Download Effect of pore-fluid on attenuation of elastic waves in rock types from

Available online at www.pelagiaresearchlibrary.com
Pelagia Research Library
Advances in Applied Science Research, 2013, 4(2):19-24
ISSN: 0976-8610
CODEN (USA): AASRFC
Effect of pore-fluid on attenuation of elastic waves in rock types from
southwestern Nigeria
Olorode D. O. and Olatinsu O. B.
Department of Physics, Faculty of Science, University of Lagos, Lagos, Nigeria
_____________________________________________________________________________________________
ABSTRACT
Laboratory attenuation measurements using pulse transmission coupled with spectral amplitude wave-ratio
technique were carried out on three sedimentary rocks namely: shale, sandstone and glauconite from Ewekoro in
Southwestern Nigeria. Attenuation coefficient (k) was measured in the frequency range of 100 Hz to 2 kHz. The rock
materials were then soaked in water and kerosene (light-oil) respectively, to observe the trends in their attenuation
patterns. In the natural rock samples, attenuation increases steadily with frequency for sandstone and glauconite but
decreases in shale. In water–saturated rock materials, shale shows no attenuation dispersion which may be due to
the pin-points getting easily disrupted by pore-fluid saturation; sandstone shows a decrease from its natural level;
which implies a strong dependence of attenuation on pore-fluid; glauconite manifests a step-wise decrease and later
increases around 1 kHz. The rock samples were saturated with kerosene (light oil) and their characteristic curves
changed. Shale completely dissolved making it impossible to observe its attenuation pattern; sandstone attenuates
more than glauconite. These results show that pore-fluid in the different rock materials have great influence on the
attenuation coefficient of the materials.
Key words: Attenuation coefficient, pore-fluid, pulse transmission, sedimentary rocks, seismic waves.
_____________________________________________________________________________________________
INTRODUCTION
The fact that elastic waves propagating through the earth are attenuated is a common observation. As these elastic
waves travel deeper they lose energy unlike in spherical spreading, where energy is spread across a wider area, and
reflection and transmission of energy at boundaries, where redistribution takes place in the upward or downward
directions. This energy loss depends on frequency, that is higher frequencies are absorbed more rapidly than lower
frequencies. In addition, attenuation appears to vary with the lithology of the medium [1]. Elastic wave attenuation
has great potential as a tool to yield a better understanding of the anelastic properties, and hence the physical state,
of rocks in the earth. Because of this potential, an expanding body of laboratory work has concentrated on bringing
to fruition the diagnostic capabilities of attenuation measurements [2-5]. Two important reasons could be advanced
for the need to investigate and understand the attenuation properties of the earth. Firstly, as elastic waves propagate
through the subsurface, their amplitudes are reduced. Secondly, attenuation characteristics, when determined, could
reveal useful information on the type of rock as well the presence and degree of fluid saturation of rocks.
There is an appreciable overlap in the attenuation values of different rocks, but it is evident that sedimentary rocks
are generally more absorptive than other types of rock. Amplitude analysis of elastic waves in sedimentary rocks is a
common practice in rock Physics. Changes in reservoir seismic properties can be connected with fluid type and
changes within the rock [6]. Low-frequency wave propagation in partially saturated rocks is still not well understood
because of the lack of precise and reliable experimental techniques [7]. Biot theory which is the most commonly
used theory for studying wave propagation in saturated porous rocks is not without its limitation. This is because the
theory estimates attenuation fairly for frequencies higher than seismic frequencies. To resolve the problem of
limitation of very important to develop simple and inexpensive experimental approach to measure attenuation at low
19
Pelagia Research Library
Olorode D. O. et al
Adv. Appl. Sci. Res., 2013, 4(2):19-24
_____________________________________________________________________________
frequencies. Our studies analyse wave attenuation in limestone, shale and glauconite of Ewekoro Formation,
southwestern Nigeria. The frequency range is from 100 Hz to 2 kHz.
2. Theory of Attenuation in Rocks
A commonly used measure of attenuation is the attenuation coefficient α , which is the exponential decay constant
of the amplitude of a plane wave propagating in a homogeneous medium. The amplitude of this plane wave may be
given as
Ar = Ao exp(−αr )
(1)
where Ar is the amplitude at any distance r from the source,
attenuation coefficient.
Ao is the initial or reference amplitude and α is the
Attenuation coefficient is expressed as
α=
πf
(2)
Qv
where Q is the wave quality factor and is the other commonly used measure of attenuation,
is the frequency.
v is the velocity and f
The quality factor Q is defined as
Q=
Q=
(3)
2π
∆E
E
(4)
For a single cycle
Q=
π
δ
(5)
where δ is the logarithmic decrement and is defined as the natural logarithm of the ratio of the amplitude of two
consecutive cycles, i.e.
