In-Situ Monitoring of Paraffin Wax Crystals Formation and Growth

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In-Situ Monitoring of Paraffin Wax Crystals Formation and Growth Samira Haj-Shafiei, Benjamin Workman, Milana Trifkovic, and Anil K Mehrotra Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.9b00052 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019

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Crystal Growth & Design

In-Situ Monitoring of Paraffin Wax Crystals Formation and Growth Samira Haj-Shafiei, Ben Workman, Milana Trifkovic*, Anil K. Mehrotra* Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada *Corresponding Authors: Milana Trifkovic Tel.: 1-403-220- 8779, Email: [email protected] & Anil K. Mehrotra, Tel.: 1-403-220-7406, Email: [email protected] Abstract The crude oil temperature in the hot flow regime is higher than the wax appearance temperature (WAT), whereas it is lower than the WAT in the cold flow regime. Under the cold flow regime, heavier paraffins in the crude oil precipitate out as crystals, resulting in a solid–liquid suspension. A new approach is presented for scrutinizing the wax crystal structure and crystal growth kinetics, during the cooling of prepared multicomponent wax–solvent mixtures from above the WAT to below the pour point temperature (PPT). The time-resolved microscale structural attributes, such as the onset of nucleation, crystal size distribution, precipitated paraffin wax volume fraction and fractal dimension, are compared under various cooling rates ranging from 0.05 to 6 °C min–1 via laser scanning confocal microscopy (LSCM). At faster cooling rates, a larger number of crystals were formed, but with a smaller average crystal size. Volume fraction and crystal size were higher at lower cooling rates, but with slower crystal growth kinetics, while the fractal dimension converged to the same value at the final temperature irrespective of the cooling rate. These findings are important for understanding crystal formation and solid deposition from ‘waxy’ mixtures in pipelines. Keywords: Paraffin wax crystallization, crystal growth, wax deposition, cold flow, fractal dimension, morphology.

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1. Introduction Normal alkanes, the main building blocks of lipids, surfactants, liquid crystals, polymers, and many other more complex organic compounds, comprise of linear hydrocarbon chains. Alkanes are also of interest to industry as they are the basic constituents of petroleum crude oil and many petrochemicals. Petroleum waxes from crude oil are obtained by separating heavy distillate fractions of crude oil 1. These are complex mixtures of hydrocarbons, consisting mainly of normal alkanes along with some branched and cyclo-alkanes with carbon numbers of 18-65 or higher 2. When highly paraffinic crude oils, called ‘waxy’ crude oils, are cooled to a temperature below their wax appearance temperature (WAT), a decrease in the solubility of paraffins causes their deposition and crystallization. The WAT, or the cloud point temperature (CPT), is the temperature at which the first wax crystals start to appear while cooling the crude oil. The deposition of waxy solid on to the pipeline wall leads to flow assurance issues 2-5. A further lowering of temperature provides the driving force for nucleation of new wax crystals and overall crystal growth. The wax crystals grow in size and form a three dimensional network structure, with entrapped liquid hydrocarbons, leading to the gelation of crude oil 6, 7. The gelation could happen with a crude oil wax content of even 2 mass% 8. The degree of crystallinity has a major influence on the hardness, density, and transparency of the material. The crystallinity equilibrium of the precipitated wax crystals depends on the applied cooling rate. Hammami and Mehrotra

9, 10

showed that paraffin wax precipitation and

crystallization generally proceed non-isothermally; for example, crude oils experience a gradual decrease in temperature when transported through pipelines in a colder environment. At low cooling rates, the different paraffins have relatively more time to diffuse and/or interact with one another, thereby forming more stable crystals of the lowest configurational energy possible. In contrast, the same paraffins would freeze readily in a less perfect unstable crystalline structure at 2 ACS Paragon Plus Environment

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fast cooling rates; hence, the non-ideal behaviour is less prominent in these cases

9, 10.

Based on

NMR 11 and x-ray diffraction analyses 12, the solid phase of gelled crude oils has been shown to be predominantly crystalline with only a small amorphous fraction 6. Furthermore, the crystalline fraction can be classified as fractal objects

6, 13-15.

