Effect of Flow Field on the Wax Deposition and Performance of Wax

Tulsa University Paraffin Deposition Projects, McDougal School of Petroleum Engineering,. 2450 East Marshall, Tulsa, Oklahoma 74110, United States...
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Effect of the Flow Field on the Wax Deposition and Performance of Wax Inhibitors: Cold Finger and Flow Loop Testing Yuandao Chi, Nagu Daraboina,* and Cem Sarica Tulsa University Paraffin Deposition Projects (TUPDP), McDougall School of Petroleum Engineering, The University of Tulsa, 2450 East Marshall Street, Tulsa, Oklahoma 74110, United States S Supporting Information *

ABSTRACT: Chemical inhibition is one of the methods to mitigate deposition of wax in pipelines; however, the efficiency of the inhibitors needs to be validated in the laboratory prior to field applications. Cold finger, as the most commonly used experimental setup in the field, has quite a different shear regime and temperature field compared to the flow loop and field production pipeline. This paper investigates the flow field (cold finger and flow loop) effect on the wax deposition and the performance of wax inhibitors under the same initial temperature difference and comparable shear stress conditions. The normalized deposit mass, wax content, carbon number distribution, and wax mass flux were investigated in these two different flow fields, and the performance of wax inhibitors was also investigated. Moreover, the results from this study are expected to serve as a basis for selecting proper inhibitors for field applications based on laboratory testing.

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The most commonly used experimental setup in the field is a cold finger apparatus5,9,22−25 or cold disk.26−28 In the cold finger setup, the hot oil is circulating around a static cooled cold finger probe. This can form a temperature gradient to provide the driving force for wax deposition. However, they can have quite different shear regimes and temperature gradients compared to the laboratory flow loop and field production pipeline. The deposition data cannot be collected continuously; only one time-point deposition result can be obtained after each test. Despite these, they are still the most common method used for evaluating wax inhibitors as a result of the easy operation, small sample requirement, and simultaneous multiple tests. Among previous cold finger studies, there are some inconsistencies on the effect of wax inhibitors on wax deposition. Most of the researchers argue about the influence of inhibitors on the wax content and hardness of the deposit.3,9,23,27 To reproduce conditions (temperature gradient and shear regime) more close to the field pipelines, a laboratory flow loop system is used to evaluate the efficacy of wax inhibitors.3,25,29−32 In the flow loop setup, the hot oil is flowing inside of a pipe-in-pipe configuration, while a counter-current cold coolant is flowing in the outside. However, the cost can be significant to operate even a small-scale flow loop considering the requirement of labor power, time, and oil sample. Most previous wax inhibition flow loop studies only investigated the deposit mass and thickness in the presence of wax inhibitors. There is limited information provided on checking the wax content and carbon number distribution; however, they are critical to estimate the deposit yield stress related to the deposit strength.3,8,33 To select proper inhibitors, further work is necessary to statistically and quantitatively compare cold finger and

INTRODUCTION A review of different wax prevention and remediation methods has been provided by several researchers.1−6 Chemical treatment, one of the three most commonly used techniques (mechanical, thermal, and chemical treatments) in the field, is especially beneficial in certain cases where applying the mechanical and thermal treatment is difficult.7−9 The typical wax inhibitors can be divided into four groups: wax crystal modifiers, dispersants/surfactants, surface treatment agents, and solvents. Wax crystal modifiers can incorporate with the wax crystals and alter their surface characteristics to inhibit deposition,10 via providing various types of crystalline domains. The poly(ethylene butane) (PEB) and ethylene−vinyl acetate copolymer (EVA) provide crystalline domains along the backbone; thus, the frequency of branches along the backbone indicates the average degree of crystallinity. The maleic anhydride copolymer (MAC) provides crystallinity domains via alkyl side chains; thus, the degree of crystallinity is characterized by the length of the alkyl appendage.11 Dispersants and surfactants act partly like wax crystal modifiers but primarily disperse the wax particles and reduce the tendency to aggregate with each other.11−13 Surface treatment agents are able to form a coat on the surface of the equipment to prevent the adsorption of the wax molecules.11 Chemical solvents to remove wax deposits are also commonly applied in the field.1 Solvents such as carbon tetrachloride have been proven to dissolve and/or melt away wax deposits.1,2,14 The chemicals considered in this study are wax crystal modifiers. Several wax inhibitors have been evaluated by previous studies.3,15−21 Among these inhibitors, EVA and MAC show promising results toward wax inhibition, which are used in this study. Even though many studies were reported in the literature,1,3,4,12,15,17 the exact mechanism of wax inhibitors is still not completely understood. Therefore, different experimental methods are used to investigate the effects of wax inhibitors on wax deposition. © 2017 American Chemical Society

