Review of Paraffin Deposition Research under Multiphase Flow

Paraffin deposition in subsea pipelines is one of the flow assurance problems for oil and ... Gas–oil and oil–water paraffin deposition models, ex...
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Review of Paraffin Deposition Research under Multiphase Flow Conditions Cem Sarica* and Ekarit Panacharoensawad Petroleum Engineering Department, Tulsa University, 800 South Tucker Drive, Tulsa, Oklahoma 74104, United States ABSTRACT: Paraffin deposition in subsea pipelines is one of the flow assurance problems for oil and gas production. A reliable paraffin deposition prediction tool is needed to develop mitigation strategies. Most of the studies address single-phase paraffin deposition. However, in practice, multiphase flow is a common occurrence during oil and gas production. Paraffin deposition prediction under multiphase flowing conditions is largely ignored. The current practice is to use single-phase paraffin deposition models in conjunction with multiphase flow hydrodynamic and thermal models. Thermal models used mostly do not consider the flow pattern effects rigorously. The use of a single-phase paraffin deposition model for multiphase flow is not proper and may lead to significant uncertainty in predictions. Thus, there is a need to better understand paraffin deposition under multiphase flow conditions. A limited number of research studies has been conducted. This paper reviews the current state-of-the-art in multiphase paraffin deposition. Gas−oil and oil−water paraffin deposition models, experimental data, deposition testing techniques, and deposit characterization methods are summarized and discussed. This review also discusses the key challenges and the areas for the advancement of multiphase paraffin deposition research.

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of either Singh et al.’s model6 or Lee’s model,8 at least one experiment is required. The value of the fitting parameter is obtained by minimizing the error in the wax fraction and deposit thickness predictions. The fitting parameters of Singh et al.’s model6 and Lee’s model8 change with the operating conditions. Therefore, both Singh et al.’s model6 and Lee’s model8 require either interpolation or extrapolation of fitting parameters to be effectively used as a predictive tool. For the interpolation of the fitting parameters, at least two test data points for different conditions are required. Unlike Lee’s model,8 Matzain9 provides a semi-empirical wax deposition model for the case of turbulent single-phase and gas−oil twophase flows. The model is developed on the basis of wax deposition in the first 24 h of South Pelto crude oil in a 2 in. inner diameter pipe. Even though Matzain’s model can be used as a predictive tool without the requirement of experimental data, it cannot predict the change of deposit wax fraction with time.9 Matzain’s model contains three empirical constants that allow the model prediction to be matched with the experimental data. The original values of these three constants based on his experimental data are given in the study by Matzain.9 In contrast to many studies on single-phase paraffin deposition,1,3,8−33 gas−oil34−37 and oil−water14,38−43 paraffin deposition studies are very limited. There is no published study on three-phase gas−oil−water wax deposition. However, there is a need to understand paraffin deposition under multiphase flowing conditions, because the actual subsea conditions are mostly multiphase flow and wax deposition is a flow-patterndependent phenomena.35,43 The flow pattern is a strong

INTRODUCTION Paraffins (interchangeably referred to as waxes) are alkanes of carbon number ranging from about 20 to 70 or even higher.1 Despite the fact that crude oils are extremely complex systems, it is generally accepted that the crystallizing materials that form paraffin deposit are primarily n-alkanes.2−4 Paraffin deposition is a serious flow assurance problem for oil and gas production. This problem is more pronounced as the production moves to a deeper subsea environment and flow lines become longer. Temperature and pressure of the produced fluid decrease along the subsea pipeline because of heat loss to the environment and frictional and gravitational pressure losses. The heat loss from the fluid in the pipeline to the environment causes a radial temperature gradient. The solubility of paraffin decreases as the temperature decreases.5 Thus, the radial temperature gradient, in pipeline, will cause the uneven precipitation of paraffin. The near wall region will have less wax dissolved in the liquid phase compared to the bulk fluid region because of the temperature gradient. The concentration gradient and flow will cause wax molecules to convectively transport to the deposit interface.6 The concentration profile of waxes dissolved in the liquid phase is needed to predict wax deposition. For the case of laminar flow, Singh et al.6 predicted wax deposition using heat- and masstransfer analogy to calculate wax mass flux to the deposit. The wax concentration at the deposit interface is assumed to be at the thermodynamics equilibrium and calculated from the solubility curve. The heat and mass analogy means that temperature and concentration profiles are independent.7 For the turbulent flow case, Lee8 incorporated the precipitationrate-fitting parameter to estimate the dissolved wax concentration profile. The model needs two fitting parameters, which are the wax crystal aspect ratio, originally coming from Singh et al.’s model,6 and the precipitation rate. No closure relationship for these parameters is provided. To find the fitting parameters © 2012 American Chemical Society

Special Issue: Upstream Engineering and Flow Assurance (UEFA) Received: January 27, 2012 Revised: May 18, 2012 Published: May 22, 2012 3968

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fluid to the coolant decreases as the deposit become thicker because the deposit acts as an insulator. The accuracy of this method is dependent upon the accuracy of the temperature measurement and the knowledge of deposit thermal conductivity, which is unknown until the deposit wax content is analyzed.16 The online LD−LD method is based on the volume displacement of the fluid from the test section to another identical reference section. This method does not require depressurization of the system, but the flow has to stop. The test section will be filled completely with oil. Then, the test section will be raised to the vertical position, and the volume of oil that goes to the reference section will be used to back calculate the thickness of the deposit. The uncertainty of this method is reported as ±0.2 mm.16 The post-deposition testing methods are the deposit thickness measurement, deposit surface investigation, and characterization of deposit and oil samples. The deposit surface is investigated using a boroscope to visually observe the deposit surface inside the spool piece.16,36 The boroscope inspection allows for a better visual inspection of the deposit surface and the deposit geometry than trying to inspect the deposit from outside the spool piece. After the visual inspection, the offline LD−LD method and the direct deposit mass measurement can be performed. The offline LD−LD has the same principle as the online LD−LD. The spool piece and the pipe with the identical inner diameter are used for the offline LD−LD method. The spool piece is filled with water. Then, water is pushed to the reference section using nitrogen gas. The displaced volume of water is used to back calculate the deposit thickness. The uncertainty of this method is due to the amount of water stayed on the deposit surface. The direct deposit mass measurement is usually performed by directly scraping the deposit from the spool piece after melting the deposit by heating the spool piece.43 For oil−water deposit testing, the deposit sample is used for both wax content and deposit water fraction analyses. Bruno42 suggested to use n-heptane as a solvent to extract water from the deposit. The mixture of the dissolved wax in heptane and the non-dissolved fraction of the deposit was separated using a centrifuge. The free water layer left after centrifugation is considered as the water content of the deposit. The minimum detection limit of this method is higher than the Karl Fischer titration method. However, the solvent extraction method is suitable for the case of deposit water content characterization because, if a very small amount of water is trapped in the deposit, the effect of the deposit water fraction on wax deposition will be negligible. The deposit wax content and composition are usually characterized using differential scanning calorimetry (DSC) and high-temperature gas chromatography (HTGC) techniques.11,12,49−57 The DSC method detects the heat of crystallization of waxes in the deposit. The wax fraction of the deposit can be back-calculated from a typical value of heat of crystallization of wax deposit. The value of 200 J/g is typically used for a rough estimation.11,12 It is considered as a rough estimation because a heat of crystallization can vary in a wide range depending upon the composition of waxes of the deposit.58 Hansen et al.2 revealed that the enthalpy of crystallization of wax in North Sea crude oil can vary from 100 to 297 J/g. The modified Universal Oil Products (UOP) 46-64 method or so-called acetone precipitation technique was used for deposit wax content characterization.52,54,59 HTGC with flame ionization detector (FID) is widely used to analyze the deposit composi-

function of pipe inclination. For the case of air−water flow at atmospheric pressure, intermittent flow becomes a dominant flow pattern even for the case of slightly upward flow (+0.25°). For a slightly downward flow (−1°), stratified flow becomes a dominant flow pattern.44 Thus, the wax deposition study in these two major flow patterns is of interest for the actual field conditions.

