A method and device for calculating thermal conductivity of rock based on finite volume method

Abstract

The present invention discloses a method and device for calculating thermal conductivity of rock based on finite volume method. The method constructs a constant temperature field experimentally, sets a constant temperature heat source satisfying the first type of boundary condition at one axial end, tests the relationship between the temperature rise inside the rock and time, and obtains the relationship between the temperature rise inside the rock and time; then constructs a golden section search calculation model and an objective function calculation model to calculate the thermal conductivity of the rock. The calculation method and device of the present invention have a high degree of automation, reliable and stable measurement results, and are easy to operate. According to the evolution relationship between the temperature rise and time of the temperature measurement point inside the coal rock mass, it comprehensively uses the finite volume method and the golden section search algorithm and other algorithm designs, solves the problem of inverse solution of the second-order nonlinear partial differential equation, and improves the calculation accuracy and efficiency of the thermal conductivity of the rock.

Description

Technical Field

[0001] The present invention relates to the field of rock geothermal utilization, and in particular to a rock thermal conductivity calculation method, a calculation device and an operation method based on a finite volume method. Background Art

[0002] Geothermal resources refer to the thermal energy in rocks that can be scientifically and rationally developed from the earth's crust under current technical, economic and geological environmental conditions. As a renewable clean energy source, geothermal extraction technology is one of the technologies that support the goal of carbon neutrality. Thermal conductivity is an important indicator for evaluating the efficiency of rock geothermal extraction. Therefore, accurate determination of rock thermal conductivity is the basis for research on geothermal energy extraction from rock formations and is of great significance.

[0003] At present, the main way to determine the thermal conductivity of a material is experimental research. In theory, thermal property testing is mainly divided into steady-state method and non-steady-state method. The steady-state method has poor accuracy and a long test cycle. For example, patent CN101984349A discloses a loose coal oxidation heat test method, which calculates the thermal conductivity of the coal at different temperatures by temperature, time, density, specific heat capacity, and porosity. It requires many parameters, resulting in a long test cycle. The non-steady-state method has stricter requirements on equipment and samples, and manual operation and calculation are more cumbersome. The test sample for measuring thermal conductivity using a laser thermal conductivity meter is in the form of a thin sheet, and the equipment is expensive.

[0004] Therefore, designing a method to test the thermal conductivity problem that can increase the measurement efficiency is of great significance for the development and utilization of geothermal resources. Summary of the invention

[0005] In view of the above-mentioned technical deficiencies, the purpose of the present invention is to provide a method and device for calculating the thermal conductivity of rocks based on the finite volume method, construct a reasonable temperature field, comprehensively use the finite volume method and the golden section algorithm, solve the problem of inverse solution of the second-order nonlinear partial differential equation, and improve the measurement accuracy and efficiency of the thermal conductivity of rocks.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for calculating thermal conductivity of rock based on finite volume method comprises the following steps:

[0008] S1: The experiment constructs a constant temperature field, sets a constant temperature heat source that meets the first type of boundary conditions at one end of the axis, tests the relationship between the temperature rise inside the rock and time, and obtains the contact time t between the heat source and the sample. 0 The temperature at the lower measuring point is T test (t 0 );

[0009] S2: Construct a calculation model for the search path and obtain the first thermal conductivity path value K 1 and the second thermal conductivity path value K 2 , the search path calculation model is:

[0010]

[0011] in, is the golden ratio, K low is the minimum rock thermal conductivity, K high is the maximum thermal conductivity of rock;

[0012] S3: Get t 0 At the same time, the thermal conductivity is K 1 and K 2 The temperature T(K,t 0 );

[0013] S4: Construct the objective function calculation model S, and transform T(K,t 0 ) and T test (t 0 ) into the calculation model and calculate K 1 and K 2 The corresponding objective function calculation model value S(K 1 ) and S(K 2 ), the objective function calculation model S is:

