Frequency-Dependent Seismic Waves in Fluid-Saturated Fractured Rock

Abstract:

Fractures are the natural and essential elements of rock. Fracture systems are the most important features that define rock permeability and strength, as well as their anisotropy properties. Recent advancement in induced fracturing is a core part of the gas/oil shale technology, where fracture monitoring and control became a special topic of interest.

Krauklis wave (K-wave) is the result of interaction between a fluid mass and elasticity of fracture walls, and it propagates primarily along the fracture systems in the fluid. At the fracture tips and fracture intersections it partially converts into the body waves. It is quite clear that incorporation of K-waves in a theory of wave propagation in fractured rock is one of the most important problems to solve for understanding of their seismic properties.

One of the most fundamental properties of fractured rock is a fractal fracture distribution and it is rarely, if ever, taken into account in existing wave propagation theories. However, this property exists on a widest variety of scales and in particular reveals itself in a form of Gutenberg-Richter Law experimentally proven, starting from laboratory measurements and up to the global seismicity.

We computed P and S-wave velocities of the rock containing fluid (and proppant) filled fractures, considering the effect of extremely slow and dispersive wave propagation within individual fractures. This was made possible by introducing the concept of “effective fracture-wave volume,” and by evaluating the elastic constants of rock containing a complex, fractal network of fractures. These velocities were used to compute seismic waves reflected normally from a fractured reservoir. We demonstrate that by taking into account the Krauklis wave phenomenon for the fractally distributed fluid-filled fractures, it is possible to explain the observed low-frequency anomalies above the underground natural reservoirs. These anomalies include increase of amplitude and a phase delay of reflected waves as frequency approaches zero.