Energy Fuels 2009, 23, 4529–4532 Published on Web 07/23/2009
: DOI:10.1021/ef900427k
New Experimental Technique To Measure the Efficiency of Drag Reducer Additives for Oil Samples Marcelo A. da Silva,† Nelson de O. Rocha,‡ Carlos H. Carvalho,‡ and Edvaldo Sabadini*,† † Department of Physical-Chemistry, Institute of Chemistry, University of Campinas, UNICAMP, P.O. Box 6154, 13084-862, Campinas, SP, Brazil, and ‡CENPES, PETROBRAS, Cidade Universit aria Q.7 Ilha do Fund~ ao, 21941-598, Rio de Janeiro, Brazil
Received May 11, 2009. Revised Manuscript Received July 3, 2009
A comparative study about the efficiency of five commercial products used to facilitate the transport of oil through pipelines was developed using a new experimental technique. The technique is based on the applied torque necessary to keep the samples rotating in turbulent flow. The hydrodynamic drag reduction is proportional to the difference on the torque applied in oil samples with and without the additive. The experiments were developed in a Couette cell of a rheometer, which is sensitive to determine levels of drag reduction with high accuracy. The method was tested by using five commercial samples of drag reducers added to a Brazilian oil sample. Their efficiency, as well as their optimum concentrations, was compared. The method has proven very attractive mainly due to the low amount of sample and the short time required for the measurements.
considerable engineering interest to save energy in pumping processes.6-10 Probably the most emblematic application of the Toms Effect is the pumping of oil from Prudhoe to Valdez bays, along the 1287 km of the Trans-Alaska pipeline.10 Quantitative measurements of drag reduction are usually carried out by measuring the pressure drop along pipes in loops installed in facilities, or directly in commercial pipelines.11 Experiments in such systems are laborious and need significant amounts of material.12,13 It is not uncommon to find situations in which the efficiency of different additives and their optimum concentrations are required for a specific oil sample. In such situations, quick experiments and a low amount of samples are very attractive prerequisites. In this paper we describe a new versatile experimental technique to measure the hydrodynamic drag reduction promoted by additives in oil samples. The technique is based on the torque applied by the rotor of a rheometer to keep the oil without and with the additive rotating in a Couette cell. In turbulent flow, the torque is lower for the oil containing a drag reducing additive. To demonstrate this experimental technique, we analyzed the performance of five commercial additives to reduce the hydrodynamic drag in a Brazilian oil sample.
1. Introduction When a liquid is submitted to turbulence, the velocityfluctuation in a three-dimensional velocity field can be dispersed in a range of wavelengths, in which the smallest scales (smallest vortices) dissipate the energy of the flow. In 1948, B. A. Toms found that a very diluted high-molecular weight polymer solution under turbulent flow required a lower pipe flow pressure gradient than the pure solvent to produce the same flow rate.1,2 The theories for the Toms effect are still inconclusive, although some qualitative aspects are very wellknown. According to Tabor and de Gennes,3 the Toms Effect can be explained by the interaction of the polymer chain with the small vortices created within the turbulent flow. The process of stretching-contraction of the polymer chain affects the evolution of the vortices cascade (which dissipates the kinetic energy of the fluid) by storing some of the turbulent energy in the chain. The effect is also observed for liquids with dispersed fibers and with giant micelles.4,5 As the phenomenon requires a very small amount of additives, it has become of *To whom correspondence should be addressed. E-mail: sabadini@ iqm.unicamp.br. (1) Toms, B. A. Proc. 1st Congress on Rheology; North-Holland Publishing Co.: Amsterdam, 1948; pp 135-141. (2) Virk, P. S.; Merrill, E. W.; Mickley, H. S.; Smith, K. A.; MolloChristensen, E. L. J. Fluid Mech. 1967, 30, 305–328. (3) Tabor, M.; de Gennes, P. G. Europhys. Lett. 1986, 2, 519–522. (4) Zakin, J. L.; Lu, B.; Bewersdorff, H. W. Rev. Chem. Eng. 1998, 14, 253–320. (5) Kamei, R. K.; da Silva, M. A.; Sabadini, E. Langmuir 2008, 24, 13875–13879. (6) Alkschbirs, M. I.; Bizotto, V. C.; Oliveira, M. G.; Sabadini, E. Langmuir 2004, 20, 11315–11320. (7) McCormick, C. L.; Hester, R. D.; Morgan, S. E.; Safieddine, A. M. Macromolecules 1990, 23, 2132–2139. (8) Bailey, F. E.; Koleske, V. J. Poly(ethylene oxide); Academic Press: New York, 1976. (9) Figueredo, R. C. R.; Sabadini, E. Colloids Surf. A 2003, 215, 77– 86. (10) Kulicke, W. M.; Gragem, H.; Kotter, M. Drag Reduction Phenomenon with Special Emphasis on Homogenous Polymer Solutions Polymer Characterization/Polymer Solutions; Springer-Verlag: Berlin, 1989. r 2009 American Chemical Society
