the in situ thermal remediation process, conduction and convection as well as evaporation are considered under the effect of heating wells and vacuum wells. Conduction is the main mechanism in the process. Convection is also studied because there is groundwater flow. The parameters are given in

Table 1. Summary of parameters.

Element	Density (kg m−3)	Conductivity (W m−1 K−1)	Specific Heat (J kg−1 K−1)	Porosity
Dry soil	2650	1.41	1750	0.35
Liquid water	1000	0.648	4177	-
Insulation	2500	0.2	4200	-

.

2.3.2. Simulation Cases

In the actual remediation process, water has a considerable impact on the heat transfer and the remediation period because of its high specific heat. When the soil is heated, the liquid water will evaporate, decreasing the water content in the soil and causing liquid water from the unheated area to seep into the heated zone. The different groundwater flows lead to different temperature distributions. Meanwhile, different heat transfer performances result from different groundwater flows, initial water contents, and so on. Therefore, factors such as groundwater flows, water seepage boundaries, and initial water contents were studied. The simulation cases are presented in

Table 2. Case 1 for different groundwater flows.

No.	Heating Power (kW)	Heating Well Space (m)	Groundwater Flow (m s−1)	Porosity	Initial Water Content (%)
1	28	2	1 × 10−7	0.35	20
2	28	2	2 × 10−7	0.35	20
3	28	2	3 × 10−7	0.35	20

,

Table 3. Case 2 for lateral water seepage.

No.	Heating Power (kW)	Heating Well Space (m)	Groundwater Flow (m s−1)	Porosity	Initial Water Content (%)	Number of Lateral Water Seepages
1	28	2	1 × 10−7	0.35	20	0
2	28	2	1 × 10−7	0.35	20	1
3	28	2	1 × 10−7	0.35	20	2

,

Table 4. Case 3 for initial water content.

No.	Heating Power (kW)	Heating Well Space (m)	Groundwater Flow (m s−1)	Porosity	Initial Water Content (%)
1	28	2	1 × 10−7	0.35	15
2	28	2	1 × 10−7	0.35	20
3	28	2	1 × 10−7	0.35	25
4	28	2	1 × 10−7	0.35	30

,

Table 5. Case 4 for heating well spacing.

No.	Heating Power (kW)	Heating Well Space (m)	Groundwater Seepage (m s−1)	Porosity	Initial Water Content (%)	Heating Well Depth (m)
1	28	1.7	1 × 10−7	0.35	20	4.5
2	28	2	1 × 10−7	0.35	20	4.5
3	28	2.3	1 × 10−7	0.35	20	4.5

and

Table 6. Case 5 for heating well depth.

No.	Heating Temperature (K)	Heating Well Space (m)	Groundwater Seepage (m s−1)	Porosity	Initial Water Content (%)	Heating Well Depth (m)
1	893 K	2	1 × 10−7	0.35	20	3.5
2	893 K	2	1 × 10−7	0.35	20	4
3	893 K	2	1 × 10−7	0.35	20	4.5

.

2.3.3. Definition of Boundary Conditions

The water mass flow is set up at the bottom of the soil. The vacuum well pressure is 3000 Pa. The heating wells operate at constant power or constant temperature. Natural convection heat transfer is defined on the upper surface of the soil. The internal heat source is set up as Equation (13) and the initial soil temperature is 293 K.

3. Results and Discussion

3.1. Case 1: Influence of Groundwater Flow on Heat Transfer Performance

Water poses a major problem in enabling a high rate of soil temperature increase during the soil heating process. Water requires a considerable amount of heat during the heating process owing to its high specific heat capacity and latent heat. Convection caused by water flowing also changes the heat transfer in the soil. Groundwater will flow into heated soil when the water content decreases. This section addresses the influence of groundwater flow on heat transfer.

