Theory of Matrix and Fracture Flow Regimes in Unsaturated, Fractured Porous Media

by John J. Nitao, Lawrence Livermore Natl Lab, Livermore, United States,



Document Type: Proceeding Paper

Part of: High Level Radioactive Waste Management 1991

Abstract:

The flow behavior of a two-dimensional, unsaturated fracture-matrix system is characterized by a critical flux q_f^* = ?(S_s - S_i)D_m where ? is matrix porosity, S_s maximum matrix saturation, S_i initial saturation, and D_m matrix imbibition diffusivity constant. If the flux q_f into the fracture satisfies q_f > q_f^*, the flow field is fracture-dominated; whereas, if q_f < q_f^*, the flow is matrix-dominated, and the system behaves as a single equivalent medium with capillary equilibrium between fracture and matrix. If the fracture entrance is ponded, the critical fracture hydraulic conductivity K_f^*, or corresponding critical aperture 2b^* from the 'cubic law,' controls the flow behavior instead of the critical flux. Rocks with fracture apertures 2b that are sufficiently large, b³ > b^*3, have flow that is fracture-dominated while rocks with small aperture fractures, b³ < b^*3, will be matrix-dominated. Numerical modeling verifies the theory and tests approximate analytical solutions predicting fracture front movement.

Subject Headings: Cracking | Hydraulic fracturing | Porous media flow | Numerical models | Matrix (mathematics) | Radioactive wastes | Mathematical models | Nevada | United States

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