estimation of gas hydrate and free gas saturation

School of Natural Sciences and MathematicsCenter for Lithospheric Studies

Estimation of Gas Hydrate and Free Gas Saturation,Concentration, and Distribution from Seismic Data

UT Dallas Author(s):

Shaoming LuGeorge A. McMechan

Rights:

©2002 Society of Exploration Geophysicists

Citation:

Lu, S., and G. A. McMechan. 2002. "Estimation of gas hydrate and free gassaturation, concentration, and distribution from seismic data." Geophysics67(2): 582-593.

This document is being made freely available by the Eugene McDermott Libraryof the University of Texas at Dallas with permission of the copyright owner. Allrights are reserved under United States copyright law unless specified otherwise.

GEOPHYSICS, VOL. 67. NO. 2 (MARCH-APRIL 2002): P. 582-S93. 12 FIGS. 10. I I L)0/1.14686 I Y

Estimation of gas hydrate and free gas saturation, concentration, and distribution from seismic data

Shaoming Lu* and George A. McMechan*

ABSTRACT

Gas hydrates contain a major untapped source of en- ergy and are of potential economic importance. The theoretical models to estimate gas hydrate saturation from seismic data predict significantly different acoustic/ elastic properties of sediments containing gas hydrate; we do not know which to use. Thus, we develop a new approach based on empirical relations. The water-filled porosity is calibrated (using well-log data) to acoustic impedance twice: one calibration where gas hydrate is present and the other where free gas is present. The water-filled porosity is used in a combination of Archie equations (with corresponding parameters for either gas hydrate or free gas) to estimate gas hydrate or free gas saturations.

The method is applied to single-channel seismic data and well logs from Ocean Drilling Program leg 164 from

the Blake Ridge area off the east coast of North America. The gas hydrate above the bottom simulating reflector (BSR) is estimated to occupy -3-8% of the pore space ( - 2 4 % by volume). Free gas is interpreted to be present in three main layers beneath the BSR, with average gas saturations of 11-14%, 7-11%, and 1-5% of the pore space (6-8%, 4 6 % , and 1-3% by volume), respectively. The estimated saturations of gas hydrate are very similar to those estimated from vertical seismic profile data and generally agree with those from independent, indirect estimates obtained from resistivity and chloride measurements. The estimated free gas saturations agree with measurements from a pressure core sampler. These results suggest that locally derived empirical relations between porosity and acoustic impedance can provide cost-effective estimates of the saturation, concentration, and distribution of gas hydrate and free gas away from control wells.

INTRODUCTION

Gas hydrates are icelike solids composed of natural gases (mainly methane) and water that occur under appropriate conditions of pressure and temperature (usually high pressure and low temperature). Because of their large volumes trapped in shallow sediments, gas hydrates are a potential source of en- ergy, submarine geologic hazards, and a factor in global climate change (Kvenvolden, 1998). However, the estimated amounts of in-situ gas hydrates worldwide are highly speculative and range widely from 3.1 x loL5 m3 to 7.6 x 10l8 m3 (Kvenvolden, 1988). Although the figure has converged to about 2.0 x 10l6 m3 in recent years (Makogon, 1997; Kvenvolden, 1998), accurate estimates are difficult because knowledge of the distribution and saturation of gas hydrates in sediments is very incomplete.

Most occurrences of gas hydrates are in deep oceanic regions and are generally recognized on the basis of bottom simulating reflectors (BSRs) on seismic sections. BSRs are strong reflections that are approximately parallel to the sea-floor reflection

and are believed to mark the base of gas hydrate stability zones. Beneath this stability zone, free gas may be present, which pro- duces a large impedance contrast. The amount of free gas below the BSRs can be large (Dickens et al., 1997) and therefore po- tentially economically important. We show that a reasonable estimate of the distribution and saturation of gas hydrate above the BSRs and free gas below the BSRs from seismic sections is technically feasible.

Various theoretical, semiempirical, and ad hoc models have been proposed to relate gas hydrate saturation to seismic velocity. Wood et al. (1994), Yuan et al. (1996), and Korenaga et al. (1997) use Wyllie et al.’s (1958) time average equation to estimate gas hydrate saturation after the velocity structure is obtained from seismic data. Lee et al. (1993,1996) use a weighted equation, and Ecker et al. (2000) use a theoretical rock model (Ecker et al., 1998) to estimate gas hydrate saturation. How gas hydrate modifies the acoustic/elastic properties of hydrated sediments is poorly known (Andreassen et al., 1995; Makogon, 1997), and the predictions obtained using different models vary

Manuscript received by the Editor August 19,2000; revised manuscript received May 29,2001. *University of Texas at Dallas, Center for Lithospheric Studies, PO. Box 830688 (FA 31), Richardson, Texas 75083-0688. E-mail: [email protected]. @ 2002 Society of Exploration Geophysicists. All rights reserved.

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Estimation of Gas Hydrate and Free Gas 583

widely even within one area. For example, estimates of gas hydrate saturation in the Blake Ridge area, offshore South Carolina, range from 50% of the pore space by using the time average equation (Wood et al., 1994; Yuan et al., 1996) to 10-15% of the pore space by using the weighted equation (Lee et al., 1993). Thus, we resort to derivation and use of empirical relations based on observations from the site being studied to provide internally consistent predictions of gas hydrate and free gas saturation and concentration.

