JP5334221B1 - Analysis method and analysis program for thermal response test and pumping test - Google Patents

Abstract

The present invention proposes a thermal response test analysis method capable of obtaining the thermal conductivity of a formation based on the thermal response test results in a short time and with high accuracy.
In an analysis method of a thermal response test, a measured value by a thermal response test is input to a computer. A parameter identification program is installed in the computer, and by using the nonlinear optimization method based on Powell's conjugate gradient method, an arbitrary value is set for the parameter to be identified, and the integral form of the exponential function. Calculate the temperature rise amount for calculating the temperature rise amount of the formation by calculating the analytical solution for the thermal response test given in step 30 up to the 30th term, and calculate the error between the calculated value and the measured value obtained by the thermal response test The parameter is identified by repeating the process of changing the parameter value so that the error is minimized. The thermal conductivity of the formation can be calculated using the parameters after identification.
[Selection] Figure 4

Description

  The present invention relates to an analysis method and an analysis program for a thermal response test and a pumping test. More specifically, the present invention relates to an analysis method and an analysis program that can perform a reverse analysis by parameter identification by applying a conjugate gradient method, and can accurately evaluate the heat exchange characteristics and groundwater flow characteristics of the ground in a short time.

  In recent years, the use of natural energy (renewable energy) has been reviewed as a clean energy alternative to nuclear power and thermal power. One of them is increasing interest in the use of geothermal heat. In contrast to the outside air temperature, which varies with the season, the underground temperature is stable at about 15 ° C throughout the year. An example of an effective use of underground heat having such characteristics is a underground heat pump (hereinafter referred to as GeoHP) system. This is an air-conditioning / hot-water supply system using geothermal heat. Focusing on the characteristics of geothermal heat that can supply stable heat, it releases heat into the ground as a cooling in the summer and uses it as a heat source for heating in the winter.

  However, in Japan, the spread of the GeoHP system is delayed compared to Europe and America. Reasons for this are low recognition, problems of initial costs in drilling wells, etc. and, unlike Europe and the United States, thermophysical values differ depending on the climate of the land, so an economic system is still established. It is not done. For this reason, in order to popularize the GeoHP system, it is essential to improve the efficiency of the system in order to reduce the initial cost.

  A thermal response test is known as a ground investigation test for improving the efficiency of the system. The thermal response test is mainly a test for evaluating the thermal conductivity of the formation and the thermal resistance of the heat exchange well, and is essential information for predicting the heat exchange behavior of the underground heat exchange well. Performing a thermal response test to determine the appropriate number and length of wells is extremely important for reducing the initial cost of the GeoHP system.

  The thermal response test for ground investigation is mainly targeted at the vertical underground heat exchange well in the closed type. A thermal response test apparatus for this purpose heats a heat medium with an electric heater in a water tank on the ground and circulates the inside of a pipe with a circulation pump. Since the heated heat medium dissipates heat when passing through the underground part, the temperature difference between the inlet and outlet of the U-shaped tube is measured to evaluate the heat exchange characteristics of the formation. Such a thermal response test apparatus is disclosed in Patent Document 1, and a thermal response test method using the thermal response test apparatus is disclosed in Non-Patent Document 1.

JP 2004-301750 A

"Standard test method of thermal response test by heating method for borehole type underground heat exchanger ver.2", Katsunori Nagano, edited by the study group of underground heat utilization and heat pump system, heat pump and heat storage center

Here, as a typical analysis method of the thermal response test, there are an analytical method based on a Kelvin source function or a cylindrical heat source function, and an analysis method based on a numerical model using a finite difference method or a finite element method. The most commonly used method in the analytical method of the thermal response test is a drawing method based on the Kelvin source function because of the ease of data observation and the ease of analysis. There are two methods of plotting, one is the method using time-dependent change of temperature data of the heat medium during circulation and the other is the method using the recovery data of underground temperature after the circulation stop, but analysis using the data at the time of circulation is generally performed. . The analysis theory of the thermal response test based on the Kelvin source function will be described below.

Homogeneous with no groundwater flow, isotropic, it is assumed that the given heat load at a constant amount Q _H isobaric into the well that fully penetrate into the formation with infinite extent. When the unsteady heat conduction equation is converted into a cylindrical coordinate system, it is expressed by equation (1).

On the other hand, assuming that the radius of the well is r _w , the initial conditions and boundary conditions are given by the following equations (2) to (4).

When the temperature rise amount of the formation is set to T _r = T−T ₀ , the following equations (5) to (8) are obtained by rewriting equation (1), initial conditions, and boundary conditions.

  When equation (5) is solved under the above initial conditions and boundary conditions, the following equations (9) to (11) are obtained.

  Equation (9) is called a Kelvin source function, and E (X) is an exponential integral. E (X) in equation (11) is approximated by the following equation (12) when X is sufficiently small, generally when X <0.05 and the error is 2.5% or less.

  Therefore, the equation (9) is approximated by the following equation (13).

In equation (13), the only variable that changes with time under the condition that the heat exchange amount is constant is only time t. Therefore, when arranged into terms that do not depend on time and terms that do not depend on time, equation (13) can be expressed as Become.

  In Expression (14), when ln (x) = 2.3log (x), the natural logarithm is converted into a common logarithm, and the following Expression (15) is obtained.

  Here, the slope m of the equation (15) is expressed by the following equation (16).

  In this case, the apparent thermal conductivity λ of the formation is expressed by the following equation (17).

  In the plotting method using the circulation data, the m value is determined from the slope of the semilogarithmic graph showing the temporal change of the heat medium average temperature based on the equation (16), and the thermal conductivity λ of the formation is calculated from the equation (17). Ask. In addition, considering that analysis is performed using approximate solutions and that the initial stage is affected by underground heat exchangers and fillers, the m value is obtained from data in a section where sufficient time has elapsed since the start of the test. To decide. However, there is no clear standard for selecting the data section to be analyzed, and it is determined by the person performing the analysis.

Thus, in the analysis by the drawing method of the thermal response test that is generally performed, the m value is determined from the slope of the semilogarithmic graph showing the change with time of the heat medium average temperature, and the formation is calculated from the above equation (17). The apparent thermal conductivity λ is obtained. The slope of the graph here is data of a straight line portion that is seen after several tens of hours have passed since the start of the test. However, there are the following problems in the analysis by the drawing method.
(1) Since the time t when the error is within the allowable range of 2.5% is unknown, there is no clear standard for selecting the straight section for determining the slope m, and which section of data is determined as the straight section Since this depends on the subjectivity of the person performing the analysis, the analysis results vary from person to person.
(2) Since all data in the initial stage is discarded, it is necessary to take a long test period, leading to an increase in cost.
(3) The analytical solution used in the drawing method does not take into account groundwater flow and ground temperature gradient. Therefore, when there is a groundwater flow or when there is a ground temperature gradient, it is not possible to obtain an accurate thermal conductivity. Therefore, the thermal conductivity obtained by the analysis of the thermal response test is often an apparent thermal conductivity including an error.

  In view of these points, an object of the present invention is to provide a thermal response test analysis method and analysis program based on parameter identification to which a conjugate gradient method is applied in order to shorten time and improve accuracy of heat exchange characteristics evaluation of the ground. It is to propose.

  Another object of the present invention is to focus on the sameness between the analytical solution of the pumping test and the analytical solution of the thermal response test that are generally performed as an in-situ test for determining groundwater flow parameters such as the permeability coefficient and the storage coefficient. Then, in order to shorten the time and improve the accuracy of groundwater flow characteristics evaluation of the ground, it is to propose an analysis method and analysis program for pumping tests using parameters to which the conjugate gradient method is applied.

