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.

翻译：模拟水力压裂过程的能力是优化处理设计和提高现场作业效率的重要工具。在大多数实际情况下，水力裂缝在多岩层地层中扩展。因此，需要在压裂模型中纳入这种非均质性的影响，以实现精确预测。为捕捉岩石的层状结构，水力压裂模拟器通常需要精细网格，这导致计算性能大幅下降。另一种选择是使用更复杂的模型，即使在相对粗糙的网格上也能提供合理准确的预测。在裂缝扩展建模中，模拟的关键组成部分是考虑地层层状结构的裂缝前沿追踪算法。因此，本文旨在扩展已建立的隐式水平集算法（ILSA），以考虑尖端渐近线中多个应力层的影响。增强的前沿追踪算法引入了应力校正渐近线，该渐近线纳入了近尖端区域内应力层的影响。为进一步扩大应力校正渐近线的有效区域，引入了应力松弛因子，并检验了其准确性。数值算法通过与参考半解析解及实验观测结果进行了验证。此外，我们研究了裂缝几何形状对网格尺寸的敏感性，以证明基于应力校正渐近线的前沿追踪算法在粗糙网格上仍能保持其准确性。