Appendix A
Thermodynamic Properties of Ammonia-Water Mixture
A.1 INTRODUCTION
Ammonia-water mixture is a working fluid used in Kalina cycle system
(KCS) and vapor absorption refrigeration (VAR) plants. Unlike for pure components,
binary mixtures additionally need mixture concentration to assess thermodynamic
properties. In ammonia-water mixture, ammonia will boil at low temperature as it has
low boiling point. Ammonia-water mixture as zeotropic nature will have the tendency
to boil and condense at a range of temperatures possessing a closer match between
heat source and working fluid mixture. Thermodynamic properties have been
generated from correlations and derivations and formed as MATLAB subroutines.
These properties are used in thermodynamic evaluation of KCS plants. The
temperature-concentration, specific volume-concentration, enthalpy-concentration,
entropy-concentration and exergy-concentration graphs for ammonia-water mixtures
are plotted up to 100 bar pressure.
A.2 THERMODYNAMIC PROPERTIES
The first step in evaluating thermodynamic properties of ammonia-water
mixture is to find the bubble point temperature (BPT) and dew point temperature
(DPT). With BPT and DPT, specific volume, specific enthalpy, specific entropy and
specific exergy values of saturated liquid and vapour properties are predicted. The
available correlations are used for the evaluation of properties (Ziegler and Trepp,
1984; Patek, 1995; Xu and Goswami, 1999 and Alamdari, 2007). These correlations
will help in avoiding the tedious iterations required in the complicated fugacity
method.
A.2.1 BUBBLE AND DEW POINT TEMPERATURES
Figure A.1 shows the details of bubble point and dew point temperature
variations with ammonia concentration at a fixed pressure. The loci of all the bubble
points have called as the bubble point curve and the loci of all the dew points have
126
called as the dew point curve. The bubble point curve is the saturated liquid line and
the dew point curve is the saturated vapor line and the region between the bubble and
dew point lines is the two-phase region where both liquid and vapor coexist in
equilibrium. The region below the saturated liquid line is sub cooled liquid region and
the region above the saturated vapor line is superheated vapor region.
The bubble and dew point temperatures of the ammonia-water mixture have
been determined from the equations (1) and (2). The coefficient values for equations
A.1 and A.2 are given in table A.1 and A.2 respectively for bubble point temperature
and dew point temperature.
Tb P, x   T0  a i 1  x 
mi
i
Td P, y   T0  a i 1  x 
mi
i
  P0
ln  P
 
  P0
ln  P
 






ni
(A.1)
ni
(A.2)
Fig.A.1 Property regions on temperature-concentration diagram for ammonia-water
mixture at constant pressure
127
Table A.1 Coefficients for equation (A.1) to determine bubble point temperature
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
mi
0
0
0
0
0
1
1
1
2
4
5
5
6
13
ni
0
1
2
3
4
0
1
2
3
0
0
1
0
1
ai
+0.322302  101
-0.384206  100
+0.460965  10-1
-0.378945  10-2
+0.135610  10-3
+0.487755  100
-0.120108  100
+0.106154  10-1
-0.533589  10-3
+0.785041  101
-0.115941  102
-0.523150  10-1
+0.489596  101
+0.421059  10-1
Table A.2 Exponents and coefficients of equation (A.2) to determine dew point
temperature
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
mi
0
0
0
0
1
1
1
2
2
3
3
4
4
5
5
6
7
ni
0
1
2
3
0
1
2
0
1
0
1
0
2
0
2
0
2
128
ai
+0.324004  101
-0.395920  100
+0.435624  10-1
-0.218943  10-2
-0.143526  101
+0.105256  101
-0.719281  10-1
+0.122362  102
-0.224368  101
-0.201780  102
+0.110834  101
+0.145399  102
+0.644312  100
-0.221246  101
-0.756266  100
-0.135529  101
+0.183541  100
Start
Input of P, T and x
BPT and DPT
Properties of ammonia (liquid and vapor)
Properties of water (liquid and vapor)
Properties of ammonia and water mixture (liquid and vapor)
Yes
Assign properties of liquid
mixture (saturated)
Yes
Assign properties of liquid
mixture (sub-cooled)
Yes
Assign properties of vapor
mixture (saturated)
T = BPT
No
T < BPT
No
T = DPT
No
Yes
T > BPT and T < DPT
BPT
No
T > DPT
Yes
Assign properties of
liquid vapor mixture
Assign properties of vapor
mixture (superheated)
Property data and charts
End
Fig.A.2 Flowchart for thermodynamic properties of ammonia-water mixture at five
regions
129
Figure A.2 shows the flowchart to solve the properties in the five regions viz: sub
cooled region, saturated liquid region, two-phase region, saturated vapor region and
superheated region.
The actual state out of five regions has been identified from the given
temperature, pressure and concentration. It can be done by comparing the temperature
with bubble point and dew point temperatures. If the temperature is less than the
bubble point temperature, the region is sub cooled or compressed liquid. If the
temperature is equal to the bubble point temperature, it is a saturated liquid region. In
case the temperature lies between bubble point temperature and dew point
temperature, the region is liquid-vapor mixture. Saturated vapor region is the one
obtained when the temperature obtained is equal to the dew point temperature.
Finally if temperature exceeds the dew point temperature, it is a superheated region.
A.2.2 SPECIFIC ENTHALPY AT LIQUID PHASE
The energy and exergy properties have derived from Gibbs free energy
function. In liquid phase the Gibbs free energy for both liquid and gas phases have
determined from equations (A.3) and (A.4), respectively.
h m  xh m
L
NH
 (1  x) h L
H O
2
3
 hE
(A.3)
The following equations (A.4) to (A.14) have specified the liquid enthalpy
calculation. TB=100 K, PB=10 bar, Tr=T/ TB, Pr=P/ PB respectively.
 
