A Generalized Rheological Model for Drilling Fluids With Cubic Splines

Abstract

SummaryIn drilling-fluid rheological characterization and hydraulics modeling, selecting a proper rheological model and obtaining rheological parameters with viscometers are critically important. Bingham plastic, power law, and yield power law are the most commonly used standard models for drilling-fluid rheology because they are mathematically simple to use. However, because of 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 that are 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 were 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 was also developed to assist the calculations. The results obtained from the model were validated with experimental data to verify the effectiveness of the proposed model.One can implement the model introduced in this paper for any fluids. 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 deepwater and Arctic environments.