Rock physics of a gas hydrate reservoir. Gas hydrates are solids composed of a hydrogen-bonded ROUND TABLE

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1 ROUND TABLE Rock physics of a gas hydrate reservoir JACK DVORKIN and AMOS NUR, Stanford University, California, U.S. RICHARD UDEN and TURHAN TANER, Rock Solid Images, Houston, Texas, U.S. Gas hydrates are solids composed of a hydrogen-bonded water lattice with entrapped guest molecules of gas. There are convincing arguments that vast amounts of methane gas hydrate are present in sediments under the world s oceans as well as in onshore sediments in the Arctic. This hydrate is possibly the largest carbon and methane pool on earth. As such, methane hydrate may be the principal factor in global climate balancing. One may also treat this methane pool as a potential energy source. These considerations ignite the scientific and business community s interest in quantifying the amount of methane hydrate in the subsurface. Gas hydrate reservoir characterization is, in principle, no different from the traditional hydrocarbon reservoir characterization. Similar and well-developed remote sensing techniques can be used, seismic reflection profiling being the dominant among them. Seismic response of the subsurface is determined by the spatial distribution of the elastic properties. By mapping the elastic contrast, the geophysicist can illuminate tectonic features and geobodies, hydrocarbon reservoirs included. To accurately translate elastic-property images into images of lithology, porosity, and the pore-filling phase, quantitative knowledge is needed that relates the rock s elastic properties to its bulk properties and conditions. Specifically, to quantitatively characterize a natural gas hydrate reservoir, we must be able to relate the elastic properties of the sediment to the volume of gas hydrate present and, if at all possible, the permeability. One way of achieving this goal is through rock physics effective-medium modeling. Rock physics models in perspective. Several attempts to construct a relation between hydrate concentration and the compressional velocity in sediments have followed the path of modifying the popular Wyllie s time average equation which states that total traveltime through rock is the volumeweighted sum of traveltimes through the solid phase and the fluid phase considered independently of each other; i.e., V P = (1-φ)V PS + φv PF, where φ is the total porosity, V P is the P- wave velocity in the rock, and V PS and V PF are the P-wave velocity in the solid and in the pore-fluid phases, respectively. The original work of Wyllie et al. (1956) is based on laboratory measurements of ultrasonic wave propagation through a pile of alternating lucite and aluminum disks set parallel to one another. The individual disk thickness varied between 1/16 and 1/2 inch. As expected, total traveltime through such a layered system was the sum of traveltimes through lucite and aluminum considered independently of each other. Next, by examining a large data set of artificial and natural liquidsaturated porous samples, Wyllie et al. (1956) established a remarkable and somewhat unexpected fact that the velocity data can be approximately described by the time average, as if the mineral grains and the pore space in rock were arranged in relatively thick layers normal to the direction of wave propagation. Obviously, this is not what the pore space structure of many natural sediments appears to be, which means that Wyllie s Figure 1. Velocity versus porosity in water-saturated sand. The symbols are from well log data light and dark blue from cemented sand intervals, red from an unconsolidated sand interval. The curves are Wyllie s time average (WTA) and the Dvorkin and Nur (1996) model (DN). WTA is not appropriate for soft sediment. Figure 2. P- (left) and S-wave (right) velocity versus porosity in sediments with gas hydrate. Porosity by definition is the space not occupied by the mineral phase. It includes both water and gas hydrate. The symbols are from onshore well log data. The high-velocity data highlighted by yellow come from hydrate-saturated sand. The blue curves are from the DN model for water-saturated shale (the lower curve) and sand (the upper curve). The red curves are from GHM, as described in the text, for 40% gas hydrate saturation (the lower curve) and 60% gas hydrate saturation (the upper curve). time average is a useful and simple but physically deceptive way of summarizing extensive experimental data. Therefore, further exploiting this equation by summing up traveltimes through the mineral components of the solid phase and/or through the components of the pore-filling material (such as water and gas hydrate) cannot be justified by first-principle physics and thus is likely to be erroneous. Also remember that Wyllie s time does not work in unconsolidated sediments where apparently most methane hydrate is concentrated. Nevertheless, various modifications of Wyllie s time average, and weighted combinations of Wyllie s time average and Wood s (1941) relation, have found their way into the gas hydrate reservoir characterization literature. Generally, by fine-tuning the input parameters and weights, these equations can be forced to fit a selected data set. The problem with such fitting is that equations that are not based on first physical principles provide little or no physical insight. More important, they are not predictive because it is difficult to establish a systematic pattern of adapting free model parameters to site-specific conditions in the exploration mode.

