In petrophysics, Archie's law is a purely empirical law relating the measured electrical conductivity of a porous rock to its porosity and fluid saturation.
It is named after Gus Archie (1907–1978) and laid the foundation for modern well log interpretation, as it relates borehole electrical conductivity measurements to hydrocarbon saturations.
) of a fluid saturated, porous rock is described as where This relationship attempts to describe ion flow (mostly sodium and chloride) in clean, consolidated sands, with varying intergranular porosity.
Electrical conduction is assumed to be exclusively performed by ions dissolved in the pore-filling fluid.
Electrical conduction is considered to be absent in the rock grains of the solid phase or in organic fluids other than water (oil, hydrocarbon, gas).
standing for total) is the resistivity of the rock saturated with the fluid and
In case the fluid filling the porosity is a mixture of water and hydrocarbon (petroleum, oil, gas), a resistivity index (
The cementation exponent models how much the pore network increases the resistivity, as the rock itself is assumed to be non-conductive.
If the pore network were to be modelled as a set of parallel capillary tubes, a cross-section area average of the rock's resistivity would yield porosity dependence equivalent to a cementation exponent of 1.
Common values for this cementation exponent for consolidated sandstones are 1.8 <
In carbonate rocks, the cementation exponent shows higher variance due to strong diagenetic affinity and complex pore structures.
The saturation exponent models the dependency on the presence of non-conductive fluid (hydrocarbons) in the pore-space, and is related to the wettability of the rock.
It is meant to correct for variation in compaction, pore structure and grain size.
is called the tortuosity factor and is related to the path length of the current flow.
The value lies in the range 0.5[citation needed] to 1.5, and it may be different in different reservoirs.
However a typical value to start with for a sandstone reservoir might be 0.6[citation needed], which then can be tuned during log data matching process with other sources of data such as core.
In petrophysics, the only reliable source for the numerical value of both exponents is experiments on sand plugs from cored wells.
) Archie's law can be written Hence, plotting the logarithm of the measured in-situ electrical conductivity against the logarithm of the measured in-situ porosity (Pickett plot), according to Archie's law a straight-line relationship is expected with slope equal to the cementation exponent
and intercept equal to the logarithm of the in-situ fluid electrical conductivity.