2 - Eccentric, Nonrotating, Annular Flow

Abstract

This chapter presents a self-contained mathematical model describing the flow of Newtonian, power law, Bingham plastic, and Herschel–Bulkley fluids through eccentric annular spaces. Numerical solutions for the nonlinear, two-dimensional axial velocity field, and its corresponding stress and shear rate distributions, are obtained for eccentric annular flow in an inclined borehole. The homogeneous fluid is assumed to be flowing unidirectionally in a wellbore containing a nonrotating drillstring. A fast, second-order accurate, unconditionally stable finite difference scheme was used to solve the nonlinear governing PDEs. The formulation uses exact boundary conforming grid systems that eliminate the need for unrealistic simplifying assumptions about the annular geometry. Calculations for several non-Newtonian flows using numerous complicated annular geometries were performed. The results, which agree with empirical observation, were computed in a stable manner in all cases. The cross-sectional displays show an unusual amount of information that is easily interpreted and understood by petroleum engineers.