Controlled Shear Stress and Controlled Shear Rate Nonoscillatory

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Controlled Shear Stress and Controlled Shear Rate Nonoscillatory Rheological Methodologies for Gelation Point Determination Yansong Zhao,*,† Kristofer Paso,† Lalit Kumar,† Jamilia Safieva,† Mior Zaiga B. Sariman,‡ and Johan Sjöblom† †

Ugelstad Laboratory, Department of Chemical Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway ‡ Petronas, 50088 Kuala Lumpur, Malaysia ABSTRACT: An experimental rheometric investigation is performed to assess the utility of various gelation point determination methodologies. Controlled shear stress and controlled shear rate methods are developed to investigate gelation processes in waxy oils. The nonoscillatory rheological method exhibits high reproducibility for model wax oils as well as for real crude oils. In addition, the nonoscillatory methods are in good agreement with standard oscillatory gel point determination methods. The effect of imposed shear stress, imposed shear rate, and cooling rate on gelation point is investigated with two types of model oils: 5 wt % macrocrystalline wax in Primol 352 and 5 wt % macrocrystalline wax in dodecane. In addition, the effect of wax content on gel temperature of macrocrystalline wax in dodecane is investigated. Moreover, the effect of additives (A3 and A4) on gelation point of a real crude oil UL-YS1 is investigated. Finally, the gelation temperatures of 5 wt % macrocrystalline wax in Primol 352, crude oil UL-YS1, and Se-7-E06 are investigated by three methods: constant imposed shear stress, constant imposed shear rate, and oscillatory G′−G″. Gel point results are obtained with the various protocols for real and model oil systems. The nonoscillatory rheological method is applicable for gel point determination of model wax oils as well as real crude oils. Hence, due to its high repeatability and instrumental accuracy, the nonoscillatory rheological method is a promising method for gel point determination.

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required for a gel to form.13 Limitations of the visual method include an absence of rheological information and a lack of accuracy for physical gels. Limitations of oscillation methods include imposition of detrimental cyclic strain. Limitations of the infinite extrapolation include a necessitated time dependence for polymer solutions, which is inapplicable to physical gels that form immediately upon attaining the pertinent percolation state. At the gel point for chemically cross-linked polymer solutions, the dynamic oscillatory viscosity follows a power law function upon frequency due to entropy-driven chain dynamics in solution. However, physical wax gel formation is driven by paraffin precipitation and subsequent van der Waals attractive forces between crystals. Therefore, chain dynamic relations per se are inapplicable to gel point determination. However, the G′−G″ method can be utilized to reveal oscillatory mechanics of wax gels, thereby affording an oscillatory measure of Tgel, albeit with cyclic degradation effects. Al-Zahrani and Al-Fariss18 suggest that the viscosity of waxy oils can be predicted as a function of shear rate, temperature, and wax concentration as follows:

INTRODUCTION A physical gel is an open network semirigid material that exhibits viscoelastic properties. Gelation processes are central to several disciplines, including food science,1,2 petroleum science,3 polymer science,4 biology,5 and medicinal science.6 Within the petroleum production industry, pipeline shut-in and restart operations impart significant risk to both planned and emergency outage scenarios.7−12 Physical wax−oil gels may form during the shut-in process of waxy crude oil pipelines. Paraffin wax−oil gels consist of volume-spanning networks that entrap the remaining organic fluid within the crystals. Gelation temperature (Tgel) is an important parameter that characterizes the gelation formation process. Tgel is a complex function of thermal and shear history during the cooling process, and as such is not a constant value as is the pour point (PP). In polymer science, the gelation temperature establishes the temperature above which a gel will not form.13 However, for physical gels, the gelation temperature exhibits a strong dependence on nucleation kinetics, precipitation kinetics, shear history, baric history, and thermal history, and as such does not infer an equilibrium condition. Instead, for physical gels such as wax−oil gels, the gelation temperature infers a mechanical change from fluid behavior to yielding behavior. Various gelation temperature measurement methods have been development by several researchers.13−17 Three common methods are used for cross-linked polymer solutions: (1) visual determination of gel formation under defined thermal conditions to estimate Tgel; (2) measuring the oscillatory storage modulus (G′), loss modulus (G″), and phase angle (δ); and (3) infinite tgel extrapolation, where tgel denotes the time © 2013 American Chemical Society

