Article pubs.acs.org/EF
Structural Behaviors of Waxy Crude Oil Emulsion Gels Guangyu Sun, Jinjun Zhang,* and Hongying Li National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban Oil & Gas Distribution Technology, China University of Petroleum (Beijing), Beijing 102249, China ABSTRACT: At low ambient temperatures in offshore environments, the water-in-oil emulsions of waxy crude oil develop a combined structure of wax crystals and water droplets, resulting in gelling and other complicated flow problems which may severely challenge flow assurance of the multiphase production and transportation system. In this study, the viscoelastic and yield behaviors of waxy crude emulsion gels were investigated, and analyses were then made by investigating the roles of wax particles and water droplets. Small amplitude oscillatory measurements were first carried out to study the effects of dispersed water on the structure and its evolution with time elapsing. Then, creep and recovery tests were conducted within the linear viscoelastic region to further investigate the viscoelastic behaviors of the emulsion gels. Further, the influence of dispersed water on the yield behaviors was studied by stress sweep measurements, and the effects of temperature, i.e., the precipitated wax, on the yield stress and yield strain were investigated by shear-rate-controlled loading measurements. The emulsion was found to become more elastic with the increase of the water cut, exhibiting phenomena such as the loss angle decreasing, storage modulus growing-up, the emulsion gelling at higher temperature, and strain recoverability increasing. The creep and recovery behavior may well be described by a mechanical analogy model with one Maxwell model and two Kelvin−Voigt models associated in series. Compared to the brittle structure of the gelled waxy crude oil as was reported in previous studies, the emulsion gels become more ductile with the increase of the water cut. The yield stresses of both the crude oil and the emulsion gels increase monotonically with the increase of the precipitated wax, and the yield strain of the emulsions with few precipitated wax particles increases with decreasing temperature, which is contrary to the waxy crude oil and the emulsions with low water cut, and interestingly the yield strain of emulsions may show both of these opposite trends, first increasing and then decreasing with the continuous decrease of temperature. All structural behavior differences between the emulsions and the waxy crude oil may be attributed to the roles that the dispersed water droplets may play and the interactions of the wax particles and the water droplets.
1. INTRODUCTION In petroleum production, the formation of crude oil emulsions, which is mainly caused by flow turbulence and high shear encountered at the production facilities, is quite common and may cause significant flow assurance problems. These crude oil emulsions can be very stable with polar components such as resins and asphaltenes serving as the natural surfactants.1−3 For a waxy crude oil at low ambient temperature in subsea environments, the paraffinic wax in the crude oil precipitates out due to its decreased solubility and forms a threedimensional spongy-like network, leading to the gelation of the crude oil and the emergence of structural rheological behaviors such as viscoelasticity and yielding.4−8 Particularly, for waxy crude oil emulsions the interfaces of dispersed droplets provide bonding sites for the paraffin crystalline particles,8,9 making the emulsions easier to gel and thus bringing more severe flow assurance problems to the subsea production and transportation systems. Therefore, the rheological behaviors of waxy crude oil emulsion gels are of great importance to the petroleum industry. However, so far most of the rheological studies on waxy crude oil emulsions are focused on the flow properties of liquid state emulsions, such as the emulsion viscosity as a function of the dispersed water fraction,10−12 and little attention has been paid to the viscoelastic and yield behaviors of gelled crude oil emulsions, except for the work of Visintin et al.8 Using small amplitude oscillatory measurements, Visintin et al.8 demonstrated that the pour point, which was defined as the © 2014 American Chemical Society
temperature at which the storage and loss modulus crossed by these authors, rose obviously with the increase of the dispersed water when the water cut exceeded 35%, and at temperatures below the pour point the storage and loss moduli of emulsion gels were found to grow with time in isothermal conditions. And after the structure of emulsion gels reached equilibrium, for the emulsion gels with a water cut above 35%, a power law relation existed between the storage modulus and the volume fraction of water. They attributed these rheological behaviors to the strong absorption of wax particles at the interface and the resultant entrapment of water droplets, rendering the entire volume spanned by a wax crystal network eventually. At present, studies on the creep and recovery of waxy crude oil emulsion gels have not been presented in the literature. Similar studies were mainly reported in the field of food emulsion gels.13−17 More recently, Haj-shafiei et al. 18 investigated the creep and recovery of model oil emulsion gels. Their study showed that the emulsions with high water cut deformed less and recovered more due to the inherent recoverable nature of water droplets under stress, and conversely the emulsions with low water cut recovered less since the wax crystal network dominating the emulsions at low water cut was more brittle and irreversibly yielded. Received: March 7, 2014 Revised: May 19, 2014 Published: May 20, 2014 3718
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Diverse results have been reported when the yield characteristics of waxy crude oil emulsions are referred to. Some research reported that the yield stress of waxy crude oil emulsion gels increased monotonically with the increase of dispersed water,8,19 whereas others indicated that the yield stress did not monotonically increase with increasing water cut when the fraction of precipitated wax crystals was low,6,20 and instead a water cut existed at which the structural strength of the emulsion gels was at its maximum. Moreover, Paso et al.6 found that the yield strain increased from about 1.5% in the absence of emulsified water to nearly 20% at the water cut of 70%, indicating that significant deformation of water droplets occurred before the maximum yield stress was attained. From the above reviews, it can be seen that there has been a lack of study on the structural behaviors of waxy crude oil emulsion gels. First, little is known about the creep and recovery