Page 184 - Introduction to Petroleum Engineering

RESISTIVITY LOGS 171

Resistivity (ohm·m)
10 100 1000 10000
4000

4010

Zone of
filtrate
4020 invasion
Depth (ft)

4030

4040

4050

FIGuRE 9.6 Illustration of resistivity log. The three resistivity traces are for shallow,
medium, and deep resistivity measurements. Compare with the GR log in Figure 9.4 and the
porosity logs in Figure 9.5.

In situ brine in a formation contains several inorganic salts that are ionized in
water. The presence of ions in brine greatly enhances electrical conductivity. Pure
water is a poor conductor of electricity. The presence of dissolved salts significantly
increases the conductivity of water. The conductance of a material is inversely
proportional to its resistance. Conductance S in siemens is given by

S =1/ R (9.6)
where R is resistance in ohms. The units are related by 1 Siemen = 1 mho = 1/ ohm.
Resistance R (ohms) is the proportionality constant between voltage V (Volts) and
current I (Amperes) in the linear relationship

V = IR (9.7)
where Equation 9.7 is Ohm’s law.
Resistivity is often used to quantify the ionic environment. If we consider a
uniform conducting medium with electrical resistance R (ohms), length L (m), and
e
cross‐sectional area A (m ), resistivity of the conducting medium ρ (ohm⋅m) is
2
A
ρ = R (9.8)
e L