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

Abstract

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