Coalbed methane surface well gas production and heat exchange mutually enhance efficiency device and method

Abstract

This invention discloses a device and method for mutually promoting and enhancing the gas production and heat exchange efficiency of coalbed methane surface wells, relating to the field of coalbed methane extraction technology. The device includes: a vertical water pump with its inlet connected to a drainage riser installed inside the production well, and a filter installed at the bottom of the drainage riser; a vertical water pump with its outlet connected to the evaporator inlet of a heat pump unit, and the evaporator outlet of the heat pump unit connected to a reinjection interface located at the top of the vertical section of the horizontal well; a water temperature sensor installed at the outlet of the vertical water pump; and a gas extraction pump with its inlet connected to the extraction interface at the top of the production well, and an extraction monitoring sensor installed at the inlet of the gas extraction pump. This invention uses an intermittent circulating heat exchange process to change the coal seam temperature field, improve coal seam permeability and gas desorption capacity, and alleviate the problem of low gas production in the later stages of surface well production.

Description

Technical Field

[0001] This invention relates to the field of coalbed methane extraction technology, specifically to a device and method for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells. Background Technology

[0002] Surface well extraction technology is a common method for pre-extraction of coalbed methane and prevention of gas disasters. With the development and progress of technologies such as drilling and completion, fracturing, and directional drilling, my country has established a mature coalbed methane surface well development technology system, including surface vertical wells, cluster wells, U-shaped wells, and L-shaped wells, which are widely used in coal mining areas. Coalbed methane surface well drainage and production typically goes through four stages: drainage and pressure reduction, stable production, production decline, and depletion. The gas production capacity in the middle and later stages of drainage is crucial to the efficiency of surface well extraction; however, there is currently a lack of technical means to improve the gas production capacity in this stage, resulting in surface well projects reaching their service life prematurely, which wastes engineering resources and reduces the effectiveness of coalbed methane extraction.

[0003] Existing research indicates that coal permeability and gas desorption capacity are crucial factors affecting coalbed methane production. Under high stress conditions, temperature significantly impacts both permeability and desorption capacity; therefore, controlling coalbed temperature can improve surface well production. Heat pump technology has been successfully applied in the utilization of medium-deep geothermal energy in my country. It can extract underground heat and alter the underground temperature field through processes such as coaxial casing and downhole water reinjection. Therefore, surface well gas production can be increased by altering the geothermal field through heat exchange. Application publication number CN 117905421 A proposes an integrated method for deep coalbed methane extraction without roadways and deep geothermal resource exploitation. Based on U-shaped wells constructed within the coal seam, it achieves deep coalbed methane extraction and deep geothermal resource exploitation through double-casing gas and heat separation. However, it does not address the improvement of gas and heat extraction processes on the development effectiveness of both resources, and the problem of reduced production in the later stages of U-shaped well extraction remains unresolved. Increased coalbed methane production reduces coal seam gas content, which in turn decreases the thermal resistance of the coal and rock mass, thus improving the thermal conductivity of the coal seam. In other words, increased coalbed methane production can improve the heat exchange efficiency of the coal seam. Therefore, it is necessary to coordinate the implementation of underground heat exchange and gas extraction technologies to improve the gas production effect of surface wells. Summary of the Invention

[0004] The purpose of this invention is to provide a device and method for mutually promoting and enhancing the gas production and heat exchange of coalbed methane surface wells in order to solve at least one of the above-mentioned technical problems.

