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arXiv · 2311.05170

A Local Parallel Finite Element Method for Super-Hydrophobic Proppants in a Hydraulic Fracturing System Based on a 2D/3D Transient Triple-Porosity Navier-Stokes Model

Luling Cao·Jian Li·Zhangxin Chen·Guangzhi Du
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Abstract

A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local parallel and non-iterative finite element method based on two-grid discretizations is proposed. The underlying idea behind utilizing the local parallel approach is to combine a decoupled method, a two-grid method and a domain decomposition method. The strategy allows us to initially capture low-frequency data across the decoupled domain using a coarse grid. Then it tackles high-frequency components by solving residual equations within overlapping subdomains by employing finer grids and local parallel procedures at each time step. By utilizing this approach, a significant improvement in computational efficiency can be achieved. Furthermore, the convergence results of the approximate solutions from the algorithm are obtained. Finally, we perform 2D/3D numerical experiments to demonstrate the effectiveness and efficiency of the algorithm as well as to illustrate its advantages in application.

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Luling Cao, Jian Li, Zhangxin Chen, Guangzhi Du. 2023-11-09. A Local Parallel Finite Element Method for Super-Hydrophobic Proppants in a Hydraulic Fracturing System Based on a 2D/3D Transient Triple-Porosity Navier-Stokes Model. https://arxiv.org/abs/2311.05170

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