Effect of Carbon Number Distribution of Wax on the Yield Stress of

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Effect of Carbon Number Distribution of Wax on the Yield Stress of Waxy Oil Gels Chengyu Bai and Jinjun Zhang* National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban Oil & Gas Distribution Technology, China University of Petroleum, Beijing 102249, China S Supporting Information *

ABSTRACT: Wax deposition is one of the most important problems in flow assurance of petroleum pipelines. Pigs are commonly employed for the removal of wax deposit (actually a wax−oil gel consisting of liquid oil and solid wax particles) on the pipe wall. Understanding of the wax deposit strength, which may be a function of the carbon number distribution of wax, assists in preventing the pig from getting stuck in the pipeline. This study focuses on the effect of the carbon number distribution of wax on the yield stress of waxy oil gels. Waxes with different carbon number distribution were dissolved into a crude oil to prepare the model oils. The vane method was used to determine the yield stress of waxy oil gels formed under quiescent or shear conditions, in which an applied shear stress was maintained during the process of cooling and isothermal holding. The results showed that the yield stresses dramatically decrease with increase of average carbon number of wax regardless of the quiescent or shear conditions. However, the applied shear stress has little effect on the yield stress of the wax−oil gel 12.5% W1 + oil-A and no effect on the yield stresses of 12.5% W2 + oil-A and 12.5% W3 + oil-A. Under quiescent conditions, the changing rate of the yield stress with respect to the solid wax content reduces as the average carbon number of wax increases. The morphology and structure of the wax crystals were also observed using optical microscopy. Microscopic observation indicated that the average size and boundary fractal dimension of the wax crystals decrease but the aspect ratio increases with the increase of the average carbon number of wax.

1. INTRODUCTION Crude oil is a complex mixture containing waxes, aromatics, resins, asphaltenes, etc. Among these components, waxes, which are the compounds of n-paraffins (C17−C55), tend to deposit on the cold wall of the pipeline, especially on subsea pipelines. In fact, the wax deposit does not consist solely of solid wax particles, but is actually a wax−oil gel consisting of liquid oil that is entrapped by the solid wax particle network.1 Wax deposition could result in reduction of the flow of a line section or even blockage of a pipeline. Pigs (pipeline inspection gauges) are widely used to remove the wax deposit.2 However, if the wax deposit becomes too hard, the pigs will be unable to break the deposit and will get stuck in the pipeline, causing further blockage. A better understanding of the wax deposit strength will be helpful in making a suitable pigging schedule. Several models of wax deposition have been developed.3−7 These models may accurately predict the thickness and the wax content of a wax deposit. However, none of them address the wax deposit strength. The strength of a wax deposit is affected by several factors. One of the main factors is the carbon number distribution of the deposited wax. In wax deposition, the critical carbon number (CCN) is the minimum carbon number of paraffins diffusing into the deposit, and it depends on the composition of the crude oil as well as operating conditions.8 Thus, the carbon number distribution of wax in the deposit varies with the crude oil composition and operating conditions of a pipeline. For example, as the flow rate increases, the average carbon number of wax increases,9 and the deposit becomes thinner and harder.1,10,11 However, it cannot be concluded that a higher © 2013 American Chemical Society

average carbon number of wax results in harder deposits because the wax content of a wax deposit also increases with the increase of flow rate.1,10 The increase of wax content could lead to hardening of the deposit.1,12 However, the effect of the average carbon number of wax on the deposit strength is not clear. Another factor affecting the deposit strength may be the shear stress from the flow stream. Since there are differences in the morphology of the wax crystals with different carbon number distributions, the effect of shear stress on the deposit strength may also be different. Therefore, it is necessary to study the effect of carbon number distribution of wax on the wax−oil gel strength (characterized by the yield stress) under quiescent and shear conditions. There are reports in the literature on the effect of single paraffins (>C17) or mixtures of paraffins on the yield stress of model oils, as well as the morphology and structure of the crystals. Guo et al.13 observed that the crystals formed in solutions of pure paraffins (i.e., C36, C32, C28, C24) and C10 appeared as large crystals, either as a three-dimensional “house of cards” for C36/C10 and C32/C10 or as long bars for C28/C10 and C24/C10. However, for the systems of binary paraffin mixtures and C10, separated crystal lamellae were observed. They also found that the yield stresses of the mixed paraffin solutions were much lower than that of each single paraffin solution. However, Imai et al.14 observed that the yield stress of Received: Revised: Accepted: Published: 2732

