Valorisation of low-temperature heat: Impact of the heat sink on performance and economics

Applied Thermal Engineering 50 (2013) 1543e1548

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Valorisation of low-temperature heat: Impact of the heat sink on performance and economicsq Oliver Buchin, Felix Ziegler* Technische Universität Berlin, Institut für Energietechnik, KT 2, Marchstraße 18, D-10587 Berlin, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 June 2011 Accepted 3 October 2011 Available online 14 October 2011

Low-grade heat is available everywhere; consequently, the valorisation of this heat seems to be attractive in terms of economics. However, irrespective of the form of energy which is produced, any valorisation comes along with the production of another stream of waste heat with even lower value. The dumping of this reject heat often turns out to be the issue which determines cost. This presentation will elaborate on the influence of the heat sink temperature both on conversion efficiency and cost. It first will give a frame on a very generic level. It is easy to reproduce the well-known fact that the change in COP of a compression heat pump with heat sink or source temperatures is in the order of some %/K. The same order of magnitude holds for all generic cycles with one important exception: the influence of the heat sink temperature on the COP of a thermally driven cooling machine is about twice the impact of the other temperatures. In addition, simple equations to account for the cost of heat exchange are presented. They show that heat pumps, be it work driven or heat driven, exhibit the best efficiency-to-cost ratio. In order to leave the generic level, a more detailed analysis is given for an absorption cooling system. It is confirmed that the impact of the heat sink temperature on capacity and COP is significantly larger than that of the other temperatures; in the nominal point a rise in heat sink temperature reduces the cooling capacity by over 10%/K. Finally, the influence of the humidity of the ambient air on performance is presented in a first order approach, also. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: First cost Operating cost Thermodynamics Temperature Characteristic equation

1. Introduction Valorisation of low-temperature heat is a broad area. It covers heat recovery by compression heat pumps, sorption heat pumps, and heat transformers, as well as conversion into cold or mechanical energy. The means to do so are abundant as well: conventional conversion systems use thermodynamic mono-fluid cycles (closed steam cycles, open steam cycles, or even gas cycles), or dual-fluid cycles such as sorption cooling processes or sorption power processes. Some options which are state of the art, or technically feasible, or at least in discussion, are listed in Table 1. The numbers (#1, 2, etc.) which are listed in Table 1, refer to Fig. 1, in which the nature of the duty to be fulfilled by these cycles is depicted on a temperature scale.

q A large part of this paper has been published before at the 2nd European Conference on Polygeneration, March 30theApril 1st 2011, Tarragona, Spain. * Corresponding author. Tel.: þ49 (0) 30 314 22387; fax: þ49 (0) 30 314 22253. E-mail address: [email protected] (F. Ziegler). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.10.002

The first aim of this paper is to give an order to the said options and then to elaborate on the impact of the heat sink, and that of the other temperatures, too. It has to be distinguished between the impact on power density, efficiency, and cost. This will be done using generic equations. In a more technical approach, absorption chillers will be discussed in detail. 2. Generic thermodynamic approach 2.1. Options for revalorisation These options could be discussed in terms of exergy, but we keep using energy and temperature as describing parameters. First two definitions or clarifications are in order: lowtemperature heat is heat with a temperature above ambient (at least two times the temperature gradient across a heat exchanger!). The heat sink is defined by the ambient, as well. It may include humidity, so it may be the dry bulb temperature or the wet bulb temperature. In order not to complicate things, in the first part of the paper we do not distinguish this.

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Table 1 Options for valorisation of low-temperature heat. Mono-fluid

No fluid

Multi-fluid

Air cycle

#1

Absorption cycle

#2, 4, 5

Rankine cycle Steam jet cycle Stirling cycle Vapor compression cycle Vuilleumier cycle

#3 #2, 5 #1, 3 #1 #2, 4, 5

Adsorption cycle Chemical cycle Hybrid sorption cycle Rankine sorption cycle

#2, 4, 5 #2, 4, 5 #1 #3

Peltier cooler Magnetocaloric cooler Thermoelectric generator

#1 #1 #3

2.2. Performance Temperature of heat flow

in

work: T→∞

out

in

drive: T4 upgraded: T3

#1: compression heat pump #2: heat-driven heat pump #3: power cycle #4: heat transformer #5: heat-driven refrigerator

out

out

in

in

source: T2

out

sink: T1

in

in

in

out

out

out

#3

#4

#5

cold: T0

in #1

#2

Fig. 1. Generic options to valorise heat of temperature T2.