δ = ln
δ = αλ =
(6)
αv
(7)
f
Laboratory measurements of attenuation in rocks show that Q correlates with rock type and fluid type, hence the
estimation of Q can be used as a diagnostic tool for rock type discrimination and the effect of fluid. Q values for
most sedimentary rocks ranges from 20 to 200 [8]. The lower value of Q indicates higher attenuation while higher
Q value means the opposite.
The spectral ratio technique originally developed by [9] was used to estimate P and S wave attenuation. This
procedure assumes that Q is constant over the experimental frequency range and thus it is frequency independent.
Hence there is no consideration for dispersion in the spectral ratio model. However, laboratory experiments
conducted on several natural rocks have revealed different dispersion and attenuation mechanisms in rocks as caused
by intrinsic anelasticity, scattering, and diffraction which can cause changes in velocities and attenuation and as a
result affect Q estimates. The accuracy of determining Q across the frequency spectrum is a function of the
dispersion characteristics of the waves, which depends on the frequency and the nature of the rocks that disperse the
waves.
20
Pelagia Research Library
Olorode D. O. et al
Adv. Appl. Sci. Res., 2013, 4(2):19-24
_____________________________________________________________________________
Incorporating the dependence on frequency into attenuation equation (1), leads to
Ar = GRAo exp(−αr )
Ar = GRAo exp(−
πfr
Qv
(8)
)
(9)
where G and R are the geometric spreading factor and the energy partitioning respectively at interface.
MATERIALS AND METHODS
Laboratory measurements were carried out on samples of sandstone, glauconite and shale collected from Ewekoro
near Abeokuta, Ogun state, Nigeria. These were made available in a prepared form with dimensions 8cm × 5cm ×
3.5cm, for use in the laboratory. The experimental set-up is as shown in Figure 1. The experiment was performed
using pulse transmission technique in which the amplitude decay of elastic wave signals travelling through a rock
sample is measured. Only one way transmission effects were measured. For the fluid saturation measurement, the
samples were immersed in the fluid for 24 hours to ensure the uniformity of saturation. The pulse transmission
technique is most suited for use in saturated samples, provided correction can be made for geometric factors such as
beam (waves) spreading and reflection. We used the pulse transmission technique and measure attenuation of the
sample by using equation (3).
Figure 1: Experimental setup.
The sine-audio signal generator generates the sinusoidal wave, which is passed into the rock sample via transducers
in contact with opposite faces of the rock samples. The transducer alloy pair was used to conduct signals from signal
generator to the rock sample and from the other face of the rock sample to the Y channel of the oscilloscope. Each
plate has a connecting wire soldered to it for wave’s transmission. Proper care was taken to insulate the rock
samples from any unwanted stray signals. The rocks samples were connected electrically by gently pressing with a
G-camp on the transducers for proper connection to the rock samples. A double-beam oscilloscope was used to
analyze the elastic waves. Its Y1 channel was used to observe the input signal directly from the signal generator
while the output from the rock sample was fed into the Y2 channel of the oscilloscope. The amplitudes of the
incident (Ai) and transmitted (At) waves were recorded and a measure of attenuation made using the expression in
Equation (3).
RESULTS AND DISCUSSION
Figure 2 show the plot of attenuation for the dry rock samples. It is observed that attenuation increases steadily with
frequency for sandstone. For glauconite, there is a slight drop in attenuation from 100-400 Hz and thereafter
21
Pelagia Research Library
Olorode D. O. et al
Adv. Appl. Sci. Res., 2013, 4(2):19-24
_____________________________________________________________________________
increases with frequency. Attenuation in the dry shale sample decreases to about 1 kHz and shoots up again to 1.5
kHz and decreases further to around 2 kHz.
Glauconite_dry
Shale_dry
sandstone_dry
-0.4
-0.6
-0.8
Attenuation
-1.0
-1.2
-1.4
-1.6
-1.8
-2.0
-2.2
-2.4
-2.6
0
500
1000
1500
2000
Frequency Hz
Figure 2: Plots of attenuation versus frequency for the dry rocks.
There is clear deviation in the behavior of the rocks from the dry condition. Shale showed no attenuation dispersion
which may be due to the fact that its pin-points get easily disrupted by pore-fluid saturation. Water-saturated
sandstone shows an almost opposite response (decrease in attenuation) to that in the dry condition which means a
strong dependence of attenuation dispersion on pore fluids. But for glauconite, the response of the saturated sample
shows a stepwise decrease and later increases around 1 kHz.
