An interpretation of induced electric currents in long

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An interpretation of induced electric currents in long

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AN INTERPRETATION OF INDUCED ELECTRIC CURRENTS IN
LONG PIPELINES CAUSED BY NATURAL GEOMAGNETIC
SOURCES OF THE UPPER ATMOSPHERE
W A L L A C E H. C A M P B E L L U.S. Geological Survey MS 964, Denver Federal Center, Box 25046, Denver, CO 80225, U.S.A.
Abstract. Electric currents in long pipelines can contribute to corrosion effects that limit the pipe's lifetime. One cause of such electric currents is the geomagnetic field variations that have sources in the Earth's upper atmosphere. Knowledge of the general behavior of the sources allows a prediction of the occurrence times, favorable locations for the pipeline effects, and long-term projections of corrosion contributions. The source spectral characteristics, the Earth's conductivity profile, and a corrosionfrequency dependence limit the period range Of the natural field changes that affect the pipe. The corrosion contribution by induced currents from geomagnetic sources should be evaluated for pipelines that are located at high and at equatorial latitudes. At midlatitude locations, the times of these natural current maxima should be avoided for the necessary accurate monitoring of the pipe-to-soil potential.
1. Introduction
With the introduction of long manmade electric conductors on the Earth's surface over 100 yr ago, there arose a concern about the surging electric currents of natural origin that sporadically appeared in such systems. It was soon realized that the spontaneous currents in telegraph wires were associated with aurorae and geomagnetic storms (Barlow, 1849; Clement, 1860; Prescott, 1860, 1866; Hansteen, 1860; Burbank, 1905; Chapman and Bartels, 1940; Harang, 1951; and Stormer, 1955). Similar current fluctuation problems were reported in submarine communication cables (Saunders, 1880, 1881; Axe, 1968; and Meloni et al., 1983) and long power transmission lines (Davidson, 1940; Slother and Albertson, 1967; Albertson and Van Baelen, 1970; Albertson et al., 1974; Akasofu and Merritt, 1979; Akasofu and Aspnes, 1982; Boerner et al., 1983; and Pirjola, 1983). Although the existence of natural induction currents in pipelines had been reported at an early date (Varley, 1873, reported in Lanzerotti and Gregori, 1985), it has been only in recent years, concurrent with the construction of very long oil and gas transmission systems and with the concern for pipe corrosion protection, that research started on this effect (Gideon et al., 1970; Campbell and Doeker, 1974; Hessler, 1974; Cambell, 1978; Peabody, 1979; Cambell and Zimmerman, 1980; Campbell, 1980; Barker and Skinner, 1980; Smart, 1982; Brasse and Junge, 1984).
A detailed corrosion analysis of a particular pipeline section can be rather complicated. Nevertheless, it is relatively easy to understand the important physical processes that are responsible for the electric currents in a long conduction pipe during geomagnetic field disturbances. These fields are a result of source currents flowing above the Earth's surface. With every changing magnetic field there is an associated electric field of identical frequency and related amplitude and phase. The
Surveys in Geophysics 8 (1986) 239-259. 9 1986 by D. Reidel Publishing Company.

240

WALLACE H. CAMPBELL

electric fields enter the Earth's surface to a depth that is dependent upon the source frequency and the penetration region conductivity. Electric currents driven by these 'internal' processes have associated magnetic and electric fields that add to the observations at the Earth's surface. Small-scale conductivity irregularities at the surface modify these Earth currents (and its driving potential difference). A grounded conductor, such as a pipeline, represents a low resistivity path for the flow of Earth-induced currents. Corrosion occurs at a grounded pipe, in contact with suitable ions of the soil, whenever the current through this location is large enough, of the correct frequency, and in the proper direction. In the following sections, the above process will be outlined in greater detail.
Three subjects are to be covered in this review. First, I will discuss some of the most important source-field characteristics, focussing upon the variability with location, spectral composition, direction, time-of-day, season, and solar cycle predictions. Second, I will review the effects of these varying fields upon both the current flow and the corrosion in a long grounded pipeline. Third, some measurement methods for pipe current and pipe-to-soil potential will be given. Battery effects of pipe contact with the soil, lightning strike and induction phenomena, or manmade causes of pipeline currents, are not within the subject or this presentation. The focus of this paper is upon the understanding of the physical processes that cause natural electric currents to flow in long pipelines during times of geomagnetic field fluctuations; it is not the purpose of this paper to give detailed pipe current analysis or protection techniques for pipeline engineers.

