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1.
结合化学反应方程式,并应用多孔多相介质溶混污染物输运过程的数值模型,对多孔多相介质中含均相/非均相化学反应传质过程进行了数值模拟。化学反应主要包含均相快速/慢速和非均相快速/慢速等5种化学反应过程,溶质输运行为的控制机制主要考虑对流、扩散及降解、吸附等。基于原有的隐式特征线Galerkin离散化的有限元方法,求解模型控制方程的边值初值问题,求解过程中把均相化学反应物质中按照反应物和生成物分开,非均相反应物质按照固相和液相分开,对均相反应物及非均相液相物质浓度耦合求解,而均相生成物和非均相固相物质独立求解。使方程组按照其不同类型进行分类,同时可减少未知数的个数。对于含有非线性内状态变量的右端项进行迭代求解。数值例题结果验证了所提出的数值方法的有效性、计算精度和稳定性。 相似文献
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After the application of a Laplace–Hankel transform, the governing equations of Biot’s consolidation are solved analytically by using the eigenvalue approach. Then the analytical layer-element of a single soil layer can be obtained in the transformed domain by synthesizing the generalized displacements and stresses, which are both expressed by six arbitrary constants. The elements of the analytical layer-element only contain negative exponential functions, which leads to a considerable improvement in computation efficiency and stability. The global stiffness matrix equation of multilayered soils is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Laplace–Hankel transform after the solution in the transformed domain is obtained. Numerical examples are given to demonstrate the accuracy of this method and to study the influence of the layered soil properties and time history on the consolidation behavior. 相似文献
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Thermomechanical model of hydration swelling in smectitic clays: I two-scale mixture-theory approach
Mrcio A. Murad 《国际地质力学数值与分析法杂志》1999,23(7):673-696
A thermomechanical theory of hydration swelling in smectitic clays is proposed. The clay is treated as a three-scale swelling system wherein macroscopic governing equations are derived by upscaling the microstructure. At the microscale the model has two phases, the disjoint clay platelets and adsorbed water (water between the platelets). At the intermediate (meso) scale (the homogenized microscale) the model consists of clay particles (adsorbed water plus clay platelets) and bulk water. At the macroscale the medium is treated as an homogenized swelling mixture of clay particles and bulk-phase water with thermodynamic properties defined everywhere within the macroscopic body. In Part I, the mesoscopic model governing the swelling of the clay particles is derived using a mixture-theoretic approach and the Coleman and Noll method of exploitation of the entropy inequality. Application of this procedure leads to two-scale governing equations which generalize the classical thermoelastic consolidation model of non-swelling media, as they exhibit additional physico-chemical and viscous-type terms accounting for hydration stresses between the adsorbed fluid and the clay minerals. In Part II the two-scale model is applied to a bentonitic clay used for engineered barrier of nuclear waste repository. The clay buffer is assumed to have monomodal character with most of the water essentially adsorbed. Further, partial results toward a three-scale thermomechanical macroscopic model including the bulk phase next to the swelling particles are derived by homogenizing the two-scale model with the bulk water. A notable consequence of this three-scale approach is that it provides a rational basis for the appearance of a generalized inter-phase mass transfer between adsorbed and bulk water. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
4.
T. Kuppusamy 《国际地质力学数值与分析法杂志》1993,17(7):457-469
Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed. 相似文献
5.
An isogeometric analysis (IGA) based numerical model is presented for simulation of thermo-hydro-mechanically (THM) coupled processes in ground freezing. The momentum, mass and energy conservation equations are derived based on porous media theory. The governing equations are supplemented by a saturation curve, a hydraulic conductivity model and constitutive equations. Variational and Galerkin formulation results in a highly nonlinear system of equations, which are solved using Newton-Raphson iteration. Numerical examples on isothermal consolidation in plane strain, one-dimensional freezing and heave due to a chilled pipeline are presented. Reasonably good agreements were observed between the IGA based heave simulations and experimental results. 相似文献
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An integrated linear/non-linear flow model for the conduit-fissure-pore media in the karst triple void aquifer system 总被引：2，自引：0，他引：2
Most karstic aquifer media may be characterized as the triple-void media with highly-varied hydraulic properties, including matrix pore, fissure and conduit, in which liner flow may co-exist with non-linear flow. In this paper, an attempt is made to couple linear flow with non-linear flow in a single unified flow governing equations by introducing the concept of equivalent hydraulic conductivity (EHC) and deriving a general Darcys law for various flow. The expression of EHC in the karst conduit and fissure are also derived. The procedures of numerical implementation are demonstrated via an ideal model and a case study of karst aquifer system in the Beishan Ore Formation area, Guangxi Autonomous Region, China. 相似文献
7.
