SOCAR Proceedingsproceedings.socar.az/uploads/pdf/31/Sliva-029-042.pdf · inner pipe was...

29

SOCAR ProceedingsReservoir and Petroleum Engineering

journal home page httpproceedingssocaraz

1 IntroductionThese days the energy demand is constantly

rising therefore potential energy resources are being searched increasingly One of the ways is consumption of the geothermal energy stored in the ground a natural reservoir of heat Energy of the rock mass can be acquired by using borehole heat exchangers Such exchangers and heat pumps make it possible to obtain quality heat suitable for users (eg residential buildings public buildings) This solution allows obtaining heat from low-temperature sources Scientific studies on BHEs were performed by many authors including [1-4]

Most commonly used are exchangers of a single or a double U-tube structure (fig1a and 1b) This type of heat exchangers is usually allocated for boreholes with shallow depth (up to 200-300 m) Single plate exchangers are being used by individual customers such as small individual households or small enterprises In order to increase the heating power a larger area of the rock mass is provided by installing the U-tubes in several neighboring holes In some cases more than thousand holes can operate for the provision of heat and cold [5]

Deep BHEs needs another approach For deep boreholes ranging from several hundred to several thousand meters the most reasonable application is the centric structure of the heat exchanger (fig1c) Implementation of this structure bases on introduction of a centric tube column made of a material characterized by a low thermal conductivity into an existing borehole Such installations have a chance to succeed eg in old and worn out boreholes originally used for oil and gas production as well as in negative wells which have been equipped with steel casing of a high thermal conductivity Drilling new holes for a deep borehole heat exchanger is unprofitable

Deep BHEs can be used for producing geothermal The method of performing such exploitation of heat is not fraught with risk as in the case of geothermal waters where problems such as corrosion absorption and precipitation of minerals may arise [6] Geothermal energy is considered as a source of renewable energy but continuous consumption of the heat by using BHEs can reduce during long-term operation temperatures in the heat storage [78] The natural regeneration of heat resources may not be enough especially with a large number of the BHEs [9] To remedy this problem various artificial methods

STUDY ON THE EFFICIENCY OF DEEP BOREHOLE HEAT EXCHANGERS

TSliwa1 TNowosiad1 OVytyaz2 ASapinska-Sliwa1 1AGH University of Science and Technology in Cracow Cracow Poland

2Ivano-Frankivsk National Technical University of Oil and Gas Ivano-Frankivsk Ukraine

SOCAR Proceedings No2 (2016) 029-042

A b s t r a c t The following paper shows results of several studies carried out with the Earth Energy Designer program (EED321) Having used the EED analyses on efficiency of the heat extraction were conducted and measurements of productivity were taken in dependence of variable parameters of a theoretical deep coaxial borehole heat exchanger The depth of 1000 m and the constant heating load 80 MWh per year were assumed for the borehole exchanger The variables analyzed were type of the heat carrier fluid flow rate of the heat carrier diameter of the borehole wall thickness of the inner tube (insulation) diameter of the inner tube thermal conductivity of the inner tube material wall thickness of the outer tube diameter of the outer tube and thermal conductivity of the outer tube material Due to mathematical basis of the EED program results of the calculations can be considered as diminished To operate correctly the program can use parameters from a borehole not deeper than 300 meters At greater depths of borehole heat exchangers results are understated Therefore the results of analyses presented below can be seen as a pessimistic scenario of the calculations

Keywords Geothermal heat exploitation Borehole heat exchangers (BHE) Heat pumpsLow-temperature geothermal heat

copy 2016 laquoOilGasScientificResearchProjectraquo Institute All rights reserved

E-mail sliwaagheduplhttpdxdoiorg105510OGP20160200276

30

of recovery of heat resources in the ground can be used eg using solar collectors [10] If so the energy obtained from the reservoir is no longer only a geothermal energy

A heat carrier in the centric system is introduced into the annular space and flows to the surface in the inner tube - the centric column The energy obtained in this way may satisfy the heat demand for bigger consumers [5] It is however characterized by a large capital for the investment Usage of the existing boreholes minimizes the costs and allows to reuse the old wells instead of liquidation which is connected with new costs so the process may be economically advantageous Currently the energy generation described above is not financially viable but getting experience in implementation and operation of these systems will pay off at the time when energy will be more expensive when fossil energy sources will be close to completion

When analyzing oil boreholes held for liquidation and located near to potential sources

of the heat if liquidation costs can be allocated to adaptation the economic balance of the deep borehole exchangers may be beneficial [11-13] A matter of insulation for the internal column pipes however may be problematic The pipe can be either well insulated and expensive or cheaper and poorly insulated [14] The costs will increase if there is a need to use the equipment with a large lift capacity (using a double steel tube)

For operational analysis and prediction of the deep BHEsrsquo exploitation a number of mathematical models has been created [15-18]

2 Examples of deep borehole heat exchangers

In recent years due to the increasing energy demand numerous innovations for constructing designing and locating borehole heat exchangers were created It is increasingly popular around the world to use the coaxial heat exchangers by using a number of unexploited boreholes [19] In Poland tests on redevelopment of old boreholes

TSliva et al SOCAR Proceedings No2 (2016) 029-042

Fig1Schemes of the borehole heat exchangers design a) single U-tube b) double U-tube c) coaxial heat exchanger A - surface area B - rock mass 1 - wall of the hole 2 - filling the hole 3 - U-tube heat exchanger 4 - outer tube of the centric system

5 - annular space of the centric system 6 - inner tube of the centric system 7 - inner pipe interior

1 1 1

2 2

2

3 3

45

6

7

AB

31

to obtain geothermal energy were carried out in some cases [1120] In many countries energy harvesting using borehole exchangers (eg in Germany Sweden Switzerland the USA) becomes an important branch of energy industry Examples of deep borehole heat exchangers usage from around the world are presented in the following chapters

