Page 59 - Applied Process Design For Chemical And Petrochemical Plants Volume II

48 Applied Process Design for Chemical and Petrochemical Plants

Equilibrium curve: L = mols of liquid per unit time, or liquid return to
ax (8 - 50) column
= 1+ (a-1)x P = distillate drawoff percentage = 100/(R + 1)
Pi = pure component vapor pressure, mm Hg
Operating line: y = x + b (see Reference 129 for dia- R = reflux ratio (liquid returned to column)/(distil-
gram). They intersect at x = k. late drawoff) ; subscripts indicate number of
plates, Rmin
V = vapor rate up column, mols per unit time
ak
-
Then,y = = k + b,whenx = k (8 8'7) 0 = time
1+ (a - 1) k
where b = (ak/c) - k Batch with Constant Reflux Ratio, Fixed Number
c = 1 + (CX - l)k Theoretical Plates in Column, Overhead Composition
Varies
a xs
Then, xp + b = At any time 8 [1311:
D + (a - 1) x, 1
S
Coordinates: In (W, /Wo) =In - (8-91)
=
XI' = XI - k
where So = mols originally charged to kettle
y' = y - (b + k) S = mols in mixture in still (kettle) at time 0
XD = mol fraction of a more volatile component in the
xp' = xp - k distillate entering the receiver at time 0
xs0 = mol fraction of a more volatile component in the
For the more volatile component at any time: initial kettle charge
xs = mol hction of a more volatile component in the ket-
XI = (FXF - WxS)/D (8 - 88) tle at time 0
D = mols of distillate at time 0
b = ys - xP
To solve the right side of the Raleigh-like equation, inte-
02 = (W / G)S(SI (dx, / b), time, hrs for refluxed distillation grate graphically by plotting:
XW
- xs) vs. 4
Fixed Number Theoretical Trays: Constant Reflux Ratio
and Variable Overhead Compositions The area under the curve between xs0 and x, is the value
of the integral. Plot the equilibrium curve for the more
Raleigh equation form [ 1301 : volatile component on x - y diagram as shown in Figure
&33. Then, select values of XD from the operating line hav-
~~~I/WO)=~~~ (8 - 90) ing the constant slope, L/V, from equation
d%v/(xD-xw)
L, + 1 = Ln + D
where W, = mols liquid mixture originally charged to still
W1 = mols final content in still are drawn from the intersection of XD and the diagonal.
G~ = Initial mol fraction of more volatile component Then from these L/V lines, draw steps to the equilibrium
in mixture curve, the same for a binary McCabe-Thiele diagram
x, = composition of liquid in still, mol fraction [130]. The proper operating line is the one that requires
xi = mol fraction of component in liquid phase the specified number of theoretical plates (stages) in mov-
x = mol fraction of more volatile component in liquid ing stepwise down from the initial desired distillate com-
XD = instantaneous mol fraction of the component in position to the composition of the mixture initially
the distillate that is leaving the condenser at time 0.
XD~ = initial distillate composition, mol fraction charged to the kettle (or pot or still). The kettle acts like
xi = mol fraction component in liquid phase and is counted as one theoretical stage or plate. The inter-
yi = mol fraction of component in the vapor phase section of the last horizontal step (going down the col-
D = mols of distillate per unit time, or mols of distil- umn) from XD with the equilibrium curve is the still or ket-
late at time 0, or distillate drawoff. tle bottoms composition, XW, at the completion of this
KA,KB = equilibrium vaporization constants for A and B, batch distillation. Using the system material balance and
respectively the constant reflux ratio used (L/V), calculate the total