Distillation with Reflux When operation of a distillation column begins, vapor i

Question

Distillation with Reflux

When operation of a distillation column begins, vapor is generated at the bottom of the column, flows upward through the column, and leaves the top of the column to be condensed in a heat exchanger. During the startup phase, all of the condensate is allowed to flow back into the top of the column as reflux where it contacts the upward-flowing vapor. When conditions in the column begin to stabilize, a valve controlling the flow of reflux to the column is opened, and a fraction of the condensate is allowed to leave the system as product instead of reentering the column as reflux. The ratio of the flow rate of condensate returned to the column (reflux) to the product withdrawal rate is 2.75. A mixture of 89.0 mol% ethanol, and the remainder water enters the condenser at a rate of 140.0 lb-mol/h. The ethanol-water condensate has a density of 49.9 lbm/ft3. When operated at steady-state conditions, the tank collecting the condensate is half full, and the mean residence time in the tank is 10.0 minutes. Using the following figure as a guide, write a general mass balance around a system consisting of the condenser, condensate tank, and splitter. From the information given, determine the product withdrawal rate at steady state the volume of the tank in gallons

Explanation / Answer

Basis: 10 minutes of operation

Given, 140 lb moles per hour

Therfore, for 10 minutes of operation the total molar flow rate is 23.333 lb moles

89% ethanol water system out of 23.333 lb moles 89% is ethanol i.e, 20.766 lb moles

And rest of them are water i,e 2.566 lb moles

Ratio of reflux to product is 2.75 writing there mole balance

X+2.75x=23.333

X=6.22 lb mole per 10 minutes

Per hr = 37.32 lb mole

Therfore product stream flows rate is 37.32 lb mole/hr

Molecular wt of ethanol is 46.06

Of water is 18

There fore total mass of ethanol water solution is 20.766*46.06 + 2.56*18 =1002.6798lbm

Density of solution = 49.9lbm/ft3

There fore volume = mass/density= 20.093ft3

This is half tank volume therefore full tank volume is 40.1875 ft3 i.e, 300.6233 gallon

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