⎤1/ n B1 ⎡⎛ γ + A1 ⎞ ⎢⎜ η= ⎟ − 1⎥ e(C / T ) + DW γ ̇ ⎢⎣⎝ A1 ⎠ ⎦⎥

(1)

Received: December 12, 2012 Revised: March 5, 2013 Published: March 12, 2013 2025

dx.doi.org/10.1021/ef302059f | Energy Fuels 2013, 27, 2025−2032

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where η is the viscosity, γ̇ is the shear rate, T is the temperature, and W is the percentage of wax. A1, B1, C, and D are model parameters obtained from nonlinear regression analysis. Pedersen and Rønningsen19 suggest that the apparent viscosity of oil phase with suspended wax particles can be described as follows: ⎡ η = η′exp(E Φwax )⎢1 + ⎢⎣

F Φwax dvx /dy

+

GΦwax 4 ⎤ ⎥ dvx /dy ⎥⎦

and A4, proprietary, from Champion Technologies, Inc.) are also used in this work. Two samples, 5 wt % macrocrystalline wax in dodecane and 5 wt % macrocrystalline wax in Primol 352, are prepared. Primol 352 (from ExxonMobil) is a high-viscosity purified mixture of liquid saturated hydrocarbons. The properties of Primol 352 are shown in previous work of Zhao et al.21 In addition, samples of macrocrystalline wax in dodecane with wax content as high as 10 wt % are also prepared. In order to investigate the effect of additives on gelation point of real crude oil, samples of 100 ppm A3 and A4 in crude oil ULYS1 are prepared. Rheological Experiments. Rheological experiments are performed on a rheometer (Anton Paar Physica 301, Austria). Several protocols are employed to investigate gelation processes of model wax oils and crude oils. Protocols a−e utilize a 4-cm diameter 2° cone and plate geometry.11 (a) Constant Imposed Shear Stress Method. A sample is loaded between the cone and plate. Prior to loading, the sample and geometry are maintained at a temperature of at least 20 °C above the wax appearance temperature (WAT) to ensure a liquid paraffin state. The sample is cooled to a liquid temperature TL (40 °C for 5 wt % macrocrystalline wax in dodecane and crude oil UL-YS1; 45 °C for 5 wt % macrocrystalline wax in Primol 352; 65 °C for crude oil Se-7E06) at a cooling rate of 20 °C/min under a constant imposed shear stress value τG. Subsequently, the sample is cooled to 4 °C at 1 °C/ min under an identical shear stress τG. The value of τG ranges from 0.001 to 30 Pa. (b) Constant Imposed Shear Rate Method. The protocol is similar to protocol a. During the first and second cool-down stages, a single shear rate of γ̇G is imposed on the sample. The value of γ̇G ranges from 0.001 to 1 s−1. (c) Effect of Cooling Rate Protocol. The protocol is similar to protocol a. During the cool-down stage from TL (40 °C for 5 wt % macrocrystalline wax in dodecane; 45 °C for 5 wt % macrocrystalline wax in Primol 352) to the final gel formation temperature 4 °C, the cooling rate ranged from 0.1 to 20 °C/min. (d) Effect of Wax Content Protocol. Various model fluid samples are prepared containing macrocrystalline wax in dodecane with wax contents ranging from 0 to 10 wt %. The rheometric protocol used is similar to protocol a. In each experiment, a constant shear stress of 0.01 Pa is imposed while the model fluid sample is cooled to 40 °C at a rate of 20 °C/min. Subsequently, a constant shear stress of 0.01 Pa is imposed while the model fluid sample is cooled to 4 °C at 1 °C/min. (e) G′−G″ Method Protocol. A sample is loaded between the cone and plate. Prior to loading, the sample and geometry are maintained at a temperature of at least 20 °C above the wax WAT to ensure a liquid paraffin state. The sample is cooled to TL (45 °C for 5 wt % macrocrystalline wax in Primol 352; 40 °C for UL-YS1; 65 °C for Se7-E06) at a cooling rate of 20 °C/min. Subsequently, the sample is cooled to 4 °C at 1 °C/min with a constant oscillation frequency of 1 Hz and an imposed strain of 0.2%. (f) Effect of Geometry Protocol. This protocol is utilized to investigate the effect of geometry type on gel temperature measurements. The geometries available include t (1) cone and plate, (2) plate and plate, and (3) concentric cylinder. A sample is loaded into the geometry. Prior to loading, the sample and geometry are maintained at a temperature of at least 20 °C above WAT to ensure a liquid paraffin state. The sample is cooled to 4 °C at 1 °C/min under a constant imposed shear stress of 0.01 Pa.

(2)

where η′ is the viscosity of the oil phase without consideration of wax particles, Φwax is the volume fraction of wax in oil sample, dvx/dy is the shear rate, and E, F, and G are empirical constants.19 As mentioned above, viscosity of waxy oils is shear ratedependent. However, strain-dependent viscosity can be considered independent of the shear rate at relatively low shear rates. In addition, viscosity at low shear rates can be described by a modified Eyring’s theory as follows:11 η=

2 ⎛ ε + εS ⎞ hN ⎛⎜ δ ⎞⎟ ⎟ exp⎜ 0 ⎝ RT ⎠ V ⎝a⎠

(3)

where h is the Planck constant, N is the Avogadro number, V is the molar volume of the system, ε0 is the activation energy, and εS accounts for changes in total solid−liquid interfacial area arising from thermodynamic solubility effects. R is the ideal gas constant, T is absolute temperature, and δ and a are length parameters.11,20 Equation 3 shows that viscosity exhibits an Arrhenius model. This demonstrated Arrhenius dependence holds regardless of measuring protocol. For example, in constant imposed shear stress rheometric probing techniques, the nonoscillatory shear rate follows the expressed form of eq 3 through γ̇ = τ/η. However, T, δ, and a are variable parameters during the gelation process. Similarly, for constant imposed shear rate rheometric probing techniques, the dynamic nonoscillatory shear stress follows from τ = ηγ̇. Therefore, if a constant stress is imposed, the shearing rate will diminish during the gel formation process. Shear rate measurements can be used to investigate the gel point. Similarly, if a constant shear rate is established during measurement, the shear stress may change due to gel formation. Hence, shear stress probing techniques can also be used for gel point determination. For both methods, viscosity correlations are altered at the gel point. Therefore, viscosity plots can also be utilized to determine the gel point. In summary, the gel point can be derived according to changes in shear stress, shear rate, and/or viscosity. In this work, a dynamic nonoscillatory gel point determination method is developed utilizing constant imposed shear stress or constant imposed shear rate conditions during the gelation process. The method is developed for model fluids containing macrocrystalline wax in Primol 352 or dodecane, as well as real crude oils UL-YS1 and Se-7-E06. In addition, the method can also be used to measure the gel point of other soft materials that exhibit temperature-dependent mechanical behavior.

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RESULTS AND DISCUSSION Constant Imposed Shear Stress Method. Repeatability of Method. Protocol a is used to follow the gelation process of 5 wt % macrocrystalline wax in Primol 352 at a cooling rate of 1 °C/min and with an imposed shear stress value of 0.2 Pa. Two runs are performed to confirm the reproducibility of the method. Temperature and shear rate values are plotted in Figure 1 as a function of time during the final cool-down stage, demonstrating adequate experimental repeatability. The tem-

EXPERIMENTAL SECTION

Materials. Dodecane is obtained from Sigma−Aldrich and the mass fraction purity (CAS 112-40-3) is ≥0.990. Macrocrystalline wax (Sasolwax 5405 from Sasol Wax GmbH), crude oil UL-YS1 (proprietary), crude oil Se-7-E06 (proprietary), and additives (A3 2026


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Figure 1. Measured shear rate values during gelation of 5 wt % macrocrystalline wax in Primol 352 with an imposed shear stress of 0.2 Pa and of 5 wt % macrocrystalline wax in dodecane with an imposed shear stress of 0.5 Pa.

