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Erosion-corrosion and its mitigation on the internal surface of the expansion segment of N80 steel tube

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  • Corresponding author:

    Xian-kang Zhong    E-mail: zhongxk@swpu.edu.cn

  • Received: 25 February 2020Revised: 6 May 2020Accepted: 7 May 2020Available online: 9 May 2020
  • We investigated erosion-corrosion (E-C) and its mitigation on the internal surface of the expansion segment of N80 steel tube in a loop system using array electrode technique, weight-loss measurement, computational-fluid-dynamics simulation, and surface characterization techniques. The results show that high E-C rates can occur at locations where there is a high flow velocity and/or a strong impact from sand particles, which results in different E-C rates at various locations. Consequently, it can be expected that localized corrosion often occurs in such segments. The E-C rate at each location in the expansion segment can be significantly mitigated with an imidazoline derivative inhibitor, as the resulting inhibitor layer significantly impedes the electrochemical reaction rate. However, we found that this inhibitor layer could not effectively reduce the difference in the erosion rates at different locations on the internal surface of the expansion segment. This means that localized corrosion can still occur at the expansion segment despite the presence of the inhibitor.
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Erosion-corrosion and its mitigation on the internal surface of the expansion segment of N80 steel tube

  • Corresponding author:

    Xian-kang Zhong    E-mail: zhongxk@swpu.edu.cn

  • 1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
  • 2. Department of Electronics Technology, Budapest University of Technology and Economics, Budapest H-1111, Hungary

Abstract: We investigated erosion-corrosion (E-C) and its mitigation on the internal surface of the expansion segment of N80 steel tube in a loop system using array electrode technique, weight-loss measurement, computational-fluid-dynamics simulation, and surface characterization techniques. The results show that high E-C rates can occur at locations where there is a high flow velocity and/or a strong impact from sand particles, which results in different E-C rates at various locations. Consequently, it can be expected that localized corrosion often occurs in such segments. The E-C rate at each location in the expansion segment can be significantly mitigated with an imidazoline derivative inhibitor, as the resulting inhibitor layer significantly impedes the electrochemical reaction rate. However, we found that this inhibitor layer could not effectively reduce the difference in the erosion rates at different locations on the internal surface of the expansion segment. This means that localized corrosion can still occur at the expansion segment despite the presence of the inhibitor.

    • Erosion-corrosion (E-C), considered to be one of the greatest safety threats in the petroleum and natural gas industry, causes pipeline thinning, leakage, and even perforation, which result in serious economic losses and can even have catastrophic consequences. The expansion of the internal diameter of a tube is often designed for a certain number of wells for which some production parameters must be adjusted. For example, tubing with various internal diameters may be used in one well due to the need to adjust the flow and production rates. Additionally, a threaded connection can cause changes in the internal diameters of the tube. For example, the internal structure of the America Petroleum Institute thread connection is usually characterized by different internal diameters [1]. When fluid flows through a tubing segment with variable diameters, the hydrodynamic parameters, such as the flow velocity or shear stress on the internal surface, obviously change [24], especially when solid particles are carried in the transmission medium, which results in serious E-C damage in these segments. As such, changes in the hydrodynamics parameters can cause further mass loss, which poses a huge safety risk. Therefore, it is important to understand E-C behavior and develop corrosion inhibition strategies for pipeline segments with variable diameters to ensure safe production and effective management in the petroleum industry.

      E-C is considered to be a result of the coupling effect between corrosion, originating from the electrochemical reaction, and erosion, which is a mechanical effect. Owing to the coupling effect between erosion and corrosion [56], the weight loss of materials caused by E-C is usually higher than the sum of the material loss from electrochemical corrosion and erosion [78], i.e., corrosion can enhance erosion and vice versa [510]. Corrosion enhanced erosion is mainly reflected in the following aspects: it increases surface roughness [6,10], which generates corrosion products that easily fall off by erosion, thus weakening the grain and phase boundaries [1011]. Erosion can also accelerate the corrosion process by changing the mass-transfer process, which results in the elimination of corrosion products and increases in the surface roughness of the metal [6,10,12].