3.1.1. Influence of Groundwater Flow on the Temperature Distribution

The temperature distribution under different groundwater flow rates are studied. Figure 3, Figure 4 and Figure 5 show the temperature distributions under different numbers of heating days of groundwater flow for $v_0=1\times {10}^{-7}$, $v_0=2\times {10}^{-7}$ and $v_0=3\times {10}^{-7}$, respectively. Panels marked a show four figures representing the temperature distribution in the vertical direction. Panels marked b are composed of four figures representing the temperature distribution in the horizontal direction temperature 3 meters from the soil bottom. The legend color range is from 50 to 500 °C. Blue represents low temperature and red represents high temperature.

Figure 3, Figure 4 and Figure 5 show the temperature distribution after 20, 30, 40, and 50 days for different groundwater flows. It is clear that the temperature distribution is symmetrical along both sides of heating wells when heating time is 20 days (Figure 3a). With increasing number of heating days, the temperature distribution is offset, with larger high-temperature areas being close to the middle vacuum wells. Meanwhile, it is obvious that heat transfer is influenced by bottom groundwater seepage. The bottom soil area near the heating wells has fewer high-temperature areas.

Because of the negative pressure of the vacuum well, liquid migrates from the overheated soil to the vacuum well, which leads to an irregular temperature distribution. Heat transfer in the insulation is slower than in the soil owing to the insulation’s low conductivity. Insulation reduces heat loss to a large extent during the heating period. With increasing groundwater flow, the temperature distribution deviation becomes more obvious. Figure 3b shows temperature distribution in the horizontal direction. Soil located between the heating well and the vacuum well has a higher temperature than that on the other side. When the heating time is 50 days, the average temperature of the soil located between the four heating wells is 320 °C.

3.1.2. Influence of Groundwater Flow on Water Content in the Soil

Figure 6 shows the water content distribution during the soil heating period. The water content ranges from 0 to 0.2. Red represents high water content and blue represents low water content. Figure 6a shows four figures along the heating well for heating periods of 16, 20, 24, and 28 days, respectively.

When the heating period is 16 days, the water content of the soil around the heating wells first decreases because of the fast temperature rise. The dry area gradually expands with increasing heating time. When the heating period is 28 days, there is moderate water content at the bottom of the soil. The concentration distribution is asymmetrical, and groundwater flowing into the soil has a major impact on water evaporation from the bottom soil. Figure 6b shows the water content distribution in the horizontal direction temperature 3 meters from the soil bottom. The temperature distribution difference leads to water content differences.

3.1.3. Influence of Groundwater Flow on the Heating Process

The relationship between temperature as well as the water content and the number of heating days is shown as Figure 7. The x axis represents the number of heating days, the left y axis represents the average soil temperature ranging from 280 to 700 K, and the right y axis represents the water content ranging from 0 to 0.2 in the soil. The three curves circled by the red dotted oval represent the average soil temperature and the other three curves stand for the water content in the soil. The target temperature (650 K) is represented by the gray dotted line.

Jiang et al. studied the remediation effect of in situ thermal remediation technology desorption on chlorobenzene in soil through experimental test. And the experimental result is shown in Figure 7a [26]. Figure 7a represents the temperature change of different monitoring points. The temperature trend of Figure 7a is consistent with Figure 7b. As shown by Figure 7b, the water seepage boundary condition is type 3 and the temperature exhibits three stages. First, the soil temperature rises to 100 °C, then stays at 100 °C for a period of time, and finally reaches the target temperature. In this first stage called the heat-up stage, the average soil temperature increases linearly from ambient temperature (25 °C) to the water boiling temperature (100 °C). The evaporation of liquid water is ignored, and conduction is the main mechanism at this stage. The liquid water evaporates and changes to water vapor when heated during the boiling stage, and the average temperature stays constant at 100 °C. In the superheating stage, groundwater flowing in the bottom soil has a great influence on the temperature distribution deviation. The average soil temperature ranges from the water boiling temperature (100 °C) to the target temperature (377 °C) with increasing heating time.