Received: January 24, 2017 Revised: March 23, 2017 Published: April 10, 2017 4915

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used to obtain the deposit thickness in the flow loop test. For more information on these methods, please refer to the studies by Panacharoensawad and Sarica36 and Chi et al.3 Agilent 7890A hightemperature gas chromatography (HTGC) was used to characterize the collected deposits. The details on this method can be found elsewhere.24 Test Matrix. For both cold finger and flow loop experiments, two wax inhibitors (PI-A and PI-B) with a concentration of 500 ppm and a no inhibitor case were conducted. The durations of experiments are 2, 8, 20, and 24 h. The bulk temperatures of both cases are 35 °C to avoid the thermal restriction (deposits stop growing when the interface temperature reaches the WAT). In addition, the initial inner wall temperature for cold finger tests is assumed the same as the coolant temperature of 25 °C, and the initial inner wall temperature was maintained as 25 °C for flow loop tests. Tables 2 and 3 show the detailed test matrix for all cold finger and flow loop experiments.

flow loop results under comparable temperature and shear conditions. In this work, the effect of the flow field (cold finger and flow loop) on the deposit mass, wax content, carbon number distribution, and wax mass flux were investigated, and their effects on the performance of two different wax inhibitors (PI-A and PI-B) were also compared. For the first time, the cold finger and flow loop experiments were conducted under the same initial temperature difference and comparable shear stress, to investigate the flow field effect on wax deposition with and without the presence of wax inhibitors.

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EXPERIMENTAL SECTION

Fluid Characterization. The Caspian Sea (CS) condensate from a gas field in Azerbaijan was used in this study.3 The important properties of CS condensate are shown in Table 1. The CS condensate has a wax appearance temperature (WAT) value of 44 °C, as measured by the cross-polarized microscopy technique.34

Table 2. Test Matrix for the Cold Finger Experiments

Table 1. Properties of the CS Condensate inhibitor wax content (wt %) API gravity (deg) flash point (°C) density at 35 °C (kg/m3)

9.5 43 10 807.2

no PI

500 ppm PI-A

Two wax inhibitors, ethylene−vinyl acetate copolymer (PI-A) and olefin−maleic anhydride copolymer (PI-B) were used in this study. Structures and other detailed information on EVA and MAC are provided elsewhere.3 Facility Description. The experiments were conducted in a cold finger apparatus (CF) (Figure 1) and a newly built laboratory-scale

500 ppm PI-B

time (h)

rotational speed (rpm)

shear stress (Pa)

ΔT (°C)

Tbulk (°C)

Tinterface (°C)

