Scaling functions of polymer‐induced turbulent drag reduction focusing on the polymer–solvent interaction

Based on turbulent drag reduction characteristics of polystyrene and polyisobutylene in a pipe flow and a rotating‐disk flow, respectively, a relationship between polymer concentration and drag reduction at a given Reynolds number was considered. The universal drag reduction equation of a three‐parameter relationship between drag reduction and polymer concentration was modified using intrinsic concentration and intrinsic viscosity, and it was then found to be the most useful formula for correlating DR data, especially for polymer–solvent interactions in a turbulent flow. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1836–1839, 2003     

The effect of added salt on the flow of highly dilute solutions of poly(ethylene oxide) polymers

Early transition, early turbulence, and drag reduction were detected in flowing solutions of high molecular weight poly(ethylene oxide) condensates. Progressive addition of salt (magnesium sulfate) increased the onset point characterizing deviations from Newtonian flow for 1 ppm Polyox Coagulant solutions and eliminated early transition in the 10 ppm WSR-35 solutions. No further drag reduction was observed when the salt molarity reached the 0.65 level. In the Coagulant solutions the onset wall shear stress characterizing the flow deviation was an inverse function of the intrinsic viscosity of the polymer in the salt solution.     

The drag reduction of dilute polymer solutions as a function of solvent power,viscosity, and temperature

The frictional drag reduction of high molecular weight poly(ethylene oxide) and polystyrene solutions under turbulent flow conditions has been studied as a function of temperature, solvent power, and solvent viscosity. A rotating-disc apparatus was used to make the drag reduction measurements. For aqueous poly(ethylene oxide) solutions, at concentrations well above that needed to produce maximum drag reduction, all drag reduction data reduced to a common curve when per cent drag reduction was plotted against the Reynolds number for the flow. However, for poly(ethylene oxide) solutions below this optimum concentration, the drag reduction-versus-Reynolds number curves showed decreasing drag reduction with increasing temperature. The data are explained primarily in terms of the inverse temperature solubility characteristics of poly(ethylene oxide) in water. The per cent drag reduction of polystyrene in nonaqueous liquids was found to be greater in good solvents than in poor ones. It was also found that increases in solvent viscosity and decreases in temperature increased the per cent drag reduction. The results are discussed in relation to the current drag reduction theories and are shown to be in opposition to Virk's theory. It is concluded from the data that drag reduction is very likely a function of a relaxation time phenomenon involving the polymer molecules and the flow system. The results also emphasize the importance of considering solvent power, viscosity, and temperature in the design of an efficient drag reduction system.     

On the real molecular weight of polyethylene oxide of high molecular weight in water

It is shown that water is close to being a theta solvent for polyethylene oxide which is highly aggregated in this solvent. This result is in agreement with the behaviour observed by hydrodynamic measurements (turbulent drag reduction and concentration and shear dependence of the viscosity). With the molecular weight correction proposed in this work, the onset drag reduction data obtained with Polyox agree well with Virk's theory.     

Flow-assisted degradation in dilute polystyrene solutions

The flow-assisted degradation behavior of polystyrene was studied as a function of solvent, polymer concentration, molecular weight, and molecular weight distribution. To obtain data at concentrations as low as 100 parts per million by weight, turbulent drag reduction measurements were used to augment the usual analytical techniques of viscosity and gel permeation chromatography. Turbulent flow measurements were found to be a valuable technique for evaluating the effects of degradation: the drag reduction onset point provides information about the largest molecules in the sample while the flow rate dependence is related to the shape of the top part of the molecular weight distribution. For the polymers and flow conditions studied, the degradation causes a shift in the distribution to lower molecular weights with little change in the shape. This suggests a complex mechanism where the probability of bond scission is not random but varies along the polymer backbone.     

