Drag reduction in transportation of hydrocarbon liquids: From fundamentals to engineering applications

1. Introduction

The problem of transporting oil from the field to oil refineries is one of the key problems in oil industry. For continental countries, this problem is solved through construction of well-developed pipeline network that were and are being constructed in Europe, Asia, the USA and Africa. At the same time, oil transportation by itself is associated with big expenses. Natural striving to increase flow velocity and construction of big diameter pipes causes onset of turbulence that spikes hydrodynamic losses and decreases effectiveness of energy consumption. Therefore, there is also a natural tendency to suppress turbulence in various ways. It appears that the most effective technique is the so-called Toms effect well-known (Toms, 1949). Its essence is that addition of extremely low concentrations of certain agents into a low-viscosity medium (water, organic liquids) dramatically reduces hydrodynamic resistance to flow within the range of large Reynolds numbers. In general, the role of such agents is performed by high molecular weight (МW) polymers which are soluble in a fluid. As a result of injection of Drag Reducing Agents (DRA) in the amount of about 10 ppm, flow capacity in oil pipelines increases essentially - for tens of percent - thus specific pumping energy consumption decreases.

The DR phenomenon can be considered as some kind of multiphase flow of immiscible liquids including multi-layer flows and/or flow of oil as emulsions (Zadymova et al., 2016, Malkin et al., 2016) The concept of multiphase flow as the mechanism of DR was discussed and successfully explored in series of original publications and reviews (Al-Sarkhi, 2010, Al-Sarkhi, 2012, Al-Sarkhi et al., 2011, Al-Yaari et al., 2009, Al-Yaari et al., 2012, Al-Yaari et al., 2013).

The main factor that impacts drag reducing (DR) activity is the size of macromolecular coil in solution: the greater it is, the more efficient DRA. The main contributors to that size are mentioned above - MW and high solubility. Under the latter term we mean the factors that promote larger end-to end distance of macromolecule of a constant MW. It can be reached by lowering salt concentration in a water for water-soluble polymers, or increasing pH for polyacids that cause repulsion of ionized acid groups. It can be also deasphaltizing or heating of heavy crude as well as internal flexibility of polymer chain.

By means of microdoses of polymer, it is possible to ‘enlarge’ bottlenecks of a pipeline network, replenish delivery volumes after a forced downtime, react to season increase in consumption of one or another petroleum product. DRA can help to reduce time required for tanker loading and offloading. Besides it can be considered as additional energy material to response to pumping power shortages in one region or another. By metaphorical comparison of a pipeline network to a blood vascular system of a living organism, results of DRA addition can be compared to a bolt of adrenalin increasing vascular blood flow.

Reviews (Virk, 1975, Little et al., 1975, Nadolink and Haigh, 1995, Graham, 2004, Wang et al., 2011; Hong et al., 2015) provide a fairly comprehensive idea about the present-day views in this area. Although discussions concerning Drag Reduction (DR) mechanism continue up until today (Hamouda, 2007, Sher and Hetsroni, 2008, Manzhai et al., 2014), the undisputable fact is that injection of macromolecules into a liquid flow reduces turbulence level in near wall regions or, what amounts to the same thing, contributes to flow laminarization.

In world practice of oil pipeline transportation this effect was used for the first time in operation of Trans-Alaskan pipeline in 1979 (Burger et al., 1982).

Found empirical regularities facilitated a wide application of the Toms effect in transportation of crude oil, diesel fuel and gas condensate through the pipelines. DRA world market for hydrocarbon liquids is estimated to be hundreds of millions of dollars.

Original observations of this effect were described for hydrocarbon medium in particular. However, at a later stage after effective water drag reducing agents (polyethylene oxide, polyacrylamide) were discovered and used in oil production, shipping industry and military hardware, overwhelming majority of publications on the subject (several thousand papers!) is accounted for water systems.

