- Email: [email protected]
Upgrading of heat through absorption heat transformers
Int. J. Refrig. Vol. 18, No. 7, pp. 439-446, 1995
II~UTTERWORTH I'VE I N E M A N N
Copyright © 1995 Elsevier Science Ltd and IIR Printed in Great Britain. All rights reserved 0140-7007/95/$10.00 + .00
Upgrading of heat through absorption heat transformers I. M . l s m a i l
M e c h a n i c a l Engineering D e p a r t m e n t , F a c u l t y o f Engineering, Assiut University, Assiut 71516, E g y p t Received 8 March 1993; revised 6 June 1995
In this paper, we study the performance of absorption heat transformers for upgrading low-level heat. A mathematical model was developed utilizing the equation of state to calculate the properties of ammoniawater mixture. The performance of the heat transformer is defined by COP and circulation ratio. The parameters that affect the performance are level of waste heat, condenser temperature, and effectiveness of heat exchangers. This study leads to identification of the field of the operating conditions. (Keywords: absorption heat transformer; circulation ratio; Gibbs free energy; upgraded heat; waste heat level; coefficient of performance)
Revalorisation de chaleur grace aux transformateurs de chaleur fi absorption On a dtudi~ la performance des transformateurs de chaleur h absorption pour la valorisation de chaleur defaible niveau. On a ~labor~ un modble math~mathique qui utilise l'~quation d'~tat pour le calcul des propri~tks d'un m~lange ammoniac-eau. La performance du transformateur de chaleur est ~valu~e selon le COP et le taux de circulation. Les paramktres ayant une influence sur cette performance sont: le niveau de chaleur perdue, la tempOrature du condenseur et l'efficacit~ des ~changeurs de chaleur. Cette Otude permet l'identification du champ des conditions de fonctionnement.
(Mot clrs: r+cup+rateurde chaleur ~iabsorption; taux de circulation;6nergie libre de Gibbs; revalorisationde chaleur; intensit~ de chaleur perdue; coefficientde performance)
Absorption heat transformers (AHTs) for upgrading of heat are useful for heat recovery of low-level heat energy, especially in petrochemical and chemical plants, where a large portion of the energy is wasted in many processes. The technology of heat transformers is now sufficiently developed to justify their future applications. The objective of this work is to analyse AHTs thermodynamically and to determine the performance as a function of the operating levels of temperatures. A schematic diagram of an AHT is shown in Figure I. This arrangement, without mixture heat exchanger (MHE) or refrigerant heat exchanger (RHE), is similar to that reported in ref. 1. The M H E and RHE are implemented to improve the performance of the unit. The AHT works on a reversed absorption refrigeration cycle. Heat is supplied at an intermediate temperature level to both the generator and evaporator. Part of this heat is rejected at a lower temperature level through the condenser. The remaining heat is delivered at a high temperature level; this is the upgraded heat. Both the evaporator and the absorber work at high pressure while the condenser and the generator work at low pressure. Waste heat is supplied to both the generator and the evaporator, while upgraded heat is extracted from the absorber. The rectifier will not be considered in this work. The performance of the unit is identified in this paper by the COP and the circulation ratio.
The thermodynamic properties of ammonia-water mixture are calculated by means of a computer program based on the equation of state reported in ref. 2 and on the saturation pressure-temperature relation given in ref. 3. This method is tedious and complicated, but it is fundamental and allows a wide range of properties, which is necessary for AHT calculations. Also, the automated calculations of properties based on the equations are much more convenient than the tabular data formats previously available. Mathematical model
Heat and mass balances on the absorber give m4 = m3 + ml2 m4x 4 =
m3x 3 + mlzY12
Qa = mTh12 + mlh] - mrh4
(1) (2)
(3)
Similarly, heat and mass balances on the generator lead to
m6 = ml + rn7
(4)
m 6 x 6 = m T y 7 -4- m i x 1
(5)
Qg = mthl + ruth7 - m6h6
(6)
439
440
I.M. Ismail
Nomenclature
Ai, Bi, Ci, Di, gi
Dimensionless coefficients Coefficient of performance Molar specific heat at constant pressure (kJ kmol- 1 K- ~) Circulation ratio Gibbs free energy (kJ kmol- 1) Enthalpy (kJ kg -1) Mass flowrate (kg s- 1) Pressure (bar) Heat transfer rate (kW) Molar entropy (kJ kmo1-1 K -1) Temperature (K) Ammonia mass fraction in liquid phase Ammonia mole fraction in liquid phase Ammonia mass fraction in vapour phase Ammonia mole fraction in vapour phase
COP
f
g h
m P
Q S T
x 2 Y
"
Condenser
a c e g o r R
Generator6~5
f -- --m6
Diagrammesch~matiqued'untransformateurde chaleurh absorption From Equations (1), (2), (4) and (5) we get
ylx4 ---~2 1)
Qa (9)
The effectiveness of the mixture and refrigerant heat exchangers M H E and RHE are defined respectively as
-
T T - Ts T7 - Tlo
-
B
l o g P = A - -~
By the solution of Equations (3), (4) and (8), the mass of refrigerant circulating in the cycle, mr (mr = roT) can be expressed as mr = hi2 - h4 + (h3 - h4)(y7/x4 - 1)/(1 - x1/x4)
The circulation ratio f is proportional to the pumping power, clarified in Appendix A. Evaluation o f f is more useful than pumping power because it indicates more clearly the variations in flowrates. The saturation pressure of the water-ammonia mixture as a function of saturation temperature is given by Bourseau and Bugarel 3 as
(7)
(8)
mT( y7-\x6 1)=m,(l--~6)
(13)
m7
Qg
Figure 1
T3 - / ' 2 ~l- T4-/'2
Absorber Condenser Evaporator Generator Reference state Refrigerant Reduced, dimensionless
In general, pump power is very small compared with the other energy rates, and therefore it can be neglected at this stage in the calculation of COP, without significant error. In the case of COP for a heat transformer, pumping power is added to Qg and Q~; then it is acceptable to ignore it. The order of magnitude of pumping power is less than 0.4% of (Qg -k- Qe). 10 The circulation ratio f is given by
Schematicdiagram of absorption heat transformer (AHT)
m3( 1 --x~):-m7(
Liquid Ideal gas state Vapour
Subscripts
]
Qc
Figure1
1 o v
~Qa
Qe
9
Superscripts
(I0)
(11)
assuming the specific heat capacities of the mixture are independent of temperature. The coefficient of performance of the AHT for upgrading of heat is defined as
(14)
where A = 10.44 - 1.767x + 0.9823x 2 + 0.3627x 3
(15)
and B = 2013.8- 2155.7x + 1540.9x 2 - 194.7x 3
(16)
The equation of state of ammonia-water mixture consists of separate Gibbs free energy expressions for the liquid and vapour phases. The liquid and vapour specific Gibbs free energies take reduced dimensionless forms 2. They are given as a function of ammonia mole fractions ~, y. The relation between mole fraction and mass fraction is given by 9 2 =
x x + (1 -
(17)
where 17.03 18.015
(Lq~) - - _ _
COP -
Q" Qg + Qe
(12)
The reduced dimensionless specific Gibbs free energy for
441
Upgrading of heat through absorption heat transformers the liquid phase is given by g~ = (1 - x ) g ~ . : o + xgRN~3 + { ( 1 - 2) In(1 - g) + X'ln(2)] + gex R
(18)
The reduced dimensionless specific Gibbs free energy for the vapour phase is given by g~ = (1 - y ) g ~ . 2 0 + Yg~ N.,
+ [(1 - :f)ln(1 - y) +pin(y)]
(19)
Enthalpies of the vapour and liquid phases of the mixture (in kJ kmol -l) are given by hRmix = - - T R
hlmix =
gR(TR,PR,Y)/Ta
(20)
--T2[o--~RglR(TR,PR,2)/TR]
(21)
1 ga, gav and gex R are given in Appendix B.
