ASSESSING PIPELINE VULNERABILITY TO TELLURIC CURRENTS

D.H. BotelerGeomagnetic Laboratory, Geological Survey of Canada

7 Observatory Crescent, Ottawa, Ontario K1A 0Y3, Canada

ABSTRACT

Telluric currents produce variations in pipe-to-soil potential (PSP) that take the pipeline outside thevoltage range for cathodic protection and interfere with potential surveys. The size of the PSPvariation depends on a variety of factors related both to the natural environment and thecharacteristics of the pipeline itself. This paper presents a methodology for assessing how differentpipeline features influence the vulnerability of the pipeline to telluric effects. Derivation of thedistributed-source transmission line (DSTL) equations for induction in a pipeline show that thecritical parameters are the series impedance of the pipeline steel and the parallel conductance toground through the pipeline coating. Large PSP variations occur where there is a disruption in theflow of telluric currents along the pipeline, such as happens at the end of the pipeline, at flanges, atbends, and changes in pipeline characteristics. A series of plots are presented showing thedependence of PSP variations on coating conductance, changes in series impedance and bends inthe pipeline. Also examined are how the PSP variations are modified when overlapping effectsoccur. Finally, the paper considers the effect of various mitigation strategies and presents modelresults of the reduction in PSP variations that can be achieved.

Keywords: cathodic protection, telluric currents, pipeline modeling, risk assessment

INTRODUCTION

Telluric currents in pipelines create variations in pipe-to-soil potential (PSP) that make it difficultto monitor cathodic potentials and, if large enough, raise concerns about the amount of time asection of a pipeline may not be cathodically protected. For engineers, encountering telluic currentsfor the first time they may seem a capricious phenomenon, coming and going in an apparentlyrandom way and with size varying from time to time and place to place. An understanding of thephenomenon is not helped when the only measurements often made on a pipeline are spot valuesor short-interval recordings as part of CP surveys. However, systematic longer-term multi-siterecordings of PSP have helped to identify that there are patterns to when telluric PSP variations are

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seen on a pipeline [1,2]. This has been coupled to modeling work that has provided the theoreticalframework for understanding the PSP produced by telluric currents [3]. Thus a lot is now knownabout telluric currents and this understanding can be used to mitigate their effects. The causes oftelluric currents and environmental factors influenced their severity are described in a companionpaper [4]. This paper examines how the pipeline structure contributes to the size and location oftelluric PSP variations on a pipeline.

Modeling

Telluric current effects on pipelines can be modeled using distributed source transmission line(DSTL) theory in the same way as is done for AC induction [5]. The electrical properties of thepipeline are described by the series impedance of the steel and the parallel conductance through thecoating to ground. These are used to define the propagation constant, (, and the characteristicimpedance, Zo:

The voltage and current along the pipeline are then given by

Differentiation and substitution leads to the equations for voltage on the pipeline

When the electric field is uniform over the length of the pipeline then equation (4) reduces to

This equation has a solution of the form

where P1 and P2 are the positions of the ends of the pipeline and A and B are constants dependenton the conditions at the ends of the pipeline. The constants A and B are derived in [6] and are givenby

These constants depend only on the characteristic impedance, propagation constant, and length ofthe pipeline, and the impedances of any ground connections at the ends of the pipeline. Therefore

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it is a simple matter to calculate values for A and B and insert them in equation (5) to determine thevoltage profile along a pipeline for any specified telluric electric field. The effects of multiplesections can be considered by representing the adjacent pipeline sections by their Theveninequivalent circuit [7]. This enables model calculations to be made for complete pipeline systems.The assumption of a uniform field is used here to more clearly show the effect that the pipelinestructure has on the amplitude of telluric PSP variations. Non-uniform electric fields can occurbecause of spatial variations in the geomagnetic field variations and changes in the earthconductivity. The effect of these on telluric PSP variations is the subject of current research.

The model equations are used to calculate the voltage profiles for a variety of situations. All of thePSP in the situations shown will depend on the size and direction of the telluric electric field, E. Thefactors affecting the size of the electric field are explained in a companion paper [4]. Here the intentis to show how the pipeline structure influences the telluric PSP variations. Accordingly a value ofE of 1 mV/km has been used throughout. This represents a small value of telluric electric field butmakes it easy to scale up the model results to give the PSP produced by larger electric fields. Theother point to note is that telluric currents vary considerably, typically reversing direction every fewseconds or minutes. The results presented here are for an instant in time when the electric field isat a maximum in a positive direction. A short time later, when the electric field reverses, all the PSPwill reverse. Also the results shown represent only the PSP variation due to telluric currents. ThesePSP variations would need to be added to the PSP produced by the cathodic protection system togive the actual voltages that would be observed.

