Nonlinear Differential Equations of Chemically Reacting Systems

Nonlinear Differential Equations of Chemically Reacting Systems PDF

Author: George R. Gavalas

Publisher: Springer Science & Business Media

Published: 2013-03-13

Total Pages: 116

ISBN-13: 3642876439

DOWNLOAD EBOOK →

In recent years considerable interest has developed in the mathe matical analysis of chemically reacting systems both in the absence and in the presence of diffusion. Earlier work has been limited to simple problems amenable to closed form solutions, but now the computer permits the numerical solution of complex systems of nonlinear differ ential equations. The numerical approach provides quantitative infor mation, but for practical reasons it must be limited to a rather narrow range of the parameters of the problem. Consequently, it is desirable to obtain broader qualitative information about the solutions by in vestigating from a more fundamental mathematical point of view the structure of the differential equations. This theoretical approach can actually complement and guide the computational approach by narrow ing down trial and error procedures, pinpointing singularities and suggesting methods for handling them. The study of the structure of the differential equations may also clarify some physical principles and suggest new experiments. A serious limitation ofthe theoretical approach is that many of the results obtained, such as the sufficient conditions for the stability of the steady state, turn out to be very conservative. Thus the theoretical and computational approaches are best used to gether for the purpose of understanding, designing, and controlling chemically reacting systems. The present monograph is intended as a contribution to the theory of the differential equations describing chemically reacting systems.

Analysis of Kinetic Reaction Mechanisms

Analysis of Kinetic Reaction Mechanisms PDF

Author: Tamás Turányi

Publisher: Springer

Published: 2014-12-29

Total Pages: 369

ISBN-13: 366244562X

DOWNLOAD EBOOK →

Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.

Transport Processes in Chemically Reacting Flow Systems

Transport Processes in Chemically Reacting Flow Systems PDF

Author: Daniel E. Rosner

Publisher: Butterworth-Heinemann

Published: 2013-10-22

Total Pages: 571

ISBN-13: 1483162680

DOWNLOAD EBOOK →

Transport Processes in Chemically Reacting Flow Systems discusses the role, in chemically reacting flow systems, of transport processes—particularly the transport of momentum, energy, and (chemical species) mass in fluids (gases and liquids). The principles developed and often illustrated here for combustion systems are important not only for the rational design and development of engineering equipment (e.g., chemical reactors, heat exchangers, mass exchangers) but also for scientific research involving coupled transport processes and chemical reaction in flow systems. The book begins with an introduction to transport processes in chemically reactive systems. Separate chapters cover momentum, energy, and mass transport. These chapters develop, state, and exploit useful quantitative ""analogies"" between these transport phenomena, including interrelationships that remain valid even in the presence of homogeneous or heterogeneous chemical reactions. A separate chapter covers the use of transport theory in the systematization and generalization of experimental data on chemically reacting systems. The principles and methods discussed are then applied to the preliminary design of a heat exchanger for extracting power from the products of combustion in a stationary (fossil-fuel-fired) power plant. The book has been written in such a way as to be accessible to students and practicing scientists whose background has until now been confined to physical chemistry, classical physics, and/or applied mathematics.

Material Balances for Chemical Reacting Systems

Material Balances for Chemical Reacting Systems PDF

Author: R.L. Cerro

Publisher: CRC Press

Published: 2022-12-05

Total Pages: 432

ISBN-13: 1000649644

DOWNLOAD EBOOK →

Written for use in the first course of a typical chemical engineering program, Material Balances for Chemical Reacting Systems introduces and teaches students a rigorous approach to solving the types of macroscopic balance problems they will encounter as chemical engineers. This first course is generally taken after students have completed their studies of calculus and vector analysis, and these subjects are employed throughout this text. Since courses on ordinary differential equations and linear algebra are often taken simultaneously with the first chemical engineering course, these subjects are introduced as needed. Teaches readers the fundamental concepts associated with macroscopic balance analysis of multicomponent, reacting systems Offers a novel and scientifically correct approach to handling chemical reactions Includes an introductory approach to chemical kinetics Features many worked out problems, beginning with those that can be solved by hand and ending with those that benefit from the use of computer software This textbook is aimed at undergraduate chemical engineering students but can be used as a reference for graduate students and professional chemical engineers as well as readers from environmental engineering and bioengineering. The text features a solutions manual with detailed solutions for all problems, as well as PowerPoint lecture slides available to adopting professors.

Modelling of Chemical Reaction Systems

Modelling of Chemical Reaction Systems PDF

Author: K.H. Ebert

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 399

ISBN-13: 3642682200

DOWNLOAD EBOOK →

For rather a long time numerical results in chemical kinetics could only be obtained for very simple chemical reactions, most of which were of minor practi ca 1 importance. The avail abil ity of fast computers has provi ded new opportunities for developments in chemical kinetics. Chemical systems of practical interest are usually very complicated. They consi st of a great number of different el ementary chemi cal reacti ons, mostly with rate constants differi ng by many orders of magni tude, frequently with surface reacti on steps and often wi th transport processes. The deri vati on of a 'true' chemical mechani sm can be extremely cumbersome. Mostly this work is done by setting up 'reaction models' which are im proved step by step in comparison with precise experimental data. At this early stage mathematics is involved, which may al ready be rather complicated. Mathematical methods such as pertubation theory, graph theory, sensitivity analysis or numerical integration are necessary for the derivation and application of optimal chemical reaction models. Most theoretical work aimed at improving the mathematical methods was done on chemical reactions which mostly were of little practical im portance. Chemi cal engi neers, who evi dently k now well how important the chemical model s and their dynamics are for reactor desi gn, have al so to be convinced not only on the theoretical work but also on its practical applic abil ity.

Determination of Complex Reaction Mechanisms

Determination of Complex Reaction Mechanisms PDF

Author: John Ross

Publisher: Oxford University Press

Published: 2006

Total Pages: 239

ISBN-13: 0195178688

DOWNLOAD EBOOK →

In a chemical system with many chemical species several questions can be asked: what species react with other species: in what temporal order: and with what results? These questions have been asked for over one hundred years about simple and complex chemical systems, and the answers constitute the macroscopic reaction mechanism. In Determination of Complex Reaction Mechanisms authors John Ross, Igor Schreiber, and Marcel Vlad present several systematic approaches for obtaining information on the causal connectivity of chemical species, on correlations of chemical species, on the reaction pathway, and on the reaction mechanism.Basic pulse theory is demonstrated and tested in an experiment on glycolysis. In a second approach, measurements on time series of concentrations are used to construct correlation functions and a theory is developed which shows that from these functions information may be inferred on the reaction pathway, the reaction mechanism, and the centers of control in that mechanism. A third approach is based on application of genetic algorithm methods to the study of the evolutionary development of a reaction mechanism, to the attainment given goals in a mechanism, and to the determination of a reaction mechanism and rate coefficients by comparison with experiment. Responses of non-linear systems to pulses or other perturbations are analyzed, and mechanisms of oscillatory reactions are presented in detail. The concluding chapters give an introduction to bioinformatics and statistical methods for determining reaction mechanisms.