Results and discussion
A computer program was written in BASIC and the calculations were carried out on a PC. The following assumptions were considered: the absorber temperature is considered as the temperature of the strong mixture leaving the absorber; the generator temperature is considered as the temperature of the weak mixture leaving the generator; the concentration of the vapour leaving the evaporator and the concentration of the vapour leaving the generator are both set to 99% in order to match the mass balance. This is not the real case. Rectification is required. It will increase the generator heat by up to 10-20%. The mixture leaving the condenser is saturated liquid at the condenser temperature 7. The mixture leaving the evaporator is saturated vapour at evaporator temperature. A capacity of 60kW rate of upgraded heat at the absorber temperature was assumed. As the residence time in the generator is not long enough to achieve the equilibrium condition, a temperature difference of 4 K was therefore assumed between the weak solution and the boiling solution at equilibrium concentration. There is also a temperature difference of 4 K between the strong solution leaving and the solution
at equilibrium inside the absorber 4. Two cases will be considered in this study: the first one is without a pressure drop, and the second considers a pressure drop in the piping. Although the pressure drop in the piping depends upon the velocity of flow, the pipe diameter and the length of pipes between components, the pressure loss in the pipe between the evaporator and the absorber is expressed as 5 Ap
= 0.075 (22) P where P is the exit pressure from the pipe. For the pressure drop between the generator and the condenser the value of AP/p is taken as 0.05. The values are taken from the reference unchanged as we are not going to consider the piping dimensions, and this value is kept constant irrespective of the value of refrigerant flowrates. First of all, the values of the properties of the ammonia-water mixture calculated in this work were compared with other published work using the same technique6. This comparison has shown a good agreement, as shown in Table 1.
Effect of waste heat level As mentioned above, the rate of upgraded heat at the absorber was assumed to be 60kW. Figure 2 gives the values of the heat supplied to the generator and the evaporator (Qg and Qe) and the heat rejected by the condenser, Qc, against the absorber temperature. It is clear from the figure that for each level of waste heat, Tg, there is a range of upgraded temperature at the absorber through which Qg is almost constant. This range increases as Tg increases. (Ta ranges from 70 to 93 °C for Tg = 60 °C and from 100 to 144 °C for Tg = 90 °C.) It is obvious that Qe and Qc are more sensitive to the variations in both Ta and Tg. Also, as Tg increases, a larger range of Ta could be attained with acceptable variations in Qe and Qc. For given generator, evaporator and condenser temperatures, there is a maximum absorber temperature (maximum upgraded value) that corresponds to approximate equalizations of ammonia concentrations of the solution flowing into and out of the absorber. This temperature can be called the maximum cut-out temperature at which the generator duty increases sharply
Sample results of mixture properties for comparison between AMMWAT 3 and this work Tableau 1 Quelques r~sultats des essais sur les propridtOs de rn~langes permettant de faire une comparaison entre A M M W A T et le prOsent travail
Table 1
Enthalpy (kJ/kg)
Temp. (°C)
Pressure (bar (105 Pa))
Mass fraction NH 3
State
AMMWAT 131
Present work
132.2 76.67 54.40 75.56 110.0 77.78 50.56 26.67 54.40 184.4
20.678 20.678 4,825 20.678 20.678 20.678 20.678 20.678 4.825 20.678
0.102 0.120 0,401 0.401 0.401 0.9936 0.9936 0.9936 0.9936 0.102
Liquid Liquid Liquid Liquid Liquid Vapour Liquid Liquid Vapour Liquid
493.80 251.73 8.180 105.92 267.02 1372.24 239.05 121.00 1396.5 728.78
493.71 251.34 7.50 105.08 266.10 1383.58 238.88 120.44 1391.00 728.85
442
I. M Ismail
140 -- ~ - - - Q c
II
oa
Table 2
"
.,
--~Qe 130
Without pressure drop
120
Tg = Te T¢ = 25°C E=0.8
ll0
Tg,°C !60
!'i'
,o 1:8o.7o
i
i: J: l
i
90
//,Ii I
g0 70 I 80
60
[ 100
I
120
l 140
Figure 2 Qg, Q, and Q¢ as a function of absorber temperature for the given generator temperatures without piping pressure loss Figure 2 Qg, Qe et Qc en fonetion de la tempdrature de l'absorbeur pour des tempdratures donndes de gOndrateur, sans prise en compte des pertes de pression darts des tuyauteries
Qg ~
]'
,'
- -qc
I
'1
II
:j
,
!'
i:
I/
II 'I
I•
~I
II
t3o 120 --
,lO ~
°
.I
TdC
I00
'f
60,'70 1,80.'90 .I I ,,
I' ,i
h " , 'i J l e I
so
!: /:l,:l !:1 ,: I /, l , ,4 I,' } / T--'r,
60
I 80
9o
E=O.8
i 100
I 120
I 140
With pressure drop
Ta (°c)
Qg (kW)
Qe (kW)
Qc (kW)
Qg (kW)
Q¢ (kW)
Qc (kW)
ll0 115 120 125 130 135 140 145 150 152 155 157
69.36 69.45 69.60 69.85 70.21 70.76 71.63 73.12 76.22 78.64 86.36 103.9
69.62 70.29 71.46 73.25 75.98 80.08 86.53 97.62 120.68 138.94 196.25 326.65
78.97 79.74 81.06 83.10 86.19 90.84 98.16 110.74 136.90 157.57 222.63 370.56
69.07 69.19 69.40 69.71 70.19 70.95 72.27 75.03 84.87 100.85
68.39 69.34 70.89 73.25 76.86 82.55 92.55 113.34 187.52 308.05
77.45 78.54 80.30 82.97 87.06 93.50 104.80 128.36 212.38 348.90
180
Ta (°C)
140
Qg, Q~ and Q~ as a function of Za
I:
J 160
Ta (°C) Figure 3 Qg, Qe and Qc as a function of absorber temperature for the given generator temperatures with pressure drop in piping Figure 3 Qg, Qe et Qc en fonction de la tempOrature de l'absorbeur pour des tempdratures de gdn~rateur donndes, avec prise en compte des pertes de pression dans les tuyauteries
beyond an acceptable value (e.g. for Tg = 70 °C and 90°C, the cut-out absorber temperature equals 119 °C and 159°C respectively). This is because, as the temperature increases, the ability to absorb ammonia vapour in the absorber decreases. The effect of pressure drop in the piping is shown in Figure 3. It is obvious that the main effect of pressure loss in the piping is the reduction in the range of Ta for constant Qg. Also, pressure loss leads to a reduction in cut-out temperature (e.g. for Tg = 70 °C and 90 °C, cut-out temperature = 114 °C and 153 °C respectively). As a design criterion (for a given condition defined by Tg, T~ and T0, the absorber cut-out temperature based
