3.3.3. Well

(a) Exergy loss due to heat transfer process *Ex*,*Q*:

$$\begin{cases} E\_{\mathbf{x},Q} = E\_{\mathbf{x},Q\_H} - E\_{\mathbf{x},Q\_L} \\ E\_{\mathbf{x},Q\_H} = (1 - \frac{T\_0}{T\_H})Q\_1 \\\ E\_{\mathbf{x},Q\_L} = (1 - \frac{T\_0}{T\_L})Q\_2 \end{cases} \tag{38}$$

*Ex*,*QH* is the calorific exergy of *Q*1 at the temperature *TH* and *Ex*,*QL* is the calorific exergy of *Q*2 at the temperature of *TL*. *Q*1 and *Q*2 are considered equal calculated in Appendix B(a), while the amount of heat transferred in the heat transfer process varies in each stage. And the calculation of *TH* and *TL* are in Appendix B (d).

(b) Exergy loss of non-isothermal heat release is caused by temperature change of exhaust gas when flowing in the well:

$$E\_{x,Q\_1} = T\_0 G\_\text{c} c\_{p,w} \ln \frac{T\_{w,\text{in}}}{T\_{w,\text{out}}} \tag{39}$$

(c) Exergy of exhaust gas that flows from the outlet of the well to the environment is connected to the energy and temperature of exhaust gas:

$$E\_{w,out} = Q\_{w,out} (1 - \frac{T\_0}{T\_{w,out} - T\_0} \ln{\frac{T\_{w,out}}{T\_0}}) \tag{40}$$

3.3.4. Soil

(a).Exergy loss of non-isothermal heat absorption *Ex*,*Q*<sup>2</sup> is caused by temperature change of soil at three stages: In the first stage, the soil temperature rises from the initial temperature (environment temperature) *T*0 to the boiling point of water 373K. The soil keeps the temperature of 373K unchanged in the second stage. The third stage is to heat soil to increase the soil temperature to final temperature *Ts*:

$$\begin{cases} \begin{array}{c} E\_{\rm x,Q\_2,1} = \, T\_0 m\_s c\_{p,s} \ln \frac{373}{T\_0} \\\ E\_{\rm x,Q\_2,II} = 0 \\\ E\_{\rm x,Q\_2,III} = \, T\_0 m\_{\rm psc} c\_{p,p} \ln \frac{T\_s}{373} \end{array} \end{cases} \tag{41}$$

(b) *Es,a* is the exergy that the soil eventually uses to heat up:

$$E\_{s,d} = E\_{s,in} - E\_{x,Q\_2} - E\_{s,l} \tag{42}$$

3.3.5. Exergy Utilization Ratio

Exergy utilization ratio as performance indicators of the exergy analysis were calculated by the exergy that the soil ultimately uses and exergy value of 1 km of NG:

$$
\eta\_{c\infty} = \frac{E\_{s,a}}{E r} \tag{43}
$$

#### *3.4. Process of Parameters Calculation in the Models*

As Figure 7 shows, the calculation process of parameters of energy analysis starts at the thermal requirements and ends at the energy. The calculations of excess air coefficient α and mass flow rates *Ge* and *GNG* are given in Appendix B (a). These three parameters are used to solve the time needed of flowing 1 km natural gas (NG). The thermal flux has been modeled in Section 3.2. The calculation process of parameters of exergy analysis is similar to that of energy analysis.

**Figure 7.** The flowchart of the parameters calculation in energy analysis.

## **4. Results and Discussions**

In order to compare the effects of energy-saving strategies, the cases shown in Table 2 are designed. The traditional polluted-soil thermal remediation system, also named basic method (BM), is the fundamental case, Case BM. Case VCM applied energy-saving strategy for variable-condition mode with different exhaust gas temperatures at different stages. Energy-saving strategy for heat-returning mode is divided into 4 cases, among Case 3.1, Case 3.2 and Case 3.3, the difference is the rate of heat return. Case 3.4 combines variable-condition mode and heat-returning mode two energy-saving strategies. Energy-saving strategy for air-preheating mode is also divided into 4 cases, the difference is preheating ratio of air in Case 4.1, Case 4.2 and Case 4.3. As a comprehensive strategy for energy saving like Case 3.4, Case 4.4 combines variable-condition mode and air-preheating mode.


