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Rheological Behavior and Structural Interpretation of Waxy Crude Oil Gels Ruben F. G. Visintin,‡ Romano Lapasin,‡ Emanuele Vignati,° Paolo D’Antona,† and Thomas P. Lockhart*,† DICAMP, Universita` di Trieste, piazzale Europa 1, 34127 Trieste, Italy, CSGI-Politecnico Milano, piazza Leonardo da Vinci, Milano (MI), Italy, and EniTecnologie, via Maritano 26, 20097 San Donato Milanese (MI), Italy Received March 16, 2005. In Final Form: May 2, 2005 A waxy crude oil which gels below a threshold temperature has been investigated under static and dynamic conditions, using a combination of rheological methods, optical microscopy, and DSC. Particular attention is given in this work to the influence of the mechanical history on gel strength and to describing the time-dependent rheological behavior. The gels display a strong dependence of the yield stress and moduli on the shear history, cooling rate, and stress loading rate. Of particular interest is the partial recovery of the gel structure after application of small stress or strain (much smaller than the critical values needed for flow onset) during cooling, which can be used to reduce the ultimate strength of the crude oil gel formed below the pour point. A second focus of this study is to further develop the physical interpretation of the mechanism by which wax crystallization produces gelation. Gelation of the waxy crude oil studied is suggested to be the result of the association between wax crystals, which produces an extended network structure, and it is shown that the system displays features common to attractive colloidal gels, for one of which, fumed silica (Aerosil 200) in paraffin oil, rheological data are reported. The colloidal gel model provides a simple and economical basis for explaining the response of the gelled oil to various mechanical perturbations and constitutes a fruitful basis from which to develop technologies for controlling the gelation phenomenon, as suggested by the rheological results reported.
Introduction The phase separation of waxy (paraffinic) solids from crude oil constitutes a major operating issue for the petroleum industry.1,2 While crude oils are extracted as a single organic phase from the reservoir, low temperatures encountered at the surface or during transport in subsea pipelines can lead to the separation of highermolecular-weight paraffins, mostly covering the range from C18 to C65.3 The phase stability of the wax component of crude oils (or distillates such as diesel) is defined by the cloud point, CP, the temperature at which the first wax crystals appear during cooling. Below the CP, many oils undergo a gel transition at what is referred to as the pour point (PP). Below the PP, the oil no longer flows but rather displays the rheological properties of a viscoelastic solid. Under flow conditions, wax deposits can form upon pipe walls at temperatures below the CP, leading ultimately to severe or total loss of flow. Where the surrounding ambient conditions are lower than the PP, a condition frequently encountered in subsea pipelines, interruption of flow will lead to cooling of the oil and, ultimately, gelation. In this case, successful restart of production depends on the ability to pressurize the pipeline sufficiently to cause gel breakdown and flow. In rheological terms, the restart problem is connected with the yield behavior of the oil; much investigation has been dedicated to this property of crude oils and to * Author to whom correspondence should be addressed. E-mail:
[email protected]. ‡ Universita ` di Trieste. ° CSGI-Politecnico Milano. † EniTecnologie. (1) Moritis, G. Oil Gas J. 2001, 99, 1, 67. (2) Venkatesan, R.; Singh, P.; Fogler, H. S. SPE J. 2002, 7, 349. (3) Srivastava, S. P.; Handoo, J.; Agrawal, K. M.; Joshi, G. C. J. Phys. Chem. Solids 1993, 54, 639.
predicting pipeline flow from rheological data.4-7 Interestingly, a recent study has suggested that the wax deposits formed on pipeline walls at temperatures intermediate between the CP and the PP possess a gel-like structure and that their properties (including sensitivity to shear) will be similar to those of the bulk gels formed below the PP.8 In the present paper, emphasis is placed upon better defining the low-temperature structural and rheological characteristics of gelled crude oils, with particular reference to the influence of the mechanical history on gel strength, the response of the gels to shear forces, and time-dependent phenomena. We will show that the waxy crude oil gel studied possesses properties found for associative colloidal gels, including their sensitivity to shear and partial recovery, and identify possible routes to reducing the pressure required to restart flow in plugged pipelines. Crystalline Structure of Waxy Systems. Though paraffin crystallization in waxy crude oils has been the object of study for more than 80 years,9 controversies still exist regarding the characteristics (shape and average size) of the crystals, principally because of problems related to the repeatability of sample preparation and measurement, misleading image interpretation, and the strong dependence on the conditions of crystallization (e.g., speed (4) Wardhaugh, L. T.; Boger, D. V. J. Rheology 1991, 35, 1121. (5) Rønningsen, H. P. J. Pet. Sci. Eng. 1992, 7, 177. (6) Chang, C.; Boger, D. V.; Nguyen, Q. D. Ind. Eng. Chem. Res. 1998, 37, 1551. (7) Chang, C.; Nguyen, Q. D.; Rønningsen, H. P. J. Non-Newtonian Fluid Mech. 1999, 87, 127. (8) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J. 2000, 46, 1059. (9) Padgett, F. W.; Hefley, D. G.; Henriksen, A. Ind. Eng. Chem. 1926, 18, 832.