on the generator capacity does not represent the only physical limit; there are two other restrictions on the value of absorber temperature. One is based on the evaporator capacity, which has more potential than the generator capacity, as Te = Tg in this work, and waste heat is supplied for both. The other is based on the condenser capacity. The capacity of the condenser could be the weighting factor for the determination of maximum working absorber temperature. The absorber temperature depends upon an acceptable size of condenser from an economical view of initial unit cost. The relationship between the condenser and evaporator capacities is clear. As a result of this discussion, the cut-out temperature may be based on the evaporator and the condenser capacities (i.e. based on the size and initial cost of the unit). This could be clarified by the values of heat duties given in Table 2. Sample results of capacities shown in the table are calculated at Tg = Te = 90 °C and Tc = 25 °C. As an example, for the case where pressure drop is considered, we cannot sacrifice the performance as an increase of 65% of heat should be supplied to the evaporator for a 5 °C rise in temperature from 145 °C to 150 °C. For zero pressure drop in the piping, the increase in evaporator heat will be 23%. This increase in heat will be reflected in both the initial and the operating costs. To clarify the steep rise in generator duty, an expression for the difference ( Q g - Qa) can be developed by solving Equations (3), (6) and the heat balance equation of the mixture heat exchanger. This will give Qg - Qa = mr(h7 - - hi2)
(23)
Equation (23) can also be easily found by just applying the energy equation around the right-hand side of the unit, as shown in Figure 1. Referring to this equation, for low absorber temperature, the mass rate of refrigerant has small values and its variation is not significant. But for high absorber temperature, mr increases steeply, as shown in Figure 4. This will lead to a steep rise in the generator duty according to the equation. In Figure 5, COP is plotted against absorber temperature for the given generator temperature. It is evident that there is a range of absorber temperature through which high COP is attained. This range increases as Tg increases, and will be reduced due to pressure drop in the
Upgrading of heat through absorption heat transformers Zero press, drop - - - with press, drop
0.20
/ 90
0.18 i
T c = 25°C
0.16
Te=Tg E=0.8
0.14 -~
!80
0.12 I
I
l/
|l
0.10
,l
/2 y . j 70
I 90
I 100
I 110
I 120
I 130
I Zero press, drop I - - - With press, drop Tg,°C 160 T c = 25"C Te= T t E--0.8
22I
170
18
i/: 0
f 14
,I / /
| 140
I 150
I
6
t. ,J
, .90
:/,,/ ,,/
IO
0.06 ~ I 80
26-
443
I
,'/,'/,7
T a (~'C) Figure 4 Refrigerant mass flowrate as a function of absorber temperature
Figure4 D~bitmassiquedufrigorLgbne en fonction de la temperature de l~bsorbeur
2
60
1 80
100
,I 120
I 140
I 160
T,~ (~C) Figure 6 Circulation ratio against absorber temperature for the given generator temperatures with and without pressure loss consideration
T c = 25°C
0.45
Figure 6 Taux de circulation en fonction de la temp&ature de l'absorbeur pour les tempOratures de gOn~rateur donnOes, en tenant compte ou non des pertes de pression
0.400.35 0.30 r)
0.25
0.20 Tg°C 60 0"15 I
70
o.10~
I
6o
8o
i
90
Zero press, drop - - With press, drop I 1 I 100 120 140 160 T~ ( C )
Figure 5 COP versus absorber temperature for the given generator temperatures with and without pressure loss consideration
Figure 5 COP en fonction de la temp&ature de l'absorbeur pour les tempgratures de gdn~rateur donn~es, en tenant compte ou non des pertes de pression
piping. A COP of 0.4 or more is attainable through a range of Ta from 90°C to 135 °C for Tg = 90°C. The concept of absorber cut-out temperature may also be considered here. Absorber temperature should not exceed the value at which COP drops sharply beyond an economically acceptable value. The peak value of COP at a lower generator temperature is higher than that at a higher temperature for the following reasons. The generator pressure, which is the low-side pressure, depends on the condenser temperature, and the absorber pressure, which is the high-side pressure, depends on the evaporator temperature. The latter is equal to the generator temperature. Therefore a low generator temperature means a low absorber pressure, which leads to a better COP. Also, it is well known that, for a constant evaporator temperature, COP increases with the generator temperature. Hence one can argue that the effect of the evaporator
temperature when the latter is equal to the generator temperature will override the effect of generator temperature. It is worth mentioning that the difference in concentrations between strong and weak solutions at low temperatures of the generator and the evaporator is smaller than that at higher values. This leads to large flowrates of weak solution, mr. For a given Tg, as Ta increases from a value close to Tg, mr decreases owing to the variations in concentration and enthalpies. Consequently, a slight reduction in both Qg and Qe takes place, which leads to a slight increase in COP. Maximum value of COP is attained at minimum value of mr . Then mr increases, as shown in Figure 4, and consequently COP decreases as Ta increases. At higher values of Ta, mr attains higher values and results in a steep rise in Qe and Qg, which produces a steep reduction in COP. Figure 6 shows the variations in circulation r a t i o f as a function of Ta for the given values of Tg. Increasing the absorber temperature leads to increasingf to undesirable values. The higher the generator temperature, the larger the range of Ta through which moderate values o f f are maintained. The pressure drop in piping reduces this range. (Let T~ - 90 ° C , f < 4 for Ta up to 138 °C and up to 131 °C wit~a pressure drop consideration.)
Effect of condenser temperature As the temperature of the heat sink is lowered, the range of absorber temperature through which heat duties (Qg, Qe and Qc) are kept almost constant is increased, as shown in Figure 7. This means that the absorber cut-out temperatures (based on Qg, Qe or Qc) are increased. The rise in cut-out temperature is nearly equal to the drop in condenser temperature. For a given absorber temperature, the duty of each of the condenser and evaporator is reduced, owing to lowering condenser temperature. Figure 8 shows the variations in both COP and circulation ratio f as a function of Ta for the given condenser temperatures. Decreasing the condenser temperature enhances the COP and increases the range
a a~.
I. 114. I s m a i l
140
!11~ '1 30
140
!~ Il ,~
,30
!: it !:
120
T¢,:35
,3o
Qg
120
L-.;~Q~
f
. , "~|
!! ill:,
E=0.8
1
II/:#:l
~
•%'1" // , /×""1
IO0
9°
./~;., , , /~ /~o/~
.,>-.-";-.'" )j..i 70
-
- ~
60
./,:/,/.ql I
_
..;;'?.;¢ / I
~" / ["4
~,.
/07J_/_
- ~ "- ~." f , " ,
,t"
0.810.9
70
I 90
I 100
I I10
I 120
i 130
I 140
60
I
J
90
100
,
I
I
t
I
110
120
130
140
T a (°C)
Ta (°C)
Figure 7 Qg, Qe and Qc as a function of absorber temperature for the given condenser temperatures
Figure 9 Q~, Qe and Qc as a function of absorber temperature for the given effectiveness of MHE and RHE exchangers Figure 9 Qg, Qe et Qc en fonction de la temperature de l'absorbeur pour des e~cacit~s donndes des ~changeurs M H E et R H E
Figure 7 Qg, Qe et Qc en fonction de la temperature de l'absorbeur pour des temperatures donn~es de condenseur
r,~,,.,.....
