CN104237301A - In-situ thermal response testing method for layered rock and soil thermophysical properties - Google Patents

In-situ thermal response testing method for layered rock and soil thermophysical properties Download PDF

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CN104237301A
CN104237301A CN201410479673.XA CN201410479673A CN104237301A CN 104237301 A CN104237301 A CN 104237301A CN 201410479673 A CN201410479673 A CN 201410479673A CN 104237301 A CN104237301 A CN 104237301A
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毕文明
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BEIJING HUAQING RONGHAO NEW ENERGY DEVELOPMENT CO LTD
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Abstract

The invention provides an in-situ thermal response testing method for layered rock and soil thermophysical properties. According to the in-situ thermal response testing method for the layered rock and soil thermophysical properties, a thermal response test is performed on an assembled buried tube heat exchanger, the theoretical value of the average temperature of a group of circulating fluids is calculated through introduction of buried tube parameters and related test data in a formula, the actual value of the average temperature of the group of circulating fluids is measured through equipment, and the theoretical value and the actual value are calculated with a parameter estimation method, so that layered rock and soil thermal thermophysical property parameters can be determined. The in-situ thermal response testing method for the layered rock and soil thermophysical properties puts forwards a column heat source model and is applicable to tests of the layered thermophysical property parameters. The change of thermal resistance in drilled holes in the depth direction and the change of the heat exchange power in the drilled holes in the depth direction are considered, and the rock and soil thermophysical property parameters at a certain layer can be calculated accurately.

Description

A kind of geotechnical stratified hot physical property in-situ heat response test method
Technical field
The present invention relates to technical field of ground source heat pump, refer to a kind of geotechnical stratified hot physical property in-situ heat response test method especially.
Background technology
In the prior art, all be that a line source model is regarded in the ground heat exchanger equivalence of U-shaped as by shape to the method for testing of ground thermal property parameter, by measuring the thermal physical property parameter of correlation data calculation outlet source model entirety, this model method can only make overall judgement to the thermal physical property parameter of ground.When practice of construction, the depth of burying of ground heat exchanger is darker, through more than the 100m that is everlasting, this causes burying underground in scope at ground heat exchanger, the distribution pattern of ground is uneven distribution, and underground water cut and seepage action of ground water speed also different, cause, at the rock-soil layer of different depth, there is different thermal physical property parameters, line source model cannot draw the thermal physical property parameter of the rock-soil layer in certain depth accurately, to the data that follow-up design cannot provide.
Existing post heat source model proposes based on not stratified ground thermal property parameter test method, directly can not apply mechanically and calculate layering ground thermal property parameter.Must improve on the original basis, propose a kind of newly, be applicable to the models and methods of the hot Calculation of Physical Properties of layering.
Summary of the invention
The present invention proposes a kind of geotechnical stratified hot physical property in-situ heat response test method, and the hot physical property measurement method in prior art that solves can not to the problem of specifying the thermal physical property parameter of rock-soil layer to measure.
Technical scheme of the present invention is achieved in that
The invention provides a kind of geotechnical stratified hot physical property in-situ heat response test method, comprise the steps:
The first step, ground heat exchanger is connected with geo-thermal response test instrument, form heat supplying loop, and by temperature-measuring system of distributed fibers, ground heat exchanger is measured, by geo-thermal response test instrument thermal response test carried out to ground heat exchanger and obtain the data on flows in ground heat exchanger, being obtained in ground heat exchanger the temperature data of multiple points for measuring temperature from top to bottom by temperature-measuring system of distributed fibers;
Second step, arranges temperature data, and in units of at least 5m, distance carries out layering from top to bottom to ground heat exchanger, and the length of every layer is one or several unit distance, and the temperature data of all points for measuring temperature in every layer is summed up formation data group;
3rd step, sets up plume source model, brings the data group data of kth layer into calculating formula:
T f 1 k = T 0 + Q k ( 1 4 πr i h + 1 2 πk p ln n r p n r p - ( r p - r i ) ) 1.7 πr e L + Q k 4 π λ s L ( 2 h + ln 4 z C - 4 h - α 1 k 2 α 1 k z + α 1 k - 2 2 α 1 k z ln 4 z C ) ,
By estimation λ s, ρ sc svalue calculate T f1kone group of theoretical value, wherein,
T f1kfor the theoretical medial temperature of kth layer ground heat exchanger fluid circulating;
T 0for kth layer ground initial temperature;
Q kfor the heating power of kth layer, Q k=1163*G* Δ T k, G is volumetric flow rate, Δ T kfor the import and export circulating fluid medial temperature temperature difference of kth layer;
R ifor ground heat exchanger internal diameter;
R pfor ground heat exchanger external diameter;
R efor the external radius when buret;
L is the length of unit distance;
Z is fourier coefficient, z=(a st/ (r e 2)), a s=(λ s/ (c sρ s)), a sfor the thermal diffusion coefficient of ground, λ sfor ground mean coefficient of heat conductivity; c sρ sfor ground specific heat per unit volume;
α 1k=(2 π r e2c sρ s)/(c cylinder), c cylinderfor wellhole unit length thermal resistance;
K pfor the coefficient of heat conductivity of tubing;
C=e 0.5772=e γ, C is hot-fluid short circuit correction factor, and γ is Euler's constant;
H=2 π λ sr ' g, R ' gfor unit length thermal contact resistance;
N is the pipe number quantity of ground heat exchanger.
