EngrD 2190 – Lecture 22 - Cornell University
Transcript of EngrD 2190 – Lecture 22 - Cornell University
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
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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
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alpy
(kJ/
mol
)
liquid
vapor
liquid + vapor
400°C350°C
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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
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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