UMIST Polymer Engineering Dept Report

S F Bush

Basic Principles of the Model

The basic principle is to use the finite cell method described in Bush and Dyer 1976 with some of the boundaries of a cell potentially defined within the computation. This approach keeps the flow part of the computations simplest, in turn enabling the model to represent the considerable chemical and phase change complexity adequately. The finite cell method consists of three elements:

1. definitions of cells as regions of solution space to which average values of intensive conserved quantities apply. A cell need not be simply connected;
2. transport of the conserved quantities from a cell is deemed to occur at the average values;
3. For calculating changes across the time and space interval (n, n+1) the conserved quantities are assigned values at (n+1): all other quantities (including transport quantities) are assigned values at n. This results in a matrix inversion for the conserved quantities.

Application to the Soot Formation Problem

The following physical and chemical processes are important:

1. liquid fuel injection, spray development and the simultaneous creation of a weapon jet;
2. droplet evaporation with potential approach to the critical temperature, and fractionation of the fuel components;
3. simultaneous cracking and oxidation of hydrocarbon molecules in fuel;
4. soot formation by polycondensationof cracked fragments and hydrogen abstraction from hydroboiling aromatic components in the fuel.

Systems Technology Group paper, ICI Europa

S F Bush, revised 1st June 1978 and again on 31st January 1979.

Summary

The paper describes ideas of a mathematical nature which have been developed and applied to the fundamental design of process systems, the emphasis being on those in which there is combined flow and chemical or physical state changes. The development has been designed specifically for digital computation and allows the structure of any particular model, especially its geometry and the basic processes of physical or chemical change to be as accessible to alteration as individual parameter values commonly are. The structure is designed to simulate real systems directly rather than their differential equations and in this way avoids or mitigates some important problems of a numerical-mathematical character. Examples are given. The structure is designed also to facilitate the elucidation of experimental data, particularly its scale-dependency. The overall development is exemplified by the experimental and computational analysis of chemical kinetics problems treated in Bush and Dyer (1976).

Paper published in the Proceedings of the Royal Society (A. 351, 33-53) 15th January 1976.

S F Bush with P Dyer

Thanks are due to the late Mr C A J Young, FRS, who communicated the paper.

Summary

Methods for the experimental and computational analysis of complex kinetics problems are described. Two examples which have been applied to industrial-scale design and operation are taken: high temperature chlorocarbon rearrangement and hydrocarbon cracking. Surface mechanisms are included within the treatment.

The experiments were based mainly on the continuous-flow uniform reaction cell which allowed precise control over physical conditions up to the temperature limit of interest, 1000 ^oC. The computational treatment is based on the development of a mathematical model system which permits a model structure to be varied at will, enabling radically different mechanisms to be rapidly examined. Using the methods, many thousands of computations have been carried out on a variety of systems of widely differing structures for the purposes of both research and design.

In Appendix A the model structure was used. In Appendix B the minimisation of the sum of squares by Gauss’s method was used.

See also the other items in this section Mathematics & Computation.

Group II Research Note, ICI Central Instrument Research Lab.

S F Bush with M J Shires and M A L Sita-Lumsden.

Summary

Results obtained from an examination of various aspects of the PTA process are given. These include esterification rate measurements, CP5 residence time measurements, an elucidation of the thin film results, a design of pre-polymeriser coil, a relationship between throughput, revolution speed and plate spacing in the CP5 design and an outline of a first model of the batch esterifier.