CN113515863A - Method for calculating heat quantity of middle-deep sleeve type heat exchanger based on numerical inversion - Google Patents

Method for calculating heat quantity of middle-deep sleeve type heat exchanger based on numerical inversion Download PDF

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CN113515863A
CN113515863A CN202110793294.8A CN202110793294A CN113515863A CN 113515863 A CN113515863 A CN 113515863A CN 202110793294 A CN202110793294 A CN 202110793294A CN 113515863 A CN113515863 A CN 113515863A
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heat exchanger
temperature
heat
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CN113515863B (en
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李永强
张卫东
韩永亮
孙玉亮
王义杰
汪启龙
杨永健
俞强
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Xian Research Institute Co Ltd of CCTEG
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Abstract

The invention provides a method for calculating the heat quantity of a middle-deep sleeve type heat exchanger based on numerical inversion, which comprises the following steps: step one, establishing a middle-deep sleeve type heat exchanger model, wherein the middle-deep sleeve type heat exchanger model is divided into two parts by taking a borehole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a borehole, and the other part is a stratum outside the borehole; step two, solving a formation heat conduction equation: step three, solving the temperature of the circulating water in the double-pipe heat exchanger: step four, solving the steps from step two to step three to obtain the water temperature in the double-pipe heat exchanger
Figure DDA0003161859260000011
And
Figure DDA0003161859260000012
the solution in the frequency domain. The invention is in the given placeUnder the conditions of the layer initial temperature distribution function, the heat exchanger inlet water temperature and the related physical parameters of the heat exchanger and the stratum, the distribution rule of the outlet water temperature of the double-pipe heat exchanger and the water temperature in the heat exchanger along the depth direction at any moment can be obtained, and then the change of the heat taken by the double-pipe heat exchanger along with the time can be obtained.

Description

Method for calculating heat quantity of middle-deep sleeve type heat exchanger based on numerical inversion
Technical Field
The invention belongs to the technical field of development and utilization of deep geothermal energy, relates to heat extraction, and particularly relates to a method for calculating heat extraction of a deep sleeve type heat exchanger based on numerical inversion.
Background
A mid-deep ground source heat pump system is a technology for indirectly utilizing geothermal energy, which obtains heat from the ground through a double pipe heat exchanger installed in a borehole. The double pipe heat exchanger structure is shown in figure 1. The double-pipe heat exchanger penetrates into a high-temperature rock stratum below 2000 m underground through a drill hole, cold water flows in from an annular area between the inner sleeve pipe and the outer sleeve pipe, heat is absorbed from the surrounding stratum when the cold water flows downwards, and the heated water is pumped out of the ground through the inner pipe for heating. The initial temperature of the formation rock mass around the geothermal well can reach more than 100K at most, the temperature of the formation rock mass around the drill hole is gradually reduced along with the heat extraction process of the double-pipe heat exchanger, and meanwhile, the heat extraction quantity of the double-pipe heat exchanger can also be continuously reduced. The method has the advantages that the water temperature distribution in the heat exchanger and the outlet water temperature are accurately calculated, and the method is particularly important for evaluating the heat extraction capacity of the geothermal well and optimizing the design of the geothermal well.
