Comparative Experiment of Wellbore Self-Circulation Heat Mining Capacity with Different Heat-Carrying Fluids

Liang Zhang; Linchao Yang; Songhe Geng; Shaoran Ren; Jian Lin

doi:10.2113/2021/2953458

Abstract

Based on the principle of wellbore self-circulation heat mining, the evaluation experiments of local wellbore self-circulation heat exchange laws and influencing factors were carried out. Water, SCCO₂, R134a, and heat transfer oil were screened as the heat-carrying fluids. The heat exchange laws and heat mining capacity of these four heat carrying fluids were analyzed and compared, and their heat mining rates at the field scale were estimated using the similarity criterion method according to the experimental results. The results show that R134a and heat transfer oil can obtain the largest outlet temperature and the largest heat loss ratio, while the water can achieve a higher heat mining rate and a larger convective heat transfer coefficient than the other three fluids. The heat mining capacity of CO₂ is significantly affected by the injection pressure. It is necessary to optimize the injection pressure larger than critical point to achieve the best heat mining performance. When the water is selected as the heat-carrying fluid, the heat mining rate can reach more than 1 MW if a horizontal wellbore with a length of 2000 m is applied for wellbore self-circulation at the field scale.

1. Introduction

Geothermal energy is one of the promising renewable energy resources [1–5]. Hot dry rock (HDR) is the most attractive geothermal type, which has the advantages of high temperature, wide distribution, and large reserves [6, 7]. Because of the low-permeability of HDR [8, 9], large-scale hydraulic fracturing is required to connect the injection well with the production well. Then, a large amount of water is injected into the reservoir as a heat-carrying fluid. Through water circulation and heat exchange with hot rocks [9, 10], geothermal energy is extracted for power generation. This process is called Enhanced Geothermal System (EGS). Although the research on HDR EGS has been conducted for more than 40 years, there are still the following main problems: (1) loss of heat-carrying fluid; (2) fluid flow channel blockage caused by rock-fluid interaction, resulting in reduced heat mining efficiency; (3) economic costs are high and commercial operation is difficult; (4) EGS may induce earthquake and environmental problems. New simple and economical HDR geothermal mining technologies are needed [4, 11–16].

Concentric tube has been proposed to extract heat from geothermal reservoirs. The basic principle is to inject the cold heat-carrying fluid through the annulus and return the heated one to the surface through the heat insulation tubing [17–21]. Kujawa et al. (2006) established a heat transfer model between the concentric tube heat exchanger and the formation, and the influences of different insulation materials and the mass flow of the heat-carrying fluid on the outlet temperature were analyzed [17]. Richard et al. (2013) established an analytical model of vertical temperature distribution for coaxial heat exchangers and verified the results through experimental temperature measurement [18]. Holmberg et al. (2016) compared the predicted results of the model with the experimental results; a parameter performance study was carried out on the coaxial conditions of different well depths, different flow rates, and different flow directions [19]. David et al. (2018) verified the semianalytical model by building a set of vertical coaxial wellbore heat exchangers and comparing the heat mining performance of heat exchangers with different inner diameters [20]. In recent years, referring to the concentric tube principle, the self-circulation wellbore was proposed to exploit geothermal energy from deep reservoirs. Cui et al. (2017) proposed to mine the HDR geothermal energy using a self-circulation horizontal well to increase the heat exchange area between the circulating water and hot rocks, which demonstrated a remarkable attraction to power generation [21]. Nian and Cheng (2018) assessed the heat mining capacity of abandoned oil wells by wellbore self-circulation, which can heat 10000 m² building area [22].

Because of the closed-loop condition of the concentric tube or self-circulation wellbore, it becomes possible to optimize the heat-carrying fluid in the system. Various fluids except water were assessed (e.g., CO₂ and organic working media) [23–27]. Cheng et al. (2013, 2014) analyzed the performance of different organic fluids used as the heat-carrying medium for geothermal power generation and discussed the influence of the thermal insulation performance of tubing on the heat mining effect under the condition that R134a was used as the heat-carrying fluid [26, 28, 29]. Davis and Michaelides (2009) used isobutane as the heat-carrying fluid to simulate geothermal power generation from abandoned oil wells. The results show that the operating power of the power generation system depends on the bottom hole temperature and injection pressure [30]. Nalla et al. (2005) analyzed the influence of properties of different working fluids on the heat mining effect by changing the density and specific heat capacity of heat-carrying fluids [31]. Alimonti and Soldo (2016) compared and analyzed the heat mining capacities of two different heat transfer fluids (water and heat transfer oil) through numerical models [32]. Zhang et al. (2014) studied the advantages of SCCO₂ as the heat-carrying fluid for geothermal exploitation and analyzed its application potential [33, 34]. Huang et al. (2020) established a self-circulation heat mining coupling model and investigated the variation law of CO₂ properties in the heat transfer process [35].

To sum up, the closed-loop condition of the concentric tube or self-circulation wellbore has the advantage of selecting the best heat-carrying fluid. No matter for the medium-low temperature porous formation or for the high-temperature HDR, it is very meaningful for enhancing the heat mining rate or making the heat-carrying fluid at a favorable state for power generation. Heat mining performance of different heat-carrying fluids in the self-circulation wellbore is often assessed by theoretical analysis or numerical simulation. There are few experiments conducted to screen the heat-carrying fluid and verify the results of the numerical simulation.

Therefore, in this study, we designed and built a wellbore self-circulation simulation experiment device, and a series of local wellbore self-circulation heat exchange experiments were carried out. By comparing the thermal properties of different heat-carrying fluids, SCCO₂, R134a, and heat transfer oil were selected to conduct the experiments. The heat exchange laws and the heat mining capacity of different heat-carrying fluids in self-circulation wellbore were analyzed and compared. Finally, the heat mining rates of different heat-carrying fluids at the field scale were estimated according to the similarity criterion based on the experimental results.

2. Comparative Analysis of Thermal Properties of Heat-Carrying Fluids

Existing geothermal power generation methods can be mainly divided into two categories: (1) single working fluid cycle power generation and (2) dual working fluid cycle power generation. The single working fluid cycle includes the direct power generation system (DPGS) and the flash power generation system (FPGS) [36]. In the direct power generation system, the organic working fluid flows into the injection well under the action of the pump and is heated by geothermal energy during the wellbore circulation process. When the organic working fluid leaves the production well, it becomes a supercritical state, and the supercritical fluid directly enters the turbine to generate electricity. After the pressure and temperature of the organic working fluid drop, it is cooled by the cooling water of the condenser and becomes a liquid state. The high-pressure liquid pressurized by the pump flows into the injection well again to complete the entire power generation cycle [37]. The traditional flash geothermal power generation system uses water as the working fluid, and the boiling point of water is related to the pressure. After underground heat exchange, the hot water with the temperature below 100°C is sent into a closed flash chamber to depressurize. Then, the underground hot water boils as the pressure drops. When it becomes steam, it drives the steam turbine to generate electricity [38]. The dual working fluid cycle power generation system mainly includes a ground cycle power generation system and an underground wellbore heat exchange system. The underground wellbore heat exchange system uses water as the heat-carrying fluid. After the water absorbs heat and returns to the ground, the heat is transferred to the organic working fluid with a low boiling point in the ground cycle power generation system through the heat exchanger. The organic working fluid directly enters the turbine to generate electricity after absorbing heat. At present, several geothermal power generation systems are based on the working principle of the Rankine cycle, and the heat-carrying fluid has a significant influence on the power generation efficiency of the Rankine cycle. Therefore, comparative analysis of the thermal properties of different heat-carrying fluids and selecting suitable heat-carrying fluids have an important influence on the exploitation of geothermal energy and power generation efficiency.

As a heat-carrying fluid, water has the advantages of large specific heat capacity and low cost and has been widely used in various geothermal power generation systems. The utilization of CO₂ resources is an effective measure to reduce greenhouse gas emissions and alleviate climate warming. The use of SCCO₂ to replace conventional water as the heat-carrying fluid to extract HDR geothermy is a novel geothermal development technology [23–25, 33, 34].

In the organic Rankine cycle system, commonly used organic working fluids include R245fa, R134a, R600a, and R290. In addition, there are also some studies on heat transfer oil as a heat-carrying fluid that can generate high temperatures under low vapor pressure and have good heat transfer effects [26, 27]. The physical parameters and safety of various heat-carrying fluids are shown in Table 1.

The comparison of thermal properties of heat-carrying fluids mainly considers density, specific heat capacity, thermal conductivity, and viscosity. The changes in thermal properties of various heat-carrying fluids with temperature under a pressure of 10 MPa are shown in Figure 1.

In the flow and heat exchange in the wellbore, due to changes in temperature and pressure, the phase state of the heat-carrying fluid will also change between liquid, gaseous, and supercritical states. The phase state change has an important influence on the heat mining capacity of the heat-carrying fluid. The phase state curves of various heat-carrying fluids are shown in Figure 2.

It can be seen from Table 1 that the critical temperature and critical pressure of CO₂ are 31.3°C and 7.39 MPa, respectively. When convection heat transfer occurs at the injection pressure of 10 MPa, it is easy to reach a supercritical state. And the unique thermal properties of SCCO₂ determine its obvious heat-carrying advantage. As shown in Figure 1, the density, specific heat capacity, thermal conductivity, and viscosity of CO₂ drastically change near the critical point. After entering the supercritical state, its density, thermal conductivity, and viscosity are close to its liquid and gaseous parameters, respectively. And the specific heat capacity at constant pressure is 0.3 to 1 times that of water. Secondly, temperature and pressure have a significant impact on the thermal properties of SCCO₂. During the heat mining cycle, the CO₂ density changes more than water, so there is a stronger thermosiphon phenomenon between the injection and production wellbore than water. It can provide a driving pressure difference for the ground process and reduce the power of the circulating pump. Finally, the use of SCCO₂ as the heat-carrying fluid can effectively avoid scaling problems in surface equipment, pipelines, and wellbore and reduce equipment maintenance costs.

Organic working fluid usually has a smaller heat capacity than water and can get a higher temperature to absorb the same heat and enter the supercritical state. Therefore, it is widely used in direct power generation system (DPGS) or ground power generation system of dual working fluid cycle. By comparing the five organic working fluids in Table 1, it can be seen that the critical pressures of the five organic working fluids are not much different, but the critical temperatures are quite different. The critical temperatures of R245fa and R600a are 154.1°C and 135°C, respectively. It is difficult for the heat-carrying fluid to reach the supercritical state after the formation temperature decreases. In addition, the safety levels of the two are B1 and A3, respectively, which are dangerous. Table 1 and Figure 1 show that propylene and R290 have similar thermal properties, and their critical temperatures are also lower, 91°C and 96.7°C, respectively. However, it can be seen from the specific heat capacity change curve that the specific heat capacity of the two fluids increases significantly with the rise in temperature. At 120°C, the specific heat capacity is almost equal to that of water, indicating that the temperature rise of the two fluids is smaller when the same heat is absorbed, and it is also difficult to reach the supercritical state. For R134a, its critical temperature is 101.1°C, and its specific heat capacity is similar to that of CO₂, which makes it easy to reach a supercritical state. At the same time, the safety level of R134a is A1, which has good safety. As a fluid with good thermal stability and heat transfer efficiency, heat transfer oil has a density and viscosity similar to water. And its specific heat capacity is only 0.3-0.5 times of water so that higher temperatures can be obtained under low vapor pressure.

