Experimental study and modelling of asphaltene deposition on metal surfaces with superhydrophobic and low sliding angle inner coatings

Inner coatings have emerged as a novel technique to prevent the deposition of paraffin, wax, scale, and corrosion of pipelines during oil production and transport. Few studies addressed this technique for preventing asphaltene deposition. In this study, two superhydrophobic inner coatings, including polytetrafluoroethylene (PTFE) coating and nanosilica coating, were fabricated on metal surfaces and the asphaltene deposition on these coated surfaces was examined. A model oil solution was prepared using asphaltene and heptol and the effect of static and dynamic flow states on the amount of asphaltene deposition on uncoated electrodes, PTFE coated electrodes, and nanosilica coated electrodes were investigated. The results showed that the PTFE coating is more effective in reducing asphaltene deposition than nanosilica coating. The PTFE coating could reduce 56% of the deposition in a static state and more than 70% in a dynamic state at an asphaltene concentration of 2000 ppm. For PTFE coating in a dynamic state, the deposition rate is negligible in long times. In addition, it was found that the type of flow state affects the asphaltene deposition kinetics. The results demonstrate that, in the static state, the nth-order kinetics model, and in the dynamic state, the double exponential models are in best agreement with the experimental data.

One of the major challenges in the production and processing of crude oil is the deposition of heavy hydrocarbons including asphaltenes and waxes 1 on the surface of well tubing, pipeline, and refining catalysts. Asphaltene molecules, as the heaviest and most polar components of crude oil 2 , are suspended in oil by resins under favorable conditions. Pressure, temperature, oil composition, the amount and type of injecting gas for enhanced oil recovery 3,4 , the amount of gas associated with oil, the type of flow in the porous media, and the characteristics of the fluid-containing pipes can be considered as effective factors on asphaltene precipitation and deposition 5 . Pressure is one of the most important parameters in the asphaltene deposition process, and other factors fall into the second order. The highest amount of asphaltene deposition occurs near the wellbore, where the highest pressure drop occurs with increasing production [6][7][8] . Reservoir pressure maintenance is probably the most effective technique to avoid asphaltene deposition in wells 9,10 . In oil production process, which is accompanied by a simultaneous decrease in pressure and temperature, asphaltene molecules precipitate and form sludge-like and highly adherent masses 11 . It is worth mentioning that the term deposition is commonly used to describe the process of precipitation 12 . Clarification of the differences between these two terms is important. The precipitation may be described as the formation of a solid phase from a liquid solution, while deposition can be defined as the formation and growth of a precipitated solid layer on the surface. Precipitation could be a prelude to deposition, but it does not necessarily guarantee deposition formation 13,14 . Asphaltene deposition could affect all components of the production system from the reservoir to the wellbore and up to the surface facility and pipelines. In porous media, the asphaltene deposition could plug the pore throats and alter the rock wettability 15 . The main mechanism(s) of deposition of asphaltene particles in porous media and resulting permeability damage have been investigated in the literature. In one of these studies, "surface deposition" was identified as the main

Materials and experimental procedures
