Kinetic models, development

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. 

Kelkar and McCarthy (1995) proposed another method to use the feedforward experiments to develop a kinetic model in a CSTR. An initial experimental design is augmented in a stepwise manner with additional experiments until a satisfactory model is developed. For augmenting data, experiments are selected in a way to increase the determinant of the correlation matrix. The method is demonstrated on kinetic model development for the aldol condensation of acetone over a mixed oxide catalyst. 

C ON KINETIC MODEL DEVELOPMENT, AICHE, DENVER, 1983 C PROGRAMMER - ASHOK SAND C... 

Kinetic Model Development Our kinetic model for the degradation of polypropylene Q.) is based upon the following reaction mechanism ... 

Results are shown in Figures 10 and 11. HPLC is well known as a reproducible and accurate technique for composition measurement From the point of view of kinetic model development however, the following points deserve emphasis. 

Kinetic models developed for reactor scale-up are also suitable for reactor optimization. The development of detailed kinetic models accounting for all factors influencing process rates is a time-consuming task. Therefore, more empirical simplified models are often used for simulation and optimization of existing reactors. 

Hydrogenation of lactose to lactitol on sponge itickel and mtheitium catalysts was studied experimentally in a laboratory-scale slurry reactor to reveal the true reaction paths. Parameter estimation was carried out with rival and the final results suggest that sorbitol and galactitol are primarily formed from lactitol. The conversion of the reactant (lactose), as well as the yields of the main (lactitol) and by-products were described very well by the kinetic model developed. The model includes the effects of concentrations, hydrogen pressure and temperature on reaction rates and product distribution. The model can be used for optinuzation of the process conditions to obtain highest possible yields of lactitol and suppressing the amounts of by-products. 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

However, the detailed description of the FT product distribution together with the reactant conversion is a very important task for the industrial practice, being an essential prerequisite for the industrialization of the process. In this work, a detailed kinetic model developed for the FTS over a cobalt-based catalyst is presented that represents an evolution of the model published previously by some of us.10 Such a model has been obtained on the basis of experimental data collected in a fixed bed microreactor under conditions relevant to industrial operations (temperature, 210-235°C pressure, 8-25 bar H2/CO feed molar ratio, 1.8-2.7 gas hourly space velocity, (GHSV) 2,000-7,000 cm3 (STP)/h/gcatalyst), and it is able to predict at the same time both the CO and H2 conversions and the hydrocarbon distribution up to a carbon number of 49. The model does not presently include the formation of alcohols and C02, whose selectivity is very low in the FTS on cobalt-based catalysts. 

This limited amount of kinetic evidence suggests that the kinetic models developed for reactivity in aqueous micelles are directly applicable to reactions in vesicles, and that the rate enchancements have similar origins. There is uncertainty as to the appropriate volume element of reaction, especially if the vesicular wall is sufficiently permeable for reaction to occur on both the inner and outer surfaces, because these surfaces will have different radii of curvature and one will be concave and the other convex. Thus binding, exchange and rate constants may be different at the two surfaces. 

A unified gas hydrate kinetic model (developed at ARC) coupled with a thermal reservoir simulator (CMG STARS) was applied to simulate the dynamics of CH4 production and C02 sequestration processes in the Mallik geological zones. The kinetic model contains two mass transfer equations one equation transfers gas and water into hydrate, and a decomposition equation transfers hydrate into gas and water (Uddin etal. 2008a). 

The two-phase kinetic model developed by Karickhoff (65) is capable of fitting either the sorption or desorption of a sorbing solute. For linear isotherms, the mathematical description given by Karickhoff (1) and others (67, 70, 71) is virtually identical to that of a mass transfer process (72). 

This paper discusses the oxidation of Mn(II) in the presence of lepidocrocite, y-FeOOH. This solid was chosen because earlier work (18, 26) had shown that it significantly enhanced the rate of Mn(II) oxidation. The influence of Ca2+, Mg2+, Cl", SO,2-, phosphate, silicate, salicylate, and phthalate on the kinetics of this reaction is also considered. These ions are either important constituents in natural waters or simple models for naturally occurring organics. To try to identify the factors that influence the rate of Mn(II) oxidation in natural waters the surface equilibrium and kinetic models developed using the laboratory results have been used to predict the... 

In the studies described above the experimental conditions were chosen for experimental convenience, so they may differ greatly from those found in natural waters. To try to identify the factors that might influence Mn(II) oxidation on metal oxides surfaces in natural waters, the surface equilibria and kinetic models developed above can been used to predict the time scales for Mn(II) oxidation in these waters. 