The isothermal and non-isothermal n-alkane

crystallization results have been described with the Avrami and Ozawa models 9, 10, 16-19. Zougari and Sopkow 20 introduced a modified Ozawa model to describe the non-isothermal kinetics of wax crystallization from crude oils. They also reported that the nucleation and growth of crude oil wax strongly depend on the temperature, pressure, composition, and production rate 20. Under various conditions, the growth of crystal size is smaller for the more complex compositions 21. In addition, crude oil might contain not only n-paraffins but also iso-paraffins and cyclic compounds, which could impact the morphology, volume fraction and size distribution of the crystals. Ronningsen et al. 22 suggested that increasing iso-paraffin fractions tends to favor microcrystalline or amorphous wax solids. Visintin et al. 6 reported that n-paraffins dissolved in organic solvents display a sharp transition in gel strength at the pour point temperature (PPT), whereas the build-up in gel strength in crude oils, as a function of temperature below the PPT, is much more gradual. This behavior was explained by the addition of iso-paraffins in the n-paraffin mixture. Gao et al. 23 indicated that waxy crystals in crude oil are quasi-sphere-shaped particles instead of platelets in simple wax– solvent mixture; therefore, care should be exercised in extrapolating results obtained from simplified systems (e.g. n-paraffins dissolved in organic solvents) to crude oils. The optical microscopy images from waxy crude oils, studied by Visintin et al. 6, with the end temperature of 15°C after 4 hours of waiting time, suggested that the wax crystals cooled at a slower rate are arranged around nucleation centers, forming extended islands which are larger than those observed after the fastest cooling rate (e.g., 1°C min–1). For a faster cooling rate, the crystals 3 ACS Paragon Plus Environment


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were distributed more uniformly within the sample and collected into smaller loose clusters that tended to fill the entire space 6. They also reported that the crystal networks formed at faster cooling rates are more regular and thinner; they explained that weaker mechanical properties of the sample result from the spatial arrangement of the dispersed phase. Kané et al. 11 used transmission electron microscopy to investigate the morphology of paraffin crystals formed in crude oil both under flow and static conditions while lowering the temperature. They concluded that, in both flow and static cases, the crystal nuclei have the shape of discs with the same molecular size thickness. Under quiescent conditions, the crystals in the form of lamellas are allowed to extend and form a colloidal network, which has a high shear modulus as a result of side-by-side interactions between lamellas. On the other hand, under flow conditions, the lateral growth of the individual discs is limited, and as a result, extended lamellas were not observed 11. Normal alkanes can provide a well-defined model system for studying the complex crystallization behaviors of polymer materials, surfactants, and lipids. In general, crude oils have apparently slower crystallization kinetics when compared to polymers 20. Su et al. 24 investigated the normal alkane phase behavior in confinement to understand the crystalline phase transition and the properties of many polymeric materials, especially polyolefins

24.

Furthermore, it has been

reported that bulk n-alkanes have some unique features during the phase transition processes, such as the surface freezing phenomenon

25-28,

rotator phases, and odd-even effect in the low

temperature crystalline phases 29, 30. The flow of waxy or paraffinic crude oils in pipelines can be classified into the hot flow and cold flow regimes 2-4, 31. In the hot flow regime, the average temperature of waxy crude oil is higher than the WAT. With the pipe-wall temperature below the WAT, solid deposition occurs on the pipe–wall. The deposit thickness increases axially as the temperature of the crude oil decreases


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until a maximum deposit thickness is reached when the crude oil temperature is equal to the WAT. The cold flow regime begins when the crude oil temperature is lowered to below the WAT, and wax crystals precipitate out into the bulk crude oil, leading to a solid-in-liquid suspension. In the cold flow regime, the deposit thickness decreases axially and it approaches zero as the crude oil temperature approaches the surroundings temperature. Beyond that location, the crude oil is at a thermal equilibrium with the surroundings; consequently, without any thermal driving force, there would not be any deposition on the pipeline wall. A few recent studies have considered the cold flow concept for minimizing, or even avoiding, solid deposition from ‘waxy’ or paraffinic crude oils in pipelines and process equipment 2-4, 31. It is pointed out that there are two important rates when dealing with the pipeline flow of ‘waxy’ crude oils: the cooling rate and the flow rate. Several experimental and modeling studies have confirmed that a lower deposit thickness is achieved at a higher flow rate (or a higher Reynolds number), which has been well explained from heat transfer considerations

2, 32-34.