The heat-up stage lasts 12 days under the three different operation modes. The different groundwater flows have nearly no influence on the rise in temperature in the heat-up stage during the heating process. In contrast, in the superheating stage, the rate at which the soil temperature increases is significantly affected by the groundwater flow. In the heat-up heating stage, there is no water to evaporate, so the heated area has the same water content as the unheated soil and no groundwater flows in the soil because of the lack of concentration difference. The duration of the boiling period is slightly different under different groundwater flows. The boiling stage lasts 17, 19, and 21 days when the groundwater flows are $1\times {10}^{-7}\mathrm{m}/\mathrm{s}$, $2\times {10}^{-7}\mathrm{m}/\mathrm{s}$, and $3\times {10}^{-7}\mathrm{m}/\mathrm{s}$, respectively. The superheating stage lasts 21 days when the groundwater flow is $1\times {10}^{-7}\mathrm{m}/\mathrm{s}$, increases to 26 days when groundwater is $2\times {10}^{-7}\mathrm{m}/\mathrm{s}$, and lasts 31 days when the groundwater flow is $3\times {10}^{-7}\mathrm{m}/\mathrm{s}$. It is obvious that groundwater flow has a greater impact on the superheating stage than on the heat-up or boiling stages.

3.2. Case 2: Influence of Surrounding Water Seepage on Heat Transfer Performance

As shown in Figure 8, the entire large square is assumed to be heated soil and the remaining soil is not heated. Water in unheated soil can flow into heated soil when the water content decreases. The soil can be divided into three types based on surrounding water seepage: Type 1 boundary condition soil is influenced by two sides of water seepage and groundwater flow; type 2 boundary condition soil is affected by one side of water seepage and groundwater flow; type 3 boundary condition soil is only impacted by groundwater seepage. The following section discusses the influence of different soil boundary condition types on the temperature distribution.

3.2.1. Temperature Distribution in Type 2 Boundary Condition Soil

Figure 9 shows the temperature distribution in type 2 boundary condition soil. Figure 9a shows the vertical temperature distribution along the heating wells. The temperature distribution in the horizontal direction temperature 3 meters from the soil bottom is described in Figure 9b. The speed of water flowing from the left side into the soil is $1\times {10}^{-7}\mathrm{m}/\mathrm{s}$ in Figure 9a, and the water flows from the upper side into the soil in Figure 9b.

As can be seen in Figure 9a, when the heating period is 30 days, the temperature distribution is almost symmetrical along the heating wells. The temperature distribution then gradually changes with increasing number of heating days. Water seepage weakens the rise in the left soil temperature, altering the temperature distribution. The area closer to the water seepage boundary has a lower temperature than the other areas and the soil near the left heating well has a lower temperature.

Figure 9b shows the horizontal temperature distribution when the heating periods are 20, 30, 40, and 50 days. The 20-day temperature distribution is not significantly different from the 30-day temperature distribution. Water in the soil evaporates during this period, so most of the soil stays at the water boiling temperature. However, the soil near the heating wells can reach a higher temperature first. There is a big difference between the 40-day temperature distribution and the 50-day temperature distribution. First, the 50-day soil temperature is significantly higher than the 40-day soil temperature. Most soil can reach 300 °C. Second, a lot of heat is lost due to water seepage, so that the temperature distribution around the above two heating wells and that near the bottom heating wells are not symmetrical. Soil located below the bottom of heating wells can reach 300 °C, whereas soil located on the upper side of the above heating wells can reach only 250 °C because of water seepage. Therefore, water seepage can change the thermal radius of the heating wells. However, water seepage into the soil can also absorb heat because of evaporation, which is detrimental to soil heating.

3.2.2. Temperature Distribution in Type 1 Boundary Condition Soil

Figure 10 shows the vertical temperature distribution in type 1 boundary condition soil. The water seepage directions are shown by the arrows and the water seepage velocity is $1\times {10}^{-7}$ m/s.

