Microscopic Study of Wax Precipitation—Static Conditions - American

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Microscopic Study of Wax PrecipitationStatic Conditions Auzan A. Soedarmo, Nagu Daraboina,* Hyun S. Lee, and Cem Sarica McDougall School of Petroleum Engineering, The University of Tulsa, 2450 East Marshall, Tulsa, Oklahoma 74110, United States ABSTRACT: The scalability of available wax deposition models is still limited, partly due to the lack of mechanistic understanding on the wax deposition processes. In an attempt to enhance the understanding of wax deposition physical mechanisms, a systematic microscopic visualization experimental program is necessary. The static microscopic tests are performed with 100× magnification under controlled cooling rate conditions. An in-house MATLAB-based program is developed to enable measurements of morphological features such as size and aspect ratio. The two-dimensional (2-D) aspect ratio distribution of the crystals resembles a log-normal pattern with a mode of 2−3. Moreover, the 2-D size distribution of the crystals resembles an exponential decay pattern with a mode of 20−40 μm2. These tests also showed that there is no significant change in crystal aspect ratio during isothermal conditions over 48 h. In addition, it is also observed that the wax crystal precipitation rate is dependent on the cooling rate owing to the effect of supersaturation. Although static tests may not be directly applicable to wax deposition under flow conditions, they provide valuable insight for designing and analyzing difficult flowing visualization experiments.

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INTRODUCTION Wax or paraffin deposition is one of the major flow assurance issues, which may escalate to the extent of field abandonment in severe cases.1,2 An accurate wax deposition model is required to develop proper operating strategies. However, currently available models rarely achieve acceptable agreement with experimental data especially at turbulent conditions.3,4 The lack of mechanistic understanding on wax deposition processes is the main reason for this deficiency. Shear stress effects, mass transfer layer behavior, and morphological evolution of the wax crystals and complex interactions between them are believed to be the main contributors. A variety of diverging physical hypotheses have been proposed for wax deposition.1,2,5−9 Consequently, they lead to different governing equations and closure relationships as well. Wax Crystal Morphology. The crystal aspect ratio is first included in the wax deposition model by Singh et al.1 to quantify the effective diffusivity of wax through deposit. Their model stipulates that incoming wax flux onto the cold surface contributes to two processes: aging (increase in wax fraction in deposit) and growth (increase in wax deposit thickness). An illustration of the wax mass balance based on this model is shown in Figure 1. To date, the values of crystal aspect ratio are

is available to predetermine these values. The crystal aspect ratio (α) is defined as (d/a) as illustrated by Cussler et al. in Figure 2. For cases where the crystal length is far greater than

Figure 2. Illustration of the aspect ratio based on the Cussler equation.11

the pore length, the pore size effect (s) is negligible.11 This equation also assumes a system with homogeneous rectangular slits,11 which may not represent the actual wax deposit structure. Therefore, it is conceivable that other crystal morphological parameters such as size, orientation, and heterogeneity may also affect the aging process. Coutinho et al.12 reported an indication of Ostwald-ripening phenomena in wax crystallization. It is possible that this phenomenon may also occur in flowing wax deposition, consequently altering the crystal morphology under isothermal conditions. Several flow loop studies concluded a range of best-fit α values of 1−25 in laminar conditions,1,13 and 10−270 in turbulent conditions.14 Earlier microscopic studies reported 2-D aspect ratio values of the crystals from 2.2 to 3.81 for various model oil systems.15,16 With no closure relationship available, there is a need to guess the aspect ratio value for modeling purposes. Sensitivity of the models to the aspect ratio value is not negligible, as illustrated in Figure 3. Figure 3 is generated using TUWAX software4,17 with a model oil mixture18 as operating fluid at operating conditions shown in Table 1.19

Figure 1. Wax mass balance illustration. Received: November 18, 2015 Revised: January 4, 2016

back calculated from flow loop experiments, which may not represent the actual morphology.10 Moreover, no closure relationship © XXXX American Chemical Society

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Figure 3. Illustration of model sensitivity to aspect ratio change: (a) for thickness prediction and (b) for deposit wax content prediction.

