Poroelastic Layer Research Articles

On a model simulating lack of hydraulic connection between a man-made reservoir and the volume of poroelastic rock hosting the focus of a post-impoundment earthquake

The idea that a direct hydraulic connection between a man-made reservoir and the foci of post-impoundment earthquakes may not exist at all sites is eminently credible on geological grounds. Our aim is to provide a simple earth model and related theory for use during investigations of earthquakes near new man-made reservoirs. We consider a uniform circular reservoir which rests on the top surface of a no-hydraulic-connection earth model (NHCEM). The model comprises a top elastic (E) layer, an intermediate poroelastic (P) layer, and a bottom elastic half space. The focus of a potential earthquake in the P layer is located directly under the reservoir. The E layer disrupts the hydraulic connection between the reservoir and the focus. Depth of water in the reservoir varies as H ′ + hcos(ω t). Expressions for reservoir-induced stresses and pore pressure in different layers of the NHCEM are obtained by solving the boundary-value problem invoking full coupling between mean normal stress and pore pressure in the P layer. As an application of the derived mathematical results, we have examined and found that earthquakes on 60∘ normal faults may occur in the P-layer of a selected NHCEM at epochs of low reservoir level if the reservoir lies mostly in the footwall of the fault. The exercise was motivated by observations of such earthquakes under the man-made Lake Mead after it was impounded.

Analysis of flexural wave propagation in poroelastic composite hollow cylinder

Wave propagation in an infinitely long poroelastic composite hollow cylinder in is examined by employing Biot’s theory of wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each poroelastic material as homogeneous and isotropic. The inner and outer boundaries of composite hollow poroelastic cylinder are free from stress. The frequency equation of flexural vibrations of poroelastic composite hollow cylinder is obtained. In addition some particular cases such as poroelastic composite hollow cylinder with rigid casing, poroelastic composite bore and poroelastic bore are discussed. Non-dimensional phase velocity is computed as a function of non-dimensional wavenumber. The results are presented graphically for two types of poroelastic composite cylinders and then discussed.Keywords: Biot’s theory, poroelastic composite hollow cylinder, wavenumber, rigidity, phase velocity

Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

The presence of porosity and reinforcement in a medium is an important factor affecting seismic wave propagation and plays vital role in many geophysical prospects. Also, the presence of salt and ore deposits, mountains, basins, mountain roots, etc. is responsible for the existence of corrugated boundary surfaces of constituent layers. Such facts brought motivation for the present paper which deals with the propagation of SH-wave in a heterogeneous fluid-saturated poroelastic layer with corrugated boundaries lying over an initially stressed fibre-reinforced elastic halfspace. Closed form of dispersion relation has been obtained and is found in well agreement to classical Love wave equation for isotropic case. The effect of corrugation, wave number, undulation, position parameter, horizontal compressive/tensile initial stress and heterogeneity on phase velocity has been analysed through numerical computation and graphical illustration. Moreover, comparative study exploring the effect of presence and absence of reinforcement in half-space on dispersion curve is the major highlight of the current study.

Layer‐wise theory and finite elements for laminated poroelastic shells

AbstractIn order to consider growing expectations on vibro‐acoustic performance of products within the design process, reliable simulation tools are necessary. In this paper, we present a approach for the simulation of laminated shells composed of elastic and poroelastic layers. We assume that the shell is given by a parametrization, which allows us to work witn the exact geometry. The three‐dimensional problem is reduced to a two‐dimensional one, by choosing a set of through‐the‐thickness functions for each quantity and through‐the‐thickness integration. The implemented high order finite element approach for the reduced problem on the reference surface relays on hierarchical shape functions. In a numerical example, we show the influence of poroelastic materials attached to a aluminium shell. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The torsional surface wave in a prestressed anisotropic intermediate poroelastic layer of varying heterogeneities

The aim of this paper is to study the behavior of the torsional surface wave in a heterogeneous initially stressed vertical fluid-saturated anisotropic layer sandwiched between inhomogeneous and homogeneous porous half-spaces. It has been considered that the mass density and rigidity of the upper half-space and intermediate layer are space dependent. The proposed model is solved to obtain different dispersion relations for the torsional surface wave in a heterogeneous poroelastic medium lying between two half-spaces. The influence of compressive stress and heterogeneity on torsional surface wave dispersion is shown numerically. It has been observed that heterogeneity, porosity, initial stress of the layer and inhomogeneity of the upper and porosity of lower half-spaces affect the torsional wave speed much. The wave analysis further indicates that the torsional surface waves travel faster in elastic half-spaces in comparison than in the fluid-saturated porous layer.

