Page 201 - Separation process principles 2

166 Chapter 5 Cascades and Hybrid Systems

Combining the equations in (5-20) to eliminate all interme- the countercurrent arrangement is greater than for the cross-
diate interstage variables, x:), the final raffinate mass ratio current arrangement, and the difference increases exponen-
is given by tially with increasing extraction factor, E. Therefore, the
countercurrent cascade is the most efficient of the three
linear cascades.
For an infinite number of equilibrium stages, the limit of
Interstage values of x:) are obtained similarly from (5-28) gives two results:

Thus, unlike the cocurrent cascade, the value of XB decreases Thus, complete extraction can be achieved in a counter-
in each successive stage. For an infinite number of equilib- current cascade, but only for an extraction factor, E, greater
rium stages, (5-21) becomes than 1.

xhm)/ xF' = 1 / exp(E) (5-23)

Thus, even for an infinite number of stages, Xf) = Xim) EXAMPLE 5.2
cannot be reduced to zero.
Ethylene glycol can be catalytically dehydrated completely to
p-dioxane (a cyclic diether) by the reaction 2HOCH2CH2H0 + ,
Countercurrent Cascade H2CCH20CH2CH20 + 2H20. Water and p-dioxane have normal
boiling points of 100°C and 101.l°C, respectively, and cannot be
In the countercurrent arrangement for two stages in Fig- separated economically by distillation. However, liquid-liquid ex-
ure 5.5c, the feed liquid passes through the cascade counter- traction at 25°C (298.15 K), using benzene as a solvent, is reason-
currently to the solvent. For a two-stage system, the material ably effective. Assume that 4,536 kgh (10,000 lbh) of a 25 wt%
balance and equilibrium equations for solute, B, for each solution of p-dioxane in water is to be separated continuously by
stage are as follows. using 6,804 kgh (15,000 lbh) of pure benzene. Assuming that
benzene and water are mutually insoluble, determine the effect of
Stage 1:
the number and arrangement of stages on the percent extraction of
p-dioxane. The flowsheet is shown in Figure 5.6.
I

SOLUTION

Three different arrangements of stages will be examined: (a) cocur-
Stage 2:
rent cascade, (b) crosscurrent cascade, and (c) countercurrent cas-
cade. Because water and benzene are almost mutually jnsoluble,
(5-13), (5-21), and (5-29) can be used, respectively, to estimate
xF)/x~), the fraction of p-dioxane not extracted, as a function
of the number of stages. From the equilibrium data of Berdt and
Combining (5-24) to (5-27) with (5-14) to eliminate Y;'), Lynch [I], the distribution coefficient forp-dioxane, KbB = Ye/XB,
(2)
(1)
YB , and X, gives where Y refers to the benzene phase and X refers to the water phase,
varies from 1.0 to 1.4 over the concentration range of interest. For
this example, assume a constant value of 1.2. From the given data,
S = 6,804 kgh of benzene, FA = 4,536(0.75) = 3,402 kglh of water,
and xF) = 0.25/0.75 = 113. From (5-14),
If the number of countercurrent stages is extended to N
stages, the result is

Solvent Extract
Interstage values of x;) are obtained in a similar fashion, benzene7 r) (p-dioxanel
benzene-rich
giving mixture)
extraction
p-dioxane
Raffinate
(water-rich
As with the crosscurrent arrangement, the value of XB de- mixture)
creases in each successive stage. The amount of decrease for Figure 5.6 Flowsheet for Example 5.2.