Resistance
Electrical Properties of Rocks
and
Electrical Resistivity Methods
Definition of an OHM
An ohm is a resistance in a conductor that produces a
potential difference of one volt when a current of one
ampere is flowing through it.
R=
Ohm’s Law
Resistance vs Resistivity
Resistance is relevant only to a particular
measurement circuit. Units: ohms
Resistivity is an intrinsic property of all
physical materials Units: ohm-meters
Apparent Resistivity is a resistivity estimate based on a
assuming a half-space geometry.
Units: ohm-meters
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html#c1
Electrical Resistivity vs
Electrical Conductivity
Calculating Resistance from
Resistivity
Resistance = ρ (ohm-meters)
Conductivity = σ = 1/ρ (mho/meters)
•
http://www.cflhd.gov:80/agm/index.htm
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Factors Influencing Electrical
Conductivity in Rocks
Archie’s Law
Porosity (connected/effective - fractures or pores)
Pore saturation (% air or gas)
Hydrocarbon Fluid Saturation
Water salinity (TDS)
Clay Content
Metallic Sulfide Mineral Content
Fluid temperature
Rock Matrix intrinsic resistivity
Formation Factor
The conductivity of most geological formations can be fit
to Archie’s Law
Comparison of electric and
hydraulic properties.
Influence of Permeability
A rock with a non-conducting matrix must be permeable (connected pores) as well as porous to
conduct electricity.
Electrical
Darcy's Law:
Ohm's Law:
where
Hydraulic
Transverse resistance:
T = Σ hiρi = Hρl
Transmissivity:
Th = Σ h iki= KlH
Longitudinal conductance:
S= Σ hi/ρi = H/ρl
Leakance:
Lh=Σ ki/hi = Kt/H
Average aquifer resistivities: Avg. hydraulic conductivities:
K l , Kt
ρl , ρt
Despite the similarity between Darcy’s and Ohm’s Laws, electric currents have zero
viscosity so even a narrow crack can provide an effective electrical connection between pores that not contribute to hydraulic
permeability.
•
http://www.cflhd.gov:80/agm/index.htm
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Metallic Sulfide
Mineral Content
Effect of Water Temperature
Electrical resistivity of rocks
with various wt % of sulfide.
•
http://www.cflhd.gov:80/agm/index.htm
http://appliedgeophysics.berkeley.edu:7057/dc/figures/fig43_7.jpg
Conductivity Ranges of Various Materials
http://www.cflhd.gov:80/agm/index.htm
http://www.cflhd.gov:80/agm/index.htm
http://www.cflhd.gov:80/agm/index.htm
http://www.cflhd.gov:80/agm/index.htm
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Resistance vs Resistivity
Calculating Resistance from
Resistivity
Resistance is relevant only to a particular
measurement circuit. Units: ohms or Ω
Resistivity is an intrinsic property of all
physical materials Units: ohm-meters or Ω -m
Apparent Resistivity is a resistivity estimate based on a
assuming a half-space geometry.
Units: ohm-meters or Ω -m
•
Four Electrode Resistivity Measurement on
rock sample
http://www.cflhd.gov:80/agm/index.htm
Four electrode resistivity arrays
… are used to avoid electrode contact resistance effects
seen in two electrode measurements.
current I
C1
P1
P2
C2
http://www.cflhd.gov/agm/images/fig90.jpg
The Basic
Concept of an
Earth
Resistivity
Measurement
Electrode Contact Resistance is typically much
higher than the intrinsic earth resistivity
http://www.cflhd.gov/agm/images/fig91.jpg
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Electrode Contact Resistance is concentrated
around each electrode
Pole-Pole Array
http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf
Pole-Dipole Array
http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf
If a standard two electrode resistivity meter were
used to measure the earth’s “resistance” we only
obtain information on the quality of the electrode
contacts – not the earth’s resistivity
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
Dipole-Dipole Array
http://appliedgeophysics.berkeley.edu:7057/dc/em44.pdf
Fig. 5.4g
Fig. 5.5g
The electric potential varies as 1/r around a single
current electrode on a homogeneous half-space
Fig. 5.9g
Fig. 5.6g
Equal potential voltage surfaces between the electrodes
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Fig. 5.14g
Depth of current flow between two current electrodes
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://appliedgeophysics.berkeley.edu:7057/dc/archie/index.html
http://ece.uprm.edu/~pol/waves_review.pdf
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