(89478) Effects of Coiled Tubing Curvature on Drag Reduction of Polymeric Fluids

Copyright 2004, Society of Petroleum Engineers Inc.This paper was prepared for presentation at the SPE/ICoTA Coiled Tubing Conference and Exhibition held in Houston, Texas, U.S.A., 23–24 March 2004.This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.AbstractThis paper presents experimental results of the effects of coiled tubing curvature on the drag reduction behavior of polymeric fluids in turbulent flow. The experimental setup consists of a 10-ft section of ½-in. OD straight tubing and four coils of coiled tubing of the same diameter. Fluids investigated included water, guar, hydroxypropyl guar (HPG), and Xanthan fluids at various polymer concentrations. It is found that the coiled tubing curvature could reduce the drag reduction by 10 to 30% as compared with straight tubing, depending on the flow conditions. The curvature of tubing also delays the onset of drag reduction. The percentage drag reduction in coiled tubing may be improved if fluid is pumped at higher rates. The results of the present study were also verified with the previous full-scale experiments and are found to be representative of the drag reduction behavior of similar fluids under the field flow conditions.IntroductionFrictional pressure of fluids in tubing can be drastically reduced by adding drag-reducing additives such as certain long-chain polymers or surfactants to fluids pumped. This drag reduction property of fluids is more desirable in pumping operations through coiled tubing than through conventional straight tubing, since the flow rates through coiled tubing reels are often limited due to the small tubing diameter (coiled tubing should be small enough for the whole length of tubing string to be spooled on the reel drum). The tubing curvature will cause secondary flow, which further increases the frictional pressure drop in coiled tubing.Since the discovery of the drag reduction phenomenon of polymer solutions in pipe flow by Toms1 in 1948, there have been numerous studies on this fascinating and certainly important subject of fluids engineering. The papers by Lumley2, Hoyt3,4, Virk5, and Berman6 provide some extensive reviews on this topic. Comparatively, information on drag reduction of fluids in coiled tubing is very scarce. It would be quite logical to believe that the drag reduction behavior of polymer solutions in coiled tubing would be significantly different than in straight tubing. The centrifugal forces during fluid flow in coiled tubing will result in secondary flow in vortical forms in the cross-section of tubing.7,8 This secondary flow, superimposed on the main axial flow, will change the flow field and, for drag-reducing fluids, affect the drag reduction mechanisms.Most of the previous studies on fluid flow in coiled pipes have focused on the flow of Newtonian fluids.9 Only a few investigated the flow of non-Newtonian fluids in coiled pipes.10-13 In recent years, the rapid increase of coiled tubing applications in the oil and gas industry has driven research activities on coiled tubing hydraulics using full-scale experiments.14-16 Shah and Zhou16 investigated the drag reduction behavior using a full-scale coiled tubing test facility which was established for the Coiled Tubing Consortium supported by the industry. Useful observations on the effects of polymer concentration and coiled tubing curvature on drag reduction were provided. Note that the curvature ratios of the coiled tubing reels in the investigation were limited ― the combinations of tubing diameter and reel drum diameter resulted in a range of curvature ratio of 0.0113 to 0.0185. To include this important parameter into friction factor or drag reduction correlations, further investigation on fluid flow through coils with a wider range of curvature ratio is apparently desired. Based on this consideration, a lab-scale test loop was constructed using ½-in. OD stainless steel tubing. It consists of a 10-ft straight tubing section and four replaceable coils with curvature ratio of 0.01, 0.019, 0.031, and 