UBC Theses and Dissertations
Yield stress fluid flows in uneven geometries : applications to the oil & gas industry Roustaei, Ali
We study a set of yield stress fluid flows in channels with geometric non-uniformities, motivated by theoretical aspects and industrial applications. Methodology is primarily computational and we try to analytically investigate as much as possible. Theoretical interest arises from the self-selection phenomenon, meaning that the original flow geometry is modified by the fluid itself. This occurs due to yield stress and is accomplished via stagnant zones of the fluid attached to the boundary of original geometry. Industrial motivations stem from oil/gas well construction operations: primary and squeeze cementing and hydraulic fracturing. In all we have drilling mud, cement or a gelled fluid which exhibit yield stress. Specifically, we model a washout along the well as a non-uniform channel and extensively study flows through it. This is an enlarged segment of the well where the wellbore is washed out or collapsed. The main industrial concern is the residual mud left in the washout after primary cementing which weakens the hydraulic sealing function of the cement. Self-selection has been analytically studied for duct flows, and not much in 2D flows. Chapter 2 is a study of self-selection in wavy walled channels as a model for smooth non-uniform channels. We find similar results to duct flows, however a complete understanding eludes us. Chapter 3 looks at the flow of Bingham fluid in fractures. We study the limits of validity of Darcy approach first and then focus at the minimal pressure drop required to mobilize the fluid in fracture. We demonstrate knowing self-selection properties can greatly improve approximations here. Chapters 4-6 are step by step investigation of the flows in washout, from Stokes to inertial and finally displacement flow. In Chapter 4 we show self-selection in Stokes flow of washout and use it to estimate the residual fluid in the washout. We study the effects of inertia on it in Chapter 5, illustrating only finite amount of inertia would help in better displacement of the mud which is counter intuitive. Chapter 6 is a preliminary study of the displacement flow and we report some interesting observations.
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