Relative Viscosity of Hydraulic Fracturing Fluids Containing Nanoparticles

Abstract The concept of relative viscosity is widely used in literature for describing the rheological behavior of Newtonian and non-Newtonian fluids containing particles. Generally, nanoparticles are used at low concentrations; but Einstein equation hardly predicts the suspension viscosity values. Similarly, equations developed for high particle concentrations hardly made the predictions too. This paper presents the inability of Einstein and Krieger-Dougherty equations in predicting the relative viscosity of surfactant-based fluids (SBF), polymeric fluids, and SBF-polymeric fluid blends. Concentrations of 5% and 33 lb/Mgal guar were used for the laboratory preparation of SBF and polymeric fluids respectively, and both fluids contained 4% potassium chloride (KCl). Also, the mixture of SBF and polymeric fluids in the ratios of 3:1 (vol.) and 1:3 (vol.) resulted into Blend-A and Blend-B fluids respectively. The addition of 20 nm silica nanoparticles, at concentrations of 0.058, 0.24, and 0.4% wt., to the clean fluids generated the nano-fluids. Rheological data were gathered with Bohlin CS-50 rheometer within a temperature range of 75 to 175 °F. Silica nanoparticle concentrations of 0.058, 0.24, and 0.4% wt. were converted to 0.0083, 0.034, and 0.055 solid volume fractions respectively. Relative viscosity values could not be predicted using Einstein and Krieger-Dougherty equations. The nano-fluids display both increase and decrease in suspension viscosity; furthermore, their suspension viscosities were dependent on the solids volume fraction, temperature, and shear rate (9 to 1026 sec−1.). Lastly, relative viscosity correlations (that covered the whole range of values for which the experiments were conducted), previously developed by the authors, were included for complementary purpose. The correlations predict the viscosity of nano-suspensions as a function of solid volume fraction, temperature, and shear rate. This work provides an insight into the behavior of suspension at nano-scale level. The prediction of viscosity of nano-suspensions depends on more than one parameter. Moreover, this study will facilitate the field application of these novel hydraulic fracturing fluids.