Flow Analysis and Approximate Expressions of Factors Related to Frictional Loss for Laminar Flow of Viscoplastic Fluids through a Concentric Annulus

Abstract

The mud flow between the borehole and the drill pipe in well drilling can be regarded as the flow of nonNewtonian fluids through a concentric annulus. In recent years, the Herschel-Bulkley rheological model is recommended as a general fluid model of drilling mud because it encompasses the power law model and the Bingham plastic model. Also, in the field of well drilling, the flow through a concentric annulus is conventionally approximated by the flow between two parallel plates. However, its applicability does not seem to be examined because it is not easy to perform analysis of non-Newtonian fluid flow through a concentric annulus. For studies on laminar flow of viscoplastic fluids (fluids with yield stress) through concentric annuli, there are researches on Bingham fluid by Fredrickson & Bird and on Herschel-Bulkley fluid by Hanks. Since the equation of motion in viscoplastic fluid flow through a concentric annulus cannot be analytically solved in all of them, in their researches numerical calculations are presented by charts. However, it is not simple as a method to estimate the frictional pressure loss, because multiple charts are related. In this research, based on the results of previous authors' research7, 8), we investigate a method that can easily calculate the average wall shear-stress in laminar flows of viscoplastic fluids through concentric annuli. That is, using the results of circular pipe and parallel-plate, an approximate expression of viscosity factor in viscoplastic fluid flow through concentric annuli is derived and the error of the average wall shear-stress represented by the approximate equation is evaluated. Furthermore, a simpler approximate formula which can be calculated directly without numerical calculation is derived and its error is also evaluated. In addition, error assessment is performed to confirm the applicability of approximation by the flow in the parallel-plate for the flow in a concentric annulus, which has been conventionally done in the field of well drilling.

Keywords

• concentric annulus
• drilling mud
• hershel-bulkley fluid
• bingham fluid
• viscosity factor
• spreadsheet solution