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MICROSCOPIC STUDY OF WAX DEPOSITION: MASS TRANSFER BOUNDARY LAYER AND DEPOSIT MORPHOLOGY Auzan A Soedarmo, Nagu Daraboina, and Cem Sarica Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.5b02887 • Publication Date (Web): 29 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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MICROSCOPIC STUDY OF WAX DEPOSITION: MASS TRANSFER BOUNDARY LAYER AND DEPOSIT MORPHOLOGY Auzan A. Soedarmo, Nagu Daraboina*, and Cem Sarica McDougall School of Petroleum Engineering, The University of Tulsa KEYWORDS: mass transfer layer, wax deposition, microscopic visualization

ABSTRACT: This study presents a pioneering effort to enable visualization of in situ wax deposition process in a microscopic scale with an emphasis on mass transfer layer and deposit morphology observations. The mass transfer boundary layer study validates the existence of partial wax super-saturation near the wax deposit and oil interface. The discrepancy between the actual mass transfer layer thickness and the heat-mass transfer analogy prediction expands as the Reynolds number increases and the ∆ (temperature difference between bulk and cold interface)

decreases. This conclusion is in agreement with several flow loop data with same oil and similar flowing conditions. Morphology study reveals that under laminar conditions, the distribution of the deposit crystals aspect ratio resembles a lognormal pattern with a distribution mode between two and three. This characteristic exhibits similarity with wax crystals observed under static cooling conditions. Deposits formed under laminar conditions have a relatively rough surface and random flake structure, while turbulent deposits have a smoother surface and more uniformly layered structure. The shear stripping phenomena is not observed within the experimental

range

of

*To whom correspondence should be addressed. Tel: 1(918) 631 5146. Email: [email protected] ACS Paragon Plus Environment

this

study.

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INTRODUCTION

Wax deposition is one of the major flow assurance concerns, especially in deep water environment. It occurs when the cold interface temperature is lower than wax appearance temperature (WAT) and a negative temperature gradient on radial direction exist to drive the molecular diffusion1, 2. Severe case of wax deposition had led to field abandonment with an estimated total loss in excess of $100M3, 4. The development of fit-for-purpose operating strategies such as pigging and chemical inhibition require a reliable wax deposition model. Unfortunately, the lack of mechanistic understanding in wax deposition processes to date impedes the scalability of available wax deposition models1, 2, 5, 6. With this deficiency, trial and errors during operations are often needed to fine tune the model for a given operating condition. Areas of important mechanistic studies in wax deposition include the shear effects, deposit morphology evolution, and super-saturation in the mass transfer boundary layer6. Visualization studies are expected to provide sound physical bases for more representative wax deposition models2. However, in-situ visualization studies of wax deposition are limited, with a majority of them were performed under static conditions7-10. Some of these studies tried to emulate flow conditions by using a shear device such as shearing plate or rheometer9, Cabanillas, et al.

11

10

.

performed a microscopic visualization study under laminar conditions as a

method to measure deposit thickness instead of morphological study. Detailed explanations on heat and mass transfer interactions and shear reduction mechanisms are provided in following sub-sections. A review of the morphological study importance in wax deposition modeling is provided by Soedarmo et al.6

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Super-saturation in Mass Transfer Boundary Layer. Wax deposition is mainly driven by radial molecular diffusion3, which relies heavily on the radial wax concentration gradient. In wax deposition, the mass transfer field is thermodynamically dependent to the heat transfer field12, which results in a need to quantify the degree of super-saturation in the mass transfer boundary layer. Two extreme opposite theories are commonly called as the equilibrium model (EM) and film mass transfer (FMT). EM assumes no super-saturation (equilibrium wax in oil concentration) while FMT assumes the heat and mass transfer fields are completely independent to each other (complete super-saturation)13-15. Mathematical expressions of EM and FMT are shown in Eqs. 114, 15 and 216, respectively. =

=

Lee

4

= .

− ℎ − = = "#, − . = ! ,

Eq.1

Eq.2

suggested the precipitation kinetics concept to quantify the magnitude of super-

saturation. If wax precipitation rate is significantly faster than the cooling rate exposed to the wax-oil system, then the system will reach the thermodynamic equilibrium and vice versa. For a given cooling rate, the precipitation rate constant "$ governs the super-saturation degree. Equation 3 is used by Lee

4

to incorporate the precipitation kinetics term. An illustration of

concentration profiles predicted by EM, FMT, and precipitation kinetics is shown in Fig. 14. %&

1 = )* + , − "$ - − . /. '

Eq.3

The closure relationship to estimate "$ value is not available yet, hence it can still be

considered as a tuning parameter1. Moreover, it is important to note that the "$ values are back

calculated from experimental data, and may not necessarily represent the actual physics. The


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concentration gradient near the deposition interface and the value of mass transfer coefficient are inversely proportional to the mass transfer layer thickness16; however physical observations on the mass transfer boundary layer are still not available. Simplified approach by using FMT and EM as upper and lower bounds, respectively, at times are not viable, since the difference between EM and FMT might be very significant17. Understanding of how the super-saturation in the heat/ mass transfer layer changes with different operating conditions is important to establish proper up-scaling parameters from laboratory to field scale, considering that the thermal driving force (and conceivably equivalent cooling rate18, 19) in field conditions is considerably smaller than typical flow loop experiments20. Shear Reduction Mechanisms. The shear reduction concept is commonly used to explain the flow loop experimental data, which suggest that the pure molecular diffusion models tend to over-predict deposition rate under turbulent conditions12,

14, 21

. However, the mechanisms by

which shear forces reduce deposition rate are still not fully understood. In fact, it remains unclear what the important flow parameters are, whether it is the shear stress (τi), NRE, or other derived dimensionless numbers20. Theories to explain the shear effects generally can be grouped into shear prevention and shear stripping. Shear stripping is described as partial removal of deposit due to shear effect. Matzain 21 has developed a semi-empirical model to take the shear stripping into account. Shear stripping and sloughing terms are loosely interchangeable in literatures21-24; however, Venkatesan

12

considered sloughing as a random phenomenon, hence it was not

modeled in his study. An alternative concept of shear effect suggested that high shear stress exerted by the flow to the deposit may reduce the net deposition rate12 instead of removing parts of formed deposit. This concept assumes that reduction of the net deposition rate is caused by the reduction of


4

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incoming flux (not after the deposit is formed).

