Theoretical and Experimental Study of Multiplicity Features of Distributed Parameter Chemically Reacting Systems

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The proposed work is the logical extension of this PI's previous work on analyzing multiplicity features in nonlinear chemically reacting systems. His previous work dealt with lumped parameter systems whereas in this project he is planning to use recently developed mathematical techniques to look at more complex distributed parameter problems. Problems associated with steady-state multiplicity are encountered mainly in catalytic reactors used to carry out exothermic chemical reactions. The efficient utilization, operation and control of industrial reactors requires knowledge of all their behavioral features, such as all the possible steady states. The proposed analysis will provide a systematic approach to finding all the qualitative features of distributed parameter systems in which the interaction between the dispersion and chemical kinetics may lead to multiple steady state. This could guide the experimentalist in finding new and more profitable states and eneable the rational development or more reliable and safe control and start-up policies. The methodology developed in this work will be useful also in other areas in which the interaction between diffusion and chemical kinetics can lead to steady-state multiplicity such as combusion, chemical vapor deposition, high performance ceramic materials and design of corrosion resistant alloys. Many chemical and physical systems may reach different steady states under the sam operating conditions. A common feature of all these systems is the occurence of nonlinear flux-force relations and some feedback (communication) mechanism. The feedback in chemical systems may be caused by an auto- accelerating or self-inhibitory reaction step or feedback is due to changes in either the physical properties or reaction rate with conversion. The main difficulty in analyzing and predicting the multiplicity features of practical systems, in which several reactions occur simultaneously, is that the governing equations are highly nonlinear and contain a very large number of parameters. Thus, it is extremely difficult, and often practically impossible, to determine the multiplicity features from a parametric study in the multi-dimensional parameter space, without having suitable theoretical guidance. These mathematical difficulties have restricted most studies to limiting cases in which only a single reaction occurs, even though most practical problems associated with steady-state multiplicity are encountered in systems in which several reactions occur simultaneously, and are due to the "taking over" by an unwanted reaction. The theoretical work will center around modeling intra - as well as interpractical temperature gradients in individual catalyst pellets (thus introducing distributed parameter analysis) as well as modeling of the multiplicity features of packed bed tubular reactors. The experimental work will be used to verify these models. This information will enable a safer and more reliable design of control and start-up policies. The PI is one of the leaders in this area and the facilities are excellent. A three year continuous grant is recommended at $73,340 out of FY 86 $70,537 out of FY 87 funds, and $69,966 out of FY 88 funds.