Study on tide characteristics and mechanism of PSP in buried pipeline along the lake

The fluctuations of the Pipe-to-Soil Potential (PSP) in buried pipes are influenced by the geoelectric field induced by changes in the Earth's magnetic field, which can accelerate pipeline corrosion. Monitoring data of PSP along China's West–East Gas Pipeline near the lake indicates obvious tidal changes. This study proposes that the periodic movement of the conductivity boundary of the seepage area near the lake shore caused by tides is the fundamental cause of the tidal changes in PSP. The movement of the boundary changes the range of the H polarization of the geoelectric field, resulting in periodic changes in the PSP of the pipeline outside the seepage area. To investigate this mechanism, a dynamic boundary model of conductivity in the seepage area of Sailimu Lake in Xinjiang was established, and the characteristics of PSP at different distances from the boundary were analyzed using electromagnetic field finite element method and DSTL pipeline model. The study compared the simulation results of the model with the PSP data of the cathodic protection station and PSP monitoring station near Sailimu Lake, during a geomagnetic disturbance on September 23–24, 2016. The results of the study, as well as the corrosion of the test strips along the lake, verified the validity of the boundary change mechanism and model of the seepage zone. This study provides a theoretical basis for corrosion protection of pipelines near the lake’s edge.


Introduction
Changes in space weather, such as solar flares or coronal mass ejections, can cause geomagnetic disturbances (GMD) that create fluctuations in the Earth's magnetic field. These fluctuations induce an electric field in the geodetic medium, which can cause geomagnetically induced currents (GIC) to flow in conductive materials such as pipelines buried in the ground. The GIC in the pipeline can drive the Pipe-to-Soil Potential (PSP), which is a measure of the electrical potential difference between the pipeline and the surrounding soil (Seager, et al. 1991;Gummow and Eng 2002;Osella et al. 1998). When the pipeline coating is damaged, the GIC in the pipeline will connect the soil through the damage point to form a current loop with the earth. This can cause the PSP to increase significantly, which may aggravate the corrosion of the damaged point and reduce the service life of the pipeline (Hejda et al. 2005;Boteler and Croall 2010;Boteler 1997). The corrosion of pipelines due to GIC is a significant problem in areas with high GMD activity, and it is important to take measures to mitigate the effects of GIC on pipeline corrosion. One effective measure is to use cathodic protection, which involves applying a small electric current to the pipeline to counteract the effects of the GIC. This can help to reduce the PSP and limit the corrosion of the pipeline (Seager, et al. 1991;Gummow and Eng 2002;Osella et al. 1998). Compared with GIC, pipe ground potential PSP is a more important indicator to evaluate the corrosion risk of pipeline. With the completion of China's west-to-east gas transmission project and the frequent occurrence of accidents during the design life of gas pipelines, the level assessment of GIC in long-distance and large-scale gas pipelines has attracted the attention of domestic scholars. Large GIC and high PSP have been monitored on gas pipelines abroad (Hejda et al. 2005;Boteler and Croall 2010).
The research of domestic and foreign scholars on geomagnetic disturbance hazard pipelines mainly focuses on the influence and simulation calculation of different pipeline structures and geodetic conductivity structures on pipeline GIC and PSP under the influence of geomagnetic storms. Boteler et al. (1997) proposed to use the Distributed Source Transmission Line (DSTL) theory to calculate the pipeline electric field according to the characteristics of the pipeline as conductor and buried by high-resistance coating. Viljanen et al. (2012) calculated the wave impedance using the Spherical Basic Current System (SECS) and a large-scale one-dimensional geodetic conductivity model, and combined with geomagnetic survey data to calculate the geoelectric field . Liang Zhishan et al. (2014) applied the Melnikov method to analyze the GIC model of buried pipelines based on DSTL theory and concluded that pipeline GIC has chaotic characteristics. Boteler et al. (2014) established four different geodetic conductivity models in Quebec and calculated the electromagnetic field transfer function (wave impedance), comparing the relationship between the magnitude and phase of the geoelectric field of different models. Dong et al. (2013) used the three-dimensional finite element method to verify that the coastal effect is mainly caused by the distortion of geomagnetic H polarization on uneven transverse conductivity.
