# Physically-Data Driven Approach for Predicting Formation Leakage Pressure: A Dual-Drive Method
## 1 Introduction  
Drilling operations entail the occurrence of drilling fluid leakage into the formation through cracks (referred to as leakage channels) in the wellbore. This occurrence is commonly known as wellbore leakage. Wellbore leakage has an estimated global annual occurrence rate of approximately 25%, resulting in costs exceeding USD 4 billion for mitigation [1]. Wellbore leakage has emerged as a prevalent issue in drilling operations [2]. Wellbore leakage is a highly complex phenomenon influenced by multiple factors, such as formation properties, drilling fluid properties, drilling construction processes, and underground pressure variations [3]. Formation properties, such as rock permeability, porosity, and fractures, play a significant role in influencing the formation leakage pressure. Drilling fluid properties, particularly density and viscosity, have a direct impact on the incidence of wellbore leakage. Stress changes in the wellbore, induced by the rotation and fluctuating pressure of the drill bit during the drilling process, can lead to wellbore leakage. Wellbore leakage is a frequent and intricate subterranean incident that frequently occurs abruptly and necessitates a complex subsequent remediation process. Wellbore leakage results in the wastage of manpower and resources, along with substantial increases in drilling time and costs. In severe instances, wellbore leakage can result in blowouts, surges, or even necessitate wellbore abandonment [4]. Precise prediction of formation leakage pressure plays a crucial role in mitigating wellbore leakage [5]. Formation leakage pressure denotes the maximum pressure threshold that the wellbore can sustain under wellbore leakage conditions and serves as the upper limit for designing a safe drilling fluid density range. Investigating formation leakage pressure holds immense significance in ensuring drilling operation safety, optimizing drilling fluid performance, reducing costs, safeguarding reservoir integrity, enhancing drilling construction efficiency, and informing wellbore structural design. With the deepening of oil and gas exploration and development, research on leakage pressure has steadily progressed. In 1990, [PERSON] introduced the theory of leakage pressure and conducted an analysis of its influencing factors [6]. In 2004, [PERSON] pioneered the development of a leakage pressure model suitable for fractured formations [7]. In 2010, [PERSON] et al. developed a drilling fluid leakage model for naturally fractured formations using the Herschel-Bulkley rheological model [8]. They emphasized the importance of controlling the drilling fluid's rheology to minimize losses. Presently, numerous scholars have extensively researched various disciplines, such as geomechanics, wellbore stability, and fluid mechanics. Research methodologies encompass numerical simulation, laboratory experiments, and field observations. In recent decades, researchers have developed numerous mathematical models and empirical formulas to predict formation leakage pressure based on extensive experimental investigations and theoretical analyses. However, the applicability of these methods is limited due to the multitude of causes and complex mechanisms of wellbore leakage, resulting in the absence of a universally applicable theoretical calculation model for leakage pressure [9]. Presently, the methods used to predict formation leakage pressure primarily involve experimental analysis [5], numerical simulation [10], theoretical formulas [11], empirical formulas [9], and statistical analysis [5]. Currently, the predominant approach for determining formation leakage pressure is primarily based on understanding the leakage mechanism. It involves analyzing leakage scenarios in the target formation using statistical data and relevant empirical formulas derived from drilled wells [12]. However, in reality, wellbore leakage is influenced by numerous causes and intricate mechanisms, and the actual conditions vary among different geological formations.