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GAS−OIL/OIL−WATER DEPOSITION TESTING Flow loops used in wax deposition testing are typically a long pipe-in-pipe heat exchanger. Coolant flows in the annulus gap between the inner pipe and the outer pipe. A removable section, called spool piece, is desired on the flow loop. This section will serve as an offline measurement section and a place to take a deposit sample or investigate the deposit surface using a boroscope.9,11,12,14,16,35,36,43,45 Current deposition testing of gas−oil and oil−water paraffin deposition can be divided into three part: pre-deposition testing, actual deposition testing, and post-deposition testing. The pre-testing step is to quantify hydrodynamics, heat transfer, and the capability of the flow loop system. The operating limitation, wall shear stress, Reynolds number, and flow pattern will be determined during this time to design a proper test matrix. Once the test matrix is designed, the detailed measurement for heat-transfer characteristic35 and liquid holdup will be performed to understand the characteristic of the testing conditions. Flow patterns can be determined by many techniques. For gas−oil two-phase flow, a γ densitometer with pressure drop measurement and flow pattern calculation were used to determine the flow pattern.35 The Zhang et al. unified model46 is the current state-of-the-art model for gas−oil flow pattern prediction. For oil−water two-phase flow, a conductivity probe can be used to determine the continuous phase, regardless of the flow patterns.43 A sapphire window has also been used in a high-pressure multiphase paraffin deposition flow loop to visually determine the flow pattern.47 The liquid holdup can be measured using quick closing valves and capacitance sensors.48 Typical measurement techniques involved in the actual testing are online thickness measurement, temperature control, and flow rate control. The methods to determine the thickness during the test are the pressure drop method, energy balance method, direct deposit mass measurement from a spool piece, and liquid displacement−level detection (LD−LD) method.9,16,35,36,43,45 The pressure drop method is a back calculation of the deposit thickness based on the ratio of the online pressure value to the initial pressure value. This method is accurate for a high frictional pressure drop case but not accurate enough to determine the thickness for the low frictional pressure drop case.16 The increment in the pressure drop because of wax deposition should be at least 10 times of the minimum pressure drop measurement limit to allow for a low relative uncertainty in the measurement. Most researchers assume that the deposit surface roughness is either zero or equal to the pipe roughness for the pressure drop method calculation.9,16,35,36,43,45 This results in an error in the backcalculated wax thickness value. Therefore, the researchers use other methods along with the pressure drop method to improve the accuracy of the thickness measurement. For the Reynolds number below 30 000, Hernandez16 suggests that error in the pressure drop method because of the assumption of the smooth deposit surface is negligible. The energy balance method is based on the principle that heat loss from the test 3969

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Figure 1. Wax thickness distribution for various horizontal flow patterns.9

Figure 2. Wax thickness distribution for various vertical flow patterns.9

tion.11,12,35,52 Either carbon disulfide52 or other organic solvent56 can be used to dissolve the deposit for composition characterization with a capillary GC column.51,56 The composition analysis from HTGC is generally used to investigate the composition change during the deposition aging process and the effect of the operating condition on deposit composition and to find the process critical carbon number60 (CCN), wax molecule with carbon number above which diffuses into the deposit.

compared to each other directly because the operating conditions and the crude oil used in these studies are different.35−37 Both Matzain et al. and Kilincer used natural gas, and Gong et al. used air as a gas phase. Gong et al. did not report either the hardness information of the deposit or the deposit wax content. Usually, either the hardness information or the wax content of the deposit is reported, as in the other studies, unless no close observation is performed or the deposit sample is not collected after the test. The deposit wax content is needed to understand the deposition aging phenomenon and model validation purposes. Wax deposition is found to be a flow-pattern-dependent phenomenon for the gas−oil flow. The deposit thickness distributions along the pipe circumference and the hardness

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GAS−OIL DEPOSITION STUDIES Only three experimental studies on gas−oil paraffin deposition are currently available.35−37 The experimental results are obtained after 24 h of testing. These results cannot be 3970

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Figure 3. Thickness and hardness trends observed in horizontal flow tests.9

Figure 4. Thickness and hardness trends observed in vertical flow tests.9

variation with flow pattern from Matzain9 are shown in Figures 1−4 for South Pelto oil and Tulsa City natural gas. The comparison of deposit thickness and hardness of different flow patterns was investigated by Matzain et al.35 and Kilincer.36 The hardness description of these studies is strictly qualitative based on observations, while the deposit was scraped from the pipe. This hardness description can vary from one researcher to the other. Both studies found similar trends, even though the liquid used in their experiments was different. For horizontal stratified flow, the deposit was soft and thick. The deposit was distributed in a crescent shape, as shown in Figure 1. Horizontal intermittent flow produced a harder deposit than that of stratified flow, while annular and intermittent flow hardnesses were similar. Figure 3 illustrates

that deposit thickness decreases and hardness increases as the vSG increases at a constant vSL for intermittent flow. The deposit thickness increase and hardness remain relatively constant as the flow pattern changes from intermittent flow to annular flow by decreasing vSL and increasing vSG, as shown in Figure 3. For vertical flow, Figure 4 shows that the deposit formed under bubbly, intermittent, and annular flows have similar thickness and hardness at high vSL. Deposit thickness increases and hardness decreases as vSL decreases for intermittent flow. The deposit thickness of the intermittent flow remains relatively constant, and the deposit hardness increases when the vSG increases at a constant and low vSL.9 Thus, at a low superficial liquid velocity, the deposit of annular flow has a 3971

