| Multi fluid contacting plays an important role in the chemical process industry with absorption, distillation, reactions, wastewater treatment, and biotechnology being but a few examples. Unfortunately, limited understanding of the factors governing the evolution of drop/bubble size and interfacial area in turbulent systems restricted the rational development of acceptable design and scale up methodologies for multiphase contactors (Prince and Blanch, 1990).; In simulating the size distribution of the dispersed phase, population balance (PB) is a well-established method. This activity was triggered by the fact that very little attention was given to the sources of errors encountered while using population balance equation (PBE) for simulating multi-phase systems.; The first part of this thesis examines the factors affecting the PBE numerical solutions. A systematic investigation of the factors affecting the accuracy of PBE (numerically integrated in both the time and drop-size domains) was undertaken using the analytical drop dispersion/coalescence model developed by Rod and Misek (1981) as a reference. The PB numerical accuracy and stability were improved by minimizing the Discretization errors in the time and drop size domains. Errors as high as 800% were observed to occur when the PBE were integrated using conventional approaches. Furthermore, unstable solutions were often encountered.; The method commonly used to describe the drop size distribution, DSD, (discretization in the drop size domain) was found to constitute a significant source of computational error. This was minimized by describing the DSD as a continuous function that is sampled at several points. The accuracy of the final solution was found to increase with increasing the number of sampling points, whereas the computational requirements were found to be adversely affected as the number of sampling points increases (particularly above 300 points for 0.25% error). An optimum number of 70 sampling points is recommended in order to achieve errors less than 1%.; Finally, the concept of quasi-steady state was introduced to the numerical solution of PBE in order to systematically identify the time at which integration should stop (in order to prevent wastage of computational effort and the propagation of round-off errors encountered at excessively long computational times). (Abstract shortened by UMI.)... |
