Scale effect on porosity and permeability: Kinetics, model, and correlation

Variation of porosity and permeability by scale dissolution and precipitation in porous media is described based on fractal attributes of the pores, realization of flow channels as a bundle of uniformly distributed mean-size cylindrical and tortuous hydraulic flow tubes, a permeability-porosity relationship conforming to Civan's power law flow units equation, and the pore surface scale precipitation and dissolution kinetics. Practical analytical solutions, considering the conditions of typical laboratory core tests and relating the lumped and phenomenological parameters, were derived and verified by experimental data. Deviations of the empirically determined exponents of the pore-to-matrix volume ratio compared to the Kozeny-Carman equation were due to the relative fractal dimensions of pore attributes of random porous media. The formulations provide useful insights into the mechanism of porosity and permeability variation by surface processes and accurate representation of the effect of scale on porosity and permeability by simpler lumped-parameter models.