behavior. Second, in the studies of the yield behaviors most attention has been paid to the evolution of the yield stress with water content, while little attention has been given to the yield strain, which is also a representation of the structural characteristics. Third, there is a lack of comprehensive comparison between the structural properties of emulsion gels and those of the gelled waxy crude oil without emulsified water. The objective of this study is to understand the structural characteristics and their mechanisms of waxy crude oil emulsion gels both by exploring their viscoelasticity and yield behaviors and by comparing them with those behaviors of the crude oil. First, the small amplitude oscillatory measurements were carried out to track the evolutions of the viscoelasticity during the cooling and the subsequent isothermally holding processes, and the evolutions of the storage modulus and the loss angle of the emulsion gels were compared with those of the waxy crude oil gel. Then, creep and recovery experiments were conducted within the linear viscoelastic region for emulsions with various water cuts, and the experimental results were further analyzed by using a mechanical analogy model. And then, the yield behaviors of the emulsion gels were investigated by using two loading modes, i.e., the stress-linearly increased sweep mode and the constant shear rate loading mode. By the combination of the experimental results acquired in this study and the existing knowledge of the structural properties of the gels, the mechanisms of the structural behaviors of waxy crude oil emulsion gels were discussed and further understood.
Table 1. Physical Properties of the Studied Waxy Crude Oil parameter
value
density at 20 °C (kg/m3) pour point (°C) gelation temperature (°C) WAT (°C) wax (wt %) resins (wt %) asphaltenes (wt %)
894.7 33.0 31.3 42.2 18.16 8.13 1.91
Products - Laboratory Determination of Density - Hydrometer Method. The pour point was tested according to the standard ASTM D5853-11 Standard Test Method for Pour Point of Crude Oils. The gelation temperature, i.e., the temperature at which the loss modulus equals the storage modulus, was tested by the small amplitude oscillatory measurement while the sample was cooled at a rate of 0.5 °C/min.22−25 The wax appearance temperature (WAT) and the precipitated wax concentration were determined by the differential scanning calorimetry (DSC) technique with the apparatus of Q20 (TA Instruments, USA). Tests were performed from 80 °C to −20 °C at a cooling rate of 5 °C/ min. The calorimetric signal recorded by the computer with the software from TA Instruments was used to determine the WAT and the precipitated wax concentration at a certain temperature.26−29 The cumulative precipitated wax concentration at a given temperature was determined as follows. First, the total heat released in the phase change from WAT to the given temperature was obtained by integrating the area between the heat flow curve and the baseline. Then the corresponding precipitated wax concentration was calculated with the total released heat divided by the enthalpy of wax precipitation, which is recommended to be 210 J/g for crude oils with a complex mixture of paraffins.26,28 The cumulative precipitated wax concentrations at different temperatures are shown in Figure 1.
2. EXPERIMENTAL SECTION
Figure 1. Cumulative precipitated wax concentration vs temperature by the DSC technique.
2.1. Materials. A typical waxy crude oil with high paraffin content was used in this study to prepare emulsions. Ultrapure water was used as the dispersed phase. No emulsifier was added in the preparation of the emulsions. During the preparation of the emulsions by stirring, the volatilization of the light components of the crude oil may occur, which will inevitably influence the rheological properties of the oil and the emulsions. To eliminate this effect, the light components were first removed as follows. The crude oil was poured into a beaker without a seal and then was stirred at a rotating speed of 1000 rpm at 80 °C for 2 h to make the light hydrocarbons fully evaporate. Then, for better repeatability of experimental results, the memory effects for the thermal and shear history of the crude oil were removed by heating the oil samples up to 80 °C and holding for 2 h, and then leaving the samples cooled quiescently and maintained at room temperature for at least 48 h before they were used for experiments. 21 The main physical properties of the pretreated crude oil are listed in Table 1. The density of the oil sample was measured according to the standard ISO 3675-1998 Crude Petroleum and Liquid Petroleum
The measurements of resins and asphaltenes content were performed according to the standard ASTM D4124-09 Standard Test Method for Separation of Asphalt into Four Fractions. 2.2. Emulsion Preparation and Stability. The crude oil and water were preheated in a water bath at 50 °C for 30 min and then were added into a 200 mL beaker sequentially according to the required volume ratios. The total volume of water and crude oil was kept at 50 mL. Emulsification was performed using an IKA RW20 digital stirrer (IKA group, Germany) equipped with a four-blade paddle which was kept at a fixed position in the mixtures. A polarizing microscope (Nikon OPTIPHOT2-POL, Nikon Corp., Japan), configured with a Linkam PE60 Peltier thermal stage (Linkam Scientific Instruments Ltd., UK) with a temperature range from −20 to 90 °C and control stability within ± 0.1 °C, was used to observe the microscopic structure of waxy crude oil emulsions. The observation proceeded as follows. First, the thermal stage of the microscope was 3719
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Figure 2. (a, b) Examples of photographed microscopic images of emulsions. preheated to 30 °C for 5 min. Second, the specimen was spread by a cell scraper onto a glass slide which had been placed on the preheated thermal stage. Third, the water droplets were photographed with a CoolSNAP 3.3 M digital charge-coupled device (CCD) color camera (Roper Scientific, Inc., Sarasota, FL, US) connected to a computer. Eight photographs were taken at different positions of each slide, and two slides were prepared with every emulsion specimen, i.e., totally 16 microscopic images were obtained for each specimen. Examples of the microscopic images are shown in Figure 2. The number and size of droplets in every microscopic image were analyzed by the software Image J (National Institute of Mental Health, Rockville, US). The Sauter mean diameter was obtained by calculating all the droplets of the 16 microscopic images. Different stirring speeds were used in order to obtain similar mean droplet sizes among different water cut samples (Table 2).
