Fractal and multifractal analysis of different hydraulic flow units based on micro-CT images

Pore structure is one of the key factors affecting the transport behavior in porous media, which is mainly determined by petrophysical facies. To accurately characterize the diversity of pore structure, hydraulic flow units (HFU) based on the modified flow zone indicator data are subdivided, and experiments of mercury injection and routine core analysis are conducted for 601 sandstone samples in this study. Five samples selected from different HFU (porosity is approximately equal, however permeability varies widely) are chosen to conduct micro-computerized tomography test. Then, fractal and multifractal methods are used to characterize complex pore space of chosen samples based on the number-area model, radius-volume model and number-radius model respectively, in which the effect of image scale on the fractal dimension is investigated. Each HFU has similar box dimension and generalized fractal dimension, but has significant difference in multifractal spectrum. Specially, the different values of singularity exponent in the multifractal spectrum have a good relationship with the experimentally measured permeability. There are clear inflections points on the fractal curves from mercury injection curve. Based on the value of maximum pore throat radius, only one segment (located in the middle) can be used to calculate the fractal dimension. Fractal dimension obtained by pore network model does not satisfy the traditional relationship. Correspondingly, fractal and multifractal characteristics pore structure of different hydraulic flow units are analyzed in detail.