- Email: [email protected]
Optimal water purification using low grade waste heat in an absorption heat transformer
Desalination 220 (2008) 506–513
Optimal water purification using low grade waste heat in an absorption heat transformer Rosenberg J. Romero*, A. Rodríguez-Martínez Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Chamilpa, Cuernavaca 62100, Morelos, México Tel./Fax +52 777 3297084; email: [email protected] Received 12 April 2007; accepted 4 May 2007
Abstract A proposal for rational energy saving using wasted heat is showed in the present paper. Thermodynamicmathematical model is presented like an effort for water purification from waste heat. This paper describes computing results of heat transformer operation for water purification using low grade waste heat. Equations, parameters and simplifications used in the model are briefly described. The main parameter of the carried out study is the coefficient of performance (COP) defined for reversed heat pumps and the second main parameter is absorber temperature, both parameters has been showed and correlated between them. Main objective of this work is to show the optimal operating condition for different process which deliver low grade waste heat and requires water purification. Assisted computing simulation was used for obtain these results. The main conclusion is an ecological proposal for optimal recover of low grade waste heat. Many operating conditions are showed in graphical form and discussed for different environment conditions. Keywords: Absorption heat pump; Water purification; Waste heat; Heat transformer
1. Introduction Unfortunately the USA/Mexico border areas have very limited water resources with salinity to major problem in irrigation districts. To lack of sufficiently pure water searches to health hazard to the growing population with to negative impact on their quality of life and their capacity *Corresponding author.
for economic productivity. The Paso/Ciudad Juarez region receives an average of only 7 inches of rain per year. It supports its population by taking water from an aquifer which is projected to be depleted of low salinity water within two decades. The situation is not assisted by the practice of using relatively clean water to transport human waste to treatment facility, which is often overloaded resulting in effluent of poor quality which is subsequently used in
Presented at the conference on Desalination and the Environment. Sponsored by the European Desalination Society and Center for Research and Technology Hellas (CERTH), Sani Resort, Halkidiki, Greece, April 22–25, 2007. 0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.05.026
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
agricultural irrigation. This simulation results has been made using lithium bromide (LiBr) — water cause it is the most commercial used pair in absorption systems.
All we have required for our own construction of primary resources and energy for its transformation. All these processes use energy and in each transformation that happens a part of this energy vanishes as heat, this heat of industrial waste has temperatures between 50 and 90°C [1] that can be used for water purification [2] with the heat transformer as single stage based system [3] or an advanced system [4]. The proposal of purification process consists in a simple distillation powered by waste heat, where the heat obtained by the heat pump is recycled when the steam is condensate and this increases the temperature of the heat source. Fig. 1 shows a simplified diagram. The impure water to be distilled is heated in absorber, water steam is condensated (loosing heat) and it is collected in auxiliary condenser. In the water purification system, heat supply can be proportionated by the heat pump.
Auxiliary condenser
Condenser
Generator
The mathematical pattern that intends to describe the behavior of this system is based on the thermodynamic pattern published previously with LiBr-water solution [5]. The following assumptions have seen made in the development of the mathematical model for an heat transformer integrated to a water purification system with reference to Fig. 2. (i) There is thermodynamic equilibrium throughout the entire system. (ii) The analysis is made under steady state conditions. (iii) A rectifier is unnecessary since the absorbent does not evaporate in the temperature range under any place of the system. (iv) The solution is saturated leaving the generator and the absorb and the working flows is saturated leaving the condenser and the evaporator. (v) Heat losses and pressure drops into tubings and the components plows are considered negligible. (vi) The flow through the valves is isenthalpic. (vii) Temperatures at the exit of the main components T1, T2, T4 and T5 and the heat load in the evaporator QEV are known.
Absorber
Impure water
Surrounding cooling water
Fig. 1 shows schematically the system, which have an heat transformer integrated to complete an ecological water purification system.
3. Simulation model and assumption
2. Basic concepts
Evaporator
507
Heat source
Fig. 1. Schematic diagram of water purification heat transformer system.
4. Mathematical model (1) From assumption (i) and (ii), T1 = T7. (2) From assumption (iv) the working fluid is considered saturated leaving the condenser and evaporator, then the pressure at state
508
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513 P PATM
Auxiliary condenser 11
10
9
4
PEV
Evaporator
Absorber
3
5 8
12 2
6 7
PCO
Condenser
1
Generator 13
TCO
TGE, TEV
TAB
T
Fig. 2. Schematic diagram water purification system assisted single stage heat transformer.
points may be obtained by the following equations: P2 = P(T2) and P4 = P(T4). (3) From assumption (v) the pressure drops in the tubing and the components are consider negligible, P1 = P2 = P7 = P6 and P3 = P4 = P5 = P8. (4) From assumption (iv) the concentration of the LiBr concentrated solution leaving the generator can be estimated as follow X7 = X(P2,T7). (5) In the same way, the concentration of the LiBr diluted solution leaving the absorber can be estimated as X5 = X(P4,T5). (6) Cause there is not mass transfer between generator and absorber X7 = X8 and X5 = X6.