2. Experimental Section 2.1. Sample Preparation. Five commercial drag-reducing additives were studied, and polyisobutylene (PIB) with molecular weight 4.7 106 g mol-1 was also used as a standard drag reduction agent. Initially, stock solutions containing 200 ppm of the additives were prepared in toluene. The solutions were kept under gentle stirring until their complete dissolution. These stock solutions were used to prepare the final solutions in mixtures of oil (with API = 17) and toluene. The studies were
(11) Cuenca, F. G.; G omes, M.; Dı´ az, M. B. Energy Fuels 2008, 22, 3293–3298. (12) Bizotto, V. C.; Sabadini, E. J. Appl. Polym. Sci. 2008, 110, 1844– 1850. (13) Nakken, T.; Tande, M.; Elgsaeter, A. J. Non-Newtonian Fluid Mech. 2001, 97, 1–12.
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Energy Fuels 2009, 23, 4529–4532
: DOI:10.1021/ef900427k
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carried out in the concentration range of the additives between 0 and 100 ppm. 2.2. Rheological Measurements. The drag reduction measurements were carried out in a HAAKE rotational rheometer RS1. A Couette cell Haake Z34 Ti - DIN 53019/ISSO 3219 with inner and external diameters of 17.00 and 18.44 mm, respectively, was used. The temperature was kept fixed at 25.0 °C through an external thermostatic bath (Haake DC30). The flow curves were obtained from 80 to 3200 rpm. For the experiments with the solutions of PIB in toluene and n-heptane a double-gap cell (Haake DG43-Ti) was used. Its characteristics are: the internal and external diameters of the cup and of the rotor were 17.75, 21.70 and 18.35, 20.99 mm, respectively. Figure 1. Schematic representation of a Couette cell (left) with the flow structures named Taylor vortices (adapted from Nijman, J. Taylor Flow in Concentric Cylinder System, Technical note of Thermo Fisher Scientific) and a schematic flow curve (right) for a pure Newtonian fluid (continuous line) and for the fluid containing a drag-reducing agent (dashed line). The regions corresponding to the onset points for the Taylor vortices (I) and for the turbulent region (II) are indicated. The %DR is estimated directly from the curves.
3. Results and Discussion The magnitude of hydrodynamic drag reduction is usually determined by measuring the pressure drop along the pipe, in which the turbulence level can be correlated with the Reynolds number as in eq 1. QF ð1Þ Re ≈ πRη where: Q, R, F, and η are, respectively, the volumetric flow, the radius of the pipe, and the density and the viscosity of the fluid. Recently, Nakken et al.13 demonstrated that levels of drag reduction can be determined by using a rheometer, measuring the difference in the applied torque in sample without and with a drag reduction agent. Zakin et al.14 also used such a technique to measure levels of drag reduction in aqueous solution containing giant micelles, and Sabadini et al.5 used it to determine their thermal stability. Experiments in such a system are very suitable for the study of the Toms Effect, mainly due to its high accuracy ((3%).13 A detailed description of the technique can be obtained elsewhere.12,13 A schematic representation of a Couette cell (with the flow structures, named Taylor vortices) and a schematic flow curve for a fluid without and with a drag-reducing agent is shown in Figure 1. The flow curve is obtained by shearing a solution in a range of angular velocity, Ω (which is proportional to the Reynolds number, Re) and measuring the correspondent torque (τ). As shown in Figure 1, for a Newtonian fluid, beyond the laminar flow regime (characterized by a straight line) the increase in the applied torque is due to the dissipative flow structures, named Taylor vortices (which consists of two counter-rotating pairs of vortices overlapped with the Couette flow).15,16 On increasing the angular velocity (therefore, Re), the flow field eventually becomes chaotic and turbulent. The pattern of the flow curve in the turbulent regime is changed if a drag-reducing agent is present in the solution. As shown in Figure 1, the torque required to keep the angular velocity is significantly lower in the presence of a drag-reducing additive. The Reynolds number for the flow produced in the Couette cell can be determined using eq 2.17 2 γ3 ðRo - Ri Þ F Re ≈ η
Figure 2. Flow curves (torque as a function of Reynolds number) for samples of oil/toluene (50%, w/w) without and with different concentrations of additive A. The measurements were carried out at 25 °C. Inset depicts the onsets of Taylor vortices (I) and the turbulent regime (II).
