A distillation column is being used to separate a liquid mixture of ethanol (mor

Question

A distillation column is being used to separate a liquid mixture of ethanol (more volatile) and water (less volatile).

A vapor mixture containing 89.0 mole% ethanol and the balance water enters the overhead condenser at a rate of 100 lb-mole/h. The liquid condensate has a density of 49.0 lbm/ft3, and the reflux ratio is 3 lbm reflux/lbm overhead product. When the system is operating at steady state, the tank collecting the condensate is half full of liquid and the mean residence time in the tank (volume of liquid/volumetric flow rate of liquid) is 10.0 minutes.

Determine the overhead product volumetric flow rate (ft3/min) and the condenser tank volume (gal).

Explanation / Answer

In a separetor's design process I use a rigorous method but we can use a quick inference that should help to find this two specific unknowns.

Qg = gas volumetric flow rate = Wg/pl

where:

Wg is the weigth og vapor mixture (lbm/hr)

pl = liquid density (lbm/ft3)

If 100 lbm/hr - 11%

X = 809.1 lbm/hr

Then,

Qg = (809.1lbm/hr) / (49lbm/ft3)

Qg = 16.51 ft3/hr

---------------------------------------------------------------------------------------------------------------------------------------------------

tank volume = 1/60 * Ql * Tr

where:

1hr takes 60 mins

Ql is the liquid flow rate

Ql = 100 lbm/hr / 49 (lbm/ft3)

Ql = 5.667*10^-4 ft3/min

---------------------------------------------------------------------------------------------------------------------------------------------------

Tr is the reflux time

tank volume = 1hr/60min * (2.04ft3/hr) * 10min

tank volume = 0.3401 ft3 * 7.48 gal/ft3 = 2.54412468 US Gallon

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