Dilute Species Transport During Generalized Newtonian Fluid Flow in Porous Medium Systems

Dilute species transport in generalized Newtonian fluids (GNFs) is typically described using explanatory empirical approaches assuming a traditional Fickian form, which is an approach that lacks predictive ability for systems and conditions not specifically investigated. Dilute species transport was investigated for a wide range of Cross and Carreau fluids flowing through a set of monodisperse and polydisperse sphere pack porous media. Both microscale and macroscale simulations were performed to demonstrate that GNF fluid flow can be predicted based upon Newtonian characterization of the media and rheological characterization of the fluid. Dilute species transport was shown to have a Fickian limit with dispersivity dependent on the porous media, fluid properties, and the flow rate in a nonlinear fashion. Dimensionless analysis and symbolic regression was used to deduce an explanatory and predictive function to describe dispersivity in terms of relevant system properties, enabling prediction of dilute species transport for GNFs flowing through porous media that does not require any non-Newtonian experiments or parameter estimation.