Inferring the Properties of Fluid-Filled Fractures using Tube Waves

We present a methodology to infer the geometry of fluid-filled fractures (both aperture and length) using the interaction between tube waves in cylindrical fluid-filled conduits and trapped waves in fractures intersecting the conduit. This approach could be applied to study engineered fractures in oil and gas reservoirs as well as volcanic systems. We specifically investigate the reflection and transmission of tube waves, propagating along the cylindrical conduit, from fractures. Pressure changes carried by the tube wave can couple to resonant oscillations of the fractures, and the spectral properties of these oscillations carry information about fracture geometry. The fracture is coupled to the conduit at the fracture mouth by balancing pressure and conserving mass as fluid flows into or out of the fracture. In our linearized theory, the fracture response is quantified through a frequency-domain transfer function relating fluid pressure and velocity at the fracture mouth. For a given transfer function, tube wave seismograms can be obtained using a single, inverse fast Fourier transform. Fracture transfer functions are obtained from numerical simulations of wave propagation along fluid-filled cracks. These simulations rigorously couple an approximate version of the linearized Navier-Stokes equation for a viscous, compressible fluid to the elastic wave equation in the surrounding medium. To solve this problem, we have developed a two-dimensional high-order finite difference method capable of handling complex fracture geometries. Fracture resonance is associated with standing crack waves (also known as Krauklis waves) propagating along the fracture. We find that although details of fracture properties can be revealed by recorded pressure or seismic signals, reductions in aperture, as occur at crack tips, can reduce the amplitude of high frequency resonant modes through increased viscous dissipation.