Sabine Stichel

Numerical methods for flow in fractured porous media

We present a numerical technique for the simulation of salinity- as well as thermohaline-driven flows in fractured porous media. In this technique, the fractures are represented by low-dimensional manifolds, on which a low-dimensional variant of the PDEs of variable-density flow is formulated. The latter is obtained from the full-dimensional model by the average-along-the-vertical. The discretization of the resulting coupled system of the full- and low-dimensional PDEs is based on a finite-volume method. This requires a special construction of the discretization grid which can be obtained by the algorithm presented in this work. This technique allows to reconstruct in particular the jumps of the solution at the fracture. Its precision is demonstrated in the numerical comparisons with the results obtained in the simulations where the fractures are represented by the full-dimensional subdomains.

Forchheimer’s correction in modelling flow and transport in fractured porous media

The scope of this manuscript is to investigate the role of the Forchheimer correction in the description of variable-density flow in fractured porous media. A fractured porous medium, which shall be also referred to as “the embedding medium”, represents a flow region that is made macroscopically heterogeneous by the presence of fractures. Fractures are assumed to be filled with a porous medium characterized by flow properties that differ appreciably from those of the embedding medium. The fluid, which is free to move in the pore space of the entire flow region, is a mixture of water and brine. Flow is assumed to be a consequence of the variability of the fluid mass density in response to the generally nonuniform distribution of brine, which is subject to diffusion and convection. The fractures are assumed to be thin in comparison with the characteristic sizes of the embedding medium. Within this framework, some benchmark problems are solved by adopting two approaches: (i) the fractures are treated as thin but

Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum

\mathrm{d}

An overview of models of density-driven flow in fractured porous media

d-dimensional flow subregions, with

Models and simulations of variable-density flow in fractured porous media

d

Simulation of densitydrivenflow in fractured porous media

d being the geometric dimension of the embedding medium; (ii) the fractures are regarded as