      In recent decades, the E-C mechanism has been extensively studied [1328], corresponding models have been established, and the effects of fluid dynamics parameters on E-C have also been discussed [1314]. Postlethwaite et al. [1516] proposed that the total loss of material by E-C has two parts, one is mechanical erosion and the other electrochemical corrosion. The effect of the mass-transfer process under turbulent conditions on E-C behavior has also been investigated and a corresponding prediction model successfully established [1519]. Nesic et al. [2021] explored the effects on E-C of fluid dynamics characteristics in multi-phase or single-phase flow in a tube with variable diameters. These authors divided E-C into four components: (1) corrosion originating from an electrochemical reaction, (2) erosion caused by a mechanical effect, (3) erosion-enhanced corrosion, and (4) corrosion-enhanced erosion [21]. They also discussed the synergy between erosion and corrosion. Rajahram et al. [22], Neville et al. [23], and Zhang et al. [24] determined the interaction between erosion and corrosion by quantitative analysis, and then discussed the effects of the material properties, fluid dynamics, and environmental factors on the electrochemical and mechanical factors of E-C [2224]. In recent decades, the development of E-C research has been rapid [2528]. For example, it has been proposed that COMSOL Multiphysics software is used with the stress-dependent erosion equation to predict the E-C of pipelines used in the oil and gas industry [26]. In addition, Zeng et al. [10,2728] studied the effect of thioureidoimidazoline on E-C behaviors and the four E-C components at pipe elbows by combining weight-loss measurement and electrochemical techniques.

      In this work, we studied the E-C behaviors in an expanding tube segment using the electrode-array technique, electrochemical impedance spectroscopy (EIS), linear polarization resistance (LPR), weight-loss measurement, computational fluid dynamics (CFD) simulation, and surface analysis. In addition, we investigated the use of an inhibitor at the expansion segment to mitigate E-C behaviors.

    2.   Experimental
    • We used N80 tubing steel as the material in this study, the elemental composition of which is listed in Table 1. For the electrochemical measurements, we used a cylindrical electrode, with an exposed area of 0.196 cm2. For weight-loss measurement, we used a sample with an exposed end area of 1 cm2, which is much larger than that of the samples used in the electrochemical measurements, because a more obvious weight loss can be observed when using a bigger exposed area. Before the experiment, we ground the end surface of the electrodes/samples using 800-grit silicon carbide sandpaper (electro-coated silicon carbide waterproof abrasive paper made by SuiSun Company Ltd., China), rinsed them in turn with distilled water and ethanol, and dried them in N2 gas flow.

      CSiMnPSCrMoNiNbVCuFe
      0.240.220.1190.0130.0040.0360.0210.0280.0060.0170.019Bal.

      Table 1.  Chemical composition of N80 steel wt%

      The test solution was prepared based on the ionic components of formation water from a Chinese oilfield, the corresponding chemical composition of which is listed in Table 2. The term “formation water” refers to the water produced along with the oil and gas from the wellbore. Prior to the test, the solution was first purged using a continuous CO2 (99.95%) gas flow for 24 h to remove O2 from the solution. At the beginning of the test, the solution pH value was 6.14. During the test, the evolution of the pH was not monitored. The CO2 gas-purging continued during the whole test period to saturate the solution with CO2 and thereby prevent ingress of O2 into the solution. The sand content in the solution was 0.15vol%, and the diameter of the sand particles ranged from 300 to 500 μm.

      NaClKClCaCl2Na2SO4MgCl2·6H2ONaHCO3
      17.240.540.430.370.503.98

      Table 2.  Chemical composition of test solution g/L

    • A homemade loop system was employed to investigate the E-C behaviors at the expansion segment, a detailed description of which can be found in our previous work [29].

      First, we filled a 25-L tank with the solution, and then circulated the solution using a pump (model IHG65-100I, China. Rated power of 3 kW and maximum flow rate of 50 m3/h), which operated throughout the experiment. In this loop system, the flow velocity of the solution was adjusted by adjusting the rotational speed of the pump. The flow velocity of the solution was set to 3 m/s, which was real-time measured using a magnetic flow meter (NRLD-DN50, Nanjing Ruiyi Automation Co., Ltd., China). The experiment segment was made of polytetrafluoroethylene and the other pipes were polycarbonate tubes with an internal diameter of 50 mm. Fig. 1 shows a schematic diagrams of the internal structure of the test segments, with one used for electrochemical measurements and the other for weight-loss measurement. The dimensions of the test segments are also shown in Fig. 1. To obtain an obvious weight loss during a time-limited test period, a larger surface area is required. Therefore, the number of samples used in the weight-loss measurement was smaller than that used in the electrochemical measurements. After pretreatment, the electrodes/samples were installed in the test segment using epoxy resin. The most important requirement for the installation of electrodes/samples is that exposed surface be consistent with the internal surface of pipelines. Along the direction of fluid flow, we placed 14 electrodes in the test segment to enable electrochemical measurement. For the weight-loss measurements, we used just 10 samples. To perform the electrochemical measurements in the E-C loop system, we also introduced counter and reference electrodes, which were installed in the test segment, and are labeled electrodes 15 and 16, respectively, in Fig. 1(a).