2 8 20 24 2 8 20 24 2 8 20 24

750

0.35

10

35

25

750

0.35

10

35

25

750

0.35

10

35

25

Table 3. Test Matrix for the Flow Loop Experiments inhibitor no PI

500 ppm PI-A

Figure 1. Cold finger apparatus in the TUPDP lab. 500 ppm PI-B

flow loop (FL) at Tulsa University Paraffin Deposition Projects (TUPDP). The detailed information on the laboratory-scale flow loop has been described elsewhere.3,24 The cold finger apparatus has also been extensively used by TUPDP to select oil and investigate paraffin deposition.35,36 Briefly, the cold finger apparatus consists of a jacketed vessel (7.6 cm inner diameter) and a cold finger probe (1.71 cm inner diameter). The oil temperature in the jacketed vessel and the cold finger probe temperature were maintained by external chillers. The temperature difference between the oil and probe can generate a gradient and provide the driving force for wax deposition. The oil in the vessel was homogenized with a Thermolyne Cimatec magnetic stirrer (operating range of 60− 1000 rpm). This stirrer can generate a circular flow field around the cold finger probe to impose a shear on the surface of the cold finger probe. The length and diameter of the stirrer are 3.78 and 0.75 cm, respectively. Deposit Analysis and Characterization. The wax deposits were collected after each test for both cold finger and flow loop experiments. A mass-based method and a pressure drop method were

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time (h)

flow rate (kg/s)

shear stress (Pa)

ΔT (°C)

Tbulk (°C)

Tinterface (°C)

2 8 20 24 2 8 20 24 2 8 20 24

0.12

0.4

10

35

25

0.12

0.4

10

35

25

0.12

0.4

10

35

25

RESULTS AND DISCUSSION The concentration driving force and shear field are known to be two key factors that affect the wax deposition.11,37 To investigate the flow field effect on the wax deposition, operating parameters, such as the temperature difference and shear stress (Figure 2), should be consistent or at least comparable to each other. The initial temperature conditions were maintained the same in all cold finger and flow loop experiments, as discussed in the test matrix part, and the temperature difference in the bulk of both facilities was maintained at 10 °C. Computational fluid dynamics (CFD) simulations were used to obtain the shear stress exerted on the probe surface. The actual cold 4916

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Figure 2. Shear stress in cold finger and flow loop. Figure 4. Normalized deposit mass for the cold finger and flow loop deposits at Tbulk = 35 °C and Tinterface = 25 °C.

finger flow characteristics were used to mimic the simulations, and results are shown in Figure 3. More computational

driving force. Because the initial temperature difference has been maintained the same, one plausible explanation behind this observation is that the concentration gradient in the flow loop may be higher than that in the cold finger. The composition of collected deposits was analyzed with HTGC after each experiment. Figure 5 is the wax content

Figure 5. Wax content for the cold finger and flow loop deposits.

comparison between the flow loop and cold finger, revealing that the cold finger deposits have a higher wax content than the flow loop deposits. Aging is a counterdiffusion phenomenon, with wax molecules into the deposit and oil out of the deposit simultaneously.37 The harder deposits result from the overlap and interlocking of thin wax crystal flakes when the size and density of them reach a critical value. Therefore, it is possible that the ordering process of wax crystals in the cold finger developed much faster than that in the flow loop. This can also be explained with Figure 4, in that the lower thickness in the cold finger attributes to the higher temperature gradient across the deposit gel, which leads to a higher solid wax content eventually. The comparison of the carbon number distribution of the cold finger and flow loop is presented in Figure 6. It can be seen that cold finger deposits tend to have more high carbon number components (>28) than flow loop deposits. Generally, if the wall temperature falls below WAT, the heavier n-alkane components precipitate first as a result of lower solubility and create a concentration gradient in the boundary layer for the diffusion of each component. As the temperature falls even lower, more and more lighter n-alkanes start to precipitate out depending upon the solubility and molecular diffusivity of

Figure 3. Shear stress in cold finger using CFD simulation.

specifications on the CFD simulation are provided in the Supporting Information. As a result, the average shear stress across the cold finger probe (τrθ = 0.35 Pa) is comparable to the shear stress calculated in the flow loop (τrz = 0.4 Pa) at the chosen operating conditions. Flow Field Effect on Wax Deposition. To understand the effect of the flow field in these two different geometries on the wax deposition, the normalized deposit mass (deposit mass per unit area) was calculated to eliminate the deposition area effects (Figure 4). The flow loop deposits have a higher normalized deposit mass compared to the cold finger deposits. The higher normalized deposit mass definitely results from the higher 4917

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Figure 6. Comparison of carbon number distribution of deposits for the cold finger and flow loop deposits for 24 h experiments.

