120712ChE128-2-VLEReview

Goal 1: Design a flash drum

How big should the drum be?What height should the nozzle be?What T and P should the drum be?What T and P should the feed be?

Vapor-liquid equilibrium (VLE)Consider a binary (i.e., 2-component) system with 2-phases:

Tvap, Pvap

yA, yB

Tliq, Pliq

xA, xB

What do we know?

yA + yB = 1 xA + xB = 1

yA ≠ xA

At equilibrium: Tvap = Tliq

Pvap = PliqGibbs’ Phase Rule:

degrees of freedom = # components (C) - # phases (P) + 2

For a binary, 2-phase system: 2 – 2 + 2 = 2

We can specify only 2 intensive variables (all others are fixed, by VLE)

Specify P and T

From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 2-3 Temperature-composition diagram for ethanol-water

superheated vapor

subcooled liquid

2-phase region

saturated vapor line

saturated liquid line

2 graphs in one:T vs. xA

T vs. yA

A subcooled liquid feed of composition zA, heated to temperature TA, will separate spontaneously into 2 phases, of composition xA and yA

TA

xA

• •

yA

•

zA•

From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 2-3 Temperature-composition diagram for ethanol-water

bubble point

dew point

xE,initial yE,initial

boiling range

1. Consider a sub-cooled binary liquid that is 40 mol% ethanol. What is its bubble point? What is the composition of the first bubble?

2. Consider a superheated binary vapor that is 40 mol% ethanol. What is its dew point? What is the composition of the first drop?

3. What is the boiling range of this mixture?

Boiling point, dew point, bubble pointPure liquids have a boiling point; mixtures have a boiling range, delimited by their bubble point and dew point.

Useful definitions• Boiling/bubble point Tbp: temperature at which the average

liquid molecule has just enough kinetic energy to escape from the surface of the liquid into the gas phase– Recall that kinetic energy follows a Boltzmann distribution, so

molecules with higher than average kinetic energy can still escape from the surface at T < Tbp, by evaporation

• Saturated liquid: a liquid at its boiling/bubble point• Dew point Tdp: temperature at which the average vapor

molecule has just enough kinetic energy to condense• Saturated vapor: a vapor at its dew point• Vapor pressure: pressure at which the liquid and vapor phase

are in equilibrium at a given temperature• Azeotrope: a constant-boiling mixture, i.e., a mixture that

behaves like a single component

How much liquid and vapor will the flash drum produce?

mass balance method

total mass balance (TMB):F = L + V

component mass balance (CMB):F zA = L xA + V yA

rearrange:

OR inverse lever-arm method

F, L and V are extensive variables

•L

•M

•V

isotherm

For a given F, we can now compute L and V.

From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 2-2 McCabe-Thiele diagram for ethanol-water

y=x

T incr.

K = yE/xE

volatility = K = K(T, P, zi)≈ K(T)

azeotrope: K = 1.0

how can we “break” an azeotrope?

Specify P and one composition (xA)

For a binary system at constant P, if one composition (xA or yA) is chosen, all others are fixed:

VLE line

VLE: K = yA/xA

mole balance:xA + xB = 1yA + yB = 1

VLE line always lies above y=x line if plotted for the more volatile component

Specify two of (P, T, volatility)to

tal

pres

sure

temperature

K = 1.0

DePriester Chart

• for a given P, find Tbp (i.e., K = 1)

• for a given T, find P0 (i.e., K = 1)• for a given P, T, find K

K > 1 prefers vapor phaseK < 1 prefers liquid phase

Don’t extrapolate beyond the range of the chart.

Tbp

P0

pure compound

Consider a pure compound:T´

P´ K > 1

T*P* K < 1

Figure 2-11 Modified DePriester chart (in S.I. units) at low temperatures (D. B. Dadyburjor, Chem. Eng. Prog.,85, April 1978; copyright 1978, AIChE; reproduced by permission of the American Institute of Chemical Engineers)

From Separation Process Engineering, Third Edition by Phillip C. Wankat (ISBN: 0131382276) Copyright © 2012 Pearson Education, Inc. All rights reserved.

At 2000 kPa, what is the boiling point of ethane?

volatility

At 15 °C, what is the saturated vapor pressure of isobutane?

At 0 °C and 500 kPa, what is the volatility of n-hexane?

Using data from vapor pressure tables

Raoult’s Law ideal liquid:non-ideal liquid:

Dalton’s Law ideal gas:non-ideal gas:

activity coefficient

fugacity coefficient

vapor pressure

Bubble point calculationfor multi-component mixtures

Trial-and-error methodGiven the composition of a subcooled liquid and PTOTAL,

find Tbp and (yi)bp

VLE:

mole balance:

Algorithm:

1. Pick a temperature T and find the corresponding Ki(T) values for each component

2. Calculate the yi value for each Ki(T)3. Check to see if Syi = 14. If not, pick a new temperature, repeat

How to pick a temperature? How to pick the next temperature?

To achieve rapid convergence:

Initial guess: (weighted average of boiling points of pure

components)

Next guess:pick a reference

component (A)

find Tnext using DePriester Chart

Dew point calculationfor multi-component mixtures

Trial-and-error methodGiven the composition of a superheated vapor and PTOTAL,

find Tdp and (xi)dp

VLE:

mole balance:

Algorithm:

1. Pick a temperature T and find the corresponding Ki(T) values for each component

2. Calculate the xi value for each Ki(T)3. Check to see if Sxi = 14. If not, pick a new temperature and repeat

Relative volatility

volatility strong function of temperature

not a strong function of temperature; often

assumed independentrelative volatility

for a binary system, substitute and rearrange:

Bubble point calculationusing relative volatility

definition of relative volatility:

solve for yi:

solve for Kref:

sum:

Algorithm:given a solution composition (xi values), find relative volatilities (ai values), then

1. guess Tinitial

2. calculate Kref

3. find T = Tbp corresponding to Kref

Ex.: Finding Tbp using relative volatilitiesFind the bubble point of a mixture of n-pentane (xP = 0.3), n-hexane (xX = 0.3) and n-heptane (xH = 0.4), at 1 atm total pressure. Find the composition of the first vapor bubble.

Designate n-pentane as the reference. At 71 °C, KP = 2.8.

Find Tbp corresponding to KP = 2.0 (read from DePriester Chart): Tbp = 58 °C

Check: