Three-dimensional cementing displacement efficiency prediction based on domain-decomposed physics-informed neural network

Abstract

Efficient displacement of drilling fluid by cement slurry is essential for ensuring cementing quality, and accurate flow-field prediction is crucial for improving displacement efficiency. Although computational fluid dynamics (CFD) is widely used to investigate displacement mechanisms, high-fidelity three-dimensional simulations are computationally expensive and inefficient for rapid engineering prediction and optimization. In recent years, data-driven neural networks have attracted attention due to their high computational efficiency; however, they rely heavily on large datasets, are prone to overfitting, and may produce predictions that violate physical laws. To address these issues, this study incorporates the governing fluid dynamics equations into the loss function of a deep neural network to impose physical constraints on flow-field evolution. Furthermore, a domain-decomposed physics-informed neural network (DD-PINN) is developed by dividing the computational domain into multiple coupled subdomains. Through parallel training and collaborative solving, the method alleviates convergence difficulties and instability commonly encountered by conventional PINNs in complex three-dimensional flow problems. Numerical experiments based on multi-condition three-dimensional datasets show that DD-PINN achieves higher prediction accuracy for pressure, velocity, and cement slurry volume fraction fields compared with purely data-driven models. For example, in predicting cement slurry volume fraction, the mean absolute error (MAE) is reduced from 1.27 × 10 −2 to 2.35 × 10 −3 . Compared with conventional PINNs, the proposed method also significantly improves computational efficiency while maintaining comparable accuracy. Additionally, it enables quantitative evaluation of displacement efficiency and provides guidance for parameter optimization in cementing operations.