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

1993 ◽  
Vol 115 (4) ◽  
pp. 710-716 ◽  
Author(s):  
Idir Azouz ◽  
Siamack A. Shirazi ◽  
Ali Pilehvari ◽  
J. J. Azar
Keyword(s):  
Laminar Flow ◽  
Cross Section ◽  
Power Law ◽  
Annular Flow ◽  
Flow Behavior ◽  
Arbitrary Cross Section ◽  
Curvilinear Coordinates ◽  
Eccentric Annulus ◽  
Power Law Fluids ◽  
Eccentric Annuli

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.

Non-Newtonian Flow in Eccentric Annuli

1990 ◽  
Vol 112 (3) ◽  
pp. 163-169 ◽  
Author(s):  
M. Haciislamoglu ◽  
J. Langlinais
Keyword(s):  
Velocity Profile ◽  
Power Law ◽  
Flow Rate ◽  
Pressure Loss ◽  
Annular Flow ◽  
Flow Behavior ◽  
Drilling Fluids ◽  
Viscosity Term ◽  
Power Law Fluids ◽  
Eccentric Annuli

A common assumption for annular flow used in the petroleum industry is that the inner pipe is concentrically located inside the flow geometry; however, this is rarely the case, even in slightly deviated wells. Considering the increasing number of directional and horizontal wells, the flow behavior of drilling fluids and cement slurries in eccentric annuli is becoming particularly important. In this paper, the governing equation of laminar flow is numerically solved using a finite differences technique to obtain velocity and viscosity profiles of yield-power law fluids (including Bingham plastic and power law fluids). Later, the velocity profile is integrated to obtain flow rate. Results show that the velocity profile is substantially altered in the annulus when the inner pipe is no longer concentric. Stagnant regions of flow were calculated in the low side of the hole. Viscosity profiles predicted for an eccentric annulus show how misleading the widely used single-value apparent viscosity term can be for non-Newtonian fluids. Profiles of velocity and viscosity in concentric and varying eccentric annuli are presented in 3-D and 2-D contour plots for a better visualization of annular flow. Frictional pressure loss gradient versus flow rate relationship data for power law fluids is generated using the computer program. Later, this data is fitted to obtain a simple equation utilizing regressional analysis, allowing for a quick calculation of friction pressure losses in eccentric annuli. For a given flow rate, frictional pressure loss is reduced as the inner pipe becomes eccentric. In most cases, about a 50-percent reduction in frictional pressure loss is predicted when the inner pipe lies on the low side.

Analysis of Yield-Power-Law Fluid Flow in Irregular Eccentric Annuli

1998 ◽  
Vol 120 (3) ◽  
pp. 201-207 ◽  
Author(s):  
Q. E. Hussain ◽  
M. A. R. Sharif
Keyword(s):  
Power Law ◽  
Flow Rate ◽  
Axial Flow ◽  
Computer Code ◽  
Exponential Model ◽  
Curvilinear Coordinates ◽  
Power Law Fluids ◽  
Annular Geometry ◽  
Eccentric Annuli ◽  
Flow Blockage

Fully developed laminar axial flow of yield-power-law fluids in eccentric annuli has been investigated numerically. The annuli may be fully open or partially blocked. General nonorthogonal, boundary-fitted curvilinear coordinates have been used to accurately model the irregular annular geometry due to the presence of a flow blockage. A computer code has been developed using a second-order finite-difference scheme. An exponential model for the shear stress, valid for both yielded and un-yielded regions of the flow, is used in the computation. The effects of pressure gradient, eccentricity, and blockage height on the flow rate have been studied and the results are presented. The flow rate is found to increase with increasing eccentricity for eccentric annuli without any blockage. For partially blocked eccentric annuli, the flow rate at a particular eccentricity decreases as the blockage height is increased.

Numerical Analysis of Annular Flow of Yield-Power-Law Fluids

1998 ◽  
Author(s):  
Quazi E. Hussain ◽  
Muhammad A. R. Sharif
Keyword(s):  
Power Law ◽  
Flow Rate ◽  
Axial Flow ◽  
Computer Code ◽  
Exponential Model ◽  
Curvilinear Coordinates ◽  
Power Law Fluids ◽  
Annular Geometry ◽  
Eccentric Annuli ◽  
Flow Blockage

Abstract Fully developed laminar axial flow of yield-power-law fluids in eccentric annuli has been investigated numerically. The annuli may be fully open or partially blocked. General non-orthogonal, boundary-fitted curvilinear coordinates have been used to accurately model the irregular annular geometry due to the presence of a flow blockage. A computer code has been developed using a second-order finite-difference scheme. An exponential model for the shear stress, valid for both yielded and unyielded regions of the flow, is used in the computation. The effects of pressure gradient, eccentricity, and blockage height on the flow rate have been studied and the results are presented. The flow rate is found to increase with increasing eccentricity for eccentric annuli without any blockage. For partially blocked eccentric annuli, the flow rate at a particular eccentricity decreases as the blockage height is increased.

Electroosmotic Flow of Power-Law Fluids in a Slit Microchannel

2009 ◽  
Author(s):  
Cunlu Zhao ◽  
Chun Yang
Keyword(s):  
Shear Stress ◽  
Double Layer ◽  
Power Law ◽  
Dynamic Viscosity ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Flow Behavior Index ◽  
Power Law Fluids ◽  
Hyperbolic Cosine ◽  
Behavior Index

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity and velocity distributions. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a mathematical expression for the average electroosmotic velocity is derived for large values of the dimensionless electrokinetic parameter, κH, in a fashion similar to the Smoluchowski equation. Hence, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Finally, calculations are performed to examine the effects of κH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

Laminar flow of power-law fluids past a rotating cylinder

2010 ◽  
Vol 165 (21-22) ◽  
pp. 1442-1461 ◽  
Author(s):  
Saroj K. Panda ◽  
R.P. Chhabra
Keyword(s):  
Laminar Flow ◽  
Power Law ◽  
Rotating Cylinder ◽  
Power Law Fluids
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