China University of Petroleum (Beijing) conducted longterm monitoring of PSP data from multiple pipelines across the country and found that the daily variation of pipeline PSP in coastal areas of Shandong, China, showed obvious tidal fluctuations (赵耀峰 2016; 熊树海 2017), and the PSP of multiple monitoring points of the West-to-East Gas Pipeline in the Serimu Lake area of Xinjiang showed different similar tidal fluctuations in the magnetostatic day (邓越 2018), and the PSP amplitude fluctuation range was large, which caused harm to pipeline safety.
Many scholars around the world have studied tidal electrical signals more (Harvey et al. 1977;Chave et al. 1989;Palshin et al. 1996), and ocean geomagnetic tidal responses have also been observed in satellite data (Tyler et al. 2003;Maus and Kuvshinov 2004;Kuvshinov and Olsen 2005). Some scholars believe that the reciprocating motion of lake water will cut the magnetic field lines of the geomagnetic field, resulting in an induced electric field (Longuet-Higgins and Deacon 1949;Weaver 1965;Liang et al. 2016), and derive the formula of the induced electric field generated by the tidal motion of seawater and the analytical solution of the induced ground electric field generated by the motion of the waves. However, according to the calculation of seawater parameters, the amplitude of the above two electric fields is less than 10-3 V/km, and their influence on the geoelectric field in the near water area is minimal. The tidal variation range of lake water is smaller than that of seawater, and it cannot produce a geoelectric field similar to the tidal fluctuations of monitoring data (邓越 2018). Domestic scholars Huang Qinghua and Tao et al. (黄清华and刘涛 2006) applied spectrum analysis methods and BAYTAPG analysis methods to obtain multi-period characteristics of tidal response of geoelectric field. Qing et al. (2007) found that most geoelectric fields have a 12-h periodic component. Tan Dacheng and Xin Jiancun et al. (2010, 2011, 2017 believed that the periodic change of the geoelectric field near the water area was affected by the solid tide, and established a periodic change model of the filter electric field caused by the seepage of fractured water, and Liu et al. (2019) used Tan's filter electric field model to explain the tidal variation characteristics of PSP in oil and gas pipelines in coastal areas of Shandong. The PSP pipe, which is more than 5 km away from the water, also has obvious tidal changes, and the lake water is difficult to affect the electric field several kilometers away through nearby rock fractures, and the scientific validity of its model needs to be further verified.
There are rich research results on the tidal change characteristics of geoelectric field at home and abroad, and there are many explanations for its formation, but the mechanism of tidal change has not been revealed (谭大诚, 赵家骝 2010;谭大诚 2011;辛建村and谭大诚 2017;Liu et al. 2019;Jacob 1972). At the same time, there are few studies on the mechanism of tidal changes in pipeline PSP. After studying a large number of pipeline PSP data, this paper proposes a new PSP tidal mechanism, establishes a model of PSP tidal effect along the lake pipeline, analyzes the PSP and corrosion of three monitoring stations of the West Second Line pipeline near Serimu Lake in Xinjiang, and verifies the correctness of the model by comparing the monitoring data and simulation results. The objective of this study is to investigate the mechanism of tidal changes in pipe-ground potential (PSP) and establish a PSP tidal effect model along the lake pipeline. Specifically, the study aims to propose a new PSP tidal mechanism, analyze the PSP and corrosion at three monitoring stations of the West Second Line pipeline near Serimu Lake in Xinjiang, and validate the model by comparing monitoring data with simulation results.

Boundary change mechanism of seepage area
There is a certain amount of moisture in the pores and fissures of rocks near waters such as lakes, and the movement of these water in the pore and fracture medium is called seepage. The area through which water moves is called the seepage zone, and the geodetic conductivity in this area is significantly higher than that of dry soil far from the water, forming a conductivity boundary with dry soil. According to Bear, there is a certain relationship between the water width x and water level h in the terrestrial seepage (Jacob 1972), as shown in Fig. 1.
With the relative motion of the Earth and the Moon, the tidal force Ft at a certain point on the Earth's surface is constantly changing. Figure 2a shows a schematic diagram of the tidal force Ft on the Earth's surface relative to different positions on the Moon. When the lake and its surrounding geodetic medium are subjected to tidal forces, the lake water level h and the pores and fissures in the earth rock will change periodically, resulting in a change in the width x of the seepage zone. As shown in Fig. 1, when the lake water level h is at the lowest point A', the width x is the smallest, and the boundary between the seepage zone and the dry soil is at A; when the lake water level h is at the highest point C', the width x is the largest, and the conductivity boundary between the seepage zone and the dry soil is at C. After one rotation of the Earth, the conductivity boundary shifts periodically between A and C, forming a curve as shown in Fig. 2b.

Formation of PSP cycle changes in pipelines along the lake
The induced ground electric field undergoes H-polarization in the boundary region where conductivity changes (Dong et al. 2013;Weaver 1963;Louis 1953;d'Erceville and Kunetz 1962). Tidal forces cause the conductivity boundary of the seepage area around the shore of the lake to move periodically, and the area where the H polarization effect of the induced ground electric field also moves synchronously, so that the amplitude of the geoelectric field at the location of the pipeline near the boundary of the seepage zone changes periodically, and the change mechanism is shown in Fig. 3.
The pipeline runs in an east-west direction, closer to the shore of the lake, passing through the south shore of the lake, the earth around the lake is a humid area formed by seepage, with extremely high conductivity, and dry soil to the east of the seepage area. Figure 3a shows the boundary between the seepage zone and the dry soil at different times. Figure 3b shows the change in the spatial distribution of the geoelectric field along the pipeline when the boundary of the seepage zone changes. Figure 3c shows the 12-h period curve formed by the amplitude of the ground electric field at a point P of the pipeline with time. Assuming that the moon is a full moon, the lake is located at 0:00 local time, the center of the earth, the moon  and the lake is located in a line, the tidal force makes the lake water level the lowest (low tide), the conductivity boundary of the seepage area is at A, at this time the pipe P point is the farthest from the boundary, and the geoelectric field EP is the minimum value; As the Earth rotates, the lake begins to rise tide, and at 3:00 local time, the boundary of the seepage zone moves to B, and the geoelectric field EP at point P gradually increases. By 6:00, the lake water level is highest (high tide), the conductivity boundary of the seepage zone moves to C, the P point of the pipe is closest to the boundary, and EP reaches the maximum. From 6:00, the lake begins to ebb tide, and by 9:00, the water level gradually decreases, the boundary of the seepage zone retreats to B, and the geoelectric field EP at point P gradually decreases. Until 12:00, the lake water level is lowest (low tide), the conductivity boundary of the seepage zone retreats to A, and EP reaches the minimum value. From 12:00 to 24:00, the lake water undergoes another ebb and flow according to the above process, and the geoelectric field forms a 24-h "double-peaked valley" daily change. The pipeline PSP, which is directly driven by the geoelectric field, thus forms periodic changes consistent with its characteristics. Due to the large difference between the conductivity of the seepage zone and the dry rock, the distortion range of the geoelectric field caused by H polarization can reach 10-20 km (Liu et al. 2019;Dong et al. 2015), so the pipeline PSP in a large range outside the seepage zone of the lake has the characteristics of periodic variation.

Pipeline PSP calculation method
In order to study the periodic variation mechanism of pipeline PSP caused by the boundary movement of conductivity in seepage area, it is necessary to establish a three-dimensional geodetic conductivity model in the lake area, decompose the actual geomagnetic station observation data by Fourier, obtain multiple excitation source solution models in the frequency domain geoelectric field for time-domain superposition and bring it into the DSTLbased pipeline model to solve PSP.

