Problem Statement: The following is a schematic diagram of an N-stage counter-current extraction operation, where E is the extract stream, R is the raffinate stream.
y1 +-----+ y2 yi +-----+ yi+1 yN +-----+ yN+1
E <----| |<----- ... <-----| |<----- ... <-----| |<----- E
|stage| |stage| |stage|
| 1 | | i | | N |
R ---->| |-----> ... ----->| |-----> ... ----->| |-----> R
x0 +-----+ x1 xi-1 +-----+ xi xN-1 +-----+ xN
The following equations describe this counter-current extraction process.
xi-1 - (1+S)*xi + S*xi+1 = 0 for i=1..N
yi=K*xi
where x = the composition of the raffinate phase, R
y = the composition of the extract phase, E
K = the partition coefficient
S = K*E/R
N = the number of stages
Another equivalent form of the first equation is:
x0-xN SN+1-S
------ = -------
x0-xN+1 SN+1-1
Given E=200 lb/hr, R=300 lb/hr, K=3, and inlet raffinate and
extract compositions of x0=0.03 and yN+1=0,
respectively, write a program to determine the number of
stages, N, required for the process to achieve an exit raffinate
composition of xN=0.001. (Note that N is an integer
-- you either have a stage or you don't.) Furthermore, output the
composition of the raffinate phase at each stage.
Solution:
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