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the system C32 + C30/n-butyl myristate (n-BM) was much higher than that of C32/n-BM. Microscopy showed that, compared with the crystals in gel C32/n-BM, many more steps were observed on the crystal surface in the system of C32 + C30/n-BM. Similarly to a study by Imai et al., Paso et al.15 observed that polydisperse n-paraffin crystals exhibited nanoscale surface roughness crystals, while the crystals composed of a single chain length component exhibited ordered surfaces and sharp edges, providing minimal crystal−crystal contacts and weak interactions. Léoffé et al.16 observed that the size of wax crystals in systems of pure paraffins and crude oil matrix was small (1−3 μm) and depended upon the length of paraffinic chains. To further study the effect of the carbon number distribution on the yield stress, different carbon numbers of paraffins were mixed to obtain binary paraffin mixtures with diverse carbon number distributions. Guo et al.13,17 observed that the yield stress of the solution 2% C36 + 2% C32/C10 was higher than that of the solution 2% C36 + 2% C28/C10. Microscopic results showed that C36 and C32 were able to cocrystallize and to form larger crystals.13 However, in contrast to results by Guo et al., Senra et al. 18 found that cocrystallization of paraffins resulted in a smaller size and a weaker network of the crystals. However, there was little work examining the effect of the continuous carbon number distribution of waxes (C17−C55) on the yield stress. A few studies have investigated the effect of the applied shear stress on the yield stress of oil gels,12,19,20 but these studies were not in agreement. This might be attributed to the different compositions of the oils used in these studies. Venkatesan et al.12 used a model oil consisting of wax and mineral oil, and the sample was cooled under an applied shear stress. The results showed that the application of shear stress resulted in two competing effects: the tendency to aggregate the precipitating crystals (increase the yield stress) and the tendency to break down the growing crystals (decrease the yield stress). By studying waxy oil, Visintin et al.19 found that the influence of the applied shear stress on the gel structure was related to the difference between the values of the applied shear stress and the yield stress of gels. Ding et al.20 used waxy crude oil in their experiments. They found that the effect of the applied shear stress on the yield stress was associated with the temperature of the sample. The objective of this study was to examine the effect of the carbon number distribution of wax on the yield stress of waxy oil gels formed under either quiescent or shear conditions. Waxes with different carbon number distributions were dissolved in a crude oil to prepare the wax−oil gels. The yield stresses of the wax−oil gels were measured by using the vane method. To provide insights into the yield stress results, the morphology and structure of wax crystals were observed by using polarizing optical microscopy. Further, the relationship between the yield stress of a wax−oil gel and the characteristic parameters of the wax crystals, i.e., the average size, aspect ratio, and boundary fractal dimension, was presented.

Figure 1. Carbon number distribution of waxes W1, W2, W3, W-A, and W-B.

Information. The average carbon numbers of the waxes W1, W2, and W3 were 25.7, 28.8, and 33.2, respectively. The average carbon number (n)̅ was evaluated as follows: n̅ =

∑

nφn

(1)

n = 17

where φn is the mass fraction of n-paraffin in the wax (wt %) and n is the carbon number of the n-paraffin. 2.1.2. Crude Oils. Two crude oils (oil-A and oil-B), produced from the Tuha oil field in China, were used in this work. The wax appearance temperature (WAT) and other oil properties are summarized in Table 1. The carbon number distribution of Table 1. Properties of Oil-A and Oil-B parameter

oil-A

oil-B

density at 20 °C (kg/m3) wax content at −20 °C (wt %) solid wax content at 5 °C (wt %) WAT (°C) asphaltene content (wt %) resin content (wt %) viscosity at 20 °C (mPa·s)