SYNERGISTIC EFFECTS OF ANIONIC SURFACTANT AND NONIONIC POLYMER ADDITIVES ON DRAG REDUCTION

Turbulent drag reduction (DR) behavior of mixed nonionic polymer and anionic surfactant solutions in water was studied in a pipeline set up to explore the synergic effects of mixed additives on DR. The concentration of polymer polyethylene oxide (PEO) was varied from 0 to 2000 ppm and the concentration of surfactant sodium dodecyl sulfate (SDS) was varied from 0 to 5000 ppm. The critical aggregation concentration (CAC), where the interaction between the polymer and the surfactant begins, and the polymer saturation point (PSP), where the polymer molecules become saturated with the surfactant, were determined using electrical conductivity and surface tension measurements. As the polymer concentration was increased the CAC decreased but the PSP increased. The relative viscosity showed a remarkable increase upon the addition of surfactant to the polymer solution due to extension of polymer chains caused by the formation of micelles on the backbone of the polymer molecules. The data exhibited a considerable increase in DR in the case of mixed polymer/surfactant systems. The percent reduction in friction factor was as high as 79 when 3000 ppm or more surfactant was added to the 500 ppm polymer solution. Furthermore, the drag reduction behavior of the polymer solution changed from so-called Type A to Type B. In Type A drag reduction, a transition from laminar to turbulent regime is observed with a clear-cut onset point. In Type B drag reduction, no transition or onset point is observed; the data fall on a gradual extension of the laminar line.     

Viscosities of moderately concentrated solutions of polyethylene in ethane,propane, and ethylene

The viscosities of moderately concentrated solutions of low-density polyethylenes in ethane, propane, and ethylene have been measured at low shear rate in the temperature range of 150–250°C and in the pressure range of about 15000–30000 psi. Within the precision of the measurements, the relative viscosity is independent of pressure over the range investigated but increases as the solvent is changed from propane through ethane to ethylene. The activation energy for the relative viscosity in ethane varies from about 0.5 to 2.5 kcal/mole as the concentration changes from 5 to 15 g/dl. Effects of polymer concentration and molecular weight on solution viscosity in ethane at 150°C have been determined, and all of the data can be represented by a single straight-line plot of the logarithm of relative viscosity versus the intrinsic viscosity (in p-xylene at 105°C) times concentration. This simple relation is valid over wide ranges of polymer concentration and molecular weight and over more than two orders of magnitude of relative viscosity. The solution viscosities of the polyethylenes in the three supercritical fluid solvents used appear surprisingly low at first sight. This behavior is partly a result of the low solvent viscosities but also might mean that the polymer has an abnormally low segmental friction factor compared to that in solutions under more familiar conditions.     

Prediction of osmotic pressures of polymer solutions

A theory which has been developed to account for the effects of concentration on the equivalent hydrodynamic volumes of dissolved polymers has been combined with a statistical mechanical relation for the virial coefficients of dilute suspensions of rigid spheres. With a scaling factor for solvent goodness, osmotic pressures of polymer solutions can be predicted with good accuracy. The input parameters needed are the number-average molecular weight of the polymer sample and its intrinsic viscosity in the solvent of interest, as well as its intrinsic viscosity under theta conditions. The intrinsic viscosities can be estimated with sufficient accuracy from tabulated Mark–Houwink coefficients. The model developed contains no adjustable parameters. Comparisons of predicted and reported experimental osmotic pressures are presented, and a method for prediction of second virial coefficients is described.     

Study of oil soluble polymers as drag reducers

This investigation was undertaken to find the most effective material which would reduce the friction coefficient in turbulent flow when added in small quantities to oil pipelines. For this purpose, a series of oil-soluble polymers, namely homopolymers and copolymers of alkyl methacrylates, alkyl acrylates, and alkyl styrenes were synthesized. Emulsion polymerization techniques were used. Commercially available alkyl methacrylate and alkyl acrylate monomers were used in the synthesis. Monomeric alkyl styrenes were synthesized and structures established prior to polymerization. Intrinsic viscosities were measured and viscosity average molecular weights were calculated for several of the homopolymers synthesized in this study. Reduction of factional drag and resistance to shear degradation were measured by pumping a solution of the polymer in a hydrocarbon solvent through a pipe and recording the pressure drop across the pipe. Drag-reducing properties of several of the polymers were correlated in terms of their viscosity average molecular weights. Drag reduction of poly (isodecyl methacrylate) was studied in various hydrocarbon solvents. Drag-reducing behavior of polymers prepared in this study exhibited a strong dependence on molecular weight; increasing the molecular weight increased the drag reduction for a given polymer concentration and pipe size. Several of these polymers were found to be superior to commercially available polyisobutylene as drag reducers, especially in terms of shear stability.     

