126 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
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126
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
127
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.
i
i
n
0m
i
i0bP
Plnx1aTx,PT
(A.1)
i
i
n
0m
i
i0dP
Plnx1aTy,PT
(A.2)
Fig.A.1 Property regions on temperature-concentration diagram for ammonia-water
mixture at constant pressure
128
Table A.1 Coefficients for equation (A.1) to determine bubble point temperature
i mi ni ai
1 0 0 +0.322302 101
2 0
1 -0.384206 100
3 0 2 +0.460965 10-1
4 0 3 -0.378945 10-2
5 0 4 +0.135610 10-3
6 1 0 +0.487755 100
7 1 1 -0.120108 100
8 1 2 +0.106154 10-1
9 2 3 -0.533589 10-3
10 4 0 +0.785041 101
11 5 0 -0.115941 102
12 5 1 -0.523150 10-1
13 6 0 +0.489596 101
14 13 1 +0.421059 10-1
Table A.2 Exponents and coefficients of equation (A.2) to determine dew point
temperature
i mi ni ai
1 0 0 +0.324004 101
2 0
1 -0.395920 100
3 0 2 +0.435624 10-1
4 0 3 -0.218943 10-2
5 1 0 -0.143526 101
6 1 1 +0.105256 101
7 1 2 -0.719281 10-1
8 2 0 +0.122362 102
9 2 1 -0.224368 101
10 3 0 -0.201780 102
11 3 1 +0.110834 101
12 4 0 +0.145399 102
13 4 2 +0.644312 100
14 5 0 -0.221246 101
15 5 2 -0.756266 100
16 6 0 -0.135529 101
17 7 2 +0.183541 100
129
Fig.A.2 Flowchart for thermodynamic properties of ammonia-water mixture at five
regions
Properties of ammonia (liquid and vapor)
Start
T = BPT
Properties of water (liquid and vapor)
Properties of ammonia and water mixture (liquid and vapor)
BPT and DPT
T < BPT
T = DPT
T > BPT and T < DPT
BPT
T > DPT
Assign properties of liquid
mixture (saturated)
Assign properties of liquid
mixture (sub-cooled)
Assign properties of vapor
mixture (saturated)
Assign properties of
liquid vapor mixture
Assign properties of vapor
mixture (superheated)
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Input of P, T and x
Property data and charts
End
130
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.
EL
O2
H
m
3NH
m
Lhhx)1(hxh (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.
Prr
r
r
2
rBT
G
TTRTh
(A.4)
T
T
pP
P
T
T
poo
ooo
dTT
CTvdpdTCTshG (A.5)
131
2
ro
2
r2
ror
2
r4r31
r
2
ro
2
r3
rorr2
ro
rr1
3
ro
3
r32
ro
2
r2
ror1
L
ror
L
ro
L
r
PP2
APPTATAA
TTT2
BTTTB
T
TlnTB
TT3
BTT
2
BTTBsTh
G (A.6)
2
ro
2
r
r
2rorr43
r
1
2
ro
2
r3
ror2
ro
r1
r
3
ro2
r
3
r
2
ro
r2
r
ro
1
L
ro
r
L
ro
r
L
r
PPT2
APPTAA
T
A
TT2
BTTB
T
TlnB
T
TT
3
B
T
TT
2
B
T
T1Bs
T
h
T
G (A.7)
2
ro
2
r2
r
2ror2
r
14r32
r
3
ro3
r3
2
r
1
2
r
2
ro2
2
2
r
ro12
r
L
ro
r
L
r
r
PPT2
APP
T
AATB
T
T
3
B
T23
BB
T
B
T2
TB
2
B
T
TB
T
h
T
G
T (A.8)
2
ro
2
r2
ror1
2
r4
3
r
3
ro
32
r
2
ro2
rro1
L
ro
r
r
r
2
r
PP2
APPATA
TT3
BTT
2
BTTBh
T
G
TT (A.9)
2
ro
2
r2
ror1
2
r4
3
r
3
ro
32
r
2
ro2
rro1
L
ro
B
L
PP2
APPATA
TT3
BTT
2
BTTBh
RTh (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
x11x2F1x2FFG2
321
E
r (A.11)
2
r
6
r
5rr43r211
T
E
T
ETPEEPEEF (A.12)
2
r
12
r
11rr109r842
T
E
T
ET)PEE(PEEF (A.13)
132
2
r
16
r
15r14133
T
E
T
EPEEF (A.14)
x,Pr
E
r
r
2
rB
E
r
T
G
TTRTh
(A.15)
2
r
16
r
15r1413
2
2
r
12
r
11r87
2
r
6
r
5r21
B
E
T
3E
T
2EPEE-1)2x(
T
3E
T
2EPEE-1)2x(
T
3E
T
2EPEE-
)x1(TRh (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.
