?#@21.AB%6(.05#@ A 55A6%A366(.71C#Dhk0460/data/dokumente_2008/E_ON_Seminar_2008... ·...
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W. Bilgic 1) ,V. Schmetan 1) , A. Bressanutti 1) , D. Erni 1) , C. Fausten 2) , W. Pascher 3) , H.-G. Schöneich 4) und H.-W. Theilmeier-Aldehoff 4) « Kathodischer Korrosionsschutz » eingeladener Vortrag, TGLK-Sonderthemenrunde, E.On Ruhrgas AG, Essen, 29. August 2008 1) Allgemeine und Theoretische Elektrotechnik (ATE), Fakultät für Ingenieurwissenschaften, Universität Duisburg-Essen, Bismarckstr. 81, 47057 Duisburg. 2) Allgemeine und Theoretische Elektrotechnik, Fakultät für Mathematik und Informatik, FernUniversität in Hagen, Universitätsstr. 27, 58084 Hagen. 3) Institut für Hoch- und Höchstfrequenztechnik, Fakultät für Elektrotechnik und Informationstechnik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg. 4) E.ON Ruhrgas AG, Gladbecker-Str. 404, 45326 Essen. « Kathodischer Korrosionsschutz » eingeladener Vortrag, TGLK-Sonderthemenrunde, E.On Ruhrgas AG, Essen, 29. August 2008 Inhalt: Im aktiven Korrosionsschutz für erdverlegte Rohrleitungen spielen die Ausbreitungswiderstände der Fehlstellen (Kontaktstellen mit dem Erdreich) eine herausragende Rolle für die Effektivität der Korrosions-Prävention. Die Größe des Widerstandes wird maßgeblich durch die geometrische Form, den umgebenden Raum und durch die sogenannte Phasengrenze bestimmt. In dem Vortrag werden zu den bekannten approximativen Formeln mathematisch exakte Formeln der Ausbreitungswiderstände zu elliptischen und ellipsoiden Formen wiedergegeben. Darüber hinaus konnte qualitativ (analytisch und numerisch) nachgewiesen werden, dass die Größe des Widerstandes einer Fehlstelle auch noch von dem Nahfeld anderer Fehlstellen abhängig ist. Grundlage der vorhergenannten Untersuchungen war ein kartesisches Halbraum-Modell, in welchem die Fehlstellen “plan” auf der Grund!äche lagen. Eine Überführung auf ein zylindrisches Rohrleitungs-Modell mit variablem Durchmesser konnte mit Hilfe von Geodäten durchgeführt werden. Die Summe der gewonnenen Erkenntnisse !ießt in eine Approximationskette ein, welche in mehreren Umwandlungsschritten von der verständlichen planaren Fehlstelle zu der zylindrischen Grund!äche mit variablem Durchmesser geht. Den Abschluss bildet die Suche nach kritischen Fehlstellen-Kon"gurationen mit Hilfe eines iterativen Evolutions-Algorithmus unter Einbettung der nichtlinearen Stromdichte-Spannungs-Charakteristik an der Phasengrenze einer jeden Fehlstelle. 1 2 Frei’a)* ,. ./’ober 2008
Transcript of ?#@21.AB%6(.05#@ A 55A6%A366(.71C#Dhk0460/data/dokumente_2008/E_ON_Seminar_2008... ·...
W. Bilgic 1), V. Schmetan 1), A. Bressanutti 1), D. Erni 1), C. Fausten 2), W. Pascher 3), H.-G. Schöneich 4) und H.-W. Theilmeier-Aldehoff 4)
« Kathodischer Korrosionsschutz »eingeladener Vortrag, TGLK-Sonderthemenrunde, E.On Ruhrgas AG, Essen, 29. August 2008
1)Allgemeine und Theoretische Elektrotechnik (ATE), Fakultät für Ingenieurwissenschaften,Universität Duisburg-Essen, Bismarckstr. 81, 47057 Duisburg.
2)Allgemeine und Theoretische Elektrotechnik, Fakultät für Mathematik und Informatik,FernUniversität in Hagen, Universitätsstr. 27, 58084 Hagen.
3)Institut für Hoch- und Höchstfrequenztechnik, Fakultät für Elektrotechnik und Informationstechnik,Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg.
4) E.ON Ruhrgas AG, Gladbecker-Str. 404, 45326 Essen.
