Distillatn

8/10/2019 Distillatn

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REVIEW of the following BASICS of BINARY

.

.

-.

4 A li i n f n h l - n n r i n i r m

FLASH distillation of a BINARY mixture

5. Steam distillation

26. Differential distillation / Rayleigh distillation


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7. Continuous multistage fractionation of binary mixtures

-

number of stages

d)Minimum reflux ratio

3


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8. Continuous multistage fractionation of binary mixtures

-

4


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Distillation: Technique of preferential separation of

s rom

VOLATILE COMPONENT(s) by PARTIAL

, .

(vapour-liquid equilibrium).

Distillation column consists of:

olumn hav ng trays or pack ng and su table nternals

Reboiler

Condenser

5


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Functioning of distillation column:

Feed enters at a suitable point.

Reboiler partially vaporises the liquid received from

.

,

at the column top and enters into overhead condenser.

A part of the condensate is withdrawn as TOP

PRODUCT and the rest is fed back to the column as

REFLUX that flows down the trays (or packings).

6


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Intimate contact between UPFLOWING vapour and

qu occurs on e rays or

packing).

EXCHANGE of mass takes place between the liquid

. . .

L.V.C. from vapour liquid.

7


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VapourTypicals a oncolumn

2 Reflux D

1Feed F: Feed (L, V, or a mixture of

D: Distillate or top productW: Bottom product

1: Distillation column

2: Feed preheater

5Steam

3: Condenser

4: Reflux drum

8Condensate

W


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Vapour-Liquid Equilibrium

Under a given set of conditions, the equilibrium vapourcomposition is related to the liquid composition.

Gibb's Phase RuleF C P 2

P number of phases

F degrees of freedom

9


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Example

Aqueous solution of C2H5OH in a closed vessel fitted

H2O + C2H5OH

Vessel put in a constant temperature bath for sufficient

S stem reaches e uilibrium

L and V com ositions

and PT in the vapour space attain unique constant

values

10


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Number of Components = 2 (C2H5OH and H2O)

Number of Phases = 2 (L and V)

Degrees of Freedom = 2

Total number of parameters = 4 (T, PT, L

,

system COMPLETELY

11


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Accurate Vapour-Liquid Equilibrium (VLE) data are

essen a or re a e es gn o a s a on co umn.

(multicomponent systems), a suitable predictive method

, , .

,

experiments to determine the VLE.

12


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Constant T& Constant PBinary V-L Equilibria

TB H VAPOURM1

H

T-y

(dew point)

M

L VG

T-x a

F

TA

L1V1

G1LIQUID

(bubble point)

x z

1

Dia onal

y =x

Equilibrium (x-

13

x(0, 0) 1


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At constant P: Boiling Temperature versus liquid

compos on -x u e po n curve

composition T-y (dew point) curve

Liquid at Point Gheated gradually Point M

heating continued Liquid becomes progressively

Li uid Boilin Point bubble oint increases

Last li uid dro let at M

14


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Final VAPOUR at N1

further heating gives SUPERHEATED vapour

Same description can be given for LV, L1V1, G1H1

15


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F = amount of two-phase mixture, kmol (zF = mole

rac on

,

,

=

= +

len th of secy * zL Vtion F

ma ng :length of secV z x Ftion L

F

16


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Raoults Law: vapour-liquid equilibria for Ideal

o u ons:

v v vp x P p x P 1 - x Pand

v vTotal pressure p p x P 1 - x P

Mole fraction of A in vapour phase y

v p P x P P

The above equation can is used to compute V-Lequilibrium data for IDEAL BINARY mixtures.

17


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Deviation from Ideality and Formation of Azeotropes

POSITIVE deviation: a liquid mixture exerting an

computed by ideal equation.

NEGATIVE deviation: a liquid mixture exerting an

computed by ideal equation.

18


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AZEOTROPES

LARGE POSITIVE deviation from ideality: vapour

,

TOTAL PRESSURE CURVE may have a MAXIMUM

mixture minimum boiling AZEOTROPE.

x-PT and y-PT curves touch at Azeotropic Composition.

x-T and y-T curves pass through a common minimum.

The equilibrium curve crosses the diagonal line at the

azeotro ic com osition.

19

V L E ilib i f Mi i B ili A t ( th l b )


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V-L Equilibria of a Minimum-Boiling Azeotrope (ethanol-benzene)

x-PT curve

x-PB curve

essure

ax-PA curvebr

iumpr

Ideal

behaviourEquil

1

Azeotropic

=

20

,

x(0, 0) 1


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LARGE NEGATIVE deviation from ideality: partial

pressures o n v ua componen s are ea va ues,

the TOTAL PRESSURE CURVE may have a

boiling mixture MAXIMUM boiling AZEOTROPE.

x-PT and y-PT curves touch at Azeotropic Composition.

x-T and y-T curves pass through a common minimum.

