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Internal energy flow analysis within a single effect sorption heat pump
International Journal of Refrigeration 24 (2001) 185±191
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Internal energy ¯ow analysis within a single eect sorption heat pump Bernard Spinner a,*, MikhaõÈl Sorin b, Driss Stitou a a
CNRS-IMP (Institut de Science et GeÂnie des MateÂriaux et ProceÂdeÂs), Rambla de la Thermodynamique, Tecnosud, 66100 Perpignan, France b Energy Diversi®cation Research Laboratory, CANMET, 1615 Lionel Boulet, PO Box 4800, Varennes, QueÂbec, Canada JX 1S6 Received 21 June 2000; received in revised form 28 August 2000; accepted 28 August 2000
Abstract The knowledge of the characteristics of unused, excess and untapped exergy allows a thorough analysis of internal energy ¯ows distribution within a sorption heat pump. It can be applied to any system based on gas±liquid absorption, adsorption or solid±gas reaction as well as to any process based on the internal recycling of the energy ¯ux. It can also be applied for the case of a simple eect ideal machine, in particular in the de®nition of processes where the COP is larger than 2: the levels at which the initial exergy is downgraded on the one hand, as well as, the upgraded excess exergy produced on the other allows the designer to make a judicious choice of a system. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Heat pump; Sorption; Internal energy ¯ow; Exergy characteristics; Exergy yield
Analyse des ¯ux energeÂtiques internes de pompes aÁ chaleur aÁ sorption simple eet ReÂsume L'analyse des ¯ux eÂnergeÂtiques internes mis en úuvre dans une pompe aÁ chaleur aÁ sorption, qu'elle soit aÁ absorption gaz± liquide, adsorption ou reÂaction gaz±solide, permet la caracteÂrisation des exergies non utiliseÂes, en exceÁs ou inexploiteÂes, ainsi que les possibiliteÂs de recirculations internes de ¯ux eÂnergeÂtiques. Il est ainsi possible, dans le cas de machines ideÂales aÁ simple eet, de de®nir des proceÂdeÂs de COP supeÂrieurs aÁ 2 : les degreÂs de deÂvalorisation de l'exergie d'entreÂe et d'exceÁs de potentiel valorise permettent de guider l'opeÂrateur dans ses choix de systeÁmes. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : Pompe aÁ chaleur ; Sorption ; Flux internes d'eÂnergie ; CaracteÂristiques d'exergies ; Eectivite exergeÂtique
1. Introduction Heat pumping, refrigeration and chilling-heating as well as, heat transformation in sorption machines are * Corresponding author. Tel.: +33-468-55-6855; fax: +33468-55-6869. E-mail address: spinner@univ- perp.fr (B. Spinner).
managed by the thermal energy ¯ows involved in the following physico-chemical processes: . . . .
phase change of gas±liquid absorption/desorption of gas±solution adsorption/desorption of gas±solid reversible solid±gas chemical reaction.
In accordance with a well de®ned system design, the
0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00076-1
186
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
Nomenclature
Ti
COP COPHP COPR ew xe H Q Tout min Tin max T0
Greek letters exergy yield yield T0 CARNOT factor 1 ÿ T
coecient of performance coecient of performance for a heat pump coecient of performance for a refrigerator speci®c excess and untapped exergy downgraded exergy factor enthalpy of transformation (J molÿ1) heat (J) produced temperature at minimum level (K) sink temperature at maximum level (K) reference temperature (K)
endothermic or exothermic processes may take place at four dierent temperature levels T1 < T2 < T3
temperature (K)
Subscripts a absorption or adsorption c condensation d desorption or decomposition e evaporation
analysis of the internal and external energy ¯ows. As was mentioned in the previous works [4,18±22], this analysis is applied to an ideal system. 2. Thermodynamic performance criteria for an ideal sorption machine Gas±solution and gas±solid (adsorption as well as chemical reaction) could be represented in a Clausius± Clapeyron diagram at four temperature levels Td,Ta,Tc and Te. It is also for a machine based on the heat generated from a monovariant solid±gas reaction. Taking into account that the desorption temperature levels T and that the absorption T are related to the ®nal state of desorption and absorption/adsorption processes, some assumptions have to be mach to justify the stability of the temperature levels. In the case of absorption, several authors like Kumar and Devotta [23], Tozer and James [24,25], Alefeld and Radermacher [3] relied up on a very large heat exchange surface. In the case of adsorption Meunier et al. [26], the use of entropy temperature was applied. Fig. 1 shows the internal energy ¯ux distribution in the operation of a heat pump. In this case, the external and internal heat ¯ux distribution can be represented as [4]: Qd Qda Qc Qa Qda Qe
1
with respect the heat balance according to the conservation of energy: Qd Qe ÿ Qa ÿ Qc 0 where Qda is that part of the heart ¯ux Qd which has passed towards the absorber (or adsorber or reactor in the case of chemical process) and is equal to Qd ÿ Qc, or Qa ÿ Qe. Qc and Qe are the ¯ux at the condenser outlet
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
187
untapped exergy of the upgraded energy ¯ux Qe is de®ned by the relation: 11ÿ12ÿ13ÿ14 6ÿ15ÿ16ÿ7 1ÿ3ÿ4ÿ6 ÿ in ÿ out Qe max ÿ e a ÿ min Qd d
ew
Fig. 1. Energy ¯ux distribution in a sorption heat pump. Fig. 1 Distribution des ¯ux energeÂtiques dans une pompe aÁ chaleur.