[0005] In a first aspect, embodiments of the present invention provide a coalbed methane surface well gas production and heat exchange mutually promoting efficiency enhancement device, applied to a U-shaped coalbed methane production well, wherein the coalbed methane production U-shaped well includes a vertical well for drainage, a horizontal well section, and a horizontal well section; the device includes: a vertical water pump, a drainage riser, a heat pump unit, a water temperature sensor, a gas extraction pump, and an extraction monitoring sensor; wherein, the inlet end of the vertical water pump is connected to the drainage riser, the drainage riser is installed inside the vertical well for drainage, and a filter is installed at the bottom end of the drainage riser; the outlet end of the vertical water pump is connected to the heat pump... The evaporator inlet of the unit is connected, and the evaporator outlet of the heat pump unit is connected to the reinjection interface located at the top of the vertical section of the horizontal well; the water temperature sensor is located at the outlet of the vertical water pump; the air inlet of the gas extraction pump is connected to the extraction interface at the top of the drainage vertical well, and the extraction monitoring sensor is located at the air inlet of the gas extraction pump; the water temperature sensor is used to monitor the water temperature at the outlet of the vertical water pump; the extraction monitoring sensor is used to monitor the methane gas concentration and flow rate at the air inlet of the gas extraction pump.

[0006] Furthermore, the heat pump unit includes a screw-type heat pump unit.

[0007] Furthermore, the evaporator inlet of the heat pump unit is equipped with a heat pump inlet valve; the outlet of the vertical water pump is equipped with a drain valve.

[0008] Secondly, embodiments of the present invention also provide a device for mutually promoting and enhancing the gas production and heat exchange efficiency of coalbed methane surface wells, applied to vertical surface wells for coalbed methane extraction; the device includes: a vertical water pump, a drainage riser, a heat pump unit, a water temperature sensor, a gas extraction pump, and an extraction monitoring sensor; wherein, the inlet end of the vertical water pump is connected to the drainage riser, the drainage riser is installed inside the vertical well, and a filter is installed at the bottom end of the drainage riser; the outlet end of the vertical water pump is connected to the evaporator inlet of the heat pump unit. The evaporator outlet of the heat pump unit is connected to the reinjection interface located at the top of the drainage well; the water temperature sensor is located at the outlet of the vertical water pump; the air inlet of the gas extraction pump is connected to the extraction interface at the top of the drainage well; the extraction monitoring sensor is located at the air inlet of the gas extraction pump; the water temperature sensor is used to monitor the water temperature at the outlet of the vertical water pump; the extraction monitoring sensor is used to monitor the methane gas concentration and flow rate at the air inlet of the gas extraction pump.

[0009] Thirdly, embodiments of the present invention also provide a method for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells, applied to the device for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells provided in embodiments of the present invention; the method includes: when the gas production monitored by the extraction monitoring sensor is lower than a preset production threshold, starting the heat pump unit and increasing the pumping rate of the vertical water pump, so that the underground hot water in the drainage well is transported by the vertical water pump to the heat pump unit for heat exchange; when the water temperature monitored by the water temperature sensor is lower than a preset temperature threshold, shutting down the heat pump unit and reducing the pumping rate of the vertical water pump to stop the heat exchange operation; when the water temperature monitored by the water temperature sensor meets a preset condition with the highest water temperature at the time of the last heat exchange start-up, restarting the heat pump unit and increasing the pumping rate of the vertical water pump.

[0010] Furthermore, when the gas production monitored by the extraction monitoring sensor is lower than the preset production threshold, the heat pump unit is started and the pumping rate of the vertical water pump is increased, including: when the average daily gas production monitored by the extraction monitoring sensor for several consecutive days is lower than the preset production threshold, the heat pump unit is started and the pumping rate of the vertical water pump is increased; the preset production threshold includes 40% of the historical maximum daily gas production value.

[0011] Furthermore, after the underground hot water in the drainage shaft is transported to the heat pump unit by the vertical pump for heat exchange, the cooled water after heat exchange flows back to the drainage shaft or the vertical section of the horizontal shaft through the reinjection interface.

[0012] Furthermore, the preset temperature threshold is no greater than 15°C.

[0013] Furthermore, the preset conditions include: T n -T0≥0.7*(T n-1 -T0)≥10℃; where, T n T is the water temperature monitored before the nth start-up of the heat exchanger. n-1 T0 is the highest water temperature during the (n-1)th heat exchange start-up, and T0 is the preset temperature threshold.

