Comparison with Kinetic Models

Fig. 13. Copolymerization DADMAC/acrylamide in aqueous solution. Comparison of experimental results with kinetic models (Data taken from [38])...

Nonequilibrium thermodynamics was chosen as a main object for comparison, though an essential part of conclusions drawn below is useful in MEIS comparison with the models of chemical kinetics, synergetics, theory of dynamic systems and other models, model engineering and theories of motions. Comparison is made from two standpoints (1) a scope of areas of effective applications and (2) simplicity and fruitfulness of computing experiments. 

Simplification of the solution or complete exclusion of the problem of dividing the variables into fast and slow is a great computational advantage of MEIS in comparison with the models of kinetics and nonequilibrium thermodynamics. The problem is eliminated, if there are no constraints in the equilibrium models on macroscopic kinetics. Indeed, the searches for the states corresponding to final equilibrium of only fast variables and states including final equilibrium coordinates of both types of variables with the help of these models do not differ from one another algorithmically. With kinetic constraints the division problem is solved by one of the three methods presented in Section 3.4, which are applied in the majority of cases to slow variables limiting the results of the main studied process. 

R. W. J. Westerhout et al. Kinetics of the low-temperature pyrolysis of polyethene, polypropene, and polystyrene modeling, experimental determination, and comparison with literature models and data. Industrial and Engineering Chemistry Research, 36, 1955-1964 (1997). 

Fig. 6. Comparison of kinetic model predictions with experimental measurements of C-in-dene metabolites for Rhodococcus KYI cells obtained from a chemostat at steady state obtained with a dilution rate of 0.065 h and 100 ppm indene air feed concentration. Reaction rate constants used in the kinetic model were determined from flux estimates as described in the text...

Model building is considered here as an adaptive process (cf. Fig. 2.18) It involves stepwise fitting of the parameters, fe, and discrimination of the function, /, itself. All of the models in this chapter should be considered as working hypotheses. The nature of formal kinetic descriptions means that other mathematical functions can always be found that serve the same descriptive function to within the precision of the measurements (see Esener et al, 1983). The lack of basic content in formal kinetic models in comparison with structured models (Harder and Roels, 1981 Roels and Kossen, 1978) can to some extent be compensated for by subsequent analysis (Esener et al., 1983 A. Moser, 1978b, 1984a). 

To facilitate the use of methanol synthesis in examples, the UCKRON and VEKRON test problems (Berty et al 1989, Arva and Szeifert 1989) will be applied. In the development of the test problem, methanol synthesis served as an example. The physical properties, thermodynamic conditions, technology and average rate of reaction were taken from the literature of methanol synthesis. For the kinetics, however, an artificial mechanism was created that had a known and rigorous mathematical solution. It was fundamentally important to create a fixed basis of comparison with various approximate mathematical models for kinetics. These were derived by simulated experiments from the test problems with added random error. See Appendix A and B, Berty et al, 1989. 

This section is divided into three parts. The first is a comparison between the experimental data reported by Wisseroth (].)for semibatch polymerization and the calculations of the kinetic model GASPP. The comparisons are largely graphical, with data shown as point symbols and model calculations as solid curves. The second part is a comparison between some semibatch reactor results and the calculations of the continuous model C0NGAS. Finally, the third part discusses the effects of certain important process variables on catalyst yields and production rates, based on the models. 

We computed the percentage errors between the reaction rate computations based on the experiments with those based on the kinetic model. Note that, like the pressure and temperature comparisons, the accuracy of the calculations for reaction rates decreases as we compare Test 1 with Test 2 and Test 3- In Test 1 the error ranges from 3 to 21, in Test 2 it was 10 to 21, in Test 3 it ranged from 5 to 36. ... 

Most published studies relate only to isothermal experiments. Hence, in order to make such comparisons we modified our computations to assume isothermal conditions. Figure 11 compares our kinetic model with data by Hui and Hamielec for styrene thermal polymerization at 1A0°C. Figure 12 compares out kinetic model with data by Balke and Hamielec (7) for MMA at 90 C using 0.3 AIBN. Figure 13 compares our kinetic model with data by Lee and Turner ( ) for MMA at 70°C using 2% BPO. Our model compares quite favorably with these published experiments. The percent error was less than S% in most of the ranges of conversions. 

In this paper, we first briefly describe both the single-channel 1-D model and the more comprehensive 3-D model, with particular emphasis on the comparison of the features included and their capabilities/limitations. We then discuss some examples of model applications to illustrate how the monolith models can be used to provide guidance in emission control system design and implementation. This will be followed by brief discussion of future research needs and directions in catalytic converter modeling, including the development of elementary reaction step-based kinetic models. 

Figure S.11. Comparison between the predictions of a micro-kinetic model and measurements on a Cu(lOO) model catalyst with a real methanol synthesis catalyst. The full line represents the ideal match between model and experiment. [Adapted from P.B. Rasmussen, P.M. Holmblad, T. Askgaard,...

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

A simple algorithm [17] makes it possible to find the probability of any fragment of macromolecules of Gordonian polymers. Comparison of these probabilities with the data obtained by NMR spectroscopy provides the possibility to evaluate the adequacy of a chosen kinetic model of a synthesis process of a particular polymer specimen. The above-mentioned probabilities are also involved in the expressions for the glass transition temperature and some structure-additive properties of branched polymers [18,19]. 

Fig. 17. Comparison of the variation of the time-average S02 conversion and the maximum bed temperature predicted for stationary cycling condition by an unsteady-state and a steady-state kinetic model for a packed-bed S02 converter operating with periodic flow reversal...

The absorption bands measured by the flash spectrographic method are often assigned by (a) comparison with known singlet-singlet absorption spectra, (b) comparison of the lifetime of the species responsible for the absorption with the phosphorescence lifetime, (c) comparison with calculated energies and intensities of the various possible absorptions by semi-empirical molecular orbital methods, and (d) comparison with published triplet absorption spectra and decay kinetics of model compounds. 

Bokkers, G. A., Van Sint Annaland, M., and Kuipers, J. A. M., Comparison of continuum models using kinetic theory of granular flow with discrete particle models and experiments extent of particle mixing induced by bubbles. Proceedings of Fluidization XI, May 9-14, 2004, 187-194, Naples, Italy (2004). 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

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