Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Todd J. Arbogast. Vita. Includes bibliographical references. Also available from UMI.

This dissertation considers the effect of measuring randomly varying local hydraulic conductivity K(x) on one's ability to predict transient flow within bounded domains, driven by random sources, initial head distribution, and boundary functions. The first part of this work extends the steady state nonlocal formalism by Neuman and Orr [1992] in order to obtain the prediction of local hydraulic head h(x, t) and Darcy flux q(x, t) by means of their ensemble moments <h(x, t)> (c) and <q(x, t)>(c)conditioned on measurements of K(x). These predictors satisfy a deterministic flow equation which contains a nonlocal in space and time term called a "residual flux". As a result, <q(x, t)>(c) is nonlocal and non-Darcian so that an effective hydraulic conductivity K(c) does not generally exist. It is shown analytically that, with the exception of several specific cases, the well known requirement of "slow time-space variation" in uniform mean hydraulic gradient is essential for the existence of K(c). In a subsequent chapter, under this assumption, we develop analytical expressions for the effective hydraulic conductivity for flow in a three dimensional, mildly heterogeneous, statistically anisotropic porous medium of both infinite extent and in the presence of randomly prescribed Dirichlet and Neumann boundaries. Of a particular interest is the transient behavior of K(c) and its sensitivity to degree of statistical anisotropy and domain size. In a bounded domain, K(c) (t) decreases rapidly from the arithmetic mean K(A) at t = 0 toward the effective hydraulic conductivity corresponding to steady state flow, K(sr), K(c), exhibits similar behavior as a function of the dimensionless separation distance ρ between boundaries. At ρ = 0, K(c) = K(A) and rapidly decreases towards an asymptotic value obtained earlier for an infinite domain by G. Dagan. Our transient nonlocal formalism in the Laplace space allows us to analyze the impact of other than slow time-variations on the prediction of <q(x, t)>(c),. Analyzing several functional dependencies of mean hydraulic gradient, we find that this assumption is heavily dependent on the (relaxation) time-scale of the particular problem. Finally, we formally extend our results to strongly heterogeneous porous media by invoking the Landau-Lifshitz conjecture.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.

Thesis (DTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2013 / The flow of reactive viscous fluids in porous media presents a theoretically challenging problem and has a broad range of scientific, technological and engineering applications. Real life areas where such flow systems are encountered include drying of food, geothermal energy extraction, nuclear waste disposal, the flow of heat and fluid inside human organs, insulation of buildings, groundwater movement, oil and gas production, astrophysical plasmas, magnetohydrodynamic (MHD) pumps and generators, metal extraction and granulation of metals, aerospace and ship propulsion and automobile exhaust systems. The reactions within such flow systems are inherently exothermic. It is in this view that we carry out studies of thermal effects and thermal stability criteria for unsteady flows of reactive variable viscosity non-Newtonian fluids through saturated porous media. The study focuses on non-Newtonian fluids mainly because the majority of industrial fluids exhibit non-Newtonian character. Particular focus will be on fluids of the differential type exemplified by third grade fluid. Both analytical and numerical techniques were employed to solve the nonlinear partial differential equations that were derived from the conservation principles, namely the principles of conservation of mass, momentum and energy balance. Graphical representations were adopted in trying to explain the response of solutions to various flow parameter variations. In chapter 1 we defined important terms and expressions, laid down a summary of important applications, carried out literature survey, stated the statement of the problem, the aims and objectives of the study as well as an outline of the envisaged research methodology. Chapter 2 focuses on the derivations of the fundamental equations that derive the flow system. These are the continuity equation, the momentum equation and the energy equation. In chapter 3 we computationally investigated the unsteady flow of a reactive temperature dependent viscosity third grade fluid through a porous saturated medium with asymmetric convective boundary conditions. The response of velocity and temperature fields to each of the various flow parameters was analysed and interpreted. A transient increase in both the velocity and temperature profiles with an increase in the reaction strength, viscous heating and fluid viscosity parameter was observed. On the other hand, a transient decrease in the field properties was observed with increase in non-Newtonian character and the porous medium shape parameter. The reaction was noticed to blow-up if, depending on other flow parameters, the reaction strength is not carefully controlled.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.

Thesis submitted in fulfillment of the requirements for the degree Doctor of Technology: Mechanical Engineering Cape Peninsula University of Technology, 2013 / Fluid flow through a porous channel and cylindrical pipe walls are important area of research due to its wide applications in transpiration cooling, gaseous diffusion technology, cooling of rocket, mechanized irrigation and filtration processes. It is therefore necessary to examine the effect of Navier slip, combined effects of buoyancy forces and variable viscosity on the entire flow structure. Analyzing the magneto- hydrodynamics (MHD) of unsteady flow with buoyancy effect and also investigate numerically the entropy generation in an unsteady flow through porous pipe. We have also examined the thermal stability and entropy generation in the system. The problems were investigated theoretically using appropriate mathematical models for both transient and steady state scenario. Both analytical techniques and numerical methods are employed to tackle the model nonlinear equations derived from the law of conservation of mass, momentum and energy balance. Some definitions of terms to come across and introduction to fluid flow are given in chapter 1, together with literature reviews, statement of problem and objectives of the study. Chapter 2 lays the foundation for basic fundamental equations governing fluid flow. In chapter 3, the combined effect of suction/injection and asymmetric Navier slip on the entropy generation rate for steady flow of an incompressible viscous fluid through a porous channel subjected to different temperature at the walls are investigated. Chapter 4 analyze combined effects of buoyancy forces together with Navier slip on the entropy generation in a vertical porous channel wall with suction/injection wall. Analysis of MHD unsteady flow through a porous pipe with buoyancy effects are carried out in chapter 5, while chapter 6 investigates numerically entropy generation of unsteady flow through a porous pipe with suction and chapter 7 gives concluding remarks.

Peatlands cover a total area of approximately 3 million square kilometers and are one of the largest natural sources of atmospheric methane (CH4) and carbon dioxide (CO2). Most traditional methods used to estimate biogenic gas dynamics are invasive and provide little or no information about lateral distribution of gas. In contrast, Ground Penetrating Radar (GPR) is an emerging technique for non-invasive investigation of gas dynamics in peat soils. This thesis establishes a direct comparison between gas dynamics (i.e. build-up and release) of four different types of peat soil using GPR. Peat soil blocks were collected at peatlands with contrasting latitudes, including the Everglades, Maine and Minnesota. A unique two-antenna GPR setup was used to monitor biogenic gas buildup and ebullition events over a period of 4.5 months, constraining GPR data with surface deformation measurements and direct CH4 and CO2 concentration measurements. The effect of atmospheric pressure was also investigated. This study has implications for better understanding global gas dynamics and carbon cycling in peat soils and its role in climate change. / by Anastasija Cabolova. / Thesis (M.S.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

In this work, flow through synthetic arrangements of contacting spheres is studied as a model problem for porous media and packed bed type flows. Direct numerical simulations are performed for moderate pore Reynolds numbers in the range, 10 ≤ Re ≤ 600, where non-linear porescale flow features are known to contribute significantly to macroscale properties of engineering interest. To first choose and validate appropriate computational models for this problem, the relative performance of two numerical approaches involving body conforming and non-conforming grids for simulating porescale flows is examined. In the first approach, an unstructured solver is used with tetrahedral meshes, which conform to the boundaries of the porespace. In the second approach, a fictitious domain formulation (Apte et al., 2009. J Comput. Phys. 228 (8), 2712-2738) is used, which employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. Detailed grid convergence studies of both steady and unsteady flow through prototypical arrangements of spheres indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach, which also does not require complex grid generation techniques. Next, flows through both random and structured arrangements of spheres are simulated at pore Reynolds numbers in the steady inertial ( 10 ≲ Re ≲ 200) and unsteady inertial (Re ≈ 600) regimes, and used to analyze the characteristics of porescale vortical structures. Even at similar Reynolds numbers, the vortical structures observed in structured and random packings are remarkably different. The interior of the structured packings are dominated by multi-lobed vortex rings structures that align with the principal axes of the packing, but perpendicular to the mean flow. The random packing is dominated by helical vortices, elongated parallel to the mean flow direction. The unsteady dynamics observed in random and structured arrangements are also distinct, and are linked to the behavior of the porescale vortices. Finally, to investigate the existence and behavior of transport barriers in packed beds, a numerical tool is developed to compute high resolution finite-time Lyapunov exponent (FTLE) fields on-the-fly during DNS of unsteady flows. Ridges in this field are known to correspond to Lagrangian Coherent Structures (LCS), which are invariant barriers to transport and form the skeleton of time dependent Lagrangian fluid motion. The algorithm and its implementation into a parallel DNS solver are described in detail and used to explore several flows, including unsteady inertial flow in a random sphere packing. The resulting FTLE fields unambiguously define the boundaries of dynamically distinct porescale features such as counter rotating helical vortices and jets, and capture time dependent phenomena including vortex shedding at the pore level. / Graduation date: 2013

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / When considering flow through porous media, different flow regimes may be identified. At very small Reynolds numbers the relation between the pressure gradient and the velocity of the fluid is linear. This flow regime ...