(7) From assumption (iii), the concentration of the absorbent in the vapor leaving the generator is zero, then X1 = X2 = X3 = X4 = 0. (8) The enthalpies at the exit of absorber and generator can be estimated by H5 = H(T5,X5) and H7 = H(T7,X7). (9) From assumption (iv), the enthalpies at the exit of the condenser and the evaporator can be estimated as follow H2 = H(T2) and H4 = H(T4). (10) Considering that the vapor upon leaving the generator is superheated H1 = H(P2,T1). (11) Because the absorbent does not evaporate in the temperature range under operating conditions, from mass balance in generator
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
and absorber, the flow ratio (RF) can be rewritten for this system by X7 M FR = AB = M WF X 7 − X 5 (12) Carrying out mass and energy balances in the to absorber and using FR definition, the mass flow rate of the working fluid can be calculated by the following equation: M WF =
QAB H 4 − H 8 + FR ( H 8 − H 5 )
(13) From FR definition:
QPU = m9 [(h12 – h11) + (h13 – h12)] therefore QAB = m9 (h13 – h11). (19) Then the enthalpy based coefficient of performance for to it single stage heat transformer is defined COPEnt =
MGE = MAB − MWF (15) Considering that the process though the expansion valve is isenthalpic (vi) H5 = H6 and H3 = H2 (16) From mass and energy balances in the main components, the amount of heat supplied or delivered can be estimated from the following equations:
QCO = M WF ( H1 − H 2 ), QEV = M WF ( H 4 − H 3 ) and QGE = M WF H1 + M GE H 7 − M AB H 6 . (17) The getting power into the absorber has been transferred to the water purification system as shown in Fig. 2, the impure water flow rate is m9, then QPU = QAB; where QPU = m9 (h11 – h10). (18) The condensation power of purified vapour water obtained into the auxiliary condenser goes to the evaporator and to the generator
QAB QGE + QEV
(20) And the water purification coefficient of performance for the proposal water purification system using low grade waste heat is COPWP =
MAB = MWFFR (14) From mass balance in the absorber or generator side
509
QAB QGE + QEV − QAB
5. Discussion Theoretical works of mathematic modeling about heat transformers assume that generator and evaporator’s temperature is the same value [6] because heat exchanger’s area is infinite and a fluid goes through it at the same temperature in a long time value. Experimental research about heat transformers evidence that internal temperatures into the generator and the evaporator are always different due to equilibrium conditions in each one [5,7,8]. It had been shown in different temperature data of the heat transformer. In the simulation carried out, it is shown that it is feasible the purification of water by means of simple evaporation of water starting from water with dissolved solids, in which heat is guaranteed with a superior temperature at 105°C provided in the absorber of the system. The simulation shows all operating possible conditions with absorber temperatures higher than 105°C till 115°C, for guarantee water purification. The evaporator temperature has values from 60 and 75°C, else generator temperature presents values from 60 to 80°C with condensation temperature of 25 and 30°C. In Fig. 3 the behavior for aqueous LiBr-water is shown for operating conditions with condenser
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R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
0.700
0.900 0.800
0.600
TEV = 70°C
TEV = 75°C
0.700
0.500 COP (dim)
COP (dim)
0.600 0.400 0.300
TEV = 65°C
TEV = 75°C TEV = 70°C
0.500 0.400 0.300
0.200 0.200 0.100 0.000 105
0.100
TG = 65°C TC = 25°C
106
107
COP_Ent COP_WP
108
109
110 111 TAB (°C)
112
113
114
115
116
TG = 70°C TC = 25°C
COP_WP (dim) COP_Ent (dim)
0.000 104
106
108
110 TAB (°C)
112
114
116
Fig. 3. COP_WP and COP_Ent against TAB for TGE = 65°C, TCO = 25°C for two different constant values of TEV.
