Drilling fluids serve many applications in the oil-drilling process, including the removing of cuttings, drill bit cooling and the prevention of fluid transfer to and from the rock strata. With the addition of nanoparticles it is possible to facilitate in-situ control of the drilling fluid rheology, increasing the hydraulic efficiency of drilling campaigns and reducing costs in a variety of reservoir environments. This paper proposes a first-principles approach to the rheology of smart drilling fluids containing

The demand for more efficient and reliable oil and gas drilling fluid systems drives their development with unprecedented sophistication: the key challenge is to achieve predictable rheological properties, but also to enable their judicious customization, particularly for High Temperature High Pressure) (HTHP) applications and tough environments. This study presents the development and validation of a first-principles multivariate rheological model, allowing yield stress and viscosity prediction for new drilling fluids with iron oxide nanoparticles (NP). Previous studies show that water-bentonite suspensions of variable Fe3O4 NP concentration exhibit non-Newtonian shear-thinning behavior, accurately captured via a tri-parametric nonisothermal Herschel-Bulkley (HB) rheological model form; nonlinear least squares regression yields reliable parameter sets. The resulting fluid shear stress and viscosity are expressed as explicit functions of independent variables (shear rate, temperature, NP concentration) and the correlations are validated against experimental data. A new parameter set must be computed by nonlinear regression for each combination of conditions, a necessity compromising the predictive potential of this data-driven rheological modeling approach. To obtain truly predictive, first-principles rheological models, a systematic strategy is presented: shear stress and viscosity have now been expressed as physics-based (not data-driven) multivariate correlations of the aforementioned independent variables, using microscopic arguments for colloidal particle behavior, as confirmed by Transmission/Scanning Electron Microscopy (TEM/SEM) images. Shear stress is thus studied by distinguishing key additive contributions, on the basis of explicit bounds on colloidal inter-particle distances: our novel functional forms consistently capture the non-Newtonian fluid behavior, but require only one parameter set computation for the entire dataset.