According to the thermal properties of various heat-carrying fluids and considering the safety in the experiment, CO₂, R134a, and heat transfer oil are selected as heat-carrying fluids to conduct wellbore heat exchange experiments. And the heat mining capacity of different heat-carrying fluids is compared.

3. Experimental Equipment and Methods

3.1. Experimental Equipment

The schematic diagram of the wellbore self-circulation heat exchange experimental system is shown in Figure 3. The heat-carrying fluid enters the heat exchange tube through the advection pump, flows down in the annulus, and exchanges heat with the inner wall of the casing. Because the experimental section is short, it can only simulate the heat exchange law of the partial well section. Therefore, the experiment section did not consider the influence of temperature gradient. In addition, the experiment did not consider the impact of the cement layer on the heat transfer between the geothermal reservoir and the outer wall of the casing. After the fluid flows to the annulus bottom, it enters the tubing from the small hole at the bottom and flows out of the tubing outlet into the low-temperature water bath. The low-temperature water bath is set to a cooling temperature of 20°C. After cooling, the fluid enters the heat exchange tube again through the plunger metering pump for circulating heat mining.

3.2. Experimental Materials

In the experiment, SCCO₂, R134a, and heat transfer oil were selected as the heat-carrying fluid for heat exchange experiments, and the granite with the best heat conductivity was selected to simulate the geothermal reservoir (as shown in Figure 4). It is heated by a high-temperature thermotank to simulate a high-temperature geothermal reservoir. The maximum heating temperature of the thermostat is 200°C. The width of the granite jacket is 22 cm, the height is 55 cm, and the middle part has an aperture of 7 cm in diameter. The gap between the heat exchange tube and the hole diameter of the stone jacket is filled with thermally conductive mud so that the stone jacket can completely wrap the heat exchange tube. The heat exchange tube is made of 304 stainless steel. Due to equipment limitations, the effect of the cement layer on heat transfer was not considered in the experiment. Table 2 lists the thermal properties of the selected experimental materials at room temperature and pressure.

3.3. Experimental Procedure

The steps of the wellbore self-circulation heat exchange experiment are as follows:

(1)
Turn on the advection pump and inject the circulating heat-carrying fluid into the heat exchange system at a rate of 10 ml/min, drive all the air out of the circulation system, then close the outlet of the loop, and continue injecting the fluid into the loop to increase the pressure to 10 MPa; then, close the inlet of the loop
(2)
Set the heating temperature of the thermotank and the cooling temperature of the low-temperature water bath to 150°C and 20°C, respectively, and turn on the thermotank to fully heat the simulated heat reservoir
(3)
When the pressure and temperature in the heat exchange tube reaches steady state (the additional pressure may need to be released due to the temperature increase), start the plunger metering pump to circulate the heat-carrying fluid in the heat exchange tube at a rate of 106.7 ml/min
(4)
Open the computer and the data acquisition box to record temperature and pressure data every 10 s. When the outlet temperature reaches steady state 2 h later, the experiment is over

According to the monitored data, the parameters that characterize the heat exchange performance of the self-circulation wellbore, including the heat mining rate at the outlet, the wellbore heat flux, the average convective heat transfer coefficient of the wellbore, and the heat loss ratio from the bottom of the annulus to the outlet of the inner tubing in the heat mining process can be calculated.

The heat mining rate at the outlet (⁠

Q_{w}

⁠, W) is determined by the inlet and outlet temperatures of the heat exchange tube and the volumetric flow rate of the water [39], which is calculated as follows:

\begin{matrix} (1) & Q_{w} = V_{w} ρ_{w} c_{w} (T_{out} - T_{in}), \end{matrix}

where

V_{w}

is the volumetric flow rate of water, m³/s;

ρ_{w}

is the density of water, kg/m³;

c_{w}

is the specific mass heat capacity of water at constant pressure, J/(kg·K);

T_{in}

and

T_{out}

are the temperatures of water at the inlet and outlet of the heat exchange tube, respectively, °C.

In order to avoid the variation of heat flux at different radius due to the variation of cross-sectional area, the heat flux (⁠

q_{w}

⁠, W/m) is often calculated according to unit pipe length in engineering for the convenience of calculation [22]. Hence, taking the average heat flux of the casing annulus, for example, it can be calculated as follows:

\begin{matrix} (2) & q_{w} = \frac{V_{w} c_{v w} (T_{bottom} - T_{in})}{L_{c}}, \end{matrix}

where

c_{v m}

is the volumetric heat capacity of the water, J/(m³·K);

T_{bottom}

is the temperature at the bottom of the casing annulus, °C;

L_{c}

is the length of the heat transfer segment (casing), m.

When the outlet temperature reaches steady state, the heat produced at the outlet is equal to the heat transferred through the casing wall from the heat storage media, regardless of the influence of the heat stored in the casing and tubing. Hence, the average convective heat transfer coefficient (⁠

h_{w}

⁠, W/(m²∙K)) between the casing wall and the water in the annulus can be calculated using the following formula [40]:

\begin{matrix} (3) & h_{w} = \frac{Q_{w}}{∆ T_{m} \cdot π d_{c i} L_{c}}, \end{matrix}

where

∆ T_{m}

is the average heat transfer temperature difference between the water and the inner wall of the casing, °C;

d_{c i}

is the inner diameter of the casing, m.

