Figures

	Figure 1. Schematic diagram of a harmonic loading applied to a rock sample. T denotes the torque applied to one end of the sample. The resulting stress, σ (red) lags behind the strain, ε (blue) by a phase angle δ.
	Figure 2. Shale samples cut in specific directions to compute Č44=Č55 and Č66.
	Figure 3. The shear (a) storage modulus (C'55), (b) inverse quality factor (1/Q55), (c) C'66, and (d) 1/Q66 of the kerogen-rich shale.
	Figure 4. (a) C'55 (triangles), C'66 (squares) and γ (diamonds) (b) Q55 (triangles), Q66 (squares) and γQ (circles) of the kerogen-rich shale at a frequency of 0.3 Hz.
	Figure 5. The SH-wave (a) velocity anisotropy parameter γ, and (b) attenuation anisotropy parameter γQ in the kerogen-rich shale.
	Figure 6. C'55 of the lean shale measured under (a) confining axial stress and (b) constant axial stress.

Introduction

A vast unexploited source of hydrocarbons is oil shales, i.e., shales rich in kerogen. The Schlumberger Oilfield Glossary defines kerogen as "the naturally occurring, solid, insoluble organic matter that occurs in source rocks and can yield oil upon heating." The US Office of Naval Petroleum and Oil Shale Reserves estimates there are some 1.6 trillion barrels of oil contained in oil shales around the world, with 60-70% of reserves (1.0-1.2 trillion barrels) in the United States. Technical challenges and environmental concerns, however, hinder their exploitation. Environmental considerations, for example, have rendered surface-mining unfeasible. This calls for in-situ recovery, which poses new technical challenges. The most promising in-situ project is being carried out by Shell Oil Company under the name of the Mahogany Research Project in Colorado, which uses electrical heating. A heating element is lowered into the well and allowed to heat the kerogen over time, slowly converting it into oils and gases, which are then pumped to the surface.

Seismic techniques can play an important role in monitoring changes in these oil shale reservoirs. Heating and steamflooding will change physical properties such as modulus, anisotropy, and attenuation, which can have a substantial effect on seismic wave propagation. The response of oil shales under varying temperature and pressure to seismic waves, however, is not well understood. To address this problem, we study the shear behavior of oil shales in the seismic frequency band by conducting torsional experiments under varying temperature and frequency.

The Experiment

Measurements are carried out using a shear rheometer. The rock sample is clamped at both ends, and measurements are conducted with the sample dry and under no lateral confining stress. A sinusoidal torsional strain is applied on one end, and the resulting stress is recorded on the other end, which is fixed. The experiment is schematically shown in Figure 1. When a viscoelastic material is subjected to a sinusoidally varying strain, a steady state will be reached when the resulting stress is also sinusoidal, with the same angular frequency, but with a phase lag of δ, which is a measure of attenuation of that body (O'Connell and Budiansky, 1978). For an elastic material, δ=0, and for a viscous fluid, δ can approach π/2, while δ for a viscoelastic body has a value between these two limits. Note that the minimum value for Q depends on how it is defined. For extremely lossy materials, Q derived from phase angle can approach 0 (O'Connell and Budiansky, 1978).

The in-phase part of the stress, σ', gives the "real" or the "storage" modulus, G', and the out-of-phase part of the stress gives the "imaginary" or "loss" modulus, G",

G' = σ'/ε, .........(1)

G" = σ"/ε. .........(2)

The quality factor, Q, which is inversely proportional to the attenuation coefficient, is defined as (O'Connell and Budiansky, 1978)

Q ≈ 1/tanδ = 2π W/W = G'/G". ......(3)

where W is the maximum elastic stored energy during a cycle of loading at the frequency under consideration and W is the energy dissipated per cycle.

Shale Samples

We analyzed two samples of shale from the same formation (Green River Formation, Colorado) with different amounts of organic content, one with ≈30% and the other with ≈5% organic content. We also examined the influence on shear wave velocity anisotropy and attenuation anisotropy. The anisotropy studies were conducted by using samples cut along three orthogonal planes (Figure 2). A sample cut parallel to the symmetry axis is used to measure the complex stiffness Č₄₄=Č₅₅ (Figure 2). As the shale is assumed to be transversely isotropic (TI), a sample cut in the vertical symmetry plane with its long axis orthogonal to the symmetry axis (Figure 2) would give Č₄₄=Č₅₅ as well. In fact, two kerogen-rich samples contained in the vertical symmetry plane, one oriented along the symmetry axis and the other perpendicular to it, gave strikingly similar results for the whole range of temperatures and frequencies studied. This supports our assumption that the shales are very likely TI. A sample cut in the isotropy plane, as shown in Figure 2, is used to obtain Č₆₆.

