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Kuwait J. Sci. Eng. 34 (1B) pp. 123-138, 2007

Thermo-economic analysis of a solar operated lithium bromide water absorption system

M. ALTAMUSH SIDDIQUI, K.A. JAMAL AND ASRAR AHMAD Department of Mechanical Engineering, Aligarh Muslim University, Aligarh (INDIA). E-Mail: [email protected] ABSTRACT

Irreversibility analysis of the lithium bromide water absorption system and economic evaluation of the ¯at plate solar collector required to operate it have been carried out to optimize the generator temperatures. The heat transfer rate, exergy ¯ow and irreversibility, along with the solar collector surface area and its cost, obtained for dierent operating conditions are exhibited graphically. The total irreversibility in the system as well as the area and cost of the solar collector show minima at certain temperatures in the generator. The optimum generator temperatures corresponding to the minimum area/cost of the solar collector are found quite close to those obtained corresponding to the minimum total irreversibility in the system. Keywords: energy; exergy; LiBr-water; optimum temperatures; solar-absorption

system.

INTRODUCTION

Commercial chillers using lithium bromide-water have been developed by many American and Japanese companies. A private organization PENZKHIMMASH in Russia has been producing the lithium bromide machines in lots. The VNII Kholodomash (All Union Scienti®c Research Institute of Refrigeration Machinery, Russia) has developed a number of air conditioning systems using the LiBr-H2O mixture as reported by Duganov et al. (1984). Russians have also been working on the development of an open cycle LiCl-H2O absorption system for cooling in the hot-dry climate of the Turkmenia desert. Presently, the leading manufacturers of the absorption machines in India are Voltas Limited, Mumbai and Thermax at Pune. Voltas Limited manufacture single as well as two stage vapour absorption machines in their own factory located at Thane. These machines are steam/hot water ®red in the range of 120 TR to 1000 TR, and direct ®red between 120 TR to 700 TR. They also import subassemblies of Koala (Direct Fired) vapour absorption machines (ranging 40 TR to 80 TR) from M/s Hitachi, Japan and assemble them in their factory at Dadar. Thermax at Pune manufactures single/double eect steam-®red vapour absorption machines in the range of 100 to 1000 TR.

124 M. Altamush Siddiqui, K.A. Jamal and Asrar Ahmad

The vapour absorption system uses low grade energy and can operate well by means of hot water and steam, gases like CNG, LPG and Biogas, liquid fuels such as kerosene and high speed diesel engine, and waste heat such as exhaust gases from the IC engines, etc. However, for economic utilization of the absorption system with maximum eciency, both energy and exergy analysis is required. According to the ®rst law of thermodynamics, all forms of energy are interconvertible. However, the second law of thermodynamics puts limitations on energy conversion. In accordance to the second law, though the work can be completely converted into heat, it is not possible to convert all the available heat into work. In the ®rst law, heat and work are de®ned as energy which is conserved, whereas, in the second law, heat and work interactions are de®ned in terms of exergy which always decreases during real irreversible processes. Irreversibilties can occur during mechanical friction in which work gets dissipated in heating eects, transfer of heat from high temperature to low temperature, and the throttling process. Similarly, mixing of two or more ¯uids are irreversible processes. Therefore, in order to increase system eciency, the irreversibility which is also known as exergy loss or exergy destruction should be minimized. Optimization of operating parameters to yield a better performance and minimum energy consumption has been published previously (Siddiqui et al. 1986, Siddiqui 1993, 1994). Optimization of generator temperature in the LiBrH2O system has been presented by Siddiqui et al. (1986). Later on, Siddiqui (1993) considered energy sources such as biogas, lique®ed petroleum gas and solar collectors with H2O-NH3, LiNO3-NH3 NaSCN-NH3 and LiBr-H2O for optimization of generator temperature. Costs of cooling the condenser and absorber were also included by Siddiqui (1994) in the energy-costs for optimizing the generator as well as the condenser/absorber temperatures along with the refrigerant absorbent ¯ow ratios. Siddiqui (1997) optimized the temperatures in each component of the absorption system along with the refrigerant absorbent ¯ow ratios by designing the entire system and then estimating their costs along with the operating costs. All the work reported by Siddiqui and his co-authors (1986, 1993, 1994, 1997) were based upon the ®rst law of energy conservation, although the real system would certainly encounter losses caused due to the irreversibilities in the system-components which can be known only through the second law or exergy analysis. Recently, second law analysis for the real systems, which estimates irreversibilities and entropy generation, has become an important area of research. A number of researchers (Anand & Kumar 1987, Karakas et al. 1990, Sozen 2001) have been concerned with the exergy analysis. However, their work seems to be limited for some speci®c conditions of the absorption system. Also, ;


