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Fluidized bed technology is employed in a wide range of industrial applications, covering the pharmaceutical, food, chemical and petrochemical industries as well as the mining and power generation industries. However in most industrial applications of fluidization, the suspension consists of non-spherical particles of different diameters and sometimes-different densities. Computational Fluid Dynamics modelling has been recognized by several in academia and industry as an indepensible tool to study multiphase systems including fluidization. CFD models that describe gas solid flow systems can be formulated at different levels of mathematical detail. The use of the Eulerian-Eulerian approach has been considered as the highest possible level of continuum modelling where both the fluid and particle phase are treated as interpenetrating continua and mass and momentum conservation equations are solved for each phase. The Eulerian-Eulerian approach has been successfully used by many researchers for tackling problems relating to the modelling of gas-solid fluidized beds coupled with using the kinetic theory of granular flow for the description of the solid phase as derived from the kinetic theory of gases. However, most of the CFD investigations carried out to date have been limited to the study of the fluidization behaviour of mono-component gas-solid systems of modelling type materials (e.g. Ballotini). The aim of this thesis is to address the computational modelling of mono-component and binary gas-solid fluidized beds with particular focus placed on industrial materials. This work, sponsored by Huntsman Tioxide, is concerned with the titanium refining industry where a bubbling fluidized bed is used for extracting titanium from naturally occurring ore. The refining process begins in a fluidized bed with the chlorination of titanium rich rutile ore which is composed of many constituents. Due to the size and density differences of all the feedstock components used in the process, there are industrial concerns about the pervasiveness of dead zones within the fluidized bed as a result of feed stock segregation. Thus, the objective of the work is to develop a model capable of predicting the degree of mixing and segregation in the fluid bed system. To this end, the following powders, slag, natural and synthetic rutile, belonging to the Geldart Group B classification and used as feedstock in the Huntsman Tioxide chlorination process, were provided for the experimental and computational investigations in this project. This work presents a new hydrodynamic model for the CFD simulations of the mono-component and binary industrial materials using a commercial code (CFX4.4). The modelling development allowed the assessment of suitable governing equations for the description of the internal stress relevant to the solid phase(s), the fluid-particle and particle-particle interphase exchange terms. For the mono-component systems, a new expression for the fluid-particle interaction term has been developed based on the fluid bed elasticity concept originally proposed by Wallis (1969). Consequently, the procedure followed to obtain a stability criterion was re-examined analytically and subsequently numerical simulations were performed to validate the ability of the model to predict the fluidization behavior of the materials investigated. As part of the development, a comparison was conducted between the model proposed in this thesis and the granular kinetic theory model in order to assess the impact of the collisional stresses on the numerical predictions. The new modelling approach was subsequently extended to the modelling of binary systems using the three fluid approach, where a separate momentum equation is solved for the fluid and each solid phase. This part of the study also assessed the effect of the particle- particle drag force on the dynamics of the binary system by comparing three different closures available in literature and catering for this contribution against a reference test case where such contribution was not accounted for. Similar to the approach followed for the mono-component systems, a sensitivity analysis on the effect of the collisional stress on the simulations of the binary systems was also performed. Furthermore, a sensitivity analysis on grid and time step resolution was also carried out. Results of these analyses enabled the qualitative and quantitative numerical investigation into the mixing and segregation behaviour of the binary mixture of the industrial materials provided for this project. In this investigation, three different average compositions, corresponding to the average mass fraction of jetsam particles of 0.25, 0.50, 0.75 in the bed were considered, so that the hydrodynamic behavior of three binary mixtures in all was studied. In addition, a new fluid-particle interaction force closure for well mixed binary systems based on the two-fluid approach, where mixture continuity and momentum equations are employed in the description of the solid phases, was also derived and corresponding CFD simulations are carried out to assess the reliability of the derived mixture models.

This thesis discusses recent advances towards the grand unification of process design, con- trol and operational optimization via multi-parametric programming techniques. First the PARametric Optimization and Control (PAROC) framework is presented together with a prototype implementation for the development of advanced receding horizon policies via multi-parametric programming and their closed-loop implementation. It is shown how state- of-the-art multi-parametric programming algorithms are utilized for the development of explicit optimization policies for a variety of problems (including control, estimation and scheduling) based on high-fidelity models and model approximation steps. Two developments are presented towards the integration of design, control and opera- tional optimization within PAROC; (i) the integration of design and control and (ii) the integration of scheduling and control. For (i) we develop receding horizon optimization for- mulations where the design variables are simultaneously considered, resulting in explicit, design–dependent policies which are then included within a Mixed-Integer Dynamic Opti- mization (MIDO) algorithm minimizing operational and investment costs. For (ii), we de- velop scheduling strategies where the process dynamics and corresponding controller designs are simultaneously considered, resulting in explicit control–dependent scheduling schemes. Surrogate/approximate models are proposed to address the time–scale mismatch between the mid–term schedule and the short–term control optimization problem. Finally, the inte- gration of (i) and (ii) is shown within an overall dynamic optimization problem. The developments are presented via a domestic cogeneration heat and power (CHP) system example and case studies of a tank, a continuously stirred tank reactor and a binary distillation column.

Experiments were carried out using glycerol-water and distilled water test solutions in a steam heated, stainless steel, natural circulation, vertical tube evaporator (i.d. 0.488 in., o.d. 0.731 in., heated length 4 ft.). The test liquid entered at its boiling point and the effects of concentration, overall temperature difference, and submergence on heat transfer were investigated. Maxima in heat transfer coefficients, due to the formation of minimum sized bubbles, were found to fade with increasing temperature difference and decreasing submergence because of the increasing influence of the forced convection mechanism over the nucleate boiling component. Experimental results from distilled water, and isopropyl alcohol-water, and normal propyl alcohol-water mixtures (from two previous workers) as well as those from water-glycerol were correlated by a modification of the Lockhart and Martinelli Parameter which included temperature and surface tension factors, and a term accounting for the distinctive features of boiling binary mixtures.

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