perature shows linear reduction with time, and the resultant shear rate shows a sharply decreasing trend driven by the gelation process. The sharp drop in shear rate at approximately 1000 s corresponds to gelation of the sample, and creeping flow is observed subsequent to gel formation. Figure 1 also shows five repeated experiments performed via protocol a with 5 wt % macrocrystalline wax in dodecane and an imposed shear stress of 0.5 Pa. An identical cooling rate of 1 °C/min is used. Again, adequate repeatability is attained. The time-based plots clearly demonstrate that gel formation is delayed past 1500 s due to the higher imposed shear stress condition as well as differences in solubility, precipitation, and viscosity deriving from the dissimilar solvent. Effect of Imposed Shear Stress. The influence of imposed shear stress magnitude on gelation temperature is investigated for 5 wt % macrocrystalline wax in Primol 352. In addition, 5 wt % macrocrystalline wax in dodecane is also used to investigate the effect of shear stress. Results are shown in Figure 2 panels a and b, respectively. The top curves in Figure 2a show an Arrhenius dependence of the shear rate upon temperature at the high-temperature liquid state. Deviation in shear rate from the Arrhenius dependence corresponds to paraffin precipitation, effectively establishing the rheometric WAT value as the sharp change in slope for the upper curves in Figure 2a. As shown in Figure 2a, shear stress does not influence the rheometric WAT value, although the WAT is difficult to observe at the lowest imposed shear stress values due to data scatter. The gelation temperature, on the other hand, is ascribed to a sharp drop in shear rate and is a complex function of the imposed shear stress. Therefore, the plots establish three regimes for the waxy oil system. At the highest temperature regime, a single liquid phase exists. The WAT value establishes the onset of wax precipitation, such that a two-phase suspension is formed. At temperatures below the WAT, the system may or may not gel, depending on the imposed shear stress condition. High shear stress values disrupt the gel formation process, while low shear stress values afford gelation very close to the WAT solubility limit. At temperature conditions below the gel point, a network structure exists, corroborating with yielding behavior. However, if a sufficiently high stress is imposed during cooling, a volume-spanning network structure will be precluded, such that the system will

Figure 2. Effect of imposed shear stress on gelation temperature: (a) 5 wt % macrocrystalline wax in Primol 352 at cooling rate of 1 °C/min; (b) 5 wt % macrocrystalline wax in dodecane at cooling rate of 1 °C/ min.

not undergo gelation, as shown for the upper curves in Figure 2a. Similarly, as shown in Figure 2b, shear stress strongly influences the gelation temperature of 5 wt % macrocrystalline wax in dodecane. For the case of the low-viscosity dodecane solvent, WAT values are difficult to establish due to the removal of paraffins from the liquid phase during precipitation, effectively counteracting the presence of a suspended solid fraction and resulting in ambiguous rheometric WAT values, as is also common for low-viscosity paraffinic gas condensate fluids. The gelation temperature, however, is readily defined as a very “sharp” drop in measured shear rate. It is evident that the imposed shear stress disrupts the gel formation process. Therefore, relatively low imposed shear stress is preferred for valid gelation point investigations reflecting field conditions in which only shrinkage flows exist in the pipeline during the shutin and cool-down stage. However, the shear stress should be sufficiently high to obtain scatter-free signals in the rheometric data acquisition. 2027


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Effect of Cooling Rate. The effect of cooling rate (0.1−20 °C/min) on gelation temperature of 5 wt % macrocrystalline wax in Primol 352 is investigated for an imposed shear stress of 0.01 Pa. As shown in Figure 3, the gelation temperature

Figure 4. Effect of cooling rate and imposed shear stress on gelation temperature of 5 wt % macrocrystalline wax in Primol 352.

