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Chapter 21

Distillation

21.1 Flash and Differential Distillation

21.2 Continuous Distillation with Reflux Principles of rectification

Material balance in plate columns Equipment

Mathematical description

Material balance

Enthalpy balances and its simplification Simplification of mass transfer process (Perfect plate and plate efficiency)

Feed plate

At the plate where the feed is admitted, the liquid rate or the vapor rate may change, depends on the thermal condition of the feed.

q is the thermal condition of the feed, defined as the moles of liquid flow in stripping section that result from the introduction of each mole of feed (fraction of saturated liquid in feed). Then q has the following numerical limits for the various conditions:

Cold feed, q > 1, γ/)(1F b pL t t c q ?+=

Feed at bubble point (saturated liquid), q = 1 Feed partially vapor, 0 < q < 1

Feed at dew point (saturated vapor), q = 0 Feed superheated vapor, q < 0 (t F > t d ),

γ/)(d F pV t t c q ??=

Total condenser, bubble point reflux

Rectifying section : RD L =

D R D L V )1(+=+=

Stripping section : qF RD qF L L +=+=

F q D R F q V V )1()1()1(?++=??=

Condenser heat duty: C C V Q γ?= Reboiler heat duty: B B V Q γ?=

Operating lines and feed line

Rectifying section operating line

Stripping section operating line

W n n Wx x L y V ?=+1 W n n x W x L y ?=+1 F

q D R Dx Fx x F q D R qF RD y D F n n )1()1()1()1(1??+????++=+ Feed line (q －line )

D F n W n n Dx Fx x L Wx x L y V +?=?=+1

n n F n Lx Vy Fx x L ?+?=+1

F n n Fx x L L y V V ??=?+)()(1

F q V V )1(??=? qF L L =?

∴ 1

1???=q x x q q y F q q (F q x x =, F q x y =) Feed line is the locus of all intersection points of the operating lines.

Effect of feed thermal condition on feed line

Enrichment of ideal (theoretical) plate

21.3 Design of Binary Mixtures Rectification Proposition

Known: F, x F, x D, x W Choice: P(α), q, R Find: number of ideal plates N and the optimum feed plate location m

Determining the number of ideal plates

Plate-by-plate calculation

（1）Total condenser, bubble point reflux

1

1112+++=+=R x x R R V Dx x V L y D D )()1(22

22y f y y x =??=αα When q n x x

≤, using V

Wx x V L y W n n ?=+1 to W n x x ≤, N is obtained.

Re-boiler at bottom of column acts as an ideal plate.

（2）Partial condenser

1y x D ≠, D x y =0,

)(00y f x =, an ideal

plate;

1y ～0x , operating

relationship.

McCabe-Thiele method

The graphical step-by-step construction utilizing alternately the operating and equilibrium lines to find the number of ideal plates is known as the McCabe-Thiele method.

（1）Locate the feed line;

（2）Calculate the y-axis intercept )1

R

x

(+

D

of the rectifying line and plot that line through the intercept and the point (x D, x D) ;

（3）Draw the stripping line through point (x W, x W) and the intersection of the rectifying line with the feed line.

Feed-plate location

After the operating lines have been plotted, the number of ideal plates is found by the usual

step-by-step construction, as shown in figure. The construction can start either at the bottom of the stripping line or at the top of the rectifying line. In the following it is assumed that the construction begins at the top and also that a total condenser is used. As the intersection of the operating lines is approached, it must be decided when the steps should transfer from the rectifying line to the stripping line. The change should be made in such a manner that the maximum enrichment per plate is obtained so that the number of plates is as small as possible. The figure shows that this criterion is met if the transfer is made immediately after a value of x is reached that is less than the x q coordinate of the intersection of the two operating lines. The feed plate is always represented by the triangle that has one corner on the rectifying line and one on the stripping line. At the optimum position, the triangle representing the feed plate straddles the intersection of the operating lines.

Optimum feed-plate location m: x F ≈x m

No back-mixing