Evaluation of Possible Corrosion Enhacement Due to Telluric Currents: Case Study for Brazilian Pipeline

Currents: Case Study for Brazilian Pipeline Joyrles Fernandes de Moraes1, Igo Paulino2, Livia Alves3, and Clezio Marcos Dinardini4 1Laboratório de Geofísica Computacional, Universidade Estadual de Campinas, Campinas, Brazil 2Unidade Acadêmica de Física, UFCG, Campina Grande, Brazil 3Divisão de Geofísica Espacial, INPE, São José dos Campos, Brazil 4Divisão de Aeronomia, INPE, São José dos Campos, Brazil Correspondence: Joyrles F. Moraes (joyrles1996@gmail.com)


Introduction
Telluric electric currents that flow within the Earth or on its surface are significantly enhanced during disturbances of the Earth's magnetic field (magnetic storms). These currents can propagate through conducting systems at the Earth's surface, such as, pipelines (Campbell Alaska pipeline), phone cables (Anderson et al., 1974), and electrical power systems (Lanzerotti et al., 1999), which in extreme events can produce blackouts (Guillon et al., 2016). 15 The Geomagnetic Induced Currents (GIC) propagation throughout pipelines can changes the pipe-to-soil potential (PSP) which changes the electrochemical environment at the pipeline surface, which can take a corrosion process. In pipelines cathodically protected, the PSP is maintained at negative potential of at least -850 mV. Fluctuations in PSP caused by GICs can lead the potential beyond -850 mV, resulting in corrosion (Seager, 1991). According to Place and Sneath (2001), PSP fluctuations also interfere in pipeline surveys. 20 Previous works on this topic were done in high latitudes, which revealed specific interactions of geomagnetic field with solar wind disturbances (Campbell, 1980;A. Fernberg et al., 2007). Effects of GICs in pipelines have been observed and published also in Argentina (Osella et al., 1998), Australia (Marshall et al., 2010) and New Zealand (Ingham and J. Rodger, 2018), where engineers had tried to find ways to dealing with the problem. Boteler and Cookson (1986) have shown that the telluric voltage induced on a pipeline can be calculated using distributed 5 source transmission line (DSTL) equations and telluric effects in pipeline is influenced not only by space weather events, but it is also dependent on the Earth's conductivity, the pipeline electromagnetic properties and geometric parameters. These calculations, when applied to modern well-coated pipelines, suggest that telluric current effects may not be as innocuous as originally thought especially for long pipelines located in high latitudes (Gummow, 2002). The DSLT theory was first described in Schelkunoff (1943) and has been used in several studies (Pulkkinen et al., 2001). 10 In this paper, the model for induced effects in pipelines proposed by Trichtchenko and Boteler (2002), using the DSLT theory, is used to compute the corrosion rates in Bolivia-Brazil gas pipeline (GASBOL) during chosen space weather events, with focus on 17th March 2015 Geomagnetic Storm. The GASBOL is the largest pipeline in Latin America, with a total extension of 3.159 km, extending from Rio Grande, Bolivia, to Canoas, Brazil. It is the main responsible by gas transportation in Brazilian territory. The GASBOL is buried about 0.5 m in the ground to ensure it integrity.  (Denardini et al., 2015). This network fills the gap with magnetic measurements available online in this sector and aims to provide magnetic data to be used to study changes in space weather. All the details on the magnetic network, type of magnetometers, data 25 resolution, data quality control, and data availability are provided by (Denardini et al., 2018).

Electric Field
The electric fields produced by geomagnetic disturbances drive electric currents in the Earth. These currents are one of the responsible to cause fluctuations in PSP. According to Trichtchenko and Boteler (2002), GICs have the effect of shielding the interior of the Earth from the geomagnetic disturbance. As the magnetic and electric fields are dependents on the conductivity uniform conductivity. The Earth model layers organized in Table 1 and used in this paper was obtained in São José dos Campos in previous geophysical surveys and published by (Padilha et al., 1991).
The electric field in the surface can be obtained from Source: Padilha et al. (1991) where H is the magnetic field component obtained from the magnetometer and z is the surface impedance obtained from the multiple horizontal layers (Trichtchenko and Boteler, 2002).

DSLT Theory
The electrical response of a pipeline can be modeled by the distributed source transmission line (DSTL) equations. In the DSTL approach, each uniform section of the pipeline is represented by a transmission line circuit element with specific series 5 impedance and a parallel admittance. The PSP can be calculated applying (Trichtchenko and Boteler, 2002) equation where x 1 and x 2 are the positions of the ends of the pipeline, A p and B p are constants dependent on the boundary conditions at the ends of the pipeline, and γ is the propagations constant along the pipeline, defined as γ = √ ZY , and Y = G + iwC is the parallel admittance and Z = R+iwL is the series impedance per unit length with G = conductance to ground, C = capacitance, 10 R = resistance of pipeline steel, L = inductance. According to Trichtchenko and Boteler (2002), the pipeline is independent of frequency, for that reason, C and L, were not necessary to apply the theory.
The termination impedances are unknown in our case, then, it was applied the theory considered 5 terminating impedances (0.1-ohm, 1 ohm, 10-ohm, 100 ohm and 1000 ohm). The circuit characteristics for the DSTL modelling of GASBOL are shown in Table 2.
15 Gummow (2002) suggested a general expression to estimate the corrosion rate (in mm/year) through a 1 cm diameter hole in pipeline coating given by: where V is the change in PSP, F(p) is the percentage of direct corrosion current due to an alternating current in a given period, 5 and F(t) is the fraction of time for which the pipe was unprotected, which is dependent of the geomagnetic activity. Gummow (2002) quoted 0.025 mm/year as the generally acceptable maximum value for corrosion rate in a pipeline. In this work, the CR was computed only for cases when the cathodic protection level was greater than -850 mV.  (Heirtzler, 2002). 20 Variations in the magnetic field, that cause changes in electric field, create GICs, which are responsible by PSP fluctuations.

