# ps_5 - DOWNSTREAM PROCESSING Problem Set#5 Problem 1...

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D OWNSTREAM P ROCESSING Problem Set #5 Problem 1 Consider the following diagram of a countercurrent extraction process in which a solute is extracted from a heavy phase with flow rate H and concentration X and into a light phase with flow rate L and solute concentration Y: a) Starting with a material balance, derive an equation showing that the recovery (R) of the solute in the light phase can be expressed as follows: 32 1 R1 EEE =− 1 + ++ where d YL L EK XH H == and E is the extraction factor and K d is the distribution coefficient. Note the light phase initially contains no solute. ( Hint: Begin your derivation around stage 3 ) 3 1 2 Y -2 Y -1 Y 0 Y 1 L H X 3 X 1 X 2 X 0 1

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b) The sum of the geometric sequence 1 + X + X 2 + X 3 + X 4 + …. . + X n can be restated as follows: n1 1X S + = Use this formula to show that a general solution to part a for the recovery of a solute from the heavy phase (H) using extraction with a particular number of stages (n) is as follows: EE R 1E + + = c) Plot recovery as a function of H/L ratio for the case in which K
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ps_5 - DOWNSTREAM PROCESSING Problem Set#5 Problem 1...

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