Effect of hydrodynamics on the inhibition effect of thioureido imidazoline inhibitor (TAI) for the flow accelerated corrosion (FAC) of X65 carbon steel elbow was studied by electrochemical measurements and surface characterization by placing array electrodes at different locations on the elbow. Compared to static condition, the inhibition efficiency of TAI for FAC is relatively low as a result of drastic turbulence flow and high wall shear stress during the FAC test. The inhibition efficiency at the outer wall is higher than that at the inner wall, which is associated with the higher flow velocity, shear stress, and turbulent kinetic energy at the inner wall of the elbow. The distribution of inhibition efficiency is in good agreement with the distribution of hydrodynamic parameters at the elbow.

Flow accelerated corrosion (FAC) is a major issue for the safety and reliability of carbon steel pipe in the oil and gas industry1-3  and nuclear industry.4-5  FAC, which is affected by many factors, is a complicated process during oil and gas transportation6-9  and in nuclear power plants.10-12  Particularly, the fluid hydrodynamics plays an important role in FAC because of the complicated relationship between the flow within a boundary layer near the solid/fluid interface and mass transfer process.13-14  FAC frequently occurs in regions with local high velocity and drastic turbulence.

Carbon steel has been widely used in the oil and gas industry because of its high strength, good weldability, and low cost.15-16  However, carbon steel is prone to corrosion under relevant service conditions. Imidazoline and its derivatives have been used successfully as corrosion inhibitors in the oil and gas fields because of their high inhibition efficiency, low toxicity, and ease of production.17-22  Therefore, the use of carbon steel in combination with inhibitors treatment is one of the most economical and effective methods to control the corrosion in oil and gas fields. The inhibitive action of these compounds is attributed to their adsorption to the metal/solution interface. However, effective inhibition of FAC under a high flow velocity has long been a challenge. The efficacy of film-forming corrosion inhibitors may be weakened under flow condition, as the fluid can hinder the adsorption process and/or disrupt protective inhibitor films that have already adsorbed on the steel surface.23-24  Moreover, hydrodynamics affects the mass transfer process of corrosive species, enhancing the availability of chlorides, etc., at the metal/solution interface. As such, the effect of hydrodynamics on inhibitor performance should be understood in order to effectively mitigate FAC.

In most pipe systems, FAC is particularly severe where the flow direction is changed, such as at elbows.25  The flow field developed at a 90° elbow is complex. The flow regime is subject to significant change in the flow direction, flow velocity, and shear stress at different locations on the elbow, thus leading to significant difference in the corrosion behavior.7,26  The hydrodynamic conditions within many pipe systems are readily emulated via a laboratory scale flow loop. In previous work,27  it was demonstrated that the corrosion rate at the inner wall is higher than that at the outer wall of an elbow. The maximum corrosion rate appears at the innermost side, while the minimum corrosion rate at the outermost side of the elbow. The distribution of the measured corrosion rate is in good agreement with the distribution of flow velocity and shear stress at the elbow.

Because of the change in flow regime at the elbow, it is expected that there would be significant difference in the mass transfer process and inhibition effect of inhibitors at different locations on the elbow. The use of an arrayed electrode, where individually accessible electrodes are distributed across the surfaces of interest, can be used to assess this heterogeneous inhibition effect at different locations along the surface of an elbow.27 

In this work, the local effectiveness of thioureido imidazoline inhibitor (TAI) on FAC of an X65 carbon steel (UNS K03014)(1) elbow was studied by electrochemical measurements and surface characterization utilizing array electrodes positioned at different locations on the elbow. Computational fluid dynamics (CFD) simulation was also performed to reveal the flow regime within the elbow, and to assess the correlation between the inhibition efficiency of TAI and hydrodynamics at different locations on the elbow.

Preparation of Array Electrodes and Solution

In this experiment, X65 carbon steel array electrodes with an exposed area of 5 mm × 6 mm were used. The chemical composition (wt%) of X65 steel utilized in this study was C 0.04%, Si 0.2%, Mn 1.5%, P 0.011%, S 0.003%, Mo 0.02%, and Fe balance. An iron wire was welded to the back of each array electrode to ensure electrical connection for electrochemical measurements. Before each FAC test, each array electrode surface was abraded with 800 grit silicon carbide paper, rinsed with deionized water, degreased with acetone, and air dried.

The testing solution, containing 90.44 g/L NaCl, 2.20 g/L KCl, 0.43 g/L CaCl2, 0.43 g/L Na2SO4, 6.33 g/L MgCl2.6H2O, and 0.49 g/L NaHCO3, was prepared from analytical grade reagents and deionized water to simulate the formation water of an oil field.28  Before FAC testing, the solution was deaerated by purging CO2 gas (purity was 99.95%) for 12 h. The pH value of the CO2-saturated solution was 5.34. As the TAI used in this study was an oil-soluble inhibitor, before being injected into the solution, TAI was dissolved into ethanol with a volume ratio of 1:4 (TAI to ethanol). After the deaerated testing solution was added to the loop system, the inhibitor was injected into the reservoir by an injector. According to previous work28  with different TAI concentrations, 100 ppm was the optimum concentration. Therefore, in this work, the inhibitor concentration was selected as 100 ppm to determine the effect of hydrodynamics on the inhibition effect of TAI for the FAC of X65 carbon steel elbow. The chemical structure of TAI was presented as follows:

formula

Loop System for Flow Accelerated Corrosion Test

The circulating loop system used for FAC testing is illustrated in Figure 1(a). It consisted of pipe, a centrifugal pump, a reservoir, a pressure gauge, a flow meter, and array electrode test section. The solution was supplied from a 30-L reservoir and circulated through the centrifugal pump. The flow velocity was controlled by adjusting the rotational speed of the pump and measured by using a flow meter. The loop system was made of poly(methyl methacrylate) pipe with an inner diameter of 50 mm. The roughness of poly(methyl methacrylate) pipe was about 10 μm. A temperature control system, which included a heater and a controller, was installed in the reservoir to control the temperature of solution. After pretreatment, array electrodes were mounted into the elbow test section with the same spacing distance in flow direction, and then sealed with silicone. Silicone sealant used was a silicone that creates no corrosion damage to the electrodes and has no effect on the flow over the electrodes. Figures 1(b) and (c) show the assembly of elbow test section, with 21 specimens at the outer wall and 9 specimens at the inner wall of the elbow. The exposed surface of each array electrode was in-plane/flush with the internal surface of pipeline, as shown in Figures 1(d) and (e). FAC tests were performed at flow velocities of 2 m/s and 4 m/s according to the operating conditions in one oil field. All of the experiments were performed at 60°C and atmospheric pressure, and lasted 5 h. The inhibition efficiency of inhibitors usually decreases with time as a result of high flow velocity, shear stress, and turbulent flow. Therefore, the test for the inhibition efficient of inhibitor under flow condition usually was performed in relatively short time.3,23  In this work, the electrochemical measurements were performed at the third and fourth hour, at which the experimental condition reaches stability under flow condition, and the experiments were completed within 5 h.

