Leaching Theory

Countercurrent stagewise processes are frequently used in industrial leaching because they can deliver the highest possible concentration in the extract and can minimize the amount of solvent needed. The solvent phase becomes concentrated as it contacts in a stagewise fashion the increasingy solute-rich solid. The raffinate becomes less concentrated in soluble material as it moves toward the fresh solvent stage.

The design equations are made up of the overall and component material balances for the entire process and for each separation stage. It is assumed that the solute-free solid is insoluble in the extracting solvent. The total system material balances are:
                                    VB + LA = VA + LB

Component:     VB YB + LA XA = VA YA + LB XB

where V = mass of liquid extractant (B entering, A leaving)
YB = concentration entering with solvent (zero if fresh solvent)
YA = concentration in solvent leaving
L = mass of retained liquid on inert solids (A entering, B leaving)
XA = concentration of solute in adhering entering liquid
XB = concentration in adhering liquid leaving process

There may be more than one solute being extracted. In the simultaneous equations for the process, there should be one overall material balance and C minus 1 component material balance equations, where C is the number of components. Also the sum of the mass or mole fractions must be equal to one for each stream because there are no chemical reactions. Similar balances apply at each stage, but the output from one stage becomes the input to the next stage. 

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School of Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180