Papers by Keyword: Poroelasticity

Abstract: In the present paper, the solution of a finite one-dimensional column with Neumann and Dirichlet boundary conditions are deduced based on the theory of mixture. The solution is obtained in the Laplace domain and the time-step method is chosen to obtain the time domain solution. The material data of Massillion sandstone are used for calculations. The column response to the dynamic loading is examined in terms of displacement, pore water pressure, and pore air pressure.

Abstract: 3D dynamic boundary-value problems of linear viscoelasticity and poroelasticity are considered. Laplace integral transform and its numerical inversion are used. Classical viscoelastic models, such as Maxwell model, KelvinVoigt model, standard linear solid model, and model with weakly singular kernel (Abel type) are considered. Boundary integral equations (BIE) method is developed to solve three-dimensional boundary-value problems. A numerical modelling of wave propagation is done by means of boundary element approach.

Abstract: The paper contains a brief introduction to the state of the art in poroelasticity models, in BIE & BEM methods application to solve dynamic problems in Laplace domain. Convolution Quadrature Method is formulated, as well as Runge-Kutta convolution quadrature modification and scheme with a key based on the highly oscillatory quadrature principles. Several approaches to Laplace transform inversion, including based on traditional Euler stepping scheme and Runge-Kutta stepping schemes, are numerically compared. A BIE system of direct approach in Laplace domain is used together with the discretization technique based on the collocation method. The boundary is discretized with the quadrilateral 8-node biquadratic elements. Generalized boundary functions are approximated with the help of the Goldshteyn’s displacement-stress matched model. The time-stepping scheme can rely on the application of convolution theorem as well as integration theorem. By means of the developed software the following 3d poroelastodynamic problem were numerically treated: a Heaviside-shaped longitudinal load acting on the face of a column.

Abstract: To describe poroelastic properties, a dynamic model of Biot’s material is used in the frame of the three-dimensional isotropic linear dynamic poroelasticity with four basic functions – displacements of the elastic skeleton and pore pressures. A direct version of the BIE method is developed. The boundary-element scheme is constructed using: regularized BIE’s, a matched element-by-element approximation, adaptive numerical integration in combination with a singularity-reducing algorithm, etc. The computer simulation is done using the boundary-element methodologies of the stepped method.

Abstract: This paper presents a consistent theoretical framework for describing the finite poroelasticity with surface effect. The underlying concept of additional pressure that is thought of as an equivalent thermodynamic pressure applying on the pore surface is used to detail the pore pressure. A nonlinear porosity laws is proposed for the finite deformation of porous material. With surface effect consideration, the corresponding constitutive equations are developed. The present model for both the swelling of the matrix and the permeability change of coal induced by adsorption of CO₂ and CH₄ are presented under different pressure conditions. It is shown that the predictions from the model are good agreement with the experimental data of sorption-induced deformation of coals.

Abstract: Variations of sorption moisture in the capillary porous materials result in strong fluid-skeleton interactions due to molecular and surface forces, which produce moisture-induced deformation. The effect of moisture sorption on the non-linear elastic behavior of hygroscopic porous building materials has been experimentally investigated showing strong influence of moisture especially in the lower moisture content range. In the framework poroelasticity moisture influence on elastic behavior is described by two poroelastic coefficients, which present the fluid-skeleton coupling. This paper presents an application of the procedure for the determination of the coupling coefficients for medieval brick.

Abstract: Based on Biot’s elastodynamic theory for poroelastic media, the dynamic response of a poroelastic half-space due to a time-harmonic concentrated vertical load applied at the free surface is investigated. Different from previous treatments of the free surface as either fully permeable or fully impermeable, the free surface of a pororelastic half-space is treated in this study as a more realistic semi-permeable boundary condition, i.e. the permeability of the free surface is considered. The governing equation for axisymmetric motion of a poroelastic half-space is solved by applying the Hankel integral transform. Numerical results are presented to show the effects of semi-permeable boundary condition on the dynamic response of poroelastic half-space.

Abstract: It is a well-known fact that an injection of the borehole fluids into surrounding porous rocks often results in fault reactivation,such as during hydrocarbon production from a reservoir, fluid injection for enhanced oil recovery, hot dry rock geothermal energy extraction, and waste disposal or carbon dioxide sequestration. However, no rigorously derived method for the description of spatial and temporal distribution of seismic events and for the estimation of the critical value of pore pressure of a porous rock sufficient for the generation of an microseismic has ever been developed. There a model developed within the context of Biot’s theory of poroelasticity is used to obtain the distribution of pore pressure, then the pore pressure is substituted into a Mohr–Coulomb failure criterion to predict the fault stability and the spatio-temporal cluster of microseismic events in a reservoir. in this model, the Biot system of equations is formulated for the radial symmetry case and is supplemented by the relevant boundary conditions, Then the solution is constructed analytically. A key advantage and the novelty of the proposed approach is it allows one to monitor an influence of pressure applied at the borehole within and surrounding reservoir and to predict the lower and upper bounds for the critical state of a natural rock, and it can be used in different reservoirs.

Abstract: This work presents a numerical simulation of the behavior of stress guided waves (GWs) propagating in a multilayer system composed of porous materials. To this end, the damped Semi-analytical Finite Element (SFE) formulation proposed in [1] is extended to take the dry porosity into account. An application of waves propagating in two squared aluminum bars jointed by a weaker layer of porous adhesive is presented. Numerical results show that variations of the adhesive's porosity modify the GWs spectro-temporal patterns. These changes could be exploited to detect the level of adhesive porosity in a total nondestructive manner for the above structures.

Abstract: The purpose of this work is to extend the equations of linear poroelasticity to the case of materials with nanopores. We consider a model of microstructure which corresponds to an assemblage of hollow spheres saturated by a fluid. The solid phase is linearly elastic and isotropic; pores are assumed to be of nanometric size. To account for the pore surface stresses, the Young-Laplace model is used. The nanopore size effects on the effective bulk modulus, Biot’ modulus and coefficient are shown. When pores are sufficiently large, the classical relations of linear poroelasticity are retrieved.