Model developed

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

Models developed with selected subsets of descriptors, instead of all possible descriptors, can be more accurate and robust. In order to select adequate descriptors for each of the four classes of protons, genetic algorithms (GA) were used, and the results were compared with those obtained when all the descriptors were used. 

The reliability of the in silico models will be improved and their scope for predictions will be broader as soon as more reliable experimental data are available. However, there is the paradox of predictivity versus diversity. The greater the chemical diversity in a data set, the more difficult is the establishment of a predictive structure-activity relationship. Otherwise, a model developed based on compounds representing only a small subspace of the chemical space has no predictivity for compounds beyond its boundaries. 

Two mechanisms for chiral separations using chiral mobile-phase additives, analogous to models developed for ion-pair chromatography, have been... 

A database management system (DBMS) is used by most LIMS systems for storing data. Examples of commercially available DBMS are DB2, DBASE, Informix, INGRES, ORACLE, and RDB. AH of these DBMS conform to the "relational" model developed by Codd (19). Eigure 3 demonstrates the use of a relational DBMS for storing LIMS data. Here data is grouped by type so customer and analysis requests are stored separately from sets of sample information which are, in turn, stored separately from sets of analysis results. Individual records are linked or related by unique identification data. 

The model developed, which has been in use for many years both for the training of professionals and speciaUsts and the preliminary education of nonspeciahsts, leads toward a universal language for odor relationships, and is named the spectmm or field of odor. This spatial model has been based on 42 reference odorants, including vanillin, and is becoming the methodological reference for describing odors (see Odormodification). 

The usual practice in these appHcations is to concentrate on model development and computation rather than on statistical aspects. In general, nonlinear regression should be appHed only to problems in which there is a weU-defined, clear association between the independent and dependent variables. The generalization of statistics to the associated confidence intervals for nonlinear coefficients is not well developed. 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

Fan, J.Y., M. Nikolaou, and R.E. White, An Approach to Fault Diagnosis of Chemical Processes via Neural Networks, AJChF Journal, 39(1), 1993, 82-88. (Relational model development, neural networks)... 

Serth, R.W, B. Srikanth, and S.J. Maronga, Gross Error Detection and Stage Efficiency Estimation in a Separation Process, AlChE Journal, 39(10), 1993, 1726-1731. (Physical model development, parameter estimation)... 

Whiting, W.B., TM. Tong, and M.E. Reed, 1993. Effect of Uncertainties in Thermodynamic Data and Model Parameters on Calculated Process Performance, Industiial and Engineeiing Chemistiy Reseaieh, 32, 1993, 1367-1371. (Relational model development)... 

Limited Data First, plant data are limited. Unfortunately, those easiest to obtain are not necessarily the most useful. In many cases, the measurements that are absolutely required for accurate model development are unavailable. For those that are available, the sensitivity of the parameter estimate, model evaluation, and/or subsequent conclusion to a particiilar measurement may be very low. Design or control engineers seldom look at model development as the primaiy reason for placing sensors. Further, because equipment is frequently not operated in the intended region, the sensitive locations in space and time have shifted. Finally, because the cost-effectiveness of measurements can be difficult to justify, many plants are underinstru-mented. 

Because the technical barriers previously outhned increase uncertainty in the data, plant-performance analysts must approach the data analysis with an unprejudiced eye. Significant technical judgment is required to evaluate each measurement and its uncertainty with respec t to the intended purpose, the model development, and the conclusions. If there is any bias on the analysts part, it is likely that this bias will be built into the subsequent model and parameter estimates. Since engineers rely upon the model to extrapolate from current operation, the bias can be amplified and lead to decisions that are inaccurate, unwarranted, and potentially dangerous. 

Analysts The above is a formidable barrier. Analysts must use limited and uncertain measurements to operate and control the plant and understand the internal process. Multiple interpretations can result from analyzing hmited, sparse, suboptimal data. Both intuitive and complex algorithmic analysis methods add bias. Expert and artificial iutefligence systems may ultimately be developed to recognize and handle all of these hmitations during the model development. However, the current state-of-the-art requires the intervention of skilled analysts to draw accurate conclusions about plant operation. 

Analysts must recognize that the end use as well as the uncertainty determines the value of measurements. While the operators may pay the most attention to one set of measurements in making their decisions, another set may be the proper focus for model development and parameter estimation. The predilec tion is to focus on those measurements that the operators Believe in or that the designers/con-trollers originally believed in. While these may not be misleading, they are usually not optimal, and analysts must consciously expand their vision to include others. 

