The rheology of drilling fluids from a non-equilibrium thermodynamics perspective

The rheological behavior of drillings fluids is usually described by the Casson or the Herschel-Bulkley models. Despite the overwhelming data highlighting the significance of their use in numerous fields, they fail to produce normal stresses, whose importance in drilling operations has only recently attracted attention. We herein introduce a continuum model for predicting the rheological behavior of drilling fluids with plate-like suspensions, based on the Hamiltonian formulation of transport phenomena for fluids with a complex microstructure. The model describes drilling fluids at a mesoscopic level by using two fields: a vectorial (the momentum density) and a tensorial one (the particle's orientation tensor). A thorough comparison against experimental data demonstrates the unique capability of the new model to accurately describe the rheological behavior of these systems, for both shear viscosity and normal stresses. Future work, aiming to improve the predictive capacity of the model at higher volume fractions and for considering the extreme temperature and pressure conditions frequently encountered in borehole operations, are also discussed.