      Figure 1.  Schematic diagrams of test segments (unit: mm) for (a) electrochemical and (b) weight-loss measurements.

    • For the EIS measurements, we used a classic configuration with three electrodes and a commercial system (CS350 system, Wuhan Corrtest Instruments Corp. Ltd., China). This three-electrode configuration was mounted in the test segment, with each N80 steel electrode acting as a working electrode, a graphite rod as the counter electrode, and a saturated calomel electrode as the reference electrode. For comparison, both the EIS and LPR measurements were performed at each working electrode in the E-C experiment. For the EIS measurements, data were collected at frequencies ranging from 10000 to 0.1 Hz using peak-to-peak 5-mV sinusoidal perturbation. Five points per decade were collected and all the EIS measurements were performed at open circuit potential (OCP). As it turned out, these frequency range settings were sufficient for determining the parameters associated with corrosion [27,30]. As such, all the measurements for the 14 electrodes were finished quickly. After the EIS measurements, LPR measurements were performed at each working electrode. The potential scanning range was from −5 to 5 mV vs. OCP, and we used a sweeping rate of 0.125 mV/s. All the EIS and LPR measurements were performed after the E-C test for 6 h. The EIS data were fitted using Z-view software, and the LPR data were analyzed using C-view software. To guarantee reproducibility, all the electrochemical measurements were repeated three times. The EIS spectrum used in this work was based on data from one of three parallel experiments, whereas the parameters fitted from the EIS data are the average values of the results obtained in the three parallel experiments.

    • The weight-loss measurements were used to obtain the total E-C rate for each sample. As shown in Fig. 1(b), ten samples were installed in the test segment to investigate weight loss. The experimental conditions were the same as those used in the electrochemical measurements. Prior to the experiments, the samples were weighed on a balance with an accuracy of 0.0001 g (ML204/02 analytical balance made by Meter Toledo Company, Switzerland). After measuring the weight loss, the samples were put into a Clarke’s solution (ASTM G103) [31] and brushed to remove corrosion products. Then, the samples were rinsed with ethanol and dried in N2 gas flow. Finally, the samples were weighed again using the analytical balance. Accordingly, the weights before and after the experiment were determined. All the measurements lasted for 6 h, with the experimental temperature maintained at 50°C. Each weight-loss measurement was repeated three times. The corrosion rate presented in this paper is the average value of the results from three parallel experiments.

    • The CFD simulation of this study was implemented using ANSYS Fluent 16.0. Based on the practical dimensions of the test segments, we constructed a geometric model using the pre-processing software ICEM CFD 16.0. We set the size of the meshes to 3–5 mm. The simulation involved the following steps.

      (1) To simulate the distribution of sand particles in the expansion section, we used a liquid flow model. The inlet flow velocity was set to 3 m/s and the outlet pressure to 101325 Pa.

      (2) The Reynolds number, which we calculated based on the flow velocity (3 m/s) and the dimensions (e.g., 50 mm in diameter) of the expansion segment, was 150000. This value is much higher than 4000, which suggests that the fluid in the test segment was turbulent. Therefore, we used the $\kappa $$\varepsilon $ turbulence model to simulate the flow of the solution. We set the following necessary parameters: turbulent kinetic energy ($\kappa $), 1 m2/s2; turbulent dissipation ($\varepsilon $), 1 m2/s3; turbulence intensity, 10%. The simulation was considered to have converged when the normalized residuals of the $\kappa $$\varepsilon $ turbulence equation were below 0.0001.