Fig. 4. COP_WP and COP_Ent against TAB for TGE = 70°C, TCO = 25°C for three different constant values of TEV.
temperature of 25°C. Generator temperature remains constant to 65°C for two operating conditions series. Left lines for evaporator temperature of 70°C and right lines for evaporator temperature of 75°C. Both series show the water purification coefficient of performance (COP_WP) with higher values than enthalpy based coefficient (COP_Ent). It is observed that for further temperatures in the evaporator bigger temperatures can be obtained in the absorber, the maximum value of the COP_WP is obtained to the smallest absorber temperature TAB of 106°C. In Fig. 4, the behavior of three different operating condition series are shown, the generator and condenser temperatures are constant for 70 and 25°C respectively for evaporator temperatures of 65, 70 and 75°C each. These three series show bigger COP_WP than COP_Ent for all conditions. It is shown that highest COP_WP for evaporator temperature of 70°C and absorber temperature of 106°C. Comparison between Fig. 4 and Fig. 5, shows that operating conditions for condenser temperature of 25°C, evaporator temperature of 70°C and absorber temperature of 106°C, higher COP_WP is obtained for higher generator temperature, means COP_WP for 70°C is bigger than for 65°C generator temperature.
Fig. 5 shows similar behaviors those shown in Fig. 3 for generator temperature of 70°C with condenser temperature of 30°C. Evaporator temperatures made two series of operation conditions, one of them at 70°C and the other one at 75°C. Both series show water purification coefficient of performance is higher than enthalpy based coefficient of performance for same operating condition. It is observed, compared this figure with Fig. 4 that when increasing the 0.800 0.700
COP (dim)
0.600 TEV = 70°C
0.500
TEV = 75°C
0.400 0.300 0.200 0.100 0.000 105
TG = 70°C TC = 30°C
106
107
COP_WP (dim) COP_Ent (dim)
108
109
110
111
112
113
114 115
116
TAB (°C)
Fig. 5. COP_WP and COP_Ent against TAB for TGE = 70°C, TCO = 30°C for two different constant values of TEV.
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
1.000 0.900 TEV = 75°C
0.800
COP (dim)
0.700
TEV = 65°C
TEV = 70°C
TEV = 60°C
0.600 0.500 0.400 0.300 0.200 0.100 0.000 104
TG = 75°C TC = 25°C
106
COP_WP (dim) COP_Ent (dim)
108
110 TAB (°C)
112
114
116
Fig. 6. COP_WP and COP_Ent against TAB for TGE = 75°C, TCO = 25°C for three different constant values of TEV.
0.900 0.800 0.700
TEV = 75°C TEV = 70°C
0.600 COP (dim)
ambient temperature causing an increase in the condensation temperature TCO, it diminishes the number of operation conditions. For these reasons and for to continue the operation of the system it has necessary to increase the evaporation temperature and smaller operation coefficients are obtained those compared in similar conditions with smaller TCO. In Fig. 6, operating conditions change those presented in Fig. 4 for an increase in generator temperature to 75°C. It is observed an increase in number of possible operating conditions presented for evaporator temperature from 60 to 75°C. With these operating conditions water purifications coefficient of performance reach closer values to 0.9 and absorber temperatures of 115°C. The highest value of COP_WP happen at absorber temperature of 106°C with evaporator temperature of 70°C. In Fig. 7 three behaviors for the water purification heat transformer are shown, where generator and condenser temperatures remain constant to 75 and 30°C respectively. These behaviors are for operating conditions of 65, 70 and 75°C compared between this and the Fig. 6, shows that when increasing the condensation temperature, the COP_WP decreases in similar conditions
511
0.500
TEV = 65°C
0.400 0.300 0.200 0.100 0.000 104
TG = 75°C
COP_WP (dim) COP_Ent (dim)
TC = 30°C
106
108
110
112
114
116
TAB (°C)
Fig. 7. COP_WP and COP_Ent against TAB for TGE = 75°C, TCO = 30°C for three different constant values of TEV.
with temperature of condensation TCO = 25°C showed in Fig. 6. It can also observe that a heat transformer is operated with smaller coefficients of performance when it diminishes the evaporation temperature. The three levels show that water purification coefficient of performance is bigger that enthalpy based coefficient of performance. When the system operates at 70°C in the evaporator it can get the longer range of possible operating conditions. In Fig. 8 water purification heat transformer possible operating conditions are shown with generator temperature of 80°C and condenser temperature of 25°C remaining constants, for evaporator temperature of 60 to 75°C as can be observed in Figs. 4 and 6. The coefficients of performance are bigger to those reported with generator temperatures of 75 and 70°C. The coefficients of performance, for temperatures of 75°C of TEV, being closer than 0.95 for the case of water purification in comparison with the COP_Ent of 0.45. All lines show that water purification coefficient of performance is bigger that enthalpy based coefficient of performance. These behaviors compared with those shown in Figs. 4 and 6, shows biggest water purifications coefficient of performance while generator
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R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
1.000 0.900 TEV = 65°C
0.800 TEV = 60°C
0.700 COP (dim)
TEV = 75°C
TEV = 70°C
0.600 0.500 0.400 0.300 0.200 0.100
TG = 80°C TC = 25°C
0.000 104
106
COP_Ent (dim) COP_WP (dim)
108
110 TAB (°C)
112
114
116
Fig. 8. COP_WP and COP_Ent against TAB for TGE = 80°C, TCO = 25°C for four different constant values of TEV.