Glauconite_H2O
Shale_H20
Sandstone_H20
0.0
-0.2
-0.4
-0.6
Attenuation
-0.8
-1.0
-1.2
-1.4
-1.6
-1.8
-2.0
-2.2
-2.4
-2.6
-2.8
0
500
1000
1500
2000
Frequency
Figure 3: Plots
of attenuation
versusfor
frequency
for water-saturated
samples.
Plots of attenuation
versus
frequency
water-saturated
rockrock
samples.
22
Pelagia Research Library
Olorode D. O. et al
Adv. Appl. Sci. Res., 2013, 4(2):19-24
_____________________________________________________________________________
Figure 3 represent the response of sandstone and glauconite when saturated with light oil (kerosene). Attenuation in
this condition is relatively more than in dry and water-saturated conditions. This is in agreement with previous
works by several authors [10-16]. It is also observed that attenuation dispersion increases for both rock types across
the frequency range of measurement. Hence there is a clear discrimination in the behavior of the two rocks is in
water and oil-saturated conditions. Shale completely dissolved in kerosene and as a result it was not possible to
study its attenuation dispersion when saturated with this light oil.
Glauconite_oil
Sandstone_oil
-1.3
-1.4
-1.5
Attenuation
-1.6
-1.7
-1.8
-1.9
-2.0
-2.1
-2.2
-2.3
-2.4
0
500
1000
1500
2000
Frequency Hz
Figure 4: Attenuation versus Frequency of light oil-saturated sandstone and glauconite
CONCLUSION
The attenuation characteristics of sandstone, shale and glauconite of Ewekoro were investigated in this work. The
three rock types behaved differently in different pore-fluid saturation. At high frequencies, attenuation is higher than
at lower frequencies. In the natural rock samples, sandstone attenuates most followed by shale and the least was
glauconite. This is in agreement with the results obtained by [17] and [18]. When the rock samples were watersaturated, shale attenuates most followed by glauconite and sandstone was the least attenuated. However, when in
kerosene (light oil), sandstone attenuates most, followed by glauconite while shale dissolved completely. Pore-fluid
in the rock matrices has a great influence on the attenuation pattern of the rock materials.
REFERENCES
[1] Chopra, S., Alexev, V, First break, 2004, 22, 31-42.
[2] Dutta, N.C, Odé, Geophysics, 1979, 44, 1777-1788.
[3] Mavko, G.M, Nur, A, Geophysics, 1979, 44(2), 161-178.
[4] Toskӧz, M.N, Johnston, D.H, Timur, A, Geophysics, 1979, 44(4), 681-690.
[5] Johnston, D.H, Toskӧz, M.N, Journal of Geophysical Research, 1980, 85, 925-936.
[6] Adam, L, Batzle, M, Lewallen, K.T, van Wijk, K, Journal of Geophysical Research, 2009, 114, B06208. doi:
10.1029/2008JB005890.
[7] Madonna, C, Tisato, N, Boutareaud, S, Mainprice, D, A new laboratory system for the measurement of low
frequency seismic attenuation, SEG Denver 2010 Annual Meeting, 2675-2680.
[8] Sheriff, R.G, Geldart, L.P; Exploration Seismology Cambridge University Press, 1995.
[9] Toskӧz, M.N, Johnston, D.H, Timur, A, Geophysics, 1979, 44, 681-690.
[10] Wyllie, M.R.J, Gardner, G.H.F, Gregory, A.R, Geophysics, 1962, 27, 569-589.
[11] Gardner, G.H.F, Wyllie, M.P.J, Droschak, D.M, Journal of Petroleum Technology, 1964,16, 189-198.
[12] O’Connell, R.J, Budiansky, B, , Geophysical Research letters, 1978, 5, 5-8.
[13] Winkler, K.W, Nur, A, Geophysical Research Letters, 1979, 6, 1-4.
[14] Murphy, W.F, III, Journal of the Acoustical Society of America, 1982, 71, 1458-1468.
[15] Tittmann, B.R, Nadler, H, Clark, V.A, Ahlberg, L.A, Spencer, T.W, Geophysical Research Letters, 1981, 38,
89-94.
23
Pelagia Research Library
Olorode D. O. et al
Adv. Appl. Sci. Res., 2013, 4(2):19-24
_____________________________________________________________________________
[16] Jones, T.D, Geophysics, 1986, 51, 1939-1953.
[17] Olorode, D. O, Ph. D. Thesis University of Ibadan (Ibadan, Nigeria, 2001).
[18] Umo, J.A, Ph.D. Thesis, University of Ibadan (Ibadan, Nigeria, 1998).
24
Pelagia Research Library