The illustrations of shear stripping and

prevention are shown in Fig. 2. Venkatesan, et al.

19

also proposed that shear stress reduces the oil gelation temperature

and therefore reduces deposition rate. Panacharoensawad

25

introduced a maximum tolerable

shear stress limit, above which the deposit growth becomes hindered. Studies by Tiwary and Mehrotra

26

reported that sloughing was not observed. They suggested that the shear forces

might deform the wax deposit crystals and consequently alter the macroscopic deposit characteristics. All of these theories are represented by different mathematical forms, which require different fitting parameters12, 25-27. Validation of these hypotheses is needed to develop or select a representative shear model in wax deposition.

EXPERIMENTAL PROGRAM Testing Fluid. A mixture of mineral oil and food grade wax used in static experimental work by Soedarmo et al.6 is also used in this study. Agarwal

28

have performed characterization of this

fluid, which is called as MO-14. The viscosity and wax precipitation curves are shown in Figs. 3 and 4, respectively, while other important properties are shown in Table 1. Facility Description. The tests are performed in the bench scale flow loop which has been described in detail elsewhere.5, 29 There are some modifications to this flow loop for this study. The rectangular test section of this loop (referred as TS-1 in the cited references) was replaced by a customized flowing cell to enable visualization from the perpendicular direction of the deposit growth and flow stream. The isometric drawings of the flowing cell is shown in Fig. 5, while the specifications are shown in Table 2. With this cell design, the oil flow is expected to be fully developed hydrodynamically at the visualization location. For this particular test cell geometry, the expected critical Reynolds number is approximately 1,70030.


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A high magnification microscope, Keyence VHX-500®, is used as the visualization device.

The boundary layer study was performed with 100-200X magnification, 50

frame/second (fps) speed, and 800 × 600 resolution.

With this resolution, the expected

minimum observable particle size is 4µm2. The morphology study was performed with 200X magnification, 15 fps speed and 1600 × 1200 resolution.

Operating Procedure. The cooling water is circulated through a bypass line until the desired temperature is reached. The oil is circulated at 54.4° C, which is 12.2° C above the wax appearance temperature (WAT), for 4 hours to ensure all of wax particles inside the flowing cell oil duct are melted. Upon complete melting, the oil temperature is reduced to the desired bulk oil temperature (in this case 44.4° C). After the desired bulk oil temperature is reached, the cooling water is redirected into the coolant duct of the flowing cell. Due to inability to drain the oil duct prior to the cooling water entrance, there will be a transient time during which the interface temperature at the oil side is decreasing towards the steady-state condition. Therefore, the wax deposition is not expected to immediately occur after the water enters the flowing cell. The video recordings were obtained from the time the water enters the flowing cell until 1 hour time duration (for boundary layer study), and until 12 hour time duration (for morphology study). The 0.88” side walls of the test cell are not insulated, however they are made from plexiglass with low thermal conductivity compared to the copper plate used as the heat transfer media. With this design, wax deposition on the side walls do not occur. However, at the observation location, both walls were drilled and the holes are covered with thin sapphire glass. Wax deposition tends to happen on these side glasses for low wall temperature cases and disturb the visual observation. To alleviate this issue, the experiments are performed with bulk


6

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temperature above WAT and the temperature inside the flow loop enclosure are kept at 85-90° F at minimum. That being said, for low interface temperature experiments, this issue is not entirely preventable and eventually limit the experiment duration. This issue will be addressed further in results and discussions section. Experimental Matrix. The experimental matrices for boundary layer, morphology, and additional shear stripping studies are given in Table 3. The calculation of important hydrodynamic and heat/ mass transfer parameters (NRE, ho, τw,cw, cooling rate, and Ti,initial) are given in the appendix. Data Analysis. Measurement of the actual mass transfer boundary layer thickness -, / is performed in this study. This thickness is defined as the distance from the cold wall where the local wax concentration reaches 99% of the bulk concentration (also known as 99% boundary layer16). This definition is analogous to the classical definition of hydrodynamic boundary layer thickness used by Blasius31. This definition differs from the equivalent mass transfer layer thickness -, / which is used in Eq. 2. The equivalent mass transfer layer thickness is

obtained by linear extrapolation of concentration gradient at the cold wall, such that the driving force can be approximated with bulk-interface concentration difference. These definitions are also applicable for momentum and heat transfer analogously. The difference between these two definitions for momentum transfer case are illustrated in Fig.6. This figure is generated using BL-01 test operating conditions, while the calculation the procedure for velocity profile is described in the appendix. The 99% boundary layer is used in this study since it is visually identifiable. Since all experiments were performed with bulk oil temperature above WAT, no crystals are expected to


