Gas Hydrates - Part II: Rock Physics, an Introduction

The world is the geologist’s great puzzle-box; he stands before it like the child to whom the separate pieces of his puzzle remain a mystery till he detects their relation and sees where they fit, and then his fragments grow at once into a connected picture beneath his hand.” – Jean Louis Rodolphe Agassiz (1807–1873), Swiss paleontologist, glaciologist, geologist

A major and obvious difference between ice and hydrate is that the hydrate is highly flammable (‘burning ice’).

It is of course the methane content in hydrate that makes it of commercial interest. In fact the difference between ice and methane hydrate is not huge: one could consider hydrate as one dash of methane gas and six dashes of pure ice. Ice has a hexagonal crystalline structure, with a density of roughly 0.92 g/cm³ at 0°C and increases to 0.93 for a temperature of -180°C. The density of methane hydrate is slightly less (0.90 g/ cm³), since there is only 1 mole of methane per 5.75 moles of ice. Another way to formulate this is to say that whereas ice has the formula H₂O, the empirical chemical formula for methane hydrate is (CH₄)8(H₂O)46.

So, if the density difference between ice and hydrate is negligible, what about other crucial seismic parameters, such as velocities?

Rock Physics Experiments

In 2001 Michael Helgerud presented a comprehensive PhD thesis at Stanford where he analyzed wave velocities in gas hydrates and sediments containing gas hydrates.

For pure gas hydrate samples made in the laboratory he measured P-wave (compressional) velocities around 3700 m/s and S-wave (shear) velocities around 1950 m/s. Only small variations with temperature and confining pressure were observed.

The ratio between P-wave velocity of pure hydrate versus ice is 0.98. For the S-wave velocity the corresponding ratio is close to 1.0. This means that, acoustically, pure ice and pure methane hydrate are very similar. This is maybe as expected since the dominant crystalline structures of the two are similar.

Compressional and shear velocity versus time. The figure shows the response to a warming of the sample from 5 to 20°C followed by a cooling back to 5°C again. Confining pressure: 9,000 psi. Source: Helgerud (2001) Compressional and shear wave velocities versus confining pressure for methane hydrate. The horizontal scale is from 4,000 to 9,000 psi. Source: Helgerud (2001)
Compressional and shear velocity versus time. The figure shows the response to a warming of the sample from 5 to 20°C followed by a cooling back to 5°C again. Confining pressure: 9,000 psi. Source: Helgerud (2001) Compressional and shear wave velocities versus confining pressure for methane hydrate. The horizontal scale is from 4,000 to 9,000 psi. Source: Helgerud (2001)

Rock Physics

Rock physics provides the connections between geophysical (elastic and electromagnetic) properties of the rock measured at the surface of the earth, within the borehole or in the laboratory, with the intrinsic properties of rocks, such as mineralogy, porosity, pore shapes, pore fluids, pore pressures, permeability, electrical resistivity, viscosity, stresses and overall architecture such as laminations and fractures. These parameters affect how seismic and electromagnetic waves/fields physically travel through the rocks. Establishing relationships between geophysical expression and physical rock properties therefore requires knowledge about the elastic/electromagnetic properties of the pore fluid and rock frame, and models for rock-fluid interactions.

Equations that attempt to describe the relationships between seismic velocities and lithology, porosity, pore fluid, etc. are either theoretical or empirical.

Zhijing Wang summarizes the tension between theoretical and empirical approaches this way: most direct measurements are carried out either in the laboratory or inside a borehole, whereas most theoretical calculations are based on the Gassmann equation (Gassmann, 1951) because of its simplicity and ease of use. Direct laboratory measurements are carried out in controlled, simulated reservoir environments and provide accurate effects of pore fluids on seismic properties. Direct borehole measurements, however, are often affected by uncontrollable factors such as stress concentration, hole washout, mud invasion/filtration, and saturation conditions. In both laboratory and borehole measurements, the wave frequencies are higher than seismic frequencies.

Jan Dewar summarizes that the crux of all this is that there are a great number of relationships between seismic velocities (and constituent elastic properties) and rock parameters, all valid to some degree but not always valid, and many that do not illuminate the physical principles involved. The trick is to try to gain a fundamental understanding so that, on a practical basis, the different relationships can be evaluated for their applicability to solving specific problems.

Theoretical rock physics modeling can also be applied to understand the physical properties of natural gas hydrate systems and accumulations. A major goal is to establish linkages between gas hydrate concentration/saturation in sediments and the measureable physical properties, like P- and S-wave velocities and electrical resistivity. Modeling the elastic properties of sediments as a function of gas hydrate content can be achieved in various ways, such as effective medium modeling or three-phase Biot theory. The effective medium theory can incorporate the effects of cement and grains. In the case of gas hydrate, the hydrate can form in various ways. The effective seismic velocities vary quite strongly depending on which formation scenario is used.

