Method for testing flow velocity of underground water by using internal heating optical cable

Abstract

The invention discloses an underground water flow velocity testing method, which utilizes equipment containing an internal heating optical cable to test the underground water flow velocity, and comprises the following steps: carrying out numerical analysis based on data information and an MILS theory, and determining finite time ranges corresponding to different flow velocity values and corresponding assumed temperature rise response curves conforming to a linear heat source theory; the internal heating optical cable is placed in a drill hole, the drill hole is backfilled with filler, DTS temperature measurement calibration and subsequent heating operation are carried out, and temperature changes of the heating optical cables at different depths within the heating duration t1 are recorded to serve as a true value temperature rise response curve; fitting a predicted value temperature rise response curve containing temperature change, calculating the flow velocity q based on the MILS theory, and taking the flow velocity consistent with the assumed flow velocity q0 corresponding to the assumed temperature rise response curve as the underground water flow velocity; according to the method, the credibility of a calculation result is ensured by verifying the consistency of calculated and preset underground water flow velocity values and ranges.

Description

Technical Field

[0001] The present invention relates to the field of groundwater testing, and in particular, provides a method for testing the groundwater flow velocity by using an internally heated optical cable. Background Art

[0002] Seepage refers to the flow phenomenon of fluids in porous media (such as rock and soil masses). In rock and soil masses, seepage may directly change their mechanical properties, reduce the stability of rock and soil masses, and trigger geological disasters such as landslides or ground collapses. In engineering construction, seepage can cause soil particles to be carried away by water flow, forming piping or quicksand, and further destroying the stability of engineering structures. At the same time, seepage may also carry pollutants to migrate and pollute groundwater.

[0003] Traditional methods for obtaining the groundwater seepage velocity of rock and soil masses include pumping tests, direct monitoring methods using piezometers, current meters, etc., and indirect inversion methods represented by isotope tracer methods, temperature tracer methods, ground penetrating radar, and electrical potential methods. The pumping test is carried out in a closed borehole within a certain depth range. By continuously pumping water from a pumping well and monitoring the water level changes in nearby observation wells, the permeability coefficient (K) of the aquifer within this depth range is calculated in combination with a mathematical model. According to the monitored hydraulic head (J), the groundwater seepage velocity can be calculated. This method is suitable for the evaluation of the characteristics of large-scale aquifers, and has a simple principle and convenient calculation. However, because it requires simultaneous pumping and monitoring of the surrounding water levels, multiple boreholes are needed for pumping tests, resulting in high costs and long time consumption. The measured groundwater seepage velocity is the average equivalent value within a certain depth range of the borehole, and the test results have multiple solutions and uncertainties, and cannot accurately reflect the groundwater seepage situation and the spatial heterogeneity of rock and soil masses. The isotope tracer method is to inject a tracer, such as a fluorescent dye or an isotope, into the groundwater, and directly calculate the seepage velocity by measuring the arrival time and concentration change of the isotope tracer in the observation well. The seepage obtained by this method is the actual groundwater velocity (pore velocity), and the Darcy velocity can be converted according to the effective porosity of the rock and soil mass as needed. The results of this method are intuitive and suitable for complex geological conditions, but it is necessary to select appropriate tracers and injection methods to reduce the impact of environmental pollution, tracer adsorption, and diffusion. The seepage meter method is a type of point sensor. By directly burying the sensor within the monitoring area, the groundwater flow velocity is monitored. The principle of the seepage meter often obtains the seepage velocity by measuring the flow rate of groundwater flowing into / out of the seepage meter, and there are also seepage meters based on electrical methods for measuring the seepage velocity. Limited by the complexity of the underground environment, seepage meters are often difficult to deploy and have a limited monitoring range. The sensors buried underground are difficult to maintain and recover, and the monitoring cost is high. The isotope tracer method has a risk of polluting the environment, and the electrical potential method and ground penetrating radar are easily affected by strong interference such as electromagnetic signal interference and high salinity areas during the monitoring process, and the measurement accuracy needs to be improved.

[0004] The temperature tracer method has the characteristics of simple theory, environmental friendliness, and convenient data collection, and is an important method for understanding the thermal conductivity of geotechnical materials and the groundwater flow velocity. Among them, the in-situ thermal response test technology (TRT) is currently the main means to obtain the in-situ thermal conductivity of geotechnical materials. By circulating water with a constant power in the heat exchange pipe and based on the infinite line source (ILS) theory according to the water temperatures at the inlet and outlet, the average thermal conductivity of the geotechnical materials at the borehole is calculated. However, this method only obtains the average thermal conductivity of the geotechnical materials within the depth range of the heat exchange pipe.