125

the eect of the energy source meant to operate the absorption system has not been considered. With this in view, economic analysis of the ¯at plate solar collector as well as the irreversibilities in the lithium bromide absorption system components have been obtained for a wide range of the operating conditions so that the optimum generator temperatures can be selected iteratively for the minimum energy cost with minimum irreversibility in the system. MATHEMATICAL MODELLING

The vapour absorption refrigeration cycle, having dierent components and state points, is shown in Fig.1. The absorbent-refrigerant solution is pumped to the generator. The anity of the absorbent-refrigerant pair is reduced at an elevated temperature and a part of the refrigerant vaporizes and condenses in the condenser. The condensate, after getting subcooled in the precooler, is throttled through TV1 to the evaporator. The refrigerant vaporizes in the evaporator and thus, cooling is produced. The subcooling in the precooler improves performance of the system. The remaining solution mixture from the generator, that is weak in refrigerant, is separated and brought to the absorber through the preheater and the throttle valve TV2. The solution in the absorber, maintained at a low temperature and pressure, absorbs the refrigerant vapour from the evaporator, and thus, the cycle gets completed.

Figure 1: Schematic view of the LiBr - H2O system

126 M. Altamush Siddiqui, K.A. Jamal and Asrar Ahmad First law analysis

With no external (shaft work) from any component and negligible kinetic and potential energies, the steady ¯ow energy equation of the ®rst law of thermodynamics gives: R dQ P mehe ÿ P mi hi where (1) e i CV Absorber: Qa m4h9 m10 h12 ÿ m1h1 (2) Condenser: Qc m4h4 ÿ h5 (3) Evaporator: Qe m4h8 ÿ h7 (4) Generator: Qg m4h4 m10 h10 ÿ m1h3 (5) Precooler: m4h5 ÿ h6 m4h9 ÿ h8 (6) Preheater: m1h3 ÿ h2 m10 h10 ÿ h11 (7) Throttle Valve 1: m4h6 m4 h7 (8) Throttle Valve 2: m10 h11 m10h12 (isenthalpic) (9) For the whole absorption cycle (Fig. 1), as a closed system, with only heat and work interaction at the system boundary: 10 Qa Qc Qe Qg Wp With negligible pumping work on the solution pump, Wp= 0, Therefore, m1h1 m1h2 11 Hence, Qa Qc Qe Qg 12 The solar collector area required to power the LiBr -- H2O system is given by: Ap 1 2Qg 1 2x12600x1TR 13 ;

:

:

:

:

Qs

:

COPa Qs

;

where 1.2 in Equation (4) is the 20% increase for storage and use during o-


127

sunshine hours. The useful heat gain from the solar collector is obtained from the following equation suggested by Siddiqui (1993): 14 Qs 0 8156S ÿ 13 665Tg 5 0 ÿ Tam :

:

:

:

Second law analysis

For the steady ¯ow of ¯uid through a component of a thermodynamic cycle to which heat dQ is added at temperature T with no external work, the irreversibility or the lost work in that component is given by: I

Z

cv

: :