Preparation of electrodes. The electrodes used in this study are made of low-carbon steels with 0.15-0.30% carbon. Metal blades were cut from a sheet with a thickness of 0.1 cm in dimensions of 2.5 cm × 10 cm. In this study, two types of electrodes, including PTFE and nanosilica coated electrodes, were used to examine the asphaltene deposition on superhydrophobic surfaces. PTFE coating includes a primer and an overcoat layer. In order to produce superhydrophobic PTFE coating with hierarchical structure and low surface energy, glass beads microparticles with an average size of 82 microns were used in the primer layer. This coating was applied on the metal surfaces by spraying process at a pressure range of 50-100 Psi. For the second type of coating, the superhydrophobic nanosilica coating was applied on the metal surfaces by a one-step electrodeposition process of a sol-gel, which contained tetraethoxysilane (TEOS) (purity ≥ 98.5%) and dodecyltrimethoxysilane (DTMS) (purity > 93%) as mixed sol-gel precursors. The precursor solution contains 1 ml TEOS, 1 ml DTMS, 10 ml potassium nitrate, and 40 ml ethanol. The solution pH was adjusted to 4 by hydrochloric acid. This solution was pre-hydrolyzed for 12 h at room temperature via strong stirring. The electrodeposition process was then performed on the surface of the metal blades. The wetting properties of the coated and uncoated surfaces are obtained by measuring the contact angle (CA) and sliding angle (SA). The CA was measured on several different samples of uncoated surfaces. The uncoated surfaces had CA of 57°-97° and SA more than 90°, and therefore had neutral and somewhat hydrophilic wetting properties (the CA reported in this study is the average of five measurements at different points on the coated and uncoated surfaces). This suggests that asphaltene deposition tests have been performed on uncoated surfaces with neutral to hydrophilic wetting properties. While both PTFE coating and nanosilica coating produced superhydrophobic surfaces, the PTFE coating reached a CA of 152 ± 0.220° and a SA of 3 ± 0.376° and a CA of 166 ± 0.481° and SA of nearly zero were obtained for nanosilica coating. It is worth noting that, what is important for the reproduction of PTFE coating processes in the spray method is the correct selection of micro particle size distribution, control of the nozzle distance from the surface www.nature.com/scientificreports/ and the injection pressure. In the reproduction of nanosilica coating by electrodiposition method, precise regulation of current density and precise control of sol-gel solution pH are important. In our study, many samples were made by each method and for all of them the wettability properties were measured and compared and in all cases the results were very consistent. The surface roughness plays a major role in wettability. An atomic force microscope (AFM) (CP II, Veeco) was used to measure the roughness of two representative coated surfaces. The scan range was 10 × 10 µm 2 . Figure 1 shows surface morphology images (Fig. 1a,d), 3D AFM images (Fig. 1b,e), and water contact angle (WCA) images (Fig. 1c,f) of PTFE and nanosilica coatings. The procedure of the current study is shown in Fig. 2.  www.nature.com/scientificreports/ Model oil preparation. Toluene and normal heptane were purchased with a purity of 99%. Crude oil samples were obtained from one of the oil reservoirs located in the southwest of Iran. The asphaltene was extracted from a crude oil sample according to the IP-143 standard method. Additional information on the composition of asphaltene extracted from crude oil based on H/C ratio, FTIR aromatic index, the heteroatoms content, the number of aliphatic chains and the XRD aromatic index are available in the literature 31 . The dried asphaltene powder was first dissolved in toluene by sonication at 40 kHz and then normal heptane was gradually added to the solution on a magnetic stirrer. The mixture was sonicated again for 5 min and was kept static for 24 h to achieve equilibrium. In this study, three different levels of asphaltene concentrations including 2000 ppm, 1000 ppm, and 250 ppm with toluene/n-heptan ratio of 1.6/38.4 (4% toluene concentration) were used to investigate the electrodeposition of asphaltene on coated and uncoated surfaces. These concentration values are initial concentrations. These values have been selected based on previous studies 32 . It should be noted that this mixture was prepared at ambient pressure and temperature. Although asphaltene particles in real crude oil show a neutral charge [33][34][35] , their charge in heptol solution depends on the concentration of toluene in the solution. It is worth mentioning that the electrodeposition process here was only used to simulate unstable asphaltene deposition.
