of Model Reactions and Statistical Modelling (original) (raw)

Determination of reaction models from experimental measurements

The Canadian Journal of Chemical Engineering, 1991

It is demonstrated through the use of transformation relations, function approximation and error limits that it is impossible to distinguish among rival gasification models using just a single temperature programmed reaction experiment. Two experiments at different heating rates must be used and the ratio between rates is important. These depend on the models to be distinguished.

MODEL FORMULATION & INTERPRETATION- FROM EXPERIMENT TO THEORY

2015

Abstract. From kinetics study of a given pair of reactants different types of mechanisms were investigated. A mathematical model was formulated. Model parameters were evaluated and assessed. Obtained results from the optimization procedure opened an interesting discussion about the limits of experiments parameters for imposed conditions, such as mecha-nism type and collecting procedure. By using of a least squares method were obtained models as best fits correlates (results shown an average of 96.6%) with experimental measurements. Comparison between experi-ments shown that the obtained model is a consistent one, all obtained parameters being in the same range of 95 % confidence interval. These results validates experimental as well as from model data. 1.

Model Formulation & Interpretation-From Experiment to Theory

2008

From kinetics study of a given pair of reactants different types of mechanisms were investigated. A mathematical model was formulated. Model parameters were evaluated and assessed. Obtained results from the optimization procedure opened an interesting discussion about the limits of experiments parameters for imposed conditions, such as mechanism type and collecting procedure. By using of a least squares method were obtained models as best fits correlates (results shown an average of 96.6%) with experimental measurements. Comparison between experiments shown that the obtained model is a consistent one, all obtained parameters being in the same range of 95% confidence interval. These results validates experimental as well as from model data.

Analytical study of an asymmetric 1D statistical model for chemical reactions

Physica A: Statistical Mechanics and its Applications, 1996

An analytical study is presented for the asymmetric FGZ reaction model, involving two different species A and B (only B can spontaneously desorb) in contact with a bath containing A and B with the same concentration. The expected values of the density and the pair correlation functions are calculated and their time behaviour is analysed in detail. This also allows to define an average time-dependent fragmentation index describing quantitatively the evolution of the topology (connectivity) of the clusters. In addition, when the system is doomed to end its evolution in the A-poisoned state, the distribution law P(T) of the times T k at which this occurs is investigated numerically. It turns out that, in the case where a single isolated B is present in the initial state, this law is well enough represented by a stretched exponential in the log variable: P(T) = C ste exp[-~t(ln T)a]. and Ray [6], relaxed the diffusion-limited assumption. Microscopic diffusion can be taken into account in some definite models using directly the concentrations of the reactants, as done by Newman . C16ment et al. [8, 9] analysed the totally symmetric case in which the two species are in equal concentration and can spontaneously desorb with equal probabilities. These authors generalized [10] the above model by including the possibility of vacant sites and also proposed a decoupling scheme to handle an infinite hierarchy of moments.

The statistical theory of multi-step compound and direct reactions

Annals of Physics, 1980

The theory of nuclear reactions is extended so as to include a statistical treatment of multi-step processes. Two types are distinguished, the multi-step compound and the multistep direct. The wave functions for the system are grouped according to their complexity. The multi-step direct process involves explicitly those states which are open, while the multi-step compound involves those which are bound. In addition to the random phase assumption which is applied differently to the multi-step direct and to the multi-step compound cross-sections, it is assumed that the residual interaction will have non-vanishing matrix elements between states whose complexities differ by at most one unit. This is referred to as the chaining hypothesis. Explicit expressions for the double differential crosssection giving the angular distribution and energy spectrum are obtained for both reaction types. The statistical multi-step compound cross-sections are symmetric about 90". The classical statistical theory of nuclear reactions is a special limiting case. The cross-section for the statistical multi-step direct reaction consists of a set of convolutions of single-step direct cross-sections. For the many step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction **lTa(p, n)181W using the statistical multi-step compound formalism.

Modelling of Chemical Reaction Systems

Springer Series in Chemical Physics, 1981

Library of Congress Cataloging in Publication Data. Main entry under title: Modelling of chemical reaction systems. (Springer series in chemical physics; v. 18). Bibliography: p. Includes index.!. Chemical reaction, Conditions and laws of Mathematical models-Congresses. I. Ebert, K. H. (Klaus Heinrich), 1928-. II.

Chapter 2: Examples of Mathematical Models for Chemical Processes

In this chapter we develop mathematical models for a number of elementary chemical processes that are commonly encountered in practice. We will apply the methodology discussed in the previous chapter to guide the reader through various examples. The goal is to give the reader a methodology to tackle more complicated processes that are not covered in this chapter and that can be found in books listed in the reference. The organization of this chapter includes examples of systems that can be described by ordinary differential equations (ODE), i.e. lumped parameter systems followed by examples of distributed parameters systems, i..e those described by partial differential equations (PDE). The examples cover both homogeneous and heterogeneous systems. Ordinary differential equations (ODE) are easier to solve and are reduced to simple algebraic equations at steady state. The solution of partial differential equations (PDE) on the other hand is a more difficult task. But we will be interested in the cases were PDE's are reduced to ODE's. This is naturally the case where under appropriate assumptions, the PDE's is a one-dimensional equation at steady state conditions. It is worth to recall, as noted in the previous chapters, that the distinction between lumped and distributed parameter models depends sometimes on the assumptions put forward by the modeler. Systems that are normally distributed parameter can be modeled under appropriate assumptions as lumped parameter systems. This chapter includes some examples of this situation. 28

MATHEMATICAL MODELS and METHODS in APPLIED SCIENCES

Mathematics plays an important role in solving real life problems. Chemistry is one of the main sciences that benefits from the development of new mathematical techniques for modelling the experimental data. In this talk I shall present two different types of approaches for determination of models for data collected in industrial environment, comparing the classical approaches with the new ones from the artificial intelligence and emphasizing the advantages of each method by the results of our research.