Problem 7.2.6
One hundred pounds of a solid,
containing 40 percent solute (A) and 60 percent inerts (I), are treated with a
solvent (S) in two stages contact extraction.
The extracted solids are then pressed.
The pressed solids contain 1.2 pounds of solution per pound of
solid. Entrainment of the solids may be
neglected. How much solute is present in
the extract phase if 340 pounds of solvent is used in each stage?
Solution: Consider 100 pounds of fresh solids.
Fresh feed contains 0.6 times
100 or 60 pounds. Underflow solution is
1.2 times 60 or 72 pounds. Total weight
of underflow stream is 72 (solution) plus 60 (inerts) is 132 pounds.
An overall-balance across the
first-stage is 100 (feed) plus 340 (solvent) minus 132 (underflow) is equal to
308 pounds of extract.
Solute balance on first stage:
Fresh feed contains 40 pounds of solute.
If concentration of solute in the solution is y1, then exit streams are y1 times (72 plus 308).
Solving this for y1
is 40 over 380 or 0.1053. Amount of solute
in the extract from the first stage is 72 times 0.1053 or 7.58 pounds.
Solute balance on second
stage: Second stage feed contains 7.58
pounds of solute. If solute concentration
in the exit stream is y2,
then exit streams are y2
times (72 plus 340). Solving this for y2 is 7.58 over 412 or 0.0184. Amount of solute in the second stage underflow
is 72 times (0.0184) or 1.32 pounds.
Overall recovery is 40 minus
1.32 over 40 is equal to 96.7 percent.