∆ T_{m}

can be calculated as follows [40]:

\begin{matrix} (4) & ∆ T_{m} = \frac{T_{bottom} - T_{in}}{\ln ((T_{c i} - T_{in}) / (T_{c i} - T_{bottom}))}, \end{matrix}

where

T_{bottom}

is the water temperature at the bottom of the casing annulus, °C;

T_{c i}

is the average inner wall temperature of the casing, °C, which can be calculated according to the average temperature of the outer wall of the casing. The formula is as follows [40]:

\begin{matrix} (5) & T_{c i} = T_{c o} - \frac{Q_{w} / A_{c} (d_{c o} - d_{c i})}{2 λ_{c}}, \end{matrix}

where

T_{c o}

is the average temperature of the casing outer wall, °C;

A_{c}

is the average wall area of the casing, m²;

d_{c o}

is the outer diameter of the casing, m;

λ_{c}

is the thermal conductivity of the casing, W/(m·K).

In addition, for the rate of heat loss (⁠

f_{t loss}

⁠, %) from the inner tubing to the casing annulus when the water flows upward in the inner tubing, it can be calculated using the following equation:

\begin{matrix} (6) & f_{t loss} = \frac{T_{bottom} - T_{out}}{T_{bottom} - 20} \times 100 % . \end{matrix}

3.4. Experimental Program

In order to compare the heat exchange laws and heat mining capabilities of different heat-carrying fluids, SCCO₂, R134a, and heat transfer oil were selected as the comparison heat-carrying fluids (The heat loss ratio of heat transfer oil is too large, and it is not suitable as the heat-carrying fluid. So, only a set of experiments under basic conditions were carried out). The granite with the best thermal conductivity is selected to simulate the geothermal reservoir, and the heat insulation condition of the tubing is vacuum insulation. The design experiment scheme is shown in Table 3.

4. Experimental Results and Analysis

4.1. Basic Laws of Wellbore Self-Circulation Heat Exchange

When analyzing the basic law of wellbore self-circulation heat exchange, the basic experimental conditions selected are as follows: (1) the reservoir type is granite; (2) the reservoir temperature is 150°C; (3) the injection pressure is 10 MPa; (4) the injection rate is 107 ml/min; (5) the heat insulation condition of the tubing is vacuum insulation; (6) water, SCCO₂, R134a, and heat transfer oil are selected as the heat-carrying fluid.

It can be seen from Figure 5(a) that the outlet temperatures of heat transfer oil and R134a at 80 min are significantly higher than those of SCCO₂ and water, which are 71.9°C and 69.3°C, respectively. The outlet temperature of SCCO₂ in the early stage is higher than that of R134a and water, but it is slightly lower than water and much lower than R134a at 80 minutes. Under the condition of 10 MPa pressure, the specific heat capacity changes of R134a and heat transfer oil are basically the same, so the outlet temperature of the two is basically the same. The specific heat capacity of CO₂ under the condition of 10 MPa changes drastically, and the temperature of the reservoir is very high at the initial stage. So the specific heat capacity of SCCO₂ is very small, resulting in its outlet temperature is relatively high. Due to the high heat mining rate in the early stage, the heat in the jacket cannot be replenished by the heat source in time. As a result, the temperature of the simulated reservoir was low, and the length of the heat exchange tube was limited, so the CO₂ temperature could only reach 50-60°C in the later stage. As shown in Figure 1, it can be seen that the specific heat capacity of CO₂ increases sharply near the critical temperature point, even much larger than that of water. It results in the outlet temperature of SCCO₂ being lower than that of the water in the middle and late stages.

Figure 5(b) shows that under the same flow rate condition, the heat mining rate of water is the highest, followed by SCCO₂, and the heat mining rates of R134a and heat transfer oil are the lowest and basically the same. When water is used as the heat-carrying fluid, although the outlet temperature is lower, the total heat mining rate is the highest because of its larger specific heat capacity.

It can be seen in Figure 6(a) that the convective heat transfer coefficient of SCCO₂ is much higher than that of the other three heat-carrying fluids, while the convective heat transfer coefficients of water, R134a, and heat transfer oil are not much different. This is because the geothermal reservoir temperature is relatively high at the initial stage, and the density and viscosity of SCCO₂ change drastically. Under the same condition of the injection rate, the flow rate of SCCO₂ increases continuously when it is heated along the annulus. It results in a high Reynolds number in the annulus. The flow state changes from laminar flow to turbulent flow, and the convective heat transfer intensity under turbulent flow is significantly more significant than laminar flow. When the heat is mined for 80 minutes, the convective heat transfer coefficients of the four heat-carrying fluids tend to be stable, the heat transfer oil is the highest, and the SCCO₂ is the lowest. It can be seen from Figure 5(b) that the heat mining rate change is not great. Because the convective heat transfer coefficient is related to the heat mining rate, the convective heat transfer coefficient of the heat conducting oil also changes little. Due to the limited heat reservoir of the granite jacket, the formation temperature is lower after the heat mining is stabilized. The SCCO₂ is slowly heated, so its convective heat transfer intensity is also low.

Figure 6(b) shows the heat loss of the four heat-carrying fluids returning from the bottom of the annulus to the outlet. It can be seen that the heat loss ratio of water in the early stage is the smallest and the heat transfer oil is the highest. As the heat mining time increases, the heat loss ratio of the four heat-carrying fluids tends to stabilize. In general, the heat loss ratio of water, SCCO₂, and R134a has little difference after heat mining stabilization, which is 27.1%, 30.9%, and 29.8%, respectively. But the heat loss ratio of heat transfer oil is significantly higher, reaching 44.09%, indicating that heat transfer oil has a worse heat mining benefit.