Asphaltene deposition process on surfaces of the electrodes. Given the mycelial structure of asphaltenes and the presence of heteroatoms and metal elements such as nickel and vanadium in the constituent structure of asphaltene molecules and functional groups, it can be assumed that these compounds have a charge 36 . Numerous experiments have shown that asphaltenes in the electric field are directly affected by the force of the electric field 37,38 . In one comprehensive study, conducted by Hosseini et al. 39 , the effect of electric fields with different strengths on three different asphaltene samples was investigated. The main purpose of this study was to determine the amount of aggregation rate and aggregation size of asphaltene particles in the electrostatic field which was done using the visual inspection method. Based on the results obtained, the higher the aggregation rate the aggregation size of asphaltene particles in the electrostatic field may cause faster deposition. According to studies conducted in the literature, in this study, an electrical deposition cell was used to simulate the asphaltene deposition on coated and uncoated surfaces. The electrical deposition cell used in this study contains 40 ml of solution in a static state, and in dynamic state experiments, a shear rate was applied using a stirring magnet in 50 ml of solution. Figure 3 shows a schematic of the device used to perform the asphaltene deposition process on the coated and uncoated electrodes. Two metal electrodes are held in parallel by a removable plastic cap. A high voltage power supply device (Oltronix LS 529R) was used to convert alternating current (AC) to direct current (DC) and create an electric field between two electrodes. During the asphaltene deposition process, an uncoated blade, which is fixed in all experiments, plays the role of the anode, and the coated and uncoated blades play the role of the cathode. In order to measure the amount of asphaltene deposition, all blades were numbered first and the weight of each was measured and recorded using the analytical weighing scale with ± 0.0001 g accuracy. The weight of the electrodes used in this study was 30 g on average. At the end of each test, after removing the blades from the solution, they were placed at room temperature to be dried completely. After drying, a uniform blackish-brown layer of asphaltene deposit was being observed on the surface of www.nature.com/scientificreports/ the blade. The weight of these blades was measured and recorded at the end of the experiment and after drying at room temperature. The difference between the weight of the blades at the end of the experiment (blades containing asphaltene deposition) and their weight at the beginning of the experiment (clean blades) indicates the amount of asphaltene deposition. The strength of the electric field was determined based on experiments performed on the uncoated sample. Based on the obtained results, the amount of asphaltene deposition on uncoated electrodes at an electric field strength of 2 kV/cm reached its maximum 32 . For this reason, in this study, 2 kV/ cm electric field strength was used to maximize the amount of deposition. In order to investigate the asphaltene deposition on coated and uncoated surfaces at different concentrations and different flow states, each electrode was exposed to an electric field at 5, 10, 20, 40, 60, 80, 120, 180 and 300 s, and the amount of asphaltene deposition at any time and in any situation was assessed. It should be noted that in order to measure the asphaltene deposition at any time, a new experiment was conducted. The experiments were repeated three times for each deposition condition, and the average values of these runs are reported here.

Kinetic models
In general, measuring, predicting, and understanding deposition rate in engineering sciences is very important. Some efforts [40][41][42][43] have been made to model the asphaltene deposition based on deposition kinetic for selecting the optimal operating conditions and the treatment of asphaltene deposition at the field scale. All these studies were conducted for uncoated surfaces 44,45 .
In order to describe the results of static and dynamic experiments at different concentrations and times, the double exponential model, diffusion equation model, Elovich's equation model, nth-order kinetics and modified second-order models were used. Although these models are suitable for modeling the adsorption process, the application of these models in this study could also provide a good insight into the kinetics of the adsorption/ deposition process. 46 and is used to describe the adsorption process with respect to both chemical and mathematical perspectives. The model links the two-step mechanism of the fast and slow adsorption process 47 as given in Eq. (1):

Double exponential model. This model was developed in 1993 by Wilczak and Keinath
where Q t and Q e , are the amount of asphaltenes at each time point of contact and the amount of asphaltene adsorbed on the surface of the electrode at equilibrium (mg/cm 2 ), respectively. D1 and D2 are asphaltene fast and slow adsorption fraction (mg/l), t is time, K D1 and K D2 are fast and slow rate constants (min −1 ) and K D1 is larger than K D2 . It is worth noting that the sum of the two parameters D 1 /m ads and D 2 /m ads is the physical equivalent of the calculated value of Q e . The rate of absorption of the absorbing material in both slow and fast states is expressed by SF and RF, respectively, and is expressed by Eqs. Diffusion equation model. The penetration of adsorbed molecules or ions into the pores is considered in order to find the appropriate kinetic model for the porous adsorbents. In many cases, the rate of absorption of (1) .
. www.nature.com/scientificreports/ a sorbent is controlled by the amount of penetration into the particles 48 . Equation (4) was expressed by Weber and Morris for this purpose.
In this equation, k p is defined as the diffusion rate coefficient and its unit is [mg/(cm 2 × min 0.5 )]. This rate coefficient could be obtained from the slope of the plots (Q t vs. t 0.5 ), and I is the intercept.
Elovich's equation model. This equation was introduced by Zeldowitsch in 1934 for absorption based on chemical bonding mechanism 49 . This equation is expressed by Eqs. (5) and (6).
