A Comprehensive Evaluation of Rheological Models for Non-Aqueous Drilling Fluids

Abstract

This article presents a comparison of Power’s law, Bingham plastic, Casson, Herschel-Bulkley, Unified Herschel-Bulkley, Robertson-Stiff, Gucuyener, Sisko and modified Sisko models using a rheological database of extensive real field and laboratory datasets. In this study, 778 field and laboratory shear rate/shear stress datasets collected from four different sources for oil-based (OBM) and synthetic-based (SBM) muds were evaluated. Rheological measurements were made using Couette coaxial cylinder rotational viscometer such as Fann-35 type viscometers, in the shear rate range of 5.11 to 1022 s−1. This study presents a simplified algorithm, called direct method, to determine the parameters of three-parameter nonlinear models. The direct method enables parameterization of three-parameter nonlinear models using the linear least squares method and significantly improves their performance. In addition, a MATLAB code based on the Gauss-Newton method was created to parameterize the nonlinear models. The nonlinear regression provided the best fit in many cases by calculating negative model parameters making the models physically senseless. The goodness of fit of the models considered here was determined by comparing the resulting mean relative error and residual mean square values. The results of this study showed that the three-parameter models predicted better rheological fit than the two-parameter models for non-aqueous drilling fluids. The fit accuracy of the three-parameter models parameterized using the direct method is very close to that obtained by nonlinear regression. The modified Sisko, Gucuyener and Sisko models gave an excellent match to most of the shear rate-shear stress data sets evaluated in this study.