Phenomenological equations (with coefficients to be determined by specified experiments) for the poroelastic behavior of a dual porosity medium are formulated and the coefficients in these linear equations are identified. The generalization from the single porosity case increases the number of independent coefficients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of different temporal and spatial scales. For very short times, both matrix and fractures behave in an undrained fashion. For very long times, the double porosity medium behaves like an equivalent single porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At an intermediate or mesoscopic scale pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measure...

Wave propagation in uid-lled porous media is governed by Biot's equations of poroelasticity. Gassmann's relation gives an exact formula for the poroelastic parameters when the porous medium contains only one type of solid constituent. The present paper generalizes Gassmann's relation and derives exact formulas for two elastic parameters needed to describe wave propagation in a conglomerate of two porous phases. The parameters were rst introduced by Brown and Korringa when they derived a generalized form of Gassmann's equation for conglomerates. These elastic parameters are the bulk modulus K s associated with changes in the overall volume of the conglomerate and the bulk modulus K associated with the pore volume when the uid pressure (p f ) and conning pressure (p) are increased, keeping the dierential pressure (p d = p p f ) xed. These moduli are properties of the composite solid frame (drained of uid) and are shown here to be completely determined in terms of the bulk modul...

Dipping permeable sandstone bodies encased in overpressured low permeability mudstone have a characteristic pressure field: sandstone pressures follow the hydrostatic gradient while mudstone pressures have a steeper (often lithostatic) gradient. This pressure distribution drives fluid into the base of the sandstone and expels it at the crest. We use mudstone pressures predicted from porosity and measured sandstone pressures to describe the spatial variation in pressure in two Eugene Island 330 reservoirs (Gulf of Mexico). In one severely overpressured reservoir, bounding mudstones are less compacted at the reservoir crest than at the reservoir base, and we interpret that flow is focused along the reservoir and expelled at the crest. In the second reservoir, mudstone is compacted around the base of the sandstone, and we interpret pore fluids were drawn into the sandstone. Dipping sandstone bodies encased in overpressured mudstone regulate hydrocarbon migration, affect borehole stability, and impact slope stability.

. Existence, uniqueness and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasi-static assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...

. The thermodynamical relations for a two-phase, N-constituent, swelling porous medium are derived using a hybridization of averaging and the mixture-theoretic approach of Bowen. Examples of such media include 2-1 lattice clays and lyophilic polymers. The homogenized field equations are obtained by volume averaging microscale field equations so that explicit relationships between the macroscale field variables and their microscale counterparts are obtained. The system of equations is closed by assuming the rate of change of the volume fraction is a dependent constitutive variable, resulting in viscoelastic behavior of the porous medium. A novel, scalar definition for the macroscale chemical potential for porous media is introduced, and it is shown how the properties of this chemical potential can be derived by slightly expanding the usual Coleman and Noll approach for exploiting the entropy inequality to obtain near-equilibrium results. Within this approach, we use Lagrange multiplier...

this paper we construct a model of the brain and ventricular system which is su#ciently complex to reproduce the behaviour of the hydrocephalic brain yet simple enough to be mathematically tractable, and use the model to analyse the onset and treatment of the condition. A review of the general area of application of poroelascticty to the brain may be found in Tenti et al. (2000)

The variables controlled and measured in elastostatic laboratory experiments (the volume changes, shape changes, confining stresses, and pore pressure) are exactly related to the appropriate variables of poroelastic field theory (the gradients of the volume-averaged displacement fields and the volume-averaged stresses). The relations between the laboratory and volumeaveraged strain measures require the introduction of a new porous-material geometrical term. In the anisotropic case, this term is a tensor that is related both to the presence of porosity gradients and to a type of weighted surface porosity. In the isotropic case, the term reduces to a scalar and depends only on the surface-porosity parameter. When this surface-porosity parameter is identical to the usual volume porosity, the relations initially proposed by Biot and Willis are recovered. The exact statement of the poroelastic strain-energy density is derived and is used to define both the laboratory strain measures and the...

Fundamental equations are derived for the mechanics of a fluidfilled porous medium under initial stress. The theory takes into account elastic and viscoelastic properties, including the most general case of anisotropy. It includes the theory of stability, and of acoustic propagation under initial stress, and by thermodynamic analogy the dynamics of a thermoelastic continuum under initial stress. Equations are also developed for a medium which is isotropic in finite strain. General variational principles are derived by which problems are easily formulated in curvilinear coordinates or in Lagrangian form by using generalized coordinates. It is shown that the variational principles are a direct consequence of the general equations of the thermodynamics of irreversible processes, and lead to real characteristic roots for instability.

. The formulation and existence theory is presented for a system modeling di#usion of a slightly compressible fluid through a partially saturated poroelastic medium. Nonlinear e#ects of density, saturation, porosity and permeability variations with pressure are included, and the seepage surface is determined by a variational inequality on the boundary. Contents 1. Introduction 2 1.1. The Semi-Linear Case 4 1.2. The Unilateral Poro-Elasticity Problem 4 1.3. The Plan 5 2. Preliminaries 5 2.1. Convex Analysis 5 2.2. Sobolev Spaces 6 3. The Initial-Boundary-Value Problem 7 3.1. The Di#usion Operator 7 3.2. The Elasticity Operator 8 3.3. Pressure-Dilation Operators 9 3.4. The Evolution system 10 4. The Cauchy Problem 12 4.1. Implicit Evolution Equations 13 4.2. A-priori estimates 14 5. The Monotone Case 15 5.1. Preliminaries 15 5.2. Uniform Estimates 16 6. Gravity-driven Flow 17 6.1. Existence for the delay equation 18 6.2. Estimates on {p h } 19 6.3. The Limit 20 References 20 Date: ...

Viscoelastic properties of wet and dry human compact bone were studied in torsion and in bending for both the longitudinal and transverse directions at frequencies from 5 mHz to 5 kHz in bending to more than 50 kHz in torsion. Two series of tests were done for different longitudinal and transverse specimens from a human tibia. Wet bone exhibited a larger viscoelastic damping tan � (phase between stress and strain sinusoids) than dry bone over a broad range of frequency. All the results had in common a relative minimum in tan � over a frequency range, 1 to 100 Hz, which is predominantly contained in normal activities. This behavior is inconsistent with an optimal ‘‘design’ ’ for bone as a shock absorber. There was no definitive damping peak in the range of frequencies explored, which could be attributed to fluid flow in the porosity of bone. �S0148-0731�00�00102-3