The heat transfer process of the intermediate-deep double-pipe heat exchanger is very complex, the involved time span is long, and the space area is large. Compared with a shallow layer buried pipe heat exchanger, the vertical variation range of the formation temperature is large, and the heat exchange process of the shallow layer buried pipe heat exchanger relates to a very complex mathematical physics problem. At present, researches on a method for calculating heat of a shallow geothermal well heat exchanger are numerous, because the depth of the shallow geothermal well is generally not more than 200m, the vertical variation of the formation temperature is very small, the formation temperature is assumed to be a constant value when the analytic solution of the shallow geothermal well heat exchanger is solved, and the vertical variation of the formation temperature is not considered. Therefore, the method for calculating the heat quantity of the shallow geothermal well heat exchanger cannot be applied to the calculation of the heat quantity of the intermediate and deep geothermal well heat exchanger.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method for calculating the heat extraction amount of a middle-deep sleeve type heat exchanger based on numerical inversion, and solve the technical problem that the method for calculating the heat extraction amount of a shallow geothermal well heat exchanger in the prior art cannot be applied to the calculation of the heat extraction amount of the middle-deep sleeve type heat exchanger.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for calculating heat quantity of a middle-deep sleeve type heat exchanger based on numerical inversion comprises the following steps:
step one, establishing a middle-deep sleeve type heat exchanger model, wherein the middle-deep sleeve type heat exchanger model is divided into two parts by taking a borehole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a borehole, and the other part is a stratum outside the borehole;
on the basis of the change of the formation temperature along with the depth, the heat transfer processes of the two parts are respectively calculated, and the two parts are coupled through the temperature of the wall of the drill hole;
step two, solving a formation heat conduction equation:
assuming that the heat conduction of the formation in the depth direction is zero, at any depth z along the axial direction of the double-pipe heat exchanger, the formation heat conduction is a one-dimensional process under a cylindrical coordinate, and can be described by the following partial differential equation:
Figure BDA0003161859240000021
boundary conditions: r → ∞ time:
Figure BDA0003161859240000022
r＝rbthe method comprises the following steps:
Figure BDA0003161859240000023
initial conditions: t when T is 0e＝az+Tair；
Solving to obtain:
Figure BDA0003161859240000024
Figure BDA0003161859240000025
Figure BDA0003161859240000026
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρeis the density of the stratum rock mass with the unit of kg/m3；
ceThe specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
Tethe temperature of the stratum rock mass at the depth z is represented by K;
Tezis the formation initial temperature in K;
t is time in units of s;
t0is a time factor of the formation temperature, dimensionless;
Tairis the surface temperature in K;
λethe heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
rbis the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
Tbis the borehole wall temperature in K;
z is the distance from the earth's surface in m;
a is the earth temperature gradient with the unit of K/m;
step three, solving the temperature of the circulating water in the double-pipe heat exchanger:
when circulating water flows in from the outer pipe and flows out from the inner pipe, the heat balance equation along the flow direction is expressed by a formula VII and a formula VIII;
inner tube heat balance equation:
Figure BDA0003161859240000031
outer tube heat balance equation:
Figure BDA0003161859240000032
wherein:
Figure BDA0003161859240000041
Figure BDA0003161859240000042
the conditions for the solution were as follows:
T2(0,t)＝Tinjformula XI;
T1(H,t)＝T2(H, t) formula XII;
in the formula:
A1is the water passing cross-sectional area of the inner pipe, and the unit is m2；
A2Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m2；
ρfIs the density of water in kg/m3；
c is the specific heat capacity of water and the unit is J/(kg. K);
T1is the temperature of water in the inner tube in unitsIs K;
T2is the temperature of the water in the outer tube, in K;
Tbis the borehole wall temperature in K;
w is the flow of water in the sleeve, and the unit is kg/s;
r1is the inner radius of the inner tube, and the unit is m;
r2is the outer radius of the inner tube, and is expressed in m;
r3is the inner radius of the outer tube, and is expressed in m;
r4is the outer radius of the outer tube, in m;
rbis the borehole radius in m;
h is the geothermal well depth, and the unit is m;
h1is the convective heat transfer coefficient of the inner wall of the inner tube and has the unit of W/(m)2·K)；
h2Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m)2·K)；
h3Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m)2·K)；
kiThe heat conductivity coefficient of the inner tube wall is W/(m.K);
kothe thermal conductivity coefficient of the outer tube wall is W/(m.K);
kgthe unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