temperature rise. Enthalpy based coefficient of performance for bigger generator temperature remains with small values changes compared those of Figs. 4 and 6. In Fig. 9 the water purification and enthalpy based coefficients of performance are shown for constant generator and condenser temperatures of 80 and 30°C respectively, for evaporator temperatures from 60 to 75°C. It is observed
that smaller coefficients of performance are obtained with compared with those obtained to temperatures of condensation of 25°C show in Fig. 8. Finally, in a comparison between Figs. 5, 7 and 9, all that with possible operating conditions at condenser temperatures of 30°C, it is observed that when proposal system operates with similar evaporator temperature an increase in generator temperature could gets similar high values of the both coefficients of performance with same operation conditions between 112 and 115°C for water purification. In the Fig. 10 water purification and enthalpy based coefficients of performance are shown in ration between them. Theoretical behavior of these coefficients suggests for any enthalpy based coefficient of performance value that water purification coefficient of performance is bigger. The COP_WP rise even two times when
1.000
0.900
0.800
0.700
0.900
TEV = 75°C
0.800 TEV = 65°C
COP (dim)
0.700 0.600
COP_WP (dimensiionless)
1.000
TEV = 70°C
TEV = 60°C
0.500
0.600
0.500
0.400
0.400 0.300
0.300 0.200 0.100 0.000 104
0.200
TG = 80°C TC = 30°C
COP_Ent (dim) COP_WP (dim)
0.100
106
108
110 TAB (°C)
112
114
116
Fig. 9. COP_WP and COP_WP against TAB for TGE = 80°C, TCO = 30°C for four different constant values of TEV.
0.000 0.000
0.100
0.200 0.300 0.400 COP_Ent (dimensionless)
Fig. 10. COP_WP against COP_Ent.
0.500
0.600
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
COP_Ent is closer to 0.5 [9], as described in point 18 of mathematical model. 6. Conclusion Theoretical behavior of possible operating conditions for an ecological water purification system was shown. The proposal system was theoretically evaluated with low grade energy with inlet temperatures from 65 to 80°C, could be from a source of industrial waste heat. Surroundings for condensate the working fluid remain for the calculations between 25 and 30°C, for guarantee absorber temperature higher than 100°C water purification. Absorber temperature for the system is the power for simple distillation of impure water, with values from 105 to 115°C which can be able for purification of brackish water. The recycled energy for latent heat of purified water purification system has a benefit effect in coefficient of performance, with the relative rise value. Enthalpy based coefficient of performance can arise from 0.3 to 0.429 water purification coefficient of performance and in similar way theoretical limit case may rise COP from 0.5 to 1.0.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Acknowledgement To the CONACYT SNI-I-52028 project for the partial support. [9]
References [1]
W. Rivera, R.J. Romero, M.J. Cardoso, J. Aguillón and R. Best, Theoretical and experimental
513
comparison of the performance of a single-stage heat transformer operating with water/lithium bromide and water/Carrol™, Int. J. Ener. Res., 26 (2002) 747–762. F.A. Holland, J. Siqueiros, S. Satoyo, C.L. Heard and E.R. Santoyo, Water purification using heat pumps, E & FN Spon, 1999. W. Rivera, R. Best, J. Hernández, C.L. Heard and F.A. Holland, Thermodynamic study of advanced absorption heat transformer, Part I. Single an two stage configurations with heat exchangers, Heat Recovery Systems & CHP, 14 (2) (1994) 173–183. W. Rivera, R. Best, J. Hernández, C.L. Heard and F.A. Holland, Thermodynamic study of advanced absorption heat transformer, Part II. Double absorption configurations, Heat Recovery Systems & CHP, 14 (2) (1994) 185–193. R.J. Romero, Theoretical and experimental studies of absorption heat transformers and optimal design for falling film absorbers (Spanish text), PhD Thesis, DEPFI-UNAM & CIE-UNAM, México, 2001. W. Rivera, Theoretical study of absorption heat transformers using lithium bromide — water blend (Spanish text), Master of Science Thesis, UACPyP — UNAM, México, 1991. R.J. Romero, Studies of lithium bromide — water and Carrol — water blends in single stage absorption heat transformers (Spanish text), Master of Science Thesis, UACPyP — UNAM, México, 1996. R.A. Huicochea, Commissioning and experimental evaluation of a portable water purification system added to an heat transformer (Spanish text), Master of Science Thesis, CENIDET, México, 2004. R.J. Romero, J. Siquerios and A. Huicochea, Increase of COP for heat transformer in water purification systems, Part II — without increasing heat source temperature, Applied Thermal Engineering, 27 (5–6) (2007) 1054–1061.