842.9 11.5 5.0 33 0.87 6.36 52.2

833.1 9.6 4.4 27 1.33 5.39 29.1

wax in oil-A and oil-B (hereinafter referred to as W-A and W-B, respectively) was determined by using high-temperature gas chromatography, and the results are shown in Figure 1. In Figure 1, 9.4 wt % C17 for oil-A indicates that 9.4 wt % of the wax in oil-A is C17 and not that 9.4 wt % of oil-A is C17. The average carbon numbers of waxes W-A and W-B were 22.4 and 22.7, respectively. 2.1.3. Model Oil Preparation. The required amounts of wax and crude oil were first placed in a glass bottle, and the bottle was sealed tightly. To completely dissolve the wax in the crude oil, the specimen was heated to 80 °C and kept isothermally for 2 h. During the isothermal holding, the bottle was shaken to prepare a homogeneous solution. Then, the sample was cooled quiescently to room temperature and kept for at least 48 h before being used in the experiments. Table 2 lists all prepared samples and their properties. In Table 2, the average carbon number of wax was based on both the pure wax (W1, W2, or W3) and the wax in oil. 2.2. Yield Stress Measurements. All yielding measurements described below were performed using a controlled stress rheometer, RheolabQC (Anton Paar GmbH, Germany), equipped with vane geometry, which has been widely used to

2. EXPERIMENTAL SECTION 2.1. Materials. 2.1.1. Waxes. Three waxes, purchased from Shanghai Hua Yong Paraffin Co., Ltd., were used to prepare model oils. The melting point ranges of these waxes are 52−54 (W1), 58−60 (W2), and 70−72 °C (W3), respectively. The carbon number distribution was measured using high-temperature gas chromatography (HTGC), as shown in Figure 1. The details of the HTGC method are described in the Supporting 2733

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Table 2. Properties of All Prepared Samples sample no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

samples a

2.5% W1 + oil-A 2.5% W2 + oil-A 2.5% W3 + oil-A 5% W1 + oil-A 5% W2 + oil-A 5% W3 + oil-A 7.5% W1 + oil-A 7.5% W2 + oil-A 7.5% W3 + oil-A 10% W1 + oil-A 10% W2 + oil-A 10% W3 + oil-A 12.5% W1 + oil-A 12.5% W2 + oil-A 12.5% W3 + oil-A (5.5% W1 + 7% W2) + oil-A (3.1% W1 + 9.4% W2) + oil-A (10% W2 + 2.5% W3) + oil-A (7.5% W2 + 5% W3) + oil-A (3.1% W2 + 9.4% W3) + oil-A 12.5% W1 + oil-B 12.5% W2 + oil-B 12.5% W3 + oil-B

average carbon no.b

WAT (°C)

solid wax content at 5 °Cc (wt %)

wax content at −20 °Cc (wt %)

23.0 23.6 24.4 23.5 24.4 25.8 23.8 25.1 26.9 24.0 25.5 27.7 24.2 25.9 28.4 25.2 25.5 26.4 26.9 27.8 24.5 26.3 29.0

35 34 38 35 35 41 36 35 42 38 40 44 38 43 46 40 − − 43 − 37 38 46

7.9 8.0 7.5 10.5 10.8 10.6 12.7 12.6 13.0 15.6 16.2 15.1 18.2 18.5 18.4 19.2 − − 18.9 − 18.1 18.2 17.9

14.9 14.4 14.4 17.0 16.5 17.7 18.8 19.2 19.9 21.9 21.9 22.5 23.9 23.4 24.5 24.2 − − 24.1 − 22.2 21.9 22.7

a

2.5 wt % of the total weight of the prepared sample is pure wax W1. All the other mass fractions of pure waxes (W1, W2, or W3) for the following samples denote the same meanings as this. bBased on both the pure wax and the wax in oil. cDetermined by differenital scanning calorimetry.

measure the yield stress of gels.21 Dimensions of the fourbladed vane were 10 mm diameter and 8.8 mm length. The temperature was controlled by a thermal bath, F32-ME (Julabo, Germany), with control stability of ±0.01 °C. The specimen already prepared was reheated to 80 °C and kept at this temperature for 30 min to completely dissolve the wax. Then it was divided into two parts. One was used for measuring the yield stress of gels, and another was used for microscopic observation of the wax crystals. After the specimen was loaded into the preheated measuring system of the rheometer, it was cooled to 5 °C and held quiescently at this temperature for a period of time (i.e., holding time). During the process of cooling and isothermal holding at 5 °C, setting of wax particles did not occur (see section 2.1 of the Supporting Information). The determination of the cooling rate and holding time is introduced in sections 2.2 and 2.3 of the Supporting Information. Finally, the cooling rate of 1 °C/min and holding time of 100 min were determined. The stress controlled mode and the rate controlled mode are commonly used for determining the yield stress. In a stress controlled mode, several stress loading paths are available, such as the logarithmic stress ramp22 and constant stress rate.21 Among these stress loading paths, the logarithmic stress ramp provides a reasonable method to probe a wide experimental range;22 therefore, it was used in this work. The initial stress was 10 Pa and the duration time between two decades of stress was 100 s. Chang et al.23 have described the yielding process of waxy crude oils as consisting of three successive steps: elastic response, creep, and fracture. The shear stress at the point of fracture is the value with engineering importance and is usually taken as the yield stress.12 This definition of yield stress was also used in our study. Figure 2 shows the rheometric responses for samples 12.5% W1 + oil-A, 12.5% W2 + oil-A, and 12.5%

