Theory of Matrix and Fracture Flow Regimes in Unsaturated, Fractured Porous Mediaby John J. Nitao, Lawrence Livermore Natl Lab, Livermore, United States,
Abstract: The flow behavior of a two-dimensional, unsaturated fracture-matrix system is characterized by a critical flux qf* = φ(Ss - Si)Dm where φ is matrix porosity, Ss maximum matrix saturation, Si initial saturation, and Dm matrix imbibition diffusivity constant. If the flux qf into the fracture satisfies qf > qf*, the flow field is fracture-dominated; whereas, if qf < qf*, 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 Kf*, 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 | Matrix (mathematics) | Porous media flow | Unsaturated flow | Two-dimensional flow | Critical flow | Rocks
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