REDUCTION OF FRICTION IN OIL PIPELINES BY POLYMER ADDITIVES A R l E RAM,’ E H U D FINKELSTEIN,* AND C H A l M ELATAS
Technion-Israel
Institute of Technology, Haifa, Israel
The capacity of oil pipelines may be increased by minute quantities of soluble polymers. The effect of the addition of polyisobutylene to crude oil and kerosine has been explored in an experimental circulation system. In turbulent flow the friction coefficient is markedly reduced. A critical Reynolds number, Re,, exists, the value of which decreases for smaller pipe diameters, higher molecular weights, and more viscous solvents. Chain elasticity is represented by a calculated relaxation time. The onset of drag reduction is characterized by a critical wall shear rate whose reciprocal should be approximately equal to the chain relaxation time. By using this criterion, some relationships were proved. The calculated values of relaxation times were found to be too large. The differences are due to the effects of shear and degradation, as well as the choice of a proper mean molecular weight. The polymers exhibited critical velocities at the range of 8.5 to 14.2 feet per second. Degradation of the long flexible polymeric chain in turbulent flow remains the bottleneck of drag reduction.
minute quantities of soluble polymers to a liquid in turbulent flow, a remarkable reduction in friction can be obtained. Utilizing this phenomenon, the possibility of increasing the capacity of oil pipelines was investigated. Recently, several articles have discussed experimental as well as theoretical analysis of the effect on pipe flow of polymer additives a t concentrations of 10 to 500 p.p.m. (2,4,5, 7, 77,20,27). Most of the experimental work was conducted in aqueous solutions. The elasticity of the polymer chain is usually believed to control the drag reduction phenomenon. Elata, Lehrer, and Kahanovitz (4) have shown that on adding polymers, the relative thickness of the laminar sublayer in a pipe increases, increasing the average velocity without changing the shape of the turbulent velocity profile in the core of the pipe. Viscoelasticity of polymer melts and solutions, which shows up in the Weissenberg effect (22), may be associated with direct measurements of normal stress differences ( 7 , 8 ) . Similar viscoelastic information may be derived from studies on the swelling of jets (3, 6, 9, 70, 78) and the entrance effects in capillary flow ( 7 7 ) . While Metzner and Park ( 9 ) point out the great experimental difficulties in estimating normal stress data for extremely dilute polymer solutions (which happens to be the range of drag reduction), Oliver (70) has recently succeeded in using the jet thrust experiments to detect normal stress differences in very dilute polymer solutions. I t is nevertheless surprising to note that Oliver (70) verified Reiner’s (74) previous findings that simple Newtonian fluids also show normal stress differences. According to Reiner (75), any fluid will exhibit elastic as well as viscous properties, provided the time scale of the experiment is shorter than the relaxation time of the fluid. For a quantitative analysis of friction reduction, criteria have been suggested which are based on molecular theory. The Y ADDING
Present address, Polymer Science and Engineering, Case Institute of Technology, Cleveland, Ohio. a Present address, Department of Chemical Engineering, Princeton University, Princeton, N. J. Present address, Hydronautics, Inc., Laurel, Md.
