Article pubs.acs.org/IECR
Yield Behavior of Waxy Crude Gel: Effect of Isothermal Structure Development before Prior Applied Stress Banglong Jia and Jinjun Zhang* National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum, Beijing 102249, China ABSTRACT: The rheological properties of waxy crude oil are dependent upon the shear and thermal histories. It would not be valuable to study the shear effect of waxy crude oil without consideration of the thermal conditions. Currently, researchers study the shear effect of waxy crude oil mainly with different cooling rates or shear temperatures; few studies have been reported about the influence of isothermal structure development on the shear effect. Present studies show that, even at constant temperature below the wax appearance temperature, the characteristics of the waxy crude gels undergo a change with quiescent duration, becoming harder and more stable. In this paper, a specimen of a typical waxy crude oil was held isothermally and quiescently for a time in the range of 0−60 min for structure development at temperatures close to the gelation temperature, followed by the application of constant stress in a wide range of 1−100 Pa at the same temperature. After subsequent cooling to below a temperature of 2 °C, the structure strength of waxy crude gel was examined by measurement of the static yield stress. This showed that the structure strength of waxy crude gel increased with isothermal aging, while the reversibility of the gel structure decreased. In cases of prior application of lower stresses (from 1 to 7 Pa), the situation of shorter aging time was easier to get a strain to overcome the critical strain, which represents the start of structure degradation, and hence induces a lower yield stress value after subsequent cooling. In cases where the specimen was prior loaded with higher stresses (from 10 to 100 Pa), the longer the aging time of structure development before prior stress application, the lower the yield stress tested after subsequent cooling.
■
INTRODUCTION It is known that, at temperatures above the wax appearance temperature (WAT), wax in the crude oil is dissolved as molecules and the waxy crude oil behaves as a Newtonian fluid. At temperatures below the WAT, more and more wax crystals precipitate from the oil with decreasing temperature because of its supersaturation. The wax crystals thus formed have a gel-like structure, formed by a three-dimensional network of interlocking paraffin crystals that creates a highly porous yet rigid structure full of entrapped oil.1,2 Accordingly, the oil changes from a Newtonian fluid to a non-Newtonian fluid and exhibits complex rheological behaviors, such as viscoelasticity, thixotropy, and yield stress. Present studies show that, even on the condition of constant temperature, the characteristics of the physical gels of waxy crude oil undergo a change with quiescent duration, becoming harder and more stable.3−10 Lopes-da-Silva and Coutinho4 analyzed the kinetics of crystallization-induced gelation with the phenomenological Avrami model. They find that the nucleation and crystal-growth mechanisms and rates are dependent on the degree of supercooling. Visintin et al.5 claimed that, at temperatures below the pour point, the waxy crude oil studied behaves as a weakly attractive colloidal gel; the structural buildup coming from crystal formation and aggregation is favored by longer time. Coussot et al.6 considered that the spatial distribution of yield stress fluids may significantly evolve in time under the combined action of thermal agitation and attractive forces. The elements of the dispersed phase may eventually find an arrangement in which they are linked to the others by attractive forces, and the potential well is, in general, significantly deeper than that in the initial disordered dispersion. Rønningsen’s research7 about North Sea crude © 2012 American Chemical Society
oils showed that the extent of recovery depended on the breakdown strain rate; in terms of percent recovery of η0−ηe after 7 h of rest, it was 73% after shearing to equilibrium at 500 s−1. Perkins and Turner8 found that the yield stress of waxy crude oil after shearing could recover to the initial value after long enough time (65 h) of rest at constant temperature. Singh et al.9 explained the mechanism of aging by a diffusion transport within the porous structure of the gel driven by temperature−composition gradients. Coutinho et al.10 studied the aging process of paraffinic crudes with X-ray diffraction, cross polar microscopy, and differential scanning calorimetry (DSC) methods and proposed Ostwald ripening as another aging mechanism of wax deposits. In addition, some scholars11−14 reported that the structure of waxy crude/ model oil did not change with time, provided that the oil was kept isothermally. Venkatesan’s research15 denoted that the structure strength would not depend on the time of rest at constant temperature any more if the cooling rate was lower than a proper value (10 °F/min). Maybe the confusion of isothermal structure development should be contributed to the various cooling rates16 and the different properties of the specimens studied. It is well-known the rheological properties of waxy crude oil are dependent upon the shear and thermal histories that affect the wax crystal structure,17−20 and it would not be valuable to study the shear effect of waxy crude oil without consideration of Received: Revised: Accepted: Published: 10977
April 22, 2012 July 24, 2012 August 2, 2012 August 2, 2012 dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
Industrial & Engineering Chemistry Research
Article
Evolution of the viscoelastic parameters of the waxy crude oil during the cooling and isothermal processes is shown in Figure 1. A sharp increase in the viscoelastic moduli was observed
the thermal conditions. Currently, researchers study the shear effect of waxy crude oil mainly with different cooling rates5,7,15,18,20,21 or shear temperatures.4,5,7,11,17,21−24 However, few studies have been reported about the influence of isothermal structure development, i.e., the structural state before prior applied shearing, on the effect of shear history. Related researches3−14 were almost focused on the variations of viscoelasticity, yield stress, and viscosity with the isothermalholding duration, which reflects the structural evolution under quiescent and isothermal conditions. The objective of this study is to examine the variation of the gel strength after a combined effect of isothermal aging and stress was applied, followed by measurement of the static yield stress with subsequent cooling.
