Chi-Chin Yang, Po- Chia Chen, and Wei-Cheng Lo

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

National Cheng Kung University

Outline

Introduction

Literature Review

Experimental Setup and Procedures

Theoretical Model

Results and Discussions

Conclusions


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.


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)


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.


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.


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).


Experimental Setup and Procedures (1/3)


Experimental Setup and Procedures(2/3)

The Brands We Use: Signal generator: Protek 9305 Digital Synthesis Arbitrary Function

Generator/Counter Amplifier: ALTEC LENSING Speaker: ALTEC LENSING Hydrophone: Brüel & Kjær

Acoustic Detections Data Collection

Moisture sensors: DECAGON DEVICES (EC-5)

Amplifier

Loudspeaker

Hydrophone

Signal spectrum analyzer

Computer

Soil moisture sensors

Data logger


Signal generator

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 change in water depth and

frequencies.


Theoretical Model

11

2 2 22 2 2 21 2 1

s s 11 12 212 2 2 2 2 2 2

2 22 1 2

22 11 222 2

2 2 211 12 1 13 2

( ) ( ) ( )

( ) ( ) ( )

4 ( ) (1.1)3

e e e eA A At t t t t t t

e e eA R Rt t t t t t

a G e a a

2 2 22 21 1 2 1

1 1 11 12 112 2 2 2 2

2 2 212 22 1 23 2

( ) ( ) ( )

(1.2)

e e eA A Rt t t t t t t

a e a a

2 2 22 22 1 2 2

2 2 21 22 222 2 2 2 2

2 2 213 23 1 33 2

( ) ( ) ( )

(1.3)

e e eA A Rt t t t t t t

a e a a

Fluid 1: Fluid 2:

Solid:

coefficients related to inertial dragcoefficients related to viscous drag

dilatation of the soil phasese uur r

1 1 2u dilatation of the fluid phase1 and phase2

ur ur ur uur2u ；

elastic coefficients


Lo et al.(2005) model:

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

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.




0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.51500Hz

DieselPolynomial (Diesel)Theoretical Values

Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5 2000HzDieselPolynomial (Diesel)Theoretical Values

Water SaturationAtte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5 2500Hz

DieselPolynomial (Diesel)

Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.53000Hz

DieselPolynomial (Diesel)

Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)


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.


0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

3500HzDieselPolynomial (Diesel)

Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.020.040.060.080.1

0.120.140.160.18

1500Hz

Soybean OilPolynomial (Soybean Oil)Theoretical Values

Water Saturation

Atte

nuat

ion

Coe

ffici

ent

(1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.050.1

0.150.2

0.250.3

2000Hz

Soybean OilPolynomial (Soybean Oil)

Water Saturation

Atte

nuat

ion

Coe

ffici

ent

(1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.050.1

0.150.2

0.250.3

0.350.4

2500Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent

(1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.10.20.30.40.50.6

3000Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent

(1/m

)


The experimental values are larger than the theoretical values.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.10.20.30.40.50.60.7

3500Hz


water saturation

Atte

nuat

ion

Coeffi

cien

t (1

/m)



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.10.20.30.40.50.6

2000Hz

Soybean OilPolynomial (Soybean Oil)DieselPolynomial (Diesel)

Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.10.20.30.40.50.6

1500Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.10.20.30.40.50.60.70.80.9

2500Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.800.10.20.30.40.50.60.70.80.9

3000Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.10.20.30.40.50.60.70.8

3500Hz


Water Saturation

Atte

nuat

ion

Coe

ffici

ent (

1/m

)

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.


Thank you


Documents

Chi-Chin Yang, Po- Chia Chen, and Wei-Cheng Lo