T 0 1 ÿ T dQ 1A

15

;

where 1A is the decrease in availability of the mass entering the control volume of the component at one state and leaving it at the other state with reference to the dead state at a temperature T0. With negligible kinetic and potential energy terms, decrease in availability of the masses entering and leaving the control volume will be: X X 1A mihi ÿ T0 misi ÿ mehe ÿ T0mese 16 i

e

:

The irreversibility in various components of the absorption cycle as a control volume, shown in Fig. 1 will thenbe: Absorber: Ia ÿQa 1 ÿ TT0a 1Aa, (17) where 1Aa m4h9 ÿ T0s9 m10h12 ÿ T0 s12 ÿ m1h1 ÿ T0s1 (18) T0 Condenser: Ic ÿQc 1 ÿ Tc 1Ac, (19) (20) where 1Ac m4h4 ÿ T0s4 ÿ h5 T0s5 ; Evaporator: Ie Qe 1 ÿ TT0e 1Ae, (21) where, 1Ae m4h7 ÿ T0s7 ÿ h8 T0s8 ; and (22) (23) Generator: Ig Qg 1 ÿ TT0g 1Ae, where 1Ag m1h3 ÿ T0s3 ÿ m10h10 ÿ T0 s10 ÿ m4h4 ÿ T0s4. (24) Decrease in availability of the masses entering and leaving the other components


in the absorption system are given by:

Precooler: 1APC m4 h8 ÿ T0 s8 m4 h5 ÿ T0 s5 ÿ m4 h9 ÿ T0 s9 ÿ m4 h6 ÿ T0 s6 , (25) Preheater: 1APH m1 h2 ÿ T0 s2 m10h10 ÿ T0 s10 ÿ m1 h3 ÿ T0 s3 ÿ m10h11 ÿ T0 s11,

(26) Pump: 1APM m1 h1 ÿ T0s1 ÿ m1h2 ÿ T0s2, (27) (28) Throttle Valve 1: 1ATV1 m4h6 ÿ T0s6 ÿ m4 h7 ÿ T0s7, and (29) Throttle Valve 2: 1ATV2 m10 h11 ÿ T0s11 ÿ m10 h12 ÿ T0s12 . Total availability of the masses in the above components from Equations (25) to (29) will be: 30 1Aext 1APC 1APH 1APM 1ATV1 1ATV2 Net availability of the masses in the absorption system or net exergy ¯ow considering all the components in the Fig. 1 will then be: 31 1Anet 1Aext 1Aa 1Ac 1Ae 1Ag Substitution of all the quantities from Equations (2) to (3) in Equations (17) to (9), the net availability 1Anet will turn to be zero and the total irreversibility in the absorption system which is given by: Itotal Ia Ic Ie Ig 1Aext 32 will then reduce to :

:

Q Q Q Q a c e g Itotal T0 T T ÿ T T a c e g

:

33

The ideal COP of the cycle with zero irreversibility and Ta=Tc will then be:

T T ÿ T e g a COPi T ÿ T Tg c e

:

34

From the above equations, it can also be shown that the actual COPa is given by:

Thermo-economic analysis of a solar operated lithium bromide water absorption system 8 > > > =

COPa COPi ÿ > TTaTTe TTg ÿÿ TT0 Itotal T >and a e Q 1ÿ 0 > > : 0 g ; g Tg 2

35

3

if T0 Ta COPa COPi 641 ÿ

I

6

;

129

Qg

total

1

ÿ TT0g

7 7 5:

36

Thus, minimum irreversibility will lead to maximum COPa close to the ideal COPi Substituting Qg A1pQ2 s form Equation (13) into Equation (35), the solar collector area can also be written in terms of irreversibility as follows: Ta 1 37 Ap Q 11 ÿ2Itotal COP s r T0 HE a where, COPr COP and HE TgTÿTg a, the heat engine eciency. COPi However, the Equations (13) and (37) remain identical in magnitude. The relations for obtaining costs of the solar collector area and the cooling water in the condenser and absorber were taken from Siddiqui (1993,1994). They are given in Appendix A. :

