Solid–liquid–air coupling in multiphase porous media

This paper addresses various issues concerning the modelling of solid–liquid–air coupling in multiphase porous media with an application to unsaturated soils. General considerations based on thermodynamics permit the derivation and discussion of the general form of field equations; two cases are considered: a three phase porous material with solid, liquid and gas, and a two phase porous material with solid, liquid and empty space. Emphasis is placed on the presentation of differences in the formulation and on the role of the gas phase. The finite element method is used for the discrete approximation of the partial differential equations governing the problem. The two formulations are then analysed with respect to a documented drainage experiment carried out by the authors. The merits and shortcomings of the two approaches are shown. Copyright © 2003 John Wiley & Sons, Ltd.     

多孔介质固液耦合相似材料的研制

为研究地下结构与富水多孔岩体的相互作用问题,根据模型试验相似理论,研制出了一种多孔介质固-液耦合相似材料,该材料由中粗砂、水泥、透水混凝土增强剂合水按一定配比均匀拌和压制而成。运用正交试验设计原理进行配比试验,制作模型小试件,进行了单轴抗压强度、渗透系数、重度、弹性模量、泊松比等参数测试,找出了相似材料各成分对配比试件的影响特征,可根据需要在物理模拟试验中选取不同配比。该配方力学指标稳定,满足一次性浇筑大尺寸模型试件的要求,适用于进行结构与围岩体耦合失效破坏模式的大型物理模拟试验,为富水条件下地下结构风险评估提供了相似试验材料     

Numerical modelling of internal erosion during hydrate dissociation based on multiphase mixture theory

It has been reported that sand production, which is a simultaneous production of soil particles along with gas and water into a production well, forced to terminate the operation during the world's first offshore methane production test from hydrate-bearing sediments in the Eastern Nankai Tough. The sand production is induced by internal erosion, which is the detachment and migration of soil particles from soil skeleton due to seepage flow. The inflow of the eroded soil particles into the production well leads to damage of the production devices. In the present study, a numerical model to predict the chemo-thermo-mechanically coupled behavior including internal erosion during hydrate dissociation has been formulated based on the multiphase mixture theory. In the proposed model, the internal erosion is expressed as mass transition of soil particles from soil skeleton to the fluidized soil particles. Since the internal erosion is considered to depend on the soil particle size, mass of soil particles are divided into several groups that have different representative particle diameters, and the constitutive equations for the onset condition and the mass transition rate of the internal erosion are formulated for each group. Also, transportation of soil particles in the liquid phase is formulated for each particle size group in the proposed model. Finally, a simulation of the methane gas production from the hydrate-bearing sediment by depressurization method is presented, and the internal erosion and the dissociation behavior are discussed.     

考虑热-水-力耦合效应多孔弹性地基的动力响应

通过对Biot波动方程的修正,得到考虑热-水-力学耦合效应的多孔弹性介质动力响应的控制方程,研究了简谐均布荷载作用下地基土体的热-水-力耦合动力响应问题。利用Fourier变换技术,得到地基中的应力、位移和孔隙水压力积分形式的解答。利用Fourier逆变换得到数值结果,分析了热-水-力学耦合条件下地基土体中温度增量、应力、位移和孔隙水压力响应的分布,并讨论了热源输入的影响, 结果表明：应力、位移和孔隙水压力随 的增大而有一定的减小。     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modeling of strongly coupled microscale multiphase flow and solid deformation

When fluid flows in porous media under subsurface conditions, significant deformation can occur. Such deformation is dependent on structural and phase characteristics. In this paper, we investigate the effect of multiphase flow on the deformation of porous media at the pore scale by implementing a strongly coupled partitioned solver discretized with finite volume (FV) technique. Specifically, the role of capillary forces on grain deformation in porous media is investigated. The fluid and solid subdomains are meshed using unstructured independent grids. The model is applied for solving multiphase coupled equations and is capable of capturing pore scale physics during primary drainage by solving the Navier-Stokes equation and advecting fluid indicator function using volume of fluid (VOF) while the fluid is interacting with a nonlinear elastic solid matrix. The convergence of the coupled solver is accelerated by Aitken underrelaxation. We also reproduce geomechanical stress conditions, at the pore scale, by applying uniaxial stress on the solid while simultaneously solving the multiphase fluid-solid interaction problem to investigate the effect of external stress on fluid occupancy, velocity-field distribution, and relative permeability. We observe that the solid matrix exhibits elasto-capillary behavior during the drainage sequence. Relative permeability endpoints are shifted on the basis of the external stress exerted.     

Poroelastic model for pile–soil interaction in a half‐space porous medium due to seismic waves

In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.     

饱和多孔介质热-水-力控制方程耦合项的意义及耦合影响分析

基于饱和多孔介质完全耦合条件下热-水-力控制方程的一般形式,对各耦合项的物理意义进行了分析。以等温条件下水-力耦合的Biot渗透固结理论和等压条件下热-力耦合的热弹性理论两种退化形式为基础,给出耦合系数的物理意义及其函数表达式。研究表明,其中一些耦合系数实际上有相同的物理意义和数学形式,因而可使控制方程得到简化。针对不同的介质特性以及热、水、力条件,给出几种特定情形下控制方程的简化形式。以无限大多孔介质中球域热源的热力学响应分析为例,对一些耦合项的影响程度进行了比较研究。     

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L ² convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.     

A finite element method for modeling coupled flow and deformation in porous fractured media

Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh‐generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd.     

泥水盾构泥膜动态形成机制研究

随着大直径泥水盾构的广泛应用,盾构掘进过程切削成层土的可能性越来越大,常规的静力平衡的方法不能有效地控制开挖面的稳定。从泥膜形成的机制入手,将泥水仓中的泥浆视为由液相和颗粒相组成的两相流,将开挖地层视为多孔介质,利用多相流在多孔介质中的渗流特性提出了泥膜动态形成的过滤模型。此模型将泥膜视为控制体,并认为泥膜形成过程中遵守质量守恒和体积守恒定律,从边界条件上认为单位时间内从单元体内排出水量与土体积的压缩量相等。过滤模型较好地揭示了泥水盾构掘进过程中泥膜的动态形成过程和开挖地层力学性质的动态变化过程,对泥水盾构正面稳定有较为重要的意义。     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

非饱和土广义有效应力原理

综述了非饱和土有效应力的沿革,并就非饱和土有效应力的研究和发展中存在的问题进行了讨论。基于多相孔隙介质理论推导得到的变形功的表达式,提出了非饱和土广义有效应力原理。该原理认为,由非饱和土中的单应力变量的有效应力或双应力变量理论很难唯一地确定非饱和土的变形和强度。广义有效应力原理实质上就是要综合考虑影响非饱和土变形和强度的三种广义应力以及与其对偶的广义变形,给出考虑因素更为全面、理论基础更为坚实的广义有效应力原理。它为非饱和土基本性质的研究和本构方程的建立奠定了坚实而科学的理论基础。     

基于分形理论的赫巴流体在多孔介质中的渗流模型

泥浆是一种用途广泛的工程浆液,在工程施工过程中会渗流进入地层,给工程带来一定的影响。为深入研究泥浆的渗流机理,把地层模拟为多孔介质,泥浆模拟为能更全面地反映其流变性能的赫巴流体,基于分形理论,建立赫巴流体在多孔介质中的渗流模型。基于渗流模型计算结果,详细分析压力梯度、流性指数、稠度系数及孔隙率等参数对多孔介质中赫巴流体瞬时平均流速的影响,指出流速变化与压力梯度、流性指数及稠度系数的变化均呈幂指数关系,与孔隙率变化呈二项式关系,且流性指数是一个影响赫巴流体渗流速度的极敏感因素。渗流模型计算结果为相关工程中泥浆方案的设计与施工奠定了一定的理论基础。     

A comparison of variational formats for porous media subjected to dynamic loading

This paper presents a comparison of two variational formats for fully saturated porous media subjected to dynamic loading, whereby the general situation of relative fluid acceleration is considered: (1) the classical three‐field ( u , p, w )‐format and (2) a novel two‐field ( u , p)‐format, where the seepage velocity w is a spatially ‘local’ field whose treatment resembles that of internal variables in material models. The limited numerical comparison shows that the ( u , p)‐format competes well with the ( u , p, w )‐format. Indeed, it is consistent with the general acceleration modeling in the full range of permeabilities. Moreover, in the low permeability regime (where the magnitude of w is insignificant), the new format reflects the situation pertinent to ‘added‐mass’ and is more efficient than the classical ( u , p, w )‐format. Finally, the ( u , p)‐formatcan conveniently be implemented in existing FE‐codes based on the ‘added mass’ formulation. Copyright © 2010 John Wiley & Sons, Ltd.     

Time‐scale analysis in unsaturated porous media under external wave loads

Extreme waves caused by tsunamis and storm surges can lead to soil failures in the near‐shore region, which may have severe impact on coastal environments and communities. Multiphase flows in deformable porous media involve several coupled processes and multiple time scales, which are challenging for numerical simulations. The objective of this study is to investigate the roles of the various processes and their interactions in multiphase flows in unsaturated soils under external wave loading, via theoretical time‐scale analysis and numerical simulations. A coupled geomechanics–multiphase flow model based on conservation laws is used. Theoretical analysis based on coupled and decoupled models demonstrates that transient and steady‐state responses are governed by pore pressure diffusion and saturation front propagation, respectively, and that the two processes are essentially decoupled. Numerical simulations suggest that the compressibility of the pore fluids and the deformation of the soil skeleton are important when the transient responses of the media are of concern, while the steady‐state responses are not sensitive to these factors. The responses obtained from the fully coupled numerical simulations are explained by a simplified time‐scale analysis based on coupled and decoupled models. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical study of boundary conditions for solute transport through a porous medium

A transition region may be defined as a region of rapid change in medium properties about the interface between two porous media or at the interface between a porous medium and a reservoir. Modelling the transition region between different porous media can assist in the selection of the most appropriate boundary conditions for the standard advection–dispersion equation (ADE). An advantage of modelling the transition region is that it removes the need for explicitly defining boundary conditions, though boundary conditions may be recovered as limiting cases. As the width of a transition region is reduced, the solution of the transition region model (TR model) becomes equivalent to the solution of the standard ADE model with correct boundary conditions. In this paper numerical simulations using the TR model are employed to select the most appropriate boundary conditions for the standard ADE under a variety of configurations and conditions. It is shown that at the inlet boundary between a reservoir and porous medium, continuity of solute mass flux should be used as the boundary condition. At the boundary interface between two porous media both continuity of solute concentration and solute mass flux should be used. Finally, in a finite porous medium where the solute is allowed to advect freely from the exit point, both continuity of solute concentration and solute mass flux should be used as the outlet boundary condition. The findings made here are discussed with reference to a detailed review of previous relevant theoretical and experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical modeling of multiphase fluid flow in deforming porous media: A comparison between two- and three-phase models for seismic analysis of earth and rockfill dams

In this paper, a fully coupled numerical model is presented for the finite element analysis of the deforming porous medium interacting with the flow of two immiscible compressible wetting and non-wetting pore fluids. The governing equations involving coupled fluid flow and deformation processes in unsaturated soils are derived within the framework of the generalized Biot theory. The displacements of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the present formulation. The other variables are incorporated into the model using the experimentally determined functions that define the relationship between the hydraulic properties of the porous medium, i.e. saturation, relative permeability and capillary pressure. It is worth mentioning that the imposition of various boundary conditions is feasible notwithstanding the choice of the primary variables. The modified Pastor–Zienkiewicz generalized constitutive model is introduced into the mathematical formulation to simulate the mechanical behavior of the unsaturated soil. The accuracy of the proposed mathematical model for analyzing coupled fluid flows in porous media is verified by the resolution of several numerical examples for which previous solutions are known. Finally, the performance of the computational algorithm in modeling of large-scale porous media problems including the large elasto-plastic deformations is demonstrated through the fully coupled analysis of the failure of two earth and rockfill dams. Furthermore, the three-phase model is compared to its simplified one which simulates the unsaturated porous medium as a two-phase one with static air phase. The paper illustrates the shortcomings of the commonly used simplified approach in the context of seismic analysis of two earth and rockfill dams. It is shown that accounting the pore air as an independent phase significantly influences the unsaturated soil behavior.     

JHomogenizer: a computational tool for upscaling permeability for flow in heterogeneous porous media

This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly.     

Dynamic response of a pile embedded in a porous medium subjected to plane SH waves

In this paper, the frequency domain dynamic response of a pile embedded in a porous medium subjected to SH seismic waves is investigated. The surrounding porous medium of the pile is described by Biot’s poro-elastic theory, while the pile embedded in the porous medium is treated as a beam and described by a beam vibration theory. Using the Hankel transformation method, the fundamental solution for a half-space porous medium subjected to a horizontal circular patch load is established. According to the fictitious pile methodology, the second kind of Fredholm integral equation for the pile is established in terms of the obtained fundamental solution and free wave field. The solution of the integral equation yields the dynamic response of the pile to plane SH waves. Numerical results indicate that the parameters of the porous medium, the pile and incident waves have considerable influences on the dynamic response of the pile and the porous medium.