Turbulent flow behaviour of dilute polymer solutions in an annulus

An experimental study has been carried out to investigate the turbulent flow behaviour of dilute polymer solutions in an annulus. The polymers used are two grades of Separan, AP30 and MG500, both are known to exhibit drag reduction characteristics in turbulent pipe flow. Similar drag reduction phenomena have been observed in annulus flow. At a given Reynolds number, the friction factor decreases with increase in polymer concentration and appears to reach a minimum (or maximum drag reduction) at certain optimum concentration. An estimate of the critical wall shear stress, which marks the onset of drag reduction, is consistent with pipe flow results, suggesting that the critical value is independent of flow geometry and size. A lower drag reduction, achieved in an annulus in comparison with circular pipes, is attributed mainly to a diameter effect.     

Poly(ethylene oxide) × polyacrylamide. Which one is more efficient to promote drag reduction in aqueous solution and less degradable?

The hydrodynamic drag reduction (HDR) in aqueous solutions containing very small amounts of poly(ethylene oxide) (PEO) and polyacrylamide (PAM, 0–100 ppm) was studied under turbulent flow. In this condition, the polymers undergo severe mechanical degradation and loose their capacity to promote drag reduction. The interpretations from a molecular point of view of the mechanical degradation of these flexible polymers under turbulent flow are not consensual. To avoid effects of polymer entanglement and to correlate the mechanical degradation with the intrinsic characteristics of the polymer chain, a polymer concentration lower than 2 ppm was used. For this purpose, a highly accurate rheometer containing a double‐gap cell was used to determine the mechanical degradation kinetics. The kinetics was measured directly from the loss of the polymer's capability to promote drag reduction. The comparisons of degradation kinetics for PEO and PAM in aqueous solution allow us to conclude that the stabilities of the two polymers are similar. This new interpretation can be useful to understand the relative mechanical stability of flexible polymers under drag reduction conditions. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Drag reduction effectiveness of macromolecules

A working hypothesis has been developed to account for observed drag reduction properties of dilute polymer solutions. Drag reduction effectiveness of polymer solutes is attributed to their ability to form a deformable network structure which inhibits the formation of microvortices in the solvent and retards their ability to migrate through the fluid, coalesce, and result in fully developed turbulence centres. The size of microvortex precursors is tentatively set in the range of 100 Å, and it is assumed that the damping (drag reduction) effect of macromolecules is due to strong association between solvent molecules and polymer chains, immobilizing many of these active precursors. The hypothesis indicates that drag reduction effectiveness of polymers should depend strongly on polymer/solvent interactions in addition to the recognized variables of molecular weight, concentration and geometry of the flow-system. The hypothesis accounts for a number of published anomalous observations and leads to new predictions of drag reduction variations with polymer molecular weight distribution, and temperature. These and related predictions are the focal points of new experimental research studies of the drag reduction phenomenon.     

