A Physics Informed Neural Network for Predicting Proppant Transport in Hydraulic Fracture

ABSTRACT: The migration and displacement of proppant in fractures is the key to maintain fracture opening and enhance fracture conductivity. Numerous numerical simulations have been conducted to investigate the hydrodynamics of proppant transport. Since the numerical simulations are computationally expensive and time-consuming, machine learning methods were introduced for proppant transport modeling. However, current methods rely solely on data-driven models, demand large datasets for training, and often yield results that are inconsistent with physical laws. Thus, this study proposed a physics informed neural network (PINN) framework to predict the proppant transport. The PINN was trained on data generated from CFD simulations and used to predict hydrodynamic parameters of proppant, such as solid phase volume fraction and particle velocity. The results indicate that the PINN reduces computation time by 98% while maintaining prediction errors below 18%. Based on the dual constraints of data and physical laws, the PINN accurately describes the four stages of proppant transport and the distribution characteristics of hydrodynamic parameters. This framework offers novel pathways for rapid prediction of proppant transport in hydraulic fractures. Furthermore, this method can also serve as a surrogate model for other particle-fluid flows. 1. INTRODUCTION Proppant distribution in hydraulic fractures is a key factor in the evaluation of the effectiveness of a hydraulic fracturing operation. Numerical simulation methods have been extensively applied in investigating proppant transport in hydraulic fractures. The Computational Fluid Dynamics (CFD) technique has been proven to be an efficient numerical method for proppant transport simulation (Zhang et al. 2022; Zhou et al. 2024). The prevailing mathematical models used for particle-fluid flow are Euler-Lagrange (E-L) model and Euler-Euler (E-E) model. The E-E model sets particles and the fluid as continuous media, and the flow field and the motion of the solid particles are described and solved by Euler's method (Hu et al. 2023). The spatial distribution of the different phases is described by the volume fraction.