Effects of medium and pore‐fluid compressibility on chemical‐dissolution front instability in fluid‐saturated porous media

Theoretical analysis and computational simulations have been carried out to investigate how medium and pore‐fluid compressibility affects the chemical‐dissolution front propagation, which is associated with a fully‐coupled nonlinear problem between porosity, pore‐fluid pressure, pore‐fluid density and reactive chemical‐species transport within a deformable and fluid‐saturated porous medium. When the fully‐coupled nonlinear system is in a subcritical state, some analytical solutions have been derived for a special case, in which the ratio of the equilibrium concentration to the solid molar density of the chemical species is approaching zero. To investigate the effect of either medium compressibility or pore‐fluid compressibility on the evolutions of chemical dissolution fronts in supercritical chemical dissolution systems, numerical algorithms and procedures have been also proposed. The related theoretical and numerical results have demonstrated that: (i) not only can pore‐fluid compressibility affect the propagating speeds of chemical dissolution fronts in both subcritical and supercritical systems, but also it can affect the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; (ii) medium compressibility may have a little influence on the propagating speeds of chemical dissolution fronts, but it can have significant effects on the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; and (iii) both medium and pore‐fluid compressibility may stabilize irregular chemical‐dissolution‐fronts in supercritical chemical dissolution systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Theoretical analyses of acidization dissolution front instability in fluid‐saturated carbonate rocks

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid‐saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.     

Theoretical analyses of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper mainly deals with the theoretical aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved‐mineral equilibrium concentration in the pore fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid‐saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when temperature variation effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. The related theoretical and numerical results have demonstrated that: (i) a temperature increase in a non‐isothermal chemical dissolution system can have some influence on the propagation speed of the planar chemical dissolution front in the system. Generally, the chemical dissolution front in the non‐isothermal chemical dissolution system propagates slower than that in the counterpart isothermal chemical dissolution system when the temperature of the non‐isothermal chemical dissolution system is higher than that of the counterpart isothermal chemical dissolution system; (ii) a temperature increase in the non‐isothermal chemical dissolution system can stabilize the chemical dissolution front propagating in the system, because it can cause a decrease in the Zhao number of the system but does not affect the critical Zhao number of the system; and (iii) the temperature gradient in the upstream direction of a chemical dissolution front is smaller than that in the downstream direction of the chemical dissolution front when the non‐isothermal chemical dissolution system is supercritical. Copyright © 2014 John Wiley & Sons, Ltd.     

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact solutions for one‐dimensional transient response of fluid‐saturated porous media

Based on the Biot theory, the exact solutions for one‐dimensional transient response of single layer of fluid‐saturated porous media and semi‐infinite media are developed, in which the fluid and solid particles are assumed to be compressible and the inertial, viscous and mechanical couplings are taken into account. First, the control equations in terms of the solid displacement u and a relative displacement w are expressed in matrix form. For problems of single layer under homogeneous boundary conditions, the eigen‐values and the eigen‐functions are obtained by means of the variable separation method, and the displacement vector u is put forward using the searching method. In the case of nonhomogeneous boundary conditions, the boundary conditions are first homogenized, and the displacement field is constructed basing upon the eigen‐functions. Making use of the orthogonality of eigen‐functions, a series of ordinary differential equations with respect to dimensionless time and their corresponding initial conditions are obtained. Those differential equations are solved by the state‐space method, and the series solutions for three typical nonhomogeneous boundary conditions are developed. For semi‐infinite media, the exact solutions in integral form for two kinds of nonhomogeneous boundary conditions are presented by applying the cosine and sine transforms to the basic equations. Finally, three examples are studied to illustrate the validity of the solutions, and to assess the influence of the dynamic permeability coefficient and the fluid inertia to the transient response of porous media. Copyright © 2010 John Wiley & Sons, Ltd.     

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe ⩽ 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright © 1999 John Wiley & Sons, Ltd.     

Assessment of acceleration modelling for fluid‐filled porous media subjected to dynamic loading

The purpose of this paper is to examine the importance of different possible simplifying approximations when performing numerical simulations of fluid‐filled porous media subjected to dynamic loading. In particular, the relative importance of the various acceleration terms for both the solid and the fluid, especially the convective contribution, is assessed. The porous medium is modelled as a binary mixture of a solid phase, in the sense of a porous skeleton, and a fluid phase that represents both liquid and air in the pores. The solid particles are assumed to be intrinsically incompressible, whereas the fluid is assigned a finite intrinsic compressibility. Finite element (FE) simulations are carried out while assuming material properties and loading conditions representative for a road structure. The results show that, for the range of the material data used in the simulations, omitting the relative acceleration gives differences in the solution of the seepage velocity field, whereas omitting only the convective term does not lead to significant differences. Copyright © 2007 John Wiley & Sons, Ltd.     