In laboratory practice the Toms effect is used not only for turbulence suppression research but also as an original physicochemical technique of research of conformational state of polymers in solution as an indicator of formation/destruction of anisotropic molecular structures (supramolecules, threadlike surfactant micelles, polymer-polymer complexes), polymer chain growth/degradation kinetics. In some cases, the Toms effect gives a unique opportunity to study extremely diluted polymer solutions at concentrations of about tenths of ppm.

The purpose of this review is to consider a correlation between structure of macromolecules and their efficiency in hydrodynamic drag reduction of hydrocarbon liquids, as well as the technological application of found regularities.

2. Experimental (laboratory) techniques of study of the Toms effect and manners of the results presentation

Technique of study of the hydrodynamic drag reduction effect can be divided into two groups. Turbulent flow characterized by averaged values as a whole is the object of research of the first group. For these purposes, turbulent rheometers and hydrodynamic benches are used to measure flow rate, pressure drop, wall shear stress, and wall shear rate from which liquid drag coefficientand the value of DR in the presence of different DRA are calculated.

Research of mechanism of DRA action refers to the second group of papers.

It should be noted that different experimental technique can give not the same evaluation of applied DRA as different measurements are performed at various flow regimes. Therefore, interpretation of results of these measurements can be ambiguous.

2.1. Turbulent rheometers

Turbulent rheometers can be divided into two groups. Devices for study of flow under pressure in which shear is generated by a pressure drop at the ends of a device (most often, a circular pipe) can be referred to the first group. In this case, conduit surface remains immobile.

In rheometers of the other type, the flow is generated by motion of a boundary surface. Shear flow occurs between a moving (usually rotating) and a motionless (or rotating in the contrary direction) surface. An example of this can be a device with coaxial cylinders (see, for example, (Chan et al., 2011)), as well as a rheometer with a rotating disk (see, for example, (Choi and Jhon, 1996)).

Rheometers of capillary and disk types are most popular in laboratory practice for a comparative evaluation of effectiveness of DRA samples. A simplified edition of a capillary rheometer (Revel-Mouroz et al., 2015) where drag reduction is evaluated through the weight of liquid flowing out of a capillary is presented in Fig. 1. Container 1 is filled with liquid under study from which it drains through a capillary 4 into a receiving container 7 under gravitational force. The capillary at the outlet is shut by an electric solenoid valve 5, the opening time for which is set by a control unit 6. The container is equipped with a Marriott pipe (3) in order to maintain a constant pressure drop.

The value of hydrodynamic drag reduction DR is calculated as(1) $D R = (1 - \frac{m_{0}^{2}}{m_{D R A}^{2}}) \cdot 100 %,$ where $m_{0}$ is the mass of pure liquid, $m_{D R A}$ is the mass of liquid with DRAflowing through a capillary at a fixed amount of time.

The general formula for Drag Reduction is(2) $D R = (1 - \frac{λ_{D R A}}{λ_{0}}) \cdot 100 % = (1 - \frac{Δ p_{D R A} \cdot Q_{0}^{2}}{Δ p_{0} \cdot Q_{D R A}^{2}}) \cdot 100 %$ where λ is the flow friction characteristic;

Δp is the pressure drop
Q is the flow rate proportional to m

Index 0 refers to the solvent, index DRA refers to polymer solution.

As Δp in turbulent rheometer is constant, the formula (2) transforms to (1).

In a turbulent rheometer with a rotating disk (Fig. 2) the value of drag reduction is evaluated according to the torque value when the disk rotates in a pure solvent (Ms) and in DRA solution (M) at the same shaft rotation:(3) $D R (%) = \frac{M_{s} - M}{M_{s}} \cdot 100 %$

The main purpose of applying compact turbulent rheometers is provision of a feedback during development of technology of ultrahigh-molecular weight polymers, as well as laboratory testing of DRA commercial samples. One of the popular ways of presenting results is a relationship between DR and DRAconcentration.