Tinjwater temperature at the inlet, in units of K;
setting the heat quantity flowing out of the borehole wall to be equal to the heat quantity obtained by the outer pipe from the stratum, the heat transfer coupling condition between the sleeve and the stratum is as follows:
Figure BDA0003161859240000051
from the formula XIII:
Figure BDA0003161859240000052
order:
Figure BDA0003161859240000053
Figure BDA0003161859240000054
Figure BDA0003161859240000055
Figure BDA0003161859240000056
Figure BDA0003161859240000057
Figure BDA0003161859240000058
Figure BDA0003161859240000059
Figure BDA00031618592400000510
in the formula:
z is a geothermal well depth factor and is dimensionless;
a is the total heat transfer coefficient factor of the inner pipe wall, and is dimensionless;
b is a factor of the total heat transfer coefficient between the outer pipe wall and the well wall, and is dimensionless;
φ1is a water temperature factor in the inner pipe, and has no dimension;
φ2is the water temperature factor in the outer tubeNo dimension;
tDthe water temperature time factor in the double-pipe heat exchanger is dimensionless;
M1、M2all are drilling aperture factors and have no dimension;
substituting formula xiv into formula viii, dimensionless the formula vii, formula viii and the conditions of the solution:
Figure BDA0003161859240000061
Figure BDA0003161859240000062
wherein:
Figure BDA0003161859240000063
φ2(0,tD)＝1；
φ1(1,tD)＝φ2(1,tD)；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
Figure BDA0003161859240000064
Figure BDA0003161859240000065
in the formula:
Figure BDA0003161859240000066
is phi1The image function of (a);
Figure BDA0003161859240000067
is phi2The image function of (a);
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
Figure BDA0003161859240000068
Figure BDA0003161859240000069
wherein:
a1、a2、k1、k2、C1and C2All are intermediate quantities;
a1＝M1s+(1+k1)A；
a2＝M1s+(1+k2)A；
Figure BDA0003161859240000071
Figure BDA0003161859240000072
C1、C2is obtained by dissolving after substituting the formula XXV and the formula XXVI under the definite dissolving condition;
step four, solving the steps from step two to step three to obtain the water temperature in the double-pipe heat exchanger
Figure BDA0003161859240000073
And
Figure BDA0003161859240000074
the solution in the frequency domain.
Compared with the prior art, the invention has the following technical effects:
according to the invention, under the condition of giving a stratum initial temperature distribution function, the heat exchanger inlet water temperature and the related physical parameters of the heat exchanger and the stratum, the distribution rule of the outlet water temperature of the double-pipe heat exchanger and the water temperature in the heat exchanger along the depth direction at any moment can be obtained, and then the change of the heat extraction quantity of the double-pipe heat exchanger along with the time can be obtained. The calculation result can be used as the basis for evaluating the heat extraction capacity of the medium-deep geothermal well and optimizing the design scheme of the geothermal well.
Drawings
Fig. 1(a) is a schematic view of a vertical sectional structure of a double pipe heat exchanger.
Fig. 1(b) is a schematic view of a horizontal sectional structure of the double pipe heat exchanger.
Fig. 2 is a graph of outlet water temperature versus time.
The meaning of the individual reference symbols in the figures is: 1-stratum, 2-drilling wall, 3-cementing cement sheath, 4-outer well, 5-inner well, 6-heat-taking circulation water inlet, and 7-heat-taking circulation water outlet.
The present invention will be explained in further detail with reference to examples.
Detailed Description
For a middle-deep geothermal well, the vertical variation of the formation temperature is large, and the assumption of constant geothermal temperature inevitably causes that the calculated value of the heat exchange medium temperature in the double-pipe heat exchanger deviates from the true value in the flowing direction thereof to be overlarge. Therefore, the influence of vertical variation of the ground temperature is necessarily considered when the heat extraction process of the middle-deep sleeve type heat exchanger is researched.
The invention aims to provide a method for calculating heat extraction quantity of a casing pipe type heat exchanger of a middle-deep geothermal well, which is characterized by comprising the following steps: vertical variation of the formation temperature is considered in the solving process, but vertical heat conduction of the formation is not considered; simplifying the convective heat transfer process in the double-pipe heat exchanger into a one-dimensional linear problem and processing according to an unsteady state; in the solving process, firstly, a heat conduction equation of a stratum is solved to obtain the temperature of the wall of the drill hole, then, the solution of a differential equation set on a frequency domain is obtained by using laplace transformation solving, and finally, the water temperature distribution in the double-pipe heat exchanger and the water temperature at an outlet are obtained by using a numerical inversion method to obtain the heat extraction quantity of the double-pipe heat exchanger. The invention provides a technical basis for simplifying the calculation method of the geothermal well heat extraction quantity, estimating the geothermal well heat extraction capacity and optimizing the geothermal well design.
