Page 185 - Introduction to Petroleum Engineering

172 WELL LOGGING
Resistivity ρ (ohm⋅m) is inversely proportional to electrical conductivity σ
(mho/m = S/m):
σ =1/ ρ (9.9)
where 1S/m = 1siemen/m = 1mho/m.
A high conductivity fluid has low resistivity. By contrast, a low‐conductivity fluid
like oil or gas would have high resistivity. A tool that can measure formation resis-
tivity indicates the type of the fluid that is present in the pore space. Resistivity in
a pore space containing hydrocarbon fluid will be greater than resistivity in the
same pore space containing brine.

Example 9.4 Ohm’s Law, Resistivity, and Conductivity
a. 0.006 C of charge moves through a circuit in 0.1 s. What is the current?
b. A 6 V battery supports a current in a circuit of 0.06 A. Use Ohm’s law to
calculate the resistance of the circuit.
C. Suppose the circuit has a length of 1 m and a cross‐sectional area of
1.8 m . What is the resistivity of the circuit?
2
D. What is the electrical conductivity of the circuit?
answer:

.
[Coulomb] 0 006 C
a. Current [Ampere] = = = 006. A
.
[Second] 01 s
×
b. Ohm’s law: Voltage V ( ) = current resistance = I ()× (ohm ) or V = IR.
A
R
=
Calculate RV /I = 6 V/00 6A =100 ohm
.
A 18 . m 2
C. ρ = R =100 ohm =180 ohm ⋅m
e
L 1 m
1 1
D. σ = = = 0 0056 mho/m. = 56 mmho/m. where mmho =
ρ 180 ohm ⋅m
milli‐mho
The resistivity R of a porous material saturated with an ionic solution is equal to
0
the resistivity R of the ionic solution times the formation resistivity factor F of the
w
porous material, thus
R = FR w (9.10)
0
Formation resistivity factor F is sometimes referred to as formation factor. It can be
estimated from the empirical relationship
, (
Fa m) = aφ − m (9.11)
where ϕ is porosity, m is cementation exponent, and a is tortuosity factor. The cemen-
tation exponent m depends on the degree of consolidation of the rock and varies