# Study on p-Wave Attenuation in Hydrate-Bearing Sediments Based on BISQ Model

Authors: Chuanhui Li; Kai Feng; Xuewei Liu
Journal: Journal of Geological Research
 (2013)

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## Abstract

In hydrate-bearing sediments, the elastic wave attenuation characteristics depend on the elastic properties of the sediments themselves on the one hand, and on the other hand, they also depend on the hydrate occurrence state and hydrate saturation. Since the hydrate-bearing sediments always have high porosity, so they show significant porous medium characteristics. Based on the BISQ porous medium model which is the most widely used model to study the attenuation characteristics in the porous media, we focused on p-wave attenuation in hydrate-bearing sediments in Shenhu Area, South China Sea, especially in specific seismic frequency range, which lays a foundation for the identification of gas hydrates by using seismic wave attenuation in Shenhu Area, South China Sea. Our results depict that seismic wave attenuation is an effective attribute to identify gas hydrates.


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## Body

## 1. Introduction

With the enhancement of exploration technology for gas hydrate resources, research on wave attenuation in hydrate-bearing sediments is being paid more and more attention. Unlike oil and gas reservoirs, hydrate reservoirs are usually found at shallow depths. In suitable conditions, hydrates form more easily within sediments with high porosity and high permeability. Gas hydrates affect the rock properties, so the wave attenuation in hydrate-bearing sediments is a complex phenomenon. In Mackenzie Delta, Canada, Guerin and Goldberg [1], Guerin et al. [2], and Pratt et al. [3] obtained high value of wave attenuation in hydrate-bearing sediments by logging data and crosshole seismic tomography results, respectively. In Nankai Trough, central Japan, Matsushima [4] also proved that elastic wave showed strong attenuation in hydrate-bearing sediments by logging data, in Blake Ridge and in the Makran Accretionary Prism, Arabian Sea, Wood et al. [5] and Sain and Singh [6] obtained week attenuation of seismic wave in hydrate-bearing sediments by using seismic data. Although the wave attenuation mechanism in hydrate-bearing sediments is not yet well explained. But the existing research results show that the wave attenuation in hydrate-bearing sediments is associated with several factors, such as the elastic properties of sediments, hydrate occurrence state, hydrate saturation, and frequency.Since the hydrate-bearing sediments always have high porosity, so they show significant porous medium characteristics. At the present, the most commonly used model to study elastic wave propagation in porous media is the BISQ model which combines the Biot flow and the squirt flow. In this model, the relationship between wave attenuation and rock properties has been discussed in a macroscopic perspective. So, we have implemented BISQ porous medium model to study Shenhu Area, South China Sea. In this paper a detailed discussion has been made to explore the gas hydrate effects on rock properties and p-wave attenuation in hydrate-bearing sediments, especially in seismic frequency range, which lays a foundation for the identification of gas hydrates by using seismic wave attenuation in Shenhu Area, South China Sea. The actual application result shows that seismic wave attenuation is an effective attribute to identify gas hydrates.


## 2. The BISQ Model

The BISQ model relates the dynamic poroelastic behavior to poroelastic constants, porosity, permeability, fluid viscosity, and the characteristic squirt flow length. It has advantages to describe the poroelastic behavior in macroscopic perspective like the Biot flow and it also predicts the elastic wave attenuation more realistically like the squirt flow. In the BISQ model, the inverse quality factor of the fast p-waveQp1-1 is given by [7, 8] as follows:
(1)Qp1-1=2Im(Y1)Re(Y1),
where
(2)Y1=-B2A+(B2A)2-CA,A=φFsqMρ22,B=((1+ρaρ2+iωcω)Fsq(2α-φ-φρ1ρ2)-(M+Fsqα2φ)×(1+ρaρ2+iωcω))(ρ2)-1,C=ρ1ρ2+(1+ρ1ρ2)(ρaρ2+iωcω),Fsq=F[1-2J1(λR)λRJ0(λR)],λ2=ρfω2F(φ+ρa/ρfφ+iωcω).
In these equations, M is the uniaxial strain modulus of the drained skeleton; α=1-Kdry/Ks is the poroelastic coefficient of effective stress; Kdry and Ks are the bulk modulus of the drained skeleton and the solid phase, respectively; J0 and J1 are Bessel functions; R is the characteristic squirt flow length; φ is the porosity of the rock; ρ1=(1-φ)ρS, ρ2=φρf, ρS and ρf are the density of the solid and the fluid phase, respectively; ρa is the inertial coupling density between the solid and the fluid; ωc=ηφ/kρf is Biot’s characteristic angular frequency; η is the viscosity of the fluid; k is the permeability of the skeleton; and F-1 is given by
(3)1F=1Kf+1φKs(α-φ),
where Kf is the bulk modulus of the fluid.From (1), we can see that elastic properties of the rock, porosity, permeability, the characteristic squirt flow length, and viscosity of the fluid, these are the key factors to determine the elastic wave attenuation. So, in order to study the p-wave attenuation in hydrate-bearing sediments, we must first study the hydrate effects on the rock properties.


