Graph and Matrix Representation of the Enthalpy Balance

The matrix C of elements C j (n e N , 7 e J) is the reduced incidence matrix of graph G, with the environment node as reference node see Chapter 3. Let us now admit the presence of energy distributors. Then the matrix D of 

Let us further partition the set J of arcs (columns of matrix C) into those incident to some splitter node 5 g S, and th remaining arcs. The first subset is, by (4.2.9 and 10), disjoint union of subsets (s g S), say 

If G is not connected then at least one of the connected components does not contain the environment node and represents a subsystem connected with the remaining nodes only via certain arcs (streams) j e J (5.2.2) recall that the whole graph G of material streams is connected. Thus all the input streams are outlet streams from some splitter, and all the output streams from the subsystem have some splitter as the other endpoint. Although such scheme is conceivable, it can be regarded as unlikely. 

In this chapter, the simplifying hypothesis (G connected) is irrelevant but see later Chapter 8. 

Let US now partition the column vector m of mass flowrates introduced in (3.1.6) as corresponds to the partition (5.2.3) 

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