Petrophysics units and saturation practice pack
PetroCalcHub · Original synthetic teaching exercise · 2026-10-24

This pack practices porosity fractions, resistivity units, Archie diagnostics and the distinction between capillary pressure and relative permeability.

Fixed controls: a = 1 dimensionless; phi = 0.2 fraction; m = 2 dimensionless; R_w = 0.1 ohm m; n = 2 dimensionless. R_t is varied as shown.

1. What is the correct porosity input for 20% when a calculator expects a fraction?

Working: ________________________________________________


2. Reproduce the baseline S_w (fraction) without rounding intermediate values.

Working: ________________________________________________


3. Compare the first and last recorded scenarios. Which input changes?

Working: ________________________________________________


4. What would be needed to apply this example to a different physical system?

Working: ________________________________________________


5. For a = 1, Rw = 0.1 Ω·m, φ = 0.2 and m = 2, calculate the full-water Rt threshold.

Working: ________________________________________________


6. With n = 2 and all else fixed, how much does doubling Rw multiply Sw?

Working: ________________________________________________


ANSWER KEY

1. 0.20. Entering 20 changes the denominator dramatically and does not represent 20% porosity.
2. a = 1; phi = 0.2; m = 2; R_w = 0.1; R_t = 1; n = 2 → S_w = 1.58113883 fraction. S_w (fraction) = 1.58113883. The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
3. True Formation Resistivity (ohm m) changes from 1 to 10. Other controls remain as stated in the premise. S_w (fraction) changes from 1.58113883 to 0.5.
4. Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. a: Tortuosity Factor (dimensionless). phi: Porosity (fraction). m: Cementation Factor (dimensionless). R_w: Formation Water Resistivity (ohm m). R_t: True Formation Resistivity (ohm m). n: Saturation Exponent (dimensionless). The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
5. Rt = aRw/φ^m = 2.5 Ω·m. Lower Rt produces an out-of-range Archie Sw under these assumptions.
6. By √2 ≈ 1.414214. This sensitivity does not establish the correct formation-temperature Rw.

Method: Replayed with the same equation record and calculation engine as /calculators/archie-water-saturation-from-resistivity-logs. Original synthetic inputs; engine outputs are saved in the downloadable record.
Sources:
Kansas Geological Survey: Archie equation and variables: https://www.kgs.ku.edu/General/Tutorial/pfeffer/archie.html
SLB: Archie equation: https://glossary.slb.com/en/terms/a/archie_equation