Steady state method/treatment/analysi

Theoretical treatments for the analysis of complex electrode reactions in terms of elementary steps can be made, as in general chemical kinetics, by the steady state [3, 5, 7] or the quasi-equilibrium methods [4, 5, 47]. 

Abstract—The question of the multiplicity of the steady states of a chemical reactor was one of the concerns in the pioneering work ofBilous and Amundson. Their diagrams showed quite clearly the geometry of the situation, and this kind of analysis sufficed for many years. It remained for Balakotaiah and Luss, using the methods of singularity theory, to give a comprehensive treatment of the question. After a brief survey, we take up the case of consecutive first-order reactions and show that up to seven steady states are possible. 

A reverse kinetic problem consists in identifying the type of kinetic models and their parameters according to experimental (steady-state and unsteady-state) data. So far no universal method to solve reverse problems has been suggested. The solutions are most often obtained by selecting a series of direct problems. Mathematical treatment is preceded by a qualitative analysis of experimental data whose purpose is to reduce drastically the number of hypotheses under consideration [31]. 

To analyze a transient heat-transfer problem, we could proceed by solving the general heat-conduction equation by the separation-of-variables method, similar to the analytical treatment used for the two-dimensional steady-state problem discussed in Sec. 3-2. We give one illustration of this method of solution for a case of simple geometry and then refer the reader to the references for analysis of more complicated cases. Consider the infinite plate of thickness 2L shown in Fig. 4-1. Initially the plate is at a uniform temperature T, and at time zero the surfaces are suddenly lowered to T = T,. The differential equation is... 

Multiple Steady States and Local Stability in CSTR.—In the two decades since the seminal work of van Heerden and Amimdson, there has been vast output of papers conoemed with the dynamic behaviour of stirred-tank reactors. Bilous and Amundson put the van He den analysis of local stability of the equilibrium state on a rigorous basis by use of linear stability theory. Their method is similar to the phase-plane treatments of thermokinetic ignitions and oscillations discussed here in Sections 4 and 3 (and preceded them dironologically). The mass and energy balance for the CSTR having a single reactant as feedstock may be expressed as ... 

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