Numerical simulation design and optimization of regional cathodic protection in a large oil and gas station

Introduction: With increasing attention from both national authorities and the oil and gas industry to corrosion protection, regional cathodic protection (CP) design and optimization have become essential for ensuring the safe operation of large oil and gas stations.

Methods: A representative large station was selected for detailed investigation, including the collection of basic information and operational conditions. Environmental medium and electrochemical tests were performed to determine the most suitable anode type. Based on the test results, a numerical simulation model of a deep-well anode CP system was established to support regional CP design and optimization.

Results: The simulation produced optimized design parameters, including the number and spatial arrangement of deep-well anodes and their required output currents. Using these results, a practical CP scheme tailored for large oil and gas stations was proposed. The optimized configuration, refined through six iterative simulations, achieved the required CP potential distribution and improved uniformity across the protected region.

Discussion: This study addresses limitations of traditional CP design approaches, such as insufficient optimization of anode layouts and inadequate consideration of current shielding effects. By overcoming these issues, it provides both theoretical insights and practical strategies to guide more effective regional CP engineering.

1 Introduction

Cathodic protection (CP) is a widely adopted technology for mitigating corrosion of metallic structures by converting the metal surface into the cathode of an electrochemical system. In underground pipelines and large oil and gas stations, CP plays a critical role in safeguarding steel structures, pipelines, and associated equipment from corrosion. The effectiveness of CP is typically evaluated using potential criteria, with commonly accepted protection potentials ranging from −0.85 V_CSE to −1.20 V_CSE. Potentials more positive than −0.85 V_CSE indicate underprotection, while potentials more negative than −1.20 V_CSE may lead to overprotection issues such as hydrogen embrittlement or coating delamination. Maintaining the surface potential within this range is essential for ensuring effective and safe corrosion control.

In large oil and gas stations, pipelines and steel structures often vary in material, geometry, and operational function. Such variations can lead to galvanic corrosion and current shielding effects, which complicate the uniform distribution of protective current (Cui et al., 2015). Traditional CP design methods, which often rely on empirical rules for anode placement and current settings, may fail to guarantee that protection potentials are achieved consistently across the entire station. Consequently, some regions may remain underprotected despite increased current output, while others may be overprotected, reflecting the limitations of conventional design practices in ensuring both safety and efficiency.

Numerical simulation has become an efficient and reliable auxiliary tool in engineering design. By constructing physical models that correspond to real-world scenarios and integrating them with electric-field theory and numerical computation algorithms, it is possible to reasonably predict the potential distribution within the system, thereby providing quantitative support and guidance for design tasks such as electrode arrangement and structural optimization. Santos et al. (Santos et al., 2016) proposed a hybrid approach that combines genetic algorithms (GA) with the method of fundamental solutions (MFS) to optimize anode layout and current output. Similarly, Cheng et al. (Cheng et al., 2022) modeled five sacrificial anode cathodic protection (SACP) systems in chloride-contaminated concrete beams to evaluate the impact of different anode configurations. Kim et al. (Kim et al., 2018) employed boundary element method (BEM) simulations, integrated with multivariate linear regression and artificial neural networks (ANN), to optimize impressed current cathodic protection (ICCP) anode arrangements.

While these studies provide valuable insights, their methodologies are not directly applicable to regional CP systems in large, complex, and multi-structured stations. BEM is particularly well-suited for CP modeling because it only requires the discretization of structure boundaries, significantly enhancing computational efficiency. This method excels in simulating potential distributions and forecasting protection performance for extensive metal systems with complex boundary conditions (Riemer and Orazem, 2005; Allahar and Orazem, 2009; Abootalebi et al., 2010; Lan et al., 2012; Santos et al., 2020; Qiao et al., 2016). Previous research has confirmed BEM’s effectiveness in optimizing anode positioning, sizing, and system performance evaluation (Abootalebi et al., 2010). For example, Kim et al. (Kim et al., 2017) optimized the layout of sacrificial anodes in seawater for a rail canal structure using BEM. Similarly, Zamani (Zamani and Chuang, 1987), Kishimoto and Miyasaka (KISHIMOTO et al., 1990; Miyasaka et al., 1990) conducted ICCP system modeling and optimization focused on current control strategies.

However, existing studies on regional cathodic protection (CP) systems for large oil and gas stations often lack systematic optimization in terms of anode quantity and current parameters. Additionally, shielding effects caused by complex internal structures are frequently overlooked, which hinders the efficiency and reliability of CP implementation.

