an application of rock physics modeling to quantify the ... · an application of rock physics...

Geosciences JournalVol. 20, No. 3, p. 321 330, June 2016DOI 10.1007/s12303-015-0044-zⓒ The Association of Korean Geoscience Societies and Springer 2016

An application of rock physics modeling to quantify the seismic response of gas hydrate-bearing sediments in Makran accretionary prism, offshore, Pakistan

ABSTRACT: Naturally occurring gas hydrates are potential futureenergy source. A significant amount of gas hydrates is interpretedthrough seismic reflection data in the form of bottom simulatingreflector (BSR) present in the sediments of the convergent continentalmargin of Pakistan. However, the seismic character of these hydrate-bearing unconsolidated sediments is not properly investigated. Sinceno direct measurements are available for quantitative estimationof gas hydrate and free gas in these sediments, therefore detailedknowledge of seismic velocities is essential. Seismic velocities of thegas hydrate-bearing sediments in the study area are estimated byusing the effective medium theory and the fluid substitution mod-eling. The results show that the presence of gas hydrates increasesthe stiffness of the unconsolidated sediments; whereas the presenceof free gas decreases the stiffness of these sediments. It is noted thatseismic velocities and density of hydrate-bearing sediments are highlyaffected by saturation and distribution pattern of gas hydrates. Thehydrate-bearing sediments seem to be characterized not only byhigh P-wave velocity (about 2800 m/s) but also by anomalously lowS-wave velocity (about 850 m/s). As pure gas-hydrates have muchhigher seismic velocities than those of host sediments, presence ofgas-hydrate increases the seismic velocities, whereas free-gas belowthe hydrate-bearing sediments decreases the velocities. Seismic reflec-tion from the BSR exhibits a wide range of amplitude variation withoffset characteristics, which depend upon the saturation and distribu-tion of hydrates above and free gas below the BSR. We have alsodemonstrated that some attributes like acoustic and shear imped-ances, and AVO can be used as important proxies to detect gashydrate saturation.

Key words: gas hydrate, effective medium theory, fluid substitution,elastic properties, AVO forward modeling

1. INTRODUCTION

Natural gas hydrates, composed of water and light hydro-carbon gases (Sloan, 1998), are stable at very low temperature(about 0 °C) and very high pressure. These hydrates normallyoccur in shallow sediments of continental slope (Kvenvolden,1993; Minshull et al., 1994), deep inland seas and perma-frost areas (Kvenvolden, 1998). The amount of methane poten-

tially trapped in gas hydrates may be significant from 1015

to 1017 cubic meters (Kvenvolden, 1998), which makes it majorinterest to explore as an alternative energy source. The dis-association of methane molecule from water molecules hasstrong influence on the climate (Paull et al., 1991; Koh andSloan, 2007). The characteristics of gas hydrates and gashydrate-bearing sediments have been described extensivelyby various researchers (Kvenvolden, 1993; Ecker et al., 1996;Kvenvolden, 1998).

The presence of hydrates can be inferred from the bottomsimulating reflector (BSR), seafloor mounds and amplitudeblanking or change in seismic velocity (Markl et al., 1970)Hovland and Judd, 1988). The BSR, which is generally marksthe base of gas hydrate stability zone (GHSZ), is the result ofa large negative impedance contrast between gas hydrate-bear-ing sediments and free gas trapped in the sediments belowthe GHSZ. Presence of gas hydrates and free gas altered theelastic and seismic properties of sediments in different way,which can be identified by various seismic attributes like ampli-tude blanking (Lee and Dillon, 2001), reflection strength andinstantaneous frequency (Taylor et al., 2000; Chopra and Mar-furt, 2005; Satyavani et al., 2008).

