Drag reduction in dilute flowing gas‐solid suspensions

Heat transfer coefficients of air-glass, argon-glass, and argon-aluminum suspensions were measured in horizontal and vertical tubes. The glass, 21.6 and 36.0-μ-dia particles, was suspended at gas Reynolds numbers between 11,000 and 21,000 and loading ratios between 0 and 2.5. The presence of particles generally reduced the heat transfer coefficient. The circulation of aluminum powder in. the 0.870-in.-dia closed loop system produced tenacious deposits on protuberances into the stream. In the vertical test section, the Nusselt number reduction was attributed to viscous sublayer thickening; in the horizontal test section to particle deposition.

Erosion in multiphase flow with entrained solid particles is a complex phenomenon due to existence of different flow patterns. Erosion experiments were conducted on an elbow specimen in a one-inch multiphase flow loop with gas, liquid and sand. Two different elbow specimens were used in the experiments. One placed downstream of a horizontal test section and one downstream of a vertical test section. Erosion tests were conducted at different gas and liquid velocities that showed a difference in erosion rates between the horizontal and vertical specimens. In order to better understand erosion results, the distribution of solid particles within the horizontal and vertical pipes just upstream of the elbows was measured across the pipe with a pitot probe. The results indicate that the distribution of sand in the pipe cross-section plays an important role in the erosion process due to the differences in velocities of the sand particles moving in the gas core and in the liquid film of the annular flow. It is observed that sand distribution in the horizontal test section is different than the sand distribution in the vertical test section for the same gas and liquid velocities. Therefore, the distribution of sand particles affects erosion test results. Based on these observations, a new mechanistic model has been developed to predict erosion in annular flow considering the effects of sand particle distribution and particle velocities in the annular film and gas core region. The experimental erosion results compare well with the model predictions.

Certain types of macromolecules added to otter and salt solutions flouting in turbulent motion can reduce the pressure gradient. Alternatively, the volumetric capacity of a pipe for these fluids is increased by the presence of these material. Examples presented show that the drag reduction can become significant. Thus, the presence of 0.28 per cent of a gum derivative in a solution of sodium chloride flowing at 200 gal/min in a 1.89- in. pipe yields a pressure drop which is 0.44 of the single-phase drop measured under the same conditions of turbulent flow; the addition of 0.1 per cent of a vinyl derivative to a 1-in. water line yields a through put capacity which is 1.78 of the single-phase capacity at the same pressure drop. It is further shown that these phenomena are distinctly different from previous observations with other classes of non-Newtonian systems. There a simple lowering of friction factors below the levels predicted from the resistance laws for Newtonian fluids is associated with a suppression of turbulent motion. A rational physical explanation for drag reduction is advanced. Briefly, the proposed mechanism is a storage by the molecular elastic elements of the macromolecules in solution of the kinetic energy of the turbulent motion. Introduction This study was inspired by a recent review of some paradoxical drag reduction phenomena in turbulent pipe flow. Under very moderate conditions of turbulent flow, the pressure gradient necessary to pump solutions containing certain specific kinds of polymers, fibers and metallic soaps may become appreciably lower than that required to pump the solvent, i.e., water or a low-viscosity hydrocarbon, under identical flow rates in the same conduit. As shown by our review, this phenomenon of drag reduction in turbulent duct flow was first noted during the second world war, apparently arising in connection with the development of flame warfare weapons. Since that time several papers illustrating this phenomenon have appeared: Toms, Oldroyd, Agoston et al., Bundrant and Matthews, Robertson and Mason, Ousterhout and Hall, Daily and Bugliarello, Lummus, Anderson, and Fox. That there are practical applications for techniques which increase discharge or decrease the pressure necessary to transport a liquid through a pipeline is illustrated in the patents which have issued which take advantage of this peculiar phenomenon, e.g., Mysels, Dever, Harbour, and Seifert. One also finds fragmentary evidence of this effect in the data pertaining to a few of the polymeric solutions studied by Shaver and Dodge. However, these investigators were concerned with the development of friction factor vs Reynolds number correlations for a variety of non-Newtonian solutions and suspensions, rather than in a study of drag reduction. A similar kind of drag reduction effect has been observed in gases. Sproull, for example, reports that adding dust to air flowing in turbulent motion through a pipe results in a lowering of the pressure gradient at identical flow rates. There are also military applications for reducing the drag on hydrodynamic vehicles. For example, the possibility of injecting a rheologically complex fluid into the boundary layers of bodies to reduce the skin friction has been investigated by Fabula and Granville. Along somewhat different lines are the drag reduction studies of Kramer. He has shown that skin friction can be reduced by covering the surface of a vehicle with a flexible skin. The effect is apparently due to the boundary layer being stabilized by the presence of the skin. Drag reduction by means of coexisting gas and liquid boundary layers, e.g., film boiling and continuous gas injection, has been proposed by Bradfield, Barkdoll, and Byrne, Cess and Sparrow, Sparrow, Jonsson, and Eckert. Here the skin friction occurs between a vapor and a surface rather than between a liquid and a surface. There are several references in the literature to friction-factor correlations for non-Newtonian solutions and suspensions: Shaver and Merrill, Dodge and Metzner, Clapp, and Thomas. SPEJ P. 203ˆ

