Diffuse interface modeling and variationally consistent homogenization of fluid transport in fractured porous media
Journal article, 2020

We critically assess diffuse interface models for fluid transport in fractured porous media. Such models, often called fracture phase field models, are commonly used to simulate hydraulic stimulation or hydraulic fracturing of fluid-saturated porous rock. In this paper, we focus on the less complex case of fluid transport in stationary fracture networks that is triggered by a hydro-mechanical interaction of the fluid in the fractures with a surrounding poroelastic matrix material. In other words, fracture propagation is not taken into account. This allows us to validate the diffuse interface model quantitatively and to benchmark it against solutions obtained from sharp interface formulations and analytical solutions. We introduce the relevant equations for the sharp and diffuse, i.e. fracture phase field, interface formulations. Moreover, we derive the scale-transition rules for upscaling the fluid-transport problem towards a viscoelastic substitute model via Variationally Consistent Computational Homogenization. This allows us to measure the attenuation associated with fluid transport on the sub-scale. From the numerical investigations we conclude that the conventional diffuse interface formulation fails in predicting the fluid-transport behavior appropriately. The results even tend to be non-physical under certain conditions. We, therefore, propose a modification of the interpolation functions used in the diffuse interface model that leads to reasonable results and to a good approximation of the reference solutions.

Author

Nele Pollmann

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

Ralf Jänicke

Chalmers, Industrial and Materials Science, Material and Computational Mechanics

European Journal of Mechanics, A/Solids

0997-7538 (ISSN)

Vol. 84 104067

Subject Categories

Geophysical Engineering

Applied Mechanics

Computational Mathematics

DOI

10.1016/j.euromechsol.2020.104067

More information

Latest update

11/10/2020