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form above the mass transfer boundary layer. Therefore, the farthest distance of observed wax crystal from the cold wall can be interpreted as the mass transfer layer boundary thickness. If the EM works, the crystals are expected to appear near the location of WAT. On the other hand, if the FMT works, the crystal are expected to present only below the mass transfer boundary layer predicted by heat and mass transfer analogy. However, Lee’s hypothesis4 suggested that the mass transfer boundary layer is located between EM and FMT predictions as shown in Fig. 7. The raw images are processed and analyzed in a similar way to Soedarmo et al.6, with additional image preparation work to filter the effects of the debris contamination. The filtering process is done manually based on visual difference between the debris and the wax crystals. However, for high flow rate experiments, these debris disturb the analysis significantly and eventually limit the range of experimental conditions performed in this study. This issue will be addressed later in the results and discussions section. The debris materials are small size dirt, which remain in the flow loop after 2 x 12 hours cycles of flow loop rinsing with the hot mineral oil without wax. Since they did not dissolve, we believe they are not hydrocarbon origin. The example of raw and analyzed images are shown in Fig. 8. For image analysis, at least 10 images are taken for each flow condition to capture the fluctuating nature of this experiment. The values presented in the results and discussions section are the averaged values with 95% confidence interval. For morphology study, quantitative analysis is only doable for 2-D aspect ratio in laminar flow conditions.

In turbulent flow conditions, the deposits conceivably have higher wax

content2, 13, 14, 32, 33, hence it is not penetrable by light. Accordingly, the deposits under turbulent flow conditions were being analyzed only qualitatively. An example of image analysis on deposits formed under laminar conditions is shown in Fig. 9.


8

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RESULTS AND DISCUSSIONS Mass Transfer Boundary Layer Study. This study requires an estimation of the mass transfer boundary layer thickness predicted by heat/mass transfer analogy -, / and the

location of WAT 12 . The calculation procedures and assumptions of these parameters are

shown in the appendix, while Table-4 shows the results. To complement the mass transfer boundary layer thickness measurement from microscope, several experimental data28 with similar range of operating conditions and same oil system are analyzed to back-calculate the mass transfer boundary layer thickness from flow loop experiments. Fig.10 shows the empirical relationship between the actual to FMT mass transfer coefficient ratio with NRE. The development of this empirical relationship is given in the appendix. Some examples of still images obtained in boundary layer study are shown in Figs. 11 13. Comparison between Figs. 11 and 12 shows that, at higher ΔT conditions (which imposes higher cooling rate), the precipitated crystals in boundary layer are observed to be smaller and denser. This observation is consistent with previous studies in static conditions6,

10, 34

.

Comparison between Figs. 12 and 13 shows that, at higher NRE, the mass transfer boundary layer thickness is lower. Fig. 13 also shows that, at higher flow rate, more debris/dirt are entrained into the flow cell. The debris contamination limits the upper range of the boundary layer study at NRE value of around 4,500. The wax crystals by nature are more transparent than the debris hence they can be differentiated visually. However, as the flow rate increases the microscope camera is losing the ability to capture the transparent nature of wax crystals due to frame rate limitation; therefore, it impedes objective quantification of mass transfer boundary layer thickness.


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The boundary layer study results are summarized in Fig. 14. This figure shows that the microscopic mass transfer boundary layer thickness -,3 / is located between 12 and , ,

which serves as the proof of Lee’s hypothesis4 of partial super-saturation. It is also observed from Fig. 14 that the magnitudes of ,3 and ,# (mass transfer boundary layer thickness based on flow loop data) within the range of experimental NRE are similar. Therefore, it enhances the confidence of mass transfer layer boundary thickness measurement quality from microscope. It is important to note that flow loop data are generated with different flow conduit geometries at different temperatures difference between bulk and cold wall (ΔT), hence, it is conceivable that the exact values of 4,3 and ,# are slightly different. Additional analysis of boundary layer study is presented in Fig. 15 by plotting the ratio between "#, and "#,3 or "#,# with NRE. This ratio indicates over-prediction of FMT if the value is greater than one. This figure shows that the FMT over-predicts mass transfer coefficient in general. This over-prediction expands with decreasing ΔT and increasing NRE. The effect of ΔT can be explained by cooling rate theory. As the ΔT decreases, the equivalent cooling rate also decreases18,

19

, therefore the system will have more time to precipitates approaching

thermodynamic equilibrium. In this condition, FMT will conceivably over-predicts the mass transfer coefficient. This finding may explain the failure of the models to predict late time deposition behavior20, during which the thermal driving force has been lessened by the deposit self-insulation effect. It also emphasizes the requirement of super-saturation parameters in upscaling flow loop results (typically at high ΔT) to field applications (typically at low ΔT). To maintain similar value of initial ΔT for various flowrates, the cooling water temperature is reduced accordingly with an increase in flowrate. Therefore, the increase in FMT over-prediction with increase in NRE is counter-intuitive from cooling rate perspective, as higher


10

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NRE should impose higher cooling rate (more super-saturation). However, as shown in Fig. 16, the effect of an increase in NRE to the shear stress is more dominant than its effect to the cooling rate. The FMT prediction is based on a constant ratio between momentum and mass diffusivity, neglecting the fact that in wax deposition, the mass transfer field is still thermodynamically dependent to the thermal field4, 19. Therefore, it is conceivable that the FMT over-prediction expands with an increase in NRE; as the over-prediction caused by the increase in momentum diffusivity outweigh the correction caused by the increase in cooling rate. This behavior is also consistent with previous experimental/ modeling studies which suggested that FMT works sufficiently well in laminar conditions3, 4.

Morphology Study. Quantitative analysis was only doable for laminar flow tests (MO-01 and MO-03). Deposits formed under turbulent flow conditions were not penetrable by light, hence preventing quantitative morphology analysis. Quantitative analysis is focused on aspect ratio distribution. Example of the deposit images obtained from laminar flow tests are shown in Fig. 17. As shown in Fig. 17, deposits formed under laminar flow tends to have flake/pebble structure with relatively random arrangement, hence the deposit surface is rough. The flake shaped clusters formation was very visible in Fig. 17 (c) and (d). The flow rate effects to the arrangement direction were not seen until later times (120 minutes). It can be inferred that, under laminar flow conditions, the shear stress exerted onto deposit surface is relatively low. Therefore the wax clusters can grow without visible alteration/hindrance. The deposit crystals aspect ratio distributions for laminar flow conditions are observed to be similar with static microscopic observation performed by Soedarmo et al.6 . The distribution mode of the crystal aspect ratio is between two and three with resemblance to lognormal pattern.