[0014] This invention provides a device and method for mutually promoting gas production and heat exchange in coalbed methane surface wells. By using an intermittent circulating heat exchange process, the temperature field of the coal seam is changed, the permeability of the coal seam and the gas desorption capacity are improved, and the problem of low gas production in the later stage of surface well production is solved. This invention also alleviates the technical problems of existing gas-heat co-extraction methods, which are difficult to achieve mutual promotion of gas production and heat extraction effects, limit the later utilization of surface well projects, and increase the cost of coalbed methane extraction. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of a coalbed methane surface well gas production and heat exchange mutually promoting and enhancing efficiency device provided in an embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram of another coalbed methane surface well gas production and heat exchange mutually promoting and enhancing efficiency device provided in an embodiment of the present invention;

[0018] Figure 3 The flowchart illustrates a method for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells, as provided in an embodiment of the present invention.

[0019] In the diagram: 1. Vertical water pump, 2. Drainage riser, 3. Heat pump unit, 4. Water temperature sensor, 5. Recharge interface, 6. Gas extraction pump, 7. Extraction interface, 8. Extraction monitoring sensor, 9. Filter, 10. Horizontal well section, 11. Drainage and extraction vertical well, 12. Rock strata, 13. Coal seam, 14. Heat pump inlet valve, 15. Drainage valve, 16. Horizontal well section, 17. Branch well section. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] Example 1

[0022] Figure 1 This is a schematic diagram of a coalbed methane surface well gas production and heat exchange mutually promoting and enhancing efficiency device according to an embodiment of the present invention. Figure 1 As shown, this device is applied to a U-shaped well for coalbed methane extraction. The U-shaped well includes a vertical drainage well 11, a horizontal well section 10, and a horizontal well section 16. The vertical drainage well 11 passes through rock strata 12 and coal seam 13. The horizontal well section 10 passes through rock strata 12 and enters coal seam 13. The horizontal well section 16 is located within coal seam 13 and connects the vertical drainage well 11 and the horizontal well section 10. Specifically, the device includes: a vertical water pump 1, a drainage riser 2, a heat pump unit 3, a water temperature sensor 4, a gas extraction pump 6, and an extraction monitoring sensor 8.

[0023] like Figure 1 As shown, the inlet of the vertical water pump 1 is connected to the drainage riser 2, which is installed inside the drainage well 11. A filter 9 is installed at the bottom of the drainage riser 2. The outlet of the vertical water pump 1 is connected to the evaporator inlet of the heat pump unit 3, and the evaporator outlet of the heat pump unit 3 is connected to the reinjection interface 5 located at the top of the vertical section 10 of the horizontal well. A water temperature sensor 4 is located at the outlet of the vertical water pump 1. The air inlet of the gas extraction pump 6 is connected to the extraction interface 7 at the top of the drainage well 11, and an extraction monitoring sensor 8 is located at the air inlet of the gas extraction pump 6.

[0024] Water temperature sensor 4 is used to monitor the water temperature at the outlet of vertical water pump 1;

[0025] The extraction monitoring sensor 8 is used to monitor the methane gas concentration and flow rate at the inlet of the gas extraction pump 6.

[0026] Optionally, the flow rate of the vertical water pump 1 is 5–800 m³ / h. 3 / h, with a head of 500~15000m.

[0027] Optionally, the thermal conductivity of the drainage riser 2 pipe material is ≤0.2W / (m·K).

[0028] Optionally, the heat pump unit 3 includes a screw-type heat pump unit. The condenser outlet temperature of the screw-type heat pump unit is 45–70°C.

[0029] Optionally, the water temperature sensor 4 monitors a temperature range of 0–120℃ and a sampling frequency of 1–60 min / time.

[0030] Optionally, the sampling monitoring sensor 8 can simultaneously monitor the concentration and flow rate of methane gas, with a sampling frequency of 1 to 60 minutes per sampling.

