Ind. Eng. Chem. Prod. Res. Dev., Vol. 18, No. 1, 1979
47
The Concentration and Friction Velocity Effects on Drag Reduction by Dowell-APE in Kerosene Nicholas D. Sylvester” and Pamela Sue Smith Resources Engineering Division, University of Tulsa, Tulsa, Olkahoma 74 104
The effects of friction velocity and concentration on t h e drag reducing abilities of Dowell-APE in kerosene were studied under turbulent flow conditions in a recycle loop experimental apparatus. The additive concentration was varied from 50 to 400 wppm and the friction velocity from 0.10 to 0.64 ft/s. For concentrations of 100 wppm and above, a maximum drag reduction of 70-75% was found to occur at a friction velocity between 0.30 and 0.40 ft/s. The data obtained using kerosene compared favorabiy with those obtained previously using hexane although the respective Reynolds numbers and viscosities differed by factors of 10. Scale-up calculations were made predicting significant drag reduction in a commercial size pipeline; however, the possibility of an important pipe diameter effect suggests the need for additional experimental study before the scale-up predictions can be used with confidence.
Introduction Drag reduction is defined as a phenomenon whereby the pressure drop of a solvent flowing through a pipe is reduced by the addition of a small amount of another material-that is, the drag reducer. Drag reduction has been produced by polymers, soaps, and solid suspensions; however, most work has been conducted using high molecular weight polymeric materials. Virk (1975) has presented a comprehensive review of the fundamentals of polymeric drag reduction. There is much less data available in the literature on nonpolymeric drag reducers. A review by Hershey e t al. (1975) gives a summary of data for soaps in aqueous solutions. They found that above a certain shear stress, drag reduction disappeared; however, when these solutions were allowed to stand, the drag reducing ability returned. Radin et al. (1969) investigated aluminum dioleate and dipalmate in toluene and found that the aging process was irreversible. This contrasts with the findings of Savins (1961) for aqueous soap solutions and marks one of the principal differences between the behavior of soaps in aqueous and nonaqueous solutions. Radin et al. (1969) also found that larger soap concentrations were required for toluene than for water in order to produce drag reduction. Other studies show that many factors affect the performance of nonpolymeric drag reducers (see, for example, Patterson et al., 1969; Baker et al., 1970; McMillan et al., 1971; Lee and Zakin, 1973; Hershey et al., 1975). Dowell-APE is the aluminum salt of an alkyl phosphate ester (Crawford et al., 1973). It was shown to be an effective drag reducer by Paz y Mino (1976) when used in hexane. It demonstrated an unusual stability when subjected to continuous shear. The purpose of this study was to further investigate the drag reducing properties of Dowell-APE in a commercial solvent (kerosene) over a range of concentrations and friction velocities. The variables studied were (1) concentration, 50-400 wppm; (2) friction velocity, 0.10-0.64 ft/s; (3) tube diameter: 0.220, 0.495, and 0.747 in. Experimental Section The experimental studies were carried out in a recycle loop apparatus. The experimental equipment and procedures have been described in detail by Smith (1977). The Dowell-APE drag reducer was provided by the manufacturer in a 10000 wppm kerosene gel. Kerosene was chosen because of its similarity to many hydrocarbon liquids, its commercial availability, and its high flash point. 0019-7890/79/1218-0047$01 .OO/O
Dowell-APE is the aluminum salt of an alkyl phosphate ester (Crawford et al., 1973)
where m = 1 to 3, n = 0 to 2, R and R are C1 to Cz0alkyls or C2 to Cz0 alkynyls. A gel, such as the stock solution, is prepared by adding an aliphatic orthophosphate ester and an aluminum compound simultaneously to h nonpolar solvent. The mixture must be agitated until a gel is formed. The aluminum activator can be sodium aluminate (38% in aqueous solution), aluminum isopropoxide, or hydrated alumina. Smith (1973) used sodium aluminate to activate a phosphate ester system used for hydraulic fracturing.