and the entry of the evaporator, respectively. It should be noted that Ta, Tc and Te are variables, while Td is a ®xed parameter; there absolute values are de®ned according to the process studied. The representation of the exergy ¯ux in the diagram of the Carnot factor vs heat ¯ux (Q) allows the following representation (Fig. 2): The heat ¯ux entering at level (d) is divided in two parts: ®rst, Qda and Qc are both downgraded from Td. This downgrading eect allows to upgrade the heat ¯ux Qe from To. Areas (1±2±8±7) and (2±3±10±9) represent the consumed exergy due to the downgrading of ¯ux Qd [4]. The area (7±12±13±16) is the produced exergy associated to the upgrading process. Being an ideal machine, there is no exergy lost: the area (1±2±3±10±9±8±7) and (12±13±16±7)are equal. Areas I and II represent the unused exergy: if the physico-chemical processes of adsorption and desorption have taken place at Ta=Tout min, the total exergy corresponding to areas I and II could be used to create an equivalent upgraded exergetic area and therefore, increasing the upgraded ¯ux Qe at given temperatures intervals. The area III is the excess exergy of the heat ¯ux Qe, which would be eliminated if the upgrading of the ¯ux took place up to the temperature Tout min. Finally, the area IV is the untapped exergy of the heat ¯ux Qe, necessarily created if a ``free'' energy source is available at Tin max. The exergy downgrading level at Qd is therefore de®ned by the ratio of the areas of the two surfaces x: 1ÿ3ÿ10ÿ9ÿ8ÿ7 1ÿ3ÿ4ÿ6 Qda d ÿ a Qc d ÿ c Qd d
xe
2
xe can be de®ned as the downgraded exergy factor which can be maximized up to 1. The speci®c excess and
3
ew can be minimized down to 0. The exergy yield is de®ned by the ratio of the exergy out produced by the upgrading of Qe ¯ux from Tin max to Tmin to the exergy provided in the desorption process. It is then de®ned by the ratio of the following areas: yield
ÿ out in ÿ max 11ÿ14ÿ15ÿ6 Qe min Qd d 1ÿ3ÿ4ÿ6
4
The yield is then equal to: yield xe ÿ ew
5
therefore can be maximized up to 1. As represented by Sorin et al. [4], a dimensionless diagram is shown in Fig. 2 using the ratio of /d and Q/ Qd (Fig. 3). The downgraded exergy factor xe can be visualized directly by the areas (1±3±10±9±8±7). Therefore the speci®c excess and untapped exergy ew is the sum of the areas (6±7±16±15) and (11±12±13±14). The yield is represented by the area (6±11±14±15). The segment (12±13) shown in Fig. 3 represents the coecient of performance of a refrigeration system de®ned by the following equation COPR=Qe/Qd, while the segment 4±15 represents the heat pump coecient of performance COPHP. The COPHP is equal to: 1+COPR as illustrated in Fig. 3. The link between yield and COPR also follows from Fig. 3: yield
ÿ out in COPR min ÿ max ÿ out d ÿ min
6
By using Eq. (5): COPHP 1 xe ÿ ew ÿ
out d ÿ min out in min ÿ max
7
3. Optimal choice of the physico-chemical processes implemented in the single eect heat pump It should be remembered that Eq. (7), the temperature in levels Td, Tout min and Tmax have been ®xed for the applied processes.