Figure 3. Effect of cooling rate on gelation temperature of 5 wt % macrocrystalline wax in Primol 352 at constant imposed shear stress of 0.01 Pa.

increases with decreasing cooling rate under the small imposed stress condition. Gel formation process is a time-dependent process in which there exists a competition between nucleation processes and crystal growth processes. Slow cooling rates promote crystal growth over nucleation and also afford sufficient time to facilitate crystal−crystal bonding, resulting in large crystal sizes and strong crystal−crystal bonds that form strong gels. Therefore, slow cooling rates promote the gelation process, and under a small imposed shear stress the stress does not significantly hinder the gel formation process. Therefore, for the conditions of small imposed shear stress, a maximum gelation temperature is obtained at a low cooling rate. For high imposed shear stress conditions, maximum gelation temperatures may be attained at higher cooling rates due to the interplay between the time-dependent gel formation process and the time-dependent rupture and degradation process with shear. Experiments with imposed shear stress of 0.01 and 0.05 Pa as well as cooling rates of 0.5 and 1 °C/min are also performed for the sample consisting of 5 wt % macrocrystalline wax in Primol 352. Results are shown in Figure 4. Under the low imposed stress condition, the cooling rate shows a significant influence on gelation temperature, demonstrating the impact of thermal history on the gel formation process. The imposed stress values, on the other hand, have a smaller impact on the gel formation process, due to the rapid network formation driven by paraffin precipitation and crystal−crystal bonding formation. Crude Oil Measurement. As shown in Figure 5, gelation temperatures of crude oils UL-YS1 and Se-7-E06 are measured at a cooling rate of 1 °C/min and an imposed shear stress of 0.01 Pa. Experiments are performed in duplicate. Results show that the repeatability of the constant imposed shear stress method is excellent, even for real produced crude oils that contain a large fraction of heavy polar components such as asphaltenes and resins. Therefore, the methods are generally applicable to measure the gelation temperature of real crude oils, as demonstrated by the nearly superimposable curves.

Figure 5. Gelation temperature measurement of crude oils UL-YS1 and Se-7-E06 by the constant imposed shear stress (0.01 Pa) method with a cooling rate of 1 °C/min.

Effect of Wax Content. The effect of wax content on gelation temperature of macrocrystalline wax in dodecane is investigated for a cooling rate of 1 °C/min and imposed shear stress of 0.01 Pa. As shown in Figure 6, the gelation temperature increases with increasing wax content from 0 to 10 wt %, as predicted by thermodynamic solid−liquid equilibrium theory. For the sample containing 0 wt % wax in dodecane, the shear rate−temperature curve is linear and no gel formation occurs. The experiments demonstrate that observed gelation temperatures are highly sensitive to overall wax content. Effect of Additives. The effect of additives (A3 and A4) on gelation temperature of crude oil UL-YS1 is investigated by the imposed shear stress method with a shear stress of 0.01 Pa and a cooling rate of 1 °C/min during the gelation process. The additives were dosed at an overall concentration of 100 ppm. As shown in Figure 7, the gelation temperature is successfully depressed by the presence of commercial additives. The selected additives are shown to be highly effective for real crude oil gelation temperature reduction purposes. 2028


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Figure 6. Effect of wax content on gelation temperature by the constant imposed shear stress (0.01 Pa) method at a cooling rate of 1 °C/min.

Figure 8. Repeated experiment of 5 wt % macrocrystalline wax in Primol 352 at constant imposed shear rate of 0.01 s−1 and cooling rate of 1 °C/min.