21 HawaiiIn 1991 a group of scientists under the

leadership of Koji Morita performed first tests on a deep BHE The experiment took 10 days between 2202-0103 [21] operations were performed on the HGP-A borehole in the Hawaiian province of Puna in order to verify the concept of using a coaxial exchanger The total borehole depth was 1962 meters in the whole lithological profile basalt formations occurred Thermal conductivity of basalt [22] is 133-229 Wm-1K-1 The inner tube was inserted to a depth of 8765m Undisturbed temperatures found at the bottom of the test section reached 110 degC In the construction of the borehole an innovative solution for the inner pipe was introduced The double vacuum inner tube was applied [23] it was composed of 74 parts with a 3frac12lsquorsquo diameter the pipe was developed in collaboration with Sumitomo Metal Industries Ltd Kawasaki Thermal Systems Inc and Kubota Ltd Based on formula (1) equivalent thermal conductivity for the constructed pipe was calculated for about 002 Wm-1K-1 (fig2)

(1)

whereλr - total heat conductivity of the insulated pipeλ123 - heat conductivities of a single elements

of the pipe

d1234 - diameters of single elements of the pipe (fig3)During the experiment water of temperature

of 30degC was injected to the borehole with flow rate about 80 dm3-min-1 The highest output temperature received during the experiment was 98 degC The maximum heating power has been observed of approximately 370 kW The experiment confirmed previously performed numerical simulations for this area [24]

22 SwitzerlandIn the nineties of the 20th century attempts

were made to use the borehole of 1600 m depth located in Weissbad Switzerland [15] for geothermal water exploitation The well was drilled in 1993 on request of the nearby hotel to explore anticipated highly productive aquifers The hole has proved to be negative therefore the idea of using it as the heat exchanger was born In the borehole a centric column was used which reached the depth of 12133 m The borehole operated as a heat exchanger in the period from 8 November 1996 to 7 November 1998 On the basis of research conducted in August 1993 the temperature at the bottom of the exchanger was determined as 45 degC As the heat transfer medium tap water was used it was pumped at a flow rate of 180 dm3-min-1 The initial assumptions based on numerical simulations predicted to obtain the temperature of 15 degC during long-term use of the heat After the analysis of the data obtained from measurements and simulations it was found that average temperatures in matching measuring periods are lower than expected of about 18 degC A number of differences between actual values and those which were used to the simulations was found The most likely cause of the irregularities was incorrect cementation of the borehole which largely increased resistance of the heat flow Therefore the data obtained from the hole were different from the previous assumptions

Another important finding was a poor choice of the inner pipe to meet the needs of the project As the inner pipe a steel pipe was used which was only the barrier between the down flow and the up flow fluid without proper thermal insulation

23 PolandIn Sucha Beskidzka directional

borehole Jachoacutewka-2k was drilled in the 1997 of a depth of 4281 m [20] The borehole originally was drilled for petroleum exploration but concentration of hydrocarbons was too small therefore researches for heat exploitation begun The centric construction of the heat exchanger was inserted to the depth of 28645


Fig2 The internal structure of the centric column used as the heat exchanger in the borehole HGP-A in Hawaii

1 - outer tube 2 - connector 3 - inner tube 4 - thread 5 - vacuum space

4

1

32 4

1 1 2 2 3 3

1 1 1r

dln

ddd d

ln ln lnd d d

λ

λ λ λ

=+ +

32

meters Results obtained during the tests were unsatisfactory due to application of steel pipes without sufficient insulation for the inner tube In the study measurements of the heat carrier self circulation were made The self flow with heat recovery at the surface and a density difference of the heat carrier was successfully obtained for one hour with a flow rate of 6 dm3-min-1 of water The whole project had the character of research its main objective was to analyze the previous assumptions As part of the subsequent work extensive analysis of the inner tubes was carried out The column with double tubes of steel with nitrogen between was analyzed Calculations of thermal expansion for both pipes in the internal column with a selection of different fillings between also were made [20] Trajectory of the borehole was an additional challenge when the internal pipe column was analyzed eg because of an additional stress [25] and application of centralizers The newly designed system of internal columns for the borehole however was not introduced due to lack of funds

Deep Borehole heat exchangers operate also in Germany where plenty of studies on models for a deep BHE was carried out More information about deep BHE is shown in the work [5]

3 The mathematical description of heat exchange in the ground

While modeling processes of heat exchange with the rock mass some assumptions need to be made Before analyzing the temperature-related issues the key concepts relating to the process

are presentedOne of the most important parameters for the

thermal process is thermal conductivity This is a property of the environment in which the process takes place largely dependent on its state It is characterized by the ability to conduct the heat in a medium When it comes to the rock mass conductivity of a layered structure should be considered [1] The thermal conductivity in the layered structures is described by the formula

(2)

whereλ ndash average thermal conductivity in a profileλ` - thermal conductivity of a single layer H - hole depthA B - the floor and the sill of each horizontal layerz - depth coordinate

However using the Eskilson model (1987) enables to adopt uniformity of the environment and exclude its layered structure which greatly simplifies the calculations without affecting the results This was also confirmed in the work [26]

Another important parameter is heat exploitation rate q(t) (the heating load) It is described by the equation

(3)

whereq(t) - heating capacityH - hole depth

Fig3 Cross section of the centric tube heat exchanger using the vacuum inner tube 1 - rock mass 2 - borehole wall 3 - filling material 4 - outer wall of the outer column 5 - outer column

6 - inner wall of the outer tube 7 - annular space of the centric heat exchanger 8 - internal column (insulation column) 9 - external wall of the outer tube in the insulating column 10 - outer tube of the

inner column 11 - vacuum space of the inner column 12 - inner tube of the inner column 13 - inner wall of the inner column 14 - inside space of the inner column


( )1`

B

A

z dzH

λ λ= int

1

14 10

2

8

12

3

94

5

67

11

13

( ) 12

b

D H

r rD

Tq t r dz

H rπ λ

+

=

part=

partint

33

A - the thickness of the surface layer of rock (depth periodic heat transfer)

T - temperaturey - distance from the axis of the bore in the

radial directionrb - hole radiusλ - thermal conductivity of rocks

Exploitation of borehole heat exchangers can be constant - one directional or cyclic seasonal - in both directions In the second case the heat can be collected from rock mass (in winter) and inserted into the rock mass (in summer) This process can be expressed by the use of the Heaviside step function [1]

(4)

whereq(t) - heat extraction rateHe(t) - the Heaviside step functionq1 - heat extraction stept - time

With reference to deep BHEs the operation can only work in one direction Entering the heat into the borehole exchanger is associated with indoor air-conditioning Owing to the temperature increase along the depth air-conditioning is not possible to apply with deep BHEs

