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:
What do we know?
Tvap, Pvap
yA , yB
yA + yB = 1
xA + xB = 1
yA ≠ xA
Tliq, Pliq
xA , xB
At equilibrium:
Tvap = Tliq
Pvap = Pliq
Gibbs’ 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
2 graphs in one:
T vs. xA
T vs. yA
superheated vapor
2-phase
region
saturated liquid line
TA
•
saturated vapor line
••
zA
•
subcooled liquid
yA
xA
A subcooled liquid feed
of composition zA,
heated to temperature
TA, will separate
spontaneously into 2
phases, of composition
xA and yA
Figure 2-3 Temperature-composition diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat
Boiling point, dew point, bubble point
Pure liquids have a
boiling point; mixtures
have a boiling range,
delimited by their
bubble point and dew
point.
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?
dew point
boiling
range
bubble point
xE,initial
2. Consider a superheated
binary vapor that is 40
mol% ethanol.
What is its dew point?
What is the composition of
the first drop?
yE,initial
3. What is the boiling range
of this mixture?
Figure 2-3 Temperature-composition diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat
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?
F, L and V are extensive variables
mass balance method
OR
total mass balance (TMB):
F=L+V
component mass balance (CMB):
F zA = L x A + V y A
rearrange: L = y A - zA
V zA - x A
inverse lever-arm method
•
L
isotherm
•
M
L MV
=
V
LM
For a given F, we can now compute L and V.
•
V
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:
K = yA/xA
mole balance:
xA + xB = 1
yA + yB = 1
VLE line always lies above
y=x line if plotted for the
more volatile component
K = yE/xE
volatility = K = K(T, P, zi)
≈ K(T)
azeotrope: K = 1.0
how can we “break”
an azeotrope?
Figure 2-2 McCabe-Thiele diagram for ethanol-water
From Separation Process Engineering, Third Edition by Phillip C. Wankat
Specify two of (P, T, volatility)
pure compound
P0
P*
K>1
K = 1.0
K<1
DePriester Chart
Consider a pure compound:
Tbp
• 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 phase
K < 1 prefers liquid phase
temperature
total
pressure
P´
T´
T*
Don’t extrapolate beyond the range of the chart.
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)
volatility
At 2000 kPa, what is the
boiling point of ethane?
At 15 °C, what is the
saturated vapor pressure
of isobutane?
At 0 °C and 500 kPa,
what is the volatility of
n-hexane?
From Separation Process Engineering, Third Edition by Phillip C. Wankat
Using data from vapor pressure tables
Raoult’s Law
ideal liquid:
non-ideal liquid:
vapor pressure
PA = x APA0 (T)
PA = g A x APA0 (T)
activity coefficient
Dalton’s Law
ideal gas:
non-ideal gas:
yA =
PA
PTOTAL
PA
yA =
f APTOTAL
fugacity coefficient
yA
PA0 (T)
PA0 (T)
KA =
=
@
x A f APTOTAL PTOTAL
Bubble point calculation
for multi-component mixtures
Trial-and-error method
Given the composition of a subcooled liquid and PTOTAL,
find Tbp and (yi)bp
VLE:
y i = Ki xi
mole balance:
åy
i
= 1.0
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 = 1
4. If not, pick a new temperature, repeat
i
How to pick a temperature? How to pick the next temperature?
To achieve rapid convergence:
T = å ziTi (K i = 1)
Initial guess:
i
(weighted average of boiling points of pure components)
Next guess:
pick a reference component (A)
K A (Tnext ) =
K A (Tprev )
å(y )
i prev
i
find Tnext using DePriester Chart
Dew point calculation
for multi-component mixtures
Trial-and-error method
Given the composition of a superheated vapor and PTOTAL,
find Tdp and (xi)dp
VLE:
yi
xi =
Ki
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 = 1
4. If not, pick a new temperature and repeat
mole balance:
åx
i
= 1.0
i
K A (Tnext ) =
K A (Tprev )
å(x )
i prev
Relative volatility
KA =
volatility
yA
= K A (T )
xA
strong function of
temperature
yA
a AB
relative volatility
K
xA
= A=
KB yB
xB
not a strong function of
temperature; often
assumed independent
for a binary system, substitute and rearrange:
y B = 1- y A
xB = 1- x A
yA =
a AB x A
1+ (a AB -1)x A
Bubble point calculation
using relative volatility
yi
definition of relative volatility:
Ki
xi
ai =
=
K ref K ref
solve for yi:
y i = ai xi K ref
sum:
åy
i
solve for Kref:
i
(
)
= 1.0 = å ai xi K ref
K ref =
i
1
åa x
i
i
i
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 volatilities
Find 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.
Tinitial = å xiTi (K i = 1) = 0.3(36) + 0.3(68) + 0.4(99) = 71°C
i
Designate n-pentane as the reference. At 71 °C, KP = 2.8.
a XP
K
1.2
= X =
= 0.43
K P 2.8
aHP =
K H 0.45
=
= 0.16
KP
2.8
1
1
K P (Tbp ) =
=
= 2.0
åai xi 0.3(1) + 0.3(0.43) + 0.4(0.16)
i
Find Tbp corresponding to KP = 2.0 (read from DePriester Chart):
y i = ai xi K ref
Tbp = 58 °C
y P = 0.3(1)(2.0) = 0.60
y X = 0.3(0.43)(2.0) = 0.26
yH = 0.4(0.16)(2.0) = 0.14
Check:
åy
i
i
= 1.0
```