Page 36 - Applied Process Design For Chemical And Petrochemical Plants Volume II

Distillation 25

Table 8-1 minimum number of stages by the Fenske equation, with a
Data for Alkyiation Deisobutanizer; Example 84 Using geometric average a of 1.261, is 16.8. The Fenske equation
Winn’s Method gives an answer that is too high by 2.3 stages or 16%.
For ideal systems following Raoult’s Law; relative volatil-
over- Equilibrium K’s ity alh = pI/ph, ratio of partial pressures.
Feed, head, Bottoms, Top For a binary distillation, a is calculated at top and bot-
Component moles moles moles tray Reboiler
tom conditions and a geometric mean used where the dif-
Ethylene 1 1 .... .... .... ferences are relatively small.
Ethane 2 2 .... .... ....
Propane 48 48 .... .... ....
Isobutane 863 848 15 0.94 3.35.
n-Butane 132 71 61 0.70 3.00
Isopentane 33 .... 33 .... .... Ester [94] recommends that the determination of a for
n-Pentane 5 .... 5 .... .... calculation as:
Alkylate 277 .... 277 .... ....
1361 970 391 .... .... (1) aavg - a evaluated at Tavg = (TtOp + TB~~)/~
Used by permission, W-inn, E W., Pet. Re$ V. 37; No. 5 (1958), p. 216, Gulf where T - “F (8- 48)
Pub. Co.
(2) aavg - a at feed tray temperature
(3) Winn’s E991 method previously discussed.
( (:) 1-b
on+* = (s) x)b ,for vapor overhead product (8- 46)
w v;, For hydrocarbon systems, the following is often used [65]

where B = mols of bottoms (8- 36A)
b = exponent in Equation 8-43
D = total mols of overhead product
n = minimum number of equilibrium trays in tower where i = any component
K = y/x = vapor-liquid equilibrium ratio for a component r = component to which all the relative volatilities are
L = mols of a component in liquid phase referred
P = vapor pressure, psia
T = absolute temperature, “R Ki = equilibrium distribution coefficient for component, i
V = mols of a component in vapor phase R, = equilibrium distribution coefficient for component
W = total mols of bottoms product to which relative volatilities are referred
x = mol fraction of a component in liquid phase
y = mol fraction of a component in vapor phase For values of a near 1.0, extreme care must be used in
a = relative volatility establishing data, as a small change in the value of a;.rp.
p = constant in Equation &43 may double the number of trays.
n: = total pressure, psia The exact procedure is to estimate a temperature pro-
L = total mols in liquid phase file from top to bottom of the column and then calculate
V = total mols in vapor phase
a for each theoretical tray or stage by assuming a temper-
ature increment from tray to tray. For many systems this,
subscripts or superscripts:
D = distillate or some variation, is recommended to achieve good sepa-
B = bottoms ration calculations.
(‘) = heavy key component
1,2 .. .= tray number YIXh
alh =- (8- 35)
XI Yh
The minimum number of theoretical stages is calculat-
ed as follows: For non-ideal systems:

(1 301) = (848/ 15) (61/71) O-’’’ (391/970)
I453 alh Y 6 1 (8-49)
n + 1 = 14.5 Yh Kh

This is exactly the number of stages obtained by tray-to- The vapor-liquid equilibrium relationship may be deter-
tray calculations with the K correlation of Winn [236]. The mined from