In

contrast, a recent study3 examined the effect of cooling rate on the amount of wax deposition. It was shown that a slower cooling rate could minimize or eliminate solid deposition in the hot flow regime, where the ‘waxy’ mixture or crude oil is transformed into a solid-in-liquid suspension. A slower cooling rate could be achieved by maintaining a small temperature difference between the oil and the coolant; and, this small temperature difference can be maintained in a heat exchanger. Other techniques could be developed for achieving low cooling rates3. Thus, the deposit thickness can be decreased by either increasing the flow rate or by decreasing the cooling rate. To develop the cold flow technology, we require an improved understanding of the nucleation, and subsequent growth of wax crystals, as well as how they affect the crude oil transportation and the wax deposition problem. The motivation for this study was, therefore, to investigate the effect 5 ACS Paragon Plus Environment


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of cooling rate on the nucleation, crystal growth and morphology of a multicomponent paraffin wax in a multicomponent paraffinic solvent using the laser scanning confocal microscopy (LSCM). This investigation associates the acquired information on paraffin wax morphology and crystallization kinetics to recent advances in the cold flow technology for minimizing wax deposition in pipelines 3. 1.1 Crystal Growth Calculations In this study, the moments of the particle population density and the crystal growth were calculated from the particle size distribution (PSD) obtained by quantifying LSCM images using imageJ (which is a Java-based image processing program). Images at eight temperatures, ranging from the nucleation temperature to 4°C, were analyzed for PSD at the cooling rates of 0.05, 0.1, and 0.37 °C min–1. The moments of the PSD were calculated as 35: ∞

𝑖=𝑛

𝜇𝑗(𝑡) ≡ ∫0 𝑟𝑗𝑛(𝑟,𝑡)𝑑𝑟 ≈ ∑𝑖 = 1𝑟𝑗𝑎𝑣𝑒,𝑖𝑁𝑖(𝑟𝑎𝑣𝑒,𝑖,𝑘)

(1)

where ri and Ni are the crystal size and number of crystals for each temperature, respectively, and k is the discrete time counter. rave,i is expressed as: 𝑟𝑎𝑣𝑒,𝑖 =

𝑟𝑖 + 𝑟𝑖 ― 1

(2)

2

The mean crystal size in the suspension is defined as the ratio of the first moment to the zeroth moment, as follows 35, 36: 𝜇1 (𝑡)

(3)

𝐿𝑗 + 1, 𝑗(𝑡) = 𝜇0(𝑡) = 𝐿1,0,𝑘

Next, the growth rate, G, is the rate of change of the mean particle size with respect to time, as follows 35: 6 ACS Paragon Plus Environment

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𝐺(𝑡)𝑒𝑥𝑝 =

𝑑(𝐿1,0) 𝑑𝑡

=

∆(𝐿1,0(𝑡)) ∆𝑡

(4)

= 𝐺𝑒𝑥𝑝,𝑘

2. Experimental Section 2.1. Materials All experiments were performed with prepared wax–solvent mixtures comprising 10 mass% paraffin wax dissolved in a multicomponent solvent. The multicomponent wax, Bernardin Parowax, was a mixture of n-alkanes with carbon numbers in the range of C21 and C58, with a melting point of 57–61 °C and a density of 912 kg m–3 (at 23 °C). The multicomponent solvent, Linpar1416V, consisted of n-alkanes with the carbon number in the range of C10 to C20 and a density of 763 kg m–3 (at 23°C). Compositional analyses of Parowax and Linpar 1416V have been reported by Kasumu and Mehrotra 37. The 10 mass% wax–solvent mixture had a WAT of 32 °C, PPT of 22 °C, and a density of 780 kg m–3 (at 23 °C). The 10 mass% wax concentration was selected for consistency with the results from the bench-scale wax deposition experiments published recently 3.



Figure 1: Compositions of multicomponent wax and solvent used for preparing the wax–solvent mixture37. 2.2.

Confocal Microscopy and Temperature Controlled Stage

Laser scanning confocal microscopy (LSCM) imaging was performed using a Leica SP8 inverted confocal microscope, equipped with an 8 kHz resonant scanner and operated using LASX software (which is a microscope imaging software from Leica Microsystems). A 50x magnification was used with an excitation laser wavelength (λ) of 405 nm and the detector range set from 415 nm to 490 nm. Laser scanning confocal microscopy was used along with a Peltier cooling system to control the sample’s temperature and cooling rate. This allowed for imaging of the system during the cooling process. The Peltier system was connected to refrigerated-heating circulators (F25), made by Julabo GmbH, to control the temperature from WAT+28 °C to WAT– 28 °C at selected cooling rates, ranging from 0.05 °C min–1 to 6 °C min–1. The reflectance confocal images were used for detecting the onset of crystallization, which was indicated by the appearance of nuclei in the reflectance image. The 638 nm laser, with a detector range of 633 nm to 643 nm, was used for the reflectance window. Perylene that had affinity for solvent was used as a fluorescent dye. For all experiments, the same amount of sample was transferred into the glass bottom microwell dishes (35 mm petri dish, 20 mm Microwell, No.1.5 coverglass (0.16-0.19 mm)), obtained from MarTek Corporation. Using these Petri dishes, the samples were not disturbed, and the crystals were free to nucleate and grow uninterrupted. 2.3.

