Temperature prediction method for fluid in pipe based on double-u-shaped pipe vertical medium-depth geothermal heat exchanger fluid model

Abstract

The invention provides an in-pipe fluid temperature prediction method based on a double-u-shaped-pipe vertical medium-depth geothermal heat exchanger fluid model. The in-pipe fluid temperature prediction method comprises the specific steps that the temperatures of a pipe A descending pipe, a pipe A ascending pipe, a pipe B ascending pipe and a pipe B descending pipe on the ground are obtained; the thermal resistance between the descending pipe of the pipe A and the wall of the drill hole, the thermal resistance between the descending pipe of the pipe A and the ascending pipe of the pipe A and the thermal resistance between the descending pipe of the pipe A and the ascending pipe of the pipe B are obtained; and carrying out dimensionless processing on the obtained numerical values, substituting dimensionless data into the model to calculate and obtain the dimensionless temperature distribution of the u-shaped pipe, and calculating and predicting the temperature of the fluid in the pipe through the obtained dimensionless temperature distribution of the u-shaped pipe. The method has the beneficial effects that the uneven distribution of the temperature of the drill hole wall along the depth is considered, the prediction model of the U-shaped pipe ground heat exchanger is established, and the temperature distribution of the circulating fluid in the U-shaped pipe under the condition of considering the change of the temperature of the drill hole wall along the depth direction is realized.

Description

Technical Field

[0001] The invention relates to the technical field of U-tube underground heat exchangers, and in particular to a method for predicting the temperature of fluid in a tube based on a fluid model of a double U-tube vertical mid-depth underground heat exchanger. Background Art

[0002] In the past few decades, clean and renewable energy has attracted worldwide attention. Buildings account for about 40% of total energy consumption, so there is a huge potential for energy saving. In order to save energy, the ground source heat pump system (GSHP) provides a good solution because of its unique characteristics of high energy efficiency, energy saving potential and environmental sustainability. Compared with traditional air source heat pumps, GSHP systems can save more than 50% energy for cooling and heating buildings. Ground heat exchanger (GHE), as a key component of GSHP system, has a great influence on the thermal performance of the entire system. Therefore, GHE using geothermal energy has received attention and rapid development in countries around the world due to the policies and financial support of various governments.

[0003] In order to predict the fluid temperature along the depth inside the GHE, the fluid heat transfer model is also important, because the inlet and outlet temperatures are directly related to the thermal efficiency evaluation and practical engineering design. The GHE fluid model has developed from the one-dimensional model originally proposed by Bose et al. to the two-dimensional model proposed by Hellstrom et al., and then to the quasi-3D model derived by Zeng et al. based on the heat transfer mechanism of the U-tube. The quasi-3D model of the wellbore can calculate the temperature variation of the circulating fluid along the depth. Therefore, this quasi-3D fluid model can analyze the thermal interference between the pipes in the wellbore, especially compared with the previous two-dimensional model. However, the 3D model still assumes that the wellbore wall temperature is independent of the wellbore depth. For shallow GHE, the initial geothermal temperature can be treated uniformly and the well temperature can be treated constant. However, for medium and shallow GHE, due to the influence of underground heat flow, the wellbore wall temperature and the heat exchange per unit length meter vary greatly in depth, and the application of the previous GHE model will produce large errors. Therefore, it is urgent to establish an analytical model of vertical UGHEs that considers the variation of wellbore wall temperature along the depth direction. Summary of the invention

[0004] The present invention solves the problem that the current GHE model will produce large errors in application because the well wall temperature is not taken into consideration.