Optimal water purification using low grade waste heat in an absorption heat transformer Rosenberg J. Romero*, A. Rodríguez-Martínez Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Chamilpa, Cuernavaca 62100, Morelos, México Tel./Fax +52 777 3297084; email: [email protected] Received 12 April 2007; accepted 4 May 2007
Abstract A proposal for rational energy saving using wasted heat is showed in the present paper. Thermodynamicmathematical model is presented like an effort for water purification from waste heat. This paper describes computing results of heat transformer operation for water purification using low grade waste heat. Equations, parameters and simplifications used in the model are briefly described. The main parameter of the carried out study is the coefficient of performance (COP) defined for reversed heat pumps and the second main parameter is absorber temperature, both parameters has been showed and correlated between them. Main objective of this work is to show the optimal operating condition for different process which deliver low grade waste heat and requires water purification. Assisted computing simulation was used for obtain these results. The main conclusion is an ecological proposal for optimal recover of low grade waste heat. Many operating conditions are showed in graphical form and discussed for different environment conditions. Keywords: Absorption heat pump; Water purification; Waste heat; Heat transformer
1. Introduction Unfortunately the USA/Mexico border areas have very limited water resources with salinity to major problem in irrigation districts. To lack of sufficiently pure water searches to health hazard to the growing population with to negative impact on their quality of life and their capacity *Corresponding author.
for economic productivity. The Paso/Ciudad Juarez region receives an average of only 7 inches of rain per year. It supports its population by taking water from an aquifer which is projected to be depleted of low salinity water within two decades. The situation is not assisted by the practice of using relatively clean water to transport human waste to treatment facility, which is often overloaded resulting in effluent of poor quality which is subsequently used in
Presented at the conference on Desalination and the Environment. Sponsored by the European Desalination Society and Center for Research and Technology Hellas (CERTH), Sani Resort, Halkidiki, Greece, April 22–25, 2007. 0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.05.026
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
agricultural irrigation. This simulation results has been made using lithium bromide (LiBr) — water cause it is the most commercial used pair in absorption systems.
All we have required for our own construction of primary resources and energy for its transformation. All these processes use energy and in each transformation that happens a part of this energy vanishes as heat, this heat of industrial waste has temperatures between 50 and 90°C [1] that can be used for water purification [2] with the heat transformer as single stage based system [3] or an advanced system [4]. The proposal of purification process consists in a simple distillation powered by waste heat, where the heat obtained by the heat pump is recycled when the steam is condensate and this increases the temperature of the heat source. Fig. 1 shows a simplified diagram. The impure water to be distilled is heated in absorber, water steam is condensated (loosing heat) and it is collected in auxiliary condenser. In the water purification system, heat supply can be proportionated by the heat pump.
Auxiliary condenser
Condenser
Generator
The mathematical pattern that intends to describe the behavior of this system is based on the thermodynamic pattern published previously with LiBr-water solution [5]. The following assumptions have seen made in the development of the mathematical model for an heat transformer integrated to a water purification system with reference to Fig. 2. (i) There is thermodynamic equilibrium throughout the entire system. (ii) The analysis is made under steady state conditions. (iii) A rectifier is unnecessary since the absorbent does not evaporate in the temperature range under any place of the system. (iv) The solution is saturated leaving the generator and the absorb and the working flows is saturated leaving the condenser and the evaporator. (v) Heat losses and pressure drops into tubings and the components plows are considered negligible. (vi) The flow through the valves is isenthalpic. (vii) Temperatures at the exit of the main components T1, T2, T4 and T5 and the heat load in the evaporator QEV are known.
Absorber
Impure water
Surrounding cooling water
Fig. 1 shows schematically the system, which have an heat transformer integrated to complete an ecological water purification system.
3. Simulation model and assumption
2. Basic concepts
Evaporator
507
Heat source
Fig. 1. Schematic diagram of water purification heat transformer system.
4. Mathematical model (1) From assumption (i) and (ii), T1 = T7. (2) From assumption (iv) the working fluid is considered saturated leaving the condenser and evaporator, then the pressure at state
508
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513 P PATM
Auxiliary condenser 11
10
9
4
PEV
Evaporator
Absorber
3
5 8
12 2
6 7
PCO
Condenser
1
Generator 13
TCO
TGE, TEV
TAB
T
Fig. 2. Schematic diagram water purification system assisted single stage heat transformer.
points may be obtained by the following equations: P2 = P(T2) and P4 = P(T4). (3) From assumption (v) the pressure drops in the tubing and the components are consider negligible, P1 = P2 = P7 = P6 and P3 = P4 = P5 = P8. (4) From assumption (iv) the concentration of the LiBr concentrated solution leaving the generator can be estimated as follow X7 = X(P2,T7). (5) In the same way, the concentration of the LiBr diluted solution leaving the absorber can be estimated as X5 = X(P4,T5). (6) Cause there is not mass transfer between generator and absorber X7 = X8 and X5 = X6.
