Parameterization of elastic stress sensitivity in shales

Abstract

Stress dependency and anisotropy of dynamic elastic properties of shales is important for a number of geophysical applications, including seismic interpretation, fluid identification, and 4D seismic monitoring. Using SayersKachanov formalism, we developed a new model for transversely isotropic (TI) media that describes stress sensitivity behavior of all five elastic coefficients using four physically meaningful parameters. The model is used to parameterize elastic properties of about 20 shales obtained from laboratory measurements and the literature. The four fitting parameters, namely, specific tangential compliance of a single crack, ratio of normal to tangential compliances, characteristic pressure, and crack orientation anisotropy parameter, show moderate to good correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance exponentially decreases. The crack orientation anisotropy parameter broadly increases with depth for most of the shales, indicating that cracks are getting more aligned in the bedding plane. The ratio of normal to shear compliance and characteristic pressure decreases with depth to 2500 m and then increases below this to 3600 m. The suggested model allows us to evaluate the stress dependency of all five elastic compliances of a TI medium, even if only some of them are known. This may allow the reconstruction of the stress dependency of all five elastic compliances of a shale from log data, for example.

Error estimates of elastic components in stress-dependent VTI media

“…The black lines in Fig. 3 are the best-fit models identical to those in Pervukhina et al (2011). The ε and δ models decrease in magnitude with increasing pressure.…”

“…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.…”

“…Error bars (calculated in the next section) accompany each c ij and s ij component. The models (black curves) show values computed using the model of Pervukhina et al (2011).…”

“…These approaches were for clastic and carbonate rocks, primarily for isotropic scenarios. However, anisotropic characterization of rock is quite important for understanding velocity dependence on directional stresses Madadi et al, 2013;Scott and Abousleiman, 2005;Shapiro and Kaselow, 2005;Verdon et al, 2008) or on fabric and stress (Ciz and Shapiro, 2009;Pervukhina et al, 2011). The latter is becoming increasingly important because of the increase in interest of extracting hydrocarbons from anisotropic shales and mudstones (Horne and Walsh, 2014;Horne et al, 2012;Miller et al, 2012;Sayers, 1994Sayers, , 2013Vernik and Liu, 1997).…”

“…In the work presented here, error bars were computed as a function of pressure for one of the sample sets (the G3 brine-saturated hard shale) in Wang (2002). The stochastic formulation began with perturbations of the best-fit rock-physics model published in Pervukhina et al (2011) on the G3 sample set. The rock-physics model simultaneously represents five compliances for all pressures .…”