A Study of mathematical models for pseudo-homogeneous chemical reactors

Abstract

In the pseudo-homogeneous models of chemical reactors, one assumes that the content of the reactor is homogeneous. These models are categorized as two-dimensional (axial and radial changes occur) and one-dimensional models (only axial changes occur). In Chapter 1 we give a short survey of the existing literature. We also propose a modification of the one-dimensional model to reconcile the boundary conditions of the problem with the practical situation. Various numerical methods to solve the problems are also discussed. In Chapter 2 a sufficient condition is derived which guarantees uniqueness for the one-dimensional problem. This result holds for general kinetics. An improved a-priori upper bound for the temperature solution is derived and this result is used to find an upper bound on the Damkohler-number which gives an improvement of 10-30 times on existing results. Upper and lower function bounds on conversion are constructed and it is used to find a lower bound on the Damkohler-number. This result is new. In Chapter 3 the bifurcation behaviour of the one-dimensional, two-dimensional and the modified one-dimensional model is examined numerically. A new method is introduced for the construction of an arc of limit points. This method enables one to examine the multiplicity behaviour of the problem as a function of the parameters. The last chapter deals with the sensitivity of the solutions. Existing criteria are evaluated and we point out their shortcomings. We propose new criteria to evaluate sensitivity a-priori and numerically.