In this equation, Q t is the amount of asphaltene adsorbed at time t, α is the initial adsorption value in gram and a is adsorption constant.
nth-Order kinetics model. In general, direct calculation of the rate constant and order of the adsorption reaction is more appropriate than assuming the reaction order, n, as 1 or 2, and therefore, using the nth-order kinetic model is much more efficient 50 . This model is expressed by Eq. (7).
where k n is the rate constant and its unit depends on the reaction order (1/min)(mg/cm 2 ) 1−n , β n is the impurity, pre-adsorbed on the surface and is defined by Eq. (8).
where θ 0 is a dimensionless surface coverage in the pre-adsorption step and is expressed by (θ 0 = Q 0 /Q e ).
Modified second-order model. Using the nth-order kinetic equation for n = 2, a modified second-order equation can be obtained 50 . This model is defined by Eq. (9).

Results and discussion
In this section, the effect of two different coatings and asphaltene concentration on the amount of asphaltene deposition at different flow states are analyzed and the results are discussed. Finally, we investigate the effect of these factors on the kinetics of asphaltene deposition on electrode surfaces. Table 1 summarizes the most important results obtained in each section.
The effect of coating type on asphaltene deposition in the static state. These experiments were performed at static state and asphaltene concentration of 2000 ppm for uncoated, PTFE coated and nanosilica coated electrodes. During these experiments, other influential parameters such as time, toluene concentration, asphaltene concentration, type of flow state, and voltage were kept constant. The parameters used in the design of the experiment are listed in Table 2. The rate of asphaltene deposition on three types of electrodes as a function of exposure time to the electric field with 2 kV/cm strength, is shown in Fig. 4. It is necessary to mention that, each data point on the asphaltene deposition rate curve, as shown in Fig. 4, was generated from an independent test. The amounts of asphaltene deposition, in this case, are shown in Table 3.
Based on our observations, the amount of asphaltene deposition on the surface of coated electrodes is lower than that of the uncoated electrode. Although the difference is not significant, the amount of asphaltene deposition on the surface of the electrode with PTFE coating is lower than that of nanosilica. It was also observed that the asphaltene deposition on the coated surfaces has low adhesion and could be easily removed from the surface after taking it out of the oil sample solution. It is worth recalling that, the asphaltene is the most polar component of crude oil and contains large amounts of active species 51 . They are known as key components of surface wettability change through the interaction of its polar functional groups with polar sites on a solid surface 52,53 . For coating created by the electrodeposition process, the wettability of the coatings largely depends on several parameters such as electrodeposition conditions of the coating such as charge transferred, applied voltage, , the alloy type and roughness of the working electrode and the surface energy of the coating 54 . Lower or negative surface energy values associated with lower or negative adhesion tendencies would be a more effective system for reducing asphaltene deposition 55 . The use of some polymer-based coatings with suitable chemically inert properties could reduce the tendency for severe asphaltene adhesion 55 . The coatings used to prevent or reduce www.nature.com/scientificreports/ asphaltene deposits must have the required surface characteristics for this purpose. The creation of superhydrophobic coatings with low surface energy could change the solid surface sites to non-polar 56,57 and ultimately reduces the tendency of asphaltene deposition on the coated surfaces [58][59][60][61][62][63][64] . Therefore, such a surface can not only prevent the deposition of minerals in formation water, but also can significantly reduce the deposition of asphaltene. Superhydrophilic surfaces could also effectively block the access of asphaltene to the surface by creating a   www.nature.com/scientificreports/ water film, and therefore reduce the asphaltene deposition 65 , however, having a water film on the surface could initiate the deposition of inorganic scales and creation of suitable sites for organic deposits and also corrosion.
The effect of flow type on the amount of asphaltene deposition. An experiment was designed to investigate the effect of shear rate on the amount of asphaltene deposition on electrode surfaces with and without superhydrophobic coating. In this regard, two parameters (flow state and type of working electrode) were considered as variables. Experiments were performed for two types of flow and working electrodes (without coating electrode and PTFE superhydrophobic coating electrode). In a dynamic state, the oil sample solution was agitated using a magnetic stirrer at 400 rpm and the amount of deposition on the surfaces with and without coating was measured. During these experiments, other influential parameters such as voltage, toluene concentration, asphaltene concentration, and time were kept constant. The parameters adjusted in the design of the experiment are shown in Table 4. The amount of asphaltene deposition on uncoated and superhydrophobic PTFE coated electrodes under static and dynamic conditions after 300 s of electrodeposition is shown in Fig. 5.
