Four environment model of mixing and chemical reaction. Part I. Model development

Abstract

A new mathematical model (the four environment model) to describe turbulent R. V. MEHTA and J. M. TARBELL flow chemical reactors with complex reactions and separate reactant feed streams is developed. The feed stream residence time distributions, the batch chemical kinetics, and a single turbulent micromixing parameter, which may be estimated Department of Chemical Engineering from direct turbulence theory, are required as input information to the model. The and Center for Air Environment Studies model is computationally efficient as it involves only ordinary differential equa-The Pennsylvania State University tions. University Park, PA 16802 SCOPEMixing and chemical reaction are concurrent phenomena in many chemical reactors, particularly those of industrial scale. The design and development of reactors with unmixed feedstreams, complicated large-scale mixing patterns, and competing chemical reactions is a challenge which often requires significant pilot-plant experience. A mathematical model capable of describing these complex chemical reactor phenomena is clearly desirable. However, most existing models are either too complex-involving many empirical parameters, or too inefficient computationally-requiring the solution of coupled partial differential equations or Monte Carlo simulations. A notable exception is the three environment model of Ritchie and Tobgy (1979), which is computationally efficient and provides a reasonable description of the mixing processes. Unfortunately, the three environment model does not properly account for the effect of micromixing on the selectivity of competing reactions--q significant problem in industrial reactor design.Our objective in this work was to develop a computationally efficient mathematical model of mixing and chemical reaction which would retain the overall structure and desirable features of the three environment model while allowing a more realistic description of the effect of micromixing on selectivity of competing reactions. CONCLUSIONS AND SIGNIFICANCEWe have developed a computationally efficient chemical reactor model (the four environment model), having an ordinary differential equation structure, which can account for competing chemical reactions, arbitrary macromixing patterns, and turbulent micromixing of unmixed reactants. The input information required by the model includes: the (perfectly mixed) batch chemical kinetics; the residence time distribution function for each reactor feedstream; and a single micromixing parameter which may be determined by a reactive tracer experiment. An analogy between the four environment model and isotropic turbulence mixing as expressed in the theories of Corrsin (1964) and Rosensweig (1964) provides a means of estimating (corre-lating) the micromixing parameter from knowledge of the reactor geometry and the power input. The four environment model is a refinement and extension of the three environment model of Ritchie and Tobgy (1979). By adding an additional "leaving environment" (the three environment model has only o...

Direct numerical simulation of chemical selectivity in homogenous turbulence

“…Mehta and Tarbell (1987) used Bourne's reaction in an unmixed feedstream multijet tubular reactor and observed that the concentration profiles (particularly the s profile) showed large deviations from the perfect mixing limit corresponding to a plug-flow reactor. Mechanistic models such as the three-environment model and four-environment model (Mehta and Tarbell, 1983) use data from these experiments to determine the value of the micromixing parameter for the models (Tarbell and Mehta, 1986). …”

Modeling of imperfect mixing and its effects on polymer properties

“…Environment models (Weinstein and Adler, 1967;Villermaux and Zoulalian, 1969;Mehta and Tarbell, 1983) represent imperfect mixing by a combination of environments, each in an extreme state of either perfect mixing or complete segregation. One or more free parameters control the amount of fluid entering each environment.…”

Mixing Characterization of Transient Puffs in a Rotary Kiln Incinerator

“…Other models in this same class include: the coalescence-redispersion model 1 (Curl, 1963); the interaction-by-exchange-with-the-mean (IEM) model (Villermaux and Devillon, 1972); and the four-environment model (Mehta and Tarbell, 1983).…”