Figure 7. Wax mass per unit area per unit time for the cold finger and flow loop.

different n-alkanes. Consequently, these mass flux differences of different components to the wax deposit interface result in a distribution of different n-alkanes in the deposit.8 Moreover, the mass flux differences are caused by the differences in the concentration driving force and diffusivities. Therefore, it is conceivable to rationalize that different temperature gradients formed in the boundary layer, whereas the temperature gradient is directly responsible for establishing the concentration gradient,38 which leads to different mass flux and, consequently, results in different distributions of n-alkanes. In addition, the lower normalized deposit mass (lower thickness) in the cold finger also results in a higher temperature gradient across the porous deposit gel, which provides a higher diffusive wax flux inside of the gel compared to the flow loop, directly leading to the peak of the carbon number distribution shifted toward the high carbon number. Wax deposition can be assumed to be quasi-steady state;37,39 thus, the wax mass flux is determined on the basis of Fick’s law of diffusion. In addition, it can be assumed that the wax concentration decreases linearly in the mass transfer boundary layer near the wall.40 With these two assumptions, the wax mass flux to the interface can be described by the following equation: J = −Dwo

C(Tb) − C(Ti) dC = Dwo dr δm

both facilities, Dwo of both cases are the same based on eq 2. As mentioned above, the bulk and interface temperatures in both facilities were also maintained the same; thus, C(Tb) − C(Ti) are the same using the solubility curve of the CS condensate. Presumably, the only possible reason is that the flow loop has a thinner mass transfer boundary layer thickness compared to the cold finger based on eq 1, as depicted in Figure 8. The different flow fields in these two geometries lead to different mass transfer boundary layer thicknesses, directly leading to a higher concentration gradient, even though they have the same concentration in both the bulk and interface, thus resulting in a higher wax mass flux. Flow Field Effect on the Performance of Wax Inhibitors. The viscosity of samples with two inhibitors (PI-A and PI-B) and five different concentrations (0, 100, 250, 500, and 750 ppm) were measured using Anton Paar SVM 3000. No significant change in viscosity of the CS condensate in the presence of inhibitors was observed in the operating region of 25−35 °C (Figure 9). Because the operating parameters (initial temperature difference and shear stress) for the cold finger and flow loop are similar and there is no significant change in the viscosity under the operating region, the experiments were conducted and further comparisons were made to investigate the inhibition effect on the wax deposition behavior in these different flow fields (cold finger and flow loop). The deposit mass results for both cold finger and flow loop experiments in the presence of no PI, PI-A, and PI-B have been reported in Tables 4 and 5. It can be seen that the deposit mass significantly decreases in the presence of wax inhibitors for both geometries (cold finger and flow loop). Even though the magnitude of the deposit mass in these two flow fields are different, the efficiency of inhibitors in decreasing the deposit mass for both cases follows the same order: PI-B > PI-A, revealing that comb-shaped inhibitors are more effective than linear inhibitors for the CS condensate under these specific conditions. One plausible explanation for this observation is that comb-shaped inhibitors (PI-B) form abundant smaller size wax crystals compared to linear inhibitors (PI-A),3,42 which facilitates the inhibition.4,21 Thus, on the basis of the phenomenon observed in the present study, it can be concluded that the cold finger apparatus can assess the efficiency of these wax inhibitors qualitatively rather than quantitatively under certain conditions. Industrially, such behavior would be desirable because the flow field seems to have little effect on the

(1)

where J is the wax mass flux to the oil−deposit interface (g/m /s), Dwo is the molecular diffusivity of wax in oil (m2/s), which is determined on the basis of the correlation of Hayduk and Minhas41 (eq 2), C is the dissolved wax concentration (g/m3), Tb is the bulk temperature (K), Ti is the oil−deposit interface temperature (K), and δm is the mass transfer boundary layer thickness (m) 2

Dwo = 13.3 × 10−8

T1.47μγ VA 0.71

(2)

where T is the bulk temperature (K), μ is the oil viscosity (mPa s), VA is the molar volume of the paraffin (m3/mol), and γ is a function of VA, as defined, γ = 10.2/VA − 0.791. Figure 7 shows the comparison of the wax mass flux in the cold finger and flow loop. The wax mass flux is the derivative of the curve of wax mass versus the time. It can be seen that the wax mass flux decreases as time progresses. The flow loop has a much higher wax mass flux than the cold finger (JFL > JCF). Because the same fluids and bulk temperature were used in 4918

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Figure 8. Concentration profile prediction in the boundary layer for the cold finger and flow loop.