The amount of the produced energy (the heat output) is also dependent on the flow rate of the heat carrier fluid The greatest efficiency of thermal exploitation is obtained if speed of the circulating medium is as high as possible Then the flow in channels is turbulent According to the above an advantageous (ie as small as possible) difference between the temperature of the fluid injected and taken out from rock formation can be obtained It is based on the dependence for heating power

(5)where

P ndash energy stream (heating power)ρ ndash specific mass of heat carrierc ndash mass specific heat of heat carrierΔT ndash temperature difference between inflow

and outflow to BHE

For an amount of heat obtained from the BHE it is obvious that the depth of the borehole has great effect In this discussion it is considered as the total depth of the hole without a periodic heat penetration depth (D) At this depth daily and seasonal temperature changes occurred under influence of external factors (temperature precipitation insulation) In Poland this depth ranges from 10 to 27 m [27]

It is essential to take into the consideration land surface temperature In the Eskilson model (1987) it is assumed that the temperature and

factors affecting it such as precipitation daily temperature fluctuations do not affect the process The average natural (undisturbed) rock temperature (Tam) is defined as the temperature at the average depth of the hole It may be described using the geothermal gradient as follows

(6)

whereTam - effective undisturbed ground temperatureTo - average air temperature at the ground

surfaceG - geothermal heat flux

When describing the possessing of the heat output in order to describe the temperature distribution in the impact zone adaptation the radial coordinate system is the most convenient The equation of the temperature distribution in the ground based on the capabilities of thermal conduction in situ is described as follows

(7)

where α - thermal diffusivity of the groundT - temperature in the groundt - timer - radial distancez - vertical coordinate

On the basis of this relationship taking into account the concept of thermal conductivity the equation of the rock mass thermal conductivity is driven from the Fourier-Kirchhoff law in the Cartesian coordinate system as [26]

(8)

whereρ - density of the environmentcp - heat capacity (steady pressure)cf - heat capacity of the fluidv - velocity of the circulating heat carrierλ ndash thermal conductivity of the grounds ndash component describing phase transitions in

the rock mass (water filtration velocity etc)

Boundary conditions for temperature are described as

(9)

(10)where

- initial temperature

- temperature at the surface

In the further discussion temperatures associated with the borehole must be taken


( ) ( ) ( ) 1 0

0 0q t q He t He t

= =

ρ= sdot sdot sdot∆P V c T

2α

minus= + sdotm o

H DT T G

2 2

2 2

1 1

αpart part part partsdot = + sdot +part partpart partT T T Tt r rr z

0== + sdotot

T T G z

( )ρ ρ λpart+ sdotnabla = nablasdot nabla +

partp fTc c v T T st

0== oz

T T

0== + sdotot

T T G z

0== oz

T T

34

into consideration [28] The temperature of the borehole wall determines the equation based on finite difference method in the cylindrical coordinates system

(11)where

q1 - heat extraction stepTb - temperature at the borehole wallRq - thermal resistance due to a heat extraction

step

Temperature of the borehole wall is a variable parameter during the process of heat exchange with the rock mass For change of this parameter many factors are significant It is expressed by terms of time-dependent heat flow resistance

(12)

whereRq - thermal resistance

- g-function

rb - borehole radiusts - steady-state extraction time

The g-function described in the model is used to bring forward the relatives in configuration of a greater number of boreholes When the g-function asymptotes undergo the analysis a decrease in resistance over time can be noted It occurs until the system reaches the equilibrium the time needed to balance the system is defined as

(13)

Then the temperature shall get a constant value it is no longer dependent on the process of exploitation In the same way on the basis of the finite differences method in the cylindrical coordinate system a relation between average temperature in the bore average temperature of the liquid and the resistance of the opening wall is obtained The above relation is defined by the formula (14) The assumption that the carrier flow is turbulent was vital Therefore it can be assumed that temperature variation in the borehole is negligibly small The described dependence is presented below

(14)

where - mean temperature of heat carrier fluid

Rb - thermal resistance between fluid and borehole wall

q - heat flowOn base of the previous considerations

temperatures of the inlet and outlet fluid can be drawn The temperatures variation along the

borehole is defined by equations

(15)

(16)where

Tf in - inlet fluid temperatureTf out - outlet fluid temperaturec

f - heat capacity of the fluid

vf

- velocity of the fluidρ

f - density of the fluid

The heat transfer fluid requires a circulation pump to let it flow into the system Self-circulation after stopping the pump is short-lived It was observed in the heat exchanger based on the borehole Jachoacutewka-2k in Poland [20] Hydraulic power in the annular space expressed using the Darcy-Weisbach formula is described by the relation below [29]

(17)

The hydraulic power inside the centric column is described as follows

(18)

whereη - viscosity of the heat carrierL - length (depth) of borehole heat exchanger - flow rate of heat carrierPin - inner diameter of the outer tubedout - outer diameter of the column centricdin ndash inner diameter of the column centric

4 Assumptions for modelingIn order to examine the effect of various

parameters on the heat carrier fluidrsquos temperature series of calculations for structural variables of construction in the heat exchanger has been conducted The calculations were made for the borehole depth of 1000 m All the assumptions for the borehole heat exchanger are shown in table 1 As a result of modeling the average temperature of the heat carrier after 10 years of continuous operation of the system was taken

5 Results and discussionThe following text describes and presents

charts of various deep BHE design parametersrsquo impact on the average heat carrier temperature after 10 years of continuous exploitation of heat with the fixed annual heating load

In the table 2 are presented the results of the simulation involving variable working mediums When analyzing the results it can be seen that the best average temperature value is obtained for water which has the best abilities to transfer heat The worst in this regard is ethanol The ability to


1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG

minus = sdotb f bT T q R


3

2 5

8 λ ρπ

sdot sdot sdot sdot=

sdot

in

in

L VPd

2 5

λ ρsdot sdot sdot sdotsdotin

in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d

1α= minus sdotb m qT T q R

2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35

transfer more heat is primarily due to differences of the heat carrierrsquos specific heat values Slightly lower temperatures were obtained for a solution of monoethylene glycol Methanol and ethanol have the lowest specific heat which causes that at the same flow rate these fluids can transport much less heat than the water

