Pressure Drop and Determination of Characterizing Coefficients for Pseudoplastic Fluid Laminar Flow in Concentric Annuli

Abstract

The flow through annuli is encountered in drilling operation, in which drilling mud flows between the borehole wall and the drilling pipe. Some drilling muds, depending on their prepared materials, exhibit nonNewtonian characteristics and in many cases may be regarded as pseudoplastic fluids. This study examines the dimensionless flow rate defined by Fredrickson and Bird (Fredrickson and Bird, 1958) on pseudoplastic fluid laminar flow in concentric annuli. A new approximation function is derived to evaluate the viscosity factor, also easy to use without numerical procedures. The function is more precise than the one, which was previously shown by the authors (Masuyama and Hatakeyama, 2003). Further, a new scheme is proposed to evaluate the characterizing coefficients, such as the pseudoplastic viscosity and the rheology constant using flow data. Furthermore, generalized formulas of the Reynolds number and the pipe friction coefficient for pseudoplastic fluid are shown for concentric annuli in order to calculate the pressure drop. They are extendable in the case of circular pipes, also parallel plates.

Keywords

• concentric annulus
• drilling mud
• pseudoplastic fluid
• pressure drop
• characterizing coefficients
• viscosity factor