Seperation processes CHEN 312 Lecture 2

8/9/2019 Seperation processes CHEN 312 Lecture 2

1/19

Ideal Solution & Raoult's Law

Raoult's Law states that, for an ideal solution, the equilibrium partial

pressure of a component at a fixed temperature T equals the product

of its vapor pressure (when it is pure) and its mole fraction in theliquid:

pA !"AxA

where

pA equilibrium partial pressure of component#A in the $as at

temperature T

!"A vapor pressure of pure liquid A at temperature T

xA liquid#phase mole fraction of component#A at temperature T

Note: The vapor pressure is a constant at constant temperature%

&ence, from the equation, we see that Raoult's Law predicts a linear


2/19

Daltons Law

alton's law states that the total pressure exerted b the mixture

of non#reactive $ases is equal to the sum of the partialpressures of individual $ases%

Total pressure, !T pA p* !"AxA !"*x*

!"AxA !"*(+ # xA) xA(!"A !"*) !"*

-f the vapor ma be ta.en as an /ideal $as0 then:

xPxP

xP

BOBAOA

BOB=

+

=

+ xPxP

xP

BOBAOA

AOA

)P(PxP

xP

OBOAAOB

AOA

+

)P(PxP

xP

OAOBBOA

BOB

+p* !T * * p*1!T

pA !T A A pA1!T


3/19

The constant-temperature phase

diagramfor an ideal solution isshown%

2or a binar mixture of A and *3

pA !"AxA3 p* !"*x* !"*(+ # xA)

The partial pressures var linearlwith xA% This is shown as pAvs% xA

and p*vs% x*

2or an ideal $as mixture, the total

pressure is the sum of the partialpressures%

Total pressure !T pA p*%

!"A

!"*


4/19

Relative olatilit!

istillation processes require a difference in volatilities of the

components% The greaterthe difference, the easierit is to separatethe components% A measure for this is termed the relative volatilit%

4olatilit of component#i: partial pressure of component#i divided b

mole fraction component#i in liquid

2or a binar mixture of A and *, therefore:

4olatilit of A pA1 xA 4olatilit of * p*1 x*

where p is the partial pressure of the component and x is the liquid

mole fraction%

Relative volatilit: the ratio of volatilit of A (5ore 4olatile 6omponent546) over volatilit of * (Lower 4olatile 6omponent L46):


5/19

Relative volatility is therefore a measure of separability of A and B.

Since xB= 1 - xA, we have

Replace with pA = yA!" # pB = $ 1 - yA %!" so as to express

everythin& in terms of the '()

*roppin& subscript +A+ for more volatile component, and

simplifyin& we obtain the euation for relative volatility


6/19

"he larger the value of above 1.,the greater the de&ree of separability,i.e. the easier the separation. Recallthat when a system has reachedeuilibrium, no further separation can

ta/e place.

"he net transfer rate from vapor toliuid is exactly balanced by thetransfer rate from liuid to vapor.

Separation by distillation is onlyfeasible within the re&ion bounded bythe euilibrium curve and the 0odia&onal line.


7/19

2rom the equilibrium curves, we see that the greater the distance

between the equilibrium curve and the dia$onal line (where x), the

greater the difference in liquid and vapor compositions and therefore

the easierthe separation b distillation%


8/19

2lash *istillation


9/19

FLASH (EQUILIBRIUM) DISTILLATION"his is de3ned as a sin&le-sta&e continuous operation

where a vapor mixture is partially condensed or a liuidmixture is partially vapori4ed. the vapour produced and theresidual liuid are in euilibrium and are then separatedand removed. "he incomin& 5uid is 3rst pressuri4ed andheated, and then fed throu&h a reducin& valve into the

5ash drum. Because of the lar&e pressure drop, part of the5uid vapori4es extremely rapidly.

Bottomsliqui

B! "A! #B

Distillate$a%or to total&o'e'ser

! A! H

Heati'gsour&e QH

Fee

F! *F! #F


10/19

2lash can be seen as a distillation operation with only onesin&le-euilibrium sta&e. "he 5ash operation stops when thevapor and the liuid stream reach the euilibrium

compositions at the 5ash pressure and temperature. "hetwo streams obtained can be easily separated.