In this study, we use borehole data from Ocean Drilling Program (ODP) leg 164 (Paull et al., 1996) and associated seismic data acquired by the U.S. Geological Survey (USGS) in 1995 on the Blake Ridge (Dillon et al., 1996). ODP leg 164 was drilled in 1995 to investigate the in-situ characteristics of hydrated sediments and to estimate the amount of gas hydrate. We use the resistivity, density, and velocity logs to develop an empirical relation to estimate water-filled porosity from acoustic impedance and then to estimate gas hydrate saturation via a combination of Archie equations. The results compare favor- ably with estimates of gas hydrate computed from resistivity and appear to be more reliable than those based on various theoretical models or on chloride concentration. We apply our method to the acoustic impedance section obtained by inversion of the seismic data. The main reason for using seismic data is that it provides information away from the wells. Near the well locations, the results from the seismic data fit closely with those from the well logs; this provides the basis for the estimates farther from the wells.

SEISMIC DATA AND WELL LOGS

The data used in this study include a single-channel seismic line, USGS95-1, and well logs from hole 994D of site 994, hole 995B of site 995, and hole 997B of site 997 (Figure 1). Detailed

information on data acquisition can be found in Dillon et al. (1996). The source-receiver offset was only 100 m, so the data are treated as if they were zero offset. Only predictive deconvolution (for a single wavelet across all traces), band-pass fil- tering (8-115 Hz), and spherical spreading compensation were applied in data processing; this preserves the relative amplitude information.

In the seismic section (Figure 2), two phenomena can be observed: a strong BSR and a reduction in amplitude (or blanking) of reflections above the BSR. The BSR has anomalously high amplitude and reverse polarity relative to the sea-floor reflection, and it mimics the relief of the sea floor. No obvious BSR is observed at site 994, while a modest to strong BSR is present at sites 995 and 997. The amplitude blanking zone above the BSR is obvious compared to the high reflectivity zone below the BSR.

Figures 3, 4, and 5 show the caliper, sonic, density, porosity, and resistivity logs recorded in holes 994D, 995B, and 997B, respectively, by Lamont-Doherty Earth Observatory of Columbia University (Paull et al., 1996). Variations in hole di- ameter reduced the quality of the density logs, but they are still useable. The porosity from the neutron logs is unreliable because they only detect the hydrogen in the borehole water (Paull et al., 1996). Resistivity logs are usually less sensitive to borehole conditions, so more reliable estimates of porosities can be obtained from resistivity logs. The total porosity 40 is estimated by Archie's (1942) relationship

where rn and a are environment-dependent empirical constants (e.g., Keller, 1987) and R,, and Ro are the resistivities of the pore water and of the formation fully saturated with water only,

i L ~~~ Leg 164 drlll slte

32000

4 3130 "-

a 0 '0 c c - (D A

3f40

1 I 1 I I b 75040 75030 7!5??0

Longitude ( " W)

a 02" 00" 70" 76" 74" 72'

Longitude ( W)

FIG. 1. Locations of the seismic line and drill sites 994,995, and 997 of ODP leg 164 in the Blake Ridge area. (a) The dark shaded area corresponds to the extent of BSRs (after Paull et al., 1996); bathymetric contours are in meters. (b) The heavy line is the location of seismic line USGS95-1 through holes 994D, 995B, and 997B.

584 Lu and McMechan

48.0 - - E 38.0

.- - d

28.0

respectively. Although equation (1) was originally proposed for clean, water-bearing formations, it is purely empirical and can be used with a variety of lithologies, provided that a and m apply to the specific environment of interest (Keller, 1987). We use Q and m obtained directly from the Blake Ridge (Paull et al., 1996) as described below. A modified Archie (1942) rela-

-

-

-

tionship is used to relate the measured formation resistivity R, to the water-filled porosity + (Paull et al., 1996); this relation is

46.0 I - 5

38.0- .- - d

30.0

Equation (2) uses the fact that R, is the same as Ro when the formation is fully water saturated (because the water-filled porosity 9 is then the same as the total porosity 40). The presence of gas hydrate or free gas in the pore space will reduce the water-filled porosity.

The value R,, in equations (1) and (2) is mainly a function of the temperature and salinity of the pore water and can be expressed by Arp's formula (Asquith and Gibson, 1982)

-

-

Rr(Tr + 21.5) R , =

T +21.5 ' (3)

FIG. 2. Single-channel seismic line USGS95-1 (Figure 1) across the Blake Ridge. The three vertical black lines are holes 994, 995, and 997 of ODP leg 164. A BSR and amplitude blanking are observed on the section.

p.

u) a in

I 1.5

70.01 \ ' I , i E

$ 60.0 -

n

- g

50.0 -

- 8 1.8- 3 .- c 6 1.6-

I I I

1.9t I -1

1.5

I I I

100 200 300 400 500 600 700 Depth (mbsf)

FIG. 3. Well logs from hole 994D. The dashed baseline in the resistivity log represents the resistivity of the formation saturated with water (Ro) . The vertical solid line marks the expected BSR location; no BSR is observed in the seismic data near the hole. The depth axis is in meters below the sea floor.

