Engineering lesson
Gassmann fluid substitution what the inputs represent
Gassmann fluid substitution relates dry-frame, mineral and fluid bulk moduli with porosity under its low-frequency connected-pore assumptions. It does not infer all those properties from one sonic log.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Assign each modulus to the correct material
Kdry describes the porous frame, Ks the solid mineral material and Kf the pore fluid. Using a saturated rock modulus as Kdry counts fluid effects twice.
All moduli must use compatible units. The Biot coefficient α = 1 − Kdry/Ks is a useful consistency check on the frame–mineral pair under the stated assumptions.
Hold the frame fixed during substitution
The simple substitution assumes changing fluid does not change the dry frame. Chemical alteration, stress changes or frequency-dependent effects can violate that premise.
The explorer varies fluid bulk modulus with porosity and frame properties fixed. It therefore illustrates the equation's sensitivity, not a prediction of every laboratory or seismic response.
Separate bulk modulus from wave velocity
A P-wave velocity also depends on shear modulus and density. A new saturated bulk modulus alone is insufficient to calculate the new velocity.
Partial saturation and fluid mixing require their own assumptions. A uniform-fluid Gassmann result should not be presented as a resolved patchy-saturation model.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/gassmann-saturated-rock-bulk-modulus. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Effective Pore-Fluid Bulk Modulus (GPa) = 2.2. K_sat (GPa): 15.0605831.
- K_sat (GPa)
Worked example
Gassmann Saturated Rock Bulk Modulus
Fixed controls: K_d = 10 GPa; K_s = 37 GPa; phi = 0.2 fraction. K_f is varied as shown.
Relation and unit basis
K_d: Drained Rock-Frame Bulk Modulus (GPa). K_s: Solid Grain Bulk Modulus (GPa). K_f: Effective Pore-Fluid Bulk Modulus (GPa). phi: Connected Porosity (fraction).
1. Define the baseline
Effective Pore-Fluid Bulk Modulus (GPa) = 2.2
Fixed controls: K_d = 10 GPa; K_s = 37 GPa; phi = 0.2 fraction. K_f is varied as shown.
2. Select the relation
K_d: Drained Rock-Frame Bulk Modulus (GPa). K_s: Solid Grain Bulk Modulus (GPa). K_f: Effective Pore-Fluid Bulk Modulus (GPa). phi: Connected Porosity (fraction).
3. Substitute the values
K_d = 10; K_s = 37; K_f = 2.2; phi = 0.2 → K_sat = 15.0605831 GPa
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
K_sat (GPa) = 15.0605831
The dry frame is fixed. Wave velocity additionally requires shear modulus and density.
Result and interpretation
K_sat (GPa) = 15.0605831
The dry frame is fixed. Wave velocity additionally requires shear modulus and density.
The fluid modulus changes while dry frame, mineral modulus and porosity stay fixed.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/gassmann-saturated-rock-bulk-modulus. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Effective Pore-Fluid Bulk Modulus (GPa) | K_sat (GPa) |
|---|---|
| 0.1 | 10.26436 |
| 0.5 | 11.28526 |
| 1 | 12.48466 |
| 2.2 | 15.06058 |
| 3 | 16.57547 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. Can Ksat alone determine P-wave velocity?
Show the worked answer
No. P-wave velocity requires density and shear modulus as well as saturated bulk modulus.
2. Reproduce the baseline K_sat (GPa) without rounding intermediate values.
Show the worked answer
K_d = 10; K_s = 37; K_f = 2.2; phi = 0.2 → K_sat = 15.0605831 GPa. K_sat (GPa) = 15.0605831. The dry frame is fixed. Wave velocity additionally requires shear modulus and density.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Effective Pore-Fluid Bulk Modulus (GPa) changes from 0.1 to 3. Other controls remain as stated in the premise. K_sat (GPa) changes from 10.2643603 to 16.575466.
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. K_d: Drained Rock-Frame Bulk Modulus (GPa). K_s: Solid Grain Bulk Modulus (GPa). K_f: Effective Pore-Fluid Bulk Modulus (GPa). phi: Connected Porosity (fraction). The dry frame is fixed. Wave velocity additionally requires shear modulus and density.
Before using the result
- Use dry-frame rather than saturated modulus.
- Keep all modulus units compatible.
- State low-frequency and fluid-distribution assumptions.
The dry frame is fixed. Wave velocity additionally requires shear modulus and density.
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.