Characterization of synthetic porous media images by using fractal and multifractal analysis

Abstract

Fractal and multifractal analysis of porous images allow the description of porous media through a scale-invariant understanding. There have been numerous works that have used these analysis techniques for the description of a great variety of real porous media. However, these studies are usually comparative, being difficult to discern the role played by the pore size and pore distribution in the results of fractal and multifractal analysis. This works develops an in-depth study of different synthetic porous media from a fractal and multifractal approach, in which both the pore size and its distribution in the medium are parameterized. Thus, a set of synthetic binary images have been generated obtaining deterministic and random structures with different fixed pore sizes and also with different rates of pore sizes. Lacunarity is also calculated in order to complete the aforementioned analysis. Results evinces that fractal dimension increases with pore size and that it is higher when the pore distribution obeys a random distribution versus a deterministic one. However, when the pore size is very large, fractal dimension is similar regardless of the pore distribution. From a multifractal approach, pore size is negatively correlated with the degree of multifractality. In fact, in images with mixtures of different pore sizes it is also found that the greater the ratio of small pores, the greater degree of multifractality. By contrast, when the ratio of large pores is relevant, the degree of multifractality also increases due to the merging of macro-pores.