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SKF 2213 Chemical Engineering Thermodynamics Chapter 10: Vapor/Liquid Equilibrium
SKF 2213 Chemical Engineering Thermodynamics
Chapter 10: Vapor/Liquid Equilibrium
It is expected that students have the ability to: Describe the behaviour of VLE and how to simplify the VLE problem. Derive and simplify equations of VLE. Apply simplified VLE equations to obtain data for P-XY, T-XY and X-
Y diagrams. Apply Raoults law and Henrys law to solve simple thermodynamic
problems. Carry out bubble and dew point calculations for a given mixture Carry out flash calculation in order to determine the vapor/liquid
fraction as well as the mixture composition of each phase at specified conditions using available K-Values etc.
Binary mixturefor species 1 and 2.
RKAC1 is vaporpressure vs. T curve for species 1
UBHC2 is vaporpressure vs. T curve for species 2
C1 and C2 are critical points for species 1 & 2
Species 1 is more volatile.
Under surface issaturated-vapor (P,T,y1 surface)
Below that is gasphase.
Top surface issaturated-liquid(P,T,x1 surface)
Above that isliquid phase.
AEDBLA givesFigure 10.2 (a)Pxy phase diagram at constant T
KJIHLK givesFigure 10.2 (b)Txy phase diagram at constant P
F (liquid solution)L (bubble point)W (dew point)G (Gas mixture)
LV = tie lineL = bubble pointW = dew point
P
Note: species 1 has higher vapor pressure or lower boiling point than species 2
Most chemical processes operate at this P, T range
Gas
Gas
Liquid
Liquid
Tieline
1 0x2y2
Commonly found shape of Pxy
diagrams at constant T
This is similar shape toFigure 10.2 (a)
Commonly found shape of Txy
diagrams at constant P
This diagram is of practical interest as
most VLE applications occur at
constant P(example in
distillation column)
This is similar shape toFigure 10.2 (b)
y1-x1 diagrams at constant P
Azeotrope
Azeotropex1=y1 x2=y2Liquid composition= Gas composition
K-value Using DePriester Chart
For light hydrocarbon mixture where Kiis essentially function of T and P only, the valuecould be simply tabulated as in DePriester chart.
Read value of K-valueat given T and Pe.g. 1000 kPa and 0 oC
for methane
Bubblepoint & DewpointCalculations
BUBL P: Calculate {yi} and P, given {xi} and T
To calculate the P when the 1st bubble appear as a result of decrease in P at constant T
To calculate the P when the last bubble disappear as a result of increase in P at constant T
DEW P: Calculate {xi} and P, given {yi} and T
To calculate the P when the 1st dew (drop of liquid) appear as a result of increase in P at constant T
To calculate the P when the last dew disappear as a result of decrease in P at constant T
BUBL T: Calculate {yi} and T, given {xi} and P
To calculate the T when the 1st bubble appear as a result of increase in T at constant P
To calculate the T when the last bubble disappear as a result of decrease in T at constant P
DEW T: Calculate {xi} and T, given {yi} and P
To calculate the T when the 1st dew (drop of liquid) appear as a result of decrease in T at constant P
To calculate the T when the last dew disappear as a result of increase in T at constant P.
Overall mole balanceT L V
Component mole balanceTzi Lxi Vyi
Let T=1 mol, so V and L are mole fractionszi Lxi Vyi zi (1V )xi Vyi (A)
Derivation
Substitute yi Kixi into (A)zi (1V )xi KixiV xi (1V VKi ) xi (1V (Ki 1))xi
zi1V (Ki 1)
Substitute xi yiKi
into (A)
zi (1V )yiKi
yiV zi Ki (1V )yi yiVKi
yi zi Ki
1V (Ki 1) (10.16)
xi yi 0zi
1V(Ki 1) ziKi
1V(Ki 1) 0
zi ziKi1V(Ki 1) 0
Bubblepoint Calculation
So at bubble point, L=1, V=0 and zi xi
(xi xiKi) 0xi xiKi xiKi 1 (10.13)
zi ziKi1V(Ki 1) 0
Bubblepoint Calculation
xiKi 1 (10.13)If Raoult's Law valid,
xiPi
sat
P 1 P xiPisat (10.2) see example 10.1
If Modified Raoult's Law valid,
xi iPisat
P 1 P xi iPisat (10.6) see example 10.3
Dewpoint Calculation
So at dewpoint, L=0, V=1 and zi yi
yi yiKiKi
0yiKi yi 0
yiKi
=1 (10.14)
zi ziKi1V(Ki 1) 0
Dewpoint CalculationyiKi
=1 (10.14) If Raoult's Law valid,
yiPi
sat
P
=1 P 1yi
Pisat
(10.3), see example 10.1
If Modified Raoult's Law valid,yi
iPisatP
=1 P 1yi
iPisat (10.7), see example 10.3
Example 10.1
Example 10.1 (cont)
Plot Px1y1 at T=75oC
lnP1sat / kPa14.2724 2945.47
T / oC224.00lnP2
sat / kPa14.2043 2972.64T / oC209.00
At 75C,P1
sat 83.21kPa P2sat 41.98kPa
Acetonitrile(1)/Nitromethane(2)Antoine Eqn,
Acetonitrile(1) is more volatile
Example 10.1 (xtra1)
Plot Px1y1 at T=75oC
Calculate P and y1, given a set of x1 and T=75oCThis is BUBL P calculation.
xiKi 1 (10.13) . For Raoult's Law, P xiPisat (10.2) P x1P1sat x2P2sat x1P1sat (1 x1)P2satP (P1sat P2sat )x1 P2sat note: a linear line (y=mx+c)
Calculate P for a set of x1 and then calculate y1using,
y1 x1P1
sat
P
Example 10.1 (xtra2)
Plot Px1y1 at T=75oC y1
x1P1sat
P
183.211750.888074.960.8750.748366.720.6750.569258.470.4750.331350.230.275041.98075y1P(kPa)x1T
P (P1sat P2sat )x1 P2sat
P1sat
P2sat
So now plot Px1y1!!