2.3. Dynamic Viscoelasticity Measurements. In this study, all the rheological measurements of the waxy crude oil and its emulsions were performed by using a HAAKE Mars III rheometer (Thermo Fisher Scientific Inc., Germany) equipped with the Z38TiP coaxial cylinder geometry. Temperature was controlled by a HAAKE AC200 circulating water bath (Thermo Fisher Scientific Inc., Germany). The sample was loaded into the measuring system preheated at 50 °C and kept for 10 min, and then it was cooled to the measurement temperature at a cooling rate of 0.5 °C/min. Rheological measurements were performed after the specimen was kept at the test temperature for 45 min to ensure that the growth of the structure reached equilibrium, shown in Figure 7 below. During the cooling and isothermal process, the small amplitude oscillatory measurement was performed at a constant frequency (1 Hz) to track the changes of viscoelastic parameters with temperature and aging time. The strain amplitude sweep tests were carried out at different temperatures to determine the linear viscoelastic region. As shown in Figure 3, the storage moduli at different temperatures stay approximately the same when the strains are less than 0.001. Therefore, the oscillatory measurements were determined to be carried out at a strain amplitude of γ = 0.0005. 2.4. Creep and Recovery Tests. Creep tests were first conducted under different stresses to determine the linear viscoelastic region at 28 °C. The results showed that the deformation of the crude oil and the emulsions could be guaranteed within the linear region under a stress of 1 Pa. Therefore creep and recovery tests were carried out by applying a constant stress of 1 Pa for 600 s and then unloading and allowing the samples to relax for 900 s. The deformation per unit stress, called compliance, was determined. 2.5. Measurements of the Yield Behaviors. In this study, we investigated the evolution of the yield behaviors not only with the increase of water cut but also with the decrease of temperature which represents the increase of the amount of precipitated wax. The controlled stress mode was used to observe the evolution of the yield behaviors with the variation of the water cut. The stress was loaded at a linearly increasing rate of 1.2 Pa/min from 0 Pa until the
Table 2. Mean Droplet Sizes of Emulsions with Different Water Cuts water cut (vol %)
D32 (μm)
10 20 30 40 50 60
6.59 6.54 6.60 6.43 6.40 6.48
Furthermore, to ensure the validity and repeatability of rheological measurements, the emulsions must be stable during the whole measurement process. For this purpose, the prepared emulsions were transferred into a colorimetric tube and maintained at 50 °C in a water bath. No water separation was observed in 6 h. Moreover, the samples in the measuring system of the rheometer were observed after every rheological experiment to ensure that no oil−water separation occurred.
Figure 3. Storage modulus vs shear strain in strain amplitude sweep tests at (a) 32 and (b) 25 °C. 3720
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sample yielded. During this process, the evolution of the strain was recorded. The controlled shear rate mode was employed to determine the yield stress and the yield strain of emulsion gels. The yield stress is defined as the maximum in the stress versus strain curve, and the yield strain is the strain at which the yield stress is reached,6,30 as illustrated in Figure 4. To eliminate the influence of the magnitude of the applied
existence of water droplets. When the temperature is lowered to 25 °C, the loss angle of the crude oil decreases to 18° rapidly, while that of the 50% water cut emulsion decreases to 11° at a slower rate. This change reflects the growing contribution of wax crystals to the elasticity. It is well-known that the formation of wax crystal structure makes the storage modulus dramatically increase with decreasing temperature for waxy crude oils. It can then be deduced that the water droplets also contribute to the formation of the structure of waxy crude oil emulsions, making the storage modulus begin to increase rapidly at higher temperatures and the loss angle become less. This can also be drawn from the change of the gelation temperature with the water cut (Figure 6).
Figure 4. Schematic of the yield point by the controlled shear rate mode. shear rate on the measured values of yield stress and yield strain, a constant shear rate of 0.1 s−1 was chosen to be applied to the sample until it yielded. According to Paso et al.,30,31 yield stress values obtained by applying a shear rate of 0.1 s−1 or less are nearly identical.