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This distribution mode value is also consistent (within similar order of magnitude) with average aspect ratio values reported in previous studies6, 7, 10. The aspect ratio distribution of wax deposit crystals formed under laminar flow tests are shown in Figs. 18 and 19. The MO-03 test was performed under very low interface temperature. This condition promotes attachment of wax crystals onto the side window, which hinders further observation at later time. Therefore, Fig. 19 only displays the results up to time equal to 15 minutes. It is possible that some crystals might not be oriented completely perpendicular to the visualization direction. These crystals conceivably appear as the low aspect ratio crystals in the histograms. Under turbulent flow conditions, flow rate is observed to profoundly affect the crystal arrangement, as the deposits tend to have more structured layers instead of random “pebble” stack. The flake shaped clusters are not observed to form on the deposit surface as part of deposit growth. Turbulent flow deposits have relatively smooth surface compared to laminar flow deposits, and the layered or stratified textures become more visible at later time. Example of deposit images obtained at turbulent flow conditions are shown in Fig. 20. It is fair to note that the 2D observations performed in this study may not be able to capture the deposit morphology as a whole. However, they still depict a reasonably physical range of crystal aspect ratio. One could compare these results to the back-calculated values from flow loop data3,

35, 36

(which vary from 1 to 270) to perform initial validation of currently

available governing equations. Moreover, the in-situ visualization capability developed in this study provides a pathway for further morphology studies to further improve aging modeling.

Shear Stripping Verification. Shear stripping study is performed with both conventional forward and reverse experiments. In a forward experiment, SS-01, SS-02, and SS-03 tests are performed separately for 12 hours each with no prior deposition. In a reverse experiment, the


12

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deposit was intentionally generated under SS-01 condition for 12 hours, then the flow rate is increased to SS-02 and SS-03 conditions for 12 hours duration each while maintaining a constant interface temperature. The shear stripping/partial removal of deposit is not observed for these conditions. However, this conclusion has to be tested with higher shear stress conditions as the maximum shear stress acting on the deposit interface in these experiments were only around 0.76 Pa. The snapshots of deposit interface during the reverse experiment are shown in Fig. 21.

CONCLUSIONS An experimental setup is designed and constructed to enable microscopic scale in-situ visualization of wax deposition process. This setup was used to perform experiments with two primary observation targets, mass transfer boundary layer and deposit morphology, and one verification study on shear stripping. The boundary layer study concluded that the actual mass transfer layer thickness is located between the EM and FMT predictions, thus proving the existence of partial super-saturation in the boundary layer. The FMT over-prediction expands with a reduction in ∆T due to decreasing degree of super-saturation. This over-prediction also expands with an increase in flow rate as the over-prediction caused by constant momentum to mass diffusion ratio assumption outweighs the correction caused by increasing cooling rate. The behavior of mass transfer boundary layer thickness observed from microscope with change in NRE is comparable to the similar value empirically obtained from flow loop data. Morphology study concluded that the aspect ratio distribution of the wax deposit crystals formed under laminar conditions have similar pattern to static conditions, with distribution mode varying between two and three. Qualitatively, the wax deposits formed under turbulent flow tend to have smoother surface and more structured layers arrangement compared to the ones formed under laminar condition. This observation shows that the flow rate affects deposit morphology


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in general.

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Shear stripping or partial removal of deposit is not observed even in reverse

experiments; however, this conclusion has to be tested for higher shear stress conditions. The boundary layer study results visually conclude that super-saturation is important in the up scaling effort. However, they do not necessarily conclude that other proposed mechanisms (e.g: shear removal) do not exist. The morphology study established a pioneering effort for insitu deposit morphology observations. The information obtained from this study enhances our understanding and aids to improve aging prediction.

ACKNOWLEDGMENT The authors would like to 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 would like to thank Mr. Rohit Imandi for his assistance in data collection. APPENDIX 1.

Calculation of NRE 567 =

567 =

B,E = ℎ

2.

M =

89 %̅& ℎ ;

; =9 >?@?ABC> =A9D

89 %̅& B,E ;

ℎ =

; =9 AFGCF =A9D 4IJ 2I + 2J

16 16 = ℎ ; =9 >ℎGP >BP> EBAA QB9B>R 89 %̅& ℎ 17 ;

N

Eq.430 Eq.537 Eq.6

Eq.737, 38

Calculation of heat transfer coefficient and initial interface temperature


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The calculation of heat transfer coefficient in the test cell is complicated by the unconventional geometry (rectangular duct with 1 cooling wall) and the thermal developing nature of the flow at the observation location. Panacharoensawad25 extrapolated Wibulswas39 data and came up with Eq. 9 for a test cell with similar aspect ratio with the one used in this manuscript. 'S∗ =

5?& = 0.719'S∗

'⁄ U '⁄ U = , 6B W WB

Z[⁄\

+ 1.3256; =9 'S∗

ℎ = 5?&

,`abc = − 3.

" U

Eq.8 Z[⁄\

> 4,

Eq.9 Eq.10

d − 4 ℎ

Eq.11

Calculation of equivalent cooling rate Singh et al18. and Venkatesan et al.19 have proposed a method to calculate the equivalent

cooling rate on a deposit as shown in Eq. 12. The equivalent cooling rate exposed to a wax molecule is conceivably analogous to how fast it travels from hot region in the bulk to the cold region closer to the wall. Mathematically, it is the multiplication of diffusion rate and the temperature gradient. The 5?⁄6 − term in Eq. 12 is simply the temperature gradient, therefore the , ⁄1 − ef term has to be replaced with a relevant molecular diffusion rate.