The figure 4 refers to the heat carrier fluidrsquos flow rate As the flow increases it becomes more turbulent thereby a higher average temperature of the fluid is possible to achieve The larger the mass stream of the media is the smaller are increases of the temperature An increase of the carrier flow rate however is correlated with a higher

flow resistance Therefore greater energy inputs are required to force circulation in the pipes The hydraulic power was calculated using the formulas (17) and (18) on basis of the calculations the plot on figure 5 was created

Figure 6 shows the average temperature obtained from the formation plotted as the function of the borehole diameter It can be seen that as the diameter is growing obtained temperatures are getting smaller This dependence is associated with the enlargement of the annular surface area between the borehole wall and the outer tube it is connected with an increase in the filling material between them The hydrated bentonite was assumed to be the filling - as for old oil bores in the Carpathian mountains The value of the thermal conductivity is considerably lower than the conductivity of rocks in the formation It is the cause of a higher resistance in the heat flow process

Then the graph of the heat carrierrsquos average temperatures compared to the thickness of the inner column was done (fig7) An increase of the thickness was assumed to result in a uniform increase in the outer diameter and a reduction in the inner diameter On basis of the above it can be seen that a rise in the wall thickness is connected with larger differences between the temperature of the fluid supplied to the ground and the fluid discharged from it This

dependence is related to the process of the medium flow in the heat exchanger - cold fluid is transported in the annular space and flows to the surface in the inner tube In such system the barrier against heat losses is the inner tube so the thickness of it has a significant effect on the average temperature if the temperature of thermal conductivity is assumed to be steady The wall thickness of the inner tube also affects the nature of the carrierrsquos flow

The next graph demonstrates temperature changes according to the inner tubersquos diameter (fig 8) There is a noticeable drop in the temperature of the heat carrier correlated with a growth of the inner pipersquos diameter A rise in the diameter is associated with a loss of the space for the medium [30] The smaller annular space is for fluid to flow the higher the velocity becomes as it overrides the need to preserve the stability of the stream thus the medium does not have the possibility to heat up because of a shorter time of the carrier in the BHE pipes The studies on the effect of the flowrsquos nature on the effectiveness of the borehole heat exchanger were described by Gałuszka The work was done on the BHE centric model in the Laboratory of Geoenergetics on


Parametr Value

Borehole diameter mm 2000

Inner tube diameter mm 900

Inner pipe wall thickness mm 46

Inner piper material heat conductivity W∙m-1∙K-1 022

Outer pipe diameter mm 1800

Outer pipe wall thickness mm 40

Outer pipe material heat conductivity W∙m-1∙K-1 040

Borehole filling heat conductivity W∙m-1∙K-1 06

Heat carrier volume flow rate dm3∙min-1 1200

Heat carrier conductivity W∙m-1∙K-1 06

Heat carrier fusion heat J∙kg-1K-1 4182

Heat carrier density kg∙m-3 9983

Heat carrier viscosity kg∙m-1s-1 0001003

Ground heat conductivity W∙m-1∙K-1 35

Ground volumetric heat capacity MJ∙m-3∙K-1 2160

Ground surface temperature degC 860

Geothermal heat flux W∙m-2 0060

Annual heat load GJrok (MWhyear) 288 (80)

Average heating power kW 2222

Average unit power Wm 2222

Time of exploitation Rok 10

Heat carrier Temperature oC

Water 1193

Methanol 1164

Monoethylene glycol 1184

Ethanol 1156

Monopropylene glycol 1163

Table 1 Basic assumptions for the implementation

of borehole heat exchanger modeling operation

Table 2 Comparison of heat carriersrsquo average

temperatures in the process

36


Drilling Oil and Gas Faculty AGH University of Science and Technology in Krakow [31]

The plot in figure 9 shows the temperature dependence on the thermal conductivity of the inner tube It can be seen the lower thermal conductivity of the inner tube material is the higher average temperatures of the heating medium can be achieved When the thermal conductivity tends to zero temperatures exploited from the bore are much higher comparing to the injected fluid temperature Such material acts as an insulator - lower heat loss occurs When the thermal conductivity tends to infinity the obtained temperature differences become smaller and tend to the zero The simulation was made for three possible materials polypropylene (λ=022 Wm-1K-1) polyethylene (λ=042 Wm-1K-1) and steel (λ=50 Wm-1K-1)

Figure 10 shows the graph of temperature profiles of the heat carrier in the annular space (inside the insulating column) depending on the heat conductivity of the columnrsquos material [32] It can be seen that the smaller the thermal

conductivity of the column is (greater insulation) the higher heating power can be produced which is manifested by an increase of the temperature difference between the fluid that enters and leaves the heat exchanger The chart concerns the borehole heat exchanger in Japan situated in a volcanic activity zone so it shows a relatively high temperature of the heat carrier

Another graph shows the average temperature dependence of the heat carrier against the outer tube thickness (fig11) Clearly the linear drop in the temperature related with an increase in value of the wall thickness - the thicker the wall is the greater the resistance for heat flow from rock to the heat carrier is generated A lower thermal conductivity results in a decrease in the temperature change of the heat carrier during the process The effect is similar to the case of increasing the borehole diameter thereby the resistance associated with the borehole sealing is increasing

In the graph in figure 12 average temperatures obtained from the borehole versus diameter of the

Fig4 Dependence of the carrierrsquos average temperatures according to flow rate

Fig5 Dependence of the hydraulic power according to the flow rate

Fig6 Dependence of the heat carrierrsquos average temperatures according to the boreholersquos diameter

Fig7 Dependence of the heat carrierrsquos average temperature according to the inner pipe wallrsquos

thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212

Wall thickenes of the oinner pipe mm

1199120

116

117

119

1204

1165

1183

200 220180Diametr of the outer pipe mm

1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37

outer tube are presented The temperature increase with an expansion of the diameter can be found An increase in the diameter is associated with two effects The first is reduction in thickness of the filling material between the external column and the borehole wall This results in greater potential for the heat conduction The second effect is higher volume of the heating medium in the annular space It contributes to a reduction of the carrierrsquos speed with maintaining constant flow rate According to the above the fluid spends longer time in contact with the outer column wall The result is therefore an increase in the carrierrsquos temperature

