In this thesis, we examine the equation describing fluid flow through saturated porous medium in order to develop a new method for approximating hydraulic head values in the subsurface. In particular, we show that under reasonable assumptions, the local explicit equation (LEE) method, an accurate, finite-difference based method that is highly sensitive to changes in the assumed location of hydraulic flow parameters, can be used to approximate hydraulic head values throughout a subsurface domain of interest. This forward solution of the fluid flow equation is solved using an altered finite difference scheme, designed to account for discontinuous jumps often encountered between subsurface material types. While the method is able to handle complicated discontinuities arising from the intermingling of various underground materials, the method determines values at nodes on an easy-to-use uniform Cartesian grid and only requires information from immediately adjacent points. The results of this research directly support the development of more accurate subsurface fluid flow models for use in a wide variety of real-world situations in areas such as water management, contaminant remediation and waste storage. Furthermore, the general development of the LEE method allows it to be used as an approximation technique for any equation where the media of interest encounters a jump.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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No description available.

This thesis presents the results of the investigations in two areas, i.e. non-Newtonian annular flow and cuttings transport in drilling annuli at various angles. In the first part of the thesis, a review of the fundamentals and the previous studies on laminar concentric annular flow of non-Newtonian fluids is given at first. Then two parallel theoretical studies are performed, respectively, on: a. Laminar eccentric annular flow of power-law and Bingham plastic fluids. In this analysis, a new method is used which treats an eccentric annulus as infinite number of concentric annuli with variable outer radius. The analytical solutions of the shear stress, shear rate, velocity and the volumetric flowrate/pressure gradient are obtained over the entire eccentric annulus. This analysis is useful in design of any engineering operations related to eccentric annular flow such as oil drilling operations. b. Laminar helical flow of power-law fluids through concentric annuli. A group of dimensionless equations are derived in this analysis for the profiles of the apparent viscosity, angular and .axial velocities, and for the volumetric flowrate. These equations are essential when one needs to simulate the helical flow conditions in various engineering operations. In addition, another group of dimensionless equations are also derived for pressure gradient calculations which can be used directly by drilling engineers to predict the reduction of the annular friction pressure drop caused by drillpipe rotation during drilling operations. The second part of the thesis is dedicated to the investigations into the problems directly related to cuttings transport through drilling annuli at various angles. First, both theoretical and experimental studies on settling velocities of drilled cuttings in drilling fluids are conducted using new approaches to account for the non-Newtonian nature of drilling fluids and for the shape irregularity of drilled cuttings. Based on experimental results, a generalised model is developed for calculating settling velocities of variously shaped particles in power-law fluids. Then, the effects of various parameters on cuttings transport during drilling operations are analysed based on the previous and the present studies. After that, an extensive theoretical analysis for the previous studies on the minimum transport velocity (MTV) in solid-liquid mixture flow through pipelines, on initiation of sediment transport in open channels and on MTV for cuttings transport in deviated wells is presented. At last, theoretical studies on the minimum transport velocity for cuttings transport in drilling annuli at various angles are conducted and two parallel general correlations are developed. When these correlations are experimentally verified and numerically established in the future, they can be served as general criteria for evaluating and correlating the effects of various parameters on cuttings transport, and as a guideline for cuttings transport programme design during directional drilling.

In this work, a code has been developed that solves the Navier-Stokes equations using the finite volume method with unstructured triangular grids. A cell-centred, finite volume method is used and the pressure-velocity coupling is treated using both the SMTLE and the MAC algorithms. The major advantage of using triangular grids is their applicability to complex geometry. A special treatment is developed to ensure good quality triangular elements around the boundaries. The numerical simulation of incompressible flow at low Reynolds number is studied in this thesis. A code for generating triangular grids using the tri-tree algorithm has been written and an adaptive finite volume method developed for calculating laminar fluid flow. The grid is locally adapted at each time step, with grid refinement and derefinement dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in reducing the numerical simulation time. The discretised equations are solved by using an iterative point by point Gauss-Seidel solver. For calculating the values of velocity and pressure at vertices of triangular grids, special interpolation schemes (averaged linear-interpolation and scattered interpolation) are used to increase the accuracy. To avoid the well known checkerboard error problems, i. e., the oscillations occurring in the pressure field, third derivative terms in pressure, first introduced by Rhie-chow (1983), are added to the mass flux velocity. Convective terms are approximated using a QUICK (Quadratic Upstream Interpolation for Convective Kinematics) differencing scheme which has been developed here in for unstructured grids. Three cases of two-dimensional viscous incompressible fluid flow have been investigated: the first is channel flow, in which the numerical results are compared with the analytical solution; the second case is the backward-facing step flow; and the third case is flow past circular cylinders at low Reynolds number (Re). The numerical results obtained for the last two cases are compared with published data. The evolution of vortex shedding is presented for the case of unidirectional flow past a circular cylinder at Re=200. In addition, drag and lift force coefficients are calculated and compared for single and multiple cylinders in unidirectional flow.

No description available.

No description available.

The hinge region of a major anticlinal fold structure in the SW Scottish Highlands was located in the eastern part of the Isle of Islay. The structure plunges gently NNW, with the hinge line measuring 02/026. The hinge region was located by mapping a 2km2 area comprised of deformed Neoproterozoic metasedimentary and metacarbonate rocks, and plotting the measurements on stereograms. The data collected was also analysed to attempt to asses evidence of refolding, and it is suggested in this thesis that the area displays evidence of at least one subsequent refolding event.

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