In drilling and hydraulic fracturing 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 commonly used as the standard models for drilling and hydraulic fracturing fluids since they are simple for mathematical modeling. However, due to the complex nature of drilling and hydraulic fracturing fluids, these models do not often fit well to the rheological data. This leads to a significant error in predicting the bottom hole pressure and pressure along the well. While searching for models based on the physical interaction between the various components of these complex fluids, 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, particularly for the time dependent 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 fluids. The main advantage of the model is it can capture all the complexity rheological response of the fluid. Hence, all readings 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 and hydraulic fracturing 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, well control operation, and hydraulic fracturing operation, especially in deep-water and arctic environments.
