Scaling of Structural Characteristics of Gelled Model Waxy Oils

Article pubs.acs.org/EF

Scaling of Structural Characteristics of Gelled Model Waxy Oils Fei Yang,† Chen Li,‡ Chuanxian Li,*,† and Dan Wang† †

College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao, Shandong 266580, People’s Republic of China College of Petroleum Engineering, Southwest Petroleum University, Chengdu, Sichuan 610500, People’s Republic of China

‡

ABSTRACT: The structural properties of gelled model waxy oils with different wax concentrations (5−20 wt %) were investigated through a differential scanning calorimetry (DSC) test, rheological measurement, and scaling model for colloidal gels. The wax precipitation curves obtained from the DSC test show that the concentration of precipitated wax crystals φW increases gradually with the decrease of the temperature, and most of the waxes dissolved in the oil phase precipitate at −20 °C. The gelation point increases gradually with an increasing wax concentration from 22 °C at 5 wt % to 26 °C at 10 wt %, then to 32 °C at 15 wt %, and 34 °C at 20 wt %. The structure of gelled waxy oils, similar to the structure of colloidal gels, transits from a strong-link regime to a weak-link regime with the increase of φW, and the value of φW at the transition point is around 1.8 wt % for all of the tested model waxy oils. In the strong-link region, G′E increases while γE decreases with an increasing φW. In the weak-link region, both G′E and γE increase with an increasing φW. The ln G′E ∼ ln φW and ln γE ∼ ln φW relations can be divided into three parts at wax concentrations of ≤10 wt %; at wax concentrations of 15−20 wt %, the relations can be divided into two parts. In the strong-link region, the fractal dimension D of gelled waxy oil was calculated through parameters A and B. In the weak-link region, the fractal dimension D was calculated through parameter B because of the good linear relationship between ln γE and ln φW. The fractal dimension D increases from very small values (less than 1) to high values (approaching 3) with an increasing φW, indicating the continuous development of the microstructure of the gelled waxy oils with an increasing φW. observation techniques.23 A more fundamental knowledge of microstructural characteristics is necessary for better understanding the complex rheological (or macrostructure) changes of gelled waxy crude oil. A scaling model has been widely used to describe the microstructures of colloidal gels since the beginning by Shih et al.24−26 Recently, the scaling model was applied to gelled waxy crude oil systems because of the colloidal nature of waxy crude oils.11,13,15 Webber et al.13 studied a gelled mineral oil system through the scaling model. It was found that the system exhibits a weak-link type of scaling, in contrast to the strong-link scaling exhibited by flocculated colloidal gels. da Silva et al.15 obtained the fractal dimension of three different gelled waxy crude oils through the scaling model. The low fractal dimensions obtained indicate elongated substructures. In a former paper,23 we introduced the scaling theory of colloidal gels and studied the structural properties of three gelled waxy crude oils through the scaling theory. The microscopic structural characteristics of the oils were obtained through the relations between ln G′E ∼ ln φW and ln γE ∼ ln φW, where G′E is the elastic modulus in the linear region, γE is the critical linear elastic strain, and φW is the concentration of precipitated wax crystals. The results showed that the gelled structure of waxy crude oils, similar to that of colloidal gels, transits from a strong-link regime to a weak-link regime with the increase of φW. The fractal dimension D increases gradually with an increasing φW. It was also found that the gel structures of three crude oils are different from each other. However, the causes leading to the difference were hard to evaluate because

