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Systematic analysis of the effect of temperature profiles on reactions in tubular reactors
Author(s) -
Wu J.,
Platzer B.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000015
Subject(s) - thermodynamics , isothermal process , laminar flow , dimensionless quantity , plug flow reactor model , arrhenius equation , mechanics , plug flow , reaction rate , heat transfer , chemistry , materials science , continuous stirred tank reactor , physics , activation energy , biochemistry , catalysis
A more or less pronounced temperature distribution existing in reactors has a strong influence on the conversion at the reactor outlet. Generally, isothermal or other strongly simplified models seem to fail. However, with their low expense of calculation they are good approaches for a rough reactor design and play an important role in books of chemical reaction engineering. Ideal isothermal models dominate the chapters of reactor design in these books. Thus, a systematic study of the influence of the temperature profile is done here. The influence of plug and laminar flow, heat transfer, reaction heat, operation states, and the temperature dependence of physical parameters is discussed. Some non‐isothermal tubular reactor models are developed for irreversible, homogeneous reactions. The models have an increasing complexity. This article focuses at first on the study of some special cases having analytical solutions. Here some new solutions are presented. Half‐analytical and numerical methods are used for the analysis, too. Beside the Arrhenius' law, a linear temperature profile is also used to calculate the reaction rate constant for small temperature differences. The analytical solutions of the concentration profiles in the reactor and the mean concentration at the outlet position are obtained for zeroth, first, and second order reactions by solving the species conservation equation. For non‐analytical integration terms (e.g. for variable viscosity problems) the relations between the mean concentration of the reactant bar c A / c Ao and the dimensionless parameter z/(LDa w ) are obtained with a numerical method. In order to find a connection between these models, an effective reaction coefficient is introduced. The results are discussed in detail.