The graph in figure 13 shows a relation between the obtained temperature and the conductivity of the outer tube It is noted that along with the increasing conductivity the average temperature of the fluid increases This is due to a reduction in the thermal resistance between the carrier and the rock

mass As for the internal column polypropylene (λ=022 Wm-1K-1) polyethylene (λ=042 Wm-1K-1) and steel (λ=50 Wm-1K-1) materials were taken as an issue

The following chart shows temperature distribution depending on thermal conductivity of the filling material (fig14) The effect is similar to the variation of the thermal conductivity of the outer tube material The increase in conductivity of the sealing material reduces the resistance of the heat transfer between the medium and the rock mass Additionally in the space between the outer tube and the borehole wall water may be present Water provides natural convection so heat transfer potential can be improved In the graph the conductivities of the following materials are

Fig9 Dependence of the heat carrierrsquos average temperature according to the inner

pipersquos heat conductivity

Fig8 Dependence of the heat carrier average temperature according

to the inner pipersquos diameter Fig10 Temperature profiles in a centric heat exchanger assuming feedback circuit for

the different conductivity of the inner tube 1 - 001 Wm-1K-1 2 - 012 Wm-1K-1 3 - 116 Wm-1K-1 4 - 461 Wm-1K-1

Fig11 Dependence of the heat carrierrsquos average temperature according to the outer

pipersquos wall thickness


Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176

2Wall thickenes of the outer pipe mm

1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34

Heat conductivity of the outer pipe mm

120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183

8070 90 100Diametr of the outer pipe mm

110

121

1203

1213

38

shown in order 1 - Dry sand (04 Wm-1K-1) 2 - Water or bentonite (06 Wm-1K-1) 3 - Compacted dry grout (12 Wm-1K-1) 4 - Saturated gravel (18 Wm-1K-1) 5 - High thermal conductivity grout (20 Wm-1K-1)6 - Saturated sand (24 Wm-1K-1)In the foregoing debates it was taken into

account that the resulting temperature in the EED is obtained as the temperature at the middle depth of the borehole This situation may be acceptable only to the depth of 300 m (fig15) It appears due to re-cooling process of the heated medium on the way back to the surface caused by the interaction with the colder fluid in the annular space In manner of performance to increase their thermal efficiency the deep borehole heat exchangers are equipped with an additional insulation of the inner pipe in the upper part What is more the heat carrier introduced into the annular space may have a higher temperature than the surrounding

subsurface rock To improve the insulation of the upper part of the borehole the cement paste characterized by low thermal conductivity is usually used as the filling material [33] In this way the BHE in Aachen was constructed

For the needs of drilling industry a number of studies covering different formulas of sealing slurries for boreholes is carried out The aforementioned practical applications are not covered by the program assumptions This discrepancy contributes to obtain the results of the simulation at lower temperatures than in reality The maximum depth at which the program is working properly is 300 m So it can be only used for typical installations with BHEs In the graph in figure 15 is shown the effect of the boreholersquos depth on the received average temperature of the heat transfer medium The graph additionally presents the unit power changes along the depth of the borehole

The calculation was made based on the Eskilson

Fig12 Dependence of the heat carrierrsquos average temperature according

to the outer pipersquos diameter



Fig14 Dependence between the average temperature and the thermal conductivity

of the borehole filling

Fig 15 Dependence showing the borehole depth influence on the obtained temperatures (1)

dependence showing the unitary power influence on the obtained temperatures (2)


Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120

Conductivity of the filling Wm-1K-1

2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39

(1987) model The model was the basis for the EED software EED is a methodology with multipole and g-function standard so it can be called quasi numerical

Numerical modeling was shown for example by Sliwa and Gonet [16] Use of the numerical method for mathematical modeling of BHEs is difficult The reason for it are dimensions of wells The diameter

the dimension in the radial direction is repeatedly smaller than the depth It generates problems when preparing the numerical grid The numerical model for BHEs is still being corrected and improved [8] The problem is with the data for calibration of the model Preparing the existing deep BHE is not cheap To this time there is not one deep BHE based on an old oil or gas well

The article was done as statutory research at the Faculty of Drilling Oil and Gas AGH University of Science and Technology in Krakow agreement no 1111190555

6 Conclusions

When analyzing the results of the above simulations impact of the design parameters in the BHE on the quality of energy produced from the rock mass could be seen The measure of this quality is the heat carrier fluidrsquos average temperature

The most efficient heat carrier is water The resulting heating power for the BHE increases with the flow rate The nature of this relationship however is non-linear The greater the heat carrierrsquos stream is the smaller are heating power increases associated with it but exponentially with flow rate growth pressure losses The thickness of the inner pipe should be as large as possible (thermal insulation - the inner tubes should be made of materials characterized by low thermal conductivity) Smaller diameter of this column is better It is important to remember that the flow resistance increases very fast with the reduction of the flow channel in the area

The situation is different with outer casing The wallrsquos thickness of the outer tube should be as small as possible When steel is the material for the casing (as always in oilgas wells) the thickness can be bigger Steel is a good heat conductor The diameter of the tube should be big (it increases the heat flow area)

The filling between the walls of the borehole and the outer pipe should be as accurate as it is possible A specially improved grout (high conducted) was used as BHE when drilling a deep borehole in Aachen Germany

The obtained results because of the mathematical model which is the basis for the EED software are understated It can therefore be considered as pessimistic predictions in the work of the BHE system The internal column whose task is to thermally insulate the stream of inside of this column should be considered as the most important parameter


40

References

1 PEskilson Thermal analysis of heat extraction boreholes PhD Thesis Sweden University of Lound 1987

2 GHellstroumlm Ground heat storage thermal analyses of duct storage systems PhD Thesis Sweden Lund Institute of Technology 1991

3 BNordell Borehole heat store design optimization PhD Thesis Sweden Lulearing University of Technology Division of Water Resources Engineering 1994

4 AGonet TSliwa SStryczek et al Metodyka identyfikacji potencjalu cieplnego goacuterotworu wraz z technologia wykonywania i eksploatacji otworowych wymiennikoacutew ciepla Krakoacutew Wydawnictwa AGH 2011

5 ASapinska-Sliwa MARosen AGonet TSliwa Deep borehole heat exchangers A conceptual review Proceedings of the World Geothermal Congress Australia Melbourne -2015 -P1-11

