1 Introduction

The aggressive environment is a big challenge to the gas exploitation in the west of China, which is characteristic of extra high temperature, high salinity and high CO2 partial pressure [1]. In the presence of salinity brine, CO2 at high temperature and elevated pressure can form highly aggressive medium with low pH, which would increase the risk of tube leakage and catastrophic accident, leading to huge economic loss [2]. Accordingly, it is essential to evaluate CO2 corrosion risk of well tubes in the exploitation process.

In fact, CO2 corrosion of well tubes is a quite complex process, which involves multiple chemical and electrochemical reactions. Its corrosion mechanism and corrosion rate can be affected by many factors, such as CO2 partial pressure, temperature, pH and flow velocity [3,4,5,6]. Among the above factors, the flow velocity is the most critical parameter, especially for determining the suitability of the tubes [7, 8]. Plenty of failure cases of stainless steel (SS) caused by the flow velocity had been reported on well-established facts [9,10,11,12,13]. However, the previous researches mainly focused on low CO2 partial pressure (< 2 MPa), low temperature (< 100 °C) and low salinity environments (Cl− concentration < 104 mg/L) [14,15,16,17]. The main reasons of the aforementioned may be due to the big challenge of the equipment and the testing methods.

To narrow the research gap, in recent years, the technology of rotating cage, which normally provides controlled mass transfer in flow for electrode kinetic studies, has developed as a compact, hydrodynamic experimental method [18]. Moreover, the maximum flow velocity is limited owing to the reliability of the equipment. Accordingly, the flow loop is designed to approach understanding the corrosion process under flow conditions [19]. However, compared to that of rotating cage, the flow loop is less convenient, efficient and more difficult to conduct. Moreover, a high-efficiency experimental method and design resources from the materials genome initiative (MGI) have been proposed to combine the merit of both the rotating cage and the flow loop technology.

The MGI can compute, produce and construct fundamental databases. It combines high-efficiency theoretical calculations with the inclusion of the functions for prediction, screening and optimization of materials by data mining from existing database [20]. The objective is to accelerate the design of new materials in an unprecedented scale and rate with low cost [21]. The design of using the high-efficiency experimental method is one of the modules of the MGI, which can be regarded as a preparation technique. This method and design have been applied to many fields and supported by many open databases [22,23,24], such as diffusion multiple approaches [25], thin-film deposition [26], the development of cladding materials [27] and the measurement of mechanical properties of samples [28].

Therefore, in the present study, the selected HP-13Cr SS, having a higher pitting corrosion resistance and excellent mechanical properties, is used in the down-hole strings. A new high-efficiency experimental method is established, which shows a relatively high efficiency, by combining the rotating cage and flow loop to conduct the various flow velocities testing in the extremely aggressive environment. Furthermore, the effect of the height, the placement and the reliability of the bump-shaped electrodes are discussed by using the computational fluid dynamics (CFD) simulation. In addition, a highly accurate correlation between the theoretical simulation and experimental results is supported by the founding of the weight loss measurement.

2 Experimental

2.1 Material and Solution

HP-13Cr SS, with its composition (wt%) of 0.003 C, 0.15 Si, 0.51 Mn, 12.77 Cr, 2.19 Mo, 0.002 S, 0.02 P, 0.047 Cu, 5.36 Ni, 0.014 V, 0.037 Al and Fe balance, is used for the following experimental study.

The testing electrolyte, simulating the formation water, was prepared using analytical grade reagents and deionized water (18 MΩ/cm in resistivity). Its chemical composition (mg/L) is 189 HCO3−, 128000 Cl−, 430 SO42−, 8310 Ca2+, 561 Mg2+, 6620 K+ and 76500 Na+.

2.2 Weight Loss Measurement

The immersion experiments of the HP-13Cr SS in the prepared formation water were carried out for 30 days in a high-temperature and high-pressure dynamic stainless autoclave with a rotating cage installed. The rotating cage is designed to imitate actual flow conditions, with rotation speed up to 810 rpm (corresponding to a calculated flow speed of 3 m/s over the specimen surface).

In general, the first critical step of application of the high-efficiency experimental design to optimize multiple flow velocities is the design of the electrodes used in the highly aggressive formation water. The schematic diagram of the bump-shaped electrode is shown in Fig. 1 and marked the surface of the bump-shaped electrode from No. 1 to No. 6 clockwise direction. In particular, No. 6 surface was toward the center axis when the bump-shaped electrode was fixed at the rotate cage. Both ends of the bump-shaped electrodes are covered with polytetrafluoroethylene in order to prevent corrosion. Moreover, the surface covered with polytetrafluoroethylene can be used as the reference surface to evaluate the thickness loss of each electrode surface encountering varied flow velocities.

Fig. 1
figure 1

Schematic of the bump-shaped electrode

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After the immersion experiments, the specimens covered with polytetrafluoroethylene were taken out of the formation water and rinsed with deionized water and anhydrous ethanol, respectively. Three aforementioned parallel specimens were descaled in the solution consisting of nitric acid (100 mL, ρ is 1.42 g mL−1), hydrofluoric acid (20 mL, ρ is 1.15 g mL−1) and deionized water (880 mL) at room temperature according to the ASTM standard G1-03 [29] to remove the sales film and polytetrafluoroethylene from the electrode surface.

Subsequently, the thickness loss of each surface of the bump-shaped electrode was obtained from the super deep scene 3D microscope (VHX-5000, Japan). The super deep scene 3D microscope has the function of the macroscopic mosaic. The outline of the surfaces both covered and uncovered by polytetrafluoroethylene could be simultaneously achieved and overlapped. As a result, the corrosion rate (Vc) can be calculated using the following equation:

$$V_{\text{c}} = \Delta H/t,$$
(1)

where \(\Delta H\) is the thickness loss of each surface of the bump-shaped electrode (mm), t is the immersion time. To ensure reproducibility, each measurement was repeated at least three times. Average corrosion rates with error bars were calculated based on three parallel specimens for each test.

2.3 Fluent Model Simulation

Numerical simulation of the flow field was conducted on the commercial software commercial CFD package, FLUENT, which is based on the finite volume approach. The SST k–ω turbulent model is used for approaching the governing equations. The surface of the specimen is defined as a non-slip solid wall with a rotation speed of 75 rad/s. The iterative calculations of the semi-implicit method for pressure-linked equations (SIMPLE) algorithm were used to solve the momentum equation (N–S equations), which can modify the pressure term in the discretized N–S equations so as to renew the velocity field and the pressure field simultaneously. The iterative calculations of the primitive variables such as flow velocity are terminated when the residual norm criteria, 10−6, was reached.

3 Results and Discussion

3.1 Effect of the Height of the Bump-Shaped Electrodes Under the Flow Condition

The velocity distribution of the bump-shaped electrodes with various heights is shown in Fig. 2, and the average flow velocity for each surface is given in Table 1. It can be seen that, regardless of the height of the bump-shaped electrode, the vortex flow forms and varies obviously when the formation water flows through each electrode surface of the bump-shaped electrode. As a consequence, the average flow rate for each surface is different with the color changes; thus, each surface can be analyzed independently. Furthermore, the diversity of the average flow rate for each surface becomes much more pronounced with an increase in the height of the bump-shaped electrodes from 1 (Fig. 2a) to 3 mm (Fig. 2c). Given that the flow velocities of surfaces of different bump-shaped electrodes are significant differences, it can be indicated that the bump-shaped electrodes are suitable to optimize the flow velocity testing, and the experimental efficiency can be improved. Furthermore, when the height of the bump-shaped is high enough (3 mm), each surface can be regarded most readily as an independent individual to be analyzed because of the biggest difference of the various velocities for the electrode surfaces. Considering the size of the rotating cage and experimental operability, a bump-shaped electrode with a height of 3 mm is preferable to be used in the experiment.

Fig. 2
figure 2

Velocity distribution of the bump-shaped electrodes with various heights: a 1 mm, b 2 mm, c 3 mm

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Table 1 Average flow velocity for each surface of the bump-shaped electrode
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3.2 Effect of the Placement of the Bump-Shaped Electrode on the Flow Condition

The high-efficiency method is implemented by combing the rotate cage and the bump-shaped electrodes. When the rotate cage is settled, the arrangement of the bump-shaped electrodes on the rotate cage is a critical parameter to ensure the uniformity of the velocity flowing through each electrode surface. Therefore, the velocity distribution of the bump-shaped electrodes is designed to be arranged symmetrically and variedly, using the CFD simulation, which is shown in Fig. 3. Figure 3 clearly shows that the velocity field around the eight bump-shaped electrodes arranged on the rotating cage is uniform and homogeneous (Fig. 3a), because of the similar color distribution around these electrodes. However, the velocity field of the four bump-shaped electrodes and four flat electrodes (Fig. 3b) is not as consistent as that of the eight bump-shaped electrodes. Consequently, the inconsistent velocity field would bring some difficulties to calculate the average flow rate for each surface of the bump-shaped electrodes. Therefore, in the high-efficiency experiment, the bump-shaped electrodes should be uniformly arranged on the rotating cage so as to guarantee the accuracy of the high-efficiency data.

