An Experimental Study on the Influence of
Fluid Saturation on the Attenuation
Coefficient of the First Dilatational Wave in
Standard Sand Saturated by an Oil-Water
Mixture
Chi-Chin Yang, Po-Chia Chen, and Wei-Cheng Lo
Department of Hydraulic and Ocean Engineering, National
Cheng Kung University, Tainan 701, Taiwan
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Outline

Introduction

Literature Review

Experimental Setup and Procedures

Theoretical Model

Results and Discussions

Conclusions
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Introduction (1/2)

Acoustic wave phenomena in fluid-containing porous media have received
considerable attention in recent years, not only because of their practical
importance in reservoir engineering, but also because of an increasing scientific
awareness of poroelastic behavior in groundwater aquifers.
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Introduction (2/2)

Propagation and attenuation characteristics of elastics waves have been applied to
measure the subsurface hydrological and geological parameters (Schrefler and
Zhan, 1991; Cosenza et al., 2002).

Energy of elastic waves has been applied to enhance the recovery of petroleum
(Beresnev and Johnson, 1994) and aquifer remediation (Lo et al., 2005)
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Literature Review (1/2)

The classical work of Biot (1956) showed that two different kinds of dilatational
waves can be found to propagate in an elastic porous medium bearing a viscous,
compressible fluid.

Brutsaert (1964) first extended upon Biot’s theory into a more complex system
wherein there are immiscible fluids permeating in soils.
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Literature Review (2/2)

Lo et al. (2005) used continuum theory to establish the theoretical model for elastic
wave propagation through unsaturated porous media;

Three different motional modes of dilatational waves were showed to exist, which
are denoted as the first, second, and third dilatational waves in the descending
order of wave speed.
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Objective

The objective of this study is to investigate the effect of the viscosity of pore
immiscible fluid mixtures on the attenuation coefficient of the first dilatational wave
in standard sand.

The computed values from our experimental study will be compared with the
theoretical values predicted by Lo et al. (2005).
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Experimental Setup and Procedures (1/3)
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Experimental Setup and Procedures(2/3)

Data Collection
Acoustic Detections

Signal generator
Hydrophone
Soil moisture
sensors
Amplifier
Signal spectrum
analyzer
Data logger
Loudspeaker
Computer
The Brands We Use:
 Signal generator: Protek 9305 Digital Synthesis Arbitrary Function
Generator/Counter
 Amplifier: ALTEC LENSING
 Moisture sensors: DECAGON
 Speaker: ALTEC LENSING
DEVICES (EC-5)
 Hydrophone: Brüel & Kjær
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Experimental Setup and Procedures (3/3)

The pore immiscible fluid mixtures are diesel-water and soybean oil-water.

Starting from an oil-saturated scenario and then gradually increasing water
saturation in a five-centimeter increment until the test sand sample fully
saturated by water nearly.

Five excitation frequencies were examined with output signal wave being
three cycles (Frequencies: 1500Hz, 2000Hz, 2500Hz, 3000Hz, and 3500Hz)

20 measurements were recorded with every
frequencies.
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change in water depth and
Theoretical Model
Lo et al.(2005) model:
Solid:
 e
 s s
t
2
 1
 A11 (
 2
t
2
 A22 (
2
t
2
2

t
 e
2
)  A12 (
2

t
2
4
3
 2
2
2
)  R11 (
 1
t
t

2
e
t
 e

t
2
 1
2
2
)  A21 (
)  R 22 (
 2
t

t
e
t
2
 e
2

t
2
)
)
G )  e  a12   1  a13   2 (1.1)
2
2
2
coefficients
related to inertial drag
coefficients related to
viscous drag
Fluid 2:
Fluid 1:
 1 1
t
2
 ( a11 
elastic coefficients
 1
 e
2
2
 1
2
 A11 (
t
2
 e

t
2
 2
2
2
)  A12 (
t
 e
2

2
t
2
)  R11 (
 1
t

e
t
 2
2
)  2 2
t
2
2
 A21 (
 a12  e  a 22   1  a 23   2 (1.2)
2
2
 1
t
2
 e

t
2
 2
2
2
)  A22 (
t
2
 e
2

t
2
)  R 22 (
 2
t

 a13  e  a 23   1  a 33   2 (1.3)
2
2
2
ur r
r   u s dilatation of the soil phase
ur ur
ur e uu
 1    u 1 ；  2    u 2 dilatation of the fluid phase1 and pha se2
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2
11
e
t
)
Theoretical Values
Elastic and hydrological parameters
of oil, water, and solid
Fitting parameter data by RETC
Dispersion relation obtained by Lo et al.(2005)
Attenuation
coefficient
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Results and Discussions (1/7)

The value of the attenuation coefficient of the first dilatational wave is the average
one between two hydrophones, such as H1 and H3 .

