Chemically induced deformation of a porous layer coupled with advective–dispersive transport. Analytical solutions

In this paper a chemically induced deformation of porous material taking place during advective–dispersive transport of a chemical is considered. Linearized governing equations are derived and analytical solutions of 2 one‐dimensional problems for a homogeneous layer with drained boundaries are developed. Numerical results for a particular clayey material and a chemical migrating through the layer showing distributions of concentration of chemical, changes in porosity of the material and pore fluid pressure, and evolution of settlement of the layer as functions of time are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Advective transport from a penny-shaped crack in a porous medium and an associated uniqueness theorem

This paper examines the problem of the advective transport of a contaminant from sources in the shape of either a penny-shaped crack or an elongated needle-shaped cavity located in a porous medium of infinite extent. The advective transport is induced by Darcy flow in the porous medium, where the internal boundary is maintained at a constant potential. The paper presents an approximate analytical solution to this problem, which is deduced from a formulation that models a cavity in the shape of either an oblate or a prolate spheroid. The results also represent one of the few spatially three-dimensional exact analytical solutions for the, albeit linear, hyperbolic problem governing the contaminant transport problem. The paper also presents a canonical proof of uniqueness for advective contaminant transport problems associated with media of infinite extent. Copyright © 2004 John Wiley & Sons, Ltd.     

Impact of single inclined faults on the fluid flow and heat transport: results from 3-D finite element simulations

The impact of inclined faults on the hydrothermal field is assessed by adding simplified structural settings to synthetic models. This study is innovative in carrying out numerical simulations because it integrates the real 3-D nature of flow influenced by a fault in a porous medium, thereby providing a useful tool for complex geothermal modelling. The 3-D simulations for the coupled fluid flow and heat transport processes are based on the finite element method. In the model, one geological layer is dissected by a dipping fault. Sensitivity analyses are conducted to quantify the effects of the fault’s transmissivity on the fluid flow and thermal field. Different fault models are compared with a model where no fault is present to evaluate the effect of varying fault transmissivity. The results show that faults have a significant impact on the hydrothermal field. Varying either the fault zone width or the fault permeability will result in relevant differences in the pressure, velocity and temperature field. A linear relationship between fault zone width and fluid velocity is found, indicating that velocities increase with decreasing widths. The faults act as preferential pathways for advective heat transport in case of highly transmissive faults, whereas almost no fluid may be transported through poorly transmissive faults.     

计算流体地球化学研究的进展

成矿作用的化学机理可以通过实验和计算机模拟进行研究。随着计算机运算能力的不断增强 ,在地球化学中正在形成一门新兴学科———计算地球化学。其中热质输运模拟、化学质量迁移数值模拟和流体输运化学反应耦合动力学研究取得了显著进展。建立在Darcy定律和守恒方程基础上的多孔介质热质输运模拟通过流函数图、等温线图及速率矢量图等 ,从古水文学和流体地球化学方面高度动态研究成矿作用。根据化学和热力学原理进行的化学质量迁移数值模拟则通过矿物和流体中化学物种的热力学数据 ,预测多组分体系中发生的流体岩石相互作用 ,定量揭示经历了复杂化学反应进程的成矿作用的化学行为。将上述两方面结合的流体输运化学反应耦合动力学 ,可以从时间和空间上模拟真实成矿流体系统复杂的动力学行为 ,是计算流体地球化学的发展方向。     

The transport of heat and matter by fluids during metamorphism

Non-dimensional solutions to the equations for the combined advective and diffusive one-dimensional transport of heat and solute in a layer are derived for fixed temperature/concentration on the boundaries and initial conditions of a linear gradient across the layer or a step function at the lower boundary. The solutions allow distinction of regimes in which advective or diffusive transport of either heat or solute predominate as a function of fluid flux, time and a length scale. The much lower diffusive coefficients for solute than heat results in a significant range of length scales and fluid flux rates characterised by advection of matter and diffusion of heat. The advective velocity of a component is a function of its fluid:rock partition coefficient. The most rapidly transported tracers which partition largely into the fluid phase, such as He, will travel orders of magnitude faster than heat or compatible solutes such as oxygen. Geochemical profiles in boundary layer regions where both advective and diffusive transport are significant are shown to be particularly informative as to properties of the rocks related to fluid flow such as porosity, permeability, time scales and fluid flux rates. The importance of advection can be directly estimated from the asymmetry of the geochemical profiles across individual layers.     

Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks

The chemical‐dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, pore‐fluid pressure and reactive chemical‐species transport in fluid‐saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re‐derived to correct this confusion in this paper. Owing to the morphological instability of a chemical‐dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical‐dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical‐dissolution front during its propagation within fluid‐saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical‐dissolution front instability problem within a fluid‐saturated porous medium. Copyright © 2007 John Wiley & Sons, Ltd.     

Solute transport through a deforming porous medium

Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co‐ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non‐linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers. Copyright © 2002 John Wiley & Sons, Ltd.     

Analytic solutions to the advective contaminant transport equation with non-linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright © 1999 John Wiley & Sons Ltd.     

Formation of bed‐scale spatial patterns in dolomite abundance during early dolomitization: Part I. Mechanisms and feedbacks revealed by reaction–transport modelling

Dolomites of varied ages exhibit metre‐scale nested patterns of lateral periodic variation in permeability and porosity and, by inference, dolomite abundance as most examples are 100% dolomite. Two‐dimensional reaction–transport modelling simulations of bed‐scale dolomitization were used to assess whether those patterns in dolomite abundance could form during near‐surface replacement dolomitization. Simulations used a 2 m high and 18 m long model domain, a low‐Mg calcite grainstone precursor and an evaporated Mississippian seawater brine (430 parts per thousand salinity) as the dolomitizing fluid. The domain was initially populated with random variations in porosity and/or grain size. Results reveal that spatial patterns in dolomite abundance emerge when there is as little as 1% dolomite formed, with similarities between the modelled patterns and outcrop‐documented patterns. The nested patterns include a near‐random component that constitutes ≤40% of the total variance, short‐range correlation ranging from 1·5 to 3·3 m and a longer‐range periodic trend with a wavelength up to 6·5 m. The emergence of pattern in dolomite abundance is the result of an autogenic self‐organizing phenomenon. It is triggered by variation in initial calcite reactive surface area that occurs due to the random heterogeneities in initial porosity and/or grain sizes. The pattern develops due to a combination of kinetic disequilibrium reactions (dolomite precipitation and calcite dissolution) and positive feedbacks between dolomite growth, calcite dissolution and fluid flow. Flow is around loci of higher dolomite, lower porosity and higher reactive surface areas, but through loci of lower dolomite, higher porosity and lower reactive surface areas. The resulting less porous/more dolomite and more porous/less dolomite structures at the metre‐scale arise from those localized interactions. This self‐organizing mechanism for pattern formation constitutes a new model for geochemical self‐organization during dolomitization and is the only self‐organization model that is proven applicable to the formation of metre‐scale patterns during early, near‐surface dolomitization.     

Modelling of rock alteration due to coupled heat and mass transport

 A three-dimensional computer model is presented for studying the interaction of heat and mass transport regarding the temporal and spatial evolution of sandstones. The model simulates coupled heat and reactive mass transport in porous rocks. In general, mineral solubilities in water are low. Therefore, large fluid volumes are required to flow through the rock to explain observed mineral cements in sandstones. Besides mass transport, pore fluids transport heat which modifies rock temperatures. Very high flow rates result in strong temperature modifications and, therefore, enhance diagenesis. Low flow rates often cannot account for observed cementation. The model results show the effect of advective, convective and conductive heat transport on temperature and diagenetic evolution of sandstones for two different flow systems in a simple geological environment. Received: 6 August 1996/Accepted: 18 December 1996     

Two‐scale modeling of solute dispersion in unsaturated double‐porosity media: Homogenization and experimental validation

