Speaker
Description
In models describing hydraulic fracturing problems by use of the Theory of Porous Media (TPM) with an integrated phase-field approach, see e. g. [1-3], fracturing scenarios such as natural fracturing and classical hydraulic fracturing processes can be reliably described. However, state-of-the-art models do not capture a local porosity change, as the fractured rock or soil particles remain in the newly created fracture region. From a physical point of view, it is expected that the solid particles will be mobilised and transported by the fluid over time in case of a (dynamic) flow in the fracture. Therefore, we propose an entropy-principle based, thermodynamically consistent description of the mass transfer processes, similar to [4], between the mobile solid particles and the pore fluid. The pore fluid itself is considered as a mixture with similar velocities between liquid water and the contained solid particles in the form of a linear viscous suspension. In this talk, we will present the methodological framework for a rigorous description of the coupled problem and discuss the numerical implementation strategy using the mixed finite-element method. Finally, we will discuss the application of the model in terms of different numerical test cases.
[1] Heider, Y., Markert, B.: A phase-field modeling approach of hydraulic fracture in saturated porous media. Mechanics Research Communications 80, 38–46 (2017).
[2] Ehlers, W., Luo, C.: A phase-field approach embedded in the theory of porous media for the description of dynamic hydraulic fracturing. Computer Methods in Applied Mechanics and Engineering 315, 348–368 (2017).
[3] Ehlers, W., Luo, C.: A phase-field approach embedded in the Theory of Porous Media for the description of dynamic hydraulic fracturing, Part II: The crack-opening indicator. Computer Methods in Applied Mechanics and Engineering 341, 429–442 (2018).
[4] Steeb, H., Diebels, S.: A thermodynamic-consistent model describing growth and remodeling phenomena., Computational Materials Science 28 ,597–607 (2003).
