Energy & Fuels 2009, 23, 1311–1315
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Time-Dependent Rheology of a Model Waxy Crude Oil with Relevance to Gelled Pipeline Restart† Jules J. Magda,*,‡ Husam El-Gendy,‡ Kyeongseok Oh,‡ Milind D. Deo,‡ Alberto Montesi,§ and Rama Venkatesan§ Department of Chemical Engineering, UniVersity of Utah, Salt Lake City, Utah 84112, and CheVron Energy Technology Company, Houston, Texas 77002 ReceiVed August 1, 2008. ReVised Manuscript ReceiVed September 28, 2008
When ambient temperatures are low, paraffinic crude oils being transported in pipelines may form gels composed of wax crystals. If pipeline flow ceases, these waxy gels may make it difficult to restart the flow without breaking the pipe. To predict the severity of this problem, we consider the rheology of a transparent model waxy crude oil for which pipeline flow visualization results are presented elsewhere. We investigate characteristics of the model oil determined by cone-plate shear flow measurements, such as the viscosity and wax appearance temperature, the gelation temperature, the elastic modulus, and the yielding behavior of the gel. The yielding behavior is a critical determinant of pipeline restart, and the time-dependent yielding behavior observed for this model oil is similar to that reported previously for North Sea crude oils. In particular, at sufficiently low-stress levels, the gel never yields, whereas the gel yields or “fractures” immediately at sufficiently high-stress levels. At intermediate-stress levels, the gel “creeps” with a delay time to fracture that ranges from seconds to hours, depending upon the imposed stress value. Some authors have suggested that waxy gels slowly degrade as they creep and that this gives rise to the very long delay times to fracture that may be observed. However, a creep-response hysteresis test on the model oil studied here shows that the gel elastic modulus does not vary with time during creep, a result which is inconsistent with the degradation mechanism.
Introduction It is generally accepted that a significant discrepancy exists between laboratory rheology measurements on waxy crude oils and pipeline field tests, with rheology measurements overestimating the upstream pressure needed to restart flow in pipelines that have become plugged with gelled oil. The three most widely proposed explanations for this discrepancy are (1) the occurrence of a pipeline pressure profile in which the pressure has a nonlinear dependence on the axial position,1 (2) the presence of voids in the pipeline because of shrinkage during gelation,2 and (3) a difference in the time scale over which the gel is subjected to a given shear stress in the rheometer and in the pipeline.3 Here, we focus on the third hypothesis. Obviously, a difference in time scale cannot explain the discrepancy unless the gel yield stress value depends upon time, and this has already been convincingly demonstrated for waxy crude oils from the North Sea4 and Australia.5,6 Unfortunately, it is difficult to visualize the restart of crude oil flow in gelled pipelines because † Presented at the 9th International Conference on Petroleum Phase Behavior and Fouling. * To whom correspondence should be addressed. Fax: 801-585-9291. E-mail:
[email protected]. ‡ University of Utah. § Chevron Energy Technology Company. (1) Davidson, M. R.; Nguyen, Q. D.; Chang, C.; Ronningsen, H. P. J. Non-Newtonian Fluid Mech. 2004, 123, 269–280. (2) Vinay, G.; Wachs, A.; Agassant, J.-F. J. Non-Newtonian Fluid Mech. 2006, 136, 93–105. (3) Chang, C.; Nguyen, Q. D.; Ronningsen, H. P. J. Non-Newtonian Fluid Mech. 1999, 87, 127–154. (4) Ronningsen, H. P. J. Pet. Sci. Eng. 1992, 7, 177–213. (5) Wardaugh, L. T.; Boger, D. V. J. Rheol. 1991, 35, 1121–1156. (6) Chang, C.; Boger, D. V.; Nguyen, Q. D. Ind. Eng. Chem. Res. 1998, 37, 1551–1559.
