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.

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.

An Accurate Model for Prediction of Turbulent Frictional Pressure Loss of Power-Law Fluids in Eccentric Geometries

2021 ◽  
pp. 1-18
Author(s):  
Vahid Dokhani ◽  
Yue Ma ◽  
Zili Li ◽  
Mengjiao Yu
Keyword(s):  
Power Law ◽  
Pressure Loss ◽  
Eddy Viscosity ◽  
Numerical Study ◽  
Axial Flow ◽  
Drilling Fluids ◽  
Eddy Viscosity Model ◽  
Friction Factors ◽  
Power Law Fluids ◽  
Eccentric Annuli

Summary The effect of axial flow of power-law drilling fluids on frictional pressure loss under turbulent conditions in eccentric annuli is investigated. A numerical model is developed to simulate the flow of Newtonian and power-law fluids for eccentric annular geometries. A turbulent eddy-viscosity model based on the mixing-length approach is proposed, where a damping constant as a function of flow parameters is presented to account for the near-wall effects. Numerical results including the velocity profile, eddy viscosity, and friction factors are compared with various sets of experimental data for Newtonian and power-law fluids in concentric and eccentric annular configurations with diameter ratios of 0.2 to 0.8. The simulation results are also compared with a numerical study and two approximate models in the literature. The results of extensive simulation scenarios are used to obtain a novel correlation for estimation of the frictional pressure loss in eccentric annuli under turbulent conditions. Two new correlations are also presented to estimate the maximum axial velocity in the wide and narrow sections of eccentric geometries.

scholarly journals Effect of the Flame Dome Depth and Improvement of the Pressure Loss in the Dump Diffuser

1998 ◽  
Author(s):  
Shinji Honami ◽  
Wataru Tsuboi ◽  
Takaaki Shizawa
Keyword(s):  
Velocity Profile ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Pressure Loss ◽  
Total Pressure ◽  
Flow Behavior ◽  
Sudden Expansion ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

This paper presents the effect of flame dome depth on the total pressure performance and flow behavior in a sudden expansion region of the combustor diffuser without flow entering the dome head. The mean velocity and turbulent Reynolds stress profiles in the sudden expansion region were measured by a Laser Doppler Velocitmetry (LDV) system. The experiments show that total pressure loss is increased, when flame dome depth is increased. Installation of an inclined combuster wall in the sudden expansion region is suggested from the viewpoint of a control of the reattaching flow. The inclined combustor wall is found to be effective in improvement of the diffuser performance. Better characteristics of the flow rate distribution into the branched channels are obtained in the inclined wall configuration, even if the distorted velocity profile is provided at the diffuser inlet.

Axial Laminar Flow of Non-Newtonian Fluids in Narrow Eccentric Annuli

1965 ◽  
Vol 5 (04) ◽  
pp. 277-280 ◽  
Author(s):  
Robert D. Vaughn
Keyword(s):  
Laminar Flow ◽  
Power Law ◽  
Flow Rate ◽  
Pressure Loss ◽  
Large Diameter ◽  
Experimental Studies ◽  
Small Diameter ◽  
Journal Bearings ◽  
Newtonian Fluids ◽  
Eccentric Annuli

Abstract The analysis of laminar flow of power-law non- Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journal bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annulus would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7.5 per cent. Introduction Non-Newtonianism and eccentricity occur simultaneously in two engineering problems:flow of lubricants in journal-bearings and pressure-reducing bushings, andflow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character - often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publications have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda and Redberger and Charles have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Caldwell and Bairstow and Berry, which is reported by Dryden, et al. Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (K less than 0.5); however, for large diameter ratios (K - 1), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden, Tao and Donovan and Piercy, et al. Tao and Donovan examined the case of flow in narrow, eccentric annuli (K - 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et al. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles and the experimental proof of Tao and Donovans both suggest that the region of large diameter ratios (K - 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. (1) This model has many disadvantages which have been pointed out; nevertheless, As simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Birds and Savins have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli. SPEJ P. 277ˆ

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.

Scaling Formulae for the Wellbore Hydraulics Similitude with Drill Pipe Rotation and Eccentricity

2021 ◽  
Author(s):  
Thad Nosar ◽  
Pooya Khodaparast ◽  
Wei Zhang ◽  
Amin Mehrabian
Keyword(s):  
Power Law ◽  
Flow Rate ◽  
Annular Flow ◽  
Rotation Speed ◽  
Drilling Fluid ◽  
Drill Pipe ◽  
Flow Loop ◽  
Annular Flows ◽  
Fluid Rheology ◽  
Pipe Rotation

Abstract Equivalent circulation density of the fluid circulation system in drilling rigs is determined by the frictional pressure losses in the wellbore annulus. Flow loop experiments are commonly used to simulate the annular wellbore hydraulics in the laboratory. However, proper scaling of the experiment design parameters including the drill pipe rotation and eccentricity has been a weak link in the literature. Our study uses the similarity laws and dimensional analysis to obtain a complete set of scaling formulae that would relate the pressure loss gradients of annular flows at the laboratory and wellbore scales while considering the effects of inner pipe rotation and eccentricity. Dimensional analysis is conducted for commonly encountered types of drilling fluid rheology, namely, Newtonian, power-law, and yield power-law. Appropriate dimensionless groups of the involved variables are developed to characterize fluid flow in an eccentric annulus with a rotating inner pipe. Characteristic shear strain rate at the pipe walls is obtained from the characteristic velocity and length scale of the considered annular flow. The relation between lab-scale and wellbore scale variables are obtained by imposing the geometric, kinematic, and dynamic similarities between the laboratory flow loop and wellbore annular flows. The outcomes of the considered scaling scheme is expressed in terms of closed-form formulae that would determine the flow rate and inner pipe rotation speed of the laboratory experiments in terms of the wellbore flow rate and drill pipe rotation speed, as well as other parameters of the problem, in such a way that the resulting Fanning friction factors of the laboratory and wellbore-scale annular flows become identical. Findings suggest that the appropriate value for lab flow rate and pipe rotation speed are linearly related to those of the field condition for all fluid types. The length ratio, density ratio, consistency index ratio, and power index determine the proportionality constant. Attaining complete similarity between the similitude and wellbore-scale annular flow may require the fluid rheology of the lab experiments to be different from the drilling fluid. The expressions of lab flow rate and rotational speed for the yield power-law fluid are identical to those of the power-law fluid case, provided that the yield stress of the lab fluid is constrained to a proper value.

Thermally Fully Developed Electroosmotic Flow of Power-Law Fluids in a Circular Microchannel

2013 ◽  
Vol 29 (4) ◽  
pp. 609-616 ◽  
Author(s):  
Y.-J. Sun ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Power Law ◽  
Joule Heating ◽  
Electroosmotic Flow ◽  
Flow Behavior ◽  
Mathematic Model ◽  
Dimensionless Temperature ◽  
Fluid Temperature ◽  
Navier Stokes Equation ◽  
Power Law Fluids ◽  
Behavior Index

ABSTRACTThis study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

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