To illustrate efficiency of applying this DRA evaluation method, two samples of one and the same polymer that was synthesized at comparable conditions but at different initial monomer content are compared in Fig. 3 (see details in figure caption). It can be seen that the polymer synthesized in mass polymerization significantly exceeds in effectiveness the one that was obtained in solution medium (Nesyn, 2007). This is due to the solvent transfer coefficient which is responsible for reducing the final MW of a polymer. Generally, DR vs. concentration curve is of an extreme nature, however, the ascending branch of curve is of interest in terms of evaluation of the DRA efficiency.

As a DRA effectiveness measure, it is convenient to take a concentration valuethat provides some set value of DR, for example, half of the maximum attainable DR value. It is called a half-effect concentration (Konovalov, 2013) and is denoted by С1/2. Fig. 4 illustrates how commercial DRA samples close in quality can be ranged with the help of this parameter.

It is convenient to apply a half-effect concentration as an instrument for optimization of a polymer synthesis technology. In such a way, Fig. 5 shows how С1/2 of the product measured in straight-run naphtha changes depending on conversion fraction of 1-octene obtained by the bulk polymerization in the presence of a Ziegler-Natta catalyst (Konovalov, 2013).

As it can be seen, the biggest efficiency (minimum of С1/2) is reached at a monomer conversion of about 57%. At higher conversion degrees, accumulation of polymer with smaller MW not active in terms of hydrodynamic DR takes place. It follows that there is no need in a complete conversion of a monomer into a polymer. Moreover, polymer synthesis process is significantly reduced while cut off at an optimum conversion value 57% which is reached in two days while an 80% conversion is reached in not less than eight days.

Another way of representing relationship of DR vs. concentration is plotting relationship of С/DR and C that turns out to be linear (Fig. 6).

A linear relationship of such type within the given coordinates is a common property of solutions of long-chain polymers in the region of low concentrations. The physical content of a reciprocal of an intercept f represents a reduced drag reduction at an infinite dilution (a formal similarity of this value with intrinsic viscosity should be pointed out). The f value can be used in order to evaluate impact of one or another factor on capability of a polymer to reduce hydrodynamic drag. An example showed in Fig. 7 demonstrates relationship of fand poly(cetyl-methacrylate) polymerization degree (Nesyn et al., 1989a, Nesyn et al., 1989b).

It can be seen from the figure that efficiency of macromolecules increases with their length. Besides, there is a minimum critical value of polymerization degree below which the polymer is not active in terms of DR. For the given case this value constitutes about 4000 that corresponds to MW of about 1.2·106.

2.2. Flow visualization technique

The Toms effect can also be applied to solve fundamental tasks related to the turbulent flow study. So, for example, it allows for evaluating details of a turbulent flow structure – average velocity profile, frequency spectrum of pulse-coupled energy, distribution of fluctuations of instantaneous velocityalong a conduit section. PIV (Particle Image Visualization) technique is used more often than other (Kulmatova, 2013). It is based on the Doppler effect when laser beam is transmitted perpendicular to flow (Fig. 8).

An example of distribution of instantaneous velocity in water flow (on the left) and DRA water solution (on the right) is shown in Fig. 9 (Hadri and Guillou, 2010). A surfactant – cetyl trimethyl ammonium chloride (CTAC) was used as a DRA in this case.

Here transition is clearly seen from a chaotic (turbulent) flow to a substantially more laminar one when DRA is injected. One can also note some increase in flow core velocity in the surfactant solution compared to a pure liquid while contours of a slow zone in the wall-adjacent region become a little wider.

2.3. Tensile technique

One of the fundamental concepts explaining increase of hydrodynamic resistance in turbulent region is the concept of fractal waves – transformation of a cascade of larger scale vortices into smaller scale ones is responsible for the increasing energy dissipation in the turbulent flow. In view of this, injection of macromolecules into a turbulent flow causes the liquid to take on viscoelastic properties at a macromolecule scale and, instead of dissipation, viscoelastic fluctuations appear (Kolmogorov, 1941, Falkovich, 2011).

