Mechanical Behavior Of Hollow Proppants Based On Finite Element Model

Proppants are being increasingly used in hydraulic fracturing, which keep the fractures open. Progress has been made in developing hollow proppants that can be transported to the far end of the fractures to improve propped fracture conductivity. Two primary mechanisms by which proppants are damaged under closure stress are embedment and crushing, leading to a remarkable reduction in fracture conductivity. In this study, finite element model (FEM), considering rock plasticity, was used to study the embedment and crushing of a hollow proppant. After comparison with the existing model and experimental data, the proposed FEM was employed to conduct sensitivity studies. The effects of the following parameters on embedment and crushing were analyzed: closure stress, distance coefficient, Young's modulus of rock and proppant, proppant size, and hollow structure. The results show that the most sensitive environmental factor is the distance coefficient, followed by closure stress and Young's modulus of rock. The embedment depth increases approximately linearly with the proppant size, and proppants with different sizes have similar crushing rates. The hollow structure has little effect on proppant embedment but significantly affects proppant crushing. Based on the data normalization method, the optimal ratio of hollow radius to proppant radius was designed to be 0.7. These results can guide the preparation of hollow proppants.