Poroelastic Theory Research Articles

Comparative Review and Outlook of Research Progress in Backscatter-based Seafloor Substrate Classification Methods

Background: The seafloor is an essential ocean boundary, and the detection of seafloor information is necessary basis for seafloor scientific research. The classification and identification of seafloor geological types is necessary for researchers to conduct seafloor research, military activities, and marine platform construction. Objective: The purpose of this paper is to summarize the progress of seafloor substrate classification research based on backscattering and to seek a new development direction for seafloor substrate classification research. Method: The literature on various types of submarine sediment attenuation geoacoustic models, backscatter intensity calculations, and submarine substrate classification is summarized, and the progress of theoretical research required for the positive and negative problems of submarine substrate classification is described that include the geoacoustic parameter models based on fluid theory, elastomer theory and poroelastic theory and submarine acoustic scattering models, including the small roughness perturbation approximation model, the Kirchhoff approximation model, the Kirchhoff approximation model and the Kirchhoff approximation model. Result: The development of the Kirchhoff approximation model, the slight slope approximation model, the volume scattering model, and the inversion methods for seafloor substrate classification are summarized, and breakthroughs in seafloor substrate classification are sought by summarizing previous studies. Conclusion: The classification of seafloor substrate based on backscattering intensity needs the support of a perfect geoacoustic model and scattering model, and the current research of low and medium-frequency scattering models and multi-layer seafloor scattering models are the further development direction in the future. Currently, the better performance of the prediction model, geo-acoustic parameter inversion results are more than 90% accuracy, sound velocity ratio and other parameters in the high-frequency band inversion accuracy of 98%, are able to better meet the measured data. Finally, some patented technologies are also reported.

Dynamic Assessment of OWT under Coupled Seismic and Sea-wave Motions

The effect of soil-monopile-structure interaction is of great importance in the design of offshore wind turbines (OWTs). Although sea waves play the most effective role in the performance of OWTs, the coupled effect of sea-wave loads and seismic motion on the performance of the OWT system in seismic-prone areas is a factor that is less investigated and should not be ignored. In this regard, a 2-D porous model based on Biot’s poro-elastic theory is considered to capture the pore water pressure generation in the soil domain surrounding the OWT foundation. The coupled effect of sea waves and seismic motion through a comparative study is considered for the reference OWT system based on the monopile foundation by using the FE program, OpenSees. The results of the analyses are presented in specific locations. Upon the obtained results, the dynamic behavior of the OWT system and the possibility of liquefaction in the soil surrounding the OWT during applied loads are investigated and compared. This comparison is a good representative of the effect of the seismic motion on the performance of the OWT system and the soil medium by considering soil-monopile-structure interaction in seismic-prone areas.

Scaled boundary perfectly matched layer for wave propagation in a three-dimensional poroelastic medium

In this paper, we introduce a novel direct time-domain artificial boundary condition, called the scaled boundary perfectly matched layer, for wave problems in 3D unbounded fluid-saturated poroelastic medium. The poroelastic medium is conceptualized as a two-phase medium composed of a solid skeleton and an interstitial fluid based on the u-p formulation of Biot's theory. The scaled boundary perfectly matched layer proposed in this work originates from an extension of a recently developed perfectly matched layer for wave problems in a single-phase solid medium. The dependence of the conventional perfectly matched layer on the global coordinate system is overcome in the present method. As a result, this method permits the utilization of an artificial boundary with general geometry (not necessarily convex) and can consider planar physical surfaces and interfaces extending to infinity. The proposed method is formulated by a mixed unsplit-field form, which includes both the mixed displacement-stress field and pore pressure-relative displacement field. The resulting scaled boundary perfectly matched layer formulation can be directly described by a system of third-order ordinary differential equations in time, which can be easily integrated into the standard finite-element framework of poroelastic theory. Finally, numerical benchmark examples are presented to demonstrate the accuracy and robustness of the proposed scaled boundary perfectly matched layer, as well as the versatility in practical engineering problems.