4th step, calculates the actual average temperature T of kth layer ground heat exchanger fluid circulating by the data group of kth group f2k;
5th step, to one group of T that the 3rd step draws f1kthe T that value and the 4th step draw f2kvalue carries out Parameter Estimation Method, calculates and determines λ s, ρ sc s.
Further, in a first step, geo-thermal response test instrument inputs constant heat flux or constant cold flow in ground heat exchanger.
Further, the temperature-measuring system of distributed fibers in the first step comprises many temperature-measuring optical fibers, and temperature-measuring optical fiber is provided with a temperature measurement node every 0.25m, is provided with 4 temperature-measuring optical fibers in every root pipe of ground heat exchanger.
Further, also comprise before the 3rd step and equivalent process carried out to ground heat exchanger, ground heat exchanger and there is following relationship between the buret: wherein, D 0for the overall diameter of ground heat exchanger, D efor the equivalent diameter when buret.
Further, in second step, the arrangement of data is comprised: give up the data recorded in first 10 hours, give up the data recorded in distance ground 5m.
Further, to the estimation in the 3rd step, comprise further: the data recorded in step 2 are brought in calculating formula and obtain T f1kabout λ s, ρ sc sa function, by c sρ sat 0 to 5*10 6between traversal, λ stravel through between 0 to 10, obtain T f1kone group of theoretical value.
Further, actual value T is calculated by the data of kth group in the 4th step f2kcomprise further: by formula to T f2kvalue calculates:
T f2k=(T in+T 2+T 3+……+T out)/N
Wherein, T infor entering temperature when recirculated water enters K layer,
T outfor temperature during recirculated water outflow kth layer,
T 2, T 3be followed successively by the average temperature data of the 3rd temperature measurement node collection on the average temperature data of second temperature measurement node collection on k layer horizontal line, K layer horizontal line
N is the number of temperature measurement node collection in k layer.
Further, Parameter Estimation Method is least square method, and least square method comprises further:
Step one, to each T f1kvalue and actual value T f2kthe calculating of variance and F is carried out by following formula:
F=∑(i=1,M){T f1ki-T f2ki} 2
Wherein M is the group number of test measurement data;
Step 2, more each T f1kthe size of the F that value draws, selects minimum F value, the T corresponding to minimum F value f1kvalue is requirements;
Step 3, searches and the λ corresponding to requirements s, ρ sc svalue, this value is and calculates λ corresponding to the ground of interval s, ρ sc svalue.
Geotechnical stratified of the present invention hot physical property in-situ heat response test method, by the degree of depth layered shaping is carried out to ground heat exchanger and respectively record is carried out to the data of every one deck, when needing to measure the thermal physical property parameter of certain depth rock-soil layer, corresponding calculating can be carried out by being brought in formula to the relevant layering test figure corresponding to certain depth rock-soil layer and underground pipe parameter, drawing the thermal physical property parameter of certain depth rock-soil layer.
Accompanying drawing explanation
In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.
