Application of unsteady couette flow of non-Newtonian power-law fluids in concentric annular wellbore

Abstract

Fluid flow phenomena that occur when the fluid is confined between two co-axial cylinders, one of which is stationary and the other is moving at a specified velocity, is known as couette flow. Such flow is representative of that which occurs in the borehole annulus where the wall of the wellbore is represented by the stationary cylinder, and the drill string or casing is represented by the moving cylinder. The fluid local velocity is dependent on the velocity of the moving cylinder or pipe. Different mathematical relations have been developed for surge and swab pressure calculations for flow of power-law fluids in the wellbore annulus. The application of couette flow equations and relationships to evaluate the surge or swab pressure has been limited. These equations are either too complex for field use or require much computation for field application. In this study, the motion equations are analytically solved for non-Newtonian power-law fluids. The solutions of the equations are presented in both dimensionless and graphical forms, which are applied to predict the surge or swab pressure encountered when running tubular goods in liquid-filled boreholes. The technique presented here is easy to use and requires minimal computational efforts for determining the surge or swab pressure for an unsteady motion of a moving inner pipe in a concentric annulus. The results of this study show that the magnitude of surge or swab pressure increases with increase in the pipe acceleration.