Chapter 6, Problem 6.90P

An ore containing 90 wt% MgSO₄(H₂O and the balance insoluble minerals is fed to a dissolution tank at a rate of 60,000 lb_m/h along with fresh water and a recycle stream. The tank contents are heated to 120°F, causing all of the magnesium sulfate monohydrate in the ore to dissolve, forming a solution 10°F above saturation. The resulting slurry of the insoluble minerals in MgSO₄ solution is pumped to a heated ?lter, where a wet ?lter cake is separated from a solids-free ?ltrate. The ?lter cake retains 5 lb_m of solution per 100 lb_m of solids. The ?ltrate is sent to a crystallizer in which the temperature is reduced to 50°F, producing a slurry of MgSO₄(7H₂O crystals in a saturated solution that is sent to another ?lter. The product ?lter cake contains all of the crystals and entrained solution in a ratio of 5 lb_m solution per 100 lb_m crystals. The ?ltrate from this ?lter is returned to the dissolution tank as the recycle stream.

Solubility data: Saturated magnesium sulfate solutions at 110°F and 50°F contain 32 wt% MgSO₄ and 23 wt% MgSO₄, respectively.

(a) Explain why the solution is ?rst heated (in the dissolution tank) and ?ltered and then cooled (in the crystallizer) and ?ltered.

(b) Calculate the production rate of crystals and the required feed rate of fresh water to the dissolution tank. (Note: Don‘t forget to include water of hydration when you write a mass balance on water.)

(c) Calculate the ratio lb_m recycle/lb_m makeup water.