:

:

;

RESULTS AND DISCUSSION

The various parameters, de®ned by the Equations (2) to (37) were calculated by varying the generator temperatures for ®xed values of the evaporator, condenser and absorber temperatures. The temperatures in absorber and condenser were assumed to be equal because they should reject heat to the same sink by means of water circulated from the cooling pond or reservoir. For the known values of temperatures in the evaporator and the absorber, the concentration of LiBr in the LiBr--H2O mixture leaving the absorber can be calculated. However, for ®xed values of the condenser temperature, concentration in the mixture leaving the generator can be evaluated for any value of the generator temperature during the computation procedure. The range of temperatures and concentrations of the LiBr salt in the various components areo listed in Table 1. The dead state temperature was assumed to be T0 = (Ta -10) C. The properties of the speci®c enthalpy and entropy for the LiBr-H2O mixture were taken from Anand and Kumar (1987) and those of the pure liquid and


vapour of water from Arora (2000). The equilibrium pressure equations for the LiBr--H2O mixture and pure water, and the saturation temperature equations were taken from ASHRAE (1981). Table 1: Range of temperatures and concentrations in the various components

Ta C) xa(%) TcoC) TgoC) xg(%) o

35 55.5 35 72-103 56-70

Te = 5 o C

40 58.5 40 83-110 59-70

45 61.0 45 95-117 62-70

Te = 10o C

Te =15o C

35 40 45 35 40 45 52.0 55.0 57.6 48.7 51.5 54.2 35 40 45 35 40 45 66-98 77-110 88-117 60-90 71-104 82-118 53-68 56-70 59-70 50-65 53-68 56-70 Exergy analysis

Availability or exergy ¯ow

The availability or net work obtainable by any ¯uid mass stream entering a component depends upon whether there is addition or rejection of heat to that component. Accordingly, there may be either increase or decrease in the availability. In other words, there will be exergy ¯ow out (loss of exergy) in case of heat rejection and vice-versa. Thus, a positive value of 1A would mean loss of exergy ¯ow while a negative value would mean gain of exergy ¯ow in the component. Thus, decrease in availability of the masses in the system components were calculated from the Equations (18), (20), (22), (24) and (25) to (29) based on the availability of the various mass streams entering and leaving. Decrease in availability of the masses have been plotted in Fig. 2 against the generator temperature. It is seen that the decrease in availability of the mass streams entering the absorber, (1Aa in which the heat is rejected out, decreases with increase in the generator temperature, reaches to a minimum value at a certain temperature and then increases gradually. Similarly, there is also a decrease in availability of the masses entering the preheater, which decreases with Tg upto a certain value, reaches to a minimum and then increases gradually. However, changes of the availability in the preheater are quite slow as compared to those in the absorber. Unlike these components, there will be an increase in availability of the masses entering the generator and the throttle valve TV2 which show negative values in Fig. 2. For exergy, increase of availability or exergy gain in the generator (1Ag, initially increases, reaches to a maximum value and then decreases gradually. Similarly, in the throttle valve TV2 the exergy gain increases rapidly at lower values of Tg, and then becomes almost constant. On the other hand, the exergy


131

loss or gain in the remaining components, evaporator, condenser, precooder, throttle valve TV1 and the solution pump, show only minor variation with Tg. This is evidently due to the fact that operation of these components are least aected by the changes in the generator temperature, as long as their temperature and concentration remain unchanged. However, there will be loss of exergy in the condenser and evaporator, while in the precooler, gain in exergy is observed. Loss of exergy in the evaporator is due to its operation at a temperature lower than that of the atmosphere (Te < T0. Irreversibility

