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Heat exchanger optimization for geothermal district heating systems: A fuel saving approach
ARTICLE IN PRESS
Renewable Energy 32 (2007) 1020–1032 www.elsevier.com/locate/renene
Heat exchanger optimization for geothermal district heating systems: A fuel saving approach Ahmet Dagdas Department of Mechanical Engineering, Yildiz Technical University, 34349 Besiktas, Istanbul, Turkey Received 30 November 2004; accepted 8 March 2006 Available online 2 May 2006
Abstract One of the most commonly used heating devices in geothermal systems is the heat exchanger. The output conditions of heat exchangers are based on several parameters. The heat transfer area is one of the most important parameters for heat exchangers in terms of economics. Although there are a lot of methods to optimize heat exchangers, the method described here is a fairly easy approach. In this paper, a counter flow heat exchanger of geothermal district heating system is considered and optimum design values, which provide maximum annual net profit, for the considered heating system are found according to fuel savings. Performance of the heat exchanger is also calculated. In the analysis, since some values are affected by local conditions, Turkey’s conditions are considered. r 2006 Elsevier Ltd. All rights reserved. Keywords: Heat exchanger; Geothermal; Optimization; Heat transfer area; District heating
1. Introduction A geothermal resource that produces geofluid at 150 1C or less is called a ‘‘low temperature geothermal resource’’ [1]. Most of the existing geothermal resources in the world are low temperature geothermal resources. These resources are used for space and district heating, greenhouse heating, fish farming, process heating and balneological purposes. Since geothermal waters have considerable dissolved solids, indirect systems are used for heating processes. That is, the heat of the geothermal brine is transferred to fresh circulating water by means of a heat exchanger. The most commonly used heat exchanger Tel.: +90 0212 259 70 70; fax: +90 0212 261 66 59.
E-mail address: [email protected]. 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.03.008
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Nomenclature e Q_ Q_ max Cp Ch Cc _s m _ geo m LMTD Thi Tho Tci Tco U A Ca Ic CRF i n Hu Zk H be Be B YPT F NK
effectiveness of the heat exchanger heat transfer rate from geothermal brine to circulating water [W] maximum heat transfer rate in the heat exchanger [W] specific heat [J/kg 0C] thermal capacity of geothermal brine [W/0C] thermal capacity of circulating water [W/0C] mass flow rate of circulating water [kg/s] mass flow rate of geothermal brine [kg/s] log-mean temperature difference [0C] input temperature of geofluid into heat exchanger [0C] output temperature of geofluid from heat exchanger [0C] input temperature of circulating water into heat exchanger [0C] output temperature of circulating water from heat exchanger [0C] overall heat transfer coefficient of heat exchanger [W/m2 K] heat transfer area of heat exchanger [m2] annual investment cost [$/year] investment cost of unit plate heat exchanger area [$/m2] cost recovery factor interest rate heat exchanger life-time [year] lower heating value of fuel [kJ/kg] boiler efficiency [%] operational hours of the plant [h/year] specific fuel consumption [kg/kWh] specific fuel consumption [kg/kW year] total fuel consumption [kg/year] annual money savings [$/year] fuel cost [$/kg] annual net profit [$/year]
type for this purpose is the counter flow plate heat exchanger (Fig. 1). There are two main reasons to use a counter flow plate heat exchanger in a geothermal heating system. Firstly, clean and less corrosive heating fluid circulates in the heating cycle and, secondly they have high heat transfer performance [2]. The heat transfer performance of a heat exchanger is very important for geothermal systems because geothermal reservoirs are not fully ‘‘renewable’’. If geothermal reservoirs are fed by hot groundwater, they may be renewable. For this purpose, the utilized geothermal fluid must be reinjected to the reservoir. However, some important points should be considered in the reinjection application, for example the distance between the reinjection and the production wells (usually41 km). Otherwise the reinjected ‘‘cold’’ water (ThooThi) may reach the production well soon after the start of operation. From that moment on the geothermal fluid production temperature will decrease; the lower Tho, the stronger is the effect. This means geothermal reservoirs should be used as effectively as possible.
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Fig. 1. The simplified scheme of counter flow heat exchanger.
Turkey has a very rich potential in terms of low temperature geothermal resources. In Turkey, there are approximately 170 geothermal fields, and 95% of them produce lowmedium temperature geofluid. Around 1500 hot and mineralized natural springs and wells exist in Turkey [3]. Low temperature resources are often used in heating applications. Geothermal heating applications are generally indirect systems. The heat energy of the geothermal brine is transferred to fresh circulating water by means of a heat exchanger. In geothermal projects, the heat exchanger cost constitutes a considerable part of the investment cost. For this reason, the optimum heat transfer area of the heat exchanger needs to be determined. In this paper, a counter flow heat exchanger of known input temperatures and mass flow rates is considered, and a mathematical model to find the optimum heat transfer area of the heat exchanger is given. In addition, the model is applied to typical low temperature geothermal resources with 90 1C geofluid temperatures. The objective function of optimization is to find the optimum heat transfer area for a counter flow plate heat exchanger, which maximizes the annual net profit. 2. Thermodynamic analysis In conventional fossil-fuel district heating systems, boilers are generally used to supply hot water. However, in geothermal applications, counter flow plate heat exchangers are often used for this purpose. This means that fuel costs are eliminated in geothermal systems. To obtain the net profit of geothermal systems, heat exchanger investment costs are subtracted from the annual money savings (i.e. fuel costs). Thermal capacities of circulating water (cold) and geofluid (hot) are [4]; _ s :C p W 0 C , Cc ¼ m (1) _ geo :C p Ch ¼ m
0 W C .
(2)
There are two main factors in efficient utilization of geothermal heat in district heating schemes [5,6]:
The flow rate of circulating water that enters the heat exchanger must be greater than _ s 4m _ geo ). the geothermal brine’s flow rate (m Return temperature of circulating water from the heating network to the heat exchanger must be as low as possible.