The equilibrium curve crosses the diagonal line at the

azeotro ic com osition.

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RELATIVE VOLATILITY

Relative volatility of a component A in a mixtureindicates the EASE of its SEPARATION from another

component B.

Relative volatilit of A

concentration of A concentration of Bvapour

concen liqtrat uidion of A concentration of B

y y y x

AB x 1 x x 1 y

xy

22


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For IDEAL binary solutions, can be expressed in

erms o vapour pressures o e componen s:

P P

v vx 1 x

p P p P

vP va our ressure of A

v vapour pressure of BPB

23


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Equilibrium in a Multicomponent System

Hydrocarbons of a homologous series are nearly ideal.

i n

vy P p x P P pand

i 1v

j jiy

j i nP v

i ii 1

24w ere = vapour pressure o pure componenj


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Since the above equation is rewv v

P P ritten s:a

x xj j

ni n x1 v

i ijx P

P i 1j

or y rocar on m xtures, a quant ty ca e equ r umvaporisation ratio is extensively used:

vy P

i iK x

i T

25

E ilib i i id l t


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Equilibrium in a nonideal system

At equilibrium, the FUGACILITIES of component i in.

V L

f f

andV V L L 0

f F y P f F x P x g f i i i T i i i T i i i

where,

fugacity coefficient of component in vapourFi

i

i

0f fu acit of com onent at standard stai et

26


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For low-to-moderate pressures, the fugacity at

s an ar s a e can e approx ma e o e vapour

pressure at the given temperature, that is:

L vf x Pi i i i

Thus, at equilV v

: y P x Pi i T

ib iui

mi

ri

27


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ENTHALPY-CONCENTRATION DIAGRAM

Change in composition is accompanied by a changein enthalpy. For a given T and concentration x of a

liquid, the molar enthalpy HL can be calculated using

the equation:HL = cPS Mav (T T0) + HS

HL = molar enthalpy of solution at T, kJ/kmol

=

Mav = average molecular weight of solution

T0 = reference temperature, K

28S = ea o so u on a 0, mo

ENTHALPY CONCENTRATION DIAGRAM


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Since the heat of mixing of the vapour is negligible,we can use the following equation to compute the

molar enthalpy of the saturated vapour HV at a

given T and y:HV = y MA {cPA (T T0) + A}

+ (1 y) MB {cPB (T T0) + B} =

kJ/(kg K)

A, B = ea s o vapor sa on o an a

temperature T, kJ/kg

29

ENTHALPY-CONCENTRATION DATA (Example)


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Aceone (A)-Water (B) system at 1 atm total P. Integral heat of solution (15 0C) at

-,

T, 0C X y HS cPS Average specific heat of liquid

56.5 1 1 0 0.54

57 0.95 0.963 0 0.56

.

Specific heat of water = 1

kcal/(kg K). . . . .

58.2 0.8 0.898 23.88 0.61

58.9 0.7 0.874 41.11 0.66

Heat of vaporisation of acetone =

A = 128.8 (T0C 50), kcal/kg

59.5 0.6 0.859 60.3 0.760 0.5 0.849 83.56 0.75

Average heat of vaporisation of

water = B = 550 kcal/kg

. . . . .

61 0.3 0.83 171.7 0.85

62.2 0.2 0.815 187.7 0.9

66.6 0.1 0.755 159.7 0.96

75.7 0.05 0.624 106.8 0.98

30

. . . .

100 0 0 0 1

x-y-H (Enthalpy-Concentration Diagram)


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15000 kcal/mol

- V

M

PD

J

(a)x-HL curve

(HV)1

(HV)2

W

F

0

1Q

,

b

R

31x(0, 0) 1

ENTHALPY CONCENTRATION DIAGRAM


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The amount of vapour and liquid phases SEPARATED .

- .

- .

amounts are given by M and N. After MIXING, the

resultant solution is P. Hence

32

Total material balance: M + N P


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Total material balance: M + N = P

Component A balance: M zM + N zN = P zP

Enthalpy balance: M HM + N HN = PHP

Eliminating P: M/N = (zNzP)/(zP zM)

Eliminating P: M/N = (HNHP)/(HP HM)

(HNHP)/(zNzP) = (HP HM)/(zP zM)

Slope of section NP = Slope of section MP

33Points M, N, and P are collinear.