[0005] To improve the test efficiency and obtain the thermal conductivity of geotechnical materials at different depths, the active heating fiber optic thermal response test technology (ATRT) has been used in the prior art. By arranging the temperature measurement optical cable based on the distributed temperature sensing (DTS) technology and the heating cable together as a composite sensor in the formation at the same time, heating the underground environment with a constant power in the form of an infinite line source hypothesis, and obtaining the thermal conductivity at different depths according to the temperature rise curves at different depths, the distributed measurement can accurately describe the variation of the thermal conductivity with depth caused by the spatial heterogeneity of the geotechnical materials. When groundwater movement exists, the groundwater flow will further accelerate the heat dissipation process in the geotechnical materials, thereby reducing the temperature rise observed at the heat source position. Based on this principle, it can be used to estimate the groundwater flow velocity.

[0006] However, there are still some technical problems in using the moving infinite line source (MILS) theory to calculate the groundwater seepage velocity in the prior art: First, although the direct push method conforms to the MILS theory hypothesis, it is difficult to monitor the groundwater seepage at deeper depths, which limits its application scope; second, the thermal resistance generated by the borehole backfill material will affect the heat conduction process, making the groundwater seepage monitoring and calculation complicated and reducing the measurement accuracy; in addition, different forms of heat sources and cable sheaths have a significant impact on the heat transfer process, making the thermal response test process not fully conform to the theoretical hypothesis of using the MILS theory to calculate the groundwater seepage velocity, resulting in errors in the measurement results. These problems seriously restrict the accuracy and applicability of the groundwater flow velocity measurement method based on the MILS theory. Summary of the Invention

[0007] In order to overcome the defects of the prior art, the purpose of the present invention is to provide at least one novel method for testing the groundwater flow velocity.

[0008] To solve the above problems, the present invention provides a method for testing the groundwater flow velocity using an internally heated optical cable. This method uses a device containing an internally heated optical cable to test the groundwater flow velocity. The groundwater flow velocity test method includes the following steps:

[0009] S1. Perform numerical analysis based on data information and MILS theory to determine the finite time range corresponding to different flow velocity values and the corresponding temperature rise response curve that conforms to the assumptions of the line heat source theory.

[0010] S2. Implement ATRT, including placing the internal heating optical cable in the borehole, backfilling the borehole with filler, calibrating DTS temperature measurement, and subsequent heating operations, and record the temperature change of the heating optical cable at different depths within the heating duration t1 as the true value temperature rise response curve.

[0011] S3. Fit the predicted value temperature rise response curve including temperature change within the heating duration t1 according to MILS theory.

[0012] S4. Calculate the flow velocity q based on MILS theory, record the assumed flow velocity q0 corresponding to the assumed temperature rise response curve corresponding to the predicted value temperature rise response curve. If the flow velocity q is consistent with the assumed flow velocity q0, the flow velocity q is recorded as the groundwater flow velocity q; otherwise, discard the flow velocity q.

[0013] In some embodiments, in step S3, calculate the RMSE between the predicted value and the true value in real time. When RMSE < 0.1K, record the fitting data and execute step S4; otherwise, stop executing step S4.

[0014] In some embodiments, in step S1, the data information includes one or more of the heating power of the heating optical cable, the borehole diameter, and the filler.

[0015] In some embodiments, the heating power is 10 - 50 W / m, and the borehole diameter is 150 mm.

[0016] In some embodiments, the filler is selected from one or more of medium sand, fine sand, silt, clay balls, and cement, and the permeability coefficient of the filler is less than 0.0001 m / s.

[0017] In some embodiments, in step S3, the heating duration t1 is continuous and uninterrupted, and the initial value is greater than 1 h, and the temperature rise does not reach the maximum value at the end point.

[0018] In some embodiments, during the heating duration t1, the true value temperature rise response curve gradually increases, and the predicted value temperature rise response curve gradually increases.