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In this study, it is assumed that the mass flow rate of circulating water is greater than the mass flow rate of geofluid. Hence the thermal capacity of circulating water is greater than the thermal capacity of geofluid (i.e. Cc4Ch). Under these assumptions, the variation of temperature related to the heat transfer area of the heat exchanger can be drawn as in Fig. 2. Since the thermal capacity of geofluid is smaller, its temperature difference will be greater. That is, the fluid with the smaller thermal capacity has a bigger slope in the temperature-area graph. The heat transfer rate from geofluid to circulating water in the heat exchanger is determined as [4,7] Q_ ¼ C h :ðT hi T ho Þ.
(3)
The heat rate that is taken by circulating water is Q_ ¼ C c :ðT co T ci Þ.
(4)
According to heat transfer law [4,7,8] ðT hi T co Þ ðT ho T ci Þ , Q_ ¼ U:A: ln ðT hi T co Þ=ðT ho T ci Þ
(5)
ðT hi T co Þ ðT ho T ci Þ . ln ðT hi T co Þ=ðT ho T ci Þ
(6)
LMTD ¼
The heat that is given off by the geofluid must be equal to the heat that is taken by the circulating water. That means, C h :ðT hi T ho Þ ¼ C c :ðT co T ci Þ. Solving for Tco in Eq. (7) and substituting into Eq. (5) with Eq. (3) gives ðT hi T ci Þ C h =C c ðT hi T ho Þ Ch Ch ln . ¼1 T ho T ci U:A Cc
Fig. 2. The relationship between temperature and heat transfer area in counter flow heat exchanger.
(7)
(8)
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Re-arranging Eq. (8): ðT hi T ci Þ C h =C c ðT hi T ho Þ 1 1 ln ¼ U:A: . T ho T ci Ch Cc If D is defined as [4] 1 1 D ¼ U:A: , Ch Cc
(10)
Eq. (9) becomes ðT hi T ci Þ C h =C c ðT hi T ho Þ ¼ D, ln T ho T ci then
(9)
ðT hi T ci Þ C h =C c ðT hi T ho Þ ¼ eD . T ho T ci
If Eq. (12) is arranged, it becomes T hi : 1 C h =C c T ci :ð1 eD Þ . T ho ¼ eD C h =C c
(11)
(12)
(13)
With Eq. (13), we can easily find output temperatures of fluids from the heat exchanger, if the input temperatures of fluids are known. Eq. (13) can be written as T ho ¼ T hi ðT hi T ci Þ
ð1 eD Þ . C h =C c eD
(14)
From Eq. (14) ðT hi T ho Þ ¼ ðT hi T ci Þ
ð1 eD Þ . C h =C c eD
(15)
2.1. Heat Exchanger Effectiveness (e) The effectiveness of the heat exchanger is formulated as [4,7] e¼
Q_ , _ Qmax
(16)
where Q_ max is the maximum heat transfer rate from geofluid to circulating water if the heat transfer area were infinite. When Q_ max is calculated, the output temperature of the fluid that has the smaller heat capacity is taken as being equal to the other fluid’s input temperature (i.e. T ho ¼ T ci ). Hence, Q_ max is calculated as; Q_ max ¼ C h :ðT hi T ci Þ ½W.
(17)
If Ch4Cc, the output temperature of the geofluid is equal to the input temperature of the circulating water. So, Q_ max ¼ C c :ðT hi T ci Þ.
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In conclusion, the most generally state of Q_ max is Q_ max ¼ C min :ðT hi T ci Þ, where Cmin smaller heat capacity. In the system considered, it is assumed that Cmin ¼ Ch. According to Fig. 2, effectiveness of heat exchanger can be written as e¼
C h :ðT hi T ho Þ C c :ðT co T ci Þ Q_ ¼ . ¼ _ Qmax C h :ðT hi T ci Þ C h :ðT hi T ci Þ
Then, e¼
ðT hi T ho Þ . ðT hi T ci Þ
(18)
Substituting Eq. (15) into Eq. (18), ð1 eD Þ . C h =C c eD
e¼
(19)
The effectiveness of the heat exchanger can be written as a function of NTU (Number of Transfer Units) and heat capacity ratio (R). NTU is a dimensionless parameter, which expresses the size of heat exchangers and is commonly used in heat exchanger analysis. In general, NTU and heat capacity ratio (R) are expressed as [4,7] NTU ¼
R¼
U:A , C min
C min . C max
For the geothermal system considered, these parameters can be written as NTU ¼
R¼
U:A , Ch
Ch . Cc
(20)
(21)
If coefficient D, in Eq. (10), is written as a function of NTU and R, it becomes D ¼ NTU:ð1 RÞ.
(22)
Hence the effectiveness of the heat exchanger can be expressed as e¼
ð1 eNTU:ð1RÞ Þ . ðR eNTU:ð1RÞ Þ
(23)
In heat exchangers, effectiveness varies in the range 0–1 (0 e 1). 3. Cost analysis of geothermal district heating heat exchanger In this section, cost analysis of the heat exchanger, which is used in geothermal district heating system, is performed and the optimum heat transfer area, which gives maximum annual net profit, is determined.
