This thesis presents the results of investigations in two areasA) Laminar helical flow of Herschel Bulkley fluids in annular space; and B) Cuttings transport in deviated wellbores. Description of area A: This is a theoretical study that consists of the modelling of non-Newtonian fluid flowing through annular space. The rheology of the fluid is represented by a three-parameter fluid model to account for a non-linear behaviour of the rheologic curve followed by the presence of a yield stress. Two distinct methodologies were used to study the effects of inner pipe rotation and inner pipe eccentricity on the velocity profiles of the annular flow. I. Laminar Helical Flow of a Herschel-Bulkley Fluid in a Concentric Annulus and its Extension to a Narrow Eccentric Annulus: The method consists of the use of the boundary conditions to enable the numerical integration of the motion equation. The subsequent extension to eccentric annuli is based on division of the annulus into sectors, where each sector is treated as an equivalent sector of a concentric annulus. Profiles of velocity presented in 2-D and 3-D contour plots explain the effects of eccentricity, inner pipe rotation and yield stress in many different situations. This analysis is useful to simulate the flow field in a borehole during directional drilling and primary cementing particularly for narrow eccentric annuli. II. Laminar Helical Flow of a Herschel-Bulkley Fluid in an Eccentric Annulus and The Special Case of a Pure Axial Flow: A new methodology to obtain the governing equations is proposed here as a first step to the solution of this complicated problem. It consists of eliminating the unknown radial and tangential pressure gradients from the equation of motion by defining vorticity between these two components of the velocity vector. The vorticity equation and the remaining axial component of the motion equation, written in bipolar co-ordinates, are then made discrete using two different finite difference approaches. Firstly, the inertial terms of both equations are made discrete using a modified upwind scheme proposed by O. Axelsson and I. Gustafsson, while the viscous terms are made discrete using central difference approximation. Secondly, the moving boundary conditions are set by enforcing continuity of pressure on the inner annular wall. The future solution of these equations will provide a very accurate model, unavailable until now, that accounts for both effects, the eccentricity and rotation of the drill string, to simulate the flow field of drilling mud in directional and horizontal wells. Description of area B: The fluid models developed are incorporated in the development of two semi-empirical correlations to predict the critical conditions of cuttings transport in deviated weI/bore. The numerical fluid models are modified to predict the velocity of the fluid at the vicinity of the cutting that is at the point of being transported. An extensive bank of data of the critical conditions of transport, emulating many different field conditions, was used in this analysis. The experimental data was provided by an industry sponsored project which did four years of experimental work in a simulated testing column to generate the data. The two semi-empirical correlations developed in this research are based on: • a dimensional analysis of the variables involved in two distinct mechanisms of transport experimentally observed: 1. Rolling or Sliding and 2. Suspension; • a force balance applied to a cutting resting on the low-side wall of an inclined annulus, under fluid dynamic conditions. The semi-empirical correlations can be used 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.

Drilling is crucial to many industries, including hydrocarbon extraction, CO2 sequestration, geothermal energy, and others. During penetrating the subsurface rocks, drilling fluid (mud) is used for drilling bit cooling, lubrication, removing rock cuttings, and providing wellbore mechanical stability. Significant mud loss from the wellbore into the surrounding formation causes fluid lost-circulation incidents. This phenomenon leads to cost overrun, environmental pollution, delays project time and causes safety issues. Although lost-circulation exacerbates wellbore conditions, prediction of the characteristics of subsurface formations can be obtained. Generally, four formation types cause lost-circulation: natural fractures, and induced fractures, vugs and caves, and porous/permeable medium. The focus in this work is on naturally fractured formations, which is the most common cause of lost circulation. In this work, a novel prediction tool is developed based on analytical solutions and type-curves (TC). Type-curves are derived from the Cauchy equation of motion and mass conservation for non-Newtonian fluid model, corresponding to Herschel-Bulkley model (HB). Experimental setup from literature mimicking a deformed fracture supports the establishment of the tool. Upscaling the model of a natural fracture at subsurface conditions is implemented into the equations to achieve a group of mud type-curves (MTC) alongside another set of derivative-based mud type-curves (DMTC). The developed approach is verified with numerical simulations. Further, verification is performed with other analytical solutions. This proposed tool serves various functionalities; It predicts the volume loss as a function of time, based on wellbore operating conditions. The time-dependent fluid loss penetration from the wellbore into the surrounding formation can be computed. Additionally, the hydraulic aperture of the fracture in the surrounding formation can be estimated. Due to the non-Newtonian behavior of the drilling mud, the tool can be used to assess the fluid loss stopping time. Validation of the tool is performed by using actual field datasets and published experimental measurements. Machine-Learning is finally investigated as a complementary approach to determine the flow behavior of mud loss and the corresponding fracture properties.

