Page 76 - Separation process engineering

5. Calculate h (T drum , x) and H (T drum , y) from Eqs. (2-8) or (2-9a) and (2-10) or from the enthalpy-
v
L
composition diagram.
6. Check: Is the energy balance equation (2-7) satisfied? If it is satisfied, we are finished. Otherwise,
return to step 2.

The procedures are similar for other trial variables.
For binary flash distillation, the simultaneous procedure can be conveniently carried out on an enthalpy-
composition diagram. First calculate the feed enthalpy, h , from Eq. (2-8) or Eq. (2-9b); then plot the feed
F
point as shown on Figure 2-9 (see Problem 2-A1). In the flash drum the feed separates into liquid and
vapor in equilibrium. Thus the isotherm through the feed point, which must be the T drum isotherm, gives
the correct values for x and y. The flow rates, L and V, can be determined from the mass balances, Eqs.
(2-5) and (2-6), or from a graphical mass balance.

Figure 2-9. Binary flash calculation in enthalpy-composition diagram

Determining the isotherm through the feed point requires a minor trial-and-error procedure. Pick a y (or
x), draw the isotherm, and check whether it goes through the feed point. If not, repeat with a new y (or x).

A graphical solution to the mass balances and equilibrium can be developed for Figure 2-9. Substitute the
overall balance Eq. (2-5) into the more volatile component mass balance Eq. (2-6),
Lz + Vz = Lx + Vy

Rearranging and solving for L/V

(2-25)

Using basic geometry, (y – z) is proportional to the distance on the diagonal line and (z – x) is
proportional to the distance FL. Then,

(2-26)

Equation (2-26) is called the lever-arm rule because the same result is obtained when a moment-arm
balance is done on a seesaw. Thus if we set moment arms of the seesaw in Figure 2-10 equal, we obtain