the oils are opaque. Therefore, one of our principle objectives in the current work is to show that transparent model waxy crude oils can be formulated that exhibit the same qualitative features of fracture and time-dependent yield already reported for waxy crude oils.4-6 We also estimate the reproducibility of yield stress measurements and compare it to the reproducibility of other model oil properties that can be measured by cone-plate rheometry. One of the most striking features of the timedependent rheology reported for waxy crude oils4 and also observed for our model oil is the phenomenon of “delayed yield”, in which the creeping gel may yield many hours after a constant stress is first imposed on the sample in the rheometer. Note that the delay time to yield can be much longer than the linear viscoelastic relaxation time, which we show below using stress relaxation data is on the order of seconds. The microscopic level changes (if any) that occur in the gel as it creeps over long periods of time and that give rise to such long delay times to yield have never been definitively pinpointed. In their excellent analysis of gelled pipeline restart, Chang et al.3 envision the creeping gel as degrading over time with a timedecreasing static yield stress value. However, if this is true, it presents problems for the validity of laboratory rheology testing, because it implies that at most a single rheological characterization test can be performed on a given gel sample before it degrades. Therefore, we probe the elastic modulus of the gel as it creeps to see if any evidence of degradation effects on this quantity can be detected. Experimental Section A transparent model waxy crude oil was prepared by dissolving 5 wt % wax in Superla mineral oil (specific gravity of 0.85 at 25 °C). Figure 1 shows the carbon number distribution in the added
10.1021/ef800628g CCC: $40.75 2009 American Chemical Society Published on Web 11/17/2008
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Magda et al.
Figure 1. Carbon number distribution in wax used to formulate model oil as measured by high-temperature gas chromatography.
wax as measured by high-temperature gas chromatography (HP 5890). To avoid potential evaporation problems, no volatile components, such as kerosene, were included in the formulation. Rheological measurements were performed using cone-and-plate fixtures (40 mm in diameter and 2° cone angle) on a controlledstress rheometer (AR 550 from TA Instruments, Newcastle, DE). The sample temperature and cooling rate were controlled using the rheometer Peltier plate. A systematic procedure was followed for preheating the sample above the wax disappearance temperature, loading it into the rheometer, cooling it, and performing tests, such as small-amplitude oscillatory shear and creep-recovery measurements. According to the rheology measurements (see below), the model oil has a WAT of 25-26 °C. This value was confirmed by Fourier transform infrared (FTIR) measurements (PerkinElmer Spectrum RX I).7 Therefore, the model oil sample was first heated at 55 °C for at least 30 min to melt all crystallites, loaded into the rheometer at 35 °C, and cooled at a rate that was typically 0.5 °C/ min. This cooling rate was chosen to match the cooling rate present in complementary model pipeline flow visualization experiments on the same model oil.8 It is also similar to the cooling rate employed by Chang et al.6 in their cone-plate rheology study of crude oils, a study to which our results will be compared. Most gel-yielding measurements were performed at 2 °C, which is approximately 20 °C below the gelation temperature according to the rheology gelation test (see below). The sample was aged for at least 30 min at 2 °C before yield tests were started.
Results and Discussion Oil Characterization Using Small-Amplitude Oscillatory Shear. Linear viscoelastic rheology tests are designed to probe material properties using only small and reversible distortions to the sample equilibrium structure.9 In linear viscoelastic shear, an oscillatory shear stress of sufficiently small amplitude and frequency is applied to the sample and the strain response of the sample is used to calculate the elastic shear modulus G′ and the viscous shear modulus G′′ as a function of the temperature. For a viscous liquid, the viscous modulus G′′ exceeds the elastic modulus G′, whereas the reverse is true for an elastic gel.9 Hence, if a waxy oil is cooled at a sufficiently low cooling rate, the gelation temperature can be identified as the temperature below which G′ first becomes greater than or equal to G″. The gelation temperature thus obtained has been shown by Venkatesan and co-workers to approximately equal the pour point.10 Figure 2 shows the results of this rheological gelation test obtained for the model waxy oil using oscillatory (7) Roehner, R. M.; Hanson, F. V. Energy Fuels 2001, 15, 756–763. (8) Deo, M.; Oh, K.; Magda, J.; Guimeraes, K.; Venkatesan, R.; Montesi, A. The 8th International Conference on Petroleum Phase Behavior and Fouling, Pau, France, June 10-14, 2007. (9) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley: New York, 1980.
