Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.

Exploring the physicochemical basis of cheese texture, rheology and functionality, with emphasis on cation-casein interactions

The physicochemical properties of cheese and milk gels are greatly influenced by molecular interactions between the casein proteins involving calcium. Novel experiments were designed to investigate the relationship between insoluble caseinbound cations and rheological properties of Cheddar cheese and rennet-induced milk gels. Cheddar cheese and rennet-induced milk gels were supplemented with Mg2+ or Sr2+ to compare their effects on their rheological properties to those previously reported in literature for Ca2+ supplementation. Sr2+ displayed behaviour similar to Ca2+ as observed by its ability to increase the rigidity of cheese and rennet milk gels and also decrease cheese meltability. Mg+2 had no influence on cheese rheological properties and was greatly inferior to Ca2+ and Sr2+ in its ability to increase rennet milk gel elasticity. Cheddar cheese was supplemented with the calcium-chelating salts trisodium citrate, disodium hydrogen phosphate or disodium EDTA, in an attempt to reduce the CCP content of cheese and thereby modify its rheological and functional properties. TSC and EDTA were successful in decreasing cheese CCP, whereas DSP caused an initial increase in CCP content. Cheddar cheese was supplemented with chlorides of iron, copper and zinc at salting to investigate the effects of concentrations of these elements in excess of those found innately or commonly in fortification studies, with emphasis on mineral equilibria changes and resultant alteration of rheological properties. Zinc addition was the only added metal that significantly influenced cheese rheological properties, leading to an increase in cheese rigidity and decreased cheese melt at elevated temperatures. Gum tragacanth was used as a fat-replacer in the manufacture of reduced-fat Cheddar cheese, in an attempt to improve the rheological, functional and sensory properties of reduced-fat Cheddar. Overall, the experimental work reported in this thesis generated new knowledge and theories about how casein-mineral interactions influence rheological properties of casein systems.