Multi-parameter step-by-step decoupling inversion method for underground heat exchanger based on thermal response test

Abstract

The present invention discloses a multi-parameter step-by-step decoupling inversion method for a buried pipe heat exchanger based on thermal response testing, and belongs to the technical field of ground source heat pumps. The inversion method integrates three key elements, namely, a short-time heat transfer model of a buried pipe heat exchanger, multiple objective functions, and a lexicographic optimization method. On the basis of sensitivity and linear correlation analysis, the inversion method reduces the coupling of multiple parameters estimated simultaneously in a step-by-step manner to obtain a more stable and reliable multi-parameter inversion result. The step-by-step decoupling inversion method proposed in the present method does not need to rely on cumbersome steps such as regularization and repeated iterations, and has high robustness. The present invention is used to calculate the thermal physical properties of shallow underground rock and soil and backfill materials, and provides technical support for improving efficiency and energy saving in the design of ground source heat pump systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of ground source heat pumps, and specifically refers to a multi-parameter step-by-step decoupling inversion method for a buried pipe heat exchanger based on thermal response testing. Background Art

[0002] The thermophysical parameters of shallow underground rock and soil and backfill materials in boreholes are the main factors affecting the underground heat transfer process of ground source heat pumps, and are also key parameters for designing ground source heat pump systems and buried pipe heat exchangers. Accurately determining these parameters is of great significance for the application of ground source heat pumps. At present, in-situ thermal response tests combined with parameter inversion are widely used to estimate the thermophysical parameters of underground rock and soil and backfill materials. The inversion of thermophysical parameters using experimental data is a typical heat transfer inverse problem, which is a type of ill-posed problem in mathematics and is difficult to solve. Although domestic and foreign researchers have conducted extensive research in this field, the following problems still need to be solved:

[0003] 1. At present, most methods are only applicable to single-parameter or double-parameter inversion calculations, such as estimating the thermal conductivity of rock and soil or estimating the thermal conductivity of rock and soil and the thermal resistance of boreholes. This is because, on the one hand, the inversion of the thermophysical parameters of the backfill material requires a complex short-time heat transfer model, and on the other hand, the increase in the number of parameters to be estimated will lead to the instability of the parameter inversion algorithm and the reduction of identifiability.

[0004] 2. A few inversion methods can calculate three or more parameters, such as using regularization to stabilize the iterative solution process of multi-parameter inversion by sacrificing data fitting accuracy. Since the multi-parameter inversion of buried pipe heat exchangers is a typical nonlinear parameter inversion problem, there is currently a lack of scientific and reasonable methods for selecting regularization parameters, which seriously limits the practicality of regularization methods.

[0005] 3. Internationally, when many parameters inversion methods for buried pipe heat exchangers involve dealing with multi-objective problems, most of them convert multiple objectives into single objectives by adding objective function weight coefficients. These weight coefficients usually need to be selected based on experience, and there is currently a lack of reasonable weight coefficient selection methods.

[0006] In summary, there is no stable and feasible multi-parameter inversion method at home and abroad for inverse calculation of thermal conductivity and thermal diffusivity of rock, soil and backfill materials required for the design of buried pipe heat exchangers through in-situ thermal response testing. Summary of the invention

[0007] The purpose of the present invention is to solve the deficiencies and shortcomings in the prior art and to propose a multi-parameter step-by-step decoupling inversion method for a buried pipe heat exchanger based on thermal response testing.

[0008] The idea of ​​the present invention is to introduce a heat transfer model suitable for a short-term buried pipe heat exchanger to accurately analyze the sensitivity and linear correlation analysis of multiple parameters during the entire thermal response test, so as to select the temperature and temperature derivative data of each time period to perform step-by-step decoupling and inversion of multiple estimated parameters, and use a lexicographic optimization method to solve the dual-objective problem after adding the temperature derivative data.

[0009] The technical solution of the present invention is as follows:

[0010] The test is carried out using a thermal response tester and a schematic diagram of the drilling cross section (see attached). Figure 1 shown).

