thermo vle part 02

5/25/2018 Thermo Vle Part 02

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VAPOR/LIQUID EQUILIBRIUM


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Review

What is bubble point?

What is dew point?

We have previously go through the 2 simplestmodels for solving VLE problems

Raoults Law

Henrys Law


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Lecture Overview

1. VLE by modified Raoults Law

2. VLE from K-value correlations

Flash calculation

3. Summary


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VLE

Raoults Law Henrys Law ModifiedRaoults Law

K-Values


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The 2ndassumption of Raoults Law is abandoned,taking into account the deviation from solution

ideality in L phase.

Thus, activity coefficient is introduced inRaoults Law

Modified Raoults Law

NiPxPy sat

iiii ,...,2,1


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Activity coefficients are function of T & liquidphase composition, x

1i iy

isatiii PxP

i

sat

iii PyP

1

For bubble point

For dew point

Since;


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Example 10.3

For the system methanol(1)/methyl acetate(2),the following equations provide a reasonable

correlation for the activity coefficients:

2

21ln Ax2

12ln Ax

Where A=2.771-0.00523T.In addition, the following Antoine equations

provide vapor pressures;

424.53

54.665,22043.14ln

424.3331.643,359158.16ln

02

01

CtkPaP

CtkPaP

sat

sat


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Find;a) P and {yi}, for x1=0.25 and T=318.15Kb) P and {xi}, for y1=0.60 and T=318.15Kc) T and {yi}, for x1=0.85 and P=101.33kPa

d) T and {xi}, for y1=0.40 and P=101.33kPae) The azeotropic pressure, and the azeotropic

composition, for T=318.15K


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a) P and {yi}, for x1=0.25 and T=318.15K

This is a BUBL P calculation.

For T=318.15K, the Antoine equations yield:

kPaPkPaP satsat 54.6551.44 21

Activity coefficients are calculated from the givenequations;

2

21ln Ax2

21ln Ax

864.175.0107.1exp)exp( 2221 Ax

072.125.0107.1exp)exp(22

12

Ax


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)64.65)(072.1)(75.0()51.44)(864.1)(25.0( P

kPaP 50.73

282.01111 P

Pxy

sat718.02222

P

Pxy

sat

b) P and {xi}, for y1=0. 60 and T=318.15K

This is a DEW P calculation.

For T=318.15K, values of Psatfrom Antoine

equations and Aare unchanged. However, liquid

composition is unknown, but is needed for

calculation of activity coefficient .


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Therefore, an iterative scheme is indicated:

1)First, assume 1=2=1.0 (Ideal solution)

2)Calculate PDEWfrom:

3)Calculate x1by x1=y1P/1P1satand then x2from

x2=1-x14)Evaluate 1and 2.

5)Using these values, go back to step (2) and

repeat the procedure.6)Iteration to convergence yield:

i

sat

iii PyP

1

P = 62.89 kPa x1= 0.8169

1= 1.0378 2= 2.0935


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(c) BUBL Tcalculation.

1)First, assume system temperature, Tusing Antoine Eqnand averaging of Tsatusing mole fraction:

T = xiTisat

2)Calculate 1, 2and a P1sat/P2

sat

3)Find a new value for P1satfrom:

4)Find new value of T from:

5)Use this T and compute from Step (2) untilStep (4).

6)Compare the Tnewobtained in Step (4) with Told.If not same, repeat procedures till you get Tnew= Told.

a /22111

xx

PPsat

1

11

1

lnC

PA

BT

sat


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BUBL PBUBL P CALCULATION

Findsat

iP

Find i

Find P from equation 10.6satsat PxPxP 222111

Find iy from equation 10.5

PPxy sat

iiii


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DEW PDEW P CALCULATION

Find satiP

Find1

& 2 . Initial guess is=1

Find P using equation 10.7

satsatPyPy

P222111

1

Find xi using equation 10.5sat

iiii PPyx

Evaluate from the given

equation

Converge?NO

YES

It is the P dew.

Find liquid phase mole fraction

satPPyx 11

& 12 1 xx

BUBL T CALCULATION


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BUBL TBUBL T CALCULATION

Find initial T from mole-fraction weighted averagesatsat

TxTxT 2211

Find satiT

For current T, find A, 1 , 2 ,satsat PP 21a

Find new value for satP1 from equation 10.6;

a 22111

xx

PPsat

Find new T from Antoine equation for species 1

1

11

1

lnC

PA

BT

sat

Converge?NO

YES

It is the T bubble.