Vapour


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VapourFLASHst at on

unit

Feed

D, xD = yD, HDBaffles

, F, F

+

Flash drum

Bottom product

34

Flash vaporisation of a BINARY MIXTURE


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If a sufficiently hot liquid is THROTTLED into a,

MVC partial separation.

The liquid is heated under Pressure, and throttled into

.

DISTILLALATE (TOP), and BOTTOM products be

F z H D x H W x H and be the rateof supply of heat exchanger:

35

Total material balance: F = D + W


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Total material balance: F = D + W

Component A balance: F zF = D xD + W xW

(D + W) zF = D xD + W xW

Enthalpy balance : F HF + Q = D HD + W HW

QH Hx z D FW F

QD x

z

H HW F W F

36

Flash Vaporisation of a Binary Mixture15000 kcal/mol


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15000 kcal/mol

y-HV

L,HV

),

ol D

(a)thalpy(

kcal/k

W

zF, F +

x-HL

0

EF1

1

,

P

b F, Fx zW D FSlope =x zD

W F

37x(0, 0) 1



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Cold feed at F1

passes through preheater

receives

(D) and liquid (W) upon throttling into the flash drum.

The enthalpy and composition of vapour (D) and liquid

through F.

The point F(zF, zF) is located on the diagonal of x-y

lot.

38

Point P is located on the equilibrium curve such that


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Point P is located on the equilibrium curve such that

e s ope o e ne = . e ne s e

operating line for flash vaporisation process.

By using the H-x-y and x-y curves, the amounts and

feed for given Q.

Alternatively, if the fraction of feed to be vaporised is

The anal sis can be extended to the case of a real sta ewith a given value of stage efficiency (How ?).

39

STEAMDISTILLATION


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DISTILLATIONun

ReceiverA

Feed

(water)Steamcoil

Open

steameamsparger

40

Steam Distillation


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Steam Distillation

For an ideal binary solution, yA = pA/PT = (xA PAV)/PT

However, if A and B are IMMISCIBLE, their mixture

individual components).

Hence the BUBBLE POINT of such a mixture < boiling

Process: Live steam is assed throu h a li uid

Avaporises leaves WITH steam condenser 2

la ers A and B se arated b decantation.

41

Applications of steam distillation:


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pp

Separation of high boiling materials (decolourisation,,

oils).

Separation and purification of hazardous materials like

Se aration of volatile im urities from waste water(removal of ammonia, VOCs)

42

Separation of A immiscible with water


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p

PT = PAV + PBV

PBV = PT PAV

If mA moles of A are volatilised by putting in mB moles

, ,

= V V = V VA B A B A T A

= V V

However if the s stem does not o erate at e uilibriumpA < PA

V

43

A factor called vaporisation efficiency E is defined =


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p y

pA A

A B A T A

requirement.

The vaporisation efficiency usually ranges from 60% to

44

BATCH DISTILLATION of a Binary Mixture


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y

eren a s a on ay e g s a on

y Coolingwater

L, LA, xKettle(still)

D,ave

Steam

45

Equilibrium is assumed in the still.


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Feed is charged to a still pot.

Heat is continuously supplied.

As boiling continues, MVC in liquid decreases with

The condensate to roduct is collected in a receiver.

At the be innin the condensate is ver rich in MVC.

46

MVC in the condensate decreases with time.


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Applicable when the components greatly differ in-

required.

47

BATCH DISTILLATION of a Binary Mixture


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Analysis is based on differential mass balance.

Let, at instance of time,

LA(t) = moles of A at any time t left in kettle liquid

LB(t) = moles of B at any time t left in kettle liquid

L = total moles of liquid left in kettle at time t, LA(t) +

L t havin mole fraction x

dL = moles of li uid va ourised between time t and t+dt

48

D = total accumulated moles of condensate up to time t


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dD = moles of condensate accumulated between time t

=

49

Consider the vaporisation of liquid taking place


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e ween me an ,

,

= = +

The mole fraction of va our hase will be com uted asfollows, only on the basis of dLA, because y(t) =

instantaneous mole fraction of va our roduced

50

moles of vapourised between time andA t t+dty


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y

mo es vapour se e ween me ano a

y y ydL xdL LdxdL dL

dL dxLdx ydL xdL Ldx dL y x dx

If distillation starts with F moles of feed (xF), and

W ,

equation is integrated as:

WdL dxdx

L x

51

F

xFF dx


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F dx

...

W

y

y x

u

xW

If x-y data is available, the RHS can be solved

ra hicall .