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The Clausius±Clapeyron diagram representation of a heat pump shown in Fig. 4 has been carried out in a monovariant mode corresponding to a chemical reaction between a solid and a gas. The same representation could be used for an absorption process, replacing Td by the ®nal desorption temperature, and Ta by the ®nal absorption temperature. For the case of an adsorption process, an entropy temperature [23] has been used. Maximising xe implies ®xing Tc and Ta as close as in possible to Tout min, minimizing ew leads to Te=Tmax. Straight lines A and B which de®ne the basic heat pump
(Fig. 4) operating between Td, Ta and Tc, Te could be modi®ed, for example, by shifting to reactant C, where the lines A and C are parallel, the temperatures Te and Td remaining constant; therefore, xe increases. Heat ¯ux distribution are presented in Fig. 5: it can be noted here that the path between the points d and a, has been eliminated, because Qda=0, as shown in Eq. (1). The corresponding diagram /d=f(Q/Qd) is presented Fig. 6. The value of COPR =1 and the value of COPHP are increased relative to the basic case (Fig. 3) and reach the value of 2. In order to improve the COPHP for the ®xed temperatures Td and Te, the term ew represented on Fig. 6 should be minimized: one way to achieve this is presented in Fig. 7. The ¯ux Qe is divided in two parts: Qa and (QeÿQa). Only the part Qa is upgraded from Te to Ta, the other part is upgraded only until it reaches Tc. Comparing Figs. 6 and 8, the segment 13±18 in Fig. 8 is
Fig. 2. Diagram =f(Q) of a quadri-thermal single eect sorption heat pump. Fig. 2 Diagramme =f(Q) d'une pompe aÁ chaleur simple eet aÁ quatre niveaux de tempeÂrature Fig. 4. Equilibrium lines of a monovariant heat pump according to dierent processes, in the diagram of Clausius±Clapeyron. Fig. 4 Droites d'eÂquilibre repreÂsenteÂes dans un diagramme de Clausius±Clapeyron d'une pompe aÁ chaleur monovariante.
Fig. 3. Dimensionless diagram of the valorised and downgraded exergies of a single eect sorption heat pump.
Fig. 5. Energy ¯ux distribution in a sorption heat pump with He=Ha.
Fig. 3 RepreÂsentations adimensionnelles des exergies valoriseÂes et deÂgradeÂes dans une pompe aÁ chaleur aÁ sorption aÁ simple eet.
Fig. 5 Distribution des ¯ux eÂnergeÂtiques dans une pompe aÁ chaleur aÁ sorption dans le cas ouÁ He=Ha.
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
wider than 13±12 in Fig. 6, then COPR > 1 (Fig. 8), and therefore COPHP >2. The position of the gas/solid equilibrium line for this case is shown in Fig. 4 (straight line D): the slope of the line D is lower than the slope of A. The energy ¯ux distribution corresponding to the distribution in enthalpies of transformation (Hv and Hs) is presented on the Clausius±Clapeyron diagram (Fig. 9). The solid±gas equilibrium lines with the enthalpies of transformation lower than those of the liquid±gas, were discovered by Touzain et al. [27±29]: the sulfates of iron III reacting between 6 and 12 (NH3) gives the values of the enthalpies varying from 12 to 15 kJ/mol of NH3,
189
while the enthalpies of condensation/evaporation of NH3 are of 22±24 kJ/mol according to the operating temperature or pressure. The COPHP of such a heat pump might be around 2.8. In the extreme case, when Ta =Tc=T0, and Te=Tmax in, that is when xe=1 and ew=0, one ®nds again the classical COPHP for a tri-thermal machine ae:
Fig. 8. Diagram /d=f(Q/Qd) corresponds to a heat pump process where the equilibrium lines are relative to D and A in the Clausius±Clapeyron diagram (Fig. 4).
Fig. 6. /d=f(Q/Qd) diagram in a sorption heat pump with He=Ha.
Fig. 8 Diagramme /d =f(Q/Qd) relatif aÁ une pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius± Clapeyron sont les droites D et A de la Figure 4.
Fig. 6 Diagramme: /d=f(Q/Qd ) dans le cas d'une pompe aÁ chaleur aÁ sorption ouÁ He=Ha.
Fig. 7. Heat ¯uxes correspond to a heat pump process where the equilibrium lines are relative to D and A in the Clausius± Clapeyron diagram (Fig. 4). Fig. 7 Flux de chaleur dans un proceÂde de pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius±Clapeyron sont les droites D et A de la Figure 4.
Fig. 9. Distributions in enthalpies of transformation corresponds to a heat pump process where the equilibrium lines are relative to D and A in the Clausius±Clapeyron diagram (Fig. 4). Fig. 9 Distribution des enthalpies de transformation relatives aÁ une pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius±Clapeyron sont les droites D et A de la Figure 4.