Coupled hydro-mechanical-chemical simulation of CCUS-EOR with static and dynamic microscale effects in tight reservoirs

Tight reservoir can be potentially stimulated via CO2 injection and serves as potential sites for CO2 storage. However, simplifying flow mechanisms in hydro-mechanical-chemical coupling simulations can cause significant deviations in forecasting productivity and storage performance. In this study, a coupled hydro-mechanical-chemical model with both static and dynamic microscale effects was established for the first time. We characterized the impact of micro- and nanopores on the multicomponent thermodynamics and multiphase flow of CO2 and in-situ oil by considering the critical property shift, capillary pressure, and boundary slip. The matrix and hydraulic fracture system were constructed based on the embedded discrete fracture model (EDFM). The effect of mineral reaction in the matrix and time-varying width and permeability of propped fractures were also involved in the model to address practical field-scale problems. An iteratively coupled scheme was used in a more comprehensive model to compute the flow and mechanical parameters at each time step, with the impact of different degrees of microscale effects studied by changing the proportions of micropores and nanopores. Two fluid models with different minimum miscible pressures (MMPs) were used to simulate the miscible and immiscible production processes. The stress sensitivity was analyzed based on the Biot poroelasticity theory and time-varying fracture conductivity, with the results suggesting that stress sensitivity can reduce overall production by slower outward pressure movement but can inhibit gas channeling and breakthrough to a certain extent. The detailed analysis of microscale effects, miscibility, and stress sensitivity in this work is of practical significance for tight reservoir development and CO2 geological storage.

Sensitivity of shear wave splitting to fracture connectivity

SUMMARY Shear wave splitting (SWS) is currently considered to be the most robust seismic attribute to characterize fractures in geological formations. Despite its importance, the influence of fluid pressure communication between connected fractures on SWS remains largely unexplored. Using a 3-D numerical upscaling procedure based on the theory of poroelasticity, we show that fracture connectivity has a significant impact on SWS magnitude and can produce a 90° rotation in the polarization of the fast quasi-shear wave. The simulations also indicate that SWS can become insensitive to the type of fluid located within connected fractures. These effects are due to changes of fracture compliance in response to wave-induced fluid pressure diffusion. Our results improve the understanding of SWS in fractured formations and have important implications for the detection and monitoring of fracture connectivity in hydrocarbon and geothermal reservoirs as well as for the use of SWS as a forecasting tool for earthquakes and volcanic eruptions.

Bayesian fluid prediction by decoupling both pore structure parameter and porosity

Carbonate reservoirs exhibit complex pore structure, which significantly affects the elastic properties and seismic response, as well as the prediction of physical parameters. As one of the main factors impacting fluid prediction, pore structure parameter directly involves in few inversion methods. In order to directly predict pore structure parameter in inversion, a novel quantitative reflection coefficient formula is proposed, that integrate Russell's poroelasticity theory with Sun's petrophysical model. This formula separates fluid bulk modulus from porosity and pore structure parameter, allowing for accurate determination of pore-fluid distribution through Bayesian framework. Both theoretical model analysis and multi-component digital core experiments of carbonates validate the importance of pore structure parameter on fluid identification. The practical application of carbonate reservoirs in Sichuan Basin demonstrates that the proposed fluid factor, eliminating the prediction illusion caused by heterogeneity in porosity and pore structure parameter within strata, provides more precise and reliable predictions compared to the Russell fluid factor. Furthermore, the similarity between the Russell fluid factor obtained directly from the Russell approximation and the Russell fluid factor calculated indirectly from the proposed method confirms the stability and accuracy of the new reflection coefficient formula.