If y = f(x) is available, RHS can be solved analytically /

numerically.

If = Ave, then RHS can be solved analytically, as

follows:

52

xWF dx


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xW x xF 1 1 x

x 1 x 1 xln ln

1 x 1 x 1 xW F F

In a more convenient form,

F 1 xFxFF

ln ln

W W

53

The above equation involves 4 quantities: F, W, xF, xW.


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The AVERAGE composition of the ACCUMULATED

material balances:

Total material balance: F = Dfinal + W

Component material balance:

FxF = DyD,Ave + WxW

54


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Continuous Multistage

Fractional Distillation of

55

Vapour


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QCEnvelope 1

Envelope 2tify

in

ction

To roduct

nRes

F, zF, HFD, xD, HD

f

n

xnHL,n

n+1

yn+1HV,n+1

m Lmxm

Vm+1ym+1

Envelope 3

VapourNHL,m HV,m+1 Envelope 4

p

ping

t

ion

+QBBottom product

Str

se

56

W, xW

, HW

MATERIAL AND ENERGY BALANCE EQUATIONS


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The determination of number of stages is based on

as shown in the Figure.

L & V: liquid and vapour flows ABOVE the feed

.

location.

Ln & Vn = molar liquid and vapour flow rate LEAVING

nth sta e.

57

HL,n & HV,n = molar liquid and vapour enthalpy

n s age


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n s age.

0

signifies that the stream is as if coming from a

th .

=C .

=

the liquid leaving the bottom stage).

F = feed rate to the column.

58

zF = mole fraction of MVC in feed.


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D = rate of distillate removal from reflux drum.

xD = mole fraction of MVC in distillate.

W = rate of bottom product removal from reboiler.

xW = mole fraction of MVC in bottom product.

L0/D = R= reflux ratio.

59

Vapour: V1, y1, HV1


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Envelope 1QC

HL0Stage 1

0,x0,

D, xD, HDflux

:

R

60

ENVELOPE 1

con enser re ux rum


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con enser re ux rum

vera a ance:

V1 = L0 + D = R D + D = D (R + 1)

Component A balance:

1 y1 = 0 x0 xD

y

V1

HV1

= L0

HL0

+ D HD

+ QC

C = + V1 L0 D

61

ease no e: y1

= xD

= x0

or o a con enser

Vapour


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QC

Envelope 2

Stage n

section

Top productD, xD, HD

Lnx

Vn+1yn+1

HL,n HV,n+1

62

ENVELOPE 2

part o rect y ng sect on + con enser


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vera a ance:

Vn+1 = Ln + D


n+1 yn+1 = n xn + xD

n a py a ance:

Vn+1

HV,n+1

= Ln

HL,n

+ D HD

+ QC

If you put n = 0, equations for Envelope 1 are obtained !

63


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ing

on

Stage m

Envelope 3Lm Vm+1trip

sect

Vapour

m

HL,m

m

HV,m+1

+QB o om pro uc

W, xW, HW

64

ENVELOPE 3

part o str pp ng sect on + re o er


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vera a ance:

Lm = Vm+1 + W


m xm = m+1 ym+1 + xW

n a py a ance:

Lm

HL,m

+ QB

= Vm+1

HV,m+1

+ W HW

65

Vapour

C


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C

Top product:

Rectifyingsection

, D, DFeed:

F, z , HFeedstage

Strippingsection

Vapour

Bottom productW, xW, HW

+QB

66

ENVELOPE 4

ent re co umn + con enser + re o er


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vera a ance:

F = D + W


zF = xD + xW

n a py a ance:

F HF

+ QB

= D HD

+ W HW

+ QC

67

Above the FEED POINT: Vapour is enriched OR

pur e y scar ng e n o e


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p y g

downflowing liquid

MVC concentration in

OR enriching section.

Below the FEED POINT: MVC is removed or

concentration in vapour is less than that in the feed

68

Flow rate, composition, state of FEED: T, P, phase, etc.

ee may e , , or wo-p ase .


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QUALITY or PURITY.

Reflux ratio and the condition of the reflux: The ratio of

WITHDRAWN. Reflux may be SATURATED liquid or-

69

Operating pressure and allowable pressure drop across

e co umn: opera ng pressure a so e erm nes e


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TEMPERATURE of column.

P =f(type, number of hydraulic design of trays OR

.

LOWER PRESSURES.

Tray / packings type: determine the efficiency of

se aration.

70

Number of Trays: McCabe-Thiele Method


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Developed in 1925: graphical solution of material

relation x-y (or equilibrium data).

