Barbara Cannon The Wenner-Gren Institute , Stockholm University
Ohm’s Law Resistance vs ResistivityElectrical Resistivity vs Electrical Conductivity ... Wenner...
Transcript of Ohm’s Law Resistance vs ResistivityElectrical Resistivity vs Electrical Conductivity ... Wenner...
1
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
2
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
3
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
5
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
6
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
7
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)