3. RESULTS AND DISCUSSION 3.1. Contribution of the Dispersed Water to the Viscoelasticity of Emulsion Gels. For waxy crude oils, it has been known that the storage and loss moduli increase dramatically with decreasing temperature.22,23,32 Figure 5 illustrates the evolutions of the storage modulus and the loss angle with temperature for emulsions with different water cuts. It is clear that the viscoelastic changes of the emulsions with temperature have the same trend as those of the waxy crude oil. However, the storage modulus grows up and the loss angle decreases with the increase of the dispersed water. Meanwhile, the storage modulus begins to increase and the loss angle begins to decrease rapidly at higher temperatures with increasing water cut. For instance, the storage modulus of the waxy crude oil tends to increase rapidly at about 26 °C, while for the 20% water cut emulsion this temperature is about 28 °C, and it rises to about 32 °C for the 50% water cut emulsion. At the WAT (42.2 °C), the loss angle of the crude oil is almost 90°, while that of the 50% water cut emulsion is only 49°, which reflects the enhancement of elasticity due to the
Figure 6. Gelation temperature of waxy crude oil emulsions with the water cut.
During the isothermal holding after a waxy crude oil is cooled to required temperature, the storage modulus increases rapidly in the early period, and then the increasing rate gradually slows with time elapsing. This phenomenon of storage modulus growth is called aging.25,32 Coutinho33 and Silva25 et al. maintained that the aging of wax is related to the Ostwald ripening of the paraffin crystals, a mechanism by which the large crystals grow at the expense of the melting of the small crystals with higher energy. Figure 7a demonstrates that the storage modulus of the emulsions above the WAT almost stays unchanged with time elapsing, which means no aging happens during this period when the paraffin crystals have not yet precipitated. After paraffins precipitated from the waxy crude oil emulsions, whether above (Figure 7b) or below (Figure 7c) the gelation temperature, the aging phenomenon exists. By defining the time needed for the storage modulus to grow up to 95% of the final value as the aging time, it can be observed from Figure
Figure 5. (a, b) Evolutions of storage modulus and loss angle with water cut during the cooling process. 3721
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Figure 7. (a−c) Evolution of storage modulus with isothermal holding time.
where G′ is the storage modulus of the emulsions, Pa; G0′ is the storage modulus of the waxy crude oil at the corresponding temperature, Pa; φ is the volume fraction of the dispersed water; A and B are fitting parameters whose values at different temperatures are listed in Table 3. In eq 2, parameter A represents the storage modulus’s dependence on the dispersed droplets. It decreases with decreasing temperature, which means the contribution of droplets to the structural strength is reduced while the contribution of wax crystals is enhanced with increasing precipitated wax. For example, at 38 °C, the storage modulus of the 60% water cut emulsion is 130.6 times larger than that of the waxy crude oil, but at 25 °C, the ratio is reduced to 6.8. Mathematically, the parameter B in eq 2 represents the ratio of G′ to G0′ when the water cut φ is reduced to 0. Therefore, B should equal to unity physically. However, we can see from Table 3 that B increases with decreasing temperature. The deviation of B from unity and its increase with decreasing temperature may be attributed to the interactions between the wax crystals and the water droplets. More specifically, the amount of wax crystals is little at 38 and 36 °C, so the contribution of wax crystals is tiny. But when the precipitated wax is abundant, e.g., 3.19 wt % at 25 °C, besides the interactions among wax crystal particles themselves and further the formation of the wax crystal network, part of the crystals will absorb at the interface of water droplets.6,8,18,35,36 This absorption strengthens the interface, contributing largely to the G′ and hence the elasticity of the emulsions. 3.2. Creep and Recovery Behaviors. In order to further understand the viscoelasticity of the emulsion gels, the creep and recovery tests were carried out within the linear viscoelastic region with the results shown in Figure 10. In the literature, the Burger mechanical-analogy model, i.e., the association in series of a Maxwell model and a Kelvin− Voigt model, was often used to describe the creep behaviors of gels.14,15,37,38 For some food emulsion gels, it was found that
8 that the aging time becomes shorter with the increase of the dispersed water. This phenomenon is similar to that reported
Figure 8. Aging time vs water cut.
by Haj-shafiei et al. 18 who found the time needed for the yield stress to reach equilibrium was shorter for higher water cut emulsion gels of model oil. After the structure equilibrium is reached, a good exponential relation exists between the storage modulus and the water cut at each temperature, as is shown in Figure 9. By referring to the definition of the relative viscosity for the disperse system,34 we define a relative storage modulus by dividing the storage modulus of the emulsion by that of the waxy crude oil at the corresponding temperature, as is shown in eq 1. Then the relation of the relative storage modulus with the water cut can be well expressed by eq 2. Gr′ =
G′ G0′
Gr′ = Be Aφ
(1) (2) 3722
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Figure 9. (a−d) Storage modulus vs water cut at different temperatures.