**Table 2.** Cases set of basic method (BM) and energy-saving strategies.

Next, the effect analysis of three energy-saving strategies is established in Sections 4.1–4.3, respectively. In Section 4.4, a comprehensive analysis of the energy-saving strategies will be presented.

#### *4.1. Energy Analysis and Exergy Anlysis of Variable-Condition Mode*

The most effective part of the variable-condition mode is that under the premise of the same heating demand and heating time, high amounts of natural gas (NG) can be saved. Table 3 lists the results of the mass flow rates of exhaust gas and NG, as well as the calculated excess air coefficient. The number of mass flow rates in the first stage of variable-condition mode (VCM) is 0.0299 km per second, much smaller than 0.1124 km per second of basis method (BM). The differences of mass flow rates and excess air coefficient of basic method (BM) and variable-condition mode (VCM) result from different temperatures of exhaust out of the well.


**Table 3.** Results of mass flow rates and excess air coefficient.

Besides savings in the amount of natural gas (NG) usage, this paper is mainly focused on improving the energetic and exergetic performance of the polluted-soil thermal remediation system depending on energy-saving strategies. Energy utilization ratios and exergy utilization ratios, two of the performance indicators of the analysis, were calculated as the important results of the mathematical model. The energy utilization ratios and exergy utilization ratios of the BM and VCM varies from different stages as well as different modes of heat convection. Detailed results of energy utilization ratios and exergy utilization ratios are shown in Tables 4 and 5. Modes of heat convection affects energy performance and exergy performance obviously. It can be observed that the energy utilization ratio of forced convection each stage is 2.6% lower than that of free convection, and exergy utilization ratio is 0.9% lower as well. It is because that the forced convection causes more loss of thermal leakage. While the two exergy utilization ratios of VCM is identical. It is because that the thermal leakage of forced convection is bigger, but the temperature of the outer wall of burner is lower. The larger quantity of thermal leakage and the lower temperature of thermal leakage lead to the same exergy loss.


**Table 4.** Energy utilization ratios of Case BM and Case VCM.

**Table 5.** Exergy utilization ratios of Case BM and Case VCM.


Next, we assessed the energy and exergy efficiency using two curves more intuitively, as indicated in Figure 8. The utilization ratios' values of forced convection and free convection are different from the tables above, but the trend is the same, so the following analysis takes forced convection as an example. The energy utilization ratios of forced convection of the three stages are plotted in Figure 8a, while exergy utilization ratios of forced convection of the three stages are plotted in Figure 8b. We combine the two curves of BM and VCM together to make our analysis simpler to understand.

**Figure 8.** Energy utilization ratio and exergy utilization ratio comparisons of variable-condition mode (VCM) and basic method (BM): (**a**) Energy utilization ratio comparisons of variable-condition mode (VCM) and basic method (BM); (**b**) Exergy utilization ratio comparisons of variable-condition mode (VCM) and basic method (BM).

Figure 8a shows that energy utilization ratios of stage I in BM is not so very different from that of stage II. The lower temperature soil is heated by the higher temperature exhaust gas, which brings higher energy utilization ratios, but in stage III, the energy utilization ratio decreases significantly for maintaining the same temperature of exhaust gas, while the temperature of soil becomes higher and it becomes difficult to heat the soil. In VCM, stage II is the stage guaranteed the best performance of the whole heating process, as it maintains the highest values of the energy utilization ratio compared to other stages. In VCM, the energy utilization ratios of stage I and stage II are better than that of the same stage in BM, but stage III is worse because the temperature of exhaust gas in VCM is higher than that in BM bringing more heat loss due to exhaust gas and lower energy utilization ratio.

