2 kinetic analysis method model system complexity

In order to estimate high-temperature rate constants, it is necessary to establish the kinetic behaviour of reactions over as wide a temperature range as possible. Modelling is very important to show what physics or chemistry is missing, to test experimental uncertainties, and to provide a view outside the window of experimental observation. Alteration of the physical and chemical properties of water upon heating (see section 15.2) makes kinetic analysis of reacting systems rather complex. A convenient method for extrapolation of the kinetic data is provided by the Noyes relationship. ... 

Application of computer analytical methods. Extensive use of computer analytic methods are thought to intensify theoretical analysis drastically. They will be applied, in particular, to study kinetic models of complex reactions that can be represented by systems of non-linear algebraic equations, for the detailed bifurcation analysis, etc. 

The information needed about the chemical kinetics of a reaction system is best determined in terms of the structure of general classes of such systems. By structure we mean quahtative and quantitative features that are common to large well-defined classes of systems. For the classes of complex reaction systems to be discussed in detail in this article, the structural approach leads to two related but independent results. First, descriptive models and analyses are developed that create a sound basis for understanding the macroscopic behavior of complex as well as simple dynamic systems. Second, these descriptive models and the procedures obtained from them lead to a new and powerful method for determining the rate parameters from experimental data. The structural analysis is best approached by a geometrical interpretation of the behavior of the reaction system. Such a description can be readily visualized. 

Some tours deforce of these methods have been presented in several publications, (see [6,7] and references therein). The studies of Tyson and coworkers are focused on the kinetic analysis of the budding yeast cell cycle. The molecular mechanism of cell cycle control is known in more detail for budding yeast, Saccharomyces cerevisiae, than for any other eukaryotic organism. Many experiments have been done on this system over many years there are about 125 references cited in [6]. The biological details are second to stressing the enormity of this task. The model has nearly twenty variables and that many kinetic equations, and there are about fifty parameters (rate coefficients, binding constants, thresholds, relative efficiencies). A fair number of assumptions need to be made in the cases of absence of any substantiating experimental evidence, and a fair number of approximations need to be made to simplify the kinetic equations. The complexity of this system is indicated in fig. 13.3 and its caption. 

In theory, enzyme reactions may tolerate reversibility, the activation/ inhibition by substrates/products, and even thermo-inactivation of enzyme. From a mathematic view, it is still feasible to estimate parameters of an enzyme reaction system by kinetic analysis of reaction curve if the roles of all those factors mentioned above are included in a kinetic model (Baywenton, 1986 Duggleby, 1983, 1994 Moruno-Davila, et al., 2001 Varon, et al, 1998). However, enzyme kinetics is usually so complex due to the effects of those mentioned factors that there are always some technical challenges for kinetic analysis of reaction curve. Hence, most methods for kinetic analysis of reaction curve are reported for enzymes whose actions suffer alterations by those mentioned factors as few as possible. 

When estimating the kinetic significance of individual steps of complex reaction mechanisms today, the greatest progress is achieved by using the method of analysis of parametric sensitivities [3,7,22-58]. Obviously this is associated with its successful combination with numerical methods in the study of kinetic models. The sensitivity analysis method allows to interprete more intelligently the numerical data, while modeling chemical reaction systems. 

The progress in computer modeling and numerical methods has made it possible to perform not only qualitative but also to a certain extent quantitative analysis of complex nonlinear chemical systems. Computer modeling of complex processes of hydrocarbon oxidation described by mechanisms composed of hundreds of elementary chemical reactions provides a pattern of the formation and interaction of many intermediate products, thereby opening up entirely new prospects of controlling the kinetics of complex chemical processes. 

Fundamental or theoretical modeling is based on the formulation of transport models analyzing the transport phenomena occurring in the membrane module as well as within the membrane. An exhaustive analysis of such a complex behavior, however, is rather onerous and time consuming for practical purposes, since the resulting system of nonlinear partial differential equations can only be solved by means of numerical methods. Moreover, some of the interactions between the fluid and the membrane structure or related to the actual kinetics, in the case of membrane reactors, are not yet completely understood and, therefore, are very difficult to interpret by proper mathematical relationships. For these reasons, several simplified approaches have been proposed in the literature to describe the behavior of real membrane systems. 

The input of the problem requires total analytically measured concentrations of the selected components. Total concentrations of elements (components) from chemical analysis such as ICP and atomic absorption are preferable to methods that only measure some fraction of the total such as selective colorimetric or electrochemical methods. The user defines how the activity coefficients are to be computed (Davis equation or the extended Debye-Huckel), the temperature of the system and whether pH, Eh and ionic strength are to be imposed or calculated. Once the total concentrations of the selected components are defined, all possible soluble complexes are automatically selected from the database. At this stage the thermodynamic equilibrium constants supplied with the model may be edited or certain species excluded from the calculation (e.g. species that have slow reaction kinetics). In addition, it is possible for the user to supply constants for specific reactions not included in the database, but care must be taken to make sure the formation equation for the newly defined species is written in such a way as to be compatible with the chemical components used by the rest of the program, e.g. if the species A1H2PC>4+ were to be added using the following reaction ... 

There are two approaches to ERS design. One is system modeling, which identifies the cause of a pressure rise from a hazard analysis. It uses approximate models—allvapor flow, all-liquid flow, or two-phase flow—to simulate the pressure increase of the reacting system vs. time and to determine vent size. The method is complex since it must identify the stoichiometry, the mechanism, and the kinetics of the decomposition causing the pressure rise. Two pressure models are used for vent sizing ... 

Another indication of the problems associated with modularization of complex systems is the small number of formal mathematical methods that allow one to simplify kinetic models. The existing methods are all based on time-scale separation in the system which allows for the decomposition of the system into a module composed of fast processes and one composed of slow processes. Then the fast processes can be considered in the absence of the slow processes. The slow processes are then considered with the fast processes either in steady state or thermodynamic equilibrium (Klonowski 1983 Segel and Slemrod 1989 Schuster and Schuster 1991 Kholodenko etal. 1998 Stiefenhofer 1998 Schneider and Wilhelm 2000). Two successful approaches to modularization of complex networks do not consider dynamics. One is purely stmctural while the other is applicable only to systems in steady state and concerns the analysis of control. 

Saguy and Karel (1980) stated that improvements have been made possible by the increase in knowledge on the kinetics of food deterioration using advanced analytical methods and by the availability of computer modeling. The latter can simulate behavior of complex systems and save the time and expense of actual experiments. When no correction of the model is anticipated, the formulated model may be used for optimization, prediction and analysis. 

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