GLQ3205 Géophysique appliquée 2 Méthodes Électriques...GLQ3205 Géophysique appliquée 2 Méthodes Électriques Gabriel Fabien-Ouellet [email protected] Été 2018

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

mailto:[email protected]

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

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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

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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

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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

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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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Les équations constitutives en électrique

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• 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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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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Loi d’Ohm

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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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11

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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


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


Équipotentiels et lignes de courant dans le sol

Les lignes de courant traversent perpendiculairement les équipotentiels, exactement comme en hydrogéologie!

14


Équipotentiels et lignes de courant dans le sol

Les lignes de courant traversent perpendiculairement les équipotentiels, exactement comme en hydrogéologie!

15


• Définition de la densité de courant

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Résumé des équations en électrique

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Variable Symbole Unités

Champ électrique


Densité de courant

Conductivité

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• Équation de Maxwell-Gauss:

• Définition du potentiel électrique

densité de charge!

• Relation résistivité/conductivité

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16


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


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


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.


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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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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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.


Résistivité effective d’un milieu hétérogène

Résistivité transversale (résistances en série)

Résistivité longitudinale (résistances en parallèle)

25

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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>


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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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



Loi d’Archie: paramètres

29



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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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


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


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


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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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


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="M+hO9e7eTUTWBtTS50oLhiOFris=">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</latexit>

<latexit sha1_base64="BpJmkkKeVwnIfID8eNisHFG5ibE=">AAADa3iclVJNT9tAEH2J20LTUgjcWg5WIyTEIXJQK3qM1EuPUDUEiUaVbTZg4S/Z60AU8Qt6LT+u/6A99D/0zdRBIBQV1nI8++a9tzOTDfI4Kq3n/Ww0nSdPny0tP2+9eLnyanWtvX5YZlURmkGYxVlxFPiliaPUDGxkY3OUF8ZPgtgMg/OPkh9OTFFGWfrFTnMzSvzTNBpHoW8JHXz+ttbxurvvPS73ftDrero6qNd+1m7s4CtOkCFEhQQGKSzjGD5KPsfowUNObIQZsYJRpHmDK7SorcgyZPhEz/l7yt1xjabci2ep6pCnxHwLKl1sUZORVzCW01zNV+os6CLvmXpKbVN+g9orIWpxRvR/ujnzoTrpxWKMD9pDxJ5yRaS7sHapdCpSuXurK0uHnJjEJ8wXjENVzufsqqbU3mW2vuZ/KVNQ2Yc1t8LvusqUyIVOK9H6U7rPiAtzworkPxspIj5jPUN8AyouFRfHUqs0NxMQfKLMxys7PPHq1tPiPZxfNndxcLjb7Xnd3sG7Tr9f38hlvMFbbNNvD318wj4G2td3/MB184+z4bx2Nv9Rm41as4E7y9n6C8v6sBI=</latexit>

<latexit sha1_base64="Mtl/1o+7FiYuc9sp6Ge3WLGqpjc=">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</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 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

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<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

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<latexit sha1_base64="Mtl/1o+7FiYuc9sp6Ge3WLGqpjc=">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</latexit>

39

https://www-ig.unil.ch/c_diaf.htm


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

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Modèle de la cellule électrochimique

41


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 !

42


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 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


Source de courants telluriques (~100 mv)

Vents solaires

Éclairs

Résonance ionosphère45


Bruits anthropiques

Vents solaires

46


(Naudet, 2004)

Points importants

47

• 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


Documents

GLQ3205 Géophysique appliquée 2 Méthodes Électriques...GLQ3205 Géophysique appliquée 2 Méthodes Électriques Gabriel Fabien-Ouellet [email protected] Été 2018