Acoustic wave propagation in a porous medium saturated with a Kelvin–Voigt non-Newtonian fluid

SUMMARYWave propagation in anelastic rocks is a relevant scientific topic in basic research with applications in exploration geophysics. The classical Biot theory laid the foundation for wave propagation in porous media composed of a solid frame and a saturating fluid, whose constitutive relations are linear. However, reservoir rocks may have a high-viscosity fluid, which exhibits a non-Newtonian (nN) behaviour. We develop a poroelasticity theory, where the fluid stress-strain relation is described with a Kelvin–Voigt mechanical model, thus incorporating viscoelasticity. First, we obtain the differential equations from first principles by defining the strain and kinetic energies and the dissipation function. We perform a plane-wave analysis to obtain the wave velocity and attenuation. The validity of the theory is demonstrated with three examples, namely, considering a porous solid saturated with a nN pore fluid, a nN fluid containing solid inclusions and a pure nN fluid. The analysis shows that the fluid may cause a negative velocity dispersion of the fast P(S)-wave velocities, that is velocity decreases with frequency. In acoustics, velocity increases with frequency (anomalous dispersion in optics). Furthermore, the fluid viscoelasticity has not a relevant effect on the wave responses observed in conventional field and laboratory tests. A comparison with previous theories supports the validity of the theory, which is useful to analyse wave propagation in a porous medium saturated with a fluid of high viscosity.

A novel hydraulic fracturing model for the fluid-driven fracture propagation in poroelastic media containing the natural cave

Hydraulic fracturing is an efficient technology to extract hydrocarbon within natural caves. However, these caves can markedly affect the fracture propagation behavior. This paper proposes a novel hydraulic fracturing model to simulate the fracture propagation in poroelastic media containing the natural cave, utilizing the strengths of the phase-field method. By coupling the Reynolds flow with cubic law in fracture domain, free flow in cave domain, and low-permeability Darcy flow in reservoir domain, the fracture-cave-reservoir flow governing equations are established. The Biot poroelasticity theory and fracture width are the links of hydro-mechanical coupling. The smooth phase-field is introduced to diffuse not only the sharp fracture but also the sharp cave edge. The fully coupling model is solved by a staggered scheme, which independently solves the pressure field and displacement field in inner cycle, and then independently solves the phase field in outer cycle. The proposed model is verified by comparing with the Khristianovic–Geertsma–de Klerk (KGD) model and Cheng's hydraulic fracturing model. Then, the interaction between hydraulic fracture and natural cave is investigated through several two-dimensional and three-dimensional cases. The result shows that the cave effect can make the hydraulic fracture deflect and raise its propagation velocity. Increasing the fracture-cave distance, injection rate, and in situ stress difference can all decline the cave effect. The displayed cases also substantiate the capability and efficiency of the proposed model.

An Electrochemical-Thermal-Mechanical Model for Large Format Lithium Ion Batteries

The intercalation reaction in Lithium-Ion batteries causes significant volume changes in the active material phases during cycling. Due to spatial limitations in common battery applications, this entails mechanical stresses on different length scales and thereby influencing performance and lifetime of the battery[1]. Mechanical effects are closely linked to electrochemical and thermal processes in the cell, giving rise to complex interactions that are difficult to predict. Moreover, large cell dimensions, which become ever so common in today’s battery industry, further increase complexity due to local variations of state variables. Therefore, modeling is essential to enhance understanding of the governing- and limiting processes.In this contribution we present a fully coupled multi-scale-, multi-physics-model that combines an electrochemical model on the particulate electrode level, namely an extended Newman model featuring a particle size distribution, and a homogenized cell material model, displaying anisotropic electrical-, thermal- and mechanical properties. To include mechanical effects into a multi-physics-model[2] a new approach is considered. We apply the poroelastic theory to describe the mechanical behavior governed by the interaction of the porous electrode matrix and the infiltrated electrolyte. The use of homogenization techniques allows to keep the computational effort in check, while still doing justice to the complexity of a three-dimensional-, multi-scale-, and multi physics problem. The model is parametrized in-house by applying different electrochemical-, mechanical-, and microstructural characterization methods. The model, its parameterization and validation as well as selected simulation results will be presented. Acknowledgements This work was funded by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the research training group SiMET (281041241/GRK2218).[1] Y. Zhao, P. Stein, Y. Bai, M. Al-Siraj, Y. Yang, B.-X. Xu, Journal of Power Sources 2019, 413, 259–283.[2] A. Schmidt, D. Oehler, A. Weber, T. Wetzel, E. Ivers-Tiffée, Electrochimica Acta 2021, 393, 1–14.

