Chemical reactions, mathematical modeling

Chemistry, Organic—Synthesis. 2. Chemical reactions—Mathematical models. I. Christoph, B. II. Series,... 

Chemical reactions—Mathematical models. 2. Chemical reactions—Computer simulation. 1. Caracotsios, Michael. II. Title. 

I. Multiphase flow - Mathematical models. 2. Chemical reactions - Mathematical models. 3. Transport theory. 4. Dispersion - Mathematical models. 1. Fox, Rodney O., 1959-... 

Chemical reactions — Mathematical models I. Title II. Toth, J. III. Series 541.3 9 0724 QD501... 

Operability analysis and control system synthesis for an entire chemical plant Mathematical modeling of transport and chemical reactions of combustion-generated air pollutants... 

A survey of the mathematical models for typical chemical reactors and reactions shows that several hydrodynamic and transfer coefficients (model parameters) must be known to simulate reactor behaviour. These model parameters are listed in Table 5.4-6 (see also Table 5.4-1 in Section 5.4.1). Regions of interfacial surface area for various gas-liquid reactors are shown in Fig. 5.4-15. Many correlations for transfer coefficients have been published in the literature (see the list of books and review papers at the beginning of this section). The coefficients can be evaluated from those correlations within an average accuracy of about 25%. This is usually sufficient for modelling of chemical reactors. Mathematical models of reactors arc often more sensitive to kinetic parameters. Experimental methods and procedures for parameters estimation are discussed in the subsequent section. 

Another issue that could be probed is the establishment of meaningful relationships between chemical and mathematical models of chemical kinetics by students. Probably the major aspects to be investigated here would be whether and how students conceptualise the existence of relationships between reaction rate data and rate equations. Are they able to interpret diagrams of empirical data or to establish relationships between empirical data, diagrams and mathematical equations As part of the research in this area, the ways teachers and textbooks deal with models represented in different modes might be investigated, as well as how such information is understood by students. It seems that alternative ways to introduce mathematical models, or even the use of different mathematical models produced from the results of such research, would be more understandable by students than those currently reported in the literature. 

Reaction mechanisms (Chemistry) 2. Chemical kinetics-Mathematical models. I. Martoian, G. A. (Gagik Ashotovich) II. Tide. 

This article describes a combination of chemical and mathematical modelling applied to the adsorption of Carbon Dioxide on Platinum surfaces, but a similar procedure can be applied to any chemical or electrochemical mechanism involving unimolecular reactions. Moreover, mathematical theorems about eigenvalues, eigenvectors, diagonalization, Jordan canonical forms, etc., and chemical laws, particularly Lavoisier s law of mass conservation can be combined to solve inverse causation and stability problems. 

The tools that we need to help the modelling of complex reaction systems have to fill the gap between chemical and mathematical modelling. They also should allow the chemist to gain practical and effecient access to the required mathematical knowledge. Finally, those tools should be able to take into account the specific features and properties of chemical reaction equations, and, at the same time, to do this using a chemical language to describe the expected behaviour and dynamical structure of the model, for instance, in terms of chemical network, reaction processes, autocatalysis, activation or inhibition. We are far from that, which indicates that we are still lacking theoretical methods to handle those problems. Moreover, even well established mathematical theories are still not usually implemented in effecient practical procedures. 

The direct problem of chemical kinetics always has an analytical solution if a reaction mathematical model is a linear system of ordinary first-order differential equations. Sequences of elementary first-order kinetic steps, including ones complicated with reversible and competitive steps, correspond to such mathematical models. Let us mark off the classical matrix method firom analytical methods of solving such ODE systems. 

An R-matrix has a series of interesting matheinatical properties that directly reflect chemical laws. Thus, the sum of all the entries in an R-matrix must be zero, as no electrons can be generated or annihilated in a chemical reaction. Furthermore, the sum of the entries in each row or column of an R-matrix must also he zero as long as there is not a change in formal charges on the corresponding atom. An elaborate mathematical model of the constitutional aspects of organic chemistry has been built on the basis of BE- and R-matriccs [17. ... 

Those based on strictly empirical descriptions Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinefics) are frequently employed in optimization apphcations. These models are conceptually attractive because a gener model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input-output data without any physiochemical analysis of the process. For... 

Dente and Ranzi (in Albright et al., eds.. Pyrolysis Theory and Industrial Practice, Academic Press, 1983, pp. 133-175) Mathematical modehng of hydrocarbon pyrolysis reactions Shah and Sharma (in Carberry and Varma, eds.. Chemical Reaction and Reaction Engineering Handbook, Dekker, 1987, pp. 713-721) Hydroxylamine phosphate manufacture in a slurry reactor Some aspects of a kinetic model of methanol synthesis are described in the first example, which is followed by a second example that describes coping with the multiphcity of reactants and reactions of some petroleum conversion processes. Then two somewhat simph-fied industrial examples are worked out in detail mild thermal cracking and production of styrene. Even these calculations are impractical without a computer. The basic data and mathematics and some of the results are presented. 

In this work the development of mathematical model is done assuming simplifications of physico-chemical model of peroxide oxidation of the model system with the chemiluminesce intensity as the analytical signal. The mathematical model allows to describe basic stages of chemiluminescence process in vitro, namely spontaneous luminescence, slow and fast flashes due to initiating by chemical substances e.g. Fe +ions, chemiluminescent reaction at different stages of chain reactions evolution. 

In this chapter The background of shock-induced solid-state ehemistry eonceptual models and mathematical models chemical reactions in shock-compressed porous powders sample preservation. 

Horie and his coworkers [90K01] have developed a simplified mathematical model that is useful for study of the heterogeneous nature of powder mixtures. The model considers a heterogeneous mixture of voids, inert species, and reactant species in pressure equilibrium, but not in thermal equilibrium. The concept of the Horie VIR model is shown in Fig. 6.3. As shown in the figure, the temperatures in the inert and reactive species are permitted to be different and heat flow can occur from the reactive (usually hot) species to the inert species. When chemical reaction occurs the inert species acts to ther-... 

Gal-Or and Hoelscher (G5) have recently proposed a mathematical model that takes into account interaction between bubbles (or drops) in a swarm as well as the effect of bubble-size distribution. The analysis is presented for unsteady-state mass transfer with and without chemical reaction, and for steady-state diffusion to a family of moving bubbles. 

C.G. Vayenas, S. Brosda, and C. Pliangos, Rules and Mathematical Modeling of Electrochemical and Chemical Promotion 1. Reaction Classification and Promotional Rules,/. Catal., in press (2001). 

Any numerical experiment is not a one-time calculation by standard formulas. First and foremost, it is the computation of a number of possibilities for various mathematical models. For instance, it is required to find the optimal conditions for a chemical process, that is, the conditions under which the reaction is completed most rapidly. A solution of this problem depends on a number of parameters (for instance, temperature, pressure, composition of the reacting mixture, etc.). In order to find the optimal workable conditions, it is necessary to carry out computations for different values of those parameters, thereby exhausting all possibilities. Of course, some situations exist in which an algorithm is to be used only several times or even once. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

It is important that chemical engineers master an understanding of metabolic engineering, which uses genetically modified or selected organisms to manipulate the biochemical pathways in a cell to produce a new product, to eliminate unwanted reactions, or to increase the yield of a desired product. Mathematical models have the potential to enable major advances in metabolic control. An excellent example of industrial application of metabolic engineering is the DuPont process for the conversion of com sugar into 1,3-propanediol,... 

C. E. Lapple, Electrostatic Phenomena with Particulates J. R. Kittrell, Mathematical Modeling of Chemical Reactions... 

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