Problem 7.2.5

One hundred pounds of a solid, containing 40 percent solute (A) and 60 percent inerts (I), are treated with a solvent (S) in a single-stage contact extraction. The extracted solids are then pressed. The pressed solids still contain 1.2 pounds of solution per pound of solid. Entrainment of the solids may be neglected. Calculate the solvent of amount that is needed to perform this operation. What would be the mass of the solute in the extract phase if 90 percent of solute in the feed is recovered?

Solution: Consider 100 pounds of fresh solids.

Desired recovery of extract is 90 percent, so amount of solute in the extract is 0.9 times 40 or 36 pounds. Amount of the extract in the underflow is 40 minus 36 or 4 pounds. As all of the inerts are leaving with underflow, the amount remains as 60 pounds. Amount of solution retained with inerts is, thus, 1.2 times 60 or 72 pounds.

This solution contains 72 minus 4 or 68 pounds of solvent. The concentration of solute is 4 or 72 or 0.055 pound of solute per pound of solution. Note that the same solution is present in the extract. Amount of extract (solution) is 36 over 0.055 or 648 pounds. Amount of solvent in the extract is 648 minus 36 or 612 pounds.

Amount of solvent required for this operation is 612 plus 68 or 680 pounds.