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One of the most important pieces of equipment in a geothermal district heating system is the heat exchanger. Annual investment cost of the heat exchanger (Ca) can be found as C a ¼ I c :A:CRF $=year (24) in which CRF is the capital recovery factor of investment, Ic is the cost of heat exchanger per unit. CRF is found as [9] CRF ¼
ð1 þ iÞn :i ð1 þ iÞn 1
(25)
in which i is the interest rate, n is the average heat exchanger life. It should be noted that the heat exchanger life-time can strongly depend on local conditions, mainly due to the chemical composition of the geothermal fluid. In this analysis, the heat exchanger life-time is assumed to be 15 years, typical for Turkish geothermal water conditions. When geothermal energy is used for district heating, there is considerable fuel cost savings compared to a conventional fossil-fuel district heating system. For this reason, adding a heat exchanger to a geothermal system instead of a boiler to a conventional system provides financial savings due to the elimination of fuel cost. Annual money saved equals the annual fuel cost used to produce the same amount of heat energy in a conventional heating system. Specific fuel consumption (be) of a conventional district heating system is be ¼
3600 H u :Zk
kg=kWh ,
(26)
in which Hu is the lower heating value of fuel and Zk is the boiler efficiency. Specific annual fuel consumption (Be) is Be ¼ H
3600 H u :Zk
kg=kW:year .
(27)
_ annual fuel consumption (B) can be found as To acquire heat rate of Q, 3600 B ¼ Q_ H H u :Zk
kg=year ,
(28)
in which H is the operational hours of the plant [h/year]. When a conventional system is used for heating, the revenue of annual fuel consumption is equal to the annual money saved in a geothermal system, over the same time. Annual saved money (YPT) can be found as YPT ¼ Q_ H
3600 F H u :Zk
$=year ,
(29)
where F is the fuel cost [$/kg]. Therefore, the net profit (NK) that supplied geothermal district heating system can be found as [10] NK ¼ YPT C a
$=year .
(30)
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Table 1 Characteristic values used in computer simulation Input temperature of geofluid
76 1C
Mass flow rate of geofluid Input temperature of circulating water Mass flow rate of circulating water Return temperature of circulating water Specific heat capacity of water (Cp) Overall heat transfer coefficient of HX (U) Boiler efficiency (Zk) Cost of heat exchanger per unit (Ic) Lower heating value of fuel (Hu) Fuel Cost (F) Heat exchanger life (n) Interest rate (i)
222.3 kg/s 50 1C 540 kg/s 48 1C 4186 J/kg K 5100 W/m2 K 0.85 350 $/m2 41900 kJ/kg 0.5 $/kg 15 years 0.10
4. Numerical analysis A mathematical model of the counter flow heat exchanger is prepared and the simulation is performed. Simulation data is given in Table 1. Input temperature and mass flow rate of geothermal water entering the heat exchanger are 76 1C and 222.3 kg/s, respectively. There are many geothermal resources in this temperature range in Turkey, particularly, in the Aegean Region of Turkey. It is possible to use these geofluids for district heating applications. This type of geothermal heating system has been successfully and efficiently applied all over the world [6,11–13]. Input temperature and mass flow rate of circulating water entering the heat exchanger are assumed to be 50 1C and 540 kg/s, respectively [14]. 5. Results of analysis After computing, the optimum heat transfer area of a counter flow heat exchanger is found as 1612 m2 (Fig. 3). As can be seen, a counter flow heat exchanger with this heat transfer area maximizes the net profit of the system. If a district heating heat exchanger has this area, annual money saved, investment cost of heat exchanger and annual net profit can be found as US$ 4.350 million/year, US$ 74,178/year and US$ 4.276 million/year, respectively (Table 2). Under these conditions, the output temperatures of geofluid and circulating water from heat exchanger are 50.08 1C and 60.58 1C, respectively. The output temperature variations of geofluid and circulating water are shown in Fig. 4. The output temperature of the geofluid is high enough for some cascaded uses. For example; balneological, swimming pool and aquaculture applications, snow and ice melting, heat pump applications etc. However, some important points should be considered in evaluation of the waste geofluid. For instance, the waste geofluid cannot be just fed to surface drainage because of environmental concerns. The reinjection process must be applied. Sometimes further use of the waste geofluid is not suitable for sustainability of the geothermal reservoir. The colder reinjection fluid cools the geothermal reservoir. In Fig. 5, the variations of the annual net profit related to heat transfer area can be seen.
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Ca ($/year)
95000
4.365x106
90000
4.360x106
85000
4.355x106 YPT
80000
4.350x106
Max NK
4.345x106
75000
4.340x106
70000 Ca
4.335x106
65000 60000 55000 1300
YPT ($/year)
A. Dagdas / Renewable Energy 32 (2007) 1020–1032
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4.330x106
Aopt=1612 m2 1400
1500
1600
1700
1800
1900
4.325x106 2000
A (m2) Fig. 3. Optimum heat transfers area, maximizes net profit of geothermal system.
Table 2 Results of simulation (at optimum conditions) Output temperature of geofluid Output temperature of circulating water Investment cost (Ca) Annual saved money (YPT) Annual net profit (NK) Capital recovery factor (CRF) Specific fuel consumption (be)
50.08 1C 60.58 1C 74,178 $/year 4,350,500 $/year 4,276,385 $/year 0.1315 0.1011 kg/kWh
50.7
60.6
50.6
60.5
50.4 50.3 50.2
60.45
Tco (C)
Tho (C)
60.55
Tco
50.5
Tho 60.4
50.1
Aopt=1612 m2 50 60.35 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 A (m2)
Fig. 4. The output temperatures of geofluid and circulating water from heat exchanger vs. Heat transfer area (at optimum conditions).
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4,278x106 4,276x106
NK ($/year)
4,274x106 4,272x106 4,270x106 4,268x106 4,266x106
Aopt=1612 m2
4,264x106 1300
1400
1500
1600
1700
1800
1900
2000
A (m2) Fig. 5. Net profit vs. heat transfer area.
