This work presents a numerical model for simulating the response of a geothermal reservoir to exploitation. The techniques developed are more efficient and in many ways superior to those of previous investigators. The model is capable of yielding a description of transient mass and heat flow in either a one- or two-dimensional reservoir defined by Cartesian or cylindrical coordinates. The techniques enable simulation of a geothermal flow in all three thermodynamic states – compressed water, two-phase and superheated steam regions – and transitions between these states. The model is able to simulate a geothermal system where the presence of carbon dioxide as a second component influences exploitation response. Results are presented for a range of reservoir states. The effects of different physical parameters are considered. The usefulness of the model for looking at real systems is demonstrated by simulating the development of Wairakei and Broadlands geothermal areas in New Zealand.

This thesis considers the scattering of small amplitude water waves, obliquely incident on a set of floating elastic plates occupying the entire water surface. The problem is twodimensional and assumes invariance in the width of the plates. All non-linear physical effects are neglected. The plates are floating on a body of water of finite depth and each plate has uniquely defined properties. The problem is formulated by imposing boundary conditions on the eigenfunction expansion of Laplace’s equation. A set of transmission and reflection coefficients is generated, which is solved by applying the edge conditions and matching at each plate boundary. We label this solution method the Matched Eigenfunction Expansion Method (MEEM). The problem is solved for a variety of edge conditions including free, clamped, sliding, springed and hinged. To verify the MEEM results, the problem is also solved using a Green Function Method. The convergence of the two methods is compared and found to be almost identical. The MEEM is used to simulate wave–ice interaction in the Marginal Ice Zone (MIZ). The model removes the resonance effects and predicts that the transmitted energy is independent of floe length, provided the wavelength is more than three times the floe length. The model predicts an exponential decay of wave energy with distance of propagation through the MIZ, which agrees with experimental findings. The results have been summarised in a graph with the attenuation coefficient expressed as a function of period for various floe thicknesses. We also provide an estimate of the attenuation coefficient using an approximation theory. The displacements of the MEEM are compared against a series of laboratory experiments performed in a two-dimensional wave-tank and show good agreement. The attenuation model results are compared against a series of field experiments carried out in the Arctic and off the West Antarctic Peninsula. Generally, the decay rates of the model agree well with the field experiments in diffuse ice. We suggest that factors other than wave scatter are relevant in models of wave-attenuation in non-diffuse ice.

This thesis is a study of the large scale flows of water and heat which give rise to the geothermal fields in the Taupo Volcanic Zone (TVZ), New Zealand. To carry out this study, a super-critical equation of state module has been developed for the geothermal simulator TOUGH2, which can describe the flow of water at the conditions expected deep in the TVZ. The code is used to simulate the behaviour of a range of idealised TVZ models in 2D and 3D settings. Hydrothermal plumes which remain stable for periods comparable to the lifetime of the TVZ can occur when there is a contrast between the high permeability of the inner TVZ 'infill' region and the lower permeability exterior region. In this case, downflows of cool surface fluid in the inner TVZ 'sweep' the geothermal heat across the TVZ at depth to the permeability barrier, where the heated fluid ascends to the surface in discrete plumes. This behaviour occurs in 2D models, where separate plumes form at each side of the high permeability infill region, and also in 3D models of caldera-like structures, where perhaps four hot plumes can form around the perimeter of the caldera. This notion is then applied to the complete TVZ hydrological system, where a permeable ‘envelope’ is defined by the location of the Taupo Fault Belt and the currently known volcanic centres in the TVZ. The permeability within this envelope varies spatially according to the geothermal heat flux, and the region outside has relatively low permeability. The spatial variation of the geothermal heat flux is obtained by summing the measured heat flows from the geothermal fields for a number of areas across the TVZ. In this model, the geothermal fields form about the boundary of the envelope, as in the TVZ, and bear a striking resemblance to the actual TVZ geothermal fields. Finally, a new simulation code, NaCl-TOUGH2, is developed to provide a tool for future modelling involving the commonest chemical species in the TVZ - salt. The code incorporates the complete phase diagram for salt-water mixtures and involves liquid, vapour and solid phases over a wide range of temperatures, pressures and salt concentrations. The code is used to solve a number of simple geothermal and mathematical problems.

