Implicit level set schemes for modeling hydraulic fractures using the XFEM

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…A similar scheme can be used for 2D fracture in a much simpler way as the fracture front reduce to single points in that case (see Gordeliy and Peirce (2013b); Lecampion and Desroches (2015a)). The algorithm has also been extended to mixed mode I+II for plane-strain fractures.…”

“…Implicit schemes using the knowledge of the hydraulic fracture tip behaviour have been successfully developed for 2D problems, properly reproducing semi-analytical solutions in the different propagation regimes without leak-off (Gordeliy and Peirce, 2013b).…”

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

“…In the recent paper by Lecampion et al [38] it was shown that the algorithms which utilize the appropriate multiscale hydraulic fracture tip asymptote perform much better than those that do not apply it. The advantages of employing enhanced asymptotic representation in the numerical algorithm have been demonstrated in [17,27,30] (special tip element), [2,8,21,22,23,37,67] (BEM and XFEM formulations).…”

Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference

“…A key advantage of XFEM is that in such problems the finite element mesh does not need to be updated to track the crack path, and discontinuous enrichment functions are used to approximate the displacement discontinuity across the crack surface, which significantly reduced the computational costs and projection errors associated with conventional finite element methods that restricting the discontinuities to mesh edges [6]. Since the introduction of this method, the XFEM has been used to model complex, nonplanar hydraulic fracture propagations by many authors [7][8][9][10].…”