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.

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.

Annular Frictional Pressure Losses During Drilling—Predicting the Effect of Drillstring Rotation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Arild Saasen
Keyword(s):  
Rheological Properties ◽  
Pressure Loss ◽  
Drilling Fluid ◽  
Axial Flow ◽  
Drilling Fluids ◽  
Unstable Flow ◽  
Pressure Losses ◽  
Shear Dependent Viscosity ◽  
Water Based ◽  
Dependent Viscosity

Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. To predict these pressure losses, however, is not straightforward. First of all, the pressure losses depend on the annulus eccentricity. Moving the drillstring to the wall generates a wider flow channel in part of the annulus which reduces the frictional pressure losses significantly. The drillstring motion itself also affects the pressure loss significantly. The drillstring rotation, even for fairly small rotation rates, creates unstable flow and sometimes turbulence in the annulus even without axial flow. Transversal motion of the drillstring creates vortices that destabilize the flow. Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Naturally, the rheological properties of the drilling fluid play an important role. These rheological properties include more properties than the viscosity as measured by API procedures. It is impossible to use the same frictional pressure loss model for water based and oil based drilling fluids even if their viscosity profile is equal because of the different ways these fluids build viscosity. Water based drilling fluids are normally constructed as a polymer solution while the oil based are combinations of emulsions and dispersions. Furthermore, within both water based and oil based drilling fluids there are functional differences. These differences may be sufficiently large to require different models for two water based drilling fluids built with different types of polymers. In addition to these phenomena washouts and tool joints will create localised pressure losses. These localised pressure losses will again be coupled with the rheological properties of the drilling fluids. In this paper, all the above mentioned phenomena and their consequences for annular pressure losses will be discussed in detail. North Sea field data is used as an example. It is not straightforward to build general annular pressure loss models. This argument is based on flow stability analysis and the consequences of using drilling fluids with different rheological properties. These different rheological properties include shear dependent viscosity, elongational viscosity and other viscoelastic properties.

Numerical Simulation of Drag Reducing Turbulent Flow in Annular Conduits

1997 ◽  
Vol 119 (4) ◽  
pp. 838-846 ◽  
Author(s):  
Idir Azouz ◽  
Siamack A. Shirazi
Keyword(s):  
Annular Flow ◽  
Eddy Viscosity ◽  
Oil And Gas ◽  
Drilling Fluid ◽  
Drill String ◽  
Cuttings Transport ◽  
Frictional Losses ◽  
Eddy Viscosity Model ◽  
Friction Factors ◽  
Variable Damping

Inadequate transport of rock cuttings during drilling of oil and gas wells can cause major problems such as excessive torque, difficulty to maintain the desired orientation of the drill string, and stuck or broken pipe. The problem of cuttings transport is aggravated in highly inclined wellbores due to the eccentricity of the annulus which results in nonuniformity of the flowfield within the annulus. While optimum cleaning of the borehole can be achieved when the flow is turbulent, the added cost due to the increased frictional losses in the flow passages may be prohibitive. A way around this problem is to add drag-reducing agents to the drilling fluid. In this way, frictional losses can be reduced to an acceptable level. Unfortunately, no model is available which can be used to predict the flow dynamics of drag-reducing fluids in annular passages. In this paper, a numerical model is presented which can be used to predict the details of the flowfield for turbulent annular flow of Newtonian and non-Newtonian, drag-reducing fluids. A one-layer turbulent eddy-viscosity model is proposed for annular flow. The model is based on the mixing-length approach wherein a damping function is used to account for near wall effects. Drag reduction effects are simulated with a variable damping parameter in the eddy-viscosity expression. A procedure for determining the value of this parameter from pipe flow data is discussed. Numerical results including velocity profiles, turbulent stresses, and friction factors are compared to experimental data for several cases of concentric and eccentric annuli.

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.

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