4,300x106 Ic=250$/m2 4,290x106
NK ($/year)
4,280x106
Ic=300$/m2
4,270x106 4,260x106
Ic=350$/m2
4,250x106 Ic=450$/m2
4,240x106 4,230x106
4,220x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2) Fig. 6. The variation of annual net profit related to heat transfer area, at various heat transfer unit costs.
Table 3 Determined optimum heat transfer areas for various heat exchanger unit costs Heat exchanger unit cost (Ic) ($/m2)
Optimum heat transfer area (Aopt) (m2)
250 300 350 450
1716 1659 1612 1534
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4,290x106
NK ($/year)
4,280x106
i=0.08
4,270x106 i=0.10
4,260x106
i=0.12
4,250x106 4,240x106
i=0.14
4,230x106 4,220x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2) Fig. 7. The variation of annual net profit related to heat transfer area, at various interest rates.
Table 4 Determined optimum heat transfer areas for various interest rates Interest rate (i)
Optimum heat transfer area (Aopt) (m2)
0.08 0.10 0.12 0.14
1648 1612 1578 1546
Some sensitivity analyses have been made as follows. For i ¼ 0.10 and F ¼ 0.50 $/kg, the effects of various unit heat exchanger costs (Ic) on optimum heat exchanger area are as shown in Fig 6. As can be seen in Fig. 6 and Table 3, while heat exchanger unit cost rises, optimum heat transfer area decreases (for i ¼ 0.10). For Ic ¼ 350 m2 and F ¼ 0.50 $/kg, the effects of various interest rates above optimum heat transfer area, like shown in Fig. 7. As can be seen in Fig. 7 and Table 4, as the interest rate rises, optimum heat transfer area and net profit of the system decrease (for Ic ¼ 350 $/m2). For Ic ¼ 350 $/m2 and i ¼ 0.10, at various unit fuel costs, the variation of annual net profit above heat transfer area is shown in Fig. 8. The optimum heat transfer areas determined for various unit fuel costs and determined to maximize net profit are shown in Table 5. According to these values, as unit fuel cost raises, annual net profit of geothermal district heating system and optimum heat transfer area of the heat exchanger increase. 6. Conclusions There are a lot of studies involving heat exchanger optimization in the literature. Most of them are confusing and not practical for the manufacturer. In this article, an easy
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NK ($/year)
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4,800x106 4,700x106 F=0.55 $/kg 4,600x106 4,500x106 4,400x106 4,300x106 4,200x106 F=0.50 $/kg 4,100x106 4,000x106 3,900x106 3,800x106 F=0.45 $/kg 3,700x106 3,600x106 3,500x106 3,400x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2)
Fig. 8. The variation of annual net profit related to heat transfer area, at various unit fuel costs.
Table 5 Determined optimum heat transfer areas for unit fuel costs Unit fuel cost (F) ($/kg)
Optimum heat transfer area (Aopt) (m2)
0.45 0.50 0.55
1579 1612 1642
approach is presented for determining optimal heat transfer area of a counter flow heat exchanger. Especially, this approach can be used for pre-feasibility studies in geothermal district heating applications. According to the analysis, utilization in a district heating application, a geothermal resource, which produces geofluid at 76 1C and 222.3 kg/s, requires a 1612 m2 heat transfer area in the heat exchanger. This value is an optimum result. With this size heat exchanger, the maximum annual revenue point of view fuel savings will be supplied from the geothermal heating application. It should be noted that this analysis considers only a single set of inlet temperatures and flow rates. Therefore, optimization results could also be expected by varying these factors. In all the regions of Turkey, these geothermal water values could be obtained very easily. Acknowledgement The Author thanks Prof. Dr. Bahri S- ahin for reviewing and any technical information. References [1] Barbier E. Geothermal energy technology and current status: an overview. Rene Sustain Energy Rev 2002;6(3):65. [2] Dai C, Liang J. Optimum design and running of PHEs in geothermal district heating. Heat Transfer Eng 1999;20(4):52–61.
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[3] Simsek S, Mertoglu O, Bakir N, Akkus I, Aydogdu O, Geothermal energy utilization, development, and projections- Country update report (2000–2004) of Turkey. Proceedings of the world geothermal congress, Turkey, 2005. p. 1–10. [4] Stoecker WF. Design of thermal systems. New York: McGraw Hill; 1989. [5] Harrison R, Mortimer ND, Smarason OB. Geothermal heating. Brussels: Pergamon Press; 1990. [6] Dimitrov K, Dimitrov O, Geothermal district heating schemes in the Republic of Macedonia. Proceedings World Geothermal Congress, Japan, 2000 p., 3401. [7] Incropera FP, Dewitt DP. Basics of the heat and mass transfer. Istanbul: Literatur Publishing; 2001 [in Turkish]. [8] Shvets IT, Tolubinsky VI, Kirakovsky NF, et al. Heat engineering. Moscow: Mir Publishing; 1975. [9] Aybers N, Sahin B. The cost of energy. Istanbul: Yildiz Technical University Press; 1995. [10] S- ahin B, Vardar N. Recovery of exhaust heat at marine systems with diesel engine. Turkish Lloyd serial conf 1991:91–103. [11] Dai C, Liang J, Direct and indirect low temperature geothermal district heating systems. Proceedings world geothermal congress, Japan, 2000 3395. [12] Wang W, A successful example of a retrofit to a geothermal district heating system. Proceedings world geothermal congress, Japan, 2000 p. 3585–3588. [13] Gunnlaugsson E, Frimannson H, Sverrissson G, District heating in Reykjavik- 70 years experience. Proceedings world geothermal congress, Japan, 2000 p. 2087–2092. [14] Dagdas A, Improvement of the optimal usage model for geothermal energy resources and the local application. PhD thesis. Department of Mechanical Engineering, Yildiz Technical University, Istanbul; 2004 [in Turkish].
