Separation Unit Operations - Domande ed Esercizi

BOIL

The addition of the feed leads to a sort of discontinuity in the mole fraction graphs.

3. Azeotropic distillation process. Extractive distillation process.

An example of the azeotropic distillation process is the water-ethanol distillation:

1.​ It is assumed to have a water-ethanol mixture feed with an azeotropic composition (

) → it is injected into the first column

= 89%

2.​ Benzene is injected from the top of the column

3.​ Ethanol, which is not affine to benzene, exits from the bottom of the column,

practically pure

4.​ a mixture whose composition is that of the triple azeotrope exits from the top 34

5.​ the mixture is cooled causing an immiscibility between the benzene and the water,

with the separation of two mixtures

a mixture rich in benzene which, after being enriched with a make-up, is

➢​ injected back into the column

a mixture rich in water

➢​

6.​ the mixture rich in water enters a second distillation column

7.​ at the top of the column a mixture is formed whose composition is that of the triple

azeotrope and is then recycled together with the same mixture exiting the first column

8.​ at the bottom of the column a binary mixture of water and ethanol exits

9.​ the mixture of water and ethanol enters a third column, whose behavior is that of a

normal water-ethanol distillation column

10.​Pure water comes out from the bottom

11.​A mixture whose composition is that of the azeotrope comes out from the top

An example of a extractive distillation process is the distillation of water-ethanol with the

addition of ethylene glycol:

1.​ ethylene glycol is charged from the top of the column

2.​ almost pure ethanol comes out from above, in the form of distillate

3.​ a mixture of water and ethylene glycol comes out from the bottom (since they are two

similar compounds)

4.​ the liquid phase enters the second column to be separated and recycle the ethylene

glycol 35

5.​ practically pure ethylene glycol comes out from the bottom (it is the least volatile

compound)

6.​ water comes out from the top, which is the most volatile compound

7.​ the ethylene glycol is recycled and re-charged into the first column together with a

make-up

4. Assumptions, derivation and significance of the Kremse-Brown-Souders

equation for absorption and stripping processes

Normally, to find the design solution, McCabe Thiele's graphical method is used. There is a

case in which it is possible to solve the problem through an analytical solution.

In the case of the absorption of a diluted gaseous stream, the concentration of B in the various

phases is such ( ) that it is possible to replace the molar ratios X with the mole fractions

→ 0

x ( ) and the flow rates of the inerts with the total flow rates .

∼ ∼

Under these conditions the equilibrium curve and the operating line of the process are straight

lines in the mole fraction graph and an analytical solution for the number of stages exists.

( ) ( )

The material balance is written around a stage j: .

− = −

−1 +1

Considering the general equilibrium equation , which also applies to

=

from which and

−1

= = =

−1

−1 −1 ( ) ( )

Substituting these relations within the material balance: →

− = −

−1 +1

( )

( ) ( ) ( )

→ →

−1

− = − − = −

+1 −1 +1

−

−1 =

−

+1

where is called “absorption factor”.

= −

Writing the same balance for the next stage and multiplying the two balances

+1 =

−

+2 +1 2

− − − ( )

together we obtain: →

−1 +1 −1

· = · =

− − −

+1 +2 +1 +2 +1

Performing this procedure for all stages we obtain the final relation

− ( )

=

−

●​ mx represents the fictitious composition of a vapor in equilibrium with the liquid

e

entering the column (of composition x )

e

●​ y represents the composition of the vapor just after entering the column

NP 36

Within the relationship just found, y is an unknown value and must be expressed as a

NP

function of the other variables. ( ) ( )

We start from the global material balance is: where so

− = − =

from the equilibrium curve → .

= =

Replacing the report within the balance sheet:

( )

( ) ( ) ( )

→ and the y is isolated:

− = − − = − NP

( )

= + −

− ( )

Substituting this relation within we obtain

=

−

−

( ) ( )

which is usually written

= 1 − + 1

−

− +1

− (Kremser-Brown-Souders equation)

= +1

− −1

●​ y -y is the separation achieved

e u

●​ mx is the minimum achievable value of y that can be obtained starting from y → y

e u e e

- mx e

The same derivation can be obtained for the stripping process knowing that is

=

called “stripping factor” →

− − +1

( ) ( ) −

or

= 1− − 1 = .

+1

−1

−

−

5. Tray columns and packed columns: comparison, schemes including

construction details, and pros/cons analysis

In a tray column, the liquid phase goes down in the column through the downcomers and in

every tray it forms a column in which the vapor goes through forming bubbles and eventually

foam.

The geometry of a tray column is:

●​ the downcomer is the part of the column that allows the liquid to descend into the next

tray

●​ the weir is positioned higher than the plate to ensure that a certain column of liquid is

formed

●​ a hydraulic guard prevents steam from rising through the downcomer

●​ h (tray-downcomer height) is the small opening through which the liquid passes

pd

from the downcomer to the tray

●​ A is the area of ​

the column (the one directly linked to the diameter D)

t

●​ A is the downcomer area

d

●​ A is the net area without considering the downcomer → = −

n

●​ A is the active area from which steam can pass → = − 2

a 37

●​ A is the perforated area, i.e. the one in

f

which there are holes that allow the passage of

steam

●​ A that's the actual area of ​

the holes

h

In a packed column, the liquid distributes on

the surface of the packings as a film while the

vapor rises through the vacuum of the

packings making a contact with the liquid

phase.

The packed column is constituted by different

parts.

The liquid distributor from which distributes

the liquid over the packings that could be:

●​ a comb distributor

●​ holes and chimneys where there are

two types of holes:

○​ from the smallest the vapor

rises ○​ from the biggest the liquid goes

down

●​ weir distributor which assures a

constant liquid flowrate even if the inlet liquid

phase could have big fluctuations in flowrate

The support grid should have a great

mechanical resistance and a high degree of vacuum. There are different types of grid, like:

●​ plastic grid

●​ bars net

●​ structure grid which is constituted by particular packings

A packed column could be filled with:

●​ random packings, where the packings are randomly positioned in the column. They

are commonly less expensive than the structured one

●​ structured packing, where the packings are positioned in the column with precised

structures. Even if they are more expensive, their efficiency is higher than the random

packings.

The differences between a tray column and a packed column are:

●​ the structured packed column has the highest efficiency (lower HETP) → pro

●​ the pressure drop is greater in tray columns → con

●​ the wetting necessary for the column for adequate operation is high to be obtained in

random packings column → con

●​ the most expensive column is the structured packed column (due to the cost of

packings) → con

●​ corrosive mixtures:

tray columns are usually made of metal, which corrodes easily → con

➢​ packing are usually made in plastic → pro

➢​ 38

●​ the temperature can usually reach higher values ​

in the tray column as it is made of

metal (instead plastic can decompose) → pro

●​ if the process produces a lot of heat it is easier to insert cooling components (such as

coils) inside a tray column, for example between one plate and another → pro

●​ foam-forming mixtures: packed columns present a lower risk of flooding → pro

●​ mixtures with suspended solids: tray columns are easier to clean → pro

●​ the greatest hold-up is present in the tray column

6. Definition of NETP and HETP. Definition of NTU and HTU, and their

calculation

The NETP is the number of theoretical plates of a column.

The HETP is the height of a theoretical plate.

The height of the packings can be calculated using .

= ·

The lower the value of the height of a theoretical plate the higher the efficiency of the mass

transfer in that portion of the column.

,