An implicit level set method for modeling hydraulically driven fractures

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

“…The results obtained with such a scheme compared extremely well with known semi-analytical solutions (Peirce and Detournay, 2008;Peirce, 2015). They have shown extremely good convergence properties when compared to other numerical codes .…”

“…We very briefly outline here the basic idea of these schemes. A complete description of such implicit algorithms using either a boundary element or an extended finite element discretization of the elasticity equation can be found in a recent review (Peirce, 2016), see also Peirce and Detournay (2008); Peirce (2015); Dontsov and Peirce (2017) for details and examples.…”

The Impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference Solutions

“…The Implicit Level Set Algorithm (ILSA) This algorithm [22] models the evolution a hydraulic fracture with an arbirarily shaped boundary that is assumed to propagate in a plane (a planar fracture in a 3D elastic medium), which is typically perpendicular to the minimum principal stress direction. The three dimensional elastic equilibrium equations are discretized using the dispacement discontinuity boundary integral method in which the fracture within the plane is represented by constant width rectangular elements that are collocated at element centres.…”

An Eulerian moving front algorithm with weak‐form tip asymptotics for modeling hydraulically driven fractures

“…Once the front location process has converged, the time is advanced, which allows more fluid into the fracture, and the front location process described above is repeated. An alternative algorithm to locate the front is presented in [32].…”

“…On the boundary between the channel region and the tip region, the fluxes are evaluated to determine the volume of fluid in each tip element. These tip fluid volumes are then used to locate the fracture front by exploiting the property that, for a smooth front, the asymptotic behavior of the solution close to the tip corresponds to a one-dimensional fracture propagating in a state of plane strain [32]. For example, if the applicable asymptotic power law is of the form (ˆ ) ∼ cˆ , then the tip volume V ( ) can be expressed in the form (16) whereˆ is the distance from the local fracture front, (ˆ ) is the local dimension of the current element in a direction parallel to the front, and is the distance between the front and the opposite vertex of the tip element.…”