Amos Nur

Effects of porosity and clay content on wave velocities in sandstones

The ultrasonic compressional (Vp) and shear (Vs) velocities and first‐arrival peak amplitude (Ap) were measured as functions of differential pressure to 50 MPa and to a state of saturation on 75 different sandstone samples, with porosities ϕ ranging from 2 to 30 percent and volume clay content C ranging from 0 to 50 percent, respectively. Both Vp and Vs were found to correlate linearly with porosity and clay content in shaly sandstones. At confining pressure of 40 MPa and pore pressure of 1.0 MPa, the best least‐squares fits to the velocity data are Vp(km/s)=5.59-6.93ϕ-2.18C and Vs(km/s)=3.52-4.91ϕ-1.89C. Deviations from these equations are less than 3 percent and 5 percent for Vp and Vs, respectively. The velocities of clean sandstones are significantly higher than those predicted by the above linear fits (about 7 percent for Vp and 11 percent for Vs), which indicates that a very small amount of clay (1 or a few percent of volume fraction) significantly reduces the elastic moduli of sandstones. For shaly...

The effect of saturation on velocity in low porosity rocks

Abstract V p and V s are often significantly lower near atmospheric pressure than at pressures of a few kilobars for dry rocks with porosity in the form of cracks. When such cracks are filled with water, however, this lowering of velocity is significantly diminished for compressional waves. In contrast, V s is unaffected by the presence of fluid; low velocity persists at low pressure. The shape of the pores in typical crystalline rocks plays an important role: increase in V p due to saturation of pores occurs when the pores are in the form of cracks but not when they are in the form of round holes. As differences in V p of dry and saturated rock at low pressure may approach 50 per cent, the degree of saturation of rocks must be taken into account in many engineering and shallow seismic applications.

Aftershocks Caused by Pore Fluid Flow

Large shallow earthquakes can induce changes in the fluid pore pressure that are comparable to stress drops on faults. The subsequent redistribution of pore pressure as a result of fluid flow slowly decreases the strength of rock and may result in delayed fracture. The agreement between computed rates of decay and observed rates of aftershock activity suggests that this is an attractive mechanism for aftershockss.

Elasticity of high-porosity sandstones : Theory for two North Sea data sets

We have analyzed two laboratory data sets obtained on high‐porosity rock samples from the North Sea. The velocities observed are unusual in that they seem to disagree with some simple models based on porosity. On the other hand, the rocks are unusually poorly‐cemented (for laboratory studies, at least), and we investigate the likelihood that this is the cause of the disagreement. One set of rocks, from the Oseberg Field, is made of slightly cemented quartz sands. We find that we can model their dry‐rock velocities using a cementation theory where the grains mechanically interact through cement at the grain boundaries. This model does not allow for pressure dependence. The other set of rocks, from the Troll Field, is almost completely uncemented. The grains are held together by the applied confining pressure. In this case, a lower bound for the velocities can be found by using the Hertz‐Mindlin contact theory (interaction of uncemented spheres) to predict velocities at a critical porosity, combined with th...

Elastic‐wave velocity in marine sediments with gas hydrates: Effective medium modeling

We offer a first-principle-based effective medium model for elastic-wave velocity in unconsolidated, high porosity, ocean bottom sediments containing gas hydrate. The dry sediment frame elastic constants depend on porosity, elastic moduli of the solid phase, and effective pressure. Elastic moduli of saturated sediment are calculated from those of the dry frame using Gassmanns equation. To model the effect of gas hydrate on sediment elastic moduli we use two separate assumptions: (a) hydrate modifies the pore fluid elastic properties without affecting the frame; (b) hydrate becomes a component of the solid phase, modifying the elasticity of the frame. The goal of the modeling is to predict the amount of hydrate in sediments from sonic or seismic velocity data. We apply the model to sonic and VSP data from ODP Hole 995 and obtain hydrate concentration estimates from assumption (b) consistent with estimates obtained from resistivity, chlorinity and evolved gas data.