FIGURE 1.

Schematic diagram of the loop system and array electrodes for FAC test: (a) loop system, (b) schematic of elbow test section, (c) assembly of the elbow test section, (d) array electrodes at the inner wall, (e) array electrodes at the outer wall, and (f) the electrodes’ number at the elbow.

FIGURE 1.

Schematic diagram of the loop system and array electrodes for FAC test: (a) loop system, (b) schematic of elbow test section, (c) assembly of the elbow test section, (d) array electrodes at the inner wall, (e) array electrodes at the outer wall, and (f) the electrodes’ number at the elbow.

Close modal

Electrochemical Measurements

An electrochemical test system was used for in situ electrochemical measurements during the FAC tests. A three-electrode electrochemical cell was constructed in the test section with the array electrodes as working electrodes (WE), a platinum plate counter electrode (CE), and a saturated calomel (SCE) reference electrode (RE), as shown in Figure 1. To determine the inhibition efficiency at each array electrode, the system was allowed to stabilize for 3 h, after which electrochemical impedance spectroscopy (EIS) measurements were performed at open circuit potential (OCP) with a sinusoidal alternating amplitude of 10 mV (peak to peak) from 10,000 Hz to 0.1 Hz. This frequency range was demonstrated to be wide enough to permit determination of the charge transfer resistance and ensured that the EIS tests for all 30 electrodes in the array were finished in 1 h.29  Furthermore, it had been confirmed that the experimental data was insensitive to the sequence in which the electrodes were measured. The charge transfer resistances (Rct) of all of the array electrodes were determined by fitting the EIS data with an electrochemical equivalent circuit by using ZSimpWin software. Then, the inhibition efficiency (η%) was determined by the charge transfer resistance according to Equation (1):

formula

where is the charge transfer resistance with inhibitor, and is the charge transfer resistance without inhibitor. To study the inhibitive mechanism of inhibitor, EIS measurements were also performed on Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) with the frequency from 10,000 Hz to 0.01 Hz at the fourth hour (i.e., upon completion of the scans discussed earlier) of the FAC tests. The electrodes scanned in this second experiment corresponded to specific hydrodynamic conditions defined by the CFD simulation.

Potentiodynamic polarization curves were also conducted on this subset of electrodes by scanning potential from −250 mVOCP to 250 mVOCP with a scan rate of 1 mV/s. The relatively quick scan rate was used in order to shorten the time for measurement, and then shorten the time difference at different electrodes during the measurements. A scan rate of 1 mV/s was also applied in other literature.19,30-31  The corrosion current density was extracted from each polarization curve, then used to calculate the inhibition efficiency according to Equation (2):

formula

where and icorr are the uninhibited and inhibited corrosion current densities, respectively, which were determined by performing a least square fit to the measured data in the weak polarization region (at the range from 0.02 VOCP to 0.07 VOCP and from −0.02 VOCP to −0.07 VOCP) by using Cview software.

As the inhibition efficiencies at different locations under static condition are supposed to be equivalent, only a single electrode was used to perform the electrochemical measurements under static condition. The static experiments were performed in a three-electrode electrolytic cell with the same temperature and solution as FAC experiments. All of the experiments under static and flow conditions were repeated three times in this study. The experimental variance was shown as error bar in the figures.

Surface Characterization of Representative Array Electrodes After Flow Accelerated Corrosion Tests

After FAC tests, the surface morphologies of array electrodes were observed by scanning electron microscope (SEM). The accelerating voltage was 10 kV with a spot size of 3.0 nm.

Professional fluid simulation software Fluent was used to perform CFD simulation. Pre-processing software Gambit was used to establish a geometric model according to the practical pipeline system used for FAC test. The straight section upstream of the elbow entrance (θ = 0°) was set as 1 m in order to reach a steady, full-developed flow before the elbow. The straight section downstream of the elbow exit (θ = 90°) was set as 0.5 m to avoid possible recirculation flow at the outlet of the elbow. Volume meshes were constructed with the interval size of 0.004 m. A geometric model for CFD simulation was shown in Figure 2. A flow velocity of 2 m/s or 4 m/s at the inlet and outflow at the outlet were the boundary conditions. The fluid was assumed to be incompressible. The Reynolds number (Re), which was calculated according to the geometrical dimension of pipeline and flow velocity, was 99,521 at 2 m/s and 199,043 at 4 m/s, respectively. The Reynolds number was much higher than 4,000, indicating a turbulent flow in this system. Then a κ-ε turbulent model (double equation model) was used to numerically solve the simulation.6,32  Turbulent kinetic energy κ, which was the energy produced by the velocity fluctuation, was set as 1 m2/s2. Turbulent dissipation rate ε, which was the transformation rate from the turbulent kinetic energy to the molecular thermal motion kinetic energy, was set as 1 m2/s3. Turbulence intensity (I) was 3.8% at 2 m/s and 3.5% at 4 m/s, which were calculated according to an empirical equation ().33-34  Wall roughness was set as 10 μm according to the roughness of the poly(methyl methacrylate) pipe. The κ-ε turbulence equation was solved by iterative method with a convergence criterion of 1 × 10−10.

FIGURE 2.

Geometric model for CFD simulation.

FIGURE 2.

Geometric model for CFD simulation.

Close modal

Hydrodynamics at the Elbow by Computational Fluid Dynamics Simulation

Figure 3 shows the three-dimensional distribution of flow velocity, shear stress, and turbulent kinetic energy at the elbow with an inlet flow velocity of 2 m/s. The three-dimensional distribution of all three hydrodynamic parameters along the elbow was found to be symmetric with respect to the central plane of pipe. These hydrodynamic parameters are generally higher at the inner wall than at the outer wall. The maximum (2.59 m/s of flow velocity, 15.8 Pa of shear stress, 0.043 m2/s2 of turbulent kinetic energy) appears at the innermost side (Electrode 26), while the minimum (1.08 m/s of flow velocity, 5.3 Pa of shear stress, 0.018 m2/s2 of turbulent kinetic energy) appears at the outermost side (Electrode 11).

FIGURE 3.

CFD simulation in a 90° elbow at 2 m/s: (a) three-dimensional vector of flow velocity (m/s), (b) three-dimensional contour of wall shear stress (Pa), and (c) three-dimensional contour of turbulent kinetic energy (m2/s2).

