multi component distillation

Mass transfer process of separation based on distribution between the vapor and liquid phases.

ABC

Distillate (D)

Feed (F)

Vapor rate (V)

bottoms

3

BOTH involve mass transfer & equilibrium

Differences- 1) All components in the mixture transfer during distillation (this complicates equilibrium calculations). Vap/Liq Equilibrium = All components exist in both phases Gas/Liq Equilibrium = Only 1 component exists in both phases

2) Addition of heat is required for distillation

3) Degrees of freedom for distillation of a binary mixture (2 components) F=C-P+2 = 2-2+2= 2 (Absorption has 3 degrees of freedom)

4) Only 1 feed stream in distillation (2 in absorption/stripping)

• Most of the distillation processes deal with multicomponent mixtures

• Multicomponent phase behaviour is much more complex than that for the binary mixtures

• Rigorous design requires computers

• Short cut methods exist to outline the scope and limitations of a particular process

As in binary mixtures calculations of equilibrium stages usage multi component mixtures also requires

material balances for each component overall and for each stage

one enthalpy balance overall and one for each stage

complex phase Equilibria

variables No. to be specified

Feed rate (F) 1

Feed composition 3

Quality of feed 1

Distillate 1

Bottom product 1

Reflux ratio 1

Reflux condition 1

Optimum feed plate 1

Total 10 (= C+6)

Distribution Coefficient or K factorsK's = fn(T, P, comp) Ki = yie/xie

If Dalton’s law and Roult’s law hold thenKi = Pi’/P

We can Use Relative volatility for each component in system instead of K's

Relative volatility for each component based on one base component key

IIJ

J

m

m

Bubble point

Dew point

*

,

,

1.0i

i j ii

i j i

y

xy

x

*

,

,

1.0

/

/

i

i i ji

i i j

x

yx

y

Vaporizing a definite fraction of liquid Evolved vapor in equilibrium with

residual liquid Separate vapor from liquid and then

condense No reflux

1FiDi Bi

x fy x

f f

11Di Fi

iBi Bi

y xK f

x f x

1 1

1( 1) 1

Nc NcFi

Bii i i

xx

f K

Tools: Material balance Energy balance

Thermodynamic equilibrium Bubble point / dew point summation

Specifications: PurityRecovery

In multi component separation involving n species, n-1 columns are needed to totally separate all n species

Computers usually used because of the large number of variables (T,P, composition, flow rates) and because iterative solution is necessary

Two different Methods are commonly used to specify computer input

I. specify feed condition, desired separation between 2 components, and reflux ratio II. specify feed condition, no. of stages, and reflux ratio

Light key : designated by L Heavy key : designated by H

Only KEY components are present in significant amounts in both Distillate and Bottom

Usually, L & K are adjacent in rank order of volatility. This is called a "sharp" separation

• Components that are present in both the distillate and the bottoms product are called distributed components

- The key components are always distributed components

• Components with negligible concentration (<10-6) in one of the products are called undistributed

A B C D E G

key components

heavy non-distributed components(will end up in bottoms product)

light non-distributed components(will end up in the overhead product)

Assumption: relative volatilities of components remain constantthroughout the column

1ln

ln

,

,

,

,

,

min

HKLK

HKD

HKB

LKB

LKD

x

x

x

x

N

LK – light componentHK – heavy component

)(

)()(, TK

TKT

HK

LKHKLK

xN+1yN

x1yo

1

N

Total Reboiler

)(

)()(, TK

TKT

HK

LKHKLK

Choices for relative volatility:

B

T

1) Relative volatility at saturated feed condition

)(,, F

FHKLK T

HKLK

2) Geometric mean relative volatility

)()(,,, B

BD

DHKLK TT

HKLKHKLK

3, )()()(

,,, BB

DD

FF

HKLK TTTHKLKHKLKHKLK

HKB

HKDNHKi

iB

iD

x

x

x

x

,

,1,

,

, minHK

iHKi K

K,

HKB

HKDNHKi

HKB

HKDNHKiiF

iD

Bx

Dx

Bx

DxFx

Dx

,

,1,

,

,1,,

,

min

min

1

•Maximum ratio which require infinite no. of trays for desired separation• •At the minimum reflux ratio condition invariant zones occurs above and below the feed plate, where the number of plates is infinite and the liquid and vapour compo-sitions do notchange from plate to plate

