Question

Using Archie’s equation, if the water saturation (Sw) increases while the porosity (phi) remains constant, how must the measured true resistivity (Rt) change?

Accepted Answer

Archie’s equation is defined as Rt = (a * Rw * phi^-m) / (Sw^n), where Rt is the true resistivity of the formation, a is the tortuosity factor, Rw is the resistivity of the formation water, phi is the porosity, m is the cementation exponent, Sw is the water saturation, and n is the saturation exponent. In this relationship, the water saturation Sw is in the denominator of the equation. Because the porosity phi, the cementation exponent m, the tortuosity factor a, and the resistivity of the formation water Rw are all held constant, the expression (a * Rw * phi^-m) acts as a fixed constant value. Therefore, Rt is inversely proportional to the saturation exponent of the water saturation, which is written as Rt proportional to 1 / (Sw^n). As the water saturation Sw increases, the value of the denominator Sw^n also increases. Mathematically, dividing a constant by a larger number results in a smaller output. Consequently, if the water saturation increases while porosity remains constant, the measured true resistivity Rt must decrease. An example of this is a reservoir zone becoming more water-wet; since water is more conductive than hydrocarbons, the increased volume of water in the pore space lowers the overall electrical resistance of the rock, leading to a lower measured resistivity value.

Home → All Courses → Science and Mathematics Courses → Petroleum Geology → Flashcard

Using Archie’s equation, if the water saturation (Sw) increases while the porosity (phi) remains constant, how must the measured true resistivity (Rt) change?