It is to be understood that all parts, devices and apparatus of the present invention, unless otherwise specified, are intended to be included within the scope of the present invention as defined in the appended claims.
The following embodiments of the present invention are provided, and it should be noted that the present invention is not limited to the following embodiments, and all equivalent changes based on the technical solutions of the present invention are within the protection scope of the present invention.
Example (b):
the embodiment provides a method for calculating the heat extraction quantity of a middle-deep double-pipe heat exchanger based on numerical inversion, which comprises the following steps:
step one, establishing a middle-deep sleeve type heat exchanger model, wherein the middle-deep sleeve type heat exchanger model is divided into two parts by taking a borehole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a borehole, and the other part is a stratum outside the borehole;
on the basis of the change of the formation temperature along with the depth, the heat transfer processes of the two parts are respectively calculated, and the two parts are coupled through the temperature of the wall of the drill hole;
step two, solving a formation heat conduction equation:
assuming that the heat conduction of the formation in the depth direction is zero, at any depth z along the axial direction of the double-pipe heat exchanger, the formation heat conduction is a one-dimensional process under a cylindrical coordinate, and can be described by the following partial differential equation:
Figure BDA0003161859240000091
boundary conditions: r → ∞ time:
Figure BDA0003161859240000092
r＝rbthe method comprises the following steps:
Figure BDA0003161859240000093
initial conditions: t when T is 0e＝az+Tair；
Solving to obtain:
Figure BDA0003161859240000094
Figure BDA0003161859240000095
Figure BDA0003161859240000096
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρeis the density of the stratum rock mass with the unit of kg/m3；
ceThe specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
Tethe temperature of the stratum rock mass at the depth z is represented by K;
Tezis the formation initial temperature in K;
t is time in units of s;
t0is a time factor of the formation temperature, dimensionless;
Tairis the surface temperature in K;
λethe heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
rbis the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
Tbis the borehole wall temperature in K;
z is the distance from the earth's surface in m;
a is the earth temperature gradient with the unit of K/m;
step three, solving the temperature of the circulating water in the double-pipe heat exchanger:
when circulating water flows in from the outer pipe and flows out from the inner pipe, the heat balance equation along the flow direction is expressed by a formula VII and a formula VIII;
inner tube heat balance equation:
Figure BDA0003161859240000101
outer tube heat balance equation:
Figure BDA0003161859240000102
wherein:
Figure BDA0003161859240000103
Figure BDA0003161859240000104
the conditions for the solution were as follows:
T2(0,t)＝Tinjformula XI;
T1(H,t)＝T2(H, t) formula XII;
in the formula:
A1is the water passing cross-sectional area of the inner pipe, and the unit is m2；
A2Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m2；
ρfIs the density of water in kg/m3；
c is the specific heat capacity of water and the unit is J/(kg. K);
T1the temperature of water in the inner tube is expressed in K;
T2is the temperature of the water in the outer tube, in K;
Tbis the borehole wall temperature in K;
w is the flow of water in the sleeve, and the unit is kg/s;
r1is the inner radius of the inner tube, and the unit is m;
r2is the outer radius of the inner tube, and is expressed in m;
r3is the inner radius of the outer tube, and is expressed in m;
r4is the outer radius of the outer tube, in m;
rbis the borehole radius in m;
h is the geothermal well depth, and the unit is m;
h1is the convective heat transfer coefficient of the inner wall of the inner tube and has the unit of W/(m)2·K)；
h2Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m)2·K)；
h3Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m)2·K)；
kiThe heat conductivity coefficient of the inner tube wall is W/(m.K);
kothe thermal conductivity coefficient of the outer tube wall is W/(m.K);
kgthe unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
Tinjwater temperature at the inlet, in units of K;