Figure 9. Viscosity of samples with different concentrations of PI-A and PI-B.

Table 4. Results for the Cold Finger Experiments inhibitor no PI

500 ppm PI-A

500 ppm PI-B

time (h)

deposit mass (g)

2 8 20 24 2 8 20 24 2 8 20 24

0.9 1.4 1.6 1.7 0.8 1.0 1.4 1.6 0.5 0.7 0.8 0.9

PIE_deposit (%)

Table 5. Results for the Flow Loop Experiments PIE_wax (%)

inhibitor no PI

18.8 31.7 16.8 7.9 50.5 51.6 46.9 45.6

13.3 19.2 14.0 4.2 28.8 29.8 32.9 26.5

500 ppm PI-A

500 ppm PI-B

time (h)

deposit mass (g)

PIE_deposit (%)

PIE_wax (%)

2 8 20 24 2 8 20 24 2 8 20 24

61.5 171.0 262.2 294.9 69.5 166.2 244.1 257.4 7.2 18.4 28.1 38.8

0 2.8 6.9 12.7 88.3 89.2 89.3 86.8

0 0 8.5 16.4 69.6 66.0 65.3 57.5

Because the only variable parameter between these two flow fields is the temperature gradient during the experiment, it is possible that the changing temperature gradient might affect the performance of these inhibitors. Figure 11 shows the wax content for all cold finger and flow loop experiments. It can be seen that the wax content in both the cold finger and flow loop follows the order of PI-B > PI-A > no PI. The wax content of the deposits is significantly higher in the presence of wax inhibitors, which has also been observed in the literature.3,9,23,27 One interesting phenomenon can be

performance trend of these wax inhibitors, if the deposit mass was used to evaluate the efficiency of wax inhibitors.16,28,29,43,44 In addition, the deposition area effects were also eliminated, and the normalized deposit mass in both geometries was compared, as shown in Figure 10. The normalized deposit mass of PI-A in the flow loop is higher than that in the cold finger, which would be consistent with what was observed in the no PI case. However, the normalized deposit mass of PI-B was observed to be lower in the flow loop, revealing the evidence for the higher efficiency performance of PI-B in the flow loop. 4919

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Figure 10. Comparison of deposit mass per unit area between the cold finger and flow loop.

Figure 11. Comparison of the wax content between the cold finger and flow loop.

under flowing conditions.3 Considering these concepts, it seems pertinent to say that the size of wax crystals decreases with the addition of wax inhibitors, and they become easier to overlap on the flakes, fill the pore spaces inside of the deposit, and increase the wax content. Figure 12 shows the wax content versus the normalized deposit mass in both the cold finger and flow loop in the presence of no PI, PI-A, and PI-B, which can be used to understand the growth and aging characteristics of wax deposition in the presence of these inhibitors. The combined results under all of the conditions are provided in the Supporting Information. It can be seen that, in the presence of no PI and PI-A, the normalized deposit mass of flow loop deposits increased significantly, while the wax content only slightly increased. In contrast, the wax content increased significantly, while the

observed that both PI-A and no PI in the cold finger have a higher wax content than those in the flow loop, except PI-B. Singh et al.37 reported that the thinner deposits contribute to a higher wax flux as a result of a higher temperature gradient across the deposit gel, resulting in a harder deposit in comparison to the flow loop. This may also be the reason for a higher wax content in the presence of PI-B in the flow loop (Figure 10). It is also observed that the wax content in the presence of PI-B is higher than that of PI-A in both the cold finger and flow loop. This may be due to the overlap and interlock of thin wax crystal flakes. It has been reported that the size of wax crystals in the presence of PI-B is smaller than that of PI-A.42 The wax deposit with small wax crystals requires a higher wax content to resist the shear stress compared to that with a larger crystal size 4920

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Figure 13. Carbon number distribution of all cold finger samples in the presence of no PI, PI-A, PI-B, and PI-C for 24 h experiments.