Figure 8b shows that the exergy utilization ratios of stage II in BM is smaller than that in stage I and stage III because the thermal requirement in stage II is larger and the loss of irreversible combustion is larger as well. Comparing BM and VCM, we can find it that the exergy utilization ratios of VCM in stage I and stage III are lower for the reason of small mass flow rates. That is because the small mass flow rates resulting in the bigger flow time. Thermal flux calculated by formulas multiplied by time is the eventual thermal leakage energy. In stage II, when the mass flow rates of BM and VCM is similar, the exergy utilization ratios of VCM is larger.

The utilization ratio curves express intuitively the energy saving situation, but where the specific embodiment of energy savings is to be analyzed from the diagrams of energy flow and exergy flow. From the calculation results obtained, the data of energy loss and exergy loss of each component are used to draw energy flow diagrams and exergy flow diagrams of basic method (BM) and variable-condition mode (VCM) representing the flow of energy and exergy visually. The following analysis is concentrated on forced convection. The thickness of the arrows represents the size of the value. Regarding energy of 1 km natural gas (NG) as 100%, the energy and exergy distribution fraction of various losses in each component of the system is presented in the Figure 9, so that comparing the losses of the two strategies is not di fficult. The meanings of the parameters in all flow diagrams, including Figure 9, list in Table A2.

**Figure 9.** Flow diagrams of forced convection in stage I of of BM and VCM: (**a**) Energy flow diagram of forced convection in stage I of BM; (**b**) Energy flow diagram of forced convection in stage I of VCM; (**c**) Exergy flow diagram of forced convection in stage I of BM; (**d**) Exergy flow diagram of forced convection in stage I of VCM.

Comparing Figure 9a,b, it is observed that the energy in the exhaust gas is smaller in VCM compared with BM. The reason is that the temperature of exhaust gas in VCM is 200 ◦C, lower than that in BM with the value of 450 ◦C and this is the key to saving energy for VCM. It can be found by comparing Figure 9c,d that the exergy loss of irreversible combustion in BM is smaller than that in VCM. The reason is that exergy loss of irreversible combustion is associated with the adiabatic combustion temperature. The higher the adiabatic combustion temperature, the smaller the exergy loss of irreversible combustion. The adiabatic combustion temperature in VCM is lower in stage I, so that the exergy loss of irreversible combustion is bigger. Relative to energy, the energy saving strategy reduces more exergy loss of exhaust gas than energy loss. That is because the low temperature and the low energy of exhaust gas bring double e ffect of low exergy of exhaust gas. The increase of exergy loss impacted by mass flow rates is reflected in heat transfer process, non-isothermal heat release of exhaust gas and non-isothermal absorption of heat of soil. For example, when computing the exergy loss of non-isothermal heat release of exhaust gas of 1 km of natural gas (NG), the quantity of heat of non-isothermal heat release is an important factor. While the total quantity of heat of non-isothermal heat release in the first stage is settled, which is decided by the thermal requirements, in other words, the state of the soil. In the case of the same heat requirements and the same heating time, changing the temperature of exhaust gas from 450 ◦C to 200 ◦C in the first stage due to energy saving purpose results in the small amount of natural gas (NG). The total quantity of heat release maintained invariant, so that the exergy loss of one kilogram natural gas (NG) on average is bigger.

#### *4.2. Energy Analysis and Exergy Anlysis of Heat-Returning Mode*

The energy-saving strategy for heat-returning mode is returning the exhaust used to discharge to the atmospheric environment directly to the burner as the air in a certain proportion, Case 3.1 is with the rate of heat return of 0.1, Case 3.2 with the rate of 0.2 and Case 3.3, the rate 0.3. Using curves to assess the energy and exergy e fficiency is the more intuitive way, as shown in Figure 10. And the specific distribution of energy and exergy loss as well as energy and exergy flow comparing with basic method (BM) are shown in Figure 11.