[0005] To achieve the above object, the present invention provides the following solutions: A method for predicting the wellbore wall temperature based on a fluid model of a double U-tube vertical mid-depth geothermal heat exchanger, wherein two U-tubes connected in series are placed vertically and parallelly in a wellbore, namely, tube A and tube B, and the connecting lines of the tube openings of the tube A downcomer, the tube A riser, the tube B riser, and the tube B downcomer form a rhombus, the tube A downcomer and the tube B downcomer are adjacent in the rhombus, and the tube A downcomer and the tube B riser are opposite in the rhombus; The specific steps include: S1. Obtain the temperature of the downcomer of tube A, the riser of tube A, the riser of tube B and the downcomer of tube B at the ground; Obtain the thermal resistance between the downcomer of tube A and the borehole wall, the thermal resistance between the downcomer of tube A and the riser of tube A, and the thermal resistance between the downcomer of tube A and the riser of tube B; S2. Non-dimensionalize the value obtained in S1 to obtain the dimensionless temperature at the ground of the downcomer of tube A. , dimensionless temperature at the ground of tube A riser , dimensionless temperature at the ground level of tube B riser and the dimensionless temperature at the ground level of the downcomer of tube B ; The dimensionless thermal resistance between the downcomer tube A and the borehole wall is obtained as , dimensionless thermal resistance between tube A downcomer and tube A upcomer And the dimensionless thermal resistance between the downcomer of tube A and the upcomer of tube B is ; S3. Substitute the dimensionless data into the model to calculate the dimensionless temperature distribution of the U-tube. The calculation model is as follows: Where Z is the dimensionless depth of the wellbore; is the empirical coefficient; is the dimensionless temperature of the borehole wall at depth Z; S4. The dimensionless temperature distribution of the U-tube obtained , , and Calculate and predict the temperature of the fluid in the tube.

[0006] As a preferred solution, the model is an energy balance model established by Laplace transformation; The energy balance equation is: Where z is the depth of the wellbore, c is the specific heat capacity of the fluid under constant pressure, M is the mass flow rate of the fluid in the U-tube, is the temperature distribution along the depth of the downcomer tube A, is the temperature distribution along the depth of the riser tube A, is the temperature distribution along the depth of the riser tube B, is the temperature distribution along the depth of the downcomer of tube B; is the heat transfer resistance from the fluid in the downcomer tube A to the borehole wall; is the heat transfer resistance between the downcomer of tube A and the upcomer of tube A, The heat transfer resistance between tube A (downcomer) and tube B (upcomer).

[0007] As a preferred solution, the empirical coefficient It can be calculated by the following formula: .

[0008] As a preferred solution, the empirical coefficient It can be calculated by the following formula: As a preferred solution, the empirical coefficient It can be calculated by the following formula: Furthermore, the empirical coefficient It can be calculated by the following formula: As a preferred solution, the empirical coefficient It can be calculated by the following formula: Furthermore, the empirical coefficient It can be calculated by the following formula: As a preferred solution, the empirical coefficient It can be calculated by the following formula: As a preferred solution, a temperature curve distribution diagram of the circulating fluid in the U-tube under different parameters is drawn according to the model to analyze the influence of different parameters on the heat transfer performance of the U-tube buried pipe heat exchanger.

[0009] The beneficial effects of the present invention are: The embodiment of the present invention takes into account the uneven distribution of the fluid temperature in the tube along the depth, establishes a prediction model for a U-tube buried tube heat exchanger, and realizes the temperature distribution of the circulating fluid in the U-tube while considering the change of the fluid temperature in the tube along the depth direction. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 It is a structural schematic diagram of the present invention.

[0011] Figure 2 It is a schematic diagram of the position of the U-shaped tube of the present invention.

[0012] Figure 3 FIG. 4 is a temperature distribution diagram of the fluid in the pipe established in an embodiment of the present invention.

[0013] Figure 4 A schematic diagram of the influence of thermal conductivity of the backfill material provided in an embodiment of the present invention.

[0014] Figure 5 Schematic diagram of the influence of thermal conductivity of U-shaped tube material provided in an embodiment of the present invention.

[0015] Figure 6 A schematic diagram of the relationship between the hole depth and temperature distribution of a U-shaped tube provided in an embodiment of the present invention.

[0016] Figure 7 A schematic diagram of the trend of Reynolds number and convective heat transfer coefficient changing with mass flow rate provided in an embodiment of the present invention.

[0017] Figure 8 A schematic diagram of the influence of mass flow provided in an embodiment of the present invention.