6 BTomaszewska LPajak Geothermal water resources management-economic aspects of their treatment Mineral Resource Manager (Gospodarka Surowcami Mineralnymi) -2012 -Vol28 -P59-70

7 SSignorelli TKohl LRybach Sustainability of production from borehole heat exchanger fields Proceedings of the 29th Workshop on Geothermal Reservoir Engineering CA USA Stanford Stanford University 2004 -P1-6

8 MJaszczur TSliwa The analysis of long-term borehole heat exchanger system exploitation Computer Assisted Methods in Engineering and Science -2013 -Vol20 -No3 -P227-235

9 MJaszczur IPolepszyc ASapinska-Sliwa Numerical analysis of the boundary conditions model impact on the estimation of heat resources in the ground Polish Journal of Environmental Studies -2015 -Vol24 -No5A -P60-66

10 TSliwa MARosen Natural and artificial methods for regeneration of heat resources for borehole heat exchangers to enhance the sustainability of underground thermal storages A review Sustainability -2015 -Vol7 -No10 -P13104-13125

11 TSliwa Techniczno-ekonomiczne problemy adaptacji wykorzystanych odwiertoacutew na otworowe wymienniki ciepla PhD Thesis Krakow AGH University of Science and Technology in Krakow 2002 (Technical and economic problems of adaptation of used wells into borehole heat exchangers PhD Thesis Krakow AGH University of Science and Technology 2002)

12 TSliwa JKotyza Application of existing wells as ground heat source for heat pumps in Poland Applied Energy -2003 -Vol74 -P3-8

13 AGonet TSliwa Possibilities of heating and air-conditioning of buildings in the mountain areas Geomatics Landmanagement and Landscape -2014 -No3 -P55-63

14 TSliwa AGonet The closing wells as heat source Acta Montanistica Slovaca -2004 -Vol9 -No3 -P300-302

15 TKohl MSalton LRybach Data analysis of the Deep Borehole Heat Exchanger Plant Weissbad (Switzerland) Proceedings of The World Geothermal Congress Japan Kyushu-Tohoku 2000 -P3459-3464

16 TSliwa AGonet Theoretical model of borehole heat exchanger Journal of Energy Resources Technology -2005 -Vol127 -P142-148

17 RAl-Khourya TKoumllbelb RSchramedeic Efficient numerical modeling of borehole heat exchangers Computers amp Geosciences -2010 -Vol36 -Issue 10 -P1301-1315

18 APriarone MFossa Modelling the ground volume for numerically generating single borehole heat exchanger response factors according to the cylindrical source approach Geothermics -2015 -Vol58 -P32-38

19 TSliwa MARosen ZJezuit Use of oil boreholes in the Carpathians in geoenergetics systems historical and conceptual review Research Journal of Environmental Sciences -2014 -Vol8 -P231-242

20 JSokolowski RFlorek AGoacuterka et al Metodyka i technologia uzyskiwania uzytecznej energii geotermicznej z pojedynczego otworu wiertniczego Krakoacutew Instytut GSMiE PAN Pracownia Geosynoptyki I Geotermii 2000 (Methodology and technology of obtaining usable geothermal energy from a single borehole Krakow The Mineral and Energy Economy Research Institute of the Polish Academy of Sciences 2000)


41

21 KMorita WSBollmeier HMizogami An experiment to prove the concept of the downhole coaxial heat exchanger (DCHE) in Hawaii Transactions of the Geothermal Resources Council -1992a -Vol16 -P 9-16 15

22 TBloomberg JClaesson PEskilson et al Earth Energy Designer (EED v32) BLOCON 2015 httpwwwbuildingphysicscommanualsEED3pdf

23 KMorita WSBollmeier HMizogami Analysis of the results from the downhole coaxial heat exchanger (DCHE) experiment in Hawaii Transactions of the Geothermal Resources Council -1992b -Vol16 -P17-23

24 KMorita MTago Development of the downhole coaxial heat exchanger system Potential for fully utilizing geothermal resources The Geothermal Resources Council bulletin -1995 -Vol24 -No3 -P 83-92

25 DKnez Stress state analysis in aspect of wellbore drilling direction Archives of Medical Science -2014 -Vol59 -P71-76

26 TSliwa MJaszczur AGonet Analiza numeryczna wplywu wlasnosci goacuterotworu na transport ciepla wokoacutel otworowego wymiennika ciepla Proceedings of XIV Sympozjum Wymiany Ciepla i Masy Polska Akademia Nauk Wydawnictwo Uczelniane ZUT Szczecin 2010 -P551-562 (Numerical analysis of the rock properties effect on the heat transport around borehole heat exchanger Proceedings of XIV Sympozjum Wymiany Ciepla i Masy Polska Akademia Nauk Wydawnictwo Uczelniane ZUT Szczecin 2010 -P551-562)

27 SPlewa Rozklad parametroacutew geotermalnych na obszarze Polski Krakoacutew Wydawnictwo CPPGSMiE PAN 1994 (Distribution of geothermal parameters in the area of Poland Krakow Wydawnictwo CPPGSMiE PAN 1994)

28 JWoloszyn Badania wplywu rozmieszczenia wymiennikoacutew na efektywnosc podziemnych magazynoacutew energii PhD Thesis Krakow AGH University of Science and Technology 2014 (Research of impact the exchangers location on efficiency the underground energy storages PhD Thesis Krakow AGH University of Science and Technology 2014)

29 AGonet JMacuda Wiertnictwo hydrogeologiczne Krakoacutew Wydawnictwa AGH 1995 (Hydrogeology drilling Krakow Wydawnictwa AGH 1995)

30 TSliwa LGaluszka Study of the effect of medium flow parameters on heat transfer in the laboratory coaxial model of a borehole heat exchanger AGH Drilling Oil Gas -2013 -Vol30 -No4 -P 421-431

31 TSliwa DKnez AGonet et al Research and teaching capacities of the Geoenergetics Laboratory at Drilling Oil and Gas Faculty AGH University of Science and Technology in Krakoacutew (Poland) Proceedings of the World Geothermal Congress -2015 Australia Melbourne 2015 -P1-14

32 KMorita MTago SEchara Case studies on small-scale power generation with the downhole coaxial heat exchanger Proceedings of the World Geothermal Congress Turkey Antalya 2005 -P1-8

33 SStryczek RWisniowski AGonet AZlotkowski JZiaja Influence of polycarboxylate superplasticizers on rheological properties of cement slurries used in drilling technologies Archives of Medical Science -2013 -Vol58 -P719-728

34 LDijkshoorn SSpeer RPechnig Measurements and design calculations for a deep coaxial borehole heat exchanger in Aachen Germany International Journal of Geophysics -2013 -Vol2013 -Article ID 916541

35 AGonet TSliwa SStryczek et al Methodology for the identification of potential heat of the rock mass along with technology implementation and operation of the borehole heat exchangers Krakow Wydawnictwa AGH 2011

36 KJaszczur TSliwa The analysis of long-term borehole heat exchanger system exploitation Computer Assisted Methods in Engineering and Science -2013 -Vol20 -No3 -P227-235


42

Исследование эффективности глубинных скважинных теплообменников

TСлива1 TНовосиад1 OВитязь2 AСапинска-Слива1

1AGH Научно-технический университет им Станислава Сташица Краков Польша2Ивано-Франковский национальный технический университет нефти и газа

Ивано-Франковск Украина

Реферат

В статье представлены результаты исследований проведенных с помощью программно-го средства Earth Energy Designer (EED321) на эффективность отвода тепла и выполнены измерения производительности в зависимости от переменных параметров теоретическо-го глубинного коаксиального скважинного теплообменника Для скважинного теплооб-менника предполагалась глубина 1000 м и постоянная тепловая нагрузка 80 МВтч в год Проанализированы следующие переменные тип жидкого теплоносителя расход теплоно-сителя диаметр ствола скважины толщина стенки внутренней трубы (изоляция) диаметр внутренней трубы теплопроводность материала внутренней трубы толщина стенки наруж-ной трубы диаметр наружной трубы и коэффициент теплопроводности материала внеш-ней трубы Благодаря математической основе программы EED результаты расчетов можно рассматривать как сокращённые Для корректной работы программа может использовать параметры из скважины глубиной не более 300 метров Для более глубинных скважинных теплообменников результаты занижены Таким образом результаты анализов представлен-ных в статье можно рассматривать как пессимистический сценарий расчетов

Ключевые слова использование геотермального тепла глубинные скважинные теплооб-менники (ГСТ) тепловые насосы низкотемпературное геотермальное тепло

Dərinlik quyu istilik muumlbadiləsi avadanlığının səmərəliliyinin tədqiqi

TSliva1 TNovosiad1 OVityaz2 ASapinska-Sliva1

1AGH Stanislav Staşits adına Elm və Texnika Universiteti Krakov Polşa2İvano-Frankovsk Milli Neft və Qaz Texniki Universiteti

İvano-Frankovsk Ukrayna

Xuumllasə

Məqalədə Earth Energy Designer (EED321) proqram vasitəsinin koumlməyi ilə istiliyin oumltuumlruumllməsinin səmərəliyi uumlzrə keccedilirilmiş tədqiqatların nəticələri təqdim olunmuş nəzəri dərinlik koaksial quyu istilik muumlbadiləsi avadanlığın dəyişən parametrlərindən asılı olaraq məhsuldarlığın oumllccediluumllməsi yerinə yetirilmişdir Quyu istilik muumlbadiləsi avadanlığı uumlccediluumln 1000 m dərinlik və 1 il ərzində 80 MBtsaat daimi istilik yuumlkuuml nəzərdə tutulmuşdur Aşağıdakı dəyişənlər təhlil edilmişdir maye istilik daşıyıcısının noumlvuuml istilik daşıyıcısının sərfi quyu luumlləsinin diametri daxili boru divarının qalınlığı (izolə etmə) daxili borunun diametri daxili borunun materialının istilik keccedilirməsi xarici boru divarının qalınlığı xarici borunun diametri və xarici borunun materialının istilik keccedilirmə əmsalı EED proqramının riyazi əsaslandırılmasına goumlrə hesablamaların nəticələrinə qısaldılmış formada baxmaq olar Dəqiq nəticələrin alınması uumlccediluumln proqramda 300 metrdən dərin olmayan quyuların parametrlərindən istifadə olunmalıdır Daha dərin quyu istilik muumlbadiləsi avadanlıqları uumlccediluumln nəticələr azaldılıb Beləliklə məqalədə təqdim edilmiş təhlilin nəticələrinə hesablamaların pessimist ssenarisi kimi baxmaq olar

Accedilar soumlzlər geotermal istiliyin istifadəsi dərinlik quyu istilik muumlbadiləsi avadanlığı istilik nasosları aşağı temperaturlu geotermal istilik


30

of recovery of heat resources in the ground can be used eg using solar collectors [10] If so the energy obtained from the reservoir is no longer only a geothermal energy

A heat carrier in the centric system is introduced into the annular space and flows to the surface in the inner tube - the centric column The energy obtained in this way may satisfy the heat demand for bigger consumers [5] It is however characterized by a large capital for the investment Usage of the existing boreholes minimizes the costs and allows to reuse the old wells instead of liquidation which is connected with new costs so the process may be economically advantageous Currently the energy generation described above is not financially viable but getting experience in implementation and operation of these systems will pay off at the time when energy will be more expensive when fossil energy sources will be close to completion

When analyzing oil boreholes held for liquidation and located near to potential sources

of the heat if liquidation costs can be allocated to adaptation the economic balance of the deep borehole exchangers may be beneficial [11-13] A matter of insulation for the internal column pipes however may be problematic The pipe can be either well insulated and expensive or cheaper and poorly insulated [14] The costs will increase if there is a need to use the equipment with a large lift capacity (using a double steel tube)

For operational analysis and prediction of the deep BHEsrsquo exploitation a number of mathematical models has been created [15-18]

2 Examples of deep borehole heat exchangers

In recent years due to the increasing energy demand numerous innovations for constructing designing and locating borehole heat exchangers were created It is increasingly popular around the world to use the coaxial heat exchangers by using a number of unexploited boreholes [19] In Poland tests on redevelopment of old boreholes


