Extraction Nomograph for SoluteFree Solvents D. S. DAVIS Wayne University, Detroit, Mich.
I
m = number of cells or units in battery
N THEIR discussion of the theory of continuous counter-
a
current extraction under equilibrium conditions Badger and McCabe (1) quoted Baker’s equation (2) for the case of solute-free solvents:
F = 1 + a,(l where F
=
of liquid by solids within system and is constant for all cells except the last n = number of any cell except the last a,,, = value of a for cell m S D = weight of solute in solution adhering t o solids discharged from system, lb./lb. inert solid ,s = weight of solute in solution on fresh solids fed to system, lb./lb. inert solid 8, = weight of solute in solution overflowing from nth cell, lb./lb. inert solid ss = weight of solute in solution in underflow from nth cell, lb./lb. inert solid
1
+ a + +. . . a2
= Sn/sn,. which is predicated upon constant retention
am-1)
the ratio of unextracted solute to solute entering with fresh solids
SD/S,,
In a form explicit i n m this equation becomes ,
ri -
(1
- P)(IFa,
lop a
The determination of the number
of cells, m, required to satisfy given
2
conditions is facilitated by the nomograph which, for convenience, deals with 1 / F rather t h a n F , although based upon Equations 1 or 2. The use of the chart is illustrated as follows: How many units are needed when 1 / F , the ratio of solute entering with the fresh solids to the unextracted solute, is 220, and a, and a have the values of 2 and 3.2, respectively? Following the arrows, connect 2 on the a, scale with 220 on the l / F scale and project the isopleth to meet the vertical line for a = 1. Then proceed horizontally until a n intersection with the vertical line for a = 3.2 is attained. The intersection is just below the curve for m = 5 , showing that four cells are insufficient and that five cells provide a little more capacity than is required.
-i
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06j 05
Literature Cited and McCabe, ”Elements of Chemical Engineering”, p. 426, New York, McGraw-Hill Book Co., 1936. ( 2 ) Baker, E. M., Chem. h Met. EPW.,42, 669-671 (1935). (1) Badger
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2
3
4
6
a
1014
8 1 0
,
