Accurate numerical modeling of surge and swab pressures in concentric annuli is proposed. The numerical scheme is developed for the laminar flow occurring during the drillstring axial movement. The model incorporates Yield Power Law (YPL) fluids, which is a good representation of the most of the drilling fluids. A commercial computational fluid dynamics (CFD) package is used to validate the developed numerical model. Also, the mathematical model and CFD analysis are compared with the existing models from literature.

A high order finite difference numerical model is developed that accurately captures the physics of laminar flow due to surge and swab phenomena in concentric annuli. The numerical scheme is prepared such that it accounts for both Newtonian and non-Newtonian fluids. YPL model is incorporated in the proposed scheme, and it accurately estimates the drilling fluid behavior in both high and low shear rates. CFD analysis is conducted using a commercial software to validate the accuracy of in house developed numerical model. The velocity profiles across the annulus are compared in order to verify the precision of the model.

The proposed model for the surge and swab pressures is more accurate than narrow slot approximation model which is most commonly used in the drilling industry. With this proposed modeling, the physics of surge and swab pressures are better captured, because it accounts for the effect of curvature in annular geometries. The model is well-validated with the CFD analysis and the velocity profile comparison of the numerical solution and CFD analysis yields less than 5% average absolute percent error. With this work, dimensionless velocity profiles are presented which better explain the flow during surge and swab in concentric annuli, while the inner pipe is reciprocating in steady-state.

Pulling out or running tubulars in the vertical section, or running casing with centralizers approximates the position of tubular to concentric. It is very important to accurately calculate these pressure losses to avoid fracturing the formation or having an influx from the formation. Therefore, CFD analysis and mathematical modeling of surge and swab pressures presented in this study has potential to optimize the tripping operations that will help avoid hole problems.

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