Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 445-452
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Effect of Pipe Diameter on Polymer Drag Reduction Robert H. J. Sellin’ and Mike Olils Department of Civil Engineering, University of Brlstol. Bristol BS8 1 TR, U.K.
Tests were conducted in six different pipe diameters (from 1 to 50 mm) with the same polymer. This was a polyacrylamide of only moderate drag reducing abilii to ensure that the onset point could be determined directly wherever possible and that the results in the polymeric zone were unaffected by the maximum drag reduction region. Standardized solution preparation was adopted throughout and Granville’s method of scale-up proved, with some limitations, to give the best and most convenient method of performance prediction. Attempts to explain drag reduction differences between large and small pipes were only partially successful.
1. Introduction In order to improve our ability to predict the behavior of drag reducing polymer additives in industrial applications (pipelines),a better understanding of the scaling laws for such fluid flows is required. Normal (Newtonian) fluid pipe flow can be scaled by considering the friction coefficient X to be a function of the flow Reynolds number Re and, for rough pipes, the relative wall roughness, t l d . It must be remembered that X is defined by the DarcyWeisbach equation which is based on the pipe diameter rather than the pipe hydraulic radius. All these parameters with the possible exception of e can be easily quantified. With dilute solutions of drag reducing polymers, however, the following additional parameters need to be considered: (1)d/v’/tv, a dimensionless ratio between the pipe diameter d, the solution viscosity v, and the polymer relaxation time t. This variable grouping may be regarded as the characteristic time of the polymer-solvent-pipe system; (2) c, the concentration of the polymer in the solution; (3) P, defining the state of the polymer species used including the distribution of different molecular weights present and its degree of dissolution. All these give a functional relationship for the friction coefficient X = f [ R e ,d f i , c , P, e / d ]
The normal treatment of a multiparameter relationship of this type is to assume that one chosen parameter group is dominant and that the influence of the other is of only secondary importance. This approach has been demonstrated to be unsatisfactory for drag reduction flows. The parameters t and P depend upon the polymer used. It is not uncommon for these parameters to vary with different batches of what is nominally a consistent commercial grade of polymer. To avoid this problem in the present experimental program, which involved testing solutions of the same polymer in five different diameter laboratory pipes, all the tests made with one polymer were carried out by using solutions prepared from the same batch at the same time and tested between 24 and 48 h after dissolution. The tests were conducted in new, smooth-walled stainless steel or PVC pipes which all behaved as hydraulically smooth so removing the parameter t l d as a variable in this program. The Reynolds number is defined as Re = V d / u (2) in which Y is always taken as the solvent viscosity for convenience as the change of solution viscosity at low polymer concentrations (I40 wppm, parts per million by 0198-432118311222-0445$01.50/0
weight) can be considered small. Drag reduction, at constant Re value, is defined as
(3) in which A, is the friction coefficient for the polymer solution and X, is that for the solvent in the same pipe and at the same Re value. Drag reduction can be expressed as a function of the pipe shear velocity (4) in which iois the wall shear stress inside the pipe and p is the fluid density. Using 1, the characteristic polymer molecule length, a dimensionless group of variables may be constructured, uJ/u to replace the group d/v’/tv in eq 1. 2. Experimental Drag Reduction Data The behavior of dilute solutions of the most effective polymers is well-known for small pipes (less than 150 mm diameter) from numerous published accounts of laboratory studies. A more limited number of investigations have been reported in the literature involving larger pipes which cover the range of sizes of potential industrial applications. Results of tests carried out in pipes over the range 150-300 mm, prior to 1974, are reviewed by Sellin (1974), while more recent experiments in the 1.6-m diameter Trans Alaska Pipeline (TAPS) are reported by Burger et al. (1980). In this the diameter and length of pipe used far outstrips that in any previous drag reduction tests. Earlier writers, extrapolating trends discernible in smaller pipe sizes, have predicted little or no drag reduction in pipes of this size and so it is interesting to note that drag reduction in the range 20-25% is consistently obtained in TAPS using 20 wppm of an appropriate oil-soluble polymer. In order to obtain flow data against which the various predictive methods could be tested, experiments were carried out in pipes whose nominal diameters were 1, 2, 5, 10, 25, and 50 mm. In the final analysis the data collected in the 1-mm pipe were discarded as they were largely concerned with the transitional region between laminar and turbulent flow as well as the laminar flow region itself. The polymer solution concentrations c tested were: 1.25, 2.5, 5, 10, 20, and 40 wppm, and initially three polymers were selected for study. These were: (1)Union Carbide’s Polyox WSR-301, a poly(ethy1ene oxide) with a M , 4 X lo6, of nonionic character, supplied as a fine powder; (2) Allied Colloid’s Magnafloc-1011, a poly(acrylamide), M , > lo6 with a 30% anionic character; this was supplied in
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6 1983 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 3, 1983
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