Practice and answer pack
Petrophysics units and saturation practice pack
This pack practices porosity fractions, resistivity units, Archie diagnostics and the distinction between capillary pressure and relative permeability.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Make every denominator explicit
Write porosity as a fraction when the equation expects a fraction. Keep saturation on the same pore-volume basis and Rw and Rt in matching units.
The baseline deliberately includes an out-of-range Archie result. The task is to diagnose it, not clip it into a physical interval.
Explain each parameter choice
A complete answer names a, m and n and states whether they were assumed or calibrated. Water resistivity also needs a temperature basis.
The additional questions compare equal-porosity rocks and distinguish a change in model parameters from a change in observations.
Separate electrical and flow properties
Relative permeability is dimensionless, capillary pressure has pressure units and absolute permeability has area units. Similar saturation axes do not make these quantities interchangeable.
Print the page for a tutorial or reveal each answer individually. The synthetic numbers are intended for unit and interpretation checks rather than a particular reservoir.
Explore the example
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.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
True Formation Resistivity (ohm m) = 1. S_w (fraction): 1.58113883.
- S_w (fraction)
Worked example
Archie Water Saturation from Resistivity Logs
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.
Relation and unit basis
S_w = ((a / phi^m) * (R_w / R_t))^(1 / n)
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).
1. Define the baseline
True Formation Resistivity (ohm m) = 1
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.
2. Select the relation
S_w = ((a / phi^m) * (R_w / R_t))^(1 / n)
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).
3. Substitute the values
a = 1; phi = 0.2; m = 2; R_w = 0.1; R_t = 1; n = 2 → S_w = 1.58113883 fraction
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
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.
Result and interpretation
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.
Use the invalid baseline to practice a diagnostic explanation before moving to the additional numerical exercises.
Exact scenario data
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.
| True Formation Resistivity (ohm m) | S_w (fraction) |
|---|---|
| 1 | 1.581139 |
| 2 | 1.118034 |
| 2.5 | 1 |
| 5 | 0.7071068 |
| 10 | 0.5 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Practice problems and answer key
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. What is the correct porosity input for 20% when a calculator expects a fraction?
Show the worked answer
0.20. Entering 20 changes the denominator dramatically and does not represent 20% porosity.
2. Reproduce the baseline S_w (fraction) without rounding intermediate values.
Show the worked answer
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. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
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. What would be needed to apply this example to a different physical system?
Show the worked answer
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. For a = 1, Rw = 0.1 Ω·m, φ = 0.2 and m = 2, calculate the full-water Rt threshold.
Show the worked answer
Rt = aRw/φ^m = 2.5 Ω·m. Lower Rt produces an out-of-range Archie Sw under these assumptions.
6. With n = 2 and all else fixed, how much does doubling Rw multiply Sw?
Show the worked answer
By √2 ≈ 1.414214. This sensitivity does not establish the correct formation-temperature Rw.
Before using the result
- Convert percent to fraction when required.
- Retain the formation-temperature Rw basis.
- Explain out-of-range outputs.
The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.