  In order to solve the above-mentioned problems, in the thermal response test analysis method and analysis program of the present invention, in the Kelvin source function that defines the temperature rise of the ground, the power series expansion formula of the exponential integral E (X) If at least the 16th term, preferably the 30th term, is taken into consideration, the calculation value (semi-analytical solution) close to the actual measurement value is obtained in the initial stage of the thermal response test, and is obtained in the initial stage of the thermal response test. By applying a nonlinear optimization method using Powell's conjugate gradient inverse analysis to the measured values, the unknown parameters of the Kelvin source function that defines the temperature rise are identified, and the heat conduction of the ground The rate is calculated. That is, using the nonlinear optimization method based on Powell's conjugate gradient method, the calculated value of the temperature rise obtained when the unknown parameter is set to a predetermined value and the temperature rise measured by the thermal response test Inverse analysis of the parameters is performed so that the error from the measured value is minimized.

  Also, in the pumping test analysis method and analysis program of the present invention, attention is paid to the identity of the thermal response test analysis solution and the pumping test analysis solution, and in the well function of Tyce that defines the groundwater level drop amount of the ground, the index Considering that the power series expansion formula of the integral W (u) takes into account at least the 16th term, preferably the 30th term, a calculated value (semi-analytical solution) close to the actual measured value can be obtained in the initial stage of the pumping test. An unknown parameter of the well function of Tyce that defines the groundwater level drop by applying a nonlinear optimization method using Powell's conjugate gradient inverse analysis to the measured value obtained in the initial stage of the pumping test And the water permeability coefficient of the ground is calculated.

(Powell's conjugate gradient method)
In the present invention, in the analysis method of the thermal response test or the pumping test, the inverse analysis by the optimization method is used. As described above, the positive analysis based on the groundwater model has a structure that calculates the groundwater level, the groundwater temperature, the concentration of substances, etc. using the water permeability coefficient, thermal conductivity, or dispersion coefficient as known parameters. However, it is difficult to directly measure these parameters with high accuracy. Rather, the concentration and groundwater temperature that should be obtained as a solution can be measured and measured more easily and accurately. In the present invention, inverse analysis is used to identify various parameters using a non-linear optimization method so that the calculated values coincide with actual measured values such as groundwater level and groundwater temperature. In the inverse analysis, each parameter is obtained by first setting objective functions and minimizing them.

  For the objective function F (x) minimized by the optimization method, the square sum of the measured value and the calculated value represented by the following equation (20) is used.

  In the present invention, the Powell conjugate gradient method is adopted as a nonlinear optimization method. Powell's conjugate gradient method does not require a derivative for each parameter of the objective function required by many other optimization techniques, and can determine the optimal parameter using only the objective function. High versatility.

  In Powell's conjugate gradient method, when a minimum point of positive quadratic form is found in the direction of v from two distant points, the vector connecting the minimum points x1 and x2 obtained by each is conjugate with v. It takes advantage of the nature of being. Using this property, the minimum point can be found by repeating the direct search n times. Fig. 1.1 shows a schematic diagram of the conjugate direction, and Fig. 1.2 shows the basic algorithm of Powell's conjugate gradient method.

(Semi-analytical solution of thermal response test)
The analytical solution of the thermal response test can be expressed by the following equations (21) to (23).

In the conventional analysis method of the thermal response test, an approximate solution that approximates the asymptotic solution of the Kelvin source function to the second term is used. Increasing the term of the asymptotic solution of Kelvin's source function approaches the exact solution. FIG. 2.1 shows a graph in which the vertical axis is E (X), the horizontal axis is 1 / X, and the asymptotic solution term is gradually increased from the second term. From the graph, it can be seen that when the term of the asymptotic solution is increased, the period in which the approximate solution and the exact solution show the same curve becomes longer and approaches the accurate solution. In this graph, a graph in which the term of the asymptotic solution is increased to the 30th term is drawn, but the 16th term and thereafter are almost coincident with the accurate solution.

  FIG. 2.2 is a list of relative errors with respect to the approximate solution obtained by approximating the asymptotic solution up to the 30th term. As a whole, the error tends to increase as the value of 1 / X decreases, but it can be seen that the error varies depending on the number of terms to be approximated, and the error decreases as the number of terms increases. It should be noted that the portion with “−” is omitted because the error value becomes too large.

  From the above, it can be seen that by increasing the number of terms in the asymptotic solution, a semi-analytical solution closer to the accurate solution than the conventional approximate solution is obtained. In the present invention, an asymptotic solution (quasi-analytical solution) that approximates the asymptotic solution of the Kelvin source function to at least the 16th term, preferably to the 30th term is used.

(Parameters to be identified in analysis of thermal response test)
Next, in the thermal response test, ΔT, Q _H and b are known as observation data, and r, ρc and λ are unknown. In the present invention, α1 and α2 are obtained as follows, and the inverse analysis is performed by an identification program incorporating a conjugate gradient method.

Here, when formula (21) is rewritten using α ₁ and α ₂ , the following formulas (24) to (26) can be obtained.

  Further, as the evaluation scale, the following expressions (27) and (28) can be used. Expression (27) is an Euclidean norm obtained by raising the sum of the square error of the calculated value and the actually measured value to the power of 1/2. Formula (28) divides the sum of the absolute value errors of the calculated value and the actually measured value by the total number of data, and represents the error per piece of data.

(Application to pumping test analysis: identity between pumping test analysis solution and thermal response test analysis solution)
Next, the thermal response test and the pumping test both derive analytical solutions based on the heat conduction theory. Therefore, the thermal response test analysis method and analysis program of the present invention can be applied to the pumping test analysis. Below, the identity of the pumped water test analysis solution and the thermal response test analysis solution will be described.

  The pumping test is most commonly performed in the field as an in-situ test for determining groundwater flow system parameters such as a permeability coefficient and a storage coefficient. Here, we derive the exact solution of Thais (Theis, 1935), which is still widely used as an analytical solution for the unsteady groundwater flow equation when pumping water from a well with a screen in a confined aquifer, Confirm the identity with the thermal response test analysis solution.

Homogeneous isotropic certain amount Q _W groundwater from the well that fully penetrate into the formation with infinite extent at equal pressure is assumed to be pumped. When the horizontal two-dimensional groundwater flow in the homogeneous and isotropic confined aquifer is converted into a cylindrical coordinate system, it is expressed by the following equation (31).

On the other hand, assuming that the well radius is r _W , the initial conditions and boundary conditions are given by the following equations (32) to (34).

When the groundwater level lowering amount is set to s = h ₀ −h, the equation (31), the initial condition, and the boundary condition are rewritten as the following equations (35) to (38).

here,
In particular, Theis (1935) solved Equation (34) under the above initial and boundary conditions to obtain the following equation. When equation (31) is solved under the above initial conditions and boundary conditions, the following equations (39) to (41) are obtained.

  Equation (39) is called the Ties well function. W (u) in equation (39) is an exponential integral, and is approximated by the following equation (42) in a range where u is sufficiently small (generally u> 0.05 and error is 2.5% or less).

  Therefore, the equation (39) is approximated by the following equation (43).

  Equation (43) is called Jacob's approximate solution.

As described above, the thermal response test analysis solution and the pumping test analysis solution are based on the heat conduction theory if traced back to the original, and b (ρc) and bλ of the thermal response test analysis solution are S _c , Although T, the form of the formula is the same, and the identity of both was confirmed. Thereby, it turns out that the analysis method of the thermal response test by this invention can be similarly applied to a pumping test.