[0019] In some embodiments, in step S4, calculating the flow velocity q based on MILS theory includes the following steps:

[0020] When considering convective heat transfer, the one-dimensional heat diffusion equation that satisfies the homogeneous assumption in the heat response process is:

[0021]

[0022] Let \(T\) be the temperature in \(K\), \(t\) be the heating time in \(s\), \(\lambda\) be the thermal conductivity of the rock and soil mass in \(W / (m\cdot K)\), \(\rho\) be the density of the rock and soil mass in \(kg / m\) 3 ; \(c\) be the specific heat capacity of the rock and soil mass in \(J / (kg\cdot K)\), \(q\) be the groundwater flow velocity in \(m / s\), \(\rho\) w , \(c\) w be the density of water in \(kg / m\) 3 ) and the specific heat capacity in \(J / (kg\cdot K)\);

[0023] When the water flow participates in heat transfer and reaches a steady state, there is:

[0024]

[0025] Let \(U\) be the equivalent velocity used to replace the moving velocity of the heat source in \(m / s\), \(\alpha\) be the thermal diffusivity of the rock and soil mass in \(m\) 2 / s;

[0026] Under the ideal condition of a constant heat input \(p\) in \(W / m\) per unit length in the borehole, the instantaneous relative temperature change of the line heat source is:

[0027]

[0028] \(\Delta T=T - T_0\), where \(T_0\) is the initial temperature in \(K\), \(D\) is the thermal diffusivity of the homogeneous medium in \(m\) 2 / s, \(r\) is the radius of the heat source in \(m\), \(W\) is the Hantush well function;

[0029] When the time \(t\) approaches infinity, the corresponding steady-state final temperature \(\Delta T(t\) ∞ ) can be expressed as:

[0030]

[0031] \(K_0\) is the modified Bessel function of the second kind of order zero, \(\Delta T(t\) ∞ ) can be approximately reached after heating for a sufficient long time in the heat response test, and its value is only related to the thermal conductivity and groundwater flow velocity in the aquifer; then the temperature rise of the line heat source can be expressed through the relationship with \(\Delta T(t\) ∞ ) as:

[0032]

[0033] The parameter \(\Delta T(t\) ∞ ), \(A\), \(r / B\) converge to a unique value. By combining Equation (0 - 25) and Equation (0 - 26), the calculation formula for the groundwater flow velocity can be obtained:

[0034]

[0035] The beneficial effects of the present invention are:

[0036] Compared with the prior art, the underground water flow velocity testing method provided by the present invention proposes to use a numerical simulation method to determine the finite time range corresponding to different flow velocity values, and ensure the credibility of the calculation results by verifying the consistency between the calculation and the preset underground water flow velocity values and ranges. Further, the heat transfer stages of the active heating optical fiber in the borehole are separated, and the effects of the optical cable sheath, backfill, and surrounding rock and soil masses on the heat source diffusion are comprehensively considered in sequence. The heat conduction stage that can neglect the effects of the sheath and backfill and conforms to the moving line heat source theory (MILS) is separated to calculate the underground water flow velocity. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1a is a schematic diagram of the TRT device;

[0038] Figure 1b is a schematic diagram of the ATRT device;

[0039] Figure 2a , 2b is a schematic diagram of the temperature distribution of the ATRT device in the porous medium in the first embodiment of the present invention;

[0040] Figure 3 is a schematic diagram of the division of different groundwater seepage temperature rise stages in the first embodiment of the present invention;

[0041] Figure 4 is a flowchart of the underground water flow velocity testing method in the first embodiment of the present invention;

[0042] Figure 5 is a schematic diagram of the results measured by using the underground water flow velocity testing method provided by the present invention in the first embodiment of the present invention.

[0043] The present invention will be further described below in conjunction with the drawings and specific embodiments. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] The specific embodiments of the present invention given below can further clearly understand the present invention, but they do not limit the present invention.

[0045] This embodiment provides an underground water flow velocity testing method, which conducts on-site testing in an investigation borehole near a certain Yangtze River bank collapse section in Zhenjiang to measure the underground water flow velocity in rock and soil masses at different depths. A copper mesh inner heating optical cable is vertically U-shaped arranged in the borehole and backfilled with low-permeability quartz sand for ATRT testing. When there is no groundwater movement, as the heating time increases, the temperature gradually accumulates in the rock and soil masses and the influence of the borehole can be ignored. The temperature response curve shows a linear trend in the latter section on the semi-logarithmic scale, and the temperature rise rate gradually reaches a constant value.