悬浮颗粒的浓度对其在饱和多孔介质中迁移和沉积特性的影响

多孔介质中悬浮颗粒迁移和沉积特性的研究对地下污染物净化、石油开采、核废料处置、水土保持等有很重要的意义。对4种不同浓度的悬浮颗粒在3种不同的渗流速度下进行室内试验,研究悬浮颗粒的浓度对其迁移和沉积特性的影响。结果表明,在一定的悬浮颗粒浓度下,随着渗流速度的增加,穿透曲线中的悬浮颗粒的相对浓度也增大。同时,渗流速度一定时,悬浮颗粒的浓度存在一个临界值,小于该临界值,穿透曲线中的相对浓度随悬浮颗粒的浓度增大而增大;大于该临界值时,相对浓度随悬浮颗粒的浓度增大而减小。另外,悬浮颗粒的临界浓度是与渗流速度相关的,随着渗流速度增加,悬浮颗粒的临界浓度也逐渐增大     

General coupling extended multiscale FEM for elasto‐plastic consolidation analysis of heterogeneous saturated porous media

This paper presents a general coupling extended multiscale FEM (GCEMs) for solving the coupling problem of elasto‐plastic consolidation of heterogeneous saturated porous media. In the GCEMs, the numerical multiscale base functions for the solid skeleton and fluid phase of the coupling system are all constructed on the basis of the equivalent stiffness matrix of the unit cell, which not only contain the interaction between the solid and fluid phases but also consider the time effect. Furthermore, in order to improve the computational accuracy for two‐dimensional problems, a multi‐node coarse element strategy for the GCEMs is proposed, and a two‐scale iteration algorithm for the elasto‐plastic consolidation analysis is developed. Some one‐dimensional and two‐dimensional homogeneous and heterogeneous numerical examples are carried out to validate the proposed method through the comparison with the coupling multiscale FEM and standard FEM. Numerical results show that the newly developed GCEMs can almost preserve the same convergent property as the standard FEM and also possesses the advantages of high computational efficiency. In addition, the GCEMs can be easily applied to other coupling multifield and multiphase transient problems. Copyright © 2014 John Wiley & Sons, Ltd.     

On computation of strain‐dependent permeability of rocks and rock‐like porous media

Determination of transport properties of geomaterials is an important issue in many fields of engineering analysis and design. For example, in petroleum engineering, in situ permeability of an oil reservoir may be crucial in establishing its viability for exploitation, whilst prevention of leakage from underground storage facilities for oil and gas, nuclear waste as well as viability of CO₂ sequestration projects crucially depends on its long‐term values. Permeability is indirectly related to the porosity, pore‐size distribution and pore architecture of the porous media. These parameters evolve when a strain field is imposed. Physical measurement of permeability under a strain field in laboratory conditions is difficult, expensive and prone to a number of uncertainties. In the past, pore network models have been used to compute permeability of materials under stress/strain‐free conditions. In this paper, we propose an enhanced pore network model to compute permeability of rocks and rock‐like porous media under a stress/strain field. Data of pore‐size distribution obtained from mercury intrusion porosimetry are used to compute permeability of rock samples from various unspecified oilfields in the world. It is shown that the two permeabilities can be predicted from the model with sufficient accuracy. A hypothesis for change in porosity, pore‐size distribution and pore architecture as a result of imposed mechanical strains is then proposed. Based on this, permeability is computed again for one of the rock samples under uniaxial and triaxial compressive and tensile strain fields. It is shown that depending on the state of strain field imposed, permeability evolves in an anisotropic manner. Permeability under tensile strain field increases dramatically compared with the reduction that takes place under compressive strain field of the same magnitude. Copyright © 2014 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Interaction between different internal length scales in strain localization analysis of fully and partially saturated porous media—the 1‐D case

The paper analyses the interaction between two internal length scales during dynamic strain localization in multiphase porous materials. The first internal length is introduced in the mathematical model by the gradient‐dependent plasticity for the solid skeleton, while the second one is naturally contained in the multiphase model and is due to the seepage process of the water via Darcy's law, which induces a rate‐dependent behaviour of the solid skeleton. Numerical results of a one‐dimensional example of water saturated porous medium demonstrate the competing effect between these two length scales. The porous medium is here treated as a multiphase continuum, with the pores filled by water and air, the last one at constant atmospheric pressure. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical study of two‐phase fluid distributions in fractured porous media