Table 1. Operating Data for TUWAX Simulation Q [m3/s] ID [m] NRe [-] Tb [°C] Ti,initial [°C]

0.0014 0.04 12 400 35.0 32.6

NPr [-] NSc [-] hout [W/m2·K] model shear reduction term

42.5 10 600 5000 Singh et al. 2000 0

Wax Mass Transfer Layer. The wax deposition rate is proportional to the concentration gradient near the cold wall or oil−deposit interface.1,20 In the wax deposition process, the mass transfer field is dependent on the heat transfer field to some extent.2,7 The degree of supersaturation is one of the parameters which governs the dependency of mass transfer on heat transfer. One could assume a no supersaturation condition such that the radial concentration profile always follows the thermodynamic equilibrium or solubility curve. This approach is commonly known as the equilibrium model (EM).4 On the other hand, a complete supersaturation approach assumes that the mass transfer field is completely independent of the heat transfer field. In this assumption, a form of heat and mass transfer analogy is used. This approach is also known as the film mass transfer (FMT).4 For most oil applications, the Lewis number (Le) is greater than 1; hence, the FMT will predict a steeper concentration gradient and higher mass transfer rate compared to EM.7 Most of the experimental data reported that FMT tends to overpredict while EM tends to underpredict the deposition rate.2,17,21 Therefore, it can be inferred that, assuming no shear reduction effects, the actual concentration profile is possibly located between EM and FMT prediction. The degree of supersaturation is a function of the precipitation kinetics2 and cooling rate applied to the system. In this paper, the cooling rate is emphasized. A wax−oil system exposed to fast cooling will not have enough time to complete the precipitation process and consequently become supersaturated; on the other hand, a slow cooling process will provide sufficient time for the system to reach the thermodynamic equilibrium. An illustration of the expected cooling rate effect in the concentration profile is shown in Figure 4. It can be seen from Figure 4 that as the cooling rate decreases, the concentration profile is expected to be more dependent on the temperature profile. Figure 5 illustrates that the discrepancy between FMT and EM may be very significant such that operational decisions cannot be made by simply using these two extremes as upper and lower bounds, respectively. Figure 5 is generated using the same method and data as Figure 3. The cooling rates in actual wax deposition experiments are not directly measured, as there is no thermal transient in a given fluid control volume. However, it can be interpreted as a function of flow rate and temperature difference (ΔT).22,23

Figure 4. Illustration of the cooling rate effect on the concentration profile in the boundary layer.

Static microscopic tests are required as the initial stage for cooling rate effects investigation as they allow more precise cooling rate control. Microscopic Experiments in Wax Application. Due to the time-consuming nature of wax deposition experiments and difficulties mimicking field conditions in the laboratory, available data in the literature are still not sufficient to develop reliable predictive tools. Research efforts in microscopic scale to enhance understanding on wax deposition mechanisms are required to complement flow loop experimental data.24 Microscopic-scale experimentation is relatively new in wax deposition research compared to flow loop type experiments. Most of the morphology studies are performed under static conditions. Kane et al.25 performed experiments using a transmission electron microscope (TEM) with the cryotechnique. The discs size based on this study are between 15 and 40 nm. Leiroz26 conducted microscopic visualization experiments with magnification up to 1000×. The wax−oil mixture was suspended in a 2 mm thick chamber with a one-sided cooling wall. No quantitative analyses were made on the crystal morphology. Paso et al.15 and Venkatesan et al.16 used a cross-polarized microscope with 50× magnification. The samples were placed above a cooling plate controlled with a Peltier device. These studies concluded that, at the terminal condition, the length of wax crystals varies from 7 to 19 μm. Some of these studies also artificially mimicked the flow effects using shearing plates.16,25 Cabanillas et al.27 performed laminar microscopic visualization limited to deposit thickness measurement (not extended to morphological scale). Even under static conditions, the raw images produced in different studies can be dissimilar qualitatively. Correspondingly, the conclusion on wax crystal size can vary from nanometer25 to micrometer scale15,16 depending on the visualization technique. Wax deposition visualization under flowing conditions is expected to be more difficult as the effects of flow B

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Figure 5. Illustration of the discrepancy between FMT and EM under a turbulent condition, neglecting shear reduction: (a) thickness prediction and (b) wax content prediction.

rates, vibrations, and compaction of the deposit may complicate the observations further. These issues emphasize the needs of a reliable experimental procedure and analysis technique under static conditions prior to performing flowing experiments.

