Archie's law An empirical law which relates, for a clay-free sediment, the electrical resistivity ρ of a porous rock containing water and cement to the fraction of the pore space that is filled with water. ρ = ρo−mS−n, where ρo is the resistivity of the water and s is the fraction of pore space filled with water. The exponent n is usually about 2.0 if one-third of the pore space is filled with water, and exponent m usually varies between 1.3 for unconsolidated sediments to approaching 2.0 for a well-cemented sediment. In the oil-bearing rocks, the remaining pore space is considered to be filled with either oil or gas and the law is usually expressed as Sw = (Rw/Rt)0.5φ, where Sw is the fraction of pore space filled by water with a resistivity Rw in a rock with a true resistivity of Rt and a porosity φ.
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