# Modeling of Swab and Surge Pressures: A Survey
## 2 Literature Review of Five Prominent Works on Swab and Surge Models
### Automatic Prediction of Downhole Pressure Surges in Tripping Operations  
In this work by [PERSON] et al. [8], the authors implemented an Ensemble Kalman Filter (EnKF) to predict the downhole pressure surges in a tripping operation based on the proposed medium-order dynamic model. Equations (22) to (37) represent the conceptual model. Different parts of the drill string with different outer and inner diameters are used in these equations. Table 2 summarizes the variables involved in the model. \[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}\Big{)},\quad j=1,2, \ldots(n_{s}-2) \tag{22}\]  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}-Q_{n}-Q_{(j)}-v_{s}A_{C}\Big{)},\quad j =n_{s} \tag{24}\]  
\[\dot{P}_{I}=\frac{K}{V_{I}}(Q_{n}-Q_{I}+v_{s}A_{IM}) \tag{25}\]  
\[Q_{n}=\min\Biggl{\{}0,C_{n}A_{n}\sqrt{2\Big{(}P_{I}-P_{(n_{s})}\Big{)}/\rho} \Biggr{\}} \tag{26}\]  
\[R_{1(j)}=D_{M}/2,\qquad j=1,\ldots,(n_{s}-1) \tag{27}\]  
\[R_{1(j)}=D_{C}/2,\qquad j=n_{s} \tag{28}\]  
\[R_{2(j)}=D_{I}/2,\qquad j=1,\ldots,(n_{s}-1) \tag{29}\]  
\[R_{2(j)}=D_{B}/2,\qquad j=n_{s} \tag{30}\]  
\[F_{f(j)}=A_{u1(j)}\tau_{u1(j)}+A_{u2(j)}\tau_{u2(j)},\qquad j=1,\ldots n_{s} \tag{31}\]  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]0  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]1  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]2  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]3  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]4  
\[\dot{P}_{(j)}=\frac{K}{V_{(j)}}\Big{(}Q_{(j+1)}-Q_{(j)}-v_{s}(A_{M}-A_{C}) \Big{)},j=n_{s}-1 \tag{23}\]5  
Since there are several uncertain and/or slowly changing parameters in this model, some sort of calibration of the model is necessary to achieve good agreement with the data. A problem in tripping operations is that measuring data is often unavailable in real-time because the mud-pulse telemetry system is not transmitting when circulation is off. However, if circulation is turned on while running the string before a tripping operation, measuring data for calibrating the model for consecutive runs can be achieved. Conservation of Mass: This work defined \(Q_{(j+1)}\) as the output flow at top of element \(j+1\), and into element \(j\). \(V_{(j)}\) is the volume of fluid of element \(j\), and \(K\) is the mud bulk modulus. \(A_{M}\) and \(A_{C}\) are the outer cross-section of the drill string and collars with their respective diameters as \(D_{M}\) and \(D_{C}\). The conservation of mass is presented as Equations (22) to (24). Because of the check valves in the string, the flow through the bit nozzle is always negative or zero. Therefore, it is given by the static expression, Equation (26). Conservation of Momentum in the Annulus: This work divided every segment in the elements into two parts as primary and secondary part. For the main part, the radius is defined by Equations (27) and (28). Equations (29) and (30) are for the secondary part. The outer diameter/surface is not homogeneous as the outer diameter in the real BHA is not homogeneous. For model simplification, this work uses a normal averaging of the outer diameter of the BHA. This work separately computes the viscous friction forces in each segment of the primary and the secondary part. Their basic equation for friction forces is given by Equation (31). For precise computation of the transient pressure forces on the fluid, the pressure at the position where the cross-sectional area changes must be known. This work assumes steady-state conditions. The resultant pressure force obtained from the main part of the cross-section area was modified by an additional term dependent on the share wall stress.