Frequency-dependent mechanical modelling of poro-elastic materials for sound transmission loss simulations

Multilayer panels made of sheet steel, a poro-elastic layer and an impervious mass are widely used in noise control for increasing sound insulation. A complete description of the vibro-acoustical behavior of the poro-elastic material used in these panels requires knowledge of mechanical parameters (i.e. complex modulus and Poisson's ratio) in order to model the wave propagation through the elastic structure constituting its skeleton. Although many of the materials used for noise and vibration control have viscoelastic behavior, prediction models currently make use of the linear elasticity theory. As a consequence, acoustical quantities, such as sound transmission loss, are predicted by using static or quasi-static values of mechanical properties. In this research, an experimental time domain approach in combination with an analytical model for linear viscoelasticity is utilized for determining the frequency-dependent complex modulus and increasing the accuracy of sound transmission loss simulations in practical applications.

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

ABSTRACTThe present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.

Wave propagation of buried spherical SH-, P1-, P2- and SV-waves in a layered poroelastic half-space

Few studies have investigated the wave propagation of spherical sources in a layered half-space. In this paper, based on Biot's theory of poroelastic media, the exact anti-axisymmetric (cylindrical SH-waves) and axisymmetric (cylindrical P1-P2-SV waves) stiffness matrices for a layered poroelastic half-space are derived. Then the dynamic responses due to buried spherical SH-, P1-, P2- and SV-waves in a layered poroelastic half-space are studied by using the direct stiffness method combined with the Hankel transform. The present solutions are in good agreements with those in a uniform pure elastic half-space as well as a uniform poroelastic half-space. These solutions have the advantages that all of the parameters in the solutions have explicit physical meanings and the thickness of discrete layers does not affect the precision of calculation; thus, the presented formulations are very convenient for engineering applications. Numerical calculations are performed in both the frequency and time domains by taking buried spherical SH-, P1- and SV- waves in a uniform poroelastic half-space and in a single poroelastic layer over a poroelastic half-space as examples. The numerical results show that wave propagation of spherical sources in a layered half-space can be significantly different from that in a uniform half-space; the dynamic responses are highly dependent on the saturated parameters, vibration frequency and the surface drained condition; the presence of the underlying half-space makes the time histories of the dynamic responses in a single layered half-space much more complicated with much longer duration.

An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.

Mathematical models of dynamic systems that include layered watered poroelastic foundations

New mathematical models including an oscillation generator and semi-bounded non-uniform in depth foundation possessing porosity, fluid saturation, and viscoelasticity, are considered. The foundation is represented by a poroelastic layer saturated with gas-liquid mixture, a heterogeneous layer with a viscoelastic coating, and a heterogeneous layer with a subsurface liquid sheet. The foundation of the pack of layers is hard. The operation of the surface oscillator is represented as Fourier series, and the problem of steady-state oscillatory conditions is solved. Applying the Fourier integral transform to the equations that describe continuous media under satisfying boundary conditions allows the construction of integral formulas describing the stress-strain condition in the layer package. A numerical algorithm to study the dependence of the ground-wave propagation on the mechanical and geometrical characteristics of the problem is proposed. The models described are widely used in Geophysics, seismic exploration, construction, railway design, and new material designing.

