glq3205 géophysique appliquée 2 méthodes Électriques...glq3205 géophysique appliquée 2...
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GLQ3205 Géophysique appliquée 2
Méthodes Électriques Gabriel [email protected]
Été 2018
Plan du cours
1. Équations constitutives du DC 2. La résistivité électrique 3. Les source de courants terrestres 4. La méthode de la polarisation
spontanée
1
L’échec des mesures ponctuelles
10 points de mesure $ Interpolation linéaire
à
Mesures géophysiques
La géophysique apporte un image floue de moindre précision, qui permet cependant de mieux discerner la structure globale.
Révision: Introduction
2
Mesures indirectes
Propriété géophysique: Une propriété physique mesurée ou estimée par une méthode géophysique. La plupart du temps, c’est une mesure que l’on dit indirecte, c’est-à-dire qu’elle n’est pas un propriété géologique en soi.Ex: La densité telle que mesurée en gravimétrie
Les liens entre les propriétés géophysiques et les propriétés géologiques se nomment les relations pétrophysiques.
Les mesures géophysiques comportent des avantages et inconvénients:
Inconvénients • Résolution limitée• Intégration quantitative difficile• Mesures parfois ambiguës • Demande un personnel
spécialisé• Échec possible des levés
Avantages • Continuité spatiale des mesures• Ratio volume investigué/coût
élevé• Mesures non-destructives
3
Révision: Introduction
Propriétés physiques et modèles physiques
En géophysique, nous voulons faire la mesure de quantités observables afin d’inférer les propriétés physiques de la sous-surface pour en faire un interprétation géologique.
Questions importantes: • Quelles quantités observables peuvent être reliées à quelles propriétés physiques ? • Quel est l’impact des incertitudes des mesures sur l’estimation des propriétés
physiques ? • Est-ce que les mesures requises sont réalisables ?
Modèle physiquePropriétés physiques
Quantités Observables Inversion
géophysique
Propriétés géologiques
4
Révision: Introduction
Méthodes géophysiques classiques
Famille Loi physique Observable Propriété
Gravimétrie Loi de la gravité Accélération gravitationnelle Densité
Sismique Mécanique des milieux continus Vibrations Modules élastiques
Magnétisme
Équations de Maxwell
Champ magnétique
Champ électrique
Potentiel électrique
Perméabilité magnétique
Électrique Résistivité électrique
Électromagnétique Résistivité électrique
Géoradar Permitivité diélectrique
Résonance nucléaire Contenu en eau
5
Révision: Introduction
Roc peu profond (Shale)
Vallée SpiritWood large
Tributaire ?
Chenal central profond
Système à chenaux multiples
Conducteur
Résistant
La géophysique en 7 étapes
1. Formulation du problème
2. Choisir les propriétés géophysiques à mesurer
3. Sélectionner une méthode géophysique
4. Acquérir les données
5. Traiter les données
6. Interpréter les résultats
7. Synthèse
6
Révision: Introduction
1. Les équations constitutives en électrique
7
Champ électrique
• Équation de Maxwell-Gauss:
• Pour une charge élémentaire, la solution est
• Une charge placée dans ce champ subira une force donnée par:
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8
Les équations constitutives en électrique
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Potentiel électrique
• Il est plus commode de résoudre les équations d’électrodynamique à l’aide du potentiel électrique
• La direction du champ électrique est perpendiculaire aux équipotentiels
• La magnitude du champ électrique est proportionnel à la densité des équipotentiels
Équipotentiels Champ électrique
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9
Les équations constitutives en électrique
Densité de courant
• Des charges libres dans un champ électrique subiront une force, qui causeront un déplacement de charges. Ce flux s’appelle la densité de courant:
• La conductivité est le rapport de la densité de courant par rapport au champ électrique
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10
Les équations constitutives en électrique
Loi d’Ohm
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<latexit sha1_base64="3+/lmJzg4zGfqQD4QBNdK68sP08=">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</latexit>
• On se souvient de la loi d’Ohm
• L’expression locale de cette loi n’est autre que
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11
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Les équations constitutives en électrique
Conductivité électrique
• La conductivité électrique est un propriété intrinsèque, tandis que la résistance dépend de la géométrie de l’object.