■
EXPERIMENTS
Material. The crude oil used in this study was a kind of typical waxy crude oil produced in the Daqing oilfield, the largest one in China, with a wax content of 24.1 wt %, a WAT of 39.0 °C, a pour point of 37 °C, and a specific gravity of 0.8624 at 20 °C. The WAT and wax content of the specimen were tested with the DSC method reported in our former work.17 The pour point was determined according to the ASTM method (D-5853). The conditioning treatment for the waxy crude oil prior to testing involved heating the sample to 80 °C for 2 h with stirring in a sealed glass bottle and cooling the sample naturally in the laboratory for measurement 2 days later. This method was first proposed by Yan and Luo.25 Rheometer Measurement. Rheological measurements were carried out using a coaxial cylinder sensor system Z41Ti of the HAAKE RS-150H controlled stress rheometer, which has an inner cylinder rotating in a stationary outer cylinder. A bob with a length of 55.00 mm and a diameter of 41.42 mm and a jacketed cup with a diameter of 43.40 mm were used to form a gap width of 0.99 mm. The temperature was controlled by a programmable water bath (F8/C35) with an accuracy of 0.1 °C. The procedure follows: (1) preheat the specimen and test segment of the rheometer to 50 °C; (2) load the specimen (12 mL) into the rheometer; (3) keep the specimen isothermally for 15 min; (4) cool the specimen to 34 °C at a constant rate of 0.5 °C/min; (5) age the specimen for 0, 30, or 60 min; (6) shear the specimen with a constant stress in the range of 1−100 Pa for 10 min; (7) cool the specimen to 32 °C at a constant rate of 0.5 °C/min and age it for 30 min; (8) measure the static yield stress at 32 °C with a ramping rate of 0.5 Pa/s; (9) change to a fresh specimen. In addition, the amount of crystallized wax was 1.53 and 2.19 wt % at temperatures of 34 and 32 °C, respectively.
■
Figure 1. Viscoelastic parameters versus time during the cooling and isothermal processes under quiescent conditions.