Point b
Example 10.1 (xtra3)
a liquid solutionor subcooled
liquid mixture
b sat liquid solution or bubblepointPb is by BUBL P
c sat vapor mixtureor dewpointPd is by DEW P
d gas mixtureor superheated
vapor mixtureData from previous slide
Example 10.1 (xtra4)
DEW P calculationCalculate Pd and x1, given y1 and T
So lets calculate Pd at z1=0.6 and T=75oC.This is point c in previous Px1y1 diagram. Note: z1=y1
Then calculate x1 using,
x1 y1PdP1
sat 0.6(59.74)83.21 0.43
yiKi
=1 (10.14) If Raoult's Law valid, Pd 1yiPi
sat (10.3)
Pd 10.683.21
0.441.98
59.74kPa
Example 10.1 (xtra5)
Plot Tx1y1 at P=70kPa
T1sat / oC 2945.47
14.2724 lnP / kPa 224.00
T2sat / oC 2972.64
14.2043 lnP / kPa 209.00
so at 70kPa,T1
sat 69.84C T2sat 89.58C
Acetonitrile(1)/Nitromethane(2)
Antoine Eqn,
Acetonitrile(1) is more volatile
Example 10.1 (xtra6)
Plot Tx1y1 at P=70kPaChoose T between T1sat and T2sat , calculate P1sat and P2sat and use these to calculate x1 by the following eqn.
xiKi 1 (10.13) . For Raoult's Law, P xiPisat (10.2) P x1P1sat x2P2sat x1P1sat (1 x1)P2sat
x1 P P2sat
P1sat P2sat
Calculate x1 for a set of T and then calculate y1 using,
y1 x1P1
sat
P
Example 10.1 (xtra7)
Plot Tx1y1 at P=70kPa y1
x1P1sat
P
0 (x2=1)0.14240.31840.51560.73781 (x2=0)x1
0 (y2=1)89.58 T2sat700.240186700.474282700.675978700.848474701 (y2=0)69.84 T1sat70y1T(oC)P (kPa)
So now plot Tx1y1!!
x1 PP2sat
P1sat P2sat
Example 10.1 (xtra8)
c sat vapor mixtureor dewpointTd is by DEW T
d gas mixtureor superheated
vapor mixture
a liquid solutionor subcooled
liquid mixture
b sat liquid solution or bubblepointTb is by BUBL T
Data from previous slide
Example 10.1 (xtra9)
BUBL T calculationCalculate Tb and y1, given x1 and P.
So lets calculate Tb at z1=0.6 and P=70kPa.This is point b in previous Tx1y1 diagram. Note: z1=x1
xiKi 1 (10.13), For Raoult's Law, Pb xiPisat (10.2) Pb xiPisat Pksat xi Pi
sat
Pksat = Pksat xiik
Pksat Pb
xiik (A) , where ik Pi
sat
Pksat Relative volatility
lnik ln Pisat
Pksat =lnPi
sat-lnPksat = Ai
BiT Ci
- Ak Bk
T Ck
The solution is not straightforward as T is unknown.
Example 10.1 (xtra10)
BUBL T calculationSolution is through iteration,
1. Start with an initial guess of T
T xi Tisat2. Arbitrarily pick a component, e.g. k=2
3. Calculate ik, (note: Number of ik is equal to number of component)
lnik Ai BiT Ci
- Ak Bk
T Ck
T 0.6(69.84)0.4(89.58)77.74oC
12 1.9611 22 1
Example 10.1 (xtra11)
BUBL T calculation
5. Calculate new value of T,
6. Stop if this is equal or close to earlier value of T, else use this value as a new guess. Repeat step 3,4 & 5 until converge.
T Bk
Ak lnPksatCk T
2972.6414.2043 ln44.3977 20976.53
oC
4. Calculate Pksat using eqn A, Pksat P
xiik P2
sat Px112 x222
= 700.6(1.9611)+0.4(1)
=44.3977kPa
Example 10.1 (xtra12)
BUBL T calculation
7. Finally, calculate yi using Raoults law (Use Antoine Eqn for Pisat)
y1=0.7472 (point b)
76.4244.221.971776.4376.4344.241.970376.53TP2sat12T
Answer(point b)
Example 10.1 (xtra13)
Example 10.1 (xtra14)
DEW T calculation
Calculate Td and x1, given y1 and P.
Calculate Td and x1 for z1=0.6 and P=70kPaSee example 10.1 page 356 for the solution (by iteration)DEW T calculation.
Answer: Td =79.58oC (point c)x1=0.4351 (point c)
Example 10.1 (xtra15)
Example 10.1 (xtra16)
Example 10.2 (Henrys law)
Example 10.3 (Modified Raoults law)
Example 10.3 (cont)
Example 10.3 (cont)
Example 10.3 (cont)
Example 10.4 (K-value correlations)
Example 10.5 (Flash calculations)
