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Annular displacement flows in turbulent and mixed flow regimes Maleki Zamenjani, Amir


This thesis presents a comprehensive, yet practical, two-dimensional model for the displacement of viscoplastic fluids in eccentric annuli in laminar, turbulent and mixed flow regimes. The motivations originally stem from primary cementing of oil and gas wells, as well as other types of wells such as those in Carbon Capture and Storage applications. During primary cementing, cement slurries are placed in an annular region between a steel casing and a wellbore to provide mechanical stability and hydraulic isolation. Several complications may arise due to the eccentricity of the annular region, as well as the viscoplastic nature of the fluids involved. The existing 2D and 3D models of primary cementing assume the flow is laminar, while in practice, turbulent and more importantly, mixed flow regimes are common. In this thesis, we fill this gap in knowledge. More specifically, we expand the laminar model of Bittleston et al. (2002) and develop a new formulation that includes turbulent and mixed flow regimes. This new formulation considers scaling based on the disparity of length-scales, which allows a narrow-gap averaging approach to be effective. With respect to the momentum equations, the leading-order equations correspond to a turbulent shear flow in the direction of the modified pressure gradient. With respect to the mass transport equations that model the miscible displacement, to leading-order turbulence effectively mixes the fluids. Changes in concentrations within the annular gap arise due to the combined effects of advection with the mean flow, anisotropic Taylor dispersion (along the streamlines) and turbulent diffusivity. This new extension allows us to understand the process of cementing more deeply, and resolve several questions that have been left unanswered for many years. In particular, we show that many simple statements/rules that are often employed in industry do not stand up to serious analysis. Instead, modelling approaches such as the one developed here can incorporate specific features of wells in the simulations, and therefore, yield more accurate predictions.

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