10.1021/la050705k CCC: $30.25 © 2005 American Chemical Society Published on Web 06/11/2005
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of cooling and crude oil composition).10 The main categories of crystalline forms that have been visualized in different paraffinic systems are plates, needles, and spherulitic and ill-defined masses of crystals, where these crystal masses are approximately spherical in shape and appear to be comprised of very thin wax sheets (cluster cross section ca. 2-10 µm). Examination of the photomicrographs reported by Ferris et al.11 and others12-14 (and in the present work) suggests that these crystalline masses can be classified as fractal objects. NMR10 and X-ray diffraction analyses15 have shown that the solid phase of gelled crude oils is mainly crystalline, with only a small amorphous fraction. Crude oils generally contain considerable amounts of branched and cyclic paraffins; in some oils prone to gelation, these even dominate over the respective n-paraffins.16 Observations on one crude oil showed that the paraffin wax solids were composed not only of n-paraffins but also of isoparaffins and cyclic compounds, which in fact constituted the largest fraction;16 Rønningsen et al. have suggested that increasing isoparaffin fractions tend to favor microcrystalline or amorphous wax solids.16 The ways in which these influence gelation remains to be fully clarified. We have found, however, that n-paraffins dissolved in organic solvents display a sharp transition in gel strength at the PP, whereas for crude oils, the buildup in gel strength as a function of temperature below the PP is much more gradual. This behavior can be obtained by addition of isoparaffins.17 Certainly, care should be taken in extrapolating results obtained for highly simplified systems (e.g., n-paraffins dissolved in organic solvents) to crude oils. The extreme compositional complexity of and the differences between crude oils18,19 constitute a particularly challenging aspect of studies on crude oil behavior and suggest that some degree of variation in aggregate structures and physical behavior may be expected, a priori, for different oils. In terms of their PP, some crude oils gel as high as 30 °C while others remain fluid to below -20 °C. Also, the difference in temperature between the CP and PP for a given oil can range from 10 to 60 °C. In general terms, disk-shaped or sheetlike crystals are most commonly found, with dimensions typically of the order of a few micrometers or less,10,15 although they are most often present as densely associated crystalline masses as noted above. By means of DSC14,20 and other techniques,21 it has been found that gelation of crude oil and oil distillates takes places when as little as 1-6% of wax solids have separated from solution.10,14,16,22,23 (10) Kane´, M.; Djabourov, M.; Volle, J.; Lechaire, J.; Frebourg, G. Fuel 2003, 82, 127. (11) Ferris, S. W.; Cowles, H. C. Ind. Eng. Chem. 1945, 37, 1054. (12) Chang, C.; Boger, D. V.; Nguyen, Q. D. SPE J. 2000, 5, 148. (13) He´naut, I.; Vincke´, O.; Brucy, F. SPE 56771, SPE Annual Technical Conference and Exhibition, October 3-6, 1999, Houston, Texas. (14) Le´toffe´, J. M.; Claudy, P.; Kok, M. V.; Garcin, M.; Volle, J. L. Fuel 1995, 74, 810. (15) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Fuel 1998, 77, 1253. (16) Rønningsen, H. P.; Bjorndal, B. Energy Fuels 1991, 5, 895. (17) Manuscript in preparation. (18) Kalichevsky, V. A.; Kobe, K. A. Petroleum Refining with Chemicals; Elsevier Publishing Company: Amsterdam, 1956. (19) Thanh, N. X.; Hsieh, M.; Philp, R. P. Org. Geochem. 1999, 30, 119. (20) Hansen, A. B.; Larsen, E.; Pedersen, W. B.; Nielsen, A. B.; Rønningsen, H. P. Energy Fuels 1991, 5, 914. (21) Hansen, A. B.; Larsen, E.; Pedersen, W. B.; Nielsen, A. B.; Rønningsen, H. P. Energy Fuels 1991, 5, 908. (22) Holder, G. A.; Winkler, J. J. Inst. Pet. 1965, 235. (23) Webber, R. M. Ind. Eng. Chem. Res. 2001, 40, 195.
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At a more microscopic level, wax crystallization and gelation proceeds in several phases, the first of which is believed to be the formation of lamellar subcrystals comprised of a solid solution of the paraffinic components in which mismatches between the length of the molecules comprising the crystal and in the thickness of the packing layer cause conformational disorder in the interlamellar regions of the crystals.8 Evidence from several sources indicates lamellar thicknesses of ca. 1.5-3 nm,10,15,24 corresponding roughly to the length of a linear C20 paraffin, and interlamellar distances from 30 to 100 nm.10 The disorder in the interlamellar region favors growth of these subcrystals in two dimensions as sheetlike crystals. The next stage in the process is the subject of some debate, although we note that the presence of spherulites or massed, sheetlike crystals suggests that these subcrystals further associate into a second sort of “elementary structure” of micrometer-size incorporating a large volume of solvent. These finally aggregate to form the large spacefilling network seen in photomicrographs (see also below). Clearly, the crystallization and aggregation processes invoked could be influenced by shear at many stages. Colloidal Gels and Waxy Crude Oil Gels. With the term colloidal gel, we refer to a coherent dispersed system comprised of at least two components, one of which is a liquid present in significant amount, that displays solidlike linear viscoelasticity and a series of yield properties (e.g., yield stress). At least three types of colloidal gels can be defined on the basis of the physical interactions underlying their formation. Where there are attractive interactions between the particles, the gels can form even at very low volume fractions and the particles form fractal clusters: the dispersed component extends continuously throughout the whole system, which ultimately percolates to form space-filling networks.25,26 A second class of colloidal gels forms in the presence of polymeric compounds, which can also promote particle aggregation, either through their adsorption (bridging flocculation) or nonadsorption (depletion flocculation) at the particle surface.27 A third class of gels can be formed when there are repulsive interactions between the particles: at a sufficiently high dispersed phase concentration, the double layers surrounding the colloidal particles overlap, at least partially, reducing particle diffusion and leading to the formation of a stiff repulsive gel28 (“colloidal glass” would be a more correct term for this case). Of these three, strong electrostatic interactions are unlikely in the essentially nonpolar medium of the crude oil, ruling out this mechanism for gelation. The second class, based on bridging or depletion flocculation, also seems difficult to apply to crude oil in which high-molecular-weight components are essentially absent (although the moderately surface-active asphaltene and resin fraction can have average molecular weights of up to ca. 1000 g/mol);29 most convincingly, gels with rheological properties similar to crude oils can be prepared by dissolving mixed n- and isoparaffins in organic solvents in which no polymeric species are present.17 The gelation of waxy crude oils has long been attributed to interactions between the wax crystals, although the (24) Radlinski, A. P.; Barre´, L.; Espinat, D. J. Mol. Struct. 1996, 51, 383. (25) Varadan P.; Solomon, M. J. Langmuir 2001, 17, 2918. (26) Almdal, K.; Dyre, J.; Hvidt, S.; Kramer, O. Polym. Gels Networks 1993, 1, 5. (27) Burns, J. L.; Yan, Y.; Jameson, G. J.; Biggs, S. Colloids Surf., A 2000, 162, 265. (28) Wierenga, A.; Philipse, A. P.; Lekkerkerker, H. N. W.; Boger, D. V. Langmuir 1998, 14, 55. (29) Sheu, E. Y.; Mullins, O. C. Asphaltenes: Fundamentals and Applications; Plenum Press: New York, 1995.
