Validation of the model

Modeling of Processes and Reactors for Upgrading of Heavy Petroleum 

FIGURE 4.3 Iterative procedure for the solution of equations of the gasification model. 

Proximal and Elemental Analyses of the 4.3°API Vacuum Residue Used for Validating the Gasification Model 

FIGURE 4.4 Comparison of predicted ( ) and experimental ( ) composition of the synthesis gas (dry basis). 

These results clearly demonstrate that the equilibrium model is suitable for estimating the composition of synthesis gas and other process parameters for the gasification of vacuum petroleum residue. 

NIR models are validated in order to ensure quality in the analytical results obtained in applying the method developed to samples independent of those used in the calibration process. Although constructing the model involves the use of validation techniques that allow some basic characteristics of the model to be established, a set of samples not employed in the calibration process is required for prediction in order to confirm the goodness of the model. Such samples can be selected from the initial set, and should possess the same properties as those in the calibration set. The quality of the results is assessed in terms of parameters such as the relative standard error of prediction (RSEP) or the root mean square error of prediction (RMSEP). 

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However, more experiments using a wider range of stress ratios will be required to achieve a more complete data set, in order to verify the validity of the model under a wide range of stress conditions. 

A linear regression analysis should not be accepted without evaluating the validity of the model on which the calculations were based. Perhaps the simplest way to evaluate a regression analysis is to calculate and plot the residual error for each value of x. The residual error for a single calibration standard, r , is given as... 

Despite their popularity, these methods normally have an inherent limitation—the fluid dynamics information they generate is usually described in global parametric form. Such information conceals local turbulence and mixing behavior that can significantly affect vessel performance. And because the parameters of these models are necessarily obtained and fine-tuned from a given set of experimental data, the validity of the models tends to extend over only the range studied in that experimental program. 

The validity of the model was demonstrated by reacting 35 under the same reaction conditions as expected, only one diastereoisomer 41 was formed, the structure of which was confirmed by X-ray analysis. When the vinylation was carried out on the isothiazolinone 42 followed by oxidation to 40, the dimeric compound 43 was obtained, showing that the endo-anti transition state is the preferred one. To confirm the result, the vinyl derivative 42 was oxidized and the intermediate 40 trapped in situ with N-phenylmaleimide. The reaction appeared to be completely diastereoselective and a single diastereomer endo-anti 44 was obtained. In addition, calculations modelling the reactivity of the dienes indicated that the stereochemistry of the cycloaddition may be altered by variation of the reaction solvent. 

Constructing the model is an area where innovative effort is needed to maximize the validity of the model. The model will vary from industry to industry, but a simple one can start with a relationship between the number of employee hours and the output produced in each discrete activity area on the site, e.g. 

It is important to test models, and in the above case, figures were obtained for other plants and the validity of the model confirmed. 

Recorded kinetic curves were fitted to the five-parameter Equation (1). The parameters pj with their errors and the standard deviation of regressions are summarized in Tables 1-6. Comparison of the data confirm the previously reported (refs. 8,12) similarity in the behavior of the two isomers in the presence of strong bases in spite of the different shape of the kinetic curves. The relatively good agreement of exponents p2, P4 computed for the diastereomers at the same temperature and amine concentration demonstrates the validity of the model used. From comparison of Equations (4) and (7) it follows that both reaction must give the same exponent. 

Calculating the exact response of a semiconductor heterostructure to an ultrafast laser pulse poses a daunting challenge. Fortunately, several approximate methods have been developed that encompass most of the dominant physical effects. In this work a model Hamiltonian approach is adopted to make contact with previous advances in quantum control theory. This method can be systematically improved to obtain agreement with existing experimental results. One of the main goals of this research is to evaluate the validity of the model, and to discover the conditions under which it can be reliably applied. 

For an initial validation of the model presented in Section 13.3, a number of low-molecular-weight MA-grafted BR mbbers with MA graft levels ranging from 5 to 25 wt%, that are commercially available from Sartomer/Cray Valley, were selected. The values of 8 were calculated and converted... 

