Nonlinear terms linearising

One would notice that there are a number of nonlinear terms in the above constraints, specifically in the contaminant balance constraints. The linearisation technique used to remove these nonlinearities is that proposed by Quesada and Grossman (1995), the general form of this linearization technique can be found in Appendix A. During the application of the model to the illustrative examples,... 

The application of the maximum outlet concentration condition (Savelski and Bagajewicz, 2000) allows for the simplification of constraint (9.5) and subsequent linearisation of two nonlinear terms present in the resulting constraint. This is done as follows. 

With the usual nonlinear terms, which are either of the form of a squared term or the product of two species concentrations, there are two approaches. One of them is to approximate the nonlinear terms by linearised terms. The approximations are different for CN and Laasonen. 

We can also choose not to linearise the nonlinear term by an approximation, in which case we do not run the (minimal) risk of adding errors to the simulation by the linearising approximation. The same example as used above (8.57) and again choosing CN as the method, the dynamic (8.58) is discretised as... 

One of the problems mentioned in Chap. 8 is that of second-order homogeneous chemical reactions, which give rise to nonlinear terms in the transport equations. One such system is the Birk and Perone reaction [10, 11], in which a light flash produces an electroactive substance in solution, which decays with a second-order reaction while it is electrolysed. If CN is used to simulate this, the term in Cj can be linearised to a good, second-order approximation. If one does not choose or is prevented from linearisation, a Newton approach, as described in that chapter, must... 

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