The modeling is used first to show how the basic properties of the pipeline: its length, the pipelinedimensions and the type of coating, affect the telluric PSP. Other pipeline features, such as bendsand changes from two to one pipelines as occurs upstream of compressor stations are then examined.All these features have already been identified as contributing to telluric PSP variations on a pipeline[5,6]. The purpose of this paper is to quantify the relation between the telluric PSP and differentpipeline characteristics to provide a guide for assessing the significance of particular features withregard to maintaining effective cathodic protection of a pipeline.

EFFECT OF PIPELINE STRUCTURE

Pipeline Length

For an isolated straight pipeline of length L the PSP produced by a telluric electric field E is givenby equation (5). This is used to calculate the PSP produced by a telluric electric field of 1 mV/kmin different lengths of pipeline (Figure 1). The results in Figure 1a show a change from anexponential variation at each end of a long pipeline to a linear variation in PSP for a short pipeline.Equation (5) shows that the PSP is given by two terms that represent the voltages produced by theinterruption of current flow at each end of the pipeline. When the pipeline is “electrically long”these parts do not overlap and the PSP is given by an exponential fall off from each end of thepipeline with a region of zero PSP in the middle. For shorter pipelines these two terms overlaps.When the pipeline is “electrically short” the exponential terms overlap to give a linear variation inPSP. Thus, whether a pipeline is long or short compared to the adjustment distance has a significanteffect on the telluric PSP produced in the pipeline [7]. Figure 1b shows how the peak PSP (at the

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end of the pipeline) varies with the length of the pipeline. For electrically long (EL) pipelines thepeak PSP becomes independent of pipeline length. For electrically short (ES) pipelines the peak PSPis proportional to pipeline length.

Parallel Admittance

The parallel admittance of a pipeline is determined by the circumference of the pipeline and theconductance of the coating. The effect of coating conductance on telluric PSP variations can beillustrated by examining the PSP produced at the end of an electrically-long pipeline with noterminating resistance to ground. Figure 2 shows the PSP near the end of the pipeline for fivedifferent values of coating conductance. These results show that the peak voltage occurs at the endof the pipeline and falls off exponentially with distance from the end of the pipeline. The adjustmentdistance increases as the coating conductance is reduced. Figure 2b shows the dependence of theend voltage on the coating conductance and shows that the end voltage increases with decreasingcoating conductance.

Series Impedance

The series impedance is determined by the cross-sectional area of the pipeline and the resistivity ofthe pipeline steel. The resistivity of the steel is typically assumed to be constant. The cross-sectional area depends on the pipe radius and the wall thickness. These are usually fixed for aparticular pipeline. However, an increased wall thickness is often used for river crossings or othersensitive areas. To illustrate the effect of a change in wall thickness model calculations were madefor a long pipeline with a 1 km section where the pipe wall thickness was doubled (Figure 3). Thisshows that a small PSP variation is produced that peaks at the start and end of the thick-wall section.Along the thick-wall section there is a linear variation in PSP. This produces a potential gradientalong the pipeline that partly cancels the electric field to reduce the current flow in this section tothe same as that in the normal wall sections.

Another scenario that involves a change in series impedance is the change from two pipelines to asingle pipeline upstream of a compressor station. Going from one to two pipelines halves the seriesimpedance and doubles the parallel conductance. In the calculation of the propagation constantthese changes cancel leaving the propagation constant unchanged, however the characteristicimpedance is halved. Figure 4 shows that a linear variation in PSP is produced along the single-pipeline section with the peak voltages occurring where the changes from two to one pipelines andfrom one to two pipelines occurs. In the double-pipeline sections, on either side, the PSP falls offexponentially with distance away from the single-pipeline section.

Bend in the Pipeline

A bend in a pipeline also gives rise to telluric PSP variations. For an electric field E aligned withone section of pipeline, there will be a smaller component of E along the pipeline after the bend.These different electric fields will drive different currents in the pipeline before and after the bend.This current difference leads to an accumulation of charge at the bend that changes the potential ofthe pipeline, modifying the current flow along the pipeline and diverting some current out of thepipeline to ground.

