Poromechanics: from Linear to Nonlinear Poroelasticity and Poroviscoelasticity

Bemer, E.; Boutéca, M.; Vincké, O.; Hoteit, N.; Ozanam, O.

doi:10.2516/ogst:2001043

Cited by 23 publications

(27 citation statements)

References 8 publications

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“…Treatments of a nonlinear poroelastic solid containing a fluid are much more limited, perhaps because of the complexity of the topic. Nonetheless, there are a number of studies [Biot and Willis, 1957;Morland, 1972;Biot, 1973;Lewis and Schrefler, 1978;Ehlers, 1992;de Boer, 2000, p. 377;Bemer et al, 2001;Cheng and Abousleiman, 2008] from which to draw upon when treating a nonlinear poroelastic medium. [53] In what follows I shall generalize an approach based upon strain invariants, as presented by Goldenblat [1962].…”

Section: Appendix A: Constitutive Relationshipsmentioning

confidence: 99%

“…[53] In what follows I shall generalize an approach based upon strain invariants, as presented by Goldenblat [1962]. As in the works by Biot [1973] and Bemer et al [2001], I include variables for fluid pressure and volumetric fluid content. As a starting point, consider a fluid-filled porous medium with fairly general relationships between the solid stress tensor , solid strain e, the fluid pressure P f , and the change in volumetric fluid content…”

Section: Appendix A: Constitutive Relationshipsmentioning

confidence: 99%

“…For example, Biot's [1973] study of a semilinear porous solid and a follow-up study by Bemer et al [2001] produced the expressions…”

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

“…This approach of Biot [1973] and Bemer et al [2001] was formulated for a semilinear solid in which the solid constituents of the porous medium deform linearly while the material as a whole may deform nonlinearly. The idea is that the solid grains behave in a linear elastic manner, but the rock as a whole, containing microcracks and interacting grains, behaves elastically but not linearly.…”

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

“…In order to express equations (A21) and (A22) in a manner compatible with the work of Biot [1973] and Bemer et al [2001] and so that they will agree with the expressions for linear poroelastic media, I write them as…”

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

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On the propagation of a quasi‐static disturbance in a heterogeneous, deformable, and porous medium with pressure‐dependent properties

Vasco

2011

Water Resources Research

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.[1] Using an asymptotic technique, valid when the medium properties are smoothly varying, I derive a semianalytic expression for the propagation velocity of a quasi-static disturbance traveling within a nonlinear-elastic porous medium. The phase, a function related to the propagation time, depends upon the properties of the medium, including the pressure sensitivities of the medium parameters, and on pressure and displacement amplitude changes. Thus, the propagation velocity of a disturbance depends upon its amplitude, as might be expected for a nonlinear process. As a check, the expression for the phase function is evaluated for a poroelastic medium when the material properties do not depend upon the fluid pressure. In that case, the travel time estimates agree with conventional analytic estimates and with values calculated using a numerical simulator. For a medium with pressure-dependent permeability I find general agreement between the semianalytic estimates and estimates from a numerical simulation. In this case the pressure amplitude changes are obtained from the numerical simulator.

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Section: Appendix A: Constitutive Relationshipsmentioning

confidence: 99%

Section: Appendix A: Constitutive Relationshipsmentioning

confidence: 99%

“…For example, Biot's [1973] study of a semilinear porous solid and a follow-up study by Bemer et al [2001] produced the expressions…”

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

Section: Vasco: Propagation In a Medium With Pressure-dependent Propementioning

confidence: 99%

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On the propagation of a quasi‐static disturbance in a heterogeneous, deformable, and porous medium with pressure‐dependent properties

Vasco

2011

Water Resources Research

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New method for measuring compressibility and poroelasticity coefficients in porous and permeable rocks

2017

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Over the last decades, a large understanding has been gained on the elastic properties of rocks. Rocks are, however, porous materials, which properties depend on both response of the bulk material and of the pores. Because in that case both the applied external pressure and the fluid pressure play a role, different poroelasticity coefficients exist. While theoretical relations exist, measuring precisely those different coefficients remains an experimental challenge. Accounting for the different experimental complexities, a new methodology is designed that allows attaining accurately a large set of compressibility and poroelasticity coefficients in porous and permeable rocks. This new method relies on the use of forced confining or pore fluid pressure oscillations. In total, seven independent coefficients have been measured using three different boundary conditions. Because the usual theories predict only four independent coefficients, this overdetermined set of data can be checked against existing thermodynamic relations. Measurements have been performed on a Bentheim sandstone under, water‐ and glycerine‐saturated conditions for different values of confining and pore fluid pressure. Consistently with the poroelasticity theory, the effect of the fluid bulk modulus is observed under undrained conditions but not under drained ones. Using thermodynamic relations, (i) the unjacketed, quartz, and skeleton (Zimmerman's relation) bulk moduli fit, (ii) the drained and undrained properties fit, and (iii) it is directly inferred from the measurements that the pore skeleton compressibility Cϕ is expected to be constant with pressure and to be exceedingly near the bulk skeleton Cs and mineral Cm compressibility coefficients.

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Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

Ashworth

Doster

2020

Num Anal Meth Geomechanics

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Summary Dual‐continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual‐scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual‐material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the DC model against fine‐scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine‐scale simulations show that anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show that the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine‐scale representations.

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Poromechanics: from Linear to Nonlinear Poroelasticity and Poroviscoelasticity

Cited by 23 publications

References 8 publications

On the propagation of a quasi‐static disturbance in a heterogeneous, deformable, and porous medium with pressure‐dependent properties

On the propagation of a quasi‐static disturbance in a heterogeneous, deformable, and porous medium with pressure‐dependent properties

New method for measuring compressibility and poroelasticity coefficients in porous and permeable rocks

Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

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