2 Figure 3. P-wave impedance in km/s g/cc (left) and Poisson s ratio (right) versus porosity and gas hydrate saturation of the pore space in water-saturated sand with 10% clay content. Color coding is by the impedance (left) and Poisson s ratio (right). of the saturated sediment are calculated using Gassmann s fluid substitution. The model accurately describes velocity-porosity trends present in well log data from soft unconsolidated clastic sediments and is not appropriate for fast sands with diagenetic cement (Figure 1). It is shown in the same figure that Wyllie s time average can be used for describing fast sands but fails in soft sediments. Prasad and Dvorkin (2001) establish the applicability of the DN model to unconsolidated marine sediments in many geographic locations. The DN model can be modified to include the effect of gas hydrate present in the pore space on the elastic moduli. In the resulting gas hydrate model (GHM), the hydrate is simply treated as part of the load-bearing frame i.e., its presence acts to reduce the porosity and, at the same time, alter the elastic properties of the composite solid matrix phase. The net effect is an increase in the P- and S-wave velocity in water-saturated rock where part of the pore space is filled with gas hydrate (Figure 2). Figure 4. Hydrate concentration in rock (the color code) versus the P-wave impedance (in km/s g/cc) and Poisson s ratio for water-saturated sand with 10% (left) and 20% (right) clay content. The color coding is by the hydrate concentration. Highest hydrate concentration domains are circled. An effective-medium model. Helgerud et al. (1999) used a physics-based effective-medium model to quantify methane hydrate concentration from sonic and check-shot data in a well drilled through a large offshore methane hydrate reservoir at the Outer Blake Ridge in the Atlantic. Sakai (1999) used this model to accurately predict methane hydrate concentration from well log P- and S-wave data as well as VSP data in an onshore gas hydrate well in the Mackenzie Delta in Canada. Ecker et al. (2000) used the same model to successfully delineate gas hydrates and map their concentration at the Outer Blake Ridge from seismic interval velocity. This effective-medium model for sediment with gas hydrate is based on the Dvorkin and Nur (1996) model (DN), which relates the elastic moduli of soft unconsolidated clastic sediment to the porosity, pore fluid compressibility, mineralogy, and effective pressure. The model assumes that at the critical porosity of 30-40%, the effective elastic moduli of the dry mineral framework of the sediment can be calculated using the Hertz-Mindlin contact theory for elastic particles. This end point is connected with the zero-porosity, pure mineral, end point by the modified lower Hashin-Shtrikman (HS) bound which is appropriate for the description of uncemented rock. For porosity above the critical porosity, the critical porosity end point is connected with the 100% porosity end point (zero elastic moduli) by the modified upper HS bound (Dvorkin et al., 1999). In a common case of mixed mineralogy, the elastic constants of the solid phase are calculated from those of the individual mineral constituents using Hill s average equation. Once the dry-frame elastic moduli are known, those Putting numbers into the model. Here GHM is used to predict the elastic properties of sand with porosity ranging from 20 to 40% filled with solid methane hydrate with the hydrate saturation in the pore space ranging from zero to 100%. The rest of the pore space is filled with brine. The assumed mineralogy is 90% quartz and 10% clay. The results in Figure 3 indicate that the larger the gas hydrate concentration at fixed porosity the larger the P-wave impedance and the smaller the Poisson s ratio (PR). The two plots in Figure 3 can be used to extract both the total porosity and gas hydrate concentration from elastic well log or impedance inversion data. The net amount of the hydrate in a unit volume of rock (hydrate concentration in rock), which is likely to be the ultimate goal of gas hydrate exploration, is the product of the total porosity and gas hydrate saturation of the pore space. This quantity is modeled and plotted versus the P-wave impedance and Poisson s ratio in Figure 4 for sands with 10 and 20% clay content. Small variations of clay content in hydrate-bearing sand do not dramatically change the range of elastic attributes within which high gas hydrate concentration can be found. These ranges for PR and P-wave impedance are and 7-9 km/s g/cc, respectively. The rock physics model used here helps discriminate sediments with commercial gas hydrate concentration from the background water-saturated rock and sands with free gas in the elastic attribute space. In Figure 5 (left), the sand-withhydrate domain in the impedance-pr plane is color-coded by hydrate concentration in the rock while the sand-withfree-gas domain is yellow and the sand/shale-with-water domain is cyan. The target, sand with a large hydrate con-

