Hydraulic Fracturing Model Based on Nonlinear Fracture Mechanics: Theory and Simulation

Abstract

Abstract Recent advancements of hydraulic fracturing in complex formations indicate the limitations of traditional fracturing models stem from Linear Elastic Fracture Mechanics (LEFM) theory, which obeys small-scale yielding rule. This rule breaks down in the crack tip region where the strain is extremely large, so Nonlinear Fracture Mechanics (NLFM) is required in studying fracture initiation and propagation phenomena for ductile rocks and pseudo-brittle rocks. The model in this paper studies fracture initiation angle of an inclined fracture/perforation (the term "inclined" is defined as the crack or perforation that does not coincide with the principal stress direction) based on R-criterion, which assumes that fracture propagates in a direction where the distance from crack tip to the elastic/plastic boundary is minimum. The crack tip opening displacement is solved with the combination of Dugdale model and R-criterion. The simulation results indicate that fracture initiation angle for the ductile and pseudo-brittle rock is less than that of a brittle rock. Furthermore, a crack tip opening displacement decreases with inclination angle and minimum in-situ stress and increases with increasing perforation depth. The hydraulic fracturing model presented in this paper opens a door to understanding why/how fracture gets twisted and narrowed near inclined borehole, why/how skin factor increases sharply near wellbore in hydraulic fracturing and helps us learn how to avoid undesired fracture geometry and "screenout" during hydraulic fracturing treatment execution and to maximize ultimate recovery. It is recommended to alleviate fracture twist by increasing pumping pressure and extending perforation depth by about 30% (based on the perforation of 1ft) when the in-situ stresses distribution is not clear. This model finds large application prospect in fracturing formations that are rich in clay or are high pressure high temperature (HPHT) formations.