Renewable Energy 32 (2007) 1020–1032 www.elsevier.com/locate/renene
Heat exchanger optimization for geothermal district heating systems: A fuel saving approach Ahmet Dagdas Department of Mechanical Engineering, Yildiz Technical University, 34349 Besiktas, Istanbul, Turkey Received 30 November 2004; accepted 8 March 2006 Available online 2 May 2006
Abstract One of the most commonly used heating devices in geothermal systems is the heat exchanger. The output conditions of heat exchangers are based on several parameters. The heat transfer area is one of the most important parameters for heat exchangers in terms of economics. Although there are a lot of methods to optimize heat exchangers, the method described here is a fairly easy approach. In this paper, a counter flow heat exchanger of geothermal district heating system is considered and optimum design values, which provide maximum annual net profit, for the considered heating system are found according to fuel savings. Performance of the heat exchanger is also calculated. In the analysis, since some values are affected by local conditions, Turkey’s conditions are considered. r 2006 Elsevier Ltd. All rights reserved. Keywords: Heat exchanger; Geothermal; Optimization; Heat transfer area; District heating
1. Introduction A geothermal resource that produces geofluid at 150 1C or less is called a ‘‘low temperature geothermal resource’’ [1]. Most of the existing geothermal resources in the world are low temperature geothermal resources. These resources are used for space and district heating, greenhouse heating, fish farming, process heating and balneological purposes. Since geothermal waters have considerable dissolved solids, indirect systems are used for heating processes. That is, the heat of the geothermal brine is transferred to fresh circulating water by means of a heat exchanger. The most commonly used heat exchanger Tel.: +90 0212 259 70 70; fax: +90 0212 261 66 59.
E-mail address: [email protected]. 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.03.008
ARTICLE IN PRESS A. Dagdas / Renewable Energy 32 (2007) 1020–1032
1021
Nomenclature e Q_ Q_ max Cp Ch Cc _s m _ geo m LMTD Thi Tho Tci Tco U A Ca Ic CRF i n Hu Zk H be Be B YPT F NK
effectiveness of the heat exchanger heat transfer rate from geothermal brine to circulating water [W] maximum heat transfer rate in the heat exchanger [W] specific heat [J/kg 0C] thermal capacity of geothermal brine [W/0C] thermal capacity of circulating water [W/0C] mass flow rate of circulating water [kg/s] mass flow rate of geothermal brine [kg/s] log-mean temperature difference [0C] input temperature of geofluid into heat exchanger [0C] output temperature of geofluid from heat exchanger [0C] input temperature of circulating water into heat exchanger [0C] output temperature of circulating water from heat exchanger [0C] overall heat transfer coefficient of heat exchanger [W/m2 K] heat transfer area of heat exchanger [m2] annual investment cost [$/year] investment cost of unit plate heat exchanger area [$/m2] cost recovery factor interest rate heat exchanger life-time [year] lower heating value of fuel [kJ/kg] boiler efficiency [%] operational hours of the plant [h/year] specific fuel consumption [kg/kWh] specific fuel consumption [kg/kW year] total fuel consumption [kg/year] annual money savings [$/year] fuel cost [$/kg] annual net profit [$/year]
type for this purpose is the counter flow plate heat exchanger (Fig. 1). There are two main reasons to use a counter flow plate heat exchanger in a geothermal heating system. Firstly, clean and less corrosive heating fluid circulates in the heating cycle and, secondly they have high heat transfer performance [2]. The heat transfer performance of a heat exchanger is very important for geothermal systems because geothermal reservoirs are not fully ‘‘renewable’’. If geothermal reservoirs are fed by hot groundwater, they may be renewable. For this purpose, the utilized geothermal fluid must be reinjected to the reservoir. However, some important points should be considered in the reinjection application, for example the distance between the reinjection and the production wells (usually41 km). Otherwise the reinjected ‘‘cold’’ water (ThooThi) may reach the production well soon after the start of operation. From that moment on the geothermal fluid production temperature will decrease; the lower Tho, the stronger is the effect. This means geothermal reservoirs should be used as effectively as possible.
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Fig. 1. The simplified scheme of counter flow heat exchanger.
Turkey has a very rich potential in terms of low temperature geothermal resources. In Turkey, there are approximately 170 geothermal fields, and 95% of them produce lowmedium temperature geofluid. Around 1500 hot and mineralized natural springs and wells exist in Turkey [3]. Low temperature resources are often used in heating applications. Geothermal heating applications are generally indirect systems. The heat energy of the geothermal brine is transferred to fresh circulating water by means of a heat exchanger. In geothermal projects, the heat exchanger cost constitutes a considerable part of the investment cost. For this reason, the optimum heat transfer area of the heat exchanger needs to be determined. In this paper, a counter flow heat exchanger of known input temperatures and mass flow rates is considered, and a mathematical model to find the optimum heat transfer area of the heat exchanger is given. In addition, the model is applied to typical low temperature geothermal resources with 90 1C geofluid temperatures. The objective function of optimization is to find the optimum heat transfer area for a counter flow plate heat exchanger, which maximizes the annual net profit. 2. Thermodynamic analysis In conventional fossil-fuel district heating systems, boilers are generally used to supply hot water. However, in geothermal applications, counter flow plate heat exchangers are often used for this purpose. This means that fuel costs are eliminated in geothermal systems. To obtain the net profit of geothermal systems, heat exchanger investment costs are subtracted from the annual money savings (i.e. fuel costs). Thermal capacities of circulating water (cold) and geofluid (hot) are [4]; _ s :C p W 0 C , Cc ¼ m (1) _ geo :C p Ch ¼ m
0 W C .
(2)
There are two main factors in efficient utilization of geothermal heat in district heating schemes [5,6]:
The flow rate of circulating water that enters the heat exchanger must be greater than _ s 4m _ geo ). the geothermal brine’s flow rate (m Return temperature of circulating water from the heating network to the heat exchanger must be as low as possible.
