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    Mathematical modelling of fluid flow and heat and pollutant transport in a porous medium with embedded objects : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy (PhD) in Mathematics, Institute of Natural and Mathematical Sciences, Massey University, Albany, New Zealand
    (Massey University, 2018) Kubra, Khadija Tul
    How does heat and/or pollutant transfer from objects embedded in the ground depend on their size, shape and burial depth, and how does the dispersion of heat and/or pollution in groundwater aquifers depend on the soil properties, the speed of the groundwater flow, etc.? In detail, the aims of present study are: - To investigate how the size, shape and position of an object or set of solid or partially pervious objects, e.g., fluid tanks, pipes, etc., embedded in a porous medium affect the local speed and shape of the flow. - If heat is ejected from the solid objects e.g., fuel storage cylindrical tanks, radioactive waste reservoirs in deep geological formations, etc., and/or a pollutant is released from, or removed by, the pervious object, e.g., septic tanks, disposal of drums of contaminants, etc., how does the subsequent dispersal through a groundwater aquifer depend on the various parameters involved (e.g., the object size, object's burial depth, perviousness of the object, the aquifer's depth, the fluid flow rates, etc.)? - What is the effect of the non-homogeneity in matrix properties (e.g. permeability or hydraulic conductivity) on fluid flow, pollutant and heat transport rates? This study pursues answers to these questions. The porous medium fluid flow equations, and the advection-dispersion equations that model the heat and/or species transport, have coeffients that depend mainly on depth. Generally, analytic solutions are not possible. In order to investigate the effects of various objects of different shapes embedded in a porous medium, I have developed numerical algorithms and used some special mathematical techniques for two-dimensional models, namely conformal mappings within the framework of complex analysis. The velocity potential and (2-D) stream function satisfy Laplace's equation. Central and one-sided finite difference methods are applied to solve this equation subject to a chosen combination of constant-head or constant-flux boundary conditions. Results are discussed for various embedded shapes in homogeneous and layered groundwater aquifers. A Matlab command "contour" is used to depict the streamlines and equipotential lines, and the resulting temperature or pollutant concentrations. Steady-state and time-dependent forced convection heat/pollutant transfer from some cylinders embedded in groundwater are explored numerically using finite difference methods. The results show that the size, shape, position, perviousness and burial depth of the cylinder affect the pressure drop, as well as the pollutant and/or heat transfer. Moreover advection and dispersion depend on the permeability structure and the fluid speed.
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    Solute movement associated with intermittent soil water flow : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Soil Science at Massey University
    (Massey University, 1991) Tillman, Russell Woodford
    The movement of nutrients within the root zone of orchard crops is important in determining both fruit yield and quality. Currently much of the research on solute movement in field soils concerns movement of chemicals to ground water. Little attention has been paid to smaller scale movement. In this study the movement of solutes in response to intermittent soil water flow was investigated in columns of repacked silt loam in the laboratory and in a similar soil in the field. In the laboratory study a 5mm pulse of a solution of potassium bromide and urea in tritiated water was applied to columns of repacked soil, left for three or ten days, and then leached with 30 mm of distilled water. Twelve days after the solute pulse was applied, the distributions of water, tritiated water, applied and resident nutrients and pH were measured. The bulk of the bromide and tritiated water was moved to between 50 and 1 50 mm depth in both water treatments. As the nitrogen applied in urea was mainly in the form of ammonium after three days, the water applied then caused little movement of nitrogen. But the water applied after 10 days caused the nitrogen, now in the form of nitrate, to move in a similar fashion to the bromide. The soil solution anion concentration determined the amount of cations leached. Calcium and magnesium were the dominant cations accompanying the nitrate and bromide downwards. The added potassium remained near the soil surface. Given the soil hydraulic properties, the behaviour of water and solutes could be simulated by coupling the water flow equations with the convection-dispersion equation, and by using solute dispersion , diffusion and adsorption parameters derived from the literature. The model assumed the Gapon relationship for cation exchange, and that hydrogen ion production during nitrification reduced the effective cation exchange capacity. It was able to simulate closely the experimental data. Two field experiments were conducted. The first involved application of a 5 mm pulse of potassium bromide solution followed by 50 mm of water to pasture plots of contrasting initial water content. Twenty-four hours later core samples of soil were collected and the distribution of water and bromide measured. Bromide applied to initially dry soil was much more resistant to leaching than bromide applied to moist soil. The second experiment lasted 12 days and was essentially an analogue of the laboratory experiment. The final nutrient distributions however differed considerably from those obtained in the laboratory, due to non-uniform flow in the structured field soil. Coupling a mobile-immobile variant of the convection-dispersion model with a description of the water flow provided a mechanistic model. When combined with the submodels developed in the laboratory study describing nutrient interactions and transformations, this model successfully described the solute movement under the four different field regimes of water and solute application. Evaporation and plant uptake, and diffusion between mobile and immobile phases emerged as key processes affecting nutrient movement. It is suggested some control over nutrient movement is possible by varying the relative timing of water and fertiliser applications.