h  RTB Tr2 
 Tr
 Gr

 Tr


 Pr
(A.4)
 Cp 
G  h o  Tso   C p dT   vdp T   dT
T 
To
Po
To 
T
P
130
T
(A.5)

Gr
L

Gr
Tr
L



B3 3
B2 2
 L

L
2
3


h

T
s

B
T

T

T

T

Tr  Tro 
ro
r
ro
1
r
ro
r
ro

2
3


 Tr 
B3 2


2
  B 2 Tr Tr  Tro  
 B1Tr ln 
Tr  Tro Tr 

2
 Tro 




A
2
2
2
 A1  A 3 Tr  A 4 Tr Pr  Pro   2 Pr  Pro

2







2
 h ro L
 T  B 
T  B
L
 s ro  B1 1  ro   2  Tr  ro   3

Tr  2 
Tr  3

 Tr

T 
B

2
2
  B1 ln  r   B 2 Tr  Tro   3 Tr  Tro 
T
2
 ro 

 A

 1  A 3  A 4 Tr Pr  Pro   A 2 Pr 2  Pro 2


 Tr
2Tr






(A.6)
 2 Tro 3 
 Tr 



T
r










(A.7)
 h ro L
T 2  B
T  B
B
 2  B1  ro2   2  B 2  ro 2   1  B 2  3 2Tr 

L
3
  G r   Tr
 Tr  2
 2Tr  Tr


Tr  Tr   B  T 3 

A1 
A2
2
2
3  ro 






B
T

A

P

P

Pr  Pro
3
r
4
r
ro
2 
2
 3 T2 

Tr 
2Tr

 r 


2   Gr

Tr
Tr  Tr



B
B

L
2
2
3
3
 h  B1 Tro  Tr   2 Tro  Tr  3 Tro  Tr
  ro
2
3
  
  A T 2  A P  P   A 2 P 2  P 2
4 r
1
r
ro
r
ro

2







B
B

L
2
2
3
3
 h ro  B1 Tro  Tr   2 Tro  Tr  3 Tro  Tr


2
3
h L  RT B 
A
 A T 2  A P  P   2 P 2  P 2
4 r
1
r
ro
r
ro

2




















(A.8)
(A.9)
(A.10)
The above equation (A.10) is used for finding liquid enthalpy for water and ammonia.
The Gibbs excess energy GrE for liquid mixtures has been expressed in equation A.11


G r  F1  F2 2x 1  F3 2x 1 1  x 
E
2
F1  E1  E 2 Pr  E 3  E 4 Pr Tr 
E5 E6

Tr Tr 2
F2  E 4  E 8 Pr  (E 9  E10 Pr )Tr 
131
E11 E12
 2
Tr
Tr
(A.11)
(A.12)
(A.13)
F3  E 13  E14 Pr 
E 15 E 16
 2
Tr
Tr

 
h  RTB Tr 

 Tr
E
2
 GrE

 T
 r
(A.14)




 Pr ,x
(A.15)


2E 5 3E 6 
 2  
 - E1  E 2 Pr 

Tr
Tr 





2E11 3E12  

E
h  RTB (1  x )(2x  1) - E 7  E 8 Pr 
 2   
T
Tr  
r




(2x  1) 2  - E  E P  2E15  3E16 
14 r
2
 13

Tr
Tr 



(A.16)
A.2.3 SPECIFIC ENTHALPY AT VAPOR PHASE
Similarly the equation of state for pure component in the vapor phase has
identified in the following equation.
h mv  xh vNH3  (1  x) h Hv 2O
(A.17)
For the gas phase, Gibbs free energy equation is given below:

Gr
v



D3 3
D2 2
 v

v
2
3
h ro  Tr s ro  D1 (Tr  Tro )  2 Tr  Tro  3 Tr  Tro 


 Tr 
 Pr  
D3

2
2
D1Tr ln  T   D 2 Tr (Tr  Tro )  2 (Tr  Tro )  Tr ln  P   
 ro 
 ro  




P

 (A.18)
4
P
3
P
T
C1 Pr  Pro   C 2  r3  ro3  ro 4 r  

 Tr

T
T


ro
ro




  Pr 12Pro 11Pro Tr  C 4  Pr 3 12Pro 3 11Pro 3 Tr  


 



C 3  11 
11
12 
11
11
12


 
Tro
Tro  3  Tr
Tro
Tro
  Tr
 
132
2
3
 h ro v

Tro  D 3  2 Tro 
 Tro  D 2 
v





 
 s ro  D1 1 
Tr 

Tr 




T
2
T
3
T
 Tr

r 
r 
r 





2




Tro
T 
D
  ln  Pr  
 D1 ln  r   D 2 Tr  Tro   3  Tr 

P 


v
T
2
T


ro
r
ro




Gr




 (A.19)
Tr
 P



 C1
4Pro
3Pro 
12Pro 11Pro 
 r
 Pr
 Pr  Pro   C 2  4  3  4   C 3  12  11  12 
Tro Tr Tro 
Tro Tr Tro 
 Tr
 Tr
 Tr


3
3
3
12Pro
11Pro 
 C 4  Pr


 12 


12
12

Tro Tr
Tro 
 3  Tr

2
3
 h ro v
T 
T  D  T  D 
 1 
 2  D1  ro2   2 1  ro2   3  2Tr  ro2   D1  
 T 
T  2 
 Tr
Tr  3 
Tr 
 r
 r 



2
v








Tro
D
4P
C
4P
  Gr  
  D 2  3 1  2   12 Pr  Pro   C 2   5r  3 ro 2    (A.20)
 T
Tr  Tr  
2 
Tr  Tr
Tro Tr  
r