[0031] like Figure 1 As shown, in an optional embodiment of the present invention, a heat pump inlet valve 14 is provided at the evaporator end inlet of the heat pump unit 3; and a drain valve 15 is provided at the outlet end of the vertical water pump 1.

[0032] Example 2

[0033] Figure 2 This is a schematic diagram of another coalbed methane surface well gas production heat exchange mutual promotion and efficiency enhancement device provided according to an embodiment of the present invention. This device is applied to a vertical surface well for coalbed methane production. Figure 2 As shown, the surface vertical well for coalbed methane extraction includes a drainage vertical well 11 and a branch section 17 connecting the lower part of the drainage vertical well 11 to the coal seam 13. Specifically, the equipment includes: a vertical water pump 1, a drainage riser 2, a heat pump unit 3, a water temperature sensor 4, a gas extraction pump 6, and an extraction monitoring sensor 8.

[0034] like Figure 2 As shown, the inlet of the vertical water pump 1 is connected to the drainage riser 2, which is installed inside the drainage well 11. A filter 9 is installed at the bottom of the drainage riser 2. The outlet of the vertical water pump 1 is connected to the evaporator inlet of the heat pump unit 3, and the evaporator outlet of the heat pump unit 3 is connected to the reinjection interface 5 located at the top of the drainage well 11. A water temperature sensor 4 is located at the outlet of the vertical water pump 1. The air inlet of the gas extraction pump 6 is connected to the extraction interface 7 at the top of the drainage well 11, and an extraction monitoring sensor 8 is located at the air inlet of the gas extraction pump 6.

[0035] Water temperature sensor 4 is used to monitor the water temperature at the outlet of vertical water pump 1;

[0036] The extraction monitoring sensor 8 is used to monitor the methane gas concentration and flow rate at the inlet of the gas extraction pump 6.

[0037] like Figure 2 As shown, in an optional embodiment of the present invention, a heat pump inlet valve 14 is provided at the evaporator end inlet of the heat pump unit 3; and a drain valve 15 is provided at the outlet end of the vertical water pump 1.

[0038] Example 3

[0039] Figure 3 This is a flowchart illustrating a method for mutually enhancing the gas production and heat exchange efficiency of coalbed methane surface wells according to an embodiment of the present invention. This method is applied to the device for mutually enhancing the gas production and heat exchange efficiency of coalbed methane surface wells provided in this embodiment of the invention. Figure 3 As shown, the method specifically includes the following steps:

[0040] Step S302: When the gas production monitored by the extraction monitoring sensor is lower than the preset production threshold, start the heat pump unit and increase the pumping rate of the vertical water pump so that the underground hot water in the drainage well is transported to the heat pump unit for heat exchange by the vertical water pump.

[0041] In one optional embodiment of the present invention, when the average daily gas production monitored by the extraction monitoring sensor for several consecutive days is lower than a preset production threshold, the heat pump unit is started and the pumping rate of the vertical water pump is increased. For example, the preset production threshold includes 40% of the historical maximum daily gas production value.

[0042] In this embodiment of the invention, after the underground hot water in the drainage shaft is transported to the heat pump unit by the vertical pump for heat exchange, the cooled water after heat exchange flows back to the drainage shaft or the vertical section of the horizontal shaft through the reinjection interface.

[0043] Specifically, in the coalbed methane surface well gas production and heat exchange mutual promotion and efficiency enhancement device provided in the above embodiment one, the cooling water after heat exchange flows back to the horizontal well vertical section through the reinjection interface, then continues to exchange heat with coal and rock through the horizontal well section, and then returns to the production vertical well, and so on.

[0044] Specifically, in the coalbed methane surface well gas production heat exchange mutual promotion and efficiency enhancement device provided in the above embodiment 2, the cooling water after heat exchange flows back to the double-layer casing in the production well through the reinjection interface, and part of it enters the rock strata and coal seam through the branch well section to continue heat exchange, and so on.

[0045] Step S304: When the water temperature monitored by the water temperature sensor is lower than the preset temperature threshold, the heat pump unit is turned off and the pumping rate of the vertical water pump is reduced to stop the heat exchange operation.