ASSUMPTIONS:

1. CONSTANT MOLAR OVERFLOW of liquid (andr fr m n r n h r r n i n f

the distillation column, that is:

L0 = L1 = L2 = ... = Ln = L (RECTIFYING section);

71Lm = Lm+1 = ... = LN = L (STRIPPING section)

AND


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V1 = V2 = V3 = ... = Vn+1 = V (RECTIFYING section);

Vm+1 = Vm+2 = ... = VN+1 = V (STRIPPING section)

2. Heat loss from distillation column is negligible. (If

,

within the column, leading to a corresponding variation

72

Steps:


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(1) Draw equilibrium curve using available x-y data

(2) Draw operating lines for the rectifying and the

and the operating lines to find out the number of

73

The RECTIFYING Section


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ENVELOPE 2 (part of rectifying section + condenser)

Component A balance: Vn+1 yn+1 = Ln xn + D xD

Since CMO: constant molar ovL0R

D Derfl wo

xL D L D Dy x x x

DxR

n 1 n1R R 1

74

The above equation is a STRAIGHT line,


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Slope = R/(R+1)

Y-intercept = xD/(R+1)

The line satisfied by xn = xD; yn+1 = xD

This equation is called the operating line for

75

The STRIPPING Section


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ENVELOPE 3 (part of stripping section + reboiler)

Component A balance: L xm = V ym+1 + W xW

V L WSince

y x x

m 1 m WV V

y x xm 1 m WL W L W

76

The above equation is a STRAIGHT line,


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Slope = L/(LW)

The line satisfied by xm = xW; ym+1 = xW

This equation is called the operating line for

.

77

The FEED line


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Consider the plate ON WHICH the feed is introduced.

L H , ,

HF

L, HL,fV, HV,f+1

78

Total material balance: F + L + V = L + V


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Enthalpy balance:

F HF + L HL,f1 + V HV, f+1 = L HL,f+ V HV,f

Assuming Uniform Enthalpy:

HL,f1

HL,f

HL , ,

F H + L H + V H = L H + V H

L L H = VV H + F H

79

Eliminating V and V ,

L L V F


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q sayF H H

heat required to convert 1 mole of

qheat required to convert 1 mole of

heat required to conv

ert 1 mole of

molar heat of vaporisation

80

LL = increase in the liquid flow rate across the feed

s age as a resu o n ro uc on o e ee


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heat required to convert 1 mole of o sa ura e vapour

q molar heat of vaporisationAlso,

Feed at its bubble point (saturated liquid): q = 1

Feed at its dew point (saturated vapour): q = 0

If feed is a two-phase mixture, q = fraction of liquid in

81

the feed (1 q) = quality of the feed

If the point of intersection of RECTIFICATION

opera ng ne an opera ng ne s x, y ,


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then:

V y = L x + D xD and Vy = Lx W xW

Subtracting the above equations, and using the equation

for component balance for the complete column (F zF =

D xD + W xW), we get:

= + + = +

Total material balance on feed late:

F + L + V = L + V

82

Using the above two equations, and the definition of q,

we ge e equa on o :


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z

, pass ng t rougy x z , zF Fq 1 q 1

83

The number of IDEAL STAGES are determined by step

s a rcase cons ruc on e ween e equ r um curve


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and operating lines.

(xn, yn): on equilibrium curve.

(xn, yn+1): on operating line.

Construction may start from either D (xD) or W (xW).

When the FEED LINE is crossed, a CHANGEOVER

from one o eratin line to the other is done that is atransition from RECTIFICATION to STRIPPING

section or vice versa .

84

1. If feed is Superheated Vapour: feed line has +VE slope

(q < 0): Explain.


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. ee s a ura e apour: ee ne s or zon a

(q = 0): Explain.

3. If feed is Liquid + Vapour: feed line hasVE slope

.

.

(q = 1): Explain.

5. If feed is Subcooled Liquid: feed line has +VE slope

>

85

Various Types of Feed Lines

4


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Subcooled L

V+L(, +)

+,

F2

Saturated V (0, +)

,

1H HL L V Fq

F H H

uper eate(+, +) Feed line:

zq Fy xq 1 q 1

86

Feed Tray Location and Number of Ideal Trays

N S


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N S

M

FS

Feed =aturated L qu d

87

TOTAL REFLUX

If th li id f h d d i TOTALLY


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If the liquid from overhead condenser is TOTALLY,

run at total reflux. Also no product is drawn from

.