c o P ~ /
16
,
135
0.,*5
,30
0.40 14
0.351
,,_
12 II Zeropress. drop / 1 1 ~
0.30
!0
~ 0.25 0.20
--
0.15
_
6
4 0.10
'
_
80
2O
~ .'-.~// o o c I
90
I
I
100 II0 T a (°C)
aa
-,
, 120
', ; Vl 'l"~0.gl
'°
s
" Io,l
,
o.,oF |
,
,E=0.9 A~ 1~'r"l
-
25 130
/
I ~"12 0.201"-
.'/,~J,."~ ,' ," Ii OI / ",,ZP"/
Z~mp~.,L,op 1,~. 1, ,1.~ ,V, --With'press. drop ~\1~ A
0.301-025~
lilt ,vll /~/1 / f
2
X V
I
140
Figure 8 COP and f versus absorber temperature for the given condenser temperatures with and without pressure loss consideration Figure 8 COP et f e n fonction de la tempkrature de l'absorbeur pour des ternpdratures de condenseur donn~es, en tenant compte ou non des pertes de pression
of absorber temperature for high COP. Also, the value of f is reduced by lowering the condenser temperature. It is clear that there is an absorber cut-out temperature for each condenser temperature at which COP drops sharply. The cut-out temperature gets lower values as the pressure drop is taken into account. When accounting for the pressure drop in the piping, the absorber pressure will be less than the evaporator pressure by the value of the pressure drop for the pipes in between. Also, the pressure in the generator will be greater than the condenser pressure by the amount of pressure drop in the piping between them. Accordingly, the pressure difference between absorber and generator will be less
.-f~
~
,;
|
1
I
I
I
I
I
so
9o
1oo
~1o
12o
13o
m40
T a (°C) Figure 10 COP and f versus absorber temperature for the given effectiveness of MHE and RHE exchangers Figure 10 COP et f en fonction de la tempdrature de l'absorbeur pour des efficacitds donndes des dchangeurs M H E et RHE
than the case of zero pressure drop. This is the reason for having a better COP when pressure drop is taken into consideration. This is valid for values of Ta close to Tg and up to a certain value of Ta for which COP takes the same value for both cases. This temperature depends on the value of Tc and exchanger effectiveness as shown in F i g u r e s 8 and 10. Beyond this value of Ta, COP with pressure drop becomes less than COP without pressure drop. For values of Ta close to Tg, Qg and Qe with pressure drop have lower values than without pressure drop. As Ta increases the circulation ratio increases. In the case of pressure drop consideration, f increases more
Upgrading of heat through absorption heat transformers significantly than that of zero pressure drop, as shown in Figure 6. This results in a relatively rapid reduction in COP with pressure drop till the two values o f COP become equal, as shown in Figures 8 and 10. At this point, the effect of circulation ratio overrides the effect of reduced pressure difference (Pa - Pg). It is worth noting that while f is increasing with Ta, (Pa - Pg) is constant for given values of Te and To.
2
Effect o f effectiveness o f heat exchangers
6
Variations in the duties of condenser, evaporator and generator for the effectiveness of M H E and R H E exchangers as a function of absorber temperature are shown in Figure 9. The higher the effectiveness of both M H E and RHE, the larger the range of absorber temperature through which moderate duties of condenser, evaporator and generator are required. Also, for a given absorber temperature, as the effectiveness increases the duty of each of evaporator and condenser decreases, Figure 9 represents the case of no pressure loss in piping. Reduction in heat exchanger effectiveness leads to an increase in Qe and Qg, especially at high values of Ta, and consequently the absorber cut-out temperatures based on reasonable values of Qg, Qe or Qc will be reduced. Figure 10 shows COP a n d f as a function of T~ for the given exchanger effectiveness. Increasing the effectiveness of M H E and R H E increases the operating range of absorber temperature for high COP. High effectiveness produces high COP of AHT. Pressure drop in piping reduces this effect. The value o f f does not depend on the effectiveness of exchangers.
Conclusion A parametric study of A H T was carried out in this work. COP, f and duties of generator, evaporator and condenser were calculated for a required upgraded heat rate at the absorber. Better COP and a wide range of upgraded heat temperature (extracted from the absorber) can be achieved with high generator and evaporator temperatures and low condenser temperature. Under the given operating conditions, the absorber temperature can be increased up to a certain value equal to the lowest limit of the following: 1. cut-out absorber temperature, defined by the economical size or capacity of the condenser and evaporator; 2. the limit of the absorber temperature, identified by an acceptable value of COP and circulation ratio f ; 3. variations in the above limits due to variations in condenser temperature, especially for units using aircooled condensers; 4. variations in those limits due to reduction in effectiveness of M H E and R H E exchangers during operation, which may be due to scaling as an example.
3 4 5
7 8 9 l0
445
Ziegler,B., Trepp, Ch. Equation of state lbr ammonia-water mixtures Int J Refrig (1984) 7 (2) 101-106 Bourseau,P., Bugarei, R. Refrigerationpar cycle~ absorptiondiffusion: comparaison des performances des syst~mes NH 3H20 et NH3-NsSCN Int J Refrig (1986) 9 206-213 An-JinMing Optimizationof ammonia absorption refrigeration process: effectsof seasonal ambient temperaturefluctuationsInt J Refrig (1991) 14 341-344 Avares,S. G., Trepp, Ch. Simulation of a solar driven aquaammonia absorption refrigerationsystem,Part 1: Mathematical description and systemoptimization Int J Refrig (1987) 10 40 48 Herold,K.E., Han, K., Moran, M. J. Ammwal: a computer program for calculatingthe thermodynamicproperties of ammonia and water mixtures using a Gibbs free energy formulation ASME Winter Annual Meeting (1988) AES 4 65-75 Ataer,O. E., Gogus,Y. Comparativestudy of irreversibilitiesin an aqua-ammonia absorption refrigerationsystem Int J Re[rig (1991) 14 86-92 Cohen,G., Rojey, A. Valorisation de chaleur fi bas niveau thermique Revue de I'Institut Franfais du Pktrole (1981) 36 (3) 349-365 Bogart,M. Ammonia Absorption Refrigeration in Industrial Processes Gulf Publishing Company (1981) George,J. M., Murthy, S. S. Experimentson a vapour absorption heat transformer Int J Refrig (1993) 16 (2) 107-119
Appendix A Power of weak solution pump = vim 1(Pa - Pg) Power of refrigerant pump v9m9(P a Pg) Total pump power = vlmlAP + v9m9AP = m 9 A P ( m l v l / m 9 + V9) = m9AP[( f - l)vl +v9] = m 9 A P [ f v l - (Vl - Vg)] where A P = (Pa - Pg), f = mr/m7, m 9 = m 7 and m6 = ml + m 7, For large values of f , say f > 5, the term (Vl - v 9 ) could be neglected, and then the pump power becomes directly proportional to the circulation r a t i o f for a given AP.
Appendix B g l = hloR _ TR SIR q_
-- TR
T,,R
/ TR
d R d TR ToR
CIpR/TR dTR + (A, + A3TR + A4T2R)
X (PR - PoR) + A2(P 2 - P2oR)/2 where C~R = Bl + B2TR + B3T 2
g~ = hVR - TRSoR -l-
C;~ d T R ToR
-
-
~ R / T R dTR + T R In(PR/PoR )
TR ~oR
+ CI(PR - PoR) + C 2 ( P R / T 3 -- 4PoR/7o3R
References
+ 3PoRTR/T4oR) + C3(PR/T~t' - 12PoR/Tlo 1 12
Franzen, P. Warmetransformateur erzeugt Nutzwarme aus Abwarme Erdol und Kohle Erdgas Petrochemie (1979) 32 (11) November
3
11
3
11
+ l l P o R T R / T o R ) + C 4 ( P R / T ~ -- 12PoR/ToR 3
12
+ l lPoRTR/ToR)/3
446
I. M. Isma#
w h e r e CpV~ = D 1 + D2TR + D3 T2. gexR = .2(1 -- .2){E 1 -k- E2P R + ( E 3 -k- E4PR)TR
+ Es/TR + ~6/T~ + (2.2 - 1)[E7 + E8PR
+ (E9 + E~oP~)TR + E ~ / & + t:~2/T~J + ( 2 ~ - 1)2[E13 + El4P R -~_EI5/TR Values o f coefficients are given in ref. 2.
_j_ EI6/T2]}
II~UTTERWORTH I'VE I N E M A N N
Copyright © 1995 Elsevier Science Ltd and IIR Printed in Great Britain. All rights reserved 0140-7007/95/$10.00 + .00
Upgrading of heat through absorption heat transformers I. M . l s m a i l
M e c h a n i c a l Engineering D e p a r t m e n t , F a c u l t y o f Engineering, Assiut University, Assiut 71516, E g y p t Received 8 March 1993; revised 6 June 1995
In this paper, we study the performance of absorption heat transformers for upgrading low-level heat. A mathematical model was developed utilizing the equation of state to calculate the properties of ammoniawater mixture. The performance of the heat transformer is defined by COP and circulation ratio. The parameters that affect the performance are level of waste heat, condenser temperature, and effectiveness of heat exchangers. This study leads to identification of the field of the operating conditions. (Keywords: absorption heat transformer; circulation ratio; Gibbs free energy; upgraded heat; waste heat level; coefficient of performance)
Revalorisation de chaleur grace aux transformateurs de chaleur fi absorption On a dtudi~ la performance des transformateurs de chaleur h absorption pour la valorisation de chaleur defaible niveau. On a ~labor~ un modble math~mathique qui utilise l'~quation d'~tat pour le calcul des propri~tks d'un m~lange ammoniac-eau. La performance du transformateur de chaleur est ~valu~e selon le COP et le taux de circulation. Les paramktres ayant une influence sur cette performance sont: le niveau de chaleur perdue, la tempOrature du condenseur et l'efficacit~ des ~changeurs de chaleur. Cette Otude permet l'identification du champ des conditions de fonctionnement.
(Mot clrs: r+cup+rateurde chaleur ~iabsorption; taux de circulation;6nergie libre de Gibbs; revalorisationde chaleur; intensit~ de chaleur perdue; coefficientde performance)
Absorption heat transformers (AHTs) for upgrading of heat are useful for heat recovery of low-level heat energy, especially in petrochemical and chemical plants, where a large portion of the energy is wasted in many processes. The technology of heat transformers is now sufficiently developed to justify their future applications. The objective of this work is to analyse AHTs thermodynamically and to determine the performance as a function of the operating levels of temperatures. A schematic diagram of an AHT is shown in Figure I. This arrangement, without mixture heat exchanger (MHE) or refrigerant heat exchanger (RHE), is similar to that reported in ref. 1. The M H E and RHE are implemented to improve the performance of the unit. The AHT works on a reversed absorption refrigeration cycle. Heat is supplied at an intermediate temperature level to both the generator and evaporator. Part of this heat is rejected at a lower temperature level through the condenser. The remaining heat is delivered at a high temperature level; this is the upgraded heat. Both the evaporator and the absorber work at high pressure while the condenser and the generator work at low pressure. Waste heat is supplied to both the generator and the evaporator, while upgraded heat is extracted from the absorber. The rectifier will not be considered in this work. The performance of the unit is identified in this paper by the COP and the circulation ratio.
The thermodynamic properties of ammonia-water mixture are calculated by means of a computer program based on the equation of state reported in ref. 2 and on the saturation pressure-temperature relation given in ref. 3. This method is tedious and complicated, but it is fundamental and allows a wide range of properties, which is necessary for AHT calculations. Also, the automated calculations of properties based on the equations are much more convenient than the tabular data formats previously available. Mathematical model
Heat and mass balances on the absorber give m4 = m3 + ml2 m4x 4 =
m3x 3 + mlzY12
Qa = mTh12 + mlh] - mrh4
(1) (2)
(3)
Similarly, heat and mass balances on the generator lead to
m6 = ml + rn7
(4)
m 6 x 6 = m T y 7 -4- m i x 1
(5)
Qg = mthl + ruth7 - m6h6
(6)
439
440
I.M. Ismail
Nomenclature
Ai, Bi, Ci, Di, gi
Dimensionless coefficients Coefficient of performance Molar specific heat at constant pressure (kJ kmol- 1 K- ~) Circulation ratio Gibbs free energy (kJ kmol- 1) Enthalpy (kJ kg -1) Mass flowrate (kg s- 1) Pressure (bar) Heat transfer rate (kW) Molar entropy (kJ kmo1-1 K -1) Temperature (K) Ammonia mass fraction in liquid phase Ammonia mole fraction in liquid phase Ammonia mass fraction in vapour phase Ammonia mole fraction in vapour phase
COP
f
g h
m P
Q S T
x 2 Y
"
Condenser
a c e g o r R
Generator6~5
f -- --m6
Diagrammesch~matiqued'untransformateurde chaleurh absorption From Equations (1), (2), (4) and (5) we get
ylx4 ---~2 1)
Qa (9)
The effectiveness of the mixture and refrigerant heat exchangers M H E and RHE are defined respectively as
-
T T - Ts T7 - Tlo
-
B
l o g P = A - -~
By the solution of Equations (3), (4) and (8), the mass of refrigerant circulating in the cycle, mr (mr = roT) can be expressed as mr = hi2 - h4 + (h3 - h4)(y7/x4 - 1)/(1 - x1/x4)
The circulation ratio f is proportional to the pumping power, clarified in Appendix A. Evaluation o f f is more useful than pumping power because it indicates more clearly the variations in flowrates. The saturation pressure of the water-ammonia mixture as a function of saturation temperature is given by Bourseau and Bugarel 3 as
(7)
(8)
mT( y7-\x6 1)=m,(l--~6)
(13)
m7
Qg
Figure 1
T3 - / ' 2 ~l- T4-/'2
Absorber Condenser Evaporator Generator Reference state Refrigerant Reduced, dimensionless
In general, pump power is very small compared with the other energy rates, and therefore it can be neglected at this stage in the calculation of COP, without significant error. In the case of COP for a heat transformer, pumping power is added to Qg and Q~; then it is acceptable to ignore it. The order of magnitude of pumping power is less than 0.4% of (Qg -k- Qe). 10 The circulation ratio f is given by
Schematicdiagram of absorption heat transformer (AHT)
m3( 1 --x~):-m7(
Liquid Ideal gas state Vapour
Subscripts
]
Qc
Figure1
1 o v
~Qa
Qe
9
Superscripts
(I0)
(11)
assuming the specific heat capacities of the mixture are independent of temperature. The coefficient of performance of the AHT for upgrading of heat is defined as
(14)
where A = 10.44 - 1.767x + 0.9823x 2 + 0.3627x 3
(15)
and B = 2013.8- 2155.7x + 1540.9x 2 - 194.7x 3
(16)
The equation of state of ammonia-water mixture consists of separate Gibbs free energy expressions for the liquid and vapour phases. The liquid and vapour specific Gibbs free energies take reduced dimensionless forms 2. They are given as a function of ammonia mole fractions ~, y. The relation between mole fraction and mass fraction is given by 9 2 =
x x + (1 -
(17)
where 17.03 18.015
(Lq~) - - _ _
COP -
Q" Qg + Qe
(12)
The reduced dimensionless specific Gibbs free energy for
441
Upgrading of heat through absorption heat transformers the liquid phase is given by g~ = (1 - x ) g ~ . : o + xgRN~3 + { ( 1 - 2) In(1 - g) + X'ln(2)] + gex R
(18)
The reduced dimensionless specific Gibbs free energy for the vapour phase is given by g~ = (1 - y ) g ~ . 2 0 + Yg~ N.,
+ [(1 - :f)ln(1 - y) +pin(y)]
(19)
Enthalpies of the vapour and liquid phases of the mixture (in kJ kmol -l) are given by hRmix = - - T R
hlmix =
gR(TR,PR,Y)/Ta
(20)
--T2[o--~RglR(TR,PR,2)/TR]
(21)
1 ga, gav and gex R are given in Appendix B.
Results and discussion
A computer program was written in BASIC and the calculations were carried out on a PC. The following assumptions were considered: the absorber temperature is considered as the temperature of the strong mixture leaving the absorber; the generator temperature is considered as the temperature of the weak mixture leaving the generator; the concentration of the vapour leaving the evaporator and the concentration of the vapour leaving the generator are both set to 99% in order to match the mass balance. This is not the real case. Rectification is required. It will increase the generator heat by up to 10-20%. The mixture leaving the condenser is saturated liquid at the condenser temperature 7. The mixture leaving the evaporator is saturated vapour at evaporator temperature. A capacity of 60kW rate of upgraded heat at the absorber temperature was assumed. As the residence time in the generator is not long enough to achieve the equilibrium condition, a temperature difference of 4 K was therefore assumed between the weak solution and the boiling solution at equilibrium concentration. There is also a temperature difference of 4 K between the strong solution leaving and the solution
at equilibrium inside the absorber 4. Two cases will be considered in this study: the first one is without a pressure drop, and the second considers a pressure drop in the piping. Although the pressure drop in the piping depends upon the velocity of flow, the pipe diameter and the length of pipes between components, the pressure loss in the pipe between the evaporator and the absorber is expressed as 5 Ap
= 0.075 (22) P where P is the exit pressure from the pipe. For the pressure drop between the generator and the condenser the value of AP/p is taken as 0.05. The values are taken from the reference unchanged as we are not going to consider the piping dimensions, and this value is kept constant irrespective of the value of refrigerant flowrates. First of all, the values of the properties of the ammonia-water mixture calculated in this work were compared with other published work using the same technique6. This comparison has shown a good agreement, as shown in Table 1.
Effect of waste heat level As mentioned above, the rate of upgraded heat at the absorber was assumed to be 60kW. Figure 2 gives the values of the heat supplied to the generator and the evaporator (Qg and Qe) and the heat rejected by the condenser, Qc, against the absorber temperature. It is clear from the figure that for each level of waste heat, Tg, there is a range of upgraded temperature at the absorber through which Qg is almost constant. This range increases as Tg increases. (Ta ranges from 70 to 93 °C for Tg = 60 °C and from 100 to 144 °C for Tg = 90 °C.) It is obvious that Qe and Qc are more sensitive to the variations in both Ta and Tg. Also, as Tg increases, a larger range of Ta could be attained with acceptable variations in Qe and Qc. For given generator, evaporator and condenser temperatures, there is a maximum absorber temperature (maximum upgraded value) that corresponds to approximate equalizations of ammonia concentrations of the solution flowing into and out of the absorber. This temperature can be called the maximum cut-out temperature at which the generator duty increases sharply
Sample results of mixture properties for comparison between AMMWAT 3 and this work Tableau 1 Quelques r~sultats des essais sur les propridtOs de rn~langes permettant de faire une comparaison entre A M M W A T et le prOsent travail
Table 1
Enthalpy (kJ/kg)
Temp. (°C)
Pressure (bar (105 Pa))
Mass fraction NH 3
State
AMMWAT 131
Present work
132.2 76.67 54.40 75.56 110.0 77.78 50.56 26.67 54.40 184.4
20.678 20.678 4,825 20.678 20.678 20.678 20.678 20.678 4.825 20.678
0.102 0.120 0,401 0.401 0.401 0.9936 0.9936 0.9936 0.9936 0.102
Liquid Liquid Liquid Liquid Liquid Vapour Liquid Liquid Vapour Liquid
493.80 251.73 8.180 105.92 267.02 1372.24 239.05 121.00 1396.5 728.78
493.71 251.34 7.50 105.08 266.10 1383.58 238.88 120.44 1391.00 728.85
442
I. M Ismail
140 -- ~ - - - Q c
II
oa
Table 2
"
.,
--~Qe 130
Without pressure drop
120
Tg = Te T¢ = 25°C E=0.8
ll0
Tg,°C !60
!'i'
,o 1:8o.7o
i
i: J: l
i
90
//,Ii I
g0 70 I 80
60
[ 100
I
120
l 140
Figure 2 Qg, Q, and Q¢ as a function of absorber temperature for the given generator temperatures without piping pressure loss Figure 2 Qg, Qe et Qc en fonetion de la tempdrature de l'absorbeur pour des tempdratures donndes de gOndrateur, sans prise en compte des pertes de pression darts des tuyauteries
Qg ~
]'
,'
- -qc
I
'1
II
:j
,
!'
i:
I/
II 'I
I•
~I
II
t3o 120 --
,lO ~
°
.I
TdC
I00
'f
60,'70 1,80.'90 .I I ,,
I' ,i
h " , 'i J l e I
so
!: /:l,:l !:1 ,: I /, l , ,4 I,' } / T--'r,
60
I 80
9o
E=O.8
i 100
I 120
I 140
With pressure drop
Ta (°c)
Qg (kW)
Qe (kW)
Qc (kW)
Qg (kW)
Q¢ (kW)
Qc (kW)
ll0 115 120 125 130 135 140 145 150 152 155 157
69.36 69.45 69.60 69.85 70.21 70.76 71.63 73.12 76.22 78.64 86.36 103.9
69.62 70.29 71.46 73.25 75.98 80.08 86.53 97.62 120.68 138.94 196.25 326.65
78.97 79.74 81.06 83.10 86.19 90.84 98.16 110.74 136.90 157.57 222.63 370.56
69.07 69.19 69.40 69.71 70.19 70.95 72.27 75.03 84.87 100.85
68.39 69.34 70.89 73.25 76.86 82.55 92.55 113.34 187.52 308.05
77.45 78.54 80.30 82.97 87.06 93.50 104.80 128.36 212.38 348.90
180
Ta (°C)
140
Qg, Q~ and Q~ as a function of Za
I:
J 160
Ta (°C) Figure 3 Qg, Qe and Qc as a function of absorber temperature for the given generator temperatures with pressure drop in piping Figure 3 Qg, Qe et Qc en fonction de la tempOrature de l'absorbeur pour des tempdratures de gdn~rateur donndes, avec prise en compte des pertes de pression dans les tuyauteries
beyond an acceptable value (e.g. for Tg = 70 °C and 90°C, the cut-out absorber temperature equals 119 °C and 159°C respectively). This is because, as the temperature increases, the ability to absorb ammonia vapour in the absorber decreases. The effect of pressure drop in the piping is shown in Figure 3. It is obvious that the main effect of pressure loss in the piping is the reduction in the range of Ta for constant Qg. Also, pressure loss leads to a reduction in cut-out temperature (e.g. for Tg = 70 °C and 90 °C, cut-out temperature = 114 °C and 153 °C respectively). As a design criterion (for a given condition defined by Tg, T~ and T0, the absorber cut-out temperature based