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higher hardness than the intermittent flow. Currently, dispersed bubble flow deposition is not investigated for vertical flow.35,36 For stratified flow, only the oil-wetted portion of the pipe can have wax deposition.35−37 For stratified wavy flow, the deposition at the gas−oil interface is thicker than that of the adjacent region, as shown in Figure 5.35,36 The deposit is found to be soft and contains a large amount of trapped oil.35,36

the temperature gradient caused by the increase in the actual oil velocity as the gas velocity increases. They claimed that the deposition-promoting effect is higher than the hindering effect; therefore, the deposit volume becomes higher as superficial gas velocity increases. However, for the single-phase laminar flow case, the general deposit thickness trend is that the deposit becomes thinner and harder as the flow velocity increased.6 If the laminar flow in the stratified gas−oil case is the same as the single-phase case, the deposit should be thinner and harder as the actual liquid-phase velocity increased. This is contrary to the speculations by Gong et al. Therefore, we propose another possible explanation of the observed trend. The increase in superficial gas velocity with a constant superficial liquid velocity spreads the liquid phase along the pipe circumference, increasing the contact area between the oil and wall, even though the total liquid holdup may decrease. Moreover, the increase in the fluid velocity can increase the inner wall temperature and reduce the thermal driving force if the coolant temperature and flow rate are kept constant. A further study is required to elucidate the behavior of two-phase stratified flow. The investigation on stratified flow wax deposition will help in the prediction of wax deposition for most of the horizontal and downward flow cases. For the upward intermittent flow, the deposit is found to be uniform circumferentially in both South Pelto crude oil35 and also Garden Bank crude oil.36 Matzain et al.35 and Kilincer36 found that the top part of the deposit is thicker and softer than the bottom part of the deposit for the horizontal intermittent flow. Further heat- and mass-transfer analyses can help to understand why the deposits at the top and bottom of the pipe for the case of intermittent flow are different. Gong et al. found that the deposit is almost uniform circumferentially and showed that the deposit thickness tends to decrease with the superficial gas velocity for the case of constant superficial liquid velocity. They also reported that the deposit thickness increases, reaches a maximum, and then decreases as the superficial liquid velocity increases for a constant superficial gas velocity. However, the thickness versus time trends can cross each other at a certain time, as seen from the results by Matzain et al. (Figure 7). Thus, the trend of decreasing or increasing of the deposit thickness is dependent upon the time of the measurement. For annular flow, the deposit on the pipe circumference is uniform, as seen in Figure 8.35,36 The thickness versus time trends crossover each other at a certain time, similar to the intermittent flow. A high superficial liquid velocity case exhibits

Figure 5. (Left) Stratified smooth and stratified wavy cases.35 (Right) Stratified wavy case.36

Gong et al.37 conducted the deposition tests for air−crude oil stratified flow. They reported the equivalent thickness of the deposit, the thickness back-calculated from the deposit volume by assuming that the deposit covers the circumference of the pipe uniformly. The assumption that the deposit covers the entire pipe circumference uniformly results in the underestimation of the deposit thickness, especially for the case of the stratified flow. The equivalent thickness of the stratified flow increased with the superficial gas velocity, as seen from Figure 6. Gong et al.37 speculate that the increase of the equivalent thickness or deposit volume are caused by the combination of the deposition-promoting factor and deposition-hindering factor. The deposition-hindering factor was attributed to the decrease of the oil−pipe contact area when the measured liquid holdup decreases as superficial gas velocity increases. However, the gas−liquid interface of stratified flow does not need to be flat. In fact, the gas−liquid interface is concave at a high gas flow rate, and the liquid film will creep up the sides of the pipe at a high gas flow rate.46 The assumption in the study by Gong et al.37 that the oil−pipe contact area decreases as the measured liquid holdup decreases ignores the possibility of film spreading along the pipe circumference, as discussed in the study by Zhang et al.46 The deposition-promoting factor in the study by Gong et al.37 was defined to be the increase in heat transfer or

Figure 6. Equivalent wax deposit thickness versus gas superficial velocity (vSG) at the liquid superficial velocity (vSL) of (a) 0.0626 m/s and (b) 0.0939 m/s for stratified flow in a 1 in. inner diameter pipe.37 3972

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flow behavior means that the deposit growth rate is smaller than a single-phase turbulent flow case initially but decreases slower than the single-phase turbulent flow case, such that the thickness at the end of the test is higher than the turbulent case. For the bubbly flow case, only two deposition tests were found: one from Matzain et al. and another one from Kilincer.36 Matzain et al. found that the thickness development trends are similar to a single-phase turbulent flow case. Kilincer also found that the deposit is thin, hard, and fragile.