• La conductivité décrit la facilité des charges à se déplacer dans un matériau, tandis que la résistivité décrit la résistance au déplacement de ces charges.
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12
Les équations constitutives en électrique
Analogie avec la loi de Darcy
La loi de Darcy:
Équation de la continuité:
La loi d’Ohm:
Équation Maxwell-Gauss (sans charge)
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13
Les équations constitutives en électrique
Équipotentiels et lignes de courant dans le sol
Les lignes de courant traversent perpendiculairement les équipotentiels, exactement comme en hydrogéologie!
14
Les équations constitutives en électrique
Équipotentiels et lignes de courant dans le sol
Les lignes de courant traversent perpendiculairement les équipotentiels, exactement comme en hydrogéologie!
15
Les équations constitutives en électrique
• Définition de la densité de courant
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Résumé des équations en électrique
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Variable Symbole Unités
Champ électrique
Potentiel électrique
Densité de courant
Conductivité
Résistivité<latexit sha1_base64="t2sbM8MUKAuIRk9eIDPjMq2LJT8=">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</latexit>
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• Équation de Maxwell-Gauss:
• Définition du potentiel électrique
densité de charge!
• Relation résistivité/conductivité
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16
Les équations constitutives en électrique
Points importants
17
• Les différences de potentiels électriques induisent des courant électriques dans le sol.
• Les courants électriques peuvent être de nature naturelle, anthropique ou induite.
• La distribution du courant dans le sol dépend de sa résistivité électrique
• Les méthodes électriques mesurent les courants et/ou les différences de potentiels
Les équations constitutives en électrique
2.0 La résistivité électrique des matériaux poreux
18
Définition
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• On se souvient de la loi d’Ohm
• L’expression locale de cette loi n’est autre que
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19
La résistivité électrique des matériaux poreux
Mécanismes de conduction
20
• Conduction électronique: • Significative en présence de métaux uniquement
• Conduction ionique: • en présence d’une solution électrolytique dans les pores • déplacement des ions par diffusion
• Conduction de surface • Conduction dans la double couche d’Helmoltz • Proportionnelle à la surface spécifique des pores • Devient significative dans les silts et argiles
La résistivité électrique des matériaux poreux
Conduction électronique
21
• Certain minéraux sont naturellement conducteurs. • Les métaux possèdent des électrons libres, qui ne sont pas liés par aucun
atome, et peuvent donc former un courant. • Le porteur de charges est l’électron.
La résistivité électrique des matériaux poreux
Conduction ionique
La conductivité d’une solution électrolytique:
• : densité de charges • : charge • : viscosité du fluide • : rayon effective de l’ion
22
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La résistivité électrique des matériaux poreux
Conduction ionique: effet de la température
Pour l’eau, on peut réduire la formule précédente à:
• : solides dissous (mg/L) • : température °C
23
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La résistivité électrique des matériaux poreux
Conduction de surface
24
• La double couche d’Helmoltz contient des ions permettant la conduction d’un courant électrique
• Plus le ratio surface/volume des pores est élevé, plus la conductivité de surface est élevée.
La résistivité électrique des matériaux poreux
Résistivité effective d’un milieu hétérogène
Résistivité transversale (résistances en série)
Résistivité longitudinale (résistances en parallèle)
25
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La résistivité électrique des matériaux poreux
Exercice: Conductivité des trois mécanismes
Quel mécanisme domine pour ce matériau poreux ?
