I am designing a distillation column and am optimising the total annualised cost by varying the number of stages and by varying the R/Rmin and by varying the inlet feed tray. I am very confused as to how I should go about with looking for the best combination of stages, R/Rmin and inlet feed tray. These variables are all dependent on each other.
I have started with the short cut method by hand, and I have obtained a certain reflux ratio but when I run it in rigorous simulation on Aspen plus, the purity in the distillate and bottom product differed from my target. Hence, I used design specification to fix my target purity by varying the reflux ratio. I got a reflux ratio much higher than the one I calculated from the short cut method, which is 2.15Rmin calculated from the short cut method. This deviated from the optimum R/Rmin range which is 1.1-1.5. I don't know why it is much higher.
The problem I have in looking into how the no. of stages affect the cost is that when I change the no. of stages on aspen, I am also required to input the position of the feed tray. The position of the feed tray for a given number of stage can greatly affect how effective the separation is hence the operating and capital costs. f I keep the feed stage constant, the no of stages with the wrong feed stage would perform worse which of course would increase the cost. Hence I dont think it's fair to keep the feed position constant. But I dont know how I can figure out the inlet feed position for every no. of stage. Would it be appropriate if I use the kirkbride correlation to calculate the new feed tray location? Someone suggested that I could increase or decrease the feed tray by the same amount as when i increase or decreases the no. of stages from my original no. of stages. However, I feel like this is an unreliable way that I could not justify why this is appropriate. Someone suuggests that I divide my no. of stages by half to get the feed point which I dont think it's appropriate too. How can I figure out the feed location when I vary the no. of stage?