Table 3. Fitting Parameters of eq 2 at Different Temperatures temperature (°C)
A
B
R2
38 36 32 25
8.316 7.672 3.499 1.826
1.0308 1.1061 1.6802 2.2120
0.990 0.992 0.966 0.996
Figure 11. Comparison of the experimental values and the curve fitted by the Burger model for the 40% water cut emulsion gel.
J (t ) =
⎡ ⎛ −tG ⎞⎤ 1 1 ⎢ 1 ⎥ ⎟⎟ + 1 − exp⎜⎜ η G0 G1 ⎢⎣ ⎝ 1 ⎠⎥⎦ +
Figure 10. Creep-recovery behavior of the waxy crude oil and its emulsion gels at 28 °C.
⎡ ⎛ − tG ⎞⎤ 1 ⎢ t 2 ⎥ ⎟⎟ + 1 − exp⎜⎜ η0 G2 ⎢⎣ ⎝ η2 ⎠⎥⎦
(3)
where J(t) represents the overall compliance at any moment t; G0 is the instantaneous elastic modulus of the Maxwell element; G1 and G2 are the elastic moduli of the two Kelvin−Voigt elements, called retarded elastic moduli; η0 is the residual viscosity of the dashpot of the Maxwell element; η1 and η2 are the internal viscosities of the dashpots of the two Kelvin−Voigt elements respectively. This model can well depict the creep behavior in the whole process. As an example, the result for the 40% water cut emulsion gel is shown in Figure 13. The fitted parameters of the emulsion gels with different water cuts are listed in Table 4. As is shown in Table 4, both the instantaneous elastic modulus G0 and the retarded elastic moduli G1 and G2 increase with the increase of the water cut, and the viscosities of the
creep behaviors may be better described by the association in series of one Maxwell model and two Kelvin−Voigt models.13,17,39 However, the creep and recovery behaviors of waxy crude oil emulsion gel has not been studied yet. In this study, we first applied the Burger model to describe the creep behaviors of the crude oil and its emulsion gels. But the fitting results showed that this model cannot describe well the incipience of loading (see Figure 11 for details). So another Kelvin−Voigt model was associated in series with the Burger model, as is shown in Figure 12, and the equation of the compliance of this model is shown as eq 3. 3723
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Figure 12. Schematic of the mechanical analogy model consisted of one Maxwell model and two Kelvin−Voigt models in series.
Figure 14. G0, G1, and G2 in eq 3 vs water cut. Figure 13. Comparison of the measured values and the curve fitted by eq 3 for the 40% water cut emulsion gel.
dashpots also increase with the water cut. Similar phenomena were observed by Dolz et al.14 and Yilmaz et al.15 in their studies on food emulsion gels. Furthermore, the relations between the three moduli (G0, G1, and G2) and the water cut φ are illustrated in Figure 14, showing exponential relations similar to the G′ obtained from the small amplitude oscillatory measurement (Figure 9). The existence of dispersed droplets was considered to be the reason for the increase of the storage moduli and the viscosities.13−15,40 The spherical water droplets undergo deformation when shear stress is applied. However, the recoverable nature of the water droplets, i.e., the spontaneous tendency that the deformed droplets restore to their original spherical shape, leads to increased resistance to further deformation and makes them return to their original form once the stress is removed.41−43 As a result, the emulsion becomes more elastic with the increase of water cut. Moreover, the dragging activity of the water droplets makes deformation harder to happen in emulsion gels than in crude oil, resulting in the increase of the viscosities. As to recovery after creep, the deformation or compliance can be divided into three sections, as is shown in Figure 15, where JSM is the instantaneous recovery and corresponds to the spring of the Maxwell element; JKV is the retarded recovery due to the Kelvin−Voigt element, tending toward an asymptote for t → ∞; J∞ is the residual deformation due to the sliding of the Maxwell dashpot, indicating permanent deformation resulting from the irreversibility of the viscous deformation.
Figure 15. Recovery of the 20% water cut emulsion gel after the removal of the applied stress.
According to the theory of mechanical analogy, the recovery behavior is expected to be symmetrical to the creep behavior if the deformation is within the linear viscoelastic region. However, it was often observed that the recovery process cannot be described by the same parameter values determined from the creep phase.14,15,17,44,45 In this study this asymmetry also emerged, so the compliance equation of the association in series of one Maxwell model and two Kelvin−Voigt models was reused to fit the recovery data, as is shown in eq 4.
