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Characterization of the flow for a single fluid in an excavation damaged zone. (English) Zbl 1176.76128

Summary: The aim of this note is to quantify the change of characteristics of the media of an Excavated Damaged Zone (EDZ) affected by several fractures. For this, we consider Darcy flow through matrix blocks and fractures with permeability of order \(\varepsilon^{2}\delta ^{\theta }\) and 1 respectively. \(\varepsilon\) is the size of a typical porous block, \(\delta \) representing the relative size of the fracture and \(\theta \) is a parameter characterising the permeability ratio. We derive the global behavior from the limit as \(\varepsilon\) and \(\delta \) tend to zero. The resulting homogenized equation is of dual-porosity type for \(\theta =2\), but it is a simple-porosity model with effective coefficients for \(\theta >2\), and there is no flow at the macroscopic level when \(0<\theta <2\).

MSC:

76S05 Flows in porous media; filtration; seepage
76M50 Homogenization applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74R99 Fracture and damage
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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