Selection of an Accurate Rheological Model to Predict Pressure Drop of Drilling Fluids

Abstract

Drilling operations rely on the continuous circulation of drilling fluids, which consist of a base fluid mixed with various additives. Pressure losses within the drill pipe and annulus are major factors affecting overall drilling performance. Accurate pressure predictions require a suitable rheological model that can represent fluid behavior under varying flow conditions. This study focuses on identifying the most appropriate model for estimating pressure losses in both the drill pipe and annulus. In this study, the model proposed by Guria and Gautam [1] was employed, in which Fann viscometer measurements are used to determine shear rates through a phenomenological relationship of the form ω(τ) = K(τ − τ0), where ω denotes the rotor angular velocity, τ represents shear stress, τ0 is the yield stress, and K is the consistency index. This approach differs from the conventional shear rate expression, γ˙(s−1) = 1.7N, where N denotes the viscometer rotor’s rotational speed (rpm). The resulting shear rates are then used to estimate the parameters of various rheological models, including Bingham Plastic (BP), Power Law (PL), Herschel–Bulkley (HB), and Robertson–Stiff (RS). The rheological models mentioned above are used with different parameters to estimate pressure losses in both the pipe and the annulus under laminar and turbulent flow conditions. The predicted results are subsequently validated against the experimental findings of Okafor and Evers [2]. The above rheological models, with different parameters, are used to calculate pressure drops in pipes and the annulus in laminar and turbulent flow regimes. The results are compared with the experimental data of Okafor and Evers [2]. The accuracy of the rheological models is assessed using the mean square error (MSE) and the coefficient of determination (R2). The results show that the HB- and RS-models fit the experimental data for the pipe and annulus very well in both laminar and turbulent flow regimes. In both cases, shear rates predicted by the phenomenological model yield pressure drops that are more accurate than those predicted by the conventional model.