where γ· is the shear rate, and Ro and Ri are the outer and inner radius of the cylinders, respectively. It must be emphasized that the critical Reynolds number for laminar to turbulent flow in pipes is different from that in a Couette flow. Whereas the critical Re is close to 3000 for pipes, the transition for Couette flow is observed at Re = 300.17 Figure 2 shows flow curves (Re from 0 to 2500) for a mixture of oil/toluene (50%, w/w) containing different concentrations of one of the drag reducing agents (generically named as A). The addition of the toluene was necessary due to the high shear viscosity of the pure oil, for which the maximum torque applied by the rotor is not enough to produce significant turbulence. Additionally, toluene was chosen to dilute the oil sample, because the components of the oil are soluble in this solvent.18 At low Re, the applied torque is practically the same for all samples, and this is because the amount of additive is small and the shear viscosity of the solutions are close to that of the oil/toluene without the additive. The onset
:
ð2Þ
(14) Ge, W.; Zhang, Y.; Zakin, J. L. Exp. Fluids 2007, 42, 459–469. (15) Groisman, A.; Steinberg, V. Phys. Rev. Lett. 1996, 77, 1480–1483. (16) Taylor, G. I. Proc. R. Soc. London 1936, A157, 537–546. (17) Goodwin, J. W.; Hughes, R. W. Rheology for Chemists ; An Introduction; Royal Society of Chemistry: Cambridge, 2000. (18) Loh, W; Mohamed, R. S.; Gonc-alves, R. In Crude Oil Asphaltenes: Colloidal Aspects. Encyclopedia of Surface and Colloid Science; Somasundaram, P. Ed.; Taylor & Francis: New York, 2007; Vol 1 (1), 1-18.
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Figure 4. The percentage of drag reduction for 40 ppm of additive A and for PIB as a function of Re for mixtures of oil/toluene in proportions 50, 25, and 10% (w/w). The temperature of the experiments was 25 °C. Figure 3. Efficiency of drag reduction additives, expressed in terms of percentage of drag reduction (%DR) for oil/toluene samples, containing 40 ppm of the additives. For this experiment Re = 2000 and the temperature is 25 °C.
high shear rates. In a Couette flow the experiments cannot be extended to Re higher than 2500, where effects of larger magnitude for DR are expected. This is because the mechanical instability, characterized by sample centrifugation, is observed beyond this Re value. To verify the influence of toluene on the drag reduction level, the additives A, B, C, D, and PIB were studied in two other oil/toluene proportions: at 10 and at 25%. For this study the concentrations of the additives were fixed at 40 ppm. The behaviors for the four commercial additives are quite similar, regardless of the oil/toluene proportion. The results for additive A and for PIB are shown in Figure 4 (the results for the other additives were not shown in order to preserve the clarity of the graph). Apparently, for A the dependence of the %DR as a function of Re can be adjusted by a master curve, but for PIB important differences are observed when the content of toluene in the mixture is changed. The percentage of drag reduction is higher for a lower proportion of toluene, and a possible explanation for this result can be inferred considering the thermodynamic properties of the solvent. The Hildebrand’s solubility parameters are 16.5,19 15.3,20 and 18.320 (MPa)1/2 for PIB, heptane, and toluene, respectively. This means that alkenes are a better solvent for PIB than toluene. In a good solvent, the gyration radius of the polymer is expanded, and its ability to reduce the hydrodynamic drag is higher.12 The proportion of aromatic and aliphatic compounds in the Brazilian oil sample are 31 and 15% (w/w), respectively. Therefore, the quality of the solvent for PIB becomes worse as the content of toluene in the mixture with the oil is enhanced. To check this hypothesis, the flow curves for 40 ppm of PIB in toluene and in n-heptane were obtained (Figure 5). As the shear viscosity for the solutions in both solvents are low, a double-gap cell was used to improve the accuracy of the torque measured. The result was expressed in terms of torque as a function of angular velocity because the flows in the outer and inner compartments of the double-gap cell are different.16 The result of Figure 5 confirms the hypothesis, as in all ranges of the flow curve, the torque for PIB/n-heptane is lower in comparison to that for PIB/toluene.
