Two-Dimensional Mode I Crack Propagation in Saturated Ionized Porous Media Using Partition of Unity Finite Elements

Hydraulic fracturing and its peculiarities

“…From a comparison of results obtained with different methods by other authors, it appears that in some situations a particular adopted method hides the problems discussed in this paper because the required refinements clash with the raison d'être of such methods like XFEM or PUFEM (adoption of rough meshes). This is the reason why 'the physical phenomenon challenges the numerical scheme' [18] and why several authors dealing with hydraulic fracturing have not noticed the peculiar behaviour shown here. Also, two-step procedures may introduce some bias in the solution.…”

“…The stepwise advancement and flow jumps were also found by Kraaijeveld [20] with a strong and a weak discontinuity model for flow. In [18], the stepwise advancement in mode I crack propagation is difficult to see because a continuous pressure profile across the crack is used. However, continuous pressure profile only works for sufficiently fine meshes.…”

“…Cavitation is found in both papers, also due to the impervious boundary conditions chosen. Partition of unity finite elements (PUFEM) are used for 2D mode I crack propagation in saturated ionized porous media by Kraaijeveldt et al [18]. A pull test, a delamination test and an osmopolarity test are simulated with rather fine regular meshes (quadrangular elements with side length of the order of 2 mm and lower) and time step size down to 0.1 s. The time and space discretizations, including the element threshold number used for the solutions, are extremely important for catching the phenomena described next.…”

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

“…In the third example we only use the ELP model. For the details about the X-FEM model we refer to the work of Kraaijeveld et al [25]. In the first example, we inject a constant volume in an opened fracture.…”

“…The X-FEM was successfully applied to fracturing in porous materials, see e.g. [23][24][25]. Recently, Mohammadnejad and Khoei [26] developed a X-FEM model for cohesive crack growth in multiphase porous materials.…”