Figure 2. Typical results of yield stress tests at 5 °C for samples 12.5% W1 + oil-A, 12.5% W2 + oil-A, and 12.5% W3 + oil-A. x-axis values of the open symbols are for yield stress.

W3 + oil-A when determining the yield stress. Initially, the applied shear stress is far below the yield stress, and the resulting viscosity is essentially infinite since no sample movement can be recorded. When the shear stress increases further, the point of fracture will be reached and manifested in the form of a sudden decrease in the viscosity. The results of yield stress measurements were reproducible within 17.9%. 2.3. Optical Microscopy. 2.3.1. Observation of Wax Crystals. A polarizing microscope (Nikon OPTIPHOT2-POL, Nikon Corp., Japan) configured with a Linkam PE60 Peltier thermal stage (Linlam Scientific Instruments Ltd., U.K.) with a temperature range from −20 to 90 °C and control stability within ±0.1 °C was used to observe the morphology and structure of the wax crystals in waxy oil gels. The observation proceeded as follows. First, a specimen mentioned in the second paragraph of section 2.2 was cooled from 80 to 50 °C at 2734

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a rate of 1 °C/min and kept at 50 °C isothermally for the second and third repeated experiments. Second, the specimen was quickly spread by a cell scraper onto a glass slide that was placed on the preheated thermal stage of the microscope. The sample was cooled from 50 °C to the measurement temperature of 20 °C at a rate of 1 °C/min. Third, images were captured with a CoolSNAP 3.3 M digital charge coupled device color camera (Roper Scientific, Inc., Sarasota, FL) connected to a computer. Because of the intricacy of the morphology and structure of the wax crystals, many micrographs of wax crystals were needed for ensuring reliability of the observation results. To do so, the glass slide was moved by using tweezers, and 20 images of wax crystals were obtained for each slide. In addition, the second and third repeated experiments were carried out. Hence, 60 images were obtained for a specimen. 2.3.2. Characteration of Wax Crystals. All images were processed and analyzed with the software Image J (from Wayne Rasband, at the Research Services Branch, National Institute of Mental Health, Rockville, MD) to extract the parameters of the wax crystals, i.e., the size, aspect ratio (AR, to characterize the shape), and the boundary fractal dimension (D, to characterize the structure). In Image J, an ellipse is assumed as the shape of each individual crystal. AR is calculated as the ratio of the major axis to the minor axis. The boxing-counting method is used for extracting D. For more details about the determination of D, one may refer to the paper by Gao et al.24 The parameter values of the wax crystals in 60 images were averaged. 2.4. Differential Scanning Calorimetry (DSC). The DSC technique is widely used to experimentally quantify the WAT and the precipitated wax concentration.16,25−27 The experimental apparatus used in this study was a DSC Q20 (TA Instruments, New Castle, DE). Tests were performed from 80 to −20 °C at a rate of 5 °C/min. A cooling rate of 5 °C/min might produce an undercooling effect. However, a very low scanning rate would give reduced sensitivity as the DSC signal is the time derivative of the heat flow.28 Therefore, a cooling rate of 5 °C/min was used in this paper. The calorimetric signal was recorded and stored by the software for use off-line. Figure 3 shows typical DSC curves of samples 12.5% W1 + oil-A, 12.5% W2 + oil-A, and 12.5% W3 + oil-A. The temperature at which the curve deviated from the baseline is the WAT. The repeatability of WAT measurements was calculated to be within 2 °C.