Stabilized isogeometric formulation of the multi-network poroelasticity and transport model (MPET[formula omitted]) for subcutaneous injection of monoclonal antibodies

The MPET2 model couples the multi-network poroelastic theory (MPET) with solute transport equations and provides predictions of the material deformation, fluid dynamics, and solute transport in different compartments of a deformable multiple-porosity medium. MPET2 offers a comprehensive framework for understanding complex porous media across multiple disciplines. Examples of its applications include studying rock formations, soil mechanics and subsurface reservoirs, investigating biological tissues, modeling groundwater flow and contaminant transport, and optimizing the design of porous materials. Despite the wide range of applications of the model, its numerical discretization has received little attention. Here we propose a stabilized formulation of the MPET2 model. To address the unique challenges posed by the discretization of the MPET2 model, we use multiple techniques including the Fluid Pressure Laplacian stabilization, Streamline Upwind Petrov–Galerkin stabilization, and discontinuity capturing. Our spatial discretization is based on Isogeometric Analysis with higher-order continuity basis functions. The fully discretized governing equations are solved simultaneously with a monolithic algorithm. We perform a convergence study of the proposed formulation. Then, we conduct a series of simulations of subcutaneous injection of monoclonal antibodies under different injection conditions. Our simulations show that the stabilized MPET2 formulation can provide oscillation-free solutions for tissue deformation, fluid flow in the interstitial tissue, blood vessels, and lymphatic vessels, drug absorption in blood vessels and lymphatic vessels, as well as drug transport in each compartment. We also study the effects of different injection conditions on drug absorption, showing the potential of the proposed model and algorithm in the future optimization of injection strategy.

Time-dependent longitudinal responses of a shield tunnel induced by surcharge load: Theoretical prediction and analysis

The surcharge load at the ground surface inevitably breaks the original equilibrium state between the underneath tunnel and the surrounding soil, which will impact the service performance of a subway tunnel. This paper presents a novel semi-analytical approach for assessing the time-dependent, longitudinal responses of a subway tunnel in soft soil strata induced by the surcharge load. The solution is developed based on the framework of the classical “two-stage method” but innovatively incorporates the effects of ground stratification, the consolidation process, and the longitudinal stiffness reduction of the lining. Biot’s poroelastic theory in conjunction with the Laplace-Fourier transform technique is selected to model the deformation of the stratified ground, while the Timoshenko beam on a Pasternak foundation is employed to model the mechanical responses of the tunnel. The proposed semi-analytical solution is validated not only by comparison with benchmark solutions and a finite element model, but also by predicting a well-documented field measurement. Parametric analyses are conducted to investigate the effects of the elastic modulus and the permeability coefficient of the stratified ground on the longitudinal responses of the tunnel. It is expected that the proposed solution can serve as a useful tool for evaluating the effects of the surcharge load on the longitudinal responses of a subway tunnel.

Vertical vibration characteristics of an offshore end-bearing pile embedded in saturated soils

Pile foundations have increasingly been used extensively for the foundations of offshore engineering structures such as cross-sea bridges, offshore wind turbines and gas infrastructure. Meanwhile, pile integrity testing (PIT) is an important method for evaluating the safety of the pile foundation. In this study, the vertical vibration characteristics of an offshore end-bearing pile embedded in saturated soils is studied by a semi-analytical method. The upper water is assumed to be an ideal compressible fluid and the lower soil is assumed as saturated soil and satisfies Biot's theory of poroelasticity. The dynamic governing equations of the ideal compressible fluid and the saturated soil governing equations are decoupled by introducing potential functions and Helmholtz decomposition using the Laplace transform. Analytical solution for the offshore end-bearing pile vertical vibration is obtained in the frequency domain. The semi-analytical solution for an offshore pile excited by a half-sine wave in the time domain is then obtained by means of inverse Fourier transform. By downscaling the pile-water-soil model to a pile-soil model, the accuracy of the proposed solution was verified. A parametric study is conducted to investigate the influences of water depth, pile radius, soil shear modulus, soil porosity, and soil permeability on the vertical dynamic responses of offshore pile, including complex impedance, the admittance of velocity, and time domain velocity response. The results indicates that the water depth, pile size and soil properties have considerable influence on the response of offshore pile vertical vibration.

