Fractures and resurgences in porous media
Abstract
Geological porous media are heterogeneous materials which in addition contain discontinuities such as fractures and conduits which facilitate fluid transport.
Fractures are relatively plane objects which strongly interact with the surrounding porous medium because of their large contact surface. A different situation occurs in karsts where distant regions of the medium can be connected by relatively thin conduits which have little if any hydrodynamic interaction with the porous medium that they cross, except at their ends; such conduits are called here resurgences. A distinctive feature of fractures is that they occur usually in large numbers which makes a statistical approach feasible. Below a certain density called the percolation threshold, the fractures form finite clusters and the macroscopic permeability is dominated by the matrix permeability. Above this threshold, the flow properties are dominated by the fracture properties. Close to the threshold, it will be shown that the properties fluctuate largely. This threshold also plays a crucial role in other phenomena such as barometric pumping. The output is of a completely different order of magnitude when the fractures percolate or not. Moreover, when the fracture density increases, the media are shown to behave as homogeneous media. Usually, resurgences are only a few, hence, a statistical approach is unrealistic and specific cases are studied. A double structure is assumed, namely a continuous porous medium described by the classical Darcy law and the resurgences modeled by conduits with impermeable walls which relate distant points of the continuous medium. When non steady regimes are considered, it is necessary to confer a capacity to these conduits in addition to their hydrodynamic resistance. The flow equations in the two structures are related by the unknown flow rates jn(t) (n = 1,2, …, N) depending on time at the nth vertices of the network. Application of the conservation law at the vertices yields a system of integral equations for jn(t) whose structure depends on the network structure. The Laplace transformation yields a linear algebraic system. When this system is solved, the flow rates jn(t) can be constructed by the inverse Laplace transform. Some of the most important characteristics of these models will be described.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFM.H34F..02A
- Keywords:
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- 1838 Infiltration;
- HYDROLOGYDE: 1847 Modeling;
- HYDROLOGYDE: 1865 Soils;
- HYDROLOGYDE: 1875 Vadose zone;
- HYDROLOGY