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Chemical Process Design

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SHORT CUT for DISTILLATION COLUMS SIZING<br />

Fenske's equation applies to any two components lk and hk at infinite reflux and is<br />

defined by N min , where αij is the geometric mean of the α's at the T of the feed,<br />

distillate and the bottoms.<br />

( α )<br />

lk / hk<br />

R min is given by Underwood with two equations that must be solved, where q is<br />

the liquid fraction in the feed..<br />

Gilliland used an empirical correlation to<br />

calculate the final number of stage N from<br />

the values calculated through the Fenske<br />

and Underwood equations (N min , R, R min ).<br />

The procedure use a diagram; one enters<br />

with the abscissa value known, and read<br />

the ordinate of the corresponding point on<br />

the Gilliland curve. The only unknown of<br />

the ordinate is the number of stage N.<br />

⎛ x Dlk / x ⎞ Blk<br />

log ⎜⎜<br />

x Dhk / x ⎟⎟<br />

Bhk<br />

N min =<br />

⎝<br />

⎠<br />

α lk / hk = D lk / hk F lk / hkα<br />

log<br />

( ) 3 / 1<br />

α α<br />

B lk / hk<br />

16

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