0.076 respectively. This range of curvature ratio is believed to be able to cover the curvature ratios encountered in the field operations. Besides the saved costs of running the full-scale experiments, better quality controls can be achieved concerning the fluid preparation, fluid degradation as well as testing conditions with the present lab-scale tests.The objective of this paper is to present the new experimental results of coiled tubing curvature on the drag reduction behavior of polymeric fluids in coiled tubing.ExperimentalExperimental Setup. The experimental setup used in this study is illustrated in Fig. 1. The flow loop consists of the following components:• A 1000-gal polyethylene tank for fluid mixingand storage.SPE 89478Effects of Coiled Tubing Curvature on Drag Reduction of Polymeric FluidsY. Zhou, SPE, S.N. Shah, SPE, and P.V. Gujar, SPE, Well Construction Technology Center, University of Oklahoma2 SPE89478• A Moyno pump for pumping fluids.• A centrifugal pump was used to feed the Moyno pump.• A 10-ft straight tubing section and four replaceable reels of coiled tubing with different curvature ratios.Both the straight and coiled tubings are ½-in. ODstainless steel tubing. The ID is 0.435 in. Thedimensions of the four reels are given in Table 1.• MicroMotion flow meter. The MicroMotion® Elite Model CMF050 Sensor is capable of measuring flowrate in the range of 0 – 30 gal/min, fluid density withaccuracy of ± 0.0005 g/cc, and temperature withaccuracy of ± 1°C or ± 0.5% of reading in °C.• Pressure transducers for measurement of frictional pressure losses in the straight tubing section and in thecoils. The measurement range can be set up to work indifferent ranges between 0 to 100 psi.• An absolute pressure sensor to measure the working entry pressure of the system. The present flow loop hasa working pressure limit of 1200 psi.• A Fluke Hydra data logger system is used for data acquisition. The data collected is transmitted to apersonal computer in the control room and displayedlive on the computer screen. This helps the monitoringand quality control during the testing.Testing ProcedureFluid Preparation. The fluids were prepared and stored in the 1000-gal polyethylene tank. The mixing procedures recommended by polymer product suppliers were followed. Gel was allowed adequate time to hydrate in the mixing tank for proper gelation. Samples of fluid were collected and measured using a model 35 Fann viscometer to check fluid viscosity.After the polymer solution was prepared, water was first circulated through the flow loop to conduct system check. This will make sure the pressure transducer settings and the parameter settings of the data acquisition computer are set properly. Water was pumped through both straight and coiled tubing at various flow rates and corresponding pressure drop readings were recorded. The results of water tests will also be used as the baselines for gel flow analysis.Then, water in the flow loop was displaced by pumping the test fluid (gel). Once the system was filled with polymer fluid, the drain valve was closed and thus the fluid was pumped in the recirculation mode ― from tank to the pump, then through the straight and coiled tubing, and then back to the tank. The flow rate was set at a desired value and the steady state pressure drop data across straight and the coiled tubing were recorded at the corresponding flow rates. The flow rate was changed and corresponding pressure drops were recorded. This procedure was followed for various flow rates. At each flow rate, adequate flow time was allowed for the flow to reach steady state condition. This was achieved by monitoring the live display of measured flow rate and pressure drop signals.Fluid samples were collected from the mixing tank at the start of each test. Another sample was collected at the end of the test. The rheology of the samples was evaluated using the model 35 Fann viscometer. By comparing the samples taken before and after the test, any change in rheology due to polymer degradation and viscous heating can be detected.After testing with one coil