Figure 14. Carbon number distribution of all flow loop samples in the presence of no PI, PI-A, PI-B, and PI-C for 24 h experiments.

the same as no PI. Similar results are observed in the flow loop. It is fair to note that the normalized deposit mass (thickness) of PI-B in the cold finger and flow loop are much lower compared to PI-A and no PI, which leads to a higher temperature gradient across the deposit, furthermore facilitating the precipitation of more high carbon number (28−50) components. As far as we know, the strength of the deposit is also an important concern during the pigging process in pipelines.3,8,9,27,32,45 Therefore, it is necessary to take the wax content into consideration when evaluating the effect of the flow field on the performance of wax inhibitors. Because both deposit mass and wax content are significantly affected by the type of inhibitor, it is necessary to take both parameters into account to evaluate the inhibition efficacy. PIE based on deposit mass (eq 3) was widely used to evaluate the efficacy of wax inhibitors on wax deposition quantitatively.16,27,43 However, previous results also showed that the inhibitors also affect the aging process significantly.3,9 Thus, PIE based on wax mass (eq 4) is also used in this study W − Wt PIE_deposit (%) = f × 100 Wf (3)

Figure 12. Wax content versus normalized deposit mass for the cold finger and flow loop with (a) no PI, (b) PI-A, and (c) PI-B.

normalized deposit mass only slightly increased in the cold finger. On the basis of these observations, it is evident that more incoming wax flux contributed to the aging rather than growth in the cold finger compared to the flow loop at these conditions. However, with PI-B, both the cold finger and flow loop behave similarly, in that the wax content increased more significantly compared to the normalized deposit mass. This might be on account of the high inhibition performance of PI-B in the flow loop, resulting in a lower deposit thickness. Figures 13 and 14 show the carbon number distribution results of cold finger and flow loop experiments in the presence of no PI, PI-A, and PI-B after 24 h. The other test duration results are summarized in the Supporting Information. It can be observed in the cold finger that PI-B has more high carbon number components (>28) than no PI, while PI-A has nearly

PIE_wax (%) =

Wfw − Wtw × 100 Wfw

(4)

where Wf and Wt are the deposit mass without and with paraffin inhibitor cases, respectively, and Wfw and Wtw are the wax mass without and with paraffin inhibitors, respectively. 4921

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Figure 15. Comparison of wax mass flux between the cold finger and flow loop.

When the inhibitor is taken into consideration, the efficiency of PI-A and PI-B in decreasing the deposit mass for both flow fields follows the same order: PI-B > PI-A, which indicates that the cold finger apparatus can assess the efficiency of wax inhibitors qualitatively rather than quantitatively under certain conditions. However, the wax content in the cold finger is always higher than that in the flow loop, except PI-B. One possible reason is that the thinner deposits in the cold finger contribute a lot to a higher wax flux as a result of a higher temperature gradient across the gel. The plausible reason why PI-B behaves differently in this case is also due to its lower thickness in the flow loop. The difference in the carbon number distribution in the wax deposit results from the mass flux differences of different components to the wax deposit interface. The temperature gradient as a result of the different deposit thicknesses, which leads to different wax mass flux, consequently results in different distributions of n-alkanes. The PIE based on wax mass and average wax mass flux was calculated and compared. Even though PI-B has a higher inhibition efficacy in both flow fields compared to PI-A, it has a significantly high wax content in the flow loop, which is also a big concern in the field. After the deposit mass, wax content, and carbon number distribution were taken into consideration, the cold finger cannot reveal the deposition behavior of the flow loop, even though they showed the same performance trend of wax inhibitors. Thus, it seems pertinent to suggest that the flow field should be taken into consideration appropriately when evaluating the performance of wax inhibitors.

