## 1 Introduction  
Swab and surge pressures are created during the drill string tripping out and into the wellbore, respectively. The magnitude of the hydrostatic pressure fluctuation due to the swab/negative and surge/positive depends on, among others, the tripping speed. An unoptimized tripping speed may induce wellbore instability, leading to well collapse or formation fracturing, as well as control issues, which increase the nonproductive time (NPT) and hence the overall drilling budget. The precise prediction of well pressures is crucial, especially in deep-water and horizontal drilling, where a narrow well stability margin poses significant challenges. In addition to tripping speed, fluid properties, geometry, eccentricity, and flow rates also control the well pressure. Moreover, the prediction of the optimum maximum and minimum tripping speeds reduces undesired nonproductive times. Over the years, researchers have conducted numerous studies of swab and surge phenomena during tripping in and out of the wellbore. They have conducted several experiments and also developed various models based on assumptions such as steady-state and transient conditions, non-slip at the wall, different flow scenarios, fluid rheological properties, well configurations, and operational parameters. [PERSON] et al. (2022) [1,2] extensively reviewed existing swab and surge models, including contributions from [PERSON] (1961) [3], [PERSON] (1964) [4], [PERSON] and [PERSON] (1974) [5], [PERSON] (1988) [6], [PERSON] (2008) [7], [PERSON] (2010) [8], [PERSON] (2012) [9], [PERSON] (2013) [10], [PERSON] (2016) [11], [PERSON] (2012) [12], [PERSON] (2015) [13], [PERSON] (2016) [14], [PERSON] (2018) [15], [PERSON] (2018) [16], [PERSON] (2020) [17,18], [PERSON] (2021) [19], and [PERSON] et al. (2023) [20]. However, these models did not consider all the parameters that affect the swab and surge, and their applicability to estimate experimental data is limited to the specific assumptions and setup conditions. During drilling and tripping operations, the well pressure is normally determined by the hydrostatic pressure and by the pressure loss due to fluid flow. The equivalent circulation density in specific gravity (sg) is given as ([PERSON] et al., 2011) [21]:  
\[\text{ECD}=\rho_{\text{static}}+\frac{\Delta\text{P}_{\text{annulus}}}{0.0981. \text{TVD}} \tag{1}\]  
where \(\Delta\text{P}_{\text{annulus}}\) is the pressure loss (bar) in the annulus due to fluid flow and \(\rho_{\text{static}}\) is the static drilling fluid density (sg). TVD is the true vertical depth (m). The pump pressure is also determined from the pressure losses across circulation flowlines. The pressure loss in the annulus is given as ([PERSON] et al., 2011) [21]. \[\Delta\text{P}_{\text{annulus}}=\frac{2f\text{P}\text{V}_{\text{Q}}^{2}}{\text {D}_{\text{H}}}\text{L} \tag{2}\]  
where VQ = Q/A is the velocity of the fluid flow, D\({}_{\text{H}}\) is the hydraulic fluid flow through the annulus (D\({}_{\text{Well}}\)D\({}_{\text{Pipe}}\)), L is the length of the flow line, and f is the friction factor. The friction factor f is a function of the Reynolds number, and the surface roughness is given by [PERSON] (1983) [22]:  
\[\frac{1}{\sqrt{\text{f}}}=-1.8\log\left[\left(\frac{\varepsilon/\text{D}}{3. 7}\right)^{1.11}+\frac{6.9}{\text{Re}}\right] \tag{3}\]  
where \(\varepsilon\) is the surface roughness coefficient (\(\varepsilon\) = k/d), k is the surface roughness, and D is the diameter of the pipe. The friction factor parameter is sensitive, and its prediction is difficult as it is a profile. The theoretical calculation of pressure losses in a wellbore requires knowledge of fluid properties at various temperatures and the shear rates as the fluid flows through each interval of a borehole. To determine the rheological properties of the drilling fluids and the ECD, there are several models available in the industry's commercial software.