3
3



12
P

12
P
   12Pr

12Pro  C 4 
ro
r


C 3  13  11 2  

13
11
2
Tro Tr  3  Tr
Tro Tr 
  Tr



Tr
2
  G r
Tr  Tr

v



 pr


  G r
Tr  Tr

v



 pr

D3
D2 2

v
2
3
3
 h ro  D1Tro  2 Tr  Tro  3 2Tr  Tro

 D T  D T 2  D 3 T 2  T 2  C P  P  
2 r
r
ro
1 r
ro
 1 r
2

  12P 12P 
 RTB   4Pr 4Pro 
r

C



C
 11ro 
3
 2
3
3
11


T
T
T
Tro 
ro 
  r
 r

3
3
 C 4   12Pr 12Pro 
 3  T 11  T 11 

ro
 r


2



h v  RTB Tr

D3
D2 2


v
2
3

h

D
T

T

T

2Tr3  Tro 
ro
1
ro
r
ro

2
3


D T  D T 2  D 3 T 2  T 2  C P  P  

2 r
r
ro
1
r
ro
 1 r

2


  12P 12P 
   4Pr 4Pro 

ro 
r

C 2   3  3   C 3  11  11 

T
Tro 
Tro 
  Tr

 r


3
3
 C 4   12Pr 12Pro 


 3 

11
11 
Tro 


 Tr
133

(A.21)












(A.22)
A.2.4 SPECIFIC ENTROPY AT LIQUID AND VAPOR PHASES
The molar entropy of the liquid and vapor phases is specified and simplified
from equation (A.23) to (A.33).
 G
s  R  r
 T
 r



 Pr
(A.23)


 Tr

B3  2 
B2
L



s

B

(
2
T
)

3
T

B
ln

1





1
r
1
G r

2
3  r 
 ro

 Tro


 (A.24)
Tr
B


B 2T  T   3 3T 2  T 2  (A  2A T ) (P  P )


r
ro
3
4 r
r
ro 
 2
r
ro 
2




L
 G L
 r
L
s  R 
 T
r







Pr


 
B2
L
2Tr   B3  3Tr 2    B1 ln Tr  1 
 s ro  B1 
2
3 
Tro
 
 



B3  2


2 
 R B 2 2Tr  Tro  
 3T  T  

r
ro
2 



 A  2A T P  P 

4 r
r
ro
 3



(A.25)


 G E
s E  R  r
 Tr
G r
Tr
E



 Pr,x
(A.26)


E
2E 
E
2E 
 E 3  E 4 Pr  52  36   (2x  1) E 9  E10 Pr  112  12

3 


Tr
Tr 
T
T
r
r


 1  x 

 E



2
E
2
15
16 
 (2x  1)   2  3 

Tr 


 Tr
(A.27)
134
 G r E
s E  R 
 Tr




 Pr,x


E
2E 
 E 3  E 4 Pr  52  36  



Tr
Tr 





E
2E 
 R 1  x (2x  1) E 9  E10 Pr  112  12
3 

T
T
r
r





 E



2
E
2
15
16 
 (2x  1)   2  3 

Tr 


 Tr
s mix  Rx ln( x )  (1  x ) ln(1  x )
s mL  xs aL  (1  x )s Lw  s E  s m ix
G
V
r
Tr







T 
 s V  D1  D 2 Tr  D 3 T 2  D1 1  ln r   D 2 2Tr  Tro 
r
Tro 
 ro








 3P
P 
3P 
 D3  2

2 
ro
r 
r


 
 C 

 3T  T   ln

r
ro
2


4
4
 T

P

T
 2 

 ro 

r
ro 






 11P 3 11P 3 
  11P 11P 


r
ro
C 4 
C  

ro 
r





 3

12
12 
12
12

3  T
T
T

  Tr



ro
r
ro



 

 G r V
v
s 
 Tr




Pr


Tr  
V
2
 
 s ro  D1  D 2 Tr  D 3 Tr  D1 1  ln
T
ro

 


P  
D3  2


2
 r  
D 2 2Tr  Tro   2  3Tr  Tro   ln  P  


 ro  













3P
3P
11P 11P
 R 

ro 
ro 
r
r


 C3 

 
 C 2  4 
 T
 T 12 T 12 
T 4 





r
r
ro
ro






 

3
11P 3 
  11Pr

ro
C4  



 3 

12
12 
T

  Tr

ro

 

s mv  xs aV  (1  x )s Vw  s m ix
135
(A.28)
(A.29)
(A.30)
(A.31)
(A.32)
(A.33)
A.2.5 SPECIFIC VOLUME AT LIQUID AND VAPOR PHASES
The specific volume of the liquid and vapor phases is simplified from
equation (A.34) to (A.43).
RTB
PB
v
G r
RTB
v 
PB
 G r L

 Pr

2
Pr

(A.35)

  RTB A  A T  A T 2  A P
1
3 r
4 r
2 r

PB
 Tr


RTB
v 
PB
E
(A.34)
 A1  A 3 Tr  A 4 Tr  A 2 Pr
E
G r


 Tr

L
Pr
L
 G r

 Pr
 G r E

 Pr

(A.36)



 Tr , x
(A.37)
 E 2  E 4 Tr   2x  1E 8  E10 Tr   2x  1 1  x E14 
2
E
RTB  G r
v 
PB  Pr

E

  RTB

PB
 Tr
E
(A.38)


 E 4 Tr   2x  1E 8  E10 Tr   2x  1 E14  1  x 
2
2
(A.39)
vLm  xvaL  (1  x)vLW  vE
(A.40)
G Vr
T
C
C
C P2
 r  C1  32  113  411r
Pr
Pr
Tr Tr
Tr
(A.41)
RTB
v 
PB
v
 G r V