To understand the seismic and elastic response of gashydrate-saturated sediments, different rock physics modelsand approaches have been proposed, including hydrate pore-filling model (Hyndman and Spence, 1992), time averageequation (Miller et al., 1991; Bangs et al., 1993; Wood et al.,1994), weighted equation proposed by Lee and Collett (2001),cementation model (Dvorkin and Nur, 1993; Sakai, 1999)and effective medium modeling (Helgerud et al., 1999; Jakob-sen et al., 2000). All these models considered the gas hydratesas part of the pore fluids or part of rock matrix and the freegas may be distributed either uniformly or in the form ofpatches throughout the pore spaces (Dvorkin et al., 1999;Helgerud et al., 1999). The distribution pattern of free gasyields different seismic behavior because of velocity dispersionin partially gas-saturated sediments (White, 1975; Lee, 2004;

Muhammed Irfan Ehsan*

Nisar AhmedPerveiz KhalidLiu Xue Wei

Mustansar Naeem

}

School of Geophysics and information Technology, China University of Geosciences (Beijing), 100083 Beijing, China

Institute of Geology, University of the Punjab, Lahore 54590, Pakistan

School of Geophysics and information Technology, China University of Geosciences (Beijing), 100083 Beijing, ChinaInstitute of Geology, University of the Punjab, Lahore 54590, Pakistan

*Corresponding author: [email protected]

322 Muhammed Irfan Ehsan, Nisar Ahmed, Perveiz Khalid, Liu Xue Wei, and Mustansar Naeem

Fig. 1. (a) Regional tectonic and geology map of Makran coastal area of Pakistan. AFP African plate, ARP Arabian plate, AS ArabianSea, COFS Chaman Oranch Fault System, CS Caspian Sea, GA Gulf of Aden, GO Gulf of Oman, INO Indian Ocean, INP Indian plate,MAW Makran accretionary wedge, OMFZ Owen Murray Fault Zone, PG Persian Gulf, RS Red Sea, and ZSZ Zagros Suture Zone(modified after Mokhtari et al., 2008). Dashed line is the political boundary between Pakistan and Iran. (b) Stratigraphic chart of Makrancoastal area of Pakistan (modified after Harms et al., 1982).

Rock physics modeling of gas hydrates, Pakistan 323

Ahmed et al., 2015a). The Makran accretionary wedge comprises of the south-

ern part of Pakistan and Iran between Sonmiani Bay and theStraits of Hormuz (Fig. 1a). The Makran accretionary wedgewas formed by the subduction of the oceanic crust of theArabian Plate under the Eurasian Plate by making a triple

plate junction at the eastern side of the subduction zoneinvolving the Indian, Eurasian and Arabian plates (Quirtmeyerand Kafka, 1984). The subduction started in the Paleocence(Platt et al., 1988), followed by accretion in the Eocene (Byrneet al., 1992). The Makran acceretionary prism is about 170km wide, extending from the Siahan Range southward to the

Fig. 2. (a) Location map of the study area. (b) Interpreted seismic section showing the location of bottom simulating reflector (BSR)below sea floor in Makran area.


Central Makran Coastal Ranges. The Makran area is high-lighted as an active trench arc system in which subduction iscontinuously going on. According to Powell (1979), the Makrancoast is uplifting at a rate of about 1.5 mm/yr. This upliftingis due to sediment accretion and underplating (Platt et al., 1988).The stratigraphic chart of the Makran area is shown in Figure1b. From the figure, it is evident that towards the Makranoffshore the sediments become younger and underlying bythe mud/mudstone (Harms et al., 1984; Kadri, 1995).

The study area is a part of the Makran accretionary prism(Fig. 2a). The presence of gas hydrates and free gas in theMakran accretionary prism has been inferred on multi-chan-nel marine seismic data by mapping an anomalous BSR asshown in Figure 2b (Minshull and White, 1989; Sain et al.,2000; Schlüter et al., 2002; Ojha and Sain, 2008; Ojha et al.,2010). However, the seismic properties of these inferredhydrate- and gas-bearing sediments are not properly inves-tigated (Ghosh and Sain, 2008). In this study, we appliedGassmann’s fluid substitution (Gassmann, 1951) and the effec-tive medium modeling (Helgerud et al., 1999) to investigatevariation in seismic and elastic properties of sediments sat-urated with gas hydrate and free gas.

