Stability of Stress Shadow Simulation

ABSTRACT: This study investigates the stability of the numerical solution describing hydraulic fractures growing simultaneously with significant stress shadow interaction. A simplified model consisting of two parallel blade-like (PKN) fractures is considered, where each fracture experiences additional local compressive stress from the neighboring one. First, an explicit method is examined, where the stress shadow is calculated using the fracture width distribution from the previous time step. It is shown that this method requires excessive time step refinement to maintain stability. Second, an implicit method is considered. It is implemented using an iterative process combined with relaxation and Aitken 6-squared extrapolation. Finally, it is demonstrated that the implicit method provides a stable solution 140 times faster than the explicit one for the same grid resolution in the cases considered. The proposed implementation of the implicit method does not require a major rework of the explicit algorithm, thereby reducing development effort.