## 3. Hydrate Effects on the Rock Properties

In suitable conditions, gas hydrates form more easily within sediments with high porosity and high permeability. Usually hydrates are always attached to the rock skeleton, which will result in the decrease of porosity, affecting the permeability and the characteristic squirt flow length of the rock. Meanwhile, hydrates in contact with rock skeleton will certainly affect the solid elastic properties of the rock. But the fluid properties of the rock, such as fluid density, bulk modulus, and viscosity, can be considered without any change.


### 3.1. Hydrate Effect on the Permeability

Generally, permeability of porous media is related to the pore geometry. Based on this concept, a lot of empirical and semiempirical formulas have been proposed and the most famous and widely used is Kozeny-Carman equation. The Kozeny-Carman equation provides a method to estimate permeability using porosity, specific surface area, particle size, and pore tortuosity. According to the Kozeny-Carman equation, the permeability of porous mediaκ is defined as follows [9]:
(4)κ=Bφ3(1-φ)2d2,
where B is constant, φ is the porosity of the medium, and d is particle diameter.When hydrates are attached to the rock skeleton, the porosity will decrease and the particle diameter will increase. Provided thatφ and φ′ refer to the porosity of the sediments before and after hydrate formation and that d and d′ refer to the particle diameter of the rock before and after hydrate formation, so, we have
(5)φ′φ=(1-Sh),d′d=(1-φ′1-φ)1/3.
According to (4), the permeability of the sediments after hydrate formation κ′ becomes
(6)κ′=Bφ′3(1-φ′)2d′2.
By using (5), the relationship between the permeability of sediments after and before hydrate formation is
(7)κ′κ=(1-Sh)3(1-φ1-φ+φSh)4/3.
From (7), we can see that the ratio between the permeability of sediments after and before hydrate formation is related to the hydrate saturation and the porosity of original sediments. Figure 1 is the representation of (7). We can see that with the increase of hydrate saturation, the permeability of the rock reduces rapidly, and with the increase of original porosity, the rate of the reduction also rises.Figure 1
The relationship between the permeability of the sediments after and before the hydrate formation.


### 3.2. Hydrate Effect on the Characteristic Squirt Flow Length

The characteristic squirt flow length is the average length of the squirt flow. It is a macroscopic description of microscopic characteristics of porous media, independent of frequency and fluid properties [8]. The formation of hydrates makes the rock solid phase volume increase, resulting in the increase of the average length of the squirt flow. Provided that R and R′ refer to the characteristic squirt flow length of the sediments before and after hydrate formation, so, we have
(8)R′2R2=1-φ′1-φ,
where φ and φ′ refer to the porosity of the sediments before and after hydrate formation. According to (5), we can get
(9)R′R=1-φ+φ·Sh1-φ.
As shown in (9), the ratio between the characteristic squirt flow length of sediments after and before hydrate formation is also related to the hydrate saturation and the porosity of original sediments. Figure 2 shows the representation of (7). We can see that with the increase of hydrate saturation, the characteristic squirt flow length of the rock increases, and with the increase of the original porosity, the rate of the increase also rises.Figure 2
The relationship between the characteristic squirt flow length of the sediments after and before the hydrate formation.


