Geometric model of the fracture as a manifold immersed in porous media

摘要: In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing fractures with complex geometries. We model coupled fracture-porous system where linear Darcy is considered and nonlinear Forchheimer equation used inside fracture. develop a to examine geometries variable thickness on Riemannian manifold. The fracture represented as normal variation surface immersed R3. Using operators Laplace–Beltrami type geometric identities, an that describes A reduced obtained low dimensional boundary value problem. then couple media. Theoretical numerical analyses have been performed compare solutions between original reservoirs prove two are close and, therefore, can be effectively large scale simulators for long thin complicated geometry.