Fig. 1 is the connection device schematic diagram of the embodiment of geotechnical stratified of the present invention hot physical property in-situ heat response test method;
Fig. 2 is the calculation procedure process flow diagram of the embodiment of the geotechnical stratified hot physical property in-situ heat response test method of Fig. 1;
Fig. 3 is the time-temperature curve schematic diagram of the geotechnical stratified hot physical property in-situ heat response test method of Fig. 1; And
Fig. 4 is the temperature survey schematic diagram of the kth layer of the geotechnical stratified hot physical property in-situ heat response test method of Fig. 1.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.
The geotechnical stratified hot physical property in-situ heat response test method of the present embodiment comprises the steps:
The first step, as shown in Figure 1, ground heat exchanger 1 is connected with geo-thermal response test instrument 2, form heat supplying loop, and measured by temperature-measuring system of distributed fibers 3 pairs of ground heat exchangers 1, carry out thermal response test by geo-thermal response test instrument 2 pairs of ground heat exchangers 1 and obtain the data on flows in ground heat exchanger, being obtained in ground heat exchanger 1 temperature data of multiple points for measuring temperature from top to bottom by temperature-measuring system of distributed fibers 3;
Second step, arranges temperature data, and in units of at least 5m, distance carries out layering from top to bottom to ground heat exchanger 1, and the length of every layer is one or several unit distance, and the temperature data of all points for measuring temperature in every layer is summed up formation data group;
3rd step, sets up plume source model, brings the data of kth group data group into calculating formula:
T f 1 k = T 0 + Q k ( 1 4 πr i h + 1 2 πk p ln n r p n r p - ( r p - r i ) ) 1.7 πr e L + Q k 4 π λ s L ( 2 h + ln 4 z C - 4 h - α 1 k 2 α 1 k z + α 1 k - 2 2 α 1 k z ln 4 z C ) ,
By estimation λ s, ρ sc svalue calculate T f1kone group of theoretical value;
4th step, calculates the actual average temperature T of kth layer ground heat exchanger fluid circulating by the data group of kth layer f2k;
5th step, to one group of T that the 3rd step draws f1kthe T that value and the 4th step draw f2kvalue carries out Parameter Estimation Method, calculates and determines λ s, ρ sc s.
The geotechnical stratified hot physical property in-situ heat response test method of the present embodiment, regards the Equivalent Column pipe of equivalence as, there is relational expression between ground heat exchanger 1 and Equivalent Column pipe by ground heat exchanger 1 wherein, D 0for the overall diameter of ground heat exchanger 1, D efor the equivalent diameter when buret.For Equivalent Column pipe, utilize the model that Carslaw proposes, meet expression formula one:
T p-T 0=(Q/λ sL)*G(z,p),
In order to the problem of the image and ground heat exchanger 1 quantity of revising two pipe fitting hot-fluids short circuit in ground heat exchanger 1, after the basis of temperature difference formula with the addition of hot-fluid short circuit correction factor C and U-tube number N, there is expression formula two:
ΔT P=T f-T P={Q(R C+R P)}/(2πr e*L*C*N),
Expression formula one and expression formula two are combined and can obtain expression formula three:
T f=T 0+{(Q/λ sL)*G(z,p)}+{[Q(R C+R P)]/(2πr e*L*C*N)}。
For the thermal resistance R of Equivalent Column pipe bthere is expression formula four:
R b = R c + R p = ( 1 / ( 4 π r i h ) ) + ( 1 / 2 π k p ) * ln { ( n r p ) / [ n r p - ( r p - r i ) ] } ,
Meanwhile, when the z value in expression formula one is greater than 0.5, expression formula one can also be expressed as expression formula five:
T p-T 0=(Q/(4πλ sL)){2h+ln(4z/C)-[(4h-α 1)/(2*α 1*z)]+[(α 1-2)/(2*α 1*z)]*ln(4z/C)}。
Expression formula four and expression formula five are brought into the calculating formula that expression formula three i.e. cocoa draws individual layer mean flow:
T f 1 k = T 0 + Q k ( 1 4 πr i h + 1 2 πk p ln n r p n r p - ( r p - r i ) ) 1.7 πr e L + Q k 4 π λ s L ( 2 h + ln 4 z C - 4 h - α 1 k 2 α 1 k z + α 1 k - 2 2 α 1 k z ln 4 z C )
In calculating formula, the meaning of each symbol is as follows:
T f1kfor the theoretical medial temperature of kth layer ground heat exchanger fluid circulating;
T 0for kth layer ground initial temperature;
Q kfor the heating power of kth layer, Q k=1163*G* Δ T k, G is volumetric flow rate, Δ T kfor the import and export circulating fluid medial temperature temperature difference of kth layer;
R ifor ground heat exchanger internal diameter;
R pfor ground heat exchanger external diameter; ,
R efor the external radius when buret;
L is the length of unit distance;
Z is fourier coefficient, z=(a st/ (r e 2)), a s=(λ s/ (c sρ s)), a sfor the thermal diffusion coefficient of ground, λ sfor ground mean coefficient of heat conductivity; c sρ sfor ground specific heat per unit volume;
α 1k=(2 π r e2c sρ s)/(c cylinder), c cylinderfor wellhole unit length thermal resistance;
K pfor the coefficient of heat conductivity of tubing;
C=e 0.5772=e γ, C is hot-fluid short circuit correction factor, and γ is Euler's constant;
H=2 π λ sr ' g, R ' gfor unit length thermal contact resistance;
N is the pipe number quantity of ground heat exchanger.