In Figure 10, it can be seen that all three case have higher utilization ratios than the basic method (BM), and the utilization ratios increase with increasing rate of heat return. The Case 3.3 with the largest rate of heat-returning has the best energy utilization ratio and exergy utilization ratio no matter what stage, which means the most significant energy-saving e ffect. However, the rate of heat return cannot always be increased without limit due to equipment and practical conditions. Compared with utilization ratios of Case 3.2 for Case 3.1, the Case 3.3 for Case 3.2 is more significant.

**Figure 10.** Energy utilization ratio and exergy utilization ratio comparisons of Case 3.1, Case 3.2 and Case 3.3 of heat-returning mode and basic method (BM): (**a**) Energy utilization ratio comparisons of Case 3.1, Case 3.2 and Case 3.3 of heat-returning mode and basic method (BM); (**b**) Exergy utilization ratio comparisons of Case 3.1, Case 3.2 and Case 3.3 of heat-returning mode and basic method (BM).

**Figure 11.** Flow diagrams of forced convection in stage I of BM and Case 3.3 of heat-returning mode: (**a**) Energy flow diagram of forced convection in stage I of BM; (**b**) Energy flow diagram of forced convection in stage I of Case 3.3 of heat-returning mode; (**c**) Exergy flow diagram of forced convection in stage I of BM; (**d**) Exergy flow diagram of forced convection in stage I of Case 3.3 of heat-returning mode.

The Case 3.3 with the best energy saving effect of the three cases of energy-saving strategy for heat-returning mode is selected to draw the energy flow diagram. From Figure 11a,b, there is a backflow of energy to the burner that is most obvious in Case 3.3, and it represents the heat-returning mode of exhaust. A Sankey diagram is a good way to show the flow of energy and the thickness of the arrows represents the size of the value in the diagram. With an initial energy of 1 km of natural gas, it is using the regenerative energy that to make more energy go into the system initially and it also results in more energy being used to heat the soil ultimately. While the energy loss of heat leakage of each component in Case 3.3 is bigger than that in BM for the reason of the higher temperature caused by more initial energy in the polluted-soil thermal remediation system. By comparing Figure 11c,d that the exergy loss of irreversible combustion in Case 3.3 is smaller than that in BM as a result of higher adiabatic combustion temperature. And the analysis of exergy loss of heat leakage is the same as the energy analysis above, the higher temperature, the more energy loss, and the more exergy loss.

#### *4.3. Energy Analysis and Exergy Anlysis of Air-Preheating Mode*

The energy-saving strategy for air-preheating mode is setting preheaters to air-preheating mode using residual heat of the system. The cases in this section selected two places with high temperature and enough space to set the preheaters. In Case 4.1, the ratio of air through preheater 1 to be preheated is 0.1, the ratio of air through preheater 2 to be preheated is 0, and the ratio of air that does not pass through the preheater directly into the burner is 0.9. In Case 4.2, the ratio of air through preheater 1 to be preheated is 0.3, the ratio of air through preheater 2 to be preheated is 0, and the ratio of air that does not pass through the preheater directly into the burner is 0.7. In Case 4.3, the ratio of air through preheater 1 to be preheated is 0.1, the ratio of air through preheater 2 to be preheated is 0.1 as well, and the ratio of air that does not pass through the preheater directly into the burner is 0.8. Curves are

used to assess the energy and exergy efficiency as shown in Figure 12. And the specific distribution of energy and exergy loss as well as energy and exergy flow comparing with basic method (BM) are shown in Figure 13.

**Figure 12.** Energy utilization ratio and exergy utilization ratio comparisons of Case 4.1, Case 4.2 and Case 4.3 of heat-returning mode and basic method (BM): (**a**) Energy utilization ratio comparisons of Case 4.1, Case 4.2 and Case 4.3 of heat-returning mode and basic method (BM); (**b**) Exergy utilization ratio comparisons of Case 4.1, Case 4.2 and Case 4.3 of heat-returning mode and basic method (BM).

