Extraction - Principles of Chemical Separations with Environmental Applications - page 151

After Stage 1, we can assume constant flowrates. Hence, the Kremser equation,
Equation (3.51), can be applied:

ln x b −

ln x b −

x b

x a

N = .

x b − x a − x a x a

So,

ln 4

10 − 1 ln 4 10 − 1

10 − 4 10 − 3 10 − 4 10 − 1 . 5 × − 1 . 2 × . 5 × − 1 . 0 ×

N = = 4 . 6 .

. ×

10 − 2

− . × . ×

10 − 3

− . ×

3 9 1 0 1 2 1 0

=

Rounding up to the next integer N 5. Including Stage 1, the number of equilibrium-

limited stages is six.

10 − 4

( S -150)kg hr

x =4.5 ×

x =0.05 Extract

S kg hr

x =3.0× 10 −3

100kghr Diluent

Raffinate Stage N Stage 1 x =0.25wax

Figure 5.29 Schematic solvent flow diagram, Example 5.7.

650 kg hr
x a = ?

500 kg hr
x = 0.05

x b =4.5× 10 −4 650 kg hr

Extract

Raffinate
250 kg hr
x *

250 kg hr
x a =0.1

100 kg hr
x a =0.25

Diluent

= ?

Stage N Stage 1

Figure 5.30 Redrawn schematic for Example 5.7.

5.12 Remember

Extraction is a UNIT OPERATION. Regardless of what chemicals are being separated,
the basic design principles for extraction are always similar.
The assumption that stages in an extraction column are in equilibrium allows calculations
of concentrations and temperatures without detailed knowledge of flow patterns and heat
and mass transfer rates. This assumption is a major simplification.
Extraction requires different solubilities of the solute in the two liquid phases. It also
requires that the two phases have different densities so that they may also be separated.