polymer chain dimensions are represented by the statistical radius of gyration. The viscoelastic character is related to equivalent relaxation times. Typical relaxation times for dilute polymer solutions may be calculated by using the theoretical derivations of Rouse (76) or Zimm (23). I t has been found (4, 20) that the product of the maximum relaxation time and the shear rate at the wall may serve as a criterion for the onset of friction reduction. The choice of the proper polymer for practical use depends on economic considerations. The added polymer should be stable during the time the fluid is passing through the pipe; its concentration should be below the regulated limit of contamination. I n the case of crude oil, addition of polymers is permissible. The tolerance for refined oils, like kerosine o r gasoline, is very low, however. The results of this work point to some valuable correlations between flow and polymer characteristics. The degradation of the long polymer chains in turbulent flow is still a limiting factor. Experimental Work
The solvents used in the experiments were crude petroleum oil (Iranian) and refined kerosine. The added polymers were commercial polyisobutylenes (PIB), provided by Badische Anilin & Soda Fabrik. Oppanol B-100 (Molecular weight 1.4 X 106) Oppanol B-150 (Molecular weight 2.5 X lo6) Oppanol B-200 (Molecular weight 5.0 X 106)
ivo,
The molecular weights, of these polymers were found from intrinsic viscosity measurements of solutions in cyclohexane. Viscosities of the polymer solutions were measured by a rotational viscometer (Epprecht Rheomat 15) and the intrinsic viscosities calculated from the measured viscosities in low shear capillaries (Ubbelohde) . The experiments were conducted in a circulation system as shown in Figure 1. The fluid is pumped by an internal gear pump into the test section in which the pressure drop is measured at four stations. Four different pipe test sections (smooth brass tubes) were used, with internal diameters of 3.15, 5.8, 10.2, and 13.7 mm. The length-diameter ratios were about 100. VOL. 6
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'
I
( T OIRCIRCULATION REL:iINE TAN1
8 4
5
/
/ /
/
FROM PIPE/' LWMLIRIL + PI ET-"""TAP TO MANOMETER
'
CIRCULAR TANK STRAINER 3. CIRCULAR PUMP 4. HIGH FLOW- RATE ROTAMETER 5. LOW FLOW -RATE ROTAMETER, 6. TEST SECTION 7. MANOMETER 8. AIR RELIEF BOX IO. VALVES I I. AIR RELIEF VALVE 12. ORIFICE PLATE 13. ORIFICE PLATE MANOMETER 14. FLOW RATE REGULATOR 15. BY-PASS 16. TANK CUT-OFF VALVE IZ SYSTEM BLOW-DOWN VALVE I. 2.
-
F ' I Z Z I Figure 1.
Experimental system for friction reduction
Additional measurements were made with a high shear capillary viscometer, described by Ram and Tamir (73). With this instrument end-correction effects were observed in the dilute polymer solutions at laminar flow, while friction reduction was measured in the turbulent flow regime. The experimental results are shown in Figures 2 to 8. I n Figure 2 the friction reduction effect in capillaries is shown. No friction reduction in the laminar region was observed. I n Figure 3 typical results are presented for solutions of the various polymers in the circulation system. The arrows indicate the sequence of the measurements. Degradation is obviously existing. Figures 4, 5, and 6 describe typical curves of Fanning friction coefficients, f, us. Reynolds number, Re, for the three polymers in kerosine and crude oil. The marked effect of pipe diameter is seen in Figure 7. Figure 8 presents some of the data in a I / - R e $diagram.
t 60 50
40
30
20 10 -D
0.5
Figure 2.
Friction reduction in capillary flow
Discussion
A* = a(
98(9
- 7s) M
(1)
(q,C)0.586 atRT
are the eigenvalues: a1
= 4 . 0 4 ; a2 = 1 2 . 7 9 ; as = 24.2,
etc.
The expression (q - qs)/q,C may be replaced by the intrinsic viscosity, [q], at small polymer concentrations. [ q ] is usually related to the molecular weight, M , by an expression of the form: [q] = 310
-
Polymer
The existence of a critical Reynolds number, Re,, a t the onset of friction reduction is apparent from the experiments. Re, decreases when molecular weights increase and pipe diameters decrease. The relaxation times for dilute polymer solutions are, according to Zimm (23),
KMa
(2)
I L E C PROCESS DESIGN A N D DEVELOPMENT
2.0
Capillary length. 224 mm. Capillary diameter. 0.57 mrn. Solvent. Kerosine
q7
where
I.o 1.5 FLOW RATE (gr/sec)
0
V
0
B-1 00 8-1 00 8-1 00
8
8-200
A
Concentration, P.P.M.