Figure 2. Rheological detections of oil gelation temperature. The waxy model oil was cooled at 0.1 °C/min during oscillatory shear testing. The gel point is identified as the temperature below which the elastic modulus exceeds the viscous modulus (≈21-22 °C).
shear parameters similar to those shown to be appropriate by Venkatesan et al.:10 stress oscillation amplitude, 0.3 Pa; oscillation frequency, 0.126 rad/s; cooling rate, 0.1 °C/min. In this gelation test, we chose a lower cooling rate than in other rheology experiments, so that comparison to Venkatesan et al.10 could be made. In Figure 2, the value of G′ becomes as large as G′′ when the temperature of the cooled sample reaches 21-22 °C, which we therefore indentify as the gelation temperature of the mineral oil containing 5 wt % added wax. When the same experiment is repeated on the mineral oil without added wax, G′′ lies above G′ over the entire temperature range. The value of the dynamic shear viscosity η′ is defined as G′′/ω, where ω is the oscillation frequency. According to rigorous linear viscoelasticity theory,9 the low-frequency value of η′ must equal the low-shear-rate value of the steady shear viscosity η for all liquids. This was verified for the model waxy oil using the higher temperature data in Figure 2, from which we conclude that the frequency (0.126 rad/s) and the stress amplitude (0.3 Pa) were low enough to obtain linear viscoelastic results. Figure 3 contains an Arrhenius-type plot of log η′ versus 1/T, where the values of η′ for the model oil were calculated using the G′′ values already given in Figure 2. Also shown are results for the mineral oil without added wax. All of the results for the mineral oil fall on a straight line. The slope of this line, according to the Arrhenius prediction, is E/R, where E is the apparent flow activation energy and R is the gas constant.9 The results for the model waxy oil conform to the same line at high temperatures but begin to depart from this line beginning about 26 °C, because of the incipient formation of wax crystals. Therefore, we estimate the WAT to be 26 °C based on the oscillatory shear rheology results, an estimate that was verified by FTIR using the method of Roehner and Hanson based on intensity measurements of methylene rocking vibrations.7 Measurement of the Elastic-Limit Yield Stress and Static Yield Stress Values. According to Chang et al.,6 gels formed from waxy crude oils often have three distinct yield stresses values: elastic-limit yield stress value, static yield stress value, and dynamic yield stress value. Here, we are concerned with the first two, which are the ones most relevant for the initial fracture of gels in pipeline flow restart. If the shear stress imposed on a given waxy crude oil gel is below its elasticlimit yield stress value (τe), then the gel by definition only exhibits elastic response. However, if the shear stress imposed (10) Venkatesan, R.; Singh, P.; Fogler, H. S. SPE J. 2002, (December), 349–352.
Time-Dependent Rheology of a Waxy Crude Oil
Figure 3. Rheological detection of the WAT. The model oil with and without added wax was cooled at 0.1 °C/min during oscillatory shear testing. The viscosity of the wax-free oil exhibits Arrhenius-type behavior (- - -) over the entire temperature range. The WAT of the waxy oil is identified as the temperature (26 °C) at which the viscosity departs from the Arrhenius prediction.
Figure 4. Shear strain versus time measured for model waxy oil gel in the creep-recovery experiment at 2 °C. A shear stress of 80 Pa was suddenly imposed on the gel at time equal zero and suddenly removed at time equal 60 s.
