Water Saturation Calculator: Archie’s Equation for Sw From Resistivity

Calculate water saturation from Archie’s equation using porosity and true resistivity, build a layered model across several depth points to map a saturation profile, or solve backward for the water resistivity, resistivity, or porosity a target saturation requires. Everything updates live.

How Archie’s Equation Works

Water saturation is the fraction of pore space occupied by water rather than hydrocarbon, and Archie’s equation is still the standard starting point for estimating it from resistivity logs. The equation ties water saturation to porosity and true resistivity through three rock dependent constants, the tortuosity factor, cementation exponent, and saturation exponent. This tool solves it directly, forward and in reverse, plus a layered model for scanning a saturation profile across several depth points at once.

Start with a single depth using the quick convert tab. Build a layered model to compare porosity and resistivity across several depth points and flag likely hydrocarbon zones. Or solve backward, enter a target water saturation and find the water resistivity, true resistivity, or porosity that would be consistent with it.

Archie’s equation states that water saturation equals the tortuosity factor times water resistivity, divided by porosity raised to the cementation exponent times true resistivity, all raised to the power of one over the saturation exponent. In plain terms, a low true resistivity relative to what clean water bearing rock at that porosity would show means more conductive water in the pore space, and a high true resistivity signals more resistive hydrocarbon displacing that water.

The three Archie constants, a, m, and n, are not universal, they depend on rock texture and pore geometry. A tortuosity factor and cementation exponent near 1 and 2 are common defaults for clean sandstone, but carbonates with vuggy or fractured pore systems often need different values, usually calibrated from core measurements rather than assumed from a textbook default.

Reading the Layered Model

Running Archie’s equation down a series of depth points turns a single calculation into a saturation profile. A water bearing interval typically shows low true resistivity and water saturation near 100 percent, while a hydrocarbon bearing interval shows resistivity climbing sharply as water saturation drops. Bulk volume water, porosity multiplied by water saturation, is a useful side check, it tends to stay roughly constant across a clean reservoir once saturation reaches its irreducible level, so a big swing in bulk volume water within a supposedly uniform rock type is worth a second look.

The tight gas preset in this tool illustrates a common trap, low porosity rock can show a high computed water saturation from Archie’s equation even in a genuine gas zone, since the equation is sensitive to the porosity term as well as resistivity, and low porosity intervals need extra care with cutoffs and calibration.

Solving Backward From a Target Saturation

Sometimes the direction of the question flips, a target or known water saturation is available from a core or a nearby correlated zone, and the question becomes whether an assumed water resistivity, a measured true resistivity, or an assumed porosity are consistent with it. Since Archie’s equation is a single algebraic relationship between four unknowns, any one of water resistivity, true resistivity, or porosity solves directly from the other three plus the target saturation, no iteration required.

Common Mistakes

Applying default Archie constants, typically a=1, m=2, n=2, to carbonate or fractured reservoirs without calibrating against core data, since these rock types often need meaningfully different exponents.

Ignoring shale volume in a shaly sand, since Archie’s equation as written assumes a clean formation and does not itself correct for the added conductivity that shale contributes.

Treating a computed water saturation near 100 percent as automatically wet without checking whether it instead reflects a genuinely low resistivity contrast, or a porosity value that does not match the interval.

Comparing water saturation values across zones with different porosity without also checking bulk volume water, since porosity differences alone can make two zones look different in saturation when the same fluid distribution is present.

Who Uses This

Petrophysicists and log analysts computing water saturation from resistivity logs and screening zones for likely hydrocarbon content.

Reservoir engineers estimating hydrocarbon pore volume inputs for a volumetric or reserves calculation.

Geologists cross checking resistivity based saturation estimates against core or mud log shows.

Students and early career geoscientists learning how Archie’s equation connects resistivity, porosity, and fluid saturation.

Try It Above

Use the quick convert tab for a single depth calculation with Archie’s equation, move to the layered model to scan a saturation profile across several depth points and flag likely hydrocarbon zones, or use the solve target Sw tab when a known saturation is available and you need to check an assumed resistivity or porosity.

Related Calculators and References

Continue building your workflow with the Porosity Calculator. For background on the formulas used above, see AAPG Wiki: Archie equation.