Region of reversible distillation

The regions of reversible distillation and regions of the identical order of components are especially signihcant for the analysis of possible cases of separation by distillation. 

As one can see in Fig. 4.2, the trajectory of each section at sharp reversible distillation consists of two parts the part, located inside the (n -1) component boundary element C i of concentration simplex, lying between the product point Xd or xb and the tear-off point of the trajectory from this boundary element x[, and the part located inside concentration simplex C , lying between the tear-off point of the trajectory and the feed point xp. Only the second part should be located inside a region of reversible distillation Reg y orRegJ g, and product point Xd or xb can lie outside this region. 

Therefore, the concentration simplex can contain one or several regions of reversible distillation Reg v.r or for each section. 

The region of reversible distillation can contain one or several reversible distillation trajectory bundles (lines of stationarity). Some of these bundles can be true some of them can be fictitious. Fictitious bundles always have two node points and true ones have one node point or no node point. 

This result also remains valid for azeotropic mixtures. A necessary condition for exhausting of the some component in the intermediate (extractive) section at reversible distillation consists of the fact that the whole trajectory of intermediate (extractive) section should be located in the region where this component is intermediate in phase equilibrium coefficient (in the region of reversible distillation of the intermediate section Reg J. The segment of the side containing only the component separated as top product and component brought in as an entrainer is a boundary element of this region Reg l. ... 

I. Define the main notions (1) region of reversible distillation of top Reg g bottom Reg -e, and intermediate sections Reg g (2) regions of trajectory tear-off Reg and Reg (3) region of possible product points of sharp reversible distillation Reg, Reg, and Reg and (4) node of trajectory bundle of reversible distillation Nrev-... 

Trajectories of adiabatic distillation at finite reflux for given product points should be located in concentration space in the region limited by trajectories at infinite reflux and by trajectories of reversible distillation (Petlyuk, 1979 Petlyuk Serafimov, 1983). 

Figure 4.8 shows the regions of components order Reg d and of reversible distillation Reg gv or Reg g for this example. In all points of one trajectory in Fig. 4.7b, liquid-vapor tie-lines are directed from one and the same point of the r< -... 

If product point Xd or xp belongs to the possible product point region Reg or Regg, the condition [Eq. (4.19) or (4.20)] is valid in one or two points along the trajectory of reversible distillation located at (n - 1) component boundary element C i of the concentration simplex (i.e., there is one tear-off point xj v of the trajectory or there are two x )- In the last case, right side of the expression [Eq. (4.19) or (4.20)] should have an extremum. 

If the feed point lies on the a-line, a-surface, or a-hypersurface, then the liquid-vapor tie-Une of feeding is directed to some (n — 2)-component boundary element or from some (n — 2)-component boundary element. It along with that the liquid-vapor tie-Une is directed to the possible product composition region at this boundary element or from this region, then the product of reversible distillation section can contain n — 2 components. For example, if the feed point in Fig. 4.10c lies on the 23-Une within the true bundle of bottom section trajectories then the liquid-vapor tie-Une of feeding is directed to vertex 1 [i.e., the component 1 = Reg can be a product of the section (the product contains n — 2 components)]. 

We previously examined the process of reversible distillation for a given feed point. Below we examine trajectories of reversible distillation sections for given product points located at any -component boundary elements Q of the concentration simplex (xd e C or xg e Q). If / < (n - 1), then in the general case such trajectories should consist of two parts the part located in the same -component boundary element where the product point lies and the part located at some (k+ l)-component boundary element adjacent to it. Along with that, the product point should belong to the possible product composition region Reg or Reg for the examined ( )-component boundary element, and the boundaries of this region can be defined with the help of Eqs. (4.19) and (4.20). 

The diagrams of reversible distillation were constructed for some types of three-component azeotropic mixtures. It is interesting that some types of mixtures with one binary azeotrope and with two distillation regions [types 3 and 5 according to classification (Gurikov, 1958)] permit sharp separation into component and binary zeotropic mixture at some feed compositions. The mixture acetone(l)-benzene(2)-chloroform(3) is an example of such mixture. 

