Abstract
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.
Highlights
In recent decades, hydraulic stimulation, often called hydraulic fracturing in the context of shale gas production, has become a prom ising technology for the production of deep geothermal energy in a carbon neutral economy
The material response associated with diffusive fluid transport in sub-scale fracture networks in sharp or diffuse formulation can be directly used for FE2 type simulations of the seismic wave propagation experiment
We introduce the simplification that pressure diffusion associated with fluid transport in the pores and fractures is a local process within the Representative Volume Element (RVE)
Summary
Hydraulic stimulation, often called hydraulic fracturing in the context of shale gas production, has become a prom ising technology for the production of deep geothermal energy in a carbon neutral economy. We aim at investigating how well fluid transport in fracture networks embedded in fluid-saturated porous media can be predicted using diffuse interface formulations such as the fracture phase field model. During hydraulic stimulation, a tool is provided for monitoring the fracturing process, i.e. the generation of induced fracture networks Another reason to focus on that particular sub-problem is that there are well-established formulations available which treat the frac tures as sharp interfaces (e.g. using interface elements) and which can be used to benchmark the phase field approach quantitatively. The material response associated with diffusive fluid transport in sub-scale fracture networks in sharp or diffuse formulation can be directly used for FE2 type simulations of the seismic wave propagation experiment.
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