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nature of these have remained poorly defined. Holder and Winkler,22,30 for example, cited the “overlapping and interlocking” structure of the platelets (formed in distillates). Others have referred to the formation of a “network” of wax crystals resulting from the “strong interaction and affinity” between the crystals8 or invoked the “flocculation” of wax crystallites as soon as they form in the solution.15 However qualitative, these descriptions are certainly compatible with a colloidal gel model for waxy oils, i.e., gelation resulting from attractive interparticle forces. Rønningsen, on the other hand,5 recalled an earlier model in which gelled oil is compared to polymer gels, and the yielding behavior likened to the “rupture of bond linkages within the network.” He´naut et al. invoked the aggregation of wax crystals as responsible for network formation and suggested that crude oil gels belong to the class of thermoreversible strong gels.13 In a recent study on gels formed from what can be considered a highly idealized, model system (single carbon number, high-molecular-weight n-paraffins dissolved in an n-paraffin solvent), it was pointed out that London dispersion forces are the sole attractive interaction present in the system.31 We note that the micrometer-sized wax crystals formed, and their marked tendency to associate into dense crystalline masses, together with the low concentration of wax solids required for gelation, provide important clues that waxy crude gels belong to the broad family of attractive colloidal gels. A rather different structural hypothesis was recently formulated by Kane´ et al.,10 who presented transmission electron microscopy (TEM) results interpreted as providing evidence for the growth, in quiescent conditions, of the molecular-thickness subcrystals to continuous, macroscopic dimensions via “overlapping” of the growing subcrystals. This was hypothesized to result in the formation of tightly bound, spatially continuous layers, in which the interaction between the lamella is responsible for the high shear modulus. TEM images on crude oil sheared strongly during cooling and then quenched at low temperature revealed only sub-micrometer-sized aggregates. Shear forces were thus interpreted as preventing gelation by blocking lateral growth of the individual disks. In this model, an essential distinction is made between the wax crystal fragments and the larger structures whose formation during gelation is required to generate a reticulated network. This description would appear to rule out the possibility of gelation after shearing (at constant temperature), inasmuch as the basic structural unit essential to gelation (i.e., extended, continuous lamellae) has been destroyed or prevented from forming. Nevertheless, the authors themselves report that, “upon halting shearing there was a rapid increase in the storage modulus and the suspension recovers a solid-like behavior by ‘healing’ of the structure.” We report below on the rehealing of crude oil gels, which shows that the sheared gels still contain the essential elements (i.e., the constituent colloidal wax solids) required for gelation. Experimental Section Materials. The sample investigated is a paraffinic crude oil (Oil A) whose chemical physical properties are given in Table 1. Its rheological properties were studied in the temperature range between 5 and 60 °C. The minimum temperature considered is lower than the PP (21 °C) determined. The conditioning treatment for Oil A prior to testing involved heating the sample to 50 °C for 1 h while stirring in a beaker. Observation under optical microscopy indicated that no wax (30) Holder, G. A.; Winkler, J. J. Inst. Pet. 1965, 228. (31) Abdalla, D. J.; Weiss, R. G. Langmuir 2000, 16, 352.
Visintin et al. Table 1. Physical-Chemical Properties of Oil A parameter
standard test method
value
API gravity [°API] pour point [°C] cloud point [°C] wt% wax wt% asphaltene
table ASTM D ASTM D97/93 by DSC measurement BP 237/90 IP 143/96
25 21 30 6 4
existed after the samples were heated to the selected maximum temperature, and experimental results showed good repeatability. The fumed silica employed to form colloidal gels was Aerosil A200 (Degussa), characterized by a superficial area of 200 ( 25 m2/g and an average particle diameter of 12 nm. The fumed silica was first dried in an oven at 105 °C for at least 48 h in order to remove all humidity and then mixed into mineral oil (Paraffin Oil 76235, CAS Number 8012-95-1, from Fluka) by means of a four-blade mechanical stirrer. Bubbles, when present, were eliminated prior to rheological measurement via centrifuging of the sample. DSC. All analyses were performed using a Perkin-Elmer DSC-7 differential scanning calorimeter. The temperature scale was calibrated using a two-point calibration, measuring the onset temperatures of indium and zinc standards. The enthalpy scale is calibrated using the observed ∆H from an accurately known amount of indium. Crude oil samples were transferred in aluminum pans, typically between 0.5 and 30 mg: to obtain a good signal-to-noise ratio, almost 10 mg of sample was employed for each measurement. A blank pan was used on the reference side. The cooling rates used were 10, 5, 2, and 1 °C/min. Data acquisition and processing was carried out using Perkin-Elmer software (Pyris). Microscopy. Oil A was heated to 50 °C for 1 h before being placed in the measurement cell at 50 °C. Samples were observed with an Olympus IX70 inverted microscope with a 100× oil immersion objective and photographed with an Olympus DP50 digital camera. Images were analyzed with the video acquisition/ elaboration software Image-Pro Plus 4.5 (Media Cybernetics). The microscope was operated with polarized light in the crossedpolarizers configuration; thus, only light coming from the sample’s depolarizing areas reached the detector. The sample was kept in a temperature-controlled custom cell mounted on the microscope’s stage. A short description of the experimental setup follows. An aluminum slab with a central hole was thermally connected to a Peltier modulus (CP 1.4-71-06L, Melcor) driven by a temperature-controlled modulus (LFI-3751, Wavelength Electronics). The sample’s temperature was measured by a thermistor attached to the slab, which was insulated by thick Teflon layers. The sample was placed between two microscope coverslides, one of which was in thermal contact with the slab and aligned with the central hole in order to allow for observation. The temperature-control modulus, wired to a PC, was controlled by a custom software developed in Labwindows-CVI (National Instruments). Both fast (up to 10 °C/min) and very slow thermal ramps with fixed rate are possible, the temperature set point being changed automatically every minute. The system was calibrated by placing a small thermistor within the sample and recording differences between the temperature set-point and the sample temperature in order to allow compensation during measurements. The custom cell is able to keep the sample temperature fixed for days with suitable precision (0.1 °C). Rheology. Rheological measurements were carried out using controlled-stress (DSR200 by Rheometric Scientific and RS 150 by Haake) and controlled-strain rheometers (RFSIII by Rheometric Scientific) equipped with different geometries (helical, vane, couette, cone and plate, and parallel plate) depending on the temperature and viscosity of the sample. Helical, vane geometries and serrated parallel plates were used to avoid slippage effects at low stress/strain, particularly at low temperature. Temperature was controlled by a thermal bath. The rheometer geometries providing the greatest control over temperature are those based on parallel plates and cone/plate. Temperature control of the bottom plate is optimal, with negligible deviations from the set point. To eliminate possible effects of air currents on the temperature imposed, a glass cover was placed over the cell.
