Advanced Separation Process

To batch crystallise benzoic acid from solutions of ethanol, water is added to the system to reduce the solubility of benzoic acid, thereby creating a supersaturated solution. The solubility of benzoic acid in the solvent mixture at 25C, as a function of the water content, is given by: c=0.6850.227w where c is solubility ( kg benzoic acid/ /kg ethanol) and w is the water content (kg water /kg ethanol). At the start of each batch, a saturated solution of benzoic acid in 5,000kg of ethanol at 25C is prepared (corresponding to a concentration of 0.584kg benzoic acid /kg ethanol). When 2,500 kg of water have been added, the batch is seeded with 50kg of 20m seed crystals of benzoic acid. Following seeding, the water addition rate is controlled to ensure that the supersaturation remains constant at the value reached at the point of seeding. Assume that nucleation is negligible, and that the growth kinetics of benzoic acid in this system are given by G=0.35c1.2 where G is the linear crystal growth rate in m/s, and c is the supersaturation in kg benzoic acid /kg ethanol. (i) Derive an analytical equation to allow the determination of the water addition rate at any time during the batch. (ii) Evaluate the water addition rate after 60,120 and 180 minutes