The molecular diffusion rate is again depends on whether EM or FMT assumption is used. Eq. 13 describes the cooling rate calculation if FMT is used while Eq. 14 is used for EM.

6 =

, 5? − , = > 1 − ef 6

Eq. 12


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6 = 4.

6 =

ℎ 5? − , = > U 6

− 5? − , = g5? h > U − 6

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Eq.13

Eq.14

Calculation of wall shear stress. Knight and Patel40 proposed Eq. 15 to calculate the shear stress acting on the width side

of a rectangular duct (in this case, the cooling wall), while the average wall shear stress required in this equation is calculated in a similar way with pipe flow system. The calculation of friction factor for non-circular ducts is proposed by Jones37 and shown in Eq. 16.

1

p=

5.

k1 m.no i̅ ,4 Z4 I Zj = 1.025 g + 1h M1 − B \S l N. i̅

J

= 2 log[t -0.64 5u. p=/ − 0.8; =9 >?@?ABC> 64 ; =9 AFGCF 5u.

Eq.15

Eq.16.

Boundary layer thickness calculation. The definition of boundary layer thickness in rectangular duct is somewhat vague, as

what usually matters for practical purposes are the equivalent transport layer thicknesses for calculation of shear stress, heat flux and mass flux. Several steps are performed to calculate the theoretical mass transfer boundary layer thickness and the location of WAT in the test cell. Shah38 has proposed an analytical solution for velocity profile of a laminar flow in rectangular duct as shown in Eq. 17.


16

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128%̅& 1 %& R = x \ −1 \ w C `[,\,…

`Z[ ` y1

Cw} l I ~ cos jCw} l − CwJ I cosh j l I cosh j

Eq.17

Eq. 17 gives the hydrodynamic boundary layer thickness and velocity profile in the boundary layer. The velocity profile inside the rectangular duct for BL-01 and -05 tests in this manuscript are shown in Fig. 22 and Eq. 18. The extrapolation of Eq. 18 derivative at the wall to

the value of %& R = %&,3b leads to Eq. 19. It is concluded that for BL-01 and 05 test conditions: %&,3b ≈ 0.174

3

, ≈ 12440 ;, and ≈ 4700 ;. Given its definition, the

value of can be verified using the relationship between wall shear stress and centerline velocity as shown in Eq. 20. This equation yields ≈ 5170 ; which indicates a fairly good

agreement with Eq. 17.

%& R R \ R k R = 0.8 g h − 2.45 g h + 2.65 g h, %&,3b %& 1= ) , M N R R t %&,3b i ,4 = ;

%& %&,3b ≈ ; R t

Eq.18

Eq.19

Eq.20

For turbulent flows, unfortunately analytical solution is not easily attainable. Given that the experiments in this work are performed at relatively low NRE (< 4,000), it is reasonable to assume that the normalized velocity profile (Eq. 18) inside the boundary layer does not change significantly with the flow rate in the experimental range of this investigation. The boundary layer thickness itself, however, is strongly dependent on the flow rate. This assumption is reasonable as even though the flow is turbulent, the flow inside the boundary layer is still strongly affected by viscous effects such that the analytical solution is still valid. The


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Page 18 of 39

calculation is performed using Eqs. 17 and 20, which has taken account of the flow regime change between laminar and turbulent. Finally, the hydrodynamic boundary layer thickness

is back-calculated using Eq. 19. Once the hydrodynamic boundary layer thickness is obtained, the thermal and mass transfer boundary layer thicknesses can then be obtained with the analogy relationship as shown in Eq. 21. =

; =9 >ℎBFA @9?CFR AFRB W [/\

= [/\ ; =9 FPP >FCP=B @9?CFR AFRB E

Eq.21

Correspondingly, an analogous form of Eq.18 is also usable to estimate the temperature profile inside the thermal boundary layer as shown in Eq.22, after the thermal boundary layer thickness is obtained. − R \ R k R = 0.8 g h − 2.45 g h + 2.65 g h − 6.

Eq.22

Calculation of mass transfer boundary layer thickness based on flow loop data. Several flow loop experimental data28 consisting of deposit mass and wax fraction

information are analyzed for comparison with the mass transfer boundary layer thickness measurement from microscope. Eq. 23 is used to back-calculate the actual mass transfer coefficient. Considering the Eq. 3 described earlier in the manuscript and the assumption of laminar velocity profile inside the boundary layer, the mass transfer boundary layer thickness based on flow loop data -,# / can be obtained with Eq. 24. The value of "#, is estimated using Harriott and Hamilton

41

equation as the Schmidt number for this case is far greater than

1000.


