A multiscale model of distributed fracture and permeability in solids in all-round compression

TL;DR

This paper introduces a multiscale microstructural model for permeability in fractured solids, capturing hierarchical fault networks and enabling explicit analytical predictions of porosity and permeability, especially relevant for hydraulic fracturing applications.

Contribution

The model uniquely describes hierarchical fracture networks and provides explicit formulas for permeability, advancing understanding of flow in fractured porous media.

Findings

Hierarchical fault networks significantly influence permeability.

Explicit analytical expressions for porosity and permeability are derived.

Model applicability to hydraulic fracturing in low-permeability reservoirs.

Abstract

We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear resistance in the undamaged material. Secondary faults may form in a hierarchical orga- nization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the dam- aged material. The approach is particularly appealing as a means of modeling low permeability oil and gas reservoirs stimulated by hydraulic fracturing.