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In this study, it is assumed that the mass flow rate of circulating water is greater than the mass flow rate of geofluid. Hence the thermal capacity of circulating water is greater than the thermal capacity of geofluid (i.e. Cc4Ch). Under these assumptions, the variation of temperature related to the heat transfer area of the heat exchanger can be drawn as in Fig. 2. Since the thermal capacity of geofluid is smaller, its temperature difference will be greater. That is, the fluid with the smaller thermal capacity has a bigger slope in the temperature-area graph. The heat transfer rate from geofluid to circulating water in the heat exchanger is determined as [4,7] Q_ ¼ C h :ðT hi T ho Þ.
(3)
The heat rate that is taken by circulating water is Q_ ¼ C c :ðT co T ci Þ.
(4)
According to heat transfer law [4,7,8] ðT hi T co Þ ðT ho T ci Þ , Q_ ¼ U:A: ln ðT hi T co Þ=ðT ho T ci Þ
(5)
ðT hi T co Þ ðT ho T ci Þ . ln ðT hi T co Þ=ðT ho T ci Þ
(6)
LMTD ¼
The heat that is given off by the geofluid must be equal to the heat that is taken by the circulating water. That means, C h :ðT hi T ho Þ ¼ C c :ðT co T ci Þ. Solving for Tco in Eq. (7) and substituting into Eq. (5) with Eq. (3) gives ðT hi T ci Þ C h =C c ðT hi T ho Þ Ch Ch ln . ¼1 T ho T ci U:A Cc
Fig. 2. The relationship between temperature and heat transfer area in counter flow heat exchanger.
(7)
(8)
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Re-arranging Eq. (8): ðT hi T ci Þ C h =C c ðT hi T ho Þ 1 1 ln ¼ U:A: . T ho T ci Ch Cc If D is defined as [4] 1 1 D ¼ U:A: , Ch Cc
(10)
Eq. (9) becomes ðT hi T ci Þ C h =C c ðT hi T ho Þ ¼ D, ln T ho T ci then
(9)
ðT hi T ci Þ C h =C c ðT hi T ho Þ ¼ eD . T ho T ci
If Eq. (12) is arranged, it becomes T hi : 1 C h =C c T ci :ð1 eD Þ . T ho ¼ eD C h =C c
(11)
(12)
(13)
With Eq. (13), we can easily find output temperatures of fluids from the heat exchanger, if the input temperatures of fluids are known. Eq. (13) can be written as T ho ¼ T hi ðT hi T ci Þ
ð1 eD Þ . C h =C c eD
(14)
From Eq. (14) ðT hi T ho Þ ¼ ðT hi T ci Þ
ð1 eD Þ . C h =C c eD
(15)
2.1. Heat Exchanger Effectiveness (e) The effectiveness of the heat exchanger is formulated as [4,7] e¼
Q_ , _ Qmax
(16)
where Q_ max is the maximum heat transfer rate from geofluid to circulating water if the heat transfer area were infinite. When Q_ max is calculated, the output temperature of the fluid that has the smaller heat capacity is taken as being equal to the other fluid’s input temperature (i.e. T ho ¼ T ci ). Hence, Q_ max is calculated as; Q_ max ¼ C h :ðT hi T ci Þ ½W.
(17)
If Ch4Cc, the output temperature of the geofluid is equal to the input temperature of the circulating water. So, Q_ max ¼ C c :ðT hi T ci Þ.
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In conclusion, the most generally state of Q_ max is Q_ max ¼ C min :ðT hi T ci Þ, where Cmin smaller heat capacity. In the system considered, it is assumed that Cmin ¼ Ch. According to Fig. 2, effectiveness of heat exchanger can be written as e¼
C h :ðT hi T ho Þ C c :ðT co T ci Þ Q_ ¼ . ¼ _ Qmax C h :ðT hi T ci Þ C h :ðT hi T ci Þ
Then, e¼
ðT hi T ho Þ . ðT hi T ci Þ
(18)
Substituting Eq. (15) into Eq. (18), ð1 eD Þ . C h =C c eD
e¼
(19)
The effectiveness of the heat exchanger can be written as a function of NTU (Number of Transfer Units) and heat capacity ratio (R). NTU is a dimensionless parameter, which expresses the size of heat exchangers and is commonly used in heat exchanger analysis. In general, NTU and heat capacity ratio (R) are expressed as [4,7] NTU ¼
R¼
U:A , C min
C min . C max
For the geothermal system considered, these parameters can be written as NTU ¼
R¼
U:A , Ch
Ch . Cc
(20)
(21)
If coefficient D, in Eq. (10), is written as a function of NTU and R, it becomes D ¼ NTU:ð1 RÞ.
(22)
Hence the effectiveness of the heat exchanger can be expressed as e¼
ð1 eNTU:ð1RÞ Þ . ðR eNTU:ð1RÞ Þ
(23)
In heat exchangers, effectiveness varies in the range 0–1 (0 e 1). 3. Cost analysis of geothermal district heating heat exchanger In this section, cost analysis of the heat exchanger, which is used in geothermal district heating system, is performed and the optimum heat transfer area, which gives maximum annual net profit, is determined.
