# A Novel Adaptive Transient Model of Gas Invasion Risk Management While Drilling
###### Abstract  
The deep and ultra-deep oil and gas resources often have the characteristics of high temperature and high pressure, with complex pressure systems and narrow safety density windows, so risks such as gas invasion and overflow are easy to occur during the drilling. In response to the problems of low management efficiency and large gas kick by traditional gas invasion treatment methods, this paper respectively established and compared three intelligent control models for bottom hole pressure (BHP) based on a PID controller, a fuzzy PID controller, and a fuzzy neural network PID controller based on the non-isothermal gas-liquid-solid three-phase transient flow heat transfer model in the annulus. The results show that compared with the PID controller and the fuzzy PID controller, the fuzzy neural network PID controller can adjust the control parameters adaptively and optimize the control rules in real-time; the efficiency of the fuzzy neural network PID controller to deal with a gas kick is improved by 45%, and the gas kick volume in the process of gas kick is reduced by 63.12%. The principal scientific novelty of this study lies in the integration of a fuzzy neural network PID controller with a non-isothermal three-phase flow model, enabling adaptive and robust bottom hole pressure regulation under complex gas invasion conditions, which is of great significance for reducing drilling risks and ensuring safe and efficient drilling. gas kick; fuzzy neural network; PID control; bottom hole pressure; intelligent control 2025202515725620  
(NMPC) and L1 adaptive control. [PERSON] et al. developed an automatic MPD system to treat gas kicks efficiently [9]. [PERSON] et al. used a linear model predictive control (MPC) algorithm to regulate pump flow and choke pressure to manage and maintain BHP [10]. [PERSON], [PERSON], and [PERSON] et al. proposed a method of BHP control using the NMPC algorithm, which can track BHP set-point during normal operations and switch to flow control mode automatically in abnormal situations [11; 12; 13; 14; 15]. [PERSON] and [PERSON] et al. designed an integrated estimator to calculate BHP in real-time and developed an L1 adaptive controller to regulate BHP automatically [16; 17]. [PERSON] et al. presented a robustness analysis framework for pressure control in MPD and an approach to search for controller tuning parameters [18]. In addition, [PERSON] et al. and [PERSON] et al. used fault trees, Bayesian networks, multiple linear controllers, etc., to regulate BHP [19; 20; 21]. [PERSON] et al. proposed a nonlinear predictive generalized minimum variance (NPGMV) controller to regulate BHP [22]. These advanced methods can provide accurate BHP tracking, especially in abnormal situations. However, they rely heavily on accurate and often complex multiphase flow models, which are governed by nonlinear partial differential equations (PDEs) [23; 24]. As a result, they often suffer from high computational burden, model sensitivity, and limited robustness in real-time applications. For the PID controller, [PERSON] presents three control schemes to stabilize the BHP role, including PI control, feed-forward PI control, and adaptive feed-forward PI control, and the results show that the adaptive PI controller exhibits less tracking error and fewer oscillations [25; 26; 27; 28]. [PERSON] et al. considered the thixotropic behavior of drilling fluids and developed a preview-based feedback PI controller to regulate BHP [29]. [PERSON] developed a nonlinear hydraulic model based on PID capturing only the main pressure and flow dynamics [30]. [PERSON] et al. established an adaptive PID switching controller to regulate BHP, which can choose the right PID parameter based on the data measurement [31]. [PERSON] et al. identified the process of MPD as a low-order transfer function model, generating the gain, the time constant, and the delay to set the PID controller for BHP [32]. [PERSON] et al. put forward an improved particle swarm optimization PID neural network (IPSO-PIDNN) model to control BHP [33].