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We consider the flow of two immiscible fluids in a thin inclined channel subject to gravity and a change in pressure. In particular, we focus on the effects of Navier slip along the channel walls on the long-wave linear stability. Of interest are two different physical scenarios. The first corresponds to two incompressible fluid layers separated by a sharp interface, while the second focuses on a more dense fluid below a compressible gas. From a lubrication analysis, we find in the first scenario that the system is stable in the zero-Reynolds number limit with the slip effects modifying the decay rate of the stable perturbation. In the case of the Rayeligh-Taylor problem, slip along the less dense fluid wall has a destabilizing effect. In the second scenario, fluid inertia is pertinent, and we find neutral stability criteria are not significantly affected with the presence of slip.

Micropores can constitute up to 100% of the total porosity within carbonate hosted hydrocarbon reservoirs, usually existing within micritic fabrics. There is, however, only a rudimentary understanding of the contribution that these pores make to reservoir performance and hydrocarbon recovery. To further our understanding, a flexible, object-based algorithm has been developed to produce 3D computational representations of end-point micritic fabrics. By methodically altering model parameters, the state-space of microporous carbonates is explored. Flow properties are quantified using lattice-Boltzmann and network modelling methods. In purely micritic fabrics, it has been observed that average pore radius has a positive correlation with single-phase permeability and results in decreasing residual oil saturations under both water-wet and 50% fractionally oil-wet states. Similarly, permeability increases by an order of magnitude (from 0.6md to 7.5md) within fabrics of varying total matrix porosity (from 18% to 35%) due to increasing pore size, but this has minimal effect on multi-phase flow. Increased pore size due to micrite rounding notably increases permeability in comparison to original rhombic fabrics with the same porosity, but again, multi-phase flow properties are unaffected. The wetting state of these fabrics, however, can strongly influence multi-phase flow; residual oil saturations vary from 30% for a water-wet state and up to 50% for an 80% oil wet fraction. flow when directly connected. Otherwise, micropores control single-phase permeability magnitude. Importantly in these fabrics, recovery is dependent on both wetting scenario and pore-network homogeneity; under water-wet imbibition, increasing proportions of microporosity yield lower residual oil saturations. Finally, in grain-based fabrics where mesopores form an independently connected pore network, micropores do not affect permeability, even when they constitute up to 50% of the total porosity. Through examination of these three styles of microporous carbonates, it is apparent that micropores can have a significant impact on flow and sweep characteristics in such fabrics.

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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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.

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