for the Taylor vortices is observed at Re = 150, and beyond specific Re the turbulence is attenuated by the additives. The longer macromolecular chains, which compose the formulation of the additives, absorb the energy of the vortices and inhibit the development of the turbulent cascade. The optimum concentration for additive A is close to 40 ppm; as for higher concentration, the shear viscosity increases and no additional benefit is obtained. This is a very attractive point of this technique as different formulations can be quickly tested in order to determine their optimum concentrations. As the shear viscosities of the samples are close (which is approximately the viscosity of oil/toluene), a linear correlation between the torques applied for the sample without (τOP) and with (τOA) additives allows an estimation of drag reduction percentage (%DR, eq 3). %DR ≈
ðτOP - τOA Þ τOP
ð3Þ
Figure 3 shows the %DR for the five studied additives and the result for PIB as a function of their concentrations. For such study, the Re was kept fixed at Re = 2000 and the concentrations of the additives were changed from 0 to 100 ppm. For the majority of the additives, the optimum concentration was in the range between 40 and 60 ppm. The maximum percentages were in the range of 20%, which is much higher than that obtained for PIB. Considering the accuracy of the technique (which is (3%), the following trend for the performance of the additives (at 40 ppm) in promoting drag reduction can be established: A ≈ B ≈ C > D ≈ E > PIB The additive D reaches the same efficiency as that for A, B, and C in higher concentrations (60 ppm). Considering the large amount of additive used during oil pumping operations, the determination of their optimum concentration is economically relevant and, in this sense, this new technique can give a quick answer. Higher %DR can be obtained in real conditions during the oil pumping operations, because they are usually performed at
(19) Sperling, L. H. Introduction to Physical Polymer Science, 4th ed.; Wiley-Interscience: New Jersey, 2006. (20) Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed.; CRC Press: Boca Raton, 1991.
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4. Conclusions The new experimental technique consists in measuring the difference in the torque require to impose a given flow rate for oil samples with and without a specific drag reduction additive. The technique is very suitable to quantify the efficiency of additives to promote hydrodynamic drag reduction. Although measurements in pipes are still essential, the proposed method helps to screen the yield and optimum concentrations of the drag reducers for different oil samples. The main advantages of the technique are the small amounts of samples required, resulting in low level of waste, its versatility to run quick experiments, and simplicity. The high accuracy of the technique allowed the verification of the effects of thermodynamic properties of the solvent on the capability of the additives to promote drag reduction. Acknowledgment. The authors thank the Fundac-~ ao de Amparo a Pesquisa do Estado de S~ ao Paulo (FAPESP, S~ ao Paulo, Brazil), the Conselho Nacional de Desenvolvimento Cientı´ fico e Tecnol ogico (CNPq, Brası´ lia, Brazil) for financial support and fellowships. This work was also supported by PETROBRAS. The authors are grateful to CENPES/PETROBRAS for the donated material and technical assistance.
Figure 5. Flow curves (torque as a function of the angular velocity) for 40 ppm of PIB in toluene and in n-heptane. The temperature of the experiments was 25 °C.
At Ω = 1200 rpm, the %DR measured were approximately 20 and 5% for PIB in heptane and toluene, respectively.
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