Environmental Engineering Reference
In-Depth Information
V , y R
L , x 1
b , x A, b
Figure 3.32 Bottom stage of a cascade.
derived for the cascade described above [11]. A constant value of the relative volatility,
α AB (see Equation (3.23)), is assumed for each stage.
Consider the bottom of any equilibrium-stage process as shown in Figure 3.32, where L
is the liquid stream exiting the cascade, b is the product stream, and V is the stream which
is vaporized and fed back into the cascade.
From the definition of a separation factor (Equation (2.9)), one can write
y A
y B
R = α R x A
b ,
(3.52)
x B
where A and B denote the two components of a binary mixture. A mass balance yields
Vy R =
Lx 1
bx A , b .
(3.53)
The case of minimum number of equilibrium stages corresponds to infinite flow from and
back into the cascade, such that no product is removed. In this case
=
=
.
V
L
and
b
0
The mass balance, then, reduces to
y R =
x 1 .
(3.54)
Substitution back into the separation factor equation gives
x A
x B
1 = α R x A
b .
(3.55)
x B
To relate equilibrium Stage 2 to equilibrium Stage 1 and the final stage R , one can write
x A
x B
2 = α 1 x A
1 = α 1 α R x A
R .
(3.56)
x B
x B
This development can be followed to the top of the cascade for N equilibrium stages
x A
x B
N = α N α N 1 ...α 1 α R x A
b ,
(3.57)
x B
Search WWH ::




Custom Search