[0018] The numbers in the figure are 1. Tube A is the downcomer; 2. Tube A is the upcomer; 3. Tube B is the upcomer; 4. Tube B is the downcomer. DETAILED DESCRIPTION

[0019] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Example Please refer to Figures 1 to 8 As shown, this embodiment is located in Dongchangfu District, Liaocheng City, Shandong Province, China. The test will be carried out from early March to mid-March 2024. This project adopts a hybrid buried pipe system, and the heat source is a medium-shallow buried pipe heat exchanger (220m double U-tube). Temperature sensors are installed on the well wall along the depth direction to test the initial well wall temperature and the change of well wall temperature over time. The optical fiber is placed on the outer wall of the U-tube borehole and placed together with the U-tube. The temperature is read and recorded every 20 meters, and the outlet temperature is collected every 5 minutes. The U-tube parameters are shown in the table.

[0021] U-tube parameter table Two U-shaped tubes connected in series are placed vertically and parallelly in the borehole, namely tube A and tube B. The connecting line of the center of the tube openings of tube A downtube 1, tube A riser 2, tube B riser 3 and tube B downtube 4 forms a rhombus. The tube A downtube 1 and tube B downtube 4 are adjacent to each other in the rhombus, and the tube A downtube 1 and tube B riser 3 are opposite to each other in the rhombus. In this project, optical fiber is buried in the borehole wall along the depth direction to test the initial surface temperature and the pipe wall temperature changing with time. The optical fiber is set on the outer wall of the U-shaped tube and lowered with the U-shaped tube to read and record the temperature every 3 meters.

[0022] The specific steps include: S1. Get the ground temperature of tube A downcomer 1, the ground temperature of tube A riser 2, the ground temperature of tube B riser 3 and the ground temperature of tube B downcomer 4; Obtain the thermal resistance between the tube A downcomer 1 and the borehole wall, the thermal resistance between the tube A downcomer 1 and the tube A upcomer 2, and the thermal resistance between the tube A downcomer 1 and the tube B upcomer 3; S2. Non-dimensionalize the value obtained in S1 to obtain the dimensionless temperature of the ground of tube A downcomer 1 , dimensionless temperature at the ground level of tube A riser 2 , dimensionless temperature at the ground of tube B riser 3 and the dimensionless temperature at the ground level of tube B downcomer 4 ; The dimensionless thermal resistance between tube A downcomer 1 and the borehole wall is obtained as , dimensionless thermal resistance between tube A downcomer 1 and tube A upcomer 2 And the dimensionless thermal resistance between tube A downcomer 1 and tube B upcomer 3 ; S3. Substitute the dimensionless data into the model to calculate the dimensionless temperature distribution of the U-tube. The calculation model is as follows: Where Z is the dimensionless depth of the wellbore; is the empirical coefficient; is the dimensionless temperature of the borehole wall at depth Z; S4. The dimensionless temperature distribution of the U-tube obtained , , and To calculate and predict the temperature of the fluid in the pipe.

[0023] The empirical coefficients in this embodiment are calculated by the following formulas: The new analytical solution model was verified by comparing with the actual ground source heat pump experimental data. The absolute average error was 0.56 and the root mean square error was 0.61, proving that the model is effective. Using the newly established U-tube ground heat exchanger model, the influence of different parameters on the heat transfer performance of the U-tube ground heat exchanger was studied. The temperature change curve of the circulating fluid in the U-tube ground heat exchanger under different tube fluid temperatures, backfill material thermal conductivity, U-tube material thermal conductivity, U-tube hole depth, Reynolds number and convection heat transfer coefficient and mass flow rate was drawn, as shown in the figure. Figures 3 to 8It can be seen that increasing the thermal conductivity of the slurry and the pipeline will increase the temperature of the circulating fluid at the bottom and outlet of the U-tube, thereby improving the thermal performance of the U-tube. Changing the drilling depth will significantly change the temperature distribution of the circulating fluid in the U-tube, and the temperature of the circulating fluid at the bottom and outlet of the tube will increase, which will also improve the thermal performance of the U-tube. In addition, the mass flow rate is negatively correlated with the temperature at the bottom of the U-tube, but it does not lead to a significant decrease in the temperature of the circulating fluid at the outlet of the U-tube.

[0024] In the existing quasi-three-dimensional heat transfer model of U-tube borehole, it is assumed that the temperature of the fluid in the tube is uniform, which is inconsistent with the actual heat transfer situation and has a certain error. In the medium-shallow U-tube buried pipe heat exchanger, due to the existence of geothermal gradient, the borehole wall temperature will increase significantly with the increase of depth. Therefore, the present invention proposes a new analytical solution model for heat transfer in the borehole of medium-shallow U-tube heat exchangers. This model abandons the traditional assumption of uniform hole wall temperature, improves the existing U-tube quasi-three-dimensional model, and takes into account the uneven vertical distribution of the fluid temperature in the tube. The developed analytical solution model was verified by experiment, and the results showed that the results of experimental measurement of the circulating fluid temperature calculated by the analytical model are basically consistent.

