Dynamic hydraulic fracturing in partially saturated porous media

The well-known phase-field approach applied to fracturing solids has recently been embedded in the Theory of Porous Media for the description of dynamic hydraulic fracturing scenarios based on fully saturated porous media. This method has further been enhanced by the introduction of a crack-opening indicator to distinguish between open and closed cracks accompanied by a switch between Darcy-type and Navier–Stokes-type flow situations in the unbroken porous domain and in fully broken areas. Based on these achievements, the present article extends the challenging matter of fully saturated media by the introduction of partially saturated scenarios, where the pore space contains both a liquid, such as water or oil, and a pore gas, such as air or natural gas. Proceeding from the Theory of Porous Media, the setup of the model is based on first principles of continuum mechanics, while the numerical study proceeds from the Finite-Element Method, where coupled problems of fracturing multi-component and multi-phasic media are treated by a monolithic solution strategy provided by a solver for coupled problems. By use of this procedure, it can be shown by comparison of fully and partially saturated porous media that the existence of pore gas slows down the fracture evolution. It is furthermore pointed out that the existence of closed precracks combined with external loads does not only lead to opening and evolving fractures, but also to fractures that do not open as a result of compressive boundary conditions.