Extending Kozeny-Carman permeability model to highly porous media

Abstract

Anomalous normalised permeability as a ratio of permeability to square of particle size for snow, diatomite, kieselgel was considered using Kozeny-Carman model and tortuosity factor defined as the square of average tortuosity pathway. Since the Kozeny-Carman model is based on the geometrical models of a capillary tube, the model adopted for high porous media with shaped particles (often with fractal properties) becomes complex. To show how the problem of permeability may be complex, two types of particles are analysed in porous media: snowflakes and diatomite and kieselguhrs. Snowflakes are typical fractal particles, whereas diatomite and kieselguhr can form pores with fractal tortuosity. Based on theoretical investigation a model including fractal measurements for void and solid phases and dependence of tortuosity on packing porosity is proposed. The obtained results show that within the developed model we can describe a wide range of porous media with different fractality and tortuosity. Based on presented numerous examples it was concluded that further experimental investigation should be useful to improve the model and validate the application range.