[0014] S=[T test (t 0 )-T(K,t 0 )] 2

[0015] S5: To K low and K high Re-assign, compare S(K 1 ) and S(K 2 ), when S(K 1 )>S(K 2 ), let K low =K 1 ; When S(K 1 )<S(K 2 ), let K high =K 2 ;

[0016] S6: Repeat steps S1 to S5 until |S(K 1 )-S(K 2 )|<1×10 -6 When K 1 and K2 Substitute the value into the following formula to calculate the thermal conductivity K of the rock ture :

[0017] K ture =(K 1 +K 2 ) / 2

[0018] Furthermore, step S3 obtains the temperature T(K,t 0 ) using the finite volume method, finite difference method, finite element method or infinite element method.

[0019] Furthermore, step S3 uses the finite volume method to obtain the calculation point t 0 Temperature at time T(K,t 0 ), the specific method is as follows:

[0020] The mesh division inside the sample is to treat the sample as a one-dimensional control volume, and the sample is meshed along the axial direction to divide it into n control volumes.

[0021] Constructing discrete equations, the discrete equations in the temperature field can be obtained based on the energy conservation equation, that is, the heat change in the control volume i per unit time is equal to the heat flowing into the left boundary minus the heat flowing out of the right boundary. The simplified result is as follows:

[0022]

[0023] In the formula, subscript i represents the i-th control volume, superscript j represents the j-th time step; △t is the time step, s; △x is the distance between the control volume and the midpoint of the previous control volume, m; T is the temperature, °C; ρ is the apparent density of the coal, kg / m 3 ; C is the specific heat capacity of rock, J / kg℃; k is the thermal conductivity of rock, W / m℃.

[0024] Subject to boundary conditions, δx 1 ,δx n Satisfied:

[0025]

[0026] Where: d 1 is the length of the first control body, m; d n is the length of the nth control volume, m;

[0027] Discrete equation solution: According to the above formula, combined with the corresponding boundary conditions and initial conditions, n linear equations with n unknowns can be listed; then, the equations are solved by iteration to obtain the temperature of each control body at the next moment. After that, the temperature value at the measuring point in the whole period can be obtained by advancing the time. Take t0 The temperature of the measuring point at the moment is T(K,t 0 ).

[0028] Another object of the present invention is to provide a device for calculating thermal conductivity of rocks based on the finite volume method, characterized in that the device is used to construct a constant temperature field in the above step S1, and a constant temperature heat source satisfying the first type of boundary condition is set at one axial end thereof to test the relationship between the temperature rise inside the rock and the time;

[0029] It comprises an electric slide rail, on which a transverse slide block seat is installed, and on which a sample is installed, so that the sample can move transversely;

[0030] A temperature measuring thermal resistor is installed inside the sample to measure the sample temperature in real time and record it by a data processor;

[0031] A metal heat source plate is installed at one end of the electric slide rail, and the metal heat source plate is on the same horizontal plane as the sample and is used to heat the sample to a constant temperature.

[0032] Furthermore, the sample is cylindrical and its surface is radially insulated, the inner layer of the thermal insulation layer is a silicone layer, the outer layer is a stainless steel layer, and the interlayer is a nano-insulation material; thermal conductive silicone grease is applied to the junction between the temperature measuring thermal resistor and the sample to reduce contact thermal resistance.

[0033] The third object of the present invention is to provide an operating method of a rock thermal conductivity measuring device based on a finite volume method, characterized in that the steps are as follows:

[0034] S1: The rock is prepared into a cylindrical sample, in which a temperature measuring thermal resistor is installed 50mm from the heat source end. The radial direction of the rock sample is insulated and placed in a constant temperature environment, and the ambient temperature and the temperature of the measuring point inside the sample are recorded;

[0035] S2: Place a metal heat source plate heated to a constant temperature on one side of the electric slide rail, and apply thermal conductive silicone grease on the contact surface between the metal heat source plate and the sample;

[0036] S3: Turn on the electric slide rail and record the corresponding moment when the constant temperature metal heat source plate contacts the sample;

[0037] S5: Use the data collector to record the time t 0 The temperature at the lower measuring point is T test (t 0 ).

