Numerical model for predicting the surge and swab pressures for yield-power-law fluids in an eccentric annulus

Abstract

Of all of the rheological parameter models for drilling fluids, the yield-power-law (YPL) model is the best one for performing actual calculations. However, no exact general analytical solution has been found for YPL fluids in both concentric and eccentric annuli because currently, all of the published methods for predicting the surge and swab pressures for YPL fluids apply the narrow-slot approximation technique.To analyze the actual flow characteristics of YPL fluids in an eccentric annulus, this paper introduces an exact model for predicting the surge and swab pressures based on fluid mechanics and the properties of YPL fluids. This model fully analyzes the effects of the rheological parameters of drilling fluids, of the geometric parameters of the annulus and of the pipe velocity on the surge and swab pressures. The results show that the maximum velocity weakens with an increased clearance (θ) when the main flow path is in the range of θ = 0 ∼ 120 deg, that the surge and swab pressures decrease with an increase in the eccentricity of the annulus but increase rapidly with an increase in the diameter ratio, and that the surge and swab pressures are most sensitive to changes in the fluid behavior index (n) when 0.7 < n < 1.When the results of this model are also used to evaluate the validity of the narrow-slot model, it is found that the accuracy of the narrow-slot model, which is slightly affected by the rheological parameters (τ0, K and n), is high when the diameter ratio is larger than 0.8 (i.e., the accuracy is within 2% error). However, when the diameter ratio is less than 0.6, the accuracy is influenced by only a few factors, among which Bingham plastic fluids (n = 1) has the most effect, followed by power-laws fluid (τ0 = 0).