Modelling of geomagnetic induction in pipelines

International audienceGeomagnetic field variations induce telluric currents in pipelines, which modify the electrochemical conditions at the pipe/soil interface, possibly contributing to corrosion of the pipeline steel. Modelling of geomagnetic induction in pipelines can be accomplished by combining several techniques. Starting with geomagnetic field data, the geoelectric fields in the absence of the pipeline were calculated using the surface impedance derived from a layered-Earth conductivity model. The influence of the pipeline on the electric fields was then examined using an infinitely long cylinder (ILC) model. Pipe-to-soil potentials produced by the electric field induced in the pipeline were calculated using a distributed source transmission line (DSTL) model. The geomagnetic induction process is frequency dependent; therefore, the calculations are best performed in the frequency domain, using a Fourier transform to go from the original time domain magnetic data, and an inverse Fourier transform at the end of the process, to obtain the pipe-to-soil potential variation in the time domain. Examples of the model calculations are presented and compared to observations made on a long pipeline in the auroral zone

Earth conductivity structures and their effects on geomagnetic induction in pipelines

Anomalous, large pipe-to-soil potentials (PSP) have been observed along a natural gas pipeline in eastern Ontario, Canada, where there is a major geological contact between the highly resistive rocks of the Precambrian Shield to the west and the more conductive Paleozoic sediments to the east. This study tested the hypothesis that large variations of PSP are related to lateral changes of Earth conductivity under the pipeline. Concurrent and co-located PSP and magnetotelluric (MT) geophysical data were acquired in the study area. Results from the MT survey were used to model PSP variations based on distributed-source transmission line theory, using a spatially-variant surface geoelectric field. Different models were built to investigate the impact of different subsurface features. Good agreement between modelled and observed PSP was reached when impedance peaks related to major changes of subsurface geological conditions were included. The large PSP could therefore be attributed to the presence of resistive intrusive bodies in the upper crust and/or boundaries between tectonic terranes. This study demonstrated that combined PSP-MT investigations are a useful tool in the identification of potential hazards caused by geomagnetically induced currents in pipelines

Earth conductivity structures and their effects on geomagnetic induction in pipelines

Anomalous, large pipe-to-soil potentials (PSP) have been observed along a natural gas pipeline in eastern Ontario, Canada, where there is a major geological contact between the highly resistive rocks of the Precambrian Shield to the west and the more conductive Paleozoic sediments to the east. This study tested the hypothesis that large variations of PSP are related to lateral changes of Earth conductivity under the pipeline. Concurrent and co-located PSP and magnetotelluric (MT) geophysical data were acquired in the study area. Results from the MT survey were used to model PSP variations based on distributed-source transmission line theory, using a spatially-variant surface geoelectric field. Different models were built to investigate the impact of different subsurface features. Good agreement between modelled and observed PSP was reached when impedance peaks related to major changes of subsurface geological conditions were included. The large PSP could therefore be attributed to the presence of resistive intrusive bodies in the upper crust and/or boundaries between tectonic terranes. This study demonstrated that combined PSP-MT investigations are a useful tool in the identification of potential hazards caused by geomagnetically induced currents in pipelines

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries

Present day challenges in understanding the geomagnetic hazard to national power grids

Power grids and pipeline networks at all latitudes are known to be at risk from the natural hazard of geomagnetically induced currents. At a recent workshop in South Africa, UK and South African scientists and engineers discussed the current understanding of this hazard, as it affects major power systems in Europe and Africa. They also summarised, to better inform the public and industry, what can be said with some certainty about the hazard and what research is yet required to develop useful tools for geomagnetic hazard mitigation

The variation of geomagnetic storm duration with intensity

Variability in the near-Earth solar wind conditions can adversely affect a number of ground- and space-based technologies. Such space-weather impacts on ground infrastructure are expected to increase primarily with geomagnetic storm intensity, but also storm duration, through time-integrated effects. Forecasting storm duration is also necessary for scheduling the resumption of safe operating of affected infrastructure. It is therefore important to understand the degree to which storm intensity and duration are correlated. The long-running, global geomagnetic disturbance index, aa , has recently been recalibrated to account for the geographic distribution of the component stations. We use this aaH index to analyse the relationship between geomagnetic storm intensity and storm duration over the past 150 years, further adding to our understanding of the climatology of geomagnetic activity. Defining storms using a peak-above-threshold approach, we find that more intense storms have longer durations, as expected, though the relationship is nonlinear. The distribution of durations for a given intensity is found to be approximately log-normal. On this basis, we provide a method to probabilistically predict storm duration given peak intensity, and test this against the aaH dataset. By considering the average profile of storms with a superposed-epoch analysis, we show that activity becomes less recurrent on the 27-day timescale with increasing intensity. This change in the dominant physical driver, and hence average profile, of geomagnetic activity with increasing threshold is likely the reason for the nonlinear behaviour of storm duration

Modelling of geomagnetic induction in pipelines

Geomagnetic field variations induce telluric currents in pipelines, which modify the electrochemical conditions at the pipe/soil interface, possibly contributing to corrosion of the pipeline steel. Modelling of geomagnetic induction in pipelines can be accomplished by combining several techniques. Starting with geomagnetic field data, the geoelectric fields in the absence of the pipeline were calculated using the surface impedance derived from a layered-Earth conductivity model. The influence of the pipeline on the electric fields was then examined using an infinitely long cylinder (ILC) model. Pipe-to-soil potentials produced by the electric field induced in the pipeline were calculated using a distributed source transmission line (DSTL) model. The geomagnetic induction process is frequency dependent; therefore, the calculations are best performed in the frequency domain, using a Fourier transform to go from the original time domain magnetic data, and an inverse Fourier transform at the end of the process, to obtain the pipe-to-soil potential variation in the time domain. Examples of the model calculations are presented and compared to observations made on a long pipeline in the auroral zone.Key words. Geomagnetism and paleomagnetism (geo-magnetic induction