Page 196 - Fundamentals of Gas Shale Reservoirs

176 GEOMECHANICS OF GAS SHALES

C 44 V sv 2 (8.4) TABLE 8.1 Anisotropic parameters obtained for various
types of shales in different studies
C 12 C 11 C 66 (8.5) Types of shales ε γ δ

C 55 C 44 (8.6) Jurassic shale (Hornby, 1995) 0.24 0.47 0.11
Kimmeridge shale (Hornby, 1995)
0.20
0.58
0.38
Cretaceous shale (Jones and 0.28 0.39 0.06
where ρ is the density of rocks, V and V are the horizontal Wang, 1981)
ph pv
and vertical P‐wave velocities and V and V are horizontal Maikop clay (Slater, 1997) 0.25 0.73 0.1
sh sv
and vertical S‐wave velocities. The estimation of the fifth Pirre shale (White et al., 1983) 0.2 0.18 0.3
independent elastic constant C requires various measure­ Mesaverde clayshale (Roberson 0.33 0.73 0.58
13
ments of P‐ and S‐wave velocity at an off‐axis angle. Thus, and Corrigan, 1983)
this parameter can be estimated by the method presented by Wills Point shale (Roberson and 0.22 0.32 0.28
Helbig (1994). Corrigan, 1983)
It is convenient to describe anisotropy in terms of the
anisotropy parameters of Thomsen (1986). Thomsen intro­
duced a more effective and scientific measure of anisotropy apply this type of analysis to study the anisotropy of gas
in 1986. He introduced three constants ε, γ, and δ as effec­ shale reservoirs.
tive parameters for measuring anisotropy. According to As location accuracy depends on the quality of the stack
Thomsen, the δ parameter is the most critical measure of of all seismic traces used for processing, utilization of an
anisotropy, and it does not involve the horizontal velocity in anisotropic velocity model should result in a better move‐out
its definition. Therefore measuring δ is very important for of the traces, which should subsequently result in a positive
processes like depth imaging. Thomsen’s parameters are effect on both the amplitude of a seismic event as well as the
presented as follows:
signal‐to‐noise ratio.
C 11 C 33 (8.7)
2 C 33 8.4 WELLBORE INSTABILITY IN GAS SHALE
RESERVOIRS
C 66 C 44 (8.8)
2 C 44 The strength properties of bedded rocks have been known
for many years. In fact, the results of a number of studies
(C C ) 2 (C C ) 2 demonstrated how most of the sedimentary rocks, such as
13 44 33 44 . (8.9) shale, display a strong anisotropy in their strength behavior
(
2 CC C )
33 33 44 resulting in instability in the weaker strength direction
(Colak and Unlu, 2004; Donath, 1964; Horino and Ellickson,
While Thomsen’s parameter ε takes only positive values, 1970; Kwasniewski, 1993; McLamore and Gray, 1967;
δ is observed to have both positive and negative values, a Ramamurthy, 1993). Therefore, compressive strength and
phenomenon that is not well understood. Parameter δ deformability of these rocks need to be estimated as impor­
appears to be sensitive to the conformity of the contact tant design parameters. In fact, deformation and strength
regions between clay particles as well as to the extent of dis­ behavior of these materials are strongly dependent on loading
order in their orientation (Sayers, 2005). Anisotropy for orientation with respect to their bedding planes. As was
wave propagation in a vertical direction is mostly governed mentioned in previous section, this type of behavior is
by this parameter. Downhole applications, utilizing domi­ referred to as VTI behavior (Hudson and Harrison, 1997),
nantly horizontal propagation, on the other hand, are more observed in many types of formations including shale rocks,
affected by parameter ε, which does not seem to be corre­ in which five independent stiffness parameters need to
lated to δ (Thomsen, 1986). However, as the signal travels to be determined. Jaeger (1960) gave a thorough analysis of
surface stations with larger offsets, the propagation path various loading scenarios that explain bedding failure.
involves an increasing horizontal component, therefore Considerable attention has been paid to the strength differ­
increasing the influence of ε. ences, failure modes, and failure criteria of anisotropic rocks
If these anisotropy parameters can be determined (Bagheripour et al., 2011; Gatelier et al., 2002; Jyh Jong
through seismic measurements by first arrival time pick­ et al., 1997; Nasseri et al., 2003; Nova, 1980; Saroglou and
ing of P‐ and S‐wave in horizontal and vertical directions, Tsiambaos, 2008; Tavallali and Vervoort, 2010; Tien et al.,
VTI parameters of shales can be determined. Table 8.1 2006). A considerable amount of research work has have
presents the results of several attempts made in the past to also been carried out to measure the strength anisotropy of