where R, is the resistivity of seawater at a given salinity at reference temperature T, and T is the formation temperature in degrees Celsius, which can be calculated from the geothermal gradient and the sea-floor temperature. For the data from the Blake Ridge considered below, we use measured values (Paull et al., 1996) of the salinity of the pore water (32 000 ppm), the

a m fn

- 8 1.8- 3 .- : 2 1.6-

1.8-

Y

>= - 1.6

I I I

~~

100 200 300 400 500 600 700 Depth (mbsf)

FIG. 4. Well logs from hole 995B. The dashed baseline in the resistivity log represents the resistivity of the formation saturated with water (Ro) . The vertical solid line marks the depth of the BSR. The depth axis is in meters below the sea floor.


geothermal gradient (3.85"C/100 m). and the sea-floor temperature (3°C). The seawater resistivity R, used is 0.24 ohm-m at T, = 18°C (GuCrin et al., 1999). Collett and Ladd (2000) suggest that the geothermal gradient may be lower (3.35- 3.68"C/lOO m).

The density logs in Figures 3-5 have been edited and smoothed to reduce effects caused by locally enlarged holes. The porosity logs in Figures 3-5 are estimated from the measured resistivity log by using equation (2) and therefore indicate the water-filled porosity. The original P -wave velocity log in hole 997B (the dashed line in the V , plot in Figure 5 ) has one low-velocity zone and one high-velocity zone below 560 m below the sea floor (mbsf), which do not correlate with any observed feature in the seismic data or the other logs. These anomalies are likely to be caused if the acoustic tool incorrectly selects velocities from the recorded sonic waveforms (Paull et al., 1996). The (solid line) P -wave velocity log plotted in Figure 5 includes estimated velocities for these two abnormal zones obtained by assuming the V,-p relation is similar to the regions right above and below the abnormal values.

The well logs from the three holes (Figures 3-5) have some common characteristics. The P -wave velocity continuously in-

K u) m - I ' I ' I 2 1.6

c 0 - Q 1.2 .- c UY UY .-

0.8

70.0 1 I -I

Q 5 :::I >-

28.0 , I . 1 100 200 300 400 500 600 700

Depth (mbsf)

FIG. 5. Well logs from hole 997B. The dashed baseline in the resistivity log represents the resistivity of the formation saturated with water (Ro) . The dashed line in the V , profile is the original data prior to correction for time picking errors (see text). The vertical solid line marks the depth of the BSR. The depth axis is in meters below the sea floor.

creases to the depth of the BSR and has an abrupt drop at the BSR. In the resistivity logs, there are high values above the BSR and a drop at the BSR. Above the BSR, water-filled porosity values are low compared to the normal compaction curve. Since there is no lithology change across the BSR (Paull et al., 1996), all these anomalies are considered to be indicators of differences in the pore fluid contents (gas hydrate, water, and free gas).

GAS HYDRATE SATURATIONS FROM RESISTIVITY LOGS AND CHLORIDE PROFILES

Formations containing gas hydrate have high resistivity anomalies and low chloride concentration anomalies in the pore water. These anomalies have been used to estimate gas hydrate saturation from both resistivity logs and chloride profiles (Paull et al., 1996; Yuan et al., 1996; Collett, 1998; GuCrin et al., 1999; and Collett and Ladd, 2000). In this section, we illustrate the estimation of gas hydrate saturation from these traditional measurements as the basis of comparison for the new estimates from seismic impedance presented in the following section.

Estimation of gas hydrate and free gas saturation from resistivity logs

Like ice, gas hydrates are electrical insulators (Pearson et al., 1983). Gas hydrate-bearing zones have relatively high electrical resistivities in comparison with water-saturated formations (see the dashed resistivity baselines in Figures 3-5). If we as- sume that the high resistivity above the BSR is caused by the presence of gas hydrate and that pores are filled partly with gas hydrate and partly with water, the gas hydrate saturation S is given by Archie's (1942) equation,

1

S = l - S , , = l - - , (y (4)

where S,,, is water saturation and Rl) is the resistivity of the formation fully saturated with water (for S,,, = 1 and S = 0). In the Blake Ridge area, the regional background resistivity profile R o ( Z ) is assumed to be the same at all points along the seismic line and is determined approximately for hole 995B (Paull et al., 1996; Collett and Ladd, 2000) by a least-squares linear fit with depth:

RO = 0.8495 + (2.986 x lOP4)Z, ( 5 )

where Z is the depth below the sea floor in meters; Ro is the dashed baselines in the resistivity plots of Figures 3-5; R, is the measured resistivity ( R , = Ro if S, = 1); and n is an empirical parameter. Thus, the amount of high-resistivity material (gas hydrate or free gas) in the pores is indicated by the amount of shift of R, above Ro. For hydrated clastic sediments, n = 1.9386 (Pearson et al., 1983). The form of equation (4) can also be used to estimate the free gas saturation in the zones containing free gas beneath the BSR. In the free gas zones we use n = 1.62 (GuCguen and Palciauskas, 1994).

Estimation of gas hydrate saturation from chloride profiles

Like ice, the formation of gas hydrate excludes the ions of dissolved salts. In an open system, the excluded ions diffuse away sometime after the formation of gas hydrate. Similarly, the

586 Lu and McMechan

salinity of the water is temporarily diluted after the dissociation of gas hydrate. Water samples recovered from a gas hydrate zone after gas hydrate dissociation during drilling have lower salinity than those from zones that do not contain gas hydrate (Kvenvolden and Barnard, 1983; Kvenvolden and Kastner, 1990; Paull et al., 1996).