on the gel exceed its static yield stress value (τs), then the gel “fractures” and exhibits continuous flow. For imposed stress values in between τe and τs, the waxy crude oil gel is expected to exhibit slow “creep”. Both τe and τs can be determined by performing creep-recovery experiments. Figure 4 shows a typical creep-recovery curve obtained at a low shear stress value for the gelled model oil. The qualitative features of Figure 4 are similar to those reported for crude oils in similar creep tests performed by Chang et al.6 After loading the model oil into the rheometer at 35 °C, the oil sample was cooled under static conditions to 2 °C at a rate of 1 °C/min and then aged for 11 min at 2 °C. At time equal zero, the shear stress on the sample was increased from 0 to 80 Pa as rapidly as possible (within milliseconds). The first 60 s of the curve in Figure 4 gives the time-dependent shear strain of the gel as it “creeps” in response to a controlled stress of 80 Pa. At time equal 60 s, the shear stress on the sample was suddenly reduced to zero. Hence, the final 30 s of the curve in Figure 4 gives the “recovery” strain of the gel as it partially recoils back to its initial shape. Strictly speaking, given that the creep strain displayed in Figure 4 never reaches a steady value, the behavior corresponds to that of a viscoelastic liquid and not a solid, albeit one of
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Figure 5. Strain versus time during creep tests on model oil cooled at 1 °C/min to the testing temperature of 2 °C. At constant stress of 40 Pa, the gel reaches a steady strain value, whereas at 80 Pa, the gel creeps and the strain never reaches a steady value. Therefore, the elasticlimit yield stress value of the gel is in the range of 40-80 Pa.
Figure 6. Strain versus time for the same model oil sample studied in Figure 5 but at higher stress levels. At constant stress of 150 Pa, the strain curve exhibits an inflection point and fracture-like behavior occurs when the strain reaches about 1%. Thus, the static yield stress value of the gel lies in the range of 120-150 Pa.
extremely high viscosity. Analogy may be made with similar creep curves observed for molten synthetic polymers.9 Hence, we interpret the curve in Figure 4 as showing a rapid elastic increase in strain at times t less than 5 s, followed by a much slower linear rise in strain corresponding to viscous creep. One may calculate an elastic shear modulus for the gel using the initial jump in strain: Ge ) 80 Pa/0.000 35 ) 230 000 Pa. After the stress is removed, the gel only recovers about 50% of the total strain imposed during creep. The recovery time is about 5 s, which is consistent with the time scale of the initial elastic response during creep. Thus, the mean viscoelastic relaxation time of the gel is of the order 5 s. The creep response of the same gel sample is compared at four different stress values in Figures 5 and 6. In all four cases, a constant stress was applied for a time period of 60 s. For each curve, the initial jump in strain is consistent with an elastic shear modulus value Ge of about 200 000 Pa. However, the viscous portion of the creep curve has a slope that monotonically increases with an increasing imposed stress value. At the lowest imposed stress value (40 Pa), the slope is zero within experimental error; i.e., there is no viscous creep. Therefore, the value of the elastic-limit yield stress τe is approximately 40 Pa for the model oil gel. At higher stress values in Figure 6, the sample exhibits an increasing rate of viscous creep. However, even at 120 Pa, the total shear strain
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Magda et al. Table 1. Reproducibility of Rheological Measurements
sample number
η′ at 30 °C (mPa s)
WAT (°C)
gelation temperature (°C)
τe elastic-limit yield stress (Pa)
τs static yield stress (Pa)
Ge elastic modulus (Pa)
γcrit critical strain at fracture
1 2 3 4 average
17.6 17.1 17.0 16.8
25-26 25-26 25-26 25
22 22 23 22-23
40-80 40-80 40-80 80-120 70 ( 20
160-200 80-120 80-120 200-240 150 ( 50
200000 220000 115000 200000 185000 ( 50000
0.017 0.009 0.004 0.005
is still only 0.002 after 60 s of creep. Thus, the creeping gel cannot be said to be “flowing” in any practical sense. However, at an imposed shear stress of 150 Pa, the creep curve exhibits an inflection point at time t ) 35 s, and then the creep strain rapidly rises by many orders of magnitude. Presumably, this behavior corresponds to “fracture” of the brittle model oil gel, the same fracture phenomenon reported for waxy crude oil gels needed for gelled pipeline flow restart.3,5,6 It is difficult to determine visually whether the model oil gel fractures at the cone surface (“adhesive fracture”) or in the gel interior (“cohesive fracture”), but cohesive fracture is probably occurring for gels formed at the cooling rates employed in this study.11 Therefore, our model oil gel has a static yield stress value τs of approximately 150 Pa, provided that one is willing to wait about 60 s for fracture to occur. Evaluation of Reproducibility. Fracture