Study on Permeability Calculation Method Based on J Function and Fractal Theory

Abstract

Permeability is a required parameter for studying aquifer properties. However, for sandstone aquifers with low permeability, it is difficult to measure permeability directly through experiments. Based on fractal theory and the J function, a new method to calculate the permeability of a sandstone aquifer is derived. This work first solves the J function under each water saturation according to its definition. Combined with mercury pressure data, the J function and logarithmic curve equation of water saturation are then fitted by the drawing method, and the fractal dimension and tortuosity of the aquifer are further solved. Finally, the aquifer's permeability is calculated using the new permeability calculation method. To verify the accuracy of the proposed method, 15 rock samples from the Chang 7 Group, Ordos Basin, are taken as research objects. The permeability is calculated using the new method combined with mercury injection data and aquifer characteristic parameters, and the results are compared with the real permeability. The relative error of most samples is <20%, which shows the permeability calculated by this method is accurate and reliable. The effects of fractal dimension, tortuosity, and porosity on permeability are also analyzed.