# Modeling of Swab and Surge Pressures: A Survey
## 2 Literature Review of Five Prominent Works on Swab and Surge Models
### Experimental Study of Swab and Surge Pressures in Horizontal and Inclined Wells
Ignoring the effects of ballooning and loss circulation, the fluid displaced rate can be expressed as in Equation (63). For the representation of wellbore geometry, the annular clearance \(h(\theta)\) and the mean slot width (W) is defined in Equation (64). Modeling Flow in Eccentric Annulus: Eccentric annulus is represented by many narrow, variable-range slots (h) from earlier discussions. The annulus is split into 360 segments of \(1\) degree each at the center-point of each segment with a clearance determined (Equation (54)). By rearranging Equation (65), the outer diameter is computed using the estimated height (h). The dimensionless flow rate is calculated by (Equation (63)). Because of the symmetry, half of the annulus was calculated. For each segment computations, the equations are updated (Equation (65)). The technique for the iteration of a certain pressure gradient systematically varies to alter after slot height computation. The total annular flow in dimensionless form can be expressed as in Equation (66), where \(\overline{q}_{t}(\theta)\) is the total dimensionless flowrate for the segment. The maximum possible value for \(y_{2}\) is equal to the slot thickness, which equals \(1\) in the dimensionless form. In the model development phase, they recognize that with an increase in eccentricity values, the error in \(\bar{y}_{2}\) is considerable. Therefore, they made a check to the maximum value of \(\bar{y}_{2}\) and maintained it at \(1\). The maximum value of \(\bar{y}_{1}\) is set to \(0\). Therefore, by using the expression \(\pi_{2,\max}=\bar{y}_{2,\max}-\bar{y}_{1,\min}\), it is obvious that the maximum possible value of \(\pi_{2,\max}\) is \(1\). Circumferential Wall Shear Stress Variation: [PERSON] and [PERSON] [14] developed an eccentric model on the basis of many concentric annuli with varying outer radii. This method only takes into account the change in shear stress readily. Therefore, with increasing eccentricity, each segment's circumferential share stress change becomes significant. [PERSON] et al. [15] accounted for the radial shear stress variations and made a correction factor as in Equation (67). The following assumptions were presumed during the model formulation:  
* The fluid is incompressible (constant density);
* Steady state and isothermal Couette flow conditions;* Laminar flow;
* Drill pipe moving at a constant speed, \(Vp\);
* Negligible wall slippage effects. Analysis of the Work by [PERSON] et al. Since the whole point of the models was to do experimental studies, the authors [10] used an existing small-scale setup. The setup is explained in detail, and the figures compare the experimental results with their models' predictions. The authors then moved on to parametric study between two hypothetical fluids, power-law fluid, and yield-power law fluid. The figures also show surge pressure predictions as a function of pipe velocity for both concentric and eccentric annulus. These figures show that the surge pressure increases with the diameter ratio due to decreased annular clearance. The numerical model developed in this study precisely predicts swab and surge pressures, simulating downhole pressure fluctuations that occur during tripping in inclined and horizontal wells. The model utilizes the existing variable narrow-slot approximation technique to account for pipe eccentric in surge pressure calculation. The conclusions of this work are:  
* The present model predicts swab and surge pressures of a yield power-law fluid in the eccentric annulus (i.e., eccentricity ranging from 0 to 90%) with reasonable accuracy (maximum discrepancy of 14%);
* Eccentricity has considerable effects on swab and surge pressures.