Poroelastic Theory Research Articles

Energy management and stability analysis of the inhomogeneous viscoelastic doubly-curved system via efficient 3D poroelasticity approach

This study investigates multi-scale hybrid laminated nanocomposite reinforced (MHLNR) structures, promising metamaterials which can be used for absorbing energy. The structure is able to absorb energy by means of its elastic deflection. For this problem, dynamic stability and absorbed energy for a MHLNR curved panel resting on a non-polynomial viscoelastic base are studied utilizing three-dimensional poroelasticity theory. In order to study the stability analysis, a viscoelastic base is presented as a non-polynomial viscoelastic. The effect of such parameters as the torsional parameter, Winkler-Pasternak parameters, the volume fraction of carbon fiber, porosity, length to radius ratio, span angle, the coefficient for friction, damping factor, compressibility coefficient, as well as initial axially stress on the dynamic responses of the MHLNR panel which is curved and rested on a non-polynomial viscoelastic are studied in detail. It is notable from the results that the radial stress has little dependence on the value of the parameters related to the foundation for the energy absorption. In addition, heightening the porosity, compressibility, as well as friction coefficients can lead to a decrease in the possibility of energy absorption of the sandwich curved panel.

Seismic wave equation formulated by generalized viscoelasticity in fluid-saturated porous media

Biot’s theory of poroelasticity describes seismic waves propagating through fluid-saturated porous media, so-called two-phase media. The classic Biot’s theory of poroelasticity considers the wave dissipation mechanism as being the friction of relative motion between the fluid in the pores and the solid rock skeleton. However, within the seismic frequency band, the friction has a major influence only on the slow P-wave and an insignificant influence on the fast P-wave. To represent the intrinsic viscoelasticity of the solid skeleton, we incorporate a generalized viscoelastic wave equation into Biot’s theory for the fluid-saturated porous media. The generalized equation that unifies the pure elastic and viscoelastic cases is constituted by a single viscoelastic parameter, presented as the fractional order of the wavefield derivative in the compact form of the wave equation. The generalized equation that includes the viscoelasticity appropriately describes the dissipation characteristics of the fast P-wave. Plane-wave analysis and numerical solutions of our wave equation reveal that (1) the viscoelasticity in the solid skeleton causes the energy attenuation on the fast P-wave and the slow P-wave at the same order of magnitude and (2) the generalized viscoelastic wave equation effectively describes the dissipation effect of the waves propagating through the fluid-saturated porous media.

PredictingVpand constrained modulus reduction curve based onVsand shear modulus reduction curve in accordance with poroelastic theory

The compression wave velocity (Vp) of sediments plays a key role in seismic wave amplification of vertical motion and is required in site response analysis. However, such information is usually lacking during field exploration (e.g. the surface wave method) because only shear wave velocity (Vs) is obtained. This aim of this study is to predict Vpbased on Vsempirically and theoretically, particularly focusing on saturated conditions. The empirical approach is to establish the Vpcorrelation dependency on Poisson's ratio and Vs, and the theoretical approach is based on poroelastic theory that accounts for the interaction between fluid and soil skeleton. The engineering geological database for the Taiwan strong motion instrumentation program and the Kiban Kyoshin network database in Japan are adopted to establish an empirical model and validate poroelastic theory. The validated poroelastic approach is used to develop a constrained modulus reduction curve dependency on the porosity, Vs, Poisson's ratio and degree of saturation with a shear modulus reduction curve. The proposed approach can be used to develop generic Vpprofiles and constrained modulus reduction curves for the site response to vertical motion given a site-specific Vsprofile.

Effect of formation strength anisotropy on wellbore shear failure in bedding shale

The shale gas/oil is playing an important role in the current energy resources. However, the wellbore instability problems bring a high risk to drilling engineering especially in the formation with bedding planes. A normal wellbore stability analysis approach is based on elasticity, which is not enough to recognize the mechanisms. In this paper, the poroelasticity was adopted to present the hydro-mechanical coupling effect in shale formation, meanwhile, the permeability anisotropy which could affect the effective stresses around the well was considered. A three-dimensional finite difference model was developed to simulate arbitrary directional well in shale by the coordinate transformation method. The jointed material model was proposed to character the strength anisotropy and plastic behavior of bedding shale. Additionally, the effects of well trajectory, bedding plane orientation and mud weight on shale wellbore stability were discussed, thus some implications for improving wellbore stability in bedding shale formation were obtained from the proposed model. • The jointed material model is proposed to analyze the shear failure region in bedding shale. • The poroelastic theory is adopted to represent the hydro-mechanical coupling effect in the formation. • A finite difference three-dimensional model is established to simulate the wellbore failure behavior. • The effects of well trajectory, bedding plane orientation and mud weight on wellbore stability are evaluated.

