Development and parameter estimation for an enhanced multivariate Herschel-Bulkley rheological model of a nanoparticle-based smart drilling fluid

Smart drilling fluids containing iron oxide nanoparticles have advantages toward increasing the energy and hydraulic efficiency of drilling operations in reservoir environments. Exploring and optimizing the rheological behavior of such new drilling fluids is critical, implying direct and significant economic savings in developing new oil and gas fields. A experimental campaign analyzing the rheology of a bentonite-based fluid produced a new multiparametric dataset, considering a wide range of realistic reservoir conditions. Non-Newtonian behaviour is confirmed by yield stress computation for all these cases. Heating and rotation induce temperature and concentration gradients at drilling depth: it
is hence essential to obtain an accurate but also versatile multivariate rheological model, which will enable viscosity prediction for the analyzed and other similar drilling fluids. The enhanced Herschel-Bulkley model is developed on a multiplicative assumption, postulating and analysing candidate equations which quantify the effect of shear rate, temperature and nanoparticle concentration on drilling fluid shear stress and viscosity. Parameter estimates have been subsequently determined via systematic optimisation, using statistical metrics to quantify and compare uncertainty and predictive potential. The trivariate shear stress and viscosity models proposed are similar in form: each
requires six parameters used to combine a Herschel-Bulkley yield stress expression, an Arrhenius exponential of temperature and a linear model for nanoparticle concentration.