Fig1Schemes of the borehole heat exchangers design a) single U-tube b) double U-tube c) coaxial heat exchanger A - surface area B - rock mass 1 - wall of the hole 2 - filling the hole 3 - U-tube heat exchanger 4 - outer tube of the centric system

5 - annular space of the centric system 6 - inner tube of the centric system 7 - inner pipe interior

1 1 1

2 2

2

3 3

45

6

7

AB

31




(1)


of the pipe











4

1

32 4

1 1 2 2 3 3

1 1 1r

dln

ddd d

ln ln lnd d d

λ

λ λ λ

=+ +

32







(2)




(3)






( )1`

B

A

z dzH

λ λ= int

1

14 10

2

8

12

3

94

5

67

11

13

( ) 12

b

D H

r rD

Tq t r dz

H rπ λ

+

=

part=

partint

33





(4)




(5)where


and outflow to BHE




(6)




(7)



(8)




(9)

(10)where





( ) ( ) ( ) 1 0

0 0q t q He t He t

= =


2α

minus= + sdotm o

H DT T G

2 2

2 2

1 1


0== + sdotot

T T G z



0== oz

T T

0== + sdotot

T T G z

0== oz

T T

34


(11)where


step


(12)


- g-function



(13)


(14)






(15)

(16)where



vf




(17)


(18)








1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG



3

2 5

8 λ ρπ


sdot

in

in

L VPd

2 5


in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d


2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




31




(1)


of the pipe











4

1

32 4

1 1 2 2 3 3

1 1 1r

dln

ddd d

ln ln lnd d d

λ

λ λ λ

=+ +

32







(2)




(3)






( )1`

B

A

z dzH

λ λ= int

1

14 10

2

8

12

3

94

5

67

11

13

( ) 12

b

D H

r rD

Tq t r dz

H rπ λ

+

=

part=

partint

33





(4)




(5)where


and outflow to BHE




(6)




(7)



(8)




(9)

(10)where





( ) ( ) ( ) 1 0

0 0q t q He t He t

= =


2α

minus= + sdotm o

H DT T G

2 2

2 2

1 1


0== + sdotot

T T G z



0== oz

T T

0== + sdotot

T T G z

0== oz

T T

34


(11)where


step


(12)


- g-function



(13)


(14)






(15)

(16)where



vf




(17)


(18)








1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG



3

2 5

8 λ ρπ


sdot

in

in

L VPd

2 5


in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d


2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




32







(2)




(3)






( )1`

B

A

z dzH

λ λ= int

1

14 10

2

8

12

3

94

5

67

11

13

( ) 12

b

D H

r rD

Tq t r dz

H rπ λ

+

=

part=

partint

33





(4)




(5)where


and outflow to BHE




(6)




(7)



(8)




(9)

(10)where





( ) ( ) ( ) 1 0

0 0q t q He t He t

= =


2α

minus= + sdotm o

H DT T G

2 2

2 2

1 1


0== + sdotot

T T G z



0== oz

T T

0== + sdotot

T T G z

0== oz

T T

34


(11)where


step


(12)


- g-function



(13)


(14)






(15)

(16)where



vf




(17)


(18)








1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG



3

2 5

8 λ ρπ


sdot

in

in

L VPd

2 5


in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d


2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




33





(4)




(5)where


and outflow to BHE




(6)




(7)



(8)




(9)

(10)where





( ) ( ) ( ) 1 0

0 0q t q He t He t

= =


2α

minus= + sdotm o

H DT T G

2 2

2 2

1 1


0== + sdotot

T T G z



0== oz

T T

0== + sdotot

T T G z

0== oz

T T

34


(11)where


step


(12)


- g-function



(13)


(14)






(15)

(16)where



vf




(17)


(18)








1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG



3

2 5

8 λ ρπ


sdot

in

in

L VPd

2 5


in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d


2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




34


(11)where


step


(12)


- g-function



(13)


(14)






(15)

(16)where



vf




(17)


(18)








1

2πλ

= sdot

bq

s

rtR gt H

2

9=s

HtG



3

2 5

8 λ ρπ


sdot

in

in

L VPd

2 5


in

L V

b

s

rtg

t H

( ) ( )in in

3

3 22

8 λ ρ

π


sdot minus sdot +

a

out out

L VPD d D d


2 ρ= minusfin f

f f f

qHT Tc V

2 ρ= +fout f

f f f

qHT Tc v

35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




35









Parametr Value























Water 1193

Methanol 1164


Ethanol 1156






36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




36












thickness

Tem

pera

ture

o CTe

mpe

ratu

re o C

Tem

pera

ture

o C

120

116

112

1156

1112

2

1182

3 4 5 6

1212


1199120

116

117

119

1204

1165

1183


1193

240 260

1181174

Hyd

raul

ic p

ower

W

1000

400200

0

600

3000

2000

0Flow rate dm3min-1

Flow rate dm3min-1

10

400200100

12

11

0 300

13

14

37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




37













Tem

pera

ture

o CTe

mpe

ratu

re o C

Temperature oC

Tem

pera

ture

o C 120

119

117

118

1209

1185

1176


1193

3 4 5 6

121

1201

Dee

pth

m

1

50

1000

100 2000

300

500

3500

2500

2

3000

2000

1500

0 150 250

34


120

100

77880

11931141

100101001

120

119

118

117

1193

1172

1183


110

121

1203

1213

38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




38















Tem

pera

ture

o C

Tem

pera

ture

o C

Tem

pera

ture

o C

Temperature oC

Bore

hole

dee

pth

m

Uni

tary

pow

er W

m-1

120

40

-15 0

1000900800700600500400300200

-10 10-5 5 15

60

80

100

120


2

120

118

116

114

112

05 2010 15 25

120

1188

1164

1196

1139

1198


120

116

11201 1010 100

1224

1193

1141

120

116

112

108

1218

1165

1133

1096


1193

39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




39





6 Conclusions







40

References






















41


















42





Реферат







Xuumllasə




40

References






















41


















42





Реферат







Xuumllasə




41


















42





Реферат







Xuumllasə




42





Реферат







Xuumllasə




SOCAR Proceedingsproceedings.socar.az/uploads/pdf/31/Sliva-029-042.pdf · inner pipe was...

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Transcript of SOCAR Proceedingsproceedings.socar.az/uploads/pdf/31/Sliva-029-042.pdf · inner pipe was...