[0011] Multi-parameter step-by-step decoupling inversion method for buried pipe heat exchanger based on thermal response test (see Appendix) Figure 2 ), which includes:

[0012] Step 1: Obtain known parameters of the U-shaped ground heat exchanger for the on-site thermal response test and the collected inlet and outlet temperatures of the circulating fluid in the U-shaped ground heat exchanger;

[0013] Step 2: Calculate the average temperature of the circulating fluid, that is, the measured value of the temperature, and then use numerical derivation to calculate the logarithmic time derivative of the measured temperature value, that is, the measured value of the temperature derivative;

[0014] Step 3: Identify the thermophysical parameters and geometric parameters that need to be inverted and calculated on site, i.e., the parameters to be estimated, assign initial values ​​to the parameters to be estimated, input the known parameters and the initial values ​​of the parameters to be estimated into the short-time heat transfer model of the ground pipe heat exchanger, calculate the relative sensitivity coefficients of temperature and temperature derivatives to the parameters to be estimated, construct a sensitivity coefficient matrix, and analyze the sensitivity of temperature and temperature derivatives to all parameters to be estimated and the linear correlation between the parameters to be estimated;

[0015] Step 4: According to the sensitivity and linear correlation analysis, a subset of the measured values ​​of the temperature and the measured values ​​of the temperature derivative are selected, and the temperature objective function and the temperature derivative objective function are formed with the corresponding average temperature and the model calculated value of the temperature derivative for the dual-objective lexicographic optimization method;

[0016] Step 5: According to the dual objective function, the parameters to be estimated are decoupled and inverted step by step by combining the lexicographic optimization method through linear fitting, nonlinear equation solving, and curve fitting steps;

[0017] Step 6: Output the step-by-step decoupling inversion results of the parameters to be estimated.

[0018] Furthermore, the step 1 specifically includes:

[0019] Step 11: The known parameters include: initial temperature T0 of rock and backfill material, radius r of underground pipe drilling b, drilling length L, U-tube outer diameter r o 、Inner diameter r i , center distance 2D, thermal conductivity of tube wall k p , the volume heat capacity of the circulating fluid C f , volume flow rate V f , the average heating rate of the heater is q.

[0020] Furthermore, the step 2 specifically includes:

[0021] Step 21: The average temperature of the circulating fluid is the arithmetic mean of the inlet and outlet temperatures of the ground heat exchanger:

[0022]

[0023] Where T i represents the average temperature of the circulating fluid at the i-th moment, T i，in and T i，out is the inlet and outlet fluid temperature of the heat exchanger at the i-th moment;

[0024] Step 22: Calculate the logarithmic time derivative of temperature using the central difference scheme and variable step size method:

[0025]

[0026] Where n is the number of central difference derivatives, usually 6 to 12, m i is the minimum time interval (usually m i 1) can be taken to represent the minimum time step There are i Should meet:

[0027]

[0028] Furthermore, the step 3 specifically includes:

[0029] Step 31: According to the design parameters of the ground heat exchanger on site, the parameters to be estimated should include the following parameters: thermal conductivity of rock and soil k s , thermal diffusion coefficient of rock and soil a s , thermal conductivity of backfill material k b , and the thermal diffusion coefficient a of the backfill material b ;

[0030] Step 32: The short-time heat transfer model of the U-shaped buried pipe heat exchanger is an infinite length composite medium line heat source model:

[0031]

[0032] Where G(t) represents the thermal response function of the unsteady heat transfer process from the outer wall of the U-tube to the semi-infinite medium; k bIndicates the thermal conductivity of the backfill material; a b represents the thermal diffusion coefficient of the backfill material; u represents the integral variable; t represents the time; i represents the summation index; r A =Dr o and r B =D+r o are the radial coordinates of the two calculation points with the center of the drilling circle as the coordinate origin; J 2i represents the 2i-order Bessel function; D represents the radial coordinate of the center of the ∪-shaped tube; k and a are dimensionless parameters, k = k s / k b , a=(a b / a s ) 1 / 2 ; a s represents the thermal diffusion coefficient of rock and soil; J n and Y n denote the first and second n-order Bessel functions respectively; J n ′ and Y n ′ represents J n and Y n The first derivative of b Indicates the drilling radius; T f is the circulating fluid temperature; T0 is the initial temperature of the rock and soil; q l It represents the heat flux density per unit length of the heat exchanger (W / m); / N represents the number of ∪-shaped tubes in the borehole; R p Represents the steady-state thermal resistance of the U-tube; k p is the thermal conductivity of the U-tube; r o and r i are the inner and outer diameters of the U-tube respectively; α represents the convection heat transfer coefficient in the tube;

[0033] Step 33: Use the difference method to calculate the relative sensitivity coefficients of temperature and temperature derivatives to the estimated parameters at different times:

[0034]

[0035] Among them, β represents a parameter to be estimated, X β，T and X β，D Respectively represent the relative sensitivity coefficients of temperature and temperature derivative, T f Indicates the temperature value calculated by the model simulation;

[0036] Step 34: Based on the relative sensitivity coefficient obtained in step 33, perform parameter sensitivity analysis and linear correlation analysis.