2. METHODOLOGY

In this section we have described a complete quantitativework flow used to compute different seismic and elastic prop-erties of gas hydrate-bearing sediments. To model the P andS wave velocities and AVO response, we need to computethe elastic properties (bulk and shear modulus) of dry rockas well as the pore fluid and fluid-saturated rock. All inputparameters used in Gassmann fluid substitution and rockphysics modeling are given in Table 1. The bulk and shearmoduli of dry sediments (Kdry, Gdry respectively) are determinedby using the modified Hashin-Shtrikman-Hertz-Mindlin the-ory (Dvorkin and Nur, 1996):

, (1a)

, (1b)

where Z is auxiliary parameter, KHM and GHM are effectivebulk and shear moduli of dry frame at critical porosity (c)respectively and are determined by following equations:

, (2a)

, (2b)

. (2c)

In the above equations, Gm is the shear modulus of solidphase and is calculated by using Hill’s approach (Hill,1952) whereas ν, n and P are the Poisson’s ratio, numberof grains per contact and pressure respectively. The pres-sure P depends on density of solid (ρs), density of fluid (ρf),depth (h) beneath the sea floor and the acceleration (g)under gravitational pull:

, (3)

when gas hydrates are part of fluid, then original porosity() of rock is unaffected which is greater than criticalporosity (c). Above this porosity grain-to-grain contact islost i.e., the sediments are not grain supported and shearstrength vanishes.

The elastic properties of solid matrix (rock forming minerals)depend on the volume fraction ( f i), bulk modulus (Ki) andshear modulus (Gi) of individual minerals. The bulk mod-ulus (Km) and shear modulus (Gm) of matrix are

, (4a)

. (4b)

Since gas hydrates are assumed to be part of fluid, therefore,the fluid modulus (gas hydrates + water or gas + water) canbe computed by using Wood (1941), Voigt (1910), Reuss (1929)and Hill (1963) relationships.

Kdry1 – / 1 c–

KHM43---GHM+

----------------------------------- c– / 1 c–

43---GHM

-------------------------------------+43---GHM–=

Gdry1 – / 1 c–

GHM Z+-----------------------------------

c– / 1 c– Z

-------------------------------------+1–

Z–=

KHMGm

2 n2 1 c– 2

182 1 – 2-------------------------------P

1/3

=

GHM5 4–

5 2 – -------------------

3Gm2 n2 1 c– 2

22 1 – 2----------------------------------P=

ZGHM

6----------

9KHM 8GHM+KHM 2GHM+

-------------------------------=

P 1 – s f– gh=

Km12--- fiKi

i 1=

m

fi

Ki

------i 1=

m

1–

+=

Gm12--- fiGi

i 1=

m

fi

Gi

------i 1=

m

1–

+=

Table 1. Parameters used in effective medium modeling when gashydrates are part of fluids

Parameters Symbols Numerical Values Units

Porosity ϕ 39 %

Critical prosity ϕc 36 %

Dry rock bulk modulus Kdry 1.028 GPa

Dry rock shear modulus Gdry 1.432 ͦGPa

Number Grains per contact n 9

Quartz bulk modulus Kq 37 GPa

Quartz Shear modulus GS 45 GPa

Clay bulk modulus Kc 20.9 GPa

Clay shear modulus Gc 6.85 GPa

Quartz Density ρq 2.65 g/cm3

Clay Density ρc 2.58 g/cm3

Gas hydrate bulk modulus Kh 6.41 GPa

Gas hydrate shear modulus Gh 2.54 GPa

Gas hydrate density ρh 0.91 g/Cm3

Gas bulk modulus Kg 0.067 GPa

Gas density ρg 0.20 g/cm3

Water bulk modulus KW 2.25 GPa

Density of water ρw 1.0 g/cm3


, (5a)

, (5b)

, (5c)

whereas Sw, Sh and Sg are the saturation of water, gas hydrateand gas respectively, and KW, Kh and Kg are the bulk modulusof water, gas hydrate and gas. KW, KV and KVRH representthe fluid modulus calculated by Wood’s, Voigt’s and Voigt-Reuss-Hill’s approaches respectively. In case of free gassaturation, the bulk modulus is calculated by simply replacingSh with Sg and Kh with Kg in the above equations.