26
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Modèle simplifié d’un pore<latexit sha1_base64="Ou+Y7Hr74CWdILppoysunkmuKC8=">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</latexit>
La résistivité électrique des matériaux poreux
Loi d’Archie
27
Lorsque la conduction est totale est dominée par la conduction ionique, Archie a empiriquement observé la loi suivante:
• : Facteur de formation • : Porosité • : Saturation en eau
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La résistivité électrique des matériaux poreux
Loi d’Archie: paramètres
28
• a: dépend de la tortuosité proche de 1 (0.6< a <1.5)
• m: facteur de forme • dépend de la forme des
pores et de leur connexion
• n: dépend du fluide • eau=2 • huile = 2.08
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La résistivité électrique des matériaux poreux
Loi d’Archie: paramètres
29
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La résistivité électrique des matériaux poreux
Loi d’Archie: Avec conduction de surface
30
Des corrections sont possibles lorsque la conduction de surface devient importante
• : ratio surface/volume des pores
• : Mobilité des ions • : Densité volumique des
charges des ions dans la double couche
+ d'argile
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La résistivité électrique des matériaux poreux
Résistivité des roches et des sols
31
Résistivité (Ωm)
Conductivité (mS/m)100000 10000 1000 100 10 1 0.1 0.01
1000001000010001001010.10.01Sulfures
GraphiteRoches éruptives
Roches métamorphiquesArgiles Sables
Eau salée Eau douce
Shales
Lignite, charbon
Permafrost
Grès conglomérats
Roches éruptives et métamorphiques
Dolomite, calcaire
BOUCLIERROCHES NON ALTÉRÉES
COUCHE ALTÉRÉE
SÉDIMENTS GLACIAIRES
ROCHES SÉDIMENTAIRES
EAU, AQUIFÈRES
La résistivité électrique des matériaux poreux
Résistivité électrique: points importants
La résistivité électrique est principalement affectée par:
• la porosité• la teneur en argile• la forme des grains composant la
matrice
Mais est aussi grandement influencée par:
• la conductivité de l’eau• la saturation• la température
32
La résistivité électrique des matériaux poreux
2. Le potentiel électrique terrestre
33
Les sources de potentiel électrique
Dans le cas de la loi de Darcy, la gravité contrôle les charges hydrauliques.
Dans le cas du potentiel électrique, plusieurs sources naturels existent:
• Altération des sulfures
• Contacts géologiques de roches de différentes compostions
• Activité bioélectrique du matériel organique
• Corrosion
• Gradients thermiques
• Écoulement de fluides souterrains
34
Le potentiel électrique terrestre
Les sources de potentiel électrique
Nous regrouperons les potentiels en 3 catégories:
• Les potentiels électrocinétique
• Les potentiels électrochimiques
• Les potentiels de minéralisation
La méthode de la polarisation spontanée se base sur ces trois potentiels. Notons qu’il existe d’autres sources naturelles, qui seront considérées comme des bruits.
• Le potentiel bioélectrique
• Les potentiels telluriques
35
Le potentiel électrique terrestre
Potentiel électrocinétique
• La parois des grains de matériaux poreux se charge en présence d’une électrolyte
• Ceci crée une double couche électrochimique. La couche près de la paroi est une couche immobile.