РАСЧЕТЫ ДЕЙСТВИЯ СИЛЫ НА ПОРОУПРУГОЕ ТРЕХФАЗНОЕ ПОЛУПРОСТРАНСТВО

The mathematical formulation of the boundary value problem in the images of the linear three-dimensional isotropic dynamic theory of poroelasticity is given when the material of the medium is partially saturated. The poroelastic medium is represented by a model of a heterogeneous material consisting of a phase of an elastic matrix and two phases of fillers – liquid and gas filling the pore system. A method for the numerical inversion of the Laplace transform is described. The description of the boundary-element approach is given. A regularized boundary integral equation is given. A discrete analogue of the boundary integral equation is written down. The discrete analog is parametrized by the complex variable of the Laplace integral transform. As an example, the problem of the action of a vertical force uniformly distributed on a square area on a partially saturated poroelastic half-space is considered. The choice of the computational boundary-element model made it possible to obtain verified numerical results. The effect of saturation on the amplitudes of the nonstationary wave response and on the velocities of the response waves is noted. The behavior of the wave response with an isotropic, homogeneous, poroelastic half-space moving away from the loading source is demonstrated. The problem of the action of a vertical force on a partially saturated poroelastic half-space weakened by a cubic cavity is considered. The influence of half-space attenuation on the wave surface response is analyzed. There is an analysis of the influence of depth on the dynamic wave response, as well as the influence of the phase of the poroelastic material.

Прямая и обратная динамическая задача пороупругости

In applied problems related to propagation of elastic waves, it is often necessary to take into account porosity, fluid saturation of the media, and the hydrodynamic background. Real geological media are multiphase, electrically conductive, fractured, porous, etc. When propagating, seismic waves dissipate due to the absorption of energy. In this paper, the wave propagation process occurs in terms of partial densities of phases, stress tensor, pore pressure, and velocities of the corresponding phases. In the first section, for completeness, the presentation presents a quasilinear system of equations of the poroelasticity theory [1-3]. In the second section, the corresponding linear system of equations of the poroelasticity theory for a homogeneous medium is obtained. In the third section, we construct a fundamental solution for the system of equations of the poroelasticity theory obtained in the second section. In the final section, the inverse poroelasticity problem of determining the distributed source in a half-space using additional information about the free surface mode is considered.

Numerical study of seabed response and liquefaction around a jacket support offshore wind turbine foundation under combined wave and current loading

The seabed instability induced by the transient liquefaction when exposed to wave-current may threaten the safety of offshore structures. In this study, the Reynolds-averaged Navier–Stokes (RANS) equations with the k–ε turbulence model were used to imitate the fluid dynamics, and Biot's poro-elastic theory was used to simulate the transient seabed response. An in-house solver (porous-fluid–seabed–structure interactions–field operation and manipulation) integrating the flow model and seabed model with the finite volume method was developed. The present model was confirmed with published experimental results and then used to analyze the dynamic process of the fluid–seabed–structure interactions as well as seafloor liquefaction around the jacket foundation under wave-current loading. The simulated results showed that the depth and range for the liquefaction area around the jacket foundation tended to increase at first and then declined as the wave propagated forward in the absence of current. In addition, the results demonstrated that the liquefaction depth under current and wave in the same orientation was greater than that without current. It is worth mentioning that the downstream piles were more prone to liquefaction than the upstream piles when the forward current existed.

Numerical investigation of non-cohesive seabed response around a mono-pile by crossing wave-current

The interaction between waves and currents in the ocean often complicates the flow field around structures. In this study, a three-dimensional integrated numerical model was established to investigate the seabed response and liquefaction around a mono-pile under different wave–current interaction angles. In the present model, the Reynolds-averaged Navier–Stokes equations were used to simulate the flow field, and the Biot's poro-elastic theory was adopted to calculate the seabed response caused by crossing wave-current loading. Unlike previous studies, the load on the mono-pile was considered, and the wave–current interaction angle was extended to 180°, which was more in line with practical engineering problems. The numerical results were in a good agreement with the experimental measurements. The results indicated that waves interacted with currents in a large angle could result in a large momentary liquefaction depth of the seabed. The parametric studies proved that the position of the front and two sides of the pile was relatively safer compared with that of the leeside of the pile, and the surface of the seabed downstream of the pile was liable to liquefy.