18

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"#,# =

ef ⁄> w ! −

, ,e "#,# = ≅ "#, ,e ,#

Eq.23

Eq.24


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NOMENCLATURES Variables

⁄

⁄ ⁄'

⁄

6 B,E !

U

: Radial concentration gradient [kg/m3/m] : Concentration derivative with respect to temperature [kg/m3/°C] : Axial concentration gradient [kg/m3/m] : Radial temperature gradient [°C /m] : Wax concentration in oil [kg/m3] : Equivalent cooling rate at flowing conditions [°C/min] : Effective diameter of a channel flow in laminar conditions [m]

: Effective diameter of the pipe, reduced by deposit thickness [m] : Hydraulic diameter of the rectangular duct [m] : Diffusivity of wax in oil [m2/s]

,

: Effective diffusivity of wax in trapped oil inside deposit [m2/s]

ℎ

: Convective heat transfer coefficient [W/m/°C]

ef ⁄>

: Experimental wax mass deposition rate [kg/s]

I

"#

: Test cell height [m]

"$

: Precipitation rate constant [s-1]

: Pipe length [m]

NRE

: Reynolds number [-]

: Peclet number [-]

WB

: Mass transfer coefficient [m/s]

: Wax deposition flux [kg/m2/s]

E

: Mass flow rate [kg/min]

: Time [min]

ℎ

: Schmidt number [-]

%&

: Temperature [°C]

>

: Sherwood number [-]

: Axial velocity [m/s]


20

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Energy & Fuels

%̅&

J

: Average axial velocity [m/s]

R

: Dimensionless distance from wall [-]

'S∗

: Axial position inside the pipe or duct [m]

'

: Test cell width [-]

: Characteristic length of the rectangular duct on the axial direction [-]

Greek Letter

: Hydrodynamic boundary layer thickness [m or µm]

: Location of WAT relative to the cold wall [m or µm]

: Thermal boundary layer thickness [m or µm]

∆ *

: Temperature difference between bulk and interface [°C]

i

: Shear stress acting on the wall [Pa]

8

: Viscosity [Pa.s]

12

;

: Mass transfer boundary layer thickness [m or µm]

: Mass transfer eddy diffusivity [-]

: Density [kg/m3]

Subscript F% @

E

: Average : At bulk fluid

ED

: Cooling water

G

: Precipitation model

7

: Cold wall

BE

: At equilibrium

9

: Initial

GCG

e

e

: At deposit and fluid interface

: Oil : Back-calculated from flow loop data : Calculated with film mass transfer or heat/mass transfer analogy theory : Observed from microscope

Superscript


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B

Page 22 of 39

: Equivalent transfer layer

REFERENCES 1. Sarica, C.; Panacharoensawad, E., Review of Paraffin Deposition Research under Multiphase Flow Conditions. Energy Fuels 2012, 26, 3968-3978. 2. Dwivedi, P.; Sarica, C.; Shang, W., Experimental Study on Wax Deposition Characteristics of a Waxy Crude Under Single-Phase Turbulent Conditions. Oil Gas Facil. 2013, 2, (04), 61-73. 3. Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N., Formation and Aging of Incipient Thin Film Wax-Oil Gels. AIChE J. 2000, 46, (5), 1059-1074. 4. Lee, H. S. Computational and Rheological Study of Wax Deposition and Gelation in Subsea Pipelines. Dissertation, The University of Michigan, Ann Arbor, 2008. 5. Panacharoensawad, E., Wax Deposit Surface Characteristics under Single-phase and Water-in-Crude-Oil Flow Conditions. In Offshore Technology Conference, SPE: Houston, 2014. 6. Soedarmo, A. A.; Daraboina, N.; Lee, H. S.; Sarica, C., Microscopic Study of Wax Precipitation: Static Conditions. Energy & Fuels 2016, DOI: 10.1021/acs.energyfuels.5b02653. 7. Paso, K.; Senra, M.; Yi, Y.; Sastry, A. M.; Fogler, H. S., Paraffin Polydispersity Facilitates Mechanical Gelation. Ind. Eng. Chem. Res. 2005, 44, 7242-7254. 8. Leiroz, A. T. Study of Wax Deposition in Petroleum Pipelines (Portuguese). Dissertation, Pontificia Universidade Catolica do Rio de Janeiro Rio de Janeiro, Brazil, 2004. 9. Kane, M.; Djabourov, M.; Volle, J. L.; Lechaire, J. P.; Frebourg, G., Morphology of Paraffin Crystals in Waxy Crude Oils Cooled in Quiescent Conditions and under Flow. Fuel 2002, 82, 127-135. 10. Venkatesan, R.; Nagarajan, N.; Paso, K.; Yi, Y.-B.; Sastry, A. M.; Fogler, H. S., The Strength of Paraffin Gels Formed Under Static and Flow Conditions. Chem. Eng. Sci. 2005, 60, 3587-3598. 11. Cabanillas, J. L. P.; Leiroz, A. T.; Azevedo, L. F. A., Paraffin Deposition in Laminar Channel Flow, in the Presence of Suspended Crystals. In ABCM 19th International Congress of Mechanical Engineering, Associacao Brasileira de Engenharia e Ciencias Mecanicas - ABCM: Brasilia, DF, 2007. 12. Venkatesan, R. The Deposition and Rheology of Organic Gels. Dissertation, University of Michigan, Ann Arbor, MI, 2004. 13. Dwivedi, P. An Investigation of Single Phase Wax Deposition Characteristics of South Pelto Oil Under Turbulent Flow. Thesis, The University of Tulsa, Tulsa, OK, 2010. 14. Karami, H. Investigation of Single Phase Paraffin Deposition Characteristics Under Turbulent Flow. Thesis, The University of Tulsa, Tulsa, OK, 2011. 15. Singh, A. Experimental and Field Verification Study of Wax Deposition in Turbulent Flow Condition. Thesis, The University of Tulsa, Tulsa, OK, 2013. 16. Huang, Z.; Zheng, S.; Fogler, H. S., Wax Deposition: Experimental Characterizations, Theoretical Modeling, and Field Practices. CRC Press: Boca Raton, FL, 2015. 17. Soedarmo, A. A. Mechanistic Study of Wax Deposition: Boundary Layer and Deposit Morphology. Thesis, The University of Tulsa, Tulsa, OK, 2015.