[0046] In one optional real-time mode provided in this embodiment of the invention, the preset temperature threshold is no greater than 15°C.

[0047] Step S306: When the water temperature monitored by the water temperature sensor meets the preset conditions with the highest water temperature during the last heat exchange start-up, the heat pump unit is restarted and the pumping rate of the vertical water pump is increased.

[0048] In one optional embodiment provided by the present invention, the preset conditions include:

[0049] T n -T0≥0.7*(T n-1 -T0)≥10℃

[0050] In the formula, T n T is the water temperature monitored before the nth start-up of the heat exchanger. n-1 T0 is the highest water temperature during the (n-1)th heat exchange start-up, and T0 is the preset temperature threshold.

[0051] Example 4

[0052] This invention also provides another method for mutually enhancing the gas production and heat exchange efficiency of coalbed methane surface wells. This method is applied to the device for mutually enhancing the gas production and heat exchange efficiency of coalbed methane surface wells provided in this invention. Specifically, the method includes the following steps:

[0053] Step 1: After the surface well is completed, connect the coalbed methane surface well gas production and heat exchange mutual promotion and efficiency enhancement device provided in this embodiment of the invention, close the heat pump inlet valve, open the drainage valve, start the vertical water pump and gas extraction pump and operate them according to the surface well extraction conditions, adjust the pumping volume of the vertical water pump to maintain the bottom flow pressure between 1 and 5 MPa, and drain the gas through the surface well casing; the bottom flow pressure can be maintained at a high value during the drainage and pressure reduction stage, and the bottom flow pressure can be reduced when entering the stable production stage;

[0054] Step 2: When the average daily gas production monitored by the extraction monitoring sensor for 7 consecutive days is less than 40% of the historical maximum daily gas production, open the heat pump inlet valve and close the drain valve, start the screw heat pump unit and increase the pumping rate of the vertical pump. The underground hot water in the extraction shaft is transported to the screw heat pump unit by the vertical pump. After heat exchange at the evaporator end, the cooling water flows back to the extraction shaft or the vertical section of the horizontal shaft through the reinjection interface to continue heat exchange with the coal and rock. Then, the vertical pump installed in the extraction shaft transports the underground hot water to the screw heat pump unit again, and so on.

[0055] Step 3: When the water temperature monitored by the water temperature sensor reaches T0, shut down the screw heat pump unit and reduce the pumping rate of the vertical water pump, close the heat pump inlet valve and open the drain valve to stop the underground heat exchange operation; T0 is set according to the actual ground temperature of the coal seam where the surface well is located. In this embodiment of the invention, T0≤20℃.

[0056] Step 4: Under the influence of geothermal heat flow, the temperature around the surface well rises. When the water temperature T monitored by the water temperature sensor... n Compared to the highest water temperature T during the last heat exchange start-up n-1 Satisfying T n -T0≥0.7*(T n-1 -T0)≥10℃, repeat steps 3 and 4 until the life cycle of the surface well gas production operation is completed.

[0057] As described above, this invention provides a device and method for mutually promoting gas production and heat exchange in coalbed methane surface wells. By using an intermittent circulating heat exchange process, it changes the coal seam temperature field, improves coal seam permeability and gas desorption capacity, and addresses the problem of low gas production in the later stages of surface well production. This alleviates the technical problems of existing gas-heat co-extraction methods, which struggle to achieve mutual promotion between gas production and heat extraction, limit the later-stage utilization of surface well projects, and increase the cost of coalbed methane extraction.