According to the present invention, compared with the conventional drawing method, it is objective in a short time (that is, without waiting for the heat transfer to be stable and the slope of the curve representing the change over time in the temperature rise to be constant). In addition, the thermal conductivity of the ground can be obtained with high accuracy. Moreover, according to this invention, the same effect can be acquired also in calculation of the water permeability coefficient by a pumping test. Specifically, according to the analysis method and analysis program of the present invention, the following effects can be obtained.
(1) By using the inverse analysis to which Powell's conjugate gradient method is applied, the parameters in the thermal response test and the pumping test can be evaluated objectively and accurately unlike the conventional drawing method.
(2) In the analysis of the thermal response test, in addition to the thermal conductivity, the volumetric heat capacity that could not be obtained by the conventional analysis can be obtained.
(3) By using a semi-analytical solution, it is possible to reproduce the initial test results that could not be evaluated with the conventional approximate solution. Therefore, the test period can be greatly shortened compared to the conventional drawing method. Thus, cost reduction can also be achieved.
(4) By using the analysis program of the present invention, parameters can be easily identified using a personal computer compared to the conventional method.
(5) The influence on the f / N value and thermal conductivity due to ground temperature gradient, groundwater flow can be confirmed.
(6) By using the data at the initial stage of the test, it is possible to obtain the thermal conductivity that is not affected by the flow and the earth temperature gradient.
(7) By using the analysis result of the thermal response test of the present invention and the analysis result obtained by the analysis program, it is possible to determine an appropriate well arrangement by drawing the heat transfer distribution by the quasi-analytic solution.

It is a conceptual diagram which shows the conjugate direction in the conjugate gradient method of Powell. It is explanatory drawing which shows the basic algorithm of the conjugate gradient method of Powell. It is the graph which compared the source function of Kelvin and the approximate solution. It is a table | surface which shows the relative error with respect to the approximate solution which approximated the asymptotic solution of the source function of Kelvin to the 30th term. It is a list which shows the conditions of the test case for verifying the validity of the identification program by this invention. It is a graph which shows the change of F value and DIF value in the test case 1. FIG. 7 is a graph showing changes in the value of bλ and the value of br ² (ρc) in test case 1. 6 is a graph showing a comparison result between a calculated value and a set value in test case 1. 6 is a list of analysis results of test case 1. 7 is a graph showing changes in F value and DIF value in test case 2. 7 is a graph showing changes in the value of bλ and the value of br ² (ρc) in test case 2. 6 is a graph showing a comparison result between a calculated value and a set value in test case 2. 10 is a list of analysis results of test case 2. It is explanatory drawing which shows an example of a thermal response test apparatus. It is a hydrogeological sectional view around the first point. It is a list of the 1st thermal response test conditions of the 1st point. It is a list of the 2nd thermal response test conditions of the 1st point. It is a list of the specifications of the measuring device and test device of the thermal response test of the 1st point. It is a graph which shows the 1st thermal response test result of a 1st point. It is a table | surface of the identification result by the reverse analysis of the 1st thermal response test of a 1st point. It is a graph which shows the comparison of the calculated value and actual value of the 1st thermal response test of a 1st point. It is a graph which shows the analysis result by the drawing method of the 1st thermal response test of a 1st point. It is a graph which shows the 2nd thermal response test result of the 1st point. It is a table | surface of the identification result by the reverse analysis of the 2nd thermal response test of a 1st point. It is a graph which shows the comparison of the calculated value and actual value of the 2nd thermal response test of a 1st point. It is a graph which shows the analysis result by the drawing method of the 2nd thermal response test of a 1st point. It is a graph which shows the temperature logging result of the 2nd point. It is a list of the thermal response test conditions of the 2nd point. It is a graph which shows the thermal response test result of the 2nd point. It is a table | surface of the identification result by the reverse analysis of the thermal response test of a 2nd point. It is a graph which shows the comparison of the calculated value and actual value of the thermal response test of a 2nd point. It is a graph which shows the analysis result by the drawing method of the thermal response test of the 2nd point. It is a list of the thermal response test conditions of the 3rd point. It is a graph which shows the thermal response test result of the 3rd point. It is a table | surface of the identification result by the reverse analysis of the thermal response test of a 3rd point. It is a graph which shows the comparison of the calculated value and actual value of the thermal response test of a 3rd point. It is a table | surface of the analysis result of the 1st time in a 1st point, and the 2nd thermal response test. It is a table | surface of the analysis result of the 2nd time of a 1st point, and the thermal response test of a 2nd point. It is a graph which shows the temperature logging result of the 2nd time of a 1st point, and a 2nd point. It is a table | surface of the analysis result of the 2nd time of a 1st point, and the thermal response test of a 3rd point. It is a graph which shows the analysis result at the time of changing the analysis data area in the 2nd thermal response test of the 1st point. It is a graph which shows the analysis result at the time of changing the analysis data area in the thermal response test of the 3rd point. It is a graph which shows the analysis result at the time of using initial stage data and latter half part data in the 2nd time of the 1st point. It is a graph which shows the analysis result at the time of using an initial stage data and latter half part data in a 2nd point. It is a graph which shows the analysis result at the time of using initial stage data and latter half part data in a 3rd point. It is a graph which shows the change of the heat conductivity with respect to the test period in the 1st time of a 1st point. It is a graph which shows the change of f / N value with respect to the test period in the 1st time of the 1st point. It is a list of the analysis result of each test period in the 1st time of the 1st point. It is a graph which shows the analysis result with respect to the test period in the 1st time of the 1st point. It is a graph which shows the change of the heat conductivity with respect to the test period in the 2nd time of a 1st point. It is a graph which shows the change of f / N value with respect to the test period in the 2nd time of the 1st point. It is a table | surface of the analysis result of each test period in the 2nd time of a 1st point. It is a graph which shows the analysis result with respect to the test period in the 2nd time of the 1st point. It is a graph which shows the change of the heat conductivity with respect to the test period in a 2nd point. It is a graph which shows the change of f / N value with respect to the test period in a 2nd point. It is a table | surface of the analysis result of each test period in a 2nd point. It is a graph which shows the analysis result with respect to the test period in a 2nd point. It is a graph which shows the change of the heat conductivity with respect to the test period in a 3rd point. It is a graph which shows the change of f / N value with respect to the test period in a 3rd point. It is a table | surface of the analysis result of each test period in a 3rd point. It is a graph which shows the analysis result with respect to the test period in a 3rd point. It is a table | surface of the pumping test conditions of a 1st aquifer. It is a table | surface of the pumping test conditions of a 2nd aquifer. It is a graph which shows the pumping test result of a 1st aquifer. It is a table | surface of the identification result by the reverse analysis about a 1st aquifer. It is a graph which shows the comparison of the calculated value and actual value about a 1st aquifer. It is a graph which shows the pumping test result of a 2nd aquifer. It is a table | surface of the identification result by the reverse analysis about a 2nd aquifer. It is a graph which shows the comparison of the calculated value about a 2nd aquifer, and a measured value.

  Embodiments of the present invention will be described below with reference to the drawings.

[Verification of parameter identification program using conjugate gradient method]
The present inventors applied the identification program developed to execute the parameter identification method by the conjugate gradient method adopted as the analysis method of the thermal response test to the test case, and verified the validity of the identification program.