In this case, in order to evaluate the role of solution elasticity in DR, measurements of viscoelastic (relaxation) properties of dilute solutions should be used. Experimentally, it is quite difficult to perform this at shear conditions, but viscoelasticity of a solution at single-axial extension can be evaluated. This method is based on high speed visualization of the kinetics of thinning the finer under extension as shown in Fig. 10 and analytical treating experimental results in the frames of the non-linear model of visco-elastic medium (Bazilevsky et al., 1981, Bazilevsky et al., 1990, Entov and Hinch, 1997). In the initial stage of stretching, the thinning process is governed by viscous forces while the further stage of stretching takes place under superposition of capillary forces and elasticity of a fluid. During this part of the extension, a dependence of the jet radius on time can be described by a spectrum of relaxation times. As the first approximation, one-mode relaxation model can be used and the decrease of the radius is described by an exponential law which gives this characteristic relaxation time as a measure of viscoelasticity of a fluid.

There are many technical realizations of this approach which remains actual for studying dilute solution (Anna and McKinley, 2001, Niedzwiedz et al., 2010, Ardekani et al., 2010, Castrejón-Pita et al., 2012, Mackley et al., 2017).

The essence of this technique is demonstrated in Fig. 10. During extension, a neck is formed that becomes thinner with time so that a fiber is formed. Eventually, the fiber breaks. Based on tensile kinetics viscoelastic properties of a diluted solution can be found and one of its main characteristics is its “lifetime”, i.e., fiber stability before its breaking. This technique was suggested for pre-award evaluation of DRA efficiency before injecting into the pipeline (Burden, 2012). It is interesting to note that worm-like micelles solutions that can also be used as DRA attribute analogous viscoelastic properties to liquid (Bhardwaj and Miller, 2007).

The essence of measuring device is that a laser thickness gauge (www.thermo.com.cn) is used to observe changing a liquid thread diameter of a sample containing a DRA after its abrupt extension (Fig. 11).

Further mathematical treating gives the value of the solution elongation viscosity using which a good quality prediction can be made. This will make it clear if the agent will reduce hydrodynamic resistance for this oil. Fig. 12illustrates changing of reduced fiber thickness with time for two solutions of different DRA in samples of initial crude oil and oil with DRA additives (Milligan et al., 2011).

DRA based on 2-ethylhexylmethacrylate polymer is highly soluble in the oil sample under study and the time until fiber breaking (Fig. 12 b) is next longer, than break time of a crude oil jet (Fig. 12a). As for a conventional agent based on alpha-olefins (the results are given for Liquid Power sample), its injection did not introduce noticeable changes into viscoelastic properties of oil (Fig. 12c). Not surprisingly, Liquid Power showed a zero result when being tested in an oil pipeline even at a concentration of 187 ppm, while adding poly(2-ethylhexyl-methacrylate) at a concentration of 50 ppm resulted in DR of about 30% (Milligan et al., 2011).

2.4. DRA efficiency at the Reynolds diagram

In order to get a hydrodynamic picture, drag reduction data is usually plotted as a relationship of the friction coefficient CF vs. the Reynolds number Re. In these coordinates, the data lie within the zone limited by the Blasius (Karman) law, the Poiseuille law and the Virk maximum DR asymptote (MDRA). Based on the curve trajectory that the points fit, DRA is referred to either A or B type depending on whether it emanates from the Blasius linear rule or the Virk asymptote.

In B case, the trajectory emanates from the laminar flow to the mode of maximum DR avoiding the transient zone. Fig. 13 shows an example of a B type behavior where relationship of CF = f (Re) is represented for water solution of polysaccharide (xanthan gum) of a fixed concentration in pipes of different diameters (Gaslievic et al., 2001).

Type of interaction of DRA with turbulent vortices, structure of a wall-adjacent layer, as well as impact of degradation on DR is assessed from the curve pattern.