• La distribution de charges crée un potentiel électrique qui décroit avec la distance
• Le potentiel d’adsorption , aussi appelé le potentiel zeta , est le potentiel à l’interface de la couche stationnaire et diffusive
https://wiki.anton-paar.com/en/zeta-potential/36
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Le potentiel électrique terrestre
Potentiel électrocinétique
• Lorsque l’électrolyte s’écoule dans le milieu poreux, les ions positifs de la couche diffuse sont entrainés par le courant. Les charges positives s’accumulent et crée une différence de potentiel, créant à son tour un courant de conduction dans la couche de Stern de sens opposé à l’écoulement. Le potentiel électrique créé est donnée par:
: Pression : Potentiel d’adsorption : Viscosité du fluide : Permittivité électrique
https://wiki.anton-paar.com/en/zeta-potential/
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37
Le potentiel électrique terrestre
Potentiel de diffusion
Le potentiel de diffusion est donné par
: charge/ion : Nombre d’Avogadro : Température absolue : Mobilité des anions (cations) : Constante de Faraday : Concentration des solutions 1 et 2
Pour NaCl à 25 C:
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<latexit sha1_base64="dcbGWgxHNr8C+kghF8UZYeOS6pk=">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</latexit>
<latexit sha1_base64="If6+UyS+Ufye/SHdkbwmbpzw8y0=">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</latexit>
<latexit sha1_base64="0zM5A/pwzbjCWCaXBr59pIYX/KY=">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</latexit>
<latexit sha1_base64="QIyXY4yY5eQ8oz808uDVRRsqH8w=">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</latexit>
<latexit sha1_base64="M+hO9e7eTUTWBtTS50oLhiOFris=">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</latexit>
<latexit sha1_base64="BpJmkkKeVwnIfID8eNisHFG5ibE=">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</latexit>
<latexit sha1_base64="Mtl/1o+7FiYuc9sp6Ge3WLGqpjc=">AAADa3iclVLLTttQED2JC4VAeZQd7cIiQkJdRA4ClWWkbroEiQASRMg2N2Dhl+zrtCjiC9jCx/EHdNF/6JnBQVQVolzL8dwz55w7M7lBHkel9bz7RtN5NzX9fma2NTf/YWFxafnjQZlVRWj6YRZnxVHglyaOUtO3kY3NUV4YPwlicxhcfpP84cgUZZSl+/YqN4PEP0+jYRT6ltDe/ulS2+tsbntc7r9Bt+PpaqNeu9ly4wtOcIYMISokMEhhGcfwUfI5RhcecmIDjIkVjCLNG1yjRW1FliHDJ3rJ33Pujms05V48S1WHPCXmW1DpYp2ajLyCsZzmar5SZ0Ff8h6rp9R2xW9QeyVELS6IvqabMP9XJ71YDLGjPUTsKVdEugtrl0qnIpW7z7qydMiJSXzGfME4VOVkzq5qSu1dZutr/kGZgso+rLkVftVVpkR+6LQSrT+l+5i4MEesSP6zgSLiM9QzxDeg4qfi4lhqleZpAoKPlPl2ZZsnXj97WryHk8vmvhwcbHa6Xqe7t9Xu9eobOYNPWMMG/b6ih+/YRV/7usEt7pq/nRVn1fn8SG02as0K/lrO+h/SCLAU</latexit>
Cause: Différence de mobilité entre les anions et les cations de deux solutions en contact de concentration différente
38
https://www-ig.unil.ch/c_diaf.htm
Le potentiel électrique terrestre
Le potentiel de Nernst est donné par
: charge/ion : Nombre d’Avogadro : Température absolue : Constante de Faraday : Concentration des solutions 1 et 2
Pour NaCl à 25 C:
Potentiel de Nernst
<latexit sha1_base64="n9442Q4WxO+w6k2MB6M9aDov8Y4=">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</latexit>
<latexit sha1_base64="NFbZXSDrTe1LenfQEQkKyzdzyDo=">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</latexit>
Cause: Deux solutions de concentration différente séparée par une membrane sélective, qui diffuse uniquement les cations, et crée une différence de potentiel
<latexit sha1_base64="0zM5A/pwzbjCWCaXBr59pIYX/KY=">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</latexit>
<latexit sha1_base64="QIyXY4yY5eQ8oz808uDVRRsqH8w=">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</latexit>
<latexit sha1_base64="M+hO9e7eTUTWBtTS50oLhiOFris=">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</latexit>