[0037] Furthermore, the step 4 further specifically includes:

[0038] Step 41: The temperature objective function composed of the temperature measured value and the temperature model calculated value:

[0039]

[0040] The derivative objective function composed of the temperature derivative measured value and the temperature derivative model calculated value is:

[0041]

[0042] Where S T and S D are the temperature objective function value and the derivative objective function value respectively, β represents the parameter vector to be estimated, p and q are the point sets for selecting temperature data and derivative data time respectively.

[0043] Furthermore, the step 5 specifically includes:

[0044] Step 51: Use the traditional line source model to perform linear fitting on the temperature measured data at the end of the thermal response test (generally after 10 hours), and then calculate the thermal conductivity k of the rock and soil based on the slope a and intercept b of the obtained straight line. s and drilling thermal resistance R b , the formula used is as follows:

[0045]

[0046] Step 52: Given the initial value of the thermal diffusivity of the rock and soil Under the condition of b The value and R b The nonlinear solution of model formula 16 obtains the thermal conductivity of the backfill material The value is calculated using the following formula:

[0047]

[0048] Among them, R a is the unsteady-state thermal resistance of the backfill material, and the dimensionless variable σ is defined as (k b -k s ) / (k b +k s ), the dimensionless variable η can usually be 0;

[0049] Step 53: The thermal conductivity of the backfill material determined in step 52 is and thermal response test temperature data, by minimizing the temperature objective function β1 = [a s a b ], and obtain the parameter inversion value based on temperature and the minimum value of the temperature objective function

[0050]

[0051] Step 54: Under the constraint of the minimum value of the temperature objective function in step 53 (where k is the adjustment coefficient, ranging from 1.0 to 1.1), according to The value and temperature derivative data are obtained by minimizing the derivative objective function β2 = [a s k b ], and obtain the parameter inversion value based on temperature derivative The minimum value of the derivative objective function

[0052]

[0053] Compared with the prior art, the advantages of the present invention are: it innovatively combines the short-time heat transfer model of the buried pipe heat exchanger, multiple objective functions and the lexicographic order optimization method, can effectively solve the ill-posed problem of multi-parameter inversion of the buried pipe heat exchanger, can make full use of the high-sensitivity thermal response test data in the early stage, and improve the efficiency of the on-site thermal response test and the reliability of parameter inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the thermal response tester and drilling cross section of the present invention

[0055] Among them: 1 is a thermometer; 2 is a heating device; 3 is a water pump; 4 is a flow meter

[0056] Figure 2 The main program flow chart of the method of the present invention is

[0057] Figure 3 This is a flowchart of the sensitivity and linear correlation analysis process described in the embodiment of the present invention.

[0058] Figure 4 The relative sensitivity coefficient time-varying diagram of the estimated parameter in the embodiment of the present invention is

[0059] Figure 5 This is a flowchart of the step-by-step lexicographic decoupling inversion process described in an embodiment of the present invention.

[0060] Figure 6 The parameter inversion results and fitting effect diagram described in the embodiment of the present invention are shown in FIG. DETAILED DESCRIPTION

[0061] The present invention is further described and verified below in conjunction with the accompanying drawings and embodiments.

[0062] Taking Beier's international standard sandbox as an example, the circulating fluid temperature data and physical property parameter reference values ​​obtained by the thermal response test conducted using the standard sandbox experiment.

[0063] The thermal response tester and the cross-sectional diagram of the drilling hole according to the embodiment of the present invention (see attached) Figure 1 shown).

