Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Network-inspired versus Kozeny-Carman based permeability-porosity
  relations applied to Biot's poroelasticity model   Water injection in the aquifer induces deformations in the soil. These
mechanical deformations give rise to a change in porosity and permeability,
which results in non-linearity of the mathematical problem. Assuming that the
deformations are very small, the model provided by Biot's theory of linear
poroelasticity is used to determine the local displacement of the skeleton of a
porous medium, as well as the fluid flow through the pores. In this continuum
scale model, the Kozeny-Carman equation is commonly used to determine the
permeability of the porous medium from the porosity. The Kozeny-Carman relation
states that flow through the pores is possible at a certain location as long as
the porosity is larger than zero at this location in the aquifer. However, from
network models it is known that percolation thresholds exist, indicating that
the permeability will be equal to zero if the porosity becomes smaller than
these thresholds. In this paper, the relationship between permeability and
porosity is investigated. A new permeability-porosity relation, based on the
percolation theory, is derived and compared with the Kozeny-Carman relation.
The strongest feature of the new approach is related to its capability to give
a good description of the permeability in case of low porosities. However, with
this network-inspired approach small values of the permeability are more likely
to occur. Since we show that the solution of Biot's model converges to the
solution of a saddle point problem for small time steps and low permeability,
we need stabilisation in the finite element approximation.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio