WOLFRAM|DEMONSTRATIONS PROJECT

Solute Extraction Cascade with Solvent Recycle

​
λ
1
stage
1
h
50
solute composition versus time
This Demonstration analyzes a solute extraction process. A raffinate stream with volumetric flow
R
containing an unwanted solute enters a five-stage extraction cascade that is connected to a tank holding the extraction solvent. The solvent container is modeled as a perfectly mixed tank such that the solute composition leaving the tank at any time is the same as the composition in the tank at that time. This problem was solved analytically by Ugo Lelli [1]. Here a numerical solution using Mathematica is given that lets you examine how two key parameters for the extraction process influence the system performance. You can see the effect of varying different values of the solvent container residence time
τ
(expressed as a dimensionless parameter
h
) and the dimensionless parameter
λ=R/(mE)
(related to the volumetric flow rates
R
and
E
in the raffinate and extract phases).
The Demonstration shows how the equilibrium composition (in the raffinate phase) of each stage in the cascade varies with extraction time, expressed in terms of the dimensionless variable
*
t
. At the start
*
t
=0
, there is no solute in the solvent stream and thus
Y
1
=
Y
6
=0
. Then at
*
t
=
+
0
, the raffinate stream has a step change in solute concentration
X
1
(
+
0
)=1
. For very large values of the residence time or dimensionless parameter
h
, we get the usual equilibrium cascade behavior without recycle and
Y
6
(t)≈0
for all
t
and
h=100000
. In contrast, for small values of residence time (or
h
), solvent saturation is observed at large values of the dimensionless time
*
t
.