Primary cementing of a highly deviated oil well

In this thesis we study laminar displacement flows of one fluid by another in a horizontal annulus. The study comes from the primary cementing of highly deviated oil and gas wells. Highly deviated wells are those in which part of the well bore is nearly horizontal. Primary cementing is a critical process in the construction of a well. The objective is to provide zonal isolation, i.e., a hydraulic seal between the well and the surrounding rock. This is essential to protect the environment and increase the productivity of the well. Therefore, an understanding of the process is indispensable. We model primary cementing displacement flows using a Hele-Shaw approach, and provide simple scientific tools to improve the design of cementing jobs. The contribution of the thesis comes in three parts. Firstly, we analyse the displacement of one viscoplastic fluid by another in a near-horizontal eccentric annulus with a fixed inner pipe. We present examples that illustrate the differences between vertical and horizontal displacements. We then derive a 1D lubrication model which gives analytical conditions that predict when the flow will stratify, according to the fluid properties and the annulus geometry. Secondly, we derive a 2D displacement model for Newtonian fluids which includes rotation and reciprocation of the inner cylinder. This is a common practice in the industry and not well understood. Using an asymptotic approach, we find steady-state traveling wave solutions for nearly- flat interfaces. Then we use numerical simulations to understand the flow dynamics for more elongated interfaces. In particular, we show that casing rotation can lead to local instabilities and mixing, which can shorten the length of the interface. Finally, we generalise this moving casing model to viscoplastic fluids. Using a lubrication- type model we explore the effects of casing motion, again deriving conditions for there to be steady solutions.Science, Faculty ofMathematics, Department ofGraduat