Porous Fluid-saturated Medium Research Articles

Application of the Dorovsky model for taking into account the fluid saturation of geological media

The discovery of oil deposits with complex internal structures requires an improvement of available seismic survey methods. The development of modern high-performance computing systems provides an opportunity to use more sophisticated mathematical models. This paper aims to investigate seismic wave propagation in porous fluid-saturated media. The Dorovsky three velocity model was formulated in the two-dimensional case and its numerical solution was obtained with the grid-characteristic method. The computational domain consisted of three layers with different rheology: a water layer, a porous fluid-saturated layer, and an elastic layer. Explicit contact conditions were derived between them and successfully applied with the help of Riemann invariants. The curvature of geological layers was taken into consideration by means of structured hexahedral grids. The time evolution of the spatial distribution of stress tensors and material velocity vectors were calculated and analyzed. These signals contain a mixture of volume, surface, transmitted and reflected waves.

Problem of Acoustic Diagnostics of a Damaged Zone

The problem of seismic wave propagation from a source located in a well is considered. Acoustic equations are used to describe the dynamic behavior of the fluid. The damaged zone is described as a porous fluid-saturated medium by applying the Dorovsky model. The elastic approximation is used to describe the dynamic behavior of the surrounding rock. A unified algorithm based on the grid-characteristic approach with curvilinear grids is proposed for full-wave modeling in the entire computational domain. Its distinctive feature is that the necessary contact conditions on the boundary between media with different rheological properties are stated explicitly. The possibility of acoustic diagnostics of the heterogeneity of the damaged zone is numerically explored.

Optimal bounds for attenuation of elastic waves in porous fluid-saturated media.

Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions.

On effective characteristic of Rayleigh surface wave propagation in porous fluid-saturated media at low frequencies

The analytical dispersion and waveform solutions of Rayleigh surface wave for the Biot fluid-saturated model are obtained at low frequencies for a homogeneous half space. The equivalent solution is also obtained by the equivalent-viscoelastic representation of the fluid-saturated model based on a single viscoelastic element for each wave modulus. The effective characteristics of the validations and limitations for the equivalent-viscoelastic model are analyzed by comparison of the numerical solutions of the fluid-saturated model and the equivalent model for the surface wave propagations. Our calculations show that the free boundary effects on the frequency dependent dispersion and time dependent dynamical waveforms of the surface wave in the Biot model are well fitted in a relative narrow low frequency band by the Zener elements in case of the frequency is much lower than the critical frequency fc of the porous material. The effective characteristics for air filled cases with a higher fc show a better result. Furthermore, if the critical frequency fc is low, always with high permeability κ under near surface condition, at low frequencies (e.g. the seismic frequency band <200Hz) the surface fluid drainage conditions influence Rayleigh-wave propagations obviously. The frequency range must hence be carefully checked for the viscoelastic representations. When the validated frequency range is defined, the viscoelastic elements can solve the transient surface wave propagation in porous media effectively. The convolution integral in wave modeling can be replaced by memory variables, which makes the field quantities calculated at every time step need not be stored. The effective representation saves the consumptions of computer time and storages, and supplies a more convenient approach to apply the surface wave considering poroelasticity.

On effective characteristics of wave propagation in a porous fluid-saturated medium containing entirely fluid inclusions

SUMMARY To investigate the behaviour of seismic wave propagation in natural rocks and soils, a model for the elastic properties of a heterogeneous porous medium containing uniform fluid inclusions is useful. The problem has already been addressed before, utilizing Biot’s theory of poroelasticity, and there have been some analytical and numerical results obtained for the different types of cavities. However, as it is shown in this paper, immediate passage within heterogeneous porous media from spherical porous heterogeneities to continuous fluid or solid inclusions cannot be performed on the basis of previously developed models. In this paper, we extend the results for wave scattering in porous media due to a random ensemble of spherical porous inclusions to allow for continuous fluid inclusions instead. To consider this case, we first obtain the single scattering series. Then we utilize multiple scattering theory to find the effective wavenumber due to an ensemble of inclusions. Our results make it possible to analyse wave attenuation and velocity dispersion at low frequencies due to the presence of entirely fluid inclusion heterogeneities within a porous material. Explicit analytical expressions for solution of single scattering problem for a fluid cavity, and effective propagation velocity and attenuation factor in a porous medium with random ensemble of these cavities constitute main results of this work.

Reservoir permeability from seismic attribute analysis

In case of porous fluid-saturated medium the Biot's poroelasticity theory predicts a movement of the pore fluid relative to the skeleton on seismic wave propagation through the medium. This phenomenon opens an opportunity for investigation of the flow properties of the hydrocarbon-saturated reservoirs. It is well known that relative fluid movement becomes negligible at seismic frequencies if porous material is homogeneous and well cemented. In this case the theory predicts an underestimated seismic wave velocity dispersion and attenuation. Based on Biot's theory, Helle et al. (2003) have numerically demonstrated the substantial effects on both velocity and attenuation by heterogeneous permeability and saturation in the rocks. Besides fluid flow effect, the effects of scattering (Gurevich, et al., 1997) play very important role in case of finely layered porous rocks and heterogeneous fluid saturation. We have used both fluid flow and scattering effects to derive a frequency-dependent seismic attribute which is proportional to fluid mobility and applied it for analysis of reservoir permeability.

On the homogenization of a diffusion–deformation problem in strongly heterogeneous media

We consider a porous fluid-saturated medium with periodic distribution of heterogeneities where the value of permeability decreases with the scale parameters. Homogenization of such double-porous material is performed using the method of periodic unfolding. The resulting homogenized macroscopic model is featured by the fading memory effect in the viscoelastic behaviour.

Symmetric Oscillations of a Porous-Elastic Strip with Free Surfaces for the Case of Closed Pores

Dispersion characteristics of the natural modes of a porous-elastic strip with free surfaces for the case of closed pores are studied in the context of the Biot theory. Due to the existence of the three types of waves in a porous fluid-saturated medium, the dispersion spectrum, even obtained without consideration of the dissipative effects, is considerably more complicated than the spectrum of a perfectly elastic strip. This spectrum is distinguished by existence of infinitely many pure imaginary roots at a specified frequency. In addition, there are two real branches passing through the coordinate origin in a porous-elastic strip with closed pores.

NUMERICAL ANALYSIS OF THE INTERPHASE INTERACTION IN A POROUS ELASTIC FLUID-SATURATED MEDIUM

We consider dynamical processes in a two-phase porous fluid-saturated medium. The equation of the Biot–Frenkel model, which accounts for the influence of the elastic, inertial, and viscous interaction between the liquid and solid phases, is used for modeling the dynamics of the soil layer (flat deformation) with the finite-element method in cases of steady and nonstationary effects. For a layer under a uniaxial stress, we give numerical examples of the displacements of the soil skeleton and interstitial fluid.

Propagation of compression waves in a porous fluid-saturated medium

Propagation of compression waves in a porous fluid-saturated medium

Waves in a partially saturated layered half-space: Analytic formulation

Abstract Rayleigh waves in partially saturated layered half-spaces are investigated under plane strain conditions. The analytical model is based on Biot9s theory of wave propagation in porous fluid-saturated media. The dispersion relation is derived using methods from propagation of free waves in layered media. For limiting cases of the dimensionless frequency, it is shown that the problem reduces to more simplified forms discussed in previous works. Further, it is shown that for zero pore pressure, the problem reduces to known results of elastodynamics.