From the temperature distribution curves of the four heat-carrying fluids along the wellbore, it can be seen that due to large thermal conductivity and small specific heat capacity, the heat transfer oil heats up quickly when flowing along the wellbore. The temperature at the bottom of the annulus is 109.7°C in 80 minutes, which is much higher than the other three heat-carrying fluids. However, the heat loss is also significantly higher during the process of returning from the bottom of the annulus to the outlet, indicating that the heat transfer oil is not suitable as the heat-carrying fluid in the wellbore self-circulation system. Therefore, it is no longer considered when evaluating the influence of different factors on the heat mining capacity of the heat-carrying fluid. Figures 7(b)–7(e) show the changes of four heat-carrying fluids along the wellbore, viscosity, flow velocity, and Reynolds number. The density of water, heat transfer oil, and R134a does not change much with temperature, so the flow rate and Reynolds number changes along the wellbore are also small. The thermal properties of SCCO₂ drastically change. When heat mining is stable, from the inlet of the heat exchange tube to the bottom of the annulus, its density decreases from 898.7 kg/m³ to 267.8 kg/m³, and the viscosity decreases from 0.082 mPa·s to 0.022 mPa·s. As a result, the flow rate along the wellbore increased from 0.14 cm/s to 0.47 cm/s, and the Reynolds number increased from 773 to 2810. It can be seen that when SCCO₂ flows and exchanges heat along the wellbore, its flow rate and Reynolds number rise significantly. This significantly influences the heat transfer intensity between the SCCO₂ and the tube wall, so the convective heat transfer coefficient in the early stage is much higher than that in the later stage.

4.2. Influence of Injection Rate

When analyzing the influence of injection rate, the basic experimental conditions selected are as follows: (1) the reservoir type is granite; (2) the reservoir temperature is 150°C; (3) the injection pressure is 10 MPa; (4) the injection rate is 27, 53, 107, 213, and 533 ml/min, respectively; (5) the heat insulation condition of the tubing is vacuum insulation; (6) the heat-carrying fluids are water, SCCO₂, and R134a.

From Figure 8(a), it can be seen that the outlet temperature of the three heat-carrying fluids basically decreases linearly with the increase of the injection rate. The outlet temperature of R134a is significantly higher than that of water and SCCO₂. Under the condition of 107 ml/min, the outlet temperatures of water, SCCO₂, and R134a are 56.9°C, 50°C, and 69.3°C, respectively. When the injection rate is low, the outlet temperature of SCCO₂ changes little with the increase of injection rate and has a small difference from the outlet temperature of the water. Figure 8(b) shows the relationship between the heat mining rate of the three heat-carrying fluids and the injection rate. The heat mining rate of water is the highest, but the outlet temperature is low, while the R134a can obtain a high outlet temperature due to its small specific heat capacity, but the heat mining rate is the lowest. When the injection rate is small, the heat mining rate difference between water and SCCO₂ is very small. But as the injection rate increases, the increase in heat mining rate obtained by water is significantly higher than that of SCCO₂ and R134a. This shows that water has a greater heat mining advantage under the condition of a high injection rate.

Figures 9(a) and 9(b) respectively describe the relationship between the convective heat transfer coefficient and heat loss ratio of the three heat-carrying fluids with the injection rate. It can be seen from the figure that the convective heat transfer coefficient of water is higher than that of R134a and SCCO₂. The convective heat transfer coefficients of the three heat-carrying fluids all increase with the injection rate, but the convective heat transfer coefficient of SCCO₂ increases with the injection rate much smaller than that of water and R134a. When the injection rate was increased from 27 ml/min to 533 ml/min, the convective heat transfer coefficients of water and R134a increased by 12.8 times and 13.2 times, respectively. The SCCO₂ only increased by 5.8 times, indicating that increasing the injection rate has a relatively small effect on the convective heat transfer intensity of SCCO₂.

The heat loss ratio curve shows that when the injection rate is less than 213 ml/min, the heat loss ratio of the three heat-carrying fluids increases slowly with the increase of the injection rate. The heat loss ratio of SCCO₂ and R134a is basically the same, but the water is slightly lower. When the injection rate increases from 213 ml/min to 533 ml/min, the heat loss ratio of the three heat-carrying fluids all increase significantly, and the water, SCCO₂, and R134a reach 36.4%, 36.8%, and 35.8%, respectively. This indicates that the heat mining rate cannot be increased by increasing the injection rate indefinitely. Therefore, an appropriate injection rate should be selected when the wellbore self-circulation heat mining is used.

4.3. Influence of Reservoir Temperature

When analyzing the influence of reservoir temperature, the basic experimental conditions selected are as follows: (1) the reservoir type is granite; (2) the reservoir temperature is 60, 90, 120, 150, and 180°C, respectively; (3) the injection pressure is 10 MPa; (4) the injection rate is 107 ml/min; (5) the heat insulation condition of the tubing is vacuum insulation; (6) the heat-carrying fluids are water SCCO₂ and R134a.

Figures 10(a) and 10(b) respectively describe the relationship between the outlet temperature and heat mining rate with the reservoir temperature. It can be seen from the figure that the outlet temperature of the three heat-carrying fluids basically rises linearly with the increase of the reservoir temperature, and the R134a is the highest. When the temperature is low, the outlet temperature of the water and SCCO₂ is basically the same, and the outlet temperature of the water is slightly higher than that of SCCO₂ as the temperature increases. When the reservoir temperature is 180°C, the outlet temperatures of water, SCCO₂, and R134a are 64.9°C, 60°C, and 79°C, respectively. The heat mining rate curve shows that although the outlet temperature of R134a is very high, the heat mining rate is significantly lower than that of water and SCCO₂. When the reservoir temperature is 180°C, the heat mining rates of water, SCCO₂, and R134a are 332.6 W, 254.8 W, and 191.3 W, respectively, and the heat mining rate of R134a is only 57.5% of that of water.