Einige eigenschaften der makromoleküle von reibungsreduzierenden polymeren

The drag reducing (DR) properties of PIB Oppanol B 200 solutions in toluene and in xylene-benzene mixture (40:60) (200 ppm) have been studied. In both solutions PIB has shown equal intrinsic viscosity and thus the coil dimensions of PIB in both solutions are identical. It was settled that DR values in both solutions were different. At low Reynolds numbers the differences are due to the earlier beginning of DR in toluene solution than in xylene-benzene. At high Reynolds numbers the differences are very small and they are due to the known small differences in the physical properties of the solutions. For the studied solutions series of values determining the sizes of polymer coils were calculated. It was established that DR values are quite independent of the manner how the PIB solutions in toluene were obtained: dissolving the polymer in the entire quantity of the solvent to achieve the desired concentration; dissolving the polymer in 10 times lower quantity of the solvent and then dilution to the desired concentration 3 or 4 h before testing; dissolving the polymer in 10 times lower quantity of the solvent and dilution just before testing. On the basis of these results and the product of concentration with intrinsic viscosity the existing of individual macromolecules of the drag reducing polymers was assumed.     

Evidence for molecular interactions in drag reduction in turbulent pipe flows

Experiments which test the concentration and molecular weight dependence of turbulent pipe flow drag reduction for random coiling polymers in dilute solutions show correlations with concentration to the one-half power and molecular weight to the 0.8 power for good solvents. This result is not consistent with a model of extension of single1 molecules, but could be related to the increase in bulk viscosity of interacting molecules after some extension. In this work, measurements for very low amounts of drag reduction for rigid rod molecules arc reported, and the effect of tube diameter on the amount of drag reduction is examined for fiexible rod molecules. No diameter effect is observed for the rigid rods, but an increase in drag reduction with increase in pipe diameter is found for the flexible polyeleetrolytes. In all cases, the volume occupied by spheres which circumscribe the molecules is greater than the actual volume when drag reduction is found. The results indicate that combined effects of individual molecule stretching and molecular interactions are present in drag reduction for random coiling or flexible rod molecules.     

Thermal stability of polymers based on acrylamide and 2-acrylamido-2-methylpropane sulfonic acid in different temperature and salinity conditions

Partially hydrolyzed polyacrylamide (PHPA) is the most widely used polymer in enhanced oil recovery (EOR) applications. However, under conditions of high temperature and salinity, the PHPA molecules become hydrolyzed, causing a drastic reduction of the viscosity of the polymer solution due to the presence of negative charges, making the molecules more susceptible to interactions with cations. In this sense, in order to increase the stability of these polymers, an anionic monomer more resistant to cations such as 2-acrylamido-2-methylpropane sulfonic acid (AMPS) has been incorporated into the HPAM molecules. This work evaluated the thermal stability of a copolymer (acrylamide and AMPS - AN125) and a terpolymer (acrylamide, acrylate, and AMPS-FP5115) in the time course of 360 days. The tests were carried out in typical conditions of Brazilian offshore reservoirs, such as absence of oxygen, high temperature, and high salt concentration. The test method involved measurements of intrinsic viscosity in function of time and determination of the hydrolysis degree of the polymers by elemental analysis. The copolymer AN125 was more stable under the test conditions than the terpolymer FP 5115 due to the presence of a higher concentration of AMPS in the copolymer. The AMPS group was hydrolyzed to AA at a temperature of 100 °C, however, the increase in salt concentration delayed the onset of this degradation. The tests indicated that the presence of a higher AMPS content in the copolymer does not prevent the polymer from undergoing hydrolysis, but delays the polymer precipitation step in the solution.     

An analysis of unsteady one-dimensional stretching of a viscoelastic fluid

The time-dependent response of a viscoelastic liquid to unsteady one-dimensional stretching deformations was examined. Oldroyd's three-constant model for a viscoelastic fluid was used. Two cases representing two different stretching histories were analyzed: a sine stretching pulse and a step stretching pulse. The results show that high elongational viscosity may be easily reached in both cases. As the relaxation time of the liquid becomes comparable to the pulse width, elongational viscosity increases with the increase in maximum stretching rates. Conditions to maintain high levels of elongational viscosity at a subsequently reduced stretching rate were given as functions of the relaxation time and initial stretching rates. In view of recent turbulent boundary layer data, the results were used to discuss possible explanations of turbulent drag reduction in polymer solutions. It was concluded that the basic mechanisms for drag reduction in polymer soluations. It was concluded that the basic mechanisms for drag reducation may be related to the effects of high elongational viscosity and local stabilization of small shear disturbances.     