Wave attenuation in partially saturated rocks

A model is presented to describe the attenuation of seismic waves in rocks with partially liquid‐saturated flat cracks or pores. The presence of at least a small fraction of a free gaseous phase permits the fluid to flow freely when the pore is compressed under wave excitation. The resulting attenuation is much higher than with complete saturation as treated by Biot. In general, the attenuation increases with increasing liquid concentration, but is much more sensitive to the aspect ratios of the pores and the liquid droplets occupying the pores, with flatter pores resulting in higher attenuation. Details of pore shape other than aspect ratio appear to have little effect on the general behavior provided the crack width is slowly varying over the length of the liquid drop.

Dynamic poroelasticity; a unified model with the squirt and the Biot mechanisms

The velocities and attenuation of seismic and acoustic waves in rocks with fluids are affected by the two most important modes of fluid/solid interaction: (1) the Biot mechanism where the fluid is forced to participate in the solids motion by viscous friction and inertial coupling, and (2) the squirt-flow mechanism where the fluid is squeezed out of thin pores deformed by a passing wave. Traditionally, both modes have been modeled separately, with the Biot mechanism treated in a macroscopic framework, and the squirt flow examined at the individual pore level. We offer a model which treats both mechanisms as coupled processes and relates P-velocity and attenuation to macroscopic parameters: the Biot poroelastic constants, porosity, permeability, fluid com-pressibility and viscosity, and a newly introduced microscale parameter--a characteristic squirt-flow length. The latter is referred to as a fundamental rock property that can be determined experimentally. We show that the squirt-flow mechanism dominates the Biot mechanism and is responsible for measured large velocity dispersion and attenuation values. The model directly relates P-velocity and attenuation to measurable rock and fluid properties. Therefore, it allows one to realistically interpret velocity dispersion and/or attenuation in terms of fluid properties changes [e.g., viscosity during thermal enhanced oil recovery (EOR)], or to link seismic measurements to reservoir properties. As an example of the latter transformation, we relate permeability to attenuation and achieve good qualitative correlation with experimental data.

Postseismic Viscoelastic Rebound

The sudden appearance of a dislocation, representing an earthquake, in an elastic layer (the lithosphere) overriding a viscoelastic half space (the asthenosphere) is followed by time-dependent surface deformation, which is very similar to in situ postseismic deformation. The spectacular postseismic deformation following the large Nankaido earthquake of 1946 yields for the asthenosphere a viscosity of 5 x 1019 poise and a 50 percent relaxation of the shear modulus. Large thrust type earthquakes may provide, in the future, a new method for exploring the rheology of the earths upper mantle.

Elasticity of High-porosity Sandstones: Theory For Two North Sea Datasets

We analyze two laboratory datasets obtained on high-porosity rock samples from the North Sea. The first set is from the Oseberg field and represents slightly cemented quartz sands. The second set represents unconsolidated and almost uncemented sands from the Troll field. We find that dry-rock ultrasonic velocities in the Oseberg samples can be well modeled by the cementation theory where the grains mechanically interact through quartz cement. In the Troll samples contact cement is almost absent and grains are held together primarily by confining pressure. In this case velocities can be modeled by a combination of the Hertz-Mindlin contact theory (interaction of two smooth uncemented spheres) and the modified Reuss average (an isostress model for suspensions). The latter approach allows us to introduce pressure dependence in the velocity model. This theoretical model generally underestimates the observed Troll velocity values. For dry rock at high pressure the error may be as large as 15 percent. This error reduces to 10 percent in saturated rock. An important result is that this Hertz-Mindlin-Reuss model can accurately predict the high Poisson`s ratios generally observed in saturated loose sediments. Both theoretical methods have analytical expressions and are ready for practical use.

Seismic attenuation: Effects of pore fluids and frictional‐sliding

Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in term...