Geoelectric field solution of three-dimensional geodetic conductivity model
The change frequency of the geomagnetic field when disturbed by magnetic storms is generally between 0.0001 and 0.01 Hz (Kappenman 2003), and the field control equation in complex form can be obtained by ignoring Maxwell's equation of displacement current (1) 1 0 ∇ × ∇ ×Ȧ + ∇̇+jȦ =̇J The above equation is difficult to solve, and the electromagnetic field distribution of the model needs to be calculated by the finite element method, adopt Ȧ − the Galerkin weighted margin equation expressed is: where V is the entire solution domain, S is the border, V c is the medium area, scalar weight function w is basis function, vector weight function Ẇ is w is the unit vector of the Cartesian coordinate system ̇e x , ̇e y and ̇e z three vector weight functions obtained by multiplying. Suppose the shape function on each region is N i (i = 1,2···, n p, i is n p total number of nodes in the cell, then ⃗ A and the interpolation function on each region is The sequence of basic functions can be obtained by superimposing shape functions on all regions, and then adding them on nodes ⃗ A and , this allows the approximation functions to be substitutional into Eqs. (10) and (11) to form a system of equations. Current density, magnetic induction, and electric field strength can be obtained by solving for all ⃗ A and .

Pipeline PSP calculation
According to the distributed source transmission line (DSTL) theory proposed by Boteler et al. (1997), a pipeline equivalent circuit model is established, and each kilometer length of pipeline is used as a basic unit, and a long straight pipeline can be regarded as the series of n-segment basic units. The GIC and PSP matrix equations are established by using Kirchhoff's law loop circuit method or nodal voltage method, and the results of the geoelectric field distribution calculated by the Gallegin FEM are taken out parallel to the pipeline direction, and the distribution source of the DSTL pipeline model is used to solve the circuit, and the space-time distribution of the pipeline PSP during the magnetic storm can be obtained.

Land model establishment and pipeline PSP calculation in the Serimu Lake area
In order to verify that the boundary change mechanism of the seepage zone proposed in this paper is the root cause of the PSP cycle fluctuation of pipelines near Serimu Lake, this section establishes a geodetic model of pipelines along the lake according to the trend of the West Second Line pipeline near Serimu Lake and the geodetic conductivity structure, and calculates the spatial changes of PSP in different pipeline locations in the model.

Geodetic structure and pipeline distribution
The research pipeline area is located in the western region of the West Tianshan Mountains in Xinjiang, from Khorgos on the Sino-Kazakh border in the west, through the Ili and Serimu massifs in the east, and to the fault zone at the northern edge of the Zhongtianshan Mountains in the east, belonging to the Serimu Lake-Boroholo area, as shown in Fig. 4. The blue line indicates the western pipeline of the West Second Line, which is about 240 km long. There are 2 cathodic protection stations and several PSP monitoring stations. The specific locations of Station H, Station J and Station S are shown in the red circle in Fig. 4. Station H is about 45 km from Lake Serimu, Jinghe Station is about 70 km from Lake Serimu, and Station S is about 5 km from the nearest lakeshore.
Station H and Station J are far from Serimu Lake, and there are no obvious oceans, lakes and other waters around, while Station S is closer to Serimu Lake and belongs to a typical pipeline along the lake.