### 3.3. Hydrate Effect on the Solid Properties of the Rock

When hydrates are in contact with the rock skeleton, the solid density of the rock will change. Provided thatρs refers to the solid density of the rock without hydrate, so the density of the solid consisting of hydrates is
(10)ρs′=fhρh+(1-fh)ρs,
where ρh is the density of hydrate and fh is the volume fraction of hydrate in the solid phase and it can be calculated as follows:
(11)fh=φSh1-φ+φSh,
where φ is the porosity of the original sediments without hydrate and Sh is the hydrate saturation.When hydrates are attached to the rock skeleton, the bulk and shear moduli of the solid phase mixed with hydrate can be calculated by Voigt-Reuss-Hill average [10] as follows:
(12)K=12[fhKh+(1-fh)Ks+(fhKh+1-fhKs)-1],G=12[fhGh+(1-fh)Gs+(fhGh+1-fhGs)-1],
where Ks and Gs are the solid bulk and shear moduli of the sediments without hydrate and Kh and Gh are the bulk and shear moduli of the hydrate.


### 3.4. Hydrate Effect on the Elastic Moduli of the Drained Skeleton

When hydrates are attached to the rock skeleton, the porosity of the rock decreases fromφ to φ′. According to the modified Hashin-Shtrikman-Hertz-Mindlin theory [11], the elastic moduli of the drained skeleton can be calculated in the following two cases: (1) for the porosity φ′ below the critical porosity φc, the drained moduli are determined as
(13)Kdry=[φ′/φcKHM+(4/3)GHM+1-φ′/φcK+(4/3)GHM]-1-43GHM,Gdry=[φ′/φcGHM+Z+1-φ′/φcG+Z]-1-Z.(2) If the porosity φ′ is above the critical porosity φ′, the drained moduli can be calculated as follows:
(14)Kdry=[(1-φ′)/(1-φc)KHM+(4/3)GHM+(φ′-φc)/(1-φc)(4/3)GHM]-1-43GHM,Gdry=[(1-φ′)/(1-φc)GHM+Z+(φ′-φc)/(1-φc)Z]-1-Z,
where Z=(GHM/6)[(9KHM+8GHM)/(KHM+2GHM)] and KHM and GHM are the effective moduli at critical porosity and they are given by [12–14] as follows:
(15)KHM=[G2n2(1-φc)218π2(1-ν)2P]1/3,GHM=5-4ν5(2-ν)[3G2n2(1-φc)22π2(1-ν)2P]1/3,
where K and G are the solid bulk and shear moduli of the sediments and they can be calculated by (12). The Poisson’s ratio is given by ν, n is the average number of grain contacts, P is the effective pressure P=(1-φ)(ρs-ρf)gh, ρs and ρf are the solid and fluid density, the depth below the seafloor is given by h, and g is the gravity acceleration.


### 3.5. Analysis with Actual Data

The hydrate-bearing sediments in Shenhu Area are at about 200 m depth below the seafloor. Table1 shows the mineral composition of the sediments, and the core data analysis shows that there is little change in the mineral composition near the hydrate-bearing sediments.Table 1
The mineral composition of the sediments in Shenhu Area.
Mineral component
Bulk modulus (Gpa)
Shear modulus (Gpa)
Density  (g/cm3)
Volume fraction
Quartz
36.6
45
2.65
0.3
Muscovite
61.5
41.1
2.79
0.2
Plagioclase
75.6
25.6
2.63
0.08
Clay
20.9
6.85
2.58
0.22
Calcite
76.8
32
2.71
0.2According to the bulk modulus, shear modulus, density and the volume fraction of each mineral in Table1, by using (10) to (15), we can calculate gas hydrate effects on rock elastic properties, as shown in Figure 3. Figures 3(a)–3(c) show the solid density, solid bulk, and shear moduli versus hydrate saturation. We can see that solid phase elastic properties reduce with the increase of the hydrate saturation, because the density and the elastic moduli of hydrates are much lower than the common mineral. Figures 3(d) and 3(e) are the representation of bulk and shear moduli of the drained skeleton. We can see that the elastic moduli of the drained skeleton rise with the increase of the hydrate saturation.Rock elastic properties versus the hydrate saturation. (a) Solid density, (b) solid bulk modulus, (c) solid shear modulus, (d) bulk modulus of the drained skeleton, and (e) shear modulus of the drained skeleton.
(a)
(b)
(c)
(d)
(e)


