Multicomponent Mixtures-Distilation-Lecture Slides, Slides of Chemical Separation Processes

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Process Mass & MomentumProcess

Mass & MomentumTransfer

DISTILLATIONDISTILLATION

Dr. Muhammad Tayyeb Javed

DCE-PIEASDCE PIEAS

Multicomponent Mixtures^ „^ Equilibrium Data^ ‰^

For a binary mixture under constant pressure conditionsthe vapour liquid equilibrium curve for either component isunique (Simple method of McCabe-Thiele) ‰ With a ternary system the conditions of equilibrium aremore complex, for at constant pressure the mole fractionof two of the components in the liquid phase must beof two of the components in the liquid phase must begiven before the composition of the vapour in equilibriumcan be determined, even for an ideal systemThus the mole fraction y

in the vapour depends not only

‰^ Thus

the^ mole

fraction

yin the vapour depends not onlyA^

on xA

in the liquid, but also on the relative proportions of

the other two components

Multicomponent Mixtures „^ Feed & Product Compositions^ ‰^

With a binary system, if the feed compostion x

and the topf^

product composition x

are known for one component, thend

the^ composition

of^ the

bottom

xcanw^

have

any^

desired

value, and a material balance will determine the amounts ofth^ t^

d b^ tt

d^ t^

D^ d W

the top and bottom products D and W ‰ This freedom of selecting the compositions does not applyfor mixtures with three or more components ‰ Gilliland and Reed have determined the number of degreesof^ freedom

for

the

continuous

distillation

of^

a

multicomponent mixture ‰ For the common case in which the feed composition, natureof feed, and operating pressure are given, there remain onlyfour variables that may be selected

Multicomponent Mixtures „^ Feed & Product Compositions… Contd..^ ‰^ If the reflux ratio R is fixed and the number of plates above and below the feedplate are chosen to give the best use of the plates

then only two variables

plate are chosen to give the best use of the plates, then only two variablesremain ‰ The complete composition on neither the top or bottom product can then befixed at will ‰ This means that some degree of trial and error is unavoidable in calculatingthe number of plates required for any separation ‰ Thus^ if a trial composition is taken

and it is found that for a given bottom

‰^ Thus, if a trial composition is taken, and it is found that for a given bottomcomposition the desired top composition is not obtained with the selectedreflux ratio, then an adjustment must be made in the bottom composition ‰^ An exact fit in a calculation of this kind is not essential since the equilibriumdata and the plate efficiency will be known with only limited accuracy ‰^ This problem is frequently simplified if a sharp cut is to be made between thecomponents, so that all of the MVC appear in the top and all of the LVC in thebottom productbottom product

No of Plates^ „^ One of the most successful methods for calculatingthe number of plates necessary for a given separation

p^

y^

g^

p

is due to Lewis and Matheson „ This is based on Sorel-Lewis method „ If the composition of the liquid on any plate is known,then the composition of the vapour in equilibrium iscalculated from a knowledge of the vapour pressurescalculated from a knowledge of the vapour pressuresor relative volatalities of the individual components „ The composition of the liquid on the plate above isth^

f^ d b

i^

ti^

ti^

t

then found by using an operationg equation, separateequation for each component

No of Plates

1

+^

+^

+^

+^ ......

1

A^

B^

C^

D

y^

y^

y^

y

+^

+^

+^

+^

=^1 .... C A^

B^

D y y^

y^

y +^

+^

+^

+^

=....

B^

B^

B^

B^

B

y^

y^

y^

y^

y

1

C

A^

B^

D x

x^

x^

x

a^

a^

a^

a

+^

+^

+^

+^

=....