(Verification procedure)
Verification of the validity of the parameter identification program using the developed conjugate gradient method was performed according to the following procedure.
1) In the two test cases shown as a list in FIG. 3.1, arbitrary values are given in advance to the two parameters α1 and α2, and the semi-analytical solution (formulas (24) to (26) is calculated by the calculation software “Excel”. ), Considering up to the 30th term). The amount of temperature change per hour is used as verification data.
2) With respect to α1 (= br ² (ρc)) and α2 (= bλ) as identification parameters, values other than arbitrary given values are given as initial values.
3) Parameters α1 and α2 are identified by inverse analysis.
4) DIF ≦ 0.0000001 is set as the calculation end condition.
(DIF = F _i −F _i−1 : difference between i-th F value and i−1th F value)

(Evaluation of parameters)
<Test case 1>
Fig. 3.2 is a graph showing the F value and DIF value at the number of searches, Fig. 3.3 is a graph showing bλ, br ² (ρc) at the number of searches, and Fig. 3.4 was obtained by inverse analysis. It is a graph which shows the comparison with the calculated value using parameter (alpha) 1 and (alpha) 2, and a setting value. FIG. 3.5 is a list of analysis results.

  The search is repeated so that the F value becomes the minimum value, and the search is terminated when the value no longer changes. The DIF value represents the difference from the previous F value, and shows a value close to zero where the F value does not change.

  In test case 1, the initial estimated value was doubled with respect to the set value and analyzed. From FIG. 3.3, it can be seen that the search is repeated and the parameter value approaches the set value, and from FIG. 3.4, the calculated value and the set value agree very well. Further, as shown in FIG. 3.5, the f / N value (error per data) is almost equal to zero, and it can be seen that a highly accurate result can be obtained.

<Test case 2>
3.6 is a graph showing the F value and DIF value in the number of searches, and FIG. 3.7 is a graph showing α2 (= bλ) and α1 (= br ² (ρc)) in the number of searches. .8 is a graph showing a comparison between the calculated value using the parameters α1 and α2 obtained by the inverse analysis and the set value. FIG. 3.9 is a list of analysis results.

  In test case 2, the initial estimated value for the set value was halved for analysis. From FIG. 3.7, it can be seen that the values of the parameters α1 and α2 approach the set values by repeating the search. From FIG. 3.8, it can be seen that the test value in Test Case 2 also matches the calculated value very well as in Test Case 1. Further, as shown in FIG. 3.9, the f / N value (error per data) is almost equal to zero, and it can be seen that a highly accurate result was obtained.

  Although verification was performed using two test cases with different default values and effective depths for the set values, very high accuracy results were obtained in both test cases, and the validity of the identification program of the present invention was verified. Was made. It was also confirmed that the results of the initial stage can be reproduced by using the semi-analytical solution.

1. In-situ thermal response test The present inventors analyzed a thermal response test conducted at three points using a parameter identification program using the conjugate gradient method according to the present invention. Below, the structure of the used thermal response test apparatus and the implementation procedure of the test will be described, and then the geological conditions, test conditions, and analysis results of the site sites at the three locations where the thermal response test was performed will be described.

[Configuration of thermal response test equipment]
FIG. 4 is an overall configuration diagram showing an example of a thermal response test apparatus for calculating the thermal conductivity of the ground from the actual measurement value of the thermal response test. The thermal response test apparatus 1 has a known configuration mainly for a vertical underground heat exchange well A in a closed type, and heats a heat medium and circulates the circulation system 2 and heat. It consists of a measurement system 3 that measures medium temperature, power consumption, circulating flow rate, and the like. The main components of the circulation system 2 are a circulation pump 4, an electric heater 5, a water tank 6, and the like, and the measurement system 3 is a temperature sensor 7, 8, 9, a flow meter 10, a data logger 11, a personal computer 12, and the like.

  In the thermal response test apparatus 1 having this configuration, the heat medium is heated by the electric heater 5 in the water tank 6 on the ground, and the heat medium is circulated in the pipe 13 by the circulation pump 4. Since the heated heat medium dissipates heat when passing through the borehole hole 15 formed in the ground 14 to be tested, the temperature difference between the inlet and outlet of the U-shaped tube 16 is measured by the temperature sensors 8 and 9, respectively. Evaluate the heat exchange characteristics of the formation.

  Connected to the personal computer 12 of the measuring instrument 3 are an input device 17 such as a keyboard and a mouse, a monitor such as a liquid crystal display, and an output device 18 such as a printer. The personal computer 12 is installed with a thermal response test analysis program according to the present invention (in the following description, it may be referred to as an “identification program”). By executing the analysis program, the heat exchange characteristics of the ground to be tested (e.g., the calculation process of the thermal conductivity of the ground) is performed based on the measurement data captured from the data logger 11.

  Here, an electric heater 5 connected to a power source having a stable voltage is used as the heat load. The electric heater 5 needs to have a capacity capable of applying a thermal load equivalent to that in the actual use of the GeoHP system. Further, the electric heater 5 is provided with a thermostat and a thermal fuse as a safety device to prevent a heating accident. The circulation pump 4 has the ability to circulate a flow rate equivalent to that in actual use, and is provided with a valve or an inverter for adjusting the flow rate. The flow meter 10 is preferably an electromagnetic flow meter with an accuracy of ± 0.5% or less. Also, platinum temperature resistors are used for the temperature sensors 8 and 9 for measuring the heat exchange well inlet / outlet temperature. The accuracy is desirably ± 0.1 ° C. or less in the assumed temperature range.

  If the heat insulation of the above-ground pipe 13 is insufficient, the load is not stable. Therefore, the length of the above-ground pipe 13 is minimized, and a heat insulating material is wound to provide sufficient heat insulation and waterproofing. An air vent valve 19 is provided at the top of the pipe, and an expansion tank 20 is provided to prevent water leakage due to thermal expansion of the heat medium. Further, the gas-liquid separator 21 separates the mixed gas and liquid in the circulation cycle. The data logger 11 is made to record heat exchange well inlet / outlet temperature, outside air temperature, and flow rate data.

[Procedure for thermal response test]
The execution procedure of the thermal response test in the vertical U-tube type underground heat exchange well using the thermal response test apparatus 1 is shown below.
(1) After excavating and finishing the heat exchange well, leave the heat exchange well for at least 3 days to restore the soil temperature to the natural state. Make sure that no other excavation work is being conducted in the vicinity of the heat exchange well to be tested, and if there is any groundwater pumping in the vicinity, stop it.
(2) Before designing the thermal response test apparatus 1, the temperature inside the mine (natural ground temperature) is measured from the ground surface to the bottom of the pit using a thermometer having a sensitivity of ± 0.1 ° C. The measurement depth sensation is desirably 10 m or less. (3) The thermal response test apparatus 1 and the heat exchange well A are connected with a heat-insulated hose or the like, and after the inside of the pipe 3 is filled with a heat medium, the air is vented. As the heat medium, water that is inexpensive and easy to handle is suitable, but a heat medium that is actually used after the system is completed may be used.
(4) The temperature sensors 7 to 9 and the flow meter 10 are connected to the data logger 11. It is desirable to measure the temperature of the heat exchange well entrance / exit of the heat medium at a position as close as possible to the entrance / exit of the heat exchange well (possibly below the ground surface).
(5) Fill the heat medium and leave it for several hours. After the heat medium temperature becomes equal to the formation temperature, energization of the heater 5 and circulation of the heat medium are started. The flow rate is the same as that used in actual system use, but the flow rate of the heat medium is in the turbulent region (reynolds number calculated with the diameter length of the U-shaped tube 16 as the representative length is 2,300 or more), temperature In consideration of measurement error (± 0.1 ° C.), if possible, it is desirable to set the temperature difference at the heat exchange well entrance / exit to be 4 ° C. or more.
(6) It is recommended that the heat load by the heater be close to the load of the GeoHP system to be actually installed, and the heating period is 60 hours as a standard and 48 hours as the shortest.
(7) After the circulation is completed, the thermal response test apparatus 1 and the ground pipe 13 are drained, and the thermal response test apparatus 1 is withdrawn.