Han et al. reviewed the previous methods of determining the precipitated wax concentration, and the limitations of these methods were also evaluated.29 Furthermore, they proposed a theoretically correct method (GC-centrifuge method) to quantify the precipitated wax concentration at a certain temperature. In fact, this method is suitable to measure the concentration of precipitated wax in liquid oil. However, for the wax−oil gels with strong structures, it was limited because the wax crystals in gels cannot be separated by centrifugation. Finally, DSC was used to measure the precipitated wax concentration of wax−oil gels in this study although it has some limitations. Literature studies have described the details of measurement of the precipitated wax concentration by DSC.16,25,26 It includes determining the total heat released (J/g) during the cooling process and the enthalpy (J/g) of wax precipitation. The total heat released in the temperature ranges from the WAT to a given temperature is proportional to the area enclosed by the DSC curve and the baseline, and it can be easily calculated by integration. The enthalpy of wax precipitation depends on the carbon number distribution of wax. However, using the complex mixture of paraffins, it was found that the average value of enthalpies of wax precipitation is close to 200 J/g.16 This constant value was also used in our study. The precipitated wax concentration at a given temperature can be finally calculated by dividing the total released heat by the average value of enthalpy of wax precipitation. The experimental results of the precipitated wax concentration were reproducible within 1.6 wt %. The solid wax content in the following sections means the mass concentration of precipitated wax at 5 °C (i.e., the temperature at which the yield stress was measured). The WAT, solid wax content, and wax content at −20 °C of all samples were determined by DSC, as shown in Table 2. It can be found that, for the specimens consisting of the same amount of the pure waxes (W1, W2, or W3) and a crude oil, the differences of the solid wax content are within the experimental error. Therefore, the solid wax content was averaged for these samples.

3. RESULTS AND DISCUSSION 3.1. Yield Stress under Quiescent Conditions. Samples 7−15 in Table 2 were used to study the effect of the carbon number distribution of wax on the yield stress. The yield stresses of wax−oil gels were measured under quiescent conditions; i.e., the sample was not subjected to any shear stress during cooling and isothermal holding. The averaged solid wax contents were 12.8, 15.6, and 18.4 wt % for samples 7−9, 10−12, and 13−15, respectively. Figure 4 shows the variation of the yield stress with the average carbon number of wax. As can be seen, at the same solid wax content, the yield stress of wax−oil gels dramatically decreases with increase of the average carbon number of wax. Taking the gels with solid wax content of 18.4 wt % as an example, the yield stress reduces from 106 490 to 15 960 Pa when the average carbon number of wax increases from 24.2 to 28.4. To confirm this conclusion, validated experiments were carried out from two aspects. On one hand, the carbon number distribution of wax was changed by respectively blending W2 with W1 and with W3 at different mass ratios. The mixture of wax was dissolved into oil-A, and then the yield stresses at 5 °C were measured. Figure 5 shows the dependence of the yield stress on the average carbon number of blended wax. As can be

Figure 3. Typical results of DSC tests for samples 12.5% W1 + oil-A, 12.5% W2 + oil-A, and 12.5% W3 + oil-A. 2735

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Figure 4. Decrease in the yield stress with increasing average carbon number of wax at 5 °C. The data points from left to right represent W1 + oil-A, W2 + oil-A, and W3 + oil-A.

Figure 6. Increase in the yield stress with increase of solid wax content for samples W1 + oil-A, W2 + oil-A, and W3 + oil-A at 5 °C.

S=

Δτy Δϕ

=

τy(ϕ2) − τy(ϕ1) ϕ2 − ϕ1

(2)