Procedure and Experimental Design

For each experiment, the 50x magnification objective was located below the glass bottom micro well dish that contained the 10 mass% wax–solvent mixture and the Peltier was placed on top of the sample. The samples first were heated to 60 °C and kept at this temperature for 1 h to melt the crystals and erase any thermal history. The samples were then cooled to 40 °C at 3.5 °C 8 ACS Paragon Plus Environment

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min-1 cooling rate. From 40 °C to 4 °C, the samples were cooled at 6 different cooling rates of 0.05, 0.1, 0.2, 0.37, 3.5, and 6 °C min–1. 2-D and 3-D images were taken at the same axial location for each experiment continuously throughout the cooling process. 3-D images were obtained using the z-drive by taking a stack of 11 images at 1.275 µm delta z with the total physical length of 14.02 µm. The stack of the 2-D images was then converted to a 3-D image using LASX software. The sample temperature was then maintained at 4 °C for 30 min, during which confocal images were taken at 5-min intervals to examine the crystal growth isothermally. After the 30-min holding time, the sample was heated back to 60 °C and the procedure was repeated. The experiments were repeated in triplicates at each of the cooling rates of 0.05, 0.1, 0.2, 0.37, 3.5, and 6 °C min–1. The images were analyzed for their fractal dimension, volume fraction, and crystal size. 2.4.

Image Post-Processing and Analysis

In order to determine the fractal dimension of an image, a series of imaging process steps were applied to extract a boundary image of the formed crystals, and the box-counting algorithm was applied to this boundary image. The analysis of 2-D images was carried out using Matlab (which is a programming language developed by MathWorks). The images at different stages of processing are shown in Figure 1. Confocal microscope images were imported into Matlab as grayscale images (Figure 1a). A box filter was applied to reduce the level of noise (Figure 1b). A kernel size of 8x8 pixels was chosen as this was on a similar length scale as the observed crystals. Choosing a kernel size similar to the size of the objects reduced the chance of features being lost during this step. A symmetrical boundary condition was applied to the box filter to prevent a loss of intensity near the edge of the image. Next, the image was binarized using Bradley’s method 38, which applied a large area mean filter to the image prior to segmentation (Figure 1c). This allowed for adaptive thresholding, where the large area mean 9 ACS Paragon Plus Environment


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filter was used to calculate the local threshold used for segmentation. The volume fraction of wax crystals, fwc, was then calculated by: 𝑓𝑤𝑐 =

𝑝1

(5)

𝑝1 + 𝑝0

where p1 is the number of white pixels, representing wax crystals, and p0 is the number of black pixels, representing the absence of wax crystals. The border of the binarized objects was extracted using 8-connectivity (Figure 1d). The box counting algorithm was then applied to the border image to extract the fractal dimension. The first step in the box counting algorithm was to pad the image with background pixels so that the image sides were of equal length and so that length was a power of 2. First, a box size equal to the length of the newly padded image was chosen and the number of boxes that contain a boundary pixel were counted. Then, the box size was decreased by a factor of 2 and again the number of boxes that contain a boundary pixel were counted. This process of decreasing box size and counting pixels was repeated until the box size is that of a single pixel. The relationship of log(N) (N = the number of boxes) vs log(D) (D = the size of those boxes) was plotted and fitted linearly using the least square method. Finally, the slope of the fitted line gave the box counting fractal dimension. The slope of the line ranged between 1 and 2, where 1 corresponds to a straight line and 2 refers to a wavy line that could fill up a 2-D plane. A steeper slope corresponds to a more fractal object, meaning that as the box size decreases, the smaller boxes are utilized to capture details that appear at small scales. A shallower slope means that the object is closer to a straight line and less fractal, and that the smaller boxes are not capturing more details in the object as their size decreases. ImageJ was used to extract the particle size distribution of paraffin wax for four different cooling rates of 0.05, 0.1, 0.2 and 0.37 °C min–1 at various temperatures. First, the line selection tool was used to draw a line on the 10 µm scale bar. The known distance of the line (10 µm) was 10 ACS Paragon Plus Environment

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set in the "Know Distance" field, where imageJ tool converts the distance to number of pixels. The unit of the measurement (µm) was also set. The images were then converted to 8-bit grayscale. A built-in plugin Bandpass Filter was used to filter out large structures (shading correction) and small structures (smoothing) of the specified size by gaussian filtering in fourier space. Next, the line selection tool was used to draw lines on top of crystals and the lengths of the lines were obtained through the measure tool in the analyze option.