when the temperature reached a certain value below the WAT. Because the sol−gel transition was defined as the point at which the storage modulus became greater than the loss modulus,16 according to this criterion, the observed gelation temperature was 34.5 °C for the specimen. The isothermal structure development of the waxy crude oil was performed at 34 °C, in order to remain close to the gelation temperature. Li et al.27 proposed the relationship between the storage modulus and the isothermal duration, under quiescent conditions and based on the Zhongyuan waxy crude oils, as m (ln Gt′ − ln G∞′)/(ln G0′ − ln G∞′) = e−ct , where Gt′ is the storage modulus at time t, G0′ the initial modulus value (at t0), and G∞′ the pseudoequilibrium storage modulus. The variation of the storage modulus was fitted with this model, on the condition that the specimen was isothermally and quiescently held at 34 °C. The fitting result is shown Figure 1 (black triangles), where G0′ is 30.6 Pa, G∞′ is 752.4 Pa, c is 0.0378, and m is 0.5719. It should be found that the model can fit the experimental data well. Stress Application. After being held isothermally and quiescently for different times (0−60 min) at 34 °C, which represented different states of the waxy crystal structure, the specimens were loaded with stresses in the range of 1−100 Pa for 10 min. The strain rates of the waxy crude gels before removal of the loading stress are reported in Figure 2. It should be noted the gel fracture occurrence was observed if the applied stress was above 10 Pa, inasmuch as the strain rate was above 10 s−1, regardless of how long the isothermal duration for the structure development was before the stress loading. In cases where the stress loaded was in the range of 1−7 Pa, the gel fracture did not occur during the 10 min of stress application if the specimen aged for 30 min or more because the strain rate was less than 10−3 s−1. Besides, the specimens without isothermal structure development before the loading of stress ranged from 3 to 7 Pa yielded during the stress application. Accordingly, the prior loading stress was classified into two grades, the lower (1−7 Pa) and the higher (10−100 Pa), for subsequent analysis. It can be found that the longer the aging time before stress application, the lower the strain rate of the
RESULTS AND DISCUSSION
Isothermal Structure Development. Small-amplitude oscillatory shear was performed as preliminary and accessorial measurements to track the evolution of the wax crystal structure during the cooling and isothermal processes. The oscillation amplitude was controlled to obtain a 5 × 10−4 maximum strain in the specimen, which was the minimum reported in the literature,4,10,16,20,26 in order to avoid perturbation of the structure development caused by the measurement of solicitation. It has been previously shown that similar systems are quite sensitive to the applied strain and that this value is within the linear viscoelastic regime.24 The oscillation frequency was 0.5 Hz. 10978
dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
Industrial & Engineering Chemistry Research
Article
Figure 2. Strain rates of waxy crude gels before removal of the constant loading stress in the range of 1−100 Pa, after being isothermally and quiescently held for 0, 30, and 60 min at 34 °C.
waxy crude gel before removal of the lower stress, while the aging time has no obvious influence on the strain rate of the waxy crude gel before removal of the higher stress. Criterion of Yielding. After removal of the prior stress application, the specimen was cooled to 32 °C with a rate of 0.5 °C/min. Then, the yield stress of the gelled oil was determined after 30 min of aging, with the method of stress ramping at a rate of 0.5 Pa/s from 0. Nowadays, there exist different criteria for yielding judgment of the gelled crude oil. Venkatesan et al.15 took the inflection at which the strain begins to increase dramatically as the yield point. Chang et al.28 defined the inflection at which the strain rate starts to increase dramatically as the yield point. Howard et al.29 noted that the material creeps slowly at low stresses, while the apparent viscosity decreases exponentially after yielding. Figure 3 shows the evolution of the strain, the strain rate, and the apparent viscosity of gelled waxy crude gel upon stress ramping at 32 °C, on condition that the specimen was cooled quiescently without prior applied stress. In this study, we took the criterion for determining the yield point used by Venkatesan et al.15 The yield stress of the specimen without stress application was 38 ± 2 Pa at 32 °C, and the measurement was repeated four times to ensure reproducibility. Yield Behavior after the Lower Stress Application. The yield stresses of waxy crude gels, prior loaded with lower stresses at 34 °C after different isothermal durations and subsequent cooling to 32 °C, are shown in Figure 4. In the case of stress application without isothermal duration, the yield stress of the waxy crude gel was lower than that with isothermal durations of 30 and 60 min. If the gels were aging for 30 or 60 min before the prior stress loading, the yield stresses increased first and then decreased with an increase of prior loaded stress in the range of 1−7 Pa; accordingly, partial yield stresses were higher compared with the original yield stress of 38 Pa on average determined without prior stress application, while others were lower. Figure 5 reports the strain evolution during the prior stress application at 34 °C of waxy crude gels, which did not yield before removal of the prior loaded stress reported in Figure 2 (i.e., the waxy crude gels that had been isothermally and quiescently held for 30 and 60 min before the prior loading with stresses from 1 to 7 Pa and the gel prior loaded with a stress of 1 Pa without isothermal structure development). This
Figure 3. Evolution of the strain, strain rate, and apparent viscosity of the waxy crude gel upon stress ramping at 32 °C. The specimen was cooled from 50 to 32 °C at a rate of 0.5 °C/min quiescently and then aged for 30 min.
