A numerical comparison of linear elastic and cohesive fracture models for hydraulic fracturing based on assumed enhanced strain (AES) method

Geomaterials are porous, and there are air, water and other liquids inside the pore space. Pore pressure fluctuation may result in the change of contact forces between the solid grains. The deformation of solid skeleton changes the size of pore and therefore the fluid flows inside the pore space. The coupled process is often described with the mixture theory in continuum mechanics. Localized deformation may lead to the displacement discontinuity or the fracture, increasing the complexity of the whole fluid-solid coupled process. Numerical simulations of the complex processes in the subsurface are essential in understanding many geoengineering systems, such as hydraulic fracturing, geological fault reactivation, waste water management, geothermal energy extraction and CO2 sequestration and so on. This paper presents an assumed enhanced strain (AES) finite element method to model the fracture evolution in porous media, where the discontinuous function enrichments are introduced into the displacement approximation to simulate fracture deformation. The enriched degrees of freedom can be removed by the standard static condensation method, which means the method does not introduce additional global system of equations. The mass and stress coupling is described by the standard Biot's poro-elasticity theory. The numerical method is verified by the mesh sensitivity studies and comparisons with analytical solutions. Particularly, with the AES framework, we have numerically compared the cohesive fracture model and linear elastic fracture mechanics model for simulating hydraulic fracture propagation in porous media.