A two‐scale modeling of solute transport in double‐porosity (DP) media under unsaturated water flow conditions is presented. The macroscopic model was developed by applying the asymptotic homogenization method. It is based on theoretical and empirical considerations dealing with the orders of magnitude of characteristic quantities involved in the process. For this purpose a physical model that mimics the behavior of DP medium was built. The resulting two‐equation model relies on a coupling exchange term between micro‐ and macro‐porosity subdomains associated with local non‐equilibrium solute concentrations. The model was numerically implemented (Comsol Multiphysics^®) to simulate the macroscopic one‐dimensional physical process taking place into the porous medium of 3D periodic microstructure. A series of dispersion experiments of NaCl solution under unsaturated steady‐state flow conditions were performed. The experimental results were used first to calibrate the dispersion coefficient of the model, and second to validate it through two other independent experiments. The excellent agreement between the numerical simulations and the measurements of the time evolution of the non‐symmetrical breakthrough curves provides a proof of predictive capacity of the developed model. Copyright © 2010 John Wiley & Sons, Ltd.     

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that(1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.     

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that (1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy’s law satisfactorily; (2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.     

Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection

This paper presents three-dimensional finite element simulations to evaluate diffusion and dispersion tensors in periodic porous media in the presence of an advective velocity field. These tensors are evaluated in the framework of the double-scale expansion technique. Two problems, a Newtonian flow and a vector-valued advection–diffusion equation, have to be sequentially solved at the pore scale. Finite element techniques to approximate these problems are proposed and analyzed. Numerical results in three-dimensional networks of spheres are presented to quantitatively assess the impact of the pore morphology and of the advection velocity on the diffusion and dispersion tensors.     

The use of laboratory experiments for the study of conservative solute transport in heterogeneous porous media

 Laboratory experiments on heterogeneous porous media (otherwise known as intermediate scale experiments, or ISEs) have been increasingly relied upon by hydrogeologists for the study of saturated and unsaturated groundwater systems. Among the many ongoing applications of ISEs is the study of fluid flow and the transport of conservative solutes in correlated permeability fields. Recent advances in ISE design have provided the capability of creating correlated permeability fields in the laboratory. This capability is important in the application of ISEs for the assessment of recent stochastic theories. In addition, pressure-transducer technology and visualization methods have provided the potential for ISEs to be used in characterizing the spatial distributions of both hydraulic head and local water velocity within correlated permeability fields. Finally, various methods are available for characterizing temporal variations in the spatial distribution (and, thereby, the spatial moments) of solute concentrations within ISEs. It is concluded, therefore, that recent developments in experimental techniques have provided an opportunity to use ISEs as important tools in the continuing study of fluid flow and the transport of conservative solutes in heterogeneous, saturated porous media. Received, December 1996 · Revised, July 1997 · Accepted, August 1997     

Copper‐gold mineralisation in New Guinea: Numerical modelling of collision,fluid flow and intrusion‐related hydrothermal systems

Two‐ and three‐dimensional numerical modelling techniques, constrained by key geodynamic data, provide insights into the controls on development of porphyry‐related Cu–Au mineralisation in the Tertiary collision zone of New Guinea. Modelling shows that the creation of local dilation to facilitate magma emplacement can be caused by reactivation of arc‐normal transfer faults, where they cut the weakened fold belt. Additionally, dilation occurs where fluid overpressuring is caused by collision‐related, south‐directed fluid flow being localised into the more permeable units of the Mesozoic passive‐margin sedimentary succession. Rapid uplift and erosion, which may be a mechanism for magmatic fluid release in these systems, is shown to be greatest in the west of West Papua, where the stronger Australian crust acts as a buttress. Within the Papuan Fold Belt, uplift is greatest near the margins, where the weaker fold belt abuts the stronger crust and/or major faults have been reactivated. Increased orographically induced precipitation and erosion exposes the lower parts of the stratigraphy within or on the margins of these uplifted zones. On a smaller scale, 2–D coupled fluid‐flow ‐ thermal‐chemical modelling uses a scenario of fluid mixing to calculate metal precipitation distribution and magnitude around an individual intrusive complex. Modelling highlights the interdependence of the spatial permeability structure, the regional temperature gradient, and the geometry of the convection cells and how this impacts on the distribution of metal precipitation.     