[0046] When there is groundwater movement, the temperature response curve becomes non-linear on a semi-logarithmic scale. As time increases, the temperature rise rate gradually decreases to zero to reach the maximum temperature rise. Under the action of groundwater flow, the heat generated by the heat source and the heat diffused into the rock and soil mass reach a dynamic equilibrium, and this equilibrium will be reached earlier as the flow velocity increases. At this time, heat can be injected into the surrounding rock and soil mass earlier and faster, and the heat source can meet the linear heat source assumption conditions earlier relative to the rock and soil mass. At this time, it is necessary to confirm the finite time range corresponding to the aforementioned dynamic equilibrium for different flow velocity values.

[0047] As shown in Figure 2, during the test, the ATRT in the backfilled borehole can be regarded as a transient heat transfer process of multi-layer media. The porous difference in temperature in the direction parallel to the linear heat source is caused by the vertical thermal conductivity of the medium. The isotherms on the cable sheath near the heat source can be regarded as straight lines parallel to the linear heat source, and the difference gradually becomes prominent outward. The temperature difference in the direction perpendicular to the linear heat source is controlled by different materials. Under a constant heating power, the heat generated by the internal heating optical cable will gradually diffuse outward due to the temperature gradient, and the heat accumulates in the borehole and around it and gradually decreases with the radial distance. The non-linear temperature gradient reflects the different thermophysical properties of the sheath, borehole backfill, and porous medium around the heat source. The presence of groundwater movement will further accelerate the heat dissipation process in the rock and soil mass and reduce the temperature rise observed at the heat source location.

[0048] During the thermal response test, heat gradually diffuses outward and accumulates among multi-layer media. According to the proportion of heat in each layer of medium in the total heat, the heat transfer process can be divided into four stages. When only considering heat conduction, the four stages correspond to:

[0049] ① Initial stage (Sc), this stage is mainly affected by the material of the internal heating optical cable, with a short duration and a rapid temperature rise. The heat source and the sheath are heated, reflecting the low thermal conductivity of the sheath.

[0050] ② Borehole-dominated heat transfer stage (Sb), at this time, the borehole dominates the heat transfer, and the heat propagates radially along the backfill.

[0051] ③ Stage of joint influence of borehole and rock and soil on heat transfer (Sj), as a transition stage, the proportion of heat absorbed by the backfill becomes less and less, and the influence of the rock and soil on heat transfer becomes greater and greater. The duration of this stage.

[0052] ④ Rock and soil-dominated heat transfer stage (Sg), in this stage, the rock and soil play a leading role in heat transfer, and the heat absorbed by the backfill can be ignored. Based on the temperature data of this stage, the heat source meets the linear heat source assumption conditions relative to the rock and soil mass (under ideal borehole conditions, the linear heat source is in direct contact with the porous medium without extra heat transfer media), and the corresponding hydrothermal parameters can be solved based on the linear heat source theory.

[0053] S1. In this embodiment, for a device with a heating power of 20 W / m, the drilling hole diameter is 150 mm, and the filler is quartz sand with a permeability coefficient less than 0.0001 m / s. Based on the foregoing data and MILS theory, numerical analysis is carried out to determine the finite time range corresponding to different flow velocity values and the corresponding temperature rise response curve that conforms to the assumptions of the line heat source theory. This only needs to be done once for each different ATRT device. Therefore, a separate and comprehensive analysis of common ATRT devices will effectively simplify practical applications.

[0054] S2. Implement ATRT, including placing the internal heating optical cable in the drilling hole, backfilling the drilling hole with filler, DTS temperature measurement calibration, and subsequent heating operations. Record the temperature changes of the heating optical cable at different depths within 72 hours of heating, and make a two-dimensional diagram of temperature rise - time.

[0055] S3. Fit the temperature change curve (i.e., the two-dimensional diagram of temperature rise - time) within the previously defined preset time range according to the Moving Infinite Line Sources (MILS) theory, and simultaneously calculate the RMSE (RMSE, that is, Root Mean Square Error, used to quantify the deviation degree between the predicted value and the true value, which is the square root of the mean square of the prediction error). In the time period when heating starts, at this time RMSE will ≥0.1 K, because this short time is in the Sc - Sj stage, resulting in a deviation between the fitting curve and the measured temperature. When the threshold RMSE < 0.1 K, it indicates that the Sg stage starts at this time, and the corresponding hydrothermal parameters can be solved, record the fitting data and execute step S4; otherwise, stop executing step S4.

[0056] When considering convective heat transfer, the one-dimensional heat diffusion equation that satisfies the homogeneous assumption in the heat response process is:

[0057]

[0058] In the formula: T is the temperature, K; t is the heating time, s; λ is the thermal conductivity of the rock and soil mass, W / (m·K); ρ is the density of the rock and soil mass, kg / m 3 ; c is the specific heat capacity of the rock and soil mass, J / (kg·K); q is the groundwater flow velocity, m / s; ρ w 、c w are respectively the density of water (kg / m 3 ).) and specific heat capacity (J / (kg·K)).

[0059] When the water flow participates in heat transfer together and reaches a steady state, there is:

[0060]

[0061] Where: U is the equivalent velocity used to replace the moving velocity of the heat source, m / s; α is the thermal diffusivity of the rock and soil mass, m 2 / s.

[0062] According to the MILS theory assumptions: ① Under ideal borehole conditions, the line heat source is in direct contact with the porous medium, without any extra heat transfer medium; ② The porous medium is homogeneous and infinite; ③ The groundwater flow velocity in the porous medium is uniform and stable, conforming to Darcy flow; ④ The thermophysical properties of groundwater do not change with temperature. By solving the analytical solution of Equation (0-22), under the ideal condition of a constant heat input p (W / m) per unit length in the borehole, the instantaneous relative temperature change of the line heat source is:

[0063]

[0064] Where: ΔT = T - T0, T0 is the initial temperature, K; D is the thermal diffusivity of the homogeneous medium, m 2 / s; r is the radius of the heat source (m), and W is the Hantush well function.

[0065] When the time t approaches infinity, the corresponding steady-state final temperature ΔT(t ∞ ) can be expressed as:

[0066]

[0067] Where: K0 is the second-kind modified Bessel function of the zero order, and ΔT(t ∞ ) can be approximately reached after heating for a long enough time in the thermal response test, and its value is only related to the thermal conductivity in the aquifer and the groundwater flow velocity. By combining Equation (0-24) and Equation (0-28), the temperature rise of the line heat source can be expressed through its relationship with ΔT(t ∞ ) as:

[0068]

[0069] If the temperature rise in the thermal response test is fitted with Equation (0-29), the parameters ΔT(t ∞ )、A、r / B converge to unique values. By combining Equation (0-25) and Equation (0-26), the calculation formula for the groundwater flow velocity can be obtained:

[0070]

[0071] Step S4, calculate the flow velocity q based on Equation (0-31). If the flow velocity q is consistent with the corresponding flow velocity range in Step S1, then the flow velocity q is recorded as the effective flow velocity q; otherwise, discard the flow velocity q.

[0072] According to the test method proposed in this patent, the test device and test results are as Figure 5As shown. The maximum and minimum temperature rises recorded at 25.5 m in the silt layer and 75.5 m in the gravel layer correspond to the low-flow velocity and high-flow velocity sections, respectively.

[0073] The depth of the borehole test is 82 m. The bottom high-permeability aquifer is mainly composed of loose sediments such as gravel and sand. According to the steady pumping test of a single-hole incomplete well and the water level of the Yangtze River, the groundwater flow velocity in the aquifer within the depth range of 12.8 - 45.6 m is about 9×10 -7 -5×10 -6 m / s.

[0074] Within the depth range of 5 - 78 m, the average groundwater flow rate calculated in this patent is 3.6×10 -6 m / s. The flow velocity of groundwater is usually higher in gravel sand, and the average flow rate can reach 4.0×10 -6 m / s, showing good consistency with the lithology of the formation. The measured groundwater flow velocity is relatively stable within the range of 5 - 48.8 m, with an average value of 3.3×10 -6 m / s, which is consistent with the results independently obtained from the pumping test within the aquifer range of 12.8 - 45.6 m (9×10 -7 m / s - 5×10 -6 m / s).

[0075] Compared with the prior art, the test method provided in this embodiment separates each heat transfer stage of the thermal response test of the active heating optical fiber carried out in the borehole, and comprehensively considers the effects of the cable sheath, backfill, and surrounding rock and soil masses on the heat source diffusion in sequence. It separates the heat conduction stage that can ignore the effects of the sheath and backfill and conforms to the moving line heat source theory (MILS) to calculate the groundwater flow velocity. It proposes to use the numerical simulation method to determine the finite time range corresponding to different flow velocity values, and ensures the credibility of the calculation results by verifying the consistency between the calculated results and the preset groundwater flow velocity values and ranges.