In this study, a regional cathodic protection optimization method using deep-well anodes for large-scale oil and gas stations is proposed. The method is established on numerical simulation results and integrates engineering design experience with on-site constraints to achieve both scientific rigor and practical applicability. Using a representative large oil and gas station as a case study, the fundamental information and operating conditions of the site were first collected, and the medium environment parameters together with electrochemical polarization test data were introduced as boundary conditions. Subsequently, a computational model of the regional cathodic protection system with deep-well anodes was developed through numerical simulation, and systematic parameter optimization was carried out to determine the number, spatial arrangement, and output current of the anodes. As a result, an optimized regional cathodic protection design scheme suitable for large oil and gas stations was established. This approach effectively avoids the resource waste often caused by “black-box” optimization algorithms with massive ineffective iterations and provides a practical improvement path to address the shortcomings of traditional cathodic protection methods, such as insufficient optimization of anode number, position, and current output, the lack of a systematic design procedure, and the neglect of shielding effects within the station area.

2 Numerical simulation and optimization methods

2.1 Numerical simulation method

The potential field within the cathodic protection system was described using the Laplace equation (Equation 1). (Adey and Niku, 1992):

$\kappa {\nabla }^2\phi =0(1)$

Where $\mathit{\phi }$ is the electric potential, and $\mathit{\kappa }$ is the electrical conductivity (the reciprocal of resistivity) of the medium within the studied region Ω. To obtain a unique solution, the boundary conditions on the enclosing surface Γ must be defined. Surface Γ was divided into three types (as shown in Figure 1): Γ₁ represents insulated surfaces (e.g., the ground surface or other completely insulating structures) where a constant current density boundary condition is applied; since no current flows through these surfaces, the current density is zero. Γ₂ corresponds to auxiliary anodes in an impressed current cathodic protection system, where the boundary condition is given by the output current density—calculated as the total anode output current divided by its working area. Γ_c represents the cathodic region, including the external surfaces of the protected structures such as pipelines and grounding electrodes. The boundary condition at Γ₃ is typically defined by a polarization function, which describes the relationship between the polarization current density i and the polarization potential E. This function can be experimentally determined. For coated pipelines, the effective polarization current density should be multiplied by the coating defect ratio to account for the damaged areas.

Figure 1

Figure 1. Boundary conditions for the cathodic protection computation.

Based on the above boundary conditions, the governing equations are typically solved using numerical methods such as the Boundary Element Method (BEM) and the Finite Element Method (FEM). Several commercial software packages have integrated these numerical techniques for the simulation of cathodic protection potentials, including BEASY Corrosion & CP and Elysca. In this study, the BEASY Corrosion & CP V21 software, which is based on the Boundary Element Method, was employed for modeling and computation. The main procedures include constructing the structural model, performing mesh generation to form the boundary integral equations, setting the corresponding boundary conditions, and finally carrying out the numerical solution (Duan et al., 2024; Gadala et al., 2016).

2.2 Anode position selection and output current optimization

To efficiently determine the appropriate number, locations, and output of anodes, this study proposes a simulation-based closed-loop decision-making method. The specific optimization process is illustrated in Figure 2. The optimization process consists of two principal stages: 1) preliminary determination of anode locations based on potential-field analysis, 2) automatic optimization of anode output currents through a feedback control algorithm.

Figure 2

Figure 2. Flowchart of regional cathodic protection design using deep anode wells in oil and gas stations.

First, based on the basic information and operating conditions of the station, soil resistivity and polarization tests are conducted to obtain the parameters required for constructing the numerical model. These parameters include the precise geometric distribution of buried facilities within the station, the soil resistivity, and the electrochemical polarization curves of key materials. Based on these data, a cathodic protection numerical model of the station is established in the boundary element software BEASY, with the corresponding boundary conditions appropriately defined.

$N=\frac{I_{total}}{I_{\mathit{max}}}(2)$

The number of anode wells, denoted as N, is initially determined using Equation 2, where I_total represents the total protective current required, calculated from the total surface area of the protected structures and the desired protection current density, and I_max denotes the maximum allowable output current of a single anode well. Subsequently, the potential data obtained from the galvanic corrosion simulation are imported into MATLABV13 to generate equipotential contour maps. By analyzing the density and distribution patterns of these equipotential lines, regions with similar potential characteristics are grouped together. Based on this classification, the entire station area is divided into N zones, and the center or the point with the most unfavorable potential in each zone is preliminarily identified as a candidate location for the deep anode wells.