      (3) To obtain the contours of the erosion rate in the expansion section, we used the discrete phase model (DPM). The mass flow rate for the sand particles was 13 g/s, which was determined based on a sand loading of 1.5vol‰ in the loop system during the E-C experiment. The erosion rate function in the DPM, as given by Edwards et al. [32], is as follows:

      where Rerosion represents the erosion rate, i is the number of particles, i = 1 means the first particle, n is the total number of particles, mi is the quality of particle i, C(di) is a function of particle diameter, di is the diameter of particle i, $f({\alpha _i})$ is a function of the impact angle, αi is the angle of particle i, vi is the velocity of particle i with respect to the wall, $b({v_i})$ is a function of the particle relative velocity, and Ai,face is the area of particle i erosion on the wall.

    • After the test in the loop system, we extracted several representative electrodes/samples from the test segment, and dried them in N2 gas flow. The micro morphologies of the electrodes/samples were examined using a ZEISS EVO MA 15 scanning electron microscope (SEM, Germany) and the components of the corrosion products were determined using a VG Multilab2000 X-ray photoelectron spectroscopy (XPS, America).

    3.   Results and discussion
    • Fig. 2 shows the EIS data obtained at each working electrode at various locations in the expansion segment. In addition, the electrode location and flow direction are shown in the inset in Fig. 2. The figure clearly shows that each Nyquist plot is a capacitive semicircle and an inductive loop. The capacitive semicircle can be attributed to the charge-transfer process at the interface of the solution and metal surface, and the inductive loop is considered to be related to the adsorbed intermediate products generated during the electrode corrosion process [30,3334]. Based on the size of the capacitive semicircle, these EIS data can be roughly categorized into three groups, with the first group consisting of electrodes 1–5 and 9–11. The sizes of the capacitive semicircles of these electrodes are very similar, which suggests that their corrosion rates are similar as well. The second group includes electrodes 7 and 8, which are located at the slope region and the starting end of the pipe with a bigger diameter, respectively. The diameters of the capacitive semicircles of both these electrodes are larger than those of the first group, which yielded lower corrosion rates for both electrodes than those of the other electrodes. In the last group of electrodes (electrodes 6 and 12–14), the sizes of the capacitive semicircles are smaller than the electrodes in the first and second groups, which indicates higher corrosion rates.

      Figure 2.  Typical Nyquist plots of electrodes at different locations. The insets are the schematic diagram of the distribution of electrodes and the equivalent ciruit for EIS fitting.

      Based on the Nyquist plots (Fig. 2), we proposed equivalent circuits shown in the inset in Fig. 2 for fitting the EIS data. In this circuit, Rs represents the resistance of the solution, CPE is the constant phase element, which differs from the ideal pure capacitance, Rct is the charge-transfer resistance, RL is the inductance resistance, and L is the inductance. Fig. 2 also shows the plot of the fitted data, for which the related parameters are listed in Table 3, where Y0 is the capacitance of CPE and n is an exponent related to the non-uniform distribution of current resulting from surface defects or surface roughness [35]. As noted above, CPE differs from the pure capacitance. If n = 1, CPE is equal to the pure capacitance, whereas if 0 < n < 1, CPE does not reflect an ideal pure capacitance.

      Electrode No.Rs / (Ω·cm2)Y0 / (Ω−1·cm−2·sn)nRct / (Ω·cm2)L / (H·cm−2)RL / (Ω·cm2)
      16.020.000490.86125.712.4928.16
      25.960.000480.86125.611.8028.31
      35.410.000410.88124.014.9026.18
      46.150.000500.86120.911.0627.99
      56.520.000510.85119.912.0529.72
      66.810.000420.87103.9 9.5623.89
      76.420.000400.86131.215.4815.48
      86.440.000390.87132.615.6027.12
      95.530.000480.87120.5 9.4424.21
      104.960.000410.88117.812.5633.03
      116.090.000360.89114.512.1530.12
      125.700.000480.87107.5 9.4423.70
      134.970.000460.89108.012.3522.96
      146.900.000410.87108.4 8.6325.98

      Table 3.  Electrochemical parameters fitted from the EIS data (shown in Fig. 2) of each electrode

      The Rct value of an electrode is recognized as being reversely proportional to the corrosion rate [36]. Therefore, it is important to analyze the distribution of Rct in the expansion segment. From Table 3 and Fig. 3(a), we can see that the smallest Rct occurred at electrode 6, and hence the maximum corrosion rate is present. The average Rct values of electrodes 7 and 8 are 131.2 and 132.6 Ω·cm2, respectively, which are larger than those of the other electrodes. This indicates that these electrodes had lower corrosion rates than the other electrodes.