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To examine how large a PSP is produced by a bend, model calculations were made for pipelineswith bends of 30 , 45 , 60 , 75 , and 90 degrees . These results are shown in Figure 5a and show thatthe peak PSP occurs at the bend with the PSP decreasing exponentially with distance on either sideof the bend. Larger PSP occur with the greater bend angle as shown in Figure 5b.

Sometimes two bends, in opposite directions, occur close together. For example, a pipeline in agenerally east-west direction may turn north-south for a river crossing and then turn back to the east-west direction on the other side of the river. In this case the two bends may be only 100 metresapart. To examine this situation the model was set up with two bends. Figure 6 shows the PSPproduced where there are two bends separated by a distance ‘s’. Calculations were made for bendseparations of 10, 20, 30, 40 and 50 km (Figure 6a). Each bend produces a variation in PSP oneither side of the bend, however the two bends are in opposite directions so produce PSP withdifferent sign. Thus where the PSP from the two bends overlap the different sign means that theytend to cancel each other. Thus the largest PSP variations occur for the largest bend separationwhere the overlap is least. For smaller bend separations the overlap is greater, so there is greatercancellation of the PSP from the two bends. Thus the peak PSP increases with increasing bendseparation (Figure 6b).

MITIGATION OF TELLURIC EFFECTS

An early suggestion for mitigation of telluric effects was to install insulating flanges to block theflow of currents along the pipeline. To examine this option, model calculations were made for a 400km long pipeline, first with no flanges, and then with flanges to split the pipeline into 2, 4 or 8sections (Figure 7a). The result for a pipeline with no flange shows the characteristic PSP variationwith peak PSP at the ends of the pipeline. When there is a flange in the middle of the pipeline, eachsection behaves as a separate pipeline with the characteristic response pattern. As more flanges areintroduced each pipeline section becomes shorter and the PSP variation along each section changesto the linear variation characteristic of an electrically-short pipeline as already shown in Figure 1.

Installing flanges in a pipeline creates more sites where large PSP variations occur (Figure 7a). Asthe number of flanges is increased the length of the pipeline sections is decreased and this causesa reduction in the peak PSP produced at the end of each section (Figure 7b). However, there needsto be many flanges installed in a pipeline for the reduction in PSP size to be significant, and theintroduction of flanges creates many more sites on the pipeline where these PSP variations occur.Thus the use of flanges is not now regarded as an effective method of mitigating the effects oftelluric currents.

If flanges are not used to block telluric currents and if any other flanges, such as used to isolate valvesites, are jumpered around so that the pipeline is electrically continuous, the telluric currents canflow from one end of the pipeline to the other and the largest PSP variations occur at the ends of thepipeline where the telluric currents flow on and off the pipeline. The PSP produced represents thepotential drop produced by the flow of telluric current through the resistance of the pipeline coating.This telluric PSP can be reduced by providing the telluric currents with a lower resistance path toground through a grounding connection at each end of the pipeline. Figure 8a shows the PSPvariations near the end of a long pipeline with end resistances of 100 ohm, 10 ohm, 1 ohm, 0.1 ohm

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and 0.01 ohm. The peak PSP, as shown earlier, occurs at the end of the pipeline. Figure 8b showsthat the size of this peak PSP decreases significantly for end grounding resistances less than 1 ohm.

Bends in the pipeline can also lead to large PSP variations in the pipeline in the vicinity of the bend.As with the ends of the pipeline, these PSP variations are associated with telluric currents flowingon and off the pipeline. Again, providing a grounding connection provides a low resistance path toground for the telluric currents. Figure 9a shows the PSP produced around a 90 degree bend withgrounding resistances of 10, 1, 0.1 and 0.01 ohms at the bend. Comparing these results with thosefor a bend with no grounding resistance (Figure 5a) shows that a 10 ohm ground has virtually noeffect on the PSP in the vicinity of the bend. A 1 ohm grounding only produces a slight reductionin peak PSP. However, a ground connection with a resistance of 0.1 or less produces a significantreduction in the peak PSP. Figure 9b shows that the grounding resistance at the bend produces asimilar reduction in peak PSP to that produced at the end of the pipeline (Figure 8b).