2.5. The Toms effect as a research tool

In a row of practical aspects of the Toms phenomenon, it should be mentioned the use of DR testing as laboratory technique to research macromolecular reactions at extremely low concentrations. The Toms effect gives an opportunity to investigate polymer formation or conversion in the solution in the range of about several ppm. When the solvent has close to polymer hydrocarbon nature, it seems there is no any method that allows to research macromolecular reactions in such a dilute state.

This technique allows to study polymerization kinetics (Malkin et al., 2001) especially at the very beginning of a reaction (Malkin et al., 2000) that may help, for example, to clear up mechanism of the initiation. Likewise the Toms effect is very sensitive to macromolecular conformation transitions, polymer-polymer interactions, cross-linking of macromolecules in very dilute solutions. So, it can be effectively used for scientific purposes.

3. Scaling – effect of pipeline diameter and length

The issue of scaling of laboratory research when studying DRA role in hydrodynamic DR has always been fundamental. Having summed up their observations and literature data, authors (Gaslievic et al., 2001, Gasljevic et al., 1999) found a simple empirical technique of predicting a DR value in a pipe of a certain diameter. It turned out that data of relationship of DR and linear flow velocity of a given solution fits onto one curve for any value of a pipe diameterboth for polymer solutions (Fig. 14) and surfactant solutions (Fig. 15).

As is seen, there is almost no spread of data obtained for a certain medium (for example, diesel fuel) using a laboratory bench for pipes of different diameters for a linear flow velocity not exceeding 6 m/s. Therefore, it can be projected with a good accuracy onto 300 and 500 mm pipelines where linear velocitydoes not exceed 3 m/s. The only critical condition is a single-flow (non-cyclic) configuration of a laboratory pipeline to exclude agent degradation at the pump.

The pipeline length can make a difference only at a big length where effects of polymer degradation start to have an impact. Fig. 16 shows change of DR along the length of a 1000 mm pipeline where DRA is based on a copolymer of higher alpha-olefins was injected into a pipeline at a section length of 500 km (Lisin et al., 2013).

The diagram above shows that the curves reach their peak at a distance of 50 km from the injection point. DRA was initially polymer slurry in a non-solvent medium, therefore the presence of the peak is indicative of competing processes of polymer dissolution and degradation that are at equilibrium state at a maximum point. Relative decrease in the maximum efficiency at the section from 50th to 500th km makes the value of about 1.8 and does not depend on DRA concentration. It should be noted that these data is unique according to such a long distance between pump stations.

At laboratory level, degradation effects are studied using either a disk type rheometer running quite a time-consuming test or a capillary rheometer at a multiple flowing of one and the same solution. The first method is more preferable as it creates time-stable flow while at a multiple tests through a capillary are attended with inlet/outlet degradation by themselves which is difficult to take into account.

Mechanical degradation is a general feature of polymers. A decrease in the chain length always has a negative impact on the efficiency of DR. This is why the DR effect becomes weaker along the pipe line. The tendency to mechanical degradation depends on the nature of a polymer chain. So, it is important to have the objective characteristic of this process. This approach has been developed in (Bizotto and Sabadini, 2008) where a method of extrapolation to zero concentration of a polymer was proposed. It appeared that two different polymers – poly(ethylene oxide) and polyacrylamide are equally inclined to mechanical degradation. However the behavior of more concentrated solutions can be different due to formation of entanglements and supramolecular structure. So it is necessary to control the efficiency of a chosen polymer in real technological conditions using the flow in a long pipe.

Degradation effects can be decreased by generation of macromolecules of a specific architecture. In such a way, graft-copolymers are more resistant to mechanical destruction than their linear analogues (Brostow et al., 2007). The same paper gives a qualitative interpretation of time-dependent polymer destruction in turbulent flow.

It is essential to note that complexes of polymers and surfactants can have a higher resistance to destruction than each component taken individually (Hayder et al., 2015). Generally speaking, development of destruction resistant DRA is the task of a high practical importance since all polymer agents known to present day lose their ability of DR completely when passing through a main line pump.