Figure 4. Yield stresses of waxy crude gels prior loaded with constant stresses in the range of 1−7 Pa at 34 °C, after different isothermal durations and subsequent cooling to 32 °C.
denotes that, with the same isothermal duration for the structure development before stress loading, the higher the loading stress, the higher the accumulated strain during the prior stress application; with the same loading stress, the longer the isothermal duration for the structure development before stress loading, the lower the accumulated strain during the prior stress application. On the basis of Figures 4 and 5, it can be found that, in cases where the accumulated strain during the prior stress application was in the range of 8.14 × 10−3−3.49 × 10−2, the yield values after subsequent cooling to 32 °C were 41.5−45.6 Pa. These values were higher (approximately 9−20% increase) compared with the original yield stress of 38 Pa on average at 32 °C determined without prior stress application. When the 10979
dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
Industrial & Engineering Chemistry Research
Article
higher stresses at 34 °C after different isothermal durations and subsequent cooling to 32 °C are shown in Figure 6.
Figure 5. Strain evolution of the waxy crude gels during the prior application of constant stresses in the range of 1−7 Pa at 34 °C. The specimens contain those held isothermally for 30 and 60 min before stress application and that loaded with the stress of 1 Pa without aging. Figure 6. Yield stresses of waxy crude gels prior loaded with constant stresses in the range of 10−100 Pa at 34 °C, after different isothermal durations and subsequent cooling to 32 °C.
−2
accumulated strains were in the range of 9.3 × 10 −1.26, lower yield values (31.4−35.5 Pa) were measured compared to the original value of 38 Pa on average (about 7−17% decrease). Besides, the accumulated strain of the gel prior loaded with a stress of 1 Pa after 60 min of aging was 6.5 × 10−3; the yield value after subsequent cooling to 32 °C showed no difference from the original. In the study of Oh et al.,11 the model oil gels were prior loaded with a stress of 90 Pa at 10 °C and cooled subsequently to 5 °C followed by the static yield stress measurement. It was found that, in cases of prior stress application in the creep compliance range of 1 × 10−4−4 × 10−4 Pa−1 (namely, in the creep strain range of 9 × 10−3−3.6 × 10−2) at 10 °C, the static yield values were much higher (approximately 16−32% increase) compared with the original yield stress determined without prior stress application, while when the compliance was increased to 5 × 10−4 Pa−1 (that is, a strain of 4.5 × 10−2), lower yield values were measured. This demonstrates that the effects of creep strain on the yield stress of the waxy crude oil and the model oil after subsequent cooling show the same regularity. The analyses above impart that there is a critical value of strain; that prior stress application in the limit of the critical strain may induce an increase in the compactness of the gel network, resulting in an increase of the gel yield stress after subsequent cooling. If the accumulated strain attributed to the prior stress application is above the critical strain, partial degradation of the gel strength results in a lower value of the yield stress after subsequent cooling. Because the network structure of the waxy crude gel undergoes a change to become harder during the aging time, a shorter time of aging before prior stress application can induce a higher value of accumulated strain, under the premise that the situations of stress application are the same (i.e., the stress loaded and the loading time are the same). Consequently, the situation of shorter aging time is easier to get a strain under the loading of lower stresses, which dominates over the critical strain and induces a lower yield stress value after subsequent cooling. According to the study of Oh et al.,11 the critical strain may be the threshold of the tertiary creep. Yield Behavior after the Higher Stress Application. The yield stresses of waxy crude gels prior loaded with the
In cases of stress application without isothermal structure development, the yield stress of the waxy crude gel was higher than that with isothermal durations of 30 and 60 min. This phenomenon was just contrary to that of the lower stress application. Besides, with the same prior loading stress and loading time, the longer the aging time of structure development before prior stress application, the lower the yield stress tested after subsequent cooling to 32 °C. Under each aging time of structure development before prior stress application, the yield stress at 32 °C decreased first and then increased with an increase in the prior loaded stress in the range of 10−100 Pa. Further, no matter how long the aging time before prior stress application was, the inflection point of the yield stress