A Model of the Fractal Fluid Loss Coefficient and its Effect on Fracture Length and Well Productivity

Loss of the fracturing fluid in hydraulic fracturing is a complex flow process that impacts the effectiveness of the technology, affecting such factors as fracture length and gas-well productivity. Many computational models have been constructed for the fluid loss coefficient, but the models do not account for the fractal character and tortuosity of the porous medium. This study considers these two parameters and proposes a fractal model to calculate the fluid loss coefficient. Fractal permeability is calculated based on the capillary-pressure curves of nine core samples. The permeability values based on fractal theory agree well with the measured values. The fluid loss coefficient determined by the fractal model is higher than the coefficient obtained by standard calculations because of high tortuosity of the porous medium. Predictions of fracture length and gas-well productivity, which depend on the fluid loss coefficient, are discussed and compared, and it is suggested that accurate determination of this coefficient is essential for optimizing hydraulic fracturing.