The acoustic velocity of CO2-saturated sandstone at the top of the CO2 reservoir has been estimated in many different studies and is still debated (e.g. Arts et al., 2004; Carcione et al., 2006; Ghaderi & Landro, 2009). These studies, discussed below, have estimated the acoustic velocity either using observations from the seismic reflection surveys, or rock physics mod-elling.
Four estimates of the seismic velocity of CO2-saturated sandstone have been made using seismic observations: Chadwick et al. (2004a) obtained a value of 1420 m s−1 based on the observed pushdown of reflective horizons beneath seismic chimneys; Williams & Chadwick (2012) calculated a velocity of 1478 m s−1 based on reflectivity of the upper boundary of the shallowest CO2 layer by exploiting higher resolution two-dimensional seismic profiles acquired in 2006; Furre et al. (2015) suggest that a velocity of 1400 m s−1 yields the optimal agreement between their thickness measurements and other studies; and finally Chadwick et al. (2016) measured a velocity of 1431 ± 62 m s−1 by correlating synthetic models with very small time shifts of reflections from the upper and lower boundaries of the shallowest layer on the 2010 broadband survey.
The acoustic velocity of seismic waves through CO2-saturated sandstone can also be esti-mated using rock physics models. When modelling the velocity of seismic waves through
CO2-saturated rocks, an important consideration is whether CO2 saturation within the reser-voir rock is ‘uniform’ or ‘patchy’ (Chadwick et al., 2004a; Boait et al., 2012). These terms describe the extent to which the CO2 is mixed with the ambient brine in the reservoir, rela-tive to the frequency of the seismic signal. The critical length scale, Lc, for mixing of fluids in the reservoir imaged with a seismic signal of frequency, f , is given by
Lc= s
kKf l
f η (2.3)
where k is the permeability of the medium, and Kf l and η are the bulk modulus and viscosity of the most viscous fluid, respectively (Mavko & Mukerji, 1998). For a mixture of CO2 and brine in the Utsira Formation, where k = 2×10−12m2, Kf l = 2.3×109 Pa, η = 7×10−4Pa s, this length scale has been estimated to be ∼0.5 m for a seismic wave with f = 30 Hz (Boait et al., 2012). This length scale defines the distance that seismic wave induced pore-pressure gradients can equilibrate during one seismic period.
If fluids are mixed at scales less than Lc (i.e. saturation is uniform), the increased pore pres-sure can diffuse away within a seismic period. However, if saturation is heterogeneous over length scales larger than Lc(i.e. saturation is patchy), then seismic wave induced flow, driven by spatial gradients in pore-pressure, can cause attenuation and velocity dispersion of the seismic wave (Toms et al., 2007). Patchy saturation might be caused by viscous fingering, spatial variation in wetability, or variable mud content within the rock (Mavko & Mukerji, 1998).
For uniform CO2 distributions, and sufficiently low seismic frequencies (i.e. . 100 Hz), the Gassmann model using the Reuss average for the effective fluid bulk modulus can be used to describe the velocity of seismic waves through CO2-saturated rocks (Figure 2.11; Sengupta
& Mavko, 2003). However, if saturation is patchy, the Voigt model provides an upper bound on the acoustic velocity, suggesting that it will vary approximately linearly between end-members (Figure 2.11; Rubino et al., 2011; Williams & Chadwick, 2012). A more useful estimate of the seismic velocity for patchy CO2 saturation is given by the Brie model, which
Figure 2.11: Velocity of seismic waves through CO2 saturated sandstone at the Utsira Formation calculated using the Gassmann model. Solid line = Effective fluid bulk modulus, Kf l, calculated using Reuss average. Dashed line = Kf l calculated using Brie average. Dotted line = Kf l calculated using Voigt average. See Appendix A for more details.
is an empirical model that suggests that there are only significant differences between patchy and uniform models for CO2 saturations lower than 40 % (Figure 2.11; Carcione et al., 2006;
Mavko et al., 2009). The differences between the model are due to the different approaches taken to averaging of the fluid properties within the pore space. A detailed description of these models is provided in Appendix A.
Evidence for the existence of patchy saturation is provided by measurements of push-down on the base of the Utsira Formation. Attempts to match the total push-down on the base of the reservoir due to the presence of CO2 suggest that CO2 is distributed in highly saturated, thin layers between regions with more diffuse, and possibly patchy, saturation (Chadwick et al., 2005; Boait et al., 2012). The existence of high saturation layers is supported by lab-oratory centrifuge experiments on core material from the Utsira Formation, which suggest that CO2-saturation within each thin layer is likely to be high with a very thin capillary fringe along its base (Figure 2.12; Chadwick et al., 2005). Rubino et al. (2011) found that the effect of patchy saturation on acoustic velocity increased when saturation was low. These authors also concluded that wave-induced flow effects can be neglected when considering the thin, highly CO2-saturated layers within the reservoir. Because this work mostly concen-trates on the regions thought to contain uniform CO2 saturation, a Gassmann model with a
Figure 2.12: Estimated CO2 saturation against thickness of CO2 layer. Saturation is estimated to be high apart from thin capillary fringe at the base of the layer. Solid line = saturation at thickness above base. Dashed line = mean saturation of layer. Figure adapted from Chadwick et al. (2005).
Reuss-averaged effective fluid bulk modulus is used to calculate the seismic velocity for CO2 saturated sandstone in this analysis. However, it is important to stress that this estimate is a lower bound, and that changes in the distribution of CO2 can cause the velocity of seismic waves through CO2 saturated media to increase. The patchy saturation model acts as an upper bound for this velocity.
Variations in pore fluid pressure triggered by CO2 injection could also affect the acoustic ve-locity of CO2 itself. Pore fluid pressure variations have been inferred from temporal changes in amplitude signals at the Snøvit CO2 injection site (Eiken et al., 2011). However, no such changes have been observed within the Sleipner field, which is consistent with the high per-meabilities and porosities of the Utsira formation (Chadwick et al., 2005).
Estimates of the acoustic velocity of a sandstone layer that is uniformly saturated with CO2
calculated using these models lie between 1400 and 1500 m s−1 (Arts et al., 2004; Chadwick et al., 2005; Ghaderi & Landro, 2009; Williams & Chadwick, 2012). There are two significant outliers of 1600 m s−1 and 1150 m s−1 (Eiken et al., 2000; Carcione et al., 2006). Here, the Gassmann model for uniformly saturated CO2 is used to obtain a value of 1428 ± 95 m s−1 for a CO2 saturation of 80 %. The quoted uncertainty reflects the range of estimates found in the literature for different input parameters (Appendix A). This value embraces almost all of the estimates that are based on seismic observations as well as those estimated from rock physics modelling.