Page 75 - Separation process engineering

(2-21)

For binary systems,

y = 1 – y , x = 1 – x A
B
A
B
and the relative volatility is

(2-22a)

Solving Eq. (2-22) for y , we obtain
A

(2-22b)

If Raoult’s law is valid, then we can determine relative volatility as

(2-23)
The relative volatility α may also be fit to experimental data.

If we solve Eqs. (2-21) and (2-11) simultaneously, we obtain

(2-24)

which is easily solved with the quadratic equation. This can be done conveniently with a spread sheet.

2.4.2 Simultaneous Solution and Enthalpy-Composition Diagram

If the temperature of the feed to the drum, T , is the specified variable, the mass and energy balances and
F
the equilibrium equations must be solved simultaneously. You can see from the energy balance, Eq. (2-7)
why this is true. The feed enthalpy, h , can be calculated, but the vapor and liquid enthalpies, H and h ,
F
v
L
depend upon T drum , y, and x, which are unknown. Thus a sequential solution is not possible.
We could write Eqs. (2-3) to (2-8) and solve seven equations simultaneously for the seven unknowns y, x,
L, V, H , h , and T drum . This is feasible but rather difficult, particularly since Eqs. (2-3) and (2-4) and
v
L
often Eqs. (2-8) are nonlinear, so we resort to a trial-and-error procedure. This method is: Guess the
value of one of the variables, calculate the other variables, and then check the guessed value of the trial
variable. For a binary system, we can select any one of several trial variables, such as y, x, T , V/F, or
drum
L/F. For example, if we select the temperature of the drum, T drum , as the trial variable, the calculation
procedure is:

1. Calculate h (T , z) [e.g., use Eq. (2-9b)].
F F
2. Guess the value of T drum .

3. Calculate x and y from the equilibrium equations (2-3) and (2-4) or graphically (use temperature-
composition diagram).
4. Find L and V by solving the mass balance equations (2-5) and (2-6), or find L/V from Figure 2-8 and
use the overall mass balance, Eq. (2-5).