arXiv subjects

A. V. Valov

Publications and source records attributed to A. V. Valov.

3 recordsLinked to original sources

arXiv2026

Acceleration methods for the planar 3D ILSA hydraulic fracturing model

Planar 3D models of hydraulic fracturing provide a practical balance between models with restrictive geometric assumptions and fully 3D simulators, capturing fractures with arbitrary planar footprints at moderate computational cost. Nevertheless, applications such as treatment design optimization and mini-frac test interpretation require large ensembles of simulations, for which the cost of planar 3D models remains a significant bottleneck. This work presents acceleration strategies for the planar 3D Implicit Level Set Algorithm (ILSA) to reduce simulation runtime while preserving numerical accuracy. A unified planar 3D ILSA scheme that consolidates the nested loops of the elastohydrodynamic solver and the front tracking algorithm into a single iterative process is introduced. A matrix splitting approach is applied to the linearized elastohydrodynamic system, moving the dense part of the elasticity operator to the right-hand side and yielding a sparse system matrix that can be solved more efficiently. Anderson acceleration is incorporated into the solution of the elastohydrodynamic system to improve convergence under varying fracture geometry. Additionally, a predictor--corrector scheme is examined with the proposed methods to assess their combined effect. Each technique is evaluated individually and in combination on both the reference and unified planar 3D ILSA schemes across five benchmark cases. Numerical experiments demonstrate that the unified scheme alone delivers an average 2.5x speedup, reaching 5.7x for the sandglass geometry. The combined application of all techniques achieves an average 4x speedup and up to 11x for the sandglass case, with the relative discrepancy in fracture aperture below 5% compared with the reference scheme.

physics.geo-ph↗

arXiv2023

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

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.

physics.geo-ph↗

arXiv2023

On the layer crossing problem for a semi-infinite hydraulic fracture

This paper analyses the problem of a semi-infinite fluid-driven fracture propagating through multiple stress layers in a permeable elastic medium. Such a problem represents the tip region of a planar hydraulic fracture. When the hydraulic fracture crosses a stress layer, the use of a standard tip asymptotic solution may lead to a considerable reduction of accuracy, even for the simplest case of a height-contained fracture. In this study, we propose three approaches to incorporate the effect of stress layers into the tip asymptote: non-singular integral formulation, toughness-corrected asymptote, and an ordinary differential equation approximation of the non-singular integral formulation mentioned above. As illustrated in the paper, these approaches for stress-corrected asymptotes differ in computational complexity, the complexity of implementation, and the accuracy of the approximation. In addition, the size of the validity region of the stress-corrected asymptote is evaluated, and it is shown to be greatly reduced relative to the case without layers. In order to address the issue, the stress relaxation factor is introduced. This, in turn, allows for enhancing the accuracy of the layer-crossing computation on a relatively coarse mesh to utilize the stress-corrected asymptote in hydraulic fracturing simulators for the purpose of front tracking.

physics.geo-ph↗