where S is the changing rate of the yield stress with respect to the solid wax content (Pa/wt %), τy is the yield stress of wax− oil gels (Pa), and ϕ is the solid wax content (wt %). From Figure 6 and eq 2, it could be concluded that lower carbon number of wax in the gel renders higher values of S. For instance, as the solid wax content increases from 15.6 to 18.4 wt %, the S values of the gels W1 + oil-A, W2 + oil-A, and W3 + oil-A are 26 176, 16 840, and 2660 Pa/wt %, respectively. It is obvious that S is much higher for the gels with lower carbon numbers of wax, as will be explained in section 3.3. 3.2. Morphology and Structure of Wax Crystals. 3.2.1. Average Size of Wax Crystals. Figure 7 shows microscopic images of the wax crystals in wax−oil gels oil-A, 12.5% W1 + oil-A, 12.5% W2 + oil-A, and 12.5% W3 + oil-A. Figure 8 shows the average size of the wax crystals versus the average carbon number of wax. These results reveal that the average size of the wax crystals decreases with increase of average carbon number of wax. For example, with the same solid wax content of 18.4 wt % , the average size of the wax crystals in gel W1 + oil-A is 1.6-fold higher than that of the crystals in gel W3 + oil-A. Several published papers have investigated the effect of the cooling rate,12,30 shear,12 and composition13 on both the yield stress and the crystal size. It has been reported that larger wax crystals render higher values of yield stress.12,13,30 In this study, the effect of the carbon number distribution of wax on the crystal size was examined. As noted above, larger crystals are formed in the gels with smaller average carbon numbers of wax. This could result in a stronger gel. Therefore, the decrease of the average size of the wax crystals is the first reason why the yield stress decreases with increase of the average carbon number of wax (Figure 4). 3.2.2. Aspect Ratio of Wax Crystals. The shape of the wax crystals is another important element affecting the yield stress of waxy oil gels. In this work, the aspect ratio was used to characterize the shape of the wax crystals. Higher values of aspect ratios indicate the presence of rodlike crystals. Figure 9 shows the aspect ratio of the wax crystals as a function of the average carbon number of wax. As can be seen, the aspect ratio of the wax crystals increases with increase of the average carbon number of wax. One may also see from Figure 7 that the wax

Figure 5. Variation of yield stress with average carbon number of blended wax at 5 °C for samples 13−20. The solid wax content was 18.4 wt % for all wax−oil gels.

seen, the gel with higher average carbon number of blended wax exhibits lower yield stress. On the other hand, another crude oil (oil-B) was used to further validate this conclusion. Specimens 21−23 were used, and the yield stresses were also tested at 5 °C. At the solid wax content of 18.1 wt %, the yield stresses of wax−oil gels 12.5% W1 + oil-B, 12.5% W2 + oil-B, and 12.5% W3 + oil-B are 63 096, 48 640, and 10 890 Pa, respectively. It can also be found that lower yield stress is observed for the gels with higher carbon numbers of wax. 3.3.1. Changing Rate of Yield Stress with Solid Wax Content. The wax deposit in pipeline ages with time due to the diffusion of wax molecules into the deposit. The increase of solid wax content due to the aging process is expected to increase the yield stress of the wax deposit. However, the changing rate of the yield stress with respect to the solid wax content may be associated with the carbon number distribution of wax. To study this point, different amounts of the waxes W1, W2, and W3 were dissolved in oil-A. The yield stresses of wax− oil gels were measured at 5 °C. Figure 6 shows the variation of the yield stress with solid wax content for the gels with different carbon number distributions of wax. The changing rate of the yield stress with regard to the solid wax content is calculated as follows: 2736

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Figure 7. Microscopic images of wax crystals from waxy oil gels: (a) oil-A, (b) 12.5% W1 + oil-A, (c) 12.5% W2 + oil-A, and (d) 12.5% W3 + oil-A.

Figure 9. Aspect ratio of wax crystals versus average carbon number of wax. The data points from left to right represent W1 + oil-A, W2 + oilA, and W3 + oil-A.

Figure 8. Average size of wax crystals versus average carbon number of wax. The data points from left to right represent W1 + oil-A, W2 + oilA, and W3 + oil-A.

crystals in gels with higher average carbon numbers of wax will be more rodlike (i.e., higher aspect ratio). It is mechanistically consistent that rodlike crystals provide smaller areas of interactions between crystal faces and ends, resulting in weaker crystal−crystal “anchoring” interactions. When the higher average carbon number wax crystallizes from the solution, more rodlike wax crystals are formed. For these crystals, the “anchoring” interactions between the crystal faces and ends are weaker, leading to a fragile network of wax crystals. Therefore, the increase of the aspect ratio of the wax crystals is the second reason why the yield stress decreases as the average carbon number of wax increases (Figure 4).

3.2.3. Boundary Fractal Dimension of Wax Crystals. The boundary fractal dimension is extremely useful in quantifying the degree of structure complexity.31 Higher values of the boundary fractal dimension suggest more complex structures. Figure 10 shows the variation of the boundary fractal dimension with the average carbon number of wax. As can be seen, the boundary fractal dimension of the wax crystals decreases as the average carbon number of wax increases. It has been experimentally observed that a higher fractal dimension results in a stronger gel.32 Therefore, the decrease of the boundary fractal dimension of the wax crystals is the third reason why the 2737

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Figure 10. Boundary fractal dimension of wax crystals versus average carbon number of wax. The data points from left to right represent W1 + oil-A, W2 + oil-A, and W3 + oil-A.

