Wave-induced Fluid Flow Effects Research Articles

Dispersion and attenuation characteristics of an obliquely incident SV wave in a fluid-saturated porous rock containing aligned penny-shaped fractures

Owing to the complex structural characteristics of aligned fractured rocks with a fluid-saturated porous background, many existing single-wave attenuation mechanism models cannot accurately characterize measuring multiband shear vertical (SV) wave data. Moreover, the coupled effect of wave-induced fluid flow between fractures and the background (FB-WIFF) and elastic scattering (ES) from the fractures leads to ambiguity in the elastic response of the SV wave. Using Biot’s theory and mixed boundary constraints, the exact solutions of the scattering problem for a single penny-shaped fracture with an obliquely incident SV wave are derived. Furthermore, a theoretical model for a set of aligned fractures is developed by using Foldy’s scheme. The numerical results indicated that the FB-WIFF, ES of fractures, and their coupling effects were mainly responsible for wave dispersion and attenuation. The FB-WIFF occurs primarily in the low-frequency seismic exploration frequency band, whereas the ES of the fracture surface depends on the relationship between the wavelength and fracture size. In addition, by comparing our model with an existing interpolation approximation model and previous experimental measurements, the accuracy and effectiveness of the model was validated. The results of this work can explain the acoustic response of SV-wave experimental data in different frequency bands and theoretically support fracture detection and characterization.

An Experimental Study on Scale-Dependent Velocity and Anisotropy in Fractured Media Based on Artificial Rocks with Controlled Fracture Geometries

The scale of the fractures can vary, making the seismic velocity and anisotropy substantially scale dependent. Two mechanisms of the scale-dependent phenomenon may be considered: scattering and wave-induced fluid flow. In this study, we measure the scale-dependent velocity and anisotropy effects through laboratory experiments on porous and non-porous artificial rocks containing aligned fractures. This allows us to isolate the effects of these two mechanisms for the first time, yielding some insights into the scale-dependent phenomenon. For short-wavelength waves, scattering dominates with less wave-induced fluid flow effects. For intermediate- and long-wavelength waves, the P-wave is strongly scale dependent mainly due to wave-induced fluid flow mechanism, and the slow shear-wave is also strongly scale dependent but due to both scattering and wave-induced fluid flow. However, the fast shear-wave is almost scale independent. Moreover, a multi-scale equivalent medium theory can model the P-wave propagation accurately.

Wave propagation in double-porosity dual-permeability materials: Velocity and attenuation

This study considers the propagation of harmonic plane waves in a double-porosity solid saturated by a viscous fluid. Two different porosities are supported with different permeabilities to facilitate the wave-induced fluid-flow in this composite material. The variation of the fluid content in the pores due to the wave-induced flow is expressed in terms of the dilatation of constituent particles in the porous aggregate. This fluid-flow can be considered through the constitutive relations with modified anelastic coefficients. The modified coefficients, being frequency dependent and complex, illustrate the dispersive and anelastic behaviour of double-porosity dual-permeability materials. Relevant equations of motion are solved to explain the propagation of three longitudinal waves and one transverse wave in double-porosity dual-permeability medium. A numerical example is considered to illustrate dispersion in velocity and attenuation of the four waves. Effect of wave-induced fluid-flow is analysed with changes in wave-inhomogeneity, pore-fluid viscosity and double-porosity structure.

Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks

SUMMARY Using a numerical approach, we explore wave-induced fluid flow effects in partially saturated porous rocks in which the gas–water saturation patterns are governed by mesoscopic heterogeneities associated with the dry frame properties. The link between the dry frame properties and the gas saturation is defined by the assumption of capillary pressure equilibrium, which in the presence of heterogeneity implies that neighbouring regions can exhibit different levels of saturation. To determine the equivalent attenuation and phase velocity of the synthetic rock samples considered in this study, we apply a numerical upscaling procedure, which permits to take into account mesoscopic heterogeneities associated with the dry frame properties as well as spatially continuous variations of the pore fluid properties. The multiscale nature of the fluid saturation is taken into account by locally computing the physical properties of an effective fluid, which are then used for the larger-scale simulations. We consider two sets of numerical experiments to analyse such effects in heterogeneous partially saturated porous media, where the saturation field is determined by variations in porosity and clay content, respectively. In both cases we also evaluate the seismic responses of corresponding binary, patchy-type saturation patterns. Our results indicate that significant attenuation and modest velocity dispersion effects take place in this kind of media for both binary patchy-type and spatially continuous gas saturation patterns and in particular in the presence of relatively small amounts of gas. The numerical experiments also show that the nature of the gas distribution patterns is a critical parameter controlling the seismic responses of these environments, since attenuation and velocity dispersion effects are much more significant and occur over a broader saturation range for binary patchy-type gas–water distributions. This analysis therefore suggests that the physical mechanisms governing partial saturation should be accounted for when analysing seismic data in a poroelastic framework. In this context, heterogeneities associated with the dry frame properties, which do not play important roles in wave-induced fluid flow processes per se, should be taken into account since they may determine the kind of gas distribution pattern taking place in the porous rock.

Numerical analysis of wave-induced fluid flow effects on seismic data: Application to monitoring of CO2storage at the Sleipner field

[1] In this work we analyze how patchy distributions of CO2 and brine within sand reservoirs may lead to significant attenuation and velocity dispersion effects, which in turn may have a profound impact on surface seismic data. The ultimate goal of this paper is to contribute to the understanding of these processes within the framework of the seismic monitoring of CO2 sequestration, a key strategy to mitigate global warming. We first carry out a Monte Carlo analysis to study the statistical behavior of attenuation and velocity dispersion of compressional waves traveling through rocks with properties similar to those at the Utsira Sand, Sleipner field, containing quasi-fractal patchy distributions of CO2 and brine. These results show that the mean patch size and CO2 saturation play key roles in the observed wave-induced fluid flow effects. The latter can be remarkably important when CO2 concentrations are low and mean patch sizes are relatively large. To analyze these effects on the corresponding surface seismic data, we perform numerical simulations of wave propagation considering reservoir models and CO2 accumulation patterns similar to the CO2 injection site in the Sleipner field. These numerical experiments suggest that wave-induced fluid flow effects may produce changes in the reservoir's seismic response, modifying significantly the main seismic attributes usually employed in the characterization of these environments. Consequently, the determination of the nature of the fluid distributions as well as the proper modeling of the seismic data constitute important aspects that should not be ignored in the seismic monitoring of CO2 sequestration problems.

Dynamic permeability of porous rocks and its seismic signatures

In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot’s equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for.

Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.

A first-order statistical smoothing approximation for the coherent wave field in random porous media

An important dissipation mechanism for waves in randomly inhomogeneous poroelastic media is the effect of wave-induced fluid flow. In the framework of Biot's theory of poroelasticity, this mechanism can be understood as scattering from fast into slow compressional waves. To describe this conversion scattering effect in poroelastic random media, the dynamic characteristics of the coherent wavefield using the theory of statistical wave propagation are analyzed. In particular, the method of statistical smoothing is applied to Biot's equations of poroelasticity. Within the accuracy of the first-order statistical smoothing an effective wave number of the coherent field, which accounts for the effect of wave-induced flow, is derived. This wave number is complex and involves an integral over the correlation function of the medium's fluctuations. It is shown that the known one-dimensional (1-D) result can be obtained as a special case of the present 3-D theory. The expression for the effective wave number allows to derive a model for elastic attenuation and dispersion due to wave-induced fluid flow. These wavefield attributes are analyzed in a companion paper.