Design of Batch Distillation Columns Using Short-Cut Method at Constant Reflux

Table 2

Actions and equations used in batch distillation column operating at constant reflux.

Step	Action	Sundaram-Evans	Diwekar-Madhavan
0	Data needed	(a) 𝑁𝑐,𝛼𝑖𝑥𝑊,𝐼,𝑁,𝑅,𝑉,𝑊0
1 (Used to begin the cycles)	Using 𝑁 as number of stages, estimate molar fraction of reference component at distillate (𝑥𝐷,𝑟)	(b) 𝑥𝐷𝑟=𝑥𝑊𝑟∑^𝑖=𝐶𝑖=1𝑥𝑊i𝛼^𝑁𝑖,𝑟; 𝑟 = heaviest component
2 (Used to begin the cycles)	Calculate molar fraction of nonreference component at distillate	(c) Fenske: 𝑥𝐷i=𝑥𝑊i𝑥𝐷𝑟𝑥𝑊𝑟𝛼^𝑁𝑖,𝑟	(d) Hengstebek-Geddes: 𝑥^i𝐷=𝑥^i𝑊𝛼𝑖𝛼𝑟^𝐶1𝑥^𝑟𝐷𝑥^𝑟𝑊
3	Stepping forward in time and calculating new molar mass at bottom and new molar fraction of all components	(e) 𝑊^(𝑘+1)=𝑊^(𝑘)−𝑉1+𝑅Δ𝑡
		(f) 𝑥𝑊^(𝑘+1)=𝑥𝑊^(𝑘)+𝑥𝐷^(𝑘)i−𝑥𝑊^(𝑘)i𝑊^(𝑘+1)−𝑊^(𝑘)𝑊^(𝑘)
4	With Gilliland (Eduljee) and Underwood, solve simultaneously for 𝑁min and 𝑅min	(g) 𝑁−𝑁min𝑁+1=0.751−𝑅−𝑅min𝑅+1^0.5668
		(h) 𝑅min=𝛼^𝑁min1,𝑟−𝛼1,𝑟𝛼1,𝑟−1∑^𝑖=𝑟𝑖=1𝑥𝑊i𝛼^𝑁min𝑖,𝑟
5	With the new value of 𝑁min, estimate the molar fraction of the reference component at distillate	(i) 𝑥𝐷𝑟=𝑥𝑊𝑟∑^𝑖=𝐶𝑖=1𝑥𝑊i𝛼^𝑁min𝑖,𝑟
6	With the new value of 𝑁min, calculate molar fraction of nonreference component at distillate	(j) 𝑥𝐷i=𝑥𝑊i𝑥𝐷𝑟𝑥𝑊𝑟𝛼^𝑁min𝑖,𝑟
7	Repeat steps 3 to 6 for several cycles.
8	Stop