Rocks as Poroelastic Composites

ABSTRACT: In Biot's theory of poroelasticity, elastic materials contain connected voids or pores and these pores may be filled with fluids under pressure. The fluid pressure then couples to the mechanical effects of stress or strain applied externally to the solid matrix. Eshelby's formula for the response of a single ellipsoidal elastic inclusion in an elastic whole space to a strain imposed at infinity is a very wellknown and important result in elasticity. Havin poroelasticity means that the hard part of Eshel % a rigorous generalization of Eshelby's results valid for y's work (in computing the elliptic integrals needed to evaluate the fourth-rank tensors for inclusions shaped like spheres, oblate and prolate spheroids, needles and disks) can be carried over from elasticity to poroelasticity -and also thermoelasticity -with only trivial modifications. Effective medium theories for poroelastic composites such as rocks can then be formulated easily by analogy to well-established methods used for elastic composites. An identity analogous to Eshelby's classic result has been derived [Physical Review Letters 79:1142-114

PORE FLUID EFFECTS ON SHEAR MODULUS FOR SANDSTONES WITH SOFT ANISOTROPY

ABSTRACT A general analysis of poroelasticity for vertical transverse isotropy (VTI) shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. After reducing the problem to a 2 × 2 system, the analysis shows in a relatively elementary fashion how a poroelastic system with isotropic solid elastic frame, but with anisotropy introduced through the poroelastic coefficients, interacts with the mechanics of the pore fluid and produces shear dependence on fluid properties in the overall mechanical system. The analysis shows, for example, that this effect is always present (though sometimes small in magnitude) in the systems studied, and can be quite large (up to a definite maximum increase of 20 per cent) in some rocks -including Spirit River sandstone and Schuler-Cotton Valley sandstone. INTRODUCTION An important paper by Gassmann [1] concerns the effects of fluids on the mechanical properties of porous rock. His main result is the well-known fluid-substitution formula (that now bears his name) for the bulk modulus in undrained, isotropic poroelastic media. He also postulated that the effective shear modulus would be independent of the mechanical properties of the fluid when the medium is isotropic. That the independence of shear modulus from fluid effects is guaranteed for isotropic me

Aligned vertical fractures, HTI reservoir symmetry, and Thomsenseismic anisotropy parameters

The Sayers and Kachanov (1991) crack-influence parametersare shown to be directly related to Thomsen (1986) weak-anisotropyseismic parameters for fractured reservoirs when the crack density issmall enough. These results are then applied to seismic wave propagationin reservoirs having HTI symmetry due to aligned vertical fractures. Theapproach suggests a method of inverting for fracture density from wavespeed data

Frequency-dependent viscous flow in channels with fractal rough surfaces

The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to {infinity} (but has a finite cutoff), and the universal scaling of the dynamic permeability, k({omega}), needs modification. We performed accurate numerical computations of k({omega}) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k({omega}) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations

On the Relationship between Stress and Elastic Strain for Porous and Fractured Rock

Modeling the mechanical deformations of porous and fractured rocks requires a stress-strain relationship. Experience with inherently heterogeneous earth materials suggests that different varieties of Hook's law should be applied within regions of the rock having significantly different stress-strain behavior, e.g., such as solid phase and various void geometries. We apply this idea by dividing a rock body conceptually into two distinct parts. The natural strain (volume change divided by rock volume at the current stress state), rather than the engineering strain (volume change divided by the unstressed rock volume), should be used in Hooke's law for accurate modeling of the elastic deformation of that part of the pore volume subject to a relatively large degree of relative deformation (i.e., cracks or fractures). This approach permits the derivation of constitutive relations between stress and a variety of mechanical and/or hydraulic rock properties. We show that the theoretical predictions of this method are generally consistent with empirical expressions (from field data) and also laboratory rock experimental data

Pore-fluid effects on seismic waves in vertically fractured earth with orthotropic symmetry

For elastically noninteracting vertical-fracture sets at arbitrary orientation angles to each other, a detailed model is presented in which the resulting anisotropic fractured medium generally has orthorhombic symmetry overall. Some of the analysis methods and ideas of Schoenberg are emphasized, together with their connections to other similarly motivated and conceptually related methods by Sayers and Kachanov, among others. Examples show how parallel vertical-fracture sets having HTI (horizontal transversely isotropic) symmetry transform into orthotropic fractured media if some subsets of the vertical fractures are misaligned with the others, and then the fractured system can have VTI (vertical transversely isotropic) symmetry if all of the fractures are aligned randomly or half parallel and half perpendicular to a given vertical plane. An orthotropic example having vertical fractures in an otherwise VTI earth system (studied previously by Schoenberg and Helbig) is compared with the other examples treated and it is finally shown how fluids in the fractures affect the orthotropic poroelastic system response to seismic waves. The key result is that fracture-influence parameters are multiplied by a factor of (1-B), where 0 {le} B < 1 is Skempton's second coefficient for poroelastic media. Skempton's B coefficient is itself a measurable characteristic of fluid-saturated porous rocks, depending on porosity, solid moduli, and the pore-fluid bulk modulus. For heterogeneous porous media, connections between the present work and earlier related results of Brown and Korringa are also established

Evaluating bounds and estimators for constants of random polycrystals composed of orthotropic elastic materials

While the well-known Voigt and Reuss (VR) bounds, and the Voigt-Reuss-Hill (VRH) elastic constant estimators for random polycrystals are all straightforwardly calculated once the elastic constants of anisotropic crystals are known, the Hashin-Shtrikman (HS) bounds and related self-consistent (SC) estimators for the same constants are, by comparison, more difficult to compute. Recent work has shown how to simplify (to some extent) these harder to compute HS bounds and SC estimators. An overview and analysis of a subsampling of these results is presented here with the main point being to show whether or not this extra work (i.e., in calculating both the HS bounds and the SC estimates) does provide added value since, in particular, the VRH estimators often do not fall within the HS bounds, while the SC estimators (for good reasons) have always been found to do so. The quantitative differences between the SC and the VRH estimators in the eight cases considered are often quite small however, being on the order of ±1%. These quantitative results hold true even though these polycrystal Voigt-Reuss-Hill estimators more typically (but not always) fall outside the Hashin-Shtrikman bounds, while the self-consistent estimators always fall inside (or on the boundaries of) these same bounds

The 3rd Global Summit of Research Institutes for Disaster Risk Reduction: Expanding the Platform for Bridging Science and Policy Making

The Global Alliance of Disaster Research Institutes held its 3rd Global Summit of Research Institutes for Disaster Risk Reduction at the Disaster Prevention Research Institute, Kyoto University, Japan, 19–21 March, 2017. The Global Alliance seeks to contribute to enhancing disaster risk reduction (DRR) and disaster resilience through the collaboration of research organizations around the world. The summit aim was to expand the platform for bridging science and policy making by evaluating the evidence base needed to meet the expected outcomes and actions of the Sendai Framework for Disaster Risk Reduction 2015–2030 and its Science and Technology Roadmap. The summit reflected the international nature of collaborative research and action. A pre-conference questionnaire filled out by Global Alliance members identified 323 research projects that are indicative of current research. These were categorized to support seven parallel discussion sessions related to the Sendai Framework priorities for action. Four discussion sessions focused on research that aims to deepen the understanding of disaster risks. Three cross-cutting sessions focused on research that is aimed at the priorities for action on governance, resilience, and recovery. Discussion summaries were presented in plenary sessions in support of outcomes for widely enhancing the science and policy of DRR