Effective Fracture Permeability Anisotropy Calculator
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 noncritically 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 timeconsuming 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.
Here are two examples of how to use of the calculator explained as part of our fracture modeling class:
1) Effective permeability calibration in a flow simulation grid
2) Well orientation design, fracture permeability and SRV using outcrop data
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 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)

Matrixfracture 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
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