The forest harvesting problem, FHP, is described. A review of the existing literature is presented along with an analysis of the strengths and limitations of various attempted solutions. The diversity of model evident in recent papers is noted. The difference is explained between a strategic model that sets long-term harvesting goals in terms of total area to be cut each year, and a tactical model that produces a short-term schedule of actual blocks. Special attention is devoted to the development of FRI’s Forestry-Oriented Linear Programming Interpreter, FOLPI, which is currently used to formulate an LP model of the strategic planning problem. Reasons are presented for the desirability of an integrated model, embracing both strategic and tactical decisions, which is capable of optimisation. Accordingly the project then proceeds to a thoughtful and detailed construction of such a model. Particular care is taken to examine the status and function of FOLPI within this model. A column generation algorithm is then developed to solve the relaxed linear program formulation. Finally powerful constraint branching techniques are utilised to obtain the desired optimal solution to the integrated model. Throughout the development of the project the Whangapoua forest in Coromandel, New Zealand has been used as a case study. A concluding section presents numerical output from some of the exhaustive computational analysis associated with this application.

Alumina performs several functions in a modern smelter - it is used to scrub the pot gases to remove fluoride, acts as a thermal insulator on top of the cell and, when added to cryolite-based electrolytes, it is the raw material used to produce aluminium. Alumina is also expected to have good flow and handling properties, and dissolve well in the bath. Unfortunately, it does not always dissolve rapidly and this leads to the formation of "sludge", which creates operating disturbances in the cell; it is difficult to remedy this problem without a basic understanding of the process of alumina dissolution. Consequently, the objective of the work presented in this thesis was to develop an apparatus and technique that would allow the dissolution behaviour of powder alumina to be measured as realistically and objectively as possible, and then determine the important factors affecting dissolution. The method developed involved the merging of three different techniques: ● electroanalytical measurement of dissolved oxide concentrations ● recording of the associated thermal phenomena ● visual observation of the interaction of alumina with the bath which were then used to investigate the effect of a range of alumina properties and smelter operating conditions on dissolution behaviour. A series of dissolution parameters was selected to evaluate the relative dissolution behaviour of the different variables. It was found that slow dissolution behaviour resulted primarily from poor feeding and/or dispersion, coupled with poor heat transfer in the first few seconds of the dissolution process. If the flow properties of the alumina were good, alumina flowed easily out of the dropper on to the surface of the bath forming relatively thin but well-distributed rafts. If not, alumina could flow out into a localized area producing very dense rafts which clumped together and eventually sank to the bottom forming sludge. properties such as loss on ignition enhanced the dispersion of the alumina through the release of volatiles, which caused the alumina to "effervesce" on the surface. Conversely, bulk density aggravated the clumping problem as the density of the formed rafts increased with increasing bulk density. Good feeder design can help to counteract deficiencies in the flow properties of an alumina, if the importance of wide coverage and the imparting of a horizontal velocity component to the alumina are kept in mind. It was also found that if the bath agitation was increased, either by increasing the amount of existing stirring or by reducing the bath volume in the feeding area for a given bath velocity, the initial heat transfer to the alumina could be dramatically improved. The presence of bath superheat was important for maintaining optimum heat transfer conditions for fast dissolutions, as alumina was found to dissolve better when a higher proportion of the heat required was supplied from the bulk of the liquid bath as opposed to localized freezing. Increasing the initial alumina concentration in the electrolyte retarded the dissolution process, with the retardation becoming increasingly more significant at higher concentration values. Similarly, reducing the cryolite ratio, which also decreased the alumina solubility, resulted in the dissolution being inhibited in the later stages, as more alumina dissolved. In situations where the mass transfer in the bath was improved, the impact of these concentration effects was minimized. The video recordings were useful for indicating potential operating difficulties with the samples, such as excessive emissions and flow problems. Six different raft formations, characterizing the degree of bath surface coverage and the raft density or cohesion, were identified from the videos and the aluminas were classified accordingly. Preliminary heat balance calculations were performed using the data obtained in this study and were used to estimate the heat of dissolution for α-Al2O3, for a variety of alumina concentrations in cryolite-based electrolytes. The results indicated heat values of 112±15 and 55±5 kJ mol-1 for alumina concentrations in the bath of 0.43 and 2.83 wt% respectively. Further work is necessary to refine these calculations, however. Reacted ore was found to dissolve more slowly than parent virgin alumina but it was difficult to ascertain which property caused the difference - whether bulk density, flowability, influence of HF, or presence of other impurities. As a result, it is recommended that a series of dissolution runs be performed on reacted samples of different compositions to establish which property associated with reacted ore causes the problem.