[0076] What is disclosed above is only the preferred embodiment of the present invention. Of course, it cannot be used to limit the scope of the rights of the present invention. Therefore, equivalent changes made according to the scope of the patent application of the present invention still fall within the scope covered by the present invention.

Claims

1. A method for testing groundwater flow rate using an internally heated optical cable, wherein the method uses a device containing an internally heated optical cable to test groundwater flow rate, and is characterized in that: The groundwater flow rate testing method comprises the following steps: S1, based on data information and MILS theory, numerical analysis is performed to determine the finite time range corresponding to different flow rate values ​​and the corresponding temperature rise response curve that conforms to the linear heat source theory assumption; S2, implement ATRT, including placing the internal heating cable in the borehole, backfilling the borehole with fillers, DTS temperature measurement calibration and subsequent heating operations, and record the temperature changes of the heating cables at different depths within the heating time t1 as the true value temperature rise response curve; S3, fitting the predicted value temperature rise response curve including temperature change within the heating time t1 according to the MILS theory; S4, calculate the flow velocity q based on the MILS theory, and record the assumed flow velocity q0 corresponding to the assumed temperature rise response curve corresponding to the predicted value temperature rise response curve. If the flow velocity q is consistent with the assumed flow velocity q0, the flow velocity q is recorded as the groundwater flow velocity q; otherwise, the flow velocity q is discarded.

2. The groundwater flow velocity testing method according to claim 1, characterized in that: In step S3, the RMSE between the predicted value and the true value is calculated in real time. When RMSE < 0.1K, the fitting data is recorded and step S4 is executed; Otherwise, stop executing step S4.

3. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 1, characterized in that: In step S1, the data information includes one or more of the heating power of the heating optical cable, the drilling hole diameter and the filler.

4. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 3, characterized in that: The heating power is 10-50 W / m, and the drilling hole diameter is 150 mm.

5. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 3 or 4, characterized in that: The filler is selected from one or more of medium sand, fine sand, silt sand, clay balls, and cement, and the permeability coefficient of the filler is less than 0.0001 m / s.

6. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 1, characterized in that: In step S3, the heating time t1 is continuous and uninterrupted, and the initial value is greater than 1 hour, and the temperature rise does not reach the maximum value at the end value.

7. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 1, characterized in that: During the heating time t1, the real value temperature rise response curve gradually increases, and the predicted value temperature rise response curve gradually increases.

8. The method for testing groundwater flow velocity using an internally heated optical cable according to claim 1, characterized in that: In step S4, the flow velocity q is calculated based on the MILS theory, including the following steps: When considering convective heat transfer, the one-dimensional heat diffusion equation that satisfies the homogeneous assumption during the thermal response process is: T is temperature, K; t is heating time, s; λ is the thermal conductivity of rock and soil, W / (m·K); ρ is the density of rock and soil, kg / m 3 ; c is the specific heat capacity of rock and soil, J / (kg·K); q is the groundwater velocity, m / s; ρ w 、c w are the densities of water (kg / m 3 ) and specific heat capacity (J / (kg·K); When water flow participates in heat transfer and reaches a steady state: U is the equivalent velocity used to replace the moving velocity of the heat source, m / s; α is the thermal diffusion coefficient of the rock and soil, m 2 / s; Under ideal conditions of constant heat input p (W / m) per unit length in the borehole, the instantaneous relative temperature change of the line heat source is: ΔT=T-T0, T0 is the initial temperature, K; D is the thermal diffusion coefficient of the homogeneous medium, m 2 / s; r is the heat source radius (m), W is the Hantush well function; When time t tends to infinity, the corresponding steady-state final temperature ΔT(t ∞ ) can be expressed as: K0 is the second kind of zero-order modified Bessel function, ΔT(t ∞ ) can be approximately reached after a sufficiently long heating time in the thermal response test, and its value is only related to the thermal conductivity of the aquifer and the groundwater flow rate; then the temperature rise of the line heat source can be obtained by comparing ΔT(t ∞ ) is expressed as: Parameter ΔT(t ∞ ), A, r / B converge to a unique value, and the formula (0-25) and (0-26) can be used to calculate the groundwater velocity:

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