Pressure-dependent seismic velocities based on effective compliance theory and an asperity deformation model

Abstract

Seismic velocities of rocks depend strongly on confining pressure, which is often explained by the fracture compliances changes within the rocks. It is important to have an accurate model describing the relations between confining pressure and seismic velocities for applications such as time-lapse reservoir characterization. We propose a new model to address this problem by combining the existing effective compliance theory with new solutions for the pressure dependence of fracture compliances. Specifically, we assume the fracture contact surface can be represented by a set of elastic hemispheres with radii following powerlaw distribution, and the pressure dependence of seismic velocities can be expressed through pressure-dependent normal and tangential fracture compliances that are derived from Hertzian contact theory. Joint data fittings of P-and S-wave velocity laboratory data show that our model is accurate. We also implement fluid substitution using our model to explain the similar stress-induced velocity variations of fluid-saturated fractured rocks.

An effective medium model for the stress-dependence of anisotropic seismic velocities in fractured rock

“…As stress increases, additional asperities come into contact and the compliances decrease. Gao & Gibson (2012) give a detailed derivation of expressions for the compliances and results for seismic velocity for isotropic media containing randomly orientated fractures. We therefore provide a summary of these results below, drawing attention to unique new results required for applications to transversely isotropic media, beginning with a review of the effective compliance theory.…”

“…Expressions for isotropic velocities developed by Gao & Gibson (2012) to address the case where the fractures are randomly oriented are presented in Appendix A.…”

“…We have recently developed a phenomenological model for the effective elastic properties of fractured media that aims to address this more general problem of seismic anisotropy associated with fractured rock materials and to provide a solution that facilitates straightforward field scale modelling of seismic data (Gao & Gibson 2012). This model combines two general approaches.…”

“…The model therefore combines a natural and realistic description of fractures and incorporates it with a straightforward system that allows the development of solutions for fairly arbitrary combinations of multiple aligned fracture sets. Gao & Gibson (2012) also included the effects of fluid saturation on fracture compliances and applied the model to the simplest case where fractures are randomly orientated and the rock is isotropic. Inversions of laboratory data show the utility of the model.…”

Error estimates of elastic components in stress-dependent VTI media

“…One method is through the argument of closing elongated pores by modeling aspect ratios and crack densities as a function of effective pressure (Sava, 2004;Spikes, 2011). The approach considered here utilized an excess compliance method as demonstrated by several authors (Ciz and Shapiro, 2009;Gao and Gibson, 2012;Madadi et al, 2013;Pervukhina et al, 2011;Sayers and Kachanov, 1995). Pores with small aspect ratios and/or microcracks, for example, introduce excess compliance.…”