Archie Equation Calculator - Water Saturation
Enter porosity, formation-water resistivity, true formation resistivity, and Archie constants. The calculator returns water saturation.
Enter porosity, formation-water resistivity, true formation resistivity, and Archie constants. The calculator returns water saturation.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Archie water saturation estimates formation water saturation from resistivity-log measurements, porosity, formation-water resistivity, and Archie exponents.
Use it in clean sandstone or carbonate petrophysics workflows where Archie assumptions are appropriate, and calibrate formation-water resistivity plus the Archie exponents against local water, core, or log evidence where possible.
SLB Energy Glossary: Archie rock and model scopeSLB Energy Glossary: saturation exponentSolves for
S_w (fraction)
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Formula, variables, and sourceCalculate water saturation from fractional porosity
On the displayed fraction basis, enter 0.20 for 20% porosity, not 20. With a = 1, m = 2, n = 2, Rw = 0.05 ohm-m and Rt = 20 ohm-m, the formation-factor term is 1/(0.20^2) = 25. The saturation term is 25 x 0.05/20 = 0.0625, so Sw = sqrt(0.0625) = 0.25, or 25% of pore volume.
Rw and Rt must have compatible resistivity units and temperature basis and describe the interpretation being made. Do not substitute invaded-zone resistivity for true formation resistivity without changing the interpretation model. Water saturation is a pore-volume fraction, not a bulk-rock volume or a direct recoverable-hydrocarbon estimate.
Why m and n need local calibration
The cementation or porosity exponent m and saturation exponent n represent different relationships. Default values of two are convenient arithmetic examples, not evidence that both exponents fit a reservoir. SLB distinguishes petrophysically simple Archie rocks from cases where pore structure, wettability or conductive material complicates the relationships.
Holding the other default inputs fixed and changing only m gives the following sensitivity check. These values show how an uncertain exponent affects the result; they are not calibrated exponent choices or a preferred saturation interpretation.
| m | Sw (fraction) | Sw (%) |
|---|---|---|
| 1.8 | 0.212835 | 21.2835 |
| 2.0 | 0.250000 | 25.0000 |
| 2.2 | 0.293655 | 29.3655 |
Check model scope before accepting Sw
A direct clean-formation Archie calculation does not explicitly include shale conductivity. For a shaly interval, compare an appropriate shale-aware model on consistent inputs rather than forcing this result to match an expected hydrocarbon saturation. The linked shaly-sand guide explains how to choose and compare those models.
If an arithmetic result lies outside zero to one, review input fractions, resistivity selection, temperature corrections and exponent calibration. Do not silently clip it into range. A numerical result is not by itself proof of a valid geological or petrophysical interpretation.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns S_w = 0.25 fraction. Defaults demonstrate the implementation; they are not recommended field values.
1
0.2
2
0.05
20
2
Input definitions
a
dimensionlessTortuosity Factor
phi
fractionPorosity
m
dimensionlessCementation Factor
R_w
ohm mFormation Water Resistivity
R_t
ohm mTrue Formation Resistivity
n
dimensionlessSaturation Exponent
Output definitions
S_w
Water Saturation
a
Tortuosity Factor
phi
Porosity
m
Cementation Factor
R_w
Formation Water Resistivity
R_t
True Formation Resistivity
n
Saturation Exponent
Engineering use, assumptions, and limits
Use it in clean sandstone or carbonate petrophysics workflows where Archie assumptions are appropriate, and calibrate formation-water resistivity plus the Archie exponents against local water, core, or log evidence where possible.
Assumptions
- The rock is sufficiently clean for Archie behavior.
- Formation-water resistivity and Archie exponents are representative.
- Input resistivities use consistent temperature correction and units.
Limitations
- Not appropriate for shaly sands without a shale correction model.
- Sensitive to cementation and saturation exponent choices.
Common mistakes
- Applying Archie directly to conductive shaly formations.
- Using uncorrected water resistivity.
- Assuming default Archie exponents are valid for every reservoir.
Frequently asked questions
What inputs does the Archie Water Saturation from Resistivity Logs calculator need?
The calculation uses Tortuosity Factor (a), Porosity (phi), Cementation Factor (m), Formation Water Resistivity (R_w), True Formation Resistivity (R_t), Saturation Exponent (n). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is water saturation in fraction. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. Not appropriate for shaly sands without a shale correction model. Applying Archie directly to conductive shaly formations.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
Core Laboratories. 2005. Formation Evaluation and Petrophysics, Page 45.
Open source reference