[0058] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0059] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A device for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells, characterized in that, This device is applied to U-shaped wells used in coalbed methane extraction, which include a vertical well for drainage, a horizontal well section, and a horizontal well section. The device includes: a vertical water pump, a drainage riser, a heat pump unit, a water temperature sensor, a gas extraction pump, and an extraction monitoring sensor. The inlet of the vertical water pump is connected to the drainage riser, which is installed inside the drainage well. A filter is installed at the bottom of the drainage riser. The outlet of the vertical water pump is connected to the evaporator inlet of the heat pump unit, and the evaporator outlet of the heat pump unit is connected to the reinjection interface located at the top of the vertical section of the horizontal well. The water temperature sensor is located at the outlet of the vertical water pump. The air inlet of the gas extraction pump is connected to the extraction interface at the top of the drainage well, and the extraction monitoring sensor is located at the air inlet of the gas extraction pump. The water temperature sensor is used to monitor the water temperature at the outlet of the vertical water pump. The extraction monitoring sensor is used to monitor the methane gas concentration and flow rate at the inlet of the gas extraction pump.

2. The apparatus according to claim 1, characterized in that: The heat pump unit includes a screw-type heat pump unit.

3. The apparatus according to claim 1, characterized in that: The heat pump unit is equipped with a heat pump inlet valve at the evaporator end; the vertical water pump is equipped with a drain valve at the outlet end.

4. A device for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells, characterized in that, This device is applied to vertical wells used in coalbed methane extraction. It includes: a vertical water pump, a drainage riser, a heat pump unit, a water temperature sensor, a gas extraction pump, and an extraction monitoring sensor. The inlet of the vertical water pump is connected to the drainage riser, which is installed inside the drainage well. A filter is installed at the bottom of the drainage riser. The outlet of the vertical water pump is connected to the evaporator inlet of the heat pump unit, and the evaporator outlet of the heat pump unit is connected to the reinjection interface located at the top of the drainage well. The water temperature sensor is located at the outlet of the vertical water pump. The air inlet of the gas extraction pump is connected to the extraction interface at the top of the drainage well, and the extraction monitoring sensor is located at the air inlet of the gas extraction pump. The water temperature sensor is used to monitor the water temperature at the outlet of the vertical water pump. The extraction monitoring sensor is used to monitor the methane gas concentration and flow rate at the inlet of the gas extraction pump.

5. A method for mutually promoting and enhancing the efficiency of gas production and heat exchange in coalbed methane surface wells, characterized in that, The method is applied to the coalbed methane surface well gas production and heat exchange mutually promoting and enhancing efficiency device according to any one of claims 1-4; the method includes: When the gas production monitored by the extraction monitoring sensor is lower than the preset production threshold, the heat pump unit is started and the pumping rate of the vertical water pump is increased so that the underground hot water in the drainage well is transported by the vertical water pump to the heat pump unit for heat exchange. When the water temperature monitored by the water temperature sensor is lower than the preset temperature threshold, the heat pump unit is turned off and the pumping rate of the vertical water pump is reduced to stop the heat exchange operation. When the water temperature monitored by the water temperature sensor meets the preset condition with the highest water temperature during the last heat exchange start-up, the heat pump unit is restarted and the pumping rate of the vertical water pump is increased.

6. The method according to claim 5, characterized in that: When the gas production monitored by the extraction monitoring sensor is lower than the preset production threshold, the heat pump unit is started and the pumping rate of the vertical water pump is increased, including: When the average daily gas production monitored by the extraction monitoring sensor is lower than the preset production threshold for several consecutive days, the heat pump unit is started and the pumping rate of the vertical water pump is increased; the preset production threshold includes 40% of the historical maximum daily gas production value.

7. The method according to claim 5, characterized in that: After the underground hot water in the drainage shaft is transported to the heat pump unit by the vertical pump for heat exchange, the cooled water after heat exchange flows back to the drainage shaft or the vertical section of the horizontal shaft through the reinjection interface.

8. The method according to claim 5, characterized in that: The preset temperature threshold is no greater than 15℃.

9. The method according to claim 5, characterized in that: The preset conditions include: T n -T0≥0.7*(T n-1 -T0)≥10℃ In the formula, T n T is the water temperature monitored before the nth start-up of the heat exchanger. n-1 T0 is the highest water temperature during the (n-1)th heat exchange start-up, and T0 is the preset temperature threshold.

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