The accuracy of kinetic parameters estimated from batch and integral reactor data (original) (raw)
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Chemometrics and Intelligent Laboratory Systems, 2000
The common methods used by chemists to obtain the estimates of the kinetic rate constants are deterministic ones. The Ž. statistical methods, such as D-optimum design DOD , can offer a better way to deal with this problem. But the kinetic model of a reversible reaction is nonlinear, the DOD is locally optimal at the value of the initial chosen parameters. The goal of this Ž. Ž. article is to try to put different experimental design techniques, i.e., uniform design UD , orthogonal design OD and DOD into a common framework, and to attempt to gain some insight on when, where and which of these three experimental methods can be expected to work well. The extensive Monte Carlo experiments have been done in order to compare the performances of these methods. The results show that the DOD often gives the best performance, but it is easy to break down in estimation of parameters, when the initial parameters are far away from the true parameters. The OD also breaks down in some situations. The UD is the most stable, and it works well in all situations.
Chemical Engineering Journal, 2009
The proper characterization of the experimental errors is essential for the correct evaluation of estimated model parameters, model fit and model predictions based on kinetic rate expressions. However, it is common to ignore the influence of experimental errors during kinetic studies due to difficulties to characterize how experimental errors depend on the reaction conditions. The behavior of experimental error depends on the specific features of the experimental system; however, in many cases the main sources of experimental errors are the unavoidable oscillations of the input variables. This work analyzes how the experimental errors affect kinetic studies based on catalytic tests when oscillations of the input variables are the main sources of uncertainties. The first part of this work assumes that the reaction rate can be described accurately as a first-order reaction in a PFR. Analytical expressions are derived for the variance of the reactant conversion in distinct scenarios and are used to analyze the quality of the obtained parameter estimates. It is shown here that the conversion variances can be described as functions of the measured conversion values, normally presenting a point of maximum for conversion values in the range of 0.6 < X < 1.0 when observed experimental fluctuations are controlled by the fluctuations of the input variables. Constant conversion variances should be expected only when fluctuations are controlled by analytical conversion measurements. As a consequence, optimum parameter estimation may be performed either with differential or integral methods, depending on the behavior of the conversion variances.
Eurokin. Chemical Reaction Kinetics in Practice
Cattech, 2001
The chemical reactions taking place in the chemical reactor form the heart of any chemical process. Reaction kinetics are the translation of our understanding of the chemical processes into a mathematical rate expression that can be used in reactor design and rating. Because of the importance of correct and safe design of chemical reactors, chemical reaction kinetics is a key aspect of research and development in chemical industries, in research institutes, and academic centers, as well as in industrial laboratories. There is, and there will always be, a strong need for knowledge and a skill base concerning the determination of reaction kinetics and their application in the form of a kinetic model. This paper is a result of cooperation within Eurokin, a consortium of over 10 European companies and 4 universities. An industrial questionnaire in 1995 highlighted that industry is not only a little conservative in the methods it uses to determine kinetics, but also that there was a wide awareness of the scope for improvement. Eurokin was thus founded in 1998 to try and establish the best practices and to facilitate development work in kinetics and associated areas. The paper briefly explains some underlying theory of heterogeneously catalyzed chemical reactions and their kinetics. It deals specifically with the acquisition of kinetic data, and gives recommendations for the selection of the experimental reactor and conditions. A primary aim of this paper is discuss kinetic experimentation and modeling through a series of case studies, attempting to illustrate good practice, methods in kinetic modeling, pitfalls, and recommendations. The paper closes with some recommendations and a perspective on the future needs of industrial reaction kinetics.
Energy & Fuels, 1999
Detailed kinetic models for the modeling of complex chemistries, including thermal cracking, catalytic reforming, catalytic cracking, and hydroprocessing, offer the compelling advantage chemical significance at the mechanistic level. They carry a considerable burden, however, in terms of species, reactions, and associated rate parameters. This, together with the batch and the plug flow reactor balances, requires solution of a large system of either stiff ordinary differential equations (ODE) or stiff differential algebraic equations (DAE), for both homogeneous and heterogeneous processes. It is often faster numerically to solve a stiff system of ODEs and, thus, it can be useful to convert a system of DAEs to ODEs for numerical solution schemes. For heterogeneous PFR systems, the reactor steady-state balances result in a set of DAEs, and it would therefore be desirable to construct the associated set of ODEs to minimize CPU demand. To this end, we propose that such a transformation can be achieved by making the "flowing surface species" approximation. This involves approximating the overall rate of reaction of surface species, which is identically equal to zero at reactor steady state, by a spatial derivative. We show that this approximation becomes better as the system of equations becomes stiffer, and, hence, is a reverse analogy of the kinetic steady-state approximation in the case of batch systems. To validate the proposition, we analyze various contrived and real examples of mechanistic kinetics for heterogeneous systems.
Missen- Introduction To Chemical Reaction Engineering And Kinetics
Introduction to Chemical Reaction Engineering and Kinetics is written primarily for a first course in chemical reaction engineering (CRE) for undergraduate students in chemical engineering. The purpose of the work is to provide students with a thorough introduction to the fundamental aspects of chemical reactor analysis and design. For this purpose, it is necessary to develop a knowledge of chemical kinetics, and therefore the work has been divided into two inter-related parts: chemical kinetics and CRE. Included with this book is a CD-ROM containing computer software that can be used for numerical solutions to many of the examples and problems within the book. The work is primarily based on material given to undergraduate students in the Department of Chemical Engineering and Applied Chemistry at the University of Toronto.