1. INTRODUCTION A pipeline is the most economical and feasible means for the transportation of large quantities of crude oil. However, wax precipitation from the crude oil causes several problems in pipeline transportation.1 Waxes are the highest molecular weight nonpolar fraction of crude oil and can be classified as branched (isoparaffins), cyclic, or linear (normal or n-paraffins), the latter of which dominate crystallization properties.2,3 Shutdown of a pipeline may occur regularly for operational reasons and occasionally for emergency reasons. During the shutdown period, the temperature of crude oils decreases gradually, leading to the continuous precipitation of wax crystals. Because of the large aspect ratios of wax crystals, only small volume fractions (as little as 0.5 wt % wax) of wax crystals could form a network structure in the oil phase, thus impeding flow.4 Then, an applied pressure higher than the usual operating pressure is required to overcome the gel strength of the gelled crude oil.5−8 To ensure the successful restart of pipeline transporting waxy crude oils, researchers payed more attention on the structural properties of gelled waxy crude oils. During the last 2 decades, the macroscopic structural properties of gelled waxy crude oils have been studied in detail through rheological measuring methods. The gelation point9,10 of waxy crude oils was welldefined, and the effects of thermal history,11,12 shearing history,13,14 wax composition,4,15 and asphaltene16,17 and pour point depressant addition18,19 on the structure of gelled waxy oils were well-discussed on the basis of the rheological data. The microscopic structural characteristics of gelled waxy crude oils are also greatly important in explanation of the rheological (or macrostructure) changes at different conditions.20−22 However, studies on this aspect were limited because of the complicated nature of the oils and the defects of microscopic © 2013 American Chemical Society

Received: March 28, 2013 Revised: May 18, 2013 Published: June 4, 2013 3718

dx.doi.org/10.1021/ef400554v | Energy Fuels 2013, 27, 3718−3724

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model waxy oils were obtained through the temperature sweeping test under oscillatory mode. The oil samples were first heated to 40 °C [well above the wax appearance temperature (WAT) of the oils], kept at 40 °C for 20 min, and then cooled at a cooling rate of 0.5 °C/min. During the cooling process, the elastic modulus G′, the viscous modulus G″, and the loss angle δ were measured under a fixed oscillatory frequency (1 Hz) and a fixed shear strain (0.0005). The gelation point is the temperature at which G′ begins to become larger than G″ (or δ begins to become smaller than 45°).9,10 2.3.2. G′E and γE Measurements of the Model Waxy Oils. Using the AR-G2 rheometer, the effect of shear stress on the structure of gelled model waxy oils was investigated through the stress sweeping test under oscillatory mode. The model waxy oils were first heated to 40 °C (well above the WAT of the oils), kept at 40 °C for 20 min, then cooled at a cooling rate of 0.5 °C/min quiescently to the test temperature (well below the gelation point), and kept at the test temperature for another 20 min. After that, the elastic modulus G′, the viscous modulus G″, the loss angle δ, and the shear strain γ were measured at different shear stress τ under a fixed oscillatory frequency (1 Hz). The linear elastic region of the gelled waxy oils was determined by G′E, at which the value of G′ begins to decrease obviously. γE was obtained on the basis of the value of G′E.

of the compositional difference of the crude oils. Model waxy oil systems were often selected as the research object because of the simplicity of its composition. In this paper, the structural properties of gelled model waxy oils with different wax concentrations (5−20 wt %) were investigated through the scaling theory. The purpose of this paper is to disclose the effect of the wax concentration on the rheology and microstructure characteristics of gelled model waxy oils, which has important guidance on the restart of pipeline transporting waxy crude oils.

2. EXPERIMENTAL SECTION 2.1. Model Waxy Oil System. A model waxy oil was created that consisted of two components. The first component is a diesel oil used to form the continuous or matrix phase. As seen in Table 1, the diesel

Table 1. Compositions of Diesel Oila n-alkane and isoalkane (wt %)

cycloalkane (wt %)

total saturated hydrocarbons (wt %)

total aromatic hydrocarbons (wt %)

resin (wt %)

56.3

31.2

87.5

12.4

0.1

3. RESULTS AND DISCUSSION 3.1. Wax Precipitation Properties of Model Waxy Oils. The DSC curves of the model waxy oils are shown in Figure 2.

a

The composition of diesel oil was examined through methods mentioned in ASIM D2425.

oil is composed mainly by saturated hydrocarbons (87.5 wt %) and aromatic hydrocarbons (12.4 wt %). The content of resin in diesel oil is very small (0.1 wt %). The second component is a paraffin wax (Yanyu Biochemistry Co., China) with a melting point specified by the manufacturer to be between 58 and 62 °C. The composition of the wax was measured using a high-temperature gas chromatograph (Agilent Co., Santa Clara, CA). As seen in Figure 1, the paraffin wax

Figure 2. DSC curves of the model waxy oils at different wax concentrations.