v
OH
v
NH
m
v 23h x)1(xhh (A.17)
For the gas phase, Gibbs free energy equation is given below:
12
ro
r
3
ro
11
ro
3
ro
11
r
3
r4
12
ro
rro
11
ro
ro
11
r
r3
4
ro
rro
3
ro
ro
3
r
r2ror1
ro
rr
2
ro
2
r
3
rorr2
ro
rr1
3
ro
3
r
32
ro
2
r2
ror1
v
ror
v
ro
v
r
T
TP11
T
P12
T
P
3
C
T
TP11
T
P12
T
PC
T
TP3
T
P4
T
PCPPC
P
PlnT)TT(
2
D)TT(TD
T
TlnTD
TT3
DTT
2
D)TT(DsTh
G (A.18)
133
12
ro
3
ro
r
12
ro
3
ro
12
r
3
r4
12
ro
ro
r
11
ro
ro
12
r
r34
ro
ro
r
3
ro
ro
4
r
r2ror
r
1
ro
r
r
2
ro
r
3
ror2
ro
r1
r
3
ro2
r
3
r
2
ro
r2
r
ro
1
v
ro
r
v
ro
r
v
r
T
P11
TT
P12
T
P
3
C
T
P11
TT
P12
T
PC
T
P3
TT
P4
T
PCPP
T
C
P
Pln
T
TT
2
DTTD
T
TlnD
T
TT
3
D
T
TT
2
D
T
T1Ds
T
h
T
G (A.19)
2
r
11
ro
3
ro
13
r
3
r4
2
r
11
ro
ro
13
r
r
3
2
r
3
ro
ro
5
r
r
2ror2
r
1
2
r
2
ro3
2
r
12
r
3
ro
r
3
2
r
2
ro2
2
r
ro
12
r
v
ro
r
v
r
r
TT
P12
T
P12
3
C
TT
P12
T
P12C
TT
P4
T
P4CPP
T
C
T
T1
2
DD
T
1D
T
TT2
3
D
T
T1
2
D
T
TD
T
h
T
G
T (A.20)
11
ro
3
ro
11
r
3
r4
11
ro
ro
11
r
r
33
ro
ro
3
r
r
2
ror1
2
ro
2
r
32
r2r1
3
ro
3
r
32
ro
2
r
2
ro1
v
ro
prr
v
r
r
2
r
T
P12
T
P12
3
C
T
P12
T
P12C
T
P4
T
P4C
PPCTT2
DTDTD
TT23
DTT
2
DTDh
T
G
TT (A.21)
11
ro
3
ro
11
r
3
r4
11
ro
ro
11
r
r33
ro
ro
3
r
r2
ror1
2
ro
2
r32
r2r1
3
ro
3
r32
ro
2
r2
ro1
v
ro
B
prr
v
r
r
2
rB
v
T
P12
T
P12
3
C
T
P12
T
P12C
T
P4
T
P4C
PPCTT2
DTDTD
TT23
DTT
2
DTDh
RTT
G
TTRTh (A.22)
134
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).
