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The problem (one equation and two unknowns) is still solvable, but the solution is not unique. We say that the two unmeasured flows are not observable (they are unobservable). The only solution of this obstacle is to complete the measurement (at least one more stream must be measured to make the system fully observable). In practice we can meet with even more complicated situations - see Fig. 2-7d. Streams 1, 2, 4 and 5 are measured and redundant (one stream can be calculated from the others). Stream 6 is measured, but nonredundant.
Cooperating plants Thus in Fig. 3-5, the input/output streams into/from separate plants G~ and G 2 are incident to environment node no; in addition the plants G~ and G 2 are connected via certain energy stream(s), and some energy stream(s) can connect directly G 2 with n 0. We can obtain connected graph G whose node set consists of Nu~ (units of G1), Nu2 (units of G2), and n 0. The arc set J of G consists of: arcs between the units of G~ , arcs between the units of G 2, and the arcs connecting G~ and G 2 with environment node as drawn.
13. 4) 48 Material and Energy Balancing in the Process Industries The classification is complete. 1), J* (resp. J') determines that of redundant (resp. nonredundant) measured ones. In addition, the incidence matrix of G* determines the conditions the measured variables have to obey in order to have the system solvable. Taking node h~ as reference node, the reduced incidence matrix equals (cf. Fig. 7) where fil (of components rhj, j ~ J+) is the vector of a priori fixed variables. 2). 8) (having deleted reference node a), and A3:/ 1 2 5 9 10 11 11 14 15 -1 h Chapter 3- Mass (Single-component) Balance 49 (having deleted reference node f).