FIGURE 3.

CFD simulation in a 90° elbow at 2 m/s: (a) three-dimensional vector of flow velocity (m/s), (b) three-dimensional contour of wall shear stress (Pa), and (c) three-dimensional contour of turbulent kinetic energy (m2/s2).

Close modal

The distribution of three hydrodynamic parameters at the elbow with an inlet flow velocity of 4 m/s is similar to that with an inlet flow velocity of 2 m/s, with the only difference being their magnitude. All of the hydrodynamic parameters at 4 m/s are higher than those at 2 m/s. At 4 m/s, the maximum (5.25 m/s of flow velocity, 55.0 Pa of shear stress, 0.150 m2/s2 of turbulent kinetic energy) also appears at the innermost side (Electrode 26), while the minimum (2.23 m/s of flow velocity, 16.0 Pa of shear stress, 0.050 m2/s2 of turbulent kinetic energy) appears at the outermost side (Electrode 11).

Figure 4 shows the variations of these hydrodynamic parameters, as well as the distribution of secondary flow in cross section along the flow direction (increase of θ) at the elbow with an inlet flow velocity of 2 m/s. It is seen that all three hydrodynamic parameters increase along the direction of flow. Secondary flow, which is the characteristic of fluid flow at an elbow, was also observed. The secondary flow is developed from two-counter rotating vortices as the result of centrifugal effect resulting from the elbow curvature (Figure 4[d]). These two counter vortices direct the fluid flow toward the outer wall, and then back to the inner wall. The secondary flow, which leads to the formation of vortices at inner wall of the elbow, initiates at θ = 20°, strengthens at θ = 45° and 70°, and decays at θ = 90°. The variations of these hydrodynamic parameters as well as the distribution of secondary flow in cross section along the flow direction (increase of θ) at the elbow with an inlet flow velocity of 4 m/s are similar to those with an inlet flow velocity of 2 m/s, with the only high magnitude at 4 m/s.

FIGURE 4.

CFD simulation in cross section along the flow direction at the elbow at 2 m/s: (a) flow velocity (m/s), (b) wall shear stress (Pa), (c) turbulent kinetic energy (m2/s2), and (d) secondary flow (m/s).

FIGURE 4.

CFD simulation in cross section along the flow direction at the elbow at 2 m/s: (a) flow velocity (m/s), (b) wall shear stress (Pa), (c) turbulent kinetic energy (m2/s2), and (d) secondary flow (m/s).

Close modal

Corrosion Potential Measurements

Figure 5 shows the corrosion potential of Electrode 11 and Electrode 26 at different flow velocities in the absence and presence of inhibitor. It should be pointed out that Electrode 11 was located at the outermost wall and experienced the minimum flow velocities, while Electrode 26 was located at the innermost wall and experienced the maximum flow velocities observed in this work. It is seen that the presence of inhibitor results in prominently positive shift of corrosion potential. It has been suggested22,35-36  that if the shift of corrosion potential is more than 85 mV with respect to the corrosion potential in blank solution, the inhibitor should be regarded as cathodic or anodic type inhibitor. In the present work, the anodic shift of the corrosion potential after adding inhibitor exceeded 85 mV, which indicates that the TAI used in this work was an anodic type inhibitor. The corrosion potential also shifted in the positive direction with the increase of flow velocity, which suggests that the fluid accelerates the cathodic process more prominently than the anodic process. Furthermore, the corrosion potential at inner wall was more positive that that at outer wall.

FIGURE 5.

Corrosion potential of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) at various flow velocities in blank and inhibited solutions.

FIGURE 5.

Corrosion potential of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) at various flow velocities in blank and inhibited solutions.

Close modal

Potentiodynamic Polarization Results

Figure 6 shows the polarization curves of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) in the absence and presence of inhibitor at different flow velocities. It is seen that the anodic process was under activation control, while the cathodic process was under mixed control of activation and diffusion regardless of the absence or presence of inhibitor. An abrupt increase in anodic current density appeared in the presence of inhibitor when polarization potential reached a relatively positive value (at about −0.570 V), which could be attributed to the desorption process of the adsorbed inhibitor on the electrode surface.37-39  Under the anodic polarization, the adsorbed inhibitor may desorb from the electrode surface quickly as a result of an acceleration of anodic dissolution. It is also seen that TAI inhibited both the anodic and cathodic reactions by decreasing the polarization current density. However, the inhibition of anodic reaction was more significant than that of cathodic reaction, which resulted in a positive shift of the corrosion potential. This means that TAI is an anodic inhibitor, which mainly inhibits the anodic process of the steel corrosion.

FIGURE 6.

Polarization curves of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) after FAC test for 5 h in blank and inhibited solutions: (a) static, (b) 2 m/s, and (c) 4 m/s.

FIGURE 6.

Polarization curves of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) after FAC test for 5 h in blank and inhibited solutions: (a) static, (b) 2 m/s, and (c) 4 m/s.

Close modal

The values of corresponding parameters in polarization curves, such as corrosion potential (Ecorr) and corrosion current density (icorr), are listed in Table 1. The value of icorr is obtained by performing a least square fit to the measured data in the weak polarization region. The fitting errors for all parameters were ensured to be less than 1%. The inhibitor efficiency, which is determined via the corrosion current density through Equation (2), is also listed in Table 1. It is seen that the presence of inhibitor caused a positive shift of the corrosion potential. The corrosion rate in the presence of inhibitor was much less than that without inhibitor. This indicates that the inhibitor is efficient under flow condition. Moreover, the corrosion current density at Electrode 26, which was located at the innermost site of the elbow, was generally higher than that at Electrode 11, which was located at the outermost site of the elbow. Furthermore, the corrosion current density under flow condition was much higher than that under static condition, and increased with the increase of flow velocity.

TABLE 1

Fitted Parameters for the Polarization Curves and Inhibition Efficiency of Representative Array Electrodes

Fitted Parameters for the Polarization Curves and Inhibition Efficiency of Representative Array Electrodes
Fitted Parameters for the Polarization Curves and Inhibition Efficiency of Representative Array Electrodes

Electrochemical Impedance Spectroscopy Measurements

Figure 7 shows the EIS data for Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity). The Nyquist plots in blank solution are characterized by a single capacitive loop, while in the presence of inhibitor under flow conditions are characterized by a capacitive loop in high-frequency range and an inductive loop in low-frequency range. The capacitive loop has been attributed to the interfacial charge transfer process, while the inductive loop has been attributed to the poorly formed inhibitor film and/or corrosion products on the electrode surface, which was caused by insufficient inhibitor adsorbed on the electrode surface.40  The high flow velocity would cause high turbulence and wall shear stress at the pipe wall, as shown in Figures 3 and 4, and thus cause the destruction of the protective inhibitor film. The repeated adsorption and desorption of inhibitor on the metal surface leads to an unstable adsorption process, and then cause the inductive effect. The presence of inductive loop in EIS measurements under flow condition were also found by other researchers.3,40-41 

FIGURE 7.

