Jing Ba

Biot‐Rayleigh theory of wave propagation in double‐porosity media

[1] We derive the equations of motion of a double‐porosity medium based on Biot’s theory of poroelasticity and on a generalization of Rayleigh’s theory of fluid collapse to the porous case. Spherical inclusions are imbedded in an unbounded host medium having different porosity, permeability, and compressibility. Wave propagation induces local fluid flow between the inclusions and the host medium because of their dissimilar compressibilities. Following Biot’s approach, Lagrange’s equations are obtained on the basis of the strain and kinetic energies. In particular, the kinetic energy and the dissipation function associated with the local fluid flow motion are described by a generalization of Rayleigh’s theory of liquid collapse of a spherical cavity. We obtain explicit expressions of the six stiffnesses and five density coefficients involved in the equations of motion by performing “gedanken” experiments. A plane wave analysis yields four wave modes, namely, the fast P and S waves and two slow P waves. As an example, we consider a sandstone and compute the phase velocity and quality factor as a function of frequency, which illustrate the effects of the mesoscopic loss mechanism due to wave‐induced fluid flow.

Comparison of P-wave attenuation models of wave-induced flow

ABSTRACT Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with Whites and Johnsons models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.

BISQ model based on a Kelvin-Voigt viscoelastic frame in a partially saturated porous medium

Taking into account three important porous media mechanisms during wave propagation (the Biot-flow, squirt-flow, and solid-skeleton viscoelastic mechanisms), we introduce water saturation into the dynamic governing equations of wave propagation by analyzing the effective medium theory and then providing a viscoelastic Biot/squirt (BISQ) model which can analyze the wave propagation problems in a partially viscous pore fluid saturated porous media. In this model, the effects of pore fluid distribution patterns on the effective bulk modulus at different frequencies are considered. Then we derive the wave dynamic equations in the time-space domain. The phase velocity and the attenuation coefficient equations of the viscoelatic BISQ model in the frequency-wavenumber domain are deduced through a set of plane harmonic solution assumptions. Finally, by means of numerical simulations, we investigate the effects of water saturation, permeability, and frequency on compressional wave velocity and attenuation. Based on tight sandstone and carbonate experimental observed data, the compressional wave velocities of partially saturated reservoir rocks are calculated. The compressional wave velocity in carbonate reservoirs is more sensitive to gas saturation than in sandstone reservoirs.

Rock physics modeling of heterogeneous carbonate reservoirs: porosity estimation and hydrocarbon detection

In heterogeneous natural gas reservoirs, gas is generally present as small patchlike pockets embedded in the water-saturated host matrix. This type of heterogeneity, also called “patchy saturation”, causes significant seismic velocity dispersion and attenuation. To establish the relation between seismic response and type of fluids, we designed a rock physics model for carbonates. First, we performed CT scanning and analysis of the fluid distribution in the partially saturated rocks. Then, we predicted the quantitative relation between the wave response at different frequency ranges and the basic lithological properties and pore fluids. A rock physics template was constructed based on thin section analysis of pore structures and seismic inversion. This approach was applied to the limestone gas reservoirs of the right bank block of the Amu Darya River. Based on poststack wave impedance and prestack elastic parameter inversions, the seismic data were used to estimate rock porosity and gas saturation. The model results were in good agreement with the production regime of the wells.

A study on effective medium theories in tight sandstone

The tight sandstone gas reservoirs in the central Sichuan basin are characterized by wide distribution and low abundance. Sandstone samples from this area usually have low porosity and poor connectivity. This paper analyzes the laboratory data of tight sandstone samples with four different inclusion models based on effective medium theory and compares the laboratory data with the estimated value of four theoretical models with different pore shapes. The laboratory data are close to the estimated data with low aspect ratio, which reveals the sandstone pore-shapes of this area as flattened fractures or fissures. The optimal aspect ratios of the four models are all around 0.1, and the Mori-Tanaka model fits better with laboratory data than the others.

Nonlinear Acoustic Waves in Fluid-Saturated Porous Rocks – Poro-Acoustoelasticity Theory

The 3rd order constants theory in solid material was completed with the papers by Toupin and Bernstein, Jones and Kobett and Truesdell [8-10]. Truesdell used four 3rd-order elastic constants in his general theory for isotropic solid. Brugger [11] gave the thermodynamic definition of higher order elastic constants. In 1973, Green reviewed 3rd-order constants measurements of various crystals, and gave the relations between the 3rd-order constant notations in isotropic solids by different authors [12].