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COPHP
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
Td ÿ Tin Tout max max in Td Tout min Tmax
8
4. Conclusion Analysis of energy ¯ux distribution within a sorption heat pump has allowed to distinguish between up and downgraded heat ¯uxes in the process. The correspondence of the exergy content of the ¯uxes with the presentation of an ideal heat pump on a Clausius± Clapeyron diagram has been established. The temperature level of the downgraded heat ¯uxes from a level corresponding to the use of a costly external energy source which is required to attain the required temperature in the heat production is characterized by a downgraded exergy factor xe. Conversely, the temperature level at which the exergy is upgraded from the level of a free energy source which is required in the heat production is characterized by the speci®c excess and untapped exergy ew. The link between these two factors with the heat pump coecient of performance has been established: maximising xe and minimizing ew allows to improve this coecient and implies a completely new energy ¯ux distribution within a system. The theoretical possibilities to design sorption heat pumps with ideal COP larger than 2 has been demonstrated. Further eorts should be made to search for the adequate materials to reach these upgraded values. References [1] Le Go P, Rivero R. A thermal inventory of sorption heat pumps based of the exergy-multipole concept. In: Proc. ECO's 95, Istanbul, Turkey, July 1995. p. 182±187. [2] Trepp Ch. History and prospects of heat transformation. Rev Int du Froid 1983;5:309. [3] Alefeld G, Radermacher R. Heat conversion systems. CRC Press Inc., 1994. [4] Sorin M, Spinner B, Stitou D. Synthesis of single eect solid gas thermochemical refrigerators. Trans. IChem. Eng. 2000; 78 (Part A, p. 795±802). [5] Meunier F. Proc. Symp.: Solid sorption refrigeration, Paris, France, 18±20 November 1992. Inst. of Refrigeration. [6] Spinner B. Changes in research and development objectives for closed solid-sorption systems. In: Proc. of the Absorption Heat Pump Conf., MontreÂal, Canada, 17±20 September 1996. p. 81±96. [7] Meunier F. Absorption heat pump technology: possibilities and limits. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 25±35. [8] Wallin E, Berntsson T. Integration of heat pumps in industrial processes. Heat Recovery Systems and CHP 1994;14:287±96.
[9] Kozic D, Krope J, Goricanec D. Optimization of large heat pumps in long-distance transit heat transportation. Int J Power Energy Systems 1994;14:5±8. [10] Wu S., Eames I. W. Ecient use of waste heat from combined heat and power systems. Proc ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 51±7. [11] Herold KE. An analysis of the major variables impacting performance of absorption chillers and heat pumps. Proc ASME Advanced Energy Systems Division, AES 37:349± 56. [12] Ziegler F. Discussion of optimized design of endo-reversible heat transformation cycles. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 459±64. [13] Herold KE. Performance predictions of absorption cycles using an endo reversible model. In: Proc ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 465±70. [14] Le Go P, Cachot T, Renaudin V, Hornut J. La thermodynamique chimique en temps ®ni. In: Proc. J ETC 99, Carry le Rouet, France, 13±15 September 1999. p. 9 [15] Boussehain R, Feidt M. The optimization for a refrigeration system with the reservoirs. In: SeÂminaire franco-allemand, Kassel, Germany, 1±4 Oct. 1984. [16] Boussehain R, Feidt M. Optimisation theÂorique du cycle d'une machine aÁ froid endoreÂversible aÁ trois sources de chaleur. In: 1er colloque franco-maghreÂbin sur les modeÁles numeÂriques de l'IngeÂnieur, 22±23 November 1987, Alger, AlgeÂrie. [17] Feidt M. Finite time thermodynamics applied to optimization of heat pump and refrigerating machines cycles. In: 12th Imacs Work Congress on Scienti®c Computation, 1988, 18±22 July, Paris, France. [18] Spinner B, Stitou D, Sorin M. Solid±gas thermochemical systems: internal exergy ¯ow analysis. In: Proc. Conf. Heat Powered Cycle's 97, Nottingham, UK, 1997. p. 100±112. [19] Sorin M, Spinner B, Stitou D, Lambert J. Intrinsic exergy eciency of solid±gas thermochemical systems. ECO's 98 1998;1:219±23. [20] Stitou D, Spinner B, Sorin M. A new advanced exergy analysis of sorption systems: characterisation of transiting exergy and exergy yield concept. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 401±7. [21] Sorin M, Stitou D, Spinner B. Approche exergeÂtique pour la conception des reÂfrigeÂrateurs thermochimiques solide± gaz. In; Proc. Conf. SysteÁmes aÁ tempeÂrature modeÂreÂe, Ecole Polytechnique MontreÂal, 22±24 may 1999. p. 141±9. [22] Stitou D, Spinner B, Sorin M. New concept of exergetic yield involoving transiting exergy analysis in energy conversion systems. In: Proc. SFGP 99, ECCE 2, Montpellier, France, 5±7 October 1999. p. 248±71. [23] Kumar P, Devotta S. Study of an absorption refrigeration system for simultaneous cooling and heating. ASHRAE Trans 1990;96/2(3415):291±8. [24] Tozer RM, James RW. Thermodynamics of absorption refrigeration: ideal cycles. In: Proc. Int. Abs. Heat Pump Conf., AES vol. 31. ASME, 1993. p.393±400. [25] Tozer RM, James RW. Fundamental thermodynamics of ideal absorption cycles. Int J Refrig 1997;20(2):120±35.
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191 [26] Meunier F, Neveu P, Castaing-Lavignottes J. Equivalent Carnot cycles for sorption refrigeration. Int J Refrig 1998;21(6):472±89. [27] Touzain P. Thermo dynamic values of ammonia-salts reactions for chemical sorption heat pumps. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 225±38.