Nyquist ([a], [c], and [e]) and Bode ([b], [d], and [f]) plots of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) after FAC conditions at different flow velocities: (a) and (b) static, (c) and (d) 2 m/s, and (e) and (f) 4 m/s.

FIGURE 7.

Nyquist ([a], [c], and [e]) and Bode ([b], [d], and [f]) plots of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) after FAC conditions at different flow velocities: (a) and (b) static, (c) and (d) 2 m/s, and (e) and (f) 4 m/s.

Close modal

However, the Nyquist plot in the presence of TAI under static state is characterized by an extended capacitive loop, with the capacitive loop representing the inhibitor film merger with the capacitive loop representing double-layer capacitance and charge transfer resistance.42  The capacitive loop at high frequency corresponds to the formation of inhibitor film on the metal surface as the inhibitor film usually has a small time constant.19,43  The part of the curve at low frequency should result from the electrochemical corrosion process. Compared to blank solution, the larger diameter of the capacitive loop with inhibitor indicates the adsorption of inhibitor on the electrode surface.2,30  Furthermore, the diameter of capacitive loop decreases with the increase of flow velocity. The diameter of capacitive loop of Electrode 11 (at the outer wall) is larger than that of Electrode 26 (at the inner wall) in both the blank and inhibited solutions.

The Bode plots of Electrodes 11 and 26 at various flow velocities are also shown in Figure 7. It is seen that the Bode plots in blank solution are characterized by one time constant, i.e., only one phase angle peak over the entire frequency range, which corresponds to the capacitive semicircle in the Nyquist plots, while the Bode plots in presence of inhibitor under flow condition are characterized by two time constants, i.e., a phase angle peak at high frequency and a phase angle valley (negative phase angle) at low frequency. The phase angle peak at high frequency corresponds to the capacitive semicircle, and the phase angle valley at low frequency could be related to the inductive semicircle in the Nyquist plots. Under static condition, the Bode plot in the blank solution is characterized by one time constant, i.e., a phase angle peak, while the Bode plot in presence of inhibitor is characterized by two time constants, corresponding to two phase angle peaks. The phase angle peak at high frequency could be related to the capacitive loop corresponding to the formation of inhibitor film, and the phase angle peak at low frequency could be related to the capacitive loop corresponding to the electrochemical corrosion process.

To analyze and obtain the impedance parameters, electrochemical equivalent circuits, shown in Figure 8, were used for fitting the EIS data, where Rs is solution resistance, CPE is constant phase element, Rct is charge transfer resistance, RL is inductance resistance, L is inductance, and Rf is film resistance. The fitted values of these impedance parameters, along with the inhibition efficiency, are listed in Tables 2 and 3. The errors for all of the parameters in the fitting process were less than 2%. The double-layer capacitance (Cdl) can be calculated based upon the CPE via the equation:44 

formula

where Y0 and n are the CPE parameters. The parameter n is an indicator of electrode surface roughness or heterogeneity, and Y0 is the admittance of the CPE.

FIGURE 8.

Electrochemical equivalent circuits for EIS fitting: (a) for all of the EIS measured in the blank solution and the EIS measured at the frequency range from 10,000 Hz to 0.1 Hz, (b) for the EIS measured with TAI under flow condition at the frequency range from 10,000 Hz to 0.01 Hz, and (c) for the EIS measured with TAI under static state at the frequency range from 10,000 Hz to 0.01 Hz.

FIGURE 8.

Electrochemical equivalent circuits for EIS fitting: (a) for all of the EIS measured in the blank solution and the EIS measured at the frequency range from 10,000 Hz to 0.1 Hz, (b) for the EIS measured with TAI under flow condition at the frequency range from 10,000 Hz to 0.01 Hz, and (c) for the EIS measured with TAI under static state at the frequency range from 10,000 Hz to 0.01 Hz.

Close modal
TABLE 2

Fitted Parameters for EIS of the Electrodes After Corrosion in Blank and Inhibited Solutions Under Static Condition

Fitted Parameters for EIS of the Electrodes After Corrosion in Blank and Inhibited Solutions Under Static Condition
Fitted Parameters for EIS of the Electrodes After Corrosion in Blank and Inhibited Solutions Under Static Condition
TABLE 3

Fitted Parameters for the EIS and Inhibition Efficiency of Representative Electrodes at Different Flow Velocities

Fitted Parameters for the EIS and Inhibition Efficiency of Representative Electrodes at Different Flow Velocities
Fitted Parameters for the EIS and Inhibition Efficiency of Representative Electrodes at Different Flow Velocities

It is seen that the Rct value increases while the Cdl value decreases in the presence of inhibitor. The changes in Rct and Cdl could be attributed to the gradual change of electrode interface. The increase of Rct indicates that the adsorbed inhibitor increases the resistance to the metal dissolution reaction. The decrease of Cdl could be attributed to the adsorption of inhibitor on the electrode surface. When the inhibitor molecules adsorb on the electrode surface, they might eliminate the originally adsorbed water molecules on the electrode surface.45  Therefore, water molecules on electrode interface could be replaced by inhibitor molecules that have a lower dielectric constant. Meanwhile, the adsorbed inhibitor molecule layer is usually thicker than the water molecule layer. Therefore, the electrode interface adsorbed by inhibitor molecules has a lower double-layer capacitance.46 

Distribution of Charge Transfer Resistance and Inhibition Efficiency at the Elbow

Figure 9 shows the variation of the charge transfer resistances (Rct) of array electrodes along the flow direction (increase of θ) at different azimuthal angles (Φ) of the elbow. The charge transfer resistances (Rct) were determined by EIS measurements after FAC for 4 h. It is seen that the Rct in the blank solution at 2 m/s is from 86 Ω·cm2 to116 Ω·cm2, and it changes from 82 Ω·cm2 to 95 Ω·cm2 at 4 m/s. In the presence of inhibitor, the Rct at 2 m/s is from 240 Ω·cm2 to 432 Ω·cm2 and it changes from 176 Ω·cm2 to 342 Ω·cm2 at 4 m/s. The Rct in the blank solution is much less than that in the inhibited solution. Furthermore, compared to the Rct under static condition (336 Ω·cm2 in the blank solution and 3,672 Ω·cm2 in the inhibited solution, respectively, corresponding to an inhibition efficiency of approximately 90.9%), the Rct under flow condition is much smaller and decreases with increasing flow velocity. There is a slightly downward trend (decrease by approximately 1% to 22% at 2 m/s and 6% to 23% at 4 m/s in inhibited solution) in the Rct along the flow direction. The Rct at the outer wall (Φ = 130°, 180°, and 230°) are higher than those at the inner wall (Φ = 0°, 50°, and 310°) in both the blank and inhibited solutions at different flow velocities, which suggests the higher corrosion rate at the inner wall.