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OIL−WATER WAX DEPOSITION STUDIES Several oil−water paraffin deposition studies using either flow loop or coldfinger apparatus have been conducted recently.14,41−43 Anosike43 showed that the deposition for the two-phase oil−water flowing condition is a flow-pattern-specific phenomena. Different flow patterns have different deposition characteristics (Figure 9). Anosike43 observed that wax does not deposit on the bottom part of the pipe only for stratified, dispersion of oil in water and water layer (D O/W & W), and dual dispersion flows. Moreover, he found that the deposit hardness increases and thickness decreases when either vSW or vSG increases. The deposition at the top part of the pipe for the case of oil−water stratified flow with mixing at the interface is shown in Figure 10.

Figure 7. Crossing over of deposit thickness trends for horizontal and slightly upward intermittent flow tests at various vSL and vSG. vSL of cases G, H, and I is 1.22 m/s. vSL of case J is 0.31 m/s. vSG of cases G, H, I, and J is 0.31, 1.52, 4.57, and 1.22, respectively.9,35 Lines are curvefitted to the LD−LD data. The open symbols are from the online LD− LD method. The open symbols with the letters “SP” are from the offline LD−LD method using a spool piece.

Figure 8. Wax deposit under horizontal annular flow picture (left) and schematic (right). The long streak defect on the deposit is caused by scraping the deposit after the deposition test.36

Figure 10. Wax deposition under oil−water stratified flow with mixing at the interface.43

a single-phase turbulent flow thickness growth behavior.35 The turbulent flow thickness growth behavior means that the deposit growth rate is high, initially. Then, the thickness almost reaches a plateau at the end of the test. A low superficial liquid velocity case exhibits a single-phase laminar flow thickness growth behavior.35 In other words, the single-phase laminar

For the case of dispersion of water in oil (D W/O), deposition occurs all around the pipe periphery. Wax can form on the pipe wall surface, even though water is a continuous phase, as seen in the case of D O/W & W (Figure 11). For a fully dispersed of oil in water (D O/W), a thin deposit is observed all around the pipe circumference (Figure 12). The

Figure 9. Deposition map for the two-phase oil−water system.43 3973

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of each flow rate and flow pattern should be further investigated. Gao,14 Couto,41 and Zhang et al.39 did not conduct a deposit water fraction analysis and did not report any visual observation of water trapped in the deposit. However, Bruno42 conducted the deposit water fraction characterization and found that water can be trapped inside the deposit. It should be noted that Bruno42 took the samples through a sampling port that has an inner diameter of only 1.5 in. A small amount of sample for water fraction characterization can cause a high uncertainty in the measurement. More investigation on the water content of the deposit is needed. This can help determine whether there is water entrapment inside the deposit, as reported by Bruno,42 or not, as reported by Zhang et al.,39 Gao,14 and Couto.41 The deposit thickness for the case of two-phase oil−water flow decreased monotonically with water cut,41,42 while it was found that, in some cases, the thickness increased with water cut first before decreasing with higher water cuts.39 Thus, the inconsistency of the trend between water cut and thickness needs to be clarified. The consistent deposition trend found by investigators39,41 is that deposit thickness decreases with a decrease in the temperature difference between the bulk fluid and the cold surface for both single-phase and two-phase oil− water cases. However, Huang et al.30 have proven that the decrease in the temperature difference does not always decrease the deposit thickness for the case of single-phase wax deposition. They have showed that the temperature difference is not necessarily representing the driving force for wax deposition because it does not consider the shape of the solubility curve at the deposit interface temperature. Bruno42 found that the deposit wax fraction decreases with water cut for the oil continuous phase for both South Pelto oil and Garden Bank condensate. However, Couto41 found that the deposit wax fraction increases with water cut up to 60% water cut and then stays about the same. Couto reported that salt does not affect the deposition process. Zhang et al.39 did not characterize the deposit wax content but reported the deposit wax appearance temperature (WAT) instead. Zhang et al.39 refer to the WAT of the deposit as the temperature below which wax in the deposit starts to crystallize. The effect of water cut on the deposit wax content is not yet clear because the results from previous investigators do not agree with each other. For the water continuous phase, Bruno’s test with 90% water cut yielded no deposit on the pipe surface. Previous researchers14,41−43 conducted the tests by controlling the coolant and bulk fluid temperatures and changing other operating conditions. It should be emphasized that the inner wall or wax−oil interface temperature will change when fluid velocity is changed or the diameter of the pipe is changed, even though the coolant and test fluid temperatures are maintained. This is primarily due to variable heat-transfer coefficients for the different flowing velocities. The heat transfer and inner wall temperature should be investigated similar to the single-phase studies by Dwivedi11 and Mirazizi12 because the deposition is dependent upon the inner wall temperature and not the coolant temperature. Moreover, water affects the hydrodynamics of the system, and the hydrodynamics will affect the deposition; i.e., a high flow rate gives a thinner deposit than a low flow rate.6 Thus, the understanding of the water effect impacting the deposition through the change of hydrodynamics is important. A recent study from Huang et al.30 suggests that a characteristic mass flux J should be used as a correlating parameter instead of the difference in the interface temperature and bulk fluid

