A Generalized Rheological Model for Drilling Fluids Using Cubic Splines

Abstract

Abstract In drilling fluid rheological characterization and hydraulics modeling, selecting a proper rheological model and obtaining rheological parameters using viscometers are critically important. Bingham Plastic, Power Law, and Yield Power Law are the most commonly used standard models for drilling fluid rheology since they are mathematically simple to implement. However, due to the complex nature of drilling fluids, these models do not often fit well to the rheological data. This leads to a significant error in drilling fluid hydraulics modeling. While searching for models based on the physical interaction between the various components of the drilling fluid, it is very practical to find simple mathematical functions that best fit to any experimental data obtained from field viscometers. This will improve the accuracy of hydraulics modeling, in particular for time dependent drilling fluids. In this research, cubic splines have been used to fit the experimental data obtained from field viscometers. A generalized hydraulics model is presented to calculate pressure drop in pipe and concentric annulus with detailed sample calculations. A numerical simulator has also been developed to assist the calculations. The results obtained from the model have been validated with experimental data to verify the effectiveness of the proposed model. The model introduced in this paper is the generalized form of all the other commonly utilized models and can be implemented for any fluid. The main advantage of the model is that it can capture all the complex rheological response of the fluid. Hence, all readings obtained from the viscometers can provide valuable input for the hydraulic model. Also, the numerical solution is stable and straightforward to implement. The model provides drilling engineers a simple and powerful method to accurately predict the pressure distribution along the wellbore. This is highly important in drilling fluid hydraulics program optimization and well control operation, especially in deep-water and arctic environments.