Polymer-Induced Drag Reduction in Dilute Newtonian and Semi-Dilute Non-Newtonian Fluids: An Assessment of the Double-Gap Concentric Cylinder Method

Abstract

Polymer-induced drag reduction (DR) in fluids was studied using a rotational rheometer with double-gap concentric cylinder geometry. Although both polymers (polyacrylamide (PAM) and 2-acrylamido-2methylpropane sulfonic acid (SPAM)) had molecular weights of several MDa, the contrasting polymer charge, nonionic and anionic, led to different polymer overlap concentrations (c*), PAM ≫ SPAM, and fluid rheology, with PAM fluids mostly Newtonian and SPAM fluids non-Newtonian (shearthinning). Based on these differences, it was important to account for the infinite shear viscosity and normalize the polymer concentration by the intrinsic concentration (c int ) so that the DR performance of the two polymer fluids could be accurately compared. Both polymers induced DR, and the maximum DR by SPAM (DR% = 28) was slightly higher than that by PAM (DR% = 22) when Re p ∼ 1700. For PAM, the loss of DR with time diminished at higher polymer concentrations (≥100 ppm, at Re p = 3149) but was found to be sensitive to high Re p , with polymer chain scission the likely cause of the reduced performance. For the semi-dilute SPAM fluids, the shear stability contrasted that of PAM, showing negligible dependence on the polymer concentration and Re p . The apparent rapid loss of DR was predominantly attributed to a time-dependent effect and not polymer degradation. In pipe flow, the maximum DR for SPAM was higher than that measured by rheometry and was attributed to differences in the flow conditions. However, changes in the normalized DR/c with polymer concentration were found to be consistent between the two flow geometries. Furthermore, the high fluid stresses in pipe flow (at high Re p ) led to drag reduction losses consistent with PAM, as the time-dependent effect was not seen.

Estimation of Drag Reduction by Polymer Additives at High Reynolds Numbers Using Rheological Measurements

“…One possible explanation for this enhancement is related to the boundaries of the fluid, i.e., the geometry of the testing equipment, which consists of two concentric cylinders. The fluid flow of polymer solutions around curved boundaries, such as cylinders and spheres, could be linked to increased drag due to interactions between the polymer and the flow around the boundary. − In their DR study on anionic sulfonated PAM (SPAM), using a double-gap concentric cylinder with a geometry similar to the one used in this work, Michaelides et al reported drag enhancement in laminar and early turbulent regions. The enhancement was higher for higher polymer concentrations.…”

“…As for the transition from stable to unstable region, for the solvent, the shear rate at which the transition occurs is around γ̇ t = 185 s –1 (ω t ≈ 10.4 rad/s), which is consistent with the results reported by Habibpour et al As polymer concentration increases for both polymers, the shear rate at which the transition occurs also increases. To obtain expressions for the viscosity as a function of shear rate in both stable and unstable regions, the Carreau–Yasuda model is used, an empirical form that is commonly used for polymer solutions that exhibit shear-thinning behavior (e.g., see the works of Habibpour et al and Michaelides et al). The model takes the following form η ( γ̇ ) = ( η 0 − η ∞ ) false[ 1 + false( κ γ̇ false) a false] false( n − 1 false) / a + η ∞ where η 0 and η ∞ are the zero- and infinite-shear viscosity, respectively.…”

“…Nonetheless, the current use of rheometers for screening DR agents is limited, which is caused in part by the limited and relatively low range of shear rate of many commercial rheometers, in addition to the indirect measurement of DR. , When testing is performed at a low shear rate, the viscosity of the polymer solution can be orders of magnitude higher than that of the solvent. Contrary to the methods developed for linear flow devices, to the best of our knowledge, the available methods for calculating DR from rheological tests do not correct for the Re of the polymer solution by using local wall viscosity measurements but instead use the solvent’s viscosity or the infinite-shear viscosity (e.g., see the works of Michaelides et al and dos Santos et al …”

“…). As a result, friction factors are compared at different Re , leading to inaccurate interpretation of the measurements in calculating DR. For instance, in their rheological study on non-Newtonian polymer solutions of 2-acrylamido-2-methylpropane sulfonic acid (SPAM) and the nearly Newtonian solutions of polyacrylamide (PAM) in water, Michaelides et al reported apparent drag enhancement, or negative drag reduction, in both polymer solutions at low shear rates (stable flow), which had higher values for higher polymer concentrations. It was suggested that this enhancement is attributed to the use of η ∞ for estimating polymer Re , a condition that is not satisfied at low shear rates.…”

“…Nonetheless, the current use of rheometers for screening DR agents is limited, which is caused in part by the limited and relatively low range of shear rate of many commercial rheometers, in addition to the indirect measurement of DR. 14,15 When testing is performed at a low shear rate, the viscosity of the polymer solution can be orders of magnitude higher than that of the solvent. Contrary to the methods developed for linear flow devices, to the best of our knowledge, the available methods for calculating DR from rheological tests do not correct for the Re of the polymer solution by using local wall viscosity measurements but instead use the solvent's viscosity or the infinite-shear viscosity (e.g., see the works of Michaelides et al 25 and dos Santos et al 26 ). As a result, friction factors are compared at different Re, leading to inaccurate interpretation of the measurements in calculating DR. For instance, in their rheological study on non-Newtonian polymer solutions of 2acrylamido-2-methylpropane sulfonic acid (SPAM) and the nearly Newtonian solutions of polyacrylamide (PAM) in water, Michaelides et al 25 reported apparent drag enhancement, or negative drag reduction, in both polymer solutions at low shear rates (stable flow), which had higher values for higher polymer concentrations.…”