## 1 Introduction  
Poorly designed drilling operations can make drilling less efficient. This can cause problems such as damaged bits, slower drilling, twisted drill strings, and inaccurate measurement while drilling (MWD) tools. These issues can lead to unwanted round-tipping operations and drive up the cost of drilling. During tripping operations, the movement of the drill string in and out of the wellbore, making and breaking connections, results in undesired non-productive time (NPT) being spent, hence increasing drilling costs. It is logical to run the drill string up to its permissible threshold speed and shorten the time related to the tripping operation. However, drill string movement beyond the allowable speed will lead to well collapse and fluid influx to the wellbore while tripping out (the swabing effect), and well fracturing while tripping in (the surging effect). The consequence of well collapse may cause drill string sticking. When the initial and alternative drill string unsticking operations are carried out without success, the final action is to locate the point of sticking, cut the drill string at the fee point, and then sidetrack. This results in a significant increase in the well budget. Similarly, well fracturing results in drilling fluid losses. Here, the problem also increases the operational and non-productive time spent, increasing the overall drilling budget. Predicting an appropriate well pressure mitigates possible well instability issues and kick influxes. Over the years, researchers have built models to predict surge and swab effects based on different assumptions and conditions, such as steady-state and dynamic/transient conditions. [PERSON] (1961) developed a model to estimate surge and swab pressures for Bingham plastic fluids, considering steady-state conditions [1]. [PERSON] (1964) used a similar approach when developing a power law fluid model, assuming steady-state flow in a concentric annulus [2]. [PERSON] and [PERSON] (1974) developed a model to predict the swab pressure for Bingham plastic and power law fluids [3]. [PERSON] (1988) produced a dynamic model that included several new factors, such as mud rheology, the elasticity of the pipe and the cement, the formation, changing temperatures, and viscous forces [4]. [PERSON] et al. (2008) experimentally demonstrated the impact of pipe rotation on well pressure in an eccentric and concentric well filled with xanthan gum and polyanionic cellulose-based fluid [5]. [PERSON] et al. (2010) developed a simplified swab and surge model for yield-power law fluids [6]. [PERSON] et al. (2012) experimentally showed that the speed of the trip, mud properties, annular clearance, and the eccentricity of the pipe highly affect the surge and swab pressures [7]. [PERSON] et al. (2013) employed a Kalman filter to predict and calibrate surge and swab pressures in real time for Herschel-Bulkley fluids based on differential pressure equations [8]. [PERSON] et al. (2016) employed computational fluid dynamics techniques to build a swab and surge prediction model for concentric annuli. The comparison of simulations and experiments indicated an accuracy of up to 75% in predicting surge and swab pressures [9]. [PERSON] et al. (2012) utilized narrow slot geometry and regression techniques to develop a steady-state swab and surge prediction model, considering the compressibility of the fluid, formation, and pipe elasticity [10]. [PERSON] et al. (2015) built a numerical annular pressure loss estimation model for eccentric annuli [11]. He at el. (2016) employed numerical simulations and regression techniques to forecast drilling operations' swab and surge pressures. The model indicated a \(\pm\)3% maximum error compared with that of the experimental measurements [12]. [PERSON] et al. (2018) utilized artificial neural network techniques and performed parametric studies on pressure loss [13]. [PERSON] et al. (2018) developed an analytical model for calculating pressure surges caused by drill string movement in Herschel-Bulkley fluids [14]. [PERSON] et al.