Results and Discussion Figure 1 presents a plot of Fanning friction factor vs. solvent Reynolds number for the concentrations studied in the 0.495-in. tube. Although some drag reduction is seen for the 50 and 75 wppm Dowell-APE concentrations, it was in all cases considerably less than that seen for 100 wppm. As the tube size increased, decreasing the shear stress on the fluid, more drag reduction was obtained a t the low concentrations. It can be seen that for concentrations of 100 wppm and above, Virk’s (1975) maximum drag reduction asymptote is equaled or exceeded. However, as the Reynolds number and thus the shear stress increased, the curve for 100 wppm increased sharply toward higher friction factors. Similar behavior was observed for the other tube sizes (Smith, 1977). The “cross-over”, seen in Figure 1 for the 100 wppm solution, occurred a t higher Reynolds numbers with increasing tube size due to the lower shear stress in the larger tubes for a given Reynolds number. This “cross-over” effect has been reported by Savins (1969), who found that it represented the critical shear stress beyond which drag reduction ceased. It is likely that the “cross-over’’ represents the onset of shear induced degradation. Figure 2 is a plot of the Fanning friction factor vs. Reynolds number data for the 50 and 300 wppm concentrations for all three tube sizes. The 50 wppm data fall in a linear group nearly independect of pipe diameter; however, for 300 wppm a distinct diameter effect is seen. Larger drag reduction is obtained in the smaller tube for 62 1979 American Chemical Society
48
Ind. Eng. Chem. Prod. Res. Dev., Vol. 18, No. 1, 1979
n
I
I
I
I
I I I I I
PIPE DIAMETER 0 4 9 5 IN
>c/!/-
CONCENTRATION APE, wppm
FRICTION VELOCITY = 0 4 KEROCENE
+
0 300
0 400
-
SOLVENT REYNOLDS NUMBER
1 6 2 C CONCENTRATION
1001
A 0747
I
I
C \20 'ONCEN: PIPE OIAMETER,IN :~;02 L
0 0220 0
A
c-
0495
0 (I
0495
I
I
I l l l l
I I
I
I
I
I
I I 1 1 1 1
1, 1' 1 I
I
,
I I
0747
002
004 007 01 02 FRICTION VELOCITY, Vf , ( f t / s e c )
loo
200
300
400
500
APE CONCENTRATION (wppm)
Figure 1. Fanning friction factor vs. solvent Reynolds number for various APE concentrations in kerosene (tube i.d. = 0.495 in.).
APE,wPpm
0
04
07
I
Figure 3. Percent drag reduction vs. friction velocity for various tube sizes (Dowell-APE concentration = 200 wppm in kerosene).
a given Reynolds number. This type of behavior has also been observed by McMillan et al. (1971). Since drag reduction is dependent upon mean velocity and pipe diameter and not directly related to Reynolds number, Patterson et al. (1969) suggest that data can be more effectively analyzed in terms of the friction velocity: uf = ~ ( f / 2 ) ' / ~Figure , 3 shows the percent drag reduction vs. friction velocity data for the 200 wppm solution in all three tube sizes. The dashed line represents data of Paz y Mino (1976) for 200 wppm Dowell-APE in hexane. A pronounced diameter effect is clearly evident. Similar results were obtained at the other concentrations, and the severity of the diameter effect increased with increasing concentration. For concentrations of 100 wppm and above, a maximum drag reduction of 70-7570 was found. The maxima occurred at a friction velocity between 0.3 and 0.4 ft/s. Figure 4 shows the drag reduction vs. concentration data for a friction velocity of 0.4 ft/s. The percent drag reduction increases rapidly with concentrations up to 100 wppm, then levels off. Also shown are Paz y Mino's (1976)
Figure 4. Drag reduction vs. concentration for kerosene-Dowell-APE and hexane-Dowell-APE formulations ( u f = 0.4 ft/s).
