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For constant molal over flow, and used to denote low rates. Distillation of Binary Mixture. Bottom plate and re-boiler. m-1. m. Bottom plate. m+1. B x B. Re-boiler. x m+1. y r. Re-boiler plate. x B. ChE 334: Separation Processes. Dr Saad Al-Shahrani.

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Dr saad al shahrani

For constant molal over flow, and used to denote low rates

Distillation of Binary Mixture

  • Bottom plate and re-boiler

m-1

m

Bottom

plate

m+1

B

xB

Re-boiler

xm+1

yr

Re-boiler plate

xB

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

Binary Multistage Distillation

  • The vapor leaving the partial re-boiler is assumed to be in equilibrium with the liquid bottom product.

Equilibrium line

Operating line

ym

a

ym+1

b

a, b,d

bottom plate

c, d, e

Re-boiler plate

The operating line for stripping section crosses the diagonal at point (xB , xB( and its slope=

c

yr

d

xB

e

xm+1

xB

xm

Xm-1

Note: Re-boiler acts as an ideal plate

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

L

F

Binary Multistage Distillation

  • Feed plate

A feed plate is the plate over which the feed is admitted. The liquid rate over the vapor rate or both may change, depending on the thermal conditions of the feed.

Consider the 5 possible feed conditions shown in the next figures which assumes that the feed has been flashed adiabatically to feed stage pressure.

a. sub-cooed liquid feed:

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

Binary Multistage Distillation

  • As a result of this, flow of liquid in stripping section increases and flow of vapor in rectifying section decreases

b. Feed is saturated liquid (bubble point liquid feed) :

L

F

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

Binary Multistage Distillation

C. Partial vaporized feed :

L

F

The liquid portion of feed becomes liquid and the vapor portion of feed becomes vapor

= LF+VF

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

L

F

Binary Multistage Distillation

d. saturated vapor feed (dew point vapor feed) :

L

F

e. Superheated vapor feed

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

Binary Multistage Distillation

  • Cold feed q > 1.0

  • Feed at bubble point (sat. liq.), q=1.0

  • Feed partially vapor, 0 < q < 1.0

  • Feed at dew point (sat. vap.), q = 0

  • Feed superheated vapor, q < 0

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

  • q for sub-cooled feed (Tb > TF)

L

F

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

L

F

McCabe Thiele Graphical Equilibrium-Stage

  • q for superheated feed (TF > Td)

Boiling liquid

  • TF= feed temperature

  • Tb, Td= bubble and dew point of feed respectively.

  • = average latent heat of vaporization

    CpL, CpV = specific heat of liquid and vapor respectively.

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

  • Feed line

The contribution of the feed stream to the internal flow of liquid = qF

The total flow rate of liquid in the stripping section is:

and

e.g

For saturated liquid feed

For saturated vapor feed

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

The contribution of the feed stream to the internal flow of vapor =F(1- q)

The total flow rate of vapor in the rectifying section is:

,

e.g

For saturated liquid feed

,

For saturated vapor feed

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

n+1

V

yn

L

xn+1

n

McCabe Thiele Graphical Equilibrium-Stage

  • For constant molal over flow

Rectifying section

stripping section

m+1

ym

xm+1

m

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

To locate the point where the operating lines intersect,

Let yn=ym , xn+1=xm+1 and subtract equation (1) from equation (2)

FxF

Feed line

q-line

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

  • This equation represents a straight line, called the feed line on which all intersections of operating lines must fall.

  • The position of feed line depend on xF and q.

  • Its slope is and its intercept is

  • This line cross the diagonal at x= xF

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

ra cold liquid q > 1 slope +

rb saturated liquid q = 1 slope 

rc (vap. + liq.) 0 < q < 1 slope -

rd saturated vapor q = 0 slope 0

re superheated q < 0 slope +

XD

q =1

q >1

0 < q <1

b

a

c

q =0

d

r

y

e

q <1

XB

XF

XB

XD

x

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

  • Construction of operating lines

  • Locate the feed line ( ) according to the feed conditions.

  • Locate the rectifying line ( ). This line croces the diagonal at (xD, xD) and of intercept ( )

  • Draw the stripping line through point (xB, xB( an the intersection of rectifying line with the feed line.

Note: xF, xB , xD, L,D are constant

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

XD

a

b

y

c

XB

XB

XD

XF

x

McCabe Thiele Graphical Equilibrium-Stage

  • Plate Feed Location

The feed plate is always represented by the triangle that has one corner on the rectifying line and one on the stripping line

  • Note:

  • The number of plates = number of plates + re-boiler plate.

  • The liquid on the feed plate does not have the same composition as the feed.

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

1

2

3

4

Feed line

5

R.O. L

6

7

8

.

9

S.O. L

10

R

xD

xF

xB


Dr saad al shahrani

Liq. At its bubble point temperature

Vap. at its dew

point temp.

T2

Va

T1

Top

plate

La

xa

D

xD

McCabe Thiele Graphical Equilibrium-Stage

  • Heating and cooling requirements

Heat loss from a large insulated is relatively small.

  • For condenser

a. If the condensate is not su-bcooled (at Tbub)

 molal latent heat of vaporization of more volatile component

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

V

ΔL

Top

plate

T1

L

Tc

D

xD

McCabe Thiele Graphical Equilibrium-Stage

b. If Su-cooled Reflux

If the reflux is cooled below the bubble point, a portion of vapor coming to the top plate (1) must condensed to heat the reflux

ΔL that is condensed inside the column is obtained from:

Cpc=specific heat of condensation

T1= temp. of liq. On to plate bubble point of condensate

Tc= temp. of return condensate (reflux)

c= heat of vaporization of condensate for volatile component.

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

McCabe Thiele Graphical Equilibrium-Stage

The actual reflux ratio in the column is

T1 Tbc= bubble point of the condensate

ChE 334: Separation Processes

Dr Saad Al-Shahrani


Dr saad al shahrani

= steam consumption

= vapor flow rate from re-boiler

s = latent heat of steam.

 = molal latent heat of mixture at the bottom

 molal latent heat of less volatile component

McCabe Thiele Graphical Equilibrium-Stage

  • For re-boiler

Bottom

plate

condensate

B

xB

steam

ChE 334: Separation Processes

Dr Saad Al-Shahrani