## 1 Introduction  
Accurate well pressure prediction is vital, especially in deep-water and horizontal drilling, where the narrow stability window poses challenges. Factors like fluid properties, geometry, eccentricity, flow rate, and tripping speeds play a crucial role. Incorrect predictions can lead to operational issues, higher costs, and wellbore instability. The petroleum industry has made significant technological advancements, increasing drilling depth efficiency. However, nonproductive time (NPT) remains a concern, accounting for 25-30% of drilling operations according to [PERSON] et al. (2008)[1]. In deep-water environments like the Gulf of Mexico, downtime in gas wells from 1993-2003 mounted to approximately 40% of total time ([PERSON] et al., 2013)[2]. NPT incidents like lost circulation, kicks, and stuck pipes are significant contributors ([PERSON] et al., 2010)[3]. Wellbore-instability-related NPT alone increases drilling cost by 10% to 20% ([PERSON], 2009)[4]. Utilizing high-speed drill string telemetry can further improve the performance of drilling operations. High-speed telemetry allows for the reduction of nonproductive time (NPT)[1]. High-quality real-time data transfer and logging during drilling help drilling personnel make accurate, timely decisions ([PERSON] et al., 2018)[5]. For example, monitoring swabbing speed in the reservoir section can help prevent well pressure from dropping below formation and collapse pressures, averting fluid influx and well collapse. Similarly, higher surging speed can lead to excessive pressure, causing circulation loss, which can be detected and addressed promptly using real-time data. Accurate determination of tripping speed is essential for effective well-pressure management and cost reduction. Numerous swab and surge hydraulic models have been developed in the literature, considering factors like tripping speeds, fluid rheology, pipe/cement elasticity, viscous forces, well eccentricity, and string rotational speed. Based on experimental and field observations, these models address surge and swab effects under various conditions, including steady-state and dynamic/transient scenarios. Effective pressure management is essential in drilling and well construction operations, especially with improved methods and technologies to perform drilling operations in extended-reach wells, slim holes, and casing while drilling. These advancements can lead to excessive surge pressure during tripping and drilling operations in the extended reach wells where the narrow operations windows persist. Failure to detect these down-hole pressure fluctuations can result in various drilling issues, including formation fracturing, lost circulation, kicks, and blowouts. These problems directly translate to higher budgets due to nonproductive downtime, equipment damage, and costly corrective measures. Consequently, developing an accurate surge pressure model becomes essential for precisely predicting tripping and casing running speed limits. Numerous studies have been undertaken to determine surge and swab pressures to optimize tripping operations. The following highlights some of the selected studies. [PERSON] (1961) [6] developed a technique to estimate surge and swab pressures in Bingham plastic fluids, specifically emphasizing steady-state conditions. In 1964, [PERSON] utilized a comparable approach to formulate a power-law fluid model, assuming steady-state flow within a concentric annulus [7]. [PERSON] and [PERSON] (1974) devised a method of anticipating swab pressure in Bingham plastic and power-law fluids [8]. [PERSON] (1988) presented a dynamic model with several novel elements, such as viscous forces, temperature changes, formation properties, pipe and cement elasticity, and mud rheology [9]. [PERSON] et al. (2008) performed experiments to investigate the effect of pipe rotation on well pressure in concentric annuli filled with xanthan gum and polyanionic cellulose-based fluids [10]. [PERSON] et al. (2010) crafted a streamlined surge and swab model for yield-power-law fluids [11].