(7) From assumption (iii), the concentration of the absorbent in the vapor leaving the generator is zero, then X1 = X2 = X3 = X4 = 0. (8) The enthalpies at the exit of absorber and generator can be estimated by H5 = H(T5,X5) and H7 = H(T7,X7). (9) From assumption (iv), the enthalpies at the exit of the condenser and the evaporator can be estimated as follow H2 = H(T2) and H4 = H(T4). (10) Considering that the vapor upon leaving the generator is superheated H1 = H(P2,T1). (11) Because the absorbent does not evaporate in the temperature range under operating conditions, from mass balance in generator
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
and absorber, the flow ratio (RF) can be rewritten for this system by X7 M FR = AB = M WF X 7 − X 5 (12) Carrying out mass and energy balances in the to absorber and using FR definition, the mass flow rate of the working fluid can be calculated by the following equation: M WF =
QAB H 4 − H 8 + FR ( H 8 − H 5 )
(13) From FR definition:
QPU = m9 [(h12 – h11) + (h13 – h12)] therefore QAB = m9 (h13 – h11). (19) Then the enthalpy based coefficient of performance for to it single stage heat transformer is defined COPEnt =
MGE = MAB − MWF (15) Considering that the process though the expansion valve is isenthalpic (vi) H5 = H6 and H3 = H2 (16) From mass and energy balances in the main components, the amount of heat supplied or delivered can be estimated from the following equations:
QCO = M WF ( H1 − H 2 ), QEV = M WF ( H 4 − H 3 ) and QGE = M WF H1 + M GE H 7 − M AB H 6 . (17) The getting power into the absorber has been transferred to the water purification system as shown in Fig. 2, the impure water flow rate is m9, then QPU = QAB; where QPU = m9 (h11 – h10). (18) The condensation power of purified vapour water obtained into the auxiliary condenser goes to the evaporator and to the generator
QAB QGE + QEV
(20) And the water purification coefficient of performance for the proposal water purification system using low grade waste heat is COPWP =
MAB = MWFFR (14) From mass balance in the absorber or generator side
509
QAB QGE + QEV − QAB
5. Discussion Theoretical works of mathematic modeling about heat transformers assume that generator and evaporator’s temperature is the same value [6] because heat exchanger’s area is infinite and a fluid goes through it at the same temperature in a long time value. Experimental research about heat transformers evidence that internal temperatures into the generator and the evaporator are always different due to equilibrium conditions in each one [5,7,8]. It had been shown in different temperature data of the heat transformer. In the simulation carried out, it is shown that it is feasible the purification of water by means of simple evaporation of water starting from water with dissolved solids, in which heat is guaranteed with a superior temperature at 105°C provided in the absorber of the system. The simulation shows all operating possible conditions with absorber temperatures higher than 105°C till 115°C, for guarantee water purification. The evaporator temperature has values from 60 and 75°C, else generator temperature presents values from 60 to 80°C with condensation temperature of 25 and 30°C. In Fig. 3 the behavior for aqueous LiBr-water is shown for operating conditions with condenser
510
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
0.700
0.900 0.800
0.600
TEV = 70°C
TEV = 75°C
0.700
0.500 COP (dim)
COP (dim)
0.600 0.400 0.300
TEV = 65°C
TEV = 75°C TEV = 70°C
0.500 0.400 0.300
0.200 0.200 0.100 0.000 105
0.100
TG = 65°C TC = 25°C
106
107
COP_Ent COP_WP
108
109
110 111 TAB (°C)
112
113
114
115
116
TG = 70°C TC = 25°C
COP_WP (dim) COP_Ent (dim)
0.000 104
106
108
110 TAB (°C)
112
114
116
Fig. 3. COP_WP and COP_Ent against TAB for TGE = 65°C, TCO = 25°C for two different constant values of TEV.
Fig. 4. COP_WP and COP_Ent against TAB for TGE = 70°C, TCO = 25°C for three different constant values of TEV.
temperature of 25°C. Generator temperature remains constant to 65°C for two operating conditions series. Left lines for evaporator temperature of 70°C and right lines for evaporator temperature of 75°C. Both series show the water purification coefficient of performance (COP_WP) with higher values than enthalpy based coefficient (COP_Ent). It is observed that for further temperatures in the evaporator bigger temperatures can be obtained in the absorber, the maximum value of the COP_WP is obtained to the smallest absorber temperature TAB of 106°C. In Fig. 4, the behavior of three different operating condition series are shown, the generator and condenser temperatures are constant for 70 and 25°C respectively for evaporator temperatures of 65, 70 and 75°C each. These three series show bigger COP_WP than COP_Ent for all conditions. It is shown that highest COP_WP for evaporator temperature of 70°C and absorber temperature of 106°C. Comparison between Fig. 4 and Fig. 5, shows that operating conditions for condenser temperature of 25°C, evaporator temperature of 70°C and absorber temperature of 106°C, higher COP_WP is obtained for higher generator temperature, means COP_WP for 70°C is bigger than for 65°C generator temperature.
