Dimensional Model Reduction for Flow through Fractures in Poroelastic Media
نویسندگان
چکیده
We study the interaction between a poroelastic medium and a fracture filled with fluid. The flow in the fracture is described by the Brinkman equations for an incompressible fluid and the poroelastic medium by the quasi-static Biot model. The two models are fully coupled via the kinematic and dynamic conditions. The Brinkman equations are then averaged over the cross-sections, giving rise to a reduced flow model on the fracture midline. We derive suitable interface and closure conditions between the Biot system and the dimensionally reduced Brinkman model that guarantee solvability of the resulting coupled problem. We design and analyze a numerical discretization scheme based on finite elements in space and the Backward Euler in time, and perform numerical experiments to compare the behavior of the reduced model to the full-dimensional formulation and study the response of the model with respect to its parameters. Mathematics Subject Classification. 76S05, 76D07, 74F10, 65M60, 65M12. Received October 21, 2015. Accepted November 7, 2016.
منابع مشابه
A new conforming mesh generator for three-dimensional discrete fracture networks
Nowadays, numerical modelings play a key role in analyzing hydraulic problems in fractured rock media. The discrete fracture network model is one of the most used numerical models to simulate the geometrical structure of a rock-mass. In such media, discontinuities are considered as discrete paths for fluid flow through the rock-mass while its matrix is assumed impermeable. There are two main pa...
متن کاملDirect simulation of fluid-solid mechanics in porous media using the discrete element and lattice-Boltzmann methods
[1] A detailed understanding of the coupling between fluid and solid mechanics is important for understanding many processes in Earth sciences. Numerical models are a popular means for exploring these processes, but most models do not adequately handle all aspects of this coupling. This paper presents the application of a micromechanically based fluid-solid coupling scheme, lattice-Boltzmann di...
متن کاملA Three-dimensional Poroelastic Model for Water Injection into a Geothermal Reservoir
A three-dimensional poroelastic model is developed to investigate the poroelastic effect of fluid injection into a geothermal reservoir. In the model, the fluid flow in the fracture is assumed to be lubrication flow and modeled by the finite element method. The threedimensional pore fluid diffusion in the reservoir and the induced stresses are modeled by the boundary integral equation method. T...
متن کاملTwo-Dimensional Solute Transport with Exponential Initial Concentration Distribution and Varying Flow Velocity
The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...
متن کاملTwo-Dimensional Solute Transport with Exponential Initial Concentration Distribution and Varying Flow Velocity
The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The...
متن کامل