• Unlike in binary distillations, in multicomponent mixtures these zones are not necessarily adjacent to the feed plate location

y

xzf

zf

xB xD

y1

yB

xN

* Relative volatility of each component has to be the same for each invariant zone

* Constant molar overflow

* αi=Ki/Kref (Usually Kref=KHK)

The operating line equations for each section of the column become:

Underwood method

Bimi

REFimi

DiniREFi

ni

BxyK

LyV

DxyK

LVy

,,1,

,,1,

rectifying section

stripping section

Bimi

REFimi

DiniREFi

ni

BxyK

LyV

DxyK

LVy

,,1,

,,1,

rectifying section

stripping section

In the invariant zones: ,,1, inini yyy

Bii

REFi

DiiREFi

BxyK

LV

DxyK

LV

,,

,,

A

x

VKL

xy

D

V

A

x

VKL

xy

D

V

i

Bii

REFi

Bii

i

i

Dii

REFi

Diii

,,,

,,,

Underwood method

Minimum reflux ratio analysisMinimum reflux ratio analysis

A

x

B

Vy

D

V

A

x

D

Vy

D

V

i

Bii

i

i

Diii

,,

,, We are looking for a condition where

this is correct. In general there are multiple solutions

But consider the following

)1(,, qFA

xB

A

xDVV

i

Bii

i

Dii

Underwood method


)1(,, qFA

xB

A

xDVV

i

Bii

i

Dii

In other words:

A

xB

A

xD

A

xB

A

xDqF BDBD

2

,22

2

,22

1

,11

1

,11)1(

Under Underwood conditions: A=Ā, ii

A

x

A

x

A

xq

i

FiiFF

,

2

,22

1

,11)1(

Underwood method


i HKi

iFHKi

A

xq

,

,,)1(

i HKi

iDHKim A

x

D

VR

,

,,1

For a given q, and the feed composition we are looking for A satisfies this equation(usually A is between αLK and αHK.

Once A is found, we can calculate theminimum reflux ratio

Underwood method

11min

D

DmD

R

RRf

N

NN

Kirkbride equation: Feed stage locationKirkbride equation: Feed stage location

206.02

,

,

,

,

D

B

x

x

x

x

N

N

HKD

LKB

LKF

HKF

S

R

R SN N N

Complete short cut design: Complete short cut design: Fenske-Underwood-Gilliland methodFenske-Underwood-Gilliland methodGiven a multicomponent distillation problem:Given a multicomponent distillation problem:

a) Identify light and heavy key components

b) Guess splits of the non-key components and compositionsof the distillate and bottoms products

c) Calculate

d) Use Fenske equation to find Nmin

e) Calculate distribution of non key components

f) Use Underwood method to find RDm

g) Use Gilliland correlation to find actual number of ideal stages given operating reflux

h) Use Kirkbride equation to locate the feed stage

HKLK ,

Two broad categories1. Equilibrium methods

2. Rate based models

Equilibrium methods solve MESH equation simultaneously

Rate based method solve mass and heat transfer equations in terms of available driving force

MESH equations

M- Material balance equationsTotal material balance:

Component i balance:

1 1 ( ) ( ) 0n n n sn n sn nL V F L L V V

1 1 1 1 , , ,. ( ). ( ). 0n n n n n i n sn n i n sn n i nL x V y F z L L x V V y

E- Equilibrium relations

S- summation of mole fractions

and

H- Heat (Enthalpy) balance

, , , , , , 1. . (1 ). 0MG i n i n i n i n MG i n i nE K x y E y

, 1i ni

y , 1i ni

x

1 , 1 1 , 1 , , ,. ( ). ( ). 0n L n n V n n F n sn n L n sn n V n nL H V H F H L L H V V H Q

Consider that murphee efficiency of plates varies from plate to plate

A simulation program RATEFRAC available in ASPEN PLUS

In order to have stable operation in a distillation column, the vapor and liquid flow must be managed.

