Page 215 - Fundamentals of Gas Shale Reservoirs

PARTIAL SATURATION EFFECTS 195
moduli of kerogen were chosen from the best fit with the laboratory measurements of Bakken ORSs (Vernik and
experimental data as c 11 c 33 98.GPa, c 13 34.GPa, and Nur, 1992).
c 44 c 66 32.GPa. Elastic moduli of shale without organic Another reasonable possibility is to follow Sayers’s (2013a)
matter were chosen to be c 11 85 6.GPa, c 33 65 5.GPa, approach, but instead of the effective field theory, apply the
c 44 24 6.GPa, and c 66 29 7.GPa. The layered medium anisotropic differential effective medium approach (Nishizawa,
model describes the decrease in elastic moduli normal to 1982). While moduli of shale can be chosen as in Vernik and
bedding but shows much gentler decrease with increase of Nur (1992), the fitting of the kerogen moduli can be avoided
kerogen than the moduli calculated from experimentally by using measured moduli recently reported by Yan and Han
measured velocities as can be seen in Figure 9.1. Vernik and (2013). Isotropic elastic moduli of kerogen can be chosen to
Nur (1992) suggested that discontinuities in illite, distrib­ be K = 4.3 GPa and μ = 2.8 GPa, which are the mean values
uted in the form of thin (<0.5 mm) lenticular beds rather than between the upper and lower bounds of kerogen moduli (Yan
solid layers might be responsible for this discrepancy. To and Han, 2013). The results for the two host/inclusion sce­
obtain a better fit, they modified the Backus model by replac­ narios of shale/kerogen and kerogen/shale are shown in
ing illite moduli in the Backus equations for the moduli Figure 9.1 by red and black lines, respectively. The solid,
parallel to bedding with effective moduli that incorporate dashed, and dotted lines correspond to aspect ratio of inclu­
effects of both kerogen and illite and can be used as a param­ sions of 0.5, 0.2, and 0.1. Green dashed‐and‐dotted line shows
eter to fit the experimental data. the theoretical prediction for a shale/kerogen layered medium
Carcione et al. (2011) suggested an alternative model that (Backus, 1962). One can see that the modeling results for the
is based on solid–solid anisotropic Gassmann’s substitution case of kerogen(host)/shale(inclusions) are in good agreement
suggested by Ciz and Shapiro (2007) and accounts for with the experimental data for Bakken Shale shown by solid
anisotropy of the shale framework by generalization of the circles. However, the experimentally measured elastic coeffi­
empirical equation of (Krief et al., 1990) cients of Bazhenov Shale (Vernik and Landis, 1996) (open
squares) exhibit a different trend with the decrease of kerogen
s
c ij m c (1 ) A ij /(1 ) (9.2) volumetric fraction. The trend for the Bazhenov Shale cannot
ij
be modeled with the same coefficients of shale and kerogen as
where indices m and s denote elastic coefficients of shale those used for the Bakken Shale. It is worth noting that Vernik
matrix and shale with zero porosity, respectively. By visual and Landis (1996) also could not model the measured elastic
best fit, the fitting coefficients A were assumed to be equal moduli of the two different shales using the same moduli of
ij
to 1.5 and 4 for the case when i = j = 1 and the cases when inorganic shale and kerogen. They suggested using different
i = j = 4 or 6 and i = 1, j = 3, respectively. moduli for the inorganic shale constituent.
The advantage of the method suggested by Carcione Reliable estimation of elastic moduli of inorganic shale
et al. (2011) is that the solid Gassmann substitution is from its mineralogy and porosity is a long‐standing problem.
independent of the microstructures. An obvious disadvan­ A detailed review of the works on this subject can be found
tage is that the generalization of the Krief equations is in Pervukhina et al. (2011). Carcione et al. (2011) suggested
purely empirical and requires two fitting parameters to inverting the moduli of the Bakken Shale with the known
obtain a good fit. Also, unlike Gassmann’s original fluid kerogen content (Vernik and Nur, 1992) for the moduli of its
substitution, solid substitution is an approximation, whose inorganic matrix. Carcione et al. (2011) reported that the
accuracy depends on the microstructure (Makarynska et al., inversion resulted in physically nonplausible results for 4
2010; Saxena et al., 2013). out of 11 samples. On top of that, the results exhibit strong
Sayers (2013a) suggested using another effective medium scatter, namely, the samples from the adjacent depth 3271–
method of modeling ORS elastic properties that does not 3272 m show changes up to 15, 64, 35, 85, and 15% in the
require any fitting parameters. He used an anisotropic effec­ inverted c , c , c , c , and c moduli, respectively. Further
44
66
13
11
33
tive field theory developed by Sevostianov et al. (2005). The refinements in kerogen modulus measurements and imaging
effective field theory accounts for the effect of ellipsoidal of ORS microstructure might help choose the best way to
heterogeneities and allows one‐particle solution for a trans­ obtain elastic moduli of inorganic shale constituent and
versely isotropic medium. Sayers (2013a) used the same rectification of the theoretical velocity–TOC relations.
elastic anisotropic coefficients of the shale and kerogen iso­
tropic moduli as used in the original paper of Vernik and Nur
(1992). Two cases have been considered. In the first case, the 9.4 PARTIAL SATURATION EFFECTS
shale forms a continuous matrix, which hosts kerogen ellip­
soidal inclusions with aspect ratios of 0.1, 0.2, and 0.5. In the Another important and not well‐understood problem is
second case, the kerogen forms the matrix, which hosts illite how partial saturation of ORS affects their elastic properties.
inclusions of different aspect ratios. Sayers demonstrated To model partial saturation, Carcione et al. (2011) assumed
that the modeling results of the second case scenario are in a that ORSs can be modeled as a shale matrix with the pore
better agreement with the elastic moduli calculated from space filled with kerogen, gas, and oil mixture. They used