R = L0/D = L0/0 =

Operating line for Rectifying section

Dy xn 1 nR 1 R 1

Wh Slope 1, Y-ien R ,

Operating

nt

li

erce

ne c DIAGONoincid ALes

pt 0

with

88

Naturally, the number of stages corresponding to

n n e are m n mum.


89/149

distillation column till the steady state is attained.

After this, continuous flow of feed, top product, and

SIMULTANEOUSLY started.

89

Fenskes equation

U d t t th ti ll th i i b f


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Used to compute theoretically the minimum number of

or less) constant. It also assumes a total reboiler

.

w

temperature, and xW, yW are Liquid and Vapour mole

y xW W

1 y 1 xW W

90

The Vapour leaving the reboiler and entering the lowest

ray m as a mo e rac on yW o componen . e

Liq id lea ing this tra has a composition Nm ( Nm


91/149

Liquid leaving this tray has a composition xNm

(xNm,W Nm W. ,

the above equation can be rewritten as:

Nm WW1 x 1 x

Applying the same procedure to the case of tray numberm,

y x

Nm Nm

x

W

Nm Nm1 y 1 x W 1 xN Nm Wm

91

Continuing the procedure up to the top tray (where y1 =

xD , we ge :

xx y WD 1


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xx y WD 1

Nm Nm W1 x 1 y 1 xD 1 W

m WDaverage1 x 1 x

x 1 x

logx 1 x

W D

mlog

avera e

92

The above equation is called the Fenskes equation,

w c s use u or e ca cu a on o

number of trays


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number of trays.

93

Minimum Reflux Ratio

This is exactly analogous to the (L/G)min for gas

absorption This is based on the identification of


94/149

absorption. This is based on the identification of

pinch point.

m

D, D W, W

DIAGONAL of the x-y diagram. These are the

Draw the feed line throu h F from the known feedcomposition zF, and feed quality (given by q); locate the

oint of intersection of the feed line and the

94equilibrium curve (x-y diagram). Call this point M.

Join DM (operating line for rectifying section), and

ex en s ne e -ax s.


95/149

- D m . m

intercept.

At Reflux Ratio = Rm, the number of stages for the

ZERO at the PINCH POINT).

95



96/149

FE

Slope = Rm

/(Rm

+ 1)

- ntercept = xD m +

96

Sieve Tray


97/149

97

Tray Columns


98/149

98

Tray Deck


99/149

99

Reboilers


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100

Bottom

Tray

Bottom

Tray


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y y

Heating Heating

Medium

Bottoms Bottoms

Circulating Pump

ro uc

Forced Circulation Vertical Thermosiphon

101

Reboilers

Bottom Bottom


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HeatingHeating

Medium

Tray Tray

Medium

ProductBottoms

Product

Kettle Horizontal Thermosiphon

102

Feed Distributors


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103


104/149

Fouled Structured Packing Damaged Valve Tray

104


105/149

Plugged Distributor

Tray Blanking Strips

105

Valve Tray Deck


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106

Major Tray Damage


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107

Fouled Bubble Cap Tray


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108

Structured Packings


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Fair, J.R., Seibert, A.F., Behrens, M., Saraber, P.P., and Olujic, Z. Structured Packing

Performance Experimental Evaluation of Two Predictive Models,Industrial and

109

, , - .

Structured Packing Wetted Area


110/149

110

Ponchon Savarit Method (Number of Stages)

Calculations on an Enthalpy-Concentration (H-x-y).


111/149

straight and roughly parallel Latent heat of

composition

Prerequisite for constant molar

If the saturation curves show si nificant chan es incurvature constant molar overflow cannot be

assumed.

111

H-x-y diagram is more general than a McCabe-Thiele

cons ruc on, ecause a es rec accoun o e

thermal effects and does not require an assumption of.


112/149

, , -x-y diagram. The coordinates are their composition

.

112

Vapour

QCEnvelope 1

Envelope 2

ti

fyin

ct

ion

e s


113/149

To roductn

Res

F, zF, HFD, xD, HD

f

n

xnHL,n

n+1

yn+1HV,n+1

m Lm

xmV

m+1

ym+1Envelope 3

VapourNHL,m HV,m+1 Envelope 4

pping

tion

+QBBottom product

Strse

113

W, xW, HW

MATERIAL AND ENERGY BALANCE EQUATIONS

The determination of number of stages is based on


114/149

as shown in the Figure.

L & V: liquid and vapour flows ABOVE the feed

.

location.

Ln & Vn = molar liquid and vapour flow rate LEAVING

nth sta e.

114

HL,n & HV,n = molar liquid and vapour enthalpy

n s age.

0


115/149

0

signifies that the stream is as if coming from ath

.

