Notes on Methodology for Parameter Estimation

for given V, T, and P, if q0 is varied to obtain several values of fA at the outlet, the expression - [ fA + 2 ln( 1 — /A)] is a linear function of V/q, with slope kA, from which the latter can be obtained. (The integration above can be done by the substitution x = 1 fA-) 

Taking Tinto account implies the ability to operate the reactor at a particular T, and hence to measure and control T. A thermostat is a device in which T is controlled within specified and measurable limits an example is a constant-T water bath. 

In the case of a PFR, it is usually easier to vary Tin a controllable and measurable way if it is operated as a differential reactor rather than as an integral reactor. In the latter case, it may be difficult to eliminate an axial gradient in Tover the entire length of the reactor. 

In Section 3.4, traditional methods of obtaining values of rate parameters from experimental data are described. These mostly involve identification of linear forms of the rate expressions (combinations of material balances and rate laws). Such methods are often useful for relatively easy identification of reaction order and Arrhenius parameters, but may not provide the best parameter estimates. In this section, we note methods that do not require linearization. 

Generally, the primary objective of parameter estimation is to generate estimates of rate parameters that accurately predict the experimental data. Therefore, once estimates of the parameters are obtained, it is essential that these parameters be used to predict (recalculate) the experimental data. Comparison of the predicted and experimental data (whether in graphical or tabular form) allows the goodness of fit to be assessed. Furthermore, it is a general premise that differences between predicted and experimental concentrations be randomly distributed. If the differences do not appear to be random, it suggests that the assumed rate law is incorrect, or that some other feature of the system has been overlooked. 

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