Table 4. Fitted Parameters of Different Water Cut Emulsion Gels by eq 3 water cut (%)
G0 (Pa)
η0 (Pa·s)
G1 (Pa)
η1 (Pa·s)
G2 (Pa)
η2 (Pa·s)
0 20 30 40 50 60
268.6 672.9 1324.7 1667.9 3399.8 5743.6
434747 638680 1577120 1601530 1740130 2752330
891.2 1969.2 3506.9 4018.3 5733.7 10724.6
5766.1 10216.1 18130.7 34890.9 22414.8 137800.6
588.0 1314.4 2200.5 2159.3 5047.4 6255.5
69483.9 136894.8 218390.8 312105.2 363364.5 946199.4
3724
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⎛ t−t ⎞ 0 ⎟⎟ J(t − t0) = J∞ + JKV1 exp⎜⎜ − ⎝ JKV1η1 ⎠ ⎛ t−t ⎞ 0 ⎟⎟ + JKV2 exp⎜⎜ − ⎝ JKV2 η2 ⎠
(4)
where t0 is the time at which the creep is terminated, i.e., the time at which the recovery process begins; J(t − t0) is the compliance of the recovery phase at the moment t-t0; JKV1 and JKV2 are the retarded compliances of the two Kelvin−Voigt elements, respectively; η1 and η2 are the viscosities of the dashpots of the two Kelvin−Voigt elements, respectively. As an example, the fitting result of the recovery data of the 20% water cut emulsion gel can be found in Figure 15. The JKV and J∞ were obtained by the fitting of eq 4, and the JSM was obtained by using eq 5. After that, the proportion of each part of the deformation was calculated by using eq 6. The results of the deformation analysis for the emulsion gels with water cut up to 60% are shown in Table 5. JSM = JMAX − JKV − J∞
Figure 16. Evolution of the strain with applied stress at 25 °C.
gel to the ductile yielding of the emulsion gels may be interpreted from the competition of the roles of the brittle wax crystal structure and the water droplets, which will be discussed later in this section. The yield stress and yield strain at different temperatures (i.e., different amounts of precipitated wax) were measured by loading a controlled shear rate of 0.1 s−1. As expected, the yield stresses of both the crude oil and its emulsions increase monotonically with increasing amount of precipitated wax and increasing water cut (see Figures 17 and 18). Besides it should be pointed out that the emulsions above 40% water cut exhibit yield behavior even at temperatures above the WAT.
(5)
where JMAX is the maximal compliance in the whole creeprecovery process. ⎡J ⎤ %J = ⎢ element ⎥ × 100 ⎢⎣ JMAX ⎥⎦
(6)
where Jelement denotes JSM, JKV1, JKV2, or J∞, respectively. Table 5. Percentage Participation of Each Element in the Maximum Compliance water cut (vol %)
%JSM (%)
%JKV1 (%)
%JKV2 (%)
%J∞ (%)
0 20 30 40 50 60
39.18 41.95 46.72 52.38 57.50 58.11
16.21 16.18 17.06 16.36 17.38 13.32
20.38 19.62 19.26 31.22 25.11 30.03
24.23 22.26 16.96 0.03 0 0
Figure 17. Yield stress of the crude oil and its emulsions vs precipitated wax.
As can be seen from Table 5, the contribution of the Maxwell spring (JSM) to the total deformation of the emulsion gels increases with increasing water cut, and correspondingly the contribution of J∞ decreases. When the water cut is more than 40%, all deformation produced in the creep phase can actually be recovered. This clearly indicates that the elasticity of the emulsion gels increases with increasing water cut, which agrees well with the results obtained from both the small amplitude oscillatory and the creep measurements. 3.3. Yield Behavior of Emulsion Gels. For gelled waxy crude oils, because of the nature of their internal wax crystal structure, their yield behavior is somewhat like the brittle fracture.46 As to waxy crude oil emulsion gels, it can be imagined that their yield behavior will be affected by the dispersed water phase. Figure 16 shows the yield processes of the waxy crude oil gel and its emulsion gels at 25 °C when the shear stress is applied at an increasing rate of 1.2 Pa/min. Unlike the brittle fracture of the waxy crude oil gel which is characterized by the sudden increase of the strain after yielding, the increase of the strain becomes slower when yielding takes place as the water cut goes up. This change from the brittle fracturing of the wax crude oil
To further investigate the variation of the yield stress with temperature, a relative temperature ΔT is defined as follows.
Figure 18. Yield stress vs water cut at different fractions of precipitated wax. 3725
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Figure 19. (a, b) Yield stress vs relative temperature at different water cuts.
ΔT = Tm − Tg
(7)
where Tm is the measurement temperature; Tg is the gelation temperature at which the storage modulus G′ equals the loss modulus G″. Figure 19 demonstrates that the yield stress (τy) varies exponentially with the ΔT for both the crude oil and its emulsions, as is expressed in eq 8. τy = α e−β ΔT
(8)
where obviously the fitted parameter α represents the yield stress at the gelation temperature, and β characterizes the increasing rate of structural strength with decreasing temperature. The values of α and β at different water cuts are listed in Table 6. It is clear that α increases with increasing water cut,
Figure 20. Evolution of the yield strain of the emulsions with temperature above and slightly below the WAT.
