ChE 132 Homework: On Ethanol-Water Distillation Systems

two-problem post

[photo credits to wikipedia]

The system to work on

Our instructor gave us two homework problems about a week ago concerning ethanol-water distillation systems. These two problems were from the book, Principles of Unit Operations by Alan Foust et. al.

A distillation column would look like this:




Here are the problems:

7.35

An equimolar mixture of ethanol and water to be fractionally distilled to produce a distillate of composition 0.80 mole fraction ethanol and bottoms of 0.05 mole fraction ethanol. The feed is a saturated liquid and there is a total condenser and a total reboiler.

(a) As a reflux ratio of 2.0, how many equilibrium stages are required?
(b) How many stages are required at total reflux?

7.38

An amount of 1000 lb moles/hr of a 25 mole percent ethanol-water mixture is to be fractioned at 1 atm into two ethanol-rich streams of composition 60% and 80% ethanol; 98% of the ethanol in the feed is to be recovered in these two products. That is, only 2% of the feed ethanol may go out in the bottoms, which are withdrawn from the reboiler. Equal quantities (in moles) of 60% and 80% products are to be produced. The feed, the bottoms, and the 60% product are liquids at the bubble point. The 80% product is a saturated vapor withdrawn from the partial condenser. The reflux ratio (Lo/D) at the top of the column is to be 3.0. The overall plate effeciency is 25%. Assuming constant molar overflow and using the xy diagram(see pic below), calculate:

(a) The number of actual plates required for the desired separation
(b) The actual plate on which to put the feed.
(c) The actual plate from which the 60% product is withdrawn
(f) The minimum reflux ratio at the top of the column
(g) The minimum number of stages at total reflux

The graph of the system

Thoughts to ponder:

7. 35

The feed is a saturated liquid. This implies that the slope of the i-line is infinity therefore it is vertical and parallel to the y-axis.

Total reflux - according to my classmate, Renz, the line for stripping section is ignored. hence, upon applying the technique on stepping off, use only the diagonal line for the enriching section.

7.38

Plate efficiency - The equilibrium produced by an actual plate of a distillation column or countercurrent tower extractor compared with that of a perfect plate, expressed as a ratio. [weblink here]


Partial condenser versus total condenser -

A total condenser - 100% of the vapor on the top part is condensed. The vapor composition at V1 is the same as that of the distillate D.

A partial condenser - the vapor is partially condensed. D' is purely vapor. The compositions D' is different from V1 and Lo. Lo is in equilibrium with D'.

Fig 1. Configuration for partial and total condensers

[more info on weblink here]


How should i locate the streams for 60% and 80% extract?

Since it is said in the problem that the feed, bottoms, and the 60% product are liquids at bubble point, i think they're located on the stripping section or much lower. I am still thinking on putting it on the bottom of the reboiler, but i have second thoughts. If it is at its bubble point (first bubble of vapor to be formed) then it's quite near the reboiler.

Revised configuration: the 60% stream should be drawn along the stripping section, probably to the left of the diagram before the bottoms. This suggest that the picture below shows a wrong configuration. I apologize. hehe!

Fig. 2 My thoughts on the stream for the 60% product (Wrong)

The 80% feed is obviously D' (see fig. 1) It is a saturated vapor therefore it follows that it comes from the partial condenser.

Okay. if you have other thoughts please leave a comment.