Dynamic mechanical analysis of the shales was carried out for temperatures ranging from 30°C to 350°C at 20°C increments, with the frequency varying from 0.01 to 80 Hz in increments of 0.1 on the log₁₀ scale. All the measurements are carried out in the linear viscoelastic regime, at a constant strain of 8x10^-5, under a variable applied axial stress which does not allow the sample to expand vertically. This is similar to reservoir recovery conditions where the shale is heated but its expansion is restricted.

Kerogen-Rich Shale

Figures 3a-b show the real part, C'₅₅, and inverse quality factor, 1/Q₅₅, respectively, for the kerogen-rich shale, and Figures 3c-d are for Č₆₆. Velocity dispersion is relatively weak in these kerogen-rich shales evident from the small change in C'₅₅ and C'₆₆ with frequency. Both storage moduli (C'₅₅ and C'₆₆) increase with frequency, even though the increase is small with the most noticeable change in the vicinity of 150°C. At low frequencies, the shales have time to undergo deformation (relaxed state), which reduces the storage modulus, while with increasing frequency, the time available for the particles to move decreases, making the shale stiffer. Within the seismic bandwidth, however, dispersion is essentially absent and Q can be safely assumed as a constant. So the observed attenuation likely is predominantly caused by frictional dissipation owing to relative motions at grain boundaries, or at interfaces between mineral and kerogen surfaces.

Both moduli (C'₅₅ and C'₆₆) and attenuation (1/Q₅₅ and 1/Q₆₆) show a marked change with temperature. Figure 4 shows a comparison of the moduli and quality factors (along the two directions) for 0.3 Hz. C'₅₅ and C'₆₆ both drop sharply with increasing temperature up to ≈200°C, probably caused by the liquefaction of kerogen in the shale. Carcione (2000) suggested that Č₅₅ is mostly controlled by the isotropic kerogen in the shales while Č₆₆ is dominated by the clay in the layering. This explains the greater drop in C'₅₅ than that in C'₆₆. As the kerogen melts, it facilitates relative sliding between the clay layers, thus making the shale softer and more lossy as a result of increased frictional sliding. This lowers the quality factors, as seen in Figure 4b, where they drop from ≈40 at room temperature to below 5 at ≈150°C. With further increase in temperature, the kerogen is altered and partially expelled, thereby increasing the stiffness (Figure 4a) and decreasing any frictional losses as well, as evident from the increase in Q, as seen in Figure 4b.

It is especially convenient to analyze the above changes in terms of the anisotropy parameters γ and γ_Q, which can be extracted from shear-wave seismic data. The difference in moduli and attenuation along the two directions can be conveniently represented using Thomsen's SH velocity anisotropy parameter γ (Thomsen, 1986) and the SH-wave attenuation anisotropy parameter γ_Q defined by Zhu and Tsvankin (2006) as the fractional difference between the attenuation coefficients in directions orthogonal and parallel to the symmetry axis:

γ_Q = (Q₅₅-Q₆₆)/Q₆₆ .........(4)

As mentioned above, the magnitude of the effect of melting and evaporation of kerogen on C'₅₅ and C'₆₆ is different. This translates to a significant change in γ as seen in Figure 4a. As the kerogen melts, C'₅₅ drops significantly compared to C'₆₆, resulting in a jump in γ. With further increase in temperature, kerogen starts evaporating, which results in a drop in γ as the shale becomes less compliant. As with velocity anisotropy, attenuation anisotropy also shows a large change with temperature (γ_Q in Figure 4b), which again could dramatically change seismic amplitudes.

γ and γ_Q for the whole frequency and temperature range are shown in Figures 5a and 5b, respectively. SH-wave velocity anisotropy can be significantly strong, attaining values as high as 3; attenuation anisotropy can also be significant, with values nearing 2. Note that the sign of γ_Q can change. In laboratory and field conditions, γ has been found to be less than 0.5, which is significantly lower than the maximum value of γ observed by us. Note that the velocity anisotropy parameter, γ, changes by a factor of 10 which is significant and could be detectable in 4D-studies. The weak frequency dependence of Č₅₅ and Č₆₆ translates to a generally weak dependence of γ and γ_Q on frequency. γ_Q, however, shows a moderately strong dependence on frequency at high temperatures.

This experiment also shows the contribution of layering to the anisotropy of TI media. Bakulin (2003) has shown that the effect of layering on VTI anisotropy is of second order compared to that of intrinsic anisotropy, but if the contrast in moduli between the different layers is large, the layer-induced anisotropy can be significant. At room temperatures, the kerogen is solid and so the contrast in shear modulus of the solid clay (and carbonate) layers and the kerogen layers is not significant. This results in a low value of γ at room temperatures (Figure 5a). With increase in temperature, the kerogen progressively melts, thereby increasing the contrast between the layers. This results in a notable increase in γ caused by layering.