Tables 4 and 5 show the paraffin inhibition efficiency (PIE) results calculated on the basis of wax mass in the cold finger and flow loop. It can be observed that PI-B has a higher efficiency in decreasing the wax mass in both the cold finger and flow loop. The wax mass flux of the cold finger and flow loop was also calculated (Figure 15) to eliminate the influence of the deposition area and test duration. It can be seen that the wax mass flux results match with the efficiency results; the lower the wax mass flux, the higher the inhibition efficiency. However, even though both flow fields reveal that PI-B has a higher inhibition efficacy and a lower wax mass flux compared to PI-A, it has a significantly high wax content in the flow loop as a result of its higher efficiency in decreasing the deposit thickness, which is also a big concern in the field. Considering the deposit mass, wax content, and carbon number distribution, the cold finger cannot reveal the deposition behavior of the flow loop, even though they showed similar performance trends of wax inhibition. As a summary, when evaluating the wax inhibitors, one should be careful that the flow field is considered appropriately.

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CONCLUSION Both cold finger and flow loop experiments were conducted to investigate the effect of the flow field on wax deposition with and without the presence of wax inhibitors, and the conditions (initial temperature difference and shear stress) were maintained the same or comparable. Results of the normalized deposit mass, wax content, carbon number distribution, and wax mass flux in these two different flow fields were reported, and the flow field effect on the performance of wax inhibitors was also investigated. For the no PI wax deposition study, it has been observed that flow loop deposits always have a higher normalized deposit mass and lower wax content compared to the cold finger deposits. The different temperature gradients resulting from different flow fields play an important role in deposition behaviors. As concluded, the flow loop having a much higher wax mass flux than the cold finger is mainly due to the higher concentration gradient, resulting from a thinner mass transfer boundary layer thickness.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.7b00253. CFD computational specifications, parameters used in the geometry design (Table S.1), shear stress distribution along the cold finger probe with different simulation times (Figure S.1), wax content versus normalized deposit mass for the cold finger and flow loop with no PI, PI-A, and PI-B (Figure S.2), carbon number 4922

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distribution of all cold finger samples in the presence of no PI, PI-A, PI-B, and PI-C for 2 h experiments (Figure S.3), carbon number distribution of all cold finger samples in the presence of no PI, PI-A, PI-B, and PI-C for 8 h experiments (Figure S.4), carbon number distribution of all cold finger samples in the presence of no PI, PI-A, PI-B, and PI-C for 20 h experiments (Figure S.5), carbon number distribution of all flow loop samples in the presence of no PI, PI-A, PI-B, and PI-C for 2 h experiments (Figure S.6), carbon number distribution of all flow loop samples in the presence of no PI, PI-A, PI-B, and PI-C for 8 h experiments (Figure S.7), and carbon number distribution of all flow loop samples in the presence of no PI, PI-A, PI-B, and PI-C for 20 h experiments (Figure S.8) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 1-918-631-5146. E-mail: nagu-daraboina@utulsa. edu. ORCID

Nagu Daraboina: 0000-0002-6910-5295 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank all members of the TUPDP consortia for their continuous support on this research. The authors extend sincere thanks to Nalco Champion for kindly providing all wax inhibitors and ConocoPhillips for the help in viscosity measurements.

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NOMENCLATURE

Variables

∂C/∂r = radial concentration gradient (g m−3 m−1) C = wax concentration in oil (g/m3) Dwo = diffusivity of wax in oil (m2/s) J = wax mass flux to the oil−deposit interface (g m−2 s−1) T = temperature (°C) VA = molar volume of the paraffin (m3/mol)

Greek Letters

δm = mass transfer layer thickness (m or μm) ΔT = temperature difference between the bulk and interface (°C) μ = viscosity (mPa s) γ = function of VA

Subscripts

b = bulk fluid i = deposit and fluid interface CF = cold finger data FL = flow loop data

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