﻿ Numerical Solution of Power-law Fluid Flow through Eccentric Annular Geometry
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### Numerical Solution of Power-law Fluid Flow through Eccentric Annular Geometry

Nuha Hussein Ebrahim1,, Noaman El-Khatib1, Mariyamni Awang1

1Petroluem Engineering, Universiti Teknologi Petronas, Perak Darul Ridzuan, Malaysia

American Journal of Numerical Analysis. 2013, 1(1), 1-7. DOI: 10.12691/ajna-1-1-1
Published online: August 25, 2017

### Abstract

Cuttings transport modeling in inclined and horizontal wellbores is complicated due to the eccentricity of the annulus. Development of a model for cuttings transport requires a deep understanding of the drilling mud flow behavior in the eccentric annular geometry. In this paper, bipolar coordinates system is used to solve for the eccentric annular geometry due to irregular shape of the boundaries. Finite difference method is used to obtain the velocity profile of Power-law non-Newtonian fluids through eccentric annuli. The discretized dimensionless Equation of flow using the finite difference method is solved iteratively using Point Successive Over Relaxation (S.O.R.) method. The results for Newtonian eccentric annular flow with 0.0001 eccentricity are in agreement with the Newtonian concentric annular flow. The Power-law eccentric annular flow results with flow index of 1.0 are verified with Newtonian fluid eccentric annular flow results. The parametric effects of flow index, Pipe/hole radius ratio, and eccentricity are investigated. We expect the development of a new model for flow in eccentric annular geometries to be an important new tool for application in oil - well drilling and production.

### Keywords:

bipolar coordinate, eccentric annulus, Power-law fluid, Point Successive over Relaxation
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