FIGURE 9.

Variation of charge transfer resistance (Rct) of array electrodes along the flow direction at the elbow at different azimuthal angles Φ: (a) Φ = 0°, (b) Φ = 50°, (c) Φ = 130°, (d) Φ = 180°, (e) Φ = 230°, (f) Φ = 310°, (g) annotation of θ, and (h) annotation of Φ.

FIGURE 9.

Variation of charge transfer resistance (Rct) of array electrodes along the flow direction at the elbow at different azimuthal angles Φ: (a) Φ = 0°, (b) Φ = 50°, (c) Φ = 130°, (d) Φ = 180°, (e) Φ = 230°, (f) Φ = 310°, (g) annotation of θ, and (h) annotation of Φ.

Close modal

Figure 10 shows the variation of inhibition efficiency along the flow direction at different azimuthal angles of the elbow after FAC test for 4 h. There is also a slightly downward trend (decrease by approximately 2% to 11% at 2 m/s and 6% to 13% at 4 m/s, respectively) in the inhibition efficiency along the flow direction. The inhibition efficiency at 4 m/s is lower than that at 2 m/s, which suggests more difficulty for the adsorption of inhibitor at higher flow velocity. The inhibition effect of TAI at the same location on the elbow decreases with the increase of flow velocity. Furthermore, the inhibition efficiency at the outer wall is higher than that at the inner wall of the elbow. Compared to the inhibition efficiency (90.9%) under static condition, the inhibition efficiency for FAC is relatively low under flow condition, with a maximum of 76.8% at 2 m/s and 74.0% at 4 m/s, respectively. The low inhibition efficiency under flow condition could be a result of drastic turbulence flow and high wall shear stress during the FAC test, which prevents the adsorption of inhibitor and/or damages the adsorbed inhibitor film.

FIGURE 10.

Variation of inhibition efficiency of array electrodes along the flow direction at the elbow with 100 ppm inhibitor at different azimuthal angles Φ: (a) Φ = 0°, (b) Φ = 50°, (c) Φ = 130°, (d) Φ = 180°, (e) Φ = 230°, and (f) Φ = 310°.

FIGURE 10.

Variation of inhibition efficiency of array electrodes along the flow direction at the elbow with 100 ppm inhibitor at different azimuthal angles Φ: (a) Φ = 0°, (b) Φ = 50°, (c) Φ = 130°, (d) Φ = 180°, (e) Φ = 230°, and (f) Φ = 310°.

Close modal

Figure 11 shows the variation of charge transfer resistance and the corresponding inhibition efficiency of TAI on Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) with time. It is seen that both the charge transfer resistance and inhibition efficiency decrease as time elapses under flow condition, which suggests that the adsorbed inhibitor film is damaged as a result of the continuous impingement of such high turbulence flow.20,40  Then, the electrode surface that is not covered by TAI molecules could corrode at a high rate.

FIGURE 11.

Variations of (a) charge transfer resistance Rct and (b) inhibition efficiencies of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) with time in the solution with 100 ppm inhibitor.

FIGURE 11.

Variations of (a) charge transfer resistance Rct and (b) inhibition efficiencies of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) with time in the solution with 100 ppm inhibitor.

Close modal

Scanning Electron Microscope Surface Morphology After Flow Accelerated Corrosion Test

Figures 12 through 14 show the SEM surface morphologies of Electrode 11 (minimum flow velocities) and Electrode 26 (maximum flow velocities) after 5 h at different flow velocities. For the electrode under static condition, relatively compact corrosion products are formed on the electrode surface in the blank solution, which could provide some protection for the corrosion of substrate. In the presence of inhibitor, the corrosion is slight and the original scratches (produced by the abraded treatment before corrosion test) still can be observed after corrosion test.

FIGURE 12.

SEM surface morphologies of electrodes after corrosion in (a) and (b) blank solution and (c) and (d) inhibited solution with 100 ppm inhibitor under static state.

FIGURE 12.

SEM surface morphologies of electrodes after corrosion in (a) and (b) blank solution and (c) and (d) inhibited solution with 100 ppm inhibitor under static state.

Close modal

For the electrodes under flow condition, all of the electrodes were covered by corrosion products in both blank and inhibited solutions, indicating the relatively poor inhibition effect of inhibitor under such drastic turbulence. In the absence of inhibitor, more porous corrosion products were observed on the electrode surface. Apparently, the corrosion products formed during the FAC test without inhibitor do not have good protection for the corrosion of substrate. Furthermore, the corrosion products on the electrode at the inner wall (Electrode 26) appear less compact than those at the outer wall (Electrode 11). Compared to the surface morphologies at different flow velocities, it is evident that the corrosion products became less compact on the electrode surface as the flow velocity increased.

Effect of Hydrodynamics on the Inhibition Effect of Inhibitor at the Elbow

The distribution of inhibition efficiency by EIS measurements (Figure 10) indicates that the inhibition effect of TAI is different at different locations on the elbow. The CFD simulation also indicates that it is quite different in flow velocity, shear stress, and turbulent kinetic energy at different locations on the elbow.27-28  These hydrodynamic parameters are generally higher at the inner wall than those at the outer wall, and increase along the flow direction (Figures 3 and 4). Apparently, hydrodynamics play an important role in the inhibition effect of TAI for the FAC at the elbow.9,23 

For a fully developed turbulent flow, the changes in fluid field, wall shear stress, turbulence, mass transfer, and fluid interaction with the wall occur in the boundary layer. The viscous regions of the velocity boundary layer and the concentration boundary layer are where corrosion occurs and inhibitor film forms.47  All of the movements of species (such as arrival and departure from the wall) and all of the chemical reactions at the wall occur in these regions. The velocity boundary layer is the region of fluid with velocity gradient, and its thickness, σ, is the vertical distance from the wall to the position where the fluid velocity is equal to 99% of the bulk solution velocity.48  Similarly, the concentration boundary layer, also called mass transfer boundary layer, is the region of fluid with concentration gradient and its thickness, σc, is the vertical distance from the wall to the position where the fluid concentration is equal to 99% of the bulk solution concentration.49  The concentration boundary layer is usually thinner than the corresponding velocity boundary layer because mass transfer by molecular diffusion is generally a much slower process than momentum transfer.50  Therefore, the concentration boundary layer is the control factor with respect to the mass transfer process of the inhibitor and corrosive species.