After computing elastic properties of dry sediments andbulk modulus of fluid phases, we can find the bulk modulusof saturated rock (Ksat) by Gassmann’s fluid substitutionformulas (Gassmann, 1951)

, (6)

, (7)

where Kdry is the bulk modulus of dry rock, Km is the bulkmodulus of rock matrix. Gsat and Gdry are shear moduli ofsaturated and dry rock respectively. The bulk modulus ofsaturated rock under patchy distribution of gas is computedby using Gassmann-Hill approach (Hill, 1963).

. (8)

Here, Ksatw and Ksatg are the bulk moduli when patches arefully saturated with water and free gas respectively. Thesebulk moduli can be computed simply by replacing Kf withKw and Kg in Equation (6). In patchy and homogeneous sat-uration, shear modulus is not affected thus; Gsat has thesame value as given in Equation (7). When elastic moduliare known, then P- and S-wave velocities are computed as

, (9)

, (10)

where ρb = (1 – )ρs + ρf is the bulk density (ρs is the den-sity of rock-forming minerals and ρf is the density of porefluid). To compute the P-wave reflection amplitude as func-tion of incident angle (RPP(θ)), we have used the Zoeppritzequation (1919).

3. RESULTS

The above described methodology is applied on the realdata set taken from the Makran accretionary prism of Pakistan.The results categorized into various sections are discussedbelow.

3.1. Effect of Gas Hydrates Saturation on Bulk Modulus and Seismic Velocities

One of the important goals of rock physics modeling ofgas hydrate-bearing sediments is to trace out the sensitivityof seismic signatures of the sediments due to pore fluid typeand saturation. Different fluids in reservoir have differentincompressibility and make a strong effect on seismic prop-erties such as P- and S-wave velocities. The accumulative bulkmodulus of fluid in a reservoir depends on the saturationand incompressibility of individual fluids (Mavako et al., 2009).We have elaborated fluids accumulative incompressibilityresponse in gas hydrate/water layer and gas/water layer. Kf

has been computed by using Wood (1941) or Reuss (1929),Voigt (1910) and Voigt-Reuss-Hill relations represented byKW, KV and KVRH respectively (Eq. 5) and is plotted in Figure3 as a function of gas hydrate saturation (gas hydrates/watersaturation case) and free gas saturation (gas/water case). KV

marked the upper bond whereas KW or KR marked the lowerbond of bulk modulus of two fluid mixtures (Kf). The fluidmodulus has opposite trend for saturation of gas hydrate andsaturation of free gas. Kf increases with increase in Sh as shownin Figure 3a; whereas Kf decreases with increase in Sg (Fig. 3b).This behavior of fluid modulus shows that the increase in Sh

may increase the stiffness of effective bulk modulus of gashydrate-bearing sediments and increase in Sg may decrease thestiffness of effective bulk modulus of free gas-bearing sediments.

As we know that the effective bulk moduli of saturated orpartially saturated sediments are direct image of the fluidmoduli present into the pore spaces (Khalid et al., 2014),therefore; fluid moduli are injected into the fluid substitutionequations (Eqs. 6–8) under uniform and patchy saturation.The saturated bulk modulus of marine sediments is plottedin Figure 4 as function of gas hydrates saturation and freegas saturation. As it was expected the saturated bulk modulusshowed opposite trend to gas hydrate saturation than freegas saturation. The saturated bulk modulus is about 13 GPaat 100% gas hydrates saturation; whereas at 100% gas sat-uration, it is merely 1.3 GPa. The results demonstrate that Ksat

for patchy case has higher value as compared to uniform sat-uration, except at end points where both approaches givethe same values. The maximum relative difference between Ksat

homogenous and Ksat patchy is about 2.66 GPa at Sg ~ 0.1.To interpret seismic data in terms of hydrate concentration,

one needs to establish a relation between hydrates satura-tion in sediments and their velocity. P-wave velocity (VP)depends on the saturated bulk and shear modului as well asthe bulk density of the sediments. The compressional wavevelocity and shear wave velocity (VS) of gas hydrate-bearingsediments are computed by using Equations (9) and (10)and are presented in Figure 5. These velocities correspondto a composition of 13% clay and 87% quartz. The backgroundvelocity at 0% hydrates saturation is taken as 2000 m/s at39% porosity. In Figure 5a, these velocities are plotted as a

KWSw

Kw

------Sh

Kh

-----+1–

=

KV SwKw ShKh+ =

KVRH12--- SwKw ShKh+

Sw

Kw

------Sh

Kh

-----+1–

+=

Ksat KmKdry 1 + KfKdry/Km– Kf+

1 – Kf Km KfKdry/Km–+-------------------------------------------------------------------=

Gsat Gdry=

KsatSw

Ksatw 4/3Gsat+---------------------------------

1 S– w

Ksatg 4/3Gsat+---------------------------------+

43---Gsat–=

VPKsat 4/3Gsat+

b

-------------------------------=

VS Gsat/b=


function of gas hydrates saturation and in Figure 5b, bothvelocities are plotted against free gas saturation. VP and VS

show increasing trend with increase in gas hydrate saturation.The hydrate-bearing sediments can be characterized not onlyby high value of VP (about 2800 m/s at 100% gas hydratessaturation) but also by very low value of VS (about 850 m/s at100% gas hydrates saturation). The underlying free gas-bear-ing layer has low value of VP (about 1390 m/s) but high valueof VS (about 950 m/s). However, variation in P-wave velocitywith saturation is higher as compared to shear wave veloc-ity which causes to increase their ratio (VP/VS) that may bea good indicator for detection of gas hydrates concentration.P-wave velocity variation with gas saturation in gas/watercase is entirely different than that of gas hydrates/water case.An abrupt decrease in VP is noted at small interval of gassaturation (Sg < 0.15) as shown in Figure 5b. Presence of even

small amount of free gas below the BSR reduces the P-wavevelocity appreciably and hence decreases the seismic imped-ance as well as amplitude. Above Sg ~ 0.20, the P-wave veloc-ity is almost unchanged. However, in case of gas hydrate/water, such type of decrease in VP with increase in hydratesaturation is missing as shown in Figure 5a. P-wave veloc-ity decreases slowly with decrease in hydrate saturation. Itis interesting to note that VP has opposite trend in hydrate/water case than that of gas/water case.

Since P-wave velocity in hydrate-bearing sediments ismuch higher than that of underlying free gas-bearing sedimentsand S-wave velocity in hydrate-bearing sediments is lowerthan that of free gas-bearing sediments, therefore, a largenegative P-wave impedance contrast and positive S-waveimpedance contrast are expected in AVO modeling. P-waveacoustic impedance (IP) also increases with increase in gas

Fig. 3. Bulk modulus of incompressibility of (a) gas hydrates and water as function of gas hydrates saturation (Sh) and (b) free gas andwater as function of free gas saturation (Sg) estimated by using Voigt (KV), Russ (KR), Wood (KW) and Hill (KVRH) approaches.

Fig. 4. The effective saturated bulk modulus (Ksat), computed by busing Gassmann-Wood (GW) or homogenous saturation andGassmann-Hill (GH) patchy saturation as a function of (a) gas hydrate saturation (gas hydrate and water case), (b) free gas saturation(free gas and water case). The input rock physics parameters used are given in Table 1.


hydrate saturation. On the other hand, S-wave acoustic imped-ance decreases with increase in gas hydrate saturation (Fig.6a). Poisson’s ratio, which is directly related to VP and VS,is also increased with increase in gas hydrate saturation as

shown in Figure 6b. After analyzing the behavior of VP and VS in two phase

fluid, we have analyzed three phase case by considering asmall amount of free gas (1% of total saturation) present ingas hydrate/water layer. In Figure 7, it is depicted that smallamount of free gas in gas hydrate/water layer made an intensiveeffect in the reduction of P-wave velocity. In this situation,P-wave velocity decreases with increase in free gas saturation.This decrease is maximum when water is absent and only gashydrates and free gas is present in gas hydrate saturation zone(percentage of gas hydrates and free gas is 99% and 1%respectively).