 Pr


  RTB

PB
 Tr
2
T
C P 
 r  C  C 2  C3  4 r 
1
3
11
11
 Pr
Tr
Tr
Tr 

v mv  xv av  (1  x ) v vw
136
(A.42)
(A.43)
Table A.3 Coefficients for the equations for the pure components
Coefficient
A1
A2
A3
A4
B1
B2
B3
C1
C2
C3
C4
D1
D2
D3
hL
hv
sL
sv
Tro
Pro
Ammonia
Water
3.971423  10-2
2.748796  10-2
-1.790557  10-5 -1.016665  10-5
-1.308905  10-2 -4.452025  10-3
3.752836  10-3 8.389246  10-4
1.634519  101
1.214557  101
-6.508119
-1.898065
1.448937 2.911966  10-2
-1.049377  10-2 2.136131  10-2
-8.288224 -3.169291  101
-6.647257  102 -4.634611  104
-3.045352  103
0.0
3.673647
4.019170
9.989629  10-2 -5.175550  10-2
3.617622  10-2 1.951939  10-2
4.878573
21.821141
26.468879
60.965058
1.644773
5.733498
8.339026
13.453430
3.2252
5.0705
2.0000
3.0000
The coefficient values for equations A6, A.12, A.13, A.14, A.18, A.24, and
A.31, are given in table A.3 and A.4.
Table A.4 Coefficients for the equations used for Gibbs excess energy function
Coefficients
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10
E11
E12
E13
E14
E15
E16
-41.733398
0.02414
6.702285
-0.011475
63.608967
-62.490768
1.761064
0.008626
0.387983
0.004772
-4.648107
0.836376
-3.553627
0.000904
21.361723
-20.736547
137
Fig.A.3 Bubble and dew point temperature up to 100 bar
Fig.A.4 (a) Specific volume of saturated liquid and (b) Specific volume of saturated
vapor
138
Fig.A.5 Ammonia-water enthalpy concentration diagram
Figure A.3 is the plot for bubble and dew point temperature up to 100 bar
pressure. Figure A. 4(a) shows the changes in saturated liquid specific volume with
ammonia mass fraction at various pressures. The specific volume has been calculated
at bubble point temperature for the given pressure and ammonia mass fractions. The
trend increases with the increase in pressure. Similarly Fig A.4(b) is the saturated
vapor specific volume diagram. It is generated with the bubble point temperature and
vapor ammonia mass fraction.
139
Fig.A.6 Ammonia-water entropy concentration diagram
Figure A.5 is an enthalpy-concentration plot as function of ammonia mass
fraction, at a fixed pressure.
140
Fig.A.7 Ammonia-water exergy concentration diagram
The upper curve is the vapor curve, resulted from liquid concentration and
dew point temperature. The lower curve is the liquid enthalpy plot, resulted from the
bubble point temperature and liquid ammonia concentration. The auxiliary curve is
resulted from bubble point temperature and vapor ammonia concentration. The
curves are generated from 0.2 bar to 100 bar pressure.
141
Figure A.6 is an entropy-concentration plot as function of ammonia mass
fraction and pressure. The entropy values are decreasing with increase in pressure, in
liquid and vapor regions.
Exergy analysis is the maximum useful work resulted from iteration of a
system with equilibrium state.
E = h - Tos
(A.44)
The exergy - concentration plot for ammonia-water mixture at various
pressures is shown in figure A.7. In liquid region, the curves are widened at low
concentration side.
A.3
ALGORITHM TO FIND THE PROPERTIES OF AMMONIAWATER MIXTURE
The algorithm has been prepared to find the property regions for thermodynamic
properties generation using MATLAB codes.
%DIFFEENT PHASES OF AMMONIA-WATER MIXTURE
if(((T-Tbp)>=-0.05)&&((T-Tbp)<=0.05))||(T==Tbp)
%1. saturated liquid mixture
df=0;
RGN=1;
elseif(T<Tbp&&T<Tdp)
%2. sub cooled liquid mixture
df=0;
RGN=2;
elseif(((T-Tdp)>=-0.05)&&((T-Tdp)<=0.05))||(T==Tdp)
%3. saturated vapor mixture
df=1;
RGN=3;
elseif(T>Tbp&&T<Tdp)
%4. liquid-vapor mixture
RGN=4;
elseif(T>Tdp)
%5. superheated mixture
df=1;
RGN=5;
end
switch(RGN)
case 1
hm=(1-df)*hf+df*hg2;
sm=(1-df)*sf+df*sg2;
vm=(1-df)*vf+df*vg2;
Tdp=Tdp-273.15;
Tbp=Tbp-273.15;
case 2
142
if(((Tbp-Tdp)>=-1)&&((Tbp-Tdp)<=1))
df=1;
end
hm=(1-df)*hf+df*hg2;
