Gassmann Saturated Bulk Modulus Calculator
Calculate Gassmann saturated rock bulk modulus from drained frame, grain and fluid moduli in GPa and connected porosity as a fraction.
Calculate Gassmann saturated rock bulk modulus from drained frame, grain and fluid moduli in GPa and connected porosity as a fraction.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Compute saturated rock bulk modulus from drained-frame modulus, solid-grain modulus, connected porosity and effective pore-fluid modulus. Gassmann's relation provides a low-frequency rock-physics calculation, not a saturated sonic-log-to-static-modulus conversion.
Use independently established frame and grain properties to evaluate the effect of a selected pore fluid. Obtain the effective fluid modulus on a compatible pressure and temperature basis, then check whether pressure equilibration and connected pores are reasonable.
COMSOL: porosity-dependent Biot-Willis stiffness boundSolves for
K_sat (GPa)
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Formula, variables, and sourceCheck frame, grain and fluid separately
Using K_d = 10 GPa, K_s = 37 GPa, K_f = 2.2 GPa and phi = 0.20 gives 15.060583 GPa for K_sat. The numerator is dimensionless, while every term in the storage denominator has inverse-modulus units; their ratio is therefore a modulus.
The minus sign on K_d/K_s squared in the denominator matters. An independent check uses alpha = 1 - K_d/K_s and M = 1/[phi/K_f + (alpha - phi)/K_s], giving K_sat = K_d + alpha squared times M. This reproduces the default without changing the frame or grain inputs.
Prepare a fluid-substitution comparison
For a second fluid, keep the drained frame, mineral properties and connected porosity fixed only if that assumption is physically justified. Evaluate K_sat again with the replacement fluid modulus at the selected conditions. The change in bulk modulus alone is not a P-wave velocity change: shear modulus and saturated density are also required.
When two pore fluids are pressure-equilibrated, the linked Wood calculator supplies a harmonic effective fluid modulus. Do not apply that value to a patchy-saturation case without checking the appropriate rock-physics treatment. Input validation rejects zero moduli, zero porosity and a nonpositive storage denominator; it cannot establish the validity of a rock sample model.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns K_sat = 15.060583 GPa. Defaults demonstrate the implementation; they are not recommended field values.
10
37
2.2
0.2
Input definitions
K_d
GPaDrained Rock-Frame Bulk Modulus
K_s
GPaSolid Grain Bulk Modulus
K_f
GPaEffective Pore-Fluid Bulk Modulus
phi
fractionConnected Porosity
Output definitions
K_sat
Saturated Rock Bulk Modulus
Engineering use, assumptions, and limits
Use independently established frame and grain properties to evaluate the effect of a selected pore fluid. Obtain the effective fluid modulus on a compatible pressure and temperature basis, then check whether pressure equilibration and connected pores are reasonable.
Assumptions
- The rock is macroscopically isotropic with connected, pressure-equilibrated pores in the low-frequency limit.
- The selected pore fluid does not alter the frame, all bulk moduli share the same units, and K_d <= (1 - phi) K_s satisfies the porous-material stiffness bound.
Limitations
- This is a saturated-modulus evaluator, not a complete two-state fluid-substitution or seismic-velocity workflow.
- Isolated pores, anisotropy, patchy saturation and fluid-frame chemical interactions can invalidate the selected model.
Common mistakes
- Using saturated log-derived bulk modulus as K_d, or confusing porous-frame and mineral-grain properties.
- Mixing GPa and psi, using percent porosity as a fraction, or changing fluids while silently changing frame properties.
Frequently asked questions
What inputs does the Gassmann Saturated Rock Bulk Modulus calculator need?
The calculation uses Drained Rock-Frame Bulk Modulus (K_d), Solid Grain Bulk Modulus (K_s), Effective Pore-Fluid Bulk Modulus (K_f), Connected Porosity (phi). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is saturated rock bulk modulus in GPa. 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. This is a saturated-modulus evaluator, not a complete two-state fluid-substitution or seismic-velocity workflow. Using saturated log-derived bulk modulus as K_d, or confusing porous-frame and mineral-grain properties.
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.
Construction of 2D and 3D rock physics templates for quantitative prediction of physical properties of a carbonate reservoir in SW of Iran, Forouzan Rahmani, Mohammad Emami Niri, Golnaz Jozanikohan (2023)
Rahmani, Emami Niri and Jozanikohan (2023), Construction of 2D and 3D rock physics templates, Journal of Petroleum Exploration and Production Technology 13, 449-470. Equation 13; published online 2022.
Open source reference