Page 38 - Distillation theory

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0521820928c01 CB644-Petlyuk-v1 June 11, 2004 17:45

12 Phase Equilibrium and Its Geometric Presentation

bond chains (i.e., all the distillation subregions). For example, in Fig. 1.8c, the
distillation subregions Reg are as follows: 123 → 12 → 1, 123 → 13 → 1, 123 →
sub
12 → 2, 123 → 23 → 2, 123 → 23 → 3, and 123 → 13 → 3. Respectively, the
distillation regions Reg are as follows: 123 ⇒ 1, 123 ⇒ 2, 123 ⇒ 3, or
∞
↑ → 13 →↓ ↑ → 23 →↓ ↑ → 13 →↓
,
,
123 → 12 → 1 123 → 12 → 2 123 → 23 → 3
1.7. Lines, Surfaces, and Hypersurfaces K i = K j

In Sections 1.3 to 1.5, the residue curve bundles, which characterize the direction
of liquid–vapor tie-lines in each point of the concentration space (i.e., the phase
equilibrium field), were considered. As stated previously, such characteristics of
the phase equilibrium field and structural elements related to it (bonds, distillation
regions, and subregions) are the most important for one of the distillation modes,
in particular, for the infinite reflux mode.
However, the liquid–vapor phase equilibrium field has other important charac-
teristics that become apparent under other distillation modes, in particular, under
reversible distillation and usual (adiabatic) distillation with finite reflux.
To such characteristics are referred, first of all, lines, surfaces, and hypersurfaces
of the phase equilibrium coefficients equality (K i = K j ). For the purpose of brevity,
we will name these lines, surfaces, and hypersurfaces as α-lines, α-surfaces, and α-
hypersurfaces (or univolatility lines, surfaces, and hypersurfaces: α ij = K i /K j = 1).
Univolatility α-lines, α-surfaces, and α-hypersurfaces divide the concentration
ijk ijk
simplex into regions of order of components Reg (in Reg K i > K j > K k )
ord ord
(Petlyuk & Serafimov, 1983).
The totality of several regions of components’ order for which one and the same
component appear to be the most light volatile (K l = max K i ) or the most heavy
i l
volatile (K h = min K i ) was named as a region of reversible distillation Reg rev, s or
h i
Reg rev, r (Petlyuk, 1978). Such a name can be explained by the crucial meaning of
these regions for possibly realizing of reversible distillation (see Chapter 4).
a) 2 b) 2

y α 23
x
231
2431
213
1 3 1 α 4
13 13
13 α 13
3 2413
Figure 1.9. α-lines, α-surfaces (shaded), and regions of order
of components Reg for (a) three-component and (b) four-
ord
component mixtures. 231, 213, 2431, and 2413, regions of com-
2,3,1 2,1,3 2,4,3,1 2,4,1,3
ponent order Reg ord , Reg ord , Reg ord , and Reg ord ; x → y, tie-line
liquid–vapor for point x on α-line; arrows, direction of residium
curves; dotty lines, separatrixes.