The key phenomenon for new imaging and interpretation technologies is the field observation of strong dependence of seismic frequency response on the reservoir properties, such as fluid mobility and permeability. This observation is consistent with theory proposed in Korneev, et al. (Geophysics, 2003) suggesting a diffusive attenuation mechanism for fluid saturated rocks. The key development was expected in incorporation of double porosity-double permeability extension for Biot’s type model for porous media. However, permeability data showed that at field scales the fluid motion in fractures becomes dominant. This motion is carried by slow fluid wave, and it is not a part of any existing poro-elastic theory. There is an urgent need in developing a new approach that adequately describes behavior of fluids in rocks at field scales.

**Results**

This project involves development of theory and processing algorithms, laboratory experiments, and verification of results using field data provided by industrial partners. The theory of the frequency-dependent reflections was under investigation. For this purpose a computer code was developed, which models reflections caused by an incidence of a P-wave for two- and three-layer models. The fluid flow effects are modeled by application of Biot’s porous rock theory and are generalized to the double porosity approach by Pride. The models treat normal, as well as oblique, wave incidence. The modeling results were compared with observations in laboratory data and field experiments. It was determined that the modeling results give qualitative agreement with experiment. However, analysis of permeability values consistently demonstrate that measurements at field scale (hundreds of meters to kilometers) show an increase of several orders of magnitude compared with values obtained at laboratory scales. This behavior finds an explanation in the self-similar distribution of fractures in rock, an explanation supported by the wide-scale applicability of the Gutenberg-Richter law for distribution of earthquakes and seismic emission.

Dramatic changes in permeability suggest the predominant role of fractures in fluid-flow processes at field scales, and that at those scales one can neglect fluid flow in pores. This explains why classical Biot’s theory, while occasionally working well at laboratory scale, fails to quantitatively describe the wave properties observed in the field—it does not capture the interaction among fluid-filled fractures and an elastic, embedding matrix. Incorporation of matrix elasticity together with a model fracture filled by a viscous fluid leads to the existence of slow Stoneley guided waves with distinct dispersive properties. Stoneley guided waves are dominant in a fracture, carry most of the fluid motion energy, and are capable of producing resonances in finite fractures at low frequencies. These resonances likely cause the strong nonlinear behavior of fluid reservoirs and may be a driving mechanism for fluid mobilization in rocks. To introduce a lateral fluid flow effect, a model of two intersecting fractures was considered where a Stoneley wave propagating in a vertically oriented fracture was reflected, because of the reflection on the horizontally oriented fracture. Numerical modeling revealed that frequency-dependence pattern of such reflection is consistent with field data. An appropriate multi-fracture model needs to be developed to describe the effects in real rocks. The results will be validated by processing field data provided by industry partners.

**Benefits**

The theoretical and modeling efforts will improve understanding of reservoir properties and help to find ways for reservoir characterization.

**Summary**

The basic hypothesis of the developed theory puts the fluid flow in the rocks as a driving mechanism responsible for the frequency-dependent reflections from gas/oil reservoirs. Indeed, analysis of the normal reflection on the elastic-porous contact showed all the observed behavior for the amplitudes and phases as functions of frequency, as well as functions of reservoir properties, such as mobility. The problem is that the predicted effects are rather small in magnitudes, which needs to be explained and corrected. Double porosity models enhance the frequency-dependent effects by several times, however, not reaching the values observed in the data. The problem with double porosity theories (Barenblatt, Pride, and Berryman) is in a large set of media parameters that are hard to evaluate or measure. Application of Biot’s type equations for propagation of seismic wave implies that no (or little, as in BISQ theory) fluid motion exists in the directions lateral with respect to direction of propagation. In the same time, from hydrogeology results, it follows that some scaling rules need to be applied to laboratory permeability measurements before using them at a field scale (Clauser, 1992; Neuman, 1994). Typically, a five-orders-of-scale increase results in a corresponding five to seven orders of permeability increase. From the scale-dependence of permeability, it follows that in Biot’s equations, permeability should not be a constant but rather a function of a wavelength that determines a spatial averaging region. Fractures play a major role in determining the permeability and direction of fluid flow in rock at field scales, while pore fluid flow can be neglected.

In most rock and at all scales, fractures generally have a hierarchical self-similar distribution. Fluid-filled fractures provide waveguides in sharp contrast with dispersive Stoneley fluid waves and are likely to be capable of strongly absorbing energy from passing seismic waves. Energy absorption can be tenfold more effective when resonant conditions are met, which creates favorable conditions for nonlinear fluid-flow effects. The resonant conditions for fracture fluid waves can exist even below prospective seismic frequencies, when guided-wave velocities approach zero. There is no existing theory that adequately describes the interaction of propagating seismic waves with systems of fluid-filled fractures in rock. Interaction of slow fluid waves in intersecting fractures also produces a frequency-dependent effect that is especially strong at low frequencies. As a consequence, numerical modeling of the interaction between propagating body waves and slow fluid waves presents a major computational challenge, because of the coexistence of wavelengths that have dramatically different sizes.

The frequency-dependent data analysis was performed for a Mallik cross-well data set. The set has very high data quality and was supported by multidisciplinary international research efforts (netl.doe.gov/scngo/NaturalGas/hydrates/newsletter/HMNewsWinter04.pdf). This is the first thoroughly studied case of methane hydrate production monitoring. While conventional seismic analysis failed to find changes in the data associated with gas production, the researchers’ frequency-dependent analysis revealed such changes above 850 Hz. There, results find an explanation in surface wave propagation along the reservoir borders.

An analytically exact solution is obtained for a slow Stoneley wave together with its low-frequency asymptotic. Asymptotics behave differently, depending on viscosity of the fluid and fracture thickness (skin factor). The solution is being compared with Biot’s solution for the same model. Slow wave interaction for intersecting fractures is under numerical investigation for different values of the skin factor. Fluid effects in finite fractures are under investigation. In particular, the value of attenuation for the slow wave will allow researchers to estimate the actual amplitudes at resonant conditions. It is expected that these amplitudes will result in effects of unilateral fluid flows (fluid mobilization).