Page 48 - Distillation theory

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22 Basic Concepts of Distillation

when the distillate is removed in form of vapor; and sometimes a mixed condenser
is applied, when one part of the distillate is liquid and the other part is vapor.
Liquid from the bottom of the column goes to the reboiler where it is partially
evaporated (reboilers of this kind are called partial). The vapor in amount V 1 ,of
composition y i1 comes back to the column, and the remaining liquid in amount B
of composition x iB is removed as bottom product.
Ratio R = L N /Dis called the reflux ratio and ratio S = V 1 /Bis called the reboil
ratio. In the reboiler, there is a input of heat in amount Q R , and, in the condenser,
there is a removal of heat in amount Q con .
Thus, distillation is a two-phase (liquid–vapor) multistage counterflow poten-
tially equilibrium process (in some cases – in cases of heteroazeotropic distilla-
tion – three phases may occur on the trays: two liquid phases and one vapor phase).

2.1.2. System of Algebraic Equations of Distillation

The distillation process is described by a system of algebraic equations, for the
deduction of which let’s consider a closed- loop covering, for example, the column
overhead beginning from tray j (Fig. 2.1b).
The equation of component material balance:

V j−1 y i, j−1 = L j x ij + Dx iD (2.1)
The equation of heat balance:

V j−1 H j−1 = L j h j + Dh D + Q con (2.2)
The equations of phase equilibrium (for “theoretical” tray):

(2.3)
y i, j = K ij x ij
The summation equations:

y ij = 1, x ij = 1 (2.4)
Here, K ij = f (T, P, x 1 ... x n , y 1 ... y n ) is a coefficient of phase equilibrium.
H j = ϕ(T, P, y 1 ... y n ) and h j = ψ(T, x 1 ... x n ) are the enthalpies of vapor and
liquid, respectively.
At first sight, the system of Eqs. (2.1) ÷ (2.4) appears to be rather simple, but
it is necessary to bear in mind that the equation of phase equilibrium [Eq. (2.3)]
together with the equations of summation [Eq. (2.4)] are always nonlinear, even in
the case of the so-called ideal mixtures, with α ih = K i /K h = const (the component
relative volatilities are not influenced by temperature and composition).
In real mixtures, functions K i, j have rather complicated form (especially for
azeotropic and heteroazeotropic mixtures).
Sometimes the system [Eq. (2.1) ÷ (2.4)] is simplified with the rejection of the
heat balance equation [Eq. (2.2)] and with the adoption of the flows L j and V j
constancy within each column section (the term section refers to the part of a
column between the flow inlet and outlet points).