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[28] Descombes A. Etudes thermodynamiques d'ammoniacates de sulfates meÂtalliques et mesures de permeÂabiliteÂ. Rapport DEA, INP Grenoble, France, 1997. [29] Martin X. Conservation de l'eÂnergie thermique par adsorption d'ammoniac sur des tissus de carbone active et eÂtude thermodynamique d'ammoniacates de sulfate de fer. Rapport DEA, INP Grenoble, France, 1998.
www.elsevier.com/locate/ijrefrig
Internal energy ¯ow analysis within a single eect sorption heat pump Bernard Spinner a,*, MikhaõÈl Sorin b, Driss Stitou a a
CNRS-IMP (Institut de Science et GeÂnie des MateÂriaux et ProceÂdeÂs), Rambla de la Thermodynamique, Tecnosud, 66100 Perpignan, France b Energy Diversi®cation Research Laboratory, CANMET, 1615 Lionel Boulet, PO Box 4800, Varennes, QueÂbec, Canada JX 1S6 Received 21 June 2000; received in revised form 28 August 2000; accepted 28 August 2000
Abstract The knowledge of the characteristics of unused, excess and untapped exergy allows a thorough analysis of internal energy ¯ows distribution within a sorption heat pump. It can be applied to any system based on gas±liquid absorption, adsorption or solid±gas reaction as well as to any process based on the internal recycling of the energy ¯ux. It can also be applied for the case of a simple eect ideal machine, in particular in the de®nition of processes where the COP is larger than 2: the levels at which the initial exergy is downgraded on the one hand, as well as, the upgraded excess exergy produced on the other allows the designer to make a judicious choice of a system. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Heat pump; Sorption; Internal energy ¯ow; Exergy characteristics; Exergy yield
Analyse des ¯ux energeÂtiques internes de pompes aÁ chaleur aÁ sorption simple eet ReÂsume L'analyse des ¯ux eÂnergeÂtiques internes mis en úuvre dans une pompe aÁ chaleur aÁ sorption, qu'elle soit aÁ absorption gaz± liquide, adsorption ou reÂaction gaz±solide, permet la caracteÂrisation des exergies non utiliseÂes, en exceÁs ou inexploiteÂes, ainsi que les possibiliteÂs de recirculations internes de ¯ux eÂnergeÂtiques. Il est ainsi possible, dans le cas de machines ideÂales aÁ simple eet, de de®nir des proceÂdeÂs de COP supeÂrieurs aÁ 2 : les degreÂs de deÂvalorisation de l'exergie d'entreÂe et d'exceÁs de potentiel valorise permettent de guider l'opeÂrateur dans ses choix de systeÁmes. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : Pompe aÁ chaleur ; Sorption ; Flux internes d'eÂnergie ; CaracteÂristiques d'exergies ; Eectivite exergeÂtique
1. Introduction Heat pumping, refrigeration and chilling-heating as well as, heat transformation in sorption machines are * Corresponding author. Tel.: +33-468-55-6855; fax: +33468-55-6869. E-mail address: spinner@univ- perp.fr (B. Spinner).
managed by the thermal energy ¯ows involved in the following physico-chemical processes: . . . .
phase change of gas±liquid absorption/desorption of gas±solution adsorption/desorption of gas±solid reversible solid±gas chemical reaction.
In accordance with a well de®ned system design, the
0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00076-1
186
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
Nomenclature
Ti
COP COPHP COPR ew xe H Q Tout min Tin max T0
Greek letters exergy yield yield T0 CARNOT factor 1 ÿ T
coecient of performance coecient of performance for a heat pump coecient of performance for a refrigerator speci®c excess and untapped exergy downgraded exergy factor enthalpy of transformation (J molÿ1) heat (J) produced temperature at minimum level (K) sink temperature at maximum level (K) reference temperature (K)
endothermic or exothermic processes may take place at four dierent temperature levels T1 < T2 < T3
temperature (K)
Subscripts a absorption or adsorption c condensation d desorption or decomposition e evaporation
analysis of the internal and external energy ¯ows. As was mentioned in the previous works [4,18±22], this analysis is applied to an ideal system. 2. Thermodynamic performance criteria for an ideal sorption machine Gas±solution and gas±solid (adsorption as well as chemical reaction) could be represented in a Clausius± Clapeyron diagram at four temperature levels Td,Ta,Tc and Te. It is also for a machine based on the heat generated from a monovariant solid±gas reaction. Taking into account that the desorption temperature levels T and that the absorption T are related to the ®nal state of desorption and absorption/adsorption processes, some assumptions have to be mach to justify the stability of the temperature levels. In the case of absorption, several authors like Kumar and Devotta [23], Tozer and James [24,25], Alefeld and Radermacher [3] relied up on a very large heat exchange surface. In the case of adsorption Meunier et al. [26], the use of entropy temperature was applied. Fig. 1 shows the internal energy ¯ux distribution in the operation of a heat pump. In this case, the external and internal heat ¯ux distribution can be represented as [4]: Qd Qda Qc Qa Qda Qe
1
with respect the heat balance according to the conservation of energy: Qd Qe ÿ Qa ÿ Qc 0 where Qda is that part of the heart ¯ux Qd which has passed towards the absorber (or adsorber or reactor in the case of chemical process) and is equal to Qd ÿ Qc, or Qa ÿ Qe. Qc and Qe are the ¯ux at the condenser outlet
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
187
untapped exergy of the upgraded energy ¯ux Qe is de®ned by the relation: 11ÿ12ÿ13ÿ14 6ÿ15ÿ16ÿ7 1ÿ3ÿ4ÿ6 ÿ in ÿ out Qe max ÿ e a ÿ min Qd d
ew
Fig. 1. Energy ¯ux distribution in a sorption heat pump. Fig. 1 Distribution des ¯ux energeÂtiques dans une pompe aÁ chaleur.
