2017/03/16 by I. O. Gladkov, Igor Gladkov, Gladkov, Igor +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1703.05686
7 figures
arxiv created 2017/03/16 · openalex publication_date 2017/03/16 · arxiv updated 2017/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper contains an extension of the Khristianovich-Geertsma-de Klerk (KGD) model to the case when the confining rock pressure, which closes a hydraulic fracture, varies in the direction of its propagation. The extension is impelled by the need to simulate fracture hampering (acceleration) when it penetrates into a layer with increased (decreased) rock pressure. The paper presents the problem formulation, an efficient numerical method for its solving, examples of fractures propagating through layers with various stresses and general conclusions. It is established that when the fracture enters a layer with increased rock stresses (positive stress contrast), it actually stops. In this case, the fluid particle velocity drops practically to zero and the velocity near the tip oscillates about a small value until the fluid pressure increases to the level of the increased rock pressure. In the opposite case, when the fracture enters a layer with decreased stresses (negative stress contrast), the fracture front accelerates until the fluid pressure drops to the level of the decreased rock pressure. Physical considerations and numerical results imply that the transition through a boundary of layers with different stresses may be characterized by a simple dimensionless parameter. The latter is defined as the ratio of the average difference between the fluid and rock pressures (at the moment of reaching the contact) to the stress jump at the contact. The parameter is applicable to contacts with positive as well as negative contrasts. The model and the method developed are to serve for improvement of the popular pseudo three-dimensional (P3D) model.