AB^

BB^

CB^

DB

B^

B^

B^

B^

B

x^

x^

x^

x^

y

a^

a^

a^

a

+^

+^

+^

x^ BBB

x

α α^

∑^

=^

xBBB

y

α

,^

;^

; C^ CB

A^ AB^

D^ DB

A^

C^

D x

x^

x

Similarly

y^

y^

y a

a^

a

=^

=^

=

B x α = AAB y ∑^

= ∑

AAB B^

x

y

α

,^

;^

;

(^

)^

(^

)^

(^

)

A^

C^

D

AB^ A^

AB^ A^

AB^ A

Similarly

y^

y^

y

x^

x^

x

a^

a^

a

å^

å^

å

Composition of vapour is found from information of relative volatility and fromthis composition of liquid is found from operating line equation as in LS method

8

this, composition of liquid is found from operating line equation as in LS method

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Minimum Reflux Ratio^ „^ In^

multicomponent

distillation

there

are^ thus

two^

pinched-in-

regions. In locating these pinched in regions it may be notedth tthat:1)^ If there are no components lighter than the light key, then allof the component appear in the bottoms and the pinch in thet i

i^

ti^ ill b

th^ f^

d^ l t

stripping section will be near the feed plate2) If there are no components heavier than the heavy key, thenall of the components will appear in the top and the upperi^ h i

l^

t th^ f^

d^ l t

pinch is also at the feed plate „^ If^ both

of^ these

conditions

are^ true,

then^

the^ two

pinches

coincide at the feed plate, as for a binary system „ For a general case, a number of proposals have been made forlocating the pinched regions and hence the minimum reflux ratioR^ m

Colburn’s Method for R

m

„^ Let A and B be the light and heavy key components „^ Similar method as for binary mixture

⎫ ⎬ ⎭ ⎧^ −⎨−⎩ =^

dBAB dA m^

x x x x R

α (^1) α 1

x^ and xdA^

are the top and pinch compositions of the light key componentnA^ x^ and xdB^

are the top and pinch compositions of the heavy key componentnB^ i th l t lit

f th

li^ ht k

l ti

t^ th

h^

k^

⎭ t −^ ⎩

nB nA AB^

x x α^1

 is the volatality of the light key relative to the heavy key component AB^ „^ xnA

and^

xarenB^

known

where

the^

pinch

coincides

the^

feed

composition

(^

)^

rf

x^ approx

=^

(^

nA .) B

x x^ approx

=

r^ is the estimated ratio of key components on feed plate, for an all liquidf^ feed at its boiling point, r

(^ .)^ equals the ratio of key components in the feed,f^

(^

)(^

)

nA

f^

fh

x^ approx

r^

xa +^

+^ å^

(^

.) nB

f x^ approx

r

otherwise r

is the raio of the key components in the liquid part of the feedf^ Xis the mole fraction of each component in the liquid portion of feed fh^ heavier than the heavy keyi^ th

l t lit

f^

t^ l ti

t^ th

h^

k

^ is the volatality of component relative to the heavy key

Colburn’s Method for R

m

X^ and xm^

are the compositions of a given heavy component at thew

pinch and in the bottomd^

th^

iti^

f th^

li^ ht k

t^ t

xand xmA^

are the compositions of the light key component atwA

the pinch and in the bottomL /W is the molar ratio of the liquid in the stripping section to them b^ tt^

d^ t

bottom product is the volatality of the light key relative to the heavyAB^ key  is the volatality of the component relative to the heavykeyThe^ second

term

in^

the^ denominator

usually

may

be

neglected

Colburn’s Method for R

m

„^ The assumed value of R

is checked with the relationm ∑

−∑ == −

) (^1) )( (^1) (

1

nn mm m n

xb xb r r

α ϕ

r^ is the ratio of the light key to the heavy key in the stripping pinchm^ r^ is the ratio of the light key ot the heavy key in the upper pinchn^ ∑ b  xm

is the summation of bm^

 x^ for all components heavier than themm^

heavy key in the lower pinch ∑ bx^ is the summation of bnn^

x^ for all components lighter than light key innn^

the upper pinch

f^

f

b, bm^ n^

are the factors shown in figure

No of Plates at Total Reflux „^ By

applying

Fenske’s

equation

to^

the^

two^

key

y^ pp y

g^

q^

y

components

)() (log 1

B^ sd A xxA xxB ⎫ ⎬ ⎭ ⎧ ⎨ ⎩

)^. log( 1

AB avAB n

α

⎭ ⎩=

Relation b/w R and No of Plates Gilliland has given an empirical relation betweenthe reflux ratio R and the number of plates n, in

p^

,

which only the minimum reflux ratio R

and them^

number of plates at total reflux n

are requiredm