Torsional Vibration of a Pile in Transversely Isotropic Saturated Soil Considering Its Construction Disturbance Effect

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

Study of wave-induced seabed response around twin pipelines in sandy seabed through laboratory experiments and numerical simulations

Wave-seabed-pipelines interaction is of critical importance in the design of submarine pipelines. Previous studies mainly focus on investigating the characteristics of flow fields and hydrodynamics around a single pipeline. In this study, laboratory experiments and numerical simulations have been performed to examine the effect of burial depth and space between the centers of twin pipelines on the wave-seabed-twin pipelines interaction subject to waves. In the mathematical model, the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations are used to describe the wave motion in the fluid domain, while the seabed domain is described by using the Biot's poro-elastic theory. Numerical models are validated using these experimental measurements and available relevant experimental data. Experimental and numerical results indicate that the burial depth and relative position of twin pipelines can significantly affect the wave-averaged flow velocity field and the pore-water pressure distribution as well as effective stress.

Diagnostic and predictive analysis of production and injection‐induced fault activation

AbstractMitigating the hazard of fault reactivation during CO injection and oil production is important for ensuring environmental sustainability of geologic carbon sequestration and hydrocarbon recovery. Currently, we do not know how the Coulomb Failure Stress (CFS), which is a commonly used metric to assess the potential of inducing slip on a fault, evolves differently for gas injection and oil production scenarios. Using high‐resolution simulations of CO injection‐induced and oil production‐induced fault slip and theories of Coulomb failure and poroelasticity, we address this gap in knowledge. We analyze the fault tractions, slip, and reservoir pressure to understand how a fault is destabilized in successive steps, how hypocenter locations are selected, and how these processes differ between injection and production. We extract and summarize the characteristic features of induced fault activation in terms of the dependence of CFS and the Fault Stress Ratio (FSR) on the dimensionless reservoir pressure perturbation caused by injection or production. We apply the framework to the Farnsworth oilfield in Texas, which is undergoing CO injection and oil production, to disambiguate observations related to fault stability. Finally, we discuss how our framework can inform models that aim to forecast fluid flow‐induced slip and mitigate the induced seismicity hazard in oilfields and gas storage sites.

An efficient ADER-DG local time stepping scheme for 3D HPC simulation of seismic waves in poroelastic media

Many applications from the fields of seismology and geoengineering require simulations of seismic waves in porous media. Biot's theory of poroelasticity describes the coupling between solid and fluid phases and introduces a stiff reactive source term (Darcy's Law) into the elastodynamic wave equations, thereby increasing computational cost of respective numerical solvers and motivating efficient methods utilising High-Performance Computing.We present a novel realisation of the discontinuous Galerkin scheme with Arbitrary High-Order DERivative time stepping (ADER-DG) that copes with stiff source terms. To integrate this source term with a reasonable time step size, we utilise an element-local space-time predictor, which needs to solve medium-sized linear systems – each with 1,000 to 10,000 unknowns – in each element update (i.e., billions of times). We present a novel block-wise back-substitution algorithm for solving these systems efficiently, thus enabling large-scale 3D simulations. In comparison to LU decomposition, we reduce the number of floating-point operations by a factor of up to 25, when using polynomials of degree 6. The block-wise back-substitution is mapped to a sequence of small matrix-matrix multiplications, for which code generators are available to generate highly optimised code.We verify the new solver thoroughly against analytical and semi-analytical reference solutions in problems of increasing complexity. We demonstrate high-order convergence of the scheme for 3D problems. We verify the correct treatment of point sources and boundary conditions, including homogeneous and heterogeneous full space problems as well as problems with traction-free boundary conditions. In addition, we compare against a finite difference solution for a newly defined 3D layer over half-space problem containing an internal material interface and free surface. We find that extremely high accuracy is required to accurately resolve the slow, diffusive P-wave at a or near a free surface, while we also demonstrate that solid particle velocities are not affected by coarser resolutions. We demonstrate that by using a clustered local time stepping scheme, time to solution is reduced by a factor of 6 to 10 compared to global time stepping. We conclude our study with a scaling and performance analysis on the SuperMUC-NG supercomputer, demonstrating our implementation's high computational efficiency and its potential for extreme-scale simulations.

