An implicit level set algorithm for hydraulic fracturing with a stress-layer asymptote

• Main Authors: Valov, A. V, Dontsov, E. V, Baykin, A. N, Golovin, S. V
• Format: Journal Article
• Language: English
• Published: 23-05-2023
• Subjects: Computer Science - Computational Engineering, Finance, and Science; Computer Science - Numerical Analysis; Mathematics - Numerical Analysis; Physics - Geophysics
• DOI: 10.48550/arxiv.2305.13714

The capability to simulate a hydraulic fracturing process is an essential
tool that can be used to optimize treatment design and increase the efficiency
of field operations. In most practical cases, hydraulic fractures propagate in
a multi-layered rock formation. As a result, there is a need to incorporate the
effect of such heterogeneities in fracturing models to achieve an accurate
prediction. To capture the layered structure of rocks, a hydraulic fracture
simulator typically requires a fine mesh, which leads to a drastic reduction in
computational performance. An alternative is to use more sophisticated models
that are capable of providing reasonably accurate predictions even on a
relatively coarse mesh. In the case of fracture growth modeling, the pivotal
component of the simulation is a fracture front tracking algorithm that
accounts for the layered structure of the formation. Consequently, this paper
aims to extend the established Implicit Level Set Algorithm (ILSA) to account
for the effect of multiple stress layers within the tip asymptote. The enhanced
front tracking algorithm involves the stress-corrected asymptote that
incorporates the influence of stress layers within the near-tip region. To
further increase the validity region of the stress-corrected asymptote, the
stress relaxation factor is introduced, and its accuracy is examined. The
numerical algorithm is validated against the reference semi-analytical
solutions as well as experimental observations. In addition, we investigate the
sensitivity of the fracture geometry to mesh size to demonstrate that the front
tracking algorithm based on the stress-corrected asymptote retains its accuracy
on a coarse mesh.