ANALYSIS OF AXIALLY DISPERSED SYSTEMS WITH GENERAL BOUNDARY CONDITIONS
Abstract
Axial dispersion models have been a useful implement for the analysis of many continuous flow systems because of their capacity to amend the predictions of the plug flow model without loss of the latter's unidimensional simplicity. For proper representation of the actual flow systems, the conditions to be specified at the equipment boundaries must account for the influence of events in regions external to the equipment on the events within the equipment and vice versa. In this connection, the boundary conditions due to Danckwerts have been the subject of considerable debate in regard to their applicability. Most arguments in their justification for steady state analysis render them inapplicable for transient situations except when the extensions of the tubular equipment are unmixed. A series of alternative, physically reasonable conditions (which imply the Danckwerts conditions at steady state) to be used when there is mixing in the extensions are discussed. The transient problems formulated for various possibilities have been solved using the eigenvalues and eigenfunctions of associated axial dispersion operators. The eigenfunctions are used to construct integral transforms (similar to the Fourier transform) and their inverses which are employed to solve the transient problems. The eigenvalues in general consist of continuously distributed eigenvalues and discrete eigenvalues. The transient problems are of relevance in continuous flow systems used for a wide class of chemical engineering operations such as heat or mass exchange processes and chemical reactions. Several practical applications of the analysis are discussed. The analysis reveals many interesting features of the non-reactive and reactive axially dispersed systems. The practical utility of the analysis lies in prediction of dynamic behavior and control of continuous tubular flow systems and in identification of mixing parameters from experimental data on residence time distributions. The stability characteristics of steady states in adiabatic tubular reactors have been investigated using the information on the distribution of eigenvalues of certain 'linearized' axial dispersion operators. Stability regions of the locally stable steady states have been identified. This identification requires only prior knowledge of concentration and temperature profiles for various steady states.
Degree
Ph.D.
Subject Area
Chemical engineering
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