Non-Newtonian fluid flow in eccentric annuli and its application to petroleum engineering problems.

摘要

The fluid flow in the annular gap in oilwells is a complex problem. The geometry of the annulus is customarily simplified to concentric annular flow. In this study, a fluid flow model is developed allowing annulus to be eccentric: inner pipe located anywhere in the annulus. Thus, a more realistic representation of the actual geometry is obtained.; An equation of motion that defines flow of non-Newtonian fluids in eccentric annuli is derived. A numerical solution of this equation is presented. The velocity profiles, the viscosity profiles, and the flow rate vs frictional pressure loss gradient relationship are calculated for varying eccentricities. The velocity profiles, and the viscosity profiles are compared to widely used substitutes: the average velocity and the apparent viscosity, respectively. A correlation based on the model generated data is developed that permits for an easy calculation of the frictional pressure losses in eccentric annuli.; Generally neglected eccentricity is introduced to two problems of petroleum engineering: surge pressure calculations and displacement of a gas kick in solution in an oil-base mud. The results are found to be a strong function of eccentricity.