In this thesis, the practice of mathematical modelling is investigated. It has long been recognised that process modelling is a very imprecise craft. Because of the difficulty in representing complex physical phenomena as simple mathematical abstractions, modelling has evolved as a series of adhoc, subjective steps. The impact of this situation has often been the lack of credible and reliable mathematical models for optimal process design and operation. The goal of this work was therefore to search for a systematic methodology for modelling which will conceive models with the desirable attributes of simplicity, accuracy and functionality.
While the focus of this thesis is the development of a general modelling methodology, applications of the work are restricted to the modelling of startup and shutdown operations. Because of the complexity and critical impact on plant operation, startup and shutdown transients serve as practical examples where mathematical modelling is of value.
A new modelling methodology is proposed in this thesis which features a systematic method for model characterisation. In a two step procedure, a reference model is first built in which few simplifying assumptions are made. All conceivable physical phenomena are included in this model. Perturbation model reduction methods are then employed to identify the essential structure in this reference model. Redundant structure is then omitted from the reference model to produce a low order model with all of the desired attributes.
The key feature of this new modelling methodology is that it is systematic and a model is constructed which is commensurate with the modelling objectives. Exploitation of the reference model structure is the mechanism upon which this new methodology is based. A significant portion of this thesis is therefore devoted to the development of perturbation model reduction methods for structure identification.
Two major case studies are presented to illustrate the proposed methodology. In the first, a low order model is built for the simulation of the startup of a single stage evaporator process. The second case study involves the modelling of a three stage centrifugal compressor system for prediction of machine surge during shutdown. In both cases, an intimate knowledge of causality with the process and a substantial reduction in model size was achieved by exploiting latent model structure.
It was also recognised in this work that knowledge of process structure is of value in other situations. Two additional applications of model structure were investigated in this thesis. In the first the dependence of structure on the process parameters was quantified. The relationship between process parameters and the model structure was then used in a novel design algorithm. In this design method, the process parameters were selected to achieve a specified dynamic performance criteria.
The innovative contributions of this work to the field of mathematical modelling include: development of a systematic method for process characterisation; development of structural parameters for the identification of model perturbations within a mathematical model; the development of a continuation algorithm for association of model states with modes and the proposal of a novel process design algorithm based on the exploitation of model structure