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

1967 ◽  
Vol 7 (03) ◽  
pp. 325-332 ◽  
Author(s):  
J.M. Rodriguez ◽  
J.L. Zakin ◽  
G.K. Patterson
Keyword(s):  
Molecular Weight ◽  
Pressure Drop ◽  
Drag Reduction ◽  
Friction Factor ◽  
High Molecular Weight ◽  
Polymer Solutions ◽  
Petroleum Industry ◽  
Nonpolar Solvents ◽  
Factor Ratio ◽  
Drag Ratio

Abstract Correlation has been obtained between drag-reducing characteristics forturbulent flow in a pipe and measurable properties of several polymersolutions. Several concentrations of high molecular weight polymethylmethacrylate in toluene, high molecular weight polyisobutylene in both tolueneand cyclohexane, medium molecular weight polyisobutylene in cyclohexane andbenzene and low molecular weight polystyrene in toluene were studied. Dataobtained in these nonpolar solvents and literature data for more polar solventswere successfully correlated as the ratio of measured friction factor to purelyviscous friction factor vs the modified Deborah numbervr1/D0.2, where r1 is the first-moderelaxation time of the solution estimated by the Zimm theory. A shift factorwhich is a function of intrinsic viscosity 1/(4[?] - 1) allowed all the dataobtained with nonpolar solvents to be correlated as a single function. Forthese systems, most of the data fit a single curve to within ±5 percent of theaverage friction factor ratio. The shift factor did not give a unique functionof the data for the more polar systems. INTRODUCTION The phenomenon of drag reduction in polymer solutions was first studied byToms1 in dilute solutions of polymethyl methacrylate inmonochlorobenzene. The drag ratio for flow through circular tubes has beendefined2 as the ratio of the pressure - drop of the solution to thepressure drop of the solvent at the same flow rate. The drag ratio is less than1.0 for a drag-reducing fluid. Practical use of drag reduction is being made infracturing operations in the petroleum industry.3 A more fundamental quantity is the friction factor ratio, defined as theratio of the observed pressure drop to that predicted for a solution of thesame viscosity characteristics and density at equal flow rates using theDodge-Metzner friction factor equation.4Equation 1 Viscous solutions with drag ratios greater than 1.0 can have friction factorratios less than 1.0. For practical applications, it is drag reduction which isof interest. However, for correlation the fundamental ratio is the frictionfactor ratio. In recent years, drag reduction has been studied extensively. Recent studieshave shown that reasonable predictions of the incipience of drag reduction inpolymer solutions can be made from the properties of the solutions and the flowvariables.5 However, it has not been possible to predict accuratelythe amount of drag reduction to be expected for a given polymer solutionwithout any drag-reducing turbulent flow data on the samesolution.6

scholarly journals Applicability of the Cox-Merz Rule to High-Density Polyethylene Materials with Various Molecular Masses

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1218
Author(s):  
Raffael Rathner ◽  
Wolfgang Roland ◽  
Hanny Albrecht ◽  
Franz Ruemer ◽  
Jürgen Miethlinger
Keyword(s):  
Molecular Weight ◽  
Pressure Drop ◽  
High Molecular Weight ◽  
High Density Polyethylene ◽  
Parallel Plate ◽  
Empirical Relationship ◽  
Polymer Processing ◽  
High Density ◽  
Viscosity Data ◽  
Molecular Masses

The Cox-Merz rule is an empirical relationship that is commonly used in science and industry to determine shear viscosity on the basis of an oscillatory rheometry test. However, it does not apply to all polymer melts. Rheological data are of major importance in the design and dimensioning of polymer-processing equipment. In this work, we investigated whether the Cox-Merz rule is suitable for determining the shear-rate-dependent viscosity of several commercially available high-density polyethylene (HDPE) pipe grades with various molecular masses. We compared the results of parallel-plate oscillatory shear rheometry using the Cox-Merz empirical relation with those of high-pressure capillary and extrusion rheometry. To assess the validity of these techniques, we used the shear viscosities obtained by these methods to numerically simulate the pressure drop of a pipe head and compared the results to experimental measurements. We found that, for the HDPE grades tested, the viscosity data based on capillary pressure flow of the high molecular weight HDPE describes the pressure drop inside the pipe head significantly better than do data based on parallel-plate rheometry applying the Cox-Merz rule. For the lower molecular weight HDPE, both measurement techniques are in good accordance. Hence, we conclude that, while the Cox-Merz relationship is applicable to lower-molecular HDPE grades, it does not apply to certain HDPE grades with high molecular weight.