10 µm

(a)

(b)

(c)

(d)

Figure 1: Image processing steps for volume fraction and fractal dimension calculations at 0.1 °C min–1 and 4 °C: (a) unprocessed grayscale image, (b) image with box filter applied, (c) segmented images, where white shows wax crystals, and (d) wax crystal border image 3. Results and Discussion 3.1.

Onset of Nucleation

The onset of nucleation in this study was taken to be when nuclei or very small crystals start to show on the reflectance confocal images even before they were shown on the fluorescence confocal images. The changes that occur in the reflectance image upon nucleation for the cooling rate of 0.05 °C min–1 at 40 °C and at the nucleation temperature of 36.5 °C are shown in Figures 2a and 2b, respectively. Small changes appeared on the reflectance image, which are circled in Figure 2b. As shown in Figure 3, the nucleation temperature increases as the cooling rate 11 ACS Paragon Plus Environment


decreases. Kasumu et al.

39

also indicated that the wax appearance temperature increases with a

decrease in the cooling rate. Also, Andrade et al.

40

reported that the crystallization temperature

increases at lower cooling rates, while the dissolution temperature decreases at lower cooling rates. They also reported that the highest solid-liquid thermodynamic equilibrium temperature is considered to approach the dissolution temperature when the material is heated at a very low heating rate. However, the crystallization temperature is never equal to the dissolution temperature even if an infinite amount of time (i.e., 0 °C min–1) is allowed to the system. From Figure 5, the onset of nucleation is estimated to be 35.9 °C at the zero cooling rate (y-intercept), which was found from fitting the experimental data to an exponential equation with the corresponding line as shown. Paraffin nucleation is a stochastic process and supersaturation is needed to initiate the nucleation process. For example, the creation of crystal precipitation does not coincide with the highest thermodynamic solid-liquid equilibrium temperature. The difference between the saturation temperature and the crystallization temperature is called the degree of supercooling 40. a

b

Figure 2: Reflectance image for 0.05 °C min–1 cooling rate (a) before (40 °C) and (b) at the nucleation temperature (36.5 °C).


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Figure 3: Onset of Nucleation (°C) as a function of cooling rate (in °C min–1) for 10 mass% wax– solvent mixtures.

3.2. Crystal Morphology Examples of the LSCM images obtained from 10 mass% wax–solvent mixtures while cooling are shown in Figures 4 and 5. The two components of paraffin wax and solvent were completely distinguishable with the aid of perylene. Figures 4a to 4c show the process of crystal growth from nucleation temperature to 4 °C while cooling at the rate of 0.2 °C min–1. Visually, the crystals start as small and thin platelets at higher temperatures, and as the samples are cooled the platelets grow in both x and y directions to form chains of crystals which become interconnected. From Figures 4a to 4c, it can be inferred that both the precipitation and growth occur as the temperature is decreased. Figures 4d and 4e show the precipitated crystals at 20 °C for two different cooling rates of 0.05 and 0.37 °C min–1. At the faster cooling rate of 0.37 °C min–1, a larger number of crystals are formed but each crystal tends to have a smaller size. Thus, the crystal number density increased with an increasing cooling rate. On the other hand, at the slower cooling rate of 0.05 °C min–1, a smaller number of crystals are formed but each crystal tends to have a bigger size. From the initial



images taken at the temperature for the nucleation onset, the average numbers of crystals formed were 10 for the sample cooled at 0.05 °C min–1, 56 for 0.1 °C min–1, and 75 for the cooling rate of 0.37 °C min–1. The first solid does not precipitate out in the solution exactly at the saturation temperature and a supersaturation or supercooling is necessary for the onset of nucleation (precipitation). The conditions between the saturation and the precipitation temperature are commonly named metastable region

40.

Saturation is a thermodynamic property that does not

depend on cooling rate, but the precipitation temperature and/or metastable region width (ΔTSupersaturation) are affected by many factors such as cooling rate, solution concentration, and impurities

40.

When entering into the unstable region from the metastable region with more

precipitated paraffin wax and larger metastable region width, there is an uncontrolled nucleation at higher cooling rates. Figure 5a shows the 3-D image taken at 25 °C while cooling at 0.1 °C min–1 rate. Venkatesan et al. 41 made 3-D imaging of the gels using the z-drive by taking several 2-D images at various planes along the z-axis and then converted to a 3-D image using image processing software. From their 3-D image using the confined space between microscopic slide and cover slip (1 µm), they concluded that the thicknesses of the platelets (1 µm) are the same for various cooling rates, indicating that the crystal growth is only two-dimensional 41. On the other hand, the 3-D images, in Figures 5b and 5c, from undisturbed and unrestricted samples in the Petri dish in this study suggest that the crystals also grow in z-axis. Eleven 2-D images at 1.275 µm delta z along the zaxis were taken and processed using the confocal software to create the 3-D images with total physical height of 14.02 µm. Figures 5b and 5c show that the height of the paraffin wax crystal increased from 34 °C to 4 °C taken at the same location on the same sample for the cooling rate of 0.1 °C min–1. Therefore, the crystal growth could occur on three axis of x, y and z and as a result, 14 ACS Paragon Plus Environment

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the crystal growth is three dimensional. In general, care must be exercised when extrapolating the findings from a prepared mixture, such as a paraffin wax dissolved in a solvent, to a more complicated crude oil, because the existence of other species, such as asphaltene, could have an impact on the morphology and characteristics of paraffin crystals. Additionally, the samples were kept isothermally at 4 °C for 30 min at the end of each experiment. The 30-min waiting time did not have any significant effect on the morphology, crystal size and fractal dimension based on the confocal results. This was also shown with microscopic images by Soedarmo et al. 42, where their 48-h isothermal runs following a cooling sequence showed little change, indicating that the isothermal aging effect on crystal aspect ratio is not substantial. On the other hand, Visintin et al. 6 and Haj-Shafiei et al. 7 reported that the gel strength and zero shear rate viscosity increases with increasing holding time, while the optical microscopy images also do not show a significant difference at a glance. Visintin et al.

6

also

reported that properties of the gel system depend mainly upon temperature and are conditioned by past thermal history where different cooling rates during the gelation process lead to differences which persist even after prolonged isothermal holding times. In the cold flow regime, at temperatures below the WAT, the precipitated wax, the morphology, and the wax crystal structure are predominant factors causing the rheological behaviours of waxy crude oils to be largely complex.



a

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c

b

a

10µm

10µm

d

10µm

e

10µm

10µm

Figure 4: Images from confocal microscopy with 50x magnification and 0.2 °C min–1 cooling rate: (a) 35.7 °C, (b) 32 °C, and (c) 4 °C. Images at 20 °C for two cooling rates of (d) 0.05 and (e) 0.37 °C min–1

b

a

c

Figure 5: 3-D image of 10 mass% wax–solvent mixture cooled at the rate of 0.1 °C min–1, gray structure is the paraffin wax crystals network and the white empty space represents the solvent; (a) at 25 °C, (b) at 34 °C, and (c) at 4 °C.


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3.2.

Fractal Dimension and Volume Fraction

Figure 6a shows the fractal dimension results based on the microscopic images for the 10 mass% wax–solvent mixture, while cooling from 60 °C (i.e., higher than the WAT) to 4 °C (i.e., lower than the PPT) at various cooling rates and temperatures. The absolute mean deviations for the fractal dimension from the repeat experiments were 2.05%, 2.62%, 2.00%, 1.14%, 2.48% and 1.76% for the cooling rates of 0.05, 0.1, 0.2, 0.37, 3.5 and 6 °C min–1, respectively. The fractal dimension values are lower at higher temperature as the network is still not formed. As seen from Figure 6a, the plateau at lower cooling rates is reached at a higher temperature and changes in the fractal dimension are negligible below the PPT of ~22 °C. This is expected given that more time is allowed for the growth of crystals. For higher cooling rates of 3.5 and 6 °C min–1, the fractal dimension reaches the final fractal dimension value at temperatures below 15 °C. From Figure 6a, the difference in the fractal dimension from higher temperature to lower temperature is approximately 0.5 at slower cooling rates of 0.05 to 3.5 °C min–1 and this difference is only 0.1 for the fastest cooling rate of 6 °C min–1. At lower cooling rates, the crystals have relatively more time to diffuse and/or interact with one another, thereby forming crystals of the lowest configurational energy possible. On the other hand, the crystals at the highest cooling rate, which has a smaller difference in the fractal dimension, initially resemble more of random structure 6. However, the final fractal dimension is ~1.6 for all cooling rates, which indicates that the final structure at low temperatures is similar (i.e., wax crystals orient themselves in the same way once the critical concentration at the pour point temperature is reached regardless of their size). At the final temperature, when cooling is not the driving force for the creation of new crystals and the growth of existing ones, the precipitated crystals undergo a random walk to form aggregates. The final fractal dimension value is in agreement with the diffusion-limited aggregation (DLA) theory,