Fig. 5 shows similar behaviors those shown in Fig. 3 for generator temperature of 70°C with condenser temperature of 30°C. Evaporator temperatures made two series of operation conditions, one of them at 70°C and the other one at 75°C. Both series show water purification coefficient of performance is higher than enthalpy based coefficient of performance for same operating condition. It is observed, compared this figure with Fig. 4 that when increasing the 0.800 0.700
COP (dim)
0.600 TEV = 70°C
0.500
TEV = 75°C
0.400 0.300 0.200 0.100 0.000 105
TG = 70°C TC = 30°C
106
107
COP_WP (dim) COP_Ent (dim)
108
109
110
111
112
113
114 115
116
TAB (°C)
Fig. 5. COP_WP and COP_Ent against TAB for TGE = 70°C, TCO = 30°C for two different constant values of TEV.
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
1.000 0.900 TEV = 75°C
0.800
COP (dim)
0.700
TEV = 65°C
TEV = 70°C
TEV = 60°C
0.600 0.500 0.400 0.300 0.200 0.100 0.000 104
TG = 75°C TC = 25°C
106
COP_WP (dim) COP_Ent (dim)
108
110 TAB (°C)
112
114
116
Fig. 6. COP_WP and COP_Ent against TAB for TGE = 75°C, TCO = 25°C for three different constant values of TEV.
0.900 0.800 0.700
TEV = 75°C TEV = 70°C
0.600 COP (dim)
ambient temperature causing an increase in the condensation temperature TCO, it diminishes the number of operation conditions. For these reasons and for to continue the operation of the system it has necessary to increase the evaporation temperature and smaller operation coefficients are obtained those compared in similar conditions with smaller TCO. In Fig. 6, operating conditions change those presented in Fig. 4 for an increase in generator temperature to 75°C. It is observed an increase in number of possible operating conditions presented for evaporator temperature from 60 to 75°C. With these operating conditions water purifications coefficient of performance reach closer values to 0.9 and absorber temperatures of 115°C. The highest value of COP_WP happen at absorber temperature of 106°C with evaporator temperature of 70°C. In Fig. 7 three behaviors for the water purification heat transformer are shown, where generator and condenser temperatures remain constant to 75 and 30°C respectively. These behaviors are for operating conditions of 65, 70 and 75°C compared between this and the Fig. 6, shows that when increasing the condensation temperature, the COP_WP decreases in similar conditions
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0.500
TEV = 65°C
0.400 0.300 0.200 0.100 0.000 104
TG = 75°C
COP_WP (dim) COP_Ent (dim)
TC = 30°C
106
108
110
112
114
116
TAB (°C)
Fig. 7. COP_WP and COP_Ent against TAB for TGE = 75°C, TCO = 30°C for three different constant values of TEV.
with temperature of condensation TCO = 25°C showed in Fig. 6. It can also observe that a heat transformer is operated with smaller coefficients of performance when it diminishes the evaporation temperature. The three levels show that water purification coefficient of performance is bigger that enthalpy based coefficient of performance. When the system operates at 70°C in the evaporator it can get the longer range of possible operating conditions. In Fig. 8 water purification heat transformer possible operating conditions are shown with generator temperature of 80°C and condenser temperature of 25°C remaining constants, for evaporator temperature of 60 to 75°C as can be observed in Figs. 4 and 6. The coefficients of performance are bigger to those reported with generator temperatures of 75 and 70°C. The coefficients of performance, for temperatures of 75°C of TEV, being closer than 0.95 for the case of water purification in comparison with the COP_Ent of 0.45. All lines show that water purification coefficient of performance is bigger that enthalpy based coefficient of performance. These behaviors compared with those shown in Figs. 4 and 6, shows biggest water purifications coefficient of performance while generator
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R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
1.000 0.900 TEV = 65°C
0.800 TEV = 60°C
0.700 COP (dim)
TEV = 75°C
TEV = 70°C
0.600 0.500 0.400 0.300 0.200 0.100
TG = 80°C TC = 25°C
0.000 104
106
COP_Ent (dim) COP_WP (dim)
108
110 TAB (°C)
112
114
116
Fig. 8. COP_WP and COP_Ent against TAB for TGE = 80°C, TCO = 25°C for four different constant values of TEV.