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18. Singh, P.; Fogler, H. S.; Nagarajan, N., Prediction of the Wax Content of the Incipient Wax-Oil Gel in a Pipeline: An Application of the Controlled Stress Rheometer. J. Rheol. 1999, 43, (6). 19. Venkatesan, R.; Singh, P.; Fogler, H. S., Delineating the Pour Point and Gelation Temperature of Waxy Crude Oils. Soc. Pet. Eng. J. 2002, 349-354. 20. Venkatesan, R.; Creek, J. L., Wax Deposition During Production Operations: SOTA. In Proc. - Annu. Offshore Technol. Conf., SPE: Houston, TX, 2007. 21. Matzain, A. Multiphase Flow Paraffin Deposition Modeling. Dissertation, The University of Tulsa, Tulsa, OK, 1999. 22. Burger, E. D.; Perkins, T. K.; Striegler, J. H., Studies of Wax Deposition in Trans Alaska Pipeline. J. Pet. Technol. 1981, 33, (06), 1075-1086. 23. Hsu, J. J.; Santamaria, M. M.; Brubaker, J. P., Wax Deposition of Waxy Live Crudes under Turbulent Flow Conditions. In Proc. - Annu. Offshore Technol. Conf., SPE: New Orleans, LA, 1994. 24. Hernandez, O. Investigation of Single Phase Paraffin Deposition Characteristics. Thesis, The University of Tulsa, Tulsa, OK, 2002. 25. Panacharoensawad, E. Wax Deposition Under Two-Phase Oil-Water Flowing Conditions. Dissertation, The University of Tulsa, Tulsa, OK, 2012. 26. Tiwary, R.; Mehrotra, A. K., Deposition from Wax-Solvent Mixtures under Turbulent Flow: Effects of Shear Rate and Time on Deposit Properties. Energy Fuels 2008, 23, 1299-1310. 27. Rittirong, A. Paraffin Deposition under Two-Phase Gas Oil Slug Flow in Horizontal Pipes. Dissertation, The University of Tulsa, Tulsa, OK, 2014. 28. Agarwal, J. Single-Phase Wax Deposition Characteristics Under Turbulent Flow Conditions, TUPDP 29th Advisory Board Meeting Report, The University of Tulsa, Tulsa, 2015. 29. Panacharoensawad, E.; Sarica, C., Experimental Study of Single-Phase and Two-Phase Water-in-Crude-Oil Dispersed Flow Wax Deposition in a Mini Pilot-Scale Flow Loop. Energy & Fuels 2013, 27, (9), 5036–5053. 30. Tosun, I.; Uner, D.; Ozgen, C., Critical Reynolds Number for Newtonian Flow in Rectangular Duct. Industrial and Engineering Chemistry Research 1988, 27, (10), 1955-1957. 31. Blasius, H., Grenzschichten in Flussikeitein mit kleiner Reibung [English Translation in NACA Technical Memo, 1256] Z. Angew. Math. Phys 1908, 56, 1-37. 32. Matzain, A. Single Phase Liquid Paraffin Deposition Modeling. Thesis, The University of Tulsa, Tulsa, OK, 1996. 33. Hernandez, O.; Hensley, H.; Sarica, C.; Brill, J. P.; Volk, M.; Delle-case, E., Improvements in Single-Phase Paraffin Deposition Modeling. In SPE Annual Technical Conference and Exhibition, SPE, Ed. SPE: Denver, CO, 2003. 34. Lee, H. S.; Singh, P.; Thomason, W. H.; Fogler, H. S., Waxy Oil Gel Breaking Mechanisms: Adhesive Versus Cohesive Failure. Energy Fuels 2007, 22, 480-487. 35. Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N., Morphological Evolution of Thick Wax Deposits during Aging. AIChE J. 2001, 47, (1), 6-18. 36. Guthrie, S.; Mazzanti, G.; Steer, T. N.; Stetzer, M. R.; Kautsky, S. P.; Merz, H.; Idziak, S. H. J.; Sirota, E. B., An in situ method for observing wax crystallization under pipe flow. Am. Inst. Phys. 2004, 75, (4), 873-877. 37. Jones, O. C., An Improvement in the Calculation of Turbulent Friction in Rectangular Ducts. J. Fluids Eng. 1976, 98, 173-181.


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38. Shah, R. K. Laminar Flow Forced Convection Heat Transfer and Flow Friction in Straight and Curved Ducts - A Summary of Analytical Solution. Dissertation, Stanford University, Stanford, CA, 1972. 39. Wibulswas, P. Laminar Flow Heat Transfer in Non-Circular Ducts. Thesis, University College London, London, 1966. 40. Knight, D. W.; Patel, H. S., Boundary Shear in Smooth Rectangular Duct. Journal of Hydraulic Engineering 1985, 111, (1), 29-47. 41. Harriott, P.; Hamilton, R. M., Solid-liquid mass transfer in turbulent pipe flow. Chem. Eng. Sci. 1965, 20.


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Table 1. MO-14 Fluid Properties WAT [°F] Wax content [%] Density at 90°F [g/cc] Heat capacity [J/kg-K] Thermal conductivity [W/m-K] Molecular weight [g/mol] Molar volume [cc/mol]

106.7 ± 1 5 0.79 1919.3 0.12 521.4 567

Cross polarized microscope N/A Coriolis flow meter PVTSIM simulation PVTSIM simulation Fluid composition Fluid composition

Table 2. Specification of the flowing cell. Copper layer thickness [m] Oil duct width [m] Oil duct height [m] Water duct width [m] Water duct height [m] Length [m] Observation window diameter [m]

0.04 0.013 0.035 0.013 0.04 0.565 0.04


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Table 3. Experimental matrix for boundary layer, morphology, and shear stripping studies.