ABSTRACT GENERALIZED COUETTE FLOW OF A HERSCHEL - BULKLEY FLUID THROUGH ECCENTRIC ANNULUS - AN APPROXIMATE SOLUTION Seyidoglu, Tijen M.S., Department of Chemical Engineering Supervisor: ismail Tosun Co-Supervisor: Ahmet N. Eraslan January 2006, 134 pages Generalized Couette flow of a Herschel-Bulkley fluid in an eccentric annulus is analyzed by approximating the flow geometry as a slit of variable height. Besides an imposed pressure gradient, one of the plates is considered non-stationary to take into account the axial and/or angular motion of the inner pipe in an eccentric annulus system. Depending on the magnitude and the direction of the applied pressure gradient with respect to the plate velocity, three separate flow cases are studied in which the velocity reaches its maximum value either within the plug flow region or at the moving boundary. Velocity distributions are obtained for each case by solving the equations of continuity and motion. Volumetric flow rate expressions are obtained by integrating the velocity distribution over the cross-sectional area. At a given pressure gradient, the results indicate an increase in volumetric flow rate with an increase in eccentricity ratio. Criteria for each flow type is developed in terms of a dimensionless parameter &amp / #923 / , which takes into account the ratio of the imposed pressure gradient to the plate velocity. Volumetric flow rate expressions for Newtonian, Bingham and power-law fluids are obtained by considering the limiting values of the fluid index and yield stress. The validity of the equations are checked by considering the slit height to be a constant, i.e., flow between parallel plates. Surge/swab pressure calculations are carried out for Herschel-Bulkley, power-law and Bingham fluids and the results are expressed as a function of eccentricity ratio, radius ratio, fluid index and yield stress. The results indicate that when the fluid index and the eccentricity ratio are fixed, a slight increase in the radius ratio causes a tremendous increase in surge/swab pressure, especially for low values of fluid index. On the other hand, displacement of the inner pipe from a concentric position causes a decrease in swab/surge pressure when other parameters are held constant. Comparison with the literature values reveals the fact that flow in an eccentric annulus can be modeled as flow between a slit of variable height as long as the radius ratio is greater than 0.5 and the eccentricity ratio is less than 0.3. The results for other values of radius ratio and eccentricity ratio can be used as initial guess values in carrying out numerical calculations.

É notório que a degradação ambiental vem ao longo do tempo posicionando-se como um dos principais problemas do mundo moderno. Dentre as várias questões do interesse ambiental podemos destacar a ascensão da bolha de metano, em reservatórios hidrelétricos, desde o sedimento anóxico no fundo do reservatório até a interface água atmosfera. Neste contexto, a presente tese vêm propor uma nova modelagem matemática para a ascensão da bolha axissimétrica em fluidos newtonianos/nãonewtonianos e mostrar resultados numéricos simulados. Desta forma, o estado da arte estaria elevado a posição de permitir, via Matemática e Simulação Numérica-Computacional, a análise do transporte de metano em reservatórios de hidrelétricas através da bolha / It is well-known that environmental degradation has come along the time positioning as one of the main problems from modern world. Among several questions of the environmental interest may emphasize the methane bubble rise in hydroelectric reservoirs from the anoxic sediment in the bottom of reservoir until water interface atmosphere. In this context, the current thesis has come to propose a new mathematic modeling to the rise of the axisymmetric bubble in the newtonian/non-newtonian fluids and display numerical results simulated. Therefore, the state of art would be ascended to a position to permit, via Mathematics and Computing-Numeric Simulation, the analysis of transport of methane in hydroelectric reservoirs through of bubble

É notório que a degradação ambiental vem ao longo do tempo posicionando-se como um dos principais problemas do mundo moderno. Dentre as várias questões do interesse ambiental podemos destacar a ascensão da bolha de metano, em reservatórios hidrelétricos, desde o sedimento anóxico no fundo do reservatório até a interface água atmosfera. Neste contexto, a presente tese vêm propor uma nova modelagem matemática para a ascensão da bolha axissimétrica em fluidos newtonianos/nãonewtonianos e mostrar resultados numéricos simulados. Desta forma, o estado da arte estaria elevado a posição de permitir, via Matemática e Simulação Numérica-Computacional, a análise do transporte de metano em reservatórios de hidrelétricas através da bolha / It is well-known that environmental degradation has come along the time positioning as one of the main problems from modern world. Among several questions of the environmental interest may emphasize the methane bubble rise in hydroelectric reservoirs from the anoxic sediment in the bottom of reservoir until water interface atmosphere. In this context, the current thesis has come to propose a new mathematic modeling to the rise of the axisymmetric bubble in the newtonian/non-newtonian fluids and display numerical results simulated. Therefore, the state of art would be ascended to a position to permit, via Mathematics and Computing-Numeric Simulation, the analysis of transport of methane in hydroelectric reservoirs through of bubble