Normally adding a ground connection can be expected to reduce the telluric PSP variations.However, an unusual situation occurs when only one end of a pipeline is grounded as it may actuallyincrease the size of PSP variations at the other end of the pipeline. To illustrate this, modelcalculations were made for a variety of pipeline lengths, all with zero resistance to ground at the leftend and no ground connection at the right end (Figure 10). Figure 10a shows the exponential falloff from the ungrounded end of a long pipeline as seen in Figure 1a. For shorter pipelines thischanges to a linear variation as also seen in Figure 1a, however now the linear variation is notcentred about the mid-point of the pipeline as when both ends were ungrounded. Figure 10b showsthe peak PSP as a function of the pipeline length. For a long pipeline the same 'electrically long'limiting value is reached as in Figure 1b. For shorter pipelines the peak PSP is greater than in Figure1b. Appendix A show the derivation of the equations for this situation and shows that theasymptotic limit for a short pipeline grounded at one end is equal to E×L instead of E×L/2 for anungrounded short pipeline.

DISCUSSION

The results presented show that the largest telluric PSP variations are associate with features on thepipeline, such as changes in series impedance or bends, that disrupt the flow of telluric currentsalong the pipeline. The telluric PSP variations are associated with the potential drop produced bythe telluric currents flowing on and off the pipeline through the coating. In many realistic situationssuch features do not occur in isolation. For example, the pipe wall thickness may be increased fora river crossing, but then goes back to normal on the other side of the river. Similarly there may bea bend in the pipeline for it to take the shortest route under a river, but there is then an opposite bendon the other side of the river where the pipeline resumes its original course. In both these cases thechange in pipeline characteristics produce PSP with opposite signs. When, as in the case of a rivercrossing, the two features are close together the PSP they produce overlap and tend to cancel eachother. Thus the effect on telluric PSP of such pairs of features is much smaller than the feature inisolation. On either side of a feature the PSP amplitude decreases exponentially with a scale lengthgiven by the pipeline adjustment distance. Thus for a pair of pipeline features to have a significanteffect they must be separated by a distance that is comparable to the adjustment distances. Such asituation occurs where two gas pipelines are reduced to a single pipeline for the section upstream

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of a compressor station. Such changes in the effective series impedance of the pipeline systemproduce a “sawtooth” pattern in the PSP produced by telluric currents.

CONCLUSIONS

Modeling techniques now exist that can show where the largest telluric PSP variations will occuron a pipeline. The largest PSP variations occur where there is a disruption to the flow of telluriccurrents, such as at the ends of a pipeline, at bends or changes from two to one pipelines. PSPvariations are larger on pipelines with more resistive coatings. Mitigation is best done by installinggood connections to ground at both ends of the pipeline. Grounding only one end can make the PSPvariations larger at the other end for short pipeline. Installing flanges just increases the number ofsites where the telluric currents are deflected out of the pipeline producing significant PSPvariations.

REFERENCES

1. Edwall, H.-E. and Boteler, D.H. , Studies of Telluric Currents on Pipelines in SourthernSweden, Paper 01315, Proceedings, CORROSION 2001, NACE, Houston, March 11-16, 2001

2. Boteler, D.H. and L. Trichtchenko, L., Observations of Telluric Currents in Canadian Pipelines,Paper 01316, Proceedings, CORROSION 2001, NACE, Houston, March 11-16, 2001

3. Boteler, D.H. and Seager, W.H., Telluric currents: A meeting of theory and observation,Corrosion, 54, 751-755, 1998.

4. Fernberg, P., Trichtchenko, L. Boteler, D.H., McKee, L., Telluric Hazard Assessment forNorthern Pipelines, Proc. NACE CORROSION/2007, March 2007.

5. Boteler, D.H. and Trichtchenko, L., A Common Theoretical Framework for AC and TelluricInterference on Pipelines, Paper No 05614, Proc. NACE CORROSION/2005, April 2005.

6. Boteler, D.H. Distributed-source transmission line theory for electromagnetic induction studiesProceedings, 1997 Zurich EMC Symposium, Feb. 18-20, URSI supplement, 401-408, 1997.

7. Boteler, D.H., Seager, W.H., Johansson, C., and Harde., C., Telluric current effects on long andshort pipelines, Cold Climate Corrosion: Special Topics, ed. Perrigo, L.D., Byars, H.G.,Divine, J.R., NACE, Houston, 67-79, 1999.