[0038] The beneficial effects of the present invention are:

[0039] 1. The calculation method of the present invention uses the finite volume method and the golden section search algorithm to solve the problem of inverse solution of the second-order nonlinear partial differential equation, and improves the calculation accuracy and efficiency of the thermal conductivity of rocks. Compared with the traditional non-steady-state method, the present invention adopts a new algorithm design to increase the calculation efficiency. Compared with the steady-state method, it requires fewer parameters and a shorter test cycle.

[0040] 2. High degree of automation, reliable and stable measurement results, easy to operate; the algorithm is encapsulated through the program, and the thermal conductivity of rock can be calculated by simply entering the corresponding parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 This is a schematic structural diagram of a device for calculating thermal conductivity of rocks based on the finite volume method according to Example 1 of the present invention;

[0043] Figure 2 This is a flow chart of a method for calculating thermal conductivity of rocks based on the finite volume method according to Example 1 of the present invention;

[0044] Figure 3 The finite volume method of the embodiment 1 of the present invention obtains the calculation point t 0 Temperature at time T(K,t 0 ) flowchart;

[0045] Description of reference numerals:

[0046] 1. Metal heat source plate; 2. Temperature measuring thermal resistor; 3. Thermal insulation layer; 4. Test sample; 5. Horizontal slider seat; 6. Electric slide rail; 7. Protection plate. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] like Figure 1As shown, a device for measuring thermal conductivity of rock based on finite volume method comprises an electric slide rail 6, a metal heat source plate 1 is installed at one end of the electric slide rail 6, a transverse slider seat 5 is installed on the electric slide rail 6, and a sample 4 is installed on the transverse slider seat 5; protective plates 7 are installed at both ends of the electric slide rail 6.

[0049] The sample 4 is cylindrical, and the surface of the cylindrical sample 4 is radially insulated. The inner layer of the thermal insulation layer 3 is a silicone layer, the outer layer is a stainless steel layer, and the interlayer is a nano thermal insulation material. The temperature measuring thermal resistor 2 penetrates into the sample 4, and the sample 4 and the metal heat source plate 1 are on the same horizontal plane.

[0050] The temperature measuring thermal resistor 2 is installed on the right side of the middle of the sample 4, specifically 50 mm from the heat source end. Thermal conductive silicone grease is applied to the joint position between the temperature measuring thermal resistor 2 and the rock sample to reduce the contact thermal resistance.

[0051] Specific calculation methods include Figure 1 As shown, the following steps are included:

[0052] S1: Place the sample in a constant temperature environment, record the ambient temperature and the temperature of the measuring point inside the sample, and ensure that the temperature in the experimental environment is stable at around 30°C;

[0053] S2: placing the metal heat source plate 1 heated to a constant temperature on one side of the electric slide rail, and applying thermal conductive silicone grease on the contact surface between the metal heat source plate 1 and the sample 4;

[0054] S3: Turn on the electric slide rail and record the corresponding moment when the constant temperature metal heat source plate 1 contacts the sample 4. The corresponding moment is the initial moment of the thermal conductivity experiment. The movement trajectory of the sample is to slowly move from the far end of the slide rail to the heat source end until it contacts the heat source plate.

[0055] S4: The data collector is connected to the temperature measuring thermal resistor, and the data collector is used to record the time t 0 The temperature at the lower measuring point is T test (t 0 ).

[0056] Then, the thermal conductivity of the rock is calculated using the algorithm proposed in the present invention. A calculation model for the search path is constructed to obtain the first thermal conductivity path value K 1 and the second thermal conductivity path value K 2 , the search path calculation model is:

[0057]

[0058] in, is the golden ratio, K low is the minimum rock thermal conductivity, K high is the maximum rock thermal conductivity; set the minimum thermal conductivity Klow =0, set the maximum thermal conductivity K high =10.