shear rate, with larger shifts observed at lower imposed shear rate conditions. As is the case for the constant imposed stress method, relatively low imposed shear rates are preferred for gelation temperature measurements, in order to minimize network rupture during measurement. However, sufficiently high shearing must be used to attain scatter-free rheometric signals. For example, a poor (scattered) signal can be observed for the lower curves in both panels of Figure 9. Effect of Cooling Rate. The influence of cooling rate (0.1− 20 °C/min) on gelation temperature is investigated with imposed shearing of 0.01 s−1 for 5 wt % macrocrystalline wax in Primol 352. As shown in Figure 10, the gelation temperature increases with decreasing cooling rate, confirming that the gel formation process is a strongly time-dependent process, even for forced shearing and forced rupture conditions. At the lowest cooling rates, the rich interplay between gel formation and shear rupture is evident from the wavy nature of the shear stress curves at temperatures below the gelation point. In general, the results are similar to the constant imposed shear stress results, demonstrating a highly time-dependent process required to form strong wax gels. Viscosity-Based Method. Viscosity measurements may also be used to investigate the gelation temperature of waxy oils by the constant imposed shear stress method and/or the constant imposed shear rate method. The constant imposed shear stress (0.2−1 Pa) method is used at a cooling rate of 1 °C/min with 5 wt % macrocrystalline wax in dodecane. As shown in Figure 11a, the viscosity of the sample increases during the gelation process. At the gel point, the viscosity values sharply increase to a high plateau level due to gel formation. Hence, the viscosity change can also be used to establish the gel point. Moreover, the constant imposed shear rate (0.001−1 s−1) method is also used at a cooling rate of 1 °C/min for 5 wt % macrocrystalline wax in Primol 352. Similarly, as shown in Figure 11b, the viscosity increases sharply at the gelation point. As expected, the rich interplay between gel formation and gel breakage is evident in Figure 11b and is an artifact of the forced gel rupture conditions stemming from the controlled shearing protocol. G′−G″ Method. As shown in Figure 12, G′−G″ method is used to measure the gelation temperature of 5 wt % macrocrystalline wax in Primol 352, crude oil UL-YS1, and

Figure 7. Effect of additives on gelation temperature of crude oil ULYS1.

Constant Imposed Shear Rate Method. Repeatability of Method. Various experiments are performed at a cooling rate of 1 °C/min and an imposed shear rate of 0.01 s−1 in 5 wt % macrocrystalline wax in Primol 352. Duplicate results are shown in Figure 8. Stochastic data are observed in the controlled shear rate regime resulting from a competition between precipitation-driven gel network formation and forced shear-driven network rupture. Hence, poor repeatability of curve profiles is obtained, although resultant gel temperatures are nearly identical. The average obtained gelation temperature of the sample is 28.34 °C. Effect of Constant Imposed Shear Rate. The influence of imposed shear rate on gelation temperature is investigated at a cooling rate of 1 °C/min and at imposed shear rates ranging from 10−3 to 1 s−1 for 5 wt % macrocrystalline wax in Primol 352 and 5 wt % macrocrystalline wax in dodecane. Results are shown in Figure 9 panels a and b, respectively. Stochastic stress values are again obtained due to forced network rupture during gel formation. For the imposed shearing protocol, the imposed shear rate does not drastically influence the gelation temperature, due to similar forced network rupture in all cases. However, the magnitude of the viscosity shift does vary with 2029


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Figure 11. Viscosity-based method for gel point determination: (a) 5 wt % macrocrystalline wax in dodecane at constant imposed shear stress ranging from 0.2 to 1 Pa at cooling rate of 1 °C/min; (b) 5 wt % macrocrystalline wax in Primol 352 at constant imposed shear rates ranging from 0.001 to 1 s−1 at cooling rate of 1 °C/min.

Figure 9. Gelation temperature measurement at various shear rates ranging from 0.001 to 1 s−1 with cooling rate of 1 °C/min in various model wax oils: (a) 5 wt % macrocrystalline wax in Primol 352; (b) 5 wt % macrocrystalline wax in dodecane.

Figure 12. Gelation temperature measurement by G′−G″ method at cooling rate of 1 °C/min: (a) 5 wt % macrocrystalline wax in Primol 352; (b) crude oil Se-7-E06; (c) crude oil UL-YS1. Figure 10. Effect of cooling rate on gelation temperature of 5 wt % macrocrystalline wax in Primol 352 by constant imposed shear rate (0.01 s−1) method at cooling rates from 0.1 to 20 °C/min.

crude oil Se-7-E06 at a cooling rate of 1 °C/min. In comparison, the gelation temperatures of 5 wt % macrocrystalline wax in Primol 352, crude oil UL-YS1, and crude oil Se-72030


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E06 at cooling rate of 1 °C/min by the nonoscillatory rheological method are also obtained. For the nonosciallatory methods, constant imposed values of the stress and shear rate are 0.01 Pa and 0.01 s−1, respectively. The gelation temperatures of waxy oils acquired by the three different methods are shown in Table 1. The gelation temperature results obtained

can be used to measure the gelation temperature. The gelation temperatures obtained from cone and plate and from plate and plate geometries are similar. However, the gelation temperature obtained from the concentric cylinder geometry is somewhat smaller than the value obtained from the cone/plate or plate/ plate systems. The origin of these differences may be associated with dissimilar thermal transfer characteristics, as gel formation is ultimately a temperature-driven process. In addition, shear localization processes may occur in the larger geometry that effectively serves to suppress the large-scale gelation point to lower temperature values.