Solid particle erosion is a major problem in many industrial applications where solids are entrained in gas and/or liquid flows. For example, erosion of production equipment, well tubing and fittings is a major operating problem that costs the petroleum industry millions of dollars each year. Entrained sand particles in the oil/gas production fluid impinge on the inner surfaces of the pipes, fittings, and valves that result in solid particle erosion. In certain production situations with corrosive fluids, erosion is compounded with corrosion causing severe erosion-corrosion. Even in situations when sand control means are utilized such as gravel packing and sand screens, small sand particles can plug sand screens promoting higher flow velocities through other portions of the screens causing failure and allowing sand production. Erosion can cause severe damage to the piping and equipment wall, resulting in loss of equipment and production downtime. Solid particle erosion is a mechanical process by which material is removed gradually from a solid surface due to repeated impingement of small solid particles on the metal surface. The erosion phenomenon is highly complicated due to the number of parameters affecting the erosion severity, such as production flow rate, sand rate, fluid properties, flow regime, sand properties, sand shape and size, wall material of equipment, and geometry of the equipment. For ductile materials, erosion is caused by localized deformation and cutting action from repeated particle impacts. It is well known that solid particle erosion rates are a strong function of the impacting velocity of particles and also the mass of impacting particles. Predicting solid particle erosion in multiphase flow is a complex task due to existence of different flow patterns. The existence of different flow patterns and sand and liquid holdup in vertical and horizontal pipes means that a unique erosion model has to be developed for each flow regime if the model is to account for the number and velocity of impacting particles. The particle impact velocity is affected by the pipe geometry, carrying fluid properties and velocity, flow pattern, particle size and distribution in the flow. Among different multiphase flow patterns in horizontal and vertical flows, severe erosion damage can occur in annular and slug flows with high gas velocities and low liquid velocities. Although there is a lack of accurate mechanistic models to predict solid particle erosion, there is a need to develop engineering prediction models for multiphase flows. Earlier erosion calculation procedures in multiphase flow were primarily based on empirical data and the accuracy of those “empirical” models was limited to the flow conditions of the experiments. A framework for developing a model has been established for predicting erosion rates of elbows in multiphase flow. The model considers the effects of particle velocities in gas and liquid phases upstream of the elbow. Local fluid velocities in multiphase flow are used to determine representative particle impact velocities. Also based on data representing sand holdup for several flow regimes, the masses of impacting particles are estimated. Erosion experiments are also conducted on elbows in two-inch and three-inch large scale multiphase flow loops with gas, liquid and sand flowing in vertical and horizontal test sections. Based on the experimental data for different flow regimes including slug, wet gas and annular flow a method for improving a previous model is discussed and is being implemented to predict erosion rates in multiphase flow.

Simulating drag reduction phenomenon in turbulent pipe flows

Drag reduction in fully developed turbulent pipe flow with 4 concentrations (200 to 500 wppm or mg/kg) of low molecular weight sodium carboxymethylcellulose (CMC) in aqueous solutions was investigated experimentally. Drag reduction was determined by pressure drop measurements. Maximum drag reduction achieved was 22% using 500 wppm CMC solution. To observe the impact of the presence of CMC on the flow, ultrasound Doppler velocimetry (UDV) was employed to monitor the instantaneous velocity distributions. Experimental measurements were used to calculate Fanning friction factor and radial distributions of the axial time-averaged velocity, velocity fluctuation (turbulent intensity), and eddy viscosity. Two impacts of increasing CMC concentration on the flow field were observed. The first effect was the decrease in the mean velocity gradient, especially near the wall, with increasing polymer amount, which in turn gave rise to a lower friction factor or pressure drop. Furthermore, smaller eddy viscosities were obtained in the flow. The second impact of polymer addition was on the velocity fluctuation or turbulent intensity variation along the radial distribution. Presence of the polymer suppressed the velocity fluctuations near the wall while the intensity in the turbulent core region became stronger than in the case of lower or no polymer addition.

Experimental study of post-CHF heat transfer in a vertical tubular test section

The drag reduction induced by superhydrophobic surfaces is investigated in a turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modeled with alternating no-slip and shear-free boundary conditions at the wall. With respect to the classical turbulent pipe flow, a substantial drag reduction is observed which strongly depends on the grooves’ dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe’s circumference. The drag reduction is due to the mean slip velocity at the wall which increases the flow rate at a fixed pressure drop. The enforced boundary conditions also produce peculiar turbulent structures which on the contrary decrease the flow rate. The two concurrent effects provide an overall flow rate increase as demonstrated by means of the mean axial momentum balance. This equation provides the balance between the mean pressure gradient, the Reynolds stress, the mean flow rate, and the mean slip velocity contributions.