In the first step of the present embodiment, temperature-measuring system of distributed fibers 3 is measured the temperature in ground heat exchanger 1 by temperature-measuring optical fiber.Wherein, geo-thermal response test instrument 2 inputs constant heat flux or constant cold flow in ground heat exchanger, temperature-measuring system of distributed fibers comprises many temperature-measuring optical fibers, temperature-measuring optical fiber is provided with a temperature measurement node every 0.25m, and the temperature-measuring optical fiber be namely arranged in every root pipe of ground heat exchanger is that spacing is measured the temperature in ground heat exchanger 1 with 0.25m.Preferably, 4 optical fiber are provided with in every root pipe of ground heat exchanger.Meanwhile, the flow of corresponding in the heat supplying loop record ground heat exchanger 1 that ground heat exchanger 1 is connected recirculated water.The data on flows of the temperature data recorded by temperature-measuring optical fiber and heat supplying loop record can calculate corresponding T 0, Δ T kand Q k.In whole test process, as shown in Figure 3, in figure 3, each layer rate of curve is very close for the temperature-time curve of ground heat exchanger, this ground explanatorily around pipe laying is evenly distributed, and irregular mainly being changed by heating power of every one deck curve causes in addition.
In use, for the requirement to precision, need to give up the unstable data measured by first 10 hours, simultaneously, due to surface temperature be subject to temperature, environment etc. the impact of objective factor, in order to obtain data more accurately, better analyzing the hot physical property of ground, at least should give up the measurement data of first 5 meters of underground.
For operable qualified data, also need to carry out packet transaction, namely layered shaping is carried out to ground heat exchanger 1.In the present embodiment, need to determine unit distance to the layered shaping of ground heat exchanger 1, ground heat exchanger 1 should occur that in unit distance obvious temperature variation is beneficial to follow-up calculating.Preferably, the length of unit distance should be more than or equal to 5m.After determining unit distance, ground heat exchanger 1 is divided into M layer from top to bottom, the length of every layer is one or several unit distance, when measuring the temperature in ground heat exchanger 1, the data of each point for measuring temperature in every one deck to be summed up in one group and to form this layer of corresponding temperature data group.
When calculating the hot physical property of the rock-soil layer corresponding to kth layer, needing the data group of kth layer correspondence to be brought in calculating formula, obtaining T f1kabout λ s, ρ sc sa function, by arranging λ s, ρ sc sspan and carry out exhaustively can obtaining multiple T f1kvalue, formed T f1kone group of theoretical value.Meanwhile, as shown in Figure 4, according to the temperature data group of the kth layer that optical fiber temperature measurement system records, by expression formula six: T f2k=(T in+ T 2+ T 3+ ... + T out)/N calculates the medial temperature of the actual cycle fluid of kth layer.
When exhaustive, λ svalue travel through between 0 to 10, ρ sc sspan at 0 to 5*10 6between traversal.
Wherein, T infor entering temperature when recirculated water enters K layer,
T outfor temperature during recirculated water outflow kth layer,
T 2, T 3be followed successively by the average temperature data of the 3rd temperature measurement node collection on the average temperature data of second temperature measurement node collection on k layer horizontal line, K layer horizontal line
N is the number of temperature measurement node collection in k layer.