## 3.1. Hydrate Effect on the Permeability

Generally, permeability of porous media is related to the pore geometry. Based on this concept, a lot of empirical and semiempirical formulas have been proposed and the most famous and widely used is Kozeny-Carman equation. The Kozeny-Carman equation provides a method to estimate permeability using porosity, specific surface area, particle size, and pore tortuosity. According to the Kozeny-Carman equation, the permeability of porous mediaκ is defined as follows [9]:
(4)κ=Bφ3(1-φ)2d2,
where B is constant, φ is the porosity of the medium, and d is particle diameter.When hydrates are attached to the rock skeleton, the porosity will decrease and the particle diameter will increase. Provided thatφ and φ′ refer to the porosity of the sediments before and after hydrate formation and that d and d′ refer to the particle diameter of the rock before and after hydrate formation, so, we have
(5)φ′φ=(1-Sh),d′d=(1-φ′1-φ)1/3.
According to (4), the permeability of the sediments after hydrate formation κ′ becomes
(6)κ′=Bφ′3(1-φ′)2d′2.
By using (5), the relationship between the permeability of sediments after and before hydrate formation is
(7)κ′κ=(1-Sh)3(1-φ1-φ+φSh)4/3.
From (7), we can see that the ratio between the permeability of sediments after and before hydrate formation is related to the hydrate saturation and the porosity of original sediments. Figure 1 is the representation of (7). We can see that with the increase of hydrate saturation, the permeability of the rock reduces rapidly, and with the increase of original porosity, the rate of the reduction also rises.Figure 1
The relationship between the permeability of the sediments after and before the hydrate formation.


## 3.2. Hydrate Effect on the Characteristic Squirt Flow Length

The characteristic squirt flow length is the average length of the squirt flow. It is a macroscopic description of microscopic characteristics of porous media, independent of frequency and fluid properties [8]. The formation of hydrates makes the rock solid phase volume increase, resulting in the increase of the average length of the squirt flow. Provided that R and R′ refer to the characteristic squirt flow length of the sediments before and after hydrate formation, so, we have
(8)R′2R2=1-φ′1-φ,
where φ and φ′ refer to the porosity of the sediments before and after hydrate formation. According to (5), we can get
(9)R′R=1-φ+φ·Sh1-φ.
As shown in (9), the ratio between the characteristic squirt flow length of sediments after and before hydrate formation is also related to the hydrate saturation and the porosity of original sediments. Figure 2 shows the representation of (7). We can see that with the increase of hydrate saturation, the characteristic squirt flow length of the rock increases, and with the increase of the original porosity, the rate of the increase also rises.Figure 2
The relationship between the characteristic squirt flow length of the sediments after and before the hydrate formation.


## 3.3. Hydrate Effect on the Solid Properties of the Rock

When hydrates are in contact with the rock skeleton, the solid density of the rock will change. Provided thatρs refers to the solid density of the rock without hydrate, so the density of the solid consisting of hydrates is
(10)ρs′=fhρh+(1-fh)ρs,
where ρh is the density of hydrate and fh is the volume fraction of hydrate in the solid phase and it can be calculated as follows:
(11)fh=φSh1-φ+φSh,
where φ is the porosity of the original sediments without hydrate and Sh is the hydrate saturation.When hydrates are attached to the rock skeleton, the bulk and shear moduli of the solid phase mixed with hydrate can be calculated by Voigt-Reuss-Hill average [10] as follows:
(12)K=12[fhKh+(1-fh)Ks+(fhKh+1-fhKs)-1],G=12[fhGh+(1-fh)Gs+(fhGh+1-fhGs)-1],
where Ks and Gs are the solid bulk and shear moduli of the sediments without hydrate and Kh and Gh are the bulk and shear moduli of the hydrate.