6
10 18-110 16
I n the case of PIB in kerosine the constants were found by Siegman (79) to be K = 8.13 X lO-*and a = 0.6, when [ T ] is measured in 100 cc. per gram. When the maximum relaxation time, XI, is larger than the inverse wall shear rate, Tu, the small turbulent eddies are damped by the polymer chains. The threshold value of friction reduction should thus be determined by, say, Xl-j,
E1
The friction coefficient,f,is defined by:
f
= 2r,/pu2
(3)
-
300
/
t
/
200 0,260
220
w 140
2
60 2o
2 350 Ix) 200250 300
400
500
450
0.00II
lo3
FLOW RATE, (cm?sec)
Figure 3. Flow rate vs. pressure drop for solutions of polyisobutylene in crude oil
Figure 5. reduction
I
I
I
I
2
3
4
5 6 789104 2 RE REYNOLDS NUMBER
0
V
0.001I IO3
Figure 4. reduction
I
2
I
I
I
Polymer
8-100 B-150 B-150 B-200
200 200 635 220
I I I l l
1
I
l
l
0
Polymer 8-100
A
B-150 8-200
V
I
I
O0.001IO3
L
2 '
3
4
3 4 5 67 RE REYNOLDS NUMBER
I-
5
Concentration, P.P.M
Pipe Diameter, Mm.
200 200 220
10.2 10.2 10.2
5 6 789104 O
2 a
3
4 5 6 7a
RE REYNOLDS NUMBER
Influence of polymer molecular weight on friction
Polymer
Concentration, P.P.M.
B-100 B-150 B-200
155 150 380
Pipe Diameter, Mm.
Figure 6.
1 2 3 4
5.8 5.8
5.8
Influence of solvent viscosity on friction reduction
Polymer
Concentration, P.P.M.
B-200 B-1 00 B-200 B-1 00
220 200 250 160
Solvent Crude oil Crude oil Kerosine Kerosine
Viscosity, c.p.
Pipe Diameter, Mm.
5.3 5.3 1.25 1.25
10.2 10.2 10.2 10.2
dx
The critical friction coefficient becomes:
Therefore
(5) and
,-
Re,
I
4
2
Polyisobutylene in kerosine
1 2 3
I
3
Polyisobutylene in crude oil Concentration, P.P.M.
3 4 5 6 t89lO4
I
Influence of polymer molecular weight on friction
Pipe diameter. 1.02 mm. Length. 900 mm.
A
I l l l l
c,D .@ =
Re is proportional to the pipe diameter, D. This diameter effect is clearly shown in Table I. The two solvents, though similar in character, had different viscosities, so that for the same added polymers and pipe diameters (RedT)lj), a (l/v). As the values of f are similar in both cases, Equation 6 shows that the values of Re, for the crude oil are smaller than for kerosine. This is proved by the experiments presented in Figures 4, 5 , and 6, which also indicate the effect of different molecular weights. By substituting Equations l and 2 in Equation 6, one obtains (Re~)caM-(a+')/2 for the same solvent and pipe diameter, or,
AlV
(7)
Equation G predicts that the critical value of the product, VOL. 6
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311
Table 1. cown., P. P.M.
Polymer
B-200
B-100 B-150 B-200
e
2t I
0.001 IO3
Figure 7.
