Page 74 - Separation process engineering

affect the drum diameter and the energy needed in the preheater.
E. Check. We can check the solutions with the mass balance, Fz = Vy + Lx.

a. (100)(0.4) = 0(0.61) + (100)(0.4) checks

b. (100)(0.4) = 100(0.4) + (0)(0.075) checks
c. 100(0.4) = (66.6)(0.52) + (33.3)(0.17)
Note V = (2/3)F and L = (1/3)F

This is 40 = 39.9, which checks within the accuracy of the graph

d. Check is similar to c : 400 = 399
We can also check by fitting the equilibrium data to a polynomial equation and then
simultaneously solve equilibrium and operating equations by minimizing the residual. These
spread sheet calculations agree with the graphical solution.

F. Generalization. The method for obtaining bounds for the answer (setting the V/F equation to its
extreme values of 0.0 and 1.0) can be used in a variety of other situations. In general, the feed rate
will not affect the compositions obtained in the design of stage separators. Feed rate does affect
heat requirement and equipment diameters.

Once the conditions within the flash drum have been calculated, we proceed to the energy balance. With
y, x, and T known, the enthalpies H and h are easily calculated from Eqs. (2-8) or (2-9) and (2-10).
drum v L
Then the only unknown in Eq. (2-7) is the feed enthalpy h . Once h is known, the inlet feed temperature
F
F
T can be obtained from Eq. (2-8) or (2-9b).
F
The amount of heat required in the heater, Q , can be determined from an energy balance around the
h
heater.

(2-19)
Since enthalpy h can be calculated from T and z, the only unknown is Q , which controls the size of the
1
1
h
heater.
The feed pressure, p , required is semi-arbitrary. Any pressure high enough to prevent boiling at
F
temperature T can be used.
F
One additional useful result is the calculation of V/F when all mole fractions (z, y, x) are known. Solving
Eqs. (2-5) and (2-6), we obtain

(2-20)

Except for sizing the flash drum, which is covered later, this completes the sequential procedure. Note
that the advantages of this procedure are that mass and energy balances are uncoupled and can be solved
independently. Thus trial and error is not required.

If we have a convenient equation for the equilibrium data, then we can obtain the simultaneous solution of
the operating equation (2-9, 2-11, or 2-13) and the equilibrium equation analytically. For example, ideal
systems often have a constant relative volatility α where α is defined as,
AB AB