Concept: Process Analysis - Graphical Modeling

Context: Combined Mass & Energy Balances for Binary Mixtures: Enthalpy-Composition (H-(x,y)) Phase Maps

Defining Question: Why are tie lines on enthalpy-composition phasemaps not horizontal?

Bring a Straightedge or Ruler to Lecture 23.

EngrD 2190 – Lecture 22

60

65

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75

80

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95

100

105

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

tem

pera

ture

(°C

)

Temperature-Composition Phase Diagram for G+H Mixtures at 1 atm

xG, yG

more volatile component

pure G

b.p. ofpure G:62.5°C

pure H

b.p. ofpure H:101°C

vapor

dew point line

bubble point line

liquid

Example 1.

1

80°C3

4

L+Vtie line

x 0.39 y 0.70

Example 1: Apply the Lever Rule to the Tie Line

0.500.39 0.70

VL

0.70 0.39 0.31

0.70 0.50 0.200.11

vapor flow rate 35 mol/min.

mol/min65mol/min10031.020.0rate flow liquid

We need a graphical method for energy balances on binary mixtures.

Recall our number line for energy balances on a pure substance: H2O.

arbitrary

H2O liquidat b.p.

H2O vaporat b.p.

4.17 (100 – 0) 417 kJ/kg 417 + 2280 2697 kJ/kg2697 + 1.83 (300 – 100)

3063 kJ/kg

Create a number line for energy balances on pure G.

Arbitrarily set H 0 kJ/mol for G liquid at 25°C

25°C

Calculate H for G liquid at b.p. H 0 + CP,G liquid(T) 0 + 80 J/mol°C (62.5 – 25°C) 3.0 kJ/mol

G liquidat b.p.

Calculate H for G vapor at b.p. H 3.0 + Hvap,G 3.0 + 23 kJ/mol 26 kJ/mol

G vaporat b.p.

Calculate H for G vapor at 200°C. H 26 + CP,G vapor (T) 26 + 50 J/mol°C (200 – 62.5 °C) 32.9 kJ/mol

Hvap,G 200°C

Calculate H for G vapor at 300°C. H 32.9 + CP,G vapor (T) 32.9 + 50 J/mol°C (300 – 200 °C) 37.9 kJ/mol

300 400 500°C

Create a number line for energy balances on pure H.

Arbitrarily set H = 0 kJ/mol for H liquid at 25°C

25°C

Calculate H for H liquid at b.p. H = 0 + CP,H liquid(T) = 0 + 120 J/mol°C (101 – 25°C) = 9.1 kJ/mol

H liquidat b.p.

Calculate H for H vapor at b.p. H = 9.1 + Hvap,H = 9.1 + 38 kJ/mol = 47.1 kJ/mol

H vaporat b.p.

Calculate H for H vapor at 200°C. H = 47.1 + CP,H vapor (T)= 47.1 + 80 J/mol°C (200 – 101 °C) = 55 kJ/mol

Hvap,H 200°C

vapor

liquid

L+V

pure Gpure H

25°C

101°C

101°C

200°C

liquid

liquid+ vapor

vapor

E (kJ/mol)

25°C62.5°C

62.5°C

200°C

liquid+ vapor

vapor

dew point line

bubble point line

tie line at 80°C

tie lineat 80°C

tie lineat 62.5°C

tie lineat 101°C

Assume G and Hform an ideal mixture.

isothermat 200°C

vapor

liquid

L+V

-5

0

5

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15

20

25

30

35

40

45

50

55

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

enth

alpy

(kJ/

mol

)

liquid

vapor

liquid + vapor

400°C350°C

300°C250°C

200°C

150°C

125°C100°C

95°C90°C

85°C

80°C

75°C

70°C

65°C80°C

65°C50°C

25°C

0°C

100°C

Enthalpy-Composition Phase Diagram for G+H Mixtures at 1 atm

pure G

G liquid at b.p.

G vapor at b.p.

pure H

H liquid at b.p.

H vapor at b.p.

dew point line

bubble point line 1

2tie line at 80°C

3

4

x 0.39 y 0.70

Tie Line:total length 81.5 mmliquid arm 29 mm

mol/min64liquid

mol/min36

100mm5.81

mm29vapor

qheater:

stream 1: 3.6 kJ/molstream 2: 15 kJ/mol

H 15 3.6 11.4 kJ/mol

qheater 11.4 100 mol/min 114 kJ/min

qheater 110 kJ/min