[Example 1: Thermal response test and parameter identification results at the first point]
(1) Geological conditions Figure 5.1 is a cross-sectional view based on deep well drilling data at the first point where the thermal response test was conducted. The geology near the first point is mainly composed of gravel layers, and sandwiched between clay layers and clay-mixed sand layers. Of these, the gravel layer is an aquifer, and the clay layer and clay mixed sand layer is a non-permeable permeable layer.

  The borehole in which the thermal response test was performed has a U-tube inserted to a depth of 76 m, and substantially corresponds to the first aquifer and the second aquifer. From the results of the electrical logging shown in Fig. 5.1, there are parts with different specific resistance values even within the same aquifer, and the water permeability of the ground is uneven.

(2) Thermal response test conditions The thermal response test at the first point was conducted twice, and the test implementation period was March 25-28, 2011, and the second was November 17-20, 2011. It is. Fig. 5.2 and Fig. 5.3 show the heating period, average heating amount, average flow rate, effective depth of underground heat exchange well, initial temperature of underground heat exchange well, filler, survey hole diameter, U tube used Indicates. Fig. 5.4 shows the specifications of the measurement equipment and thermal response test equipment used. The test is carried out using the same measuring equipment for the first time and the second time.

(3) Measurement results and identification results <First time at the first point (March 25-28, 2011)>
FIG. 5.5 is a graph showing measurement data (forward temperature, return temperature, average temperature, flow rate, heating amount, outside temperature) obtained by the thermal response test. The heating period was 3 days from March 25 to 28, 2011, the average heating amount was 3557 (W), the average flow rate was 20.9 (L / min), and the effective depth was 76.0 (m). . The formation temperature before heating was stable at about 14.1 (° C.), but after 72 hours from the start of the test, the going-out temperature was about 26.5 (° C.) and the return temperature was about 23.5 (° C.).

  Fig. 5.6 is a list showing the identification results by inverse analysis, and Fig. 5.7 is a graph showing a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. The value of the thermal conductivity obtained from the inverse analysis is 2.33 (W / m / K), and the calculated value and the measured value graph using this value agree very well. The number of data used in the reverse analysis was 4320 (pieces), and the f / N value (error per data) was 0.075 (° C.).

  Fig. 5.8 is a graph showing the result of analysis by a conventional drawing method. The value of thermal conductivity obtained by the drawing method was 2.40 (W / m / K), which was close to the result obtained by inverse analysis. The data interval used for the analysis is 10.3 (h) to 72.0 (h).

<The second at the first point (November 17 to 20, 2011)>
FIG. 5.9 is a graph showing measurement data (forward temperature, return temperature, average temperature, flow rate, heating amount, outside temperature) obtained by the thermal response test. The heating period was 3 days from November 17 to 20, 2011. The average heating amount was 3,964 (W), the average flow rate was 20.2 (L / min), and the effective depth was 76.0 m. The formation temperature before heating was stable at about 14.1 ° C, but after 72 hours from the start of the test, the going-out temperature was about 27.0 ° C and the return temperature was about 24.0 ° C.

  Fig. 5.10 is a list showing the identification results by inverse analysis, and Fig. 5.11 is a graph showing a comparison between the calculated values of the quasi-analysis solution using the identification results and the actual measured values. Similar to the first result, the calculated value and the measured value are in good agreement, and the thermal conductivity value obtained from the inverse analysis is 2.52 (W / m / K). It was a little larger than the result. Incidentally, the number of data used in the inverse analysis was 4320 (pieces), and the error per one data was 0.056 (° C.).

  Figure 5.12 shows the result of analysis using the drawing method. The value of thermal conductivity obtained by the drawing method was 2.59 (W / m / K), which was close to the result obtained by inverse analysis. The data interval used for the analysis is 24.0 (h) to 72.0 (h).

[Example 2: Thermal response test and parameter identification results at the second point]
The thermal response test at the second point is conducted from December 24 to 29, 2010. Below, the geological conditions at the site, thermal response test conditions, and identification results will be described.

(1) Geological conditions Since geological confirmation by core boring has not been carried out at the second point where the thermal response test was conducted, the geology is assumed from the mining situation and existing data. The geology assumed by this excavation seems to be mainly composed of a gravel layer mixed with clay, cobblestone, etc., but as shown in Fig. 6.1, the temperature by temperature logging at a depth of around 80m or later. Since the phenomenon of increasing ascending slope is observed, it is highly likely that the rock has changed to a Neogene rock that is considered to be a basement rock. The U tube installation depth is 143.75 m.

Fig. 6.2 is a list showing the heating period, average heating amount, average flow rate, effective depth of underground heat exchange well, initial temperature of underground heat exchange well, filler, survey hole diameter, and U tube used during the test. It is. The specifications of the measuring instrument and the thermal response test apparatus used are the same as those at the first point (see FIG. 5.4).

(2) Measurement Result and Identification Result FIG. 6.3 is a graph showing measurement data (forward temperature, return temperature, average temperature, flow rate, heating amount, outside air temperature) obtained by the thermal response test. The heating period was 3 days from December 24 to 27, 2010, the average heating amount was 5,716 (W), the average flow rate was 10.4 (L / min), and the effective depth was 143.75 m. The formation temperature before heating was stable at about 16.8 ° C, but after 72 hours from the start of the test, the going-out temperature was about 34.0 ° C and the return temperature was about 26.0 ° C.

  Fig. 6.4 is a list showing the identification results by inverse analysis, and Fig. 6.5 is a graph showing a comparison between the calculated values of the quasi-analytical solution using the identification results and the actually measured values. The calculated values and the measured values are in good agreement. The value of thermal conductivity obtained from the inverse analysis is 1.79 (W / m / K), and compared with the identification results (2.33 kW, 2.51 kW) in the two tests at the first point, It became a small value. Further, the f / N value (error with respect to one piece of data) was 0.158 (° C.), which was larger than the identification result at the first point. This is thought to be due to the presence of underground conditions or heat transfer phenomena that are not considered in heat conduction theory. The number of data used at the time of reverse analysis is 4,320 (pieces).

  Fig. 6.6 is a graph showing the results of analysis using the drawing method. The value of thermal conductivity obtained by the drawing method was 1.53 (W / m / K). Incidentally, the data interval used for the analysis is 17.2 (h) to 72.0 (h).

[Example 3: Thermal response test and parameter identification results at the third point]
The thermal response test at the third point was conducted from October 13 to 16, 2011. The geological conditions, thermal response test conditions, and identification results will be described below.

(1) Geology The third point is a point where groundwater is abundant and groundwater flow is expected to exist. In the well where the thermal response test was conducted this time, a U tube was inserted to a depth of 99 m. In addition, detailed information on the geological structure was not obtained, so it will not be described here.

(2) Thermal response test conditions Figure 7.1 shows the heating period, average heating amount, average flow rate, effective depth of underground heat exchange well, initial temperature of underground heat exchange well, filler, investigation hole diameter, U tube used It is a list which shows. The specifications of the measuring instrument and the thermal response test apparatus used are the same as those at the first point (see FIG. 5.4).

