The subsurface injection of nanoparticles dispersed in stabilizing suspensions has emerged in the last 20 years as an effective and efficient remediation technique. The stabilizing suspensions used to avoid particle aggregation are shear-thinning—and hence non-Newtonian—fluids. In addition, the relatively high groundwater velocities and the high fluid viscosity do not allow for the application of the Darcy’s law, which must be replaced with the Forchheimer’s law. For these reasons, the calculation of the pressure drop in porous media has so far been performed numerically. In this article, a novel analytical formula is derived through a series of simplifying assumptions, using the Cross–Carreau formulation to describe the shear-thinning rheological behavior of the injected fluid. The validity of the formula was assessed using the numerical model MNMs. Comparison between the analytical predictions and the numerical results showed good agreement, with a substantial overlap of the results. For these reasons, the explicit formula is considered a useful tool to support the field-scale design of injection interventions.
Mondino et al. (Tue,) studied this question.