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Figure 1. Storage (thin line) and loss (thick line) moduli versus temperature for the crude oil in cure tests at two different cooling rates: 1 (a) and 0.05 °C/min (b). The rheometer was statically cooled from the starting temperature (typically 50 °C) to the testing temperature according to the programmed cooling rate (from 0.05 to 1 °C/min). Each final rheological test was performed isothermally at the test temperature. Various cooling rates under constant shear and at various isothermal holding times were performed in order to evaluate the influence of the cooling process on the wax crystal structure. More details referring to the cooling programs and the testing are described in the Results and Discussion section and in the figure captions. Both steady-state and oscillatory measurements were carried out. Steady-state measurements were conducted in order to evaluate viscosity (η0 and η∞) and yield stress from the flow curve profile η (viscosity) vs σ (stress). The stress range investigated was 0.01-1000 Pa. In the controlled stress test, each shear stress was applied long enough to reach the stationary state at each testing temperature. Oscillatory measurements at small amplitude (small enough not to disturb the waxy structure) were carried out in order to obtain information on the kinetics of gel formation as a function of temperature and on the strength of waxy oil gel formed. The strain and strain rate were measured during the oscillatory tests in order to calculate the storage modulus (G′) and the loss modulus (G′′) as a function of time (up to 4 h), temperature (from 50 to 10 °C), and frequency (from 0.1 to 100 rad/s).
Result and Discussion 7,12
As noted by others, waxy crude oils exhibit complex rheological behavior across the sol-gel transition on account of their marked shear- and time-dependent properties, which are strongly affected by the previous mechanical and thermal histories. Consequently, the experimental plan was subdivided into different segments in order to analyze separately the effect of each variable. In the latter part of this section, comparisons are made to colloidal gels and the sensitivity to shear and the partial rehealing of the waxy crude oil gels are explored. Effect of Cooling Rate. The kinetics of gelation under cooling conditions were evaluated in time cure tests performed at constant frequency (1 Hz) and at a strain amplitude, γ ) 0.0015, within the linear viscoelastic regime. Samples were loaded in the helical geometry of the control stress rheometer, heated to 35 °C for 15 min, and their viscoelastic moduli measured as they were cooled to 15 °C at a constant cooling rate of 0.05, 0.5, or 1 °C/min. Both viscoelastic moduli increase with decreasing temperature (Figure 1). The greater increase in the storage modulus (G′) during cooling leads to a crossover with the loss modulus (G′′) and then to prevailing elasticity at lower temperatures, confirming the structural transition to the
Figure 2. Time variation of G′ and G′′ under isothermal conditions (15 °C), after curing tests at different cooling rates (0.05, 0.5, 1 °C/min).
gel state. As seen in Figure 1, the slower the cooling rate, the higher is the G′ value, in accordance with Chang et al.,12 and the crossover condition is shifted to higher temperature. This means that the structural build-up arising from crystal formation and aggregation is favored by longer times and leads to more extended gel microdomains within the gel network. Figure 2 reports the isothermal change of G′ and G′′ with time for the different cooling rates after the sample has reached the reference temperature (15 °C). Noteworthy is the persistence over time of the effect of the cooling rate, which suggests that the microstructures of the gels formed are irreversibly determined by the cooling rate. The differences in G′ values in fact persisted for 16 h after the end of cooling, suggesting that the equilibrium value of the gel strength can be associated with the asymptotic plateau value G′∞ (identical considerations hold for the loss modulus). The time evolution of viscoelastic moduli can be described by a stretched exponential function:
G - G0 ) 1 - exp(-(t/tcr)n) G∞ - G 0
(1)
where n is set equal to 2/3. For both moduli, the asymptotic
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Table 2. Parameters Used in the Model Described by Eq 1 cooling rate [°C/min] 0.05 0.50 1.00
storage modulus (G′) G′∞ [Pa] t′cr [s] 22 719 10 351 8095
where
loss modulus (G′′) G′′∞ [Pa] t′′cr [s]
6923 1831 1586
7363 3005 2098
9651 1887 919
value, G∞, and the critical time, tcr, decrease with increasing cooling rate (Table 2). Optical microscopy was employed to gain further insight into the differences observed. Figure 3a and b refers to samples cooled to 15 °C with the minimum and maximum cooling rates reported above, respectively. The pictures were taken after equal holding times (4 h) under isothermal conditions. In the sample cooled most slowly (0.05 °C/min), the wax crystals are arranged around nucleation centers, forming extended islands, which are larger than those observed after the fastest cooling (1 °C/min). In the latter case, the crystals are distributed more uniformly within the sample and are collected into smaller and loose clusters that tend to fill the whole space. The lower brightness of aggregates formed at the faster cooling rate denotes lower depolarization and reflects their lower compactness. The resulting network is more regular but thinner; this different spatial arrangement of the dispersed phase can reasonably explain the weaker mechanical properties of the sample, in particular the lower G′ values observed during the isothermal test. Effect of Temperature on the Gel Strength. The previous results showing the influence of the thermal history were kept in consideration in the study of the temperature dependence of the rheological properties, in particular of the gel strength. The samples were heated to 50 °C and then statically cooled at the faster cooling rate (1 °C/min) to the temperature (between 35 and 5 °C) selected for the isothermal test. Once at the final temperature, a stepwise sequence of increasing stresses (logarithmically scaled in the range of interest) was applied. During each step, the stress was kept constant for 10 min. As shown in Figure 4, the viscous behavior of the sample changes from Newtonian (viscosity constant and independent of the applied stress) to shear thinning (viscosity decreases with increasing stress) in the range of temperature between 35 and 30 °C and becomes apparently plastic at lower temperatures. This plastic behavior is characterized by a dramatic decrease in viscosity which covers more than four decades in a narrow stress range. This means that an apparent yield stress can be arbitrarily located within this range, as though a minimum force were necessary to produce an appreciable flow of the system. Indeed, the strain rate values corresponding to the first Newtonian plateau are very low and result, at most, in quite limited deformations, even when the corresponding stress is applied for long times. The same yield condition is associated with a critical strain that must be reached in order to pass from continuous deformation to real flow; this also implies time dependence of the yield stress (see below). The flow curves can be described quite satisfactorily, as shown in the figure, with the Roberts-Barnes-Carew model:32
η - η′∞ 1 ) η′0 - η′∞ 1 + (σ/σ )m C
(2)
(32) Roberts, G. P.; Barnes, H. A.; Carew, P. Chem. Eng. Sci. 2001, 56, 5617.
