5-vapor liquid equilibrium._depriester chart
DESCRIPTION
VLETRANSCRIPT
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SKF 2213 Chemical Engineering Thermodynamics
Chapter 10: Vapor/Liquid Equilibrium
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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.
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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.
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Under surface issaturated-vapor (P,T,y1 surface)
Below that is gasphase.
Top surface issaturated-liquid(P,T,x1 surface)
Above that isliquid phase.
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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
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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
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Commonly found shape of Pxy
diagrams at constant T
This is similar shape toFigure 10.2 (a)
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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)
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y1-x1 diagrams at constant P
Azeotrope
Azeotropex1=y1 x2=y2Liquid composition= Gas composition
- For Raoults law, needs PisatTherefore requires T
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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.
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Read value of K-valueat given T and Pe.g. 1000 kPa and 0 oC
for methane
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Bubblepoint & DewpointCalculations
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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
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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
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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
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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.
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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
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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)
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xi yi 0zi
1V(Ki 1) ziKi
1V(Ki 1) 0
zi ziKi1V(Ki 1) 0
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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
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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
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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
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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
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Example 10.1
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Example 10.1 (cont)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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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)
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Example 10.1 (xtra14)
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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)
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Example 10.1 (xtra16)
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Example 10.2 (Henrys law)
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Example 10.3 (Modified Raoults law)
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Example 10.3 (cont)
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Example 10.3 (cont)
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Example 10.3 (cont)
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Example 10.4 (K-value correlations)
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Example 10.5 (Flash calculations)