sm=(1-df)*sf+df*sg2;
vm=(1-df)*vf+df*vg2;
Tdp=Tdp-273.15;
Tbp=Tbp-273.15;
hg1=0;
hg2=0;
case 3
hm=(1-df)*hf+df*hg2;
sm=(1-df)*sf+df*sg2;
vm=(1-df)*vf+df*vg2;
Tdp=Tdp-273.15;
Tbp=Tbp-273.15;
case 4
%AMMONIA-WATER LIQUID MIXTURE
hm=(1-df)*hf+df*hg2;
sm=(1-df)*sf+df*sg2;
vm=(1-df)*vf+df*vg2;
Tdp=Tdp-273.15;
Tbp=Tbp-273.15;
case 5
hm=(1-df)*hf+df*hg2;
sm=(1-df)*sf+df*sg2;
vm=(1-df)*vf+df*vg2;
Tdp=Tdp-273.15;
Tbp=Tbp-273.15;
end
A.4 AQUA-AMMONIA TABLES
A.4.1 BUBBLE AND DEW POINT TEMPERATURES
From Patek and Klomfar (1994) equations, the bubble and dew point
temperatures have been calculated and tabulated in Table A5 and Table A6
respectively. The specific enthalpy, specific entropy, specific volume and specific
exergy values are tabulated using Xu and Goswami (1999) mathematical relations
(Table A7 to A12).
143
Table A.5 Bubble point temperature, ºC
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
100
0
60.50
76.10
86.02
93.48
99.53
120.00
143.47
158.85
170.59
180.06
198.96
213.14
234.96
251.68
265.39
277.10
287.38
296.57
304.90
312.53
0.1
29.59
45.25
55.22
62.71
68.78
89.31
112.81
128.18
139.90
149.32
168.17
182.26
203.95
220.55
234.15
245.77
255.96
265.06
273.31
280.87
0.2
10.25
24.94
34.34
41.42
47.17
66.70
89.15
103.87
115.13
124.16
142.32
155.87
176.80
192.83
205.98
217.21
227.07
235.89
243.87
251.20
0.3
-6.71
7.00
15.83
22.50
27.94
46.44
67.82
81.89
92.66
101.30
118.74
131.76
151.90
167.35
180.04
190.89
200.42
208.93
216.66
223.74
0.4
-22.51
-9.54
-1.17
5.17
10.34
28.01
48.49
62.00
72.36
80.67
97.49
110.04
129.51
144.45
156.73
167.24
176.47
184.72
192.22
199.09
0.5
-36.09
-23.70
-15.68
-9.59
-4.63
12.35
32.08
45.13
55.14
63.17
79.45
91.61
110.48
124.98
136.90
147.11
156.07
164.10
171.38
178.06
0.6
-46.43
-34.49
-26.75
-20.88
-16.08
0.32
19.41
32.04
41.74
49.53
65.31
77.12
95.45
109.54
121.14
131.07
139.80
147.61
154.70
161.21
0.7
-53.26
-41.67
-34.17
-28.48
-23.84
-7.93
10.56
22.80
32.21
39.78
55.10
66.58
84.40
98.11
109.40
119.06
127.56
135.17
142.08
148.42
0.8
-57.14
-45.86
-38.57
-33.04
-28.53
-13.10
4.83
16.71
25.84
33.19
48.07
59.23
76.55
89.89
100.88
110.29
118.57
125.99
132.72
138.90
0.9
-59.25
-48.22
-41.12
-35.74
-31.35
-16.37
1.03
12.55
21.41
28.54
42.99
53.82
70.67
83.64
94.33
103.50
111.56
118.78
125.34
131.37
1
-60.78
-49.96
-43.03
-37.79
-33.52
-18.96
-2.08
9.09
17.68
24.60
38.62
49.14
65.50
78.11
88.51
97.43
105.28
112.32
118.71
124.58
144
Table A.6 Dew point temperature, ºC
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
100
0
60.50
76.10
86.02
93.48
99.53
120.00
143.47
158.85
170.59
180.06
198.96
213.14
234.96
251.68
265.39
277.10
287.38
296.57
304.90
312.53
0.1
60.99
75.79
85.26
92.41
98.22
117.93
140.48
155.17
166.31
175.40
192.95
206.24
226.25
241.38
253.68
265.10
273.19
281.26
288.53
295.17
0.2
57.77
72.39
81.75
88.81
94.54
114.00
136.25
150.75
161.76
170.73
188.06
201.19
220.96
235.91
248.07
258.37
267.35
275.33
282.53
289.09
0.3
54.69
69.01
78.16
85.07
90.69
109.74
131.55
145.77
156.57
165.38
182.40
195.30
214.74
229.45
241.41
251.55
260.39
268.24
275.33
281.80
0.4
51.53
65.47
74.38
81.10
86.56
105.09
126.32
140.18
150.70
159.29
175.90
188.50
207.48
221.86
233.56
243.48
252.13
259.82
266.76
273.09
0.5
48.01
61.57
70.21
76.72
82.01
99.94
120.47
133.86
144.04
152.35
168.42
180.63
199.02
212.96
224.30
233.92
242.32
249.78
256.52
262.67
0.6
43.76
57.03
65.43
71.74
76.84
94.11
113.82
126.65
136.41
144.36
159.75
171.43
189.05
202.40
213.27
222.50
230.54
237.70
244.16
250.06
0.7
38.27
51.44
59.65
65.77
70.71
87.27
106.02
118.17
127.39
134.90
149.41
160.41
177.00
189.57
199.80
208.48
216.06
222.80
228.88
234.44
0.8
30.74
44.03
52.14
58.10
62.87
78.65
96.22
107.51
116.03
122.96
136.29
146.39
161.58
173.08
182.43
190.37
197.29
203.45
209.01
214.09
0.9
19.26
32.75
