Shear Rate Determination from Pore-Scale Flow Fields

摘要: Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order predict Darcy-scale effective viscosity $$\mu _{\mathrm{eff}} $$ required for practical applications often, semi-empirical correlations such as Cannella or Blake–Kozeny correlation are employed. These employ an empirical constant (“C-factor”) that varies over three orders of magnitude explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons this not very well understood. derived under assumption porous media can be approximated by a capillary bundle which analytical exist. (v_{\mathrm{Darcy}} )$$ function flow velocity is then cross-sectional average local field resulting linear relationship between shear rate $$\gamma velocity. Only relationship, expressed instead rate. field, however, does general relationship. Particularly tubes, maximum at center, while tube wall indicating rather anti-correlated. sphere pack somewhat more compatible However, hydrodynamic simulations (using Newtonian fluids simplicity) performed directly pore-scale resolved digital images suggest, fields sandstone rock fall two limiting cases tubes packs do This indicates some shortcomings originate from approximation direct calculations. study also 3D represented tubes.