Correlation of Drag Reduction With Modified Deborah Number For Dilute Polymer Solutions

Rodriguez, J. M.; Zakin, J. L.; Patterson, G. K.

doi:10.2118/1678-pa

Cited by 34 publications

(10 citation statements)

References 4 publications

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“…The maximum drag reduction asymptote, its universality, and Prandtl-Karman form were first pointed out by US although the existence of a maximum possible drag reduction was independently noted by several investigators (Hoyt and Fabula, 1964;Castro and Squire, 1967;Giles, 1968). The reader should also be aware of some alternative gross flow correlation schemes, for example, those of Rodriguez, Zakin, and Patterson ( 1967), Whitsitt, Crawford, and Harrington (1968), Seyer and hletzner ( 1969), Astarita, Greco, and Nicodemo (1969).…”

Section: Sourcesmentioning

confidence: 98%

Drag reduction fundamentals

1975

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Drag reduction by dilute solutions of linear, random-coiling macromolecules in turbulent pipe flow is reviewed. The experimental evidence is emphasized in three sections concerned with the graphical display of established features of the phenomenon, data correlation and analysis, and the physical mechanism of drag reduction. P. S. VlRK Deportment of Chemical Engineering Indian Institute of TechnologyMadras 600036, India SCOPEOur objective is to acquaint the reader with the phenomenon of drag reduction, in which the skin friction caused by turbulent flow of an ordinary liquid is reduced by additives. This phenomenon, discovered ahnut 1947, has received attention because it suggests practical benefits, such as increased pipeline capacities and faster ships, and is also theoretically stimulating, in the areas of wall turbulence and molecular rheology . This review, restricted to drag reduction by polymer solutions in pipe flow, has three sections: (1) the experimental evidence, (2) correlation and analysis, and (3) mechanism. Section 1 presents experimentally established results showing the flow regimes exhibited by polymer solutions, the relationships among flow and macromolecular parameters, and the changes in mean and turbulent flow structures which accompany drag reduction. The conclusions of Section 1 are documented in Section 2. The latter concerns the empirical correlation of experimental results, with analysis (and tabulations) of the data used for this purpose. Section 2 also provides for discussion of evidence not fully enough established to be included in Section 1. Finally, in Section 3 an attempt is made to physically interpret the experimental results, to infer the nature of the polymer-turbulence interaction responsible for drag reduction and its effect on the energy balances of turbulent pipe flow. CONCLUSIONS AND SIGNIFICANCE1. Gross Flow. Drag reduction by dilute polymer solutions in turbulent pipe flow appears bounded between two universal asymptotes, namely, the Prandtl-Karman law [Equation (2)] for Newtonian turbulent flow and a maximum drag reduction asymptote [Equation (4)]. Between these limits is a polymeric regime in which the observed friction factor relations are approximately linear on Prandtl-Karman coordinates and can be characterized by two parameters-the wall shear stress at the onset of drag reduction and the slope increment by which the polymer solution slope exceeds Newtonian. For a given polymer species-solvent pair: The onset wall shear stress is essentially independent of pipe diameter, polymer concentration, and solvent viscosity, and varies inversely as the two to three power of polymer radius of gyration [Equations (19) and ( 5 ) ] . The slope increment is essentially independent of pipe diameter, varies as the square root of polymer concentration, and as the three-halves power of the number of chain links in the polymer backbone [Equation (S)], and seems unaffected by decreases in polymer excluded volume.2. Mean Velocity Profiles. On law of the wall coordinates, these posse...

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Section: Sourcesmentioning

confidence: 98%

Drag reduction fundamentals

1975

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“…Although several definitions are available for Deborah number (16,20,21) , none of them were successful in correlating flow data of SB fluids. Therefore, a new definition of Deborah number is adopted, employing the predetermined relaxation times shown in Table 3.…”

Section: Theoretical Workmentioning

confidence: 99%

Investigation of the Complex Flow Behaviour of Surfactant-Based Fluids in Straight Tubing

Kamel

Shah

2010

Journal of Canadian Petroleum Technology

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Summary In spite of their wide use in hydraulic fracturing and gravel-pack operations, the complex flow behaviour of surfactant-based (SB) fluids in straight tubing is rarely investigated. Accurate prediction of friction-pressure is essential for proper treatment design. Previous correlations from small tubing data and using simple power-law fluid model parameters alone do not scaleup to large tubing sizes for field application. The properties of one of the most popular surfactants, Aromox APA-T, are thoroughly investigated. It is a highly-active surfactant used as the gelling agent in aqueous and brine solutions. Commonly used surfactant concentrations (1.5%, 2%, 3% and 4% by volume) are studied. Rheological and viscoelastic measurements are conducted using the Bohlin rheometer. Flow tests are conducted using 1.27-cm, 3.81-cm, 6.03-cm and 7.30-cm tubing. The results show SB fluid exhibiting a non-Newtonian pseudo-plastic behaviour. Fluid concentration and pipe shear have a significant effect on fluid elasticity. The conventional Fanning friction factor vs. Reynolds number correlation is improved by including a new dimensionless group that accounts for both fluid elasticity and pipe diameter. A new definition of Deborah number is introduced. Thus, a new correlation for predicting friction factors of SB fluid in straight tubing is developed. The scaleup problem is thus alleviated with the present analysis and this provides more accurate friction-pressure estimates.

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“…Several references [4][5][6][7][8][9] that appeared in the petroleum literature indicate the importance and potential applications of drag reduction to this industry. Savins 4 reported pipe flow tests using a number of synthetic and natural polymeric materials and three tubing sizes.…”

Section: Literature Reviewmentioning

confidence: 99%

An Experimental Study of Drag Reduction of Polymer Solutions in Coiled Tubing

Zhou

2001

Proceedings of SPE/ICoTA Coiled Tubing Roundtable

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe excessive friction pressure loss due to the small tubing diameter and the curvature (which believed to cause secondary flow) of coiled tubing (CT) often limits the maximum obtainable flow rate in CT operations. This paper presents an experimental study of drag reduction performance of several polymer solutions in coiled tubing using a sophisticated fullscale coiled tubing test facility for an industry-university joint research project. The facility includes of seven reels of coiled tubing with diameters of 1", 1-1/2", and 2-3/8", fluid mixing and pumping equipment, and data acquisition system. Fluids investigated include water and solutions of polymers currently used in the well drilling and completion industry -Xanthan gum, partially hydrolyzed polyacrylamide (PHPA), guar gum, and hydroxyethylcellulose (HEC). Experimental results showed that the amount of friction drag reduction differs significantly among the different types of polymers at various concentrations. Data interpretation and analysis revealed that the CT diameter and the CT-to-reel drum diameter ratio are important geometrical parameters affecting drag reduction. The flow data indicate that the onset of turbulent flow in CT is suppressed in the polymer solutions. This paper introduces the concept of the modified drag reduction envelope for flow of polymer solutions in coiled tubing.

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Correlation of Drag Reduction With Modified Deborah Number For Dilute Polymer Solutions

Cited by 34 publications

References 4 publications

Drag reduction fundamentals

Drag reduction fundamentals

Investigation of the Complex Flow Behaviour of Surfactant-Based Fluids in Straight Tubing

An Experimental Study of Drag Reduction of Polymer Solutions in Coiled Tubing

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