# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 1 Introduction
The results demonstrated that Scheme 2 exhibited lower errors, signifying its superior performance. [PERSON] et al. utilized the South China Sea region as a case study and developed a leak-off type prediction model based on the division of leak-off speed [23]. The model employed artificial neural networks (ANNs) and big data techniques, utilizing formation properties, drilling parameters, and drilling fluid parameters as input variables. The model achieved a prediction accuracy rate of 92% in assessing wellbore leakage risk. In the domain of wellbore leakage monitoring and early warning, [PERSON] et al. devised a detection model for early wellbore leakage warning using real-time drilling data from 132 wells [24]. Multiple machine learning algorithms were employed to establish the model, which achieved a false alarm rate of only once every 5 h for wellbore leakage. [PERSON] et al. developed a software solution named RSFMc for early wellbore leakage warning [25]. The software integrates real-time drilling data with diverse artificial intelligence algorithms and offers visual representation of multiple data aspects, including formation pore pressure,-fracture pressure, and bottom hole pressure profiles. Additionally, it enables real-time monitoring of wellbore leakage. These examples illustrate the utilization of machine learning and artificial intelligence algorithms in the development of early warning systems for wellbore leakage. These systems capitalize on real-time drilling data to deliver precise and timely alerts, thereby improving the safety and efficiency of drilling operations. Presently, there is a substantial body of research focusing on the utilization of artificial intelligence techniques in conjunction with seismic, logging, and drilling data to forecast formation permeability and leak-off speed, and enable wellbore leakage monitoring and early warning. However, there is a dearth of articles that directly employ artificial intelligence methods for the prediction of formation leakage pressure. To address this research gap, the present study introduces a method that combines physics-based models and data-driven approaches to predict formation leakage pressure. The detailed workflow is illustrated in Figure 1.  
Drawing upon geomechanical theory and expert knowledge, six logging data parameters (CAL, DT, GR, VSH, Pp, and DEN) are chosen as input parameters for the model. Recognizing the presence of sequence dependency in logging data and the effectiveness of long short-term memory (LSTM) networks in managing long sequences, an LSTM-BP neural network model is developed. Spearman correlation analysis is employed to examine the correlation between the six input parameters and formation leakage pressure. Two  
Figure 1: Establishment process of LSTM-BP leakage pressure intelligent prediction model. distinct input layer schemes are devised, and for each scheme, separate modeling, training, analysis, and evaluation are performed. By integrating geological and engineering knowledge into the machine learning model, the objective is to constrain the model's predictions and enhance the reliability of formation leakage pressure forecasts, ensuring alignment with geological and engineering principles. This research plays a vital role in streamlining the prediction process of formation leakage pressure, enhancing prediction accuracy, expanding the applicability and feasibility of prediction methods, and advancing intelligent drilling engineering.