waxy crude oil decreases monotonically with decreasing temperature, i.e., with increasing precipitated wax (Figure 21a). The same trend is also observed in the 10% and 20% water cut emulsions. However, as is shown in Figure 21b, for the emulsions above 30% water cut and at temperatures below the WAT, the yield strain first increases and then decreases with decreasing temperature, i.e., with increasing precipitated wax. In addition, the turning point of the yield stain moves to lower temperature with increasing water cut. The mechanism of this phenomenon may be understood by considering the change of the yield strain with the amount of precipitated wax. Above the WAT, the emulsions above 40% water cut show yield behavior, while those emulsions with lower water cuts do not. Because of no wax precipitation and no wax crystal structure, the yield behavior can only be attributed to the damage of droplet clusters. Below the WAT, the amount of precipitated wax in the crude oil increases and the wax crystal network structure becomes more brittle with decreasing temperature, so the yield strain decreases with decreasing temperature. The emulsions with low water cuts, i.e., 10% and 20%, keep this trend as is shown in Figure 21a, but the variation rate of the yield strain with temperature above 31 °C obviously decreases with increasing water cut, showing that the role of the water droplets becomes stronger. However, when the water cut is increased to or above 30%, as the temperature decreases, the change of yield mechanism obviously occurs from the domination of the damage of droplet clusters to the domination of the fracture of wax crystal network as a result of the increased amount of precipitated wax and further the formation of wax crystal network that may entrap the dispersed water. To further understand the mechanism of the yield behavior and the phenomenon of ductility enhancement shown in Figure 16, a recovery experiment was designed as follows for emulsion
Table 6. Fitted Parameters of eq 8 for the Waxy Crude Oil and Its Emulsion Gels water cut (vol %)
α (Pa)
β (1/°C)
R2
0 10 20 30 40 50 60
5.73 5.86 6.80 8.19 10.11 10.40 10.48
0.524 0.493 0.463 0.425 0.392 0.346 0.318
0.978 0.982 0.982 0.990 0.988 0.985 0.985
which means that the structural strength of a higher water cut emulsion at its gelation temperature is stronger than that of a lower water cut emulsion, although the gelation temperature of the higher water cut emulsion is higher (Figure 6). Obviously at the gelation temperature, the precipitated wax fraction of the higher water cut emulsion is less than that of the lower water cut emulsion, but the dispersed water phase contributes to the strength of the gel structure, too. 8 It is also shown in Table 6 that β decreases with increasing water cut, indicating that the increasing rate of the yield stress with the decreasing temperature is slower at a higher water cut than at a lower water cut. This is closely related to the fact that an increase of the water cut means a decreased proportion of the oil phase and hence a decreased amount of precipitated wax at the same temperature. As to the yield strain, its evolution with temperature below the WAT is not monotonic for emulsion gels, which is analogous to neither the waxy crude oil nor the emulsions without precipitated wax. As is shown in Figure 20, at a temperature above or slightly below the WAT, the yield strain of the emulsions increases monotonically with decreasing temperature. Conversely, below the WAT the yield strain of the 3726
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Figure 21. (a, b) Evolution of the yield strain of the waxy crude oil and the emulsions with temperature below the WAT.
Figure 22. (a−c) Residual strains after recovery from different set strains.
increased (strain from 0.04 to 0.08), and finally section III when all emulsion gels had yielded (strain larger than 0.08). The residual strains of the waxy crude oil and its emulsion gels after recovery from the three sections (represented by the strains of 0.04, 0.07 and 0.10 respectively) are shown in Figure 22. It should be noted first that because recovery happens at strains above 0.04 which is far beyond the linear viscoelastic region, the relation between the residual strain and the water cut differs from that shown in Table 5, which is obtained from the creep recovery test within the linear viscoelastic region. From Figure 22a, one may see that the residual strain of the waxy crude oil is less than that of the 10% water cut emulsion gel after recovery from the strain of 0.04. But when the specimens recover from the strains of 0.07 and 0.10, the opposite results are observed; i.e., the residual strain of the waxy crude oil is higher than that of the emulsions (see Figure
gels with different water cuts. First, shear stress was applied from zero and at an increasing rate of 1.2 Pa/min to make the strain of the gels reach a certain value. Once the set strain was reached, the stress was unloaded immediately and the recovery process was recorded. The recovery of deformation generally reached equilibrium after 20 min, and the strain that could not be recovered after 20 min was designated as the residual strain. If all the samples are not yielded, their residual strains after recovery will decrease with the increase of the water cut, i.e. the increase of the elasticity. Once yielding occurs in some lower water cut sample which possesses lower yield stress, its residual strain will become larger than those higher water cut samples which are not yielded. Therefore, according to the trends of the residual strains, the ductile yielding process of the gels with different water cuts could be roughly divided into three sections, i.e., section I when all gels did not yield (strain less than 0.04), section II when the emulsion gels yielded sequentially from low water cut to high water cut as the strain 3727