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One of the most important pieces of equipment in a geothermal district heating system is the heat exchanger. Annual investment cost of the heat exchanger (Ca) can be found as C a ¼ I c :A:CRF $=year (24) in which CRF is the capital recovery factor of investment, Ic is the cost of heat exchanger per unit. CRF is found as [9] CRF ¼
ð1 þ iÞn :i ð1 þ iÞn 1
(25)
in which i is the interest rate, n is the average heat exchanger life. It should be noted that the heat exchanger life-time can strongly depend on local conditions, mainly due to the chemical composition of the geothermal fluid. In this analysis, the heat exchanger life-time is assumed to be 15 years, typical for Turkish geothermal water conditions. When geothermal energy is used for district heating, there is considerable fuel cost savings compared to a conventional fossil-fuel district heating system. For this reason, adding a heat exchanger to a geothermal system instead of a boiler to a conventional system provides financial savings due to the elimination of fuel cost. Annual money saved equals the annual fuel cost used to produce the same amount of heat energy in a conventional heating system. Specific fuel consumption (be) of a conventional district heating system is be ¼
3600 H u :Zk
kg=kWh ,
(26)
in which Hu is the lower heating value of fuel and Zk is the boiler efficiency. Specific annual fuel consumption (Be) is Be ¼ H
3600 H u :Zk
kg=kW:year .
(27)
_ annual fuel consumption (B) can be found as To acquire heat rate of Q, 3600 B ¼ Q_ H H u :Zk
kg=year ,
(28)
in which H is the operational hours of the plant [h/year]. When a conventional system is used for heating, the revenue of annual fuel consumption is equal to the annual money saved in a geothermal system, over the same time. Annual saved money (YPT) can be found as YPT ¼ Q_ H
3600 F H u :Zk
$=year ,
(29)
where F is the fuel cost [$/kg]. Therefore, the net profit (NK) that supplied geothermal district heating system can be found as [10] NK ¼ YPT C a
$=year .
(30)
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Table 1 Characteristic values used in computer simulation Input temperature of geofluid
76 1C
Mass flow rate of geofluid Input temperature of circulating water Mass flow rate of circulating water Return temperature of circulating water Specific heat capacity of water (Cp) Overall heat transfer coefficient of HX (U) Boiler efficiency (Zk) Cost of heat exchanger per unit (Ic) Lower heating value of fuel (Hu) Fuel Cost (F) Heat exchanger life (n) Interest rate (i)
222.3 kg/s 50 1C 540 kg/s 48 1C 4186 J/kg K 5100 W/m2 K 0.85 350 $/m2 41900 kJ/kg 0.5 $/kg 15 years 0.10
4. Numerical analysis A mathematical model of the counter flow heat exchanger is prepared and the simulation is performed. Simulation data is given in Table 1. Input temperature and mass flow rate of geothermal water entering the heat exchanger are 76 1C and 222.3 kg/s, respectively. There are many geothermal resources in this temperature range in Turkey, particularly, in the Aegean Region of Turkey. It is possible to use these geofluids for district heating applications. This type of geothermal heating system has been successfully and efficiently applied all over the world [6,11–13]. Input temperature and mass flow rate of circulating water entering the heat exchanger are assumed to be 50 1C and 540 kg/s, respectively [14]. 5. Results of analysis After computing, the optimum heat transfer area of a counter flow heat exchanger is found as 1612 m2 (Fig. 3). As can be seen, a counter flow heat exchanger with this heat transfer area maximizes the net profit of the system. If a district heating heat exchanger has this area, annual money saved, investment cost of heat exchanger and annual net profit can be found as US$ 4.350 million/year, US$ 74,178/year and US$ 4.276 million/year, respectively (Table 2). Under these conditions, the output temperatures of geofluid and circulating water from heat exchanger are 50.08 1C and 60.58 1C, respectively. The output temperature variations of geofluid and circulating water are shown in Fig. 4. The output temperature of the geofluid is high enough for some cascaded uses. For example; balneological, swimming pool and aquaculture applications, snow and ice melting, heat pump applications etc. However, some important points should be considered in evaluation of the waste geofluid. For instance, the waste geofluid cannot be just fed to surface drainage because of environmental concerns. The reinjection process must be applied. Sometimes further use of the waste geofluid is not suitable for sustainability of the geothermal reservoir. The colder reinjection fluid cools the geothermal reservoir. In Fig. 5, the variations of the annual net profit related to heat transfer area can be seen.
ARTICLE IN PRESS
Ca ($/year)
95000
4.365x106
90000
4.360x106
85000
4.355x106 YPT
80000
4.350x106
Max NK
4.345x106
75000
4.340x106
70000 Ca
4.335x106
65000 60000 55000 1300
YPT ($/year)
A. Dagdas / Renewable Energy 32 (2007) 1020–1032
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4.330x106
Aopt=1612 m2 1400
1500
1600
1700
1800
1900
4.325x106 2000
A (m2) Fig. 3. Optimum heat transfers area, maximizes net profit of geothermal system.
Table 2 Results of simulation (at optimum conditions) Output temperature of geofluid Output temperature of circulating water Investment cost (Ca) Annual saved money (YPT) Annual net profit (NK) Capital recovery factor (CRF) Specific fuel consumption (be)
50.08 1C 60.58 1C 74,178 $/year 4,350,500 $/year 4,276,385 $/year 0.1315 0.1011 kg/kWh
50.7
60.6
50.6
60.5
50.4 50.3 50.2
60.45
Tco (C)
Tho (C)
60.55
Tco
50.5
Tho 60.4
50.1
Aopt=1612 m2 50 60.35 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 A (m2)
Fig. 4. The output temperatures of geofluid and circulating water from heat exchanger vs. Heat transfer area (at optimum conditions).
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4,278x106 4,276x106
NK ($/year)
4,274x106 4,272x106 4,270x106 4,268x106 4,266x106
Aopt=1612 m2
4,264x106 1300
1400
1500
1600
1700
1800
1900
2000
A (m2) Fig. 5. Net profit vs. heat transfer area.