40.72
46.46
50.99
65.66
81.57
91.62
99.14
105.23
116.90
125.69
131.87
148.84
156.93
163.80
169.78
175.11
179.91
184.30
1
-60.78
-49.96
-43.03
-37.79
-33.52
-18.96
-2.08
9.09
17.68
24.60
38.62
49.14
65.50
78.11
88.51
97.43
105.28
112.32
118.71
124.58
145
A.4.2 SPECIFIC ENTHALPY VALUES
Table A.7 Saturated liquid enthalpy of ammonia-water mixture, kJ/kg
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
100
0
252.4
317.87
359.54
390.93
416.44
503.1
603.6
670.1
721.4
763.78
847.17
911.92
1012.1
1090.4
1155.6
1212.1
1262.3
1307.6
1349.1
1387.5
0.1
55.87
121.49
163.19
194.56
220.03
306.6
406.9
473.6
525.2
567.94
652.36
718.27
820.96
901.73
969.48
1028.5
1081.1
1128.8
1172.6
1213.3
0.2
-91.72
-28.97
10.89
40.88
65.25
148.1
244.4
308.6
358.4
399.83
481.88
546.23
647.03
726.78
793.99
850.72
905.28
953.10
997.14
1038.1
0.3
-221.5
-160.7
-122.2
-93.23
-69.72
10.13
102.8
164.6
212.6
252.52
331.76
394.06
491.92
569.61
635.27
692.80
744.39
791.42
834.81
875.22
0.4
-332.5
-272.1
-234.0
-205.4
-182.3
-104.1
-13.80
46.24
92.76
131.40
208.19
268.56
363.48
438.95
502.82
558.87
609.19
655.12
697.54
737.08
0.5
-414.7
-353.7
-315.5
-286.9
-263.9
-186.4
-97.53
-38.71
6.75
44.46
119.28
178.05
270.42
343.88
406.09
460.70
509.78
554.59
596.01
634.65
0.6
-458.5
-397.1
-358.7
-330.2
-307.3
-230.3
-142.5
-84.67
-40.04
-3.07
70.19
127.68
217.99
289.80
350.63
404.05
452.08
495.95
536.51
574.36
0.7
-459.6
-398.9
-361.1
-332.9
-310.3
-234.5
-148.2
-91.39
-47.57
-11.27
60.64
117.07
205.75
276.29
336.07
388.59
435.83
478.99
518.92
556.18
0.8
-421.6
-363.2
-326.8
-299.7
-277.8
-204.3
-120.3
-64.77
-21.86
13.71
84.31
139.82
227.16
296.73
355.75
407.64
454.32
497.01
536.50
573.36
0.9
-355.1
-300.9
-266.8
-241.3
-220.6
-150.7
-69.87
-16.00
25.79
60.56
129.81
184.42
270.61
339.43
397.89
449.33
495.65
538.01
577.21
613.81
1
-274.0
-226.0
-195.2
-171.9
-152.9
-87.7
-10.99
40.80
81.30
115.15
182.93
236.66
321.80
390.00
448.03
499.15
545.20
587.34
626.35
662.78
146
Table A.8 Saturated vapor enthalpy of ammonia-water mixture, kJ/kg
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
100
0
2612.2
2639.0
2655.6
2667.7
2677.2
2708.1
2739.8
2758.3
2771.1
2780.6
2796.9
2807.1
2818.9
2824.8
2827.7
2828.6
2828.4
2827.3
2825.6
2823.5
0.1
1548.1
1634.1
1690.4
1732.5
1766.3
1876.0
1989.6
2056.1
2102.8
2138.3
2200.9
2243.2
2298.7
2334.4
2359.6
2378.2
2392.4
2403.5
2412.3
2419.4
0.2
1359.8
1406.5
1439.9
1466.4
1488.7
1567.3
1658.9
1717.4
1760.4
1794.5
1856.9
1900.9
1961.1
2001.5
2031.0
2053.5
2071.1
2085.3
2096.8
2106.3
0.3
1296.3
1327.5
1349.3
1366.6
1381.2
1433.8
1498.3
1541.6
1574.5
1601.1
1651.2
1687.6
1738.8
1774.0
1799.9
1819.8
1835.5
1848.1
1858.3
1866.7
0.4
1256.9
1282.5
1299.7
1312.9
1323.9
1362.7
1409.6
1441.2
1465.5
1485.2
1522.9
1550.5
1589.5
1616.3
1635.9
1650.6
1662.0
1670.7
1677.5
1682.7
0.5
1227.0
1250.0
1265.1
1276.5
1285.8
1317.6
1354.5
1378.6
1396.9
1411.7
1439.5
1459.6
1487.3
1505.6
1518.1
1526.9
1532.9
1536.8
1539.1
1540.1
0.6
1204.9
1226.5
1240.3
1250.7
1259.1
1287.1
1318.2
1337.7
1352.1
1363.5
1384.2
1398.5
1416.8
1427.4
1433.2
1436.0
1436.4
1435.0
1432.3
1428.5
0.7
1190.4
1210.9
1224.0
1233.7
1241.5
1267.1
1294.5
1311.1
1323.0
1332.0
1347.7
1357.7
1368.5
1372.5
1372.3
1369.4
1364.4
1357.8
1350.1
1341.2
0.8
1182.2
1201.8
1214.3
1223.5
1230.8
1254.7
1279.6
1294.2
1304.3
1311.7
1323.8
1330.4
1335.3
1333.7
1328.3
1320.3
1310.3
1298.9
1286.2
1272.5
0.9
1177.7
1196.7
1208.6
1217.4
1224.4
1246.9
1269.8
1282.9
1291.6
1297.7
1306.9
1310.9
1310.7
1304.3
1294.2
1281.4
1266.8
1250.6
1233.1
1214.7
1
1174.6
1192.9
1204.4
1212.8
1219.5
1240.7
1261.9
1273.5
1281.0
1286.0
1292.5
1294.0
1289.1
1278.0
1263.1
1245.5
1225.9
1204.7
1182.2
1158.6
147
A.4.3 SPECIFIC ENTROPY VALUES
Table A.9 Saturated liquid entropy of ammonia-water mixture, kJ/kg-K