      Figure 3.  Different parameters for the electrodes: (a) Rct, (b) Rp, (c) corrosion rate calculated from Rp, and (d) electrode distribution at the test segment. The error bars indicate the standard deviation.

      For comparison, we also performed LPR measurements and obtained polarization resistance (Rp), as shown in Fig. 3(b). Obviously, the Rp value of each electrode is in good agreement with its corresponding Rct. To determine the corrosion rate at each location, we calculated the current density based on Rp using the Stern–Geary equation [36]:

      where B is the constant of proportionality (V), which is related to the anodic Tafel and cathodic Tafel slopes; in this study, we used 26 mV as the B value [36]; icorr represents the corrosion current density (A/cm2). According to Faraday’s law of electrolysis [37], the corrosion rate (v, mm/a) can be obtained using the following equation:

      where M represents the molar mass (g/mol) of Fe, ρFe is the density of pure Fe (g/cm3), F is the Faraday constant (26.8 A·h), and n is the number of electrons transferred in the Fe dissolution reaction (n = 2).

      Fig. 3(c) shows the corrosion rates of the electrodes at various locations in the expansion segment. We can see that the corrosion rates of electrodes 7 and 8 are lower than those of the other electrodes. Among all the electrodes, the corrosion rates of electrodes 6 and 11–14 are higher. These results show that there are huge differences among the corrosion rates of the electrodes, which suggests that localized corrosion may be occurring in such expansion segments. In fact, most localized corrosion such as local thinning is observed in tube segments with variation in their diameters, e.g., in segments with a threaded connection [3839]. Therefore, these findings are in agreement with those observed in the field.

      The electrochemical results only reveal the corrosion rate distribution at the expansion segment, which means that the E-C rate distribution is still unknown in this experiment. Therefore, we performed weight-loss measurements to determine the E-C rate, the results of which are presented in the following section.

    • After measuring the weight loss, the E-C rate (ve-c) can be calculated as follows [40]:

      where Δm is the difference in the weight of the sample before and after the test in the loop system (g), ρ is the density of N80 steel (g/cm3), A is the exposed area of the sample in the test solution (cm2), and ∆t is the time period of the E-C test (h).

      Fig. 4 shows the E-C rates of samples 1–10, as determined based on the weight-loss method. We note that the E-C rate obtained by the weight-loss measurement includes both the electrochemical corrosion rate and the erosion rate. The E-C rates of samples 5 and 7–10 are obviously higher than those of the other samples. Combined with the EIS, LPR, and weight-loss measurement results, we can draw the following conclusions: (1) localized corrosion may occur at the expansion segment, given the presence of huge differences in the E-C rates at various locations, (2) the lowest E-C rate occurred near the end of the pipe (sample 6) with a bigger internal diameter where the slope and the pipe meet, and (3) the highest E-C rate occurred in sample 10, likely because of the strong impact of the sand particles. To further explain the differences in the E-C rate at various locations of the expansion segment, we consider our CFD simulation results in the following section.

      Figure 4.  (a) the E-C rates of samples 1–10 obtained by weight-loss measurement and (b) the electrode distribution at the test segment. The error bars indicate the standard deviation

    • To understand the differences in the E-C rates at various locations of the expansion segment, we conducted a CFD simulation. Fig. 5 shows the contours of the flow velocity and erosion rate along the flow direction, which indicates that the expansion changes the distribution of flow velocity, i.e., the flow velocity distribution at the expansion segment is completely different from that elsewhere. This variation in the local flow velocity field leads to huge changes in the trajectories of the sand particles being carried by the fluid. Here, the likelihood of hitting the inner wall surface of the segment differs for sand particles at different locations, which results in a different erosion rate at the expansion segment (Fig. 5(b)).

      Figure 5.  Three-dimensional images of (a) flow velocity distribution and (b) erosion rate distribution along the test section.

      Figure 6.  CFD simulation data: (a) flow velocities and (b) erosion rates at the corresponding locations of electrodes used in electrochemical measurements.