Second, any analysis must recognize the nonlinearities of eqmp-ment capability. Model development must recognize that equipment fundamentals will affec4 conclusions and extrapolations. These... 

Third, any analysis must recognize that the measurements have significant uncertainty, random and systematic. These affect any conclusions drawn and models developed. Multiple interpretations of the same set of measurements, describing them equally well, can lead to markedly different conclusions and, more significantly, extrapolations. 

This matrix will contain information regarding loading characteristics such as flooding hmits, exchanger areas, pump curves, reactor volumes, and the like. While this matrix may be adjusted during the course of model development, it is a boundary on any possible interpretation of the measurements. For example, distillation-column performance markedly deteriorates as flood is approached. Flooding represents a boundary. These boundaries and nonlinearities in equipment performance must be accounted for. 

Model Development PreHminary modeling of the unit should be done during the familiarization stage. Interactions between database uncertainties and parameter estimates and between measurement errors and parameter estimates coiJd lead to erroneous parameter estimates. Attempting to develop parameter estimates when the model is systematically in error will lead to systematic error in the parameter estimates. Systematic errors in models arise from not properly accounting for the fundamentals and for the equipment boundaries. Consequently, the resultant model does not properly represent the unit and is unusable for design, control, and optimization. Cropley (1987) describes the erroneous parameter estimates obtained from a reactor study when the fundamental mechanism was not properly described within the model. 

Verneuil et al. (Verneuil, V.S., P. Yan, and F. Madron, Banish Bad Plant Data, Chemical Engineering Progress, October 1992, 45-51) emphasize the importance of proper model development. Systematic errors result not only from the measurements but also from the model used to analyze the measurements. Advanced methods of measurement processing will not substitute for accurate measurements. If highly nonlinear models (e.g., Cropley s kinetic model or typical distillation models) are used to analyze unit measurements and estimate parameters, the Hkelihood for arriving at erroneous models increases. Consequently, resultant models should be treated as approximations. 

Overview Reconciliation adjusts the measurements to close constraints subject to their uncertainty. The numerical methods for reconciliation are based on the restriction that the measurements are only subject to random errors. Since all measurements have some unknown bias, this restriction is violated. The resultant adjusted measurements propagate these biases. Since troubleshooting, model development, ana parameter estimation will ultimately be based on these adjusted measurements, the biases will be incorporated into the conclusions, models, and parameter estimates. This potentially leads to errors in operation, control, and design. 

However, given that reconciliation will not always adjust measurements, even when they contain large random and gross error, the adjustments will not necessarily indicate that gross error is present. Further, the constraints may also be incorrect due to simphfications, leaks, and so on. Therefore, for specific model development, scrutiny of the individual measurement adjustments coupled with reconciliation and model building should be used to isolate gross errors. 

Because of these limitations, different models may appear to describe the unit operation equally well. Analysts must discriminate among various models with the associated parameter estimates that best meet the end-use criteria for the model development. There are three principal criteria forjudging the suitability of one model over another. In addition, there are ancillary criteria like computing time and ease of use that may also contribute to the decision but are not of general concern. 

Aside from the fundamentals, the principal compromise to the accuracy of extrapolations and interpolations is the interaction of the model parameters with the database parameters (e.g., tray efficiency and phase eqiiilibria). Compromises in the model development due to the uncertainties in the data base will manifest themselves when the model is used to describe other operating conditions. A model with these interactions may describe the operating conditions upon which it is based but be of little value at operating conditions or equipment constraints different from the foundation. Therefore, it is good practice to test any model predictions against measurements at other operating conditions. 

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

Gill, W.N., Garside, J. and Berty, J. M., Editors, 1989, Special Issue on Kinetic Model Development, Chem. Eng, Comm. 76. 

The best fit, as measured by statistics, was achieved by one participant in the International Workshop on Kinetic Model Development (1989), who completely ignored all kinetic formalities and fitted the data by a third order spline function. While the data fit well, his model didn t predict temperature runaway at all. Many other formal models made qualitatively correct runaway predictions, some even very close when compared to the simulation using the true kinetics. 

After the preliminary tests are made on a promising catalyst and some insight gained on the process, it is time to do a kinetic study and model development. The method of a kinetic study can be best explained on an actual industrial problem. Because more can be learned from a failure than from a success, the oxidation of propylene to acrolein is an instructive attempt at process development. (Besides, to get permission to publish a success is more difficult than to solve the problem itself) Some details of the development work follow in narrative form to make the story short and to avoid embarrassing anyone. 

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