The whole system of balance equations

We have admitted the absence of certain components (chemical species) C,5 in certain material streams (arcs) j of the graph G. For any k (= 1, —, K), E,( is the subset of streams where component Q can be present. The arbitrariness in the choice of the has been limited by the stractural conditions (8.2.18), (8.2.22), and (8.2.29) see Section 8.2, first paragraph of Subsection 8.2.5. We have also limited the admissible flowrates to positive ones. [Observe that a system of balance equations that would not admit of such solutions would be technologically absurd.] 

We have further assumed, as motivated by the consideration following after (5.2.4), that the subgraph G [N-S, ] of G, obtained by deleting the 

We have considered an a priori given state of aggregation and pressure P in each of the streams J e J. Then the system of balance equations (8.2.2) with (8.2.1), and (8.3.1) has 

See the last paragraph of Section 5.2. Formally, a heat exchanger is a 

The partition of a heat exchanger (as technological unit) into two nodes (8.3.32) has been motivated by separate (generally multicomponent) mass balances of the cold and hot sides. On the other hand, it can happen that we are not interested in the (unknown) heat transfer rates. Then the latter can be eliminated by merging the nodes (8.3.32). Let us first partition the set E of net energy streams 

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The multicomponent chemical species and energy balances are mostly non-linear in the primary variables (mass flowrates, mass fractions, temperatures, possibly also pressures of the streams). The solvability analysis of non-linear systems in Chapter 8 begins with examples showing that even in simple cases, the terminology introduced for linear systems (in particular observability and redundancy) becomes somewhat vague certain problems can be not well-posed . We then first analyse the solvability of the whole system of balance equations without a priori fixed variables (Sections 8.2 and 8.3) and show that under certain plausible stractural hypotheses, the system is solvable. 

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