Fig. 1 schematically shows the thermodynamic options [1]; the only scale used is a temperature scale with temperature rising from bottom to top. Each box denotes another generic conversion process. The words "in" or "out" are related to the energy flow on the respective temperature level, entering or leaving the device. Box #1 depicts a compression heat pump which upgrades heat from T2 to T3 with input of mechanical work. Process #2 does the same upgrading, albeit with using heat of temperature T4 as drive. It depicts a heat driven heat pump. Box #3 stands for a power cycle which works between T2 and T1. Box #4 represents a heat transformer cycle which upgrades heat from T2 to T3 with degrading part of the heat to the heat sink at T1. Box #5, finally, shows a heat driven refrigerator. So, summarising, #1, #2, and #4 are heat pumps of different nature. In any case, the low-temperature heat source at T2 conveys heat into the box. Energy flows out at a higher level (#1e4) or flows in at a lower level (#5). The focus of this paper is on the processes #3 to #5 because they have to reject heat to a heat sink at a temperature T1. However, we will discuss processes #1 and #2 also shortly. Table 2 Performance of generic valorisation processes.

#1

Work-driven heat pump

#2

Heat-driven heat pump

#3

Power cycle

#4

Heat transformer

#5

Heat-driven refrigerator

Efficiency

Example

Q T3 COP ¼ 3 ¼ g W T3  T2 Q T T  T2 COP ¼ 3 ¼ g 3 4 Q4 T4 T3  T2 W T  T1 h¼ ¼ g 2 Q2 T2 Q T T  T1 COP ¼ 3 ¼ g 3 2 Q2 T2 T3  T1 Q T T  T1 COP ¼ 0 ¼ g 0 2 Q2 T2 T1  T0

COP ¼ 4:9 COP ¼ 1:1

Table 2 gives the definition of efficiency or COP and an equation to determine it in the most simple way, which is to calculate the reversible limit and multiply this with a rough measure for thermodynamic quality, g. This is done often although it is not really correct: irreversibilities, of course, change with temperature and, especially, with temperature differences. In order not to prolong this paper we will stick to a simple numerical example, just for orientation. This example uses the temperatures from Table 3 and a constant quality of g ¼ 0.5. All these equations are well-known from textbooks (e.g. [1],) or can be derived easily, so they will not be discussed here. The sensitivity of the efficiencies on the temperatures will be investigated by using the derivatives. Table 4 gives the derivatives with respect to all the relevant temperatures, normalised with the respective efficiency. From these equations it is obvious that, e.g., the impact of the source temperature, T2, on the heat pump COP is always somewhat larger than that of the sink, T3, in the work driven case (#1) because 1 > T2/T3, whereas it is smaller in the heat driven case #2 because (T4-T3)/(T4-T2) T1/T2. In the case of the heat transformer (#4) it is the other way round, again. This is understood easily, as a shift in the intermediate temperature T2 changes temperature lift and temperature thrust of the process at the same time. For the same reason, the impact of the heat sink in the case of refrigeration (#5) is the largest one. In order to quantify these findings, the derivatives according to Table 4 are plotted against the heat sink temperature for a set of other temperatures (see Table 3) in Figs. 2 to 6. The absolute value of the relative (normalised) derivatives is shown. The dashed lines display negative derivatives. The impact of the temperatures on the COP of a compression heat pump (#1, Fig. 2) between T2 and T3 is the larger, the smaller the temperature lift, (T3-T2), to be accomplished is. It is in the order of some %/K for realistic temperatures. The difference between the impact of the two temperatures is marginal. For heat driven heat pumps (#2, Fig. 3), the impact of the temperatures on the COP is in the same order of magnitude as for compression heat pumps. However, the influence of the driving temperature T4 is the smallest and it varies slightly only. For moderate temperatures, the impact of the sink T3 is the strongest, as discussed before. For a power station which is operated by low-temperature heat (#3, Fig. 4), the impact of the temperatures is reverse as compared to Fig. 2, naturally.

h ¼ 0:06 COP ¼ 0:29 COP ¼ 0:43

Table 3 Set temperatures according to Fig. 1. Temperature level

T4

T3

T2

T1

T0

Value [ C]

180

120

80

35

5

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Table 4 Relative change in COP or efficiency due to a change in one temperature.     vCOP  vh       vT  COP or vT  h; derivative with respect to. i