Let s examine the analysis of structure of reversible distillation trajectory bundles at the concrete example of four-component mixture acetone(l)-benzene(2)-chloroform(3)-toluene(4). At the beginning, the segments of the components order Regff at the edges of the concentration tetrahedron are defined by means of scanning and calculation of the values Ki (Fig. 4.13a). The corresponding regions of components order Reg in the tetrahedron are shown in Fig. 4.13b and in its faces - in Fig. 4.14. The whole face 1-2-3, where the component 4 that is absent... 

Can trajectory bundle of reversible distillation go outside the boundaries of distillation region Reg°° ... 

The main methods used in desalination units are reverse osmosis and multi-effect distillation. The energy consumption of a desalination plant using the technology of reverse osmosis depends on its size, the contents of sea water and the desired quality of the produced water and usually ranges between 5-7 kWh/m3 when sea water is used. When well water in coastal regions is used for desalination the energy consumption is less than half of the above. The nominal capacity of small-size desalination units for rural housings is of the order of 400 W. 

Between the lower and upper invariant zones, the mole fraction of both keys in the vapor phase decreases, and the ratio of light key to heavy key decreases. This region of the column serves to remove the light nonkey components from the liquid flowing down and the heavy nonkey component from the material that will flow up and form the distillate. The small amount of reverse fractionation shown for the key components is an interesting phenomenon that is often found in real columns operating at close to the minimum reflux ratio. 

Therefore, Eqs. (4.19) and (4.20) allow determination of the boundaries of the possible product composition region Reg, or Reg at sharp reversible distillation in (n - l)-component boundary elements C i of the concentration simplex. 

It follows from the aforesaid that sharp separation in a reversible distillation column is feasible only if the liquid-vapor tie-line of feeding is directed to the possible product composition region Reg at the boundary element C i of the concentration simplex and from region Reg at other boundary element... 

The location of trajectory bundles and possible product composition segments at reversible distillation of three-component mixtures determines the location of trajectory bundles, and of possible product composition regions of multicomponent mixtures and the locations of trajectory bundles of real adiabatic columns. 

Figure 4.16. Bundles of sharp reversible stripping trajectories in region reversible distillation Regjigy j for the acetone(l)-benzene(2)-chloroform(3)-tolnene(4) mixture (a) node is component 1, (b) node is azeotrope 13, and (c) nodes are component 1 and azeotrope 13.

Figure 4.24. Boundary of semisharp reversible distillation region (shaded) of acetone(l)-benzene(2)-chloro-form(3) mixture e Regjg .

For splits with distributed components, sharp split regions of two sections are different (Fig. 5.10). Reversible distillation regions Regf and RegJ, which are discussed in Chapter 4, are a particular case of sharp split regions (in this case, component h is absent in overhead and component / is absent in bottom). 

Figure 5.19. (L/V)rev as functions X2 on the reversible-distillation trajectories in rectifying section for the split 1,3 2 (for given xo in the tangential-pinch region Regu g) of the acetone(l)-...

Figure 5.20. The trajectories of rectifying section for quasisharp separation of the ideal mixture. (L/Vjs = 1, (L/V)2 > (L/V)2 > (L/V)i, the region between the reversible-distillation trajectory and the distillation trajectory underinflnite reflux is shaded. qS, quasistationary point.

For bottom product points Xb, located in this region, distillation trajectory at some values of the parameter V/L is directed to vertex 1 and at other values, bigger than them, it is directed to vertex 3 (Fig. 5.21b). It is connected with the fact that for these product points reversible distillation trajectory has two branches, one of the branches goes to vertex 1 and another branch goes to vertex 3. The point iV+ small values of the parameter V/L is located at one of the branches, and at bigger values it is located at other branches. 

In contrast to nonsharp separation in the top and bottom sections, the intermediate section has at reversible distillation trajectory not just one node stationary point, but there are saddle point Sm and node point Nm- Separatrixes of the saddle points Sm divide concentration triangle into four regions Reg t trajectory bundles of intermediate section, one of which is the working one Reg jj,t-... 

Determination of possible composition regions Reg Reg of top and bottom products at reversible distillation of all three-component constituents of initial mixture. 

Reversible distillation region of section (Regrev.n Re ev,s Re ev,e) unification of several regions of components order for which one and the same component appears to be (1) the most heavy-volatile for rectifying section, (2) the most light-volatile for stripping section, and (3) middle-volatile between top and en-trainer components for extractive section. 

---