=C .

=

the liquid leaving the bottom stage).

F = feed rate to the column.

115

zF = mole fraction of MVC in feed.

D = rate of distillate removal from reflux drum.


116/149

xD = mole fraction of MVC in distillate.

W = rate of bottom product removal from reboiler.

xW

= mole fraction of MVC in bottom product.

L0/D = R= reflux ratio.

116

Vapour: V1, y1, HV1

Envelope 1QC

Stage 1


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HL0Stage 1

0,x0,

D, xD, H

Dflu

x:

R

117

ENVELOPE 1

con enser re ux rum

vera a ance:


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V1 = L0 + D = R D + D = D (R + 1)


1 y1 = 0 x0 xD

y

V1 HV1 = L0 HL0 + D HD + QC

C = + V1 L0 D

118

ease no e: y1 = xD = x0 or o a con enser

Vapour

QC Envelope 2

section


119/149

Stage n

section

Top productD, xD, HD

Lnx

Vn+1yn+1

HL,n HV,n+1

119

ENVELOPE 2


vera a ance:


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Vn+1 = Ln + D


n+1 yn+1 = n xn + xD

n a py a ance:

Vn+1 HV,n+1 = Ln HL,n + D HD + QC

If you put n = 0, equations for Envelope 1 are obtained !

120

g Stage m


121/149

ing

on

Stage m

Envelope 3Lm Vm+1tripsect

Vapour

m

HL,m

m

HV,m+1

+QB

o om pro ucW, xW, HW

121

ENVELOPE 3


vera a ance:


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Lm = Vm+1 + W


m xm = m+1 ym+1 + xW

n a py a ance:

Lm HL,m + QB = Vm+1 HV,m+1 + W HW

122

Vapour

C

Rectifyingsection


123/149

Top product:section

, D, DFeed:F, z , H

Feedstage

Stripping

section

Vapour

Bottom productW, xW, HW

+QB

123

ENVELOPE 4


vera a ance:


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F = D + W


zF = xD + xW

n a py a ance:

F HF + QB = D HD + W HW + QC

124

Rectifying Section

ENVELOPE 2 (part of rectifying section + condenser)

Total material balance: V L + D


125/149

Total material balance: Vn+1 = Ln + D

Component A balance: Vn+1 yn+1 = Ln xn + (Vn+1Ln) zD

Ln

/ Vn+1

= (zD

yn+1

) / (zD

xn

)

Note: Reflux may be a sub-cooled liquid and hence the

com osition is denoted b z .

125

Energy balance:

Vn+1

HV, n+1

= Ln

HL,n

+ D (HD

+ QC/D) = L

nH

L, n+ D Q

D

where Q = Enthalpy removed from the TOP section of


126/149

where QD = Enthalpy removed from the TOP section of

.

= n+1 n

= + n , n n , n n n

L /V = H / H, ,

The uantit L /V is called internal reflux ratio.

126

From the above two equations:

Q Hz y D V,n 1D n 1

D n D L,n


127/149

Q H Q H

, ,z x z yD n D n 1

z , Q x , HD D n L,nThe 3 points , ,

yand , are COLLINEAR., Hn 1 V n 1

Dthe points , , and are COLLINEARL Vn n 1.Q

127

Point D (zD, QD) can be considered as a phase

o a ne y su rac ng n rom n+1 .

n+1 n.


128/149

,

composition zD, and enthalpy QD = HD + QC/D.

The stream D is a fictitious stream defined for the

D lies verticall above D because the have same

abscissa = zD.

128

If D lies below H-x curve, D is sub-cooled liquid.

Put n = 0 D, D, V1

are collinear.

Point L (x H ) is located by drawing a tie line from


129/149

Point L1 (x1, HL1) is located by drawing a tie line from

1

.

1 2,

129

Q H Q HL VD V,n 1 D L,nn n 1

V Q H L Q Hn 1 D L,n n D V,n 1

D L,0 D L,001Put n 0


130/149

L H L HPut n 0

, ,Q HD

L Q H

0 D V,1

vertical distanceQ HL D VD V,10 1R

V,1 1D

130

If the reflux ratio is given, the above relation is used

o oca e .

, D, D

distillate.


131/149

distillate.

A vertical line through zD intersects the y-HV curve at

1.

satisfied.

