# Modeling of Swab and Surge Pressures: A Survey
## 2 Literature Review of Five Prominent Works on Swab and Surge Models
### Wellbore Pressure Surges by Pipe Movement
The mean of the effective annular mud velocity is the mud velocity that creates the surge pressure's viscus drag with reference to the wellbore wall. Pressure Generated Due to the Mud Flow in an Annulus: For the Bingham plastic fluid, the plasticity for an annulus is defined by Equation (44). The Reynolds number of Bingham plastic fluid for annular flow is defined by Equation (45). By finding the friction factor using this Reynolds number, the pressure surge generated in the annulus by moving a closed-end pipe in the borehole is given by Equation (46). \begin{table}
\begin{tabular}{l l l} \hline \hline
**Notation** & **Variable** & **Equations** \\ \hline \(p\) & Pressure, psi. & (38), (39) \\ \hline \(L\) & Length of pipe section,ft. & (38), (39) \\ \hline \(\zeta\) & Mud gel strength, lb/100 \(ft^{2}\). & (38), (39) \\ \hline \(D_{i}\) & Internal diameter, in. & (38), (39) \\ \hline \(D_{p}\) & Pipe outside diameter, in. & (38), (39), (42)–(46), (48) \\ \hline \(D_{h}\) & Hole inside diameter, in. & (38), (39), (42)–(46), (48) \\ \hline \(a_{p}\) & Pipe acceleration. & (40), (41) \\ \hline \(\rho\) & Mud density. & (40), (41), (45), (46) \\ \hline \(L\) & Length of pipe section,ft. & (40), (41) \\ \hline \(g\) & Acceleration of gravity. & (40), (41) \\ \hline \(V_{d_{e}}\) & Annulus competent of velocity due to displacement, ft/min. & (42) \\ \hline \(V_{p}\) & Velocity of pipe, ft/min, in. & (42), (43), (48) \\ \hline \(V_{a_{e}}\) & Effective annular mud velocity, ft/min. & (43), (45), (48) \\ \hline \(K\) & Proportionality constant. & (43), (48) \\ \hline \(T_{0}\) & Mud yield point, lb/100 \(ft^{2}\). & (44) \\ \hline \(\mu_{p}\) & Plastic viscosity, cp. & (44) \\ \hline \(R_{e}\) & Reynolds number. & (45) \\ \hline \(\frac{\Delta P}{L}\) & Pressure gradient, psi/ft. & (46) \\ \hline \(f\) & Friction factor. & (46) \\ \hline \(q_{a}\) & Mud flow in annulus measured with respect to the fixed borehole & (48) \\  & wall, \(ft^{3}\)/min. & (49) \\ \hline \(V_{be}\) & Effective pipe bore mud velocity, ft/min. & (49) \\ \hline \(q_{b}\) & Mud flow in pipe bore measured with respect to pipe walls, & (49) \\  & \(ft^{3}\)/min. & \\ \hline \(D_{i}\) & Inside diameter of pipe, in. & (49) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The variables used in the model by [PERSON] [1]. The contribution to pressure gradients due to change in borehole or geometry of the pipe, specifically for each geometry, should be computed. Then, the total pressure would be the sum of the separate component. Viscus Drag Pressure Surges with Open Pipe Strings: The open pipe strings are defined, the strings have openings to the annulus, and the pipe bore at the string bottom, e.g., the drill string without the float sub in the assembly or a fill-up shoe in the casing string. A statement must be made regarding how the extra pipe borer mudflow channel is associated with the annular mud flow path to calculate the effective annular mud velocity, creating the viscose drag pressure-surge components. The criterion utilized to characterize this connection was that the total pressure surge created in the pipe bore must be equal to the total pressure surge generated in the annulus. The total pressure surge is given by Equation (47). In Equation (47), \(P_{b}\) is the pipe bore pressure, psi., and \(P_{a}\) is annulus pressure, psi. This equality of pressure is achieved by separating the mudflow from the two pathways in different ratios until the same pressure is created in each flow path. The ultimate pressure should be the same as the pressure that really occurred; hence, the surge pressure. Effective Mud Velocities for Pressure-Surge Generation: The effective mean mud annulus mud velocity is the total of mud displacement and the moving pipe walls. Thus, Equation (48) presents effective annulus mud velocity. The effective mean mud velocity in the pipe bore with reference to the pipe bore walls is given by Equation (49). The flow rate of the mud pipe walls \(q_{b}\) generates pressure in the pipe bore regardless of which is considered to be moving.