After determining the anode locations, an optimization program developed in MATLAB is employed to automatically adjust the output current of each anode well. The algorithm identifies the point with the most negative potential (E_c) around each anode as the key evaluation point. Its optimization objective is to adjust E_c within the target potential range (E_target), while ensuring that the output current of each anode (I_i) does not exceed the maximum allowable value (I_max).

The specific optimization steps are as follows:

Taking one anode as an example, two initial calculations are first performed, where the output current densities are denoted as I¹ and I², respectively. The sign of the current density indicates the current direction. From the simulation results, the corresponding potentials E_c¹ and E_c² are obtained. According to Equation 3, the response coefficient k can be determined, representing the current change (in kA) required to vary the potential at the key point by 1 V.

Next, the iterative optimization process begins. Based on Equation 4, the deviation between the current potential and the target potential E_target is calculated. When E_c > E_upper, the potential difference is ΔE = E_upper − E_c; when E_c < E_lower, ΔE = E_lower − E_c. Using Equation 5, the response coefficient k is applied to back-calculate the required current adjustment to eliminate this potential deviation, and the next iteration current Iⁿ⁺¹ is predicted using Equation 6.

Before applying the new current value, it must satisfy the engineering constraint Iⁿ⁺¹ (n > 2) = min [Iⁿ⁺¹ (n > 2), I_max]. Finally, an iterative convergence loop is executed: the constrained current Iⁿ⁺¹ (n > 2) is submitted to BEASY for the next round of simulation. These steps are repeated until E_c falls within the target potential range, at which point the corresponding output current I is taken as the optimized result.

$\left.\mathrm{k}=|\frac{{\mathrm{I}}^2-{\mathrm{I}}^1}{{\mathrm{E}}_{\mathrm{c}}^2-{\mathrm{E}}_{\mathrm{c}}^1}\right|(3)$

$△\mathrm{E}={\mathrm{E}}_{\mathrm{c}}^2-{\mathrm{E}}_{\text{target}}(4)$

$△{\mathrm{I}}_{\text{adjust}}=\mathrm{k}*△\mathrm{E}(5)$

${\mathrm{I}}^{\mathrm{n}+1}\left(\mathrm{n}>2\right)={\mathrm{I}}^{\mathrm{n}}-△{\mathrm{I}}_{\text{adjust}}(6)$

The optimized current values are applied to the BEASY model for global validation. At this stage, a more stringent criterion is adopted, requiring that the potentials of all protected structures within the station fall within the effective protection range. If this requirement is not satisfied, a scheme adjustment is initiated. Specifically, the number of anode wells can be increased to N + 1, after which the optimization process restarts from the step of determining the anode quantity. Alternatively, if physical conditions permit, the burial depth of the anodes may be appropriately increased to extend the protection range. The current output is then re-optimized and revalidated in BEASY until a final design scheme satisfying the global protection requirements is achieved.

3 Case study

3.1 A large oil and gas station was selected as the study object

The lengths, dimensions, burial depths, and spatial configurations of the pipelines and grounding systems within the station were collected. Based on these data, a regional cathodic protection design was carried out for the station.

3.2 Station data collection and model construction

The pipelines have diameters ranging from 133 mm to 1,600 mm and a total buried length of 6,204 m, with a combined surface area of 10,568.67 m². The grounding system spans 16,009.73 m with a surface area of 574.32 m². Grounding conductors have cross-sectional areas of 25 mm², 90 mm², and 120 mm², and are buried at depths of 0.5–1 m, while pipelines are buried at 1–3 m. These geometric and structural datasets form the foundation for subsequent numerical simulations and current optimization.

The station was divided into four regions (A1–A4) for modeling purposes. A full-scale (1:1) geometric model was established in the BEASY GiD module, reflecting the actual site dimensions (as shown in Figure 3, where the red lines represent the pipelines and the blue lines represent the grounding system). Mesh generation was performed with a node spacing of 5 m, and segments shorter than 5 m were treated as a single mesh element, resulting in a total of 10,781 mesh elements.

Figure 3

Figure 3. Geometric model diagram.

