Research Article Study on p-wave Attenuation in Hydrate-Bearing Sediments Based on BISQ Model

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1 Geological Research Volume 23, Article ID 76579, 8 pages Research Article Study on p-wave Attenuation in Hydrate-Bearing Sediments Based on BISQ Model Chuanhui Li, Kai Feng, 2 and Xuewei Liu School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 83, China 2 China National Oil and Gas Exploration and Development Corporation, Beijing 34, China Correspondence should be addressed to Xuewei Liu; liuxw3@sina.com Received 25 July 23; Revised 27 August 23; Accepted 27 August 23 Academic Editor: Umberta Tinivella Copyright 23 Chuanhui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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.. Introduction With the enhancement of exploration technology for gas hydrate resources, research on wave attenuation in hydratebearing 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 [], 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 andinthemakranaccretionaryprism,arabiansea,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 hydratebearing sediments is not yet well explained. But the existing research results show that the wave attenuation in hydratebearing 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,

2 2 Geological Research 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-wave Q p is given by [7, 8] as follows: where Q p = 2Im ( Y ) Re ( Y ), () Y = B 2A + ( B 2A ) 2 C A, A = φf sqm ρ2 2, B= (F sq (2α φ φ ρ ) (M+F sq α 2 φ ) (+ ρ a +i ω c ω )) (), C= ρ +(+ ρ )( ρ a + iω c ω ), F sq =F[ 2J (λr) λrj (λr) ], λ 2 = ρ fω 2 F (φ+ρ a/ρ f φ +i ω c ω ). In these equations, M is the uniaxial strain modulus of the drained skeleton; α= K dry /K s is the poroelastic coefficient of effective stress; K dry and K s are the bulk modulus of the drained skeleton and the solid phase, respectively; J and J are Bessel functions; R is the characteristic squirt flow length; φ is the porosity of the rock; ρ =( φ)ρ S, =φρ f, ρ S and ρ f arethedensityofthesolidandthefluidphase,respectively;ρ a istheinertialcouplingdensitybetweenthesolidandthefluid; ω c =ηφ/kρ f is Biot s characteristic angular frequency; η is the viscosity of the fluid; k is the permeability of the skeleton; and F is given by (2) F = K f + φk s (α φ), (3) where K f is the bulk modulus of the fluid. From (), 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 sedimentswithhighporosityandhighpermeability.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..HydrateEffectonthePermeability. 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 media κ is defined as follows [9]: φ 3 κ=b ( φ) 2 d2, (4) 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 that φ and φ refer to the porosity of the sediments before and after hydrate formation and that d and d refer totheparticlediameteroftherockbeforeandafterhydrate formation, so, we have φ φ =( ), d /3 d =( φ φ ). According to (4), the permeability of the sediments after hydrate formation κ becomes φ 3 (5) κ =B ( φ ) 2 d 2. (6) By using (5), the relationship between the permeability of sediments after and before hydrate formation is κ =( ) 3 φ ( ) φ+φ κ 4/3. (7) 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 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 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

3 Geological Research k /k.6.4 R /R φ φ Figure : The relationship between the permeability of the sedimentsafterandbeforethehydrateformation. Figure 2: The relationship between the characteristic squirt flow length of the sediments after and before the hydrate formation. 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 R 2 R 2 = φ φ, (8) where φ and φ refer to the porosity of the sediments before and after hydrate formation. According to (5), we can get R R = φ+φ. (9) φ Asshownin(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 Hydrate Effect on the Solid Properties of the Rock. When hydrates are in contact with the rock skeleton, the solid densityoftherockwillchange.providedthatρ s refers to the solid density of the rock without hydrate, so the density of the solid consisting of hydrates is ρ s =f hρ h +( f h )ρ s, () where ρ h is the density of hydrate and f h is the volume fractionofhydrateinthesolidphaseanditcanbecalculated as follows: f h = φ φ+φ, () where φ is the porosity of the original sediments without hydrate and 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-Hillaverage [] as follows: K= 2 [f hk h +( f h )K s +( f h + f h ) ], K h K s G= 2 [f hg h +( f h )G s +( f h + f h ) ], G h G s (2) where K s and G s arethesolidbulkandshearmoduliofthe sediments without hydrate and K h and G h are the bulk and shear moduli of the hydrate Hydrate Effect on the Elastic Moduli of the Drained Skeleton. When hydrates are attached to the rock skeleton, the porosity of the rock decreases from φ to φ. According to the modified Hashin-Shtrikman-Hertz-Mindlin theory [], the elastic moduli of the drained skeleton can be calculated in the following two cases: () for the porosity φ below the critical porosity φ c, the drained moduli are determined as φ /φ K dry =[ c φ /φ + c ] 4 K HM + (4/3) G HM K+(4/3) G HM 3 G HM, G dry =[ φ /φ c G HM +Z + φ /φ c G+Z ] Z. (3)