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EXPERIMENTAL PROGRAM

Testing Fluid. A mixture of Exxsol D-60 mineral oil and CSP-165 food-grade wax with a 95/5 weight ratio is used as the testing fluid. This fluid is also used by Agarwal19 for ongoing flow loop experiments and will be referred to further as MO-14. MO-14 has a WAT value of 41 ± 0.5 °C as measured by the cross-polarized microscopy technique. The detailed properties of MO-14 are provided by Agarwal.19 Facility Description. The static microscopic tests are performed with an AMSCOPE PZ600T cross-polarized microscope (CPM) with 100× magnification. The temperature stage INSTEC TS-62 is used to control the sample temperature from the bottom of the thin microscopic slide. This temperature stage works on Peltier-based control, which provides a temperature range from −30 to 120 °C and a cooling rate range from 0.1 °C/h to 50 °C/min. Figure 6 shows the microscopic test assembly, while Figure 7 shows the schematic drawing of TS-62.28

Figure 7. TS-62 temperature stage drawing. Image Analysis Procedure. Images obtained from the tests are analyzed with an in-house MATLAB-based program. This program is tailored to enable measurements of several morphological features such as size and aspect ratio. First, the program converts the raw image from red/green/blue (RGB) type to 8 bit. After that background noises due to contaminations such as microsize bubble or possibly dirt coming from the sample container are eliminated as necessary. Contaminants originally present on the microscopic slide are assumed to be negligible as the microscopic slide was always cleaned with acetone solution before each experiment. These nonwax objects do not disappear even after the sample is heated up to 55 °C, typically have an individual size of less than 100 sq-pixel at 100× magnification (∼5 μm2), and are relatively round in shape. These contaminations may form very fine dots once a color threshold is applied, which may be misinterpreted as objects. Therefore, the image analysis program is designed to exclude objects smaller than the above-mentioned size threshold. This size threshold is considerably smaller than estimated crystal size values reported in the literature.15,16 The program then converts the image into a binary image using the Otsu29 thresholding algorithm. This threshold value may need to be adjusted manually for some occasions, e.g., at the onset of precipitation where first crystals might not be optimally focused. Finally, the program performs detection and measurement of objects with measurement features available in MATLAB. The program is calibrated against particle size standards, and the error was found to be less than 10%. The analytical-gradepolymethacrylate microparticles from Sigma-Aldrich are used for image analysis calibration purposes. The individual particle radius is 2 μm with a manufacturer-specified standard deviation of 0.075 μm. The program is also tested against a widely used object identification software (Image-J), and the discrepancy was found to be less than 10%. The calibration example result is shown in Figure 8, and verification

Figure 6. Static tests experimental setup. Operating Procedure. The sample is prepared on a thin microscope slide after being heated to 55 °C for 20 min. The sample amount is being kept consistent at 1 drop per experiment with a dropping distance of 5 mm. The 3 mm gap between the TS-62 top cover and the bottom plate is closed by a plastic cover to minimize the ambient effects before starting the experiments. The samples are cooled from 55 to 25 °C with three different cooling rates (0.1, 0.5, and 1 °C/min). Upon reaching 25 °C temperature, the sample is kept under isothermal condition for 48 h to observe any effects of isothermal aging to crystal morphology. Each test is repeated three times to check reproducibility of the data. As the temperature stage and the CPM are not integrated to each other, representative images have to be taken manually at every intended observation temperatures. C

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Figure 11. Examples of the image processing sequence: (a) raw image, (b) binary image conversion, and (c) object identification.

Figure 8. MATLAB code calibration results example.