η′0 )
η0 1 + (σ/σ1)P
(3)
and
η′∞ ) η∞[1 + (σ/σ2)S]
(4)
where the most significant parameters are the zero-shear rate viscosity, η0, the infinite-shear rate viscosity, η∞, and the critical stress, σ1. The parameters η0 and η∞ define the two limiting Newtonian behaviors at low and high stresses, respectively, whereas σ1 can be identified with the apparent yield stress. The values of these parameters are reported in Table 3. These quantities can be conveniently plotted vs reciprocal temperature (Figure 5) in order to better define the sol/gel transition interval. Significant observations can be drawn from the linear asymptotic branches of the zeroshear rate viscosity, η0, and the infinite-shear rate viscosity, η∞. Indeed, the temperature dependence of viscosity is satisfactorily described by the Andrade-Eyring equation η ) A exp(E/RT), where A is the pre-exponential constant and E is the flow activation energy. At higher temperature (sol state), the behavior is Newtonian and characterized by low activation energy (Esol ) 27.3 kJ/ mol). In the gel state, the Newtonian viscosities η0 and η∞ diverge with decreasing temperature because of the large difference in the flow activation energies (Egel,0 ) 222 kJ/ mol vs Egel,∞ ) 27,3 kJ/mol). The connection between the two linear branches can be described by the function:
(TC/T)n η ) ηsol + (ηgel - ηsol) 1 + (TC/T)n
(5)
where TC is the sol/gel transition temperature. In the case under examination, TC ) 294.95 K and n ) 447. The yield stress undergoes a similar decrease with increasing temperature and vanishes above TC. We observe that Egel,∞ is equal to Esol and that only a slight change in the high shear viscosity is observed with decreasing temperature in correspondence with the solgel transition, the viscosity ratio ηgel,∞/ηsol being equal to 2. At high shear, the hydrodynamic forces prevail over the interparticle interactions, and consequently, the gel structure is broken down and reduced to a dispersion of separate, small structural units. These may correspond to the single massed clusters of crystals (spherulites) or possibly to small aggregates of these clusters. Wessel et al. have suggested that the residual viscosity of colloidal gels under strong shear conditions is directly related to the cluster size.33 The viscosity ratio ηgel,∞/ηsol can be interpreted also as the relative viscosity, that is, the contribution of wax crystal aggregates to the dispersion viscosity at high shear conditions.34 Its value does not depend on temperature, and hence, it can be argued that the effective volume fraction of the wax crystal aggregates, φeff, does not change appreciably as temperature decreases. In the case of (33) Wessel, R.; Ball, R. C. Phys. Rev. A 1992, 46, 3008. (34) Such a hypothesis holds on condition that the viscosity of the continuous phase at low temperature does not differ appreciably from that obtained by extrapolation of high-temperature viscosity data (ηsol) for the whole system. Indeed, the composition of the continuous phase progressively changes with decreasing temperature below the CP because of heavier paraffin crystallization, but not remarkably, the amount of solid phase being relatively low.
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Figure 3. Optical microscopy images (100× magnification and 1/10 s time of exposition) after different cooling processes. Cooling rate: (a) 0.05, (b) 1 °C/min and equal holding time (4 h) in isothermal conditions.
Figure 4. Flow curves at different temperatures (continuous lines from data fitting with the RBC model). Table 3. Some Parameters of the Roberts-Barnes-Carew Model (RBC) for the Crude Oil Investigated T (°C)
σ1 [Pa]
η0 [Pa‚s]
η∞ [Pa‚s]
5 10 15 20 22.5 25.5 26 30 35 40 50 60
1068 309 128 35.6 8.72 1.79 1.47 -
1.70 × 107 2.42 × 106 6.11 × 105 7.47 × 104 1.10 × 104 4.55 × 102 5.21 × 100 5.44 × 102 2.95 × 10-2 2.30 × 10-2 1.70 × 10-2 1.30 × 10-2
1.80 × 10-1 1.50 × 10-1 1.15 × 10-1 1.06 × 10-1 8.57 × 10-2 6.12 × 10-2 5.42 × 10-2 3.10 × 10-2 2.95 × 10-2 2.30 × 10-2 1.70 × 10-2 1.30 × 10-2
spherical aggregates, the volume fraction, φeff, can be estimated by means of the Batchelor equation to be 0.24.35 For nominal volume fractions of wax crystals comprised between 0.03 and 0.07 (from DSC), we can conclude that an appreciable state of aggregation still persists at high shear conditions, whatever cluster-cluster aggregation mechanism is assumed.36 On the other hand, we must recall that similar high shear relative viscosities can be ascribed to dilute dispersions (φ ) 0.03-0.07) of anisotropic particles for sufficiently high shape factor (above 100 for prolate and oblate ellipsoids).37 In light of this result, it seems prudent to consider φ ) 0.24 as the upper limit for the volume fraction. Conversely, at low stresses, the (35) Batchelor, G. K. J. Fluid Mech. 1977, 83, 97. (36) Meakin, P. J. Sol-Gel Sci. Technol. 1999, 15, 97. (37) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999.