of glassy polymers is sometimes modeled as a random process that occurs whenever a critical flaw or crack randomly appears within the material. Therefore, we were concerned about the reproducibility of our measured τs value. To address this concern, an identical procedure for measuring τs and other rheological properties was applied to four samples from the same batch of model oil. This procedure was chosen both to optimize the reproducibility of τs measurement and to allow us to compare the uncertainty in τs with that of other properties. First, each model oil sample was heated at 55 °C for at least 60 min to melt all crystallites. Then, each sample was loaded into the rheometer at 35 °C and cooled to 2 °C at a rate of 0.5 °C/min. To obtain WAT and gel points for each sample, small-amplitude oscillatory shear measurements were performed during this cooling step (stress amplitude, 0.3 Pa; frequency, 0.126 rad/s). As discussed in the preceding section, these oscillatory shear experiments give a value for the WAT very similar to that obtained for the quiescent sample in FTIR measurements and, thus, are not expected to distort the sample structure. Each sample was aged for 30 min at 2 °C and then subjected to a sequence of creep-recovery tests, with 60 s of creep and 30 s of recovery. The first creep test was performed at a constant stress value of 40 Pa. If no fracture was observed, then the next test in the sequence of creeprecovery tests was performed with a new constant stress value, 40 Pa larger than in the previous test. In this way, the sequence of creep-recovery tests was continued until sample fracture was observed within 60 s. Table 1 lists the results obtained in this reproducibility evaluation test for the dynamic viscosity value η′ at 30 °C, the WAT, the gel point, the elastic shear modulus Ge, the elastic-limit yield stress τe, and the static yield stress τs. Whenever fracture occurred, an inflection point was observed in the plot of creep strain versus time. Hence, Table 1 also lists the value for γcrit, defined as the strain value of this inflection point just before fracture. One observes in Table 1 that the measured values of η′, WAT, and the gel point are very reproducible. However, the measurements of the elastic modulus and yield stresses are less satisfactory: Ge ) 185 000 ( 50 000 Pa, τe ) 70 ( 20 Pa, and τs ) 150 ( 50 Pa. Given that the (11) Lee, H. S.; Singh, P.; Thomason, W. H.; Fogler, H. S. Energy Fuels 2008, 22, 480–487.
measurements were made under highly controlled conditions, a great deal of variation can be expected in gelled pipeline restart experiments with this model oil. Measurement of Delay Time to Fracture. According to Chang et al., a waxy crude oil gel that creeps under the influence of an applied shear stress will eventually fracture, given sufficient time.6 Furthermore, for creep to occur, the applied stress value must lie between τe and τs. This concept leads directly to the prediction of the CNR model that delayed restart of flow can occur in gelled pipelines.3 The creep results presented thus far are consistent with this hypothesis. As observed in Table 1, fracture during creep seems to always occur near a critical strain value γcrit of 0.005-0.02. Therefore, any model oil gel that creeps will eventually reach this critical strain value and probably fracture. The rate of creep increases with an increase in imposed stress value τ, and thus, the delay time to fracture (td) should decrease with an increasing stress level. A better test of this hypothesis can be obtained by performing creep experiments at various stress levels and allowing the gel to creep until the time of fracture. Figure 7 shows the creep results from one such test. The model oil was cooled from 35 to 2 °C at a rate of 0.5 °C/min in the rheometer, aged for 30 min at 2 °C, and then subjected to a time-independent shear stress τ of 100 Pa. As seen in Figure 7, the initial rate of creep is modest, but then the gel yields catastrophically at td ≈ 140 s. A series of similar experiments were performed at various stress values, giving the plot of td versus τ shown in Figure 8. As expected, the measured value of td appears to be diverging as τ approaches the estimated elastic-limit yield stress value (70 ( 20 Pa in Table 1), although the scatter is considerable. As expected, the measured value of td approaches zero as τ approaches the estimated static yield stress value (150 ( 50 Pa in Table 1). In one such experiment (not included in Figure 8), the model oil took over 1 h to fracture at τ ) 100 Pa. In similar experiments on crude oils, Ronningsen4 reported fracture times in excess of 5 h! The microscopic level changes (if any) that occur in the gel as it creeps over a long period of time have never been pinpointed. In the CNR model for gelled pipeline restart, the creeping gel is presumed to degrade over time until
Figure 7. Shear strain versus time for waxy model oil gel at 2 °C subjected to a time-independent shear stress of 100 Pa. After a delay time (in seconds) of over 2 min, the gel fractures catastrophically.