T4 #1 #2

T2 T4 ðT4  T2 Þ

i

T3

T2

T2  T3 ðT3  T2 Þ

1 T3  T2



T2 T3 ðT3  T2 Þ

#3 #4



T1 T3 ðT3  T1 Þ

#5

T1

T0

T4  T3 ðT3  T2 ÞðT4  T2 Þ T1 T2 ðT2  T1 Þ



1 T2  T1

T1 T2 ðT2  T1 Þ



T3  T2 ðT3  T1 ÞðT2  T1 Þ

T1 T2 ðT2  T1 Þ



T2  T0 ðT1  T0 ÞðT2  T1 Þ

T1 T0 ðT1  T0 Þ

for the other processes (be aware that the scale of the ordinate is doubled!). So, it may be stated that waste heat driven chillers are most sensitive to the respective temperatures. The impact of the heat sink temperature T1 is by far the largest. We will elaborate on these findings in a later chapter. Before we do so, we use the equations from above for another short discussion with the focus on first cost. 2.3. Impact on first cost It is very well known that low efficiency drives operating cost. However, low efficiency also drives first cost: the amount of heat which has to be put through an energy conversion system, of course, depends on its efficiency. Especially in processes which are driven by low-temperature heat the cost for heat exchange becomes a decisive issue [2]. In Table 5 equations for a specific cost ratio s are given which is defined as the ratio of the overall heat turnover to the useful energy (which may be heat or work): Fig. 2. Relative change of the COP of a compression heat pump (#1) with temperatures.

s¼

P

jQ i j Q USE

(1)

For the heat transformer (#4, Fig. 5) the relative impact of the high temperature heat sink temperature T3 does not change with temperature T2. Therefore, it is comparably small for small heat source temperatures, but for high heat source temperatures it becomes important. Then however, all derivatives are in the order of 1%/K. The most important result may be found in Fig. 6 for the refrigerators (#5): all derivatives are about a factor of 2 larger than

These equations may be combined with the equations for efficiency in Table 2; then the derivatives in Table 4 can be applied. This will not be exemplified here because it is a straightforward exercise. It shall be sufficient to state that those temperatures which have a large impact on efficiency will have a large impact on cost, also. It is interesting to note that the relative heat turnover in the case of the heat driven heat pump (#2) does not depend on the COP

Fig. 3. Relative change of the COP of a heat driven heat pump (#2) with temperatures.

Fig. 4. Relative change of the efficiency of a power station (#3) with temperatures.

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O. Buchin, F. Ziegler / Applied Thermal Engineering 50 (2013) 1543e1548 Table 5 Specific cost ratio: relative heat turnover.

Fig. 5. Relative change of the COP of a heat transformer (#4) with temperatures.

#1

Work-driven heat pump

#2

Heat-driven heat pump

#3

Power cycle

#4

Heat transformer

#5

Heat-driven refrigerator

Relative heat turnover P 1 jQ i j s¼ ¼ 2 Q COP P 3 jQ i j s¼ ¼ 2 Q P 3 2 jQ i j s¼ ¼ 1 h W P 2 jQ i j s¼ ¼ Q COP P 3 2 jQ i j s¼ ¼ 2þ Q0 COP

Example (see Table 2) 1.8 2 32 6.9 6.7

power, Q0, as well as the driving heat input, Q2, can be represented as a linear function of a temperature functional, the characteristic temperature function DDt, which, in turn, depends on the mean temperatures of the external heat carriers, driving heat t2, cooling water t1, and chilled water t0:

DDt ¼ at0  bt1 þ ct2

(2)

Q 0 ¼ S0 þ M0 DDt

(3)

Q 2 ¼ S2 þ M2 DDt

(4)

The benefit of this representation is the fact that the impact of the temperatures is directly seen. As an example a single-effect LiBr absorption chiller with a nominal cooling capacity of 10 kW shall be used. In order to bring cost into the play the heat flows are normalised by a first cost of 10,000V for this device. This, of course, is not the real price of the chiller but it is in the right order of magnitude. It renders a specific price of 1000V/kW of cooling capacity. The cost-specific heat flows (W/V) then are given by:

Fig. 6. Relative change of the COP of a heat driven refrigerator (#5) with temperatures.

q0 ¼ s0 þ m0 DDt

(5)

q2 ¼ s2 þ m2 DDt

(6)

The COP consequently is the ratio because all input heat is turned into useful heat. In all other cases, the turnover of heat can only and will be reduced by increasing efficiency. The numerical examples drastically show the problem of producing power from low-temperature heat: as the efficiency of the power plant will be relatively small, the turnover of heat as compared to the power output will be large. The heat pumps (#1 and 2), from this point of view, definitely show the best result. So we can conclude at this stage that valorisation of waste heat by pumping it to a useful, higher temperature level may be the most attractive option. This topic, however, will be covered by future investigations. In this paper cooling from waste heat will be looked at in more detail: cold is a more valuable product than heat and it is in the focus of today’s research.