[0064] The main program flow chart of the embodiment of the present invention (see attached) Figure 2 shown):

[0065] Step 1: Input the inlet and outlet temperatures and known physical properties and geometric parameters of the circulating fluid for the sandbox thermal response test;

[0066] Step 2: Calculate the arithmetic mean of the temperature data as the average temperature of the circulating fluid, which is the measured temperature value, and calculate the logarithmic time derivative value of the average temperature of the circulating fluid, which is the measured temperature derivative value;

[0067] Step 3: Call the sensitivity and linear correlation analysis subroutine;

[0068] Step 4: Based on the analysis in step 3, select 50 sets of temperature measured values ​​and temperature model calculated values ​​in the first 20 hours, and select 50 sets of temperature derivative measured values ​​and temperature derivative model calculated values ​​from the 5th hour to the 20th hour to construct the temperature objective function inversion a s with a b And derivative objective function inversion a s With k b ;

[0069] Step 5: Call the step-by-step lexicographic decoupling inversion subroutine;

[0070] Step 6: Output multi-parameter step-by-step decoupling inversion results

[0071] Sensitivity and linear correlation analysis subroutine call operation diagram (see attached) Figure 3 shown):

[0072] Step 31: Determine the parameter to be estimated as the thermal conductivity k of the rock and soil s , thermal diffusivity of rock and soil a s , Thermal conductivity of backfill material k b , Thermal diffusivity of backfill material a b ;

[0073] Step 32: Input the infinite length composite medium line heat source model of the U-shaped buried pipe heat exchanger;

[0074] Step 33: Calculate the relative sensitivity coefficients of temperature and temperature derivatives to the estimated parameters at different times (see Appendix Figure 4 shown);

[0075] Step 34: Analyze the attached Figure 4 The sensitivity of the temperature and temperature derivative to the estimated parameters and the linear correlation between the parameters are shown in the temperature graph except a bThe estimated parameters are more sensitive after 20 hours, but except for k s The linear correlation between external parameters is strong, and a s and k b The highly linear correlation during the entire period makes it difficult to estimate a unique result at the same time; the estimated parameters in the first 20 hours of the temperature derivative graph are highly sensitive and identifiable, but k b and a b Highly linearly correlated over the entire period, and k b and a b The sensitivity of varies too much to estimate a stable result.

[0076] The step-by-step lexicographic decoupling inversion subroutine call operation block diagram (see attached Figure 5 shown):

[0077] Step 51: According to the traditional linear heat source model, the thermal conductivity k of the rock and soil is obtained by linear fitting using the later temperature measurement data of more than 10 hours in the temperature measurement values. s and drilling thermal resistance R b ;

[0078] Step 52: Given the initial value of soil thermal diffusivity Under the condition of b The value and R b The model calculation formula is nonlinear to solve the thermal conductivity value of the backfill material

[0079] Step 53: Minimize the temperature objective function and invert the parameter value and Minimum value of temperature objective function

[0080] Step 54: Under the constraint of the minimum value of the temperature objective function in step 53 By minimizing the derivative objective function, the parameter value is inverted and Minimum of derivative objective function

[0081] In this embodiment, the known physical property parameters and thermophysical property parameter reference values ​​of the sandbox are shown in Table 1, where the reference value of the parameter to be estimated is k s =2.82W / (m·K), a s =k s / C s =0.881×10 -6 m 2 / s,k b =0.73W / (m·K), a b =k b / C b =0.192×10 -6 m 2 / s.

[0082] Table 1 Experimental parameters of sandbox thermal response test

[0083]

[0084]

[0085] Use the main program to perform parameter inversion on the sandbox thermal response test data, and the inversion results of each parameter and the fitting effect diagram (see attached) Figure 6 As shown), the relative error is as follows: Linear fitting result k s =2.92W / (m·K)(≈3.55%), nonlinear solution The inversion result of temperature objective function parameters is: Minimum value of temperature objective function The inversion result of the derivative objective function parameter is: Temperature objective function value Minimum value of derivative objective function

[0086] In summary, the present invention verifies the inversion method through examples, and the results show that the step-by-step decoupling method can obtain more stable and reliable multi-parameter inversion results without relying on regularization and repeated iterations; it effectively reduces the coupling between the parameters to be estimated, and has the characteristics of robustness, stability, and small amount of calculation. At the same time, by adding the derivative objective function through the lexicographic method, the thermal conductivity k of the backfill material can be effectively improved. b These are all conducive to calculating the thermal physical parameters of the shallow underground rock and backfill materials to improve the design accuracy of the buried pipe heat exchanger, so as to avoid unnecessary initial investment and improve the utilization rate of geothermal resources, and provide technical support for the design of ground source heat pump systems to improve efficiency and energy saving.

