Explicit flow velocity modelling of yield power-law fluid in concentric annulus to predict surge and swab pressure gradient for petroleum drilling applications

Exact prediction and controlling of surge/swab pressure are required during drilling of hydrocarbon reservoirs and other geological formations that often leads to well control challenges. The existing methods to predict the surge/swab pressure gradient in the wellbore are much implicitly developed, which further reduces the model accuracy. Therefore, the present research aims to develop a novel analytical model by incorporating the explicit flow velocity equations to further improve the efficiency in predicting the surge pressure gradient. The governing flow velocity equations are developed for a concentric annulus exhibiting Couette–Poiseuille flow phenomenon that subsequently used in designing a new analytical model for yield power-law fluids to predict surge pressure gradient. Detailed analysis for the validation of a newly developed model is performed using existing predictive models and experimental data of surge pressure. The statistical analysis exhibits satisfactory outcomes with a maximum error of 5.61% and R² of 0.988. A detailed analysis on the effect of relevant parameters on surge/swab pressure is also presented. The impact of fluid behaviour index and diameter ratio is found to be highly dependent on surge pressure under varying tripping speeds compared to other drilling parameters such as fluid yield point and consistency index.