Some numerical simulation of hydraulic fractures in poro-elastic media

There are several models of hydraulic fracturing in poro-elastic media. Complete models are very complex and therefore I shall discuss mainly the numerical simulation (numerical analysis and algorithms) of two simplified models: a Reynolds lubrication model and a phase field model. The first one describes the opening of an existing fracture, without width, the width being included in the fracture flow equation. Its disadvantage is that the fracture cannot propagate, but its advantage is it treats the location of the fracture with precision, and avoids meshing the interior of the fracture. The phase field model locates a region surrounding the fracture, and thus does not describe precisely the position of the fracture, but it has the advantage of being able to describe the propagation of the fracture.