Figures 11(a) and 11(b) respectively describe the relationship between the convective heat transfer coefficient and heat loss ratio with the reservoir temperature. It can be seen from the figure that the convective heat transfer coefficients of the three heat-carrying fluids increase slowly with the increase of reservoir temperature. When the reservoir temperature increases from 60°C to 180°C, the convective heat transfer coefficients of water, SCCO₂, and R134a only increase by 27.9%, 12.6%, and 26.8%, respectively. When the injection rate is constant, the heat loss ratio of water remains basically unchanged with the increase of reservoir temperature, and the R134a increases slowly with the increase of reservoir temperature. The heat loss ratio of SCCO₂ rises first and then decreases with the rise of reservoir temperature, especially at 120°C. Under the condition of a reservoir temperature of 120°C, the bottom and outlet temperatures of the annulus are 49.6°C and 42.8°C, respectively. In this temperature range, the enthalpy of SCCO₂ will suddenly decrease (as shown in Figure 12), which will significantly reduce the calculated heat mining rate. Therefore, the heat loss ratio calculated based on the difference between the bottom-hole heat mining rate and the wellhead heat mining rate is significantly larger.

4.4. Influence of Injection Pressure

When analyzing the influence of injection pressure, the basic experimental conditions selected are as follows: (1) the reservoir type is granite; (2) the reservoir temperature is 150°C; (3) the injection pressure is 5 MPa, 10 MPa, and 15 MPa, respectively; (4) the injection rate is 107 ml/min; (5) the heat insulation condition of the tubing is vacuum insulation; (6) the heat-carrying fluids are water SCCO₂ and R134a.

Figures 13(a) and 13(b) respectively describe the relationship between the outlet temperature and heat mining rate of the three heat-carrying fluids and the injection pressure. It can be seen from the figure that the outlet temperature of the water is basically unchanged with pressure, the outlet temperature of R134a increases slightly with pressure, and the outlet temperature of SCCO₂ is greatly affected by pressure. When the injection pressure is 5 MPa, 10 MPa, and 15 MPa, the outlet temperature of SCCO₂ is 44.2°C, 49.9°C, and 57.6°C, respectively. It can be seen from Figure 14 that the thermal properties of water, such as density and enthalpy, are little affected by pressure, so its heat mining rate is basically unchanged with the increase of pressure. The density of R134a and CO₂ increases with increasing pressure, but the enthalpy value decreases. When the temperature is low, the density and enthalpy of R134a are less affected by pressure. Under the experimental conditions, the heat mining rate changes little with the increase in pressure. Pressure and temperature have a great influence on the density and enthalpy of CO₂. When the pressure is 5 MPa, the enthalpy is the highest. But the density is small, so the heat mining rate is very low. When the pressure is 10 MPa and 15 MPa, and the injection temperature is 20°C, the density difference of CO₂ is small. Considering that the mass flow rate is constant during the circulation process, the enthalpy value at the inlet is similar (242.7 KJ/kg at 10 MPa, 236.8 KJ/kg at 15 MPa), but the enthalpy value at the outlet is quite different (404.14 KJ/kg at 10 MPa and 329.62 KJ/kg at 15 MPa), so the heat mining rate at 15 MPa is lower than that at 10 MPa.

Figures 15(a) and 15(b) respectively describe the relationship between the convective heat transfer coefficient and heat loss ratio of the three heat-carrying fluids with the injection pressure. It can be seen from the figure that the convective heat transfer coefficient and heat loss ratio of water remain basically unchanged with the increase of pressure. Pressure has little effect on the convective heat transfer coefficient and heat loss ratio of R134a. The convective heat transfer coefficient increases from 336.1 W/(m²·K) to 359.6 W/(m²·K) with the increase of pressure, while the heat loss ratio decreases from 30.1% to 26.4%. The convective heat transfer coefficient and heat loss ratio of CO₂ are greatly affected by pressure. The convective heat transfer coefficient first increases and then decreases with the increase of pressure, which is consistent with the change of heat mining rate. When the injection pressure is 5 MPa, the heat loss ratio of CO₂ reaches 44.5%. It decreases rapidly as the pressure increases, indicating that a higher injection pressure should be maintained when CO₂ is selected as the heat-carrying fluid. When the injection pressure exceeds 10 MPa, the heat loss ratio of the three heat-carrying fluids has very little difference.

5. Discussion

In forced convection heat transfer, there are three independent similarity criterion, namely,

N_{u}

number,

R_{e}

number, and

P_{r}

number. The physical meaning of

N_{u}

number is a criterion that expresses the intensity of convective heat transfer,

R_{e}

number determines the flow state of fluid motion, and

P_{r}

number reflects the influence of fluid thermal properties on the process of convective heat transfer. According to the second theorem of similarity, the solution of the differential equations of forced convection heat transfer can be expressed as the relationship between these three similarity criteria [40]. The formula is as follows:

\begin{matrix} (7) & N_{u} = f (R_{e}, P_{r}) . \end{matrix}

N_{u}

is the ratio of the convective heat transfer heat flow to the heat conduction heat flow through the fluid layer with a characteristic length of

l

⁠, and the calculation formula is as follows:

\begin{matrix} (8) & N_{u} = \frac{h l}{λ}, \end{matrix}

where

h

is the convective heat transfer coefficient, W/(m²·K);

l

is the characteristic length, for circular annulus section, characteristic length

l = d_{c i} - d_{to}

⁠, m;

λ

is the thermal conductivity of the heat-carrying fluid, W/(m·K).

