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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: