1. Electrical Properties
Archie’s Law

2. Formation Factor Equation
Rock containing pores saturated
with water and hydrocarbons
Non-shaly rock, 100% saturated
with water having resistivity, Rw Rt
Cube of water
having resistivity, Rw
= 20%
Sw = 20% Ro
= 20%
Sw = 100% Rw
Saturation Equation
= 100%
Sw = 100%
Resistivity
Formation Factor Equation

3. Formation Factor The formation factor (F) depends on
Porosity of the formation,
Pore geometry - tortuosity
Lithology of the formation
Degree of cementation, and
Type and amount of clay in the rock
From J. Jensen, PETE 321 Lecture Notes

4. Formation Factor Equation
Archie’s equation for formation factor is a power law model:
F=R0/Rw=a·f-m
1000
Rock type 1
100 F
Note: When  = 100%, Ro must equal Rw; thus, a = 1.0 (if a is constant)
Ro is the resistivity of a formation 100% saturated with water. If we think about a core sample, there is only one major component that conducts electricity, and that is the water in the pore space. The magnitude of the resistivity is a function of the amount of fluid (porosity and water saturation), the resistivity of the saturating fluid, and the interconnectedness of the pore space. The graph above illustrates that there is a relationship between the formation factor and porosity. The slope of the line is a function of the pore structure (or tortuosity) which is called the cementation exponent. The cementation exponent is a measure of the degree of interconnectivity of the pore space. 10
Rock type 2 1
Note: Sw=1
.01 .1
1.0 
From NExT, 1999

5. Formation Factor - Example Core Data
From J. Jensen, PETE 321 Lecture Notes

6. F=a·f-m Formation Factor a = constant  1.0 for most formations
m = cementation factor  2 for most formations
Other commonly used values
Sandstones:
F = 0.8/f2 (Tixier)
0.62/f2.15 (Humble)
Carbonates
F = 0.8/f2
From J. Jensen, PETE 321 Lecture Notes

7. Saturation Equation Power Law Model IR=Rt/R0=Sw-n
Each curve for a specific core sample
No conductive materials (clay) present
Rock type 1
Rock type 2
1000
100 10 1
.01 .1
1.0 Sw
IR = Rt R0
Note: When Sw = 100%, Rt must equal Ro
As we stated earlier, the resistivity of a formation is controlled by the water in the formation. It is a function of the amount of water, the resistivity of that water, and the interconnectivity of the pore space. Both porosity and water saturation control the amount of water in the pore space. When porosity is constant, the resistivity relationships are solely affected by water saturations. The figure above clearly shows that the ratio of resistivities is a strong function of water saturation where the saturation exponent is a measure of the interconnectivity of the fluids in the pore space (which is related to capillary pressure and relative permeability). Saturation exponent is related to the cementation exponent discussed in the previous slide.
From NExT, 1999

8. Laboratory Determination of Saturation Exponent, n
100 10 1
0.1
1.0
Sw (fraction)
Rt / Ro
n = Slope
From J. Jensen, PETE 321 Lecture Notes

9. R0 Appears in Both Equations
when Sw = 100%
when  = constant
From NExT, 1999

10. Archie’s Equation (Combined)
Empirical constant (usually near unity) a
Resistivity of formation water, -m w R
Water saturation, fraction w S
Saturation exponent (also usually near 2) n
Porosity, fraction f
Cementation exponent (usually near 2) m
True formation resistivity, -m t R
Archie’s equation is the basic equation used by petrophysicists to determine whether a formation has water or hydrocarbons in the pore space. As you can see, the water saturation is a function of several variables: the resistivity of the water in the pore space, the total composite formation resistivity, porosity, and several other variables that are a function of the rock.
From NExT, 1999

11. IDEALIZED LOG SET R = 4  = 0.30 R = 0.4 R = 8  = 0.07 Shale R = 0.3
 = 0.35
 = 0.07
R = 0.4
R = 0.3
R = 4
R = 8
Sand
Shale
IDEALIZED LOG SET
From J. Jensen, PETE 321 Lecture Notes

12. Effect of Filtrate Invasion - Rnear_well  Rt (permeability present)
Wellbore
Mud
(Rm)
Mud Cake
(Rmc)
Transition
Zone
Uninvaded
(Rt)
Invaded
Zone (Rxo)
Modified from J. Jensen, PETE 321 Lecture Notes

13. EXAMPLE LOG WITH RESISTIVITY
GRC
150
SPC MV
-160 40
ACAL 6 16
ILDC
0.2
200
SNC
MLLCF
RHOC
1.95
2.95
CNLLC
0.45
-0.15 DT
us/f 50
001) BONANZA 1
10700
10800
10900
SNC
0.2
200
MLLCF
ILDC
Deep
Resistivity
Log (ILDC), Rt
From NExT, 1999

14. Laboratory Resistance
From J. Jensen, PETE 321 Lecture Notes

15. Laboratory Resistivity
From J. Jensen, PETE 321 Lecture Notes