Dynamic modeling of explosively driven hydrofractures

Abstract

The long‐range extension of explosively driven fractures depends upon the flow of gas into the fractures as well as the nonlinear stress wave dynamics of the surrounding solid. These two interactive processes are, for the first time, modeled in a simultaneous fashion which includes solid dynamic as well as fluid dynamic considerations. At each time step in the numerical procedure, a fluid dynamics algorithm is first used to calculate the pressure distribution along the crack(s) and the rate of fluid advance, after which a solid dynamics algorithm calculates the incremental motion of the solid, the new stress field, and the opening displacement of the crack(s). To gain generality and simplicity, gas‐filled fractures are introduced using a crack porosity formulation in which local crack strains are adjusted to achieve a balance between the internal gas pressure and the local compressive stress. Comparisons with exact self‐similar solutions include cases in which the fracture speed is controlled by solid dynamic as well as fluid dynamic considerations. Example calculations include single or multiple fractures with individually calculated pressure distributions as well as more pervasive fracture swarms which are presumed to be fully pressurized. A broad range of results are presented for underground nuclear explosions which are detonated in a premined spherical cavity. As the initial radius of the cavity is increased, the explosion becomes progressively decoupled, and the primary constraint on fracture propagation changes from solid dynamics to fluid dynamics, thereby exercising the full range of the controlling physics.