on the generator capacity does not represent the only physical limit; there are two other restrictions on the value of absorber temperature. One is based on the evaporator capacity, which has more potential than the generator capacity, as Te = Tg in this work, and waste heat is supplied for both. The other is based on the condenser capacity. The capacity of the condenser could be the weighting factor for the determination of maximum working absorber temperature. The absorber temperature depends upon an acceptable size of condenser from an economical view of initial unit cost. The relationship between the condenser and evaporator capacities is clear. As a result of this discussion, the cut-out temperature may be based on the evaporator and the condenser capacities (i.e. based on the size and initial cost of the unit). This could be clarified by the values of heat duties given in Table 2. Sample results of capacities shown in the table are calculated at Tg = Te = 90 °C and Tc = 25 °C. As an example, for the case where pressure drop is considered, we cannot sacrifice the performance as an increase of 65% of heat should be supplied to the evaporator for a 5 °C rise in temperature from 145 °C to 150 °C. For zero pressure drop in the piping, the increase in evaporator heat will be 23%. This increase in heat will be reflected in both the initial and the operating costs. To clarify the steep rise in generator duty, an expression for the difference ( Q g - Qa) can be developed by solving Equations (3), (6) and the heat balance equation of the mixture heat exchanger. This will give Qg - Qa = mr(h7 - - hi2)
(23)
Equation (23) can also be easily found by just applying the energy equation around the right-hand side of the unit, as shown in Figure 1. Referring to this equation, for low absorber temperature, the mass rate of refrigerant has small values and its variation is not significant. But for high absorber temperature, mr increases steeply, as shown in Figure 4. This will lead to a steep rise in the generator duty according to the equation. In Figure 5, COP is plotted against absorber temperature for the given generator temperature. It is evident that there is a range of absorber temperature through which high COP is attained. This range increases as Tg increases, and will be reduced due to pressure drop in the
Upgrading of heat through absorption heat transformers Zero press, drop - - - with press, drop
0.20
/ 90
0.18 i
T c = 25°C
0.16
Te=Tg E=0.8
0.14 -~
!80
0.12 I
I
l/
|l
0.10
,l
/2 y . j 70
I 90
I 100
I 110
I 120
I 130
I Zero press, drop I - - - With press, drop Tg,°C 160 T c = 25"C Te= T t E--0.8
22I
170
18
i/: 0
f 14
,I / /
| 140
I 150
I
6
t. ,J
, .90
:/,,/ ,,/
IO
0.06 ~ I 80
26-
443
I
,'/,'/,7
T a (~'C) Figure 4 Refrigerant mass flowrate as a function of absorber temperature
Figure4 D~bitmassiquedufrigorLgbne en fonction de la temperature de l~bsorbeur
2
60
1 80
100
,I 120
I 140
I 160
T,~ (~C) Figure 6 Circulation ratio against absorber temperature for the given generator temperatures with and without pressure loss consideration
T c = 25°C
0.45
Figure 6 Taux de circulation en fonction de la temp&ature de l'absorbeur pour les tempOratures de gOn~rateur donnOes, en tenant compte ou non des pertes de pression
0.400.35 0.30 r)
0.25
0.20 Tg°C 60 0"15 I
70
o.10~
I
6o
8o
i
90
Zero press, drop - - With press, drop I 1 I 100 120 140 160 T~ ( C )
Figure 5 COP versus absorber temperature for the given generator temperatures with and without pressure loss consideration
Figure 5 COP en fonction de la temp&ature de l'absorbeur pour les tempgratures de gdn~rateur donn~es, en tenant compte ou non des pertes de pression
piping. A COP of 0.4 or more is attainable through a range of Ta from 90°C to 135 °C for Tg = 90°C. The concept of absorber cut-out temperature may also be considered here. Absorber temperature should not exceed the value at which COP drops sharply beyond an economically acceptable value. The peak value of COP at a lower generator temperature is higher than that at a higher temperature for the following reasons. The generator pressure, which is the low-side pressure, depends on the condenser temperature, and the absorber pressure, which is the high-side pressure, depends on the evaporator temperature. The latter is equal to the generator temperature. Therefore a low generator temperature means a low absorber pressure, which leads to a better COP. Also, it is well known that, for a constant evaporator temperature, COP increases with the generator temperature. Hence one can argue that the effect of the evaporator
temperature when the latter is equal to the generator temperature will override the effect of generator temperature. It is worth mentioning that the difference in concentrations between strong and weak solutions at low temperatures of the generator and the evaporator is smaller than that at higher values. This leads to large flowrates of weak solution, mr. For a given Tg, as Ta increases from a value close to Tg, mr decreases owing to the variations in concentration and enthalpies. Consequently, a slight reduction in both Qg and Qe takes place, which leads to a slight increase in COP. Maximum value of COP is attained at minimum value of mr . Then mr increases, as shown in Figure 4, and consequently COP decreases as Ta increases. At higher values of Ta, mr attains higher values and results in a steep rise in Qe and Qg, which produces a steep reduction in COP. Figure 6 shows the variations in circulation r a t i o f as a function of Ta for the given values of Tg. Increasing the absorber temperature leads to increasingf to undesirable values. The higher the generator temperature, the larger the range of Ta through which moderate values o f f are maintained. The pressure drop in piping reduces this range. (Let T~ - 90 ° C , f < 4 for Ta up to 138 °C and up to 131 °C wit~a pressure drop consideration.)
Effect of condenser temperature As the temperature of the heat sink is lowered, the range of absorber temperature through which heat duties (Qg, Qe and Qc) are kept almost constant is increased, as shown in Figure 7. This means that the absorber cut-out temperatures (based on Qg, Qe or Qc) are increased. The rise in cut-out temperature is nearly equal to the drop in condenser temperature. For a given absorber temperature, the duty of each of the condenser and evaporator is reduced, owing to lowering condenser temperature. Figure 8 shows the variations in both COP and circulation ratio f as a function of Ta for the given condenser temperatures. Decreasing the condenser temperature enhances the COP and increases the range
a a~.
I. 114. I s m a i l
140
!11~ '1 30
140
!~ Il ,~
,30
!: it !:
120
T¢,:35
,3o
Qg
120
L-.;~Q~
f
. , "~|
!! ill:,
E=0.8
1
II/:#:l
~
•%'1" // , /×""1
IO0
9°
./~;., , , /~ /~o/~
.,>-.-";-.'" )j..i 70
-
- ~
60
./,:/,/.ql I
_
..;;'?.;¢ / I
~" / ["4
~,.
/07J_/_
- ~ "- ~." f , " ,
,t"
0.810.9
70
I 90
I 100
I I10
I 120
i 130
I 140
60
I
J
90
100
,
I
I
t
I
110
120
130
140
T a (°C)
Ta (°C)
Figure 7 Qg, Qe and Qc as a function of absorber temperature for the given condenser temperatures
Figure 9 Q~, Qe and Qc as a function of absorber temperature for the given effectiveness of MHE and RHE exchangers Figure 9 Qg, Qe et Qc en fonction de la temperature de l'absorbeur pour des e~cacit~s donndes des ~changeurs M H E et R H E
Figure 7 Qg, Qe et Qc en fonction de la temperature de l'absorbeur pour des temperatures donn~es de condenseur
r,~,,.,.....
