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Electrical Properties of Rocksand

Electrical Resistivity Methods

ResistanceDefinition of an OHMAn ohm is a resistance in a conductor that produces apotential difference of one volt when a current of oneampere is flowing through it.

R =

Ohm’s Law

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html#c1

Resistance vs ResistivityResistance is relevant only to a particularmeasurement circuit. Units: ohms

Resistivity is an intrinsic property of allphysical materials Units: ohm-meters

Apparent Resistivity is a resistivity estimate based on aassuming a half-space geometry. Units: ohm-meters

Electrical Resistivity vsElectrical Conductivity

Conductivity = σ = 1/ρ (mho/meters)

Resistance = ρ (ohm-meters)

Calculating Resistance fromResistivity

• http://www.cflhd.gov:80/agm/index.htm

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Factors Influencing ElectricalConductivity in Rocks

Metallic Sulfide Mineral Content

Porosity (connected/effective - fractures or pores)

Clay Content

Pore saturation (% air or gas)

Water salinity (TDS)

Hydrocarbon Fluid Saturation

Rock Matrix intrinsic resistivity

Fluid temperature

Archie’s Law

Formation Factor

The conductivity of most geological formations can be fitto Archie’s Law

Influence of PermeabilityA rock with a non-conducting matrix must be permeable (connected pores) as well as porous toconduct electricity.

Darcy's Law:

Ohm's Law:

where

Despite the similarity between Darcy’s and Ohm’s Laws, electric currents have zeroviscosity so even a narrow crack can provide an effective electrical connection between pores that not contribute to hydraulicpermeability.

Comparison of electric andhydraulic properties.

Avg. hydraulic conductivities: Kl, Kt

Average aquifer resistivities:ρl, ρt

Leakance:Lh=Σki/hi = Kt/H

Longitudinal conductance:S= Σhi/ρi = H/ρl

Transmissivity: Th = Σhiki= KlH

Transverse resistance: T = Σ hiρi = Hρl

HydraulicElectrical

• http://www.cflhd.gov:80/agm/index.htm

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Electrical resistivity of rockswith various wt % of sulfide.

Metallic SulfideMineral Content

• http://www.cflhd.gov:80/agm/index.htm

Effect of Water Temperature

http://appliedgeophysics.berkeley.edu:7057/dc/figures/fig43_7.jpg

Conductivity Ranges of Various Materials

http://www.cflhd.gov:80/agm/index.htmhttp://www.cflhd.gov:80/agm/index.htm

http://www.cflhd.gov:80/agm/index.htm

http://www.cflhd.gov:80/agm/index.htm

4

Resistance vs ResistivityResistance is relevant only to a particularmeasurement circuit. Units: ohms or Ω

Resistivity is an intrinsic property of allphysical materials Units: ohm-meters or Ω-m

Apparent Resistivity is a resistivity estimate based on aassuming a half-space geometry. Units: ohm-meters or Ω-m

Calculating Resistance fromResistivity

• http://www.cflhd.gov:80/agm/index.htm

Four Electrode Resistivity Measurement onrock sample

… are used to avoid electrode contact resistance effects seen in two electrode measurements.

C1 C2

current I

P1 P2

Four electrode resistivity arrays

http://www.cflhd.gov/agm/images/fig90.jpg

The BasicConcept of an

EarthResistivity

Measurement

http://www.cflhd.gov/agm/images/fig91.jpg

Electrode Contact Resistance is typically muchhigher than the intrinsic earth resistivity

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Electrode Contact Resistance is concentratedaround each electrode

If a standard two electrode resistivity meter wereused to measure the earth’s “resistance” we onlyobtain information on the quality of the electrodecontacts – not the earth’s resistivity

http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf

Pole-Pole Array Pole-Dipole Array

http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf

Pole-Dipole Array

http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf

Wenner Array

http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf

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Schlumberger

http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf

Dipole-Dipole Array

Fig. 5.4g

The electric potential varies as 1/r around a singlecurrent electrode on a homogeneous half-space

Fig. 5.5g

Fig. 5.9g Fig. 5.6g

Equal potential voltage surfaces between the electrodes

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Depth of current flow between two current electrodes

Fig. 5.14g

Fig. 5.13g (a) Fig. 5.13g (b)

Fig. 5.13g (c) Fig. 5.12g (a)

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Fig. 5.12g (b) Fig. 5.12g (c)

Fig. 5.14g Fig. 5.15g (a)

Fig. 5.15g (b) Fig. 5.13g (b)

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Fig. 5.13g (c) Fig. 5.18g (a)

Fig. 5.18g (b) Fig. 5.18g (c)

Fig. 5.19g Fig. 5.21g (a)

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Fig. 5.20g Fig. 5.21g (b)

Fig. 5.21g (c) Fig. 5.22g

Fig. 5.23g (a) Fig. 5.23g (c)

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Fig. 5.24g (a) Fig. 5.24g (c)

Fig. 5.25g (a) Fig. 5.25g (b)

Fig. 5.26g Fig. 5.27g (a)

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Fig. 5.27g (b) Fig. 5.28g

Fig. 5.29g Fig. 5.30g (a,b)

Fig. 5.30g (c,d) Fig. 5.31g

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Fig. 5.33g (a) Fig. 5.33g (b)

Fig. 5.33g (c) Fig. 5.39g

One point removed

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C:\Shortcut to Geo-CD-ROM.exe

Airborne EM Resistivity Airborne EM Resistivity

http://ece.uprm.edu/~pol/waves_review.pdf

http://appliedgeophysics.berkeley.edu:7057/dc/archie/index.html