For the fluid flow in a pipe, the distribution of velocity (u) along radial direction can be expressed as parabolic velocity profile:51-52 

formula

where ub is the bulk fluid velocity and y is the distance from the wall. σu is the velocity boundary layer thickness.

Then the concentration boundary layer thickness can be determined from analogy theory which links the momentum and the mass transfer process:53-54 

formula

In this equation, Sc is Schmidt number (Sc = ν/D), where D is diffusion coefficient and ν is kinematic viscosity, and α is a constant. As can be assumed as a constant, concentration boundary layer thickness σc is achieved.

Because molecule diffusion occurs within the concentration boundary layer, the diffusion flux can be obtained according to Fick’s first law of diffusion:

formula

The convective mass transfer flux can be expressed as:

formula

where cσ is the concentration at the edge of concentration boundary layer, cb is the concentration in bulk solution, and Kc is mass transfer coefficient.

In steady state, the diffusion flux should be equal to the convective mass transfer flux. Substituting Equation (6) into Equation (7), the mass transfer coefficient can be expressed as:55 

formula

Then mass transfer coefficient Kc can be solved by combining Equations (5) and (8).

In present work, the flow velocity at the inner wall of the elbow is higher than that at the outer wall, which leads to the fluctuation in turbulence flow. Furthermore, the high flow velocity at the inner wall enhances the wall shear stress and surface friction, therefore reducing the concentration boundary layer thickness. Then, the concentration boundary layer thickness σc is thinner at the inner wall than that at the outer wall, and there is the same trend in velocity boundary layer thickness.56  According to Equation (8), the thinner concentration boundary layer thickness σc will result in higher mass transfer coefficient Kc, and then accelerate mass transfer process. The increased wall shear stress at the inner wall will also cause the increase of surface roughness, which may disturb the hydrodynamics within the concentration boundary layer, and accelerate the mass transfer process.52  Furthermore, the flow separation effect (Figures 4[g] and [h]), which is the characteristic of the fluid flow at an elbow, will lead to the vortices at the inner wall of the elbow, which will also disturb the concentration boundary layer and promote the mass transfer process.57  Therefore, the higher mass transfer rate is present at the inner wall of the elbow. Then, it is faster for corrosive species to reach metal/solution interface, which results in a higher corrosion rate in the inner wall at the elbow, as show in Figures 9(a) and (c).

For the adsorption of TAI on the electrode surface, it involves the replacement of the adsorbed water molecules by inhibitor molecules:28 

formula

Then, during the FAC process, the adsorbed inhibitor will combine with the dissolved Fe2+ ions to form Fe-inhibitor complex on the electrode surface:58-59 

formula
formula

Under flow condition, fluid flow has different effects on the inhibition performance of inhibitor. On the one hand, flow of fluid promotes the mass transfer of inhibitor molecules, which facilitates inhibitor molecules to reach the electrode surface.3,31  On the other hand, hydrodynamics with high shear stress and turbulence energy will remove the adsorbed [Fe–Inh]2+ complex or prevent the adsorption of inhibitor, resulting in a low inhibitor efficiency.20,23  The balance of these effects leads to the difference in the inhibition effect of TAI at different locations on the elbow. Apparently, in present work, the harmful effect of hydrodynamics dominates the inhibitor performance during the FAC process. At the inner wall of the elbow, under the impingement of the fluid with a high wall shear stress and turbulence, the adsorbed inhibitor film would be removed from the electrode surface. Moreover, the high flow velocity, and thus the high mass transfer rate, will enhance the transportation of the dissolved Fe2+ ions from the electrode surface to bulk solution, which inhibits the formation of [Fe–Inh]2+ complex on the electrode surface. However, at the outer wall of the elbow, the relatively low flow velocity results in relatively low shear stress, turbulent kinetic energy, and mass transfer rate. Then, the inhibitor film is not easily removed and higher inhibition efficiencies are observed at the outer wall of the elbow. As shown in Figure 15, at θ = 45° of the elbow, the wall shear stress decreases, while the corresponding inhibition efficiency increases with increase of azimuthal angle. The polarization curves (Figure 6) and EIS plots (Figure 7) of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) indicate that higher velocity and turbulence flow at the inner wall leads to the lower inhibition efficiency. The SEM morphologies (Figures 13 and 14) also indicate a more complete and compact corrosion product film at the outer wall of the elbow, i.e., the corrosion products are more compact at the outer wall (Electrode 11) than those at the inner wall (Electrode 26) of the elbow at various flow velocities. This suggests that protective corrosion products are not easy to form under higher wall shear stress and turbulence flow. Therefore, the positional variation in the inhibition efficiency of TAI is consistent with the distribution of hydrodynamic parameters (flow velocity, shear stress, turbulent kinetic energy, and secondary flow) at different locations on the elbow.

FIGURE 13.

SEM surface morphologies of Electrodes 11 (at the outer wall) and 26 (at the inner wall) after FAC tests in blank and inhibited solutions at 2 m/s: (a) Electrode 11, blank, (b) Electrode 11, 100 ppm inhibitor, (c) Electrode 26, blank, and (d) Electrode 26, 100 ppm inhibitor.

FIGURE 13.

SEM surface morphologies of Electrodes 11 (at the outer wall) and 26 (at the inner wall) after FAC tests in blank and inhibited solutions at 2 m/s: (a) Electrode 11, blank, (b) Electrode 11, 100 ppm inhibitor, (c) Electrode 26, blank, and (d) Electrode 26, 100 ppm inhibitor.

Close modal
FIGURE 14.

SEM surface morphologies of Electrodes 11 (at the outer wall) and 26 (at the inner wall) after FAC tests in blank and inhibited solutions at 4 m/s: (a) Electrode 11, blank, (b) Electrode 11, 100 ppm inhibitor, (c) Electrode 26, blank, (d) Electrode 26, 100 ppm inhibitor.

FIGURE 14.

SEM surface morphologies of Electrodes 11 (at the outer wall) and 26 (at the inner wall) after FAC tests in blank and inhibited solutions at 4 m/s: (a) Electrode 11, blank, (b) Electrode 11, 100 ppm inhibitor, (c) Electrode 26, blank, (d) Electrode 26, 100 ppm inhibitor.

Close modal
FIGURE 15.

Variations of inhibition efficiency and wall shear stress at the elbow along azimuthal angles Φ at θ = 45°.