The availability of masses or exergy loss or gain in any component creates irreversibility in those components. However, they are greatly aected by the magnitudes and direction of heat interaction at the component boundaries as a control volume. The irreversibilities encountered at the various components of the absorption system are plotted against the generator temperature in Fig. 3. It is found that the absorber has positive values of irreversibility, indicating loss of exergy and the generator has negative values, thereby showing gain in the exergy. The irreversibilities in the absorber and the generator are largely aected by the generator temperature, although they are insigni®cant in the condenser and the evaporator. The irreversibility in the absorber decreases at low values of Tg until it becomes minimum and then again increases with increase in the generator temperature. On the other hand, the irreversibility in the generator, initially increases with Tg, reaches to a maximum value and then decreases gradually.

Figure 2: Decrease in a availability of the masses in Figure 3: Variation in irreversibilities of the various components with Tg dierent components [availabilities: Aph (preheater), Apc (precooler), Atv1 (throttle valve 1), Atv2 (throttle [Irreversibilities: la (absorber), lg (generator), Ic valve2),Apm(pump),Aa(absorber),Ag(generator),Ac (condenser), le(evaporator), Itotal (total system)] condenser) Ae (evaporator)]


However, the total irreversibility in the absorption system, also shown in the Fig. 3, gives the total exergy loss in the system with the generator temperature which initially decreases with Tg, reaches a minimum value and then again increases. This give rise to the optimum generator temperatures for the absorption system at some speci®ed conditions with minimum irreversibility, which is essentially desirable. Interestingly, one can also see that irreversibility in the generator near the optimum values of Tg is almost negligible. This indicates that the irreversibilities caused in the system are mainly due to the absorber. The variation in total irreversibility of the absorption system with generator temperature has been plotted in Fig. 4 for dierent operating temperatures Te, Ta and Tc. One can notice the minimum irreversibilities at dierent operating conditions. The generator temperature corresponding to the minimum irreversibility in the system increases with decrease in the evaporator temperature and increase in the absorber/condenser temperature. In addition, the system irreversibility increases with decrease in the evaporator temperature and increase in the absorber/condenser temperature.

Figure 4: Total irreversibility in the system with generator temperature [Temperatures:

Te (evaporator), Ta (absorber), Tc (condenser)] Energy analysis

For the purpose of comparison, energy analysis of the absorption system was carried out. The heat transfer rates in the various components were evaluated and correspondingly the area and cost of the solar collector required for operation were


133

estimated. Figure 5 shows variation in the heat transfer rates at boundaries of the absorber, generator, condenser and evaporator with Tg at ®xed values of Te, Ta and Tc. Variation in the generator and absorber heat transfer rates with Tgare obvious, which decrease with increase in the values of Tg. However, the condenser and the evaporator loads remain unchanged with Tgbecause the calculations here are made at ®xed values of the temperatures Te and Tc in these components.

Figure 5: Variation in the heat transfer rates and the operating costs [Heat transfer rates: Qa (absorber), Qc (condenser), Qg (generator), Qe (evaporator); Costs: Cs (solar collector), Csw (solar collector + cooling water)]

The variation in the solar collector area, Ap with the generator temperature for the dierent operating conditions is shown in Fig. 6. The areas decrease initially with Tg, reach to minimum values and then increase with increase in generator temperature. The solar collector area increases and shifts towards the high generator temperatures at high condenser and absorber temperatures. However, with increased evaporator temperatures, the solar collector areas decrease and require low generator temperatures. The minimum collector areas so obtained thus become criteria for selecting the optimum generator temperatures that would lead to the economic operating conditions for the absorption system. The minimum collector area also increases with decrease in the evaporator temperature and increase in the absorber/condenser temperature. The solar collector costs follow the same trend of variation as does the solar collector area which can be seen through the plots in Fig. 5. The operating costs are shown for the solar collector area alone and also including cost of the


cooling water for the condenser and absorber. From Figs. 4 and 6 one can notice that the variations in total system irreversibility and solar collector areas follow almost the same trend. Interestingly it is also clear that the minimum irreversibility and minimum solar collector areas for the same operating conditions in the absorber, condenser and evaporator require almost the same generator temperatures.