The gas hydrate saturation S can be estimated from the chloride anomalies (Yuan et al., 1996) using

where Ph =0.9 is the value of density of pure gas hydrate in g/cm3 (Sloan, 1998). Here, CI,, is the measured chloride concentration in pore water samples, and CIS, is the chloride concentration of normal pore water (Paull et al., 1996); the latter is determined by smoothly fitting the chloride data above and below the gas hydrate zone with a low-order polynomial (Figure 6).

Results

In Figure 7, the green lines show the gas hydrate and free gas saturations estimated from resistivity logs with equation (4); the red dots show the gas hydrate saturations we estimated from chloride profiles with equation (6) for each of the three holes. The estimated gas hydrate saturation is 3-8% of the pore space. This is similar to the values obtained independently by

Paull et al. (1996). The anomalies obtained from resistivity are at locations similar to those from chloride, but the saturations estimated from resistivity are generally higher. The reason the results from chloride are lower may be because water entered the pore space during core recovery because the system was open. Thus, chloride appears to be a reliable indicator of the location of the hydrated zone but not as reliable as resistivity for quantitative estimation of saturation. We now compare the results from these indirect measurements (resistivity and chloride) with those from our new acoustic impedance method.

GAS HYDRATE SATURATION FROM ACOUSTIC IMPEDANCE LOGS

Little is known about the physical properties of hydrated sediments (Makogon, 1997), although the physical properties of pure gas hydrate (structure I) are well known (Sloan, 1998). The reason for this uncertainty is that gas hydrates are unstable at normal laboratory pressures and temperatures and become unstable during drilling and core recovery. Collett and Ladd (2000) cite decomposition of gas hydrate as a factor in the poor core recovery at all of the Blake Ridge drilling sites. Pressure core sampler (PCS) data are available from 17 depths in each of holes 995 and 997 (Dickens et al., 1997), but these are for very small (< 1 m long) samples. So they are less representative and exhibit larger variances with depth than the other estimates (Figure 7). Analysis of the PCS data also requires porosity information; the porosity data used by Dickens et al.

2s 7

z 20-

t -6 1 5 - p 10-

I "-

0 100 200 300 400 500 600 700 Depth (rnbsf)

FIG. 6. Chloride profiles from sites 994D, 99SB, and 997B. The dashed baselines represent the chloride concentration of the normal pore water. The unit of chloride concentration is mil- limoles (mM).

-- I 4.z

FIG. 7. Gas hydrate and free gas saturations estimated from the acoustic impedance log (blue), resistivity (green), and chloride (red). Measurements (black circles) from a pressure coring sampler (PCS) are also displayed for comparison. Saturation results are for (a) hole 99SB, (b) hole 994D, and (c) hole 997B.


(1997) were close (within 10 m) but not at the same locations of the PCS samples. Thus, although there is substantial indirect evidence of the presence and concentration of hydrate, direct measurements from cores are not available for comparison with predictions.

The most readily observable change in sediment physical properties resulting from the formation of gas hydrate is an increase in seismic velocity that is proportional to the amount of hydrate (Pearson et al., 1983). Ecker et al. (2000) use spatial variations in seismic velocity to estimate spatial variations in hydrate.

The output of seismic inversion is usually acoustic impedance rather than P-wave velocity. Acoustic impedance provides rock property information and has been used to discern rock types and as a direct hydrocarbon indicator (e.g., Latimer et al., 2000). Thus, it is desirable to develop a relation between gas hydrate saturation and acoustic impedance to estimate gas hydrate saturation from seismic data.

We have shown that water-filled porosity and gas hydrate saturation can be estimated from the formation resistivity by equations (2) and (4). Combining these two equations, we have a relationship between gas hydrate saturation S , water-filled porosity 4, and the resistivities of the fully water-saturated formation (Ro) and of the pore water (R,,,); this relation is

1 s = 1 - (-&-) Ro4m

(7)

Since Ro, rn, a , R,,,, and n can all be determined empirically for a particular environment, the only unknown in the right side of this equation is $. Thus, if we can establish a relationship between $ and acoustic impedance, we will be able to estimate gas hydrate saturation spatially from equation (7).

Water-filled porosity as a function of acoustic impedance

Consider a homogeneous sediment under normal compaction in the absence of gas hydrate and free gas. In this situa- tion, in the water-filled porosity versus acoustic impedance ($-I) plane we have a smooth baseline curve along which $ decreases and I increases with increasing depth (the solid line A X - G - E - B in Figure 8). Depth changes monotonically along this curve, so individual points are associated with specific depths of interest, such as the top of the gas hydrate zone and the BSR. If gas hydrate is now introduced at a representative depth C in Figure 8,$ will decrease and I will increase, moving point C to D. Point D lies above the baseline because the I of gas hydrate is larger than that of water as a consequence of its much higher velocity (-3.3 km/s compared to -1.5 km/s). Similarly, if free gas is introduced at some depth E below the BSR, both $ and I will decrease, moving point E to F .