4,300x106 Ic=250$/m2 4,290x106
NK ($/year)
4,280x106
Ic=300$/m2
4,270x106 4,260x106
Ic=350$/m2
4,250x106 Ic=450$/m2
4,240x106 4,230x106
4,220x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2) Fig. 6. The variation of annual net profit related to heat transfer area, at various heat transfer unit costs.
Table 3 Determined optimum heat transfer areas for various heat exchanger unit costs Heat exchanger unit cost (Ic) ($/m2)
Optimum heat transfer area (Aopt) (m2)
250 300 350 450
1716 1659 1612 1534
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4,290x106
NK ($/year)
4,280x106
i=0.08
4,270x106 i=0.10
4,260x106
i=0.12
4,250x106 4,240x106
i=0.14
4,230x106 4,220x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2) Fig. 7. The variation of annual net profit related to heat transfer area, at various interest rates.
Table 4 Determined optimum heat transfer areas for various interest rates Interest rate (i)
Optimum heat transfer area (Aopt) (m2)
0.08 0.10 0.12 0.14
1648 1612 1578 1546
Some sensitivity analyses have been made as follows. For i ¼ 0.10 and F ¼ 0.50 $/kg, the effects of various unit heat exchanger costs (Ic) on optimum heat exchanger area are as shown in Fig 6. As can be seen in Fig. 6 and Table 3, while heat exchanger unit cost rises, optimum heat transfer area decreases (for i ¼ 0.10). For Ic ¼ 350 m2 and F ¼ 0.50 $/kg, the effects of various interest rates above optimum heat transfer area, like shown in Fig. 7. As can be seen in Fig. 7 and Table 4, as the interest rate rises, optimum heat transfer area and net profit of the system decrease (for Ic ¼ 350 $/m2). For Ic ¼ 350 $/m2 and i ¼ 0.10, at various unit fuel costs, the variation of annual net profit above heat transfer area is shown in Fig. 8. The optimum heat transfer areas determined for various unit fuel costs and determined to maximize net profit are shown in Table 5. According to these values, as unit fuel cost raises, annual net profit of geothermal district heating system and optimum heat transfer area of the heat exchanger increase. 6. Conclusions There are a lot of studies involving heat exchanger optimization in the literature. Most of them are confusing and not practical for the manufacturer. In this article, an easy
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NK ($/year)
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4,800x106 4,700x106 F=0.55 $/kg 4,600x106 4,500x106 4,400x106 4,300x106 4,200x106 F=0.50 $/kg 4,100x106 4,000x106 3,900x106 3,800x106 F=0.45 $/kg 3,700x106 3,600x106 3,500x106 3,400x106 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 A (m2)
Fig. 8. The variation of annual net profit related to heat transfer area, at various unit fuel costs.
Table 5 Determined optimum heat transfer areas for unit fuel costs Unit fuel cost (F) ($/kg)
Optimum heat transfer area (Aopt) (m2)
0.45 0.50 0.55
1579 1612 1642
approach is presented for determining optimal heat transfer area of a counter flow heat exchanger. Especially, this approach can be used for pre-feasibility studies in geothermal district heating applications. According to the analysis, utilization in a district heating application, a geothermal resource, which produces geofluid at 76 1C and 222.3 kg/s, requires a 1612 m2 heat transfer area in the heat exchanger. This value is an optimum result. With this size heat exchanger, the maximum annual revenue point of view fuel savings will be supplied from the geothermal heating application. It should be noted that this analysis considers only a single set of inlet temperatures and flow rates. Therefore, optimization results could also be expected by varying these factors. In all the regions of Turkey, these geothermal water values could be obtained very easily. Acknowledgement The Author thanks Prof. Dr. Bahri S- ahin for reviewing and any technical information. References [1] Barbier E. Geothermal energy technology and current status: an overview. Rene Sustain Energy Rev 2002;6(3):65. [2] Dai C, Liang J. Optimum design and running of PHEs in geothermal district heating. Heat Transfer Eng 1999;20(4):52–61.
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[3] Simsek S, Mertoglu O, Bakir N, Akkus I, Aydogdu O, Geothermal energy utilization, development, and projections- Country update report (2000–2004) of Turkey. Proceedings of the world geothermal congress, Turkey, 2005. p. 1–10. [4] Stoecker WF. Design of thermal systems. New York: McGraw Hill; 1989. [5] Harrison R, Mortimer ND, Smarason OB. Geothermal heating. Brussels: Pergamon Press; 1990. [6] Dimitrov K, Dimitrov O, Geothermal district heating schemes in the Republic of Macedonia. Proceedings World Geothermal Congress, Japan, 2000 p., 3401. [7] Incropera FP, Dewitt DP. Basics of the heat and mass transfer. Istanbul: Literatur Publishing; 2001 [in Turkish]. [8] Shvets IT, Tolubinsky VI, Kirakovsky NF, et al. Heat engineering. Moscow: Mir Publishing; 1975. [9] Aybers N, Sahin B. The cost of energy. Istanbul: Yildiz Technical University Press; 1995. [10] S- ahin B, Vardar N. Recovery of exhaust heat at marine systems with diesel engine. Turkish Lloyd serial conf 1991:91–103. [11] Dai C, Liang J, Direct and indirect low temperature geothermal district heating systems. Proceedings world geothermal congress, Japan, 2000 3395. [12] Wang W, A successful example of a retrofit to a geothermal district heating system. Proceedings world geothermal congress, Japan, 2000 p. 3585–3588. [13] Gunnlaugsson E, Frimannson H, Sverrissson G, District heating in Reykjavik- 70 years experience. Proceedings world geothermal congress, Japan, 2000 p. 2087–2092. [14] Dagdas A, Improvement of the optimal usage model for geothermal energy resources and the local application. PhD thesis. Department of Mechanical Engineering, Yildiz Technical University, Istanbul; 2004 [in Turkish].