Figure 5. Newtonian viscosities in the sol state (ηsol) and the gel state at low-shear (ηgel,0) and high-shear conditions (ηgel,∞) and apparent yield stress (σ1) vs reciprocal temperature.
activation energy Egel,0 associated with the shear flow is nearly 8 times higher than Esol, and the viscosity ratio ηgel,0/ηsol diverges with decreasing temperature. It must be emphasized that the effective dispersed phase volume fraction can increase significantly with decreasing temperature since additional paraffins crystallize and the crystal aggregation state can change as well. Hence, the calculated Egel,0 value does not represent the activation flow energy of a stable dispersion with constant dispersed phase volume fraction and cannot be easily compared with activation energy values obtained for other colloidal systems. Effect of Isothermal Holding Time on the Gel Strength. In light of the previous observations on the time evolution of the linear viscoelastic moduli in isothermal conditions, similar effects are expected also for the nonlinear properties. Thus, tests were performed (flow curves at different isothermal holding times at 15 and 20 °C, respectively) in order to evaluate the effect of isothermal holding time on the viscosity profiles of the gel system, and, specifically, on its apparent yield stress at different temperatures. The values of the apparent yield stress, σ1, derived from the data correlation with the RBC model are plotted in Figure 6. It can be clearly seen that the gel strength of the system (and, in a similar manner, the zero shear rate viscosity) increases with increasing holding time and approaches an asymptotic value after 4 h, thus confirming the results obtained for the isothermal evolution of G′ (Figure 2). During the initial holding time interval, the structural features of the network formed by the paraffin crystals
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Figure 6. Yield stress vs holding time at 15 and 20 °C.
Figure 7. Optical microscopy images (100× magnification and 1/10 s time of exposition) after different holding times in isothermal conditions at 15 °C ((a) 1, (b) 4 h).
undergo a significant change so that both the linear and nonlinear properties of the system increase. Figure 7a and b reports the microscopy images obtained after 1 and 4 h for the sample cooled to 15 °C. Effect of the Stress Application Time on the Yield Stress Value. In the present investigation, the apparent yield stress which marks the transition from limited deformation to appreciable flow conditions was estimated from the η vs σ profiles through application of the RBC model. The experimental viscosity values were derived from the strain data determined through stepwise procedures composed of consecutive creep segments at increasing stress. This means that the duration of the segments becomes important in the low-stress range where the linear viscoelastic properties of the sample can play an important role on its time-dependent behavior and very long times can be required to approach a constant time derivative of strain at constant stress. To study the effect of the stress application time, a stepwise sequence of constant stresses (from 10 to 80 Pa, with 10 Pa steps) was repeated on three different samples varying the time duration of each step from 30 min to 4 h. Each sample was heated to 50 °C and then cooled to 15 °C with the fastest cooling rate (1 °C/min) and maintained at the same temperature for 4 h before measurement in order to exclude the influence of the previous thermal history. Figure 8 reports the experimental results obtained at 15 °C with 30 min and 4 h application times. It can be seen that the viscosity decay takes place at lower stresses for longer application times. Thus, the estimated value of the apparent yield stress depends quite evidently upon the experimental conditions employed. Bearing in mind the actual meaning of the yield condition and the experimental test conditions (time of stress application), the results can be re-examined and compared more conveniently in terms of strain vs time (Figure 9). In so doing, it can be noted that the transition from continuous but small deformation to significant flow falls in a narrow strain band (γ ) 1-2), independently of the application time. The strain-time curves follow similar patterns and can be superimposed, to a rough approximation, by rescaling the experimental time (not
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shown). The transition is sharp and can be easily recognized from the analysis of transients at constant stress: the shear rate monotonically decreases at small stresses and strains, whereas the sign of its time derivative changes as the applied stress exceeds the critical threshold as determined in experiments such as those reported in Figure 8 (see also ref 38). The reduction in the apparent yield stress, σy, for increasing application times can be associated also with the parallel increase in the critical time, tc, which defines the yield condition (data are reported in Table 4). The parameters σy and tc are strictly correlated with each other, and in this sense, the apparent yield stress is confirmed to be time-dependent.12,38 The yield stress marks the border between different structural conditions and rheological responses, which are characterized by time-dependent features that differ qualitatively, as well as quantitatively. Under low-stress conditions, the time evolution of deformation is coupled with the linear and nonlinear viscoelastic properties, while beyond the threshold, the applied stresses give origin to significant structural changes on the mesoscopic scale (such as the break-up of interparticle bonds in dispersed systems, or intermolecular associations in physical polymeric gels), with the consequent loss of connectivity of the system.25,33,39 These structural modifications result in timedependent responses of different sign that can be classified as thixotropic, provided that they are reversible. Similarities between Colloidal and Waxy Crude Oil Gels. Attractive colloidal gels form when the bonding interaction between colloidal particles is thermally irreversible. This results in the formation of a nonequilibrium, space-filling network of fractal aggregates or clusters, where the fractal dimension can be related to the mechanism of aggregation. These systems exhibit marked elastic components and high viscosity in the linear regime and undergo substantial structural break-down above critical deformation and stress values. Beyond a threshold value, shear conditions can produce remarkable structural reordering between and within aggregates, and such changes are only partially reversible.25,39-43 Moreover, all these processes result in an increase in aggregate compactness, and correspondingly, in the fractal dimension.25,40,44,45 Several workers have verified that different shear regimes can have a profoundly different impact on the final viscosity of the system. Varadan et al. found for organophilic colloidal silica in hexadecane that low shear applied during gelation leads to a deep modification of the long-range structure, with an increase in local density and little or no viscosity recovery after removing the shear, while greater recovery was observed at high shear rates.25 This result was interpreted as reflecting reorganization via disaggregation/reaggregation of the (larger) clusters at low shear, while at higher shear, the (smaller) clusters move essentially independently of one another, resulting in less permanent modification of the gel structure compared to gelation under quiescent conditions. In other studies on colloidal stearyl-silica spheres in benzene, (38) Fredrickson, A. G. AIChE J. 1970, 16, 436. (39) Verduin, H.; de Gans, B. J.; Dhont, J. K. G. L. Langmuir 1996, 12, 2947. (40) Rueb, C. J.; Zukoski, C. F. J. Rheol. 1997, 41, 197. (41) Uriev, N. B.; Ladyzhinsky, I. Ya. Colloids Surf., A 1996, 108, 1. (42) Van der Aershchot, E.; Mewis, J. Colloids Surf. 1992, 69, 15. (43) Buscall, R.; Mills, P. D. A.; Yates, G. E. Colloids Surf. 1986, 18, 341. (44) Meakin, P. Adv. Colloid Interface Sci. 1988, 28, 249. (45) Hanley, H. J. M.; Butler, B. D.; Straty, G. C.; Bartlett, J.; Drabarek, E. J. Phys.: Condens. Matter 1999, 11, 1369.
