Page 70 - Separation process engineering

(2-10)

where x and y are mole fractions of component A in liquid and vapor, respectively. C is the molar
A
A
P
heat capacity, T is the chosen reference temperature, and λ is the latent heat of vaporization at T . For
ref
ref
binary systems, x = 1 − x , and y = 1 − y .
A
B
B
A
2.4.1 Sequential Solution Procedure
In the sequential solution procedure, we first solve the mass balance and equilibrium relationships, and
then we solve the energy balance and enthalpy equations. In other words, the two sets of equations are
uncoupled. The sequential solution procedure is applicable when the last degree of freedom is used to
specify a variable that relates to the conditions in the flash drum. Possible choices are:
Vapor mole fraction, y

Liquid mole fraction, x
Fraction feed vaporized, f = V/F

Fraction feed remaining liquid, q = L/F
Temperature of flash drum, T
drum
If one of the equilibrium conditions, y, x, or T drum , is specified, then the other two can be found from Eqs.

(2-2a) and (2-2b) or from the graphical representation of equilibrium data. For example, if y is specified,
x is obtained from Eq. (2-2a) and T drum from Eq. (2-2b). In the mass balances, Eqs. (2-5) and (2-6), the
only unknowns are L and V, and the two equations can be solved simultaneously.

If either the fraction vaporized or fraction remaining liquid is specified, Eqs. (2-2a), (2-2b), and (2-6)
must be solved simultaneously. The most convenient way to do this is to combine the mass balances.
Solving Eq. (2-6) for y, we obtain

(2-11)

Equation (2-11) is the operating equation, which for a single-stage system relates the compositions of the
two streams leaving the stage. Equation (2-11) can be rewritten in terms of either the fraction vaporized, f
= V/F, or the fraction remaining liquid, q = L/F.
From the overall mass balance, Eq. (2-5),

(2-12)

Then the operating equation becomes

(2-13)

The alternative in terms of L/F is