Numerical simulations of simple shear with non‐coaxial soil models

This paper investigates the effects of a non‐coaxial model on simulated stress–strain behaviour of granular materials subject to simple shearing under various initial conditions. In most cases, a significant difference of predictions between coaxial and non‐coaxial modelling is found during the early stage in shearing. With the increase in shearing, non‐coaxial simulations approach and tend to coincide with coaxial simulations. It is also found that the roles of non‐coaxial modelling in simulating simple shear behaviour are considerably influenced by hardening rules, flow rules, initial static lateral pressure coefficients. In some cases, the non‐coaxial modelling gives a similar simulation as the coaxial modelling. In other cases, the non‐coaxial modelling decreases the hardening response or softening response of materials, compared with the coaxial modelling. Under certain conditions, the predicted peak strength of materials with non‐coaxial modelling is larger than that for coaxial modelling. Some of these observations can be attributed to the amount of principal stress rotation in various cases analysed. Others can be attributed to the difference between the directions of the non‐coaxial plastic flow and those for coaxial plastic flow. Copyright © 2005 John Wiley & Sons, Ltd.     

Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media

In this paper, a three‐dimensional smooth particle hydrodynamics (SPH) simulator for modeling grain scale fluid flow in porous media is presented. The versatility of the SPH method has driven its use in increasingly complex areas of flow analysis, including the characterization of flow through permeable rock for both groundwater and petroleum reservoir research. SPH provides the means to model complex multi‐phase flows through such media; however, acceptance of the methodology has been hampered by the apparent lack of actual verification within the literature, particulary in the three‐dimensional case. In this paper, the accuracy of SPH is addressed via a comparison to the previously recognized benchmarks of authors such as Sangani and Acrivos (Int. J. Multiphase Flow 1982; 8 (4): 343–360), Zick and Homsy (J. Fluid Mech. 1982; 115 :13–26) and Larson and Higdon (Phys. Fluids A 1989; 1 (1):38–46) for the well‐defined classical problems of flow through idealized two‐ and three‐dimensional porous media. The accuracy of results for such low Reynolds number flows is highly dependent on the implementation of no‐slip boundary conditions. A new, robust and numerically efficient, method for implementing such boundaries in SPH is presented. Simulation results for friction coefficient and permeability are shown to agree well with the available benchmarks. Copyright © 2010 John Wiley & Sons, Ltd.     

On the relationship between flow and suspended sediment transport over the crest of a sand dune, Río Paraná, Argentina

The links between large‐scale turbulence and the suspension of sediment over alluvial bedforms have generated considerable interest in the last few decades, with past studies illustrating the origin of such turbulence and its influence on flow resistance, sediment transport and bedform morphology. In this study of turbulence and sediment suspension over large sand dunes in the Río Paraná, Argentina, time series of three‐dimensional velocity, and at‐a‐point suspended sediment concentration and particle‐size, were measured with an acoustic Doppler current profiler and laser in situ scattering transmissometer, respectively. These time series were decomposed using wavelet analysis to investigate the scales of covariation of flow velocity and suspended sediment. The analysis reveals an inverse relationship between streamwise and vertical velocities over the dune crest, where streamwise flow deceleration is linked to the vertical flux of fluid towards the water surface in the form of large turbulent fluid ejections. Regions of high suspended sediment concentration are found to correlate well with such events. The frequencies of these turbulent events have been assessed from wavelet analysis and found to concentrate in two zones that closely match predictions from empirical equations. Such a finding suggests that a combination and interaction of vortex shedding and wake flapping/changing length of the lee‐side separation zone are the principal contributors to the turbulent flow field associated with such large alluvial sand dunes. Wavelet analysis provides insight upon the temporal and spatial evolution of these coherent flow structures, including information on the topology of dune‐related turbulent flow structures. At the flow stage investigated, the turbulent flow events, and their associated high suspended sediment concentrations, are seen to grow with height above the bed until a threshold height (ca 0·45 flow depth) is reached, above which they begin to decay and dissipate.