First-principles Rheological Modelling and Parameter Estimation for Nanoparticle-based Smart Drilling Fluids

Abstract 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 Fe 3 O 4 nanoparticles which have shown advantages to increasing drilling efficiency in a variety of reservoir environments. The model for shear stress is developed based on a force balance between the Van der Waals attractions of monodispersed Fe 3 O 4 nanoparticle spheres. The model for viscosity is developed by considering the force required to maintain the nanoparticles in suspension being equal to the drag force as calculated for Stokes flow approximation about a sphere. Both models had a candidate equation for interparticle distance under increasing shear rate. A bivariate model described the rheological effects of shear rate and Fe 3 O 4 nanoparticle concentration with a high predictive potential R 2 τ γ . ϕ = 0.993 , R 2 μ γ . ϕ = 0.999 . The trivariate model accounts for temperature with high predicative potential R 2 τ γ . ϕ T = 0.983 , R 2 μ γ . ϕ T = 0.986 . Heating effects and low nanoparticle concentrations increase standard correlation error.