3. Absorption chillers 3.1. Characteristic curves The discussion up to now, of course, suffers from the fact that the specific features of the processes which are used do not show up in the fundamental thermodynamic relationships. Therefore, in order to check the validity, a more applied approach will be shown now. The performance of absorption chillers can be presented most easily with using the characteristic equations [3e6]. The cooling

COP ¼

q0 s þ m0 DDt ¼ 0 q2 s2 þ m2 DDt

(7)

The coefficients are given in Table 6 [7]. The coefficient b gives the impact of the heat sink. It obviously is the largest one, and it is about double the size as the others. The same order of magnitude resulted from the generic approach (Fig. 6) also. The respective characteristic curves for cooling power, driving heat, and COP are shown in Fig. 7. The vertical line marks the design point of the chiller with a cooling capacity of 1W/V at a characteristic temperature difference of about 22K. Any changes in any of the three temperatures (separately or combined) may be seen as influencing cooling power or specific cost, respectively. For instance, an increase in heat source temperature t0 or driving heat temperature t2 will increase the characteristic temperature function DDt according to equation 2. Consequently, cooling power per investment, driving heat requirement per investment, and COP will increase. This means that for a given design the power increases, and for a given power

Table 6 Coefficients for characteristics of an absorption chiller. Coefficient

a

b

c

s0

m0

s2

m2

Value

1.8

2.5

1

0.09W/V

0.042W/VK

0.2W/V

0.051W/VK

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Fig. 7. Characteristic curves of a single-effect absorption chiller. Fig. 8. Sensitivity of the specific cooling power on the temperatures.

the necessary investment decreases. The reverse influence is due to the heat sink temperature t1. 3.2. Impact of temperatures on heat flows In order to see the influence of the temperatures on heat flows and the COP, again the derivatives have to be calculated. The results for the heat flows are given in Table 7. The impact of the temperatures on the driving heat are stronger than on the cooling power. Comparing the three temperatures, the influence of the heat sink temperature t1 is the largest one. The impact of the temperatures on the heat flows is almost linear as stated before, but it is a non-linear impact on the COP. Moreover, the relative impact is more interesting than the absolute one. Therefore, the relative influence of each temperature on relative cooling capacity and COP is plotted against the cost-specific cooling power q0 in Figs. 8 and 9. Again, a negative value of the derivative is indicated by a dashed line. The nominal point is marked by a vertical line. The impact of the temperatures on specific cooling capacity is in the order of 5%/K (driving heat), 8%/K (chilled water), and over 10%/ K (heat sink) in the nominal point. It increases strongly when the specific load is reduced. This happens in the case of part load, or in the case of the characteristic temperature difference being small. In this case, the required heat exchange area is relatively large, the chiller will be expensive, and the sensitivity on the temperatures will be high.

3.4. Impact of ambient humidity We now also want to exemplify the influence of the ambient conditions, namely dry bulb temperature and relative humidity, separately. The absorption chiller is coupled to the ambient via the heat sink, generally a wet or hybrid cooling tower. The cooling water temperature t1 in this case is dependent on the characteristics of the cooling tower also. We want to roughly model the system dependence using the characteristic temperature functions for the chiller. Ideal behaviour of the cooling tower is assumed: any heat flow can be rejected as long as a driving temperature difference across the exchanger exists. In order to take into account humidity, the heat sink temperature is calculated as wet bulb temperature twb of the ambient air. Furthermore the mean temperature difference between humidified air and cooling water is set to 10 K. Equation (2) in this case turns into

DDt ¼ at0  bðtwb ðta ; 4a Þ þ 10KÞ þ ct2 :

Setting mean evaporator and generator temperatures and ambient pressure constant (t0 ¼ 16.5  C, t2 ¼ 70.0  C, pa ¼ 1 bar) and taking parameters for the chiller from Table 6 the normalized cooling capacity Q0/10 kW, with Q0 according to equation (3), can easily be calculated with respect to ambient temperature and humidity (Fig. 10).

3.3. Impact of temperatures on COP The impact on the COP is significantly less than the one on the heat flows, as long as the specific load is not too small. This can be seen in Fig. 7 as well as in Fig. 9, where the impact of the temperatures on the COP is plotted against the specific cooling load, again. Once more, the derivative with respect to the heat sink temperature, t1, is the largest.

Table 7 Derivatives of the specific heat flows with respect to the temperatures. i

0

vq0 vti

a m0

0.076

-b m0

0.105

c m0

0.042

a m2

0.092

-b m2

0.128

c m2

0.051

vq2 vti

1

(8)

2

Fig. 9. Sensitivity of the COP on the temperatures.