For example, when the heating period is 60 or 70 days, the temperature distribution of a is lower than the temperature distribution of b. Most soil can reach 250 °C when the heating period is 60 days in Figure 10a, while most soil might reach above 300 °C in Figure 10b. This phenomenon is caused by the water seepage. The difference in the temperature distribution is more obvious when the heating period is 70 days.

The 20-day temperature distribution of in Figure 10a is the same as the 20-day temperature distribution in Figure 10b, but the temperature distribution has changes with increasing heating period. The temperature distribution in the horizontal direction temperature 3 meters from the soil bottom for different heating periods are shown in Figure 11. When the heating period is 20 or 40 days, the temperature distribution is almost symmetrical. The effect of water seepage becomes apparent when the heating period is 60 or 70 days, in which case the rate of increase in temperature of the soil near the water seepage boundary is weakened.

3.2.3. Influence of Different Soil Boundary Condition Types on the Heating Process

The relationship between the average soil temperature as well as water content in the whole domain and the heating period is shown in Figure 12.

The blue, green, and red curves represent type 1 boundary condition soil, type 2 boundary condition soil, and type 3 boundary condition soil, respectively. The three curves circled by the red dotted oval stand for the temperature change and the other three curves represent the water content. It is clear that the rate at which soil temperature increases is significantly affected by side water seepage. The three temperature lines exhibit the same increasing trend and the temperature change can be divided into three stages. The three types of boundary condition soil last 12 days in the heat-up stage, indicating that the heat-up stage heating time is not influenced by side water seepage. However, side water seepage has a certain impact on the boiling and superheating stages. The type 3 boundary condition soil not affected by side water seepage lasts 25 days during the boiling stage, and the type 2 boundary condition soil lasts 22 days during this period. In the superheating stage, type 3 boundary condition and type 2 boundary condition soils last 34 and 27 days, respectively. Water seepage has a larger influence on the rate at which soil temperature increases in the superheating stage.

3.3. Case 3: Impact of Initial Water Content on Heat Transfer Performance

3.3.1. Impact of Initial Water Content on the Temperature Distribution

Figure 13, Figure 14 and Figure 15 show the soil temperature distributions for different initial water content values. The heating power is 28 kW, and the groundwater flow is $1\times {10}^{-7}$ m/s. Panels marked a include four figures representing the vertical temperature distribution along the heating wells and panels marked b are composed of figures representing the horizontal temperature distribution. Figure 13b and Figure 14b show the horizontal temperature distribution of different depth when heating period is 40 days. The legend color ranges from 20 to 500 °C. The temperature distribution is offset to the middle vacuum wells and upper parts in Figure 13, Figure 14 and Figure 15. There is a large temperature gradient between the 1 m depth (from the soil bottom) section temperature distribution and the 2 m depth section temperature distribution in Figure 13b. Because the soil enters the superheating stage, the water in the soil is gone. So the soil near the bottom has slow temperature rising rate due to the rapid evaporation of groundwater. As the initial water content is 25%, it just gets through the boiling stage when the heating period is 40 days, most soils do not reach very high temperature, so this different depths temperature difference are not obvious in Figure 14b. Groundwater seepage changes the thermal radius of the heating wells, as well as the vertical temperature distribution for different initial water contents under the same heating period. When the water content increases, the heated soil has a lower temperature under a heating period of 40 days (i.e., the more moisture there is, the slower the soil temperature rises). When the initial water content is 30%, the total heating period is about 61 days. Soil stays the boiling stage as the heating period is less than 40 days, and the different depths temperature difference are not obvious. So the temperature distribution in the horizontal direction temperature 3 meters from the soil bottom of different heating periods is shown in Figure 15b. It is obviously that the temperature distribution is partial to the middle due to the effect of vacuum wells.

3.3.2. Impact of Initial Water Content on the Heating Process

The relationship between soil average temperature change as well as average water content in the whole domain and the heating period under different initial water content values is shown in Figure 16.