Figure 6: Variation in the solar collector area with generator temperature

[Temperatures: Te(evaporator), Ta (absorber), Tc (condenser)] CONCLUSIONS

The following conclusions can be reached from this study: 1 - The variation in total irreversibility of the absorption system with generator temperature gives rise to minimum irreversibility which is essentially desirable. 2 - The generator temperatures corresponding to minimum irreversibility in the system increase with decrease in the evaporator temperature and increase in the absorber/condenser temperature. 3 - The system irreversibility increases with decrease in the evaporator temperature and increase in the absorber/condenser temperature. 4 - The minimum solar collector area also increases with decrease in the evaporator temperature and increase in the absorber/condenser temperature.


135

5 - The minimum irreversibility and the minimum solar collector area fall nearly at the same values of the generator temperatures, showing compatibility of the ¯at plate solar collector with the LiBr-H2O absorption machines. Thus, the absorption system operated at the generator temperatures corresponding to the minimum energy cost and minimum exergy destruction will make it a thermo-economical system. REFERENCES

Anand, D. K. & Kumar, B. 1987. Absorption machine irreversibility using new entropy calculations. Solar Energy 39(3):243-256. Arora, C.P. 2000. Refrigeration and Air Conditioning, 2nd edition. Tata McGraw Hill Co. Ltd.,

New Delhi, INDIA, pp. 968-975. ASHRAE Handbook of Fundamentals 1981. American Society of Heating, Refrigeration and Air Conditioning Engineers, Inc., Atlanta, GA. Duganov, G.V., Timofeevskii, L.S., Rozhko, V.F. & Shtompel, A.I. 1984. Use of absorption refrigeration in mine air conditioning systems. A translation of Khimicheskoe i Neftyanoe Mashinostroenie, 19(3):11-12 December (1983). Chemical and Petroleum Engineering 19:522. Karakas, A., Egrican, N. & Uygur, S. 1990. Second law analysis of solar absorption cooling cycles using lithium bromide water and ammonia/water as working ¯uids. Applied Energy 37:169-187. Siddiqui, M. A., Prasad, M. & Sahay, B. 1986. Economic evaluation of biogas for optimizing generator temperature in a vapour absorption system. Energy Conversion and Management 26(1):83-89. Siddiqui, M. A. 1993. Optimum generator temperatures in four absorption cycles using dierent sources of energy. Energy Conversion and Management 34(4): 251-266 . Siddiqui, M. A. 1994. Economic analysis of the operating costs in four absorption cycles for optimizing the generator and the condensing temperatures. Energy Conversion and Management 35(6):517-534. Siddiqui, M. A. 1997. Economic analyses of the absorption systems: Part B-optimization of various parameters. Energy Conversion and Management 38(9):905-918. Sozen, A. 2001. Eect of heat exchangers on performance of absorption refrigeration systems. Energy Conversion and Management 42:1699- 1716. Submitted : Revised : Accepted :

21/10/2005 7/4/2006 27/5/2006

136 M. Altamush Siddiqui, K.A. Jamal and Asrar Ahmad APPENDIX A

The relations for the capital and yearly running costs of the solar collector and the cooling water, taken from Siddiqui (1993,1994) are as follows: Solar Collector

Capital cost Yearly cost Total yearly cost

: C1s = 4957 Ap : C2s= 536.5 Ap : Cs= (C1s+8.3667C2s / 15

Capital cost Yearly cost Total yearly cost Total operating cost

: : : :

Cooling Water

C1w= 1887.3 W0 361566 C2w= 595.75 W0 612887 Cw= (C1w+8.3667C2w / 15 Csw= Cs+ Cw :

:

137


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