Evaluation of friction factor correlations and equivalent diameter definitions for pipe and annular flow of non-Newtonian fluids

Friction pressure estimation is an important part of pipe and annular hydraulics useful for determining hydraulic horsepower requirements and the maximum wellhead pressure. For non-Newtonian fluids in laminar flow, the friction factor can be calculated with the Hagen–Poiseuille type equation. In turbulent flow, however, several correlations have been developed for smooth pipes. Many of these correlations are in the form of the Dodge–Metzner equation for flow in smooth pipes. The Dodge–Metzner correlation was developed using carbopol aqueous solution which is not used for oilfield operations. Previous studies on friction factor correlation comparison have been limited to the use of non-Newtonian fluid friction factor equations for smooth pipes neglecting the significant effect of pipe roughness on wellbore hydraulics. Generally, tubulars in oilfield applications have some degree of roughness which results in higher friction pressure than that for smooth pipes of the same size especially for less viscous fluids. A few studies have addressed the effect of roughness on friction pressure loss. In this study, friction factor correlations with relative roughness are compared with experimental measured friction factor data using a statistical approach as the basis for comparison. Further, equivalent diameter definitions for annular flow are evaluated to determine the friction factor–equivalent diameter combination that best describes the experimental data. The objective of this work is to recommend the non-Newtonian friction factor correlation that allows for accurate prediction of frictional pressure losses in rough pipes and annular sections.