3.3 Boundary conditions

To establish accurate boundary conditions for simulation, polarization tests and soil resistivity measurements were conducted. A three-electrode system was used, with a graphite counter electrode, saturated calomel reference electrode, and working electrodes of 20 carbon steel (20 × 10 mm) and copper grounding (20 × 16 mm). Only lateral surfaces were exposed, and other surfaces were sealed with epoxy. The experimental medium was soil sampled directly from the oil and gas station site, ensuring that the test conditions accurately reflected the characteristics of the actual environment. All electrodes were cleaned with distilled water, acetone, and ethanol before testing.

Polarization tests were conducted at multiple potentials (carbon steel: 850, −1,000, −1,150, −1,300 mV; copper: 550, −700, −850, −1,000, −1,150, −1,300 mV vs. Cu/CuSO₄) using an electrochemical workstation. Each test included a 30-min open-circuit potential stage followed by a 2-h i–t test and the final stabilized current obtained during the measurement was recorded as the current corresponding to that potential.

The soil resistivity was measured using the Wenner four-probe method. In this method, four electrodes are placed at equal intervals along a straight line on the ground surface, with the outer two electrodes used for current injection and the inner two for measuring the potential difference. Based on the measured voltage and current values, the apparent resistivity of the soil is calculated using the corresponding formula. The spatial heterogeneity and seasonal variation of soil resistivity are key factors influencing the performance of cathodic protection systems. However, for the specific station considered in this study, which is located in the coastal region of south-central China, temperature and humidity variations are relatively small. Therefore, adopting an average and stable soil resistivity value in the model remains both reasonable and feasible.

4 Results and discussion

4.1 Experimental results

Based on the E-I curves (Figure 4) of the pipeline and the grounding copper electrode, it can be observed that the pipeline’s corrosion potential is approximately −0.75 V_CSE, whereas the copper grounding electrode has a corrosion potential positive than −0.6 V_CSE. Because the pipeline potential is more negative and the copper potential is more positive, a natural potential difference is formed. As a result, the pipeline acts as the anode in the galvanic couple and undergoes self-corrosion, while the copper grounding electrode serves as the cathode and is protected. When the pipeline reaches the −0.85 V_CSE protection potential, the current supplied by the copper grounding electrode is much higher than the pipeline’s own corrosion current, approximately 2000 times greater. This implies that, under cathodic protection conditions, the majority of the protective current is carried by the grounding system.

Figure 4

Figure 4. (a) Pipeline E–I curve, (b) grounding E-I curve.

The soil resistivity test results are presented in Table 1The measurements indicate that the deep soil resistivity is relatively low, at 2 Ω m, which facilitates the dispersion of current from deep well anodes. Therefore, this station is suitable for cathodic protection using deep well anode systems. These data are used as boundary conditions in the BEASY simulations.

Table 1

Table 1. Field-measured layered soil resistivity.

4.2 Simulation of unprotected potential distribution

Multiple instances of pipelines running parallel to or intersecting with the underground grounding grid exist within the oil and gas station, forming a typical complex scenario for regional cathodic protection, commonly referred to as a “pipeline–grounding proximity” condition. Due to the large scale of the station, the extensive grounding network imposes significant interference on the cathodic protection system. During the operation of regional cathodic protection, a portion of the protective current is diverted by the grounding network, reducing the effective current reaching the pipeline. Consequently, some pipeline segments may become underprotected, potentially undermining the overall corrosion protection performance.

To address this issue, the design of the regional cathodic protection system must fully account for current losses induced by the grounding grid and evaluate their impact on protection effectiveness. To enhance both economic efficiency and engineering practicality, if a small portion of the pipeline remains below the target potential after optimization, compensatory measures—such as adding localized sacrificial anodes or insulating the grounding system—can be adopted. In this study, the system is considered compliant if the total length of underprotected pipeline segments does not exceed 5% of the overall buried pipeline length. For the current implementation, this corresponds to a permissible total underprotected length of 310 m.

The cathodic protection system is designed to maintain pipeline potentials between −950 mV and −1,200 mV. Additionally, the maximum output current for each deep well anode is limited to 30 ± 0.5 A. Based on these criteria, an optimized design and simulation analysis of the regional cathodic protection system using deep well anodes was conducted for the large station.