which predicts the final fractal dimension of 1.71 for systems in which diffusion is the primary means of molecular transport 43. Figure 6b shows the volume fraction of the precipitated wax in the samples as a function of temperature for various cooling rates from 0.05 °C min–1 to 6 °C min–1. As expected, the slower cooling rates result in an increased precipitation of wax. In the cold flow regime of crude oil transportation, this could mean that more wax would precipitate into the bulk liquid region instead of depositing on the pipe wall. At a low temperature of 4°C (much lower than PPT = 22 °C), between 20-30 percent of paraffin wax precipitated out, which is in agreement with previous wax deposition studies where the deposits contained similar amount of paraffin wax content 44. With lower cooling rates, more larger crystals precipitated out and as a result, more volume was occupied. The increase in volume fraction is very small below PPT. For example, for the 0.05 °C min–1 cooling rate, the volume fraction increased from 0 to 27 percent from the nucleation temperature to 20°C and it increased by only 3 percent from 20 °C to 4 °C. Furthermore, the absolute mean deviations for the volume fraction from repeat experiments were 7.70%, 4.90%, 4.02%, 3.52%, 6.35% and 5.71% for cooling rates of 0.05, 0.1, 0.2, 0.37, 3.5 and 6 °C min–1, respectively.

b

a


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Figure 6: (a) Fractal dimension (b) and volume fraction as a function of temperature for 10 mass% wax–solvent mixture at various cooling rates. Note that the WAT for 10 mass% wax–solvent mixture is 32 °C and the PPT is 22 °C 3. 3.3.

Paraffin Crystal Size and Kinetics

ImageJ was used to extract the particle size distribution of paraffin wax for four different cooling rates of 0.05, 0.1, 0.2 and 0.37 °C min–1 at various temperatures. Figure 7 shows the average crystal size as a function of temperature and each point refers to a specific cooling rate. In general, the crystal sizes increased from about less than 5 µm to approximately 20 µm as the temperature decreased from near the nucleation temperature to 4 °C. The absolute mean deviations for the crystal size from repeat experiments were 4.88%, 5.80%, 3.63% and 6.12% for the cooling rates of 0.05, 0.1, 0.2 and 0.37 C min–1, respectively. At a lower cooling rate of 0.05 °C min–1, the crystal sizes are larger at different temperatures when compared to the higher cooling rate of 0.37 °C min–1. At a high cooling rate of 0.37 °C min–1, the samples started with more nuclei and smaller particles. This was also visually seen previously in Section 3.2. In general, in the cold flow regime under lower cooling rate, the size of precipitated paraffin wax crystals is larger when compared to higher cooling rate. In addition, it has been reported that the yield stress of crude oil decreases with an increase in the cooling rate 22, 41. The reason for the observed decrease in the yield stress with an increasing cooling rate could be explained by considering the time available for the growth of the wax crystal network. Given the same upper and lower temperature limits, a lower cooling rate provides more time for crystal growth, resulting in the formation of larger crystals. On the other hand, under a higher cooling rate, the rate of precipitation is faster and there is not as much time for crystal growth resulting in smaller crystals 9. This is also confirmed in Figure 7, where at 35 °C, the crystal size is similar for different cooling rates, but at the final temperature of 4 °C, the lower cooling rate has the largest crystal size. Additionally, from the onset of nucleation to the PPT of ~22 °C, 19 ACS Paragon Plus Environment


the crystal size increases by about 20 µm for 0.05 °C min–1 cooling rate and by about 15 µm for 0.37 °C min–1 cooling rate. In contrast, from PPT to 4 °C, the crystal size increases by only 1.5 µm for 0.05 °C min–1 cooling rate and by about 5 µm for 0.37 °C min–1 cooling rate.