Prr
r
T
GRs
(A.23)
)PP()TA2A(TT32
BTT2B
1T
TlnBT3
3
B)T2(
2
BBs
T
G
rorr43
3
ror2
ro
r1
3
r2
1
2
ro
2
r
2
r
L
ro
r
L
r (A.24)
rorr43
3
ror2
ro
r1
3
r2
1
PPTA2A
TT32
BTT2B
1T
TlnBT3
3
BT2
2
BBs
RT
G
Rs 2
ro
2
r
2
r
L
ro
Pr
r
L
rL
(A.25)
xPr,r
E
rE
T
GRs
(A.26)
3
r
16
2
r
152
3
r
12
2
r
11r1093
r
6
2
r
5
r43
r
E
r
T
E2
T
E)1x2(
T
E2
T
EPEE)1x2(
T
E2
T
EPEE
x1T
G
(A.27)
135
3
r
16
2
r
152
3
r
12
2
r
11r109
3
r
6
2
r
5
r43
xPr,r
E
r
E
T
E2
T
E)1x2(
T
E2
T
EPEE)1x2(
T
E2
T
EPEE
x1RT
GRs (A.28)
)x1ln()x1()xln(xRsmix (A.29)
mixE
L
w
L
a
m
L sss)x1(sxs (A.30)
12
ro
3
ro
12
r
3
r
12
ro
ro
12
r
r
4
ro
ro
4
r
r
2
ro
r2
ro
2
r
2
r
V
ro
V
r
T
P11
T
P11
3
C
T
P11
T
P11C
T
P3
T
P3C
P
PlnTT3
2
D
TT2DT
Tln1DTDTDDs
T
G
43
3
ror2
ro
r13r21
r
(A.31)
12
ro
3
ro
12
r
3
r
12
ro
ro
12
r
r
4
ro
ro
4
r
r
2
ro
r2
ro
2
r
2
r
V
ro
Pr
V
r
T
P11
T
P11
3
C
T
P11
T
P11C
T
P3
T
P3C
P
PlnTT3
2
DTT2D
T
Tln1DTDTDDs
RT
Gvs
4
3
3
ror2
ro
r13r21
r
(A.32)
mix
V
w
V
a
m
v ss)x1(sxs (A.33)
136
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).
Trr
r
P
G
P
RTv
B
B
(A.34)
r2
2
r4r31
r
L
rPATATAA
P
G
(A.35)
r2
2
r4r31
B
B
Trr
L
r
B
BL PATATAAP
TR
P
G
P
TRv
(A.36)
x,Trr
E
r
B
BE
P
G
P
TRv
(A.37)
14
2
r108r42
r
E
rEx11x2TEE1x2TEE
P
G
(A.38)
x1E1x2TEE1x2TEEP
RT
P
G
P
RTv 14
2
r108r42
B
B
Trr
E
r
B
BE
(A.39)
EL
W
L
a
L
m vv)x1(xvv (A.40)
11
r
2
r4
11
r
3
3
r
21
r
r
r
V
r
T
PC
T
C
T
CC
P
T
P
G
(A.41)
11
r
2
r4
11
r
3
3
r
21
r
r
B
B
Trr
V
r
B
Bv
T
PC
T
C
T
CC
P
T
P
TR
P
G
P
TRv (A.42)
v
w
v
a
v
m v)x1(xvv (A.43)
137
Table A.3 Coefficients for the equations for the pure components
Coefficient Ammonia Water
A1 3.97142310-2
2.748796 10-2
A2 -1.790557 10-5
-1.016665 10-5
A3 -1.308905 10-2
-4.452025 10-3
A4 3.752836 10-3
8.389246 10-4
B1 1.634519 101 1.214557 10
1
B2 -6.508119 -1.898065
B3 1.448937 2.911966 10-2
C1 -1.049377 10-2
2.136131 10-2
C2 -8.288224 -3.169291 101
C3 -6.647257 102 -4.634611 10
4
C4 -3.045352 103 0.0
D1 3.673647 4.019170
D2 9.989629 10-2
-5.175550 10-2
D3 3.617622 10-2
1.951939 10-2
hL 4.878573 21.821141
hv 26.468879 60.965058
sL 1.644773 5.733498
sv 8.339026 13.453430
Tro 3.2252 5.0705
Pro 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 -41.733398
E2 0.02414
E3 6.702285
E4 -0.011475
E5 63.608967
E6 -62.490768
E7 1.761064
E8 0.008626
E9 0.387983
E10 0.004772
E11 -4.648107
E12 0.836376
E13 -3.553627
E14 0.000904
E15 21.361723
E16 -20.736547
138
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