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ABSTRACT Poroelastic modelling of micro-inhomogeneous rocks is of interest for applications in rock physics and geomechanics. Laboratory measurements from both communities indicate that the Biot poroelasticity framework is not adequate. For the case of a macroscopically homogeneous and isotropic rock, we present the most general poroelasticity framework within the scope of equilibrium thermodynamics that is able to capture the effects of micro-inhomogeneities in a natural way. Within this generalized poroelasticity framework, the concept of micro-inhomogeneity is generically related to partial localization of the deformational potential energy either in the solid phase, including the interfacial region or in the fluid phase. The former case can occur in the presence of surface roughness or multi-mineralic frame and the latter case can be related to suspended particles residing in the fluid phase. A measure for micro-inhomogeneity is the coefficient that governs the effective pressure dependence of porosity changes as described by the porosity perturbation equation of this framework. It can be therefore equivalently interpreted as porosity effective pressure coefficient or as micro-inhomogeneity parameter. We show how this parameter and the other poroelastic constants embedded in this framework can be expressed in terms of experimentally accessible poroelastic constants. [ABSTRACT FROM AUTHOR]

ABSTRACT Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non-interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P-wave and S-wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi-static poroelasticity to fluid-saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency-dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub-volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative-elementary-volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency-dependent effective moduli of realistic fracture networks. [ABSTRACT FROM AUTHOR]

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In this paper, we focus on media containing aligned compliant pores embedded in an isotropic background matrix. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. Results are also expressed in terms of Thomsen anisotropy parameters. It turns out that the P-wave anisotropy parameter ε tends to zero in the high-frequency limit, whereas the δ parameter remains the only indicator of P-S⊥ anisotropy. The S-wave anisotropy parameter γ is not affected by the presence of fluid and remains the same for all frequency ranges. A new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy. In the most important case of liquid saturation, analytical expressions are derived for elastic properties, velocity anisotropy parameters, quality factors, and attenuation anisotropy parameters. A companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress. [ABSTRACT FROM AUTHOR]

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media, however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In a companion paper, we focused on media containing aligned compliant pores embedded in an isotropic background matrix. In this paper, we investigate the case for which anisotropy results from the presence of cracks with an ellipsoidal distribution of orientations due to the application of anisotropic stress. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. In the most important case of liquid saturation, analytical expressions are derived for elastic properties and Thomsen anisotropy parameters. The main observations drawn from this model are as follows. Crack closure perpendicular to the applied stress leads to an increase in seismic velocities as a function of stress in the direction of applied stress and a decrease in squirt-flow-induced dispersion and attenuation in this direction. The anisotropy of squirt flow dispersion engenders a decrease in the degree of anisotropy with frequency. The stress-induced anisotropy remains elliptical, even in saturated media, for all frequency ranges. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a generalized effective poroelastic model for periodically layered media in the mesoscopic scale range, which accounts for both Biot's global and interlayer wave-induced fluid flow, as well as for the anisotropy associated with the layering. Correspondingly, it correctly predicts the existence of the fast and slow P-waves as well as quasi and pure S-waves. The proposed analytical model is validated through comparisons of the P-wave and S-wave phase velocity dispersion and attenuation characteristics with those inferred from a one-dimensional numerical solution of Biot's poroelastic equations of motion. We also compare our model with the classical mesoscopic model of White for a range of scenarios. The results demonstrate that accounting for both wave-induced fluid flow mechanisms is essential when Biot's global flow prevails at frequencies that are comparable or smaller with respect to those governing interlayer flow. This is likely to be the case in media of high permeability, such as, for example, unconsolidated sediments, clean sandstones, karstic carbonates, or fractured rocks. Conversely, when interlayer flow occurs at smaller frequencies with respect to Biot's global flow, the predictions of this model are in agreement with White's model, which is based on quasi-static poroelasticity. [ABSTRACT FROM AUTHOR]

ABSTRACT Quantitative interpretation of time-lapse seismic signatures aims at assisting reservoir engineering and management operations. Time-lapse signatures are thought to be primarily induced by saturation and pressure changes. Core-flooding and reservoir flow simulations indicate that a change of the driving forces during dynamic fluid injection gives rise to a varying saturation scale. This saturation scale is yet another variable controlling the time-lapse seismic signal. In this work, we investigate the saturation scale effect on time-lapse seismic signatures by analysing simple modelling scenarios. We consider three characteristic saturation scales, ranging from few millimetres to metres, which may form during gas injection in an unconsolidated water-saturated reservoir. Using the random patchy saturation model, we compare the corresponding acoustic signatures, i.e., attenuation, reflectivity, and seismic gather associated with each saturation scale. The results show that the millimetre saturation scale produces minimum attenuation and the same seismic signatures with those obtained from the elastic modelling. The centimetre saturation scale produces maximum attenuation, whereas the metre saturation scale causes highest velocity dispersion. The analyses of the time shift and amplitude change indicate that ignoring a time-dependent saturation scale can result in biased estimation/discrimination of the saturation and the fluid pressure. In particular, the 4D signal can be strongly affected by the saturation-scale change when the reservoir gas saturation is low and the effective pressure is high. In the presence of an increasing (decreasing) saturation scale during injection, interpreting an observed time shift and amplitude change using the Gassmann model will lead to underestimation (overestimation) of the change in gas saturation and fluid pressure. We show that including the effects of capillarity and residual saturation into the rock physics modelling can potentially reduce the interpretation uncertainty due to the saturation-scale change. [ABSTRACT FROM AUTHOR]