Figure 11. Wax deposition under D O/W & W picture (left) and schematic (right).43

Figure 12. Wax deposition under D O/W picture (left) and schematic (right).43

quantitative description of the surface roughness was not reported by Anosike.43 For the dual dispersion flow, deposit is found only on the top part.43 It can be seen that, when water becomes continuous, sometimes deposition can occur, i.e., D O/W & W, but sometimes no deposition occurs, i.e., the bottom part of dual dispersion flow. The deposition in the water continuous region could happen if there is a physical contact between the oil phase and pipe. We speculate that this contact occurs through the formation of a thin oil film on the inner pipe wall surface. On the basis of our speculation, the thin oil film layer may form all around the pipe for the case of D O/ W but may not form at the bottom part of the pipe wall for dual dispersion flow. The absence of the oil film at the bottom part of the dual dispersion flow could be because oil tends to float to the top part of the pipe. However, if there is enough velocity fluctuation as in the case of D O/W, then the velocity fluctuation may allow the oil phase to reach the bottom part of the pipe and form an oil film, resulting in wax deposition. Our speculation is inspired by the new flow pattern47 observed in a high-viscosity oil system. For a high-viscosity oil system, Vuong47 observed that there is a thin oil film coated the pipe wall, while a dispersion of oil in water is flowing in the pipe. The slurry of wax crystal−oil at the cold pipe wall can exhibit a high-viscosity behavior. Another factor that may cause wax to deposit in some water continuous cases but not in all cases could be the variable inner pipe wall temperatures. Anosike43 conducted the tests by controlling the coolant temperature, test fluid temperature, and coolant flow rate. The local inner wall temperature is not backcalculated. Thus, one flow pattern may cause the inner wall temperature to be hotter than other flow patterns and may lead to less deposition. The effect of the local inner wall temperature 3974

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temperature because the characteristic mass flux comes from the dimensional analysis and reflects the concentration gradient driving force, instead of the thermal gradient driving force.

diffusion path of wax in the deposit and increase the thermal conductivity of the deposit. Therefore, it is critical to understand if water can be trapped inside the deposit or not, and if water can be trapped inside the deposit, the water fraction of the deposit will be the critical parameter to be measured. The effect of oil−pipe wettability on wax deposition can be significant.62 Guo et al.62 showed that the carbon steel surface that was treated by chemical conversion treatment can trap water molecules on its surface and reduce deposition significantly for the case of two-phase oil−water wax deposition [the test fluid is crude oil with 57% (w/w) water]. The deposition tests in the study by Guo et al.62 were conducted in a self-designed apparatus based on the coldfinger method. For the flow in a pipe at a high flow rate or a single-phase oil flow, the performance of the treated surface may be different from the case shown in the study by Guo et al.62 More studies in a deposition flow loop will allow for a better understanding on the performance and limitation of the chemical-conversiontreated surface. The cost-effectiveness analysis of the chemicalconversion-treated surface is also needed to determine if the coated pipe will be economically feasible to be implemented in the field. The deposition wax mass flux from the experiments needs to be compared to the wax mass flux calculated from the solubility method, as shown in Venkatesan’s and Mirazizi’s works.1,12 This will allow us to understand whether the actual wax mass flux toward the deposit interface can be less than the minimum wax mass flux predicted by the model or not. To back calculate the wax mass flux from the experiment, the deposit wax fraction is needed. The multiplication between the deposit mass and wax fraction yields the wax mass of the deposit. The difference of deposit wax masses at two different times can be used to calculate the wax mass deposition rate. The wax mass deposition rate divided by the deposit surface area yields the deposit wax mass flux. If the wax mass flux is less than that predicted by the solubility method,8 then there has to be an additional mass flux reduction term in addition to the mass flux decrease because of the precipitation or, simply, the diffusion coefficient closure relationships do not perform well. One also has to keep in mind that the solubility curve of wax in oil is the important parameter that needs to be determined properly, as shown in the work by Han et al.,5 to have a correct wax mass flux prediction from the solubility method. Singh et al.6 found experimentally that deposit thickness decreases and the deposit wax fraction increases with the flow rate increasing. They adjust the wax crystal aspect ratio to allow for the model to give the prediction that matches with their experimental results. They assume that the wax crystal aspect ratio of the deposit starts from 1 and increases linearly with the wax fraction of the deposit. However, they did not experimentally investigate the wax crystal aspect ratio. The possible mechanism for the change in the wax crystal aspect ratio is the Ostwald ripening phenomenon.32 The crystal shape is also impacted by the presence of the isoalkane components.33 More studies on the impact of Ostwald ripening and the impact of isoalkanes and cycloalkanes on the crystal size of the wax deposit are suggested. Furthermore, the hardening of the deposit with the increase in velocity could be due to the effect of shear stress or heat transfer, instead of the effect of changing in the wax crystal aspect ratio. Different wax crystal aspect ratio fitting parameters are used for different operating conditions to fit their experimental results.6 Thus, a closure relationship