No

Boundary Layer Qo [kg/min] Tb,o [°C] Tb,c [°C] NRE [-] ho [W/m2K] τw,cw [Pa] ΔT [°C] CReq,FMT [°C/min]

BL-01 BL-02 BL-03

2.0 3.1 4.0

BL-04 BL-13 BL-05 BL-06 BL-07 BL-08 BL-09

5.0 6.0 2.0 3.1 4.0 5.0 6.0

No

18.3 17.7 17.3

44.4 44.4 44.4 44.4

31.7 31.5 18.3

1216 1988 2585

60.0 69.1 74.7

2.0 3.1 2.0

MO-04 MO-05

5.0 10.1

16.9 16.7 31.7 31.5 31.2 30.8 30.8

0.05 0.10 0.16 0.24

12.3 12.2 12.2

0.05 0.10 0.05

5.9 5.9 12.2

0.32 0.45 0.52

3280 80.2 12.2 0.60 44.4 3897 84.4 0.32 12.2 0.67 44.4 0.05 1216 60.0 5.9 0.15 44.4 1988 69.1 0.10 5.9 0.22 44.4 2585 74.7 0.16 6.0 0.25 44.4 3280 80.2 0.24 6.0 0.30 44.4 3897 84.4 0.32 6.0 0.33 Morphology Qo [kg/min] Tb,o [°C] Tb,c [°C] NRE [-] ho [W/m2K] τw,cw [Pa] ΔT [°C] CReq,FMT [°C/min]

MO-01 MO-02 MO-03

No

44.4 44.4 44.4 44.4

1216 1988 1292

60.0 69.1 60.0

0.15 0.22 0.32

3280 80.2 0.24 6.0 0.30 6561 98.8 0.76 6.0 0.45 Shear Stripping Qo [kg/min] Tb,o [°C] Tb,c [°C] NRE [-] ho [W/m2K] τw,cw [Pa] ΔT [°C] CReq,FMT [°C/min]

SS-01

3.1

SS-02 SS-03

5.0 10.1

44.4

44.4 44.4 44.4

30.8 30.3

31.5

1988

69.1

0.10

5.9

0.22

30.8 30.0

3280 6561

80.2 98.8

0.24 0.76

6.0 6.0

0.30 0.45

Table 4. Theoretical boundary layer thicknesses and WAT locations estimations summary. NRE[-] 1216 1988 2584 3280 3897 1216 1988 2584 3280 3897

Tb,o - Ti,ini [°C] 12.2 12.2 12.2 12.2 12.2 6.0 6.0 6.0 6.0 6.0

δv[µm] 12443 7169 6027 5133 4564 12443 7169 6027 5133 4564

δT[µm] 4826 2781 2338 1991 1770 4826 2781 2338 1991 1770

δC-FMT[µm] 523 302 254 216 192 523 302 254 216 192

δWAT[µm] 2437 1404 1180 1005 894 1551 894 751 640 569


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Figure 1. An illustration of radial wax concentration profiles based on the EM, FMT, and precipitation kinetics theories.

Figure 2. An illustration of shear stripping concept (a) and shear prevention concept (b).

Figure 3. MO-14 viscosity curve measured at 196 1/s shear rate28.


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Figure 4. MO-14 wax precipitation curve measured using DSC28.

Figure 5. An isometric view of the flowing microscopic test cell.


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Figure 6. Illustration of 99% hydrodynamic boundary layer and equivalent hydrodynamic boundary layer difference.

Figure 7. An illustration of mass transfer layer thickness measurement through microscope.


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Figure 8. An example of mass transfer layer thickness measurement with microscope: (a) raw image, (b) analyzed image.


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Figure 9. An example of image analysis process for morphology study: (a) raw image, (b) filtered image with Otsu (1979) method, (c) analyzed image.


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Figure 10. Relationship between actual to theoretical mass transfer coefficients based on flow loop data, as a function of Reynolds Number (NRE).

Figure 11. Raw (a) and processed image (b) from BL-05 test; NRE = 1,216 and ∆T = 6° C.


32

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Figure 12. Raw (a) and processed image (b) from BL-01 test; NRE = 1,216 and ∆T = 12.2° C

Figure 13. Raw (a) and processed image (b) from BL-04 test; NRE = 3,280 and ∆T = 12.2° C.


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Figure 14. Summary of mass transfer thickness plotted against NRE.

Figure 15. FMT over-prediction with NRE variation at two different ∆T conditions.


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Figure 16. The effects of NRE to shear stress on the cold wall and cooling rate for tests at ∆T = 6° C.


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Figure 17. Raw image examples obtained from MO-01 experiments (NRE = 1,216, ΔT= 6° C); (a) t = 2 min, (b) t = 10 min, (c) t = 13 min, (d) t = 15 min, (e) t = 30 min, (f) t = 120 min.


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Figure 18. Deposit crystals aspect ratio distribution under laminar conditions; MO-01 test, NRE = 1,216, and ΔT = 6° C.

Figure 19. Deposit crystals aspect ratio distribution under laminar conditions; MO-03 test, NRE = 1,216, and ∆T = 12.2° C.


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Figure 20. Raw image examples obtained under turbulent conditions; MO-02 test, NRE = 1,988, ΔT = 6° C; (a) t = 15 min, (b) t = 20 min, (c) t = 240 min, (d) t = 720 min.


38

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Figure 21. Snapshots of wax deposit surface under reverse experiment for shear stripping verification; (a) SS-01 (τw,cw = 0.1 Pa), (b) SS-02 (τw,cw = 0.2 Pa), (c) SS-03 (τw,cw = 0.8 Pa).

Figure 22. Fully developed laminar flow velocity profile inside the rectangular duct: (a) 2-D velocity contour on the duct cross sectional area, (b) velocity profile inside the boundary layer at x = 0 (middle of the test cell x axis).


39

Microscopic Study of Wax Deposition: Mass ... - ACS Publications

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