Darcy-Forchheimer Velocity Calculator
Calculate Darcy-Forchheimer superficial velocity from SI pressure gradient, permeability, viscosity, density and inertial resistance coefficient.
Calculate Darcy-Forchheimer superficial velocity from SI pressure gradient, permeability, viscosity, density and inertial resistance coefficient.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Solve the local one-dimensional Darcy-Forchheimer pressure-gradient balance for nonnegative superficial velocity. The expression includes viscous and inertial resistance and uses a numerically stable positive quadratic root, including the zero-inertia Darcy limit.
Enter a gravity-free driving pressure-gradient magnitude in Pa/m with compatible SI permeability, viscosity, density and inertial resistance. Use this as a local constant-property porous-flow check, not an integrated radial gas-deliverability forecast.
Solves for
v (m/s)
Best next page
Formula, variables, and sourceCheck the pressure-gradient balance
For the illustrative inputs G = 1,000,000 Pa/m, mu = 0.001 Pa.s, k = 1e-10 square metres, beta = 1e8 per metre and rho = 1,000 kg/m3, velocity is 0.003112673 m/s. Substitution gives about 31,126.729 Pa/m viscous resistance and 968,873.271 Pa/m inertial resistance, summing to the supplied gradient.
Setting beta to zero returns v = kG/mu = 0.1 m/s for the same other inputs. A zero driving gradient returns zero velocity. The rationalized positive root avoids subtracting nearly equal numbers when the inertial contribution becomes very small, and avoids division by beta at the Darcy limit.
Match the coefficient and velocity definitions
Some references absorb density into the nonlinear coefficient or express resistance through dimensionless c_F. This page explicitly uses G = (mu/k)v + beta rho v squared, with beta in inverse metres. Convert a coefficient definition before transferring it; matching a symbol name alone is not sufficient.
The output is superficial, or Darcy, velocity based on total cross-sectional area. A pore-space average velocity requires porosity and an appropriate flow interpretation. The synthetic high-permeability example is an arithmetic check, not a claim that these parameters represent a typical reservoir or fracture.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns v = 0.003113 m/s. Defaults demonstrate the implementation; they are not recommended field values.
1000000
0.001
1e-10
100000000
1000
Input definitions
G
Pa/mNonnegative Driving Pressure Gradient Magnitude (Gravity Excluded)
mu
Pa.sDynamic Viscosity
k
m^2Intrinsic Permeability
beta
1/mInertial Resistance Coefficient (Not Dimensionless c_F)
rho
kg/m3Fluid Density
Output definitions
v
Superficial Velocity Magnitude
G
Driving Pressure Gradient Magnitude
Engineering use, assumptions, and limits
Enter a gravity-free driving pressure-gradient magnitude in Pa/m with compatible SI permeability, viscosity, density and inertial resistance. Use this as a local constant-property porous-flow check, not an integrated radial gas-deliverability forecast.
Assumptions
- Single-phase, one-dimensional local flow with constant positive viscosity, permeability and density.
- The pressure-gradient input is a nonnegative driving magnitude with gravity already excluded; beta is nonnegative.
Limitations
- Does not integrate compressible gas flow, reservoir radial geometry, gravity or spatial property changes.
- Beta must be characterized for the medium; this evaluator does not estimate it from permeability alone.
Common mistakes
- Entering dimensionless c_F in place of beta in 1/m; the convention here is beta = c_F/sqrt(k).
- Entering millidarcies as square metres or cP as Pa.s, or interpreting superficial velocity as pore velocity.
Frequently asked questions
What inputs does the Darcy-Forchheimer Superficial Velocity calculator need?
The calculation uses Nonnegative Driving Pressure Gradient Magnitude (Gravity Excluded) (G), Dynamic Viscosity (mu), Intrinsic Permeability (k), Inertial Resistance Coefficient (Not Dimensionless c_F) (beta), Fluid Density (rho). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is superficial velocity magnitude in m/s. 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. Does not integrate compressible gas flow, reservoir radial geometry, gravity or spatial property changes. Entering dimensionless c_F in place of beta in 1/m; the convention here is beta = c_F/sqrt(k).
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: Modeling Darcian and Non-Darcian Flow in Porous Media (2020), equation 3. Stable positive quadratic-root rearrangement for a one-dimensional, gravity-free pressure-gradient magnitude.
Open source reference