For laminar flow heat transfer in the tube, the Sider-Tate correlation is used to calculate the

N_{u}

number:

\begin{matrix} (9) & N_{u} = 1.86 {(R_{e} P_{r} \frac{d}{L})}^{1 / 3} = 1.86 {(\frac{ρ v l c_{p} d}{λ L})}^{1 / 3}, \end{matrix}

where

R_{e}

is the Reynolds number in the tube,

R_{e} = ρ v l / μ

⁠;

P_{r}

is the Prandtl number of the heat-carrying fluid,

P_{r} = c_{p} / λ

⁠;

v

is the average velocity of annular,

v = 4 V / π ({d_{c i}}^{2} - {d_{to}}^{2})

⁠, m/s;

μ

is the dynamic viscosity of heat-carrying fluids, (N·s)/m².

According to the first theorem of similarity, phenomena that are similar to each other, the number of criteria for the same name is equal [41]. Therefore, for

N_{u 1}

under the laboratory scale and

N_{u 2}

under the field scale, there is

N_{u 1} = N_{u 2}

⁠. According to Equations () and (), we can get:

\begin{matrix} (10) & N_{u 1} = {(\frac{ρ_{1} v_{1} (d_{c i, 1} - d_{to, 1}) c_{p 1} d_{c i, 1}}{λ_{1} L_{1}})}^{1 / 3} = {(\frac{ρ_{2} v_{2} (d_{c i, 2} - d_{to, 2}) c_{p 2} d_{c i, 2}}{λ_{2} L_{2}})}^{1 / 3} = N_{u 2}, \\ (11) & N_{u 1} = 1.86 {(\frac{ρ_{1} v_{1} (d_{c i, 1} - d_{to, 1}) c_{p 1} d_{c i, 1}}{λ_{1} L_{1}})}^{1 / 3} = (\frac{h_{2} (d_{c i, 2} - d_{to, 2})}{λ_{2}}) = N_{u 2} . \end{matrix}

Substituting the formula for calculating the average flow rate of the annulus into Equation (), we can get:

\begin{matrix} (12) & V_{2} = \frac{0.0014 λ_{2} L_{2} ρ_{1} c_{p 1} d_{c i, 1} V_{1} (d_{c i, 2} + d_{to, 2}) c_{p 1} d_{c i, 1}}{λ_{1} L_{1} ρ_{2} c_{p 2} d_{c i, 2} (d_{c i, 1} + d_{to, 1})} . \end{matrix}

Substituting the formula for calculating the convective heat transfer coefficient in 3.3 into Equation (), we can get:

\begin{matrix} (13) & Q_{2} = \frac{1.86 π λ_{2} L_{2} d_{c i, 2} Δ T_{m 2}}{(d_{c i, 2} - d_{to, 2})} {(\frac{ρ_{1} v_{1} (d_{c i, 1} - d_{to, 1}) c_{p 1} d_{c i, 1}}{λ_{1} L_{1}})}^{1 / 3}, \end{matrix}

where

V_{2}

is the injection rate at field scale, m³/d;

V_{1}

is the injection rate at laboratory scale, ml/min;

Δ T_{m 2}

is the average heat transfer temperature difference between the heat-carrying fluid and the casing wall at the field scale, °C;

Q_{2}

is the heat mining rate at the field scale, W.

In the experiment, the heat exchange tube is a part of the self-circulating horizontal well section without considering fluid gravity and geothermal gradient. Therefore, only the similarity of horizontal well sections is considered. The dimensions of the wellbore at the laboratory scale and the field scale are shown in Table 4. At the field scale, the horizontal well section is assumed to be 2000 m. The parameters used to calculate the heat mining rate at the field scale are shown in Table 5 and Figure 16. Under similar geothermal reservoir and wellbore conditions, referring to the numerical simulation results of Wang [42], it is assumed that $Δ T_{m 2}$ (field scale) is twice that of $Δ T_{m 1}$ (laboratory scale).

Figure 16 is the calculation results extended from the laboratory scale to the field scale according to the similarity criterion. At the field scale, the injection rate increased from 152 m³/d to 3002 m³/d, and the heat mining rate of water increased from 677.1 kW to 2057.7 kW. Changing the reservoir temperature, the variation range of the heat mining rate is 384.1-1601.9 kW. When the injection rate is 602 m³/d, the heat mining rates of the four heat-carrying fluids are 1045.9 kW, 254.4 kW, 171.9 kW, and 192.6 kW, respectively. It can be seen that the heat mining rate of water is the highest. Compared with CO₂, R134a, and heat transfer oil, the heat mining rate increased by 311.1%, 508.4%, and 443.4%, respectively. The above analysis shows that water is the best choice as the circulating heat-carrying fluid. The higher the reservoir temperature and the faster the injection rate, the larger the heat mining rate. In the paper of Wang et al. [27], when the bottom hole temperature is 120°C and the horizontal well length is 2000 m, the heat mining rate is about 750 kW. In comparison, the heat mining rate calculated by similar criteria under the same conditions in this paper is 593.5 kW, which is lower than 750 kW. The main reason is that the heat mining rate at the field scale calculated by the similarity criterion only includes the horizontal section and does not consider the heat mining rate of the vertical section. From the above comparative analysis, the similarity criterion derived in this article is correct.