was that of prior loaded stress with a value of 30 Pa. It can be found in Figure 2 that, in cases where the prior loading stress was in the range of 10−100 Pa, the aging time of structure development before prior stress application has no obvious influence on the strain rate of waxy crude gels before removal of stress application. This means the apparent viscosities of waxy crude gels with different aging times before shearing are properly the same. According to the Krieger− Dougherty model,30 the relationship between the apparent viscosity of the suspension and the effective volume fraction is η = ηs(1 − ϕ /ϕm)−[η]ϕm, where η is the apparent viscosity of the suspension (Pa·s), [η] is the intrinsic viscosity of the solid phase, ϕm is the maximum volume fraction of solid particles, ηs is the viscosity of the liquid phase (Pa·s), and ϕ is the effective volume fraction of the solid. For the specimens held isothermally and quiescently for different periods of time before prior stress loading, the parameters [η], ηs, and ϕm are absolutely constant. Consequently, the aging time of structure development (i.e., the structural state) before prior stress application has little effect on the effective volume fraction of waxy crystals before removal of the prior loaded higher stress. Actually, the waxy crude gels were in the quasi-equilibrium state after 10 min of shearing with the constant stress in the range of 10−100 Pa, regardless of how long the aging time was before the prior stress application. 10980
dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
Industrial & Engineering Chemistry Research
Article
the diffusion coefficient yields D = RTσ1/3/(Na × 6πηraσc1/3), that is, D ∝ σ1/3. Accordingly, a higher loading stress corresponds to a smaller scale of particles,18,32 which induces intense diffusion. Therefore, with an increase of the loading stress, the strength of the initial structure of the wax crystals decreases, while diffusion of the particles/aggregates increases, which means a higher level of recovery. On the basis of the combined effect of these two different phenomena, after removal of prior stress application, the yield stress value of the waxy crude gel after subsequent cooling to 32 °C and aging for 30 min decreased first and then increased with an increase of the prior loading stress in the range of 10−100 Pa. In practice, the structural state of the waxy crude gel in the pipeline is approximately steady because of the slow rate of natural drop in the temperature, compared with the common situation in the laboratory. Once destroyed, it was quite difficult for the structure to recover to the initial state because of poor reversibility. Accordingly, restart pressures could be reduced by applying pressure during pipeline cooling, which can induce a strain dominating over the critical strain aforementioned before or yielding flow.
In the opinion of Coussot et al.,6 the spatial distribution of suspensions may significantly evolve in time under the combined action of thermal agitation and attractive forces. The aggregates/particles may eventually find an arrangement in which they are linked to the others by attractive forces. In this new arrangement, the potential well is, in general, significantly deeper than that in the initial disordered dispersion. Coutinho et al.10 present evidence indicating Ostwald ripening to be another aging mechanism of wax deposits: X-ray diffraction and cross polar microscopy indicate the kinetics of hardening of a wax crude oil kept at isothermal temperatures in the neighborhood of the pour point, to be caused by an increase of the crystallites’ size with time; but the DSC measurements do not show any detectable change of heat under isothermal conditions. Accordingly, lowly saturated thinner crystals dissolve, whereas thicker ones grow within close vicinity. According to the theories mentioned above, we can suppose that isothermal structure development in waxy crude oil attributes to the active small crystals. At constant temperatures, the active small crystals take part in the arrangement of wax crystal structures, so as to enhance the strength of the structure over the passage of time. Under yielding flow conditions, the combinations of the active small crystals with the large ones are limited because of the loading stress. Therefore, the small crystals that have not combined with the large ones still keep active after shearing and then participate in the structural recovery. Equal are the effective volume fractions of wax crystals in the waxy crude gels loaded in advance with constant stresses of 10−100 Pa for 10 min after different isothermal durations, indicating that the volume fraction of the active small crystals is tiny. However, the yield stresses of the specimens without isothermal duration before the prior stress loading are distinctly higher than those of the specimens aged for 30 or 60 min. This proves that, although