Drag Reduction of Polymer Solutions in a Pipe With a Highly Water-Repellent Wall

1999 ◽  
Author(s):  
Keizo Watanabe ◽  
Hiroshi Udagawa
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Drag Reduction ◽  
Polymer Solutions ◽  
Tap Water ◽  
Acrylic Resin ◽  
Water Repellent ◽  
Number Range ◽  
Surfactant Solutions ◽  
Laminar And Turbulent Flow

Abstract By applying a highly water-repellent wall pipe in the drag reduction of polymer solutions, a flow system in which drag reduction is obtained in both laminar and turbulent flow ranges has been realized. Experiments were carried out to measure the pressure drop in pipes with a highly water-repellent wall and an acrylic resin wall by means of a pressure transducer. The diameter of the pipe was 6mm. The polymer solutions tested were PE015 aqueous solutions in the concentration range of 30ppm∼1000ppm. The drag reduction ratio for laminar flow was about 11∼15%. To understand this effect, the pressure drop was measured by using surfactant solutions and degassed water, and by pressurizing tap water in the pipeline. It was shown that the laminar drag reduction does not occur in the case of surfactant solutions although degassed water and pressurizing tap water in the pipeline have no effect on the reduction. In the laminar flow range, the friction factor of a power-law fluid with fluid slip was analyzed by applying the modified boundary condition on fluid slip at the pipe wall, and the analytical results agree with the experimental results in the low Reynolds number range.

Drag Reduction in Three Distinctly Different Fluid Systems

1981 ◽  
Vol 21 (06) ◽  
pp. 663-669 ◽  
Author(s):  
Thomas R. Sifferman ◽  
Robert A. Greenkorn
Keyword(s):  
Pressure Drop ◽  
Drag Reduction ◽  
Polymer Solution ◽  
Flow Rate ◽  
Polymer Solutions ◽  
Tap Water ◽  
Smooth Wall ◽  
Two Phase ◽  
Fluid Systems ◽  
Flow Systems