Time-Dependent Rheology of a Waxy Crude Oil
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Figure 8. Fracture time versus applied stress value, as measured for model waxy oil samples at 2 °C. The fracture time appears to diverge as the imposed stress approaches the elastic-limit yield stress value of the gel (40-80 Pa). Figure 10. Comparison of the time-dependent strain curves for the two creep tests at 80 Pa on the same sample, as given in Figure 9.
during creep, one might expect hysteresis in the final strain value, but no such trend is apparent in Figure 9. Figure 10 compares the time-dependent creep response of the gel in the first test at 80 Pa with that in the repeat experiment on the same sample at 80 Pa. Figure 10 shows that 5 min of creep at 80 Pa has no discernible effect on either the elastic modulus Ge or the rate of viscous creep. Conclusions
Figure 9. Final value of strain after 5 min of creep versus the value of shear stress imposed on the gel during creep at 2 °C. In chronological order, the 5 min creep tests were performed at 40, 60, 80, 80, 60, and 40 Pa, all on the same sample.
the static yield stress value τs decreases to the imposed stress value τ, at which point fracture occurs.3 However, this mechanism presents problems from the viewpoint of laboratory rheology testing. For example, the estimated value of τs in Table 1 was obtained by performing a sequence of creep tests on a single sample until fracture was observed, and Chang et al.6 followed a similar procedure. One might argue that the τs value thus obtained is invalid, because the gel may have degraded after the first creep test. A similar objection could be raised against the results of stress-ramp tests.6,11 To address this possible concern, we performed a creep-response hysteresis test. A sample of the model oil was cooled from 35 to 2 °C at a rate of 0.5 °C/min in the rheometer, aged for 30 min at 2 °C, and then subjected to a sequence of six creep tests of a 5 min duration, with 15 s recovery between each test. The timeindependent stress values of the six creep tests were, in chronological order, 40, 60, 80, 80, 60, and 40 Pa. Figure 9 contains a plot of the final value of strain after 5 min of creep versus applied stress, as measured for the same gel sample in this sequence of six creep tests. If the gel degrades with time
The transparent model waxy oil studied here exhibits complex rheological behavior that includes an elastic-limit yield stress value (τe), a static yield stress value (τs), and the occurrence of delayed fracture while under an imposed shear stress. The same three qualitative rheological features have previously been reported for waxy crude oil gels.4-6 However, values of τe and τs reported here are approximately 5 times larger than reported earlier for the waxy crude oil gels.4-6 A possible reason for the difference in yield stress values between crude oils and the model oil is the presence of asphaltenes in the former, because small amounts of asphaltenes have been shown to reduce the gel yield stress.12 Creep-recovery tests show that the model waxy oil gel exhibits both elastic response and viscous creep, with a mean viscoelastic relaxation time of about 5 s. However, the delay time to fracture can be many orders of magnitude larger than this, as is also observed for waxy crude oil gels. Rheological methods can be used to estimate the WAT and gel point of the model waxy oil with excellent reproducibility. However, measurements of the static yield stress value and the delay time to fracture are much less reproducible, even under highly controlled conditions. The results of tests for hysteresis (Figures 9 and 10) show that the rheological properties of a given sample of the model waxy oil gel can probably be measured over a time period of at least 30 min without concern about sample degradation, unless of course the sample fractures in the rheometer. EF800628G (12) Venkatesan, R.; Ostlund, J.-A.; Chawla, H.; Wattana, P.; Nyden, M.; Fogler, H. S. Energy Fuels 2003, 17, 1630–1640.