Poroelastic medium with non-penetrating crack driven by hydraulic fracture: Variational inequality and its semidiscretization

A new class of unilateral variational models appearing in the theory of poroelasticity is introduced and studied. A poroelastic medium consists of solid phase and pores saturated with a Newtonian fluid. The medium contains a fluid-driven crack, which is subjected to non-penetration between the opposite crack faces. The fully coupled poroelastic system includes elliptic–parabolic governing equations under the unilateral constraint. Well-posedness of the corresponding variational inequality is established based on the Rothe semi-discretization in time, after subsequent passing time step to zero. The NLCP-formulation of non-penetration conditions is given which is useful for a semi-smooth Newton solution strategy.

Computer simulation as an aid to predict fundamental frequency of a sandwich system via discrete singular convolution method

Present article is the first attempt to analyze the vibration behavior of the composite sandwich cylindrical panels based on the integration of a statistical approaches with numerical solver of differential equations. The motion equations of the structure with functionally graded graphene-platelets reinforced composite (FG-GPLRC) face-sheets imbedded in linear and torsional spring-simulated elastic substrate and subjected to multi-orientational initial stresses are formulated based upon three-dimensional poroelasticity theory. Bi-directional discrete singular convolution method (DSCM) is implemented to find the natural frequency of the mentioned system at design-points. Then, the response surface method is utilized to acquire the closed form of the natural frequency and predict the vibration response of the system according to the reduced third-order polynomial functions. The modified format of Halpin-Tsai micromechanics is employed in order to approximate the elastic properties of the structure. The veracity of the solving procedure is verified by comparing its outcomes with those recorded by the high-quality literature. The results reveal that the span-angle of the panel plays the most important role in the free vibration response of the system compared with the other parameters whose effects are studied in this article. Additionally, it is concluded that reinforcing the face-layers of the sandwich panel by graphene-platelets (GPL) is the more effective way to increase the stiffness of the sandwich structure compared with the case of reinforcing the core section.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multitrace Bayesian amplitude-variation-with-offset petrophysics inversion in multiporosity reservoirs

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude-variation-with-offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. In general, PP-wave reflection coefficients, elastic moduli, and petrophysical parameters are nonlinearly coupled, especially in multiple-type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We have developed a new approach that combines Biot-Gassmann’s poroelasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multitrace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. Our stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of our inversion method is illustrated with synthetic examples and a real data application.

Three-Dimensional Modelling of Non-Linear Wave-Induced Seabed Response around Offshore Open-Ended Pile

This paper analyses the fluid–seabed–structure interactions (FSSI) around the open-ended pile by applying the in-house solver established on the open-source Computational Fluid Dynamics (CFD) platform. The Reynolds-averaged Navier–Stokes (RANS) equations are solved to simulate the hydrodynamic interactions between waves and open-ended piles. Biot’s poro-elastic theory (quasi-static model) is used to reproduce the wave-induced seabed responses. The parameter analysis indicates that the wave period, degree of saturation of seabed and pile diameter have a great influence on the development of the transient seabed liquefaction depth around the pile. In addition, the distribution of the pore water pressure vs soil depth in the inner zone of the pile presents a “V” shape rotated 90 degrees counterclockwise.

Unloading induced absolute negative pore pressures in a low permeable clay shale

The stability analysis of underground excavations constructed in low-permeable rocks requires a comprehensive understanding of the short- and long-term pore pressure response around the excavation. This paper presents the results of a novel in-situ experiment, which was conducted in Opalinus Clay at the Mont Terri Underground Rock Laboratory, Switzerland. The primary aim of the project was to understand unloading-induced pore pressure changes in Opalinus Clay with a focus on the possibility of the development of absolute negative pore pressures. In this experiment, the pore pressure response was initiated by overcoring a small diameter pilot borehole equipped with a pressure transducer and a full-range tensiometer. The results of the experiment showed that the stress relief was accompanied by a noticeable pore pressure drop in the core. An absolute negative pore pressure of −755 kPa was measured. To replicate the pore pressure evolution during the in-situ experiment, a 3D hydro-mechanical-coupled finite element model was developed. It is shown that the magnitude of the pore pressure drop cannot be explained by the classical poroelasticity theory for fully saturated Opalinus Clay samples. Good agreement between the experimental data and numerical results can only be achieved when unloading induced desaturation is considered. Rapid unloading may cause pore water cavitation and desaturation, which significantly increases the pore fluid compressibility. Our considerations based on the nucleation theory suggest that during unloading the required conditions for pore water cavitation in pores larger than a critical value were met.