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
0
0.83
1.03
1.14
1.23
1.30
1.52
1.77
1.93
2.05
2.14
2.32
2.45
2.65
2.80
2.92
3.02
3.11
3.19
3.26
3.32
0.1
0.46
0.68
0.80
0.90
0.97
1.22
1.49
1.66
1.78
1.89
2.08
2.23
2.45
2.61
2.74
2.86
2.96
3.04
3.12
3.19
0.2
0.14
0.35
0.48
0.58
0.66
0.91
1.18
1.36
1.49
1.59
1.79
1.95
2.17
2.35
2.49
2.61
2.71
2.81
2.89
2.97
0.3
-0.19
0.02
0.15
0.25
0.33
0.59
0.87
1.05
1.18
1.29
1.50
1.65
1.89
2.06
2.21
2.33
2.44
2.54
2.63
2.71
0.4
-0.54
-0.30
-0.16
-0.06
0.01
0.28
0.57
0.76
0.89
1.00
1.21
1.37
1.61
1.79
1.94
2.07
2.18
2.28
2.37
2.45
0.5
-0.85
-0.60
-0.45
-0.34
-0.25
0.02
0.32
0.50
0.64
0.76
0.97
1.14
1.38
1.57
1.72
1.85
1.96
2.06
2.15
2.23
0.6
-1.09
-0.82
-0.66
-0.55
-0.46
-0.17
0.13
0.32
0.47
0.58
0.80
0.97
1.21
1.40
1.56
1.69
1.80
1.90
1.99
2.08
0.7
-1.21
-0.94
-0.78
-0.67
-0.57
-0.28
0.02
0.22
0.36
0.48
0.70
0.87
1.12
1.31
1.46
1.6
1.71
1.81
0.91
1.99
0.8
-1.23
-0.96
-0.81
-0.69
-0.60
-0.29
-0.005
0.18
0.33
0.45
0.67
0.84
1.09
1.28
1.43
1.56
1.68
1.78
1.88
1.96
0.9
-1.17
-0.92
-0.77
-0.66
-0.58
-0.30
0.0003
0.19
0.33
0.44
0.67
0.83
1.08
1.28
1.43
1.56
1.68
1.78
1.88
1.96
1
-1.11
0.89
-0.75
-0.65
-0.57
-0.31
-0.02
0.16
0.30
0.41
0.63
0.79
1.05
1.24
1.40
1.53
1.65
1.75
1.85
1.93
148
100
Table A.10 Saturated vapor entropy of ammonia-water mixture, kJ/kg-K
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
40
50
60
70
80
90
0
8.18
7.94
7.79
7.69
7.62
7.39
7.17
7.04
6.95
6.89
6.77
6.69
6.57
6.48
6.41
6.35
6.29
6.24
6.19
6.15
0.1
7.98
7.75
7.61
7.51
7.44
7.22
7.01
6.89
6.80
6.74
6.62
6.54
6.41
6.32
6.24
6.16
6.09
6.03
5.97
5.90
0.2
7.78
7.54
7.40
7.31
7.23
7.01
6.80
6.68
6.59
6.53
6.41
6.32
6.17
6.06
5.95
5.86
5.76
5.67
5.58
5.49
0.3
7.55
7.31
7.17
7.08
7.00
6.78
6.57
6.44
6.36
6.29
6.15
6.05
5.88
5.73
5.58
5.45
5.31
5.18
5.04
4.90
0.4
7.30
7.06
6.92
6.83
6.76
6.53
6.32
6.19
6.09
6.02
5.87
5.74
5.52
5.32
5.12
4.93
4.73
4.53
4.34
4.14
0.5
7.05
6.81
6.67
6.58
6.50
6.28
6.06
5.92
5.82
5.74
5.56
5.41
5.13
4.87
4.60
4.34
4.07
3.80
3.52
3.25
0.6
6.80
6.56
6.42
6.33
6.25
6.03
5.80
5.66
5.55
5.45
5.26
5.08
4.75
4.42
4.10
3.77
3.44
3.10
2.76
2.42
0.7
6.56
6.32
6.18
6.09
6.01
5.78
5.55
5.40
5.29
5.19
4.98
4.79
4.43
4.07
3.71
3.35
2.98
2.61
2.24
1.86
0.8
6.33
6.09
5.95
5.85
5.77
5.54
5.30
5.15
5.03
4.94
4.72
4.54
4.18
3.83
3.49
3.14
2.78
2.43
2.07
1.71
0.9
6.08
5.83
5.69
5.59
5.52
5.28
5.04
4.89
4.77
4.68
4.48
4.31
4.00
3.71
3.41
3.12
2.83
2.54
2.25
1.95
1
5.77
5.53
5.38
5.28
5.20
4.96
4.71
4.57
4.46
4.37
4.20
4.06
3.83
3.62
3.43
3.25
3.06
2.89
2.71
2.54
149
100
A.4.4 SPECIFIC EXERGY VALUES
Table A.11 Specific exergy for saturated liquid ammonia-water mixture, kJ/kg
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
8.0
10
15
20
30
5.06
10.93
19.82
24.39
29.04
50.14
76.14
94.96
110.5
126.06
155.81
181.8
222.4
0.1
-81.21
-81.15
-75.21
-73.64
-69.03
-56.96
-37.12
-21.08
-5.24
4.72
32.52
53.73
0.2
-133.4
-133.2
-132.1
-131.9
-131.0
-123.0
-107.2
-96.68
-85.62
-73.99
-51.54
0.3
-164.8
-166.6
-166.9
-167.7
-168.0
-165.6
-156.4
-148.3
-139.0
-131.9
0.4
-171.5
-182.7
-186.3
-187.5
-185.2
-187.5
-183.6
-180.2
-172.4
0.5
-161.4
-174.9
-181.4
-185.5
-189.4
-192.3
-192.8
-187.7
0.6
-133.6
-152.7
-162.0
-166.3
-170.2
-179.6
-181.2
0.7
-99.02
-118.7
-128.6
-133.2
-140.4
-151.0
0.8
-55.06
-77.12
-85.42
-94.08
-99
0.9
-6.44
-26.74
-37.34
-44.62
1
56.78
-491.2
28.3
21.8
0
50
60
70
80
90
100
256
285.44
312.14
335.52
356.95
377.62
398.14
90.86
123.95
152.96
176.22
199.02
222.88
242.84
262.68
-34.87
0.37
26.48
51.97
72.94
97.7
115.72
135.92
153.04
-115.2
-97.64
-71.3
-44.27
-23.31
-1.54
17.27
34.5
51.07
67.64
-166.6
-152.3
-139.7
-116.3
-94.47
-75.3
-57.99
-40.45
-24.32
-8.72
6.98
-183.9
-182.0
-169.7
-161.6
-140.8
-123.9
-106.4
-90.6
-74.3
-59.29
-44.69
-29.89
-180.0
-180.1