FIGURE 15.

Variations of inhibition efficiency and wall shear stress at the elbow along azimuthal angles Φ at θ = 45°.

Close modal

Effect of Flow Velocity on the Inhibition Effect of Inhibitor at the Elbow

The inhibition efficiency at different flow velocities shows that the inhibition efficiency under flow condition is much less than that under static condition, and decreases with increasing flow velocity. Compared to static condition, the inhibition efficiency of TAI for FAC is relatively low resulting from drastic turbulence flow and high wall shear stress during the FAC test. As the flow velocity increases, the mass transfer process will be accelerated. The higher turbulence with an increasing velocity prevents the [Fe–Inh]2+ complex from adsorbing on the surface by carrying Fe2+ away, and higher wall shear stress damages the inhibitor film formed on the electrode.58-59  Therefore, the inhibition effect of inhibitor is degraded to a lower level. While in static state, a static environment without turbulence and wall shear stress facilitates firm and steady films adsorbing on the metal surface. The inductive loop in EIS plots under flow condition (Figure 7) should be related to the poor inhibitor film and/or corrosion products on the electrode surface, which is caused by insufficient inhibitor adsorbed on the electrode surface.40  Furthermore, the Rct decreases with the increase of flow velocity, which suggests that a higher flow velocity inhibits the formation of inhibitor film and protective corrosion products. Both the EIS plots and polarization curves of Electrode 11 (minimum flow velocity) and Electrode 26 (maximum flow velocity) indicate that inhibition efficiency decreases with increase of flow velocity. The SEM morphologies (Figures 12 through 14) also indicate incompact corrosion product layer under flow condition. Therefore, hydrodynamics play an important role in the inhibition effect of TAI for the FAC of pipeline steel.

  • The inhibition efficiency of TAI decreases with increasing flow velocity. The reduced inhibition efficiency has been attributed to turbulent flow, high wall shear stress, and secondary flow during the FAC test, all of which act to prevent the adsorption of inhibitor onto the metal surface and/or damages the adsorbed inhibitor film.

  • The inhibition efficiency of TAI at the inner wall was found to be lower than that at the outer wall of the elbow. This difference was found to be the result of the higher flow velocity, wall shear stress, and turbulent kinetic energy at the inner wall, as well as a result of the effect of secondary flow within the elbow. These hydrodynamic parameters affect the concentration boundary layer, thus leading to difference in mass transfer rate of inhibitor and corrosion species to both the inner and outer walls of the elbow. The positional variation in the calculated inhibition efficiencies of TAI was consistent with the distribution of flow velocity, shear stress, turbulent kinetic energy, and secondary flow.

(1)

UNS numbers are listed in Metals and Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.

Trade name.

The authors thank the support of National Natural Science Foundation of China (No. 51101065, 51371086). The authors also thank the support of analytical and testing center of Huazhong University of Science and Technology.