temperature rise. Enthalpy based coefficient of performance for bigger generator temperature remains with small values changes compared those of Figs. 4 and 6. In Fig. 9 the water purification and enthalpy based coefficients of performance are shown for constant generator and condenser temperatures of 80 and 30°C respectively, for evaporator temperatures from 60 to 75°C. It is observed
that smaller coefficients of performance are obtained with compared with those obtained to temperatures of condensation of 25°C show in Fig. 8. Finally, in a comparison between Figs. 5, 7 and 9, all that with possible operating conditions at condenser temperatures of 30°C, it is observed that when proposal system operates with similar evaporator temperature an increase in generator temperature could gets similar high values of the both coefficients of performance with same operation conditions between 112 and 115°C for water purification. In the Fig. 10 water purification and enthalpy based coefficients of performance are shown in ration between them. Theoretical behavior of these coefficients suggests for any enthalpy based coefficient of performance value that water purification coefficient of performance is bigger. The COP_WP rise even two times when
1.000
0.900
0.800
0.700
0.900
TEV = 75°C
0.800 TEV = 65°C
COP (dim)
0.700 0.600
COP_WP (dimensiionless)
1.000
TEV = 70°C
TEV = 60°C
0.500
0.600
0.500
0.400
0.400 0.300
0.300 0.200 0.100 0.000 104
0.200
TG = 80°C TC = 30°C
COP_Ent (dim) COP_WP (dim)
0.100
106
108
110 TAB (°C)
112
114
116
Fig. 9. COP_WP and COP_WP against TAB for TGE = 80°C, TCO = 30°C for four different constant values of TEV.
0.000 0.000
0.100
0.200 0.300 0.400 COP_Ent (dimensionless)
Fig. 10. COP_WP against COP_Ent.
0.500
0.600
R.J. Romero, A. Rodríguez-Martínez / Desalination 220 (2008) 506–513
COP_Ent is closer to 0.5 [9], as described in point 18 of mathematical model. 6. Conclusion Theoretical behavior of possible operating conditions for an ecological water purification system was shown. The proposal system was theoretically evaluated with low grade energy with inlet temperatures from 65 to 80°C, could be from a source of industrial waste heat. Surroundings for condensate the working fluid remain for the calculations between 25 and 30°C, for guarantee absorber temperature higher than 100°C water purification. Absorber temperature for the system is the power for simple distillation of impure water, with values from 105 to 115°C which can be able for purification of brackish water. The recycled energy for latent heat of purified water purification system has a benefit effect in coefficient of performance, with the relative rise value. Enthalpy based coefficient of performance can arise from 0.3 to 0.429 water purification coefficient of performance and in similar way theoretical limit case may rise COP from 0.5 to 1.0.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Acknowledgement To the CONACYT SNI-I-52028 project for the partial support. [9]
References [1]
W. Rivera, R.J. Romero, M.J. Cardoso, J. Aguillón and R. Best, Theoretical and experimental
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comparison of the performance of a single-stage heat transformer operating with water/lithium bromide and water/Carrol™, Int. J. Ener. Res., 26 (2002) 747–762. F.A. Holland, J. Siqueiros, S. Satoyo, C.L. Heard and E.R. Santoyo, Water purification using heat pumps, E & FN Spon, 1999. W. Rivera, R. Best, J. Hernández, C.L. Heard and F.A. Holland, Thermodynamic study of advanced absorption heat transformer, Part I. Single an two stage configurations with heat exchangers, Heat Recovery Systems & CHP, 14 (2) (1994) 173–183. W. Rivera, R. Best, J. Hernández, C.L. Heard and F.A. Holland, Thermodynamic study of advanced absorption heat transformer, Part II. Double absorption configurations, Heat Recovery Systems & CHP, 14 (2) (1994) 185–193. R.J. Romero, Theoretical and experimental studies of absorption heat transformers and optimal design for falling film absorbers (Spanish text), PhD Thesis, DEPFI-UNAM & CIE-UNAM, México, 2001. W. Rivera, Theoretical study of absorption heat transformers using lithium bromide — water blend (Spanish text), Master of Science Thesis, UACPyP — UNAM, México, 1991. R.J. Romero, Studies of lithium bromide — water and Carrol — water blends in single stage absorption heat transformers (Spanish text), Master of Science Thesis, UACPyP — UNAM, México, 1996. R.A. Huicochea, Commissioning and experimental evaluation of a portable water purification system added to an heat transformer (Spanish text), Master of Science Thesis, CENIDET, México, 2004. R.J. Romero, J. Siquerios and A. Huicochea, Increase of COP for heat transformer in water purification systems, Part II — without increasing heat source temperature, Applied Thermal Engineering, 27 (5–6) (2007) 1054–1061.