## 3.4. Hydrate Effect on the Elastic Moduli of the Drained Skeleton

When hydrates are attached to the rock skeleton, the porosity of the rock decreases fromφ to φ′. According to the modified Hashin-Shtrikman-Hertz-Mindlin theory [11], the elastic moduli of the drained skeleton can be calculated in the following two cases: (1) for the porosity φ′ below the critical porosity φc, the drained moduli are determined as
(13)Kdry=[φ′/φcKHM+(4/3)GHM+1-φ′/φcK+(4/3)GHM]-1-43GHM,Gdry=[φ′/φcGHM+Z+1-φ′/φcG+Z]-1-Z.(2) If the porosity φ′ is above the critical porosity φ′, the drained moduli can be calculated as follows:
(14)Kdry=[(1-φ′)/(1-φc)KHM+(4/3)GHM+(φ′-φc)/(1-φc)(4/3)GHM]-1-43GHM,Gdry=[(1-φ′)/(1-φc)GHM+Z+(φ′-φc)/(1-φc)Z]-1-Z,
where Z=(GHM/6)[(9KHM+8GHM)/(KHM+2GHM)] and KHM and GHM are the effective moduli at critical porosity and they are given by [12–14] as follows:
(15)KHM=[G2n2(1-φc)218π2(1-ν)2P]1/3,GHM=5-4ν5(2-ν)[3G2n2(1-φc)22π2(1-ν)2P]1/3,
where K and G are the solid bulk and shear moduli of the sediments and they can be calculated by (12). The Poisson’s ratio is given by ν, n is the average number of grain contacts, P is the effective pressure P=(1-φ)(ρs-ρf)gh, ρs and ρf are the solid and fluid density, the depth below the seafloor is given by h, and g is the gravity acceleration.


## 3.5. Analysis with Actual Data

The hydrate-bearing sediments in Shenhu Area are at about 200 m depth below the seafloor. Table1 shows the mineral composition of the sediments, and the core data analysis shows that there is little change in the mineral composition near the hydrate-bearing sediments.Table 1
The mineral composition of the sediments in Shenhu Area.
Mineral component
Bulk modulus (Gpa)
Shear modulus (Gpa)
Density  (g/cm3)
Volume fraction
Quartz
36.6
45
2.65
0.3
Muscovite
61.5
41.1
2.79
0.2
Plagioclase
75.6
25.6
2.63
0.08
Clay
20.9
6.85
2.58
0.22
Calcite
76.8
32
2.71
0.2According to the bulk modulus, shear modulus, density and the volume fraction of each mineral in Table1, by using (10) to (15), we can calculate gas hydrate effects on rock elastic properties, as shown in Figure 3. Figures 3(a)–3(c) show the solid density, solid bulk, and shear moduli versus hydrate saturation. We can see that solid phase elastic properties reduce with the increase of the hydrate saturation, because the density and the elastic moduli of hydrates are much lower than the common mineral. Figures 3(d) and 3(e) are the representation of bulk and shear moduli of the drained skeleton. We can see that the elastic moduli of the drained skeleton rise with the increase of the hydrate saturation.Rock elastic properties versus the hydrate saturation. (a) Solid density, (b) solid bulk modulus, (c) solid shear modulus, (d) bulk modulus of the drained skeleton, and (e) shear modulus of the drained skeleton.
(a)
(b)
(c)
(d)
(e)


## 4. p-Wave Attenuation Analysis in Hydrate-Bearing Sediments

The hydrate-bearing sediments in Shenhu Area occur at shallow depth below the seafloor. In this area, the unconsolidated sediments have high porosity and high permeability. The average porosity of the rock is 45%. The permeability of the rock is an average of 20Darcy and the hydrate saturation is up to 50%. According to the pervious analysis of the hydrate effects on rock properties, by using (1), we can calculate the p-wave attenuation in hydrate-bearing sediments in Shenhu Area.Figure4 gives the p-wave attenuation at different hydrate saturation within specific frequency range 0~106 Hz. From the figure, we can see clearly that the inverse quality factor of p-wave first rises and then reduces with the increase of frequency, presenting single peak characteristics, up to an extreme value at a certain frequency. With the increase of the hydrate saturation, the inverse quality factor of p-wave decreases gradually and the extreme position moves to the high frequency.Figure 4
p-wave attenuation versus frequency and the hydrate saturation.In order to further study the p-wave attenuation in hydrate-bearing sediments at seismic frequency. We calculate the curve of p-wave attenuation versus hydrate saturation at frequency 60 Hz which is the dominant frequency of the seismic data in Shenhu Area, as shown in Figure5. We can see that the inverse quality factor of p-wave reduces gradually with the increase of the hydrate saturation. So in seismic exploration, with the increase of the hydrate saturation, the p-wave attenuation reduces gradually.Figure 5
p-wave attenuation versus the hydrate saturation at frequency 60 Hz.So, we conclude that hydrates make a certain impact on the porosity, permeability, the characteristic squirt flow length, and elastic moduli of the rock, and thus they will affect the p-wave attenuation in the sediments, which lays a foundation for the identification of gas hydrates by using seismic wave attenuation. In the next section, we will use actual data in the Shenhu Area to verify our results as an application to identify gas hydrates by seismic wave attenuation.