The detailed test results are reported in Table 5. It should be noted that measurements were made at ambient pressure and temperature. According to the results, hydrophobic properties decrease the adhesion force between the surface and the deposition. The amount of asphaltene deposition in the dynamic state for the uncoated and the superhydrophobic PTFE-coated electrodes is far less than in other cases. Dynamic deposition for PTFE superhydrophobic coating is far less than the other cases.
The effect of asphaltene concentration on the amount of asphaltene deposition. An experiment was designed to investigate the kinetics of asphaltene deposition on superhydrophobic PTFE-coated electrodes for three different asphaltene concentrations. During these experiments, other influential parameters such as voltage, toluene concentration and coating type were kept constant. The parameters used in the design of the experiment are listed in Table 6. Experiments were performed for asphaltene concentrations of 2000, 1000 and 250 ppm and different exposure times up to 5 min. The amount of asphaltene deposition as a function of asphaltene concentration in the static and dynamic states for the PTFE superhydrophobic coated electrodes is shown in Fig. 6. The detailed information for this experiment can be found in Tables 7 and 8. Figures 7 and  8 also compare the amount of deposition at different asphaltene concentrations in static and dynamic states. It is observed that decreasing the asphaltene concentration and the duration of the electrodeposition process decrease the amount of asphaltene deposition in the static and dynamic states for PTFE superhydrophobic coatings. The amount of asphaltene deposition at all three concentrations and dynamic state is lower than that in the static state. As shown in Fig. 7, the amount of asphaltene deposition after 300 s at a concentration of 2000 ppm for PTFE superhydrophobic coating is lower than that for nanosilica coating. The reason for this result can be related to the functional groups on the surface of nanosilica coatings and asphaltene. H-bonding sites of surface  www.nature.com/scientificreports/ hydroxyls, in the nanosilica superhydrophobic coating, formed by modification with silane material (DTMS), can be effective in adsorbing active groups in the asphaltene surface such as carboxylic. Some studies have also confirmed the effect of interaction between surface active sites of asphaltenes and sorbent surface active sites 61 . In PTFE coating, there is no interaction between fluorine in PTFE coating and asphaltene particles, and therefore the amount of asphaltene deposition in PTFE superhydrophobic coating will be less than nanosilica superhydrophobic coating. In this experiment, due to high the concentration and opacity of the solution, the movement of asphaltene particles at a concentration of 2000 ppm at the beginning and end of the experiment was not observed. As the concentration of asphaltene decreased, the movement of the particles in the form of    Figure 6. The effect of asphaltene concentration on asphaltene deposition for PTFE coating in static and dynamic states at ambient pressure and temperature.   www.nature.com/scientificreports/ dark masses toward the electrodes became evident. In this experiment, the amount of asphaltene deposition in a short time on the superhydrophobic coated electrodes, especially PTFE superhydrophobic coated electrode, at the static state and 250 ppm, was very low and close to zero, and no traces of deposition were observed in a short time (Table 7). In contrast, the deposition rate at 250 ppm, in the static state on the uncoated electrode, was significantly high (Supplementary Fig. S.1). Experiments with dynamic states showed very small deposition rates at longer times for superhydrophobic PTFE coating (Table 8 and Fig. 8). It can be inferred that the hydrophobic property of the coating reduces the crude oil affinity for sticking to the surface 26 and therefore, at lower concentrations the amount of asphaltene deposition is very low. It should be noted that the reason for a high CA and low SA in superhydrophobic surfaces is the low surface energy along with the hierarchical structure of the surface. As these two properties are enhanced at the surface, the existing surface becomes more hydrophobic until it reaches the superhydrophobicity 66 . The superhydrophobic and low sliding angle characteristic of the produced PTFE superhydrophobic coating could be considered as the main reason for reducing asphaltene deposition. The surface roughness of the coatings was measured using the AFM method, and some roughness characteristics including average surface roughness (Ave Rough), root mean square roughness (RMS Rough) and mean height roughness (Mean Ht) of the samples were calculated. Figure 1b,e show 3D roughness images of PTFE and nanosilica superhydrophobic coatings measured by AFM. The roughness characteristics of the coatings are listed in Supplementary Table S.1. As can be seen in this table, the average surface roughness of PTFE and nanosilica superhydrophobic coatings is 1.255 µm and 611.2 nm, respectively. The roughness plays a major role in surface wettability and consequently in asphaltene deposition. Our objective in synthesizing the coatings was to obtain superhydrophobic surfaces with very low sliding angles. It was achieved by combining low surface energy and desired roughness in PTFE superhydrophobic coatings and generating a rough surface and later modifying the surface energy in nanosilica coating. Creating roughness on the surface increases the surface area and then reduces its energy. Therefore, low surface energy is considered as the main factor in superhydrophobic properties of the surface and roughness is the aggravating factor 67 .

