Estimation of effective fracture permeability anisotropy

​

The effective fracture permeability anisotropy in a cell is controlled not only by the particular fracture geometry and intensity of the fractures but also by the individual fracture apertures and stress state that affects them by making critically stressed fractures more conductive than non-critically stressed ones. This calculator takes all these aspects into account. Give it a try with your own data to get a sense of how we would calibrate a complete 3D volume derived from seismic data. You can also use this calculator to calibrate with your own measured perms at the well. For more details on how this concept is used in field scale, seismic constrained fracture modeling take a look at this publication by Michelena, et al., 2019. 

​

This calculator is a robust, fast alternative to the time-consuming workflow required to calibrate discrete fracture network (DFN) models with measured permeabilities prior to flow simulation. Typical DFN calibration workflow includes generation of discrete fractures, transmissivity adjustment, critical stress analysis, and permeability upscaling. This calculator combines all these steps without the need to explicitly model the discrete fractures.

 

Input:

• Number of fractures in each orientation (measured from North)

• Estimated fracture width for each orientation

• Orientation of maximum horizontal stress Shmax (measured from North)

• Relative fracture width multipliers for fractures parallel to stress, perpendicular to stress, and critically stressed. If all multipliers are equal to one means that there is no width enhancement enhancement due to stress.

• Measured permeability (if available) for calibration of fracture parameters

• Matrix permeability

• Cell area and volume of the cell where calibration is made.          

• Average fracture height for all fractures within a cell.

​

Assumptions: 

Critically stressed fractures occur in the vicinity of 30 degrees; estimations are based on the Oda equation; natural fractures are vertical.

 

Output:

• Circular variance and Fisher coefficient for the input fracture geometry

• Orientation of maximum permeability 

• Maximum modeled permeability (Kmax)

• Minimum modeled permeability (Kmin)

• Permeability anisotropy

• Modeled effective permeability Keff (geometric average of Kmax and Kmin plus matrix perm)

• Fracture porosity

• Fracture intensity P32  (area of fractures per unit volume)

• Sigma (matrix block shape factor)

• Matrix-fracture contact surface area assuming a cell thickness of 1 m. 

• Width_eff: Effective fracture hydraulic width estimated from Keff and P32 .

• Average fracture spacing between fractures assuming a cell size of sqrt(Area)

​

Legend of curves:

​Fractures Shmax Kmax  Kmin Keff Modeled K measured Width^3

All curves are normalized by its larger value. Permeabilities are normalized  by the maximum of K_measured and Kmax

​

This calculator is not designed to work on mobile devices

​

​

​