The red, green, dark blue, and light blue curves represent initial water contents of 15%, 20%, 25%, and 30%, respectively. The four curves framed by the dotted oval represent the average soil temperature and the other four curves stand for the water content change. The soil temperature change exhibits three stages. The soil temperature rises from the initial temperature (25 °C) to 100 °C in the heat-up stage; it stays at 100 °C for a period of time in the boiling stage; and then continues to rise to the target temperature (650 K) in the superheating stage. The heated soil exhibits different rates of temperature increase in the heat-up stage under different initial water contents. The heat-up stage lasts 11, 12, 13, and 14 days when water contents are 15%, 20%, 25%, and 30%, respectively. The heat-up stage lasts longer as the initial soil moisture increases. The boiling stage lasts 15, 18, 23, and 28 days, respectively. However, the superheating stage lasts 19 days under different initial water contents. This can be explained by the following: Soil is composed of dry soil, water, and air. The influence of air on heat transfer in the soil during the heating period is ignored in this study. The porosity of dry soil is 0.35. In the superheating stage, the soil is heated to approximately dry soil. Although the initial water contents are different, the average soil water contents are the same as the moisture has almost evaporated at this stage. Consequently, the different initial water contents have no impact on heat transfer. In contrast, the boiling stage heating time is seriously influenced by the initial water content. When the initial water content rises from 15% to 30%, the boiling stage heating period has grown to 13 days. In summary, the initial water content has a great impact on the heat-up and boiling stages, but the heat transfer behavior is not influenced by the initial water content and the soil exhibits the same rate of temperature increase in the superheating stage during the heating process.

3.4. Case 4 and Case 5: Influence of Heating System Characteristics and Arrangements on Heat Transfer Performance

The influence of water seepage and initial water content on the soil temperature distribution and rate at which temperature increases has been studied above. The site thermal design also affects the actual heating remediation process, potentially leading to energy waste if an unsuitable heating well design is chosen. This section addresses the influence of the site thermal design on the heating process, including the heating well spacing and depth.

3.4.1. Influence of Heating Well Spacing on the Temperature Distribution

The effect of the heating well spacing on the temperature distribution is investigated next. The following simulation cases are explored:

(1) Heating well spacing $S=1.7$ m.

Figure 17 shows the soil temperature distribution when the heating well spacing is 1.7 m during the heating process. Figure 17a includes four figures representing the vertical temperature distribution and Figure 17b is composed of four figures representing the horizontal temperature distribution. The horizontal section in Figure 17b has a distance of 2.5 m from the bottom. The soil between the heating wells can easily experience a high rate of increase in temperature. Likely, the temperature distribution can shift to the middle by the vacuum effect of the vacuum well, so that the high-temperature soil is more distributed in the middle region. When the heating period is 50 days, the soil located between heating wells can reach 350–400 °C, while other soil might reach only 250–300 °C. When the heating well spacing is 2 m, the soil between heating wells can reach 350 °C, while the other soil can reach 300 °C. Therefore, the uniformity of temperature distribution is not as good as in case $S=2$ m (as shown in Figure 3). In the remediation process, the soil furthest from the heating wells must be heated to reach the target temperature, so, when the heating well spacing is 1.7 m, more heating time is needed to make the whole soil region reach the target temperature. This is disadvantageous in terms of both cost and energy consumption.

(2)Heating well spacing $S=2.3$ m

Figure 18 shows the temperature distribution when the heating well spacing is 2.3 m. Figure 18a,b represent the vertical and horizontal temperature distributions, respectively. There is a difference in temperature distribution between the cases of heating well spacing $S=1.7$ m and heating well spacing $S=2.3$ m. High-temperature soil is mainly concentrated around the edge region of the heating wells. This part of the soil can reach 350–400 °C. In contrast, the soil located between the heating wells exhibits a lower temperature, with most of the soil reaching 250–300 °C when the heating period is 50 days. The high-temperature soil area is smaller than that in case $S=2$ m. In general, the case $S=2$ m, exhibiting better temperature distribution uniformity than cases $S=1.7$ and $S=2.3$ m, is the most suitable for in situ thermal remediation.