Results and Discussion
The PSP computed in the GASBOL, which is cathodically protected, are shown in Figure 3 and 4. Figure 3 shows the PSP at different sites of the pipeline with low terminating impedance (0.1 ohm). Figure 4 is observed the PSP at different locations with high terminating impedance (1000 ohm). The constants lines are the safe operation region of the pipeline (-0.85 V and -1.45 V).

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It is possible to observe that in both cases the largest variations in PSP is relative to largest variations in electric field, that occurred in main stage of the 17th March geomagnetic storm. The PSP was out of the safe region to low terminating impedance, and mainly, when the pipe was considered with high terminating impedance. The terminating impedances are responsible to allow the entrance of GICs in the pipe, and high terminating impedance is relative to the pipe connected to the ground.
From Figures 3 and 4, it was also observed that the largest PSP fluctuations were in the ends of the pipe. This result is 30 confirmed in Figure 5, which is a profile of the PSP as function of the length of the pipe at 13 UT, on 17th March 2015.
This result confirms the mathematical theory described by Boteler and Seager (1998). According to that authors, it produces a  movement of electrical charge away from one end and a buildup of charge at the other end, resulting in the S-shaped potential profile observed. During one half electric field, the negative variation of potential of the pipe with respect to the ground causes a current to flow onto the pipe; whereas at the other half, positive variation potential causes the current to leave the pipe.  30) and quiet days. The acceptble limit to corrosion rate quoted by Gummow (2002), which is 0.025mm/year, is plotted in Figure 6(a).
In Figure 6a is possible to observe that the corrosion rate during strongs geomagnetic storms was greater than 0.005 mm to terminating impedances greater than 1 ohm for both cases. Moreover, the loss of material presented constant values to  greater than 10 ohm. Figure 6b is relative to moderated storms. It shows that the 7th November reached greater values than 2.10 −5 mm for impedances equal and greater than 1 ohm/km. These results are close to loss of material observed on 23th June geomagnetic storm (Figure 6a), considered strong, however, the loss of material was not close to the 17th March storm, which was 10 times greater than the moderated storms. Figure 7a shows the corrosion rates for weak storms. It is possible to observe that the loss of material on 07th February 2015 5 geomagnetic storm was close to the result found in 01th January storm and for impedances greater than 1 ohm, the loss of  material was greater. In quiet days (Figure 7b), with no geomagnetic storms, the results was reduced related to weak storms, reaching maximum values about 2.10 5 mm in maximum impedances. In general, strongs storms presented more significant values when it compared to weak, moderate and quiet days.
A. Martin (1993) observed corrosion rates in the north region of Australia (similar latitude to Brazil). They found corrosions rate ranging between 0.01 mm/year and 0.038 mm/year. According to the author, this is responsible by a penetration in pipe of 10 in 14 years. Henriksen et al. (1978) studied a Norway pipeline with 300 telluric events found a corrosion rate of 0.04 mm/year caused by these events.
Considering that geomagnetic storms occur several times a year, there would be many days when currents are flowing along the pipes. According to Osella and Favetto (2000) this fact implies two main risks. The first one is directly correlated with the enhancement of the induced current when the pipe is embedded in more resistive media; a sector of the pipe would be 5 anodic with respect to the other, with the consequent risk that the excess of the currents could drain through the pipe to the soil. Moreover, as the common practice is to increase the current if the medium is conductive the final result would lead to an actually improper setting of the cathodic protection voltages. The other risk is related to the intensity of the currents, since values of some amperes could contribute to the degradation of the coating.

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The presented application of the DSLT theory to evaluate the metal loss in the first Bolivia -Brazil gas pipeline route has provided ways to a new understanding of telluric current effects on pipeline during extreme space weather events. The use of magnetometer data to compute the electrical field, allows to estimate the PSP and metal loss which brought the following conclusions: 1. The electrical field peaks were computed on 17th March geomagnetic storm occured in the same time of the main stage 15 of the storm, and the currents generated could arrive in Brazil by compressional waves or surface waves. 3. The GASBOL presented significant corrosion levels for terminating impedances greater than 10 ohm/km, mainly in the 17th Geomagnetic Storm. Beside the event did not exceed the accepetble level, but they can contribute to accelerate the corrosion process of the pipe. Therefore, the effects of GICs in pipelines can not be negligible, even in middle latitudes,