A physics and data dual-driven method for real-time fracturing pressure prediction

Wellhead pressure prediction is challenging due to problems such as drastic pressure fluctuations, numerous disturbing factors, and complex influencing mechanisms. Current research often adopts traditional physical models which find it difficult to capture multiple nonlinear changes and sudden fluctuations due to the oversimplification of complex formation conditions, fracture characteristics, and fluid dynamics processes, limiting their prediction accuracy and real-time responsiveness in actual operations. Artificial intelligence (AI) models, despite their strong nonlinear fitting capabilities, often lack an in-depth understanding of the physical mechanisms underlying pressure fluctuations and are less sensitive to formation and operational parameters, resulting in poor stability and insufficient interpretability under extreme or dynamically changing conditions. To address these challenges, a physics and data dual-driven prediction method was proposed to predict future pressure trends. An intelligent model based on a long and short-term memory (LSTM) neural network was constructed, integrating the equilibrium height calculations of the proppant bed within the fracture and real-time pumping data at the wellsite as model inputs to predict pressure for the next 60 seconds. Then, combined with traditional wellhead pressure inversion method, wavelet transform was used to decompose predictions from both the intelligent and traditional models. The overall trend of the LSTM model and the characteristics of mutation point in the inverse pressure calculation (IPC) model were utilized to reconstruct the wellhead pressure prediction curves that could balance the overall trend and local fluctuations. Results showed that compared to pure LSTM model, the wavelet fusion model of IPC and LSTM reduced the root mean square error (RMSE) and mean absolute error (MAE) by 37.87% and 15.29%, respectively, in wellhead pressure prediction for the next 60 seconds. The fusion model can accurately capture fracturing pressure changes during field operations, providing more reliable guidance and decision support for field operations.