and the entry of the evaporator, respectively. It should be noted that Ta, Tc and Te are variables, while Td is a ®xed parameter; there absolute values are de®ned according to the process studied. The representation of the exergy ¯ux in the diagram of the Carnot factor vs heat ¯ux (Q) allows the following representation (Fig. 2): The heat ¯ux entering at level (d) is divided in two parts: ®rst, Qda and Qc are both downgraded from Td. This downgrading eect allows to upgrade the heat ¯ux Qe from To. Areas (1±2±8±7) and (2±3±10±9) represent the consumed exergy due to the downgrading of ¯ux Qd [4]. The area (7±12±13±16) is the produced exergy associated to the upgrading process. Being an ideal machine, there is no exergy lost: the area (1±2±3±10±9±8±7) and (12±13±16±7)are equal. Areas I and II represent the unused exergy: if the physico-chemical processes of adsorption and desorption have taken place at Ta=Tout min, the total exergy corresponding to areas I and II could be used to create an equivalent upgraded exergetic area and therefore, increasing the upgraded ¯ux Qe at given temperatures intervals. The area III is the excess exergy of the heat ¯ux Qe, which would be eliminated if the upgrading of the ¯ux took place up to the temperature Tout min. Finally, the area IV is the untapped exergy of the heat ¯ux Qe, necessarily created if a ``free'' energy source is available at Tin max. The exergy downgrading level at Qd is therefore de®ned by the ratio of the areas of the two surfaces x: 1ÿ3ÿ10ÿ9ÿ8ÿ7 1ÿ3ÿ4ÿ6 Qda d ÿ a Qc d ÿ c Qd d
xe
2
xe can be de®ned as the downgraded exergy factor which can be maximized up to 1. The speci®c excess and
3
ew can be minimized down to 0. The exergy yield is de®ned by the ratio of the exergy out produced by the upgrading of Qe ¯ux from Tin max to Tmin to the exergy provided in the desorption process. It is then de®ned by the ratio of the following areas: yield
ÿ out in ÿ max 11ÿ14ÿ15ÿ6 Qe min Qd d 1ÿ3ÿ4ÿ6
4
The yield is then equal to: yield xe ÿ ew
5
therefore can be maximized up to 1. As represented by Sorin et al. [4], a dimensionless diagram is shown in Fig. 2 using the ratio of /d and Q/ Qd (Fig. 3). The downgraded exergy factor xe can be visualized directly by the areas (1±3±10±9±8±7). Therefore the speci®c excess and untapped exergy ew is the sum of the areas (6±7±16±15) and (11±12±13±14). The yield is represented by the area (6±11±14±15). The segment (12±13) shown in Fig. 3 represents the coecient of performance of a refrigeration system de®ned by the following equation COPR=Qe/Qd, while the segment 4±15 represents the heat pump coecient of performance COPHP. The COPHP is equal to: 1+COPR as illustrated in Fig. 3. The link between yield and COPR also follows from Fig. 3: yield
ÿ out in COPR min ÿ max ÿ out d ÿ min
6
By using Eq. (5): COPHP 1 xe ÿ ew ÿ
out d ÿ min out in min ÿ max
7
3. Optimal choice of the physico-chemical processes implemented in the single eect heat pump It should be remembered that Eq. (7), the temperature in levels Td, Tout min and Tmax have been ®xed for the applied processes.