In a zone containing gas hydrate, the shift of the @--I points above the baseline will indicate the amount of hydrate present in the same way that the shift of resistivity from the Ru baseline does in Figures 3-5. Similarly, in a free gas zone the shift of the $-I points below the baseline indicates the amount of free gas present. The water-filled baseline separates the $-I plane into regions containing gas hydrate (above the line) and those containing free gas (below the line). Our task is to quantify these relationships so they can be used to predict $ away from the control well.

To develop relations between water-filled porosity and acoustic impedance, we initially consider only data from hole 995B because it appears to be the most reliable of the three wells. We must separate the data by depth because there can be an overlap of $-I points from the gas hydrate zone (above the BSR) with those of the water-saturated zone below the BSR (see the hydrate trajectory G-H in Figure 8). The depth intervals in hole 995B that correspond to the gas hydrate zone and to the water-saturated zone above the gas hydrate zone are easily defined from the resistivity, acoustic impedance, and chloride profiles (Figures 4, 6, and 10). The free gas zones below the BSR can be identified by a combination of locally low V,,/ V, and locally low I (Figures 9b and 10) (GuCrin et al., 1999); the remaining points below the BSR are assumed to be water filled and thus to be approximated by the water-filled baseline (Figure 9a). The position of the water-filled baseline is difficult to define except at its ends (where water-saturated zones are known to occur) because the original baseline is destroyed by the shifting associated with the presence of gas hydrate or free gas (Figure 8). A few remnants of the baseline may remain if there are some depth intervals that contain no gas hydrate within the gas hydrate zone. It is also expected (from Figure 8) that the original baseline lay in the gap between the present gas hydrate and free gas points, so it can be located approximately, even in the absence of explicit points on the baseline (Figure 9b).

With these interpretations and guidelines, we proceed with constrained least-squares fitting of $-I curves for the data from hole 995B to obtain

4 = -26.413 + 261.712 - 866.71 + 1015.0 (8)

with standard deviation 1.34 for the water-filled baseline (Figure 9a),

9 = -0.479412 - 9.08411 + 88.3446 (9)

with standard deviation 0.89 for the gas hydrate zone (Figure 9b), and

4 = (19 .80~ 10-")12-(126.20~ w 4 ) 1 +252.44 (10)

66 - lncnulng depm

50 t I #

2.4 2.6 2.8 3.0 3.2 3.4 3.6 Acoustlc Impedance (x106 kg/m?mls)

FIG. 8. Sketch of expected porosity-impedance trajectories. Gas hydrates move points off the water-filled baseline to the right, and free gas moves points off to the left.

588 Lu and McMechan

withstandarddeviation0.78for the freegaszone (Figure9b). In equations (8)-(10), I is the acoustic impedance in kg/m3 . m/s divided by 10'. These fitted curves clearly provide only average values of 6. In principle, more accurate predictions of q5 can be made by isolating the @-I trajectories for individual layers; there appear to be some trajectories similar to C-B of Figure 8a in Figure 8c, but we have not attempted this here because of the ambiguity in selection when multiple curves are present; we fit only one average curve for the gas hydrate zone and one for the free gas zones. This simplification is the main reason for the scatter of points about the best- fit lines. The effect of propagating these standard deviations into the uncertainties in the final estimates of free gas and hydrate concentrations are described in the Discussion section. Changes in lithology will also affect the baseline and deviations from it; lithologic variations may be the explanation for the few points lying far to the left of the baseline in the hydrated zone (Figure 9b) and the obvious, but otherwise unex- plained, spread of the water-saturated points below the BSR (Figure 9a).

Estimation of gas hydrate saturation at the holes

Using functions (8)-( lo), we first estimate the water-filled porosity from the acoustic impedance well-log data at hole 995B. Then we use equation (7) to predict the gas hydrate and free gas saturations using a = 0.9 and rn = 2.7 as derived from hole 995B by Paul1 et al. (1996). Collett and Ladd (2000) independently estimate average values for a and rn of 1.05 and 2.56, respectively. The values of n used are 1.9368 for the nonfree

gas region (Pearson et al., 1983) and 1.62 for the free gas region (GuCguen and Palciauskas, 1994). The results are shown in Figure 7a. The gas hydrate saturations estimated from the acoustic impedance log (in blue) are very similar to those estimated independently from resistivity (in green) and are generally higher than those from chloride concentration (in red).

We next apply relations (8)-(10) developed using well logs from hole 995B to predict gas hydrate saturations in holes 994D and 997B. We again obtain saturation values (Figures 7b and 7c) consistent with those estimated from the resistivity and higher than those estimated from the chloride concentration. These examples show that this approach based on Archie's equations appears to work well with porosities determined from acoustic impedance by the fitting functions. With the support of this consistency check at the wells, we proceed to extend the gas hydrate and free gas estimates throughout the seismic section (Figure 2).

GAS HYDRATE SATURATION FROM SEISMIC DATA

Well-log data provide information only at the well locations. To understand the whole picture of an area such as the Blake Ridge, we can use 2-D or 3-D seismic data to extend the well information spatially. Since the acoustic impedance obtained from seismic inversion is the pseudoacoustic impedance log at every seismic trace, we can estimate the gas hydrate saturation from seismic data using the method described above, once the seismic data are inverted for acoustic impedance and calibrated with the well logs. Thus, we first invert the Blake Ridge seismic data (Figure 2) for acoustic impedance.

