Biot-Willis Coefficient Calculator
Calculate the Biot-Willis coefficient from drained rock and solid grain bulk moduli in GPa. Distinguish frame modulus from saturated log modulus.
Calculate the Biot-Willis coefficient from drained rock and solid grain bulk moduli in GPa. Distinguish frame modulus from saturated log modulus.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate the isotropic Biot-Willis poroelastic coefficient as one minus drained-frame bulk modulus divided by solid-grain bulk modulus. This gives the coefficient used in volumetric poroelastic coupling, not a fluid property or the heat-transfer Biot number.
Use drained-frame and solid-grain moduli from a consistent material characterization to determine the coefficient for a poroelastic screening calculation. Keep the modulus basis consistent and review the additional porosity-dependent bound separately.
Solves for
alpha (dimensionless)
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Formula, variables, and sourceReproduce the modulus ratio
For K_d = 10 GPa and K_s = 37 GPa, alpha = 1 - 10/37 = 0.729730. Scaling both inputs to 10,000 and 37,000 MPa leaves the dimensionless ratio unchanged. Mixing 10 GPa with a grain value entered as 37,000 without changing the unit basis does not.
A zero frame modulus gives the mathematical soft-frame limit alpha = 1. Equal frame and grain moduli give alpha = 0. The latter is not a physically appropriate result for a material with positive porosity under the usual porous-material bound; the calculator cannot check that bound without porosity.
Keep poroelastic coefficients distinct
The Biot-Willis coefficient depends on porous-frame and solid-grain stiffness. Biot modulus M additionally depends on fluid properties and porosity, while Skempton B describes a different pressure response under undrained loading. One numerical coefficient must not be substituted for another because their names occur in the same constitutive model.
The linked Gassmann calculation makes the distinction explicit by using both alpha and a storage modulus in an equivalent form. Treat the calculated alpha as one characterized input to a wider geomechanics model; it is not a standalone prediction of reservoir compaction or allowable wellbore pressure.
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 alpha = 0.72973 dimensionless. Defaults demonstrate the implementation; they are not recommended field values.
10
37
Input definitions
K_d
GPaDrained Porous Rock Bulk Modulus
K_s
GPaSolid Grain Bulk Modulus
Output definitions
alpha
Biot-Willis Poroelastic Coefficient
Engineering use, assumptions, and limits
Use drained-frame and solid-grain moduli from a consistent material characterization to determine the coefficient for a poroelastic screening calculation. Keep the modulus basis consistent and review the additional porosity-dependent bound separately.
Assumptions
- Small-strain isotropic poroelasticity is an appropriate material model.
- Frame modulus is measured under drained conditions; grain and frame moduli use compatible units and conditions.
Limitations
- No porosity input is provided, so the additional material bound phi <= alpha is not automatically checked.
- This coefficient does not replace anisotropic poroelastic characterization or determine a failure envelope.
Common mistakes
- Substituting saturated sonic-log modulus for a drained-frame measurement.
- Confusing Biot coefficient with porosity, Skempton B, Biot modulus M or a heat-transfer Biot number.
Frequently asked questions
What inputs does the Biot-Willis Coefficient from Bulk Moduli calculator need?
The calculation uses Drained Porous Rock Bulk Modulus (K_d), Solid Grain Bulk Modulus (K_s). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is biot-willis poroelastic coefficient in dimensionless. 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. No porosity input is provided, so the additional material bound phi <= alpha is not automatically checked. Substituting saturated sonic-log modulus for a drained-frame measurement.
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.
COMSOL Multiphysics 6.4 documentation, Poroelastic Material, general model for the Biot-Willis coefficient. This coefficient depends on frame and grain properties, not fluid modulus.
Open source reference