Erratum: On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer [J. Acoust. Soc. Am. 138, 748-757 (2015)

Erratum: On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer [J. Acoust. Soc. Am. 138, 748-757 (2015)

Effect of loosely bonded undulated boundary surfaces of doubly layered half-space on the propagation of torsional wave

This paper investigates the propagation of torsional wave in an initially stressed poroelastic layer with corrugated as well as loosely bonded boundary surfaces, sandwiched between a corrugated fiber-reinforced layer and a viscoelastic half-space under initial stress. The velocity equation has been obtained in closed form analytically and the substantial effect of affecting parameters on the phase velocity of torsional surface wave has been demonstrated numerically and graphically. Comparative study has been made to observe the effect of flatness parameter, reinforcement, viscoelasticity and porosity on the phase velocity, meticulously. Some particular cases have also been discussed and it is found that velocity equation is in well-agreement to the classical Love wave equation. Moreover, some remarkable observation has been made through numerical computation and graphical demonstration for fiber-reinforced layer of carbon fiber-epoxy resin, poroelastic layer of sandstone and a viscoelastic half-space.

Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach.

The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded is studied. A semi-analytical approach is presented, based on Biot's 1956 theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. This model is validated by comparing the derived absorption coefficients to finite element simulations. Numerical results are further exposed to investigate the influence of the properties of the inclusions (type, material properties, size) of this structure, while a modal analysis is performed to characterize the dynamic behaviors leading to high acoustic absorption. Particularly, in the case of thin viscoelastic membranes, an absorption coefficient larger than 0.8 is observed on a wide frequency band. This property is found to be due to the coupling between the first volume mode of the inclusion and the trapped mode induced by the periodic array and the rigid backing, for a wavelength in the air smaller than 11 times the material thickness.

Propagation of Love waves in an isotropic poroelastic layer bounded between two viscous fluids

The present paper is devoted to the study of Love wave propagation in an infinite isotropic poroelastic layer bounded between two compressible viscous liquids. The equations of motion of an isotropic poroelastic solid are formulated in the framework of Biot’s theory. An analytical solution for the complex frequency equation of Love waves is derived. The analytical expressions for phase velocity of Love waves are obtained and solved numerically for two materials, namely, sandstone saturated with kerosene and sandstone saturated with water. Further, effect of viscosity is observed by considering several particular cases.

On propagation of Love waves in an infinite transversely isotropic poroelastic layer

The present paper is devoted for the study of propagation of Loves waves in a compressible viscous liquid layer of thickness h2 and co-efficient of viscosity ηι bounded by an infinite transversely isotropic poroelastic layer and a transversely poroelastic half-space. The equations of motion in transversely isotropic poroelastic solid have been formulated in the frame work of Biots theory. The secular equation has been obtained and is discussed in the limiting case h2 → 0, ηι → 0 such that the ratio h2/ηι is a constant. Further, secular equation is observed for a case of the poroelastic layer is in welded contact with half-space when the thickness of liquid layer is zero for finite co-efficient of viscosity. Several other special cases have been discussed.

A mixed “Biot–Shell” analytical model for the prediction of sound transmission through a sandwich cylinder with a poroelastic core

A mixed “Biot–Shell” analytical model dedicated to the calculation of sound transmission through an infinite sandwich cylinder composed of orthotropic skins and a poroelastic core is proposed in this paper. The motion of the two thin orthotropic skins is described with the first-order shear deformation theory while the poroelastic core is modeled with the full 3D Biot׳s theory. The main advantage of this mixed model is that it takes into account the elasticity effects related to the skeleton of the poroelastic material. First, an analytical expression of the displacement and stress fields of the solid and fluid phases in the poroelastic layer is presented in cylindrical coordinates. Then, the poroelastic core transfer matrix relating the displacements and the stresses at the two common interfaces between the core and the skins is calculated. The coupling of the two skins is then made using the modal transfer matrix of the core, leading to the global dynamic equilibrium of the sandwich cylinder. The proposed model is finally used to calculate the sound Transmission Loss (TL) of infinite cylinders excited by an incident plane wave. Excellent agreement is observed in comparison with a finite element model. The usefulness of Biot׳s model in this type of problem is demonstrated by comparing the results with those obtained with equivalent fluid models. The mixed “Biot–Shell” analytical model is finally used to demonstrate the influence of the structural damping of each layer and to study the sound transmission in different configurations.