The key feature of successful models is that they produce results consistent with the experimental observations. Successful models capture the essential features of the systems of interest, and they customarily go beyond this simple reproduction to predict new features of the systems that may have previously escaped notice. In this latter case, the predictions provide an important means for testing the validity of the models. 

The validity of the model is tested against the experiment. A ISOOcc canister, which is produced by UNICK Ltd. in Korea, is used for model validation experiment. In the case of adsorption, 2.4//min butane and 2.4//min N2 as a carrier gas simultaneously enter the canister and 2.1//min air flows into canister with a reverse direction during desorption. These are the same conditions as the products feasibility test of UNICK Ltd. The comparison between the simulation and experiment showed the validity of our model as in Fig. 5. The amount of fuel gas in the canister can be predicted with reasonable accuracy. Thus, the developed model is shown to be effective to simulate the behavior of adsorption/desorption of actual ORVR system. 

In recent years some theoretical results have seemed to defeat the basic principle of induction that no mathematical proofs on the validity of the model can be derived. More specifically, the universal approximation property has been proved for different sets of basis functions (Homik et al, 1989, for sigmoids Hartman et al, 1990, for Gaussians) in order to justify the bias of NN developers to these types of basis functions. This property basically establishes that, for every function, there exists a NN model that exhibits arbitrarily small generalization error. This property, however, should not be erroneously interpreted as a guarantee for small generalization error. Even though there might exist a NN that could... 

Before we can apply an adaptive filter, we should define a criterion to judge the validity of the model to describe the measurements. Such a criterion can be based on the innovation defined in Section 41.2. The concept of innovation, /, has been introduced as a measure of how well the filter predicts new observations ... 

The significance of this dimensionless equation form is now that only the parameter (k x) is important and this alone determines the system dynamics and the resultant steady state. Thus, experiments to prove the validity of the model need only consider different values of the combined parameter (k x). 

The expression of chemical fate can be computerized using a code to perform the computations and predict the results when inputs simulating conditions of interest are provided. Two critical aspects of the use of computer codes for predicting geochemical fate are the verification and validation of the models on which the codes are based. 

Table 11.8. Additional reaction conditions collected for validation of the model performance...

Validation of the model. The O Flaherty Model was initially calibrated to predict blood, bone, and tissue lead concentrations in rats (O Flaherty 1991a), and subsequently modified to reflect anatomical and physiological characteristics in children (O Flaherty 1995a), adults (O Flaherty 1993) and Cynomolgus... 

Validation of the model. Output from the Leggett Model has been compared with data in children and adult subjects exposed to lead in order to calibrate model parameters. The model appears to predict blood lead concentrations in adults exposed to relatively low levels of lead however, no information could be found describing efforts to compare predicted blood lead concentrations with observations in children. 

Validation of the model. The Perbellini model was validated using a data set for venous blood /7-hexane values in volunteers exposed for 4 hours (Veulemans et al. 1982). The range in the study was 334-368 g/L during exposure to 204 ppm the model predicted a value within this range. After 4 hours exposure to 102 ppm, the predicted value for venous blood -hexane concentration was about 10% below that actually observed in humans. The authors also compared their own data from previous studies on the correlation between venous blood -hexane concentrations and workplace concentrations. From the correlation curve, exposure at 102 ppm would predict a venous blood concentration of 176 g/L the model predicted 182 g/L. The urinary excretion rate of 2,5-hexanedione predicted by the model was also compared to a data set from 13 workers followed for 24 hours from the beginning of a workday. 

Validation Of the model. Data sets for levels of -hexane in breast milk after quantified exposures to -hexane are not available so the model was not validated. 

Quality, in terms of the validity of the acceleration, becomes interwoven with the validity of the model. Generally, it is not unreasonable to argue that if the data shows a good fit to the model it is valid. However, this provides absolutely no evidence that the model itself is valid, nor that the data is valid or even relevant when applied to the intended service conditions. 

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