c o P ~ /
16
,
135
0.,*5
,30
0.40 14
0.351
,,_
12 II Zeropress. drop / 1 1 ~
0.30
!0
~ 0.25 0.20
--
0.15
_
6
4 0.10
'
_
80
2O
~ .'-.~// o o c I
90
I
I
100 II0 T a (°C)
aa
-,
, 120
', ; Vl 'l"~0.gl
'°
s
" Io,l
,
o.,oF |
,
,E=0.9 A~ 1~'r"l
-
25 130
/
I ~"12 0.201"-
.'/,~J,."~ ,' ," Ii OI / ",,ZP"/
Z~mp~.,L,op 1,~. 1, ,1.~ ,V, --With'press. drop ~\1~ A
0.301-025~
lilt ,vll /~/1 / f
2
X V
I
140
Figure 8 COP and f versus absorber temperature for the given condenser temperatures with and without pressure loss consideration Figure 8 COP et f e n fonction de la tempkrature de l'absorbeur pour des ternpdratures de condenseur donn~es, en tenant compte ou non des pertes de pression
of absorber temperature for high COP. Also, the value of f is reduced by lowering the condenser temperature. It is clear that there is an absorber cut-out temperature for each condenser temperature at which COP drops sharply. The cut-out temperature gets lower values as the pressure drop is taken into account. When accounting for the pressure drop in the piping, the absorber pressure will be less than the evaporator pressure by the value of the pressure drop for the pipes in between. Also, the pressure in the generator will be greater than the condenser pressure by the amount of pressure drop in the piping between them. Accordingly, the pressure difference between absorber and generator will be less
.-f~
~
,;
|
1
I
I
I
I
I
so
9o
1oo
~1o
12o
13o
m40
T a (°C) Figure 10 COP and f versus absorber temperature for the given effectiveness of MHE and RHE exchangers Figure 10 COP et f en fonction de la tempdrature de l'absorbeur pour des efficacitds donndes des dchangeurs M H E et RHE
than the case of zero pressure drop. This is the reason for having a better COP when pressure drop is taken into consideration. This is valid for values of Ta close to Tg and up to a certain value of Ta for which COP takes the same value for both cases. This temperature depends on the value of Tc and exchanger effectiveness as shown in F i g u r e s 8 and 10. Beyond this value of Ta, COP with pressure drop becomes less than COP without pressure drop. For values of Ta close to Tg, Qg and Qe with pressure drop have lower values than without pressure drop. As Ta increases the circulation ratio increases. In the case of pressure drop consideration, f increases more
Upgrading of heat through absorption heat transformers significantly than that of zero pressure drop, as shown in Figure 6. This results in a relatively rapid reduction in COP with pressure drop till the two values o f COP become equal, as shown in Figures 8 and 10. At this point, the effect of circulation ratio overrides the effect of reduced pressure difference (Pa - Pg). It is worth noting that while f is increasing with Ta, (Pa - Pg) is constant for given values of Te and To.
2
Effect o f effectiveness o f heat exchangers
6
Variations in the duties of condenser, evaporator and generator for the effectiveness of M H E and R H E exchangers as a function of absorber temperature are shown in Figure 9. The higher the effectiveness of both M H E and RHE, the larger the range of absorber temperature through which moderate duties of condenser, evaporator and generator are required. Also, for a given absorber temperature, as the effectiveness increases the duty of each of evaporator and condenser decreases, Figure 9 represents the case of no pressure loss in piping. Reduction in heat exchanger effectiveness leads to an increase in Qe and Qg, especially at high values of Ta, and consequently the absorber cut-out temperatures based on reasonable values of Qg, Qe or Qc will be reduced. Figure 10 shows COP a n d f as a function of T~ for the given exchanger effectiveness. Increasing the effectiveness of M H E and R H E increases the operating range of absorber temperature for high COP. High effectiveness produces high COP of AHT. Pressure drop in piping reduces this effect. The value o f f does not depend on the effectiveness of exchangers.
Conclusion A parametric study of A H T was carried out in this work. COP, f and duties of generator, evaporator and condenser were calculated for a required upgraded heat rate at the absorber. Better COP and a wide range of upgraded heat temperature (extracted from the absorber) can be achieved with high generator and evaporator temperatures and low condenser temperature. Under the given operating conditions, the absorber temperature can be increased up to a certain value equal to the lowest limit of the following: 1. cut-out absorber temperature, defined by the economical size or capacity of the condenser and evaporator; 2. the limit of the absorber temperature, identified by an acceptable value of COP and circulation ratio f ; 3. variations in the above limits due to variations in condenser temperature, especially for units using aircooled condensers; 4. variations in those limits due to reduction in effectiveness of M H E and R H E exchangers during operation, which may be due to scaling as an example.
3 4 5
7 8 9 l0
445
Ziegler,B., Trepp, Ch. Equation of state lbr ammonia-water mixtures Int J Refrig (1984) 7 (2) 101-106 Bourseau,P., Bugarei, R. Refrigerationpar cycle~ absorptiondiffusion: comparaison des performances des syst~mes NH 3H20 et NH3-NsSCN Int J Refrig (1986) 9 206-213 An-JinMing Optimizationof ammonia absorption refrigeration process: effectsof seasonal ambient temperaturefluctuationsInt J Refrig (1991) 14 341-344 Avares,S. G., Trepp, Ch. Simulation of a solar driven aquaammonia absorption refrigerationsystem,Part 1: Mathematical description and systemoptimization Int J Refrig (1987) 10 40 48 Herold,K.E., Han, K., Moran, M. J. Ammwal: a computer program for calculatingthe thermodynamicproperties of ammonia and water mixtures using a Gibbs free energy formulation ASME Winter Annual Meeting (1988) AES 4 65-75 Ataer,O. E., Gogus,Y. Comparativestudy of irreversibilitiesin an aqua-ammonia absorption refrigerationsystem Int J Re[rig (1991) 14 86-92 Cohen,G., Rojey, A. Valorisation de chaleur fi bas niveau thermique Revue de I'Institut Franfais du Pktrole (1981) 36 (3) 349-365 Bogart,M. Ammonia Absorption Refrigeration in Industrial Processes Gulf Publishing Company (1981) George,J. M., Murthy, S. S. Experimentson a vapour absorption heat transformer Int J Refrig (1993) 16 (2) 107-119
Appendix A Power of weak solution pump = vim 1(Pa - Pg) Power of refrigerant pump v9m9(P a Pg) Total pump power = vlmlAP + v9m9AP = m 9 A P ( m l v l / m 9 + V9) = m9AP[( f - l)vl +v9] = m 9 A P [ f v l - (Vl - Vg)] where A P = (Pa - Pg), f = mr/m7, m 9 = m 7 and m6 = ml + m 7, For large values of f , say f > 5, the term (Vl - v 9 ) could be neglected, and then the pump power becomes directly proportional to the circulation r a t i o f for a given AP.
Appendix B g l = hloR _ TR SIR q_
-- TR
T,,R
/ TR
d R d TR ToR
CIpR/TR dTR + (A, + A3TR + A4T2R)
X (PR - PoR) + A2(P 2 - P2oR)/2 where C~R = Bl + B2TR + B3T 2
g~ = hVR - TRSoR -l-
C;~ d T R ToR
-
-
~ R / T R dTR + T R In(PR/PoR )
TR ~oR
+ CI(PR - PoR) + C 2 ( P R / T 3 -- 4PoR/7o3R
References
+ 3PoRTR/T4oR) + C3(PR/T~t' - 12PoR/Tlo 1 12
Franzen, P. Warmetransformateur erzeugt Nutzwarme aus Abwarme Erdol und Kohle Erdgas Petrochemie (1979) 32 (11) November
3
11
3
11
+ l l P o R T R / T o R ) + C 4 ( P R / T ~ -- 12PoR/ToR 3
12
+ l lPoRTR/ToR)/3
446
I. M. Isma#
w h e r e CpV~ = D 1 + D2TR + D3 T2. gexR = .2(1 -- .2){E 1 -k- E2P R + ( E 3 -k- E4PR)TR
+ Es/TR + ~6/T~ + (2.2 - 1)[E7 + E8PR
+ (E9 + E~oP~)TR + E ~ / & + t:~2/T~J + ( 2 ~ - 1)2[E13 + El4P R -~_EI5/TR Values o f coefficients are given in ref. 2.
_j_ EI6/T2]}