Pressure drop scaling laws and structural stress contributions for complex flows of flexible polymer solutions in thick solvents

1992 ◽  
Vol 44 ◽  
pp. 55-83 ◽  
Author(s):  
U. Cartalos ◽  
J.M. Piau
1999 ◽  
Author(s):  
Keizo Watanabe ◽  
Hiroshi Udagawa

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.


1982 ◽  
Vol 104 (1) ◽  
pp. 88-91 ◽  
Author(s):  
J. Lee ◽  
C. T. Crowe

An experimental investigation was undertaken to determine those scaling parameters applicable to measuring the mass flow rate of gas-particle suspensions through venturis. It was found that Stokes number and the particle/gas loading ratio are the two most important parameters. The results show that pressure drop increases linearly with loading ratio and decreases monotonically with increasing Stokes number. The results also indicate that β-ratio and orientation of venturi do not significantly affect the pressure drop. Data for irregularly shaped pulverized coal particles show higher pressure drop compared with those for spherical particles. A quasi one-dimensional numerical model overpredicts the pressure drop, but a two-dimensional model demonstrates improved agreement.


1981 ◽  
Vol 21 (06) ◽  
pp. 663-669 ◽  
Author(s):  
Thomas R. Sifferman ◽  
Robert A. Greenkorn

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


1976 ◽  
Vol 65 (3) ◽  
pp. 1101-1108 ◽  
Author(s):  
J. P. Cotton ◽  
M. Nierlich ◽  
F. Boué ◽  
M. Daoud ◽  
B. Farnoux ◽  
...  

1967 ◽  
Vol 7 (03) ◽  
pp. 325-332 ◽  
Author(s):  
J.M. Rodriguez ◽  
J.L. Zakin ◽  
G.K. Patterson

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


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