New Simple Analytical Surge/Swab Pressure Model for Power-Law and Modified Yield-Power-Law Fluid in Concentric/Eccentric Geometry

The axial movement of pipe in and out of the well generates positive (surge) and negative (swab) pressures that will impact the well pressure. When the swab and surge effects cause well pressures outside the allowable operational limits, wellbore instability (well collapse/well fracture), kick, and induced drill string sticking issues will occur. The problems increase the operational and nonproductive time-related costs. Consequently, the drilling budget rises significantly. It is therefore, imperative to predict the differential pressures in order to mitigate the problems. Even though several models have been developed in the past, models work for the considered experimental setup and conditions. In this paper, a simple analytical model was derived for eccentric/concentric annuli. The fluid rheological behaviors were assumed to be described by power law and yielded power-law. The model is derived based on a steady state condition, and the effects of tripping speed, the power-law fluids, the yield-power-law fluids rheological parameters, and well geometries are considered. The model is compared with experimental data from the literature and with the existing model. Parametric sensitivity studies have been conducted. Results show that the model prediction exhibited quite good performance, with an average percentile error deviation of 9.9% and 6.2% for the power-law and yield-power-law fluids, respectively. However, more testing is required to determine the model’s limitations and application.