Remarks on Solvability

The complete set of balance equations comprises the component (chemical species) balances and the energy balance. In an analogous manner as in Section 3.3, having measured or otherwise fixed certain variables values, the variables can be classified into measured and unmeasured the latter are to be computed as unknowns in a system of equations. A finer classification as in Section 3.3 is, however, less obvious. 

Relatively simple is the system of equations (5.4.6). Under plausible assumptions, it can be shown that it has certain properties of regularity see later in Chapter 8. Having measured the values of certain variables thus having restricted the number of unknowns this regularity can get lost. Let us give a simple example. 

Generally, in a nonlinear system the solvability with respect to the unmeasured variables depends on the measured values and, as is frequently the case, the system is not solvable unless the measured values are adjusted by (nonlinear) reconciliation. In the above example however, a detailed analysis would show that the (iterative) reconciliation procedure would not converge for reasons of principle. Instead of speaking of observability/unobservability, one would rather say that the problem is not well-posed. See chapter 8 for more detailed discussion. 

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