setting the heat quantity flowing out of the borehole wall to be equal to the heat quantity obtained by the outer pipe from the stratum, the heat transfer coupling condition between the sleeve and the stratum is as follows:
Figure BDA0003161859240000111
from the formula XIII:
Figure BDA0003161859240000112
order:
Figure BDA0003161859240000113
Figure BDA0003161859240000114
Figure BDA0003161859240000115
Figure BDA0003161859240000116
Figure BDA0003161859240000117
Figure BDA0003161859240000121
Figure BDA0003161859240000122
Figure BDA0003161859240000123
in the formula:
z is a geothermal well depth factor and is dimensionless;
a is the total heat transfer coefficient factor of the inner pipe wall, and is dimensionless;
b is a factor of the total heat transfer coefficient between the outer pipe wall and the well wall, and is dimensionless;
φ1is a water temperature factor in the inner pipe, and has no dimension;
φ2is a water temperature factor in the outer pipe, and has no dimension;
tDthe water temperature time factor in the double-pipe heat exchanger is dimensionless;
M1、M2all are drilling aperture factors and have no dimension;
substituting formula xiv into formula viii, dimensionless the formula vii, formula viii and the conditions of the solution:
Figure BDA0003161859240000124
Figure BDA0003161859240000125
wherein:
Figure BDA0003161859240000126
φ2(0,tD)＝1；
φ1(1,tD)＝φ2(1,tD)；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
Figure BDA0003161859240000127
Figure BDA0003161859240000131
in the formula:
Figure BDA0003161859240000132
is phi1The image function of (a);
Figure BDA0003161859240000133
is phi2The image function of (a);
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
Figure BDA0003161859240000134
Figure BDA0003161859240000135
wherein:
a1、a2、k1、k2、C1and C2All are intermediate quantities;
a1＝M1s+(1+k1)A；
a2＝M1s+(1+k2)A；
Figure BDA0003161859240000136
Figure BDA0003161859240000137
C1、C2is obtained by dissolving after substituting the formula XXV and the formula XXVI under the definite dissolving condition;
step four, solving the steps from step two to step three to obtain the water temperature in the double-pipe heat exchanger
Figure BDA0003161859240000138
And
Figure BDA0003161859240000139
the solution in the frequency domain.
In the invention, a time domain solution phi of the water temperature in the double-pipe heat exchanger is obtained1And phi2Need to be aligned with
Figure BDA00031618592400001310
And
Figure BDA00031618592400001311
performing inverse laplace transform because
Figure BDA00031618592400001312
And
Figure BDA00031618592400001313
the form of the double-pipe heat exchanger is complex, laplace inverse change cannot be directly carried out, and a numerical inversion method is required to obtain a solution phi of the water temperature in the double-pipe heat exchanger on a time domain1And phi2And then T is obtained1(T, z) and T2(t,z)。
Application example:
in this application example, the change of the outlet water temperature of the double pipe heat exchanger with time is calculated by using the analytic solution of the method for calculating the heat quantity of the deep double pipe heat exchanger based on numerical inversion in the above embodiment 1, and the parameters required for calculation are shown in table 1. In addition, in the application example, the surface temperature is a constant value of 16K, the ground temperature gradient is 0.03K/m, and the water temperature at the inlet of the heat exchanger is 15K.
TABLE 1 analysis and calculation parameter table for double-pipe heat exchanger
Figure BDA0003161859240000141
Taking the first heating season as an example, the time-dependent change relationship of the outlet water temperature when the formation thermal conductivity is 2.5W/(m.K) is obtained, as shown in FIG. 2. The outlet water temperature is the same as the inlet water temperature at time zero. The outlet water temperature rose rapidly in the initial phase and was at its maximum at 0.2 days, with a maximum temperature of about 60K, at which time the heat removal was 1500 kW. Then, the outlet water temperature gradually decreases again as the heat extraction progresses. After continuously taking heat for 120 days, the outlet water temperature is 27K, and the heat taking amount is 420 kW. Compared with the analytic solution obtained by the steady-state treatment of the convection heat transfer in the double-pipe heat exchanger, the analytic solution has the trend that the water temperature at the outlet at the initial stage of calculation is increased firstly and then decreased, and the analytic solution is more in line with the actual situation.

