Significant model parameters

From this it can be concluded that it is only the temperature variation, Xj, which has a significant (95 % level) influence on the yield in the elimination experiment. 

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The purpose is to develop estimates of significant model parameters that provide the best estimate of unit operation. The unit operation is embodied in the measurements. 

Figure 8.22 shows the effect of adsorption. Based upon these simulations, the adsorption of sulfonates on fired Berea appears to be a highly significant model parameter. 

Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Statistical testing of model adequacy and significance of parameter estimates is a very important part of kinetic modelling. Only those models with a positive evaluation in statistical analysis should be applied in reactor scale-up. The statistical analysis presented below is restricted to linear regression and normal or Gaussian distribution of experimental errors. If the experimental error has a zero mean, constant variance and is independently distributed, its variance can be evaluated by dividing SSres by the number of degrees of freedom, i.e. 

Two comments can be made on the second point. For a simple mathematical reason mistakes made with the LEL value are of little consequence to the calculated value of flashpoint cc . Indeed, this mistake is not that significant since there Is a logarithm involved. Secondly, in theory no mistake is made with the stoichiometric concentration (except for nitrogenous compounds where there is an ambiguous aspect with regard to the nitrogen reaction). This second approach (with Cg) can thus provide preliminary control of the model parameters (S or the group) and there... 

For non-Newtonian fluids, any model parameter with the dimensions or physical significance of viscosity (e.g., the power law consistency, m, or the Carreau parameters r,]co and j/0) will depend on temperature in a manner similar to the viscosity of a Newtonian fluid [e.g., Eq. (3-34)]. 

As seen previously for some specific applications such as wastewater treatment plants, software sensors can be envisaged to provide on-line estimation of non-measurable variables, model parameters or to overcome measurement delays [81-83]. Software sensors have been developed mainly for monitoring bioprocesses because the control system design of bioreactors is not straightforward due to [84] significant model uncertainty, lack of reliable on-line sensors, the non-linear and time-varying nature of the system or slow response of the process. 

Body, J.E. Persson, P. Sjdberg, S. (2000) Benzene carboxylate surface complexation at the goethite (a-EeOOH)/water interface. III. The influence of particle surface area and the significance of modelling parameters. J. Cod. 

The ANOVA table shown in Table 2.14 indicates that there was no significant lack-of-fit of the model. Parameter estimates and t-statistics for this model are shown in Table 2.15. 

From the appearance of the dispersion number DjuL in this dimensionless form of the basic differential equation of the plug-flow dispersion model it can be inferred that the dispersion number must be a significant characteristic parameter in any solution to the equation, as we have seen. 

A detailed transport model for resist dissolution has been developed (169). In conjunction with standard ellipsometric equations describing multilayer films, the model provides quantitative agreement with the observed traces from the in situ ellipsometer. Model parameters are thus extracted, and their significance in terms of molecular structures of the system can be established. This model can then be extended for predictive purposes in the design and selection of resist materials. 

The question then arises as to how to explain this sharp decrease in the parameters. Boudart et al. [127,128] ascribe it to the significant decrease in the surface coverage by oxygen, but the surface coverage must depend on the parameters of the elementary processes taking place in the system the primary reason must be simply the value of the parameter. Apparently, the sharp drop in the model parameters must be attributed to the decreased number of active surface sites of the catalyst due to the formation of inactive oxides or PtC complexes [119,122]. The model must account for the catalyst deactivation [122, 125]. 

The selection of the appropriate population pharmacokinetic base model was guided by the following criteria a significant reduction in the objective function value (p < 0.01,6.64 points) as assessed by the Likelihood Ratio Test the Akaike Information Criterion (AIC) a decrease in the residual error a decrease in the standard error of the model parameters randomness of the distribution of individual weighted residuals versus the predicted concentration and versus time post start of cetuximab administration randomness of the distribution of the observed concentration versus individual predicted concentration values around the line of identity in a respective plot. 

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