Claims

1. A multi-parameter step-by-step decoupling inversion method for underground heat exchangers based on thermal response testing, characterized in that: Adopt energy treatment The short-term heat transfer model of the non-steady-state heat transfer process in the borehole of the underground heat exchanger is established. The inlet and outlet temperatures of the circulating fluid in the thermal response test are collected, and the average temperature of the circulating fluid and its logarithmic time derivative are calculated. Based on the sensitivity and linear correlation of the thermophysical parameters to be estimated, a dual-objective lexicographic optimization algorithm with the average temperature of the circulating fluid and its logarithmic time derivative as the target is adopted to invert the thermophysical parameters of the shallow underground rock and soil and the backfill material in the borehole in a step-by-step decoupling manner; The steps include: Step 1: Obtain known parameters of the U-shaped ground heat exchanger for the on-site thermal response test and the collected inlet and outlet temperatures of the circulating fluid in the U-shaped ground heat exchanger; Step 2: Calculate the average temperature of the circulating fluid, that is, the measured value of the temperature, and then use numerical derivation to calculate the logarithmic time derivative of the measured value of the average temperature, that is, the measured value of the temperature derivative; Step 3: Identify the thermophysical parameters and geometric parameters that need to be inverted and calculated on site, i.e., the parameters to be estimated, assign initial values ​​to the parameters to be estimated, input the known parameters and the initial values ​​of the parameters to be estimated into the short-time heat transfer model of the ground pipe heat exchanger, calculate the relative sensitivity coefficients of temperature and temperature derivatives to the parameters to be estimated, construct a sensitivity coefficient matrix, and analyze the sensitivity of temperature and temperature derivatives to all parameters to be estimated and the linear correlation between the parameters to be estimated; Step 4: According to the sensitivity and linear correlation analysis, a subset of the measured values ​​of the temperature and the measured values ​​of the temperature derivative are selected, and the subsets are used together with the corresponding model calculated values ​​of the temperature and the temperature derivative to form a temperature objective function and a temperature derivative objective function for a dual-objective lexicographic optimization method; Step 5: According to the dual objective function, the parameters to be estimated are decoupled and inverted step by step by combining the lexicographic optimization method through linear fitting, nonlinear equation solving, and curve fitting steps; Step 6: Output the step-by-step decoupling inversion results of the parameters to be estimated.

2. The multi-parameter step-by-step decoupling inversion method for underground heat exchanger based on thermal response test according to claim 1, characterized in that: Based on the adopted numerical derivation method, the logarithmic time derivative of the average temperature of the circulating fluid at each sampling moment is calculated using the variable step-size averaging method to reduce the amplification effect of the numerical derivation process on the measurement error and reduce the variance of the obtained temperature derivative measured value.

3. The multi-parameter step-by-step decoupling inversion method for underground heat exchanger based on thermal response test according to claim 1, characterized in that: The short-time heat transfer model of the buried pipe heat exchanger is an infinite length composite medium line heat source model, which is suitable for describing the unsteady-state heat transfer process of the U-shaped buried pipe heat exchanger during the entire thermal response test period, and is suitable for calculating the relative sensitivity coefficient of the estimated parameter during the entire thermal response test period.

4. The multi-parameter step-by-step decoupling inversion method for underground heat exchanger based on thermal response test according to claim 1, characterized in that: The lexicographic optimization method adopts the method of performing parameter inversion calculation in a certain order according to the importance and priority of the objective function, that is, first performing inversion calculation according to the temperature objective function, and then taking the minimum value of the temperature objective function as a constraint, performing parameter correction according to the temperature derivative objective function, which conforms to the physical law that the temperature objective function is the main and the derivative objective function is the auxiliary in the dual objective function.

5. The multi-parameter step-by-step decoupling inversion method for underground heat exchanger based on thermal response test according to claim 1, characterized in that: The step-by-step decoupling inversion: firstly, the temperature measured value in the later stage of the thermal response test is used to calculate the minimum value of the temperature objective function, the thermal conductivity of the rock and soil, and the borehole thermal resistance of the buried pipe heat exchanger in a linear fitting manner; Secondly, the thermal conductivity of the backfill material is preliminarily determined by solving the nonlinear equation through the borehole thermal resistance model. Then, the measured temperature value in the early stage of the thermal response test is used to calculate the minimum value of the temperature objective function and the thermal diffusion coefficient of rock and soil and backfill material by curve fitting. Finally, the minimum value of the temperature objective function is used as the constraint condition and the temperature derivative is used as the objective function. The inversion values ​​of the thermal conductivity of the backfill material and the thermal diffusion coefficient of rock and soil are corrected by curve fitting.

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