Prediction of second virial coefficients from intrinsic viscosities

One of the most readily available characteristics of a polymer sample is its intrinsic viscosity in a particular solvent. This datum can often be estimated reasonably from a single relative viscosity measurement. A number of theories permit the calculation of the second virial coefficient of a polymer/solvent mixture given the intrinsic viscosity and polymer molecular weight. The intrinsic viscosity of the polymer under theta conditions is also needed, but this can be estimated, if necessary, from the molecular weight. This article compares the efficiencies of various alternative models for the prediction of second virial coefficients of a series of polymers and solvents. The most effective technique for this purpose first calculates the concentration-dependent equivalent hydrodynamic volume of a solvated polymer coil. This value is used with a primitive statistical mechanical theory for virial coefficients of hard-sphere suspensions to calculate the osmotic pressure or turbidity of the polymer solution. These simulated experimental values are fitted with a least-squares line as in the real experiment, and the second virial coefficient is derived from the slope. The computations are relatively simple; the average deviation between observed and predicted virial coefficient was less than 16% for a variety of polymer types, molecular weights, and solvents.     

SOME MOLECULAR EFFECTS IN DRAG REDUCTION: A SUMMARY†

Dilute solutions of high molecular weight polymers have drawn a great deal of interest in recent years because of their drag reducing characteristics. It is well-known now that a substantial reduction in turbulent frictional drag can be achieved with a very small amount of polymeric additives, usually only a few parts per million by weight (ppmw) in concentration. This unique phenomenon has offered a new dimension in the design development of new marine systems for higher speed, longer range, larger payload as well as possibly quieter machinery. Although the discovery of this turbulent drag reduction phenomenon may be traced back to Toms¹ and Mysels² in the 1940's, the U.S. Navy's exploration of the turbulent drag reduction effect did not begin until the pioneering effort of Hoyt and Fabula in the 1960's. ³ During a period of several years in the early 19707apos;s, an interdisciplinary group at the Naval Research Laboratory undertook an intensive basic research effort to study the effects of polymer molecular structure on turbulent drag reduction. Model compounds were synthesized in the laboratory, and their drag reducing properties characterized. Polymers including polyacrylamide and its derivatives, polyacrylic acid, poiyphosphate and association colloids have been investigated. In this report, an attempt is made to highlight some of the results from that program in a brief summary form.     

Characterization of polymer adsorption in tube flow of drag reducing fluids

Elucidation of the polymer adsorption and flow characteristics at the tube wall is essential for an understanding of turbulent drag reduction. The polymer adsorbed onto the tube wall, in the flow of dilute solutions of linear random coiling macromolecules, also produces a concentrated fluid layer at the surface of the adsorption zone, as a result of the flow of the solvent micromolecules in the porous network comprising the adsorption zone.Velocity profiles are developed and used to determine the radial variation in the adsorption zone of porosity, as well as fractional surface coverages and mean separation or interpenetration distances between macromolecules in the various adsorption layers. The polymer concentration build-up in the concentrated fluid layer is also evaluated. Predictions of the latter for aqueous Polyox WSR-301 solutions are in qualitative agreement with experimental measurements and suggest that turbulent drag reduction is related to the level of polymer build-up in the concentrated fluid layer.     

Vortex flow of dilute polymer solutions

It has been observed that very d longchain polymers which are effective in turbulent drag reduction inhibit the formation of a vortex or air core as water drains from a tank. This paper considers the fluid mechanical velocity profile measurements have been performed. There appear to be at least two distinct mechanisms for the vortex inhibition—one involving the viscosity enhancement caused by polymer addition, and the other related to the viscoelastic properties of the polymer solutions. This second mechanism is shown to arise due to the generation of high normal stresses as the air core begins to form. The very close correlation between vortex inhibition and turbulent drag reduction suggests that normal stresses may also play an important role in this latter phenomenon.