A New Permeability Model for Smooth Fractures Filled with Spherical Proppants

Permeability modeling of filled fractures, in contrast to porous media and rough fractures, has long plagued the hydrology and energy industries. Non-Darcy flow occurs in filled fractures, and it reduces the effective permeability, making it challenging to predict the effective permeability. In this study, smooth fractures filled with ideal spherical proppants were considered as research objects. To address the challenges in characterizing the permeability of fractures filled with proppants, 150 three-dimensional fracture models filled with spherical proppants were established, and 635 effective permeability simulations of different filled fractures under various pressure gradients were performed. The effects of the fracture porosity, fracture aperture, and proppant size on the Darcy permeability of filled fractures were investigated by performing orthogonal tests using the control variables method. A new Darcy permeability model for filled fractures was developed based on the numerical simulation results. The proposed model is expressed as a power function of the porosity, fracture aperture, and proppant size. This model can more accurately predict the permeability of filled fractures with spherical proppants than conventional permeability models. A prediction model for the effective permeability was proposed using a logistic function to characterize the effective permeability under a non-Darcy flow. The effective permeability model could accurately predict the effective permeability of filled fractures under non-Darcy flow. Our study has an important reference value for the effective permeability prediction of porous media and rough fractures.