In Figure 12, it can be seen that the energy and exergy utilization ratio of Case 4.1 is smaller than that of BM, and it is proved that the air preheating through the preheater 1 is not conducive to the improvement of utilization ratio and energy saving. The energy and exergy utilization ratio of Case 4.2 is even smaller than that of Case 4.1, that is to say, the effect of the preheater 1 wasting energy increases with the proportion of air passing through it. While the preheater 2 performs better, the energy utilization ratio of Case 4.3 is bigger than that of BM and the exergy utilization ratio is similar to that of BM under the bad interference of preheater 1. The underlying reason is that preheater 1 uses the energy to flow to the next component, while preheater 2 uses the waste heat to be drained into the air, so making full use of waste heat is the wonderful way to save energy, so in the Section 4.4 comprehensive energy-saving strategies, in Case 4.4, the ratio of air through preheater 1 to be preheated is 0, the ratio of air through preheater 2 to be preheated is 0.3, and the ratio of air that does not pass through the preheater directly into the burner is 0.7.

Case 4.3 with the best energy saving effect of the three cases of energy-saving strategy for air-preheating mode is selected to draw the energy flow diagram. From Figure 13a,b, there are two backflows of energy to the burner in Case 4.3, and they represent preheated air with energy. Although the proportion of air through the preheater is not high, not much heat is brought back. The amount of energy used eventually increases a little with the increase in heat leakage accompanied by an increase in temperature.

**Figure 13.** Flow diagrams of forced convection in stage I of BM and Case 4.3 of air-preheating mode: (**a**) Energy flow diagram of forced convection in stage I of BM; (**b**) Energy flow diagram of forced convection in stage I of Case 4.3 of air-preheating mode; (**c**) Exergy flow diagram of forced convection in stage I of BM; (**d**) Exergy flow diagram of forced convection in stage I of Case 4.3 of air-preheating mode.

#### *4.4. Energy Analysis and Exergy Anlysis of Comprehensive Energy-Saving Strategies*

The comprehensive energy-saving strategies are mainly to compare air-preheating mode combined with variable-condition mode (VCM) and heat-returning mode combined with variable-condition mode (VCM), that is Case 3.4 and Case 4.4. The rate of heat return in Case 3.4 is 0.3 and in Case 4.4 the ratio of air through preheater 2 to be preheated is 0.3 as well as the ratio of air that does not pass through the preheater directly into the burner is 0.7. Because the variable-condition mode (VCM) were applied in both cases, so draw the energy utilization ratio curves for the three cases on one graph, Figure 14a, and draw the exergy utilization ratio curves on the other graph, Figure 14b, for easy comparison.

By comparing Figure 14a,b, in the three cases with variable-condition mode (VCM), the trend of energy utilization ratio and exergy utilization ratio curve is the same in the three stages. The second stage has the highest utilization ratio, then the first stage, then the third stage. The results in Figure 14a indicate that the Case 3.4 has the best energy utilization ratio in all three stages by combining the advantages of variable-condition mode (VCM) and heat-returning mode, that is to say, using two energy-saving strategies can bring the improvement of fuel saving and energy efficiency at the same time. The results of Case 4.4 have the same implications that Case 4.4 has better energy utilization ratio and exergy utilization ratio than Case VCM by combining the advantages of variable-condition mode (VCM) and air-preheating mode. If all three energy-saving strategies are combined, the structure of the system will become too complex and uncontrollable. Therefore, the combination of the two energy-saving strategies is recommendable.

**Figure 14.** Energy utilization ratio and exergy utilization ratio comparisons of Case 3.4, Case 4.4 and variable-condition mode (VCM): (**a**) Energy utilization ratio comparisons of Case 3.4, Case 4.4 and variable-condition mode (VCM); (**b**) Exergy utilization ratio comparisons of Case 3.4, Case 4.4 and variable-condition mode (VCM).
