Pseudo-three-dimensional simulations of a vertical hydraulic fracture with time-dependent injection rates

This study reports a hydraulic fracture pseudo-three-dimensional model with time-dependent injection rates in elastic layered reservoirs. The adopted solution method can capture the crack tip asymptotic behaviors. The model is validated against the PKN analytical solutions of storage and leak-off-dominated regimes. The results show good agreement between the P3D model and its corresponding PKN solutions. The validated model is then employed to conduct a series of simulations to gain insight into the variable injection rates, fracture toughness, and leak-off coefficient on the fracture propagation behavior. Results show that increasing the variable injection rate reduces the lateral growth and has slight effects on the width and vertical growth. The fracture toughness considerably increases the crack width and length, whereas the leak-off coefficient has the most impact on limiting the lateral extension. © 2021 Taylor & Francis Group, LLC.