Reservoir EngineeringPermeability

Lognormal Effective Permeability from Geometric Mean Formula

k_{eff}=k_g\exp\left[\left(\frac{1}{2}-\frac{1}{d}\right)\sigma_{\ln k}^2\right]

Lognormal Effective Permeability from Geometric Mean calculates lognormal effective permeability for permeability workflows in reservoir engineering.

Calculate

How engineers use this formula

Use this formula when the listed inputs (k_g, sigma_lnk, d_dim) are known and the assumptions behind the cited permeability relationship match the engineering case being checked.

Assumptions

Input values are representative for the well, reservoir, fluid, or equipment case being evaluated.
The declared units match the field-unit constants used in the formula.
The cited formula applies to the selected petroleum engineering workflow.

Limitations

The calculation does not replace a full engineering model or operating procedure.
Accuracy depends on the source correlation, assumptions, input quality, and unit consistency.

Common mistakes

Mixing unit systems without converting the inputs.
Using default example values as field recommendations.
Applying the formula outside the source assumptions.

Default example

Using the default inputs, k_eff equals 59.068021 mD.

k_gmD

sigma_lnkdimensionless

d_dimdimensionless

Inputs

k_g

Geometric Mean Permeability

sigma_lnk

dimensionless

Standard Deviation of Natural Log Permeability

d_dim

dimensionless

Flow-System Dimensionality

Outputs

k_eff

Lognormal Effective Permeability

k_g

Geometric Mean Permeability

sigma_lnk

dimensionless

Standard Deviation of Natural Log Permeability

d_dim

dimensionless

Flow-System Dimensionality

Source and review

reviewed

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts, Masihi, M., Gago, P.A., King, P.R. (2016)

Masihi, M., Gago, P.A., and King, P.R. 2016. Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts. Transport in Porous Media 114, 169-199.

Source