1,721,036 research outputs found
Formulation of a phase field model of multiphase flow in deformable porous media
No full textIn this contribution a new model for partially saturated porous media is presented, within the framework of gradient poromechanics, based on a phase field approach. While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of the surface tension between the wetting and the non-wetting fluid, occupying the pore space, is stated considering a regularized phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. This approach provides similar results as those of the model based on the concept of specific interfacial area. The dependence of the free energy on the gradient of the saturation also implies that Darcy law must be extended to become a fourth order partial differential equation
Dilatancy and compaction around a cylindrical cavern leached-out in a fluid saturated salt rock
No full textAfluid filled cylindrical cavern of circular cross section in a homogeneous infinite salt formation under a hydrostatic stress is set under internal pressure that differs from the confining pressure. The fluid in the cavern and in the mixture is treated as ideal and the solid as elastic. The initial state of stress is a consequence of the outside pressure and the cavern pressure. Perturbing the cavern pressure induces small changes in the solid and fluid densities.We compute these fields as functions of the radial distance from the cavern centre and show that depending on the relative stress levels the (salt) formation experiences either a dilatation or a compaction that is concentrated in a boundary layer near the cavern wall. © 2005 Taylor & Francis Group, London
A second gradient theory for deformable fluid-saturated porous media
No full textLocal dilatancy and solid-fluid surface tension are two of the driving micro-phenomena which characterize the behaviour of fluid saturated porous media. The first one is essentially due to micro-filtration occurrence and pore opening, the second one to wetting phenomena at the solid-fluid interface at the micro-level. In order to describe these phenomena at the macro-scalewe propose in this paper an extension of the classical Biot model of porous media, which includes so called second gradient effects. Starting from a mixture theory model involving two second gradient constituents, so as to describe local dilatancies in the solid as well as capillarity effects, we derive a poromechanical model, which describes not only the effects of porosity but also those of the porosity gradient. It is proven how starting from the first and the second principle of thermodynamics a suitable macro-scale potential for the skeleton can be defined in order to state a consistent formulation of constitutive relations. Moreover an extended formulation of the Darcy law is derived. © 2005 Taylor & Francis Group, London
Phase field modeling of partially saturated deformable porous media
No full textA poromechanical model of partially saturated deformable porous media is proposed based on a phase field approach at modeling the behavior of the mixture of liquid water and wet air, which saturates the pore space, the phase field being the saturation (ratio). While the standard retention curve is expected still to provide the intrinsic retention properties of the porous skeleton, depending on the porous texture, an enhanced description of surface tension between the wetting (liquid water) and the non-wetting (wet air) fluid, occupying the pore space, is stated considering a regularization of the phase field model based on an additional contribution to the overall free energy depending on the saturation gradient. The aim is to provide a more refined description of surface tension interactions.
An enhanced constitutive relation for the capillary pressure is established together with a suitable generalization of Darcy’s law, in which the gradient of the capillary pressure is replaced by the gradient of the so-called generalized chemical potential, which also accounts for the “force” associated to the local free energy of the phase field model. A micro-scale heuristic interpretation of the novel constitutive law of capillary pressure is proposed, in order to compare the envisaged model with that one endowed with the concept of average interfacial area.
The considered poromechanical model is formulated within the framework of strain gradient theory in order to account for possible effects, at laboratory scale, of the micro-scale hydro-mechanical couplings between highly-localized flows (fingering) and localized deformations of the skeleton (fracturing)
The role of edge forces in conservation laws and energy release rates of strain-gradient solids
No full textConservation laws and energy release rates for general strain-gradient elastic solids are derived in a finite deformation framework. With respect to the relevant literature new terms are derived modelling the energy release through the body edges. We show how the enlightened contributions and the presence of edge forces play a relevant role when estimating the J-integral of mode I and II crack opening problems
A second gradient model for deformable porous matrices filled with an inviscid fluid
No full textIn this paper we deal with an enlarged theory of binary mixtures: a second gradient solid constituent and a perfect fluid are considered. On the basis of this assumptions we obtain, for a linear elastic hollow cylinder, a set of density profiles of the solid matrix, parameterized by a suitable energetic coupling coefficient and characterized by the presence of boundary layers arising at the external surfaces of the body. A structural stability analysis of the partial differential equations, governing the motion of the mixture, is also developed, in a case which may be of interest in applications to underground structural engineering
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