(3) Measurement Result and Identification Result FIG. 7.2 is a graph showing measurement data (forward temperature, return temperature, average temperature, flow rate, heating amount, outside air temperature) obtained by the thermal response test. The heating period was 3 days from October 13 to 16, 2011, the average heating amount was 4,667 (W), and the average flow rate was 10.4 (L / min). The effective depth is 99.0 m. The formation temperature before heating was stable at about 17.8 ° C., but after 72 hours from the start of the test, the going-out temperature was about 28.8 ° C. and the return temperature was about 25.8 ° C.

FIG. 7.3 is a list showing identification results by inverse analysis, and the value of thermal conductivity obtained by inverse analysis was 3.01 (W / m / K). Fig. 7.4 is a graph showing a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. The graphs of the calculated value and the actually measured value have some portions that do not coincide with each other, but almost coincide as a whole. The f / N value (error per data) was 0.187 (° C.), which was a large result compared to the result at the first point. This is thought to be due to the presence of underground conditions or heat transfer phenomena that are not considered in heat conduction theory. The number of data used at the time of this reverse analysis is 4,338 (pieces).

[Consideration of test results]
(1) Calculation of analysis accuracy and volumetric heat capacity From the two thermal response tests at the first point and the analysis results by the inverse analysis method of the results, there are very small errors and highly accurate analysis results are obtained. I understand that. Also, the volumetric heat capacity that could not be obtained conventionally can be obtained if r (distance from the well) is known.

(2) Effect of groundwater level on thermal conductivity Figure 8.1 is a list showing the results of two thermal response tests at the first point. Comparing the results, the thermal conductivity is 2.33 (W / m / K) in the first round, whereas the thermal conductivity is 2.51 (W / m / K) in the second round. A little bigger. Since the same well is being tested twice, the difference will be discussed. It has been confirmed that the groundwater level on both test days was 1.5 (m) deeper in the first round than in the second round due to seasonal variations.

  According to literature values, the thermal conductivity of water and the thermal conductivity of air are 0.594 (W / m / K) and 0.0241 (W / m / K), respectively, and the thermal conductivity of water is higher. Therefore, the thermal conductivity increases as the groundwater level increases. For this reason, it is thought that the thermal conductivity of the 2nd time with a thick saturated part was larger than the 1st time.

(3) Influence of Geothermal Gradient on Thermal Conductivity Fig. 8.2 is a list showing the second analysis result at the first point and the analysis result at the second point. Comparing the two, the thermal conductivity at the second point is 1.79 (W / m / K), the second thermal conductivity at the first point is 2.51 (W / m / K), the second The thermal conductivity at the point was smaller. Further, the f / N value (error per data) is 0.158 (° C.) at the second point, 0.056 (° C.) at the second point of the first point, and data 1 at the second point. The error was about 3 times per hit.

  Therefore, the ground temperature distribution before the start of both tests was examined, and the results are shown in Fig. 8.3. From Fig. 8.3, the ground temperature distribution at the first point is almost constant regardless of the depth, whereas the ground temperature distribution at the second point is non-uniform, and the temperature increases as the depth increases from around 60m depth. Yes. Comparing the ground temperature of 20m and 140m in depth, it is about 20 ° C at 140m point compared to about 15 ° C at 20m point, and there is a temperature difference of 5 ° C. Therefore, the amount of underground heat exchange decreases as the depth increases. The ground temperature gradient is generally 0.03 (° C./m), but the ground temperature gradient at the second point is 0.053 (° C./m) and tends to be a little large.

  When there is a ground temperature gradient as in the second point, the ground temperature rises as the depth increases, and the amount of underground heat exchange decreases. Therefore, it is thought that the 2nd point which shows non-uniform ground temperature distribution showed the heat conductivity smaller than the 1st point. The f / N value (error per data) is larger than the result at the first point because it is contrary to the precondition that the underground heat exchange amount is constant in the depth direction of the source theory. It is thought that it became.

(4) Influence of groundwater flow on thermal conductivity Fig. 8.4 is a list showing the second analysis result of the first point and the analysis result of the third point. Comparing the two, the thermal conductivity at the third point is 3.01 (W / m / K), the thermal conductivity at the first point is 2.51 (W / m / K), and the thermal conductivity at the third point. The rate showed a larger value. F
/ N value (error per data) is 0.186 (° C) at the third point, 0.056 (° C) at the first point, and the difference between the theoretical solution and the measured value is larger at the third point. became.

  Looking at the topographical conditions at the third point, there is a confluence of two rivers in the vicinity, and there is abundant groundwater and groundwater flow.

  Fig. 8.5 and Fig. 8.6 are graphs showing the analysis results when the data section used for the analysis is changed to the three sections of the whole section, the latter half, and the initial stage at the first point and the third point. is there.

  In the case of the first point, no difference is seen between the thermal conductivity and the f / N value (error per data) regardless of the data section. On the other hand, in the case of the third point, there is a clear difference between the thermal conductivity and the f / N value (error per data) depending on the data section to be analyzed. Comparing the analysis results using only the initial stage data and the analysis results using the latter half of the data, there is a difference of 1.31 (W / m / K) in thermal conductivity, and the f / N value (data The error per one) is 0.09 (° C.) and 0.144 (° C.), respectively, and the f / N value (error per data) is smaller when using the initial stage data, It can be seen that the heat conduction theory agrees.

  As shown in Fig. 8.6, the effect of groundwater flow can be considered as the reason why different results were obtained depending on the data section. In the heat conduction theory, since it is assumed that all heat transfer is performed by heat conduction, the difference between the measured value and the calculated value increases as the influence of advection accompanying groundwater flow increases. At the third point, groundwater flow is considered to exist due to topographical conditions, but the f / N value (error per data) is small when using the initial stage data where heat conduction is dominant, It can be seen that the f / N value (error per piece of data) increases when using the latter half of the data where the influence of groundwater flow increases.

(5) Influence on the thermal conductivity by the analysis data section As mentioned in the discussion (4), in this analysis, it is assumed that all heat transfer is performed by heat conduction. If there is, there will be a large difference between the calculated value and the measured value. However, even when there is a movement other than the thermal conductivity, the movement due to thermal conduction is dominant because the temperature gradient is large at the initial stage when the temperature starts to rise. Therefore, the true thermal conductivity can be obtained by performing analysis using the data at the initial stage.

  Figures 8.7, 8.8, and 8.9 show the analysis results and data in the second half of the data at the initial stage at the second, second, and third points, respectively. The analysis result using is shown.

  The second value at the first point has no effect on the thermal conductivity and f / N value (error per data) even if the analysis data section changes. On the other hand, the second point and the third point are affected by the ground temperature gradient and the groundwater flow, respectively, when the analysis is performed using the data in the latter half. In addition, in the analysis results using the data at the initial stage, the thermal conductivity was close to the value in all three cases, and the f / N value (error per data) was small.

  From the above results, it can be seen that it is better to use data at the initial stage where heat conduction is dominant when it is desired to obtain true thermal conductivity that is not affected by ground temperature gradient or groundwater flow.

[Examination of accuracy of analysis results when test period is shortened]
In the analysis method according to the inverse analysis of the present invention, the test result at the initial stage that cannot be evaluated by the conventional approximate solution can be utilized by using the semi-analytical solution. For this reason, there is a possibility that a good analysis result can be obtained in a test period shorter than the conventional method. Here, the accuracy of the analysis result when the analysis is performed by reducing the number of data used in the inverse analysis method step by step is examined.