was finished, the coil was replaced by another coil with different curvature ratio. The similar testing procedure was followed to obtain pressure drop data at various flow rates for all the four coils.In this study, we tested three types of polymer fluids, i.e., guar, hydroxypropyl guar (HPG), and Xanthan solutions at various polymer concentrations, as shown in Table 2.Results and DiscussionData Reduction and Analysis. The data recorded from the Fluke Hydra wireless loggers consist of flow rate, pressure drops across straight and coiled tubings, fluid density, and fluid temperature, etc. The transient data points due to flow rate change or due to purging operations are removed so that only the steady state data points are kept.The Fanning friction factor was calculated from the following relation:221Vf wρτ= (1)in which τw = the wall shear stress and is calculated from:Lpdw4∆=τ (2)where L is the tubing length of either straight tubing or coiled tubing.Drag reduction can be defined16 as:spffDR−=1 (3)where f p and f s are the Fanning friction factors of polymer solution and solvent respectively. Both can be calculated using Equations 1 and 2.The flow behavior of each fluid will be examined from plots of Fanning friction factor versus generalized Reynolds number which is determined as:12Re8−−=npnng KVdNρ (4)Water Test. Water test was performed with all the four coils as well as the 10-ft straight section. Since water was used as the base fluid or solvent, the result of water testing will be the basis for drag reduction analysis for polymer solutions.Figure 3 is a composite plot of Fanning friction factor versus Reynolds number (N Re) for the straight tubing and the four coils. During the testing, only the coils were replaced by one another, whereas the 10-ft straight section remained the same. It was found that the pressure drop readings of the straight section during the tests of different coils are close and exhibit very good reproducibility.SPE 89478 3As shown in Fig. 3, the friction factor of the straight tubing matches closely with the Drew17 correlation for straight pipe. All the coils show higher friction than straight tubing. As the curvature ratio (a/R) increases from 0.01 to 0.076, the friction factor also increases. Published correlations18,19 were compared with the present results and it was found that the Ito18 correlation results in close agreement with the water data. The Ito18 correlation, when plotted on f vs. N Re plot, is dependent on the parameter of curvature ratio. The plot of Ito18 correlation shown in Fig. 3 was calculated using curvature ratio of 0.076. It matches well with the set of data points of coiled tubing with a/R = 0.076.Effect of Curvature Ratio on Drag Reduction. Figure 4 shows the plot of Fanning friction factor versus generalized Reynolds number for 15 lb/Mgal Xanthan fluid. The high generalized number indicates that the flow regime was turbulent. The drag reduction effect is evident in both straight tubing and coiled tubing since the data points of the straight tubing lie below the Drew17 correlation while the data points of coiled tubing are below the Ito18 correlation. For straight tubing, the first two points are close to the Virk5’s maximum drag reduction asymptote. As N Reg further increases, the data points deviate from the Virk’s asymptote line. For coiled tubing, friction factor increases with increasing curvature.Figure 5 shows the plot of percentage drag reduction versus generalized Reynolds number for 15 lb/Mgal Xanthan in the straight tubing and the four coils. Note that the percentage drag reduction for straight tubing is calculated using the straight pipe correlation for Newtonian fluid (such as Drew correlation) for f s in Equation 3. For coiled tubing, f s was estimated from coiled tubing correlation for Newtonian turbulent flow, i.e., the Ito correlation. The difference in drag reduction behavior between straight and coiled tubings is obvious.The drag reduction in coiled tubing is significantly lower than in straight tubing. At low generalized Reynolds number the difference could be as