Claims (1)

1. A method for calculating heat quantity of a middle-deep sleeve type heat exchanger based on numerical inversion is characterized by comprising the following steps:
step one, establishing a middle-deep sleeve type heat exchanger model, wherein the middle-deep sleeve type heat exchanger model is divided into two parts by taking a borehole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a borehole, and the other part is a stratum outside the borehole;
on the basis of the change of the formation temperature along with the depth, the heat transfer processes of the two parts are respectively calculated, and the two parts are coupled through the temperature of the wall of the drill hole;
step two, solving a formation heat conduction equation:
assuming that the heat conduction of the formation in the depth direction is zero, at any depth z along the axial direction of the double-pipe heat exchanger, the formation heat conduction is a one-dimensional process under a cylindrical coordinate, and can be described by the following partial differential equation:
Figure FDA0003161859230000011
boundary conditions: r → ∞ time:
Figure FDA0003161859230000012
r＝rbthe method comprises the following steps:
Figure FDA0003161859230000013
initial conditions: t when T is 0e＝az+Tair；
Solving to obtain:
Figure FDA0003161859230000014
Figure FDA0003161859230000015
Figure FDA0003161859230000016
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρeis the density of the stratum rock mass with the unit of kg/m3；
ceThe specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
Tethe temperature of the stratum rock mass at the depth z is represented by K;
Tezis the formation initial temperature in K;
t is time in units of s;
t0is a time factor of the formation temperature, dimensionless;
Tairis the surface temperature in K;
λethe heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
rbis the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
Tbis the borehole wall temperature in K;
z is the distance from the earth's surface in m;
a is the earth temperature gradient with the unit of K/m;
step three, solving the temperature of the circulating water in the double-pipe heat exchanger:
when circulating water flows in from the outer pipe and flows out from the inner pipe, the heat balance equation along the flow direction is expressed by a formula VII and a formula VIII;
inner tube heat balance equation:
Figure FDA0003161859230000021
outer tube heat balance equation:
Figure FDA0003161859230000022
wherein:
Figure FDA0003161859230000023
Figure FDA0003161859230000024
the conditions for the solution were as follows:
T2(0,t)＝Tinjformula XI;
T1(H,t)＝T2(H, t) formula XII;
in the formula:
A1is the water passing cross-sectional area of the inner pipe, and the unit is m2；
A2Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m2；
ρfIs the density of water in kg/m3；
c is the specific heat capacity of water and the unit is J/(kg. K);
T1the temperature of water in the inner tube is expressed in K;
T2is the temperature of the water in the outer tube, in K;
Tbis the borehole wall temperature in K;
w is the flow of water in the sleeve, and the unit is kg/s;
r1is the inner radius of the inner tube, and the unit is m;
r2is the outer radius of the inner tube, and is expressed in m;
r3is the inner radius of the outer tube, and is expressed in m;
r4is the outer radius of the outer tube, in m;
rbis the borehole radius in m;
h is the geothermal well depth, and the unit is m;
h1is the convective heat transfer coefficient of the inner wall of the inner tube and has the unit of W/(m)2·K)；
h2Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m)2·K)；
h3Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m)2·K)；
kiThe heat conductivity coefficient of the inner tube wall is W/(m.K);
kothe thermal conductivity coefficient of the outer tube wall is W/(m.K);
kgthe unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
Tinjwater temperature at the inlet, in units of K;
setting the heat quantity flowing out of the borehole wall to be equal to the heat quantity obtained by the outer pipe from the stratum, the heat transfer coupling condition between the sleeve and the stratum is as follows:
Figure FDA0003161859230000041
from the formula XIII:
Figure FDA0003161859230000042
order:
Figure FDA0003161859230000043
Figure FDA0003161859230000044
Figure FDA0003161859230000045
Figure FDA0003161859230000046
Figure FDA0003161859230000047
