Applications of Water-Soluble Polymers in Turbulent Drag Reduction

Exact Solutions for Non-Isothermal Flows of Second Grade Fluid between Parallel Plates

In this paper, we obtain new exact solutions for the unidirectional non-isothermal flow of a second grade fluid in a plane channel with impermeable solid walls, taking into account the fluid energy dissipation (mechanical-to-thermal energy conversion) in the heat transfer equation. It is assumed that the flow is time-independent and driven by the pressure gradient. On the channel walls, various boundary conditions are stated. Namely, we consider the no-slip conditions, the threshold slip conditions, which include Navier's slip condition (free slip) as a limit case, as well as mixed boundary conditions, assuming that the upper and lower walls of the channel differ in their physical properties. The dependence of solutions on the boundary conditions is discussed in some detail. Moreover, we establish explicit relationships for the model parameters that guarantee the slip (or no-slip) regime on the boundaries.

The Problem of Filling a Spherical Cavity in an Aqueous Solution of Polymers

The problem of filling a spherical cavity in a liquid has attracted the attention of many authors. The study of bubble behavior in liquid allows to estimate the consequences of cavitation processes, which can lead to the intensive destruction of the material surface. Regarding this connection, it becomes necessary to study the influence of impurities, including polymeric additives on the strengthening or suppression of cavitation. In this paper, this problem is considered in three models of a relaxing fluid. It is shown that for all models, the cavity filling time is finite if the surface tension is not equal to zero. This result was previously established for the cases of ideal and viscous fluids. However, the relaxation factor can significantly change the flow pattern by slowing down the filling process and lowering the level of energy accumulation during the bubble collapse.

Mitigation and Remediation Technologies of Waxy Crude Oils’ Deposition within Transportation Pipelines: A Review

Deposition of wax is considered one of the most significant culprits in transporting petroleum crude oils, particularly at low temperatures. When lowering pressure and temperature during the flow of crude oil, the micelle structure of the crude oil is destabilized, allowing oil viscosity to increase and precipitating paraffin (wax) in the well tubulars and pipeline, which increase the complexity of this culprit. These deposited substances can lead to the plugging of production and flow lines, causing a decline in oil production and, subsequently, bulk economic risks for the oil companies. Hence, various approaches have been commercially employed to prevent or remediate wax deposition. However, further research is still going on to develop more efficient techniques. These techniques can be categorized into chemical, physical, and biological ones and hybridized or combined techniques that apply one or more of these techniques. This review focused on all these technologies and the advantages and disadvantages of these technologies.

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

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-2-methylpropane 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 (shear-thinning). 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.

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

In this paper we consider the initial–boundary value problem describing the motion of weakly concentrated aqueous polymer solutions. The model involves the regularized Jaumann’s derivative in the rheological relation. Also this model is considered with non-linear viscosity. On the basis of the topological approximation approach to the study of hydrodynamics problems the existence of weak solutions is proved. Also we consider an optimal feedback control problem for this initial–boundary value problem. The existence of an optimal solution minimizing a given performance functional is proved.

Turbulent Drag Reduction with an Ultra-High-Molecular-Weight Water-Soluble Polymer in Slick-Water Hydrofracking

Water-soluble polymers as drag reducers have been widely utilized in slick-water for fracturing shale oil and gas reservoirs. However, the low viscosity characteristics, high operating costs, and freshwater consumption of conventional friction reducers limit their practical use in deeper oil and gas reservoirs. Therefore, a high viscosity water-soluble friction reducer (HVFR), poly-(acrylamide-co-acrylic acid-co-2-acrylamido-2-methylpropanesulphonic acid), was synthesized via free radical polymerization in aqueous solution. The molecular weight, solubility, rheological behavior, and drag reduction performance of HVFR were thoroughly investigated. The results showed that the viscosity-average molecular weight of HVFR is 23.2 × 10⁶ g⋅mol⁻¹. The HVFR powder could be quickly dissolved in water within 240 s under 700 rpm. The storage modulus (G′) and loss modulus (G″) as well as viscosity of the solutions increased with an increase in polymer concentration. At a concentration of 1700 mg⋅L⁻¹, HVFR solution shows 67% viscosity retention rate after heating from 30 to 90 °C, and the viscosity retention rate of HVFR solution when increasing C_NaCl to 21,000 mg⋅L⁻¹ is 66%. HVFR exhibits significant drag reduction performance for both low viscosity and high viscosity. A maximum drag reduction of 80.2% is attained from HVFR at 400 mg⋅L⁻¹ with 5.0 mPa⋅s, and drag reduction of HVFR is 75.1% at 1700 mg⋅L⁻¹ with 30.2 mPa⋅s. These findings not only indicate the prospective use of HVFR in slick-water hydrofracking, but also shed light on the design of novel friction reducers utilized in the oil and gas industry.

Polymers and Plastrons in Parallel Yield Enhanced Turbulent Drag Reduction

Despite polymer additives and superhydrophobic walls being well known as stand-alone methods for frictional drag reduction in turbulent flows, the possibility of employing them simultaneously in an additive fashion has remained essentially unexplored. Through experimental friction measurements in turbulent Taylor–Couette flow, we show that the two techniques may indeed be combined favorably to generate enhanced levels of frictional drag reduction in wall-bounded turbulence. We further propose an additive expression in Prandtl–von Kármán variables that enables us to quantitatively estimate the magnitude of this cooperative drag reduction effect for small concentrations of dissolved polymer.

Group Analysis of the Boundary Layer Equations in the Models of Polymer Solutions

The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The task includes the ratio of two characteristic length scales, one of which is the Prandtl scale, and the other is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. In the limit case, when the ratio of these two scales tends to zero, the equations of the boundary layer are exactly integrated. One of the goals of the present paper is group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the Pavlovskii model (1971). The equations of the plane non-stationary boundary layer in the Pavlovskii model are studied in more details. The equations contain an arbitrary function depending on the longitudinal coordinate and time. This function sets the pressure gradient of the external flow. The problem of group classification with respect to this function is analyzed. All functions for which there is an extension of the kernels of admitted Lie groups are found. Among the invariant solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate.

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are similar to those of motion of a usual viscous fluid. Other models can include weak discontinuities, which are retained in the course of fluid motion. Exact solutions are found by using the group analysis of the examined systems of equations. These solutions describe the fluid motion in a gap between coaxial rotating cylinders, the stagnation point flow, and the motion in a half-space induced by plane rotation (analog of the Karman vortex). The problem of motion of an aqueous solution of a polymer in a cylindrical tube under the action of a streamwise pressure gradient is considered. In this case, a flow with straight-line trajectories is possible (analog of the Hagen-Poiseuille flow). In contrast to the latter, however, the pressure in the flow considered here depends on all three spatial variables.

Polymer effects on Kármán vortex: Molecular dynamics study

We investigated the Kármán vortex behind a circular cylinder in a polymer solution by a molecular dynamics simulation. The vortex characteristics are distinctly different for short and long polymers. The solution with the long polymer exhibits a reduction in the vortex shedding frequency and broadening of the lift coefficient spectrum. On the other hand, the characteristics of the short-polymer solution are almost the same as those of the Newtonian fluid. These facts are consistent with the experiments. Because the distributions of the gyration radius and the orientational order of the long-polymer solution are highly inhomogeneous in the flow field, we conclude that the extensional property of the polymer plays an important role in changing the flow characteristics.

Role of Bio-Based Polymers on Improving Turbulent Flow Characteristics: Materials and Application

The remarkable ability of polymeric additives to reduce the level of frictional drag significantly in turbulent flow, even under extremely low dilutions, is known as turbulent drag-reduction behavior. Several bio-polymers have been assessed as promising drag-reducing agents for the potential replacement of high molecular weight synthetic polymers to improve safety and ameliorate environmental concerns. This article reviews the recent advances regarding the impact of several bio-polymer additives on turbulent drag reduction in either pipe or rotating disk flow systems, and their potential applications in the petroleum, biomedical, and agricultural industries.