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APPENDIX: GROUNDING OF LONG AND SHORT PIPELINES

The response of a pipeline to telluric currents is significantly affected by the grounding connectionsat the ends of the pipeline. When there is a low resistance ground connection at each end thevoltages on the pipeline go to zero for any pipeline length. In the case where the groundingconnections at the end of the pipeline have a high resistance such that Z1 >> Z0 and Z2 >> Z0 thenthe expressions for A and B reduce to -1 leaving the expressions for voltage on a long pipeline

For a long pipeline, when x = 0, the first term is 1 while the second term becomes e-(L which isconsiderably << 1 so can be neglected with the result that

Similarly at the other end the first term is e-(L << 1 while the second term is 1, so this time the firstterm can be neglected and the result is

Thus the effects from opposite ends of the pipeline do not affect each other.

For a short pipeline with no ground connections at the ends of the pipeline (or if the groundingresistance has a high value) then approximations can be made that lead to simpler expressions [7]showing that there is a linear variation in voltage along the pipeline passing through zero at the mid-point of the pipeline. When the pipeline is considerably shorter than the adjustment distance, thecurrent goes to zero. In this case the voltage on a short pipeline is given by

This gives

Thus again, equal and opposite voltages are produced at opposite ends of the pipeline.

When only one end is grounded interesting effects can occur. Consider the case when one end hasa low resistance ground connection, ie Z1 = 0 and the other end has a high value so that Z2 >> Z0the expressions for A and B reduce to

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Substituting these expressions for A and B into equation (A.8) gives

At one end of the pipe x = x1 e-((x-x1) --> 1 and e-((x2-x) --> e-(L so A.9 simplifies to:

e(L e-(L = 1, so the terms in the numerator in (A.10) cancel, leaving

for both long or short pipelines. This is to be expected since there is a zero resistance to ground atthis end of the pipeline.

Now consider what happens at the other end of the pipeline where the grounding resistance is high.At the other end of the pipeline, x = x2 e-((x-x1) --> e(L and e-((x2-x) --> 1 so A.9 simplifies to

The Z0Z2 terms cancel, leaving

For an electrically-long pipeline the exponential terms e-(L << 1 and is e(L >> 1 so (20) becomes

For an electrically-short pipeline the exponential terms can be approximated by e(L = 1 + (L and e-(L = 1 - (L . Substituting these in equation (13) and cancelling terms gives

Thus the end voltage is double that for a short pipeline where neither end is grounded.

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Figure 1. Dependence of telluric PSP variations on length of pipelinea) PSP produced by pipelines of lengths: 50, 100, 200, 300, 400 km

All calculations made for an electric field = 1 mV/kmb) Peak PSP as a function of pipeline length. These results show

for lengths < 50 km, pipeline is electrically short (ES)for lengths > 300 km, pipeline is electrically long (EL)

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Figure 2. Dependence of PSP on coating conductancea) Variation of PSP at end of a long pipeline for different coatingsb) Peak PSP as a function of coating conductance

Figure 3. Effect of a decrease in series impedance produced by a doubling of the pipe wall thickness for a 1 km section as shown at the top of the figure.

Figure 4. Effect of an increase in series impedance due to a change from two pipelines to one pipeline for a 50 km section as shown at the top of the figure.

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Figure 5. Dependence of PSP on angle of bend in the pipelinea) Variation of PSP around different bendsb) Peak PSP as a function of bend angle

Figure 6. Dependence of PSP on length of section between bendsa) Variation of PSP for different section lengthsb) Peak PSP as a function of length of section

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Figure 7. Effect of installing flanges on telluric PSP variations a) PSP produced in a 400 km long pipeline with 0, 1, 3, 7 flanges.

All calculations made for an electric field = 1 mV/kmb) Peak PSP as a function of number of flanges

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Figure 8. Dependence of PSP on grounding resistance at the end of the pipeline.a) Variation of PSP at end of a long pipeline for different resistancesb) Peak PSP as a function of end resistance

Calculations made for an electric field of 1 mV/km.

Figure 9. Dependence of PSP on grounding resistance at bend.a) Variation of PSP for different grounding resistanceb) Peak PSP as a function of grounding resistance

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Figure 10. Telluric PSP Variations on pipelines with zero ground resistance at left enda) PSP produced by pipelines of lengths: 50, 100, 200, 300, 400 km

All calculations made for an electric field = 1 mV/kmb) Peak PSP as a function of pipeline length. Also shown (dotted) are

the results when both ends are ungrounded.

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