the effective volume fraction is tiny, the active small crystals provide great contributions to the strength of the wax crystal structure. Maybe the active small crystals are mainly used to form the links between the aggregates. Interesting is the phenomenon that, under each aging time, the yield stress value tested at 32 °C decreases first and then increases with an increase in the stress prior loaded at 34 °C in the range of 10−100 Pa. Rønningsen7 indicated that there are two kinds of structures in the gel of waxy crude oil: a predominantly irreversible shear degradation of weak bonds taking place at low strain rates and a predominantly reversible (thixotropic) breakdown of stronger bonds at high strain rates. What merits our attention is that Richard et al.20 considered that the behavior of the wax crystal gel is characteristic of weaklink gels for which the yield occurs at links between flocs rather than internal to flocs. Snabre and Mills31 considered that the relationship between the critical scale of aggregates and the loading stress in weakly flocculated suspension satisfies the relation Rc = a(σ/σc)−1/3, where Rc is the critical scale of the aggregates (m), σ the shear stress (Pa), σc the strength of links between the particles in the aggregates (Pa), and a the scale of a single particle (m). Consequently, the higher the shear stress, the smaller the wax crystal aggregates at the equilibrium state. According to the diffusion law in colloidal chemistry, the diffusion coefficient D = RT/(Na × 6πηr), where R is the universal gas constant [J/(mol·K)], T the temperature (K), Na Avagadro's constant 6.02 × 1023 mol−1, η the viscosity of the medium (Pa·s), and r the scale of the particle (m). Substituting the equation proposed by Snabre and Mills into the equation of
■
CONCLUSION
■
AUTHOR INFORMATION
The gel behavior of the waxy crude oil was examined by measuring the static yield stress of prior stress applied gels after different times of aging and subsequent cooling. The structure strength of the waxy crude gel increased with isothermal and quiescent holding at a temperature of 34 °C, which is close to the gelation point, while reversibility of the gel structure decreased. Under the prior application of lower stresses (from 1 to 7 Pa), as the structure undergoes a change to become stronger with time evolution, the situation of shorter aging time is easier to get a strain over the critical strain, which means the start of structure degradation, and hence induces a lower yield stress value after subsequent cooling. Under the prior application of higher stresses (from 10 to 100 Pa), because of poorer reversibility, the longer the aging time of structure development before prior stress application, the lower the yield stress tested after subsequent cooling to 32 °C. On the basis of the combined effect of structure degradation and diffusion, the yield stress tested after subsequent cooling to 32 °C decreased first and then increased with an increase of prior loaded stress in the range of 10−100 Pa, under each aging time of structure development before prior stress application.
Corresponding Author
*Tel: 86-108 973 4627. Fax: 86-108 973 4627. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The authors express heartfelt thanks to Dr. Bo Yu, Dr. Lei Hou, and Dr. Hongying Li for fruitful discussions and to the Research Project for Supervisors of Beijing Excellent Ph.D. Dissertations (YB20081141401) and the National Natural Science Foundation of China (Grant 51134006) for support. 10981
dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
Industrial & Engineering Chemistry Research
■
Article
(24) Li, C. X.; Yang, Q. Z.; Lin, M. Z. Effects of stress and oscillatory frequency on the structural properties of Daqing gelled crude oil at different temperatures. J. Pet. Sci. Eng. 2009, 65, 167−170. (25) Yan, D. F.; Luo, Z. M. Rheological Properties of Daqing Crude Oil and Their Application in Pipeline Transportation. SPE Prod. Eng. 1987, 2, 267−276. (26) Magda, J. J.; El-Gengy, 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 2009, 23, 1311−1315. (27) Lin, M. Z.; Li, C. X.; Yang, F.; Ma, Y. Isothermal Structure Development of Qinghai Waxy Crude Oil after Static and Dynamic Cooling. J. Pet. Sci. Eng. 2011, 77, 351−358. (28) Chang, C.; Boger, D. V. The Yielding of Waxy Crude Oils. Ind. Eng. Chem. Res. 1998, 37, 1551−1559. (29) Barnes, H. A. The yield stressa review or ‘παντα ροι’ everything flows? J. Non-Newtonian Fluid Mech. 1999, 81, 133−178. (30) Krieger, I. M. Rheology of monodisperse lattices. Adv. Colloid Interface Sci. 1972, 3, 111−136. (31) Snabre, P.; Mills, P. Rheology of Weakly Flocculated Suspensions of Rigid Particles. J. Phys. III Fr. 1996, 6, 1811−1834. (32) Kanè, M.; Djabourov, M.; Volle, J.-L.; Lechaire, J.-P.; Frebour, G. Morphology of paraffin crystals in waxy crude oils cooled in quiescent conditions and under flow. Fuel 2003, 82, 127−135.
