CN113515863B - 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 PDFInfo
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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
And
the solution in the frequency domain. According to the invention, under the condition of giving the initial temperature distribution function of the stratum, the water temperature at the inlet of the heat exchanger and the related physical parameters of the heat exchanger and the stratum, the distribution rule of the water temperature at the outlet 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-taking quantity of the double-pipe heat exchanger along with the time can be obtained.
Description
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 is also 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 to realize:
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:
boundary conditions are as follows: r → ∞ time:
r＝r b the method comprises the following steps:
initial conditions: t =0 time T e ＝az+T air ；
Solving to obtain:
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρ e is the density of the stratum rock mass with the unit of kg/m 3 ；
c e The specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
T e the temperature of the stratum rock mass at the depth z is represented by K;
T ez is the formation initial temperature in K;
t is time in units of s;
t 0 is a time factor of the formation temperature, dimensionless;
T air is the surface temperature in K;
λ e the heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
r b is the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
T b is 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 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:
outer tube heat balance equation:
wherein:
the conditions for the solution were as follows:
T 2 (0,t)＝T inj formula XI;
T 1 (H,t)＝T 2 (H, t) formula XII;
in the formula:
A 1 is the water passing cross-sectional area of the inner pipe, and the unit is m 2 ；
A 2 Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m 2 ；
ρ f Is the density of water in kg/m 3 ；
c is the specific heat capacity of water and the unit is J/(kg. K);
T 1 the temperature of water in the inner tube is expressed in K;
T 2 is the temperature of the water in the outer tube, in K;
T b is the borehole wall temperature in K;
w is the flow of water in the sleeve, and the unit is kg/s;
r 1 is the inner radius of the inner tube, and the unit is m;
r 2 is the outer radius of the inner tube, and the unit is m;
r 3 is the inner radius of the outer tube, and is expressed in m;
r 4 is the outer radius of the outer tube, in m;
r b is the borehole radius in m;
h is the geothermal well depth, and the unit is m;
h 1 is the convective heat transfer coefficient of the inner wall of the inner tube and has the unit of W/(m) 2 ·K)；
h 2 Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m) 2 ·K)；
h 3 Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m) 2 ·K)；
k i The heat conductivity coefficient of the inner tube wall is W/(m.K);
k o the thermal conductivity coefficient of the outer tube wall is W/(m.K);
k g the unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
T inj water 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:
from the formula XIII:
order:
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;
φ 1 is water Wen Yinzi in the inner pipe, and has no dimension;
φ 2 is water Wen Yinzi in the outer pipe, and is dimensionless;
t D the water temperature time factor in the double-pipe heat exchanger is dimensionless;
M 1 、M 2 all 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:
wherein:
φ 2 (0,t D )＝1；
φ 1 (1,t D )＝φ 2 (1,t D )；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
in the formula:
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
wherein:
a 1 、a 2 、k 1 、k 2 、C 1 and C 2 All are intermediate quantities;
a 1 ＝M 1 s+(1+k 1 )A；
a 2 ＝M 1 s+(1+k 2 )A；
C 1 、C 2 is 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
And
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 capability 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 exchange process in the double-pipe heat exchanger into a one-dimensional linear problem, and processing according to 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 drill hole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a drill hole, and the other part is a stratum outside the drill hole;
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:
boundary conditions: r → ∞ time:
r＝r b the method comprises the following steps:
initial conditions: t =0 time T e ＝az+T air ；
Solving to obtain:
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρ e is the density of the stratum rock mass with the unit of kg/m 3 ；
c e The specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
T e the temperature of the stratum rock mass at the depth z is represented by K;
T ez is the formation initial temperature in K;
t is time in units of s;
t 0 is a time factor of the formation temperature, dimensionless;
T air is the surface temperature in K;
λ e the heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
r b is the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
T b is 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:
outer tube heat balance equation:
wherein:
the conditions for the solution were as follows:
T 2 (0,t)＝T inj formula XI;
T 1 (H,t)＝T 2 (H, t) formula XII;
in the formula:
A 1 is the cross-sectional area of the inner tube, and the unit is m 2 ；
A 2 Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m 2 ；
ρ f Is the density of water in kg/m 3 ；
c is the specific heat capacity of water and the unit is J/(kg. K);
T 1 the temperature of water in the inner tube is expressed in K;
T 2 is the temperature of the water in the outer tube, in K;
T b is the borehole wall temperature in K;
w is the flow of water in the sleeve, and the unit is kg/s;
r 1 is the inner radius of the inner tube, and the unit is m;
r 2 is the outer radius of the inner tube, and is expressed in m;
r 3 is the inner radius of the outer tube, and is expressed in m;
r 4 is the outer radius of the outer tube, in m;
r b in order to be the radius of the drilled hole,the unit is m;
h is the geothermal well depth, and the unit is m;
h 1 is the convective heat transfer coefficient of the inner wall of the inner tube and has the unit of W/(m) 2 ·K)；