4 4 Geological Research ρ s (kg/m 3 ) K s (GPa) G s (GPa) K dry (GPa) G dry (GPa) (a) (b) (c) (d) (e) Figure 3: 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. (2) If the porosity φ is above the critical porosity φ,the drained moduli can be calculated as follows: K dry =[ ( φ )/( φ c ) + (φ φ c )/( φ c ) ] 4 K HM + (4/3) G HM (4/3) G HM 3 G HM, G dry =[ ( φ )/( φ c ) G HM +Z + (φ φ c )/( φ c ) ] Z, Z (4) where Z=(G HM /6)[(9K HM +8G HM )/(K HM +2G HM )] and K HM and G HM are the effective moduli at critical porosity and they aregivenby [2 4] as follows: K HM =[ G2 n 2 ( φ c ) 2 /3 8π 2 ( ]) 2 P], G HM = 5 4] n 2 ( φ c ) 2 5 (2 ]) [3G2 2π 2 ( ]) 2 P] /3, (5) where K and G are the solid bulk and shear moduli of the sediments and they can be calculated by (2). The Poisson s ratio is given by ], n is the average number of grain contacts, P istheeffectivepressurep = ( φ)(ρ s ρ f )gh, ρ s and ρ f are the solid and fluid density, the depth below the seafloor is given by h,andg is the gravity acceleration Analysis with Actual Data. The hydrate-bearing sediments in Shenhu Area are at about 2 m depth below the seafloor. Table 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. According to the bulk modulus, shear modulus, density and the volume fraction of each mineral in Table,byusing ()to(5), 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 thedensityandtheelasticmoduliofhydratesaremuch lower than the common mineral. Figures 3(d) and 3(e) are therepresentationofbulkandshearmoduliofthedrained skeleton. We can see that the elastic moduli of the drained skeleton rise with the increase of the hydrate saturation. 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 2Darcy and the hydrate saturation is up to 5%. According to the pervious analysis of the hydrate effects on rock properties, by using (), we can calculate the p-wave attenuation in hydrate-bearing sediments in Shenhu Area. Figure 4 gives the p-wave attenuation at different hydrate saturation within specific frequency range 6 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

5 Geological Research 5 Table : The mineral composition of the sediments in Shenhu Area. Mineral component Bulk modulus (Gpa) Shear modulus (Gpa) Density (g/cm 3 ) Volume fraction Quartz Muscovite Plagioclase Clay Calcite Q (V p ) Q (V p ) = =2% Frequency (Hz) =4% =6% Figure 4: p-wave attenuation versus frequency and the hydrate saturation. 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. 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 6 Hz which is the dominant frequency of the seismic data in Shenhu Area, as shown in Figure 5. Wecan 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. So,weconcludethathydratesmakeacertainimpact 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 (%) Figure 5: p-wave attenuation versus the hydrate saturation at frequency 6 Hz. 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. Figure 6 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.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.

6 6 Geological Research CDP High.5.6 Time (s).7 BSR Low Figure 6: Seismic profile CDP High.6 Time (s) Low Figure 7: Instantaneous phase profile. In order to pick up the BSR accurately, we calculate the instantaneous phase of the seismic data as shown in Figure 7. 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. 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. Figure 8 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.9 s in this region there are significant low attenuation outliers which are consistent with the drilling results. In order to further verify whether the attenuation outliers are caused by hydrates or not, we calculated the instantaneous amplitude profile as shown in Figure 9. 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. 6. Conclusion () 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

7 Geological Research CDP High.6 Time (s) Low Figure 8: Seismic wave attenuation profile CDP.5.6 Time (s) Low Figure 9: Instantaneous amplitude profile. 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 pwave 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. Conflict of Interests The authors declare that they have no conflict of interests. References [] G. Guerin and D. Goldberg, Sonic waveform attenuation in gas hydrate-bearing sediments from the Mallik 2L-38 research well, Mackenzie Delta, Canada, Geophysical Research B, vol. 7, no. 5, pp. EPM - EPM -, 22. [2] G. Guerin, D. Goldberg, T. S. Collett, and Sonic attenuation in the JAPEX/JNOC/GSC, Mallik 5L-38 gas hydrate production research well, in Scientific Results From the Mallik 22 Gas Hydrate Production Research Well Program, Mackenzie Delta, Northwest Territories, Canada, S. R. Dallimore and T. S. Collett, Eds., Bulletin 585, pp. 4, Geological Survey of Canada, 25. [3] R. G. Pratt, F. Hou, K. Bauer et al., Waveform tomography images of velocity and inelastic attenuation from the Mallik 22 crosshole seismic surveys, in Scientific Results From the Mallik 22 Gas Hydrate Production Research Well Program, Mackenzie Delta, Northwest Territories, Canada, S. R. Dallimore and T. S. Collett, Eds., Bulletin 585, pp. 4, Geological Survey of Canada, 25. [4] J. Matsushima, Attenuation measurements from sonic full waveform logs in gas hydrate bearing sediments, in Proceedings of the of 74th SEG Annual International Meeting, pp , 24.

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