Figure 11. Variation of yield stress with applied shear stress at 5 °C for wax−oil gels 12.5% W1 + oil-A (□), 12.5% W2 + oil-A (○), and 12.5% W3 + oil-A (△).

yield stress decreases with increase of the average carbon number of wax (Figure 4). 3.3. Discussion of Yield Stress Changing Rate with Solid Wax Content. At the end of section 3.1, it has been concluded that the changing rate of yield stress with respect to the solid wax content is smaller for the gel with higher average carbon number of wax. This result may be well explained by the microscopic results above. The smaller size and more rodlike and simpler structure of the wax crystals are formed in the gels with higher average carbon numbers of wax, and these characteristics of the wax crystals could result in a weaker gel. Therefore, a lower yield stress changing rate is observed for the wax−oil gel with a higher average carbon number of wax. 3.4. Yield Stress under Shear Conditions. The effects of the thermal and shear histories on the properties of wax−oil gels depend on oil composition. For example, the cooling rate had different influences on the gel points of 4% C36 + mineral oil and 4% C35 + mineral oil.8 On the basis of the microscopy results above, one may infer that the different effects of the thermal-and-shear-history on the gel properties may result from the diverse crystal characteristics. Therefore, the yield stresses were also tested under shear conditions in which an applied shear stress was maintained during the cooling and isothermal holding. Applied shear stresses of 5, 10, and 15 Pa were used. Other experimental conditions including the heating temperature, cooling rate, test temperature, holding time, and stress loading path were same as those under the quiescent conditions. Figure 11 shows the effect of the applied shear stress on the yield stress. As can be seen, the applied shear stress has little effect on the yield stress of the gel 12.5% W1 + oil-A and no effect on the yield stress of the gels 12.5% W2 + oil-A and 12.5% W3 + oil-A. However, the gels with higher average carbon numbers of wax always exhibit smaller yield stress.

respect to the solid wax content also greatly reduces as the average carbon number of wax increases. Microscopic observation showed that the average size and boundary fractal dimension of the wax crystals decrease but the aspect ratio of the wax crystals increases as the average carbon number of wax increases. In other words, crystals that are more rodlike, of smaller size, and of simpler structure are formed in the wax−oil gels with higher average carbon number of wax. The smaller size and simpler structure of the wax crystals could result in a weaker gel. The more rodlike wax crystals provide the smaller areas of “anchoring” interactions between the crystal faces and ends, leading to the weaker network. The wax content of the wax deposit (actually wax−oil gel) in field pipelines increases with time, resulting in the hardening of the deposit. In addition, the carbon number distribution of wax in deposit changes with the oil composition and operating conditions of pipelines. In this study, crude oils (oil-A and oilB) were used, and the results may be closer to field application. On the basis of the findings, it may be inferred that the strength of the wax deposit and its dependency on solid wax content are strongly influenced by the carbon number distribution of wax. Therefore, when determining the pigging methods or pigging frequency, the effect of the carbon number distribution of wax on the deposit properties should be considered. However, how to quantify the strength of the deposit in field pipelines still needs further study.

■

ASSOCIATED CONTENT

S Supporting Information *

Details of the HTGC method; determination of experimental conditions of yield stress tests. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

4. CONCLUSIONS At the same solid wax content, the yield stress of waxy oil gels formed under quiescent or shear conditions always decreases with increase of the average carbon number of wax. However, the yield stress results under shear conditions indicated that the applied shear stress has little effect on the yield stress of the gel 12.5% W1 + oil-A and almost no effect on the yield stresses of the gels 12.5% W2 + oil-A and 12.5% W3 + oil-A. Under quiescent conditions, the changing rate of the yield stress with

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support from the National Natural Science Foundation of China (No. 51134006) and the Science Foundation of China 2738

dx.doi.org/10.1021/ie303371c | Ind. Eng. Chem. Res. 2013, 52, 2732−2739

Industrial & Engineering Chemistry Research

Article

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University of PetroleumBeijing (Grant LLYJ-2011-55) is gratefully acknowledged.

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dx.doi.org/10.1021/ie303371c | Ind. Eng. Chem. Res. 2013, 52, 2732−2739