-I- F

.* - ..*

a b I 8 I I I I I I I I I I I

24 26 28 3.0 32 3.4 3.6 24 26 28 3.0 b2 3.4 $6 Acaurtlc IlnpeQncs (do6 k&hh) A a W k lmpu lm (xlo" kgh?m4)

FIG. 9. Crossplots of water-filled porosity and acoustic im edance. (a) The water-filled baseline, constrained to go through the data points and between the hydrate and free gas points in (bg. (b) The hydrate and free gas zones show well-separated trends above and below the water-filled baseline, respectively.


Constrained sparse spike inversion

Inversion of the seismic data for acoustic impedance is per- formed with Jason Geosystems’ Constrained Sparse Spike In- version (CSSI) package (Torres-Verdin et al., 1999; Helgelsen et al., 2000). CSSI is based on the generalized sparse spike time-domain inversion formulation by Fullagar (1985).

Since the seismic data are band-limited, the CSSI acoustic impedance estimates do not, by themselves, have accurate low-frequency information. The low-frequency impedance information is obtained from the low-frequency trends of the impedance logs from the wells (Lindseth, 1979; Jason Geosystems, 1999) and is interpolated and extrapolated following control horizons to all other locations. The control horizons are the water bottom, the top of the hydrated zone, and the BSR; these boundaries are first identified in the holes (as described above) and then are extended laterally, guided by the geometry seen in the seismic data (Figure 2). Where the boundaries are not clearly defined, the control horizons are extended parallel to the water bottom.

CSSI finds acoustic impedance values within prescribed constraints by minimizing the objective function

F = c(ri)p + hq c(di - ~ i ) ~ (11)

at time i , where ri is the reflection coefficient (which is a function of acoustic impedance), h is the data mismatch weigh-

a m v)

I I I

0.7

0.5 >-

‘ I 0.3 I

L I 1 100 200 300 400 500 600 700

Depth (mbsf)

FIG. 10. Well logs from hole 995B. The acoustic impedance is the product of the density and V, logs. The acoustic impedance and V p / V s are used to identify the free gas zones; the three main ones discussed in the text are labeled A, B, and C and correspond to the similarly labeled features in Figures 11 and 12.

ting factor, di is the recorded seismic acoustic trace, si is the synthetic trace, and p and q are empirically determined expo- nents that weight their corresponding contributions to F . We use h =25, q =2, and p =0.9.

The input data for CSSI include the time-migrated seismic data, the seismic wavelet, interpreted control horizons, and the interpolated low-frequency impedance trend. The source- time wavelet was estimated in the frequency domain with well control by iteratively matching observed and calculated seis- mograms; the latter are based on the velocity and density well logs. A single wavelet provided a good match to the data at all three wells, so spatial or temporal variations in the wavelet are not of concern with respect to possible influence on the final results. A reasonable wavelet is important to CSSI.

The interpolation/extrapolation at any position involves weighting data from all available wells, weighted inversely proportional to the distance from each of the wells. Thus, at a well the data profile is exactly that of the well. For points between two wells, the interpolation is dominated, but not totally determined, by the profiles at those two wells. At distances far from all wells, the interpolation tends to the average profile of all of the wells (between each of the control horizons).

4.0

FIG. 11. (a) The acoustic impedance distribution obtained by CSSI. The low-impedance layers below 4.2 s are considered to be free gas zones. The water-filled porosity section (b) is estimated from the acoustic impedance section using equations @)-(lo). (c) The saturation of gas hydrate and free gas estimated using the water-filled porosity section (b), equation (7), and the appropriate parameters in the gas hydrate and free gas zones. The BSR is A; other labeled features are discussed in the text.

590 Lu and McMechan

Results

Figure 1 l a shows the acoustic impedance distribution obtained by CSSI. We apply the fitting functions [equations (8)-(lo)] to their respective regions of the acoustic impedance section to obtain the estimated water-filled porosity section (Figure 1 lb). Figure l l c shows the distribution and saturation of the gas hydrate and free gas obtained from the water-filled porosity section by using equation (7). Again, we use different values of n for the nonfree gas and the free gas zones. The zone boundaries are clearly visible in Figure 12 and correspond to the control boundaries used in extrapolating the low-frequency impedance data away from the holes.

To estimate the volume concentrations of gas hydrate (CH) and free gas (Cc), we use the relations

and

CG = 4OsG 3 (13)

where SH and SG are the hydrate and free gas saturations, respectively. Assuming that gas hydrate and free gas do not coex- ist, the total porosity can be estimated from the water-filled porosity 4 by the relations

(14) 4

40 = ~ 1 - S H

for the gas hydrate zone and

4 40 = - 1 - SG

for the free gas zone. Figure 12 shows the resulting gas hydrate and free gas volumes. The figure is obtained from the water- filled porosity section (Figure l l b ) and the saturation section

m

FIG. 12. Estimates of the volumetric concentration of (a) gas hydrate and (b) free gas obtained from the data in Figures l l b and l l c with equations (11) and (12). The corresponding estimated volumetric water distribution is shown in Figure l lb . The BSR is A; other labeled features are discussed in the text.