3.2. Effect of Gas Hydrates Saturation and Distribution Pattern on AVO Response

Amplitude versus offset or amplitude versus incident angleanalysis depends on three basic elastic properties i.e., VP, VS

and bulk density of gas hydrate-bearing sediments. The resultof variation in these properties is change in reflectivity withincident angle at gas hydrate (upper layer) and free gas (lowerlayer) interface. The influence of gas hydrate saturation and

Fig. 5. P-wave and S-wave velocities of gas hydrate-bearing sediments as a function of (a) gas hydrates saturation, with uniform (GW)distribution (gas hydrates and water case), (b) free gas saturation, with uniform (GW) and patchy (GH) distribution (free gas and watercase).

Fig. 6. (a) Variation in P- and S-wave acoustic impedances with respect to gas hydrate saturation (Sh), (b) Variation in Poisson’s ratio,P-to-S wave velocities ratio with respect to gas hydrate saturation.

Fig. 7. Effect of free gas saturation on P-wave velocity of gas hydrate-bearing sediments. The input rock physics parameters used are givenin Table 1.


its distribution pattern on AVO response of hydrate-bearingsediments is modeled by using AVO forward modeling. Theseismic velocities (VP and VS) and density estimated in pre-vious sub-section are used as input parameters in AVO for-ward modeling. The velocities and density values of lowerlayer are given in Table 2. Figure 8 shows the AVO curvesat different saturation of gas hydrates in water under uniform

saturation. These curves are drawn by using Zeoppritz equa-tions by varying hydrates saturation from 0% (100% water)to 100% (0% water) at an interval of 20% for fix gas saturationbelow the BSR. The curves show highly negative values ofintercept (amplitude at 0° incident angle) and gradient (rateof change of amplitudes with angles), thus fall in class IIIreservoir (Castagna et al., 1998; Ahmed et al., 2015b). Thereason behind high negative amplitude is the high impedancecontrast between gas hydrate layer and free gas layer presentbeneath the BSR. The reflection coefficient at 0° incidentangle has maximum negative value when pores are fully satu-rated with hydrates and has minimum negative value for 0%water saturation. Amplitudes increase negatively with offsetand the gradient increases with increase in saturation of gashydrates.

4. CONCLUSION

The quantitative seismic response of gas hydrate saturationand distribution is studied using rock physics modeling andfluid substitution in the Makran accretionary prism. The resultsshow that increase in gas hydrate saturation causes an increasein bulk modulus of fluid, which may stiffen the effectivebulk modulus of hydrate-bearing sediments. However, thepresence of free gas may decrease the stiffness of the sed-iments. It is noted that seismic velocities and density ofhydrate-bearing sediments are highly affected by saturationand distribution pattern of gas hydrates. P-wave velocity inhydrate-bearing sediments is higher than those in free gassaturated sediments. A very small amount of free gas in gashydrate layer can produce significant reduction in P-wavevelocity. Some attributes like acoustic and shear impedance,and amplitude can be used as important proxies to detect gashydrate saturation. Highly negative amplitude for gas hydrate-bearing sediments shows a good coupling with rock physicsmodels to characterize the seismic properties of gas hydrate-bearing sediments in Makran area of Pakistan, which maygive a fruitful clue for quantitative seismic interpretation ofBSR. The gradient of AVO increases with increase in gas hydratesaturation, thus intercept versus gradient crossplot may alsobe used to quantify the concentration of gas hydrates.

ACKNOWLEDGMENTS: This research work is related to Ph.D.work of Mr. Muhammad Irfan Ehsan. Mr. Irfan’s Ph.D. is sponsoredby China Scholarship Council, which is highly acknowledged. Majorportions of this work have been done at the GeoSeis Modeling Lab ofthe Institute of Geology, University of the Punjab. The authors arethankful to the Institute of Geology for providing lab facilities.

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Fluid Type VP (m/sec) VS (m/sec) ρeff (kg/cc)

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80% Gas hydrate 2540 852.165 1972.65

60% Gas hydrate 2360 850.629 1979.67

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20% Gas Hydrate 2090 847.65 1993.71

10% Gas Hydrate 2036 846.90 1997.22

100% Brine 1985 846 2000

Gas Layer 1480 823 1740

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Manuscript received February 22, 2015Manuscript accepted July 7, 2015

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