Pore scale flow simulations for numerical validation of Darcy-Forchheimer law for shear thinning fluids used in colloidal zerovalent iron delivery

The use of viscous, shear thinning fluids (eg. guar gum and xanthan gum solutions) has been recently proposed to improve colloidal stability of micro- and nanoscale zerovalent iron particles (MZVI and NZVI) for groundwater remediation. When modelling the colloidal transport of such suspensions, the rheological, non-Newtonian properties of the shear thinning carrier fluid are to be incorporated into the model, in order to correctly simulate pressure drops and viscosity of the suspension. For small flow rates, typical of laboratory column tests, the extended Darcy law is known to be applicable also to non Newtonian fluids. However, when field injection is considered, high Reynolds numbers are encountered close to the injection point, and linear flow cannot be assumed. The Darcy-Forchheimer law is known to be applicable for Newtonian flow and for simple models of shear thinning fluids (power law). However, this is not demonstrated for other, more realistic, shear thinning rheological models. In this work the validity of Darcy-Forchheimer law also for such fluids is demonstrated via pore-scale single-phase flow simulations. Simulations were conducted on synthetic two-dimensional porous media and performed via computational fluid dynamics for both Newtonian and non-Newtonian fluids, and the results are used for the extension and validation of the Darcy-Forchheimer law, herein proposed for shear thinning fluid models of Cross, Ellis and Carreau. The results of flow simulations show the superposition of two contributions to pressure drops: one, strictly related to the non-Newtonian properties of the fluid, dominates at low Reynolds numbers, while a quadratic one, arising at higher Reynolds numbers, is dependent only on the porous medium properties.