(Figure l l c ) with the corrections given by equations (12) and (13). The water concentration equals the water-filled porosity, which is plotted in Figure l lb. The estimated saturation of gas hydrate (Figure l l c ) is generally - 3 4 % of the pore space, which is similar to the 5-7% estimated from vertical seismic profile data with Lee et al.’s (1993) weighted equation (Holbrook et al., 1996). The corresponding gas hydrate concentration (Figure 12a) is -2-5% by volume. Our results are also similar to estimates of gas hydrate concentration by a pressure core sampler (PCS), which range between 0 and 9% by volume (Dickens et al., 1997).

The results also indicate the distribution and saturation of at least three low-impedance sub-BSR layers that we interpret as containing free gas (Figures 10, l l c , and 12b). The free gas saturation of the first layer (A) (immediately beneath the BSR) is about 11-14% of the pore space, with the highest concentration (&8% by volume) occurring near site 997. The second layer (B), which is also observable as a reflection in the original data (Figure 2 ) , where it parallels the BSR and cuts across the dipping lithology, has a saturation of 7-11% of the pore space and a concentration of 4 4 % by volume. The third layer (C) is not continuous, is about 30 m thick, is visible across most of the section, and has an estimated gas saturation of 1-5% of the pore space and concentration of 1-2% by volume. These estimates are higher than those obtained by Ecker et al. (2000) and Holbrook et al. (1996), which are about 1-2% of the pore space but are reasonable when compared with the results from the PCS (Figure 7), which are as high as 22% of the pore space (-12Y0 by volume) immediately below the BSR at site 997 (Dickens et al., 1997).

Near the well sites, the gas hydrate and free gas saturation estimates obtained by inversion of the seismic data (Figure 1 lc) fit very well with those from the acoustic impedance logs in the wells (Figure 7). The main advantage of using acoustic impedance as the basis of studying gas hydrate saturation is that it can be used wherever seismic data exist, provided that well logs are available for calibration. At the wells, the low-frequency component of acoustic impedance in the well logs and the low-frequency component constructed from the seismic data are identical because the latter is defined by the former.

DISCUSSION

Accuracy and limitations of the method

Our method is based on a combination of two Archie equations and an indirect empirical estimation of water-filled porosity from acoustic impedance. In equation (7), the values a , m , n , R,,,, and Ro are all determined empirically for the Blake Ridge, as described above. The method used to define these values affects the estimates of saturation. When these values are determined, the gas hydrate or free gas saturation (S) de- pends only on 4. This assumes that the reduction of water-filled porosity above the BSR is caused by the presence of gas hydrate in the pores and the reduction below the BSR is caused by the presence of free gas in the pores.

Hyndman et al. (1999) discuss the importance of account- ing for changes in pore fluid salinity with depth when using resistivity to estimate hydrate concentration. This is related to the baseline reference resistivity level Ro [equation ( 5 ) ] . GuCrin et al. (1999) argue that (at least for the Blake Ridge)


the resistivity of the water-saturated sediments (which is what we use) provides a reliable baseline that compares well with the more rigorous salinity analysis.

The water-filled porosity is estimated from acoustic impedance by the empirical equations @)-(lo). These equations were derived for the Blake Ridge site, so the coefficients are not expected to be general, but the procedure is applicable to any other data. Well-log data are needed to develop the empirical relationship between water-filled porosity and acoustic impedance in other areas. By using parameters derived for the clay-rich sediments of the Blake Ridge, the Archie equations seem to produce reasonable gas hydrate and free gas saturations (Collett and Ladd, 2000).

The standard deviations of the impedance-porosity functions [equations (9) and (10) and Figure 91 can be propagated through the subsequent calculations to provide an estimate of the corresponding uncertainties in the final volume concentrations of hydrate and free gas. Since the effect of &) on S is nonlinear [equation (7)], the corresponding uncertainties in CH and CG [from equations (12) and (13)] are of different magnitudes, depending on whether the q5 variation is above or below the fitted functions (Figure 9). The calculated uncertainties in the values of C H are +0.93 and -1.18; for Cc, they are +0.74 and -1.05.

The nature of BSRs

Whether free gas is present in the underlying sediments has been a controversial issue (Dillon and Paull, 1983; Hyndman and Spence, 1992; Singh et al., 1993). Recent studies (Ecker and Lumley, 1994; Andreassen et al., 1995, 1997; Yuan et al., 1996,1999; Ecker et al., 1998) and ODP data from legs 141,146, and 164 indicate free gas is very likely to be present beneath the BSRs.

In Figure 12b, near site 994, no free gas is predicted immediately below the gas hydrate zone, and no obvious BSR can be observed at this location in the seismic section (Figure 2). At the other two holes (995 and 997), free gas layers are predicted to be present below the gas hydrate zone, and a strong BSR can be observed in the seismic section. This result supports the model that BSRs are consistent with the presence of free gas below the gas hydrate zone.

The nature of the amplitude blanking zone

The nature of amplitude blanking is also a controversial and unsolved issue. Based on vertical seismic profiling on ODP leg 164, Holbrook et al. (1996) suggest that the amplitude blanking on the Blake Ridge may be attributed to the relative homogeneity of the sediments rather than to hydrate cementation. Other authors (Lee et al., 1993,1994; Dillon et al., 1994, 1996) conclude that amplitude blanking in the Blake Ridge area is caused by hydrate cementation, and the degree of blanking is proportional to the amount of hydrate in the pore space.