The WAT increases with the increase of the wax concentration. At a wax concentration of 5 wt %, the WAT of model waxy oil is 22 °C. As the wax concentration increases to 10 wt %, the WAT is 26 °C. With the further increase of the wax concentration to 15 wt %, the WAT increases to 32 °C. At a wax concentration of 20 wt %, the WAT is 34 °C. At temperatures below WAT, the model waxy oils release heat very quickly because of the precipitation of wax crystals. The wax precipitating peak region of model waxy oils is narrowed in comparison to that of waxy crude oils,23 perhaps because of the narrow carbon number distributions of the wax dissolved in diesel oil (see Figure 1). On the basis of the DSC curves, the concentration of precipitated wax crystals φW at different temperatures was obtained and shown in Figure 3. At temperatures above the WAT, φW equals zero, meaning that no wax crystals exist in the temperature range. At temperatures below the WAT, φW increases gradually with the decrease of the temperature. As the temperature decreased to −20 °C, φW is 4.83 wt % for 5 wt % waxy oil, 9.81 wt % for 10 wt % waxy oil, 14.74 wt % for 15 wt % waxy oil, and 19.51 wt % for 20 wt % waxy oil. It is clear that most of the waxes precipitate from the oil phase at −20 °C. 3.2. Gelation Point Determination. The variations of G′, G″, and δ of model waxy oils with the test temperature are

Figure 1. Composition of paraffin wax as determined by gas chromatography. has a continuous carbon-number distribution ranging from C20 to C38. It contains about 90 wt % n-paraffins, with the remainder being branched and cyclic paraffins, and, thus, provided a system whose interactions would be dominated by its crystalline character. The model waxy oil system was prepared by dissolving a certain amount of paraffin wax in diesel oil. The wax concentrations of prepared model waxy oils are 5, 10, 15, and 20 wt %. 2.2. Differential Scanning Calorimetry (DSC) Measurement. Using a DSC821e differential scanning calorimeter (Mettler-Toledo Co., Switzerland), the exothermic characteristics of model waxy oils having different wax concentrations were studied. The temperature scanning range is from −20 to 80 °C, and the cooling rate is fixed at 5 °C/min. The concentration of precipitated wax crystals φW at different temperatures was calculated on the basis of the DSC curves.25 2.3. Rheological Measurement. 2.3.1. Gelation Point Determination. Using an AR-G2 controlled stress rheometer (TA Co., New Castle, DE) with rotor−cylinder geometry, the gelation points of 3719


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into large plate-like particles, which favors the formation of a network structure. Then, a very small concentration of precipitated wax crystals could impede flow of the oils. Therefore, the gelation points of the model waxy oils are slightly below or the same as the WAT. 3.3. G′E and γE of the Gelled Model Waxy Oils. 3.3.1. Determination Method of G′E and γE. The effect of shear stress τ on the structure of 10 wt % gelled waxy oil under different temperatures is shown in Figure 5. G′ remains Figure 3. Concentrations of the precipitated wax crystals φW for model waxy oils at different temperatures.

shown in Figure 4. The structural transition from liquid-like to solid-like occurs with the decrease of the test temperature because of the continuous precipitation of wax crystals. At temperatures larger than WAT, the value of G′ is far smaller than G″ and the loss angle δ is great larger than 45°, indicating that the model waxy oils show a liquid-like behavior. At temperatures around the WAT, G′ increases more quickly with a decreasing temperature, leading to the rapid decrease of the loss angle δ from high values to small values (around 25°). The model waxy oils show a viscoelastic fluid behavior in the temperature range. At temperatures far below the WAT, G′ is far larger than G″ and the loss angle δ is around 10°, meaning that the model waxy oils show a solid-like behavior. The gelation points of the model waxy oils obtained from Figure 4 are nearly the same as the WAT: the gelation point is 20 °C for 5 wt % waxy oil, 26 °C for 10 wt % waxy oil, 32 °C for 15 wt % waxy oil, and 34 °C for 20 wt % waxy oil. For the model waxy oils, the contaminates (such as resin and asphaltene) are scarce and the wax crystals are easier to grow

Figure 5. Variations of G′ and γ of 10 wt % model waxy oil with shear stress τ under different test temperatures.

constant, and γ increases linearly when the values of shear stress are in the low range, indicating that the relationship between shear stress and its corresponding strain is in the linear elastic region; when the loaded shear stress increased above a certain