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The Clausius±Clapeyron diagram representation of a heat pump shown in Fig. 4 has been carried out in a monovariant mode corresponding to a chemical reaction between a solid and a gas. The same representation could be used for an absorption process, replacing Td by the ®nal desorption temperature, and Ta by the ®nal absorption temperature. For the case of an adsorption process, an entropy temperature [23] has been used. Maximising xe implies ®xing Tc and Ta as close as in possible to Tout min, minimizing ew leads to Te=Tmax. Straight lines A and B which de®ne the basic heat pump
(Fig. 4) operating between Td, Ta and Tc, Te could be modi®ed, for example, by shifting to reactant C, where the lines A and C are parallel, the temperatures Te and Td remaining constant; therefore, xe increases. Heat ¯ux distribution are presented in Fig. 5: it can be noted here that the path between the points d and a, has been eliminated, because Qda=0, as shown in Eq. (1). The corresponding diagram /d=f(Q/Qd) is presented Fig. 6. The value of COPR =1 and the value of COPHP are increased relative to the basic case (Fig. 3) and reach the value of 2. In order to improve the COPHP for the ®xed temperatures Td and Te, the term ew represented on Fig. 6 should be minimized: one way to achieve this is presented in Fig. 7. The ¯ux Qe is divided in two parts: Qa and (QeÿQa). Only the part Qa is upgraded from Te to Ta, the other part is upgraded only until it reaches Tc. Comparing Figs. 6 and 8, the segment 13±18 in Fig. 8 is
Fig. 2. Diagram =f(Q) of a quadri-thermal single eect sorption heat pump. Fig. 2 Diagramme =f(Q) d'une pompe aÁ chaleur simple eet aÁ quatre niveaux de tempeÂrature Fig. 4. Equilibrium lines of a monovariant heat pump according to dierent processes, in the diagram of Clausius±Clapeyron. Fig. 4 Droites d'eÂquilibre repreÂsenteÂes dans un diagramme de Clausius±Clapeyron d'une pompe aÁ chaleur monovariante.
Fig. 3. Dimensionless diagram of the valorised and downgraded exergies of a single eect sorption heat pump.
Fig. 5. Energy ¯ux distribution in a sorption heat pump with He=Ha.
Fig. 3 RepreÂsentations adimensionnelles des exergies valoriseÂes et deÂgradeÂes dans une pompe aÁ chaleur aÁ sorption aÁ simple eet.
Fig. 5 Distribution des ¯ux eÂnergeÂtiques dans une pompe aÁ chaleur aÁ sorption dans le cas ouÁ He=Ha.
B. Spinner et al. / International Journal of Refrigeration 24 (2001) 185±191
wider than 13±12 in Fig. 6, then COPR > 1 (Fig. 8), and therefore COPHP >2. The position of the gas/solid equilibrium line for this case is shown in Fig. 4 (straight line D): the slope of the line D is lower than the slope of A. The energy ¯ux distribution corresponding to the distribution in enthalpies of transformation (Hv and Hs) is presented on the Clausius±Clapeyron diagram (Fig. 9). The solid±gas equilibrium lines with the enthalpies of transformation lower than those of the liquid±gas, were discovered by Touzain et al. [27±29]: the sulfates of iron III reacting between 6 and 12 (NH3) gives the values of the enthalpies varying from 12 to 15 kJ/mol of NH3,
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while the enthalpies of condensation/evaporation of NH3 are of 22±24 kJ/mol according to the operating temperature or pressure. The COPHP of such a heat pump might be around 2.8. In the extreme case, when Ta =Tc=T0, and Te=Tmax in, that is when xe=1 and ew=0, one ®nds again the classical COPHP for a tri-thermal machine ae:
Fig. 8. Diagram /d=f(Q/Qd) corresponds to a heat pump process where the equilibrium lines are relative to D and A in the Clausius±Clapeyron diagram (Fig. 4).
Fig. 6. /d=f(Q/Qd) diagram in a sorption heat pump with He=Ha.
Fig. 8 Diagramme /d =f(Q/Qd) relatif aÁ une pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius± Clapeyron sont les droites D et A de la Figure 4.
Fig. 6 Diagramme: /d=f(Q/Qd ) dans le cas d'une pompe aÁ chaleur aÁ sorption ouÁ He=Ha.
Fig. 7. Heat ¯uxes correspond to a heat pump process where the equilibrium lines are relative to D and A in the Clausius± Clapeyron diagram (Fig. 4). Fig. 7 Flux de chaleur dans un proceÂde de pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius±Clapeyron sont les droites D et A de la Figure 4.
Fig. 9. Distributions in enthalpies of transformation corresponds to a heat pump process where the equilibrium lines are relative to D and A in the Clausius±Clapeyron diagram (Fig. 4). Fig. 9 Distribution des enthalpies de transformation relatives aÁ une pompe aÁ chaleur dont les droites d'eÂquilibre dans le diagramme de Clausius±Clapeyron sont les droites D et A de la Figure 4.
