Page 148 - Separation process engineering

(4-14)

Once we know /V we can obviously alternate between the operating Eq. (4-14) and the equilibrium Eq.
(4-4c, stage k).
The phase and temperature of the feed obviously affect the vapor and liquid flow rates in the column. For
instance, if the feed is liquid, the liquid flow rate below the feed stage must be greater than liquid flow
above the feed stage, > L. If the feed is a vapor, V > . These effects can be quantified by writing mass

and energy balances around the feed stage. The feed stage is shown schematically in Figure 4-3. The
overall mass balance and the energy balance for the balance envelope shown in Figure 4-3 are

(4-15)

Figure 4-3. Feed-stage balance envelope

and

(4-16)

(Despite the use of “h ” as the symbol for the feed enthalpy, the feed can be a liquid or vapor or a two-
F
phase mixture.) If we assume CMO neither the vapor enthalpies nor the liquid enthalpies vary much from
stage to stage. Thus H ~ H and h ~ h . Then Eq. (4-16) can be written as
f
f−1
f
f+1
The mass balance Eq. (4-15) can be conveniently solved for − V,

which can be substituted into the energy balance to give us

Combining terms, this is

or

(4-17)

In words, the “quality” q is