REFERENCES
(1) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Multicomponent paraffin waxes and petroleum solid deposits: structural and thermodynamic state. Fuel 1998, 77, 1253−1260. (2) Singh, P.; Fogler, H. S.; Nagarajan, N. Prediction of the wax content of the incipient wax−oil gel in a pipeline: An application of the controlled-stress rheometer. J. Rheol. 1999, 43, 1437−1459. (3) Cordoba, A. J.; Schall, C. A. Solvent migration in a paraffin deposit. Fuel 2001, 80, 1279−1284. (4) Lopes-da-Silva, J. A.; Coutinho, J. A. P. Analysis of the Isothermal Structure Development in Waxy Crude Oils under Quiescent Conditions. Energy Fuels 2007, 21, 3612−3617. (5) Visintin, R. F. G.; Lapasin, R.; Vignati, E.; D’Antona, P.; Lockhart, T. P. Rheological behavior and structural interpretation of waxy crude oil gels. Langmuir 2005, 21, 6240−6249. (6) Coussot, P.; Tocquer, L.; Lanos, C.; Ovarlez, G. Macroscopic vs. local rheology of yield stress fluids. J. Non-Newtonian Fluid Mech. 2009, 158, 85−90. (7) Rønningsen, H. P. Rheological behaviour of gelled waxy North Sea crude oils. J. Pet. Sci. Eng. 1992, 7, 177−213. (8) Perkins, T. K.; Turner, J. B. Starting Behavior of Gathering Lines and Pipelines Filled with Gelled Prudhoe Bay Oil. JPT, J. Pet. Technol. 1971, 23, 301−308. (9) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. Formation and aging of incipient thin film wax−oil gels. AIChE J. 2000, 46, 1059−1074. (10) Coutinho, J. A. P.; Lopes-da-Silva, J. A.; Ferreira, A.; Soares, M. R.; Daridon, J. L. Evidence for the aging of wax deposits in crude oils by Ostwald ripening. Pet. Sci. Technol. 2003, 21, 381−391. (11) Oh, K.; Jemmett, M.; Deo, M. Yield Behavior of Gelled Waxy Oil: Effect of Stress Application in Creep Ranges. Ind. Eng. Chem. Res. 2009, 48, 8950−8953. (12) Wardhaugh, L. T.; Boger, D. V. The Measurement and Description of the Yielding Behavior of Waxy Crude Oil. J. Rheol. 1991, 35, 1121−1156. (13) Chang, C.; Boger, D. V.; Nguyen, Q. D. Influence of Thermal History on the Waxy Structure of Statically Cooled Waxy Crude Oil. SPE 2000, 5, 148−157. (14) Ekweribe, C.; Civan, F.; Lee, H. S.; Singh, P. Effect of System Pressure on Restart Conditions of Subsea Pipelines. SPE115672 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, Sept 21−24, 2008. (15) Venkatesan, R.; Nagarajan, N. R.; Paso, K.; Yi, Y.-B.; Sastry, A. M.; Fogler, H. S. The strength of paraffin gels formed under static and flow conditions. Chem. Eng. Sci. 2005, 60, 3587−3598. (16) Lopes-da-Silva, J. A.; Coutinho, J. A. P. Dynamic rheological analysis of the gelation behaviour of waxy crude oils. Rheol. Acta 2004, 43, 433−441. (17) Ding, J. L.; Zhang, J. J.; Li, H. Y.; Zhang, F.; Yang, X. J. Flow Behavior of Daqing Waxy Crude Oil under Simulated Pipelining Conditions. Energy Fuels 2006, 20, 2531−2536. (18) Kané, M.; Djabourov, M.; Volle, J.-L. Rheology and structure of waxy crude oils in quiescent conditions and under shearing conditions. Fuel 2004, 83, 1591−1605. (19) Mewis, J.; Norman, J. W. Current trends in suspension rheology. J. Non-Newtonian Fluid Mech. 2009, 157, 147−150. (20) Webber, R. M. Yield Properties of Wax Crystal Structures Formed in Lubricant Mineral Oils. Ind. Eng. Chem. Res. 2001, 40, 195− 203. (21) Lorge, O.; Djabourov, M.; Brucy, F. Crystallisation and gelation of waxy crude oils under flowing conditions. Oil Gas Sci. Technol. 1997, 52, 235−239. (22) El-Gamal, I. M. Combined effects of shear and flow improvers:the optimum solution for handling waxy crudes below pour point. Colloids Surf., A 1998, 135, 283−291. (23) El-Gamal, I. M.; Gad, E. A. M. Low-temperature rheological behavior of Umbarka waxy crude and influence of flow improver. Colloids Surf. 1998, 131, 181−191. 10982
dx.doi.org/10.1021/ie301047g | Ind. Eng. Chem. Res. 2012, 51, 10977−10982