The kinetic model developed in this study can be used to design and analyze various chemical reactors for the hydrogenation of benzaldehyde. Although it is based on a Langmuir-Hinshelwood mechanism, it does not prove that this is the correct mechanism. 

The kinetic model developed from the detailed experimental data obtained with Pd(l 11) holds similarly for other single crystal planes as well as for the results from polycrystalline material. Without reviewing all the available measurements in detail, only two sets of data from the first study of this type with Pdf 110) will be mentioned (2). Figure 38 shows the variation of the steady-state rate of C02 formation with pco at constant oxygen pressure (Po2 = 1 x 10-7 Torr) and temperature (T= 520 K). For pco p0l, r increases linearly with the CO pressure while the simultaneously monitored LEED pattern indicates the presence of appreciable amounts of oxygen on the surface. Under these conditions case 2 is valid, whereby (15) correctly describes the observed kinetics. For pco > p0l the reaction rate becomes... 

Furthermore, since most large-scale fermentations are carried out in batch mode, the kinetic parameters determined by the chemostat study should be able to predict the growth in a batch fermenter. However, due to the significantly different environments of batch and continuous fermenters, the kinetic model developed from the CSTF runs may fail to predict the growth behavior of a batch fermenter. Nevertheless, the verification of a kinetic model and the evaluation of kinetic parameters by running chemostat is the most reliable method because of its constant medium environment. 

Accordingly, the potential dependence of the electrode kinetics is determined by the variation of the activation energy with E, which is established by the position of the transition state on the energy profile in Fig. 1.13. This key aspect has been addressed in different ways by the different kinetic models developed. In the following sections, the two main models employed in interfacial electrochemistry will be reviewed. 

A single site model assumes only one type of surface sites, i.e., the same type of sites is responsible for trichloroethylene adsorption and reduction. The kinetic model developed herein is based on the following reaction... 

While vinyl acetate is normally polymerized in batch or continuous stirred tank reactors, continuous reactors offer the possibility of better heat transfer and more uniform quality. Tubular reactors have been used to produce polystyrene by a mass process (1, 2), and to produce emulsion polymers from styrene and styrene-butadiene (3 -6). The use of mixed emulsifiers to produce mono-disperse latexes has been applied to polyvinyl toluene (5). Dunn and Taylor have proposed that nucleation in seeded vinyl acetate emulsion is prevented by entrapment of oligomeric radicals by the seed particles (6j. Because of the solubility of vinyl acetate in water, Smith -Ewart kinetics (case 2) does not seem to apply, but the kinetic models developed by Ugelstad (7J and Friis (8 ) seem to be more appropriate. 

The kinetic model developed in Sect. 2.4 for the phenol-formaldehyde reaction belongs to a wider class of kinetic networks made up of irreversible nonchain reactions. In this section, a general form of the mathematical model for this class of reactive systems is presented moreover, it is shown that the temperature attainable in the reactor is bounded and the lower and upper bounds are computed. 

The kinetic model developed here does not use any kind of adiabatic assumption, and thus is capable of rendering frequency dependencies of the SR characteristics. 

Fig. 11 Cr(VI) concentrations versus illumination time (Xe light source filtered to simulate solar spectrum). Filled symbols aerated solutions empty symbols N2- purged solutions. The lines are the results from a kinetic model developed to describe the data. The pH values and the initial concentrations in iM for Fe(III) and for oxalate are given (from [74])...

The kinetic model developed from these data for the reversible production of butanol is of the form ... 

A kinetic model developed for imseeded emulsion polymerization based on the knowledge and conclusions obtained above could explain the progress of polymerization inside both the monomer droplets and the latex particles in the seeded emulsion polymerization of St initiated by AIBN at 50 °C. 

High-resolution Si NMR spectroscopy was used to study the hydrolysis and condensation kinetics of monomeric and dimeric species in the silicate sol-gel system. Peak assignments for the kinetics experiments were determined by comparing add-catalyzed reaction solutions prepared with limited amounts of water with the synthetically prepared dimeric, trimeric, and tetrameric species. Si NMR peaks were assigned for 5 of the 10 possible dimeric species. The temporal evolution of hydrolysis and condensation products has been compared with a kinetic model developed in our laboratory, and rate constants have been determined. The results indicate that the water-producing condensation of dimeric species is approximately 5 times slower than the water-producing condensation of the monomeric species. The alcohol-producing condensation of dimeric species is comparable with that of monomeric species. 

The purpose of this review is to discuss IE kinetics in selected systems using the kinetic model developed in this author s research [26-27,45-50]. It is an attempt to demonstrate, in particular, that phenomenological regularities and criteria describing intraparticle diffusion kinetics for conventional ion exchange are not applicable for the selective ion-exchange systems. 

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