Figure FDA0003161859230000048
Figure FDA0003161859230000049
Figure FDA00031618592300000410
in the formula:
z is a geothermal well depth factor and is dimensionless;
a is the total heat transfer coefficient factor of the inner pipe wall, and is dimensionless;
b is a factor of the total heat transfer coefficient between the outer pipe wall and the well wall, and is dimensionless;
φ1is a water temperature factor in the inner pipe, and has no dimension;
φ2is a water temperature factor in the outer pipe, and has no dimension;
tDthe water temperature time factor in the double-pipe heat exchanger is dimensionless;
M1、M2all are drilling aperture factors and have no dimension;
substituting formula xiv into formula viii, dimensionless the formula vii, formula viii and the conditions of the solution:
Figure FDA0003161859230000051
Figure FDA0003161859230000052
wherein:
Figure FDA0003161859230000053
φ2(0,tD)＝1；
φ1(1,tD)＝φ2(1,tD)；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
Figure FDA0003161859230000054
Figure FDA0003161859230000055
in the formula:
Figure FDA0003161859230000056
is phi1The image function of (a);
Figure FDA0003161859230000057
is phi2The image function of (a);
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
Figure FDA0003161859230000058
Figure FDA0003161859230000059
wherein:
a1、a2、k1、k2、C1and C2All are intermediate quantities;
a1＝M1s+(1+k1)A；
a2＝M1s+(1+k2)A；
Figure FDA00031618592300000510
Figure FDA0003161859230000061
C1、C2is obtained by dissolving after substituting the formula XXV and the formula XXVI under the definite dissolving condition;
step four, solving the steps from step two to step three to obtain the water temperature in the double-pipe heat exchanger
Figure FDA0003161859230000062
And
Figure FDA0003161859230000063
the solution in the frequency domain.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270512A (en) * 2022-08-24 2022-11-01 西南石油大学 Optimal flow design method of closed-cycle geothermal utilization system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3739749A1 (en) * 1987-11-24 1989-06-08 Mueller Christa Dr Selective treatment, at the same time and place, of tumours by means of heat and radioactive emissions by two-zone combination needles
CN109800527A (en) * 2019-01-30 2019-05-24 西安交通大学 A kind of calculation method for self circulation heat exchange amount in the buried double-tube heat exchanger of mid-deep strata
CN109946103A (en) * 2019-04-23 2019-06-28 山东建筑大学 A kind of underground heat parameter test system and method based on mid-deep strata ground heat exchanger
CN111551288A (en) * 2020-05-13 2020-08-18 山东建筑大学 Prediction method for circulating liquid temperature of middle-deep layer U-shaped heat exchange well
CN112597639A (en) * 2020-12-11 2021-04-02 山东中瑞新能源科技有限公司 Heat transfer dimension reduction analysis method and system for porous ground heat exchanger

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3739749A1 (en) * 1987-11-24 1989-06-08 Mueller Christa Dr Selective treatment, at the same time and place, of tumours by means of heat and radioactive emissions by two-zone combination needles
CN109800527A (en) * 2019-01-30 2019-05-24 西安交通大学 A kind of calculation method for self circulation heat exchange amount in the buried double-tube heat exchanger of mid-deep strata
CN109946103A (en) * 2019-04-23 2019-06-28 山东建筑大学 A kind of underground heat parameter test system and method based on mid-deep strata ground heat exchanger
CN111551288A (en) * 2020-05-13 2020-08-18 山东建筑大学 Prediction method for circulating liquid temperature of middle-deep layer U-shaped heat exchange well
CN112597639A (en) * 2020-12-11 2021-04-02 山东中瑞新能源科技有限公司 Heat transfer dimension reduction analysis method and system for porous ground heat exchanger

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
A. SHTYM; I. ZHURMILOVA: ""Ground heat exchangers of geothermal heat pumps and analysis of their constructive features and types"", 《2017 INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING, APPLICATIONS AND MANUFACTURING (ICIEAM)》 *
杜甜甜等: "套管式中深层地埋管换热器传热建模及取热分析", 《可再生能源》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115270512A (en) * 2022-08-24 2022-11-01 西南石油大学 Optimal flow design method of closed-cycle geothermal utilization system
CN115270512B (en) * 2022-08-24 2024-04-16 西南石油大学 Optimum flow design method for closed circulation geothermal utilization system

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