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Figure 8. Viscosity vs time at 15 °C from stepwise sequences with different time duration of stress steps ((a) 30 min, (b) 4 h).
Figure 9. Strain vs time at 15 °C from stepwise sequences with different time duration of stress steps ((a) 30 min, (b) 1 h, (c) 4 h). Table 4. Characteristic Parameters from Figure 9 time step [min]
σy [Pa]
tc [s]
30 60 240
55 45 36
8400 14 800 49 902
changes in the organization of the aggregates induced by shear were found to remain frozen in the gel, which reformed when the shear force was removed.39 Thus, we see that the influence of shear can be profound and depends on the extent to which the clusters are modified (compacted), which may be irreversible. Counter-intuitively, this condition is found at lower, rather than higher, induced shear, the former favoring compaction and solvent expulsion from larger clusters, the latter reduction of the cluster size to a smaller, but conformationally stable state. The similarity between the rheological behaviors of waxy crude oils below the PP and colloidal gels can be better described and defined in quantitative terms, provided that the volume fraction of the dispersed phase is determined. The mass of wax solids formed can be determined by DSC measurement, since a linear correlation can be established with the latent heat of crystallization.46 Indeed, the volume fraction of the dispersed phase can be estimated in normalized terms from the measured values of crystallization heat, as φ/φgel vs Q/Qgel, using the gelation temperature as the reference condition for normalization. For known wax concentrations, this analysis can be carried out using φ/φgel as the reference variable.40 In this way, it becomes possible to correlate the most significant linear and nonlinear quantities, such as zero-shear-rate viscosity and yield stress, with the dispersed phase content through (46) Chen, J.; Zhang, H. L. Thermochim. Acta 2004, 410, 23.
Figure 10. Relative viscosity ηr,0 vs φ/φgel or Q/Qgel for waxy crude oil below gelation temperature and fumed silica dispersions in paraffin oil (at 25 °C and different concentration above 1 wt%).
scaling laws which are quite similar to those already found for other colloidal gels. Figure 10 reports a comparison between the viscosity data for the waxy crude oil below the gelation temperature and those obtained for colloidal gels formed by fumed silica (Aerosil A200) dispersed in paraffin oil at different concentrations (from 1 to 10 wt%) and 25 °C. The zero-shear-rate viscosity values are reported in terms of relative viscosity ηr,0 vs φ/φgel or Q/Qgel. In the case of the waxy crude oil, the extrapolated ηsol values were used as continuous phase viscosity to calculate ηr,0. The strict correspondence between waxy crude oil and silica gel is evident. As shown above (Figure 2) for the crude oil gels, the time evolution of both viscoelastic moduli at constant temperature after static cooling follows an exponential trend, approaching an asymptotic value for the unperturbed gel after 4 h holding time. The same condition cannot be reached or totally re-established when shearing conditions are applied either during gel formation or to the preformed gel (at isothermal conditions), however long the holding time, if the critical strain for flow onset has been exceeded. Figure 11 reports the recovery of the crude oil gel (G′) subjected to shearing at 1 and 50 s-1 after cooling to 15 °C and compares this to the development of gel strength in the same sample previously gelled under static conditions. We note that the crude oil gel recovers much, but not all, of the ca. 4 orders of magnitude of storage modulus lost during shearing and that the asymptotic values for the sheared samples are almost identical. Also
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Figure 11. Time evolution of the storage modulus of crude oil A at a temperature of 15 °C after different rheological histories. Table 5. Asymptotic Values of Viscoelastic Modulus after Different Rheological Histories experimental condition
G′ [Pa]
G′′ [Pa]
no shear during cooling equilibrated at temperature followed by shearing at 1 s-1 equilibrated at temperature followed by shearing at 50 s-1 sheared at 5.5 pa while cooling to final temperature
8095 1173
2098 513
1106
509
1200
450
evident is the slower recovery of the final modulus in the more strongly sheared sample. Table 5 reports the results of all the experiments in which the crude oil was sheared after cooling to a temperature below the PP under quiescent conditions or sheared while cooling to temperature; in all cases, the crude oil gel recovered ca. 15-25% of the asymptotic value of the unperturbed gel. While we have observed similar levels of recovery for other crude oils and a model system (on which we will report elsewhere), not all workers have reported healing of the crude oil gel following shear. Thus, some groups report finding little or no recovery for many hours following shearing,4,12,47 while others find complete48 or similar levels of recovery to those observed here.5,10 Rønningsen5 noted that this property was shear dependent for the oils he studied, lower shear (1 and 100 s-1) leading to greater changes (14-26% recovery), higher shear (500 s-1) to substantially reversible effects (74%), a trend which qualitatively recalls observations on attractive colloidal gels. Similarly, Webber found irreversible changes to shearing of mineral oil lubricant gels near the gel threshold, while the effects of shearing were reversible for oils well below the PP.23 We underscore that there is an underlying issue here of what constitutes “complete” or “irreversible” recovery; in our judgment, a 1000-fold recovery of viscosity must be considered significant, whether the final value is 25% or 100% of that prior to shear. In any event, our and others’ observations of substantial shear healing appear in sharp contrast with the structural model for gelation proposed by Kane´ et al.,10 which states that shear fundamentally perturbs the shape and size of the crystals formed in such a way that, apparently, they should no longer be able to generate an extended network (see above). (47) Cazaux, G.; Barre, L.; Brucy, F. SPE 49213, SPE Annual Technical Conference and Exhibition, September 27-30, 1998, New Orleans, LA. (48) Perkins, T. K.; Turner, J. B. J. Pet. Technol. 1971, 301.
Figure 12. Storage and loss moduli vs time under isothermal conditions (at 20 °C) for the unperturbed gel (continuous lines) and for the sheared system (recovery tests after continuous application at 10 and 20 Pa).
