Concentration drag reduction

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

In the extensive literature on polymer drag reduction, it has occasionally been reported that a continuous thread of a high-concentration polymer solution injected into the axis of a pipe produces a drag-reduction effect on the water flow in the pipe [856]. The thread seems to persist through the length of the pipe and little, if any, diffusion of polymer to the walls of the pipe is apparent. 

A polymer of the polyacrylamide type was injected as a 0.5% solution from an axially-placed nozzle at the bellmouth entrance. The experiments showed that the central thread provided drag reduction almost equivalent to premixed solutions of the same total polymer concentration flowing in the pipe. Overall concentrations of 1, 2, 4, and 20 ppm were used. Moreover, the effects were additive 2 ppm thread overall concentration plus 2 ppm premixed gave drag reductions equivalent to 4 ppm of either type. Reynolds numbers of up to 300,000 were investigated. In other experiments, a number of different polymer fluids were injected on the centerline of a water pipe-flow facility [857]. Two distinct flow regions were identified ... 

Experiments have been conducted to investigate the effect of a soapy industrial cleaner on reducing the skin friction of a Jordanian crude oil flowing turbulently in pilot-scale pipes of different sizes. Experiments showed that a concentration of only 2 ppm of the chemical additive injected into the crude oil line caused an appreciable amount of drag reduction [1165]. The effects of additive concentration and pipe diameter on drag reduction have been investigated. 

Universal drag reduction curves can be obtained in several ways, for example, by normalizing the hydrodynamic volume fraction of the polymer in solution (63). Further, a three-parameter empirical relationship between the drag reduction and concentration has been introduced (64). 

The effects of the concentration of PIB on drag reduction in different solvents have been investigated (65). Viscosity measurements of PIB with different molecular weights in two solvents, namely cyclohexane and xylene showed that a universal drag reduction equation can be used in order to describe the behavior. 

In the area of hydrodynamics the term drag reduction has become a familiar name for characterizing the reduction of friction in turbulent flow through pipes. This is not caused by an improvement in the wall properties as this would only lead to a decrease in friction of a few percent. It is possible, however, to reduce the degree of friction in turbulent flow by a considerable extent, if small amounts of a suitable additive in a concentration range of only a few parts per million by weight are used a reduction in friction of 80 percent can be reached. A tremendous change in the flow field will result, while turbulent flow still remains. 

Fig. 2. The Alaska pipeline, one of the most significant large-scale technical examples of the benefits to be gained from the drag reduction effect. Over a distance of 1287 km, polymer is injected approximately every 100 km at a concentration of 5-25 ppm...

Goren found asymptotic behaviour, which is higher for this heterogeneous drag reduction than for a premixed homogeneous solution, whereas Tullis, Ramu, and Maus reported only little influence of the concentration of the injected polymer solution on this asymptotic value. Walters and McComb (1982) found no such influence. 

However, according to Little (1969), polyethyleneoxide solutions of different molecular weights gave the same drag reduction when their concentration was proportional to the critical concentration at each molecular weight (i.e., the computed concentration for the polymer coils to touch each other). Kinnier obtained similar results but used the concept of equivalent concentrations . He found that to have equal drag reduction for different molecular weight polymer solutions, one has to have equal volumes of polymer based upon the hydrodynamic sphere considerations. 

The non-ionic surfactants have an advantage over all the drag-reducing additives studied so far. They are both mechanically and chemically stable, do not precipitate in the presence of calcium, and hence can be used in all impure waters, sea water, brackish water, or concentrated brine solutions. They have an excellent potential for drag reduction at high temperatures. 

The aim of this contribution is to investigate the influence of concentration, chain length, molecular weight distribution, chemical nature, solvent quality, aging effects, etc. on drag reduction as has been proposed, e.g., by Kulicke, Klein (1985). 

In order to obtain a higher effectiveness of drag reduction, it was therefore more convenient to produce the actual experimental solution from the more diluted stock solution. This is already an indication that the state of solution of macromolecules plays an important role in the interpretation of the results. However, a molecular weight of 10.1 106 g/mol and a concentration of 1000 ppm is just below the critical concentration c (this c is based on viscometric measurements) (Kulicke 1982). Above this critical concentration, mechanical entanglements ensure between the macromolecules. Beneath this limit, interactions between the molecules come into... 

The flow enhancement effect is completely suppressed in the presence of trivalent cations. Even at the preparation stage for aluminium sulfate (Al2(SOi)3), the polymer is precipitated at a concentration of c = 5 ppm the flakes thus formed can be clearly seen, suspended in solution. Consequently, no drag-reduction effect can be expected and the experimental solution behaves as a Newtonian fluid (Fig. 31). Therefore, it is likely that multivalent cations from complexes or ionotropic gels and that by exceeding a critical value they may precipitate out of solution. 

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