V A 0
fo
13.7 10.2 5.8 3.15 13.7 5.8 3.15 13.7 10.2 5.8 3.15
23,000 17,000 10,000 5,000 30,000 12,700 7,000 >35,000 35,000 18,500 8;OOO
0.0064 0.0068 0.0078 0.0092 0.0060 0.0073 0.0085 -0.0058 0.0058 0.0067 0.0082
264
262
271
249
184 140.5 88.1 48 23.2 108.5 64.5 >266 266 151.5 725
5 x 108
261
3.84 2.93 1.84 1 3.6 1.69 1 >3.67 3.67 2.09 1
4.35 3.22 1.84 1 4.35 1.84 1 4.35 3.22 1.84
1 0.77 0.6
1 0.63 0.56
I
14
I
I
2
3 4 5 678910
1
I I IIII
I
2 RE,REYNOLDS NUMBER
I
I I I l l >
II
3 4 5 6 7 8 9
Influence of pipe diameter on friction reduction 8-1 5 0 in kerosine Concentration, Polymer P.P.M. 200 B-150 225 8-150 150 8-1 50 150 B-150
Pipe Diameter, Mm. 13.7 10.2 5.8 3.15
I t may thus be concluded that there exists a critical velocity which depends on the polymer molecular weight and intrinsic viscosity. The appropriate critical velocities calculated for the three PIB samples in kerosine, for increasing molecular weights, were 14.2,11.0, and 8.5 feet per second, respectively. These critical velocities are usually too high for actual pipelines. Equation 7 is compared with the actual results in Table 11. While these results are satisfactory, discrepancies were found on comparing the calculated values of AI with (Table 111). This may be due to the fact that the values of [ q ]used to calculate AI in Equation 1 were taken from low shear measurements. I n high shear flow as in our pipe experiments, [ q ]may have smaller values, as was shown by Siegman (79) for PIB solutiops in kerosine. The effect of shear on intrinsic viscosity was discussed by R a m (72). A second point is that the PIB samples used in the experiments were whole polymers and not fractions. 312
Relative Diameter
Table 11. Critical Velocities for Onset of Drag Reduction Critical Velocity, W E , Cm/Sec. D = D = D = D = 13.7 10.7 5.8 3.5 "6 mm. mm. mm. mm. Cm./Sec. MV 401 439 500 400 435 1.4 X 106 344 302 344 350 335 2.5 X 106
Polymer
2
Rec
.
190 250 380 285 280 150 150
B-150
Onset of Drag Reduction
Pipe Diameter, Mm
l&EC PROCESS DESIGN A N D DEVELOPMENT
IO2
2
4 5 6 7 89103
3
RE
Figure 8.
_.-.-.-. -. .-. .-. .
----.,..........
Polymer 8-200 8-1 50 8-200 B-150 8-200 8-1 5 0
4
2
3
4 5 6
JF
vs. RE
Concentration, P.P.M. 220 200 300 150 250 280
.\/7 Solvent Crude oil Crude oil Kerosine Kerosine Kerosine Kerosine
Pipe Diameter, Mm. 10.2 10.2 5.8 5.0 10.2 13.7
The molecular weight used in Table I11 was M , based on the intrinsic viscosity, [q]. This molecular weight is close to Bw,the weight-average molecular weight. The proper average molecular weight characterizing the relaxation time should be (number average) instead of which was used here, so that
n,,
no
A=- Z N A
ZNi
Relationships between Calculated Relaxation limes and Measured Shear Rates Pipe Diameter, +WC, X1, Mm. See. -1 Sec. X 703 Solvent
Table 111. Polymer
B-200
Kerosine
13.7 10.2 5.8 3.5
B-100
Kerosine
13.7 10.2 5.8 3.15 10.2
B-200 B-150 B-100
Crude oil
10.2
10.2
a, is always smaller than w,,and in our case the ratiom,/nn (the spread) may be around 3 to 5. Furthermore, actual molecular weight during the flow experiments may be lower than the original one, because of shear degradation occurring during the flow. I n most severe cases it was found that PIB B-200 may decrease in molecular weight from 5 X 106 to 0.4 x 106 while passing for 15 minutes through the centrifugal pump. Degradation a t the gear pump was much less, however. Conclusions
1. Polyisobutylene is a n effective friction reducer in the turbulent flow of petroleum. 2. A critical Reynolds number exists, below which no friction reduction occurs. This Re, is smaller for smaller pipe diameters, higher molecular weights, and more viscous solvents. 3. By adopting the idea of a critical shear rate .izo,, = l/Xl, where XI is the chain maximum relaxation time, Re, was found to be proportional to pipe diameter D and to the inverse solvent viscosity, T ~ . For each polymer a critical velocity exists below which no friction reduction occurs. 4. The calculated values for X 1 are too high when comPossible reasons for pared with the measured values of l/.i,,,. this discrepancy are : a shear-dependent intrinsic viscosity, and shear degradation. use of lqoinstead of IF,,, Nomenclature a
= eigenvalue in Equation 1 = exponent in Equation 2
D
= pipe diameter
f
=
at
e = concentration
Fanning friction factor
G = shear modulus K = constant in Equation 2 M = molecular weight N = number of moles
R
= gas constant R e = Reynolds number T = absolute temperature u = mean velocity Y = shear rate t = viscosity
14,600 15.500 19;500 19,200 23.000 20; 600 28,500 34,600 29,500 35,000 55,000 43,000 3,300 11,700 14,300
0.069 0.064 0.051 0.052 0.044 0.048 0.035 0,029 0.034 0.028 0.018 0.023 0.03 0.09 0.07
3.9 3.9 3.9 3.9 1.29 1.29 1.29 1.29 0.51 0.51 0.51 0.51 17.4 5.75 2.3
.