6. Conclusion

In this paper, we selected the SCCO₂, R134a, and heat transfer oil to carry out the wellbore self-circulation heat exchange comparison experiment and analyzed the heat exchange law and the difference of heat mining capacity of different heat-carrying fluids. The main conclusions are as follows:

(1)
Under the basic experimental conditions, the outlet temperature of R134a and heat transfer oil is significantly higher than that of water and SCCO₂, but the heat mining rate of water is higher than that of the other three heat-carrying fluids. The convective heat transfer coefficient of SCCO₂ changes most drastically. It is significantly higher than the other three heat-carrying fluids in the early stage and is the lowest in the later stage. In addition, the heat loss ratio of heat transfer oil is much higher than that of the other three heat-carrying fluids, indicating that it has very low heat mining benefits
(2)
The outlet temperature of the three heat-carrying fluids at different injection rates is R134a>water>SCCO₂, and the heat mining rate is water>SCCO₂>R134a. And with the increase of the injection rate, the rise in heat mining rate of water is significantly higher than that of SCCO₂ and R134a. The convective heat transfer coefficients of the three heat-carrying fluids increase significantly with the increase of injection rate, while SCCO₂ is smaller. When the injection rate is less than 213 ml/min, the heat loss ratio of the three heat-carrying fluids changes little. When the injection rate increases to 533 ml/min, the heat loss ratio increases significantly
(3)
The outlet temperature of the three heat-carrying fluids at different reservoir temperatures is R134a>water>SCCO₂, the heat mining rate is water>SCCO₂>R134a, and the convective heat transfer coefficient is water>R134a>SCCO₂. The convective heat transfer coefficients of the three heat-carrying fluids increase with the increase of reservoir temperature, but the increase is very small. The heat loss ratio of water and R134a changes little with the increase of reservoir temperature. Due to the influence of thermal properties, the heat loss ratio of SCCO₂ increases first and then decreases with the increase of reservoir temperature and finally remains stable
(4)
The outlet temperature and heat mining rate of the water and R134a at different injection pressures remain basically unchanged, while the outlet temperature of SCCO₂ rises with the increase of the pressure. When the injection pressure is 15 MPa, the outlet temperature of CO₂ is higher than that of water, and the heat mining rate increases first and then decreases, indicating that the appropriate injection pressure should be selected when the SCCO₂ is used as the heat-carrying fluid. The convective heat transfer coefficient and heat loss ratio of water are basically unchanged. The convective heat transfer coefficient of R134a slightly rises with the increase of pressure, while the heat loss ratio slightly decreases. The convective heat transfer coefficient of SCCO₂ first increases and then decreases with the increase of pressure, while the heat loss ratio first significantly decreases and then remains stable
(5)
Using similarity criterion, we extended the results of laboratory-scale calculations to field-scale. Analysis shows that water as a heat-carrying fluid has the best heat mining effect. At the field scale, when the water injection rate is 602.8 m³/d and the reservoir temperature is 150°C, a 2000 m horizontal well can obtain a heat mining rate of more than 1 MW.

Data Availability

The basic data in the article is confidential.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research is supported by the Fundamental Research Funds for the Central Universities (No. 18CX05009A) and the Basic Research Program Project of Qinghai Province (No. 2020-ZJ-758), and it is also partially financed by the General Project of Shandong Natural Science Foundation (ZR2020ME090). We also appreciate Mr. Jun Kang for his contribution to the experiment works.

Exclusive Licensee GeoScienceWorld. Distributed under a Creative Commons Attribution License (CC BY 4.0).

Heat-carrying fluid	Molecular weight (g·mol^-1)	Critical temperature, °C	Critical pressure, MPa	Security
Water	18	374.3	22.05	Safe
CO₂	44	31.3	7.39	Safe
R245a	135.05	154.1	4.43	B1
R134a	102.03	101.1	4.06	A1
R600a	58.12	135	3.65	A3
R290	44.1	96.7	4.25	A3
Propylene	42.08	91	4.55	A3
Heat transfer oil	/	/	/	Safe

Heat-carrying fluid	Molecular weight (g·mol^-1)	Critical temperature, °C	Critical pressure, MPa	Security
Water	18	374.3	22.05	Safe
CO₂	44	31.3	7.39	Safe
R245a	135.05	154.1	4.43	B1
R134a	102.03	101.1	4.06	A1
R600a	58.12	135	3.65	A3
R290	44.1	96.7	4.25	A3
Propylene	42.08	91	4.55	A3
Heat transfer oil	/	/	/	Safe

Materials	Water	Air	Granite	Tank	Heat exchange tube
Density, kg/m³	998.2	1.1691	2700	7930	7930
Specific heat capacity, J/kg/K	4182	1012	653.2	500	500
Heat conductivity coefficient, W/m/K	0.62	0.024	2.7~3.2	16.2	16.2
Volume, m³	0.0008	0.2489	0.0205	0.00086	0.00128

Materials	Water	Air	Granite	Tank	Heat exchange tube
Density, kg/m³	998.2	1.1691	2700	7930	7930
Specific heat capacity, J/kg/K	4182	1012	653.2	500	500
Heat conductivity coefficient, W/m/K	0.62	0.024	2.7~3.2	16.2	16.2
Volume, m³	0.0008	0.2489	0.0205	0.00086	0.00128

Similarity conditions	Parameters	Value

Laboratory scale	Length of heat transfer section $L_{1}$ /m	0.55
	Inner diameter of casing $d_{c i, 1}$ /m	0.05
	Outer diameter of tubing $d_{to, 1}$ /m	0.03

Field scale	Length of heat transfer section $L_{2}$ /m	2000·
	Inner diameter of casing $d_{c i, 2}$ /m	0.158
	Outer diameter of tubing $d_{to, 2}$ /m	0.114

Comparative Experiment of Wellbore Self-Circulation Heat Mining Capacity with Different Heat-Carrying Fluids

Abstract

1. Introduction

2. Comparative Analysis of Thermal Properties of Heat-Carrying Fluids