much as 30%. At high generalized Reynolds number, the difference is more than 10%. It is interesting to note that the plot for the straight tubing is relatively flat, implying that increasing pumping rate (therefore increasing generalized Reynolds number) will not result in additional drag reduction. As a matter of fact, the drag reduction decreases slightly as the generalized Reynolds number increases for this case. The behavior in coiled tubing is quite different. The percentage drag reduction increases as the Reynolds number increases. The practical implication would then be that if pumping conditions permit, the percentage drag reduction can be improved by pumping at higher rates.The Modified Drag Reduction Envelope for Coiled Tubing. When the data of friction factor and Reynolds number are plotted in the Prandtl-Karman coordinates, the drag reduction behavior of a fluid can be better revealed. As an example, Fig. 6 shows the plot of 20 lb/Mgal HPG gel. Similar plots for 10 and 30 lb/Mgal HPG and guar fluids are also made. This kind of plot can be called the modified drag reduction envelope since it is modified from the Virk’s drag reduction envelope which is useful for the analysis of drag reduction in straight pipes. In this case, the zero-drag reduction line (Prandtl-Karman law) was replaced with Newtonian turbulent correlation for coiled tubing such as Ito18 correlation. As is shown in Fig. 6, the data points for coiledand straight tubings all fall on straight lines. But, the data linefor straight tubing has greater slope and higher position. As curvature ratio increases, the data lines for coiled tubing become lower and the slopes are decreased slightly. The intersections of the zero-reduction line (the Ito correlation in Fig. 6) with the data lines or their extrapolations represent the onset conditions of drag reduction. Therefore, Fig. 6 also indicates that as the curvature ratio increases, the onset of drag reduction in coiled tubing is delayed. This confirms our observation in a previous full-scale experimental investigation.16Effect of Polymer Concentration. Figures 7 and 8 show the plots of percentage drag reduction for 10, 15, 20, and 30lb/Mgal Xanthan in straight tubing (ST) and coiled tubing (CT)with curvature ratio of a/R = 0.01 respectively. These plots reveal the different effects of polymer concentration on drag reduction for tubings with different curvature ratios. For straight tubing and at higher Reynolds number, 20 and 30lb/Mgal Xanthan produce higher drag reduction than 10 and15 lb/Mgal Xanthan fluids. Since the difference in drag reduction between the 20 and 30 lb/Mgal Xanthan fluids is small, the 20 lb/Mgal Xanthan fluid appears to have an optimum concentration.Figure 8 shows that for coiled tubing with a/R = 0.01, thedrag reduction is better for less concentrated polymer solution.This is probably because the turbulence intensity in coiled tubing is suppressed by curvature and more concentrated polymer solution has more adverse viscous effect on theflow resistance.Figure 9 shows the combined effect of polymer concentration and curvature ratio for the data of 15 and 30lb/Mgal Xanthan fluids. For straight tubing, both slopes and position of data lines are drastically affected by the polymer concentration. The slope of 30 lb/Mgal Xanthan has much greater slope. For coiled tubing, the vertical position of thedata lines are more or less dominated by the polymer concentration rather than the curvature ratio. The slope doesnot change as much as in straight tubing when polymer concentration is increased from 15 to 30 lb/Mgal.Comparison with Full-scale Test. In Fig. 10, the data of 20lb/Mgal Xanthan fluid from a previous full-scale study with 1-in. coiled tubing16 are plotted together with the data of 20lb/Mgal Xanthan fluid obtained from the present study. In thefull-scale experimental setup, there were two reels of 1-in. coiled tubing. One reel has 1000 ft and is spooled on a drumof diameter of 72 in. The other reel has 500 ft and is spooledon a drum of 48 in. diameter. The internal diameter of the 1-in. tubing is 0.81 