Modeling of asphaltene deposition kinetics on coated and uncoated electrodes. The kinetic
behavior of asphaltene deposition was modeled based on the results obtained in the previous sections. These models are appropriate for adsorption processes, however, their usage for deposition/adsorption processes (this study), provides a suitable insight into the kinetics of the deposition/adsorption process. Table 9 shows the parameters of the kinetic models for the coated and uncoated electrodes at different concentrations. The results of the deposition model are as follows. Double exponential model. There are usually two steps in the asphaltene deposition process. The first involves the rapid deposition rate and the second step is related to the slow adsorption until equilibrium is reached. As the initial concentration of asphaltenes increases, this period will be longer. The initial rate of asphaltene buildup on a surface could be different from that at the later stages and this makes the two-step models a suitable choice for adsorption modeling. This behavior was also modeled in a study by Refs. 12,68 who used quartz crystal microbalance with dissipation (QCM-D) measurements and examined the process of asphaltene adsorption for short and long times. Our results show that the RF value in static and dynamic states for the uncoated electrode is higher than that of the SF, indicating that this process is faster for the uncoated electrode. For the PTFE coating, the RF and SF values in static and dynamic states do not show any particular trend. In the dynamic state for the uncoated electrode at a concentration of 2000 ppm, the RF value is almost 100.0000 and the SF value is 0.0000 and in this state, the RF value for the PTFE coated electrode in 2000 ppm, is 100.0000 and the value of SF is 0.0000. This indicates that, under these conditions, the asphaltene deposition process happens only in the first step, i.e., during the rapid step and there is no slow deposition step under these conditions. The RF value for nanosilica coating and the concentration of 2000 ppm in a static state is lower than the SF value. This indicates that the slow deposition process is faster for this coating. The RF value for the dynamic state and the PTFE coating increases with increasing initial concentration (250, 1000, and 2000), and no specific trend is observed for the static state. The range of K D1 values for the static state and dynamic state is 0.0103-0.0391 and 0.0170-0.0261, respectively. Also, the range of K D2 values for the static state is 0.0032-0.0039 and for the dynamic state is 0.0036-0.0083.
nth-Order kinetics model. The order of the deposition reaction, n, for the coatings in static and dynamic states decreases with the increasing initial concentration of asphaltene. Its value was calculated for the static state between 1.0153 and 1.2680 and for the dynamic state between 1.1091 and 1.5429. K n values were calculated for static state in the range of 0.0114-0.0794 (1/min) × (mg/cm 2 ) 1−n and 0.0166-0.0467 (1/min) × (mg/cm 2 ) 1−n for the dynamic state. The β n values for static and dynamic states were approximately 1. This means that initially there were no impurities or pre-adsorbed asphaltenes.
Elovich's equation model. www.nature.com/scientificreports/ and for this electrode at the dynamic state and concentration of 2000 ppm is 537.1581. Comparison of these results shows that by changing the flow state from static to dynamic, the deposition constant for the coated and uncoated electrodes decreases. Also, the initial deposition rate, α, for PTFE coatings at static and dynamic states increases with decreasing initial concentration. The value of this parameter for nanosilica coating in static state and concentration of 2000 ppm is 1147.4729; therefore, its value in nanosilica coating at constant state and concentration is higher than PTFE coating.  www.nature.com/scientificreports/ Evaluation of kinetic models. In this study, root mean square error (RMSE) and average absolute percent relative error (AAPRE), as two statistical parameters, were used to evaluate and compare the accuracy of kinetic models. These parameters are calculated using Eqs. (10) and (11).