Using the BEASY GiD modeling module, a full-scale (1:1) geometric model of the station was constructed, and the appropriate boundary conditions were applied. A mesh was then generated for all geometric entities. As a baseline analysis, galvanic corrosion simulations were performed under unprotected conditions, as shown in Figure 5. Based on these simulations and the relevant current demand formula, the total cathodic protection current required for all protected components within the station was calculated. As stated in Section 3.1, the total surface area of the pipeline is 10,568.67 m², while that of the grounding system is 574.32 m². Based on the polarization curves obtained from Figure 3, the current densities corresponding to a constant potential of −850 mV were conservatively selected. The resulting values are 0.06 mA/m² for the pipeline and 233.87 mA/m² for the grounding system. The expression used for current demand estimation are as shown in Equations 7, 8:

${\mathrm{I}}_{\text{total}}={\mathrm{I}}_{\mathrm{p}}+{\mathrm{I}}_{\mathrm{g}}(7)$

${\mathrm{I}}_{\text{total}}=10568.67\times 0.06+574.32\times 233.87=134950.33\text{mA}=134.95\mathrm{A}(8)$

Figure 5

Figure 5. The layout diagram of five deep well anodes divided according to the equipotential lines of galvanic corrosion.

The required cathodic protection current for the large oil and gas station, denoted as I_total, consists of two components: the current required for buried steel pipelines (I_p) and the current required for the grounding system (I_g).

A galvanic corrosion simulation without cathodic protection was first conducted to obtain the potential values at each mesh nodeBased on the potential distribution results, equipotential lines were plotted using MATLAB, as shown in Figure 6, and the region was divided into five sections according to these lines.

Figure 6

Figure 6. Simulated potential distribution of a buried steel pipeline under galvanic corrosion without cathodic protection.

4.3 Current optimization results

According to the division results of the equipotential lines in Section 4.1 and considering the maximum output current of a single anode well (30 ± 0.5 A) as the limiting condition, five anode wells were selected, denoted as I = [I₁, I₂, I₃, I₄, I₅], each with a diameter of 273 mm and an initial burial depth of 30 m. In the subsequent numerical simulation including cathodic protection, the anode models were incorporated, and the mesh was recalculated. The total output current of the five deep anode wells was set to 150 A. The simulation results, presented in Figures 7b,c, show that the most negative potentials around the five anodes, denoted as E_c = [E₁, E₂, E₃, E₄, E₅], fall within the range of −1,190 mV to −1,200 mV. Therefore, the output is considered satisfactory when E_target = [–1,190, −1,200] and I_max = 30 ± 0.5 A.

Figure 7

Figure 7. (a) Potential distribution map of the buried pipeline with five deep anode wells installed, (b) distribution of regions with buried pipeline potentials more negative than −1,200 mV after installation of five deep anode wells.

After six optimization cycles, the simulation showed that deep well anodes #2 and #3 had reached the maximum output current limit. However, the most negative potentials in their respective zones still failed to reach the target range of −1,190 mV to −1,200 mV. As a result, the program automatically terminated further current adjustments for these two anodes. The other three anodes successfully adjusted their surrounding potentials to fall within the target range.

The total output current from the five deep well anodes was 131.62 A, distributed as follows: Anode #1: 23.74 A; Anode #2: 30.42 A; Anode #3: 30.42 A; Anode #4: 24.06 A; Anode #5: 22.98 A. At this stage, the output current had been optimized (Table 2), and the overall pipeline potential was evaluated to determine whether the protection criteria were satisfied. The results indicated that 672 m of the pipeline still failed to meet the required potential range, as illustrated in Figure 8a and b According to the optimization procedure, adjustments were then made by either increasing the number of anodes or deepening their burial depth.

Table 2

Table 2. The optimized output current and current density results obtained from the developed code.

Figure 8

Figure 8. (a) Potential distribution map of the buried pipeline after output current optimization, (b) potential distribution map highlighting regions below −950 mV on the Buried Pipeline.

To address the issue of buried pipelines that failed to meet the protection criteria, the number of anodes was increased. When the five deep-well anodes operated at their maximum total output current of 131.64 A, the most negative potentials were already within the range of −1,190 mV to −1,200 mV, or some individual anodes had reached their maximum output current of 30 ± 0.5 A. Based on the unprotected pipeline surface area and the corresponding current density at a constant potential of −850 mV, the additional current demand was recalculated. The result showed that the required current was less than 30 A, and therefore, one additional deep-well anode was installed. The optimization procedure was then repeated from the step involving equipotential contour plotting and area division. The protection region was redefined into six zones, with each deep-well anode positioned at the center of its respective zone, as shown in Figure 9.