2. Source Field Characteristics
Upper atmospheric currents are a major source of the natural field variations that are of interest for the pipeline effects presented in this paper. The majority of these currents flow in an ionized region (ionosphere) at about 100 km altitude. The currents differ in character depending upon the active or quiet behavior of the Sun. Active times have been correlated with a string of solar-terrestrial phenomena that begin with observable changes on the solar surface (related to sunspots) (White, 1977) and include modifications during the flow of fields and particles to the vicinity of the Earth, deformation of the shape of the Earth's main field in space, and the development of currents that flow both at a great distance about the Earth and into the auroral region. By way of the ionosphere, the strong auroral currents (sometimes called 'electrojets') are communicated to the entire globe. A secondary concentration of these currents occurs in the equatorial region because the horizontal direction of the Earth's main field creates an ionospheric band of high conductivity there.
Two 3-hr planetary indices are commonly used to indicate the geomagnetic field
disturbance level. The Kp index has a quasilogarithmic scale of 0 to 9 that is
convenient for general indications of the activity levels. These indices are usually
converted to equivalent Ap indices which are linear with respect to field strength. As a 'rule of thumb' the Ap may be taken as an indicator of a 3-hr range of the

AN INTERPRETATION OF INDUCED ELECTRIC CURRENTS

241

TABLE I Ap geomagnetic activity index

(a) Occurence Most probable value 50% occurrence Low value, once every 2 yr Active value, once every 2 months High value, once every 2 yr
(b) Formula representations Days per year with activity _>Ap
N(high) = 4.14 • 104 Ap -zz5 +_6% (for Ap = 15 to 150) Days per year with activity - N(low) = - 52.3 + 267.4 log Ap +_4%0 (for Ap = 2 to 20)

Ap index 5
<8 0
> 52 > 150

excursions in H, the magnetic northward component of the geomagnetic field in gammas (nanoteslas), at midlatitudes. On a long time sample over many years, the occurrence of various levels of Ap indices are statistically predictable. Table I illustrates how Ap behaves over a 40-yr sample. For example, the expected number of days that Ap would be at some quiet level below a specified value is obtained from the last equation in Table I. In the pipeline corrosion studies, attempts are made to identify the induction-related currents with Ap indices. Table I then allows prediction of the statistical occurrence of such currents over the estimated lifetime of the pipeline.

k,p

Ap30-DA19YR32U-N19N6IN1GMEAN

181

20

2 ~

18~ / ~

Absolute / ~

6 ~

Joo ~oSo~rDeclinati~ 9 o=~ 10~

16

4 ~

"~

""

~

14

8 ~

12

!2 ~

IIII II III II

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

Fig. 1. 30-day running mean of geomagnetic activity index, Ap, for 1932 to 1961 (dots and scale to left) and 6 the absolute value of solar declination (curved trace) showing semiannual characteristics of the geomagnetic index with maxima at the equinoxes and the slightly greater values in northern hemisphere summer because of the dominance of northern stations that contribute to the index (figure redrawn from
Roosen, 1966).

242

WALLACE H. CAMPBELL

i fi i i i i I i [ f i I f i I t i I r [ iI

D ANvJol overo ~ Zurich II~JnspOf

numbor, Rz

] 160

MAp_> 40

JI o,p_

140

~Ap_> BO

["--"J Ap _~ IOO

120
gz100 /~ri~
80

I 115S50 O

~

~A

45 Y

.. S

-35

60 /

,O/!o 4o J

b

!~

I - 20

i . o 32 54 56 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 lO 72 74 /6 (8 80

YEAR
Fig. 2. The number of daysper year (scaleat right) in which the geomagneticindexApexceededvalues

of 40, 60, 80, or 100 in the period 1932 through 1980. Annua] sunspot number indices, Rz, are also
indicated on scale at left (figure from Allen, 1982).

