Gilliland Correlation for Actual Reflux Ratio and Theoretical Stages Feed-Stage Location

Transcription

1 Lecture 4. Approximate Multicomponent Methods (2) [Ch. 9] Minimum Reflux - In binary systems - In multicomponent systems - Underwood equation Gilliland Correlation for Actual Reflux Ratio and Theoretical Stages -Stage Location Distribution of Nonkey Components at Actual Reflux

2 Minimum Reflux in Binary Systems Minimum reflux - Infinite stages - Pinch point (or point of infinitude) - Most of the stages are crowded into a constant-composition composition zone Binary system, ideal conditions Binary system, nonideal conditions : location of pinch-point zone

3 Minimum Reflux in Multicomponent Systems Class (one pinch point): all components in the feed distribute to both the distillate and bottoms products (narrow-boiling-range range mixtures or the degree of separation between key components is not sharp) Class 2 (two pinch points): one or more of the components appear in only one product All components Not all LLK and HHK distributed (Class ) distributing (Class 2) All LLK, if any, distributing, but not all HHK distributing (Class 2) LLK: lighter than light key; HHK: heavier than heavy key : location of pinch-point zones

4 Underwood Equation for Minimum Reflux () Material balance over all stages y V x L x D i, i, i, D V L D y V x L x D j, j, j, D Phase equilibrium relation (phase compositions do not change in the pinch zone) y K x y K x i, i, i, j, j, j, V L D L D ( x id, / xi, ) ( ij, ) ( xjd, / xj, ) ( ) i, j Pinch-point zone or Class separation, flashed feed- and pinch-zone compositions are identical ( x i, xi, ) ( L ) LK, HK V L ( L / ) ( DxLK, D/ Lx LK, ) ( LK, HK) ( DxHK, D/ Lx HK, ) ( )

5 Underwood Equation for Minimum Reflux (2) Distribution of nonkey components ( L ) ( L / ) ( DxLK, D / LxLK, ) ( LK, HK) ( DxHK, D / LxHK, ) ( ) Replace LK with component i LK, HK ( L ) ( L / ) ( Dxi, D / Lxi, ) ( i, HK) ( DxHK, D / Lx HK, ) ( ) ihk, Dx id, ( ihk, ) Dx LKD, ( LKHK, ) ( ihk, ) Dx HKD, Lxi, ( LK, HK) Lx LK, ( LK, HK) Lx HK, Dx id, 0 x i, or all nonkey components in a Class separation

6 Gilliland Correlation for Actual Reflux Ratio and Theoretical Stages Gilliland correlation : empirical correlation N N{ N ( x, x, ), R ( z, x, q, ), R} Y X N N N id, ib, i, id, 544. X X exp X X R R R The value of N includes one stage for a partial reboiler and one stage for a partial condenser, if used A small initial i i increase in R above R causes a large decrease in N, but further changes in R have a much smaller effect on N

7 -Stage Location Suggestion of Brown and Martin (939) - Based on the enske equation (at total reflux conditions) - Not reliable except for fairly symmetrical feeds and separations N N R S ( NR) ( N ) S / 2 log ( xlk, D / zlk, )( zhk, / xhk, D ) log[( B ) ] / 2 log ( zlk, / xlk, B )( xhk, B / zhk, ) log[( D ) ] Empirical equation of Kirkbride 2 N z R HK, x LK, B B NS z LK, x HK, D D N R N S

8 Distribution of Nonkey Components or multicomponent mixtures at Actual Reflux - Total reflux condition: all components distribute to some extent between distillate and bottoms - Minimum reflux condition: none or only a few of the nonkey components distribute - Reflux ratio near imum: the product distribution lies between the two limits - High reflux ratio: the product distribution may lie outside the limits inferior separation