Figure 4. Variations of G′ (□), G″ (○), and δ (△) of model waxy oils with the test temperature. The wax concentration is (a) 5 wt %, (b) 10 wt %, (c) 15 wt %, and (d) 20 wt %. 3720


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Table 2. G′E and γE of 5 wt % Gelled Model Waxy Oil at the Temperature Range of 7−20 °C T (°C) γE G′E (Pa) T (°C) γE G′E (Pa)

20 1.16 × 10−4 3.036 13 9.56 × 10−6 10400

19 8.94 × 10−5 10.88 12 1.13 × 10−5 20910

18 4.57 × 10−5 20.53 11 5.48 × 10−6 51500

17 2.70 × 10−5 679 10 1.33 × 10−5 66500

value, G′ begins to decrease obviously while γ increases nonlinearly, meaning that the gel structure is partly destroyed by the loaded shear stress and the gelled waxy oil comes into the nonlinear viscoelastic region. G′E and γE, at which G′ begins to decrease obviously and γ begins to increase nonlinearly, can be well-obtained from Figure 4. At the test temperature of 26 °C, G′E is 42 Pa and γE is 9.42 × 10−5. At the test temperature of 24 °C, G′E increased to 3100 Pa while γE decreased to 1.08 × 10−5. 3.3.2. G′E and γE of the Gelled Model Waxy Oils. 3.3.2.1. G′E and γE of 5 wt % Gelled Model Waxy Oil. As seen in Table 2, the initial value of G′E is very small at 20 °C (3.036 Pa), meaning that the concentration of precipitated wax crystals is not large enough to build a strong gel structure. With the decrease of the test temperature, G′E increases greatly because of the continuous precipitation of wax crystals. γE decreases with a decreasing temperature at temperatures of ≥15 °C. At the range of temperatures of 14−12 °C, γE fluctuates around 1 × 10−5. γE achieves a minimum value (5.48 × 10−6) at 11 °C and then increases gradually with the further decrease of the test temperature. The variations of G′E and γE of 5 wt % gelled model waxy oil with the concentration of precipitated wax crystals are demonstrated in Figure 6. The figure can be divided into

16 1.36 × 10−5 1672 9 1.44 × 10−5 79580

15 9.74 × 10−6 4650 8 1.86 × 10−5 102000

14 1.21 × 10−5 7448 7 1.88 × 10−5 125000

strong-link regime in these parts. The variation rates of G′E and γE are very slow in part one but very quick in part two. Both G′E and γE increase quickly with an increasing ϕW in part three (1.91 < ϕW ≤ 2.57 wt %), meaning that the gelled model waxy oil shows a weak-link regime in this part. 3.3.2.2. G′E and γE of 10 wt % Gelled Model Waxy Oil. As seen in Table 3, the value of G′E increases quickly when the test temperature decreases from 26 to 19 °C. With the further decrease of the temperature, the decreasing rate of G′E becomes slow. γE decreases with a decreasing temperature and achieves the minimum value (4.33 × 10−6) at 22 °C. At temperatures below 22 °C, however, γE increases quickly with the further decrease of the temperature. The variations of G′E and γE for 10 wt % gelled model waxy oil with ϕW are shown in Figure 7, which can also be divided

Figure 7. Variations of G′E and γE of 10 wt % gelled model waxy oil with the concentration of precipitated wax crystals ϕW.

into three parts. In part one (ϕW ≤ 0.902 wt %) and part two (0.902 < ϕW ≤ 1.87 wt %), G′E increases while γE decreases with an increasing ϕW, indicating that the gelled waxy oil shows a strong-link regime in these parts. The variation rates of G′E and γE are slow in part one but accelerate in part two. Both G′E and γE increase with an increasing ϕW in part three (1.87 < ϕW ≤ 5.43 wt %), meaning that the gelled waxy oil shows a weaklink regime in this part. 3.3.2.3. G′E and γE of 15 wt % Gelled Model Waxy Oil. As seen in Table 4, the value of G′E first increases quickly with a decreasing temperature at temperatures of ≥26 °C and then increases slowly with the further decrease of the temperature. γE


three parts. In part one (ϕW ≤ 0.685 wt %) and part two (0.685 < ϕW ≤ 1.91 wt %), G′E increases while γE decreases with an increasing ϕW, meaning that the gelled model waxy oil shows a