The value of fluid saturation is the average one between two water moisture
sensors.
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Results and Discussions (2/7)
0.4
Diesel
Theoretical Values
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
Water Saturation
Attenuation Coefficient (1/m)
0.5
2000Hz
0.5
Diesel
0.4
Theoretical Values
0.3
0.2
0.1
0
0
0.2
Diesel
0.3
Theoretical Values
0.2
0.1
0
0.2
0.4
0.6
Water Saturation
0.8
0.6
0.8
1
3000Hz
0.4
0
0.4
Water Saturation
2500Hz
0.5
1
Attenuation Coefficient (1/m)
Attenuation Coefficient (1/m)
Attenuation Coefficient (1/m)
1500Hz
0.5
0.4
Diesel
0.3
Theoretical Values
0.2
0.1
0
0
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0.2
0.4
0.6
Water Saturation
0.8
1
Results and Discussions (3/7)
Attenuation Coefficient (1/m)
3500Hz

0.5
Diesel
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Water Saturation
0.8
1
The trend of the curve of experimental values is similar to that of
theoretical values, especially at high frequencies.

The qualitative variations in the experimental and theoretical values may be
partially due to the cause that the water saturation is calculated as the
average one in the experiment.
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Results and Discussions (4/7)
2000Hz
0.6
0.5
0.4
0.3
Soybean Oil
0.2
Theoretical Values
0.1
0
0
0.2
0.4
0.6
0.8
Attenuation Coefficient (1/m)
Attenuation Coefficient (1/m)
1500Hz
0.5
0.4
0.3
Soybean Oil
0.2
Theoretical Values
0.1
0
0
Theoretical Values
0.4
0.6
0.8
Attenuation Coefficient (1/m)
Soybean Oil
0.2
0.4
0.6
0.8
3000Hz
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
Water Saturation
Water Saturation
2500Hz
Attenuation Coefficient (1/m)
0.6
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Soybean Oil
Theoretical Values
0
Water Saturation
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0.2
0.4
0.6
Water Saturation
0.8
Attenuation Coefficient (1/m)
Results and Discussions (5/7)
3500Hz
0.8
0.7
0.6
0.5
0.4
Soybean Oil
0.3
Theoretical Values
0.2
0.1
0
0
0.2
0.4
0.6
0.8
water saturation
The experimental values are larger than the theoretical values.
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Results and Discussions (6/7)
2000Hz
0.6
0.5
0.4
0.3
Soybean Oil
0.2
Diesel
0.1
0
0
0.2
0.4
0.6
0.8
Water Saturation
Attenuation Coefficient (1/m)
Attenuation Coefficient (1/m)
1500Hz
0.6
0.5
0.4
0.3
Soybean Oil
0.2
Diesel
0.1
0
0
0.2
0.4
Soybean Oil
Diesel
0.4
0.6
Water Saturation
0.8
Attenuation Coefficient (1/m)
Attenuation Coefficient (1/m)
3000Hz
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.2
0.8
Water Saturation
2500Hz
0
0.6
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Soybean Oil
Diesel
0
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0.2
0.4
0.6
Water Saturation
0.8
Results and Discussions (7/7)
Attenuation Coefficient (1/m)
3500Hz
0.8
0.7
0.6
0.5
0.4
Soybean Oil
0.3
Diesel
0.2
0.1
0
0
0.2
0.4
0.6
0.8
Water Saturation
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Conclusions

The effect of pore fluid viscosity on the attenuation coefficient of the first
dilatational wave in standard sand saturated by two immiscible fluids was
investigated experimentally.

It was shown that the experimental data qualitatively agrees with the theoretical
values by Lo et al.(2005).

The quantitative variations in experimental and theoretical values may be due to
the consolidated state of porous media and non-uniform fluid saturation.
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Thank you
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