Table 1. Comparison of Gelation Temperatures by Three Methods in Different Samples gelation temp (°C) samplea

G′−G″ method

constant shear stress method

constant shear rate method

a b c

28.3 43.1 24.5

28.4 (0.01 Pa) 51.8 (0.01 Pa) 23.2 (0.01 Pa)

28.3 (0.01 s−1) 51.6 (0.01 s−1) 23.2 (0.01 s−1)

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CONCLUSION In this work, a nonoscillatory rheological gel point determination method is developed at constant imposed shear stress or constant imposed shear rate during the gelation process. The mechanisms for the method are that the viscosity, shear rate, and/or shear stress exhibit a sharp change at the gelation point. The effect of imposed shear rate, imposed shear stress, cooling rate, and wax content on gelation temperature of model wax oils is investigated. In addition, effect of additive on gelation temperature of crude oil UL-YS1 is also investigated. Moreover, constant imposed shear stress method, constant imposed shear rate method, and G′−G″ method are used to measure the gelation temperature of different model wax oil systems, crude oil UL-YS1, and crude oil Se-7-E06. The results shown that the gelation temperatures of the samples are similar by the three various measuring methods. It is manifested that nonoscillatory rheological methods are applicable to measure the gel point of real crude oils. In addition, due to its high repeatability and instrumental accuracy, the method will become a promising method for gel point determination. In particular, the imposed stress method accurately emulates small shrinkage flows that form during pipeline shut-in and cool-down processes, providing the most accurate measure of gelation temperature for the purposes of predicting pipeline plugging processes with waxy crude oils.

a

(a) 5 wt % macrocrystalline wax in Primol 352; (b) crude oil Se-7E06; (c) crude oil UL-YS1.

from the three various methods are similar, demonstrating that the constant imposed shear stress and constant imposed shear rate methods are applicable to measure the gelation temperature of waxy oils. In general, constant imposed stress methods result in less gel degradation during the gel formation process, as the shearing rate responds to the initial viscosity increase associated with crystal network formation. In contrast, controlled shearing rate methods are unresponsive to initial gel network formation, allowing significant degradation of the initial gel network structure. Therefore, in general, controlled stress methods are considered somewhat more accurate in the ability to capture the pristine undisturbed gelation state. The relatively similar gel point values derived from controlled stress and controlled shearing methods is a consequence of the very low selected values of imposed stress and strain rate, respectively. Effect of Geometry Type. Experiments are performed in duplicate with three different geometry types to elucidate the effect of measuring geometry on gelation temperature. Cone and plate, plate and plate, and concentric cylinder geometries are utilized. As shown in Figure 13, the repeatability of the three various geometries is excellent and all three geometries

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] or yansong.zhao2004@gmail. com. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge The Research Council of Norway, Champion Technologies, BASF, Petrobras, Petronas, and Statoil ASA for financial support.

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REFERENCES

(1) Alting, A. C.; de Jongh, H. H. J.; Visschers, R. W.; Simons, J. W. F. A. Physical and chemical interactions in cold gelation of food proteins. J. Agric. Food Chem. 2002, 50 (16), 4682−4689. (2) Foegeding, E. A. Gels and gelation: Rheology, structure and texture perception in food protein gels. In Food Colloids; Dickinson, E., Ed.; Royal Society of Chemistry: London, 2005; pp 1−15. (3) Paso, K.; Senra, M.; Yi, Y.; Sastry, A. M.; Fogler, H. S. Paraffin polydispersity facilitates mechanical gelation. Ind. Eng. Chem. Res. 2005, 44 (18), 7242−7254. (4) Christensen, S. K.; Chiappelli, M. C.; Hayward, R. C. Gelation of copolymers with pendent benzophenone photo-cross-linkers. Macromolecules 2012, 45 (12), 5237−5246.