(1) First test at the first point The test period was gradually reduced to 3.0 days, 2.5 days, 2.0 days, 1.5 days, and 1.0 days in 0.5 day increments. The thermal conductivity and f / N value (error per data) are shown in Fig. 9.1 and Fig. 9.2, respectively. Figure 9.3 summarizes the analysis results. From Fig. 9.3, even when the test period is shortened, there is no significant difference in the thermal conductivity λ (W / m / K), and the f / N value (error per data) is also 0.077-0. .071 (° C.), a highly accurate analysis result was obtained.

  Fig. 9.4 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the actual measured value. The calculated values and the actual measured values are in good agreement, and by using semi-analysis, the test results at the initial stage that could not be evaluated by the conventional approximate solution could be used.

(2) The second test period at the first point was reduced in steps of 0.5 days in steps of 3.0 days, 2.5 days, 2.0 days, 1.5 days, and 1.0 days. The thermal conductivity and f / N value (error per one data) are shown in FIG. 9.5 and FIG. 9.6, respectively. Figure 9.7 summarizes the analysis results.

  From Fig. 9.7, no significant difference is observed in the thermal conductivity λ (W / m / K) obtained even when the test period is reduced. When the thermal conductivities of the test period of 3.0 days and 1.0 day are compared, they are 2.51 (W / m / K) and 2.58 (W / m / K), respectively, and the difference is 1.028%. And small. Further, the f / N value (error per data) was as small as 0.060 (° C.) to 0.053 (° C.), and a highly accurate analysis result was obtained even when the test period was shortened.

  Fig. 9.8 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. Similar to the first result at the first point, the calculated value and the actual measured value are in good agreement, and by using the semi-analysis, the test results at the initial stage that could not be evaluated by the conventional approximate solution are utilized. did it.

(3) Second point (December 24-27, 2010)
In another response test conducted at the second point, the test period was gradually reduced to 3.0 days, 2.5 days, 2.0 days, 1.5 days, and 1.0 days in 0.5 day increments. Fig. 9.9 and Fig. 9.10 show the thermal conductivity and f / N value (error per one piece of data), respectively. Figure 9.11 summarizes the analysis results.

  From Fig. 9.11, the identified thermal conductivity value is 1.79 (W / m / K) to 2.09 (W / m / K), and the thermal conductivity value increases with increasing test period. It is getting smaller. In the formation where the test was conducted, the temperature gradient was confirmed from the results of temperature logging. Therefore, it is considered that heat is supplied at the bottom of the borehole and the apparent thermal conductivity is reduced.

  From Fig. 9.9, it can be seen that the value of thermal conductivity is not stable. Therefore, when the test period is extended, the apparent thermal conductivity is expected to be further reduced. Moreover, f / N value (error per one data) was 0.112 (degreeC)-0.168 (degreeC). This is because the heat conduction is dominant in the initial stage data as described in the discussion (4) regarding the test results.

  Fig. 9.12 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. The f / N value (error per piece of data) is smaller when the data at the initial stage is used, and the calculated value and the actually measured value are in good agreement. By using quasi-analysis, the test results at the initial stage that could not be evaluated by the conventional approximate solution could be utilized.

(4) Third point (October 13-16, 2011)
In the thermal response test conducted at the third point, the test period was gradually reduced to 3.0 days, 2.5 days, 2.0 days, 1.5 days, and 1.0 days in 0.5 day increments. Fig. 9.13 and Fig. 9.14 show the thermal conductivity and f / N value (error per piece of data), respectively. Fig. 9.15 summarizes the analysis results.

  From Fig. 9.15, the value of thermal conductivity is 2.42 (W / m / K) to 3.01 (W / m / K), and the value of thermal conductivity increases with increasing test period. Yes. The f / N value (error per one piece of data) is 0.107 (° C.) to 0.187 (° C.), and becomes larger as the test period is longer. This is considered to be the effect of groundwater flow. In the initial stage when the temperature starts rising, the thermal gradient is dominant because the temperature gradient is large, but in the latter half, the advection is dominant, the f / N value (error per data) is large, and the apparent thermal conductivity. The value of is considered to have increased.

  From Fig. 9.13, the value of thermal conductivity is not yet stable, and it is predicted that the apparent thermal conductivity will be further increased if the test period is extended. Deviation from thermal conductivity.

  Fig. 9.16 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. The f / N value (error per piece of data) is smaller when the data at the initial stage is used, and the calculated value and the actually measured value are in good agreement. By using quasi-analysis, the test results at the initial stage that could not be evaluated by the conventional approximate solution could be utilized.

2. Pumping test analysis Next, the results of applying the identification program of the present invention to the pumping test conducted on January 18, 2011 at the first point where the thermal response test was performed will be considered.

(1) Test outline In order to grasp the well capacity of the first aquifer and the second aquifer, a pumping test for each layer was conducted. The implementation date is January 18, 2011. Figures 10.1 and 10.2 show the pumping time, pumping volume, aquifer thickness, and distance between pumping well and observation well in each aquifer.

(2) Pumping test results and identification results a) First aquifer A pumping test result in the first aquifer is shown in Fig. 10.3. It represents the fluctuation of the groundwater level of the observation well at a distance of 3.8m from the pumping well. The groundwater level continued to decrease after 1 min, and a water level drop of 0.246 m was confirmed at 65 min. Since almost no change in the water level was observed after 65 min, the test was completed in 120 min.

FIG. 10.4 shows the identification result by inverse analysis. FIG. 10.5 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the actually measured value. From this figure, the calculated value and the actually measured value seem to agree with each other, but from FIG. 10.4, the f / N value (error with respect to one piece of data) is 0.045 (m), showing a slightly large value. The water permeability coefficient obtained by the inverse analysis was 1.39 (m ² / min). Further, the water permeability coefficient was 1.39 (m ² / min) divided by the aquifer layer thickness of 32.7 (m), and the water permeability coefficient was 0.042 (m / min). This value is larger than the general hydraulic conductivity value. From these, it is considered that the first aquifer is leaking. When the aquifer is leaking, it is considered that the f / N value (error per one piece of data) has increased because the Hantus-Jacob equation is generally used instead of the Theis equation. .

  In this pumping test, since the distance between the pumping well and the observation well was known, the storage coefficient could be obtained. The number of data used at the time of reverse analysis is 29 (pieces).

b) Second aquifer Fig. 10.6 shows the pumping test results in the second aquifer. It represents the fluctuation of the groundwater level of the observation well at a distance of 3.8m from the pumping well. The groundwater level continued to decrease after 1 min, and a water level drop of 0.240 m was confirmed in 90 min. Since the change in the water level was hardly seen after 90 min, the test was completed in 160 min.

FIG. 10.7 shows the identification result by inverse analysis, and FIG. 10.8 shows a comparison between the calculated value of the semi-analytical solution using the identification result and the field measurement value. Figure 10.8 shows that the calculated value and the actual measured value agree with each other, but as with the first aquifer, the f / N value (error relative to one piece of data) is 0.069 (m), indicating a large value. It was. The water permeability coefficient obtained by the inverse analysis was 0.92 (m ² / min). Moreover, the water permeability coefficient of 0.92 (m ² / min) was divided by the aquifer thickness of 21.2 (m), and the water permeability coefficient was 0.043 (m / min). This value is larger than the general hydraulic conductivity value. From these, it is considered that the second aquifer is leaking. When the aquifer is leaking, it is considered that the f / N value (error per one piece of data) has increased because the Hantus-Jacob equation is generally used instead of the Theis equation. . The number of data used at the time of reverse analysis is 34 (pieces).