[0025] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for predicting the temperature of the fluid in a tube based on a fluid model of a double U-tube vertical medium-deep geothermal heat exchanger, characterized in that: Two U-shaped pipes connected in series are placed vertically and in parallel in the wellbore, namely pipe A and pipe B, the pipe A downcomer (1), pipe A riser (2), pipe B riser (3) and pipe B downcomer (4) are connected by a line connecting the centers of the pipe openings of pipe A downcomer (1), pipe A riser (2), pipe B riser (3) and pipe B downcomer (4) to form a rhombus, the pipe A downcomer (1) and pipe B downcomer (4) are adjacent to each other in the rhombus, and the pipe A downcomer (1) and pipe B riser (3) are opposite to each other in the rhombus; The specific steps include: S1. Obtain the ground temperature of tube A downcomer (1), tube A riser (2), tube B riser (3) and tube B downcomer (4); Obtaining the thermal resistance between the tube A downcomer (1) and the borehole wall, the thermal resistance between the tube A downcomer (1) and the tube A upcomer (2), and the thermal resistance between the tube A downcomer (1) and the tube B upcomer (3); S2. Convert the value obtained in S1 to dimensionless to obtain the dimensionless temperature at the ground of tube A downcomer (1): , dimensionless temperature at the ground of tube A riser (2) , dimensionless temperature at the ground of tube B riser (3) and the dimensionless temperature at the ground level of the downcomer (4) of tube B ; The dimensionless thermal resistance between the downcomer (1) of tube A and the borehole wall is obtained as , the dimensionless thermal resistance between the downcomer (1) of tube A and the upcomer (2) of tube A and the dimensionless thermal resistance between the downcomer (1) of tube A and the upcomer (3) of tube B ; S3. Substitute the dimensionless data into the model to calculate the dimensionless temperature distribution of the U-tube. The calculation model is as follows: ； ； ； ； Where Z is the dimensionless depth of the wellbore; , , , is the empirical coefficient; is the dimensionless temperature of the borehole wall at depth Z; S4. The dimensionless temperature distribution of the U-tube obtained , , and Calculate and predict the temperature of the fluid in the tube.

2. The temperature prediction method of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1 is characterized in that: The model is an energy balance model established through Laplace transformation; The energy balance equation is: ； Where z is the depth of the wellbore, c is the specific heat capacity of the fluid under constant pressure, M is the mass flow rate of the fluid in the U-tube, is the temperature distribution along the depth of the downcomer (1) of tube A, is the temperature distribution along the depth of the riser (2) of tube A, is the temperature distribution along the depth of the riser (3) of tube B, is the temperature distribution along the depth of the downcomer (4) of tube B; is the heat transfer resistance from the fluid in the downcomer (1) of tube A to the wall of the drilled hole; is the heat transfer resistance between the downcomer (1) of tube A and the upcomer (2) of tube A, Thermal resistance of heat transfer between tube A downcomer (1) and tube B upcomer (3).

3. The temperature prediction method of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1 is characterized in that: The empirical coefficient It can be calculated by the following formula: 。 4. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: The empirical coefficient It can be calculated by the following formula: 。 5. The temperature prediction method of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1 is characterized in that: The empirical coefficient It can be calculated by the following formula: 。 6. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: The empirical coefficient It can be calculated by the following formula:

7. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: The empirical coefficient It can be calculated by the following formula:

8. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: The empirical coefficient It can be calculated by the following formula:

9. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: The empirical coefficient It can be calculated by the following formula:

10. The method for predicting the temperature of the fluid in the tube based on the fluid model of the double U-tube vertical mid-depth heat exchanger according to claim 1, characterized in that: According to the model, a temperature curve distribution diagram of the circulating fluid in the U-tube under different parameters is drawn to analyze the influence of different parameters on the heat transfer performance of the U-tube buried pipe heat exchanger.

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