Kinetic modeling case studies

In this study the oil yield decreased with reaction time, as oil was polymerized at higher temperature for Miike, Taiheiyo and Hikishima coals. Thus the kinetic models (Case 2 or 3) which involve two steps of resini-fication and coking correlated data reasonably well for above coals, whereas for Morwell and Bukit Asam coals, Case 5 is more suitable. 

A similar kinetic model has been developed for the measurement of ion complex formation kinetics and energies involving both dissociative and nondissociative electron capture, for example, the hydration of halide ions and of 02( ). The ratio of negative ions observed in NIMS can be used to determine energies of complex formation. In this case the sequential formation of the higher complexes must be added to the kinetic model. These studies are important because they demonstrate that the API mass spectrometer can be used to measure thermodynamic quantities. When we use the data for hydrates of 02(—) as an example, the kinetic expression is given by... 

Because the radiation in most cases will not penetrate the entire sample, the concentration of the reactant is unlikely to approach zero at infinite time. A plot of remaining concentration vs. time will therefore level off at a value greater than zero. This should be taken into account when selecting the kinetic model for studies of solid-state degradation (Sande, 1996). The solid-state degradation will in some cases appear to consist of a series of consecutive processes with different mechanisms and rates (Carstensen, 1974). Such a stepwise change in reaction rate is most likely caused by an alteration in sample surface and fading of subsequent layers. The concept of reaction order may not be useful for photodecomposition in the solid state (De VUliers et al 1992). 

CASE STUDY ENZYME KINETIC MODELS FOR RESOLUTION OF RACEMIC IBUPROFEN ESTERS IN A MEMBRANE REACTOR... 

The nitrosation of N-methyltyramine represents an interesting case of N-nitrosation and C-nitrosation in the same molecule. In relatively strong acid (below pH 5), C-nitrosation is predicted to be more rapid (36) but in dilute acid where there is a considerable amount of unprotonated amine available, it is not yet clear which type of nitrosation is favored. N-methyltyramine would serve as a useful model to study the competitive kinetics of N-nitrosation and C-nitrosation in dilute acid. Details of the synthesis and nitrosation of N-methyltyramine will be published elsewhere. 

Boekel, M.J.S., Kinetic modeling in food science a case study on chlorophyll degradation in olives, J. Sci. Food Agric., 80, 3, 2000. 

A lot of research has been published on hydroformylation of alkenes, but the vast majority of the effort has been focused on the chemistry of various metal-ligand systems. Quantitative kinetic studies including modeling of rates and selectivities are much more scarce. In this work, we present the approach to modeling of hydroformylation kinetics and gas-solubility. Hydroformylation of 1-butene with a rhodium-based catalyst was selected as a case study. 

In this section, we will discuss some examples from the literature, in which the approximation methods derived in this chapter have been used. In several cases, the approximations have been compared with more-accurate path integral simulations to assess their validity. This is not meant as a full review rather, several case studies have been chosen to illustrate the tools we have developed. We will first look at simpler examples and then discuss water models and applications in enzyme kinetics. 

A kinetic model based on the Flory principle is referred to as the ideal model. Up to now this model by virtue of its simplicity, has been widely used to treat experimental data and to carry out engineering calculations when designing advanced polymer materials. However, strong experimental evidence for the violation of the Flory principle is currently available from the study of a number of processes of the synthesis and chemical modification of polymers. Possible reasons for such a violation may be connected with either chemical or physical factors. The first has been scrutinized both theoretically and experimentally, but this is not the case for the second among which are thermodynamic and diffusion factors. In this review we by no means pretend to cover all theoretical works in which these factors have been taken into account at the stage of formulating physicochemical models of the process... 

Metal ions play an important role as catalysts in many autoxidation reactions and have been considered instrumental in regulating natural as well as industrial processes. In these reactive systems, in particular when the reactions occur under environmental or in vivo biochemical conditions, the metal ions are involved in complicated interactions with the substrate(s) and dioxygen, and the properties of the actual matrix as well as the transport processes also have a pronounced impact on the overall reactions. In most cases, handling and analyzing such a complexity is beyond the capacity of currently available experimental, computational and theoretical methods, and researchers in this field are obliged to use simplified sub-systems to mimic the complex phenomena. When the simplified conditions are properly chosen, these studies provide surprisingly accurate predictions for the real systems. In this paper we review the results obtained in kinetic and mechanistic studies on the model systems, but we do not discuss their broad biological or environmental implications. 

