rag reduction was defined by Savins (68, 70) as the
D increase in pumpability of a fluid caused by the addition of small amounts of another substance to the fluid. During drag reduction, therefore, the fluid with additive requires a lower pressure gradient to move it at a given bulk mean velocity in a pipe than the same fluid without additive. Drag reduction is distinct from the decreased friction factor observed by Dodge and Metzner (15) and exhibited by a purely viscous pseudoplastic fluid in turbulent flow at a given generalized Reynolds number (42). Dodge and Metzner formulated a pipe flow friction factor correlation for such fluids, which reduces to the von Karman equation for flow behavior index, n ’, of 1.O and which is expressed as follows :
dz
= [ 4 . 0 / ( n ’ ) 0 * 7 6log ]
[NRe’f(’ - n’’2)] - 0.40/(n’)l-2
Friction factors for drag-reducing flow may be far below those predicted using this correlation. Drag reduction is a phenomenon exhibited by many Newtonian and pseudoplastic solutions, gels, and suspensions, and is a departure from their “normal” viscous behavior, the pseudoplastic friction factor effect correlated by Dodge and Metzner being “normal” viscous behavior. Drag reduction occurs in turbulent flow and is, therefore, of great potential value to the processing industry, where most flows are turbulent. At this time, however, extensive use of drag reduction additives has been made only in petroleum production operations (34, 37, 47), particularly in the fracturing process, where water and oil suspensions of chemicals are pumped into the well a t high pressure and flow rate to increase permeability of the well formation. Promising applications of drag reduction are in long crude petroleum product pipelines (59), in brine disposal pipelines, in water and sewer systems (88), in fire-fighting water hoses, and in sprinkler irrigation (79). Applications are possible for processing operations, but will tend to be of a specific rather than general nature. Drag reduction may be achieved with several types of additives. The most spectacular drag reduction is that obtained through the addition of small amounts (order of ppm up to about 1%) of soluble polymers of certain types to the fluid. Polymer solution drag reduction may occur from one of two effects-the extension of laminar behavior to abnormally high Reynolds numbers, or the reduction of friction factor in fully developed turbulence. If the second behavior begins at low Reynolds number, it is difficult to distinguish from the first, unless transition to a higher friction factor finally occurs (indicating the first type of behavior). Hershey and Zakin (28) have pointed Out the difference in the two types of behavior. A second type of drag-reducing additive was observed in the use of gasoline gelled with aluminum soaps (7, 46) during World War 11. Since then, a number of other soaps have been reported to produce drag reduction (57,69, 77, 8 6 ) . A third type of drag-reducing fluid is a dilute SUSpension of properly sized solid particles (7, 12, 52,8?, 88). A completely different approach involves the use of a thin viscoelastic liquid injected near the wall to form an annular film around a viscous flowing fluid. Under the 22
INDUSTRIAL AND ENGINEERING CHEMISTRY
G.K. PATTERSON J. L. ZAKIN J. M. RODRIGUEZ
DRAG REDUCTION Polymer Solutions, Soap Solutions and Solid Particle Suspensions in Pipe Flow
A considerable reduction in the pressure drop accompanying turbulent flow in a p@eline can sometimes be achieved when certain additives are present in the fluid
proper conditions, annular flow will be maintained with very low wall friction. This technique has demonstrated drag reductions approaching 100% in the pipeline flow of very heavy crude oil (35, 59). The first three of the above drag reduction methods will be discussed in more detail below. Polymer Solution Drag Reduction
Polymers effective in drag reduction. Drag reduction obtained by the addition of soluble polymer to the fluid has received more study than the other types mentioned, possibly because of its spectacular effectiveness under certain conditions. High levels of drag reduction may be obtained in water, for short times, with only a few ppm of high-molecular-weight polyethylene oxide (PEO) (77, 21, 54, 62, 76, 83), the addition of which causes little perceptible change in viscosity or other measurable rheological properties. Other water-soluble polymers yielding high drag reduction are sodium carboxymethyl cellulose (CMC) (75, 20, 54, 67, 62, 75)) hydroxyethyl cellulose (39), guar gum (7 7, 78, 19, 54, 84),and some polyacrylamides (54, 56, 62, 73). A number of polymers, soluble in organic solvents and oils, have drag-reducing characteristics. These include high-molecular-weight polyisobutylene (PIB) in toluene, cyclohexane, benzene (25, 28, 64, 75), trichloroethylene (26)) or light mineral oil (65), and highmolecular-weight polymethyl methacrylate (PMMA) in toluene (25, 28) and in monochlorobenzene (78). The drag reduction caused by some rubbers, silicone polymers, and polyethylene oxides when added to organic solvents has been studied by Liaw (32), but the data are still being interpreted. I t is likely that many other
TABLE I. Polymer
polymers having structures similar to these are dragreducing, but specific data have not yet been reported. Polymer solutions not exhibiting drag reduction at any concentration at attainable flow rates are : water solutions of a polyacrylic acid, at several degrees of neutralization up to and including polysodium acylate, a carboxymethyl-hydroxyethyl cellulose solution (69), toluene solutions of commercial polystyrene (25, 281,low-molecularweight PIB in cyclohexane (25), and low-molecularweight PMMA in toluene (25). Molecular weight and flow rate must be known for intelligent comparisons of behavior. Table I is a partial list of polymer solutions which have been studied for drag reduction. The molecular weight, flow rate, and pipe size €or 3070 drag reduction (a significantly measurable level) are shown for each solution being compared. The effects of polymer properties and polymer-solvent interaction on drag reduction are considered below. Drag reduction correlations for polymer solutions. The variables most affecting the level of drag reduction for a given polymer solution in turbulent pipe flow are the bulk mean velocity, polymer concentration, and pipe diameter. .A strong diameter effect on drag reduction was reported by Savins (68) for the data of Toms (78) ; the Toms solutions were polymethyl methacrylate in monochlorobenzene. As shown for one concentration in Figure 1, smaller diameters yield drag reduction a t lower Reynolds numbers and greater drag reduction at the same Reynolds numbers. As will be shown, this strong diameter effect occurs because polymer solution drag reduction is not directly related to Reynolds number for dilute polymer solutions [see Liaw’s (32) definition below].
M I N I M U M VELOCITY FOR 30% DRAG REDUCTION
Mol wt, vlrcorily a v
Solvent
CMC PMMA-G
Unknown 1,500,000
Water Toluene
PMMA PIB L-80 PIB L-80 PIB L-200 Vinyl I Guar gum Guar gum PEO coagulant PEO WSR 205
1,400,000a 720,000 720,000
MCB Cyclohexane Benzene Cyclohexane Water Water Sea water Benzene Benzene
4,000,000 Unknown 1,700 ) 000 Unknown 2,750,000 400,000
%
Pipe i.d., in.
Velocity, fpr
Ref.
0.25
2.00
( 75)
0.55 0.25 0.10 0.25 0.40 0.07 0.08 0.05 0.20 0.40
0.51 0.16 0.51 0.51 1 .oo 1.oo 2.00 0.065 1.00 1.00
10 51 8 45 76 20
1 .oo
1
(69)
1.00
8
(57)
