Crystallization of gypsum takes place in a 200,000-gal stirred tank that is part of a process for flue gas desulfurization. With a single outlet to a settling tank and filter. the slurry has 15 weight percent CaSO₄ - 2H₂O and a mean particle size of about 30 μm. Pilot-plant tests under similar conditions but with double drawoff and an overflow-underflow ratio of 3.5 showed a bimodal size distribution with peaks at 20 μm and 50 μm. The classification was made with hydroclones with a cut size of 30 μm.

(a) What is the average residence time for large crystals with DDO operation relative to the average residence time for MSMPR operation?(b) What evidence is there that the supersaturation is different in the two modes of operation? 

(c) Estimate the concentrations in the overflow and underflow streams and the concentration of the combined streams.