Distillation subregions

The totality of all bonds characterizes the mixture s structure. The bond serves as the elementary nonlocal characteristic of the residue curve bundle structure. Bonds form bond chains. The bond chains of maximum length connect the unstable node A and the stable node A+ of the distillation region Reg". Let s call a polyhedron formed by aU stationary points of one maximum-length bond chain and containing aU components of the mixture a distillation subregion Reg. ... 

A bond, bond chain, distillation subregion, andregion are the nonlocal structural elements of the azeotropic mixture concentration space. 

Bonds between the stationary points (points of the components and azeotropes) and distillation subregions Reg j are the structural elements of the distillation regions. Residue curve bundle structure of multicomponent mixtures can be described with the help of a structural matrix that reflects the bonds available between the stationary points. 

However, the above-described method is unfit for splits other than the direct and indirect ones, and the number of such splits grows dramatically with the increase of n. The general methods of splits set determination are based on the usage of structural matrix and of method of product simplex for distillation subregions (Petlyuk, Kievskii, Serafimov, 1979). 

Let s show that if product points belong to the first and second types boundary elements of distillation subregion RegsH (xD e Regs B andxs RegsM ), then these product points meet the conditions of connectedness (e.g., all these splits are feasible at R = oo and N=oo, product points should lie on these boundary elements). 

Let distillation subregion correspond to the following dtain of bonds Ai... 

Let s examine the case when m = n. In this case the distillation subregion is a simplex (Reg" = Regs/mp). the amount of vertexes of which is equal to the amount of components. From the practical point of view, it is frequently convenient... 

Such simplex is analogous to an ideal mixture, components of which correspond to the stationary points of the simplex (in both cases, we have only one bonds chain). That is why at sharp separation, when product points lie in boundary elements of distillation subregion, the set of stationary points (pseudocomponents) is divided into two subsets of stationary points of the top and bottom products, just as at separation of ideal mixture, a set of components is divided into two subsets. 

At sharp separation of azeotropic mixture, the key stationary points key pseudocomponents), that is, stationary points that are adjacent in the bonds chain, play the key components. At separation without distributed pseudocomponents, the set of stationary points Ai, A2... Am is divided into two subsets Ai, A2... A and Ak+i, Ak+i-- Am- These subsets are the boundary elements of distillation subregion Reg , which the top and bottom product points belong to (Rego and Regfl). Dimensionality of these boundary elements is A - 1 and m - (k + 1), correspondingly. The summary dimensionality of these boundary elements is equal to OT -I- 2. 

Thus, if the feed point lies inside some distillation subregion (xp e Regsut) to... 

Product simplex for three-component mixtures is a triangle for four-component mixtures, it is a tetrahedron for five-component mixtures, it is a pentahedron etc. Inside one distillation subregion at m > n, product simplexes cross each other (i.e., one and the same feed point can simultaneously enter several product simplexes). 

Figure 3.16. Regions Reg°° and subregions Regsa of distillation and product simplexes B.egsimp of some structures of three-component mixtures. 1,3.4a,..., classification according to Gurikov (1958). Dotty lines with arrows, boundaries of distillation regions thin lines, boundaries of distillation subregions dotted lines, boundaries of product simplexes.

What is the difference between distillation subregion Reg5 6 and distillation region... 

What is the difference between product simplex Reg p and distillation subregion... 

How many types of boundary elements can a distillation subregion Regs 6 have ... 

Can two boundary elements of distillation subregion to which product points at R = 00 and N = oo belong have common stationary points If the answer is yes, then how many common stationary points ... 

For a mixture of acetone(l)-methanol(2)-chloroform(3)-ethanol(4), determine the location of the boundary between distillation regions. List all the distillation subregions and product simplexes for this mixture. For each product simplex, state all feasible sphts without distributed components or pseudocomponents. 

Product simplex (Reg /mp) simplex whose vertexes are stationary points of distillation subregion and their number is equal to the total number of components. 

---