in. Therefore, their curvature ratios are 0.0113and 0.0169 respectively. Fig. 10 indicates that the data of the present work represent the trend of the full-scale experimentaldata very well. The data points of ½-in. CT with a/R = 0.01 are close to the 1-in. CT with a/R = 0.0113 from the full-scale test. Similarly, the data points of ½-in. CT with a/R = 0.019 fallwell in line with the behavior of 1-in CT with a/R = 0.0169.4 SPE89478The significance of this close agreement is that the data obtained from the lab-scale tests can be applied to predict the drag reduction behavior of fluids in field-scale tubings. Besides providing data of coils with a wider range of curvature ratio, cost-saving is also one of the advantages of running the lab-scale tests.Conclusions1. The drag reduction of polymer fluids in coiled tubing canbe reduced by the coiled tubing curvature by as much as10 – 30% as compared with straight tubing.2. The percentage drag reduction of polymer fluids in coiledtubing can be improved by pumping at higher rates, while in straight tubing and within the flow rates tested, the drag reduction is not significantly affected by flow rate. In certain cases, the drag reduction may even decrease slightly as generalized Reynolds number increases.3. The modified drag reduction envelope is proved to be auseful tool for understanding the drag reduction behavior of polymer fluids in coiled tubing. It has been found that the data points of polymer fluids on the Prandtl-Karman coordinates fall more or less on straight lines. The tubing curvature increases the vertical position of the data lines and decreases slightly the slopes of these lines.4. It was also found that the tubing curvature delayed theonset of drag reduction in coiled tubing. This may be because the tubing curvature delayed the onset of turbulence. It may also be due to the secondary flow caused by the curved flow geometry.5. Comparison of drag reduction results of the present studyand a previous full-scale experimental investigation indicates that the data of the lab-scale experiments are representative of the drag reduction behavior observed in the full-scale tests. The new data of polymer fluids obtained from coils with wider range of curvature ratio will be useful for developing improved drag reduction correlations for flow in coiled tubing.Nomenclaturea = radius of coiled tubing, incha/R = curvature ratioCT = coiled tubingd = pipe diameter, inchDR = drag reduction (= 1 - f p/f s )HPG = hydroxypropyl guarf = Fanning friction factorK p = consistency index, lb f s n/ft2L = pipe length, ftn = flow behavior indexN Re = Reynolds number (=ρdV/µ)N Reg = generalized Reynolds number (=d n V2-nρ/K p8n-1)N Res = solvent Reynolds number (=ρdV/µs)p = pressure, psi∆p = pressure drop, psiR = radius of coiled tubing reel, inchST = straight tubingV = mean velocity, ft/sµ = fluid viscosity, cPµs = solvent viscosity, cPρ = fluid density, lb m/ft3τw = wall shear stressSubscriptsp = polymer solutions = solventw = wallAcknowledgmentsThe authors would like to acknowledge gratefully the research team, especially Joe Flenniken and Milt Bishop, of the Well Construction Technology Center for their help with the experiments. We also wish to thank the members of the Coiled Tubing Consortium for their continued support of the Coiled Tubing Consortium.References1. Toms, B.A.: “Some Observations on the Flow of Linear PolymerSolutions through Straight Tubes at large Reynolds Numbers,”Proc., First Intl. Congress on Rheology, North Holland, Amsterdam (1948).2. Lumley, J.L.: “Drag Reduction by Additives,” Annual Review ofFluid Mechanics, Vol. 1, Annual Reviews Inc., Palo Alto, Calif. (1969).3. Hoyt, J.W.: “The Effect of Additives on Fluid Friction,” ASMEJournal of Basic Engineering (1972) 94, No. 2, 258.4. Hoyt, J.W.: “Drag Reduction by Polymers and Surfactants,”Viscous Drag Reduction in Boundary Layers, D.M. Bushnell and J.N. Hefner (eds.), American Inst. of Aeronautics and Astronautics, Washington, DC (1990).5. Virk, P. S.: “Drag Reduction Fundamentals,” AIChE J. (1975) 21,No. 4, 189.6. Berman, N.S.: “Drag