Method to calculate the effective hydraulic aperture and permeability of rock fractures

A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:

• receiving a geometry of a 3D fracture obtained by an X-ray tomography machine;
• determining, using a computer processor, a fluid flow direction through the 3D fracture;
• dividing, using the computer processor, the 3D fracture into a plurality of 2D cross-sections oriented substantially parallel to the fluid flow direction;
• dividing, using the computer processor, each 2D cross-section into a plurality of Type I and Type II fracture segments based, at least in part, on a segment aspect ratio and a segment roughness ratio;
• determining, using the computer processor, a 2D segment hydraulic aperture for each of the plurality of Type I and Type II fracture segments;
• determining, using the computer processor, the 3D hydraulic aperture of the 3D fracture based, at least in part, on the 2D segment hydraulic apertures of the plurality of Type I and Type II fracture segments;
• and
• designing a hydraulic fracturing plan to be executed based, at least in part, on the 3D hydraulic aperture, the executed hydraulic fracturing plan comprising pumping a fluid from a hydraulic fracturing unit into a well.

A system comprising:

• an X-ray tomography machine for determining a geometry of a 3D fracture;
• a computer processor, configured to;
• receive the geometry of the 3D fracture;
• determine a fluid flow direction through the 3D fracture;
• divide the 3D fracture into a plurality of 2D cross-sections oriented substantially parallel to the fluid flow direction;
• divide each 2D cross-section into a plurality of Type I and Type II fracture segments based, at least in part, on a segment aspect ratio and a segment roughness ratio;
• determine a 2D segment hydraulic aperture for each of the plurality of Type I and Type II fracture segments;
• determine the 3D hydraulic aperture of the 3D fracture based, at least in part, on the 2D segment hydraulic apertures of the plurality of Type I and Type II fracture segments;
• and
• design a hydraulic fracturing plan based, at least in part, on the 3D hydraulic aperture;
• and
• a hydraulic fracturing unit for pumping a fluid into a well based on the hydraulic fracturing plan.