New fractal-dimension-based relation model for estimating absolute permeability through capillary pressure curves

Abstract

This paper developed a new general power-law relation model to predict absolute permeability, which innovatively integrating Poiseuille's law and fractal capillary pressure model. The proposed model took into account the assumption of Poiseuille's law and Purcell theory characterizing the porous media as capillary tubes of various radii. Kewen Li fractal capillary pressure model was preferred to characterize capillary pressure curves and derive the new permeability relation model due to its higher fitting accuracy compared with Brooks-Corey model. Further, a randomly collected dataset containing 151 rock samples was used to calibrate the coefficients and another 53 rock samples were used to validate the feasibility of this new model. The proposed permeability model can predict absolute permeability through 5 basic parameters as follows: porosity, displacement pressure, capillary pressure at irreducible wetting phase saturation, irreducible wetting phase saturation and the fractal dimension. The fractal dimension, an indicator of the porous media heterogeneity, has a great impact on flow capacity in natural rock system. For rock samples with fractal dimension Df > 3, the capillary pressure matching results of Kewen Li power-law model are much better than those of Brooks-Corey capillary pressure model. 151 mercury injection capillary pressure (MICP) curves were all well fitted by Kewen Li model to estimate the basic parameters, and the absolute permeability of these rock samples were predicted through the new relation model. Then this study performed a comparison between the measured permeability in laboratory and calculated permeability through the new relation model. The regression Coefficient of Determination (R2) for measured and calculated permeability of 151 rock samples was 0.967. Besides, the new model consistently obtained attractive prediction results for another 53 validation rock samples. The new relation model can be widely used to estimate the absolute permeability for various rock types, including limestone, sandstone, dolomite, and from tight rocks to high permeability rocks.