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An improvement of the fractal theory and its application in pore structure evaluation and permeability estimation

We present an improved fractal model for pore structure evaluation and permeability estimation based on the high pressure mercury porosimetry data. An accumulative fractal equation is introduced to characterize the piecewise nature of the capillary pressure and the mercury saturation. The iterative truncated singular value decomposition algorithm is developed to solve the accumulative fractal equation and obtain the fractal dimension distributions. Furthermore, the fractal dimension distributions and relevant parameters are used to characterize the pore structure and permeability. The results demonstrate that the proposed model provides better characterization of the mercury injection capillary pressure than conventional monofractal theory. In addition, there is a direct relationship between the pore structure types and the fractal dimension spectrums. What is more, the permeability is strongly correlated with the geometric and the arithmetic mean values of fractal dimensions, and the permeability estimated using these new fractal dimension parameters achieve excellent result. The improved model and solution give a fresh perspective of the conventional monofractal theory, which may be applied in many geological and geophysical fields.