26 9.42 × 10−5 42 19 3.35 × 10−5 175000

25 2.10 × 10−5 1700 18 4.29 × 10−5 184000

24 1.08 × 10−5 3100 17 5.20 × 10−5 195000

23 7.33 × 10−6 14890 15 8.42 × 10−5 205000 3721

22 4.33 × 10−6 63350 14 1.18 × 10−4 207000

21 8.96 × 10−6 102000 13 1.39 × 10−4 220000

20 1.83 × 10−5 148000 11 1.62 × 10−4 234000


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31 3.11 × 10−5 600 25 7.20 × 10−5 209000

30 1.37 × 10−5 20000 24 8.48 × 10−5 220000

29 7.95 × 10−6 80000 23 1.57 × 10−4 228000

28 1.25 × 10−5 124000 22 2.04 × 10−4 225000

27 2.71 × 10−5 171000 21 2.45 × 10−4 235000

26 4.07 × 10−5 190000

first decreases with a decreasing temperature at temperatures of ≥29 °C and then increases quickly with the further decrease of the temperature. The variations of G′E and γE for 15 wt % gelled model waxy oil with ϕW are demonstrated in Figure 8, which can be divided


The structures of gelled model waxy oils are different from those of gelled waxy crude oils.23 In comparison to gelled waxy crude oils, G′E of gelled waxy oils becomes larger while γE of gelled waxy oils becomes smaller. The possible reason is that the gelled waxy oil shows a more rigid and brittle structure, which is easier to be destroyed by a very small shear strain. 3.4. Microstructure of Gelled Model Waxy Oils Analyzed by the Scaling Model. On the basis of Figures 6−9 and the scaling model, the values of parameter A, parameter B, and fractal dimension D of model waxy oils were calculated and listed in Table 6. It is clear that the fractal dimension D increases with an increasing φW. For 5 wt % gelled waxy oil, G′E ∼ φW1.395 while γE ∼ φW−0.546 at φW ≤ 0.685 wt %; the calculated value of fractal dimension D is very small (0.645), indicating the formation of a very porous and loose microstructure. When φW is between 0.685 and 1.91 wt %, G′E ∼ φW5.334 while γE ∼ φW−1.499; the calculated value of fractal dimension D increases to 2.478, meaning the formation of a compact microstructure. At the range of φW of 1.91−2.57 wt % (weak-link region), the values of parameters A and B are nearly the same and the calculated fractal dimension D increases to 2.725. The variations of parameter A, parameter B, and fractal dimension D with φW for 10 wt % gelled waxy oil are similar to those for 5 wt % gelled waxy oil. The fractal dimension D increases from 0.490 to 2.300 and then to 2.700 with the increase of φW, indicating the continuous development of the microstructure with an increasing φW. In the weak-link region (1.87 < φW ≤ 5.43 wt %), the fractal dimension D was


into two parts. In part one (ϕW ≤ 1.42 wt %), G′E increases while γE decreases with an increasing ϕW. The gelled waxy oil shows a strong-link regime in part one. Both G′E and γE increase with an increasing ϕW in part two (1.42 < ϕW ≤ 6.50 wt %), meaning that the gelled model waxy oil shows a weaklink regime in this part. 3.3.2.4. G′E and γE of 20 wt % Gelled Model Waxy Oil. As seen in Table 5, the value of G′E first increases quickly with a decreasing temperature at temperatures of ≥28 °C and then increases very slowly with the further decrease of the temperature. γE first decreases with a decreasing temperature at temperatures of ≥31 °C and then increases quickly with the further decrease of the temperature. The variations of G′E and γE for 20 wt % gelled model waxy oil with ϕW are shown in Figure 9, which can also be divided into two parts. In part one (ϕW ≤ 1.81 wt %), G′E increases while γE decreases with an increasing ϕW. The gelled waxy oil shows a strong-link regime in part one. Both G′E and γE increase with an increasing ϕW in part two (1.81 < ϕW ≤ 7.70 wt %), meaning that the gelled model waxy oil shows a weaklink regime in this part.


