EAAI Journal 2026 Journal Article
Ensemble Kalman filter-driven adaptive modeling for real-time fracturing pressure forecasting
- Zhengxin Zhang
- Lei Hou
- Qian Sun
- Mao Sheng
- Fengshou Zhang
- Tingxue Jiang
- Xiaobing Bian
- Jiangfeng Luo
Accurately forecasting fracturing pressure significantly enhances the safety and efficiency of hydraulic fracturing design. Traditional machine learning methods rely on offline datasets for model training, making it challenging to accurately capture the dynamic variations in features under real-time conditions. This study presents a data assimilation-driven workflow for predicting fracturing pressure, enabling real-time capture of feature variations and adaptive model updates. By integrating the Gated Recurrent Unit (GRU) with the Ensemble Kalman Filter (EnKF), this study develops and evaluates three updating strategies: updating the GRU model parameters, updating the GRU model hidden states, and updating both the GRU model parameters and the hidden state simultaneously. Sensitivity analyses were conducted on two key parameters—process noise and ensemble size. The results demonstrate that the approach of adjusting the GRU model parameters, with a process noise of 0. 01 and an ensemble size of 50, delivers optimal performance. The optimal configuration was adopted for subsequent case studies, where improved pressure prediction accuracy in the first case and optimized fracturing design in the second confirmed the workflow's overall effectiveness. The EnKF-updated predictions reduced Symmetric Mean Absolute Percentage Error (SMAPE) from 3. 56%-6. 48% to 0. 90%-3. 02% and Root Mean Squared Error (RMSE) from 3. 51 to 6. 19 to 1. 05-2. 80, outperforming direct GRU model predictions. Furthermore, the optimized fracturing design increased the cumulative proppant volume from 124. 96 cubic meters (m3) to 147. 89 m3, a 18. 35% improvement. By capturing real-time feature variations, this new workflow provides a robust solution for improving pressure prediction accuracy, thereby enabling optimization of fracturing designs.