Parameter Estimation and Statistical Testing of Models and Parameters in Multiple Reactions [Pg.119]

Techniques for parameter estimation vary considerably. If consistent values for model parameters cannot be obtained, the investigators may decide that the model is itself unreliable and should be changed. Thus, model choice and parameter estimation are interactive. A number of workers have discussed generalised procedures [16—18]. Yeh [19] developed numerical algorithms and showed that multiple linear regression could be used successfully if the reaction scheme consisted of steps such as those shown in eqn. (41) or [Pg.125]

In this chapter, you have derived the equations governing chemical reaction equilibrium and seen how the key parameters can be estimated using thermodynamics. You have solved the resulting problems using Excel, MATLAB, and Aspen Plus. You also learned to solve multiple equations using MATLAB when there are several reactions in equilibrium. [Pg.52]

Many biochemists use the velocity equations for kinetic parameter estimates despite the fact that the rates are difficult to determine experimentally. In practice either the substrate depletion or the product formation is measured as a function of time and the rates are calculated by differentiating the data, leading to an inexact analysis (Schnell Mendoza, 1997,2000a). Alternatively, the differential equations governing the biochemical reactions may be solved or approximated to obtain reactant concentration as function of time. This approach decreases the number of experimental assays by at least a factor of live, as proved by Schnell and Mendoza (2001), because multiple experimental points may be collected for each single reaction. [Pg.15]

The above analysis is, of course, based on the assumption of simple order reactions under Tafel operation and on the availability of sufficiently accurate data ( 5-10%). With complex reaction kinetics, for example, those involving surface adsorption terms (Eq. 16), a nonlinear regression analysis would yield the best estimate of a, Uj, and for a possible kinetic model. In all cases, use of these parameters for predicting the performance of an electrochemical reactor or the selectivity of a reaction scheme should be restricted within the potential, concentration, and temperature range that they were determined. We should stress here that kinetic information is presently scanty for complex, multiple electrochemical reactions, yet it is essential for the design, optimization, and control of electrochemical processes. [Pg.286]

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