3.4.2. Impact of Heating Well Depth on the Temperature Distribution

Figure 19 shows the temperature distribution under different heating well depths. The vertical temperature distribution for a heating well depth $D=3.5$ m is presented in Figure 19a,b shows the vertical temperature distribution for a heating well depth $D=4$ m. The soil is heated at a constant temperature and the heating temperature is 893 K. There is a large temperature difference when the heating well depth is $D=3.5$ m. Heating well depth has a significant influence on the rate at which the soil temperature increases, as can be seen in Figure 19a,b.

The soil between the heating wells exhibits a similar rate of temperature increase regardless of the heating well depth, but the temperature distributions of the bottom soil are very different in Figure 19a,b. When heating period is 70 days, most soil between the heating wells can be heated to 350–400 °C when the heating well depth is 3.5 m, while the bottom soil might only reach 150 °C. Although he temperature distribution difference improves in Figure 19b where the bottom soil can reach 200–250 °C, this temperature does not break down most of the pollutants. The temperature distribution uniformity of case $D=4.5$ m is better than that of case $D=3.5$ m and $D=4$ m. In summary, $D=4.5$ m is most beneficial to soil remediation.

4. Conclusions

Thermal remediation is a commonly used technology in soil remediation. The present work has analyzed the heat transfer performance during the soil thermal remediation process. Factors including groundwater seepage, initial water content, surrounding water seepage, and site thermal design were investigated in detail by numerical simulation. The following preliminary conclusions are drawn:

(1)

Groundwater seepage has a significant influence on soil temperature and water content distribution. The temperature distribution is shifted to the middle vacuum well and is intensified with increasing groundwater flow. The heat-up stage is not influenced by groundwater seepage. The boiling stage lasts 17 days and the superheating stage lasts 21 days when groundwater flow is $1\times {10}^{-7}\mathrm{m}/\mathrm{s}$. The boiling stage lasts 3 and 6 days longer when groundwater flow increases to $2\times {10}^{-7}\mathrm{m}/\mathrm{s}$ and $3\times {10}^{-7}\mathrm{m}/\mathrm{s}$, respectively, while the superheating stage increases by 5 and 10 days.

(2)

The heat-up and boiling stages are mainly influenced by the initial water content. The heat-up stage lasts 11 days and the boiling stage lasts 14 days when the initial water content is 15%. The heat-up stage lasts 1, 2, and 3 days longer when the initial water content increases to 20%, 25%, and 30%, respectively, while the boiling stage increases by 4, 9, and 13 days, respectively. However, the superheating stage lasts 22 days regardless of the initial water content.

(3)

The heating system characteristics and arrangements are studied. When the heating well spacing is 1.7 m, the high-temperature area is centered in the middle of the heating wells, whereas when the heating well spacing is 2.3 m, the high-temperature area is mainly distributed the outside of the heated soil. When the heating well depth is 3.5 or 4 m, it becomes difficult to heat bottom soil to reach the target temperature. So $S=2$ m and $D=4.5$ m are the most beneficial to in situ soil remediation.

In summary, a method using mathematical analysis of water content and temperature distribution was presented. The influence of those factors including water seepage, initial water content, and heating system characteristics on heat transfer performance were studied by simulation. It can be found that groundwater seepage and initial moisture content have a big influence on the thermal performance. So it could be considered to take some measures to prevent water seepage from unheated soil. And adopting the solar energy to preheat polluted soil for reducing initial water content is also feasible. The combination of thermal remediation and other remediation methods may be the development trend of soil remediation technology in the future. Finally, the results presented can serve as an analysis tool and a theoretical reference for in situ thermal remediation technology.