Reduction by Polymers,” Annual Review ofFluid Mechanics (1978) 10, 47 – 64.7. Dean, W.R.: “Note on The Motion of Fluid in a Curved Pipe,”Philosophical Magazine (1927) 20, No. 20, 208.8. Dean, W.R.: “The Streamline Motion of Fluid in a Curved Pipe,”Philosophical Magazine (191928) 5, No. 30, 673.9. Zhou, Y. and Shah, S.N.: “Fluid Flow in Coiled Tubing: ACritical Review and Experimental Investigation,” paper 2002-225 presented at the Canadian International Petroleum Conference 2002, Calgary, Alberta, Canada, June 11-13, 2002.10. Mashelkar, R. A. and Devarajan, G. V.: “Secondary Flows ofNon-Newtonian Fluids: Part I – Laminar Boundary Layer Flow ofa Generalized Non-Newtonian Fluid in a Coiled Tube,” Trans.Instn. of Chemical Engineers (1976) 54, No. 2, 100.11. Mashelkar, R. A. and Devarajan, G. V.: “Secondary Flows ofNon-Newtonian Fluids: Part II Frictional Losses in Laminar Flow of Purely Viscous and Viscoelastic Fluids through Coiled Tubes,”Trans. Instn. of Chemical Engineers (1976) 54, No. 2, 108.12. Mashelkar, R. A. and Devarajan, G. V.: “Secondary Flows ofNon-Newtonian Fluids: Part III – Turbulent Flow of Viscoinelastic Fluids in Coiled Tubes: A Theoretical Analysis and Experimental Verification,” Trans. Instn. of Chemical Engineers (1977) 55, No. 1, 29.13. Mishra, P. and Gupta, S.N.: “Momentum Transfer in CurvedPipes. I. Newtonian Fluids, II. Non-Newtonian,” Ind. Eng. Chem.Process Des. Dev. (1979) 18, No. 1, 130.14. Azouz, I., Shah, S.N., Vinod, P.S., and Lord, D.L.: “ExperimentalInvestigation of Frictional Pressure Losses in Coiled Tubing,”SPE PF (May 1998), 91.15. McCann, R. C. and Islas, C. G.: “Frictional Pressure Loss duringTurbulent Flow in Coiled Tubing,” paper SPE 36345 presented atSPE 89478 5the SPE/ICoTA North American Coiled Tubing Roundtable held in Montgomery, TX, 26-28 Feb. 1996. 16. Shah, S.N. and Zhou, Y.: “An Experimental Study of Drag Reduction of Polymer Solutions in Coiled Tubing,” SPE Production & Facilities (November 2003), No. 4, 280. 17. Drew, T.B., Koo, E.C., and McAdams, W.H.: “The Friction Factors for Clean Round Pipes,” Trans AIChE (1932) 28, 56.18. Ito, H.: “Friction Factors for Turbulent Flow in Curved Pipes,” J. Basic Eng. (June 1959) 81, No. 2, 123.19. Srinivasan, P. S., Nandapurkar, S.S., and Holland, F.A.: “Friction Factors for Coils,” Trans. Instn. Chem. Engr., (1970) 48, Nos. 4-6, T156-T161.SI Metric Conversion Factor in. × 2.54* E-01 =cmft × 3.048*E-01 = m °F (°F-32)/1.8 =°C gal × 3.785412 E-03 = m 3 cP × 1.0* E-03 = Pa·s lb f × 4.448222 E+00 = N lb m × 4.535924 E-01 =kg Mgal × 3.785412 E+00 = m 3 psi × 6.894757 E+00 = kPa*Conversion factor is exact.6 SPE89478Table 1 Dimensions of CoilsTable 2 Polymer Concentrations of Fluids TestedFig. 1 Schematic of Flow LoopSPE 894787Fig. 2 Photograph of the Four Coils0.0010.010.11000100001000001000000Reynolds Number, N ReFanningFrictionFactor,fFig. 3 Friction Factor of Water8 SPE 89478100010000100000Generalized Reynolds Number, N RegFig. 4 Plot of Friction Factor vs. Generalized Reynolds Number for 15 lb/Mgal Xanthan Fluid01020304050607080100010000100000Generalized Reynolds Number, N RegD r a g R e d u c t i o n , %Fig. 5 Percentage Drag Reduction of 15 lb/Mgal Xanthan in Straight Tubing and CoilsSPE 89478 951015202530354010100100010000100000N Res f 1/2f(-1/2)Fig. 6 Drag Reduction of 20 lb/Mgal HPG Fluid in Prandtl-Karman Coordinates0102030405060708090100010000100000Generalized Reynolds Number, N RegD r a g R e d u ct i o n , %Fig. 7 Effect of Xanthan Polymer Concentration on Percentage Drag Reduction in Straight Tubing10 SPE 8947801020304050607080100010000100000Generalized Reynolds Number, N RegD r a g R e d u c t i o n , %Fig. 8 Effect of Xanthan Polymer Concentration on Percentage Drag Reduction in Coiled Tubing (a/R = 0.01)51015202530354010100100010000100000N Res f1/2f (-1/2)Fig. 9 Effects of Curvature Ratio and Polymer Concentration on Drag ReductionSPE 89478 111020304050607080901000100001000001000000Generalized Reynolds Number, N RegD r a g R e d u c t i o n , %Fig. 10 Comparison of Drag Reduction Data of 20 lb/Mgal Xanthan Fluid from Full-scale and Lab-scale Tests。