Modelling of space weather effects on pipelines
Introduction
The relatively new concept of space weather is generally understood as the time-variable conditions in the space environment that may affect space-borne and ground-based technological systems. The interaction between the solar wind and the Earth's magnetic field produces time varying currents in the ionosphere and magnetosphere. These currents cause variations of the geomagnetic field at the surface of the earth and induce an electric field which drives currents in all conductors, such as power transmission lines and oil or gas pipelines. Geomagnetically induced currents (GIC) can cause damage to power systems (Kappenman and Albertson, 1990) or give rise to corrosion and interfere with electrical surveys of pipelines Henriksen et al., 1978, Camitz et al., 1997.
There is a method for calculating GIC in discretely earthed power systems Lehtinen and Pirjola, 1985, Viljanen et al., 1999 but a satisfying theory for studies of geomagnetic effects on continuously earthed pipelines has been missing until these days. Earlier studies on pipelines have dealt with solving Maxwell's equations for an infinitely long pipeline Ogunade, 1986, Viljanen, 1989, Osella et al., 1998, Osella and Favetto, 2000 or they have been applications of methods that are more suitable for power systems (Pirjola and Lehtinen, 1985). These studies suffered from unrealistic assumptions, and they were not able to give voltage and current profiles in a pipeline network.
In this paper, we present a general method which can be used to determine the profiles for buried pipelines when the geoelectric field, the pipe geometry and the electromagnetic properties of the pipeline are assumed to be known. The method is based on the analogy between pipelines and transmission lines, which makes it possible to use the distributed source transmission line (DSTL) theory familiar from the circuit analysis. The main advantage of the analogy is the applicability of the Thevenin theorem (Ferris, 1962) needed to construct the boundary conditions for the differential equations that are used to solve the current and the voltage profiles in a pipeline section.
The DSTL theory was used for modelling AC induction in pipelines by Taflove and Dabkowski (1979). Boteler and Cookson (1986) were the first to use it for GIC in pipelines, and Boteler (1997) extended the theory to deal with discontinuities of pipelines. In this paper, we extend the earlier models to consider a pipeline network including branches. In the new method, the electric field driving GIC may be any function of space. Consequently, nonuniformities due to inhomogeneities of both ionospheric currents and the earth's conductivity can be taken into account.
Section snippets
General model
We start from the basic electromagnetic laws and derive two equations which yield a full solution for our problem: determine GIC and pipe-to-soil (P/S) voltages in a buried straight pipeline section, when the external geoelectric field and the pipe geometry and electromagnetic properties are known. Our approach leads to the transmission line analogy adopted by Boteler and Cookson (1986). As a further improvement, we will later show how this analogy can be applied to general pipeline systems.
Transmission line analogy of pipelines
The form of , is identical to the equations that give the current and the voltage in a transmission line due to an external electric field (Smith, 1987). This suggests that a pipeline can be presented as a transmission line and geomagnetic effects can be calculated using the distributed source transmission line theory (DSTL) (Boteler, 1997).
The analogy between a pipeline and a transmission line is shown in Fig. 2. The pipeline is modelled by an electric circuit which itself is presented as an
Application of the distributed source transmission line theory
The distributed source transmission line (DSTL) theory was first applied to studies of the inductive coupling between powerlines and pipelines by Taflove and Dabkowski (1979). Similar studies of inductive couplings between buried conductors and different kinds of sources have been carried out by Krakowski (1968) and Machczynski (1986). Boteler and Cookson (1986) were the first to realize that the DSTL theory can also be applied to studies of geomagnetic effects on pipelines. He used active
Application of the method to a real pipeline network
To demonstrate the use of the modelling technique for a real pipeline network, we will present results obtained for the Finnish pipeline system. We use general DSTL equations to determine the pipeline response to both, spatially constant and spatially varying geoelectric fields. The model results are then compared to measured values obtained during a study made by Gasum Oy, the owner of the Finnish pipeline network, and the Finnish Meteorological Institute (Pulkkinen et al., 2001). Furthermore,
Concluding remarks
The problem solved in this paper was to find a theoretical model in which we can, knowing the external electric field, the geometry, and the electrical characteristics of a buried pipeline, calculate the current and voltage profiles along the pipeline. We obtained an exact justification to the use of the distributed source transmission line (DSTL) theory in which the pipeline is presented as a transmission line and the basic circuit theory can be applied. Consequently, we can now model
Acknowledgements
This work was related to a collaborative project between the Gasum Oy and the Finnish Meteorological Institute, in which geomagnetic effects on the Finnish natural gas pipeline were investigated. Our thanks go to Mr. Juha Vainikka, Senior Vice President of Gasum, and to Mr. Matti Pitkänen for their great support and interest in the study.
The measurements of induced currents in the Finnish pipeline were carried out by Dr. Kari Pajunpää and Mr. Pentti Posio of the Nurmijärvi Geophysical
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