# Modeling of Swab and Surge Pressures: A Survey
## 2 Literature Review of Five Prominent Works on Swab and Surge Models
### Bottomhole Pressure Surges While Running Pipe
#### 2.2.1 Clark's Model
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Notation Variable** & **Equations** \\ \hline \(P\) & Pressure drop in psi over the length being computed. & (7), (8), (14), (18), (20), \\  & (21) \\ \hline \(l\) & Total length in feet of the diameter being considered. & (7), (8), (14), (18), (21) \\ \hline \(t_{Y}\) & Mud yield point in lbs./100 sq.ft. & (7), (10) \\ \hline \(n\) & Plastic viscosity of the mud in Centipoise. & (7), (18), (19) \\ \hline \(V\) & Mean fluid mud velocity in ft.per sec. & (7), (9), (11)–(13) \\ \hline \(D\) & Pipe ID in inches for internal flow, or, bit size minus pipe OD in inches for annular flow. & (7)–(10), (18)–(20) \\ \hline \(f\) & Pigott friction factor. & (8), (20) \\ \hline _rho_ & Mud weight in lbs./cu.ft. & (8), (9), (10), (14), \\  & (19)–(21) \\ \hline \(V\) & Mean fluid mud velocity in ft.per sec. & (8) \\ \hline \(R\) & appropriate Reynolds number in turbulent flow. & (8), (19) \\ \hline \(V_{L}C\) & Lower critical fluid velocity in ft.per.sec. & (10) \\ \hline \(Q_{A}\) & Observed mean annulus displacement rate in cu.ft/sec. & (11)–(13), (15), (16) \\ \hline \(Q_{P}\) & Observed mean internal displacement rate in cu.ft/sec. & (11)–(13) \\ \hline \(A_{A}\) & Annulus area in sq.ft alongside the considered diameter. & (11)–(13), (18)–(21) \\ \hline \(A_{P}\) & Area of internal section being considered in sq.ft. & (11)–(14) \\ \hline \(V_{P}\) & Pipe speed in ft./sec. & (11)–(13), (15), (16), \\  & (18), (19) \\ \hline \(A\) & Square feet area of the section being considered. & (14) \\ \hline \(\frac{dQ}{dt}\) & Rate of change of flow rate in cu-ft/sec./sec. & (14) \\ \hline \(S_{J}T\) & Total volume displaced in cu. up in the annulus for the joint under consideration. & (15)–(21) \\ \hline \(L_{J}T\) & Joint total length in ft. under consideration. & (15)–(21) \\ \hline \(Q_{G}\) & Average rate of displacement in cu.ft/sec. at any given point in the annulus. & (16) \\ \hline \(Q_{L}\) & Local annulus displacement rate in cu.ft/sec. & (16) \\ \hline \(A_{PR}\) & Sq.ft. area that projects outside the basic pipe size on the under consideration. & (16), (17)–(21) \\ \hline \(\frac{dQ_{G}}{dt}\) & Acceleration of annulus flow rate at any point in the annulus in cu.ft/sec./sec. & (17) \\ \hline \(a_{P}\) & Acceleration of pipe in ft/sec./sec. & (17), (21) \\ \hline \(t_{Y}\) & Yield point of the mud in lbs. /100 sq. ft. & (18) \\ \hline \(K_{L}\) & Constant from clinging effect in laminar flow (0.39 For drill pipe AND 0.46 for casing). & (18) \\ \hline \(K_{T}\) & Constant from clinging effect in turbulent flow (0.166 for drill pipe and 0.181 for casing). & (19), (20) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The variables used in the model by [PERSON] [5]. Acceleration Pressure: The pipe goes from zero speed to a maximum speed and then back to zero when dropping downpipe in the hole. Since the pipe movement makes the fluid move from rest to a peak and then return to static, there must be an increase and decrease in pressure with respect to the dropping cycle. The value of these respective increase and decrease in pressure between any two points can be calculated from Equation (14). Conversion into Measurable Values: Due to the difficulties of measuring the fluid flow variables, these should convert mostly the available values of speed and acceleration of the pipe. For buoyancy in an incompressible fluid, this relationship is given by Equation (15). Equation (15) is strictly not true when the float is not included in the bottom hole assembly; this allows the fluid to find its own path of minimum energy loss. Local Displacement: Where an expanded diameter exists on a pipe string, at these locations, there must be a movement over and above the surface-recorded displacement. This is evident, since as the projection falls, a local fluid movement must occur from the forecast to fill the gap produced behind the projection. The amount of these local fluid displacements is equal to the projection area multiplied by the pipe speed.