In this paper, a new continuum approach for the coupled hydromechanical analysis of fractured porous media is proposed. The methodology for describing the hydraulic characteristics invokes an enriched form of Darcy's law formulated in the presence of an embedded discontinuity. The constitutive relations governing the hydromechanical response are derived by averaging the fluid pressure gradient and the discontinuous displacement fields over a selected referential volume of the material, subject to some physical constraints. The framework incorporates an internal length scale which is explicitly embedded in the definition of gradient operators. The respective field equations are derived following the general form of balance equations in interacting continua. The conventional finite element method is then employed for the spatial discretization, and the generalized Newmark scheme is used for the temporal discretization. The proposed methodology is verified by some numerical examples dealing with a steady-state flow through fractured media as well as a time-dependent consolidation in the presence of a discontinuity. 相似文献
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An alternative approach for quasi‐static large deformation analysis of saturated porous media using meshfree method 
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下载免费PDF全文 An alternative coupled large deformation formulation combined with a meshfree approach is proposed for flow–deformation analysis of saturated porous media. The formulation proposed is based on the Updated Lagrangian (UL) approach, except that the spatial derivatives are defined with respect to the configuration of the medium at the last time step rather than the configuration at the last iteration. In this way, the Cauchy stresses are calculated directly, rendering the second Piola–Kirchhoff stress tensor not necessary for the numerical solution of the equilibrium equations. Moreover, in contrast with the UL approach, the nodal shape function derivatives are calculated once in each time step and stored for use in subsequent iterations, which reduces the computational cost of the algorithm. Stress objectivity is satisfied using the Jaumann stress rate, and the spatial discretisation of the governing equations is achieved using the standard Galerkin method. The equations of equilibrium are satisfied directly, and the nonlinear parts of the system matrix are derived independent of the stresses of the medium resulting in a stable numerical algorithm. Temporal discretisation is effected based on a three‐point approximation technique that avoids spurious ripple effects and has second‐order accuracy. The radial point interpolation method is used to construct the shape functions. The application of the formulation and the significance of large deformation effects on the numerical results are demonstrated through several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
11.
A new approach is proposed for incorporating solid solution reactions into mass conservation equations describing reaction paths in both closed and open systems. The method is applicable to problems involving advective, dispersive, and diffusive transport in a porous medium. By representing the continuously variable solid solution composition with a discrete set of stoichiometric solids that span composition space, combined with a kinetic formulation of their rates of reaction, a self-determining spatial and temporal evolution of the solid solution concentration and composition is obtained. It is demonstrated that equilibrium of an aqueous solution with a stoichiometric solid derived from a solid solution corresponds to equilibrium of the solid solution itself if and only if equilibrium of the stoichiometric solid is stable. One advantage of this approach is that it is unnecessary to introduce any additional compositional variables to represent the solid solution. Discretization may be over the entire range of composition space, or over some subset depending on the system. A major consequence of the kinetic discrete-composition solid solution representation is that modeling solid solutions is similar to modeling pure mineral phases with the exception of a weighting factor applied to reaction rates of stoichiometric solids corresponding to a common solid solution. With this approach, precipitation leads to a discrete zonation of the solid solution that approximates the continuous variation in composition expected for the actual solid solution. The approach is demonstrated for a hypothetical ideal and non-ideal binary solid solution AxB1−xC for a reaction path formulation and reactive transport involving advection and diffusion. 相似文献
12.
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. 相似文献
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Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion
PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each
grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global
solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies
the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated
in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that
one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An
additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times
vector product. The proposed method is tested on the MoMaS reactive transport benchmark. 相似文献
15.
S. Sadiku 《国际地质力学数值与分析法杂志》2013,37(16):2789-2800
One‐dimensional consolidation analysis of layered soils conventionally entails solving a system of differential equations subject to the flow conditions at the bounding upper and lower surfaces, as well as the continuity conditions at the interface of every pair of contiguous layers. Formidable computational efforts are required to solve the ensuing transcendental equations expressing the matching conditions at the interfaces, using this method. In this paper, the jump discontinuities in the flow parameters upon crossing from one layer to the other have been systematically built into a single partial differential equation governing the space–time variation of the excess pore pressure in the entire composite medium, by the use of the Heaviside distribution. Despite the presence of the discontinuities in the coefficients of the differential equation, a closed‐form solution in the sense of an infinite generalized Fourier series is obtained, in addition to which is the development of a Green's function for the differential problem. The eigenfunctions of the composite medium are the coordinate functions of the series, obtained computationally through the application of the extended equations of Galerkin. The analysis has been illustrated by solving the consolidation problem of a four‐layer composite, and the results obtained agree very well with the results obtained by previous researchers. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
16.
A.F. Mastryukov 《Russian Geology and Geophysics》2011,52(9):1035-1042
A spectral method for modeling high-frequency electromagnetic waves in axisymmetric geometry is proposed.The method is based on the expansion of the solutions of Maxwell’s equations in Laguerre functions in the time region.The spectral method is used to solve Maxwell’s equations for both 2D media and stratified media. In the case of stratified media, a Fourier–Bessel expansion in the radial variable is used. The effectiveness of the spectral and finite-difference methods is compared. Harmonic solutions and solitary solutions by the Laguerre method are considered, and the dynamics of monochromatic and broadband electromagnetic pulses are examined. 相似文献
17.
A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
Non-equilibrium thermodynamics and Biot poro-elasticity have been combined to give a coupled hydro-mechanical formulation for unsaturated rock. Darcy’s law for unsaturated flow has been derived from the dissipation process by using standard arguments of non-equilibrium thermodynamics, whereas Helmholtz free energy has been used to derive the relationship between stress and pore pressure changes. The resulting general framework accommodates both large and small deformation theories. When small deformations are assumed, the formulation is comparable with coupled equations derived using an alternative approach. For illustrative purposes, the formulation has been used to analyse a seasonally affected tunnel model. Numerical results for the desaturation in winter and resaturation in summer, of the zone near the tunnel wall, have been evaluated and compared with the findings of other researchers. 相似文献
20.
A finite element model is developed to simulate the behaviour of an aquifer used as storage space for a compressed air energy storage (CAES) system. The governing equations describing a two-phase flow of air and water are coupled non-linear partial differential equations and are solved by the Galerkin approach. The resulting computer model is applied to a gas percolation problem. Upon verification of the numerical results, the model is employed to simulate the air-water displacement in a storage reservoir during daily air cycling. The corresponding saturation variations and the effects of reservoir permeability on the system are presented. The results obtained are essential in establishing storage design and stability criteria for long-term operation of compressed air energy storage systems. 相似文献