Page 147 - Separation process engineering

1. The column is adiabatic.

2. The specific heat changes are small compared to latent heat changes.

(4-10)

3. The heat of vaporization per mole, λ, is constant; that is, λ does not depend on concentration.
Condition 3 is the most important criterion. Lewis called this set of conditions constant molal
overflow (CMO). An alternative to conditions 2 and 3 is

4. The saturated liquid and vapor lines on an enthalpy-composition diagram (in molar units) are parallel.
For some systems, such as hydrocarbons, the latent heat of vaporization per kilogram is approximately
constant. Then the mass flow rates are constant, and constant mass overflow should be used.

The Lewis method assumes before the calculation is done that CMO is valid. Thus Eqs. (4-8) and (4-9)
are valid. With this assumption, the energy balance, Eqs. (4-3) and (4-7), will be automatically satisfied.
Then only Eqs. (4-1), (4-2), and (4-4c), or (4-5), (4-6), and (4-4c) need be solved. Eqs. (4-1, stage j) and
(4-2, stage j) can be combined. Thus,

(4-11)

Solving for y , we have
j+1

(4-12a)

Since L and V are constant, this equation becomes

(4-12b)

Eq. (4-12b) is the operating equation in the enriching section. It relates the concentrations of two passing
streams in the column and thus represents the mass balances in the enriching section. Eq. (4-12b) is
solved sequentially with the equilibrium expression for x, which is Eq. (4-4c, stage j).
j
To start we first use the column balances to calculate D and B. Then L = (L /D)D and V = L + D. For a
1
0
0
0
saturated liquid reflux, L = L = L = L and V = V = V. At the top of the column we know that y = x .
2
1
D
1
0
2
1
The vapor leaving the top stage is in equilibrium with the liquid leaving this stage (see Figure 4-1A).
Thus x can be calculated from Eq. (4-4c, stage j) with j = 1. Then y is found from Eq. (4-12b) with j =
1
2
1. We then proceed to the second stage, set j = 2, and obtain x from Eq. (4-4c, stage j) and y from Eq.
2
3
(4-12b). We continue this procedure down to the feed stage.
In the stripping section, Eqs. (4-5, stage k) and (4-6, stage k) are combined to give
(4-13)

With CMO, and are constant, and the resulting stripping section operating equation is