      The CFD simulation results suggest that the erosion rates or velocities at various locations are quite different due to their different geometries. To clarify the relationship between the E-C behaviors and the hydrodynamic parameters of the expansion segment, Figs. 6 and 7 show the flow velocities and erosion rates simulated using CFD. Fig. 6 shows the velocity and erosion rate of each electrode used in the electrochemical measurements, and Fig. 7 shows the flow velocity and erosion rate of each sample used in the weight-loss measurements. We can clearly see that the highest flow velocity occurred at electrode 6 (sample 5), and the lowest at electrode 8 (sample 6). It also shows that the erosion rates of electrodes 12–14 (samples 9‒10) were higher than those of the other electrodes. In contrast, the erosion rates of electrodes 7, and 8 and sample 6 (0 kg·m−2·s−1, i.e., no sand particles hit these locations) were lower than those of the other electrodes/samples. The CFD simulation results are basically in agreement with the weight-loss and electrochemical measurements.

      Figure 7.  CFD simulation data: (a) flow velocities and (b) erosion rates at the corresponding locations of samples 1–10 used in weight-loss measurement.

      We also found the E-C rate to be positively correlated with the flow velocity and erosion rate (calculated using CFD). For instance, the corrosion rates are higher at electrodes 6 and 12–14 (the E-C rate of samples 5, 9, and 10), where the flow velocities or erosion rates are relatively high. The lowest corrosion rate occurs at electrode 8 (the E-C rate of sample 6), where there are relatively low flow velocities and erosion rates (Figs. 4, 5, 6, and 7). Accordingly, the distribution of the E-C rate at the expansion segment is consistent with the distribution of the flow velocity and sand-particle erosion. These findings match those of previous studies [10,2728,30].

    • Fig. 8 shows the chemical structure of the imidazoline derivative inhibitor used in this study. The synthesis of this inhibitor is described in previous work [41]. To generate a more obvious inhibition effect, we used a relatively high content of 100 mg/L. With the inhibitor, we found the diameter of the capacitive loop of every electrode to be much bigger than that in the absence of the inhibitor, which means that a protective film formed on the electrode surface (Fig. 9(a)). Furthermore, in the presence of the inhibitor, all the capacitive loops are nearly all overlapped and the shape of each Nyquist plot is one capacitive semicircle. In this case, we propose an equivalent circuit, as shown in Fig. 9(b), for fitting the EIS data, the relevant parameters of which are listed in Table 4. This clearly shows that in the presence of the inhibitor, the Rct value of each electrode greatly increases in comparison with that without the inhibitor, which demonstrates that corrosion at the expansion segment can be significantly inhibited. Fig. 10 shows a comparison of the corrosion rates obtained by electrochemical measurements with and without the inhibitor, and Fig. 11 shows the E-C rates obtained by weight-loss measurement.

      Electrode No.Rs / (Ω·cm2)Y0 / (Ω−1·cm−2·sn)nRct / (Ω·cm2)
      19.420.000120.774289
      26.280.000120.774232
      34.970.000120.764098
      45.410.000110.764018
      55.030.000110.774052
      65.630.000120.773904
      76.550.000110.774457
      85.670.000120.764508
      95.280.000110.764407
      1012.520.000130.784350
      116.770.000120.774173
      128.920.000120.784244
      1310.480.000120.774390
      148.270.000120.774324

      Table 4.  Electrochemical parameters fitted from the measured EIS data (shown in Fig. 9) of each electrode in the presence of the inhibitor

      Figure 8.  Chemical structure of the inhibitor used in this work.

      Figure 9.  (a) Typical Nyquist plots of electrodes at different locations with 100 mg/L of inhibitor. (b) Equivalent circuit for EIS fitting in the presence of the inhibitor.

      Figure 10.  (a) Corrosion rates calculated from Rp of each electrode with and without inhibitor, and (b) electrode distribution at the test segment. The error bars indicate the standard deviation

      Figure 11.  (a) E-C rate of each sample with and without inhibitor obtained from weight-loss measurement, and (b) the electrode distribution at the test segment. The error bars indicate the standard deviation

      With the inhibitor, the corrosion rates of electrodes 1–14 are much lower than those without the inhibitor (Fig. 10). The other significant characteristic associated with the inhibitor is that the difference in the corrosion rates is greatly reduced compared with that without the inhibitor. That is, the electrochemical corrosion rates of electrodes 1–14 are similar, although a slight difference can still be seen in Fig. 10. This indicates that the inhibitor not only inhibits the corrosion of the expansion segment, but also reduces the difference in the corrosion rates of all the electrodes at different locations.

