Geomechanics and FracturingNaturally Fractured Reservoirs

Lim-Aziz Anisotropic Rectangular Matrix-Block Shape Factor Formula

\alpha=\frac{\pi^2}{k_{mg}}\left(\frac{k_x}{L_{mx}^2}+\frac{k_y}{L_{my}^2}+\frac{k_z}{L_{mz}^2}\right)

Lim-Aziz Anisotropic Rectangular Matrix-Block Shape Factor calculates lim-aziz anisotropic shape factor for naturally fractured reservoirs workflows in geomechanics and fracturing.

Calculate

How engineers use this formula

Use this formula when the listed inputs (k_x, k_y, k_z, L_mx, L_my, L_mz) are known and the assumptions behind the cited naturally fractured reservoirs 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, alpha equals 0.441391 1/ft^2.

k_xmD

k_ymD

k_zmD

0.5

L_mxft

L_myft

L_mzft

Inputs

k_x

Matrix Permeability in x Direction

k_y

Matrix Permeability in y Direction

k_z

Matrix Permeability in z Direction

L_mx

Matrix Block Length in x Direction

L_my

Matrix Block Length in y Direction

L_mz

Matrix Block Length in z Direction

Outputs

alpha

1/ft^2

Lim-Aziz Anisotropic Shape Factor

k_mg

Geometric Average Matrix Permeability

L_mx

Matrix Block Length in x Direction

L_my

Matrix Block Length in y Direction

L_mz

Matrix Block Length in z Direction

Source and review

reviewed

Shape factor for regular and irregular matrix blocks in fractured porous media, Rostami, P., Sharifi, M., Dejam, M. (2020)

Rostami, P., Sharifi, M., and Dejam, M. 2020. Shape factor for regular and irregular matrix blocks in fractured porous media. Petroleum Science 17, 136-152.

Source