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TWO-PHASE WAX DEPOSITION MODELING There are very few models to predict two-phase wax deposition. The currently available two-phase gas−oil deposition models, such as the model by Apte et al.,34 are simply the application of the single-phase oil deposition models with use of two-phase heat-transfer correlations to account for the effect of two-phase flow. There is no model available that accounts for the effects of multiphase flow on paraffin deposition mechanisms. The model by Apte et al. cannot be confidently used to predict the deposit wax fraction over time because the given wax fraction correlation is only based on 24 h test results of their study. The proof that the model by Apte et al. can predict the deposit thickness and wax fraction for the case of different oils, testing conditions, or testing duration is not available. Thus, this model cannot be directly extrapolated to other oils, testing conditions and time, or a bigger pipe diameter. More studies are required to develop a comprehensive gas−oil deposition model. For the oil−water wax deposition model, the first deposition model is proposed by Couto41 and later modified by Bruno.42 Anosike43 experimentally showed that the deposition is flowpattern-dependent. Huang et al.38 proposed a deposition model strictly for stratified oil−water flow. The model by Couto/Bruno41,42 does not account for the flow pattern. The model is based on the single-phase deposition mechanism and uses two-phase oil−water properties to calculate pseudo-single-phase hydrodynamics and heat transfer. It is still not clear if the mixture viscosity or the oil viscosity should be used for the wax diffusivity calculation in the Hayduk−Minhas equation61 because this equation is not developed for a multi-component, non-isothermal, and noninfinite dilute system. More investigations on the diffusivity calculation are needed to determine if the extrapolation of the Hayduk−Minhas equation is valid. For stratified flow, Huang et al.38 used the deposition model by Singh et al.6 in their heatand mass-transfer calculations. The concentration and temperature profiles are assumed to be developed separately. Therefore, the model by Huang et al.38 has one fitting parameter inherited from the model by Singh et al.,6 which is the crystal aspect ratio in the deposit effective diffusivity calculation. Huang et al. provides only the deposition for a parallel plate flow without any experimental verification. Both Couto/Bruno and Huang et al. can be considered as the initial modeling attempts. More studies are necessary to better understand the deposition in oil−water under flowing conditions.

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OPPORTUNITIES FOR IMPROVEMENT There are several areas for two-phase wax deposition research that are necessary for further improvement and development. For gas−oil and oil−water wax deposition studies, the information of deposit composition or wax fraction versus time is needed for model verification purposes. Generally, the information of deposit thickness versus time is widely available, but the deposit wax fraction information is very limited because deposit sampling during testing is tedious. For oil−water wax deposition studies, if the water phase can be trapped inside the deposit, the water will decrease the 3975

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from the test fluid to the coolant. Because, the problem becomes two-dimensional (2D) for two-phase gas−oil flow, deposit samples along the pipe periphery are required for a full 2D problem analysis. The information on local heat transfer along the pipe periphery is also needed to understand the variation of wax deposition along the pipe periphery. The local sampling at the different pipe peripheries allows for the measurement of deposit thickness, composition, and wax fraction at the different pipe peripheries. Moreover, it is known that, for a thick deposit, the wax fraction of the deposit changes in the radial direction.63 The investigation on the change of the deposit composition in the radial direction is also important for the cases of two-phase flow that yield a thick deposit. However, with more samples for the analysis, the deposition characterization will take a longer time and become more tedious. Last but not least, for two-phase wax deposition, it is also important to understand how the chemical used to mitigate the wax deposition problem for the single-phase cases works on the two-phase cases. However, this study is in the early phase, and it requires the two-phase wax deposition results without chemical as the base case for the comparison purposes.