An analytical study on hydrodynamics of an unsteady flow and mass transfer through a channel asymmetrically lined with deformable porous layer

The present study is motivated by its possible relevance to the rheology of blood and the transport of nutrient and drug molecules (macro–microscopic level) through capillaries, venules and digestive tract under the influence of endothelial-cell glycocalyx (EG). As an approximation, we study unsteady fluid flow through a rectangular channel lined with asymmetric porous lining. In order to model a more realistic situation, we adopt biphasic mixture theory for the unsteady hydrodynamics of fluid transport in poroelastic layer(s) (EG). The flow within the lumen region between the deformable porous layers is governed by unsteady Stoke’s equation. The unsteady nature of the flow is being taken care with the Fourier series expansion analysis. Shear stress is calculated at the interface of free lumen and porous layers along with volumetric flow rate through the free lumen region. An expression for Sherwood number is derived at the said interface from the pseudo steady state solution of the mass transfer equation that quantifies the transport of solute nutrient through the lumenal space. The corresponding convection–diffusion equation is solved within the mass transfer boundary layer using similarity transformation method. It is observed that the rate of volumetric flow through the free lumen increases and interfacial shear stress (i.e., shear stress at the interface of at the porous and free lumen) decreases with stress jump coefficient at the mentioned interface. Length averaged Sherwood number deceases with increase in depth of the porous layer and increases with the constant permeation velocity when the other parameters characterizing the mass transfer process remain constant.

Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer

Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer

On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer.

The effective density fluid model (EDFM) was developed to approximate the behavior of sediments governed by Biots theory of poroelasticity. Previously, it has been shown that the EDFM predicts reflection coefficients and backscattering strengths that are in close agreement with those of the full Biot model for the case of a homogeneous poroelastic half-space. However, it has not yet been determined to what extent the EDFM can be used in place of the full Biot-Stoll model for other cases. Using the finite element method, the flat-interface reflection and rough-interface backscattering predictions of the Biot-Stoll model and the EDFM are compared for the case of a poroelastic layer overlying an elastic substrate. It is shown that considerable differences between the predictions of the two models can exist when the layer is very thin and has a thickness comparable to the wavelength of the shear wave supported by the layer, with a particularly strong disparity under the conditions of a shear wave resonance. For thicker layers, the predictions of the two models are found to be in closer agreement, approaching nearly exact agreement as the layer thickness increases.

Line source in a poroelastic layer bounded by an elastic space

SummaryThe fundamental solution of a continuous line source, injecting fluid at a constant rate over the thickness of a poroelastic reservoir bounded by infinite impermeable elastic layers, is derived in this paper. This idealized problem has applications in hydrogeology and in petroleum engineering, as it can be used to assess the mechanical perturbations caused by injection or withdrawal of fluid in the subsurface through a vertical well. Construction of the solution takes advantage of the uncoupling of the pore pressure field, which, in this particular case, is given by the classical singular solution of the diffusion equation for an infinite line source. The mechanical fields then are determined by solving an elasticity‐like problem with a body force field proportional to the time‐dependent pore pressure gradient. On account of the problem symmetries, the Navier equations of elasticity reduce to two uncoupled partial differential equations for the radial and vertical (axial) displacement components, which are solved by a twofold application of Fourier and Hankel transforms. The solution exhibits different regimes at small, intermediate, and large times. When the diffusion radius, proportional to the square root of time, is smaller than or comparable to the thickness of the permeable layer, the induced deformation is confined to a region with a characteristic dimension of the same order as the diffusion radius. At large time, when the diffusion radius is large compared with the permeable layer thickness, the deformation rate in the reservoir is essentially oedometric (uniaxial). The different regimes of solutions are justified with a conceptual model based on identifying the evolving characteristics of complementary interior and exterior domain problems. The derived solution can serve as a valuable benchmark for coupled reservoir simulators. It also provides insights in to such problems as waterflooding, shearing at reservoir/cap rock interfaces, and stress redistribution around producing wells. Copyright © 2015 John Wiley & Sons, Ltd.