The aim of this paper is to present a new numerical model to study the drilling fluid flow through eccentric annulus during tripping operations and to investigate the effect of the eccentricity on the annular velocity and apparent viscosity profiles. Many published works studied surge and swab phenomenon using simplified numerical models that do not consider the azimuthal variation of the shear stress in the eccentric annuli. In this paper, the developed numerical model takes into consideration this variation. Non-orthogonal, curvilinear coordinates were used to generate a body-fitted elliptic mesh that maps the irregular complicated eccentric annulus into a simple rectangle where flow equations can be discretized using the finite difference method then solved numerically. Besides, a commercial software (ANSYS Fluent 19R3) was used to support the findings of the numerical model. Results of these models were validated against the experimental data from literature where good agreement was observed with an average relative error of 2.6%, 3.8%, and 6.8% for the three Herschel-Bulkley fluids studied in the eccentric case. The profiles of velocity and viscosity were plotted, the contours showed that we cannot use an average velocity or a single value for the apparent viscosity to describe the drilling fluid flowing through an eccentric annulus, but, the whole profile should be used, instead.

The developed numerical model was used in a parametric study to investigate the effect of eccentricity on the relationship between surge pressure and the relevant drilling parameters namely tripping velocity, annular geometry, and fluid rheological properties. The results showed that the eccentricity decreases the surge pressure independently of the previous parameters and that the rate of decrease varies from one parameter to another. The outcome of this parametric study was used to construct a surrogate model using Random Forest Regressor. Predictions from the surrogate model fit the numerical data very well with R-squared of 0.99 and 0.97 for training and test data, respectively.