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Td ÿ Tin Tout max max in Td Tout min Tmax
8
4. Conclusion Analysis of energy ¯ux distribution within a sorption heat pump has allowed to distinguish between up and downgraded heat ¯uxes in the process. The correspondence of the exergy content of the ¯uxes with the presentation of an ideal heat pump on a Clausius± Clapeyron diagram has been established. The temperature level of the downgraded heat ¯uxes from a level corresponding to the use of a costly external energy source which is required to attain the required temperature in the heat production is characterized by a downgraded exergy factor xe. Conversely, the temperature level at which the exergy is upgraded from the level of a free energy source which is required in the heat production is characterized by the speci®c excess and untapped exergy ew. The link between these two factors with the heat pump coecient of performance has been established: maximising xe and minimizing ew allows to improve this coecient and implies a completely new energy ¯ux distribution within a system. The theoretical possibilities to design sorption heat pumps with ideal COP larger than 2 has been demonstrated. Further eorts should be made to search for the adequate materials to reach these upgraded values. References [1] Le Go P, Rivero R. A thermal inventory of sorption heat pumps based of the exergy-multipole concept. In: Proc. ECO's 95, Istanbul, Turkey, July 1995. p. 182±187. [2] Trepp Ch. History and prospects of heat transformation. Rev Int du Froid 1983;5:309. [3] Alefeld G, Radermacher R. Heat conversion systems. CRC Press Inc., 1994. [4] Sorin M, Spinner B, Stitou D. Synthesis of single eect solid gas thermochemical refrigerators. Trans. IChem. Eng. 2000; 78 (Part A, p. 795±802). [5] Meunier F. Proc. Symp.: Solid sorption refrigeration, Paris, France, 18±20 November 1992. Inst. of Refrigeration. [6] Spinner B. Changes in research and development objectives for closed solid-sorption systems. In: Proc. of the Absorption Heat Pump Conf., MontreÂal, Canada, 17±20 September 1996. p. 81±96. [7] Meunier F. Absorption heat pump technology: possibilities and limits. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 25±35. [8] Wallin E, Berntsson T. Integration of heat pumps in industrial processes. Heat Recovery Systems and CHP 1994;14:287±96.
[9] Kozic D, Krope J, Goricanec D. Optimization of large heat pumps in long-distance transit heat transportation. Int J Power Energy Systems 1994;14:5±8. [10] Wu S., Eames I. W. Ecient use of waste heat from combined heat and power systems. Proc ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 51±7. [11] Herold KE. An analysis of the major variables impacting performance of absorption chillers and heat pumps. Proc ASME Advanced Energy Systems Division, AES 37:349± 56. [12] Ziegler F. Discussion of optimized design of endo-reversible heat transformation cycles. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 459±64. [13] Herold KE. Performance predictions of absorption cycles using an endo reversible model. In: Proc ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 465±70. [14] Le Go P, Cachot T, Renaudin V, Hornut J. La thermodynamique chimique en temps ®ni. In: Proc. J ETC 99, Carry le Rouet, France, 13±15 September 1999. p. 9 [15] Boussehain R, Feidt M. The optimization for a refrigeration system with the reservoirs. In: SeÂminaire franco-allemand, Kassel, Germany, 1±4 Oct. 1984. [16] Boussehain R, Feidt M. Optimisation theÂorique du cycle d'une machine aÁ froid endoreÂversible aÁ trois sources de chaleur. In: 1er colloque franco-maghreÂbin sur les modeÁles numeÂriques de l'IngeÂnieur, 22±23 November 1987, Alger, AlgeÂrie. [17] Feidt M. Finite time thermodynamics applied to optimization of heat pump and refrigerating machines cycles. In: 12th Imacs Work Congress on Scienti®c Computation, 1988, 18±22 July, Paris, France. [18] Spinner B, Stitou D, Sorin M. Solid±gas thermochemical systems: internal exergy ¯ow analysis. In: Proc. Conf. Heat Powered Cycle's 97, Nottingham, UK, 1997. p. 100±112. [19] Sorin M, Spinner B, Stitou D, Lambert J. Intrinsic exergy eciency of solid±gas thermochemical systems. ECO's 98 1998;1:219±23. [20] Stitou D, Spinner B, Sorin M. A new advanced exergy analysis of sorption systems: characterisation of transiting exergy and exergy yield concept. In: Proc. ISHPC's (Int. Sorption Heat Pump Conf.), MuÈnich, Germany, 24±26 March 1999. p. 401±7. [21] Sorin M, Stitou D, Spinner B. Approche exergeÂtique pour la conception des reÂfrigeÂrateurs thermochimiques solide± gaz. In; Proc. Conf. SysteÁmes aÁ tempeÂrature modeÂreÂe, Ecole Polytechnique MontreÂal, 22±24 may 1999. p. 141±9. [22] Stitou D, Spinner B, Sorin M. New concept of exergetic yield involoving transiting exergy analysis in energy conversion systems. In: Proc. SFGP 99, ECCE 2, Montpellier, France, 5±7 October 1999. p. 248±71. [23] Kumar P, Devotta S. Study of an absorption refrigeration system for simultaneous cooling and heating. ASHRAE Trans 1990;96/2(3415):291±8. [24] Tozer RM, James RW. Thermodynamics of absorption refrigeration: ideal cycles. In: Proc. Int. Abs. Heat Pump Conf., AES vol. 31. ASME, 1993. p.393±400. [25] Tozer RM, James RW. Fundamental thermodynamics of ideal absorption cycles. Int J Refrig 1997;20(2):120±35.
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