Research on Helical Flow of Non-Newtonian Fluids in Eccentric Annuli

Abstract

Abstract The governing equations, the boundary and connective conditions of the helical flow of non-newtonian fluids in eccentric annuli, which are the 4th order nonlinear nonhomogeneous partial differential equations with variable coefficients expressed by the stream function and axial velocity in the bipolar coordinate system, are established theoretically and calculated numerically by using the finite difference method. The calculation steps of the above mentioned equations are given and, being as the examples of the experimental data of the aqueous solution of CMC in the laboratory, the helical flow of the non-newtonian fluid in eccentric annuli are calculated and analysed practically. The results are as follows:There is a secondary flow, which is very important for analysing cuttings carrying capacity of drilling muds in the annuli and for preventing drill pipe from being suck, in the helical flow of the non-newtonian fluid in eccentric annuli.The flow rate of the helical flow is enhanced by the rotation of the inner cylinder of eccentric annulus.The results of comparison between the numerically calculated flow rates and the flow rates measured in the experiments show that the governing equations and the method of the numerical calculation of the helical flow of the non-newtonian fluids in eccentric annuli in the paper are correct. Introduction In the oil drilling, the flow of the drilling muds in the eccentric annulus formed by the drill pipe and the casing or wellbore is helical flow. As for providing accurate hydraulic parameters for jet drilling and optimized drillIng, it is very significant that the study of helical flow is conducted. The study of the helical flow of the non-newtonian fluids in a concentric annulus was completed by the authors in 1985. In this paper, the stream function-axial velocity equations, boundary and connective conditions of the helical flow of the non-newtonian fluids in eccentric annuli will be established theoretically and calculated numerically by using the finite difference method. BASIC EQUATIONS Consider the steady, isothermal laminar and helical flow of the non-newtonian fluid in an eccentric annulus, which is formed by two infinite eccentric circular cylinders with parallel axes. The radii of the inner and outer cylinder forming the eccentric annulus are Ri and Ro respectively. The distance between the axes of the two cylinders is e. The inner cylinder rotates about its own axis with an angular velocity and a pressure gradient-P, parallel to the axes of cylinders, exists in the fluid. P. 543