APE-hexane data which are similar to the APE-kerosene data. Substantial drag reduction was only found for concentrations of 100 wppm or larger in which the solutions tended to exhibit a filament forming tendency. Gordon et al. (1973) have correlated this tendency with drag reducing ability. Scale-up Considerations. Dowell-APE has been shown to produce sighificant amounts of drag reduction in both hexane and kerosene, two hydrocarbons, with very different properties. If this level of drag reduction could be achieved in an industrial application, the energy used to pump fluids through pipelines could be reduced. For this reason it is desirable to predict the level of drag reduction that could be achieved in a pipeline from laboratory data. Patterson et al. (1969) stated that the flow velocity in a commercial pipeline must be at least as high as that in a laboratory tube to expect the same level of drag reduction. This observation was confirmed by Crowley and Witbeck (1970). An average flow velocity for a 12-in. pipeline is 6 ft/s and for a 6-in. line, 10 ft/s. If the hydrocarbon carrying pipeline is assumed to have singlephase flow, the properties of the fluid can be specified. For the purposes of the following scale-up calculations, a low density fluid with the properties of pentane and a viscous hydrocarbon were assumed. To make the calculations, the following procedure was used: (1)Calculate the Reynolds number using the velocity, pipe diameter, and fluid properties. (2) Determine the friction factor for the pure liquid. (3) Calculate the friction velocity. (4) Determine the percent drag reduction from that data for the concentration desired. The roughness value for cast iron pipe was used to obtain the pure liquid friction factors. It should be noted that the friction velocity depends much more on the average velocity than on the friction factor. The results, shown in Table I, indicate that pipeline friction velocities vary from 0.30 to 0.60 ft/s, which is well within the range studied. The most imprecise aspect of the scale-up prediction occurs in step 4, where the contribution of the diameter effect must be accessed. In the most extreme case (400 wppm), the drag reduction at uf = 0.25 could be read as anything between 25% and 65%. It is encouraging to note, however, that the decreasing portion of the curves (see Figure 3) shifts to the left as the diameter increases. For commercial pipeline diameters this portion should be well to the left of the friction velocities of interest. The downward trend of the drag reduction curves seen a t higher friction velocities begins a t about the same value of friction velocity for each concentration. This indicates that for much larger diameter pipes, the drag reduction curve does not "peak out" at low friction velocities.
Ind. Eng. Chem. Prod. Res. Dev.,Vol. 18, No. 1, 1979
Table I. Data and Results for Scale-uD Calculations (1) pipe diameter, in.
(2)
velocity, ft/s
6.0 6.0
10.0 10.0
6.0
6.0
12.0 12.0
6.0 6.0
12.0
10.0
(3)
fluid pentane hydrocarbon hydrocarbon Dentane hydrocarbon pentane
friction factor (cast iron pipe)
(8) friction velocity, ft/s
0.0058 0.0060 0.0066 0.0048 0.0053 0.0048
0.54 0.55 0.35 0.29 0.31 0.49
(7)
(4)
(5)
0.626 1.000
0.2 5.0
1 5 0 0I000 93 000
1.000
5.0
55 700
0.626 1.000
0.2 5.0
1750000 111 500
0.626
0.2
2900000
den- viscos(6) sity, ity, Reynolds no. g/cm3 CP
(9) (10) prepredicted dicted drag drag reducreduction, %a tion, %b 55.0 52.0 65.0 63.0 63.0 58.0
62.0 59.0 68.0 70.0 70.0 63.0
(11)
av drag reduction, %' 58.5 55.5 66.5 66.5 66.5 60.5
(14) predicted velocity, ft/s
predicted friction velocity, ft/s
velocity increase, %
15.5 15.0 10.4 10.4 10.4 15.9
0.54 0.55 0.35 0.29 0.31 0.49
55.0 50.0 73.0 73.0 73.0 59.0
(12)
(13)
predicted friction factor 0.0024 0.0027 0.0022 0.0016 0.0018 0.0019
(15)
F o r 200 a F o r 200 wppm APE-kerosene formulation. wppm APE-hexane formulation. ' Average of columns 9 and 10.