h 2 Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m) 2 ·K)；
h 3 Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m) 2 ·K)；
k i The heat conductivity coefficient of the inner tube wall is expressed in W/(m.K);
k o the thermal conductivity coefficient of the outer tube wall is expressed in W/(m.K);
k g the unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
T inj water 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:
from the formula XIII:
order:
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;
φ 1 is water Wen Yinzi in the inner pipe, and has no dimension;
φ 2 is water Wen Yinzi in the outer pipe, and is dimensionless;
t D the water temperature time factor in the double-pipe heat exchanger is dimensionless;
M 1 、M 2 all 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:
wherein:
φ 2 (0,t D )＝1；
φ 1 (1,t D )＝φ 2 (1,t D )；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
in the formula:
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
wherein:
a 1 、a 2 、k 1 、k 2 、C 1 and C 2 All are intermediate quantities;
a 1 ＝M 1 s+(1+k 1 )A；
a 2 ＝M 1 s+(1+k 2 )A；
C 1 、C 2 is obtained by the solution after the substitution of the formula XXV and the formula XXVI under the solution condition;
step four, solving the steps from step two to step three to obtain the water temperature in the double-pipe heat exchanger
And
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 obtained 1 And phi 2 Need to be aligned with
And
performing inverse laplace transform because
And
is in a complex form and cannot be directly usedPerforming laplace inverse change, namely obtaining a solution phi of the water temperature in the double-pipe heat exchanger on a time domain by using a numerical inversion method 1 And phi 2 And then T is obtained 1 (T, z) and T 2 (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
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 1500kW. Then, the outlet water temperature gradually decreases again as the heat extraction progresses. After 120 days of continuous heat extraction, the outlet water temperature is 27K, and the heat extraction amount is 420kW. 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 drill hole wall as a boundary, one part is a heat exchanger and a well cementation cement sheath in a drill hole, and the other part is a stratum outside the drill hole;
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:
boundary conditions: r → ∞ time:
r＝r b when the method is used:
initial conditions: t =0 time T e ＝az+T air ；
Solving to obtain:
in the formula:
q is the radial heat loss of the stratum at a certain depth and is expressed by W;
ρ e is the density of the stratum rock mass with the unit of kg/m 3 ；
c e The specific heat capacity of the stratum rock mass is expressed as J/(kg.K);
T e the temperature of the stratum rock mass at the depth z is represented by K;
T ez is the formation initial temperature in K;
t is time in units of s;
t 0 is a time factor of the formation temperature, dimensionless;
T air is the surface temperature in K;
λ e the heat conductivity coefficient of the stratum rock mass is W/(m.K);
r is the distance from the axis of the borehole in m;
r b is the borehole radius in m;
dQ is the radial heat loss of the formation at the borehole wall in units of W;
T b is 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:
outer tube heat balance equation:
wherein:
the conditions for the solution were as follows:
T 2 (0,t)＝T inj formula XI;
T 1 (H,t)＝T 2 (H, t) formula XII;
in the formula:
A 1 is the cross-sectional area of the inner tube, and the unit is m 2 ；
A 2 Is the cross-sectional area of water passing between the inner and outer tubes, and has unit of m 2 ；
ρ f Is the density of water in kg/m 3 ；
c is the specific heat capacity of water and the unit is J/(kg. K);
T 1 the temperature of water in the inner tube is expressed in K;
T 2 the temperature of water in the outer pipe is expressed in K;
T b is the borehole wall temperature in K;
w is the flow rate of water in the sleeve, and the unit is kg/s;
r 1 is the inner radius of the inner tube, and the unit is m;
r 2 is the outer radius of the inner tube, and is expressed in m;
r 3 is the inner radius of the outer tube, and is expressed in m;
r 4 is the outer radius of the outer tube, in m;
r b is the borehole radius in m;
h is the geothermal well depth, and the unit is m;
h 1 is the convective heat transfer coefficient of the inner wall of the inner tube, and has the unit of W/(m) 2 ·K)；
h 2 Is the convective heat transfer coefficient of the outer wall of the inner pipe and has the unit of W/(m) 2 ·K)；
h 3 Is the convective heat transfer coefficient of the outer tube wall, and has the unit of W/(m) 2 ·K)；
k i The heat conductivity coefficient of the inner tube wall is W/(m.K);
k o the thermal conductivity coefficient of the outer tube wall is W/(m.K);
k g the unit is W/(m.K) for the heat conductivity coefficient of the cementing material;
T inj water 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:
from the formula XIII:
order:
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;
φ 1 is water Wen Yinzi in the inner pipe, and has no dimension;
φ 2 is water Wen Yinzi in the outer pipe, and is dimensionless;
t D the water temperature time factor in the double-pipe heat exchanger is dimensionless;
M 1 、M 2 all 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:
wherein:
φ 2 (0,t D )＝1；
φ 1 (1,t D )＝φ 2 (1,t D )；
in the formula:
beta is a factor of the geothermal gradient and is dimensionless;
laplace transformations of the formulae XXIII and XXIV:
in the formula:
s is a complex variable and is dimensionless;
solving the linear differential equations of the formulae XXIII and XXIV to obtain:
wherein:
a 1 、a 2 、k 1 、k 2 、C 1 and C 2 All are intermediate quantities;
a 1 ＝M 1 s+(1+k 1 )A；
a 2 ＝M 1 s+(1+k 2 )A；
C 1 、C 2 is 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
And
the solution in the frequency domain.
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Citations (5)
| 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 |
-
2021
- 2021-07-14 CN CN202110793294.8A patent/CN113515863B/en active Active
Patent Citations (5)
| 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)
| 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)》.2017, * |
| 套管式中深层地埋管换热器传热建模及取热分析;杜甜甜等;《可再生能源》;20200720(第07期);全文 * |
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