Find satiP , A and 1 & 2

Find vapor phase mole fraction

PPxy sat1111

& 12 1 yy

DEW T CALCULATION


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DEW TW C CU ON

Find initial T from mole-fraction weighted averagesatsat TyTyT 2211

Find satiT

For current T, find A, satsat PP 21 , satsat PP21a

Find new value for satP1 from equation 10.7;

a 2

2

1

11

yyPPsat

Find new T from Antoine equation for species 1

1

11

1

lnC

PA

BT

sat

Converge?NO

YES

It is the T bubble.

Find satiP , A and 1 & 2

Find vapor phase mole fraction

PPxy sat1111 & 12 1 yy

Find satPPyx 1111 & 12 1 xx

Calculate 21 & from given correlation


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AZEOTROPE

When x1=y1, the dew

point and bubble pointcurves are tangent tothe same horizontal line

A boiling L of this

composition produce avapor exactly the samecomposition; L does notchange in composition

as it evaporates


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)8.10(22

1112

xy

xy

a

Relative volatility;

sat

sat

xP

AP

2

1

012exp

1a

AP

Psat

sat

x

exp2

1

112 1a

If one limit is >1 &the other limit is


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VLE from K-Value

i

ii

x

yK

PPK

sat

iii P

PK

sat

ii

Ki: equilibrium ratio i.e. measure of lightness

(tendency to favor vapor phase)

Raoults Law Modified

Raoults Law

Maybe determined fromcalculation or DePriester

chart


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1

1

ii

i

iii

xK

y

xKy

Bubble point

Must find thesets of Ks thatsatisfy thisequation

1

1

ii

i

iii

Ky

y

Kyx

Dew point

Must find thesets of Ks thatsatisfy thisequation


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K-valuefromDePriester

chart-Low Trange


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K-valuefromDePriester

chart-High Trange


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When given a mixture of composition at certainT or P;

Bubble point

- Insignificant L

-The given molefraction is yi

- Need to satisfy

equation 10.14

- Composition ofdew is xi=yi/Ki

Dew point

-System is almostcondensed

-The given molefraction is xi

- Need to satisfy

equation 10.13

- Composition ofbuble is yi=Kixi


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FLASH CALCULATION

V

L

Feed, F

Vapor, V

Liquid, L

Liquid at P > Pbubblepartially evaporateswhen P is reduced,

producing 2-phasesystem of V & L inequilibrium

Find; T, P, z


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FLASH CALCULATION

Find BUBL P with ii xz ; bubbleP

Find DEW P with ii yz ; dewP

Using equation 10.11, find iK

Is the given P

between

dewbubble PP & ?

NO

No need for flash

calculation

YES

Substitute iK in equation 10.17. By trial & error,

solve for V. Then L=1-V

Solve equation 10.16 for each component - iy

Solve equation 10.10 for each component - ix

Flowchart forflashpressure


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V

L

Feed, F =1 mol

Acetonitrile 0,2

Nitrometane 0,35

Aceton 0,45

Vapor, V

Liquid, L

T = 80 C

P = 110 kPaTentukan fraksi mol difaseCair dan uap!


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TUGAS:

Suatu campuran pengolahan minyak bumi

terdiri dari nC3 10%, nC4 20%, nC5 20%, nC6

30%, sisanya nC7. temperatur campuran 93 F.

tentukan kondisi bubble pointnya!

Suatu campuran terdiri dari Aceton 50%,

Acetonitrile 20%, sisanya Benzene. temperatur

campuran 75 C. tentukan kondisi bubblepointnya!


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Suatu campuran pengolahan minyak bumi

terdiri dari i-C3 20%, nC3 20%, i-C4 20%, n-C4

15%, sisanya I-C5 20%. Tekanan 120 Psia.

tentukan kondisi dew pointnya!


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V

L

Feed, F = 100kg/mol

benzen 0,5

Toluen 0,3

Acetonitril 0,2

Vapor, V

Liquid, L

T = 87 C

P = 1 atmTentukan fraksi mol difaseCair dan uap!


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thermo vle part 02

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