Figure 12. Examples of raw images from static microscopic visualization tests under 100× magnification and 0.5 °C/min cooling rate: (a) 41.2, (b) 35, and (c) 25 °C.

Figure 13. Examples of raw images from static microscopic visualization under 100× magnification at 35 °C and various cooling rates: (a) 0.1, (b) 0.5, and (c) 1 °C/min. Figure 9. MATLAB code comparison with Image-J for crystal count function.

crystal tends to have a larger size. All of the crystal size values mentioned in this paper are based on 2-D measurements. Venkatesan et al.16 tried to make 3-D projections of the crystal images using a z-drive microscope and concluded that the wax crystals resemble thin platelets with thicknesses of around 1 μm. They also concluded that platelets thicknesses for several cases are similar, indicating that the growth might be twodimensional. With this consideration, this study is progressed with 2-D measurements. Cooling rate dependency of average crystal size is confirmed quantitatively in Figure 14. Uncertainty bars with the 95% confidence interval are included in all quantitative analysis. These results are consistent with the qualitative observations by Venkatesan et al.16 and Lee et al.30 Figure 14 shows that size measurement uncertainty is considerably higher at low temperature. This issue can be explained by superposition of crystals as more of them are precipitating, as shown in Figure 12c. The image analysis program assumes the superposed crystals as one big crystal, which leads to discrepancy in individual size measurement results. Due to this deficiency, the crystal size distributions may be more suitable to describe the crystal size evolutions than average values, particularly at low temperature. Information on crystal size distributions is available in the later section of this paper. Static tests at various cooling rates also conclude that the CPM precipitation rate is cooling rate dependent as shown in Figure 15. This observation serves as a possible indication of supersaturation in wax precipitation processes. Observations on Crystals Aspect Ratio and Size Distribution. All aspect ratio values mentioned in this paper are based on 2-D measurements. Initial crystals precipitated from MO-14 solution near WAT tend to have “needle” shapes

Figure 10. MATLAB code comparison with Image-J for crystal average size measurement function. with Image-J results is shown in Figures 9 and 10, respectively. Figure 11 shows an example of the image processing and analysis sequence.

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RESULTS AND DISCUSSION Cooling Rate Effects on Precipitation Curves and Crystal Size. Examples of raw images obtained from static tests are shown in Figures 12 and 13. It can be inferred from Figure 12 that both precipitation and growth are happening as the temperature decreases. Figure 13 shows that, at a slower cooling rate, a smaller number of crystals is formed but each D

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that the compressive stress effect is negligible. Burton and Cabrera32 identified two primary mechanisms of crystal growth during the solidification process, namely, nonuniform lateral growth and uniform normal growth. In the presence of sufficient thermal driving force (in this case, cooling rate), every crystal surface element may advance normal to itself and contributes to growth of the crystal in a uniform manner. This theory serves as a plausible explanation of the experimental observation in this paper, which shows that the crystal average aspect ratio decreased with reduction of temperature. While it is possible that crystal superposition also affects the average aspect ratio values at lower temperature, Figure 16 shows that the convergence to the terminal aspect ratio value occurs at relatively high temperature where superposition of crystals is not expected yet. Moreover, the reproducibility of the average aspect ratio measurement is relatively better compared to the average size measurement, shown by the smaller error bars. The crystal aspect ratio distribution at terminal condition consistently resembles a log-normal pattern with a distribution mode of 2−3. This distribution mode value is within the same order of magnitude compared to average 2-D aspect ratio values reported by Paso et al.15 and Venkatesan et al.16 The terminal crystal aspect ratio distributions for all cooling rates are shown in Figure 17. The terminal aspect ratio distributions

Figure 14. MO-14 crystal size evolution with temperature and cooling rate (CR) variation.