3 Figure 5. Hydrate concentration in rock (HC) versus the P-wave impedance and Poisson s ratio (left) and the P-wave velocity and V P /V S ratio (right). The cases displayed include sand with gas hydrate with clay content 10% and 20%; water-saturated sand with clay content between zero and 100%; and sand with free gas with clay content 10% and 20%. The data for sand with gas hydrate are colorcoded by hydrate concentration in rock. The data for sand with free gas are yellow, and data for water-saturated sand are cyan. a b c d Figure 6. Pseudosection of earth with a dipping sand layer encased in shale. From left to right: (a) Clay content (small in the sand and large in the shale). The horizontal white bar indicates the hydrate-free gas contact. (b) P-wave impedance in km/s g/cc. (c) Poisson s ratio. (d) The inverse quality factor. centration, is characterized by a relatively high impedance and medium-to-high PR. The same model data but displayed in the V p -V p /V s domain are on the right of Figure 5. Figure 7. Pseudosection of earth with a dipping sand layer encased in a shale. The product (left) of the impedance and quality factor divided by The product (right) of the impedance and Poisson s ratio. Hydrate in a pseudosection. Consider a vertical section of earth where a dipping sand layer is encased in shale (Figure 6). The shale is fully saturated with water. The upper part of the sand layer is partially saturated with methane hydrate with the hydrate saturation of the pore space about 50%. The lower part of the sand contains free methane gas with about 20% gas saturation. Such arrangement of methane hydrate and free gas is likely in seabottom sediment where the hydrate-gas contact position corresponds to the lower boundary of the stability zone of methane hydrate. In several documented cases, a strong impedance contrast is observed between the sediment with hydrate and the underlying sediment with free gas. This contrast gives rise to a strong seismic reflection known as the bottom-simulating reflector (BSR). The elastic properties of the sediment in the vertical pseudosection under examination are calculated according to the above-described GHM model. This model becomes the DN model if no hydrate is present in the pore space. Figure 6 shows the modeled P-wave impedance and Poisson s ratio. As expected, there is a strong impedance contrast between the sand with gas hydrate and the sand with free gas. The impedance in the sand with gas hydrate is also much larger than that in the shale. This large impedance may serve as an indicator of hydrate-cemented sand in a shallow marine environment usually composed of very soft sediments. Poisson s ratio obtained from elastic impedance inversion is useful as a free gas indicator. PR in the sand with free gas falls below 0.2 while that in the sand with gas hydrate and in the shale exceeds 0.3. Also, PR in the hydratecemented sand is smaller than in the shale background and should be expected to be smaller than in water-saturated sand without gas hydrate (Figure 5). Therefore, PR, in addi-

4 Figure 8. Model-derived P-wave impedance (km/s g/cc) versus hydrate saturation color-coded by the total porosity. 5% clay content (left). 15% clay content (right). Figure 9. Pseudowell with methane hydrate. From left to right: clay content; total porosity; hydrate and gas saturation; P-wave impedance; and Poisson s ratio. The impedance and PR are calculated from porosity, clay content, and saturation according to the gas hydrate model. In the last two frames the blue curves are for the original log data and red curves represent Backus average upscaling. tion to the impedance, can serve as an indicator of hydratecemented sand. Elastic-wave attenuation, if properly extracted from seismic data, may become an important attribute for subsurface characterization. To calculate the inverse quality factor in the pseudosection under examination, we use a combination of a newly developed theoretical model of Dvorkin et al. (yet unpublished) for partially gas-saturated sediment and an empirical model of Koesoemadinata and McMechan (2001), the latter for fully water-saturated sediment. The results in Figure 6 indicate that one should expect strong intrinsic attenuation in the gas-saturated sand and very small attenuation in the hydrate-cemented sand. These attenuation modeling results are supported by analyses conducted by Rock Solid Images on real seismic data from a gas hydrate reservoir. The primary seismic elastic and inelastic attributes can be combined into hybrid attributes to better highlight various parts of the reservoir (Figure 7). For example, the product of the impedance and quality factor is large in hydrate-cemented sand because both primary attributes are large there. The opposite is true for the product of the impedance and Poisson s ratio, all of them small in sand with free gas. Hydrate saturation from impedance. The ultimate goal of the rock physics modeling presented here