Approach for a floating pile embedded in poroelasitc soil under horizontal dynamic load

The deformation mechanism in the horizontal direction of a floating pile under dynamic load should be paid extensive attention. The closed-form solution of dynamic characteristics of a floating pile in poroelasitc soil subject to horizontal dynamic load is obtained by a newly developed framework in this paper. Firstly, based on the three-dimensional continuum model and Biot’s poroelastic theory, the governing equations of the pile surrounding soil and pile end soil are respectively established. Secondly, the pile shaft reaction is calculated by use of the conventional method used in many existing literatures, and the pile base resistance is obtained with the aid of the Hankel transform technique and mixed boundary-value conditions that came from the contact interaction between a rigid massless disk with its beneath soil layer of finite thickness. Thirdly, the Timoshenko beam theory is applied to depict the pile vibration considering its shear deformation, and thus the dynamic impedance functions at pile head are derived. Subsequently, the correctness of the proposed solution is verified through comparisons with the existing results from other scholars. Finally, a parameter analysis about the thickness of the pile end soil, pile slenderness ratio and soil permeability are performed. Results suggest that the soil layer thickness and pile slenderness ratio have a pronounced effect on the pile dynamic behavior, and considering the soil permeability is more realistic to pile vibration response. The obtained results can exert great significance to the serviceability of floating pile for engineering practice.

Technique for studying in high resolution poromechanical deformation of a rocklike medium.

Pressurized fluid injection into underground rocks occurs in applications like carbon sequestration, hydraulic fracturing, and wastewater disposal and may lead to human-induced earthquakes and surface uplift. The fluid injection raises the pore pressure within the porous rocks, while deforming them, yet this coupling is rarely captured by experiments. Moreover, experimental studies of rocks are usually limited to postmortem inspection and cannot capture the complete deformation process in time and space. In this Letter we will present a unique experimental system that can capture the spatial distribution of poromechanical effects in real time by using an artificial rocklike transparent medium mimicking the deformation of sandstone. We will demonstrate the system abilities through a fluid injection experiment, showing the nonuniform poroelastic expansion of the medium and the corresponding poroelastic model that captures completely the results without any fitting parameters. Moreover, our results demonstrate and validate the underlying assumptions of the poroelastic theory for fluid injection in rocklike materials, which are relevant for understanding human-induced earthquakes and injection induced surface uplift.

Influence of partial saturation on bulk modulus and attenuation: the experiment and the theoretical model

SUMMARY Modelling the dispersion and attenuation of seismic waves in partially saturated rocks is important for quantitative interpretation of seismic data. To observe the partial saturation effects on modulus and attenuation, three sandstone samples with different porosities were used in the laboratory experiment. The samples were measured by ultrasonic testing system under different water saturation using drainage process. The experimental results show that the bulk modulus more rapidly increased at higher saturations (>80 per cent), and attenuation peaks could be observed. Then we develop a new partial saturation model based on Chapman’s theory and poroelastic theory. The new model is consistent with the Gassmann equation when the water saturation is 0 or 100 per cent. By analysing the characteristic frequency, the new model can be concluded in the form of a standard linear solid model. A comparison of the new model with the White model and the measured data is conducted. The results show that the model performed well at predicting the effective bulk modulus and attenuation of the rock with different water saturation. Finally, we discussed the impact of frequency, fluids and pore structures on the new model. The results reveal that the new model will be helpful in discussing partial saturation in rocks.

Couple-stress–based gradient theory of poroelasticity

In this research, we present a gradient theory of poroelasticity based on the couple-stress. Within the context of finite deformations and in a thermodynamically consistent manner, the constitutive equations for the porous solid are derived by including the solid vorticity gradient and its power-conjugate counterpart, namely, the couple-stress. Subsequently, a linearized theory for an isotropic porous solid is developed in which two microstructure-dependent constitutive moduli (or equivalently, two material length-scale parameters) are introduced. To investigate the gradient effects on the responses of the material, the problem of wave propagation in fluid-saturated porous solids is formulated and solved based on the proposed theory. For comparison, the wave dispersion and attenuation curves are compared with those obtained from classical theory of poroelasticity.

