4. Non-Newtonian Eccentric Annulus Flow

This problem is based on the fluid dynamics observed in the flow of drilling muds in a borehole during well drilling operations. In these operations, the mud is pumped through the hollow drill shaft to the drill bit where it enters the wellbore and returns under pressure as a rotational flow to the well surface. The primary functions of the mud are to carry rock cuttings to the surface, to lubricate the drill bit and to control subsurface pressures. The rheology of muds usually exhibits a finite yield stress and shear thinning behavior (Meuric [1]).

In this problem the drilling mud flow has a tendency to form a helical stream surrounding the drill string due the existence of radial and tangential forces. The radial force is generated by the pressure drop imposed by the mud pump and the tangential force is due to the rotational movement of the drill string. The transport of these rotational forces through the fluid layers is significantly influenced by the fluid viscosity.

Extensive numerical investigations of annuli flow were conducted by Escudier et al [2]. In this article the effects of eccentricity and inner-cylinder rotation on the flow of several Power Law fluids were studied.

Reference

[1]. Meuric, O. F. J., Wakeman, R. J., Chiu, T. W. and Fisher, K. A., 1998, Numerical Flow Simulation of Viscoplastic Fluids in Annuli, Can. J. Chem. Eng., 76: 27-40;

[2]. Escudier, M. P., Oliveira, P. J. and Pinho, F. T., Fully Developed Laminar Flow of Purely Viscous non-Newtonian Liquids Through Annuli Including the Effects of Eccentricity and Inner-Cylinder Rotation, International Journal of Heat and Fluid Flow, 2352-73;