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

vapor

139

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.

140

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.

141

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.

142

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 AMMONIA-

WATER 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

143

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).

144

x

Pressure, bar

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

Table A.5 Bubble point temperature, ºC

145

x

Pressure, bar

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

Table A.6 Dew point temperature, ºC

146

x

Pressure, bar

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

A.4.2 SPECIFIC ENTHALPY VALUES

Table A.7 Saturated liquid enthalpy of ammonia-water mixture, kJ/kg

147

x

Pressure, bar

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

Table A.8 Saturated vapor enthalpy of ammonia-water mixture, kJ/kg

148

x

Pressure, bar

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 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

Table A.9 Saturated liquid entropy of ammonia-water mixture, kJ/kg-K

A.4.3 SPECIFIC ENTROPY VALUES

149

x

Pressure, bar

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 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

Table A.10 Saturated vapor entropy of ammonia-water mixture, kJ/kg-K

150

x

Pressure, bar

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 5.06 10.93 19.82 24.39 29.04 50.14 76.14 94.96 110.5 126.06 155.81 181.8 222.4 256 285.44 312.14 335.52 356.95 377.62 398.14

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 90.86 123.95 152.96 176.22 199.02 222.88 242.84 262.68

0.2 -133.4 -133.2 -132.1 -131.9 -131.0 -123.0 -107.2 -96.68 -85.62 -73.99 -51.54 -34.87 0.37 26.48 51.97 72.94 97.7 115.72 135.92 153.04

0.3 -164.8 -166.6 -166.9 -167.7 -168.0 -165.6 -156.4 -148.3 -139.0 -131.9 -115.2 -97.64 -71.3 -44.27 -23.31 -1.54 17.27 34.5 51.07 67.64

0.4 -171.5 -182.7 -186.3 -187.5 -185.2 -187.5 -183.6 -180.2 -172.4 -166.6 -152.3 -139.7 -116.3 -94.47 -75.3 -57.99 -40.45 -24.32 -8.72 6.98

0.5 -161.4 -174.9 -181.4 -185.5 -189.4 -192.3 -192.8 -187.7 -183.9 -182.0 -169.7 -161.6 -140.8 -123.9 -106.4 -90.6 -74.3 -59.29 -44.69 -29.89

0.6 -133.6 -152.7 -162.0 -166.3 -170.2 -179.6 -181.2 -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

0.7 -99.02 -118.7 -128.6 -133.2 -140.4 -151.0 -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

0.8 -55.06 -77.12 -85.42 -94.08 -99 -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

0.9 -6.44 -26.74 -37.34 -44.62 -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

1 56.78 -491.2 28.3 21.8 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

Table A.11 Specific exergy for saturated liquid ammonia-water mixture, kJ/kg

A.4.4 SPECIFIC EXERGY VALUES

151

x

Pressure, bar

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

0 174.56 272.88 334.18 376.0 406.44 505.88 603.14 660.38 700 727.38 779.44 813.8 861.04 893.76 917.52 963.3 953.98 967.78 980.98 990.8

0.1 -829.9 -675.4 -577.3 -505.4 -450.8 -275.5 -99.38 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

0.2 -958.6 -840.4 -765.3 -711.9 -665.8 -521.6 -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

0.3 -953.6 -850.8 -787.3 -743.2 -704.8 -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

0.4 -918.5 -821.3 -762.4 -722.4 -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

0.5 -873.9 -779.3 -722.5 -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

0.6 -821.5 -728.3 -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

0.7 -764.4 -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

0.8 -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

Table A.12 Specific exergy for saturated vapor ammonia-water mixture, kJ/kg

152

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.

Fig.B.1 Flow chart of low temperature Kalina cycle system (LTKCS)

Start

High pressure from separator vapor condition

Mass, energy and exergy balancing

Performance evaluation (specific work and efficiencies)

Input of Tsep, VF and xtur

Separator concentrations (inlet and liquid outlet) from temperature and pressure

Low pressure from condenser exit condition

Economic evaluation

Stop

LTKCS performance results and graphs

153

Fig.B.2 Flow chart of medium temperature Kalina cycle system (MTKCS)

Start

Low pressure from condenser exit condition

Mass, energy and exergy balancing

Performance evaluation (specific work and efficiencies)

Input of Tsep, xss, xtur and Ptur

Separator concentrations (liquid and vapor) from temperature and pressure

Vapor fraction in separator from concentrations

Economic evaluation

Stop

MTKCS performance results and graphs

154

Fig.B.3 Flow chart of high temperature Kalina cycle system (HTKCS)

Start

Intermediate pressure from condenser exit condition

Mass, energy and exergy balancing

Performance evaluation (specific work and efficiencies)

Input of Tsep, xtur, xtur – xsep,

Tsuply and Ptur

Separator liquid concentration from temperature and pressure

Economic evaluation

Stop

Vapor fraction from concentrations

Low pressure from absorber exit condition

HTKCS performance results and graphs