A high concentration of gas hydrate (labeled D in Figures 1 1c and 12a) is predicted near site 995 at the amplitude blanking zone in the seismic section (Figure 2). However, another zone of high hydrate concentration (labeled E) is at the right end of the section, where no amplitude blanking can be observed. In other parts of the section, amplitude blanking also does not correspond to the hydrate concentration. Based on these observations, we conclude that there is no one-to-one relation-

ship between hydrate concentration and amplitude blanking. Amplitude blanking may be produced both by lithologic homogeneity and hydrate concentration.

Distribution of gas hydrate and free gas

The spatial distribution and concentration of gas hydrate and free gas are a consequence of the origin and migration of the gas (including structural controls, such as faults and impermeable layers) and the pressure/temperature stability regime of gas hydrate. Thus, we can speculate regarding the patterns shown in Figures 12a and 12b and relate them to geologic factors in the environment.

Gas hydrate can contain gas that is of biogenic or thermo- genic origin (Sloan, 1998); the gas may have formed in-situ or may have migrated to a zone where gas hydrate is formed, or both. Gas on the Blake Ridge has been interpreted to be biogenic (Sloan, 1998). Site 997 corresponds to the local structure high and is thus the expected location of gas accumulation beneath an impermeable layer. The maximum gas hydrate accumulation, however, is near site 995 (labeled D in Figure 12a), which is consistent with an observed increase in fault density [see Figures 4 and 5 of Dillon et al. (1996)], which provides high-permeability pathways for gas migration into the over- lying zone of gas hydrate stability. The increase in gas hydrate concentration at E (in Figure 12a) also coincides with both increased faulting and reduced free gas concentration in layer A (Figure 12b), which are interpreted as the cause and effect, respectively, of upward free gas seepage. The gas hydrate stability zone may itself have moved upward over time (Paull et al., 1994) as the sediment thickness increased.

The lateral distribution of gas hydrate between locations D and E (Figures 1 l c and 12a), with decreased concentration near site 997, is consistent with decreased availability of free gas away from the faulted zones by local capture of free gas by gas hydrate formation. The geometric pattern of gas hydrate is presumably also influenced by the pattern of lateral and vertical fluid permeability that controls free gas transport.

Interestingly, the base of the gas hydrate and the top of the free gas (A) are not coincident; there appears to be a small gap in between (F in Figure l lc), which has both low free gas and low gas hydrate concentrations. This is explained if the gas is confined by an impermeable (e.g.. water-saturated clay) layer as described above and the bottom of the gas hydrate stability zone is slightly shallower than the top of this impermeable layer. A more sophisticated explanation is provided by Xu and Ruppel (1999), based on fluid and methane flux rates and the solubility of methane in seawater. This model predicts a zone between the bottom of the hydrate and the top of the free gas in which methane is dissolved in the water and neither hydrate nor free gas is stable.

At the micromechanical scale, Ecker et al. (1998) propose two models of hydrate distribution. In the contact-cement model, the hydrate cements grain contacts and strongly reinforces the sediments. In the noncontact-cement model, the hydrate is located away from grain contacts and does not affect the stiffness of the sediment frame. They conclude, from seismic elastic amplitude variation with offset (AVO) compu- tations, that the noncontact-cement model is the more likely of the two. On the other hand, Helgerud et al. (1999) show better agreement, at site 995, of the contact-cement model with other independent estimates of hydrate concentration (resistivity,

592 Lu and McMechan

chloride, and evolved gas). These opposite conclusions (both based on Blake Ridge data) suggest that t he model is not yet sufficiently well understood and that more work is needed; for example, neither tested the alternative model of Xu and Ruppel (1999). The present study, as it is empirically based, does no t allow explicit discrimination between these models. Neither t he density nor the water-filled porosity is affected by the microspatial distribution of hydrate. The elastic constants (and hence velocity) a r e affected by the choice of model, but here w e use only the measured velocity and impedance profiles, which do not require knowledge of t he underlying micromechanical model.

SYNOPSIS

The presence of gas hydrate in sediments results in anomalies in resistivity, chloride concentration, P-wave velocity, acoustic impedance, and water-filled porosity. All of these anomalies can be used t o indicate the presence of gas hydrate above the BSR.

We have developed a n empirical method based on Archie’s equations to estimate gas hydrate saturation via acoustic impedance. The results are in general agreement with those obtained from resistivity and chloride and from evolved gas measurements by PCS. This also provides a feasible method t o estimate gas hydrate and free gas saturation and concentration from impedance derived by inversion of seismic data away from the control wells.

ACKNOWLEDGMENTS

The research leading t o this paper was funded by the spon- sors of the UT-Dallas Geophysical Consortium and by the Petroleum Research Fund of the American Chemical Society through grant 36706-AC. We thank Bill Dillon of the USGS for providing the seismic da t a and David Goldberg of Lamont- Doherty Ea r th Observatory of Columbia University for his V , log. Discussions with Timothy S. Collett of t he USGS have been very helpful. We also gratefully acknowledge Jason Geosys- tems for the acoustic impedance inversion software. We thank Jeff Wright, George Spence, Zhi-jing Wang, and an anonymous reviewer for constructive comments. This paper is contribu- tion 940 from the Geosciences Department a t the University of Texas at Dallas.

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estimation of gas hydrate and free gas saturation

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