Dynamic boundary model of seepage zone
Due to the complexity of the geoelectric structure, it is impossible to accurately establish a geodetic structure model that is consistent with the reality, and the modeling needs to be simplified. According to the theory of geodetic electromagnetic bathymetry and plane waves, electromagnetic waves occur vertically from space and propagate downward, and the influence of surface earth on electromagnetic waves is much greater than that of deep earth structures, so the deep earth can be assumed to be uniform conductivity distribution for easy calculation and theoretical analysis. In this paper, the "thin plate model" is used to model the conductivity of the earth, mainly considering the lateral difference in conductivity on the surface (Price 1949;Wang and Lilley 1999;Bailey et al. 2017). The surface layer of the geodetic model is divided into 8 plots according to the literature related to geomagnetism in the area, and a high seepage area is set around Lake Serimu. Lake areas and other plot areas are fixed in location, and the boundaries of seepage zones vary over time, as shown in Fig. 5. The deep earth is a uniformly layered geodetic conductivity structure, and the specific conductivity parameters are shown in Table 1.
In order to simulate the influence of tidal effect, five different geodetic conductivity models are established at different positions of the seepage zone boundary at 0:00, 1:30, 3:00, 4:30 and 6:00, finite element calculations are performed on the same input source, and then the corresponding 1.5-h change curves in one day are taken from the five model results for synthesis and smoothing, of which the maximum change distance of the seepage zone boundary is 3000 m, and finally a 24-h pipeline PSP simulation curve can be obtained. The tidal effect on pipe-ground potential refers to the phenomenon where the pipe-ground potential (PSP) of buried pipelines near water bodies, such as lakes and rivers, varies periodically due to changes in the conductivity boundary of the seepage area near the water's edge. This effect is  caused by the combined influence of the geomagnetic field, the electrically conductive properties of the soil and water, and the position of the pipeline relative to the water's edge. The tidal effect on pipe-ground potential has been observed in many different water bodies, and it can have significant implications for the corrosion protection of buried pipelines in these areas. The magnitude of the tidal effect can vary depending on various factors, such as the size and depth of the water body, the distance of the pipeline from the water's edge, and the electrical conductivity of the surrounding soil and water.

Geomagnetic data selection and PSP calculation
In our study, we used the geomagnetic 24-h data closest to Serimu Lake on a magnetostatic day as the excitation source of the model. The data were selected because it represents the most relevant and accurate data for the region under investigation. The data were processed by Fourier decomposition to obtain all frequency components with a period greater than 1 h. The PSP of pipelines at 5 km, 15 km, 25 km, and 35 km from the western boundary of the lake were then calculated using the method described in section "Pipeline psp calculation method". Figure 5 shows the dynamic boundary model of electrical conductivity established for the Selimu Lake region of Xinjiang, while Fig. 6a illustrates the selected geomagnetic data used as the excitation source. The resulting PSP data were then plotted in Fig. 6 to demonstrate the variation characteristics of pipe-ground potentials at different distances from the western boundary of the lake. This approach allowed us to analyze the variation characteristics of PSP due to the geoelectric field polarization caused by changes in the conductivity boundary of the seepage area near the lake shore. By using the geomagnetic data as the excitation source, we were able to accurately simulate the dynamics of the electric field in the region, leading to a better understanding of the underlying mechanisms of PSP changes in buried pipes.
In summary, we will ensure a more balanced presentation of the modeling and simulation approach used, while placing greater emphasis on explaining the principles and processes underlying the periodic variations in PSP.

PSP monitoring and simulation results
Due to the regulation of pipeline PSP by the cathodic protection device, the actual PSP is the combined effect of the potential induced by geomagnetic storm and the cathodic protection potential. This paper focuses on the periodic fluctuation law of PSP, so only consider the calculation of PSP fluctuation caused by geomagnetic changes through the model. Figure 7a, b is the 24 h monitoring and simulation curves of PSP at Khorgos and Jinghe stations, respectively, and it can be seen that the simulated PSP fluctuation curve is consistent with the trend of the measured data, and the two morphology is similar, and the change in one day shows a typical "peak-valley" tide pattern from 10:00 to 14:00 local time, which is a typical Sq change (徐文耀 1992;Stening and Winch 2013). The daily peak-to-valley fluctuation range of station H reached 0.4VCSE, and station J reached 0.25VCSE. Figure 7c is the 48-h PSP monitoring and simulation curve of Station S on the west side of Serimu Lake, the two trends are also consistent, the daily variation has obvious 12-h periodic change characteristics, peaks at about 6:00 and 18:00, troughs at about 12:00 and 0:00, which is a typical "daily double-peaked valley" tidal pattern, and the change amplitude of PSP reaches nearly 1VCSE, far exceeding the safe range. Therefore, the tidal fluctuations of the pipeline PSP cannot be ignored.