Here, d exp,i and d pred,i represent experimental and calculated deposition values, respectively. The results of calculated AAPRE and RMSE parameters for all kinetic models evaluated in this study are listed in Table 9. As can be seen in these figures, the diffusion model and Elovich's equation do not fit well with the experimental data and have more errors than the other ones. The selection of suitable deposition kinetics models is based on the deposition process mechanism and application of different models. Based on the deposition kinetics data, it can be concluded that at the beginning of the asphaltene deposition process, the maximum amount of deposition occurs on the electrode surface (during the first 2 min), and then the amount of deposition decreases. Also, based on these figures, it can be seen that the presence of a coating on the electrode surface caused a reduction of about 56% of the deposition in the static state at the concentration of 2000 ppm. Comparison of the amount of asphaltene deposition in the dynamic state for the coated electrodes shows more than 70% reduction in the amount of deposition at the same concentration, compared to the uncoated electrode. Regarding the RMSE values, in the static state, Elovich's equation and based on AAPRE values, the nth-order kinetics model showed the best fit to the experimental data. For the dynamic state and based on the RMSE parameter, Elovich's equation, has the best fit to the experimental data, and from AAPRE comparison, the double exponential model shows better agreement with the experimental data. Comparison of both parameters at all concentrations shows that in the static state, the nth-order kinetics model and in the dynamic state, the double exponential model, have the best agreement with the experimental data. Figure 17 shows the agreement of the experimental data and the best deposition kinetic models in static and dynamic states for PTFE coating electrodes at different concentrations. www.nature.com/scientificreports/ In this study, the adsorption kinetic modeling showed that the initial deposition rate is faster than that at subsequent times. According to the literature, most unstable fractions of asphaltenes, which have a high metal content and are more polar, react to the electric field and form the first adsorbed layer on the electrode, which will lead to subsequent deposition [69][70][71] . Other studies have also shown that polar entities of asphaltene dominate the initial adsorption mechanism 64,72-74 . Therefore, it can be said that the first layer of asphaltene particles is bonded to the electrode surface under the influence of an electric field and starts a chemical reaction with it, but other particles are mainly affected by solvent interaction due to lack of direct contact with the electrode surface.

Conclusions
The application of internal coatings with low surface energy could help to tackle organic and inorganic scale depositions in pipes. Recent efforts have been devoted to producing coatings with special surface properties to prevent or minimize asphaltene deposition on metal srfaces. In this study, two superhydrophobic coatings, including PTFE and nanosilica coatings, were fabricated simply and practically, and their performance for www.nature.com/scientificreports/ reducing asphaltene deposition was investigated. In this study, the effect of various factors including the type of coatings, fluid flow states, asphaltene concentration, and deposition time on the amount of asphaltene deposition was investigated and finally, the kinetics of asphaltene deposition in all these states were evaluated. We tried to show how the superhydrophobicity of a surface could increase its anti-scaling performance. Field application of this technique requires a comprehensive economic study based on net present value (NPV) analysis. This is an essential part of our future direction for extending the application of this technique in the field. The main findings of this study are as follows: 1. Surface wettability plays a major role in the amount of deposited asphaltene. Although both superhydrophobic coatings introduced in this study are capable of reducing the asphaltene deposits as compared to the uncoated electrode, the PTFE coating showed better performance. 2. At an asphaltene concentration of 2000 ppm and compared to the uncoated electrode the PTFE coated electrode shows a 56% decrease in asphaltene depositions at static state and more than 70% decrease in the number of asphaltene depositions at dynamic state. www.nature.com/scientificreports/ 3. The maximum amount of asphaltene deposition on the surface of the electrodes occurs during the first 120 s of the electrodeposition process. 4. The change of flow state affects the asphaltene deposition kinetics on the electrode surfaces. However, the type of electrode has no effect on the kinetics of asphaltene deposition. The results showed that the diffusion model and Elovich's equation are not in good agreement with the experimental data and the highest error is observed in these two ones. Investigation of the effect of flow type on the kinetics of asphaltene deposition showed that in the static state, the nth-order kinetics model, and in the dynamic state, the double exponential model has the best agreement with the experimental data.