As shown in Figure 4, when actual computation, T infor the average temperature data of first temperature measurement node collection on k layer horizontal line, T outfor the average temperature data of last temperature measurement node collection on k layer horizontal line.Owing to being provided with many temperature-measuring optical fibers in each pipe of ground heat exchanger, after temperature measured by the temperature measurement node of described temperature-measuring optical fiber on this horizontal line should being added together when calculating the temperature on certain level line divided by the radical of optical fiber to obtain the medial temperature on this horizontal line, improve the precision of data.
Obtaining T f1kone group of theoretical value and actual average temperature after, calculate the λ determining rock-soil layer corresponding to k layer by the least square method in Parameter Estimation Method s, ρ sc s.Least square method be specially to each theoretical value relatively and actual average temperature value to be asked by expression formula seven and calculate variance and F,
F=∑(i=1,M){T f1ki-T f2ki} 2
Wherein M is the group number of test measurement data.
Obtaining variance corresponding to each theoretical value and rear to each variance and comparing, select the minimum variance of numerical value and, this minimum variance and corresponding theoretical value are requirements, the λ that this requirements is corresponding s, ρ sc sbe the λ of the ground corresponding to k layer s, ρ sc s.
The data volume calculating design due to this portion is large, and calculate very complicated, can be completed the calculating of this part in practical operation by computing machine, calculation procedure process flow diagram as shown in Figure 2.
The geotechnical stratified hot physical property in-situ heat response test method of the present embodiment is owing to carrying out layered shaping to mathematical model, the blade diameter length ratio of model is caused greatly to increase relative to the blade diameter length ratio of line source model, directly cannot apply mechanically original line source model, need to use new account form.Geotechnical stratified in the present embodiment hot physical property in-situ heat response test method, is carrying out in the process of layering to ground heat exchanger 1, considers along depth direction boring internal thermal resistance R bchange, along the change of heat exchange power Q in depth direction boring, make the λ finally calculated s, ρ s, c s.More close to the actual thermal physical property parameter of ground, improve the computational accuracy of calculating formula.Simultaneously, the experimental formula that calculating formula in the present embodiment is different from the past, without the need to carrying out a large amount of hypothesis and loaded down with trivial details derivation, only intrinsic for underground pipe parameter and relevant test data need be brought in calculating formula and carry out calculating the theoretical value that directly can draw key parameter in least square method, with a wide range of applications and convenience, is convenient to carry out promotion and application.
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1. a geotechnical stratified hot physical property in-situ heat response test method, is characterized in that, comprise the steps:
The first step, ground heat exchanger (1) is connected with geo-thermal response test instrument (2), form heat supplying loop, and by temperature-measuring system of distributed fibers (3), ground heat exchanger (1) is measured, by described geo-thermal response test instrument (2) thermal response test carried out to ground heat exchanger (1) and obtain the data on flows in described ground heat exchanger (1), being obtained in described ground heat exchanger (1) temperature data of multiple points for measuring temperature from top to bottom by described temperature-measuring system of distributed fibers (3);
Second step, described temperature data is arranged, in units of at least 5m, distance carries out layering from top to bottom to ground heat exchanger (1), and the length of every layer is one or several unit distance, and the temperature data of all described point for measuring temperature in every layer is summed up formation data group;
3rd step, sets up plume source model, brings the data group data of kth layer into calculating formula:
T f 1 k = T 0 + Q k ( 1 4 πr i h + 1 2 πk p ln n r p n r p - ( r p - r i ) ) 1.7 πr e L + Q k 4 πλ s L ( 2 h + ln 4 z C - 4 h - α 1 k 2 α 1 kZ + α 1 k - 2 2 α 1 kZ ln 4 z C ) ,
By estimation λ s, ρ sc svalue calculate T f1kone group of theoretical value, wherein,
T f1kfor the theoretical medial temperature of kth layer ground heat exchanger fluid circulating;
T 0for kth layer ground initial temperature;
Q kfor the heating power of kth layer, Q k=1163*G* Δ T k, G is volumetric flow rate, Δ T kfor the import and export circulating fluid medial temperature temperature difference of kth layer;
R ifor ground heat exchanger internal diameter;
R pfor ground heat exchanger external diameter;
R efor the external radius when buret;
L is the length of unit distance;
Z is fourier coefficient, z=(a st/ (r e 2)), a s=(λ s/ (c sρ s)), a sfor the thermal diffusion coefficient of ground, λ sfor ground mean coefficient of heat conductivity; c sρ sfor ground specific heat per unit volume;
α 1k=(2 π r e2c sρ s)/(c cylinder), c cylinderfor wellhole unit length thermal resistance;
K pfor the coefficient of heat conductivity of tubing;
C=e 0.5772=e γ, C is hot-fluid short circuit correction factor, and γ is Euler's constant;
H=2 π λ sr ' g, R ' gfor unit length thermal contact resistance;
N is the pipe number quantity of ground heat exchanger.
