# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 1 Introduction
Consequently, it is challenging to formulate a universally applicable calculation formula, as theoretical formulas rely on specific assumptions that might not completely align with the actual drilling conditions. Consequently, the calculated results offer limited guidance for onsite operations and pose challenges when attempting to generalize and apply them [13]. Conventional empirical formulas face challenges in accurately determining empirical coefficients, and the selection of empirical parameters ishighly subjective. Conversely, statistical models demand substantial preliminary statistical work and might not fulfill the practical requirements for leakage prevention, particularly in newly developed blocks with limited relevant data and absence of reference methods. Presently, a pressing need exists for a relatively universal calculation method for accurately predicting formation leakage pressure. Such a method should enhance prediction accuracy, improve computational efficiency, and reduce operational costs. In recent years, due to the ongoing advancements in artificial intelligence technology, the extensive research and application of artificial intelligence have become prevalent across various industries [14; 15]. It offers notable advantages in addressing intricate nonlinear problems. Within the petroleum sector, the utilization of machine learning techniques for the advancement of both conventional and unconventional oil and gas fields is progressively gaining traction [16]. An increasing number of scholars are embarking on investigations into the application of artificial intelligence methods, such as machine learning and deep learning, for in-depth analyses of mechanisms and patterns related to well leakage [17]. For instance, [PERSON] et al. [18] collected data from 61 wells in the Marun oilfield in Iran to predict wellbore leakage. The dataset comprised 19 parameters, including well depth, drilling pressure, and drill bit rotation speed, resulting in a total of 1900 data points. They employed algorithms like artificial neural networks (ANNs), support vector machines (SVMs), and decision trees to develop a model for predicting wellbore leakage. The model's performance was assessed using evaluation metrics like root mean square error (RMSE) and coefficient of determination (R\({}^{2}\)). [PERSON] et al. [19] identified the four most highly correlated parameters, namely, variance, attenuation, sweetness, and RMS amplitude, from a set of 15 seismic attribute parameters. They presented a predrilling method for assessing wellbore leakage risk using machine learning techniques and three-dimensional seismic data. [PERSON] et al. [20] identified 16 out of 22 comprehensive logging parameters that were most pertinent to drilling fluid leakage. They utilized the mixture density network to evaluate and forecast drilling fluid leakage. [PERSON] et al. employed three machine learning algorithms, specifically artificial neural networks (BPNN), support vector machines (SVMs), and random forests, to predict wellbore leakage [21]. They utilized 12 parameters, including well depth, drilling fluid density, and pore pressure, as input for the models. The investigation determined that the random forest algorithm achieved the highest performance. These examples underscore the growing adoption of machine learning and artificial intelligence methods in studying and predicting wellbore leakage, promising enhanced accuracy and efficiency in the analysis and prevention of such incidents. In the context of leak-off speed prediction, [PERSON] et al. [22] utilized artificial neural networks (ANNs) to develop two models for predicting leak-off speed in natural fractured formations. In the first model (Scheme 1), the input layer parameters comprised conventional drilling parameters, including well depth, porosity, and formation permeability. In the second model (Scheme 2), additional geomechanical parameters, such as Young's modulus, were incorporated in addition to those in Scheme 1.