PSP corrosion
Potentiostats are set up at Station H and Station J, while the Lake Serimu area is not. Figure 8 shows the corrosion morphology of cathodic protection specimens set near Serimu Lake. From the corrosion effect of the test piece, it can be seen that the test piece 5 km away from Serimu Lake is seriously corroded, while the corrosion of the test piece 30 km east of the lake and 30 km west of the lake is relatively good, indicating that the cathodic protection device effectively protects the pipeline in this area. According to the above analysis of the PSP change trend characteristics of the three stations, it can be seen that the amplitude of the PSP of the H station and the J station farther away from Serimu Lake is about 0.3VCSE in the magnetostatic day, while the daily change amplitude of the PSP of the monitoring station near the lake is about 1VCSE, which is more serious than the fluctuation of the other two stations. It indicates that the risk of corrosion of pipelines near the shore of the lake is higher, which is consistent with the corrosion situation presented by the test piece.

Conclusion
Our aim was to develop a dynamic boundary model of electrical conductivity for the Selimu Lake region of Xinjiang using the finite element method and DSTL pipeline model. By utilizing geomagnetic data as the excitation source, we simulated electric field dynamics and analyzed the variations of pipe-ground potentials at different distances from the western boundary of the lake. The results indicated significant tidal fluctuations of pipeline pipe-ground potentials, signifying a higher risk of corrosion in pipelines near the lake shore compared to other areas. Nonetheless, the cathodic protection device was found to be effective in most areas, confirmed by the corrosion morphology of the test pieces. This study provides a theoretical foundation for the corrosion protection of pipelines along the water's edge and has practical implications for pipeline management and maintenance in the region. Recent studies have observed significant cyclical fluctuations in the daily variation of pipe-ground potentials in many near-water pipelines along the lake, leading to severe corrosion. However, corrosion in most of these areas, located 3-5 km away from the water, is not caused by redox due to moist soil on the shore of the lake or changes in the electric field of the shore due to periodic movement of the water body. In this study, we propose a dynamic boundary model of conductivity in the seepage area and analyze the simulation of pipe-ground potentials, monitoring data, and corrosion test piece results of pipelines at three monitoring points by establishing a geodetic model in the Selimu Lake area of Xinjiang. Our results suggest that geoelectric fields with tidal characteristics develop near lakes and other water areas due to the movement of conductivity boundaries in the seepage zone nearby water. The periodic movement of the conductivity boundary in the seepage area leads to changes in the H polarization range of the geoelectric field, resulting in the periodic change of pipeline pipe-ground potentials. The monitoring point located approximately 5 km west of the lake shore displays a "daily double-peaked valley" curve, primarily due to the periodic movement of the conductivity boundary in the seepage area. In contrast, the pipe-ground potential at stations farther from the shore of the lake presents a "noon-afternoon peak-valley" curve, mainly caused by the change in Sq current. The test piece of the monitoring point near the lake shore shows severe corrosion due to the large fluctuation of pipe-ground potentials formed by the boundary change of the seepage zone. Conversely, the test pieces at stations farther from the lake shore are in good condition, indicating that they are not affected by the movement of the seepage zone boundaries. The results suggest that changes in the conductivity boundary of the seepage area near water bodies can explain the pipe-ground potential variation, which is crucial for understanding the corrosion mechanism of pipelines in the Selimu Lake region. Our study provides significant insights for developing effective corrosion mitigation strategies for pipelines in this area.
Funding There is no funding for this paper.

Data availability
The data can be shared upon request to the corresponding author.

Conflicts of interest The authors declare no conflict of interest.
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