4th step, calculates the actual average temperature T of kth layer ground heat exchanger fluid circulating by the data group of kth layer f2k;
5th step, to one group of T that the 3rd step draws f1kthe T that value and the 4th step draw f2kvalue carries out Parameter Estimation Method, calculates and determines λ s, ρ sc s.
2. a kind of geotechnical stratified according to claim 1 hot physical property in-situ heat response test method, it is characterized in that, in a first step, described geo-thermal response test instrument (2) input constant heat flux or constant cold flow in described ground heat exchanger (1).
3. a kind of geotechnical stratified according to claim 2 hot physical property in-situ heat response test method, it is characterized in that, described temperature-measuring system of distributed fibers (3) in the described first step comprises many temperature-measuring optical fibers, described temperature-measuring optical fiber is provided with a temperature measurement node every 0.25m, in every root pipe of described ground heat exchanger, is provided with 4 described temperature-measuring optical fibers.
4. a kind of geotechnical stratified according to claim 1 hot physical property in-situ heat response test method, it is characterized in that, also comprising before the 3rd step and carry out equivalent process to described ground heat exchanger (1), there is following relationship in described ground heat exchanger (1) and described working as between buret: wherein, D 0for the overall diameter of ground heat exchanger (1), D efor the equivalent diameter when buret.
5. a kind of geotechnical stratified according to claim 1 hot physical property in-situ heat response test method, is characterized in that, comprises: give up the data recorded in first 10 hours in described second step to the arrangement of described data, gives up the data recorded in distance ground 5m.
6. a kind of geotechnical stratified according to claim 5 hot physical property in-situ heat response test method, is characterized in that, to the estimation in described 3rd step, comprises further: the data recorded in step 2 be brought in calculating formula and obtain T f1kabout λ s, ρ sc sa function, by c sρ sat 0 to 5*10 6between traversal, λ stravel through between 0 to 10, obtain T f1kone group of theoretical value.
7. a kind of geotechnical stratified according to claim 1 hot physical property in-situ heat response test method, is characterized in that, calculates actual value T in described 4th step by the data of kth group f2kcomprise further: by formula to T f2kvalue calculates:
T f2k=(T in+T 2+T 3+……+T out)/N
Wherein, T infor entering temperature when recirculated water enters K layer,
T outfor temperature during recirculated water outflow kth layer,
T 2, T 3be followed successively by the average temperature data of the 3rd temperature measurement node collection on the average temperature data of second temperature measurement node collection on k layer horizontal line, K layer horizontal line
N is the number of temperature measurement node collection in k layer.
8. a kind of geotechnical stratified according to claim 1 hot physical property in-situ heat response test method, it is characterized in that, described Parameter Estimation Method is least square method, and described least square method comprises further:
Step one, to each T f1kvalue and actual value T f2kthe calculating of variance and F is carried out by following formula:
F=∑(i=1,M){T f1ki-T f2ki} 2
Wherein M is the group number of test measurement data;
Step 2, more each T f1kthe size of the F that value draws, selects minimum F value, the T corresponding to minimum F value f1kvalue is requirements;
Step 3, searches and the λ corresponding to requirements s, ρ sc svalue, this value is and calculates λ corresponding to the ground of interval s, ρ sc svalue.
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CN112632788A (en) * 2020-12-28 2021-04-09 中国科学技术大学 Thermal response test method for rock-soil thermal conductivity distribution
CN114252475A (en) * 2020-09-22 2022-03-29 宝山钢铁股份有限公司 Method for checking efficiency of heat exchanger

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CN114252475A (en) * 2020-09-22 2022-03-29 宝山钢铁股份有限公司 Method for checking efficiency of heat exchanger
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CN112632788B (en) * 2020-12-28 2022-09-06 中国科学技术大学 Thermal response test method for rock-soil thermal conductivity distribution

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