Fenskes Method Explained

8/11/2019 Fenskes Method Explained

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1

Distillation

A separation technique based on differences in boiling point

which results in differences in vapor pressure. It is covered by

chapter 11 in the text book.

Pages to be covered in the text 599-621

Partial pressure (PA) of component A is the pressure that A would exert at the same

temperature, if present in the same volumetric concentration as in the mixture.

Daltons law: Total pressure is equal to the sum of the partial pressures

= iPPRaults law and Henrys law: Relates partial pressure to the liquid phase concentration

Raults law for high values of xi, and Henrys law for low values

iiixPP o=

iiHxP=Raults: Henrys:

Partial pressures, and Daltons,

Raults and Henrys laws

Binary system: equilibrium

Relative volatility:2

1

2

2

1

1

12K

K

xy

xy

=

Where:

( )( )11

11

2

2

1

1

2

112

1

1

yx

xy

xy

xy

K

K

===

121 =+xx 121 =+yyand

( )11 121112

1+

=

x

xy

( )11212

1

1

1y

yx

=


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Vapor liquid equilibrium (VLE):Binary system

Different types types of VLE

Distillatiom

Fn, zi,nVn, yi,n

Ln, xi,n

Stage n

Vn, yi,n

Ln, xi,n

Ln+1, xi,n+1

Vn-1, yi,n-1

Qn

Column

Reboiler

Total-

condensor

F, xF

W, xW

D, xD

rectifier

l

stripper

L

D

LR=Reflux

ratio


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Column: Binary

Balances over thewhole column

Reboiler

Total-

condenser

F, xF

W, xW

D, xDL

Total balance: WDF +=

WDF WxDxFx +=

condenserWDreboilerF QWhDhQFh ++=+Energy balance:

Component balance:

Equilibrium stage:

Binary stagen

Vn, yn

Vn+1, yn+1Ln, xn

Ln-1, xn-1

Total balance: nnnn VLVL +=+ + 11

Energy balance:

Component balance: nnnnnnnn yVxLyVxL +=+ ++ 1111

nnnnnnnn HVhLHVhL +=+ ++ 1111

Equilibrium relation: )( nn xfy =

Equilibrium stage:Binary steg n

Vn, y

n

Vn+1, yn+1Ln, xn

Ln-1, xn-1

It is assumed that there is constant molar overflow

Total balance: VLVL +=+

Energy balance:

Component balance: nnnn VyLxVyLx +=+ + 11

nnnn VHLhVHLh +=+ + 11

Equilibrium relation : )( nn xfy =


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Binary distillation: How many stages

are necessary for separation?

Reboiler

Total-condenser

F, xF

W, xW

D, xDL

1. - Sorels method

algebraic

2. - McCabe-Thieles method

graphical

McCabe-Thieles mehtodConstant molar overflow

upper operating line (system A)

F, xF

W, xW

D, xD

ym+1 xm

yn+1 xn

A

B

y L

Vx

D

Vxn n D+ = +1

R L

D=

V L D= +

L R D=

( )V R D= + 1

y R

Rx

Rxn n D+ = +

++1 1

1

1

McCabe-Thieles mehtod

Constant molar overflow

Draw in the upper operating line

in the equilibrium diagram

y R

Rx

x

Rn n

D+ = +

++1 1 1

x

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

y

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

xD

upper operating liney

n+1=x

Dx xn D=

y R

Rx xn D D+ =

+

+ =1

1

1

x n = 0

y x

Rn

D+ =

+1

1


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q line

For a two phase feed (assumed in equilibrium)

F hF = LF hL + VF hvwhere,

hF = specific enthalpy of feed

hL = specific enthalpy of saturated liquid

hv = specific enthalpy of saturated vapor

Generalize by defining q:

q = Enthalpy change reqd to vaporize 1 mole of feed/

molar enthalpy of vaporization

= (hv - hF) / (hv - hL)

q > 1Sub-cooled Liquid

q = 1Saturated LiquidhL

0 < q < 12-phase feed

q = 0Saturated Vaporhv

q


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Total reflux

Minimum reflux

Optimum reflux ratio is usually1.2-1.5 times minimum


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Merill R. Fenske, 1932

In the design of any (distillation) column it is importantto know at least two things. One is the minimum

number of plates required for the separation if no

product, or practically no product, is withdrawn from

the column. This is the condition of total reflux. The

other point is the minimum reflux that can be used to

accomplish the desired separation. While this case

requires the minimum expenditure of heat, it

necessitates a column of infinite height. Obviously, all

other cases of practical operation lie in between these

two conditions.

Multi-component distillation

The availability of large electronic computers

has made possible the rigorous solution of

the equilibirum-stage model for

multicomponent, multi-stage distillation

column to an exactness limited only by the

accuracy of the phase-equilibrium and

enthalpy data utilized.

Buford D. Smith, 1973

Binary vs. Multicomponentdistillation

Binary:

Unique equilibrium curve under constant pressure

Feed and distillate compositions for onecomponent known => bottoms product may bechoosen, D and W calculated by MB

Multicomponent:

Equilibrium depends on all components

Not same freedom of choice.

Complete composition of top and bottom productcannot be fixed => trial&error calculations


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9

Multi-component distillation

Component1

2

3

4

5

.

.

.

LK (Light Key) primary goes overhead

HK (Heavy Key) primarily goes to bottoms

tex

tex

HHK (Heavy Heavy Keys) main component in botten

LLK (Light Light Keys) main component in heads

Separation is between LK and HK

Ex: methanol, ethanol, n-propanol, water & n-butanol. Split between ethanol och water.

Minimum reflux ratio

Binary: Rm gives pinch at F

Multicomp: Two pinches, one in stripping andone in rectifying section

i. If no components lighter than LK;

stripping pinch near feed plate

ii. If no components heavier

than HK; rectifying pinch

near feed plate

F

W

D

M

Ny

LK

xLK

Multi-component distillationShort-cut method

Gillilands correlation (Stages vs Reflux)

Erbar-Maddox correlation (L/V vs. Nmin/N)

Fenskes equation (Nmin)

Underwoods method (Rmin)

Colburns method (Rmin)


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Gillilands correlation

Gilliland found a graphical correlation between N

and Ras a function of Nmin and Rmin :

56680

1750750

1

.

minmin

R

RR..

N

NN

+

=

+

Underwoods method

qx

i r,i

F,ir,i =

1

1+=

Mini r,i

D,ir,i Rx

And r is a reference component

is a root betweenLKand HK

Distillation: Rigorous methods

Fn, zi,nVn, yi,n

Ln, xi,n

stage n

Vn, yi,n

Ln, xi,n

Ln+1, xi,n+1

Vn-1, yi,n-1

Qn


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"Inside-out" algorithm

There is an inner and outer calculation loop for each tray.

In the inner loop there are calculations with

the MESH-equations. These are done using

simplified expression for equilibrium realtions

,etc..

In the outer loop these values are corrected

for the more rigourous expressions.

Example of simplified expressions

T

BAK

KK

r

rrii

=

=

ln

,

Equilibrium:

Enthalpy:*)(

*

TTDCH

HHH

iiii

iii

=

+=

Different flowsheeting programs

ASPEN

ChemCAD

Hysys - Hysim

Pro II

Massball

Gems - Wingems - Mops


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Method

Condenser

Pressure

R/Rmin

LK & HK

"Recovery":

Condenser

Pressure

Number of

trays

Feed tray


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Specification of top and bottom of column

Distillation

and reflux

rates

Temperature

in top and

bottom

Number of interations is usually 20.

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Fenskes Method Explained

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