Multibody approach for reactive transport modeling in discontinuous-heterogeneous porous media

Computational Geosciences - In the context of long-term degradation of porous media, the coupling between fracture mechanics and reactive transport is investigated. A reactive transport model in a...     

基于图像法的多孔介质双分子反应溶质运移模拟

采用图像分析法确定溶质浓度,以硫酸铜和EDTA二钠作为双分子反应物,在多孔介质模型中开展了不同粒径(1.52.0,2.53.0,3.54.0 mm)和流量(1.0,1.5,2.0 mL/s)下反应性溶质运移实验,探讨了应用不完全混合的对流弥散模型(IM-ADRE)对双分子反应溶质运移的模拟和预测,并进行了参数敏感性分析。结果表明:图像分析法可准确获取多孔介质中显色反应性溶质的浓度,灰度值与浓度的决定系数R²大于0.96;用IM-ADRE模型能够准确预测双分子反应性溶质硫酸铜和EDTA二钠在3种不同多孔介质中的运移过程,误差低于3.71%;实验条件的改变对IM-ADRE模型参数D、m和β₀的影响显著,说明模型参数依赖于环境条件,其变化规律需要根据实际环境条件进一步率定,便于IM-ADRE模型的进一步推广应用。     

A global method for coupling transport with chemistry in heterogeneous porous media

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.     

A general reduction scheme for reactive transport in porous media

We present a method to transform the governing equations of multispecies reactive transport in porous media. The reformulation leads to a smaller problem size by decoupling of equations and by elimination of unknowns, which increases the efficiency of numerical simulations. The reformulation presented here is a generalization of earlier works. In fact, a whole class of transformations is now presented. This class is parametrized by the choice of certain transformation matrices. For specific choices, some known formulations of reactive transport can be retrieved. Hence, the software based on the presented transformation can be used to obtain efficiency comparisons of different solution approaches. For our efficiency tests, we use the MoMaS benchmark problem on reactive transport.     

Numerical evaluation of multicomponent cation exchange reactive transport in physically and geochemically heterogeneous porous media

Experimental evidence and stochastic studies strongly show that the transport of reactive solutes in porous media is significantly influenced by heterogeneities in hydraulic conductivity, porosity, and sorption parameters. In this paper, we present Monte Carlo numerical simulations of multicomponent reactive transport involving competitive cation exchange reactions in a two-dimensional vertical physically and geochemically heterogeneous medium. Log hydraulic conductivity, log K, and log cation exchange capacity (log CEC) are assumed to be random Gaussian functions with spherical semivariograms. Random realizations of log K and log CEC are used as input data for the numerical simulation of multicomponent reactive transport with CORE^2D, a general purpose reactive transport code. Longitudinal features of the fronts of reactive and conservative species are computed from the temporal and spatial moments of depth-averaged concentrations. Monte Carlo simulations show that: (1) the displacement of reactive fronts increases with increasing variance of log K, while it decreases with the variance of log CEC; (2) second-order spatial moments increase with increasing variances of log K and log CEC; (3) uncertainties in the mean arrival time are largest (smallest) for negatively (positively) correlated log K and Log CEC; (4) cations undergoing competitive cation exchange exhibit different apparent velocities and retardation factors due to both physical and geochemical heterogeneities; and (5) the correlation between log K and log CEC affects significantly apparent cation retardation factors in heterogeneous aquifers.     

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.     

Reactive transport benchmark of MoMaS

We present here the definition of the reactive transport benchmark of Groupement Mathematical Modeling and Numerical Simulation for Nuclear Waste Management Problems. The aim of this benchmark is to propose a challenging test for numerical methods used for reactive transport modeling in porous media. In order to focus on numerical methods, the problem presented here is of quite a small size, both from a hydrodynamical and from a geochemical point of view. Though the chemical coefficients used in this benchmark are not taken from a real chemical system, they are realistic, and the test case is quite challenging.     

去耦合方法求解非均质地区地下水中多组分反应-运移模型

近些年来地下水中多组分反应-运移模型在地球科学及环境领域开始得到应用,但其求解较为复杂,为了提高计算效率,可以采用去耦合化方法处理,从而使模型求解得到简化。针对自然界中广泛存在的非均质地质体,提出该类条件下的去耦合化方法,即根据水-岩间、水溶组分间反应的不同,将整个研究区划分为若干子区域,获得对应的去耦合化矩阵。对化学场中各子区域间相邻边界进行设定,达到简化模型求解的目的。最后,以一维非均质介质中基于热力学平衡的反应-运移问题作为算例,基于以上方法进行求解,并与该算例经PHAST软件所示的结果较为一致。结果表明,基于去耦合化方法获得的各离子浓度随时间演变和沿空间分布特征与PHAST所示的结果较为一致,显示该方法在非均质区域模拟溶质运移等方面具有较好的适用性。     

Numerical modeling of coupled fluid flow and thermal and reactive biogeochemical transport in porous and fractured media

Subsurface contamination problems of metals and radionuclides are ubiquitous. Metals and radionuclides may exist in the solute phase or may be bound to soil particles and interstitial portions of the geologic matrix. Accurate tools to reliably predict the migration and transformation of these metals and radionuclides in the subsurface environment enhance the ability of environmental scientists, engineers, and decision makers to analyze their impact and to evaluate the efficacy of alternative remediation techniques prior to incurring expense in the field. A mechanistic-based numerical model could provide such a tool. This paper communicates the development and verification of a mechanistically coupled fluid-flow thermal-reactive biogeochemical-transport model where both fast and slow reactions occur in porous and fractured media. Theoretical bases, numerical implementations, and numerical experiments using the model are described. A definition of the “rates” of fast/equilibrium reactions is presented to come up with a consistent set of governing equations. Two example problems are presented. The first one is a reactive transport problem which elucidates the non-isothermal effects on heterogeneous reactions. It also demonstrates that the rates of fast/equilibrium reactions are not necessarily greater than that of slow/kinetic reactions in the context of reactive transport. The second example focuses on a complicated but realistic advective–dispersive–reactive transport problem. This example exemplifies the need for innovative numerical algorithms to solve problems involving stiff geochemical reactions. It also demonstrates that rates of all fast/equilibrium reactions are finite and definite. Furthermore, it is noted that a species-versus-time curve cannot be used to characterize the rate of homogeneous fast/equilibrium reaction in a reactive transport system even if one and only one such reaction is responsible for the production of this species.     