1.
R.
Malka
,
S.
Nešić
,
D.A.
Gulino
,
Wear
262
(
2007
):
p
.
791
.
2.
A.
Neville
,
C.
Wang
,
Wear
267
(
2009
):
p
.
2018
.
3.
X.
Jiang
,
Y.G.
Zheng
,
W.
Ke
,
Corros. Sci.
47
(
2005
):
p
.
2636
.
4.
W.H.
Ahmed
,
M.M.
Bello
,
M. El
Nakla
,
A.
Al Sarkhi
,
H.M.
Badr
,
Nucl. Eng. Des.
267
(
2014
):
p
.
34
.
5.
J.L.
Singh
,
U.
Kumar
,
N.
Kumawat
,
S.
Kumar
,
V.
Kain
,
S.
Anantharaman
,
A.K.
Sinha
,
J. Nucl. Mater.
429
(
2012
):
p
.
226
.
6.
G.A.
Zhang
,
Y.F.
Cheng
,
Corros. Sci.
52
(
2010
):
p
.
2716
.
7.
M.
El-Gammal
,
H.
Mazhar
,
J.S.
Cotton
,
C.
Shefski
,
J.
Pietralik
,
C.Y.
Ching
,
Nucl. Eng. Des.
240
(
2010
):
p
.
1589
.
8.
M.M.
Stack
,
G.H.
Abdulrahman
,
Tribol Int.
43
(
2010
):
p
.
1268
.
9.
R.
Barker
,
X.
Hu
,
A.
Neville
,
S.
Cushnaghan
,
Corrosion
69
(
2013
):
p
.
193
.
10.
W.H.
Ahmed
,
M.M.
Bello
,
M. El
Nakla
,
A.
Al Sarkhi
,
Nucl. Eng. Des.
252
(
2012
):
p
.
52
.
11.
M.I.
Jyrkama
,
M.D.
Pandey
,
Nucl. Eng. Des.
250
(
2012
):
p
.
317
.
12.
K.
Fujiwara
,
M.
Domae
,
K.
Yoneda
,
F.
Inada
,
Corros. Sci.
53
(
2011
):
p
.
3526
.
13.
K.
Sasaki
,
G.T.
Burstein
,
Corros. Sci.
49
(
2007
):
p
.
92
.
14.
D.
John
,
B.
Kinsella
,
S.
Bailey
,
R.
De Marco
,
Corrosion
65
(
2009
):
p
.
771
.
15.
S.
Ramachandran
,
V.
Jovancicevic
,
Corrosion
55
(
1999
):
p
.
259
.
16.
P.C.
Okafor
,
X.
Liu
,
Y.G.
Zheng
,
Corros. Sci.
51
(
2009
):
p
.
761
.
17.
Y.
Chen
,
W.P.
Jepson
,
Electrochim. Acta
44
(
1999
):
p
.
4453
.
18.
X.Y.
Zhang
,
F.P.
Wang
,
Y.F.
He
,
Y.L.
Du
,
Corros. Sci.
43
(
2001
):
p
.
1417
.
19.
M.
Heydari
,
M.
Javidi
,
Corros. Sci.
61
(
2012
):
p
.
148
.
20.
Y.
Chen
,
T.
Hong
,
M.
Gopal
,
W.P.
Jepson
,
Corros. Sci.
42
(
2000
):
p
.
979
.
21.
B.
Wang
,
M.
Du
,
J.
Zhang
,
C.J.
Gao
,
Corros. Sci.
53
(
2011
):
p
.
353
.
22.
W.H.
Li
,
Q.
He
,
S.T.
Zhang
,
C.L.
Pei
,
B.R.
Hou
,
J. Appl. Electrochem.
38
(
2008
):
p
.
289
.
23.
O.O.
Ige
,
R.
Barker
,
X.
Hu
,
L.E.
Umoru
,
A.
Neville
,
Wear
304
(
2013
):
p
.
49
.
24.
C.
Li
,
S.
Richter
,
S.
Nešić
,
Corrosion
70
(
2014
):
p
.
958
.
25.
X.H.
Chen
,
B.S.
McLaury
,
S.A.
Shirazi
,
J. Energy Resources Technol.
128
(
2006
):
p
.
70
.
26.
H.P.
Rani
,
T.
Divya
,
R.R.
Sahaya
,
V.
Kain
,
D.K.
Barua
,
Annals Nucl. Energy
69
(
2014
):
p
.
344
.
27.
G.A.
Zhang
,
L.
Zeng
,
H.L.
Huang
,
X.P.
Guo
,
Corros. Sci.
77
(
2013
):
p
.
334
.
28.
L.
Zeng
,
G.A.
Zhang
,
X.P.
Guo
,
C.W.
Chai
,
Corros. Sci.
90
(
2015
):
p
.
202
.
29.
L.
Zeng
,
G.A.
Zhang
,
X.P.
Guo
,
Corros. Sci.
85
(
2014
):
p
.
318
.
30.
F.G.
Liu
,
M.
Du
,
J.
Zhang
,
M.
Qiu
,
Corros. Sci.
51
(
2009
):
p
.
102
.
31.
D.M.
Ortega-Toledo
,
J.G.
Gonzalez-Rodriguez
,
M.
Casales
,
A.
Caceres
,
L.
Martinez
,
Int. J. Electrochem. Sci.
6
(
2011
):
p
.
778
.
32.
B.
Bozzini
,
M.E.
Ricotti
,
M.
Boniardi
,
C.
Mele
,
Wear
255
(
2003
):
p
.
237
.
33.
K.
Rup
,
P.
Sarna
,
Flow Measurement Instrum.
22
(
2011
):
p
.
383
.
34.
J.D.
Wang
,
T.T
Li
,
M.M.
Zhou
,
X.P.
Li
,
J.M.
Yu
,
Electrochim. Acta
173
(
2015
):
p
.
698
.
35.
Y.
Yan
,
W.H.
Li
,
L.K.
Cai
,
B.R.
Hou
,
Electrochim. Acta
53
(
2008
):
p
.
5953
.
36.
E.S.
Ferreira
,
C.
Giacomelli
,
F.C.
Giacomelli
,
A.
Spinelli
,
Mater. Chem. Phys.
83
(
2004
):
p
.
129
.
37.
C.
Cao
,
Corros. Sci.
38
(
1996
):
p
.
2073
.
38.
A.O.
Yuce
,
B.D.
Mert
,
G.
Kardas
,
B.
Yazici
,
Corros. Sci.
83
(
2014
):
p
.
310
.
39.
M.P.
Desimone
,
G.
Gordillo
,
S.N.
Simison
,
Corros. Sci.
53
(
2011
):
p
.
4033
.
40.
A.
Neville
,
C.
Wang
,
Wear
267
(
2009
):
p
.
195
.
41.
C.
Deslouis
,
M.C.
Lafont
,
N.
Pebere
,
D.
You
,
Corros. Sci.
34
(
1993
):
p
.
1567
.
42.
G.A.
Zhang
,
M.X.
Lu
,
Y.B.
Qiu
,
X.P.
Guo
,
Z.Y.
Chen
,
J. Electrochem. Soc.
159
(
2012
):
p
.
C393
.
43.
G.A.
Zhang
,
C.F.
Chen
,
M.X.
Lu
,
C.W.
Chai
,
Y.S.
Wu
,
Mater. Chem. Phys.
105
(
2007
):
p
.
331
.
44.
Sh.
Hassani
,
K.P.
Roberts
,
S.A.
Shirazi
,
J.R.
Shadley
,
E.F.
Rybicki
,
C.
Joia
,
Corrosion
68
(
2012
):
p
.
885
.
45.
S.-H.
Yoo
,
Y.-W.
Kim
,
K.
Chung
,
S.-Y.
Baik
,
J.-S.
Kim
,
Corros. Sci.
59
(
2012
):
p
.
42
.
46.
X.K.
He
,
Y.M.
Jiang
,
C.
Li
,
W.C.
Wang
,
B.L.
Hou
,
L.Y.
Wu
,
Corros. Sci.
83
(
2014
):
p
.
124
.
47.
J.
Lee
,
J.R.
Selman
,
J. Electrochem. Soc.
130
(
1983
):
p
.
1237
.
48.
M.F.
El-Amin
,
M.
Inoue
,
H.
Kanayama
,
Int. J. Hydrogen Energy
33
(
2008
):
p
.
7642
.
49.
C.V.
Chrysikopoulos
,
P.-Y.
Hsuan
,
M.M.
Fyrillas
,
K.Y.
Lee
,
J. Hazard. Mater.
97
(
2003
):
p
.
245
.
50.
D.
Prieling
,
H.
Steiner
,
Chem. Eng. Sci.
101
(
2013
):
p
.
109
.
51.
H.
Ahmad
,
M.F.
Baig
,
P.A.
Fuaad
,
Eur. J. Mech. B/Fluids
49
(
2015
):
p
.
250
.
52.
B.
Poulson
,
R.
Robinson
,
Int. J. Heat. Mass Transfer
31
(
1988
):
p
.
1289
.
53.
S.R.
Smith
,
Z.F.
Cui
,
Chem. Eng. Sci.
59
(
2004
):
p
.
5975
.
54.
J.B.
Xiong
,
X.
Cheng
,
Y.H.
Yang
,
Int. J. Heat. Mass Transfer
68
(
2014
):
p
.
366
.
55.
F.
Jousse
,
T.
Jongen
,
W.
Agterof
,
Int. J. Heat Mass Tranfer
48
(
2005
):
p
.
1563
.
56.
C.K.
Saha
,
W.T.
Wu
,
G.Q.
Zhang
,
B.
Bjerg
,
Computers Electronics Agriculture
78
(
2011
):
p
.
49
.
57.
M.M.
Enayet
,
M.M.
Gibson
,
A.M.K.P.
Taylor
,
M.
Yianneskis
,
Int. J. Heat. Fluid Flow
3
(
1982
):
p
.
213
.
58.
E.E.
Oguzie
,
Y.
Li
,
F.H.
Wang
,
J. Colloid Interface Sci.
310
(
2007
):
p
.
90
.
59.
D.M.
Ortega-Toledo
,
J.G.
Gonzalez-Rodriguez
,
M.
Casales
,
L.
Martinez
,
A.
Martinez-Villafane
,
Corros. Sci.
53
(
2011
):
p
.
3780
.