33 3.92 × 10−5 270 28 9.01 × 10−5 225000

32 1.50 × 10−5 5500 27 1.70 × 10−4 220000

31 8.11 × 10−6 55000 26 2.52 × 10−4 233000 3722

30 1.25 × 10−5 156000 25 3.10 × 10−4 230000

29 3.08 × 10−5 190000 24 3.35 × 10−4 235000


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Table 6. Values of Parameter A, Parameter B, and Fractal Dimension D of Gelled Model Waxy Oilsa wax concentration 5 wt %

10 wt % 15 wt % 20 wt %

range of φW (wt %)

link regime of the microstructure

A

B

D

φW ≤ 0.685 0.685 < φW ≤ 1.91 1.91 < φW ≤ 2.57 φW ≤ 0.902 0.902 < φW ≤ 1.87 1.87 < φW ≤ 5.43 φW ≤ 1.42 1.42 < φW ≤ 6.50 φW ≤ 1.81 1.81 < φW ≤ 7.70

strong-link strong-link weak-link strong-link strong-link weak-link strong-link weak-link strong-link weak-link

1.395 5.334 3.626 1.380 4.072

−0.546 −1.499 3.638 −0.586 −1.216 3.334 −0.356 2.805 −0.399 3.541

0.645 2.478 2.725 0.490 2.300 2.700 0.932 2.643 0.850 2.718

1.324 1.329

a

The fractal dimension D in a strong-link regime was calculated according to parameters A and B, while the fractal dimension D in a weak-link regime was calculated only according to parameter B.

■

calculated through parameter B because of the good linear relationship between ln γE and ln φW (see Figure 7). For 15 wt % gelled waxy oil, G′E ∼ φW1.324 while γE ∼ φW−0.356 at φW ≤ 1.42 wt %; the calculated value of fractal dimension D is 0.932. At the range of φW of 1.42−6.50 wt % (weak-link region), the fractal dimension D calculated through parameter B (B = 2.805) is 2.643, indicating the formation of a compact gel structure. For 20 wt % gelled waxy oil, G′E ∼ φW1.329 while γE ∼ φW at φW ≤ 1.81 wt %; the calculated value of fractal dimension D is 0.850. At the range of φW of 1.81− 7.70 wt % (weak-link region), the fractal dimension D calculated through parameter B (B = 3.541) is 2.718, indicating the formation of a compact gel structure

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (51204202), the Natural Science Foundation of Shandong Province of China (ZR2012EEQ002), and the Fundamental Research Funds for the Central Universities (12CX04073A).

■

4. CONCLUSION On the basis of the DSC curves, rheological data, and scaling model for colloidal gels, we systematically analyzed the structural properties of gelled model waxy oils with different wax concentrations (5−20 wt %). The wax precipitation curves measured by DSC show that φW increases gradually with the decrease of the temperature. Most of the waxes dissolved in the oil phase precipitate at −20 °C. The gelation points of waxy oils are slightly below or the same as the WATs of waxy oils. With the increase of the wax concentration, the gelation point increases gradually. The gelation point is 22 °C for 5 wt % waxy oil, 26 °C for 10 wt % waxy oil, 32 °C for 15 wt % waxy oil, and 34 °C for 20 wt % waxy oil. The structure of gelled waxy oils, similar to the structure of colloidal gels, transits from a strong-link regime to a weak-link regime with the increase of φW, and the value of φW at the transition point is around 1.8 wt % for all of the model waxy oils. In the strong-link region, G′E increases while γE decreases with an increasing φW. In the weak-link region, both G′E and γE increase with an increasing φW. In comparison to gelled waxy crude oils, G′E of gelled waxy oils becomes larger while γE of gelled waxy oils becomes smaller. The ln G′E ∼ ln φW and ln γE ∼ ln φW relations can be divided into three parts at wax concentrations of ≤10 wt %. At wax concentrations of 15−20 wt %, the relations can be divided into two parts. In the strong-link region, the fractal dimension D of gelled waxy oils was calculated through parameters A and B. In the weak-link region, the fractal dimension D was calculated through parameter B because of the good linear relationship between ln γE and ln φW. The fractal dimension D increases from very small values (less than 1) to high values (approach 3) with an increasing φW, indicating the continuous development of the microstructure of the gelled waxy oils with an increasing φW.

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Scaling of Structural Characteristics of Gelled Model Waxy Oils

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