For Archie's equation, when n = 1 and m = 2, this parameter set is appropriate for which formation lithology?

For Archie's equation, when n = 1 and m = 2, this parameter set is appropriate for which formation lithology?

• A. Sandstones
• B. Carbonates (limestone or dolomite)
• C. Shales
• D. Igneous rock

Answer: (B)

Archie’s equation models how resistivity of a rock depends on porosity, water saturation, and the rock’s pore geometry through two exponents, m and n. The equation is Rt = a * Rw * φ^(-m) * Sw^(-n) (ignoring minor constants), where m reflects how pore structure and cementation affect conduction, and n describes how sensitive resistivity is to changes in water saturation. For clean sandstones, typical values cluster around m ≈ 2 and n ≈ 2. Carbonates, however, have more complex pore systems with fractures, vugs, and variable cementation, which often produce different scaling. In many carbonate datasets, a relatively low n (around 1) with a moderate m (around 2) provides a reasonable empirical fit, capturing the linear-like influence of saturation on resistivity that can occur in these dual-porosity or fractured networks. Therefore, the pair n = 1 and m = 2 is commonly used to represent carbonate formations like limestone or dolomite, where Archie's assumptions are applied with these adjusted exponents. In contrast, sands tend to require n closer to 2, shales involve clay-related conduction not well described by Archie, and igneous rocks generally have porosity and conductivity patterns that don’t fit Archie’s framework.

Archie’s equation models how resistivity of a rock depends on porosity, water saturation, and the rock’s pore geometry through two exponents, m and n. The equation is Rt = a * Rw * φ^(-m) * Sw^(-n) (ignoring minor constants), where m reflects how pore structure and cementation affect conduction, and n describes how sensitive resistivity is to changes in water saturation.

For clean sandstones, typical values cluster around m ≈ 2 and n ≈ 2. Carbonates, however, have more complex pore systems with fractures, vugs, and variable cementation, which often produce different scaling. In many carbonate datasets, a relatively low n (around 1) with a moderate m (around 2) provides a reasonable empirical fit, capturing the linear-like influence of saturation on resistivity that can occur in these dual-porosity or fractured networks.

Therefore, the pair n = 1 and m = 2 is commonly used to represent carbonate formations like limestone or dolomite, where Archie's assumptions are applied with these adjusted exponents. In contrast, sands tend to require n closer to 2, shales involve clay-related conduction not well described by Archie, and igneous rocks generally have porosity and conductivity patterns that don’t fit Archie’s framework.