      Fig. 11 shows the E-C rates of samples 1–10 obtained by weight-loss measurement with and without the inhibitor. Like the results obtained from the electrochemical measurements, the E-C rate of each sample with the inhibitor is much lower than that without the inhibitor. We estimate that the E-C rate of each sample decreases more than tenfold, which means that the E-C rate can also be greatly mitigated by the use of an inhibitor. However, the differences in the E-C rates among all the samples could not be significantly reduced. That is, a huge difference remains between the E-C rates of samples 5 and 6 in the presence of the inhibitor. This indicates that the imidazoline derivative inhibitor can mitigate the E-C rate, but it cannot effectively reduce the difference in the erosion rates at different locations of the expansion segment. As such, the inhibition effect on the localized E-C caused by the impact of sand particles is relatively limited.

      Fig. 12 shows SEM images of the micro morphologies of a representative electrode (electrode 13) after the E-C experiments with and without the inhibitor. We can see in the images that the surface of electrode 13 with the inhibitor is very smooth and almost no corrosion products appear at the electrode surface (Fig. 12(a)). Some fine scratches that formed during the grinding process can be observed. In contrast, obvious corrosion products can be observed on the electrode surface when no inhibitor was added. This indicates that corrosion on the electrode surface was well suppressed by the inhibitor.

      Figure 12.  SEM surface morphologies of electrode 13 after E-C test (a) with and (b) without the inhibitor.

      To check for the presence of the corrosion inhibitor on the exposed surface of the electrode, we used XPS to determine the composition of the exposed surface of the electrode. As shown in Fig. 13, we obtained the XPS spectra of the N, O, and Fe elements on the electrode surface after the E-C test in the presence of the inhibitor. These XPS spectra were divided into several peaks to obtain the exact ionic states of the elements. The peak area of each component is listed in Table 5, which clearly shows that N element was present on the electrode surface. According to the peak divisions, the XPS spectrum of N 1s can be split into two peaks, i.e., the peak at 398.7 eV can be ascribed to C−N/C=N and that at 399.8 eV to the presence of NH/NH2. As shown in Fig. 8, these components could be from the imidazoline ring and amino-group [4243]. In any case, these results indicate the existence of the inhibitor on the surface of the samples and electrodes. The O 1s XPS spectrum clearly indicates that the peaks at 529.6, 531.0, and 531.9 eV could be ascribed to O2−, OH and H2O, respectively. The Fe 2p3/2 XPS spectrum can be divided into three peaks: the metal Fe peak at 706.5 eV, the Fe2O3 peak at 710.1 eV, and the FeOOH peak at 711.7 eV [44]. We note that the presence of iron oxides may be caused by contact with air when the sample was taken out of the loop system. XPS analysis indicates that the inhibitors had successfully adsorbed onto the electrode surface.

      Figure 13.  High resolution XPS spectra of the electrode surface after E-C test with 100 mg/L inhibitor: (a) N 1s; (b) O 1s; (c) Fe 2p3/2.

      SpectraComponentPosition / eVPeak area / %
      N 1sC−N/C=N398.740.97
      NH/NH2399.859.03
      O 1sO2−529.624.30
      OH531.021.73
      H2O531.953.97
      Fe 2p3/2Fe706.515.77
      Fe2O3710.143.91
      FeOOH711.740.32

      Table 5.  Binding energies and specifications of the elements by XPS analysis of electrode surface after E-C test with 100 mg/L inhibitor

      In general, the corrosion rates initiated by the electrochemical reaction are influenced by the mass-transfer and charge-transfer processes. It has been acknowledged that a high flow velocity could enhance the mass-transfer process. Moreover, the high erosion rate caused by sand particles can accelerate the removal of corrosion products and metallic material [30]. Consequently, the corrosion rates of electrodes 6 and 11–14 (the E-C rates of samples 5 and 7–10) are higher than those of the other electrodes (samples), which leads to a high localized E-C rate at the expansion segment. However, this E-C behavior can be mitigated in the presence of an inhibitor. It is well known that an adsorbed and protective layer on the steel surface can form when an imidazoline-type inhibitor is added to a corrosive aqueous solution [4547]. This layer can impede the penetration of aggressive ions from the solution into the steel surface, which greatly decreases the E-C rate.

