Anisotropy is a useful attribute for the detection and characterization of aligned fracture sets in petroleum reservoirs. Unfortunately, many of the traditional effective medium theories for modeling the seismic properties of fractured rock are insensitive to the size of the constituent fractures. For example, the same pattern of anisotropy may be produced by a high concentration of small, stiff cracks or by a lower concentration of large, compliant fractures. The distinction between these models is important for assessing permeability anisotropy because fluid flow is dominated by the largest fractures. One method to gain further insight is through the analysis of frequency-dependent shear-wave splitting in microseismic data because fracture compliance is frequency dependent, and microseismic data are relatively rich in frequency content. We compared two potential mechanisms causing frequency-dependent compliance of fractures: (1) squirt flow in fractured porous rock and (2) wave scattering over rough fractures. Both models showed a sensitivity to average fracture size or compliance of the constituent fractures, and thus they provide a potential means to differentiate between anisotropy produced by small cracks or large fractures. We used both mechanisms to model frequency-dependent anisotropy data obtained from a fractured gas reservoir and invert for fracture parameters. Under certain conditions, the squirt-flow mechanism can cause significant frequency dependence in the microseismic band. However, the model is highly sensitive to the empirically derived mineral-scale relaxation time, which is poorly known and requires laboratory measurements to constrain. Conversely, producing a similar frequency response using the scattering model requires implausible fracture parameters; therefore, the squirt-flow model appears to be the most likely mechanism for microseismic applications. At higher frequencies, however, scattering may become more significant. Care should be taken when upscaling ultrasonic laboratory results for field-scale problems because different mechanisms may be at play within different frequency bands.
Fluid Flow in Fractured Rock: Theory and Application