131

Rectifying Section D

y-HV curve

VVV 1HV


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V1V2V3Vn

Vn+1,H

H x-HL curve

LL2Ln1Ln

DTie lines

z

Operating lineSEGMENTS

132

. .,

Stripping Section

ENVELOPE 3 (part of stripping section + reboiler)

Total material balance: Lm = Vm+1 + W


133/149

Total material balance: L m V m+1 W


Lm

xm

= Vm+1

ym+1

+ (Lm

Vm+1

) xW

Ln / Vm+1 = (ym+1 xW) / ( xm xW)

133

Energy balance:

Lm

HL, m

Vm+1

HV, m+1

= W HW

QB

= W (HW

QB

/W)

Lm HL m Vm+1 HV m+1 = W QW


134/149

m L, m V m+1 V, m+1 W Q W

where QW = Enthalpy supplied to the BOTTOM section

.

= m m

L H V H = L V , ,

L / V = H / H

134

, ,

From the above two equations:

H Qy x V,m 1 Wm 1 W

m W L,m W

H Q H Q


135/149

H Q H Q, ,

y x x xm 1 W m W

The 3 points , ,x , Q x , HW W m L,m

and , are COLLINEAR.y , Hm+1 V,m+1

that is, the points , , and are COLLINEAL V Qm m+

R.1 W

135

The flow rate of phase W is also denoted by W = Lm

m+1.

purpose of graphical construction.


136/149

p p g p

W lies vertically below W, because they have same

= W.

-

the tie line drawn from W.

136

The line connecting VN+1 and Wintersects x-HL curve

a N co near y con on .

N - V

VN, and so on


137/149

N

137

Stripping Section D

V

V

VN,

HV

y-HV curveVN1


138/149

V1,

F

LN

x-HL curve

0.0 1.0zx, y

xW

Tie linesO eratin lineSEGMENTS

138W

Feed Plate

A changeover from one section to the other is necessary

, .


139/149

envelope 4, that is, entire column + condenser +

.

D + W z = D z + W x D/W = z x / z z

139

Enthalpy balance:

(D + W) HF + QB = D HD + W HW + QC

D HF + W HF = D (HD + QC/D) + W (HWQB/W)Q

CH H


140/149

H H

D F WQW Q H

W FW

z xF W F W F W D F

z z H z x z z

The 3 points W(xW, QW), F(zF, HF), and D(zD, QD)

140are collinear.

The intermediate point F(zF, HF) denotes the state of

ee n erms o compos on an en a py.

F, F .


141/149

m m+1.

= n+1 n.

F = D + W = D + W

Therefore, F, a real stream can be viewed as a stream

obtained b mixin the 2 fictitious streams Dand W.

The line DWis called feed line.

141

The steps (graphical) for obtaining the number of ideal

s ages on -x-y agram:

,

Enthalpies, Flow Rates of Distillate, Bottom Product, as


142/149

.

, , .

{drawn through W(xW, HW)} at point W.

Stages can be constructed either from D or from W.

142

A changeover has to be made after the feed line is

crosse .

stage.


143/149

Construction continues till the other end point is

.

143

The steps (graphical) for obtaining the number of ideal

s ages on x-y agram:

-

separate axes below the H-x-y diagram using matching


144/149

.

D, D W, W .

-

x and H-y curves at xn and yn+1 respectively, the point

x is oint on the o eratin line in the x-

diagram.

144

Several lines can be drawn from D and W, and for

eac o ese nes, e po n xn, yn+1 s oca e on e

x-y diagram.

All these points are joined, giving rise to two curves;


145/149

, ,

section operating curve and stripping section operating

.

constant (constant molar overflow is not applicable),

the o eratin lines are not strai ht.

Staircase construction ives the number of ideal sta es.

145


If a line through D or W coincides with tie line, the

, .


146/149

vertical distanceQ HL D V

verticaD H l dH V D

V,1

istanc

D

e

1

The above relation indicates that the smaller the

distance DV or the nearer the oint D to the H-x

curve), the smaller is the reflux ratio.

146

Most commonly, when the line DW coincides with the

e ne roug e ee po n , m n mum re ux ra o

occurs.

However, for some highly nonideal mixtures, it may


147/149

intersects the vertical line (drawn through zD) at the

. ,

taken as the true pinch point.

Once (D)min has been located on the H-x-y diagram,

then the minimum reflux ratio is com uted usin the

above relation.

147

Total Reflux

In this case, the reflux ratio is infinite.

Naturally, the points D and W are located at infinity.


148/149

Therefore, all the lines through D and W are vertical

.

Locate V verticall above z on the H- curve.

148

Draw a tie line from V1, which will intersect H-x curve

a 1.

1, -

curve at V2.


149/149

Continue the above construction till xW is reached.

This (obviously) gives the minimum number of ideal

149

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