« Kathodischer Korrosionsschutz »eingeladener Vortrag, TGLK-Sonderthemenrunde, E.On Ruhrgas AG, Essen, 29. August 2008
Inhalt: Im aktiven Korrosionsschutz für erdverlegte Rohrleitungen spielen die Ausbreitungswiderstände der Fehlstellen (Kontaktstellen mit dem Erdreich) eine herausragende Rolle für die Effektivität der Korrosions-Prävention. Die Größe des Widerstandes wird maßgeblich durch die geometrische Form, den umgebenden Raum und durch die sogenannte Phasengrenze bestimmt. In dem Vortrag werden zu den bekannten approximativen Formeln mathematisch exakte Formeln der Ausbreitungswiderstände zu elliptischen und ellipsoiden Formen wiedergegeben. Darüber hinaus konnte qualitativ (analytisch und numerisch) nachgewiesen werden, dass die Größe des Widerstandes einer Fehlstelle auch noch von dem Nahfeld anderer Fehlstellen abhängig ist. Grundlage der vorhergenannten Untersuchungen war ein kartesisches Halbraum-Modell, in welchem die Fehlstellen “plan” auf der Grund!äche lagen. Eine Überführung auf ein zylindrisches Rohrleitungs-Modell mit variablem Durchmesser konnte mit Hilfe von Geodäten durchgeführt werden. Die Summe der gewonnenen Erkenntnisse !ießt in eine Approximationskette ein, welche in mehreren Umwandlungsschritten von der verständlichen planaren Fehlstelle zu der zylindrischen Grund!äche mit variablem Durchmesser geht. Den Abschluss bildet die Suche nach kritischen Fehlstellen-Kon"gurationen mit Hilfe eines iterativen Evolutions-Algorithmus unter Einbettung der nichtlinearen Stromdichte-Spannungs-Charakteristik an der Phasengrenze einer jeden Fehlstelle.
1
2
Frei'a)* ,. ./'ober 2008
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10
11
Freitag, ,. ./t0ber 2008
0 1 2 3
Ri
Ra,12
Ra,13
Ra,1n
Ra,23
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R22
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z
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titä
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α = ArcCosh[d2 − r2
1 − r22
2r1 r2
]
G11 = 2πκ r1r2 sinh(α)∞∑
n=1
[1
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d sinh(nα)
]
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d
∞∑
n=1
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G22 = 2πκ r1r2 sinh(α)∞∑
n=1
[1
r1 sinh(nα) + r2 sinh [(n − 1)α]− 1
d sinh(nα)
]
Analytische Formel zweier Halbkugeln als Funktion der Größe, der Leitfähigkeit und des Abstandes.
RHK = RK
12πκ rHK
=1
4κ rK
rHK =2π· rK
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der Widerstände von Halbkugeln auf Kreis"ächen übertragbar ist, wenn die Ausbreitungswiderstände
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Halbkugel Kreisförmig
1 2
G11
G22
G12
Abstrahiertes Netzwerk
11
12
Freitag, ,. .ktober 2008
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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4200
220
240
260
280
300
320
Abstand in m →
R11
inΩ→
A1
=10
0cm
2
A2
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0cm
2
R11
R22
R12
!
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0.2 0.4 0.6 0.8 1.0 1.2 1.40
5000
10 000
15 000
20 000
25 000
Abstand in m →
R11
inΩ→
R22
inΩ→
Abstand in m →
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R12
inΩ→
Abstand in m →
A1
=10
0cm
2
R11
R22
R12
A2
=10
cm2
A1
=10
0cm
2
R11
R22
R12
A2
=10
cm2
A1
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2
R11
R22
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A2
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!!!!!!!!!
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]
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≈ R11(planar)[ln
(50√
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mit rp ∈[0.1m · · · 22m
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Risikokonstellationen bei vier Fehlstellen
Linien-Form
Quadratrische-Form
Dreieckige Form
0 0.5 1 1.5 2140
160
180
200
220
240
260
280
300
320
Abstand in m (Mitte,Mitte) !
Au
sb
reit
un
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tan
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Quadrat
Dreieck
Norm
Projektergebnisse - Zusammenfassung
Analytischen Widerstände für Kreis, Ellipse, Halbkugel, halber Ellipsoid
Analytisches Modell für zwei Fehlstellen
Annäherungsgleichung für Widerstände an zylindrischen Oberächen
Annäherungsgleichung für Widerstände an Phasengrenzen
Ein Programm zur Extraktion kritischer Fehlstellen Konstellationen
Ein semi-analytisch arbeitendes Programm für n Fehlstellen auf planaren Flächen zur Extraktion der Widerstandskoefzienten
Annäherungsgleichung für die Umwandlung der planaren Widerstandskoefzienten auf zylindrische Oberächen
22
23
Freitag, 3. Oktober 2008
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