Archie formula

1. Archie Formula – Archie derived the relationship in the 1940's:
F=a/
m

Where: F is the Formation Resistivity Factor,
a is an empirically derived constant
 is the porosity
m is the Cementation Factor
F= Ro/Rw
Where Ro is the resistivity of the rock sample completely saturated with brine of
resistivity Rw.
For a given porosity, Ro/Rw remains constant over a wide range of water resistivity.
For most compacted formations, a=1 and m= 2.2.
Where a rock contains hydrocarbons, Sw is the fraction of the rock containing
formation water, therefore (1-Sw) is the volume of the pore space containing
hydrocarbons .
Sw
n
= FRw/Rt
Where n is the saturation exponent and Rt is the true resistivity of the formation.
FRw=Ro when the formation is 100% saturated with water of resistivity Rw.
Thus: Sw= (Ro/Rt)
Many variations of this formula have been derived for specific circumstances:
eg The Humble Equation for unconsolidated rocks of the Gulf Coast a=0.62 and
m=2.15 gives better results.
The presence of clays or iron pyrite require considerable modification to the formula.