      Although the E-C rate can be significantly decreased by the use of an imidazoline derivative, the difference in the E-C rates of various samples cannot be effectively decreased. This can be attributed to the ineffective resistance of the adsorbed inhibitor layer to the impact of sand particles.

    • The E-C rate is known to be the sum of the pure corrosion rate, pure erosion rate, erosion-enhanced corrosion rate, and corrosion-enhanced erosion rate [10,21]. In this work, we determined the E-C rate of each sample using the weight-loss method. We determined the corrosion rate, which consists of the pure and erosion-enhanced corrosion rates, using electrochemical techniques, i.e., we calculated the corrosion rate from Rp or Rct.

      According to Eq. (1), we determine the erosion rate by the flow velocity, impact angle, and quantity of solid particles. This can explain why the CFD simulation results show that the erosion rate at the back (with a large diameter) of the expansion segment is higher than that at the front (with a small diameter), as shown in Figs. 57. Although the flow velocity at the front is higher than that at the back, the front of the expansion segment is only slightly rubbed by a small number of particles. However, the sudden change in the pipe diameter leads to sudden changes in the flow pattern of the fluid, which alters the motion tracks of the solid particles, so that more solid particles hit the pipe wall at various angles at the back of the expansion segment. The higher erosion rate means that the steel experiences more and stronger impact from sand particles. In addition, we can easily deduce that more active sites would be present on the steel surface, which could accelerate the electrochemical reaction.

      It is a common sense that for the same loop system, a higher velocity occurs at the segment with a smaller diameter, whereas a lower velocity occurs at the segment with a larger diameter. The CFD simulation results confirm this statement, as shown in Figs. 57. In general, higher velocity generates a higher corrosion rate because the flow accelerates the mass-transfer process [29]. However, the corrosion rate calculated from Rp in Fig. 3(c) shows the opposite tendency, i.e., that the corrosion rate at the back of the segment is higher than that at the front. This seems contradictory. However, as we noted above, the corrosion rate measured using the electrochemical technique consists of the pure and erosion-enhanced corrosion rates. At the back of the test segment, the erosion is much more significant than that at the front, which results in a higher electrochemical reaction rate. This means that the erosion-enhanced corrosion rate greatly increases. Therefore, the corrosion rate at the back of the test segment is higher than that at the front, as shown in Fig. 3.

      Using an inhibitor is a cost-effective way to mitigate the corrosion rate of Fe-alloy tubes in the oilfield. In this work, we also confirmed that the corrosion rate at each test segment location can be mitigated using the selected inhibitor. In particular, the difference in the corrosion rates of all the electrodes was greatly reduced. The total E-C rate was also found to decrease dramatically with the addition of the inhibitor. However, the big difference in the E-C rates of all the samples remained, as shown in Fig. 11. This may be due to the inhibitor layer being unable to effectively prevent the steel from the impact of the sand particles. Accordingly, the low erosion-rate-inhibition efficiency may be of great concern when using this inhibitor to protect Fe-alloy tubing in environments containing sand particles.

    4.   Conclusions
    • (1) A higher E-C rate occurs at the back (with a large diameter) of the expansion segment than at the front (with a small diameter) because of the enhanced impact from sand particles due to the changes in the impact angle and quantity of solid particles, despite the lower flow velocity at the back of the segment.

      (2) The corrosion rate measured using electrochemical techniques consists of the pure and erosion-enhanced corrosion rates. A higher erosion rate at the back of the expansion segment can accelerate the erosion-enhanced corrosion rate. This also explains why the corrosion rate at the back is higher than that at the front part.

      (3) In the expansion segment of the tube, different E-C rates occur at different locations. Therefore, it follows that localized corrosion can more easily occur at such segments, as compared with that in a straight tube.

      (4) The E-C rate at each location of the expansion segment greatly decreased in the presence of an imidazoline derivative inhibitor, with the resulting inhibitor layer significantly impeding the electrochemical reaction rate. However, this inhibitor layer could not effectively reduce the difference in the erosion rates at various locations of the expansion segment. This means that localized corrosion could still occur in the expansion segment, despite the presence of the inhibitor.

    Acknowledgements
    • This work is financially supported by the 111 Project (No. D18016), the Application and Fundamental Research of Sichuan Province, China (No. 2017JY0171), and the Scientific and Technological Innovation Team for the Safety of Petroleum Tubular Goods in Southwest Petroleum University (No. 2018CXTD01).

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