The partial reversibility to shear of the crude oil studied provides support for the associating colloid gel model, where the attractive interactions between clusters of particles (the masses of sheetlike wax crystals), overcome during shearing, re-establish themselves upon returning to the quiescent state. The rather similar time scale for structure development in the sheared gel, and when the gel is formed by cooling entirely under quiescent conditions (Figure 11), suggests that the build-up of the gel network involves essentially the same microscopic processes in the two conditions. Parenthetically, we note that it further suggests that the time-scale for full structure development in gels cooled under quiescent conditions is not determined by the kinetics for wax crystallization. Structural Modifications below the Critical Strain. Following suggestions that colloidal gel clusters can be profoundly modified under low-shear conditions on account of reorganization of their microstructure33,39 and with an eye toward possible technological applications, we have explored the influence of low stress/strain values on gel strength and recovery when applied below the yield threshold. These studies were encouraged by the results in Figure 8 which showed that yield was strongly determined by the time duration of stress application. Figure 12 reports a comparison of the results obtained at 20 °C for the unperturbed gel, and two gel samples sheared for 600 s at two different stress values during gelation. Both applied stress values (10 and 20 Pa) are lower than the apparent yield stress (35 Pa). In the former case, the gel structure does not undergo appreciable changes, owing to the low strain accumulated in the continuous-shear segment and recovery is immediate and complete. Conversely, structural breakdown is quite significant at 20 Pa and only partially reversible, at least on the ordinary time scale of observation. Additional tests indicated that similar effects on the final asymptotic value of gel strength are produced by different mechanical histories on the condition that shear deformations exceeding the critical strain are applied to the system. From a technological point of view, this result and those in Table 5 suggest that the possibility to expose a gelling crude oil in a pipeline to shear forces could have a very beneficial impact on restart. Of course, the greatest need arises when oil flow within the pipeline has been abruptly halted and the temperature subsequently falls below the PP. In this case, the possibility to induce shear by bulk flow of the oil is, by definition, precluded. However, shear effects could still, at least in principle, be obtained by submitting the gelling crude to oscillatory mechanical
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Figure 13. Time evolution of the storage modulus for crude oil A (cooled to 15 °C at 0.05 °C/min): one sample was monitored in quiescent condition (unperturbed sample), while the other (perturbed sample) was sheared at 1 s-1 for the time required to reach the final temperature. Both samples achieve asymptotic values, and for the unperturbed case, this value is much higher than in the latter case. The profile of G′ (measured in oscillatory conditions) during the shearing process (continuous shear rate application) cannot be displayed, but we can suppose that the profile is similar to that of unperturbed sample after 2-3 h but lower by a couple orders of magnitude.
stimuli involving no net flow, such as might be imposed by ultrasound or pressure surges. Figure 13 shows that the build-up in gel strength of the crude oil on cooling to 15 °C is significantly reduced, compared to the unperturbed system, by low-amplitude oscillatory stimulation, for strain/stress values falling just outside the linear viscoelastic region. Note that the effect, a ca. 8-fold reduction in the elastic modulus, persists indefinitely, even though the stimulus was applied only for a time equivalent to that required for development of the gel strength to its limiting value under quiescent conditions. We note that the same result should be obtained for stress less than the yield value, for still longer application times. The results shown in Figures 8, 12, and 13 suggest that the different shear histories imposed in different rheological experiments may provide the explanation for discrepancies between the results reported for the postshear recovery of crude oil gels. Thus, Chang et al.,12 who observed only slight recovery, conducted shear sweeps beginning from very low (0.015 s-1) shear rates. Under these conditions, the gelled crude was presumably exposed to subcritical stress for a prolonged period of time which, in light of the results reported here, may have deeply and permanently modified the gel structure. An interesting objective for future studies on shear healing in colloidal, as well as crude oil, gels is to verify the extent to which different rheological procedures determine recovery behavior. Conclusions At temperatures below the PP, the waxy crude oil studied behaves as a weakly attractive colloidal gel. The
structural build-up coming from crystal formation and aggregation is favored by lower temperatures and longer times. In the low-stress range, it displays very high viscosity and marked viscoelastic properties, which are strictly connected to the aggregation state of wax crystals and the formation of a three-dimensional network composed of loose clusters. When a critical strain is overcome, the applied stresses produce a significant breakdown of the structural network and hence a transition from continuous but small deformation to significant flow is observed. At constant stress, the time-dependent response of the system changes its sign and the viscosity falls dramatically. The viscosity breakdown takes place at lower stresses for longer application times, thus confirming the time-dependent nature of the apparent yield stress and the important role of the accumulated strain. The state of a colloidal gel and the relevant rheological properties are strictly determined by the mode of particle aggregation and the spatial distribution and coordination of aggregates: in other terms, by the effective volume fraction of the dispersed phase. This means that the properties of the gel system depend mainly upon temperature and are conditioned by past thermal history. In particular, different cooling rates during the gelation process lead to differences which persist even after prolonged isothermal holding times. The mechanical history exerts quite significant effects on the structural conditions and, consequently, on the rheological properties of the gel in its final state and during its formation process as well. Indeed, even small deformations and stresses above the limit of the linear viscoelastic range, but below the yield condition for flow onset, can sensibly affect the aggregation mode of paraffin crystals during the gel formation, leading to a more fragile network. The effects produced by the shearing conditions depend, even if moderately, on the intensity and duration of the applied stress and are only partially reversible. The dynamic properties of these gels have interesting technological implications, only some of which have previously been identified. Thus, it is common knowledge that a crude oil flowing in a pipeline below its PP is not necessarily at risk of blockage owing to gelation, provided that the system is kept in movement.2 On the other hand, our observations indicate that the gel strength (quantified by the yield point or G′) of the crude oil gel will be lower by a factor of 2-4 if the wax crystallization occurs while the crude oil is in movement; current practice does not consider this “benefit” for restart in the design phase. Most significantly, though, are the observations that lowenergy mechanical solicitations of the crude oil during gelation can profoundly influence the final gel properties. This result, in particular, identifies technologically interesting objectives for further studies. Acknowledgment. It is our pleasure to acknowledge the contributions of R. Piazza and P. Cioffi to this study. LA050705K