Two‐phase fluid distributions in fractured porous media were studied using a single‐component multiphase (SCMP) lattice Boltzmann method (LBM), which was selected among three commonly used numerical approaches through a comparison against the available results of micro X‐ray computed tomography. The influence of the initial configuration and the periodic boundary conditions in the SCMP LBM for the fluid distribution analysis were investigated as well. It was revealed that regular porous media are sensitive to the initial distribution, whereas irregular porous media are insensitive. Moreover, to eliminate the influence of boundaries, the model's buffer size of an SCMP LBM simulation was suggested to be taken as approximately 12.5 times the average particle size. Then, the two‐phase fluid distribution of a porous medium was numerically studied using the SCMP LBM. Both detailed distribution patterns and macroscopic morphology parameters were reasonably well captured. Finally, the two‐phase fluid distributions in a fractured porous media were investigated. The influence of the degree of saturation, fracture length, and fracture width on the fluid distributions and migration was explored. Copyright © 2015 John Wiley & Sons, Ltd.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermo‐hydro‐mechanical modeling of damage in unsaturated porous media: Theoretical framework and numerical study of the EDZ

The damage model presented in this article (named ‘THHMD’ model) is dedicated to non‐isothermal unsaturated porous media. It is formulated by means of three independent strain state variables, which are the thermodynamic conjugates of net stress, suction and thermal stress. The damage variable is a second‐order tensor. Stress/strain relationships are derived from Helmholtz free energy, which is assumed to be the sum of damaged elastic potentials and ‘crack‐closure energies’. Damage is assumed to grow with tensile strains due to net stress, with pore shrinkage due to suction and with thermal dilatation. Specific conductivities are introduced to account for the effects of cracking on the intensification and on the orientation of liquid water and vapor flows. These conductivities depend on damage and internal length parameters. The mechanical aspects of the THHMD model are validated by comparing the results of a triaxial compression test with experimental measurements found in the literature. Parametric studies of damage are performed on three different heating problems related to nuclear waste disposals. Several types of loading and boundary conditions are investigated. The thermal damage potential is thoroughly studied. The THHMD model is expected to be a useful tool in the assessment of the Excavation Damaged Zone, especially in the vicinity of nuclear waste repositories. Copyright © 2011 John Wiley & Sons, Ltd.     

我国北方型裂隙岩溶水流及污染物运移数值模拟研究进展

简要回顾了近几十年来我国北方型裂隙岩溶水流及污染物运移数值模拟方面的研究成果,评述了裂隙岩溶水资源评价和污染物运移模拟的计算方法和模拟技术,其中对一些与数值模拟相关的重要问题、近年来研究的热点问题,如模型参数识别及其尺度效应问题、数值弥散和数值振荡问题、Non-Darcy流和Non-Fickian运移问题以及随机方法研究等进行了重点评述,对已有的解决办法进行了比较和对照,并探讨了今后的研究趋势.     

Mathematical and numerical filtration–advection–dispersion model of miscible grout propagation in saturated porous media

The development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed first. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption effects. Constitutive laws such as Fick's law for diffusive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modified by taking into account filtration effects. A new surface term appears in mass balance equations as a consequence of filtration. According to the filtration laws used, an initial filtration rate is estimated on the basis of a one‐dimensional experimental campaign. The field equations are discretized by using Galerkin finite element and θ‐scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a first step to validate the model on a realistic basis. Copyright © 2001 John Wiley & Sons, Ltd.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Coupled simulation of wave propagation and water flow in soil induced by high‐speed trains

The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water‐saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd.     

Upscaling of Navier–Stokes equations in porous media: Theoretical, numerical and experimental approach

The accurate estimation of hydraulic conductivity is important for many geotechnical engineering applications, as the presence of fluids affects all aspects of soil behaviour, including its strength. Darcy’s law is the key experimental (or phenomenological) equation employed to model ground water flow. Yet, this phenomenological equation can be linked to a more fundamental microscale model of flow through the pore spaces of the porous material. This paper provides an experimental verification of the relationships between Darcy’s law (macroscale) and the Navier–Stokes equations (microscale) for actual complex pore geometries of a granular material. The pore geometries are experimentally obtained through state-of-the-art X-ray computer assisted micro-tomography. From the numerical modelling of the microscale flow based on actual pore geometries, it is possible to quantify and visualize the development of pore-scale fluid preferential flow-paths through the porous material, and to assess the importance of pore connectivity in soil transport properties.