Abstract Drag reduction was observed in three distinctly different flow systems-dilute polymer solutions, two-phase solid/liquid suspensions, and three-phase immiscible liquid/liquid flow with suspended solids - in relatively large-diameter pipes (0.027, 0.038, and 0.053 m). Galvanized pipes presented a rough wall, while glass provided a smooth wall and allowed for flow visualization. provided a smooth wall and allowed for flow visualization. By drag reduction, we mean that, for the same flow rate, there is less pressure drop per length of pipe than for the base fluid flowing, alone.Three polymers-sodium carboxymethylcellulose (CMC). polyethylene oxide (POLYOX(TM)), and guar gum) (Jaguar(TM)) were mixed with water to form solutions of various concentrations (from 0.001 to 0.3 wt%). Two nominal concentrations (5 to 10%) of silca sand also were suspended with either tap water or some of the polymers. Finally, white mineral oil and either tap water or polymer solutions were tested. Sand also was added to the oil system.Drag reductions of up to almost 80% were obtained for both the polymer systems and the oil system. Sand suspensions had a maximum of about 35% drag reduction in tap water. However, greatest reductions (more than 90% were attained with the polymer/sand suspensionsSince the sand in the polymer solutions reduced the drag even more than the polymers alone, it may be that the drag mechanism is additive and even may be the same type for both polymers and suspensions.Drag reduction occurs in the region near the wall and could occur in an intermediate layer zone that allows an effective slip velocity to result. Polymers showed significant deviation from the Newtonian velocity profiles.Less power was required to pump the polymers than water alone. Viscosity and normal stress data were obtained also. Introduction There are many interesting engineering applications of drag-reduction phenomena. For many flow situations in conduits, the use of a drag reduction agent (normally a viscoelastic soluble polymer) increases flow rate for the same pressure drop in diverse systems. Such as storm sewers, drilling operations, fire fighting, irrigation and living systems. External flows can be improved around ships and torpedoes. Proper design of solid/fluid systems to take advantage of the drag reduction associated with suspended solids can be used in transporting coal, raw sewage, and sediment. In two-phase liquid/liquid situations, such as hydraulic fracturing of oil wells and transportation of liquid petroleum. drag reduction associated with annular immiscible or emulsion flow can be used to advantage where exceptionally large reductions in pressure for a given flow rate result for viscous oils and water.To design systems to take advantage of lower energy requirements at the same flow rate, data are necessary (1) from systems large enough that diameter effects are absent, (2) at flow rates of sufficient velocity that the phenomena are present, and (3) on different systems phenomena are present, and (3) on different systems with varying physical properties. Such data re necessary to develop correlations, to understand flow mechanisms, and to develop mathematical models-all of which are necessary to interpolate and extrapolate the data for design of such flow systems. Previously, this type of data has not been available.Drag reductions is defined, at a given flow rate, as the pressure drop for a given system minus the pressure drop pressure drop for a given system minus the pressure drop for the base fluid divided by the pressure drop for the base fluid.In this paper, we report observations of drag-reduction phenomena in three distinctly different flow systems: (1) phenomena in three distinctly different flow systems:single-phase water, oil, and dilute polymer-water solutions;two-phase oil/water, oil/polymer solution, water/sand, and polymer solution/sand; andthree-phase oil/water/sand and oil/polymer solution/sand. The data were collected in 0.027- and 0.053-m Schedule 40 galvanized pipe and a 0.038-m-ID smooth-wall glass pipe. pipe. SPEJ P. 663

Experimental Study on Flow-Front Fingering Instabilities in Injection Molding of Polymer Solutions and Melts

2004 ◽  
Author(s):  
Kalonji K. Kabanemi ◽  
Jean-Franc¸ois He´tu ◽  
Samira H. Sammoun
Keyword(s):  
Molecular Weight ◽  
High Molecular Weight ◽  
Polymer Solutions ◽  
Low Molecular Weight ◽  
Flow Front ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer ◽  
Polymer Molecules ◽  
Molecular Weights ◽  
Solvent Molecules

An experimental investigation of the flow behavior of dilute, semi-dilute and concentrated polymer solutions has been carried out to gain a better understanding of the underlying mechanisms leading to the occurrence of instabilities at the advancing flow front during the filling of a mold cavity. Experiments were performed using various mass concentrations of low and high molecular weight polyacrylamide polymers in corn syrup and water. This paper reports a new type of elastic fingering instabilities at the advancing flow front that has been observed only in semi-dilute polymer solutions of high molecular weight polymers. These flow front elastic instabilities seem to arise as a result of a mixture of widely separated high molecular weight polymer molecules and low molecular weight solvent molecules, which gives rise to a largely non-uniform polydisperse solution, with respect to all the kinds of molecules in the resulting mixture (solvent molecules and polymer molecules). The occurrence of these instabilities appears to be independent of the injection flow rate and the cavity thickness. Moreover, these instabilities do not manifest themselves in dilute or concentrated regimes, where respectively, polymer molecules and solvent molecules are minor perturbation of the resulting solution. In those regimes, smooth flow fronts are confirmed from our experiments. Based on these findings, the experimental investigations have been extended to polymer melts. Different mixtures of polycarbonate melts of widely separated molecular weights (low and high molecular weights) were first prepared. The effect of the large polydispersity of the resulting mixtures on the flow front behavior was subsequently studied. The same instabilities at the flow front were observed only in the experiments where a very small amount of high molecular weight polycarbonate polymer has been mixed to a low molecular weight polycarbonate melt (oligomers).

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