Fig. 3
figure 3

Top views of the velocity distribution of the bump-shaped electrodes arranged symmetrically and variedly at the single rotate cage layer: a eight bump-shaped electrodes, b four bump-shaped electrodes and four flat electrodes

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The experimental efficiency is associated with the homogeneity of the flow condition around the bump-shaped electrodes. If the velocity distribution is uniform and each electrode can work independently, the experimental efficiency can be enhanced. In order to improve the experimental efficiency, the selection of the distance between the bump-shaped electrode and the center axis for each layer is also important, which affects the corresponding flow velocity [30]. It should be noted that the structure of the rotating cage can also affect the homogeneity of the flow condition around the bump-shaped electrodes [31], especially when the rotating cage is a single layer. Trying to not affecting the homogeneity of the flow condition around the bump-shaped electrodes and considering the dimensions and structure of the autoclave, the rotating cage is designed to a double layer, and the bump-shaped electrodes are arranged diversely but evenly for each rotating cage layer with the same axis. Figure 4 shows side views of the velocity distribution of the bump-shaped electrodes arranged at the double-layer rotate cage, obtained by the CFD simulation. It can be observed that using either the eight bump-shaped electrodes (Fig. 4a), or the four bump-shaped electrodes and four flat electrodes (Fig. 4b), the flow condition for each layer is unaffected by each other. Moreover, velocity distribution of the eight bump-shaped electrodes is also more uniform than that of the four bump-shaped electrodes and four flat electrodes. Therefore, it can be concluded that when using multilayer structure of the rotating cage (in this case, double-layer one), and adjusting the distance between the bump-shaped electrodes and the center axis for each layer simultaneously, the design of this high-efficiency experiment is feasible, and the homogeneity of the flow condition around each electrode surface cannot be affected, leading to the enhanced efficiency of the high-efficiency experiment.

Fig. 4
figure 4

Side views of the velocity distributions of the bump-shaped electrodes arranged symmetrically and variedly at the double-layer rotate cage: a eight bump-shaped electrodes, b four bump-shaped electrodes and four flat electrodes

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3.3 Reliability of the Bump-Shaped Electrodes

Besides certifying the feasibility of the bump-shaped electrodes with the CFD model, actually, the reliability of the electrodes is also important, which concerns their future application and needs to be further confirmed in practice. In this experiment, the traditional one-by-one method by weight loss tests is used for comparison. The super deep scene 3D microscope is generally used to examine the thickness loss of each surface of the bump-shaped electrode. The mosaicked macroscopic morphologies after removal of the corrosion scales are shown in Fig. 5. There is a significant difference in the thickness loss of each surface of the bump-shaped electrode. These surfaces are marked from number 1 to 6 (abbreviated Nos. 1 to 6) in clockwise order with an average thickness loss of each electrode surface 0.03, 0.07, 0.04, 0.09, 0.05 and 0.08 mm, respectively. Then, the thickness loss of each electrode surface is converted to Vc using Eq. (1). Figure 6 shows Vc as a function of different velocities obtained by both the traditional one-by-one method and this high-efficiency method. It can be seen that the Vc values obtained by these two different methods are nearly coincident. Therefore, as mentioned above, it can be concluded that it is reliable to conduct this high-efficiency experiments by combining using the bump-shaped electrodes and the rotating cage. Compared to that one-by-one method, for the bump-shaped electrodes having six surfaces, the experimental efficiency can improve six times; for the up and down double layers of the rotating cage, the experimental efficiency can improve two times. Thus, the total experimental efficiency can improve 12 (6 × 2) times. Furthermore, based on the above discussion, it is possible to design much more complicated electrodes (not limited to the bump-shaped electrodes) and extra layers (more than double) of the rotating cage to further increase the experimental efficiency under extremely aggressive environment [32]. In addition, it is believable that the goal of the project of “high-efficiency experimental method and design” of the MGI would be realized in near future [33].

Fig. 5
figure 5

Macroscopic morphologies of the bump-shaped HP-13Cr SS electrodes after removal of the corrosion scales in the extremely aggressive oilfield formation water: a global drawing, b partial enlarged drawing

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Fig. 6
figure 6

Corrosion rates of the HP-13Cr SS electrodes at different velocities measured by the high-efficiency and traditional one-by-one methods

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4 Conclusions

A new high-efficiency experiment is designed by combing selection of the bump-shaped electrodes and the double-layer rotate cage to optimize the flow velocity testing in the extremely aggressive oilfield formation water. The above findings, based on discussing the effect of the height, the placement and the reliability of the bump-shaped electrodes, allow the following conclusions:

  1. 1.

    The bump-shaped electrode is designed to optimize the flow velocity testing. When the height of this kind of electrode is high enough, there is a significant difference of flow velocity for different bump-shaped electrode surfaces; each electrode surface can be analyzed independently.

  2. 2.

    A double-layer rotate cage is designed to ensure the homogeneity of the flow condition around the bump-shaped electrodes. The electrodes are evenly arranged with varied distances from the center axis for each rotate cage layer, and the flow field around these electrodes is unaffected by each other. The velocity distribution of the eight bump-shaped electrodes is more uniform than that of the four bump-shaped electrodes and four flat electrodes.

  3. 3.

    By comparison with weight loss tests using the one-by-one method, the thickness loss is consistent with that using the traditional one-by-one method. However, the experimental efficiency is largely improved by using this designed high-efficiency experiment.