Numerical modeling of the simultaneous propagation of multiple hydraulic fractures with fluid lags

Purpose: The purpose of this paper is to develop a numerical method to model the simultaneous propagation of multiple hydraulic fractures (HFs) with fluid lags driven from a horizontal wellbore. Design/methodology/approach: Fracture propagation in solid medium is modeled with the extended finite element method and fluid flow is modeled with finite volume method. Three iteration loops are introduced to solve the nonlinear system within each time increment, i.e. a Newtonian iteration to solve the solid-fluid coupling system, a Picard iteration to determine fluid front positions and a secant iteration to update fracture lengths. Findings: The propagation of one single HF with a fluid lag is simulated and agrees well with semi-analytical solutions or other numerical results in the literature. The simultaneous propagation of two HFs are then investigated, which demonstrates the ability of the proposed method in capturing the hydraulic fracturing process with multiple fractures and fluid lags. Originality/value: With the proposed method, one can simulate the simultaneous propagation of multiple HFs with fluid lags, which play a significant role during early-time propagation or when the confinement stress is relatively low (shallow HFs). Solid deformation and fracturing, fluid flow in fractures and in the wellbore are fully coupled, and three iteration loops are introduced to solve the nonlinear system.