A1 +w,c
57 60 76 75 30 26 37 44 15 18
28 22 57 67 33
[ q ] = intrinsic viscosity X = relaxation time v = kinematic viscosity p = density T = shear stress
SUBSCRIPTS G
n s u
m
= = = = =
critical number solvent viscosity wall, weight
literature Cited (1) Adams, N., Lodge, A. S., Proc. Roy. SOG.London A256, 149
(1964). (2) Astarita, G., Znd. Ens. Chem. Fundamentals 4, 354 (1965). (3) Bagley, E. B., Storey, S. H., West, D. C., J. A$$. Polymer Sci. 7, 1661 (1963). (4) Elata, C., Lehrer, J., Kahanovitz, A,, Israel J. Technol. 4, 87 (1966). (5) Fabula, A. G., Lumley, J. L., Taylor, W. D., Syracuse University Rheology Conference, August 1965. (6) Gadd, G. E., Nature 206, 463 (1965). (7) Hershey, H. C., Zakin, J. L., Symposium on Mechanics of Viscoelastic Fluids, 58th Annual Meeting, A.I.Ch.E., Philadelphia, December 1965. (8) Markovitz, H., Trans. SOC.Rheol. 1, 25 (1957). (9) Metzner, A. B., Park, M. G., J . Fluid Mech. 20, 291 (1964). (10) Oliver, D. R., Can. J . Chem. Ens. 44, 100 (1966). (11) Philippoff, W., Gaskins, F. H., Trans. Sod. Rheol. 2,263 (1958). (12). Ram, A,, “High Shear Viscometry,” in “Rheology,” F. R. Eirich, Ed., Vol. IV, New York, Academic Press, 1967. (13) Ram, A., Tamir, A., Znd. Eng. Chem. 56, 4 (1964). (14) Reiner, M., Phys. Fluids 3, 427 (1960). (15) Reiner, M., Physics Today 17, 62 (1964). (16) Rouse, P. E., J . Chern. Phys. 21, 1272 (1953). (17) Savins, J. G., SOG. Petrol. Ens. J . 4, 203 (1964). (18) Shertzer, C. R., Metzner, A. B., Trans. Plastics Znst. London 31, 148 (1963); 32, 217 (1964). (19) Siegman, A,, M. Sc. thesis, Department of Chemical Engineering, Technion, Haifa, Israel, June 1966. (20) Tulin, M. P., private communication, 1966. (21) Virk, P. S., Pine Brook Rheology Conference, August 1965. (22) Weissenberg, K., Nature 159, 310 (1947). (23) Zimm, B. H., J. Chem. Phys. 24, 269 (1956). RECEIVED for review July 18, 1966 ACCEPTED February 10, 1967 Work partly based on the M. Sc. thesis of E. Finkelstein, submitted to the Department of Chemical Engineering, Israel Institute of Technology.
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