Scaling Law of Permeability and Porosity for Fluid Transport Phenomena in Porous PCM Media

The present paper reports the numerical results of fluid flow in porous phase change materials (PCM) media. This is an important topic in potential scientific, technological and engineering field’s especially latent heat storage. In this paper, we are only interested in the correlation between permeability and porosity of the porous media and not in latent storage. Fluid flow is characterized by many parameters mainly permeability and porosity. Many models have been proposed for the study of this phenomenon over the years. However, it can be modeled using the complex model that studies the characteristics of pore microstructure and fluid flow in porous media. This model is more accurate and realistic compared to previous models. It predicts permeability and porosity with a good agreement with experimental data. In this paper, the complex model is used to determine the impact of the tortuosity and the density of capillary distribution on the relation between permeability and porosity and check their scaling laws with universal exponents independently of other parameters. The results show that the permeability-porosity relation is proportional to the standard deviation of capillary distribution and its density. The tortuosity affects porosity proportionally, and permeability inversely. The relation between porosity and permeability follows a power law with universal exponents β = 4.06 ± 0.12 for different values of the expectation of distribution, the density of capillaries and the tortuosity; and β = 1.69 ± 0.01 for different values of the standard deviation, density of capillaries and tortuosity. The universality of these exponents further validates the complex model with various previous experimental and numerical studies.