The dynamics of viscous compressible fluid in a fracture

Solves a problem of fluid dynamics in an arbitrarily shaped fracture containing proppant. The fracture is embedded in an absolutely rigid solid. The fluid flow is induced by normal harmonic oscillations of fracture walls that are permeable, allowing the fluid to filtrate into the surrounding formation. The amplitude of oscillations can be described as a function of a spatial coordinate along the fracture. Fluid flow inside the fracture is described by Biot's modification of Darcy's law that includes both inertia and filtration terms. Filtration inside the fracture may drastically change its acoustic characteristics. The apparent acoustic velocity in the fracture is lower than sound velocity in the fluid because of coupling between the fluid and the proppant. In a fracture without proppant, fluid filtration into the surrounding rock acts to decrease resonance peaks and to increase resonance period. -from Authors