Distillation - Principles of Chemical Separations with Environmental Applications - page 95

and vapor flows up from tray n + 1totray n . The component mass balance, then, becomes

x D D = y n + 1 V − Lx n (4.14)

for any two subsequent trays.
Because the goal of the mass balance is to obtain an operating line describing the
relationship between the vapor-phase mole fraction entering and the liquid-phase mole
fraction leaving a stage, the mass balances can be combined and rearranged to give:

L
V x n +

x D ( V − L )

y n + 1 = (4.15)

V

or, in terms of liquid streams only,

L x D D

L

y n + 1 =

D x n + D .

(4.16)

+ +

L

Reflux ratio

Typically, the quantity of distillate product that is being condensed and returned to the
top of the column needs to be specified. It can be defined as either an internal or external
quantity depending upon which variables are used. The internal reflux ratio is defined in
terms of flowrates within the rectifying section of the column:

L
V =

R V = reflux ratio (internal) . (4.17)

The external reflux ratio is expressed in terms of liquid flows exiting the condenser:

L
D =

R D = reflux ratio (external) . (4.18)

The operating line for the rectifying section can, then, be expressed in terms of the external
reflux ratio. It is chosen because of the ease of measuring and controlling external liquid
flowrates compared to internal vapor ones:

R D x D

y n + 1 =

R D x n +

(operating line for the rectifying section). (4.19)

1 + 1 + R D

So, with a single point on the x - y diagram and a reflux ratio, the operating line can be
drawn. Let us look at what happens when the liquid coming from a total condenser equals
the distillate concentration. Substituting x D for x n in the operating-line equation,

L Dx D

L

y =

D x D + D =

x D , (4.20)

L + +

it can be seen that at the top of the column y = x D or the operating line intersects the di-

x D ). So, if you know x D and R D , you can draw the operating line for the
rectifying section. It is important to note that since there is more vapor than liquid in the
rectifying section (some vapor is removed as D ), the slope of this operating line is LESS
than 1. Mathematically this is apparent because the slope of R D /

agonal at ( x D ,

( R D + 1) is less than 1 .