Session: 11-02-01 Well Drilling Fluids & Hydraulics

Submission Number: 156358

On the Sources of Errors in Rheological Measurements of Non-Newtonian Fluids and the Interpretation of Yield-Power Law Rheological Model Parameters 

Drilling fluids are typically non-Newtonian and, more specifically, shear-thinning. They are often described by the Yield-Power Law (YPL) rheological model. To calculate pressure losses during fluid movement and estimate suspension capability, it is essential to obtain an accurate description of these fluids' rheological properties. This paper addresses the following questions: What are these rheological properties? How can they be measured? What do the Yield-Power Law model parameters represent? And is there an alternative rheological model more suitable for drilling fluids?

Traditionally, flow curves are measured using a concentric cylindrical (Couette) rheometer, which measures torque at a specified rotational speed. For the sake of simplicity, the rheometer provides shear rates and stresses at the wall of the bob, assuming the fluid is Newtonian. However, these values are inaccurate for non-Newtonian fluids. This paper describes methods for estimating shear rates and stresses at the wall of the inner cylinder for YPL fluids. Once corrected, these flow curves can be fitted to a rheological model. For the YPL model, this process can be particularly efficient because the flow behavior index can be derived independently of the yield stress and consistency index, allowing an optimal least-squares fit without recurring to an iterative minimization method.

The YPL model can be expressed in consistent physical quantities, providing straightforward explanations of its parameters. However, it is not easily adaptable to incorporating thixotropic effects. For this purpose, the Quemada model is better suited, as it accounts for both thixotropic viscosity and viscoelastic effects. Thixotropy introduces another source of error in drilling fluid measurements, impacting both Couette and pipe rheometer readings and should be considered during rheometer design and operation.

The more shear-thinning a drilling fluid is, the greater the effect on corrections to the flow curve measured with a concentric cylindrical rheometer. Mechanical Couette rheometers provide limited coverage of low and intermediate shear rates compared to the typical range of drilling fluid behavior. As a result, curve fitting for rheological models may often be of poor quality, highlighting the importance of using methods that yield optimal model parameters. Highly shear-thinning fluids can be particularly challenging to fit accurately. Fitting the Quemada model is also possible, though care must be taken to ensure that the fitted model remains monotonic.

Open-source code for correcting concentric cylindrical rheometer measurements and calibrating a yield-power model to the corrected flow curve is available. A reference implementation of a web-based server is also accessible to the scientific community. These resources aim to simplify the complexities of calibrating rheological models for non-Newtonian fluids based on rheometer measurements.

Presenting Author: Eric Cayeux NORCE

Presenting Author Biography: Eric Cayeux is chief scientist for the drilling and well modelling group at NORCE. After an 18 years career in the industry working with the development of expert system solutions for directional drilling and multi-disciplinary (geophysics, geology, reservoir engineering and drilling) well planning applications, he joined NORCE in 2004, where he worked with drilling automation, real-time drilling diagnostic and drilling simulators. The last decade, he has more focused on basic research and mathematical modelling of the drilling process. Cayeux holds an M.Sc. degree in civil engineering from Ecole Nationale des Travaux Publics de l’Etat, Lyon, France, an M.Sc. degree in software engineering from the University of Nice, France, and a Dr. Philos. degree in petroleum engineering from the University of Stavanger, Norway.