The onset of convection in a horizontal fluid layer, heated from below, is, examined by means of perturbation analysis. The resulting eigenvalue system of equations is solved by means of a new extension of a Fourier series technique. Two sets of coupled effects are investigated: (i) thermal buoyancy and surface-tension effects, and (ii) thermal buoyancy and solute buoyancy effects. For the first set of effects the magnetohydrodynamic problem is also studied. For the surface-tension problem, attention is focussed on the case where the lower boundary is a rigid conductor and the upper free surface is subject to a general thermal condition. It is found that for this care the surface-tension and buoyancy forces reinforce each other and are tightly coupled. Cells formed by surface tension are approximately the same size as those formed by buoyancy. The stream line patterns produced by the two agencies acting separately are again similar. When the fluid is electrically conducting and is in the presence of a vertical magnetic field, it is found that the field always has a stabilizing effect. When convection cells are formed in the presence of such a field, their horizontal dimensions are less than for cells formed in the absence of the field. The magnetic field accentuates the difference between the cells induced by surface tension and those by buoyancy, and thus reduces the coupling between the destabilizing forces. Increase of magnetic field causes the buoyancy cell pattern to become more symmetrical, but causes the streamlines in surface-tension cells to become bunched near the surface. When the magnetic field is large, the transition from one type of cell to the other type is extremely sudden, at least when the upper surface is a good thermal conductor. It has been found that, on the model considered, there can be no oscillatory for this problem. However, dimensional analysis reveals that, for a sufficiently flexible upper surface, oscillatory Instability might in fact occur. Finally the thermohaline problem, where the density varies with both temperature and the concentration of some solute, is studied. The eigenvalue equation is now found for general boundary conditions. The degree of coupling between the thermal and the solute effects again depends on the similarity between convection cells caused by the two agencies acting separately. (For one extreme case studied the coupling is zero for a certain range of parameters.) In this problem both monotonic and oscillatory instability can now occur.

The work described in this thesis represents an investigation undertaken with the two-fold purpose of (a) establishing the apparatus and techniques necessary for carrying out investigations into the response of metals to dynamic loading, and (b) examining the response of beta-brass single crystals to dynamic loading. The first part of the investigation required the development of basic apparatus for investigations of the type planned. This apparatus included a dynamic compression testing machine and apparatus for the production and preparation of metal single crystals. The second part of the investigation required the assessing of the existing knowledge of the static and dynamic properties of beta-brass and the planning of a programme aimed at contributing to this knowledge. A review of the existing literature is presented and a programme of tests is outlined. As a result of the investigation the following conclusions were drawn concerning the static and dynamic properties of beta-brass single crystals. The dynamic upper and lower yield stresses were found to be strain-rate sensitive and the upper yield stress increased by up to 4.5 times the static yield stress. The dynamic upper and lower yield stresses were found to be temperature dependent and to show the same temperature dependence as the static yield stress. Both increasing strain-rate and decreasing temperature raised the yield stress. The dynamically deformed material showed large yield drops whereas the statically deformed material did not. Both the static and dynamic work hardening behaviour were found to be orientation dependent. The rate of work hardening for the static tests increased with decreasing temperature whereas that for the dynamic tests did not. The dynamic work hardening behaviour was insensitive to strain-rate. At strains greater than 4 per cent the dynamically deformed material was found to be softer than that statically deformed the same amount. Both the statically and dynamically tested material deformed by slip and the formation of deformation bands. Twinning was not observed. Jerky flow was found to be composition and temperature sensitive.

Aluminium smelting is an energy intensive process, and as a result there has been considerable and ongoing research over a number of decades on the energy efficiency of various aspects of the process. One of the most important measures is current efficiency, which has been shown to have direct relationships with current density, cell temperature, electrolyte chemistry, and anode-cathode distance. The effects of these variables on current efficiency are generally accepted, however there remains debate over the influence of the alumina concentration in the electrolyte on current efficiency. This research relied upon the development of a laboratory scale aluminium smelting cell where the current efficiency was measured via sampling of the product gases. A modified oxygen balance was used, with gas analysis performed using online mass spectrometry. The findings of this research agreed with the accepted current efficiency trends, showing a current density influence of 17.25 %CE per A/cm2, over the range 0.3 and 1.1 A/cm2. The influence of electrolyte chemistry was -7.8 %CE per unit cryolite molar ratio, between cryolite ratios 1.99 and 3. The anode-cathode distance was shown to have no influence on current efficiency in this cell, contradicting the established findings, however this was expected because of the design of the cell with no metal pad at the cathode and therefore constant mass transfer conditions at all the anode-cathode distances used. The most significant finding concerning current efficiency is that the variation with alumina concentration is so small, -0.0376 %CE/wt% Al2O3, that there is effectively no influence. While in many other studies an influence was found, the values and direction of the relationship varied. This suggests that in many cases the observed variation in current efficiency was actually caused by a change in the level of stability in the cell, by processes such as dissolution of sludge from the cathode or the thermal disturbance of alumina feeding, whereas in this research the cell was stable under all operating conditions.

This thesis reports investigations into the stiffness of and energy loss in two series of prestressed concrete beams subjected to reversing sinusoidal cyclic end rotations of equal magnitude and direction. These rotations produced equal moments at the ends of the beams and zero moment at the centre which led to uniform shear along the length of the member. Special care was taken in the manufacture of the two series of beams to ensure essential uniformity of the properties of the beams one to another. The end rotations and the resulting moments where measured by suitable transducers and traces of the moment versus rotation relationship were recorded on an X-Y recorder at intervals during each test run. The amplitude of rotation was progressively changed during each test to ensure a steady value of the end moments. From these recordings the changes in end stiffness and energy absorption were observed and recorded against the number of cycles of moment applied. Concrete strains near the ends of the beams were recorded during the tests. The end moments were expressed as a percentage of the “ultimate” moment which would be required to fail the beams in one reverse cycle of loading. The moment rotation properties of the beams were observed to change as the number of cycles of loading were increased, this change being more rapid for higher percentages of “ultimate” moment. The energy dissipation was found to increase with an increase in the frequency of the cyclic loading, It was considered that the greater part of the energy dissipation arose from the material damping within the concrete. At higher percentages of ultimate moment, the number of cycles sustained before failure was found to increase when ties were inserted around the reinforcing wires. The results from the tests were analysed and an attempt made to relate the properties by the beans to the properties of the component materials of the prestressed members. A theoretical model was postulated with certain simplifications of the relationships of the material properties and a computer program designed to simulate qualitatively, the behaviour of the beams tested. A non-linear hysteretic stress-strain relationship was assumed for the concrete in this analysis which gave similar stress-strain traces to these found in the experimental analysis.

The fermentation of sugars from biomass to produce liquid fuels is receiving widespread attention as a renewable source of energy. For such processes to become competitive with current alternatives, technology must be improved to increase the efficiency and productivity of the operation. Using ethanol fermentation by Saccharomyces cerevisiae yeast as a model system, two aspects of the process were considered in detail. The first aspect concerned the use of cell recycle in a continuous fermentation. A new technique was developed for the rapid settling of yeast cells in the fermentation medium and involved the addition of dense, inert particles to a yeast suspension at pH 4.5, followed by a rapid change in pH to 8.0 - 9.0. Large flocs formed immediately and settled rapidly, leaving a clear supernatant. Separations of 99.9% were possible, even at yeast concentrations of 50 g/l (dry weight) and increases in settling rate of up to 1600 fold were observed. When the pH was returned to 4.5, the flocs were destroyed. Seeded settling at constant pH was possible although the flocs were smaller, the settling rates were lower and significantly more seed was required. Flocculation was also found to be influenced to a greater extent by certain components in solution. Nickel powder was used extensively in these experiments although several other materials were tested, with ground iron sand showing potential for application on a larger scale. The pH switching technique for seeded settling was used to recycle yeast cells in a semi-continuous fermentation. Application of the technique to this and similar systems is discussed. The factors affecting yeast/inert powder flocculation is discussed and a model is proposed to explain the observed experimental behaviour for flocculation, both at constant pH and with rapid pH switching. The second aspect of ethanol production considered in this thesis was the distillation stage. Equipment and techniques were developed to obtain basic mass transfer information in binary or multi-component systems. A new design of evaporation cell was used to measure the evaporation of ethanol and water mixtures into an air stream in a wind tunnel. This enabled the effect of liquid concentration on evaporation rate to be studied dynamically from batch tests. Radiochemical labelling was used to measure liquid concentrations and proved to be a relatively simple, rapid and precise analytical technique. Coupled with the direct measurement of liquid displacement, precise information on the evaporation loss of both ethanol and water components was obtained. The pure component evaporation data agreed well with literature correlations and, for the binary liquid mixtures, good agreement was found between the experimentally determined mass transfer flux ratios and those predicted from Gilliland's solution to the multi-component gas diffusion equations. The velocity dependence of the overall mass transfer coefficients enabled estimates to be made of the distribution of diffusional resistance between the gas and liquid phases. For the ethanol-water system diffusion was gas film controlled and the overall mass transfer driving forces could best be represented in terms of vapour concentration.