Lateral dynamic response of single floating piles in saturated soil layer

AbstractA closed‐form formulation for the dynamic analysis of lateral response of floating piles in a saturated finite‐thickness soil layer is presented in this paper. Governing equations of the saturated soil are established on the basis of Biot's poroelastic theory, solution to which results in the lateral resistance of surrounding saturated soil to pile deflection. Closed‐form expressions of the lateral deformations of pile along depth and the dynamic compliances at pile head are obtained by solving a system of linear equations from the boundary and continuity conditions, instead of solving sophisticated integral equations in existing boundary integral methods. The parametric study focuses on exploring the sensitivity of pile compliances and deformations to the main problem parameters, including pile‐soil modulus ratio and soil permeability.

Theory of porous media with the advection term and mass exchange between phases

Earlier modeling approaches in the field of mixtures assumed the solid phase of the mixture was the predominant constituent and simplified the constitutive laws for the fluid phase. In the field of mixtures, it has been argued that methods such as the theory of poroelasticity are incapable of accurately capturing mass exchange between phases and stress and strain fields. Mass exchange between phases and accurate stress and strain variations of each phase are indispensable to many fields of study, such as bone remodeling, fault movement in rocks, and shock waves in soils. This study presents an alternative method for capturing the stress and strain fields of mixtures, focusing on the advection term in the balance of linear momentum and mass exchange for each phase. In addition, this extended theory has the potential for measuring the shear stress field of a viscous fluid component, considering complex boundary conditions, and modeling chemical reactions between mixture phases. The capability of the model has been evaluated by analyzing 2D and 3D examples, including a realistic bone remodeling scenario. Calculations have shown a maximum difference of 20% in the displacement fields. Thus, results clearly demonstrate the importance of considering the advection term and mass exchange between phases, as its application causes significant variations in the displacement and stress fields of the mixture. The developed model of this study can be considered as a general theory, which yields the classic poroelastic model with certain manipulations.

Poroviscoelastic Gravitational Dynamics

AbstractGlobal‐scale periodic deformation has been studied using the (visco)elastic gravitational theory, which assumes a planetary body consists of solid or liquid layers. Recent planetary exploration missions, however, suggest that a global layer of a mixture of solid and liquid exists in several planetary bodies. This study provides a theory of periodic deformation of such a layer unifying the viscoelastic gravitational theory with the theory of poroelasticity without introducing additional constraints. The governing equation system and a formulation suitable for numerical calculation are given. Equations used to calculate the energy dissipation rate are also given. The analytical solutions for a homogeneous sphere are obtained using an eigenvalue approach. Simple numerical calculations assuming a homogeneous sphere reveal that a numerical instability occurs if a thick porous layer, a low permeability, or a high frequency is assumed. This instability can be avoided by choosing an appropriate interior structure model that is numerically equivalent. Different simple numerical calculations adopting a multilayered, radially varying interior profile reveal that the radial profile of the tidal heating rate for a fluid‐saturated porous layer and that for a low‐viscosity solid layer are completely different. In addition, the radial variation in porosity can lead to a factor of ∼100 increase in the local heating rate. These results indicate that future studies should consider a wider variety of detailed interior structure models.

Fiber reinforced hydrated networks recapitulate the poroelastic mechanics of articular cartilage

The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches the physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering. Statement of significancePoroelasticity drives the functional mechanics of articular cartilage (load bearing and lubrication). In this work we develop the design rationale and approach to produce a poroelastic material, known as a fiber reinforced hydrated network (FiHy™), that begins to approach the native performance of articular cartilage. This is the first engineered material system capable of exceeding isotropic linear poroelastic theory. The framework developed here enables fundamental studies of poroelasticity and the development of translational materials for cartilage repair.