Lean Shale

C'₅₅ for the lean shale under confining axial stress is shown in Figure 6a. The general trends for lean shale are similar to those for the kerogen-rich shale. The magnitudes of lean-shale moduli, however, are larger than those of the organic-rich shales because the larger clay content in the lean shale increases its modulus. This might be used as a distinguishing factor between lean and kerogen-rich shales.

Velocity dispersion is weak (Figures 6a), especially within the seismic band. Attenuation is also weakly dependent on frequency. This weak frequency dependence at intermediate temperatures (around 150°C) of attenuation implies that friction may be the dominant attenuation mechanism. Later, we will give more evidence in favor of frictional attenuation. Additional experiments, however, are necessary to find out if other mechanisms, such as "squirt flow" of fluids and viscous relaxation, are playing important roles.

With increase in temperature, till about 200°C, C'₅₅ drops more rapidly than does C'₆₆. This fall in the storage moduli is most probably due to the liquefaction of the small amount of kerogen sandwiched between the clay layers. As discussed earlier in the previous section, any change to the kerogen would influence Č₅₅ much more than Č₆₆, which explains the greater drop in C'₅₅. Below 200°C, the liquefaction of kerogen not only softens the rock, bringing down C'₅₅, but also decreases the quality factor, Q₅₅ sharply. This is because the liquid kerogen facilitates sliding, thereby decreasing the efficiency of transfer of mechanical energy between clay particles and increasing frictional loss. Like the kerogen-rich shales, these effects can be better seen by the changes in anisotropy (γ and γ_Q).

To test if friction is the dominant loss mechanism, we conducted another set of measurements to find C'₅₅ under constant axial stress, results for which are shown in Figure 6b. If friction were indeed the dominant loss mechanism, two major changes would occur. First, C'₅₅ would decrease in general. Second, for temperatures above 200°C, just as when the kerogen is lost, C'₅₅ under constant axial stress would continue to decrease. This is because under constant axial stress, after loss of some kerogen, the voids left behind are retained, which decreases C'₅₅ further. In contrast, under increasing axial stress, the voids are occupied by the expanding clay minerals as the rock is not allowed to expand. Both these effects can be seen by comparing Figures 6a and 6b, which support friction as the dominant attenuation mechanism.

Discussion and Conclusions

In-situ recovery of oil from oil shales involves thermal processes which melt the kerogen. These changes, therefore, should have a more pronounced effect on the shear-wave properties of the shales than the P-wave properties. So a study of the shear properties of these rocks is more attractive than the study of their bulk properties and thus makes acquisition of multicomponent seismic data all the more important. Our shear property measurements, as a function of temperature, should be representative of the conditions encountered during in-situ thermal cracking and steamflooding of oil shale reservoirs. Moreover, as our measurements encompass the seismic band, they should be more representative of the seismic properties of oil shales in the field.

The strong temperature dependence of the mechanical properties of oil shales makes 4D-9C seismic analysis promising. The melting of kerogen can bring down the shear velocity significantly, by as high as five times in some cases. Their quality factor can also drop by a factor of 10 when going from room temperature to ≈150°C. So reservoir areas affected by heat should show a noticeable drop in velocities accompanied by significant increase in attenuation. Seismic data can be exploited to estimate the physical state of the rock, thus the local temperature. As has already been used in many studies, the direction and extent of the steam front can also be detected from seismic data.

Oil shales have an additional property to be exploited - anisotropy. The temperature influence on C'₅₅ and C'₆₆ differs, making anisotropy an important attribute. The large changes in anisotropy observed by us could be visible in seismic data. For example, there should be a notable change in the nonhyperbolic moveout of SS-waves. Our measurements also serve the purpose of studying the contribution of layering to the anisotropy of shales, where the melting kerogen increases the contrast in properties between the layers, thereby increasing the anisotropy.

The original kerogen content in a shale also influences the behavior of the shale with temperature. From our study, we see that lean-shales have higher storage moduli and higher Q than more organic rich shales. Also the change in velocity anisotropy and attenuation anisotropy is greater in shales richer in organic content. This can potentially be used to estimate the organic content of shales.

References

Balkulin, A., 2003, Intrinsic and layer-induced vertical transverse isotropy: Geophysics, v. 68/5, p. 1708-1713.

Carcione, J.M., 2000, A model for seismic velocity and attenuation in petroleum source rocks: Geophysics, v. 65/4, p. 1080-1092.

O'Connell, R.J., and B. Budiansky, 1978, Measures of dissipation in viscoelastic media: Geophysical Research Letters, v. 5/1, p. 5-8.

Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, v. 51/10, p. 1954-1966.

Zhu, Y., and I. Tsvankin, 2006, Plane-wave propagation in attenuative transversely isotropic media: Geophysics, v. 71/2, p. T17-T30.

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