Archie m and n Calculator: Cementation and Saturation Exponents from Core Data

Every water saturation calculated with Archie's equation quietly leans on two exponents that most people never question: m, the cementation exponent, and n, the saturation exponent. The textbook defaults are m = 2 and n = 2, and to be fair, those defaults work surprisingly often. But when they are wrong, they are wrong in ways that move reserves. Get m wrong by 0.3 in a 15 percent porosity rock and your formation factor shifts by half; get n wrong in an oil-wet carbonate and you can misclassify pay as water. This calculator fits both exponents from core data instead of assuming them.

Where m comes from

The cementation exponent lives in the formation factor relationship F = a / phi^m, where F is the ratio of fully brine-saturated rock resistivity to the brine resistivity itself. Measure F on a handful of core plugs spanning a porosity range, plot log F against log porosity, and the points fall on a straight line whose slope is negative m. The intercept gives the tortuosity factor a. This calculator runs that least squares fit for you and reports both, along with an R squared so you can see whether one bad plug is dragging the line.

Where n comes from

The saturation exponent describes how resistivity climbs as water is displaced by hydrocarbon: RI = Sw^-n, where RI is the resistivity index, the ratio of true resistivity at partial saturation to the resistivity at full water saturation. In the lab this comes from a desaturation experiment, stepping a plug through decreasing water saturations and measuring resistivity at each step. Because RI is exactly 1 when Sw is 1 by definition, the fit is forced through that origin point, which is why the Sw = 1 row in the table carries no slope information.

Worked example

• Five plugs give F values of 100, 44.4, 25.0, 16.0, and 11.1 at porosities of 0.10 to 0.30
• The log-log fit returns m very close to 2.0 with a near 1.0, textbook cemented sandstone
• A desaturation series of RI = 1.56 at Sw 0.8 through RI = 11.1 at Sw 0.3 fits n close to 2.0
• With both exponents confirmed near 2, the default Archie assumptions are safe for this rock

Reading the numbers like a petrophysicist

The exponents are not just fit parameters, they are rock typing information. An m below about 1.6 usually means fractures are carrying the current, because a connected fracture is an electrical freeway compared to matrix pores. An m above 2.2 is the signature of vuggy carbonates, where big pores are poorly connected and current takes tortuous detours. On the n side, values near 2 mean water-wet behavior, while n climbing to 3 or 4 is the classic fingerprint of oil-wet rock: as water desaturates it retreats into isolated pendular rings and loses electrical connectivity fast. If your lab reports n = 3.5 and someone still runs the log analysis with n = 2, their computed water saturations will be systematically too high and they may walk away from real pay.

One practical warning that saves grief: make sure the core measurements were made at reservoir-representative brine salinity and, ideally, at overburden stress. Both m and a shift with confining pressure, and clay-bearing rocks measured with fresh brine produce fits that look precise but answer the wrong question. A tight R squared on the wrong experiment is still the wrong answer.

Related Calculators and Reference

These exponents feed directly into the Archie water saturation calculator, which is where a fitted m and n actually earn their keep. Porosity inputs for the formation factor fit usually come from the porosity calculator, and if your rock has enough clay to worry about, the shale volume calculator helps decide whether Archie is even the right model. For deeper background, the SEG Wiki entry on the Archie equation covers the assumptions and history.