for this problem perform the degree of freedom analysis for this problem and sol

Question

for this problem perform the degree of freedom analysis for this problem and solve for the unknow values. A is the Oleic acid, P is the propane and O is the cottonseed oil

A stream of 5.00 wt% oleic acid in cottonseed oil enters an extraction unit at a rate of 100.0 kg/hr. A separate stream of propane enters the unit. Propane is able to dissolve oleic acid but cannot mix with the cottonseed oil. Two streams exit the unit: One stream of propane that contains 90% of the oleic acid that enters the process; and a second stream that contains all of the cottonseed oil along with the remaining oleic acid. The concentration of oleic acid in the propane stream is 6.15 wt%. Perform the degree of freedom analysis on this problem and solve for the unknown values. Turn in your solution at the beginning of

Explanation / Answer

Basis : 100 kg/hr

Oleic acid in the sample = 5 wt%

Oleic acid = 100*5/100 =5 kg/hr

Unknowns : Propane flow rate, m* and mp*, ma*

There are three unknown( propane flow rate, mp* and m.)

Three independent equations need to be written

Propane stream mP* contains 90% of the oleic acid   entering

Oleic acid in propane rich stream= 5*0.9=4.5 kg/hr

This correspond to 6.15% of propane stream

Hence flow rate of propane stream = 4.5*100/6.15=73.17 kg/hr

Rest of the 100-6.15=93.85% is propane, hence propane is the propane rich stream= 73.17*0.9385=68.67 kg/hr

So propane is exiting through only one stream, propane entering = 68.67 kg/hr

Writing overall balance 100+68.67= 73.17+ mP

Therefore mp = 168.67-73.17=95.5 kg/hr

A ain mp*= 95.5-95= 0.5 kg/hr ( not O as mentioned)

Flow rate of A in m.= 5-0.5 =4.5 kg/hr

Remaining oleic acid = 5-4.5= 0.5 kg/hr

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