Figure 9

Figure 9. The layout diagram of six deep well anodes divided according to the equipotential lines of galvanic corrosion.

The additional anode was incorporated into the computational model, and the optimization program was re-run. As shown in Figure 10a, the total output current for the six-anode configuration was set to 136.14 A, with individual outputs as follows: Anode #1: 21.12 A; Anode #2: 25.90 A; Anode #3: 25.21 A; Anode #4: 22.16 A; Anode #5: 20.43 A; Anode #6: 21.30 A. The corresponding potential distribution and locations of underprotected segments are presented in Figure 10b. Compared to the five-anode setup, the current output of each anode decreased, suggesting that multiple anodes jointly contributed to protecting certain critical areas. This overlap reduced the required current at each location and improved the overall potential uniformity. As a result, only 150 m of pipeline remained below −950 mV, thereby meeting the system’s protection standard.

Figure 10

Figure 10. (a) Potential distribution map of the buried pipeline with six deep anode wells installed, (b) distribution of regions with buried pipeline potentials less negative than −950 mV after installation of six deep anode wells.

Another strategy explored was increasing the burial depth of the anodes to further optimize protection performance. Based on the original five-anode configuration, the burial depth was incrementally increased by 5 m, and the output currents were adjusted accordingly using the optimization program. When the burial depth was increased to 40 m (i.e., 10 m deeper than the original design), the total output current of the five anodes rose to 136.13 A, with the individual outputs as follows: Anode #1: 25.82 A; Anode #2: 29.99 A; Anode #3: 30.42 A; Anode #4: 24.08 A; Anode #5: 25.82 A.

Simulation results, shown in Figures 11a,b, indicate that Anode #3 reached its maximum output limit, while the others exhibited varying increases in current output. The overall potential field became more uniform. At this stage, only 21 m of pipeline remained below the minimum protection threshold of −950 mV, demonstrating that increasing the anode burial depth is also an effective method for significantly enhancing regional cathodic protection performance and ensuring compliance with design targets.

Figure 11

Figure 11. (a) Potential distribution map of the buried Pipeline with deep anode wells at 40 m burial depth, (b) regions with buried pipeline potentials less negative than −950 mV under 40 m burial depth.

5 Conclusion

This study proposes a optimization design process for regional cathodic protection using deep-well anodes. A comprehensive CP simulation model of the oil and gas station was established in BEASY based on the boundary element method (BEM), followed by mesh division. Based on the established optimization design process, regional cathodic protection optimization was carried out for the station, and the following conclusions were obtained.

The main findings are as follows:

1. The proposed optimization process comprehensively considers the effects of grounding interference and current shielding during the modeling stage. As a result, a standardized and systematic method for deep well anode configuration has been developed, which is particularly suitable for complex underground infrastructure environments.

2. By utilizing the galvanic coupling effects among buried steel structures, simulated potential contour maps were employed to segment the station into protection zones and determine optimal anode placements. The optimization was guided by the requirement that all protected components meet the specified target potential range. It holistically integrated anode count, spatial layout, and output current. A custom algorithm was implemented to automate the optimization of anode current distribution.

3. In comparison to conventional empirical design approaches, the proposed process markedly improves protection effectiveness, reduces design time, and lowers overall implementation costs. It offers both technical innovation and practical value, providing a robust reference framework for the design and deployment of regional CP systems in oil and gas facilities.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

RW: Conceptualization, Formal Analysis, Investigation, Visualization, Writing – original draft. JL: Data curation, Formal Analysis, Investigation, Writing – original draft. SH: Data curation, Formal Analysis, Investigation, Writing – original draft. WD: Formal Analysis, Investigation, Writing – original draft. YD: Formal Analysis, Investigation, Writing – original draft. QY: Formal Analysis, Writing – original draft. PH: Formal Analysis, Writing – original draft. XS: Formal Analysis, Writing – original draft. TG: Methodology, Supervision, Writing – original draft, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Science and technology Project of China National Petroleum Corporation Chuanqing Drilling Engineering Co., LTD. (CQ2024B-36-2-7) and the Key Research and Development Project of Sichuan Provincial Science and Technology Plan (2024YFTX0061). Chuanqing Drilling Engineering Co., Ltd. participated in the project through technical support and coordination during the research process.

Conflict of interest

Authors RW, JL, SH, WD, YD, QY, PH, and XS were employed by CNPC Chuanqing Drilling Engineering Co., Ltd.

The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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