Quantification of non-Newtonian fluids for flows in porous media in terms of energy dissipation rate: permeability, mobility and tortuosity

We propose a systematic approach in quantifying flows in a porous media with an alternative formulation of permeability, mobility and tortuosity using the energy dissipation rate . Two flow numbers (i.e., the coefficient of effective shear rate and the coefficient of energy dissipation rate), which depend nearly on the flow geometry, are adopted to quantify flow characteristics of porous flow system, independent of fluid rheology. First, the relationship of the permeability and the coefficient of energy dissipation rate will be discussed. Next, the mobility of inelastic non-Newtonian fluids (i.e., the relationship of Δp and Q ) for flows in porous media will be decomposed into the permeability and the effective viscosity, evaluated with the coefficient of effective shear rate and the coefficient of energy dissipation rate. Finally, we show that hydraulic tortuosity for quantifying sinuosity and interconnectedness of the pore space can also be expressed in terms of the two flow numbers as well as the porosity based on the energy dissipation rate.