-175.9
-168.2
-161.3
-142.5
-127.4
-114.2
-99.57
-84.32
-70.25
-56.51
-45.48
-154.1
-156.9
-154.8
-154.3
-147.9
-142.1
-128.0
-114.0
-99.01
-88.21
-73.75
-60.39
247.74
-36.84
-117.8
-118.8
-118.4
-120.2
-120.3
-115.3
-110.5
-97.66
-84.71
-70.39
-57.24
-46.32
-33.43
-23.74
-10.72
-47.76
-61.3
-69.95
-72.62
-72.55
-70.56
-69.85
-62.92
-51.23
-42.01
-28.25
-15.55
-4.99
7.57
16.97
29.73
16.96
4.68
-5.03
-6.88
-8.1
-7.03
-4.81
1.24
8.9
20.48
30.83
43.21
53.5
65.84
75.05
87.64
150
40
Table A.12 Specific exergy for saturated vapor ammonia-water mixture, kJ/kg
Pressure, bar
x
0.2
0.4
0.6
0.8
1.0
2.0
4.0
6.0
0
174.56
272.88
334.18
376.0
406.44
505.88
603.14
660.38
0.1
-829.9
-675.4
-577.3
-505.4
-450.8
-275.5
-99.38
0.2
-958.6
-840.4
-765.3
-711.9
-665.8
-521.6
0.3
-953.6
-850.8
-787.3
-743.2
-704.8
0.4
-918.5
-821.3
-762.4
-722.4
0.5
-873.9
-779.3
-722.5
0.6
-821.5
-728.3
0.7
-764.4
0.8
8.0
10
15
20
30
40
50
60
70
80
90
700
727.38
779.44
813.8
861.04
893.76
917.52
963.3
953.98
967.78
980.98
990.8
2.88
76.4
129.78
228.14
294.28
388.52
451.04
500.08
542.52
577.58
606.56
633.24
661.2
-367.5
-273.2
-203.4
-151.4
-53.28
17.54
122.44
195.62
257.9
307.22
354.62
395.64
433.96
470.28
-586.6
-459.5
-377.5
-320.3
-273.3
-181.5
-115.3
-13.44
66.46
137.06
195.7
253.12
304.46
356.38
406.5
-690.5
-583.2
-473.5
-403.4
-349.3
-308.7
-226.3
-160.0
-55.46
30.94
110.14
181.46
252.46
320.76
384.18
448.98
-684.3
-651.2
-553.8
-451.3
-385.5
-337.4
-298.8
-217.3
-152.5
-41.44
54.34
147.3
233.58
320.04
404.4
490.14
571.6
-672.8
-635.6
-603.4
-509.8
-410.2
-348.9
-301.8
-260.6
-183.2
-115.3
1.3
110.24
211.4
312.54
411.28
511.2
609.82
707.34
-672.4
-617.6
-581.1
-549.4
-455.3
-359.4
-298.1
-253.4
-214.6
-136.3
-69.71
48.36
159.36
266.72
371.1
476.36
580.02
682.58
786.92
-704.1
-613.0
-558.8
-519.8
-488.6
-396.2
-299.8
-240.5
-194.6
-160.4
-82.76
-22.52
89.66
192.36
288.28
384.58
481.86
574.76
669.34
762.92
0.9
-634.1
-540.6
-487.0
-448.4
-420.5
-326.5
-232.1
-174.3
-129.8
-96.94
-28.14
26.52
118.7
198.72
278.02
351.64
423.46
493.68
562.6
633.6
1
-544.8
-455.0
-398.8
-360.6
-330.1
-237.3
-141.6
-88.36
-48.08
-16.26
40.9
84.12
147.76
199.24
246.96
277
314.02
343.48
374.62
401.68
151
100
Appendix B
Flow Charts for Kalina plants
B.1 FLOW CHARTS FOR PLANTS
The process flow charts for three Kalina cycle systems (KCSs) are developed and
depicted in Fig.B.1, B.2 and B.3 respectively for low, medium and high temperature
heat recoveries.
Start
Input of Tsep, VF and xtur
High pressure from separator vapor condition
Separator concentrations (inlet and liquid outlet) from temperature and pressure
Low pressure from condenser exit condition
Mass, energy and exergy balancing
Performance evaluation (specific work and efficiencies)
Economic evaluation
LTKCS performance results and graphs
Stop
Fig.B.1 Flow chart of low temperature Kalina cycle system (LTKCS)
152
Start
Input of Tsep, xss, xtur and Ptur
Low pressure from condenser exit condition
Separator concentrations (liquid and vapor) from temperature and pressure
Vapor fraction in separator from concentrations
Mass, energy and exergy balancing
Performance evaluation (specific work and efficiencies)
Economic evaluation
MTKCS performance results and graphs
Stop
Fig.B.2 Flow chart of medium temperature Kalina cycle system (MTKCS)
153
Start
Input of Tsep, xtur, xtur – xsep,
Tsuply and Ptur
Intermediate pressure from condenser exit condition
Separator liquid concentration from temperature and pressure
Vapor fraction from concentrations
Low pressure from absorber exit condition
Mass, energy and exergy balancing
Performance evaluation (specific work and efficiencies)
Economic evaluation
HTKCS performance results and graphs
Stop
Fig.B.3 Flow chart of high temperature Kalina cycle system (HTKCS)
154