To model gas hydrate systems via rock physics one needs to define the elastic/electromagnetic properties of the system in terms of (i) elastic/electromagnetic properties of the (unconsolidated) sediments that host the hydrates, (ii) elastic/electromagnetic properties of the embedded gas hydrates, (iii) the concentration of hydrates in the sediments, and (iv) geometrical details of the distribution of hydrates within their host sediments. The inverse modeling problem is to infer hydrate concentration from geophysical measurements.

Acoustic well-logs with full waveform show a pronounced decrease of wave amplitude in hydrate-bearing zones.

Compressional and shear velocity versus porosity for ice. Source: Helgerud (2001) P-wave velocity versus porosity assuming that the methane hydrate is a part of the rock frame (black line), of the pore fluid (green line). The red line shows a rock which is 100% water saturated (no hydrate), the blue solid line represents 1% patch gas saturation, and the dark blue line represents 1% homogenous gas saturation. Source: Helgerud (2001)
Compressional and shear velocity versus porosity for ice. Source: Helgerud (2001) P-wave velocity versus porosity assuming that the methane hydrate is a part of the rock frame (black line), of the pore fluid (green line). The red line shows a rock which is 100% water saturated (no hydrate), the blue solid line represents 1% patch gas saturation, and the dark blue line represents 1% homogenous gas saturation. Source: Helgerud (2001)

Fluid, Frame or Cement?

Is hydrate a part of the fluid, the frame or is it cement?

We have seen that pure hydrate and ice are very similar with respect to traditional seismic parameters, such as velocities and densities. However, in nature, the hydrate is found as a part of a rock, making the rock physics relations more complex. What happens when methane hydrate enters into a sedimentary rock? Hydrate is found both in clay rich sediments and in sands. Several models have been proposed for this, varying from regarding the hydrate as a part of pore fluid fill, via being a part of the rock frame or acting as cement between sand grains. Helgerud found that the P-wave velocity is slightly higher when assuming that the hydrate is a part of the rock frame.

There are two ways of addressing this problem: either to perform measurements in wells drilled into hydrate-bearing rocks, or to inject hydrate in a controlled way into a rock in the laboratory. We will discuss both methods in the next issue of GEO ExPro.

In this box we show two examples of some of the most frequently used rock physics relations. The most famous model in rock physics is the Gassmann (1951) equation, which is used to describe the effect of gradually changing the pore fluid in, for instance, a sandstone. It needs calibration prior to use, for which we often use well logs. The figure on the right shows how the relative P-wave velocity varies as a function of water saturation, assuming that the pores are filled with either oil or water. Another key reservoir parameter is the pore pressure. For wave velocities it turns out that it is the effective pressure (which is approximately equal to the overburden pressure minus the pore pressure) that controls the velocity. The simplest version for a theoretical model that includes changes in effective pressure is the Hertz-Mindlin model. This is a contact model, where it is assumed that the rock grains are identical spheres with a given contact area that increases with the effective pressure. As this contact area increases, the velocity increases, as shown below. The black line corresponds to a Mindlin-coefficient of 1/6 and the red line to 1/10, demonstrating that also in this case we need a calibration procedure prior to practical application of this simple model. In most cases we assume that the density does not change as the pore pressure changes. However, in some cases the rock might compact or undergo stretching, and in such cases the porosity will change and hence also the density. Typical examples are chalk reservoirs that may compact by several meters, due to production. Rock physics plays a crucial part both in exploration and production geophysics: advanced and quantitative use of, for example, pre-stack seismic data require rock physics input to link the seismic parameters to key reservoir parameters such as saturation, pressure and porosity.

This article is Part II of a four part series:

References:

Dewar, J., 2001. Rock Physics For The Rest Of Us – An Informal Discussion: CSEG Recorder.
Gassmann, F., 1951. Uber die elastizitat poroser medien. Vierteljahrsschrift der Naturforchenden Gesellschaft in Zurich 96, 1-23.
Helgerud, M., 2001. Wave speeds in gas hydrate and sediments containing gas hydrate: A laboratory and modeling study, PhD thesis, Stanford University, USA.
Wang, Z., 2000. The Gassmann equation revisited: Comparing laboratory data with Gassmann’s predictions, Seismic and Acoustic Velocities in Reservoir Rocks, Vol. 3, Recent Developments, SEG Reprint Series, pp.1–23.

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Gas Hydrates – Part II: Rock Physics, an Introduction

Rock Physics Experiments

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