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22b,c). This difference may be attributed to the different natures of the wax crystal structure and the water droplets. For the waxy crude oil gel, because of the brittle nature of the wax crystal structure and the structure breakdown after yielding, the deformation of the fractured gel may recover less. For instance, for the yielded waxy crude oil gel which recovers from the strain of 0.10, only 20.4% of the strain can be recovered. This may be compared with 75.4% of the strain recovery from the strain of 0.04, which is nearly the same proportion with that in the linear viscoelastic region (Table 5). However, for waxy crude oil emulsion gels, the entire volume is spanned by a wax crystal network which entraps the dispersed water.6,8,20 As a result, the shear stress and strain are shared by both the water droplets and the wax crystal structure. Because of the contribution of water droplets, the yielded emulsion gels show stronger recoverability of deformation than the waxy crude oil gel. As to the recoverability of the emulsion gels which is dependent upon the water cut, it can be seen from Figure 22a that when the emulsion gels recover from the strain of 0.04, i.e., for the unyielded emulsion gels, the residual strain decreases with the increase of water cut. On the contrary, when the emulsion gels recover from the strain of 0.10, i.e., for the yielded emulsion gels, the residual strain increases with the increase of water cut (see Figure 22c). And accordingly when the emulsion gels recover from the strain of 0.07, a turning point appears at the water cut of 40%, as can be seen in Figure 22b. In fact, in this case the samples below the 40% water cut have yielded, but the samples with higher water cuts are unyielded. That is to say, in the unyielded region the variation of the residual strain with the water cut is consistent with that shown in Figure 22a, whereas in the yielded region the trend is just the same as that shown in Figure 22c. This may be interpreted according to the contribution of the water droplets to the elasticity of the emulsion gels. For those unyielded gels, the elasticity is increased with increasing water cut, which has been demonstrated by the above-discussed creep-recovery experiments. However, after the yielding of the emulsion gels, the initiation of flow will result in the breakage of water droplet clusters and further the coalescence of droplets, as is shown in Figure 23 by the enlarged droplet sizes. This
Table 7. Viscoelastic Parameters of the Emulsion Gels with the Water Cuts of 20% and 50% after the Stress Is Loaded to γ = 0.04 and γ = 0.10 after stress loaded to γ = 0.04
after stress loaded to γ = 0.10
water cut (vol%)
G′ (Pa)
loss angle (o)
G′ (Pa)
loss angle (o)
20 50
4110 6770
12.34 9.12
2905 3730
16.06 14.37
by 29.3%, and the loss angle increases by 30.1% when the strain is increased from 0.04 to 0.10. However, for the emulsion gel with a high water cut (50%), the storage modulus decreases by 44.9% and the loss angle increases by 57.6% under the same conditions, which means the high water cut emulsion gel loses more elasticity after yielding due to the more coalescence of droplets.
4. CONCLUSION The viscoelastic and yield behaviors of waxy crude oil and its emulsion gels were investigated, and their mechanisms were discussed based on experiments and comparisons. In summary, the rheological behaviors are dramatically changed because of the existence and deformation of the dispersed water droplets in combination with the precipitation of wax crystals and further the formation of a structure with wax crystals and water droplets. By small amplitude oscillatory measurements, it is found that the structure is strengthened and becomes more elastic after the crude oil is emulsified. Specifically speaking, as the water cut of the emulsion increases, the storage modulus grows up while the loss angle decreases, and the emulsion gels at a higher temperature. Meanwhile, the structure builds up more quickly. An exponential relation is found between the storage modulus and the water cut. The creep-recovery experiments within the linear viscoelastic region further demonstrate the enhancement of elasticity. With the increase of water cut, the residual strain after recovery decreases and even vanishes when the water cut is above 40%. Both the creep and recovery behavior may well be described by a mechanical analogy model with one Maxwell model and two Kelvin−Voigt models associated in series. However, the parameters fitted by the creep data cannot describe well the recovery behavior, as is reported in many other works. The emulsion gels show different yield behaviors from the gelled waxy crude oil. First, the yield process shows that the emulsion gel becomes more ductile with increasing water cut, compared to the brittle-fracture-like yielding of the waxy crude oil gel. Second, the yield stresses of both the crude oil and the emulsion gels increase monotonically with the increase of precipitated wax and water cut, while the yield strains show different trends. For the emulsions with few wax particles, the yield strain increases monotonically with decreasing temperature. Conversely, for the waxy crude oil and the emulsions at low water cuts, when many wax particles precipitate, the yield strain decreases monotonically with decreasing temperature. However, in the same temperature region, for the emulsions above 30% water cut, the yield strain first increases and then decreases with decreasing temperature. This is due to the change of the yield mechanism from the domination of the damage of droplet clusters to the domination of the fracture of wax crystal network with precipitated paraffins increased.
Figure 23. (a, b) Microscopic images of the 30% water cut emulsion gel after rheological tests corresponding to Figure 22, panels a and c respectively (25 °C).
leads to the emulsions becoming less elastic, and accordingly the deformation is less recoverable. And because more droplets may coalesce at higher water cuts due to the breakdown of the structure and the flow, the higher the water cut is, the more elasticity the emulsion loses after yielding. This is proved by the change of the viscoelastic parameters before and after the emulsion gels yield, as is shown in Table 7. For the emulsion gel with a low water cut (20%), the storage modulus decreases 3728
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AUTHOR INFORMATION
Corresponding Author
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[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Support from the National Natural Science Foundation of China (No. 51134006) is gratefully acknowledged. REFERENCES
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