between the wax crystal aspect ratio and operating conditions is required to complete the model. One has to keep in mind that the variation of the wax crystal aspect ratio with operating conditions does not necessarily represent physics of the phenomena because other effects on wax deposition, i.e., shear effect, heat-transfer effect, etc., are already combined into the wax crystal aspect ratio fitting parameter. For the case of single phase, the results from Dwivedi11 and Mirazizi12 show that the increase in the initial wall shear stress decreases the deposit thickness and increases the wax fraction of the deposit. However, the effects of shear stress and heat transfer are coupled together because both shear stress and heat transfer increase with velocity. To investigate only the effect of shear stress on wax deposition, the effect from heat transfer has to be decoupled from the shear stress effect. Currently, the deposition results available in the literature are from the tests in small pipe diameters, less than 2 in. The upscaling study of the wax deposition model to the case of the larger diameter is needed. Moreover, more heat- and mass-transfer analyses should be performed to understand how the crossover between the thickness versus time curves occurs and when the crossover period should end. The effect of oil composition can be investigated using different waxy oil and conducting the deposition experiment. This can help with the understanding of how to extrapolate the results obtained from tested to untested crude oils. In this case, the parameter to be varied is the crude oil. However, to be able to compare the results of different oils, the results should be compared at the same characteristic mass flux values30 or at the same initial wax concentration gradient as the deposit. For gas−oil flowing conditions, the deposition characteristic for each flow pattern should be investigated separately because deposition is a flow-pattern-dependent phenomenon. The dependent variables should be compared at the same heattransfer coefficient or at the same characteristic wax mass flux to ensure the same driving force. The effect of two-phase flow hydrodynamics on wax deposition is important to study. To purely investigate the effect of hydrodynamics, such as slug frequency, on wax deposition, the driving force of wax deposition, which is the concentration gradient at the deposit interface, needs to be controlled. However, the concentration gradient at the deposit interface is not the measurable quantity. This concentration gradient is dependent upon how much wax precipitation occurs. Practically, the initial inner wall temperature and the difference between the bulk fluid temperature and inner wall temperature should be kept constant, while the hydrodynamics of the flow is varied, so that the characteristic wax mass flux proposed by Huang et al.30 remains constant. Moreover, n-alkanes that have different chain length solidify at different temperatures. When the inner wall temperature is increased, the chain length of the shortest n-alkane existing in a solid phase (at the solid−liquid equilibrium) increases. In other words, the increase in the inner wall temperature will increase the critical carbon number of the deposit. To perform a parametric study on wax deposition, one parameter should be varied, while other parameters should be kept constant to decouple the effects of other parameters. Therefore, controlling the inner wall temperature will allow for the comparison of the deposits that have the same critical carbon number. The better instrumentation and measurement techniques will improve the experimental part of the study. The challenges for the wax deposition experiment are the measurement of the deposit thickness, inner wall temperature, and local heat flux

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CONCLUDING REMARKS The current developments in two-phase gas−oil and oil−water paraffin deposition are reviewed. The experimental techniques, deposit characterization method, and experimental data are summarized and discussed. It is found that there are a limited number of two-phase paraffin deposition studies, and they are not conclusive and do not always agree. More experimental studies are required to resolve the inconsistent deposition trends found by researchers. For two-phase gas−oil paraffin deposition, the correlating parameter proposed by Huang et al.30 representing a driving force should be explored together with the effects of hydrodynamics of the flow on wax deposition. For oil−water paraffin deposition, the inconsistent findings were reported on the trapped water inside the deposit, the effect of water cut on deposit thickness, and the wax fraction. Further targeted testing is needed to resolve the inconsistencies and advance our understanding. Once the mechanisms of the deposition are understood with the experimental investigations, better deposition models can be developed. For two-phase flow, a deposition model should be flow-pattern-dependent and incorporate a two-phase paraffin deposition mechanism, two-phase hydrodynamics, and twophase heat transfer. The models will inevitably require experimental closure relationships, such as the relationships that are used in the current models, i.e., diffusion coefficient, wax crystal aspect ratio, and precipitation rate. The experimental studies then need to focus on the closure relationship development.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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