Large-diameter,non-pumped wells filled with reactive media for groundwater remediation

A groundwater flow and contaminant transport model was used to simulate arrays of non-pumped wells with reactive media for remediating contaminated groundwater. Each array featured a minimum number of wells, with identical diameter, capable of removing a contaminant plume within a hypothetical site. Simulated well diameters ranged from 0.25 m (similar to typical remediation wells) to 1.25 m (similar to large-diameter, bucket-augered wells). Both arrays occupied a linear transect located approximately 5 m downgradient of the front of a polluted enclave and oriented 90° to the hydraulic gradient. The minimum smallest diameter array contained 23 wells, whereas the minimum largest diameter array contained only four wells. Results of this study suggest that bucket-augering technology, adapted to install non-pumped wells with reactive media, may be an effective alternative for remediating contaminated groundwater in some environments.     

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.     

连续时间随机游动理论模拟多孔介质中溶质运移的研究进展

近年来,基于连续时间随机游动(Continuous Time Random Walk, CTRW)理论所建立的模拟非均质多孔介质中溶质运移的方法已在大量的数值实验、室内实验、野外实验中得到了广泛的验证,为非均质多孔介质中的溶质运移行为提供了一种有效的模拟方法。简述了提出和发展CTRW的研究背景、基础理论以及与经典的对流-弥散方程等其他模拟方法的关系,综述了该理论在模拟溶质运移中的发展和应用,分析了实际应用中的关键问题,并展望了将其进一步发展应用于模拟反应性溶质运移的前景。     

HYTEC results of the MoMas reactive transport benchmark

A specific benchmark has been developed by the French research group MoMas in order to improve numerical solution methods applied by reactive transport models, i.e., codes that couple hydrodynamic flow and mass transport in porous media with geochemical reactions. The HYTEC model has been applied to this benchmark exercise, and this paper summarizes some of the principal results. HYTEC is a general-purpose code, applied by industrials and research groups to a wide variety of domains, including soil pollution, nuclear waste storage, cement degradation, water purification systems, storage of CO₂, and valorization of stabilized wastes. The code has been applied to the benchmark test-cases without any specific modification. Apart from the benchmark imposed output, additional information is provided to highlight the behavior of HYTEC specifically and the simulation results in particular.     

Precipitation of calcium carbonate and calcium phosphate under diffusion controlled mixing

Multi-component mineral precipitation in porous, subsurface environments is challenging to simulate or engineer when in situ reactant mixing is controlled by diffusion. In contrast to well-mixed systems, the conditions that favor mineral precipitation in porous media are distributed along chemical gradients, which evolve spatially due to concurrent mineral precipitation and modification of solute transport in the media. The resulting physical and chemical characteristics of a mixing/precipitation zone are a consequence of coupling between transport and chemical processes, and the distinctive properties of individual chemical systems. We examined the spatial distribution of precipitates formed in “double diffusion” columns for two chemical systems, calcium carbonate and calcium phosphate. Polyacrylamide hydrogel was used as a low permeability, high porosity medium to maximize diffusive mixing and minimize pressure- and density-driven flow between reactant solutions. In the calcium phosphate system, multiple, visually dense and narrow bands of precipitates were observed that were reminiscent of previously reported Liesegang patterns. In the calcium carbonate system, wider precipitation zones characterized by more sparse distributions of precipitates and a more open channel structure were observed. In both cases, formation of precipitates inhibited, but did not necessarily eliminate, continued transport and mixing of the reactants. A reactive transport model with fully implicit coupling between diffusion, chemical speciation and precipitation kinetics, but where explicit details of nucleation processes were neglected, was able to qualitatively simulate properties of the precipitation zones. The results help to illustrate how changes in the physical properties of a precipitation zone depend on coupling between diffusion-controlled reactant mixing and chemistry-specific details of precipitation kinetics.     

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.     

Local problem-based <Emphasis Type="Italic">a posteriori</Emphasis> error estimators for discontinuous Galerkin approximations of reactive transport

We consider adaptive discontinuous Galerkin (DG) methods for solving reactive transport problems in porous media. To guide anisotropic and dynamic mesh adaptation, a posteriori error estimators based on solving local problems are established. These error estimators are efficient to compute and effective to capture local phenomena, and they apply to all the four primal DG schemes, namely, symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin, incomplete interior penalty Galerkin, and the Oden–Babuška-Baumann version of DG. Numerical results are provided to illustrate the effectiveness of the proposed error estimators.     

Mixed finite element discretization and Newton iteration for a reactive contaminant transport model with nonequilibrium sorption: convergence analysis and error estimates

We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. The convergence of the scheme is analyzed. An explicit order of convergence depending only on the regularization parameter, the time step, and the mesh size is derived. We give also a sufficient condition for the quadratic convergence of the Newton method. Finally, relevant numerical results are presented.