This paper is aimed to an experimental study on the flow patterns formed by heavy crude oil (488 mPa.s, 925.5 kg/m3 at 20 °C) and water inside vertical and horizontal 1 in. pipes. The interfacial tension was 29 dynes/cm. Effort is concentrated into flow pattern characterization, which was visually defined. The similarities with gas-liquid flow patterns are explored and the results are expressed in flow maps of the superficial velocities. In contrast with other studies, the annular flow pattern (‘core annular flow’) was observed in both horizontal and vertical test sections. In fact this flow pattern typically occurs in heavy oil-water flows at low water input fractions. Because of the practical importance of core flow in providing an effective means for heavy oil production and transportation, this paper discusses two criteria that favor its occurrence in pipes.

Numerical simulations using Euler-Euler model (also known as two-fluid model) were used to predict pressure drop in pneumatic conveying (i.e., gas-solid flows) in vertical pipes. Standard \(k - \varepsilon\) turbulence model has been used for gas phase, and kinetic theory of granular flows (KTGF) was used to close solid phase stresses and solid pressure aroused due to inter-particle collisions. The model was validated by comparison with the available experimental data and good agreement was found for pressure drop prediction. The effect of important flow parameters like gas phase Reynolds number, solid loading ratio and particle density on pressure drop was investigated. It was observed that pressured drop increased with gas velocity and solid loading ratio. Finally, computed results for pressure drop are compared with the existing correlations. Present predictions showed good agreement with the correlations of (Reddy and Pei in Ind Eng Chem Fundam 8:490–497, 1969 [1], Capes and Nakamura in Can J Chem Eng 51:31–38, 1973 [2]) data.

Experimental studies of drag reduction and polymer degradation in turbulent pipe flow with dilute water solutions of unfractionated polyethylene oxide are described. Drag reduction results indicate that the magnitude of the reduction cannot be correlated on the basis of weight average molecular weight, rather the phenomenon depends strongly on the concentration of the highest molecular weight species present in the molecular weight distribution. Polymer degradation in turbulent flow is found to be severe for high molecular weight polymers causing appreciable changes in drag reduction and molecular weight with the duration of flow. Data indicates that drag reduction exists in the limit of infinite dilution suggesting that the phenomenon is due to the interaction of individual polymer molecules with the surrounding solvent and that the extent of reduction is relatively independent of pipe diameter when a comparison is carried out at equal solvent wall shear stresses. Consideration of the high viscosity obtained with solutions in an irrotational laminar flow field suggests this is due to polymer molecule deformation and that this phenomenon is central to the mechanism of turbulent flow drag reduction.

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.

Drag reduction induced by polymer in turbulent pipe flows

The optimal amplifications of small coherent perturbations within turbulent pipe flow are computed for Reynolds numbers up to one million. Three standard frameworks are considered: the optimal growth of an initial condition, the response to harmonic forcing and the Karhunen-Loève (proper orthogonal decomposition) analysis of the response to stochastic forcing. Similar to analyses of the turbulent plane channel flow and boundary layer, it is found that streaks elongated in the streamwise direction can be greatly amplified from quasistreamwise vortices, despite linear stability of the mean flow profile. The most responsive perturbations are streamwise uniform and, for sufficiently large Reynolds number, the most responsive azimuthal mode is of wave number m=1 . The response of this mode increases with the Reynolds number. A secondary peak, where m corresponds to azimuthal wavelengths λ_{θ}^{+}≈70-90 in wall units, also exists in the amplification of initial conditions and in premultiplied response curves for the forced problems. Direct numerical simulations at Re=5300 confirm that the forcing of m=1,2 and m=4 optimal structures results in the large response of coherent large-scale streaks. For moderate amplitudes of the forcing, low-speed streaks become narrower and more energetic, whereas high-speed streaks become more spread. It is further shown that drag reduction can be achieved by forcing steady large-scale structures, as anticipated from earlier investigations. Here the energy balance is calculated. At Re=5300 it is shown that, due to the small power required by the forcing of optimal structures, a net power saving of the order of 10% can be achieved following this approach, which could be relevant for practical applications.

Experiments were conducted to measure the drag reduction of the complex mixtures in the pipe flow. The friction factor was measured for bio-polymer solutions and aqueous suspensions of fine solid matter. The results indicated that the experimental data points of the test solutions diverged from the maximum drag reduction asymptote at and above Re√f ≅ 200 and aligned parallel to those of Newtonian fluids. Type B drag reduction was observed. The velocity profile in turbulent pipe flow was predicted using a semi-theoretical equation, in which the friction factors were determined using the difference between the experimental results of the tested solutions and Newtonian fluids.