Figure 7: Paraffin wax crystal size obtained from ImageJ as a function of temperature for various cooling rates. Figures 8a and 8b show the mean crystal growth rate and the cumulative crystal growth rate, respectively. The mean crystal growth rate for the three cooling rates of 0.05, 0.1, 0.2 and 0.37 °C min–1 was obtained from equations 1 to 4. As shown in Figure 8a, the mean crystal growth rate starts from zero before the nucleation temperature and reaches a maximum value and then decreases again. The maximum mean crystal growth rate is shifted to a lower temperature as the cooling rate increases. In Figure 8a, at the beginning until reaching the maximum point, the heavier molecules could have been growing while the lighter molecules grow following the maximum point. In addition, the differential scanning calorimetry results for a pure wax also showed a sequential formation of wax crystals 44. The maximum mean crystal growth rate could occur as a consequence of competing growth rates of new nuclei and existing particles. From Figure 8b, the cumulative crystal growth rate for the lower cooling rates of 0.05 and 0.1 °C min–1 reaches a


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plateau below the PPT of ~22 °C. For the cooling rate of 0.2 °C min–1, the cumulative crystal growth rate reached a plateau just after the PPT. Whereas, for the 0.37 °C min–1 cooling rate, the crystals are smaller, and the process is forced to occur faster and as a result, a gradual increase in the cumulative crystal growth rate is observed. Venkatesan et al. 41 also indicated that at a higher cooling rate, the rate of wax precipitation and growth is higher. b

a

Figure 8: (a) Mean crystal growth rate and (b) cumulative crystal growth rate as a function of temperature.

4. Conclusion Recent investigations have demonstrated that solid deposition in pipelines and process equipment from ‘waxy’ mixtures or paraffinic crude oils could be decreased substantially either by operating at high Reynolds numbers, by attaining the cold flow regime, and/or by maintaining low cooling rates. We have presented a non-invasive approach for in-situ monitoring of crystallization while cooling waxy mixtures at varying cooling rates. The effect of cooling rate on the paraffin wax crystal morphology, the onset of nucleation, and the crystallization kinetics was quantified from the acquired image data. The onset of nucleation occurred at higher temperatures 21 ACS Paragon Plus Environment


for slower cooling rates. The practical implication of this phenomenon is that the temperature of transition into the cold flow regime is inversely related to the cooling rate over the tested cooling rate range of 0.05–6.0 °C min–1. The 3-D images from undisturbed and unrestricted samples in the petri dish indicated that the crystals grow in all three directions. The acquired images were analyzed in terms of the fractal dimension, the precipitated wax volume fraction, and the crystal size. The fractal dimension reached similar values from a temperature below the PPT to 4 °C. The final structures of paraffin wax aggregates were the same at 4 °C regardless of the cooling rate used below the PPT. The cumulative crystal growth rate was observed to increase gradually at the highest cooling rate, but it reached a plateau below the PPT at the lower cooling rates. The faster cooling rates with the higher initial paraffin wax deposition showed a higher sudden increase in the mean crystal growth rate, where the formation of new nuclei and the growth of existing particles was faster. The onset of nucleation and crystal growth kinetics were used to interpret the transition between the hot flow and cold flow regimes, while cooling at fast and slow cooling rates. These results have a direct application in the development of cold flow technology for minimizing, or even avoiding, solid deposition from ‘waxy’ or paraffinic crude oils in pipelines and process equipment.

Acknowledgment Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Department of Chemical and Petroleum Engineering, University of Calgary, is gratefully acknowledged. We thank Professor Peter Kusalik for his valuable input. We also thank


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Mr. Sina Ehsani, Dr. Brandy Pilapil, Dr. Behzad Fuladpanjeh Hojaghan, and Ms. Rachel Malone for their technical support.

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"For Table of Contents Use Only"

Title: In-Situ Monitoring of Paraffin Wax Crystals Formation and Growth Authors: Samira Haj-Shafiei, Ben Workman, Milana Trifkovic, Anil K. Mehrotra

TOC Graphic

Synopsis The 3D images of multicomponent paraffin mixtures are shown at 4 °C for the cooling rates of 0.1 and 0.35 °C min–1. The resulting fractal dimensions show that, when the samples were cooled below the pour point temperature (PPT), similar crystalline structure networks were obtained for the two different cooling rates.


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In-Situ Monitoring of Paraffin Wax Crystals Formation and Growth

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