Question

Caffeine is often added to headache medications because it affects the flow of blood in vessels and may enhance the pain relieving qualities of the medication. You have been tasked with evaluating one process that extracts caffeine from a coffee slurry, and you decide to study a small scale version of the process. A coffee slurry containing a mass fraction of 0.01 g caffeine/g, 0.08 g other solids/g, and 0.91 g water/g is fed to a mixer at a rate of 710.0 g/min. Na2CO3 is added to the mixer such that the mass ratio of Na2CO3 to coffee slurry is 0.0300. This aqueous solution proceeds to an extractor where CH2Cl2 is added such that the mass ratio of CH2Cl2 to coffee slurry entering the extractor is 0.440. Two streams leave the extractor. The first is a mostly aqueous stream that leaves the process containing some caffeine, all of the other solids in the original slurry, all of the Na2CO3, all of the water and 2% of the mass of CH2Cl2 entering the extractor. The second stream contains the remaining caffeine and CH2Cl2, and enters an evaporator that completely vaporizes the CH2Cl2. The vaporized CH2Cl2 is condensed and is merged with the fresh CH2Cl2 on the way to the extractor. The dried caffeine crystals exit the evaporator and leave the process. Of the caffeine entering the process a fraction of 0.960 leaves the process in this product stream.

a) What is the mass flow rate of crystallized caffeine (g caffeine/min)?

b) What is the mass flow rate of fresh CH2Cl2 to the process (g CH2Cl2/min)?

c) What is the ratio of the flow rates of recycled CH2Cl2 to fresh CH2Cl2?

Answer 1

Coffee slurry contains 0.01 g caffeine. Total coffee slurry= 710g/min

Caffeine entering the process = 710*0.01= 7.1 gm/min

0.96 fraction entering the process leaves the products stream =7.1*0.96= 6.82 g/min

Balance caffeine= 7.1-6.82= 0.28 g/min will have to leave along with aqueous solution leaving the extractor

All the water is entering leaves through the aqueous medium, hence water in the aqueous medium= 710*0.91=646.1 gm/min

Na2CO3 added = 710*0.03 =21.3 g/min. This also leaves along with aqueous solution

Other solids in the slurry= 710*0.08=56.8 g/min

Total slurry entering the extractor= 710+ 21.3 =731.3 g/min

CH2Cl2 = 0.44*731.3=321.772 g/min

2% of this leaving the aqueous medium and hence , CH2CL2 leaving the aqueous medium= 321.772*2/100=6.44 g/min

Under steady state conditions, the CH2CL2 stream leaving aqueous stream needs to be compensated with fresh CH2Cl2. This amounts to 6.44 g/min

Total CH2Cl2 entering the extractor = 6.44 g/min. Rest of CH2CL2 is recycled which is equal to = 321.772-6.44=315.332g/min

Ratio of Recycle to Fresh CH2Cl2= 315.332/6.44=48.96