[0059] Through the above experiment, we can get t 0 Temperature at time T test (t 0 ), get t 0 At the same time, the thermal conductivity is K 1 and K 2 The temperature T(K,t 0 ); Get the calculated measuring point temperature T(K,t 0 ) using the finite volume method, finite difference method, finite element method, infinite element method or discrete element method.

[0060] Preferably, the finite volume method is used to obtain the calculation point t 0 Temperature at time T(K,t 0 ). The mesh division inside the sample is to treat the sample as a one-dimensional control volume, and the sample is meshed along the axial direction of the sample to divide it into n control volumes.

[0061] Constructing discrete equations, the discrete equations in the temperature field can be obtained based on the energy conservation equation, that is, the heat change in the control volume i per unit time is equal to the heat flowing into the left boundary minus the heat flowing out of the right boundary. The simplified result is as follows:

[0062]

[0063] Where, subscript i represents the i-th control volume, superscript j represents the j-th time step; △t is the time step, s; △x is the distance between the control volume and the midpoint of the previous control volume, m; T is the temperature, °C; ρ is the apparent density of the coal, kg / m 3 ; C is the specific heat capacity of rock, J / kg℃; k is the thermal conductivity of rock, W / m℃.

[0064] Subject to boundary conditions, δx 1 ,δx n Satisfied:

[0065]

[0066] Where: d 1 is the length of the first control body, m; d n is the length of the nth control volume, m;

[0067] Discrete equation solution: According to the above formula, combined with the corresponding boundary conditions and initial conditions, n linear equations with n unknowns can be listed. Then, the equations are solved by iteration to obtain the temperature of each control body at the next moment. After that, the temperature value at the measuring point in the whole period can be obtained by advancing the time. Take t 0 The temperature of the measuring point at the moment is T(K,t 0 ).

[0068] Construct the objective function calculation model S and transform T(K,t 0 ) and T(t 0 ) into the calculation model and calculate K 1 and K 2 The corresponding objective function calculation model value S(K 1 ) and S(K 2 ), the objective function calculation model S is:

[0069] S=[T(t 0 )-T(K,t 0 )] 2

[0070] To K low and K high Re-assign, compare S(K 1 ) and S(K 2 ), when S(K 1 )>S(K 2 ), let K low =K 1 ; When S(K 1 )<S(K 2 ), let K high =K 2 ; Repeat the discrete equation solution to the final step until |S(K 1 )-S(K 2 )|<1×10- 6 The calculation can be stopped when K 1 and K 2 Substitute the value into the following formula to calculate the thermal conductivity K of the rock ture :

[0071] K ture =(K 1 +K 2 ) / 2

[0072] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for calculating thermal conductivity of rocks based on the finite volume method. It is characterized in that The following steps are involved: S1: The experiment constructs a constant temperature field, sets a constant temperature heat source that meets the first type of boundary conditions at one end of the axis, tests the relationship between the temperature rise inside the rock and time, and obtains the contact time t between the heat source and the sample. 0 Temperature T at the lower measuring point test (t 0 ); S2: Build a calculation model for the search path and set the thermal conductivity K low With K high , get the first thermal conductivity path value K 1 The second thermal conductivity path value K 2 , the search path calculation model is: in, is the golden ratio, K low is the minimum rock thermal conductivity, K high is the maximum thermal conductivity of rock; S3: Get t 0 At the same time, the thermal conductivity is K 1 and K 2 The temperature T(K,t 0 ); S4: Construct the objective function calculation model S, and transform T(K,t 0 ) and T test (t 0 ) into the calculation model and calculate K 1 and K 2 The corresponding objective function calculation model value S(K 1 ) and S(K 2 ), the objective function calculation model S is: S=[T test (t 0 )-T(K,t 0 )] 2 S5: To K low and K high Re-assign, compare S(K 1 ) and S(K 2 ), when S(K 1 )>S(K 2 ), let K low =K 1 ; When S(K 1 )<S(K 2 ), let K high =K 2 ; S6: Repeat steps S3 to S5 until S(K 1 )-S(K 2 )<1×10 -6 When K 1 and K 2 Substitute the value into the following formula to calculate the thermal conductivity K of the rock ture : K ture =(K 1 +K 2 ) / 2。 2. According to the method for calculating thermal conductivity of rock based on finite volume method according to claim 1, It is characterized in that Step S3 obtains the calculated measurement point temperature T(K,t 0 ) using the finite volume method, finite difference method, finite element method or infinite element method.

