Simple Models for the Stress-Dependence of Anisotropic Seismic Velocities in Fractured Rock
Richard L. Gibson, Jr. and Kai Gao
Department of Geology & Geophysics, Texas A&M University, College Station, TX, USA
Time-lapse seismic methods offer strong potential for monitoring fluid movements in complex geologic media such as carbonates. Seismic detection and characterization of fracturing in such materials will be of particular interest, since fractures can control fluid flow in cases where they provide the primary conduits through which fluids move through a low permeability rock matrix. Reliable seismic reservoir characterization requires reliable models that relate fracturing and seismic velocities, but these results are complicated by several factors. For example, fractures often cause the rock to display seismic anisotropy (Pointer et al., 2000; Tod, 2001; Bakulin et al., 2002; Sayers, 2002; Guégen and Sarout, 2009), which should be taken into account in any seismic modeling or imaging applications. Furthermore, the influence of these fractures will depend on changes in stress in the reservoir during fluid movement, and the magnitude of the seismic anisotropy may also vary as a result. Reliable inversions or other analyses of field data thus require a model relating various fracture sets to the resulting seismic properties as both fluid saturations and stress distributions change during hydrocarbon production. While a number of analytic solutions for the effective seismic properties of fractured media have been proposed, there are few that consider the effects of stress variations (e.g., Pointer et al, 2000; Tod, 2001;.Maultzsch et al., 2003).
In this paper, we will present results based on a recently developed phenomenological model for the effective velocities of fractured media that aims to address this problem and to provide a solution that facilitates straightforward simulations using with field-scale reservoir models. This model combines two general approaches (Gao and Gibson, 2011). First, the stress-dependence of normal and tangential compliances of individual fractures is quantified in terms of increasing contact area of rough surfaces with a distribution of asperities. Second, these compliances are used in the general theoretical framework outlined by Sayers and Kachanov (1995) (see also Sayers, 2010), which expresses the effective seismic velocities of fractured rock in terms of these fracture compliances. This approach also makes it straightforward to develop expressions for fairly arbitrary combinations of multiple aligned fracture sets, an important and useful result for applications to fractured, carbonate reservoirs. Below we first outline the model for the seismic velocities, and then present examples of inversions of laboratory velocity measurements, both isotropic and anisotropic, using this model. The presentation will also include simulations of seismic reflections from anisotropic reservoirs with stress changes.
Effective characterization of complex carbonate reservoirs where fractures have a strong influence on fluid movement requires reliable methods for relating fracture distributions to changes in seismic reflection amplitudes. Here we outline a method that expresses the stress-dependence of fracture compliances to increasing contact area of rough-surfaced fractures. This in turn allows a simple model for the effective seismic velocities in media with isotropic or aligned fracture sets, and the resulting solution can easily represent the changes in seismic anisotropy caused by variations in stress fields. Inversions of laboratory data measuring isotropic and anisotropic seismic velocity variations demonstrate the model can easily reproduce such measurements, and it is also easily incorporated into field scale models since a relatively small number of parameters is required.
AAPG Search and Discovery Article #120034©2012 AAPG Hedberg Conference Fundamental Controls on Flow in Carbonates, Saint-Cyr Sur Mer, Provence, France, July 8-13, 2012