Although the above model was developed under non-catalytic conditions, some of the results may bear significance under natural conditions or in the presence of excess sulfite ions. Thus, the decomposition of the mono-sulfito complex was considered to be the rate-determining step in the catalytic cycle, but only estimates could be given for the rate constant in earlier studies. The comprehensive data treatment used by Lente and Fabian yielded a well established value for this parameter (106), which can then be used to improve previous kinetic models. Furthermore, the participation of reactions of the [Fe2(0H)(S03)]3+ complex was never considered in kinetic studies where excess sulfite ion was used over low iron(III) concentration in mildly acidic solution (pH 2.5-3.0). The above model predicts that in some cases the formation of the dimeric sulfito complex could make a substantial contribution to the spectral changes and omission of this species could lead to biased conclusions. Reevaluation of data sets reported earlier by including the reactions of [Fe2(0H)(S03)]3+ may resolve some of the controversies found in literature results. 

It is important to note that wastewater is subject to great variability in terms of its components and processes. Procedures 1 to 4, therefore, correspond to a typical analytical method for the determination of the characteristic components and the stoichiometric and kinetic parameters. Cases where the procedure described in Sections 7.2.1-1.2 A is either difficult or not feasible to follow may exist. A detailed knowledge on wastewater characteristics and experience from laboratory and modeling studies may be crucial in such situations for finding alternative variants of the procedures 1 to 4. 

In chapter 1, Profs. Cramer and Truhlar provide an overview of the current status of continuum models of solvation. They examine available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. They then consider a number of case studies with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter they focus attention on the subtleties of actual chemical systems and some of the danger in applying continuum models uncritically. They hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. In the last section they offer a brief overview of methods to extend continuum solvation modeling to account for dynamic effects in spectroscopy and kinetics. Their conclusion is that there has been tremendous progress in the development and practical implementation of useful continuum models in the last five years. These techniques are now poised to allow quantum chemistry to have the same revolutionary impact on condensed-phase chemistry as the last 25 years have witnessed for gas-phase chemistry. 

The main objectives of this chapter are to (1) review the different modeling techniques used for sorption/desorption processes of organic pollutants with various solid phases, (2) discuss the kinetics of such processes with some insight into the interpretation of kinetic data, (3) describe the different sorption/ desorption experimental techniques, with estimates of the transport parameters from the data of laboratory tests, (4) discuss a recently reported issue regarding slow sorption/desorption behavior of organic pollutants, and finally (5) present a case study about the environmental impact of solid waste materials/complex... 

Examples. There are by now several reactions for which the best available levels of ab initio electronic structure theory find a plateau on the PE hypersurface, in the vicinity of a singlet-state biradical. Several of these have been studied by MD simulation and/or experiment, and in each case the conclusion is that application of statistical kinetic models will give a misleading description of how the reaction really occurs. There is not room to describe each of these studies, and so just one is chosen as a representative, and described in Section 3.2.3.1. 

Although the kinetic rate and energy partitioning are qualitatively consistent with a pure ER process, other aspects of the experiments and most of the theory (see discussion below) imply that the abstraction is more properly described as a combination of ER and HA reactions. The large a for abstraction is inconsistent with theoretical studies of a pure ER process as this requires a direct hit of the incoming H(D) with the adsorbed D(H) [380,381]. There is also no way to reconcile formation of homonuclear products with a pure ER process. In addition, similar kinetic experiments on other metals, e.g., Ni(100) [146], Pt(lll) [147,382], etc., are not even in qualitative agreement with the simple ER rate law above. In those cases, it is necessary to develop more sophisticated HA kinetic mechanisms to describe the kinetics experiments [383-385]. The key parameter of these kinetic models is the ratio of reaction to non-reactive trapping, pr/ps. For pr/ p, = 1, the HA kinetics looks very much like the simple ER case, and this is the reason H(D) + D(H)/Cu(lll) has such simple kinetics. 

This represents the typical feed mixture to SCR converters when no oxidation precatalyst is applied, as for instance in the case of NOx abatement from stationary sources. With such a feed mixture the main deNOx reaction occurring over V-based catalysts is the so-called standard SCR (R6 in Table V). Transient experiments in a wide range of temperatures (50-550°Q were performed in order to develop a suitable kinetic model of the NH3-N0/02 reacting system. The study of the standard SCR kinetics was particularly focused on the characteristics that are critical for mobile applications, namely the behavior during transient operation and the reactivity in the low temperature region. 

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