Figure 15. MO-14 CPM precipitation curves at various cooling rates (CR).

with relatively high average aspect ratio values (3.4−5.7). As the temperature decreases, the average aspect ratio value converges into a terminal value. For MO-14, the terminal average aspect ratio value is observed to be around 2−2.3. Figure 16 shows the Figure 17. MO-14 terminal crystal aspect ratio distribution (25 °C).

are relatively independent of cooling rate. Small portions of high aspect ratio crystals are observed under a faster cooling rate; however, the magnitude of those is relatively insignificant. The crystal aspect ratio distributions evolution with temperature at 1 °C/min cooling rate is shown in Figure 18. Initial

Figure 16. MO-14 average aspect ratio evolution with temperature at various CR.

average crystal aspect ratio evolution with temperature at different cooling rates. These data show that the preferred crystal growth direction is not necessarily parallel to the major axis of the crystals. Kamb31 suggested that the preferred crystal orientation produces a minimum chemical potential required for equilibrium across a surface perpendicular to the axis of greatest compressive stress. In static condition, it is conceivable

Figure 18. MO-14 crystal aspect ratio distribution at near WAT, 35 °C, and 25 °C under 1 °C/min CR. E

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Energy & Fuels Table 2. Complete Crystal Aspect Ratio Distributions for Cooling Sessions 1 °C/min CR

0.5 °C/min CR

0.1 °C/min CR

aspect ratio

WAT − 0.2 °C

34 °C

25 °C

WAT − 0.2 °C

34 °C

25 °C

WAT − 0.2 °C

34 °C

25 °C

0−1 1−2 2−3 3−4 4−5 5−6 6−7 7−8 8−9 9−10 10−11

0% 0% 8% 0% 28% 44% 0% 8% 11% 0% 0%

0% 15% 42% 23% 12% 5% 2% 1% 0% 0% 0%

0% 22% 50% 19% 6% 2% 1% 0% 0% 0% 0%

0% 0% 17% 11% 72% 0% 0% 0% 0% 0% 0%

0% 23% 47% 19% 7% 2% 1% 0% 0% 0% 0%

0% 26% 53% 16% 4% 1% 0% 0% 0% 0% 0%

0% 33% 33% 17% 0% 0% 11% 0% 6% 0% 0%

0% 22% 47% 20% 7% 3% 1% 0% 0% 0% 0%

0% 27% 50% 17% 5% 1% 1% 0% 0% 0% 0%

Figure 21. Examples of images obtained from a 48 h isothermal run at 25 °C upon 0.5 °C/min cooling sequence: (a) 24, (b) 36, and (c) 48 h.

Figure 19. MO-14 crystal size distribution at terminal condition after various (CR).

Figure 22. MO-14 average crystal aspect ratio throughout 25 °C isothermal runs upon various CR. Figure 20. MO-14 crystal size distribution evolution under 1 °C/min CR.

crystals tend to have a more random aspect ratio distribution but then converges quickly into the signature distribution. The quantitative analyses for other cooling rates results lead to the same conclusion as shown in Table 2. The stochastic nature of the aspect ratio distribution near WAT is shown by the relatively larger error bars compared to lower temperature data. One of the plausible explanations behind this observation is that the major axis orientation of the initial crystals might not be completely parallel to the objective plane, leading to apparently smaller aspect ratio values. This randomness conceivably diminishes as the temperature decreases, and more crystals are available for quantitative analysis. That being said, the distribution mode near WAT is consistently greater than its value at lower temperatures (34 and 25 °C). The average crystal size measurement is observed to have high uncertainty with the current experimental setup, especially at lower temperatures, due to the superposition issue mentioned earlier.

Figure 23. MO-14 crystal aspect ratio distribution throughout 25 °C isothermal runs upon 1 °C/min CR.

Nevertheless, a resemblance to an exponential decay pattern is generally observed for the crystal size distribution, with superposed crystals inducing anomaly at the high tail end of the F