Requirements are:

vapor should flow only through the open regions of the tray between the downcomers liquid should flow only through the downcomers liquid should not weep through tray perforations liquid should not be carried up the column entrained in the

vapor vapor should not be carried down the column in the liquid vapor should not bubble up through the downcomers

Single Pass Two Pass Four Pass

Types of traysTypes of trays

1. Sieve plates

2. Bubble-cap plates

3. Valve plates

Types of traysTypes of trays

In order to get a preliminary sizing for distillation column, we need to obtain values for

the tray efficiency the column diameter the pressure drop the column height

Stage efficiency analysisStage efficiency analysis

Step 1: Thermodynamics data and methods to predict equilibrium phase compositions

Step 2: Design of equilibrium stage separation

Step 3: Develop an actual design by applying the stage efficiency analysis to equilibrium stage design


In general the overall efficiency will depend:

1) Geometry and design of contact stages

2) Flow rates and patterns on the tray

3) Composition and properties of vapour and liquid streams


Lin,xin

Lout,xout

Vout,yout

Vin,yin

Local efficiency

1*

1

nn

nnmv yy

yyE

Actual separation

Separation that would have been achieved on an ideal tray

What are the sources of inefficiencies?

For this we need to look at what actually happenson the tray


Depending on the location on the tray the point efficiency will vary

high concentrationgradients

low concentrationgradients

stagnation points

The overall plate efficiency can be characterized by the Murphreeplate efficiency:

1*

1

nn

nnmV yy

yyE

When both the vapour and liquidphases are perfectly mixed the plateefficiency is equal to the point efficiency

mvmV EE

Point efficiency


In general a number of empirical correlations exist that relate point and plate efficiencies

ce

LPe tD

ZN

2

Peclet number

length of liquid flow path

eddy diffusivity residence time of liquidon the tray


In addition we need to take in account effects of entrainment

Entrained liquid droplets

Dry Murphree efficiency can be corrected for theentrainment effects by Colburn equation:

11 mV

mVa

E

EE entrainment fraction =

entrained liquid/gross liquid flow


Finally the overall efficiency of the process defined as

ltheoretica

actualO N

NE

U C C F F F C

F F foam factor C

F forA

AF

A

Afor

A

A

DV M

f UA

A

whereA

A

floodL V

V

ST F HA F

ST F F

HAh

a

HAh

a

h

a

T

vapor

floodd

V

d

1 2

0 2

20

10 010 5 05 0 06 010

4

1

01

/

.

. . . . .

: . (typical value)

0.50

Column Height = # actual stages x tray spacing + space allowance for feed/draws + sump + top volume

Tray spacing for most applications is 18-24 inches

Circulating Pump

Heating Medium

Forced Circulation

Top Tray

Heating Medium

Vertical Thermosiphon

Top Tray

Bottoms ProductBottoms Product

Reboilers

Heating Medium

Kettle

Top Tray

Heating Medium

Horizontal Thermosiphon

Top Tray

Bottoms Product

Bottoms Product

Reboilers

Fouled Structured Packing Damaged Valve Tray

Plugged Distributor Tray “Blanking” Strips

Dis

tanc

e fr

om t

ower

top

Tra

y N

umbe

r

Tower Scan

Binary mixtures having nearly equal to 1

Separation difficult even of ideal mixtures

Third component is used

Two types:I. Extractive distillation II. Azeotropic distillation

non volatile solvent is used

Associate with one of the component and increase

Solvent selectivity:ability to enhance the separation of key component

Entrainer is added Entrainer forms an

low boiling azeotrope with one component

multi component distillation

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