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using the approach of the characteristic functions. The impact of the heat sink temperature on heat flows (capacity) and performance (COP) is about twice as large as that of the other temperatures. Finally, a first attempt has been made to include the impact of humidity via the wet bulb temperature into the calculus. This, however has to be refined further by using a realistic model of the cooling tower. Summarising, the heat sink deserves more attention in the design of processes which re-valorise low-grade heat. It can be stated that the research which is dedicated to the field of heat rejection does not match the importance within the area of energy engineering. Nomenclature

Fig. 10. Influence of ambient conditions on the normalized cooling capacity.

As expected, we see that for a given ambient temperature (dry bulb) decreasing the relative humidity results in decreasing the wet-bulb temperature and thus provoking higher cooling capacities. For a set cooling capacity, higher ambient temperatures can only be handled with lower relative humidities. The system can be operated in free-cooling mode when wet bulb temperatures are lower than the required chilled water temperature, t0. This region is shown in the upper part of Fig. 10. In the respective example free-cooling corresponds to a normalized cooling capacity larger than 1.5. Hourly ambient conditions for a moderate climate (Berlin METEONORM Test Reference Year [8]) are plotted in Fig. 10 also. It can be seen that the particular climatic conditions result in a wide possible operating range of the chiller e in this example between 0.8 and 1.5 of the normalized cooling capacity at different relative humidity, albeit at elevated dry bulb temperatures the operating range starts to be restricted to part load. At maximum dry bulb temperature (when the loads are highest) the normalized cooling capacity will not surpass 0.8 as long as the relative humidity is larger than 40%. 4. Conclusion From the fundamental relationships which have been presented in this communication it can be concluded that the impact of the temperature and nature of the heat sink on performance and economics in the field of valorisation of low-temperature heat is predominant - except, of course, in the case of simple heat pumps. In all other cases the heat flow into this sink accounts for a large fraction of the energetic turnover. For the sake of efficiency, the driving temperature difference must be small which in turn necessitates large heat transfer areas. Heat pumps seem to be the most cost-efficient devices for valorisation of low-temperature heat. Of course a rising ambient or heat sink temperature in any case reduces efficiency. This effect is especially large for heat driven cooling machines. These devices have been studied in more detail

a,b,c COP g M m Q q S s T t W

h s

coefficients [-] coefficient of performance [-] thermodynamic quality [-] coefficient [kW/K] coefficient [W/VK] heat flow [kW] specific heat flow [W/V] coefficient [kW] coefficient [W/V] temperature (process) [K] temperature (heat carrier) [K] mechanical power [kW] efficiency [-] relative heat turnover [-]

Indices: 0.4 a

temperature levels ambient

References [1] G. Alefeld, R. Radermacher, Heat Conversion Systems. CRC Press, Bocca Raton, 1993. [2] S. Köhler, F. Ziegler, Sorption cooling: best alternative for the use of low temperature heat sources?, in: Proc. of Heat Powered Cycles 2006, Newcastle upon Tyne, UK, 12th to 14th September(CD-ROM) (2006). [3] T. Furukawa, et al., Study on characteristic temperatures of absorption heat pumps, in: Proc. 20th Japan Heat Transfer Conf., June 1983 (1983), pp. 508e510 (in Japanese). [4] T. Furukawa, T. Sonoda, Characteristics of H2O/LiBr absorption heat pumps for the temperature change of external Fluids, in: Proc. XVII Int. Congress of Refrigeration, Wien, 24.-29.8.1987 (1987). [5] P. Riesch, J. Scharfe, F. Ziegler, J. Völkl, G. Alefeld, Part-Load Behavior of an absorption heat transformer, in: Proc. 3rd Int. Symp. on the Large Scale Applications of Heat Pumps, Oxford. BHRA, The Fluid Engineering Centre, Cranfield, Bedford, 1987, pp. 155e160. [6] H.-M. Hellmann, C. Schweigler, F. Ziegler, A simple method for modelling the operating characteristics of absorption chillers, in: Proc. of Eurotherm Seminar No.59, Nancy-Ville, France, 6-7 July (1998), pp. 219e226. [7] A. Kühn, F. Ziegler, Operational results of a 10 kW absorption chiller and adaptation of the characteristic equation, in: Proc. Int. Conf. Solar Air Conditioning, 6.-7. October 2005, Bad Staffelstein (2005). [8] METEONORM software documentation, software version 6.0., METEOTEST, Fabrikstrasse 14, CH-3012 Bern, Switzerland.