1 Thermal Response Test Equipment 2 Circulation System 3 Measurement System 4 Circulation Pump 5 Electric Heater (Heating Heater)
6 Water tank 7-9 Temperature sensor 10 Flow meter 11 Data logger 12 Personal computer

Claims (12)

A thermal response test analysis method for evaluating a heat exchange characteristic of the ground based on a change over time of a temperature rise amount in a ground to be investigated measured by a thermal response test,
The temperature rise of the ground is defined by the Kelvin source function expressed by equation (A), and up to at least the 16th term in the power series expansion equation of exponential integral E (X) is adopted as an approximation formula of the source function. Using the approximate expression
Using a nonlinear optimization method based on Powell's conjugate gradient method, a calculated value Tr of a temperature rise obtained when an unknown parameter included in the approximate expression is set to a predetermined value, and measured by the thermal response test Inverse analysis of the parameters is performed so that an error from the measured value Tri of the measured temperature rise is minimized.
In the inverse analysis, the parameters to be identified are expressed by the following equations (B) and (C) using the radius r, the density ρ, the specific heat c, and the thermal conductivity λ, which are unknown quantities in the source function. Α1 and α2
An analysis method of a thermal response test, wherein at least the thermal conductivity λ is calculated from the thermal conductivity λ and the volumetric heat capacity ρc of the ground using the parameters α1 and α2 identified by the inverse analysis. In claim 1,
An analysis method of a thermal response test, characterized in that an approximate expression employed up to the 30th term in the power series expansion expression of exponential integral E (X) is used as an approximate expression of a Kelvin source function. In claim 1 or 2,
Using the measured values of at least two thermal response tests conducted at different times for the same point, calculate the thermal conductivity of the formation at the same point at each time point,
An analysis method of a thermal response test, wherein a difference in the calculated thermal conductivity is obtained as an index for determining whether or not there is a change in groundwater level at each time point. In any one of claims 1 to 3,
The actual measurement value obtained by the thermal response test is divided into initial stage data from the test start time to the time when a predetermined time has passed, and the latter half data after the time,
The initial stage data is used to calculate the thermal conductivity and the f / N value that is an error per data represented by the formula (D), and the latter half data is used to calculate the thermal conductivity and the f / N value is calculated,
The difference between the two calculated thermal conductivities and the difference between the two calculated f / N values is obtained as an index for determining the presence or absence of a geothermal gradient in the formation depth direction or the presence or absence of groundwater flow. Analysis method of thermal response test. A thermal response test analysis program used for evaluating the heat exchange characteristics of the ground based on the change over time of the temperature rise in the ground to be measured measured by the thermal response test,
Approximate expression using computer up to at least the 16th term in exponential integral E (X) power series expansion expression as the approximate expression of Kelvin's source function represented by expression (A) with the temperature rise of the ground Function as a computing means to perform computations using
The computer uses a nonlinear optimization method based on Powell's conjugate gradient method to calculate a temperature rise amount Tr obtained when an unknown parameter included in the approximate expression is set to a predetermined value, and the thermal response. In order to minimize the error from the actual measured value Tri of the temperature rise measured by the test, it functions as an inverse analysis means for performing an inverse analysis of the parameters,
In the inverse analysis means, the parameters to be identified are expressed by equations (B) and (C) using the radius r, density ρ, specific heat c, and thermal conductivity λ, which are unknown quantities in the source function. Α1 and α2
Furthermore, using the parameters α1 and α2 identified by the inverse analysis, causing the computer to function as calculation means for calculating at least the thermal conductivity λ of the ground thermal conductivity λ and the volumetric heat capacity ρc. An analysis program for thermal response tests. In claim 5,
An analysis program for a thermal response test, characterized in that an approximate expression adopted up to the 30th term in the power series expansion expression of exponential integral E (X) is used as the approximate expression of the Kelvin source function. In claim 5 or 6,
By using the measured values of at least two thermal response tests performed at different times for the same point by the inverse analysis means and the calculation means, the thermal conductivity of the formation at the same point at each time point is calculated,
Furthermore, in order to determine whether there is a change in the groundwater level at each time point, the computer functions as a thermal conductivity difference calculation means for calculating the calculated thermal conductivity difference. Analysis program. In any one of claims 5 to 7,
The inverse analysis means divides the actual measurement value obtained by the thermal response test into initial stage data from a test start time to a time when a predetermined time has elapsed and second half data after the time, and uses the initial stage data. F / N value, which is an error per one piece of data represented by the formula (D), and the thermal conductivity and the f / N value are calculated using the latter half data. And
Further, in order to determine the presence or absence of a geothermal gradient in the depth direction of the formation or the presence or absence of groundwater flow, the computer obtains the difference between the two calculated thermal conductivities and the difference between the two calculated f / N values. An analysis program for a thermal response test, characterized in that it functions as a difference calculation means. An analysis method of a pumping test for evaluating the groundwater flow characteristics of the ground based on the change over time of the groundwater level drop in the ground to be investigated measured by the pumping test,
The groundwater level lowering amount of the ground is defined by the Ties well function expressed by the equation (E), and at least the 16th term in the power series expansion formula of the exponential integral W (u) is adopted as an approximation formula of the well function. Use an approximate expression,
Using a nonlinear optimization method based on Powell's conjugate gradient method, calculated by calculating the groundwater level drop when the unknown parameter included in the approximate expression is set to a predetermined value, and the pumping test. In order to minimize the error with the actual measured value of the groundwater level drop that was made, perform the inverse analysis of the parameters,
In the inverse analysis, the parameters to be identified are set to α1 and α2 represented by the following equations using the radius r, the water permeability coefficient T, and the storage coefficient Sc that are unknown quantities in the well function,
α1 = r ² Sc
α2 = T
An analysis method for a pumping test, wherein at least the water permeability coefficient T is calculated from the parameters α1 and α2 identified by the inverse analysis, among the water permeability coefficient T and the storage coefficient Sc of the ground. In claim 9,
An analysis method of a pumping test characterized by using an approximate expression adopted up to the 30th term in a power series expansion expression of exponential integral W (u) as the approximate expression of the well function of Ties. A pumping test analysis program used to evaluate the groundwater flow characteristics of the ground based on the change over time of the groundwater level drop in the ground subject to survey measured by the pumping test,
As an approximation formula for the well function of the Ties expressed by equation (E), the computer uses an approximation formula that employs up to at least the 16th term in the power series expansion formula of the exponential integral W (u). Function as a computing means to perform computations using
The computer uses a nonlinear optimization method based on Powell's conjugate gradient method to calculate a groundwater level drop obtained when each unknown parameter included in the approximate expression is set to a predetermined value, and the pumping In order to minimize the error from the actual measured value of the groundwater level drop measured by the test, it functions as an inverse analysis means for performing the inverse analysis of the parameters,
In the inverse analysis means, the parameters to be identified are α1 and α2 represented by the following equations, using the radius r, the water permeability coefficient T, and the storage coefficient Sc that are unknown quantities in the well function,
α1 = r ² Sc
α2 = T
Further, the computer is caused to function as a calculation means for calculating at least the water permeability coefficient T among the water permeability coefficient T and the storage coefficient Sc of the ground from the parameters α1 and α2 identified by the inverse analysis. Analysis program for thermal response test. In claim 11,
An analysis program for a pumping test characterized in that an approximate expression employed up to the 30th term in the power series expansion expression of exponential integral W (u) is used as the approximate expression of the well function of Ties.