Figure 13. Gelation temperature measurement by various types of geometry: (CP) cone and plate; (PP) plate and plate; (CC) concentric cylinder. 2031


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(5) Coradin, T.; Livage, J. Aqueous silicates in biological sol−gel applications: New perspectives for old precursors. Acc. Chem. Res. 2007, 40 (9), 819−826. (6) Parker, S.; Braden, M. The effect of particle size on the gelation of tissue conditioners. Biomaterials 2001, 22 (14), 2039−2042. (7) Davidson, M. R.; Dzuy Nguyen, Q.; Chang, C.; Rønningsen, H. P. A model for restart of a pipeline with compressible gelled waxy crude oil. J. Non-Newton. Fluid Mech. 2004, 123 (2−3), 269−280. (8) Davidson, M. R.; Nguyen, Q. D.; Rønningsen, H. P. Restart model for a multi-plug gelled waxy oil pipeline. J. Petrol. Sci. Eng. 2007, 59 (1−2), 1−16. (9) Phillips, D. A.; Forsdyke, I. N.; McCracken, I. R.; Ravenscroft, P. D. Novel approaches to waxy crude restart, Part 2: An investigation of flow events following shut down. J. Petrol. Sci. Eng. 2011, 77 (3−4), 286−304. (10) Phillips, D. A.; Forsdyke, I. N.; McCracken, I. R.; Ravenscroft, P. D. Novel approaches to waxy crude restart, Part 1: Thermal shrinkage of waxy crude oil and the impact for pipeline restart. J. Petrol. Sci. Eng. 2011, 77 (3−4), 237−253. (11) Zhao, Y.; Kumar, L.; Paso, K.; Safieva, J.; Sariman, M. Z. B.; Sjöblom, J. Gelation behavior of model wax−oil and crude oil systems and yield stress model development. Energy Fuels 2012, 26 (10), 6323−6331. (12) Magda, J. J.; El-Gendy, H.; Oh, K.; Deo, M. D.; Montesi, A.; Venkatesan, R. Time-dependent rheology of a model waxy crude oil with relevance to gelled pipeline restart. Energy Fuels 2008, 23 (3), 1311−1315. (13) Tosh, S. M.; Marangoni, A. G. Determination of the maximum gelation temperature in gelatin gels. Appl. Phys. Lett. 2004, 84 (21), 4242−4244. (14) Venkatesan, R.; Singh, P.; Fogler, H. S. Delineating the pour point and gelation temperature of waxy crude oils. SPE J. 2002, No. Dec, 349−352. (15) Winter, H. H. Can the gel point of a cross-linking polymer be detected by the G′− G″ crossover? Polym. Eng. Sci. 1987, 27 (22), 1698−1702. (16) Carvalho, W.; Djabourov, M. Physical gelation under shear for gelatin gels. Rheol. Acta 1997, 36 (6), 591−609. (17) Kané, M.; Djabourov, M.; Volle, J.-L. Rheology and structure of waxy crude oils in quiescent and under shearing conditions. Fuel 2004, 83 (11−12), 1591−1605. (18) Al-Zahrani, S. M.; Al-Fariss, T. F. A general model for the viscosity of waxy oils. Chem. Eng. Process. 1998, 37 (5), 433−437. (19) Pedersen, K. S.; Rønningsen, H. P. Influence of wax inhibitors on wax appearance temperature, pour point, and viscosity of waxy crude oils. Energy Fuels 2003, 17 (2), 321−328. (20) Macías-Salinas, R.; Durán-Valencia, C.; López-Ramírez, S.; Bouchot, C. Eyring-theory-based model to estimate crude oil viscosity at reservoir conditions. Energy Fuels 2008, 23 (1), 464−470. (21) Zhao, Y.; Kumar, L.; Paso, K.; Ali, H.; Safieva, J.; Sjöblom, J. Gelation and breakage behavior of model wax−oil systems: Rheological properties and model development. Ind. Eng. Chem. Res. 2012, 51 (23), 8123−8133.

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