Question

2. Lactic acid is an important pharmaceutical product that is manufactured by the fermentation of glucose: C6H1206 → CsHO Lactic acid has a melting point of 17°C so one way to separate it from the water and unreacted glucose that makes up part of the biomass is to drop the temperature below this melting point in a crystallizer. This will allow solid lactic acid to drop out of the mixture. This solid lactic acid will still be wetted with a portion of the water/glucose mix and will then be cold filtered to further concentrate the lactic acid. A mix contains 14% by mass lactic acid enters the crystallizer unit at a rate of 500 kg/hr. After crystallization, the crystal stream contains 49% by mass lactic acid and the liquid portion itself contains no lactic acid. The crystal stream than goes to the filtration unit where the solids generated contain 79% lactic acid and the liquid portion 0% lactic acid. Determine the mass flow of materials out of both streams for the crystallization and the filtration processes. (a total of 4 streams).

Answer 1

Let the flow rate of Crystal Stream coming out of crystallization unit be A kg/hr and the liquid flow rate be B Kg/hr. Let the flow rate of feed be F. F = 500 Kg/hr

At the crystallization unit balancing the flow rates.

Net flow in = Net flow out => F = A+ B ---(1)

Using the mass balance of lactic acid in crystallization unit, we get, Total Lactic Acid in = Total Lactic Acid out => 14% of F = 49% of A.

0.14 * 500 = 0.49 * A => A = 0.14 * 500/0.49

=> A = 142.85 Kg/hr.

We get B from equation (1), B = F-A => B = 500-142.85 = 357.15 Kg/hr.

Now A flows into the filtration unit and we get a liquid stream whose flow rate is C Kg/hr and our solid product whose flow rate is P Kg/hr.

Balancing the flow rates, we get A = C + P ---(2)

Using Lactic acid mass balance we get, 49% of A = 79% of P.

0.49 * 142.85 = 0.79 * P => P = 0.49*142.85/0.79

P = 88.6 Kg/hr

Using equation (2), we get C = 142.85 - 88.6 = 54.25 Kg/hr