<latexit sha1_base64="BpJmkkKeVwnIfID8eNisHFG5ibE=">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</latexit>
<latexit sha1_base64="Mtl/1o+7FiYuc9sp6Ge3WLGqpjc=">AAADa3iclVLLTttQED2JC4VAeZQd7cIiQkJdRA4ClWWkbroEiQASRMg2N2Dhl+zrtCjiC9jCx/EHdNF/6JnBQVQVolzL8dwz55w7M7lBHkel9bz7RtN5NzX9fma2NTf/YWFxafnjQZlVRWj6YRZnxVHglyaOUtO3kY3NUV4YPwlicxhcfpP84cgUZZSl+/YqN4PEP0+jYRT6ltDe/ulS2+tsbntc7r9Bt+PpaqNeu9ly4wtOcIYMISokMEhhGcfwUfI5RhcecmIDjIkVjCLNG1yjRW1FliHDJ3rJ33Pujms05V48S1WHPCXmW1DpYp2ajLyCsZzmar5SZ0Ff8h6rp9R2xW9QeyVELS6IvqabMP9XJ71YDLGjPUTsKVdEugtrl0qnIpW7z7qydMiJSXzGfME4VOVkzq5qSu1dZutr/kGZgso+rLkVftVVpkR+6LQSrT+l+5i4MEesSP6zgSLiM9QzxDeg4qfi4lhqleZpAoKPlPl2ZZsnXj97WryHk8vmvhwcbHa6Xqe7t9Xu9eobOYNPWMMG/b6ih+/YRV/7usEt7pq/nRVn1fn8SG02as0K/lrO+h/SCLAU</latexit>
39
https://www-ig.unil.ch/c_diaf.htm
Le potentiel électrique terrestre
Potentiel électrochimique
40
Le potentiel électrochimique est donné par la somme des potentiels de diffusion et de Nernst
Pour NaCl. À 25 degrés, pour un rapport de concentration 5:1, ce potentiel atteint ~50 mV
<latexit sha1_base64="D9yOPSeE/nVA1uNh249YRWod3xA=">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</latexit>
Le potentiel électrique terrestre
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Modèle de la cellule électrochimique
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Le potentiel électrique terrestre
Potentiel de minéralisation
Surface
Sens du courantO2 gazeux
H2O
tabled'eau
anomalie
H+
Fe++
Fe(OH)3
Fe(OH)3
Fe(OH)2
H+
OH-Fe+++
Fe++
FeS2
HFeO2O2 dissous
H2O2OH-
Électrons
-
+
cathode
anode
réduction
oxydation
• Le modèle du potentiel de minéralisation est basé sur la cellule électrochimique.
• Apparait surtout en présence de sulfures métalliques, de graphite et certains oxydes métalliques telle que la magnétite.
• Des différences de l’ordre de ~1V sont observées sur le terrain !
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Le potentiel électrique terrestre
Potentiel due à la biodégradation
• Le même modèle de cellule électrocinétique a été appliqué pour la biodégradation des contaminants organiques
• Les bactéries métabolisent les hydrocarbures rapidement en présence d’oxygène.
• Lorsque tout l’oxygène est consommée, la métabolisation continue plus lentement en régime anaérobique. Le fer, le souffre le nitrate sont utilisés comme accepteur d’électron, ce qui crée une zone réduite.
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Amplitude ~100mV
Le potentiel électrique terrestre
Le biopotentiel
• Les plantes pompent de l’eau par leurs racines et se nourrissent de nutriments (ions) de façon sélective
• Une différence de potentiel se crée donc entre les zones de différente couverture végétale.
• Ces anomalies sont de l’ordre de ~100 mV.
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http://landviser.net
Le potentiel électrique terrestre
Source de courants telluriques (~100 mv)
Vents solaires
Éclairs
Résonance ionosphère45
Le potentiel électrique terrestre
Bruits anthropiques
Vents solaires
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Le potentiel électrique terrestre
(Naudet, 2004)
Points importants
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• De multiples sources de potentiel existent dans la nature
• Les magnitudes des différentes sources sont souvent du même ordre. exception: Potentiel de minéralisation ~1 V
• Certaines sources sont reliées à des phénomènes géologiques d’intérêt, d’autres non.
• Étant donné la quantité de sources de potentiel et le manque de compréhension de certains mécanismes, il est difficile d’expliquer quantitativement les potentiels observés
Le potentiel électrique terrestre