is to determine gas hydrate saturation of the pore space from seismic data. We have established that there is a strong relation between the P-wave impedance and the amount of hydrate in the pore space. Therefore, impedance inversion is an appropriate technique for gas hydrate reservoir characterization. Unfortunately, multiple factors affect the elastic properties of sand with hydrate. Some (such as the bulk modulus and density of the pore fluid, and the differential pressure) are relatively easy to bound. The remaining factors (porosity, clay content, and gas hydrate saturation) are impossible to uniquely determine from the acoustic impedance. However, model-driven bounding can help bracket the results. Assume, for example, that the total porosity of a hydratecemented sand body may vary between 20 and 30% and the clay content may vary between 5 and 15%. Then model-derived nomograms (Figure 8) can provide a reasonably narrow range of hydrate saturation from impedance. For example, if the measured impedance is 7 km/s g/cc then the hydrate saturation lies between 45 and 80%. This degree of narrowing uncertainty is realistically achievable. It can only be further reduced by imposing additional stringent assumptions on reservoir properties. Even further reduction of uncertainty in gas hydrate reservoir characterization is probably possible if seismic attributes other than the acoustic impedance, such as Poisson s ratio and attenuation, can be accurately measured from field data. Once again, the model-driven approach is paramount for bracketing the results. Caveats due to seismic resolution. Rock physics models are

5 and elastic impedance data. The upscaling makes clusters of data points that correspond to the hydrate and gas sand change their position in this diagnostics crossplot. Because of the often complex stratigraphic distribution and thickness of sand/shale layers, there is no universal recipe for upscaling rock physics models and relations. The upscaling effect has to be assessed in each concrete case by synthetic seismic modeling or Backus averaging. Figure 10. Impedance versus PR from log data shown in Figure 9. The original log data (left) with the hydrate sand shown in blue and gas sand shown in red. Upscaled data (right) with the hydrate sand in green and gas sand in yellow. usually used on a point-by-point basis at the well log and/or core scale. The scale of seismic data may exceed that of well log data by 2-3 orders of magnitude. A seismic wave tends to average the small-scale reservoir elastic features observed at a smaller scale. Sharp impedance and Poisson s ratio contrasts that manifest the presence of gas hydrate and free gas become smaller and may even disappear in impedance inversion volumes. Consider a gas hydrate pseudowell where the upper part of the sand body is filled with methane hydrate and the lower part contains free gas (Figure 9). The hydrate-cemented sand is manifested by large impedance while the sand with free gas is manifested by small Poisson s ratio. Figure 9 shows the smoothing effect of the seismic wave on the elastic attributes (upscaling) simulated via Backus averaging of the elastic moduli. The sharp impedance and PR contrasts apparent at the log scale become smaller. Even the vertical positions of the extrema of the upscaled elastic properties change. Figure 10 shows an impedance-pr crossplot that can be used for identifying gas hydrate and free gas from acoustic Conclusion. The use of a first-principle-based rock physics model is crucial for gas hydrate reservoir characterization because only within a physics-based framework can one systematically perturb reservoir properties to estimate the elastic response with the ultimate goal of characterizing the reservoir from field elastic data. Rock physics relations have to be upscaled to become applicable to seismic reservoir characterization. Suggested reading. Direct measurement of in-situ methane quantities in a large gas hydrate reservoir by Dickens et al. (Nature, 1997). Elasticity of high-porosity sandstones: Theory for two North Sea data sets by Dvorkin and Nur (GEOPHYSICS, 1996). Time-average equation revisited by Dvorkin and Nur (GEOPHYSICS, 1998). Elasticity of marine sediments by Dvorkin et al. (GRL, 1999). Estimating the amount of gas hydrate and free gas from marine seismic data by Ecker et al. (GEOPHYSICS, 2000). Elastic-wave velocity in marine sediments with gas hydrates: Effective medium modeling by Helgerud et al. (GRL, 1999). Empirical estimation of viscoelastic seismic parameters from petrophysical properties of sandstone by Koesoemadinata and McMechan (GEOPHYSICS, 2001). Gas Hydrates as a Potential Energy Resource A Review of Their Methane Content by Kvebvolden (USGS Professional Paper 1570, 1993). Velocity to porosity transform in marine sediments by Prasad and Dvorkin (Petrophysics, 2001). Elastic wave velocities in heterogeneous and porous media by Wyllie et al. (GEOPHYSICS, 1956). TLE Corresponding author: jack@pangea.stanford.edu