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Energy & Fuels Table 3. Complete Crystal Aspect Ratio Distributions for Isothermal Sessions after 1 °C/min CR

after 0.5 °C/min CR

after 0.1 °C/min CR

aspect ratio

12 h

24 h

36 h

48 h

12 h

24 h

36 h

48 h

12 h

24 h

36 h

48 h

0−1 1−2 2−3 3−4 4−5 5−6 6−7 7−8 8−9 9−10 10−11

0% 26% 51% 17% 4% 1% 0% 0% 0% 0% 0%

0% 26% 51% 16% 5% 1% 1% 0% 0% 0% 0%

0% 24% 54% 16% 4% 1% 0% 0% 0% 0% 0%

0% 25% 51% 17% 5% 1% 0% 0% 0% 0% 0%

0% 23% 51% 18% 7% 0% 0% 0% 0% 0% 0%

0% 24% 51% 17% 5% 1% 0% 0% 0% 0% 0%

0% 25% 52% 17% 5% 1% 0% 0% 0% 0% 0%

0% 26% 51% 17% 4% 1% 0% 0% 0% 0% 0%

0% 28% 49% 17% 4% 1% 0% 0% 6% 0% 0%

0% 31% 49% 15% 4% 1% 0% 0% 0% 0% 0%

0% 31% 49% 15% 4% 1% 0% 0% 0% 0% 0%

0% 33% 48% 14% 4% 1% 0% 0% 0% 0% 0%

conditions, these results are necessary to design and analyze flowing visualization experiments. As the wax morphology data are relatively scarce in the literature, experimental observations are valuable, especially if agreement with previous studies is achieved. Provided that data from flowing visualization studies can be available in the future, a solid morphological database in static conditions can serve as the baseline. The image analysis technique developed during this study is expected to be useful for visualization studies in flowing conditions.

histogram. The crystal size distributions at the terminal condition (25 °C) for various cooling rates are shown in Figure 19. Figure 19 indicates that the crystal size distribution at terminal condition is not dependent on the cooling rate. It is also seen that at terminal condition the crystal size distribution mode of MO-14 is 20−40 μm2. This value is within the same order of magnitude compared to average 2-D size values inferred from Paso et al.15 Figure 20 shows the crystal size distributions at near WAT, 34 °C, and 25 °C with a 1 °C/min cooling rate. This figure shows that the distribution modes of crystal size are consistent at 20−40 μm2, despite the appearance of larger crystals as the temperature decreases. This observation implies that while the existing crystals are growing in size, the smaller new nuclei are also forming as the temperature decreases. Isothermal Experiments. Isothermal runs are performed for 48 h following a cooling sequence to verify the effect of isothermal aging to crystal aspect ratio. It is observed that there was little change throughout these isothermal runs, indicating that the isothermal aging effect on crystal aspect ratio is not substantial. Examples of images obtained during the isothermal runs are shown in Figure 21. These images qualitatively show that there is no significant change throughout the isothermal period. Figure 22 shows the average crystal aspect ratio values, while Figure 23 shows the aspect ratio distribution throughout an isothermal period upon a cooling sequence with 1 °C/min cooling rate. Quantitative analyses for other cooling rates results lead to a similar conclusion as shown in Table 3.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 918-631-5146. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the company members of TU Paraffin Deposition Project (TUPDP) consortia and McDougall School of Petroleum Engineering at The University of Tulsa for their continuous support on this research effort. We thank Dr. Ekarit Panacharoensawad of Texas Tech University for his valuable input at the start of the study.

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CONCLUSIONS Microscopic study of wax precipitation and deposition is essential to understand physical mechanisms behind the wax deposition process. An in-house MATLAB program was developed to analyze the images obtained from the microscope. The performance of this program is verified with particle size standards and commercial software. The 2-D crystal aspect ratio distributions resemble the log-normal pattern with a distribution mode of 2−3. It is also observed that the average crystal aspect ratio values tend to converge into a terminal value with a reduction in temperature. A resemblance to the exponential decay pattern for the 2-D crystal size distribution is observed with a distribution mode of 20−40 μm2. Moreover, there is no significant change in the crystal aspect ratio during isothermal conditions over 48 h. In addition, it is also observed that the wax crystal precipitation rate is dependent on the cooling rate, which supports the applicability of supersaturation theory. One should be aware that even though static tests may not be directly applicable to wax deposition under flow

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ABBREVIATIONS CR = cooling rate Le = Lewis number CPM = cross-polarized microscope h = hours REFERENCES

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