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solution The separation parameter S is determined from Eq. (3.5)

solution The separation parameter S is determined from Eq. (3.5)

Calculate aav according to Eqs. (3.7)

2. ctav = (2.904 + 1.579)/2 = 2.242 N^ = 8.137/ln 2.242 = 10.1

4. a,v = V2.904 x 1.579 = 2.141 N^ = 8.137/ln 2.141 = 10.7

5. a8V = (2.904 x 1.870 x 1.579)1'3 = 2.047 Nmin = 8.137/ln 2.047 = 11.4

6. Using Winn's methods, find Plk/hk and 0LK at the top and bottom [Eq. (3.9)]

Top Plk/hk = 0.514/(0.177)0LK Bottom Plk/hk = 2.146/(1.359)8lk Solving gives Plk/hk = 1-731, elk = 0.7011

JVmln

In 1.731

For comparison, extrapolation of rigorous computer simulation runs (Fig. 3.8) gives Nmin = 13. Also, from the simulation and Eq. (3.6), (oclr/hk^v was calculated to be 1.956. This gives

In this example, aav approximations 1 and 3 and Winn's method gave close estimates ofN^. Two of the less rigorous approximations of aav, (2 and 4), gave poor estimates. A check using Douglas's inequality gives

«top ~ <*bot = 2.904 - 1.579 _ 0 29g atop + «bot 2.904 + 1.579 " '

0.x in Si = 0.1 In 2'904 " 1579 = 0.081 < 0.296

Douglas's inequality is not obeyed; therefore, the simpler approximations of aav (such as 2, 3, and 4} can be expected to be inaccurate.

### 3.2.2 Minimum reflux

Underwood's method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 0 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination. When no distributed key components are present, the method is

1. Find 6 (which must lie between the relative volatilities of the keys) by trial and error from

2. Substitute 6 in the following equation to calculate (l,/D)min:

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