Numerical Simulation of Laminar Flow of Yield-Power-Law Fluids in Conduits of Arbitrary Cross-Section

Abstract

A numerical model has been developed to simulate laminar flow of Power-law and Yield-Power law fluids in conduits of arbitrary cross-section. The model is based on general, nonorthogonal, boundary-fitted, curvilinear coordinates, and represents a new approach to the solution of annular flow problems. The use of an effective viscosity in the governing equation of the flow allows the study of the flow behavior of any fluid for which the shear stress is a function of shear rate only. The model has been developed primarily to simulate annular flow of fluids used in drilling and completion operations of oil or gas wells. Predicted flow rates versus pressure gradient for laminar flow of Newtonian fluids in concentric and eccentric annuli, and Power-law fluids in concentric annuli compare very well with results derived from analytical expressions. Moreover, the predictions for laminar flow of Power-law and Yield-Power-law fluids in eccentric annuli are in excellent agreement with numerical and experimental data published in the literature. The model was also successfully applied to the case of laminar flow of Power-law fluids in an eccentric annulus containing a stationary bed of drilled cuttings and the results are presented herein.

Flow of power-law fluid in a partially blocked eccentric annulus

“…Thus, numerical methods are often applied to predict pressure loss and bed shear stress in a partially blocked annulus. Previous studies (Azouz et al, 1993;Hussain et al, 1998) …”

“…Previous numerical models (Azouz et al, 1993;Azouz, 1994;Hussain and Sharif, 1998) According to Azouz et al (1993), the distribution of the axial shear stress on cuttings bed surface is non-linear, which becomes flattened as n decreases from 1 to 0.6.…”

“…Later, several numerical studies (Azouz et al, 1993;Azouz 1994;Hussain and Sharif, 1998;Aworunse, 2012) were conducted using nonorthogonal, curvilinear, and boundary fitted coordinate systems. These numerical studies is proposed by Chen (2005), who formulated a semi-empirical model based on effective diameter concepts (Whitaker, 1985).…”

“…However, very limited studies (Hussain and Sharif, 1998;and Azouz et al, 1993) Due to the presence of tool joints and wellbore irregularities, drillstring is expected to have approximately 90% eccentricity. In addition, for eccentricity more than 90%, simulation studies become very difficult and computationally intensive due to numerical instability.…”

Numerical simulation of velocity profile in eccentric annulus

“…In 1992, Azouz [7] studied the flow of Newtonian and non-Newtonian fluids in conduits of arbitrary cross-section. And they also studied the characteristics of laminar flow of the Bingham fluid and the power law fluid in annulus by using the CFD software.…”