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Traditionally the reactor is recognised as the `heart' of a chemical process system and hence the focus on this part of the system is usually quite detailed. Steam reforming, however, due to the `building block' nature of its reaction products is unusual and generally is perceived as a `utility' to other reaction processes and hence the focus is drawn " towards the 'main' reaction processes of the system. Additionally as a `mature' process, steam reforming is often treated as sufficiently defined for the requirements within the overall chemical process. For both primary and secondary steam reformers several models of varying complexity were developed which allowed assessment of issues raised about previous models and model improvements; drawing on the advancements in modelling that have not only allowed the possibility of increasing the scope of simulations but also increased confidence in the simulation results. Despite the complex nature of the steam reforming systems, a surprisingly simplistic model is demonstrated to perform well, however, to improve on existing designs and maximise the capability of current designs it is shown that more complex models are required. After model development the natural course is to optimisation. This is a powerful tool which must be used carefully as significant issues remain around its employment. Despite the remaining concerns, some simple optimisation cases showed the potential of the models developed in this work and although not exhaustive demonstrated the benefits of optimisation.

Current technologies in chemical engineering focus on process intensification in order to remain cost efficient in an environmentally responsible manner. Catalytic Plate Reactors (CPRs) emerge as a novel design for intensification of conventional chemical reactors. Such a design consists of catalytically coated metal plates so that exothermic and endothermic reactions can take place in alternate channels, which have the channel height of order of millimetres and the catalyst thickness of order of micrometers. CPRs combine reaction with heat transfer in an intensified manner, representing a feasible alternative to conventional reactors. The reduced dimensions of the reacting channels minimise heat and mass transfer resistances leading to significant volume and catalyst amount reduction in comparison to conventional reactors. Suitable applications for CPRs include autothermal coupling by means of indirect heat transfer of strong endothermic processes such as hydrocarbon steam reforming, dehydrogenation, or catalytic cracking with an exothermic process, usually catalytic combustion. Despite their attractiveness CPRs have not been yet implemented in practice, and only a few experimental and theoretical studies exist. Although CPRs show important advantages compared to conventional reactors, in order to become a viable alternative it is necessary to demonstrate their feasibility and reliability. This work is an initiation in the study of CPRs. Its main objective is oriented towards formulation of accurate mathematical models utilised further to investigate such reactors for illustrative case studies. Different reaction systems are considered and explored using parametric studies. The study of the system ethane-dehydrogenation - methane combustion revealed that the ratio of catalyst loading for the two reactions is a key variable and must be carefully adjusted in order to avoid severe hot or cold spots that can lead to either reactor run-away or extinction A metallic wall with a thickness of 2 mm, due to its high thermal conductivity, makes possible an efficient heat transfer between the endothermic and exothermic channel for small temperature differences. Among all potential applications for CPR, small-scale hydrogen production is favoured due to an increasing demand of hydrogen for fuel cells. Thus, hydrogen production in a CPR from steam-reforming of methane coupled with methane catalytic combustion was investigated. It was shown that a reduction in the reformer volume by a factor of 150 and reduction for the necessary amount of catalyst by a factor of 85 could be achieved. The effectiveness factors for the chemical reactions of the reforming process are about one order of magnitude higher than in the conventional process, proving a significant reduction of intraphase resistances. The short distance between the heat source and heat sink increases the efficiency of heat transfer. The influence of channel height and catalyst thickness on reactor behaviour was also addressed. It was shown that the intraphase resistances are important and cannot be neglected. In addition, the size of channel height has to be correlated with care with the flowrates and the amount of catalyst necessary to achieve desired CPR performance. A comparison between operation in co-current and counter-current showed that overall, the heat generation and consumption is balanced better for co-current operation than for counter-current one. Although, the counter-current flow arrangement may provide better thermal efficiency, due to opposite reactant concentration depletion along the reactor local heat balance proves difficult to achieve. Successful counter-current operation needs to use a non- uniform catalyst distribution as a degree of flexibility in adjusting the rate of heat generated and consumed. Another objective of this thesis is to find criteria to identify suitable ranges for CPR design parameters and to evaluate if the reactor has a reliable and stable operation. Parametric sensitivity analysis was utilised to define such criteria and to identify the most important parameters that can affect CPR behaviour. Among the parameters studied the strongest influence comes from the activation energies followed by the inlet temperature. Sensitivity to inlet composition and velocities have moderate effect, while the lowest sensitivity was found with respect to geometrical parameters and wall thermal conductivity. A generic procedure for CPRs design is summarised based on the understanding gained during the present work. The procedure includes preliminary, detailed and optimal design steps which are shortly described and discussed. It was also aimed to use mathematical modelling in order to aid experimental work concerned with the study of catalytic combustion in small channels. Simulation of a 2 mm-diameter reacting channel having the catalyst coated on the walls, demonstrated that immersing the channel in a fluidised bed can keep the channel wall in almost isothermal conditions. It was also shown that the axial velocity profile does not affect the model accuracy. In addition, CFD simulations showed that an expansion-contraction geometry for the channel inlet eliminates recirculation patterns and minimises the experimental errors due to entrance effects.

In the past two decades a depletion of rich ore materials has led to a decrease in mining productivity and a commensurate increase in costs, as the industry moves to extraction from lower economic ores. To sustain productivity, these inherently higher energy costs and expenditures must be limited by ensuring a deep understanding of ore material composition, and optimization of extraction processes. To this end, this thesis is aimed at optimising the thermal decomposition process of cobalt-rich pyrite sourced from the Thackaringa mine in Broken Hill, being one step in the patented process of sulfur and cobalt extraction by our industry partner Cobalt Blue Holdings (Ltd). The precursor material to thermal treatment was a pyrite ore concentrate powder constituting a complex multiphase composition, which needed to be characterized in terms of materials present and particle size distribution to identify influences on pyrite thermal decomposition to pyrrhotite. Main phases of pyrite (82.7(3) wt.%), albite (8.3(2) wt.%), quartz (4.96(12) wt.%), pyrrhotite 4M (3.06(10) wt.%), and rutile (0.923(14) wt.%) were identified and found consistent across a 50 kg aliquot obtained from the ‘Pyrite Hill’ subsite. Particle size distribution is broad (1 - 1000 µm), with 50(8) wt.% of the available pyrite manifesting in the 106 - 250 µm range, which was an essential result given how particle size influences the underlying ‘unreacted core’ reaction mechanism associated with pyrite particle decomposition. Powder X-ray diffraction was the primary characterization method used here, whereby a 7-min ball milling preparation technique was optimized to attain reproduceable results within 0.3 wt.% for main phases. Analysis of thermal treatment indicated no change in gangue phases when treated between 450 - 750 °C. Reaction was seen commencing > 450 °C, though sometimes as low as 300 °C in the special case of reduced particle size and ideal particle-gas interfacing known to improve pyrite decomposition. Activation energies, as in the Arrhenius relation, of 220 - 250(50) kJ/mol and pre-exponential factors between 1.9(2)x1012 - 2.2(2)x1015 sec-1 were obtained and coincide with those found in literature. The progression of reaction is best described by a combination of volumetric shrinking sphere mechanics at < 50 - 70 % pyrite conversion, and 3-dimensional diffusion limiting mechanics at > 50 - 70 % pyrite conversion when treated between 450 - 550 °C. Enhancing interaction between concentrate particles and carrier gas appears to be greatest influence on thermal decomposition across all experimental designs increasing degree of reaction by 22% and 58% at 600- and 650 °C respectively.

We analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency.