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Hydraulic fracturing is a process for the extraction of hydrocarbons from underground formations. It involves pumping a specialized fluid into the wellbore under high pressures to form and support fractures in the rock. Fracturing stimulates the well to increase the production of oil and the natural gas which are the pillars of the energy economy. Key to this process is the use of proppants, which are solid materials used to keep the fractures open. Understanding the transport of proppant particles through a fluid is important to improve the efficiency and reduce environmental impact of fracturing. An increase of the settling velocity for instance, will impede the hydraulic fracturing process by reducing well productivity, or necessitate use of chemical additives. This thesis presents a theoretical investigation of the settling velocity of proppant particles. The effect of different parameters on the settling velocity were studied by manipulating the main factors that can influence particle transport. These include size of the particle (300 μm- 2000 μm), sphericity, density (1200 kg/m3-3500 kg/m3) and concentration. These typical values were obtained from commercially available proppants currently used in industry. Various correlations were investigated, assuming the carrier (fracturing) fluid to be an ideal Newtonian and as a power law (non-Newtonian) fluid. This will help predict the settling velocity for proppant particles in order to increase well productivity, and improve hydraulic fracturing efficiency. The models show that changing the carrier fluid viscosity and particle properties such as diameter, density, sphericity, and concentration leads to a significant change in the proppant settling velocity. For instance, reduction in particle size, density, and sphericity tend to reduce the settling velocity, while increasing the concentration of the particles and the fluid viscosity reduce the settling velocity.

[pt] Este trabalho teve como objetivo estudar as características de filtração estática e dinâmica de um fluido usado em fraturamento hidráulico à temperatura ambiente. Para sua realização foi projetado, desenvolvido e qualificado metrologicamente um simulador que permitisse efetuar testes de filtração estática e dinâmica. Foram realizadas filtrações com um fluido newtoniano (água) e um não newtoniano (HPGUAR-BO lbm/1000gal). / [en] This research intended to study the characteristcs of dynamic and static leakoff of a fluid in hydraulic fracturing at room temperature. A test apparatus was designed, constructed and metrologically qualified in order to carry out dynamic and stactic leakoff test. Leakoffs with a Newtonian fluid (water) and with a non-Newtonian one (HPGUAR-BO lbm/1000 gal) were performed.

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The velocity fields around a circular cylinder in a crossflow of drag-reducing polymeric solutions and water were experimentally investigated using a laser-Doppler velocimeter. Measured boundary-layer velocity profiles indicated that the flow parameter controlling the drag on a bluff body in drag-reducing flows is the turbulence intensity rather than the Reynolds number. For turbulence intensity less than 0.7% polymer addition induced delayed separation. For turbulence intensity over 1% the opposite effect was true. Time-averaged velocity profiles of water did not show any significant difference between self-induced and forced oscillatory flows. Heat, mass and momentum transfer of Newtonian and power-law non-Newtonian fluids were theoretically investigated using an implicit finite-difference scheme. The results clearly· indicated that shear-dependent non-Newtonian viscosity controls the entire transport processes of the power-law fluids. For the major portion of the boundary layer, it was found that the more shear thinning the material exhibits, the lower the skin friction and the higher the heat transfer result. Accounting for the motion of the stagnation point provided an improved prediction of heat transfer for Newtonian fluid. / Doctor of Philosophy

In this scientific work, we use two effective methods : Lie groups theory and the finite element method, to explain why the transition from laminar flow to turbulence flow depends on the variation of the Reynolds number. We restrict ourselves to the case of incompressible viscous Newtonian fluid flows. Their governing equations, i.e. the continuity and Navier-Stokes equations are established and investigated. Their solutions are expressed explicitly thanks to Lie's theory. The stability theory, which leads to an eigenvalue problem is used together with the finite element method, showing a way to compute the critical Reynolds number, for which the transition to turbulence occurs. The stationary flow is also studied and a finite element method, the Newton method, is used to prove the stability of its convergence, which is guaranteed for small variations of the Reynolds number. / Mathematical Sciences / M.Sc. (Applied Mathematics)

With the depletion of oil reserves and increase in oil price, the enhanced oil recovery methods such as polymer flooding to increase oil production from water flooded fields are becoming more attractive. Effective design of these processes is challenging because the polymer chemistry has a strong effect on reaction and fluid rheology, which in turn has a strong effect on fluid transport. We have implemented a well-established polymer model within the Implicit Parallel Accurate Reservoir Simulator (IPARS), which enables parallel simulation of non-Newtonian fluid flow through porous media. The following properties of polymer solution are modeled in this work: 1) polymer adsorption; 2) polymer viscosity as a function of salinity, hardness, polymer concentration, and shear rate; 3) permeability reduction; 4) inaccessible pore volume. IPARS enables field-scale polymer flooding simulation with its parallel computation capability. In this thesis, several numerical examples are presented. The result of polymer module is verified by UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability is also tested. The influence of different shear rate calculations is investigated in homogeneous and heterogeneous reservoirs. We observed that the wellbore velocity calculation instead of Darcy velocity reduces the grid effect for coarse mesh. We noted that the injection bottom hole pressure is very sensitive to the shear rate calculation. However, cumulative oil recovery and overall oil saturation appear to not be sensitive to grid and shear rate calculation for same reservoir. There are two models to model the ground water infiltration in vadose zone. One is Richard’s Equation (RE) model. And the other is two-phase flow model. In this work, we compare the two-phase model with an RE model to ascertain, under common scenarios such as infiltration or injection of water into initially dry soils, the similarities and differences in solutions behaviors, the ability of each model to simulate such infiltration processes under realistic scenarios, and to investigate the numerical efficiencies and difficulties which arise in these models. Six different data sets were assembled as benchmark infiltration problems in the unsaturated zone. The comparison shows that two-phase model holds for general porous media and is not limited by several assumptions that must be made for the RE formulation, while RE is applicable only for shallow regions (vadose) that are only several meters in depth and a fully saturated bottom boundary condition must be assumed. / text