Concept: Process Analysis - Graphical Modeling

Context: Thermodynamic Maps for Binary Mixtures -The Lever Rule and Tie Lines

Defining Questions: What is the descriptive term for the border between the ‘all vapor’and ‘liquid+vapor’ regions on a map for binary mixtures?

What is the descriptive term for the border between the ‘all liquid’and ‘liquid+vapor’ regions on a map for binary mixtures?

Bring a Straightedge or Ruler to Lecture 21.

EngrD 2190 – Lecture 20

New Homework Team AssignmentsFor New Teams: Last person listed is Team Coordinator for Homework 6.

Homework 5 due today at noon.Write team number and names of all contributing team memberson all solutions. Indicate this week’s Team Coordinator.

Homework 6 due Friday 10/22.4.5 and 4.9 graphical energy balances (Lecture 19)4.13 and 4.19 graphical analysis of flash drums (Lecture 20)

Download blank graphs and phase data from EngrD 2190 homepage:Textbook Textbook Graphs and Figures

Graphs for Chapter 4 Exercises.

Process Economics Analysis with a Spreadsheet Optimize a chemical process with respect to ROI. Your Process Plan – equipment purchases and operating parameters –

is due Friday 10/22.You must also submit your spreadsheet.

One L+V Equilbrium Stage

liquid

vaporheaterT = ?

4

liquid

vapor

21

3

1.0 atm75°C

40. mol% benzene60. mol% toluene100. mol/min

A Flash Drum

56 mol% benzene

composition?

flow rate?

flow rate?

cylinder

floatingpiston

P = 1 atm

benzene T < 80°C 80°C 80°C 80°C T > 80°C

toluene T < 111°C 111°C 111°C 111°C T > 111°C

50% benzene50% toluene T < 92°C 92°C

L: 50% BV: 70% B 95.5°C

L: 38% BV: 62% B 98.5°C

L: 30% BV: 50% B T > 98.5°C

75% benzene25% toluene T < 85.5°C 85.5°C

L: 75% BV: 88% B 87.5°C

L: 66% BV: 84% B 91°C

L: 54% BV: 75% B T > 91°C

25% benzene75% toluene T < 100°C 100°C L: 25% B

V: 45% B103.5°C L: 17% B

V: 33% B105°C L: 11% B

V: 25% BT > 105°C

How to plot these Data? A Graph?

A Graph:

x

yy f(x)

Given x, the graph gives y.

Our data: given composition and temperature,what is the phase (liquid, vapor, or liquid+vapor)?

Two independent variables - composition and temperature.

We need a map.

Benzene+Toluene Mixtures at Equilibrium

70

80

90

100

110

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x benzene, y benzene

tem

pera

ture

(C)

P = 1 atm

mol fractionof benzene

in the liquid mol fractionof benzenein the vapor

pure benzenepure toluene

A Map

liquid vapor

a tie line:ties togethertwo phases

in equilibrium.

One L+V Equilbrium Stage

liquid

vaporheaterT = ?

4

liquid

vapor

21

3

1.0 atm75°C

40. mol% benzene60. mol% toluene100. mol/min

A Flash Drum

56 mol% benzene

composition?

flow rate?

flow rate?

70

80

90

100

110

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x benzene, y benzene

tem

pera

ture

(C)

P = 1 atm

Benzene+Toluene Mixtures at Equilibrium - A Map

pure benzenepure toluene

benzene b.p.

toluene b.p.

vapor

dew point line

liquid

bubble point line

L+V

mol fractionof benzene

in the liquid mol fractionof benzenein the vapor

You are here.

destination

The lever is a tie line:the line ties together

two phases at equilibrium.

97°C

x = 0.34

L V

Example 1.

y = 0.56

Apply the Lever Rule to the Tie Line

0.400.34 0.56

L V

total lever: 0.56 0.34 0.22

lever arm to liquid: 0.40 0.34 0.06

liquid flow rate 100 0.06/0.22 27 mol/min. Okay?vapor

Vapor-Liquid Phase Map for Methanol + Water at 1 atm - Exercise 4.19

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x methanol, y methanol

tem

pera

ture

(°C

)

Vapor-Liquid Phase Map for Methanol + Water at 1 atm - Exercise 4.19

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x methanol, y methanol

tem

pera

ture

(°C

)

Do not ‘connect the dots.’

Sketch ‘best fit’lines or use

French curves.