Since friction factors, Reynolds numbers, and friction velocities can be determined for commercial pipelines, drag reduction levels can be predicted. The percent drag reduction expected for 200 wppm can be obtained from Figure 3 for the friction velocities calculated in step 3. Table I shows the level of drag reduction predicted by this study to be from 52 t o 63%. From the hexane curve a prediction of 59 to 70% drag reduction is found. The hexane values are also shown in Table I. Crowley and Witbeck (1970) showed that when a drag reducer was introduced into a pipeline, the pressure drop remained about the same, but the flow velocity increased considerably. In a rough pipe the percent drag reduction (D.R.) can be defined as 70 D.R. =
fsolvent -
f
x 100
fsolvent
By using this definition and the average values for percent drag reduction given in column 11 of Table I, the friction factor for the drag reducing solution (column 12) was calculated. Then by using the definition of friction factor, it can be shown that where u2 is the new velocity and f2 is the new friction factor. Table I shows the new velocities in column 13. It can be seen that in the 6-in. pipe the two different fluids have about the same drag reduction at 10 ft/s. When the velocity decreases to 6 ft/s, the percent drag
49
reduction increases for the hydrocarbon fluid. This is attributed to the fact that the maximum drag reduction is obtained at a friction velocity of about 0.30 ft/s. The friction velocity of 0.54 ft/s is on the decreasing side of the drag reduction vs. friction velocity curve (Figure 3). Thus, when the flow velocity decreased to 6 ft/s, the friction velocity decreased to 0.35 ft/s, giving a higher value of drag reduction. Likewise in the 12-in. pipe the same amount of drag reduction was obtained for both fluids a t 6 ft/s. When the flow velocity in the case of the pentane was increased from 6 to 10 ft/s, however, the drag reduction decreased. This occurs because the increase in velocity increased the friction velocity to 0.49 ft/s where lower drag reduction is obtained. When the flow velocity is held constant and the pipe diameter is changed, little effect is seen on the drag reduction predicted. This is because the friction velocity is principally dependent on the flow velocity. The predicted flow velocities (column 13) increased between 50 and 70% with increasing drag reduction. Although the predicted velocity increased significantly, the predicted friction velocities were almost identical with the values found for the nondrag reducing solutions (columns 8 and 14). This gives confidence that the addition of the drag reducer would not significantly change the friction velocity and thus complicate drag reducing predictions based on the drag reduction vs. friction velocity curves. It has been shown that significant drag reduction can be achieved by adding Dowell-APE to hydrocarbon fluids. Previous work (Paz y Mino, 1976) which showed low shear degradation rates coupled with high drag reducing ability for Dowell-APE was also confirmed (Smith, 1977). More experimental data are needed, however, to evaluate the behavior of Dowell-APE hydrocarbon formulations in commercial-size pipe. The Dowell-APE drag reduction additive shows promise of commercial applicability and thus certainly warrants further testing. Acknowledgment The authors would like to thank the Shell Foundation for financial support for P. S. Smith and the Dowel1 Division of Dow Chemical Company for donating materials and providing technical assistance. Nomenclature f = friction factor u = flow velocity, ft/s u f = friction velocity, ftjs Literature Cited Baker, H. R., Bolster, R. N., Leach, P. N., Little, P. C., Ind. f n g . Chem. Prod. Res. Dev., 9, 541 (1970). Crawford, D. L., Earl, R. B., Monroe, R. F., U S . Patent 3757864 (Sept. 11, 1973). Crowley. G. K., Witbeck, N. C., U S . Army Mobility Equipment Research and Development Center, Columbia Research Corp., Oct. 1970. Gordon, R. J., Balakrishnan, C., Pahwa, S., Chem. fng. Prog. Symp. Ser., No. 130, 69, 33 (1973). Hershey, H. C., Kuo, J. T., McMillan, M. L., Ind. Eng. Chem. Prod. Res. Dev., 14, 3 (1975). Lee, K . E., Zakin, J. L., Chem. fng. P r q . Symp. Ser., No. 130, 69, 45 (1973). McMillan, M. L.. Hershey, C. H., Baxter, R. A,. Chem. f n g . Prog. Symp. Ser., No. 7 1 1 , 67, 27 (1971). Patterson, G. K., Zakin, J. L., Rodrigues, J. M., Id. f n g . Chem., 61, 22 (1969). Paz y Mino, H. A,, M.S. Thesis in Chemical Engineering, University of Tulsa, 1976. Radin, I., Zakin, J. L.,, Patterson, G. K., in "Viscous Drag Reduction", C. S. Wells, Ed., Plenum Press, New York, N.Y., 1969. Savins, J. G., J . Inst. Pet., 47, 329 (1961). Savins, J. G., in "Viscous Drag Reduction", C. S. Wells, Ed., Plenum Press, New York, N.Y., 1969. Smith, C. F., SPE Preprint No. 4678, presented at 48th Annual Fall Meeting, Las Vegas, Nev., 1973. Smith, P. S.,M.S. Thesis in Petroleum Engineering, University of Tulsa, 1977. Virk, P. S.. AlChf J . , 21, 625 (1975).
Received for review February 27, 1978 Accepted September 11, 1978