Microcrack Porosity Estimation Based on Rock Physics Templates: A Case Study in Sichuan Basin, China

Low porosity-permeability structures and microcracks, where gas is produced, are the main characteristics of tight sandstone gas reservoirs in the Sichuan Basin, China. In this work, an analysis of amplitude variation with offset (AVO) is performed. Based on the experimental and log data, sensitivity analysis is performed to sort out the rock physics attributes sensitive to microcrack and total porosities. The Biot–Rayleigh poroelasticity theory describes the complexity of the rock and yields the seismic properties, such as Poisson’s ratio and P-wave impedance, which are used to build rock-physics templates calibrated with ultrasonic data at varying effective pressures. The templates are then applied to seismic data of the Xujiahe formation to estimate the total and microcrack porosities, indicating that the results are consistent with actual gas production reports.

Spatiotemporal Evolution of Pore Pressure Changes and Coulomb Failure Stress in a Poroelastic Medium for Different Faulting Regimes

AbstractSpatial distribution of aftershocks has been explained by the co‐seismic static Coulomb Failure Stress changes (ΔCFS) to some extent. In practice, the earth's crust is porous medium saturated with fluid filling pores, cavities, cracks, and faults. The pore fluid flow plays an important role in the evolution of the stress field in porous medium of the earth. The ΔCFS can be influenced by the co‐seismic pore pressure changes and the post‐seismic pore fluid flow. In order to understand such impacts, we built 3D fault‐slip finite element models to study the evolution of the pore pressure changes and the ΔCFS based on the fully coupled poroelastic theory. The strike‐slip, reverse, and normal faulting models were investigated separately. The patterns of co‐seismic ΔCFS were similar to the elastic stress changes on a homogeneous half‐space, but there were considerable differences in details especially in the near‐fault area when considering co‐seismic pore pressure change. Due to post‐seismic pore fluid flow, the near‐field stress shadow narrowed gradually in the strike‐slip model. In the reverse faulting model, both the near‐field stress shadow and enhanced areas expanded. In the normal faulting model, the stress shadow near the epicenter reduced. The pore pressure changes decayed sharply at the beginning and then gradually approached to zero because the system evolves to drained conditions. These results can help us to understand the effect of pore fluid flow on Coulomb Failure Stress evolution and might improve the understanding of earthquake triggering and aftershock forecasting.

S-wave propagation across material discontinuities in poroelasticity

The shear motion in Newtonian fluids, that is, the fluid vorticity, represents an intrinsic loss mechanism governed by a diffusion equation. Its description involves the trace-free part of the fluid viscous stress tensor. This part is missing in the Biot theory of poroelasticity. As a result, the fluid vorticity is not captured and only one shear wave (S-wave) is predicted. The missing fluid vorticity has implications for the propagation of S-waves across discontinuities. This becomes most apparent in the problem of S-wave propagation across the welded contact of an elastic solid with a porous medium. At such a contact, the no-slip condition between the elastic solid and the constituent parts of the porous medium, the solid frame and the pore fluid, must hold. This requirement translates into a vanishing relative motion of the fluid with respect to the solid frame, that is, the filtration field, at the contact. Nevertheless, our analysis indicates that for the Biot theory, in the low-frequency regime, a nonzero, although insignificantly small, filtration field exists at the contact. However, more importantly, the filtration field is noticeable when the transition to the high-frequency regime occurs. This constitutes a disagreement with the requirement of a no-slip boundary condition and renders the prediction unphysical. This shortcoming is circumvented by including the fluid viscous stress tensor into the poroelastic constitutive relations, as stipulated by the de la Cruz-Spanos poroelasticity theory. Then, a second S-wave is predicted that manifests as the fluid vorticity at the macroscale. This process is distinct from the fast S-wave, the other predicted S-wave akin to the Biot S-wave. We find that the generation of this process at the contact induces a filtration field equal and opposite to that associated with the fast S-wave. Therefore, the no-slip condition is satisfied and the S-wave reflection/transmission across a discontinuity becomes physically meaningful.