3. According to claim 2, a method for calculating thermal conductivity of rock based on finite volume method, It is characterized in that Step S3 uses the finite volume method to obtain the calculation point t 0 Temperature at time T(K,t 0 ), the specific method is as follows: The mesh division inside the sample is to treat the sample as a one-dimensional control volume, and the sample is meshed along the axial direction of the sample to divide it into n control volumes; Constructing discrete equations, the discrete equations in the temperature field can be obtained based on the energy conservation equation, that is, the heat change in the control volume i per unit time is equal to the heat flowing into the left boundary minus the heat flowing out of the right boundary. The simplified result is as follows: In the formula, subscript i represents the i-th control volume, superscript j represents the j-th time step; △t is the time step, s; △x is the distance between the control volume and the midpoint of the previous control volume, m; T is the temperature, °C; ρ is the apparent density of the coal, kg / m 3 ; C is the specific heat capacity of rock, J / kg℃; k is the thermal conductivity of rock, W / m℃; Subject to boundary conditions, δx 1 ,δx n Satisfied: Where: d 1 is the length of the first control body, m; d n is the length of the nth control volume, m; Discrete equation solution: According to the above formula, combined with the corresponding boundary conditions and initial conditions, n linear equations with n unknowns can be listed; then, the equations are solved by iteration to obtain the temperature of each control body at the next moment; thereafter, the temperature value at the measuring point in the whole period can be obtained by advancing the time. 0 The temperature of the measuring point at the moment is T(K,t 0 ).

4. A device for calculating thermal conductivity of rock based on finite volume method, applied to the method for calculating thermal conductivity of rock based on finite volume method as claimed in claim 1, It is characterized in that The measuring device is used to construct a constant temperature field in step S1, and a constant temperature heat source satisfying the first type of boundary conditions is set at one axial end thereof to test the relationship between the temperature rise inside the rock and the time change; It comprises an electric slide rail, on which a transverse slide block seat is installed, and on which a sample is installed, so that the sample can move transversely; A temperature measuring thermal resistor is installed inside the sample to measure the sample temperature in real time and record it by a data processor; A metal heat source plate is installed at one end of the electric slide rail, and the metal heat source plate is on the same horizontal plane as the sample and is used to heat the sample to a constant temperature.

5. According to the rock thermal conductivity measuring device based on the finite volume method according to claim 4, It is characterized in that The sample is cylindrical and its surface is heat-insulated radially, the inner layer of the heat-insulating layer is a silicone layer, the outer layer is a stainless steel layer, and the interlayer is a nano-insulating material; Thermal conductive silicone grease is applied to the joint position between the temperature measuring thermal resistor and the sample to reduce the contact thermal resistance.

6. A method for operating the rock thermal conductivity measuring device based on the finite volume method as claimed in claim 4, It is characterized in that Here are the steps: S1: The rock is prepared into a cylindrical sample, and a temperature measuring thermal resistor is installed inside the sample at the end far away from the heat source. The radial direction of the rock sample to be tested is insulated and placed in a constant temperature environment, and the ambient temperature and the temperature of the measuring point inside the sample are recorded; S2: Place a metal heat source plate heated to a constant temperature on one side of the electric slide rail, and apply thermal conductive silicone grease on the contact surface between the metal heat source plate and the sample; S3: Turn on the electric slide rail, and the movement trajectory of the sample is to slowly move from the far end of the slide rail to the heat source end until it contacts the heat source plate, and record the corresponding moment when the constant temperature metal heat source plate contacts the sample; S5: Use the data collector to record the time t 0 Temperature T at the lower measuring point test (t 0 ).

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