ENERGY BALANCE EQUATION:

FhF+ QH= BhB+ VHv

MATERIAL BALANCE EQUATIONS:

F = B + V; FzF= BxA+ VyA

Bottomsliqui

B! "A! #B

Distillate$a%our tototal&o'e'ser

! A! H

Heati'gsour&e QH

Fee

F! *F! #F


11/19

)onsider a binary mixture of A $'()% and B $6()%. "he feed ispreheated before enterin& the separator and 5ows throu&h apressure-reducin& valve to the separator where the separation

between the vapour and liuid ta/es place. "he uantity of Aproduced in the vapour $and in the liuid% depends on thecondition of the feed, i.e. how much of the feed is enterin& inthe vapour phase, which in turn is controlled by the extent ofheatin&. 7n other words, the de&ree of vapori4ation a8ects theconcentration $distribution% of A in the vapour phase and liuidphase.

Bottomsliqui

B! "A! #B


! A! H

Heati'gsour&e QH

Fee

F! *F! #F


12/19

"here is a relationship between the de&ree of heatin&$vapori4ation% and mole fraction of A in the vapor and liuid $yand x%. "his relationship is /nown as the 9peratin& 6ine

:uation.

7f no vapori4ation ta/es place, then the liuid leavin& theseparator will have the same composition as the feed.

7f total vapori4ation occurs, the vapour will also have the samecomposition as the feed.

Bottomsliqui

B! "A! #B


! A! H

Heati'gsour&e QH

Fee

F! *F! #F


13/19

De+'e , - mole ,ra&tio' o, t#e ,ee t#at is $a%ori*ea' .it#ra.' &o'ti'uousl as a $a%or/

"herefore, for 1 mole of binary feed mixture, $1- f% is the

mole fraction of the feed that leaves continuously as a liuid.6et

yA= mole fraction of A in vapor leavin&

xA = mole fraction of A in liuid leavin&

42= mole fraction of A in feed enterin&

Bottomsliqui

B! "A! #B


! A! H

Heati'gsour&e QH

Fee

F! *F! #F


14/19

"he distribution of A in the vapor and liuid phases $yAand xA%

depends on the amount of preheatin& that ta/es place. Basedon the de3nition of ,, the greaterthe heatin&, the largerthe

value of ,which will be obtained.

7f the feed is completely vapori4ed, then f = 1.. "hus, f variesfrom $no vapori4ation% to 1 $total vapori4ation%.

"o see how yA

and xA

chan&e as f chan&es, a material balance

is used to obtain an operatin& line euation, which relates the

Bottomsliqui

B! "A! #B


! A! H

Heati'gsour&e QH

Fee

F! *F! #F


15/19

2rom a material balance for 1 mole of feed then for the morevolatile component $A%

1. 42= f yA< $1 - f% xAf yA= 42- $1 - f% xA

Re-arran&e into

2rom the above operatin& line euation, for a &iven value off and 42, there are certain values for yA and xArespectively.

"he fraction f depends on the enthalpy of the feed and theenthalpies of the vapour and liuid leavin& the separator.

*roppin& the subscripts &ives the &eneral operatin& lineeuation

here x = 4 in case the feed is li uid

+

=

f

zx

f

f1y FAA

2xf

+x

f

f+(

+

=


16/19

2or a &iven feedcondition with a

/nown value of f and42, the above

euation is a strai&htline euation withslope = -$1-f%>f and

intercept = 42> f.

7f x = 42, and y = 42

$no separation%, "heoperatin& line

crosses the point $x2,x2% for all values of f.

"his provides onepoint on theoperatin& line. "he

other point can beobtained from the

ith 42 /nown, the operatin& line on the euilibrium curve is

constructed. "he 7'terse&tio' between the operatin& line and

the euilibrium curve yields the values for yA and xA. "his is

2xf

+x

f

f+(

+

=


17/19

The energy balance is an independent equatin! "here thenly un#n"n is Q

H"hile hF! hBand Hvcan be calculated r

read $r% an enthalpy-composton !a"#am $r thebinary %ixture&

F hF+ Q

H= B h

B+ V H

v

Fr exa%ple:

hF= x

A'

pA(T ) + x

B'

pB(T )

"he above operatin& line can also be written as:

Since and

FAA zVFx

VBy

+

=

2xf

+x

f

f+(

+

=

,F

Vf =

F

Bf =1


18/19

42

, 0 12om%lete$a%ori*atio'

, 0 3'o$a%orisatio'

Analysis of 9peratin& 6ine )han&es in 2raction(aporised

2or a &iven feed composition, x2 is 3xed. hen the

fraction of feed vapori4ed is chan&ed, the mole fraction'() in the vapor and liuid products chan&esaccordin&ly.


19/19

"he 2i&ure below shows how the temperature and mole fractionchan&e on a phase dia&ram.

Seperation processes CHEN 312 Lecture 2

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