Rule of connectedness

Let s examine the application of the rule of connectedness in a few more cases. At the beginning, the trivial case of impossible separation of the ideal three-component mixture split 2 1,3 (Fig. 3.3) does not meet the rule of connectedness. Really, stable node Nf, of top product region Reg = Q ound,D is vertex 2 and unstable node Ng of the bottom product region Regg s Reg g is vertex 1. Bond 1-2 is directed to the top but not to the bottom product. 

For an n-component mixture, the rule of connectedness in some cases can be used without graphic interpretation of the concentration simplex and without application of structural matrix (Petlyuk et al., 1977 Knight Doherty, 1990). Such elementary cases are the following (1) = Ng, and (2) and Ng are... 

As far as the stable node of boundary element Ai, A2... A (Regu) is stationary point A< (Ai = Np) and unstable node of boundary element A< +i,A< +2 - Am (Regfl) is stationary point Ak+i (Ak+i = and as far as there is bond A Ak+i Ak and Ak+i are adjacent stationary points of one bonds chain), separation into considered subsets of stationary points meets the rule of connectedness (i.e., it is feasible). In exactly the same way, it is possible to show that splits with one distributed pseudocomponent are feasible. It is noteworthy that the boundary elements Ai, A2... A and A +i, A +2... A are curvilinear, and three... 

Split is feasible if points Nf and Ng coincide with each other or if there is bond or bonds chain Nf (the rule of connectedness). This rule is fulfilled if the... 

In which way can the rule of connectedness be checked without structural matrix ... 

Split 1 2,3 is feasible in two-section column at finite reflux, which is unfeasible according to the rule of connectedness (see Chapter 3) in the mode of infinite reflux. The feasibility of such separation was shown first by means of calculation in the work (Kondrat ev et al., 1977). 

Rule of connectedness condition satisfied to product points at R = oo and N = oo. The stable node of the top product boundary element of distillation region at infinite reflux Reg and the unstable node Njj of the bottom product boundary element of distillation region at infinite reflux Reg should coincide (N = iVjj), or should be connected with each other by the bond (N — Nj ) or chain of bonds in direction to the bottom product. 

Rule 2 Each level of hierarchy is defined by the constituting (non-homeo-morphic) types of entities, and by relations between the types. In materials the relations include (but are not limited to) connectedness by primary chemical bonds, hydrogen bridges, dispersion interactions, and interactions between phases such as adhesion forces. 

If it is ascertained by means of such analyses that feed point belongs to several product simplexes, then the mixture at R = 00 and N = 00 can be separated into pseudocomponents at any border between two adjacent key stationary points of each product simplex if the rule connectedness is not broken. The splits with one pseudocomponent being distributed between products is also feasible. 

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