## 5. Actual Data Application

The gas hydrate drilling area in Shenhu Area is located in the middle of the northern slope, South China Sea. In this area, collapse caused a large relief of the submarine topography, folds, and faults in the shallow strata. Some faults extended up to the seafloor, which is conductive to the migration of the gas. Meanwhile, the geochemical analysis of the core samples in the drilling area and the surroundings shows that the biogenic gas and pyrolysis gas in the study area are well developed, which provides sufficient material for the formation of gas hydrates.Figure6 is a seismic profile in the drilling area in Shenhu Area. The red line shows the location of an actual drilling and the core results have confirmed the existence of gas hydrates at about 1.9 s. In the seismic profile, there are two obvious BSRs. But because of the large relief of the submarine topography and the complicated geological structure, BSR shows multievent, discontinuous, and poor parallelism to the seafloor. In addition, the blanking zone above the BSR is not typical. The blanking zone has many strong reflections and poor continuity, which brings difficulties for the determination of gas hydrate distribution.Figure 6
Seismic profile.In order to pick up the BSR accurately, we calculate the instantaneous phase of the seismic data as shown in Figure7. As can be seen in Figure 7, although it is observed that the BSR in seismic profile has complicated features and poor continuity, but in instantaneous phase profile, according to the break, disappearance, and disorder of the event, we can still pick up the BSR clearly, as shown in the black curve in the figure.Figure 7
Instantaneous phase profile.According to the former analysis of the seismic wave attenuation in the hydrate-bearing sediments in Shenhu Area, when the sediments contain gas hydrates, the seismic wave attenuation will reduce. Figure8 is the seismic wave attenuation calculated from seismic data. From the figure, we can see that there are indeed some white low outliers which are concentrated relatively above the BSR. Delineating the outlier concentration areas, we can gain five regions as shown in the yellow oval shaded areas, one of which is located in the actual drilling position. As we can see in the figure, at about 1.9 s in this region there are significant low attenuation outliers which are consistent with the drilling results.Figure 8
Seismic wave attenuation profile.In order to further verify whether the attenuation outliers are caused by hydrates or not, we calculated the instantaneous amplitude profile as shown in Figure9. In the instantaneous amplitude profile, the strong reflections are highlighted above BSR and the blanking zone is more obvious. Projecting the five outlier concentration areas in Figure 8 to the instantaneous amplitude profile, we can see that the outlier concentration areas in the seismic wave attenuation profile are in good agreement with the blanking zone in the instantaneous amplitude profile. So, it can be concluded that the low outliers in the seismic wave attenuation profile are indeed caused by the hydrates in the sediments.Figure 9
Instantaneous amplitude profile.


## 6. Conclusion

(1)
The BISQ porous medium model is first used to study the p-wave attenuation characteristics in the hydrate-bearing sediments. In the BISQ model, gas hydrates within the sediments make a certain impact on porosity, permeability, the characteristic squirt flow length, and elastic moduli of the rock. Due to the variation of these properties, we conclude that gas hydrates have also made a certain impact on the p-wave attenuation in the sediments.
(2)
In Shenhu Area, we notice that when the sediments contain hydrates, the seismic wave attenuation will decrease, and with the increase of the hydrate saturation, the seismic wave attenuation will reduce gradually.
(3)
The actual application result in Shenhu Area shows that the seismic wave attenuation is an effective attribute to identify gas hydrates, which lays the foundation for the next work to elaborate the quantitative analysis of the gas hydrates by seismic wave attenuation.



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*Source: 176579-2013-10-09.xml*