SPECTRAL COMPOSITION MID LATITUDE H

WINTER

EQUINOX

MINIMUM LEVEL Ap 10.0

ACTIVE LEVEL Ap 10.0

~ 2 0.1 <

~ 0.1

o.ol t: 5 10

t 30 1 2 5

o.o .5 10 I 1 ,30 1 2 .5

minutes

hours

minutes

hours

PERIOD

PERIOD

Fig. 3. Example of geomagnetic field spectral composition changes for a midlatitude H component of

field. Left: winter, minimum levelAp. Right: equinox, activelevelAp (cf, Campbell, 1973,1976b, 1977b).

AN INTERPRETATION OF INDUCED ELECTRIC CURRENTS

243

FIELD VARIATION AMPLITUDES 90

U,.I UJ O:
(.9
UJ
tm
60
UJ
o :3
t..<
,,_1

I.--

U.I
z

30

CO

<

O
LU
L9

l /Z~

/

1

/

/

/

/

i

/

"~ F
!.J7 ,,

0L.-

0.1

0.2 0.3 0.5 0.7 1

2 3 5 7 10

20

AMPLITUDE A/T (100 ,y/min)

Fig. 4. A representationof the geomagneticvariation amplitudesfor the period range of 5 min to 4 hr during a year of minimumactivity.H, D, and Z orthogonal field componentsand total fieldamplitudes,
F, are shown. The spectral amplitudes (divided by the period in minutes and multiplied by 100) are
averaged to form the amplitude scale shown here (figure redrawn from Campbell, 1976a).

Geomagnetic activity has both a seasonal and solar-cycle behavior. Figure 1 (Roosen, 1966) shows the outstanding equinoctial maxima in Ap indices; this means that the Sun-Earth alignment during March and September favors the interaction of the solar wind with the Earth's magnetosphere so that larger disturbances occur about the globe. The annual geomagnetic activity rises and falls with 10 to 11-yr cycles in general agreement with the annual average sunspot number index. Figure 2 illustrates this behavior for the period of 1932 to 1980 (Allen, 1982). Once a relationship is established between the pipeline current and the Ap index, estimates of the current activity levels in a future time or over the expected life of the pipeline are possible from the predictions of Ap available at World Data Center A for Solar Terrestrial Physics and/or the Space Environment Forecasting Center, both operated by NOAA in Boulder, Colorado, U.S.A.
As the geomagnetic levels of activity change, both the relative spectral composition and the amplitudes of the disturbance field variations change. Figure 3 illustrates this point by comparing the spectral samples of a quiet day, having Ap values near zero, to that of an active day, having Ap values near 70, for the field variation periods of 5 min to 5 hr. A clear diurnal variation of the amplitudes has also been found. Because of the unique global distribution of the geomagnetic disturbance currents

244

WALLACE H. CAMPBELL

O I<- 2.0
tr LU
E3 1.5
.,.J
Q_ 1.0 <
LU 0.5

DALLY CHANGE IN FIELD DIRECTION SAN JUAN

'

1 '

I

'

I

i

T i I

i

0 r I I I JI , II I I

Z

0

4

8

12

16 20 24

LOCAL TIME (hr)

Fig. 5. The average daily change in field direction for variations of 10 to 60 rain period at San Juan (during a time of high geomagnetic activity) displayed as the ratio of N-S component to E - W component
amplitudes (figure redrawn from Campbell, 1977a).

about the Earth there is a unique distribution of field amplitudes with latitude. In Figure 4 note the minimum field sizes between about 15 to 40 deg geomagnetic latitude, the maximum at the high latitude auroral zone, and a seondary maximum near the equator. There is some seasonal shift in these locations as well as in the amplitudes.
One further characteristic needs to be described to complete the picture of the disturbance source currents. Note in Figure 4 the change of component relative amplitudes with respect to latitude means that the source current direction is latitude dependent. There is also a time-of-day change in these current directions at all locations as illustrated for San Juan in Figure 5. If the ground conductivity is assumed to be uniform horizontally over a region that is large with respect to the source size, a pipeline grounded in the direction of the source-current flow will carry the largest induced electric current.
Another cause of the special pipeline geomagnetic effects is the ionospheric dynamo current driven by winds and thermal-tidal motions. These currents, called
Sq by geomagneticians, cause most of the 24-, 12-, 8-, and 6-hr daily variations of
field at the Earth's surface (Figure 6). The amplitude of these currents increases with
the Ap index, and therefore Sq responds to sunspot-cycle changes. Figure 7 illustrates
the expected fields from an external ionospheric dynamo current system determined for an average quiet day of each month during a year of low solar activity. Note three things in particular: there is a shift between the northward (H) and eastward (D) components at specific latitudes and seasons of the year; there is an annual amplitude
change at all latitudes and a semiannual change at low latitudes; amplitudes of Sq
fields are particularly large near the equator. With increasing activity level the
amplitudes of Sq increase two to three times in size and the phase shifts slightly. In

AN INTERPRETATION OF INDUCED ELECTRIC CURRENTS

245

D TUCSON SPECTRAL COMPOSITION

1.0

I

I

0.8
t.-
E
iii
a 0.6

_.J n

< 0.4

.<- I

E:

I--

(J iii

0.2 b

O9

March 1965

6 hr

8 hr

12 hr

24 hr

VARIATION PERIOD (weeks) ,--~.

Fig. 6. Fourier analysis spectral amplitudes in the period range of 4 weeks to 6 hr for averaged Tucson D-component daily magnetograms in March 1965.

NORTH AMERICAN Sq(H, D, Z) FROM SHA COEFFICIENTS

H COMPONENT

D COMPONENT

Z COMPONENT

i i f Fi } I I I i iI
80oL~ A ,I A ,41A ,dl 9 9 ~--.
vvvvvf/yv''"

i 8oo',i ', i i i 'i " w w W r.V A

,vvvvl]vv--,,

~ 7~

V V V V t I V'f'"

700JilliJ rrvrr.r.

. l a % ~ r r % 70. .9.~.- , - ~wA Iw W ,l~d l -.v.-. . . ~ -

~,0o~0o",~-v~-'v~" "v~"v-,-" ;-

60o. A a l l t ] 9 r vr y./,

._1

-v--r162 ;;

'v V 'v i

v

s0oAaiJ I J J

v crryt.

-yrr

v--

U

,,P], a0o~ -.. 7"

--_--._-

. - v v -v~ - - v

o 2oo.~ - * " I I l , . i j , . . ~

~0o; # # %

; -. ;*.#,.

----.--.--v--

y 9 ---

-. ; ~0o-,-v~-'v--,--,--,~-v~-,-,-

J F M AM J J A $ ON D

I I r I I I I I I IOINIDI J F M A /,A J J A S MONTH

I ] J I I I I I I I0 I P

J FM A M J J A S

N D

Fig. 7. Annualpictureofthedailyvariations (inlocaltime) ofSq from the equator to 80~latitude(bottom of top rows) displayed for H, D, and Z field components at left, center, and right sections respectively. The scale size between baselines is 50 gammas. Months of the year are indicated at the bottom of each
section (Campbell, 1983).

246

WALLACE H. CAMPBELL

~-~

/ -

HUANCAYO H

A~

28,0:397

JL ~ ~) I 0

23 March 1966

I

I

06

I

i

12

~'

I

I

I

I

18

00

Hours, UT

24 MMaarrcch 1966

I

I

06

I

I

12

l

I

I

18

O0

Fig. 8. Magnetogram of H component of field for the equatorial observatory at Huancayo, Peru, for a geomagnetically active day (23 March) and a relatively quiet day (24 March). Local time is 5 hr earlier
than the UT time given at bottom of figure.

Figure 8 we see, in sequence, a solar-terrestrial disturbance variation (23 March) and a Sq variation (24 March) at an equatorial location. For the study of pipeline effects, the most important features of geomagnetic fields in the active or quiet times are the frequency composition, the amplitudes, and the direction relative to the grounded locations of the pipeline.

3. Induction in Earth and Pipe

The depth of penetration into the Earth by the upper atmospheric source fields depends upon the frequency and Earth's conductivity profile: the lower the frequency, the deeper the penetration and the higher the conductivity, the shallower the penetration. A 'skin depth' concept is used for visualizing a comparison of the penetration of fields within a conductor. For a homogenous region of conductivity a [Siemens/meter or (~m)-1] with the period of the field oscillation given as T (minutes) we call the 'skin depth' in kilometers

= .f600 T/cr/27r,

(1)

the depth at which the amplitude of the field drops to about one-third (1/2.718) of the original size. If the conducting material is very thin with respect to 6, then we consider the electromagnetic wave to be unaffected ('not seen') by the conductor.
For the geomagnetic fields of interest here the pipe is too thin to be noticed. For example, consider a steel pipe with a conductivity of 4 to 6 x 10 6 Siemens m - 1. For field changes of 2 to 40 min periods the skin depth would be about 2 to 12 m; for field changes of 6 to 24 hr periods the skin depth would be about 30 to 74 m. Steel pipe wall thickness of even 2 cm hardly disturb these long waves. No interaction means that there is no induction process, or induction currents of importance, in the pipe directly. Yet we know that induction-like currents are measured in the pipeline so how do they get there?
Figure 9 from Campbell and Zimmerman (1980) and Figure 10 from Barker and Skinner (1980) illustrate the association of pipeline currents with the natural electric and magnetic fields. These currents occur in the pipeline because the currents induced within the Earth by the natural sources have found an easy-flowing path through the

AN INTERPRETATION OF INDUCED ELECTRIC CURRENTS

247

COLLEGE ELECTRIC POTENTIAL Eco

/

/

/

/

[_L

09

I0 \ \ \ il

12

13 UT

I

I

I

I

f

I

I

I

I

I

CHENA PIPELINE CURRENT lc. 5 AUGUST 1978

[~0o Amps

Fig. 9. Simultaneous appearance of the Earth's electric field potential, Eco, in milliwatts km- 1measured at College, Alaska, (top trace) and the Alaska oil pipeline current, I:~,, in amperes (bottom trace) measured at nearby Chena, Alaska, between 0900 and 1330 UT on 4 August, 1978. Local time is 10 hr earlier than
the UT time given (figure from Campbell and Zimmerman, 1980).

TO NAIROBI

PIPELINE CURRENT AND MAGNETIC FIELD

Pipeline Current 0

~L ~_ _ ~-""~

v

--

~

~

,,J"

2 Oct

3 Oct

4 Oct

TO MOMBASA ~

Magnetic H

Field

Change 12 16 20 24

0 04 08 12

0 04 08 12 16 20 24

LOCAL TIME

Fig. 10. Simultaneous appearance of the H component of magnetic field variations (in nanotesla) measured at Nairobi, Kenya, and the current (in amperes) in the 450 km pipeline between Mombassa and Nairobi. The period from noon 2 October to noon 4 October, 1978, local time, is shown (figure redrawn
from Barker and Skinner, 1980).

pipe. Thus, our next step toward understanding the process is to look at the frequency, amplitude, and directional effects that the induction processes play in establishing the Earth's currents.
The equations for the relationship of the orthogonal magnetic and electric fields measured for each frequency component at the Earth's surface were originally developed by Caignard (1953) and Tickhonov (1953). If a plane wave source is assumed, the relationship between the magnetic and electric field magnitudes may be represented by the formula

248

WALLACE H. CAMPBELL

E-B FIELDS AT COLLEGE

E(N-S)

217 mv/km

B(E-W)

~- 23.9 I gammas

T= 459 sec

0600

UT (hr) 16 JULY 1959

0700

Fig. 11. Correspondingnorth-south(N-S)electric(E) fields(mV km- 1)and magnetic(B) fields(gamma) for north-south and east-west (E-W) fluctuations at College, Alaska.

where By and Ex are the horizontal, orthogonal, magnetic (B), and electric (E) field
components in nT and mV km - 1, respectively; Tis the oscillatory period in minutes and a is the effective conductivity o f the model Earth in S m - 1 . Figure 11 is an example of the corresponding variations of electric and magnetic fields.
The importance of electromagnetic methods to the surveying of crustal materials has led to extensive theoretical developments in this subject (cf., Wait, 1982; Filloux, 1979). For the typical situations that are of interest at mid and low latitudes, one may consider the ionospheric currents as quite large and sheet-like with respect to the study size of a pipeline so that the source fields represent a plane wave at the Earth's surface. At the high latitude auroral region the sources are more like line currents, rather than sheet currents, and special source dimension factors need to be included in the analysis. The intense aurorally associated currents at high latitudes have an approximate size L (km) of 12 times the oscillatory period T (rain). For a given subsurface conductivity structure the amplitude and phase of the ratio for orthogonal electric to magnetic fields may be determined (cf., Wait, 1962; Jackson
EarthCurrentsFieldsPipelineField