Rate and extent of cobalt sorption to representative aquifer minerals in the presence of a moderately strong organic ligand

There is an increasing awareness that rate-limited sorption reactions can play an important role in the transport of solutes in groundwater. The rate and extent of reactions between aqueous metals and mineral surfaces are affected by many factors, including the temperature, the presence of organic chelating agents, and adsorbent mineralogy. Cobalt sorption was investigated in terms of temperature, citrate concentration, and silica sand surface coating. The kinetic sorption data were described well by two simultaneous second-order reactions. The results suggested that decreasing temperature or the presence of citrate resulted in a slower approach to equilibrium for Co sorption to the uncoated silica sand that contained small amounts of secondary minerals. Using the same sand coated with an amorphous Fe(III) oxide, increasing temperature or the presence of citrate resulted in a faster approach to equilibrium for Co sorption. The equilibrium adsorption isotherms were described well by a generalized two-layer surface complexation model. Citrate decreased the extent of Co sorption to the uncoated silica; the effect was most pronounced at low temperature. Conversely, citrate increased the extent of Co sorption to the Fe-coated silica. These results suggest that citrate decreased the rate and extent of adsorption to the uncoated silica through the formation of a stable anionic aqueous complex that has a lower affinity for the surface than Co²⁺. Conversely, the higher anion sorption capacity of the Fe-coated silica increased the rate and extent of Co sorption with citrate present, presumably through the formation of an organo-metallic ternary surface complex.     

Hydrogeochemical modeling of organo-metallic colloids in the Nsimi experimental watershed,South Cameroon

This paper presents a hydrogeochemical modeling code HYDROS, which combines the multi-component transport model with equilibrium speciation module MINTEQA2. The processes of adsorption, aqueous speciation and mineral precipitation/dissolution are represented in the model. The numerical model uses a sequential iterative approach for solving the solute transport and the equilibrium geochemistry modules. Further the transport part is solved using an operator split approach wherein a finite volume method is used for solving the advective equations while a classical finite difference method is employed for solving the dispersive equations. The model performance is evaluated by comparing it with MINTOX for a literature problem. HYDROS is then applied to the case study of the transfer of transition metals with organic colloids in the swamp groundwater system of the experimental Nsimi watershed, representative of the humid tropical ecosystem of the South Cameroon Plateau. Field observations at the site swamp system suggest that the carbon is mainly transferred as organic colloids (i.e., dissolved organic carbon) produced by the slow biodegradation of the swamp organic matter. Using HYDROS, the behaviour of Al(III) and Fe(III) elements in the base flow system is simulated during inter rain events of a short rainy season (May–June 1996). The elemental time-series for Al, Fe, Cl, pH compare well with the simulation results. The colloids are found to have a strong impact on the mobilization and transfer of Al(III) and Fe(III), which are considered to have low mobility in weathering environment.     

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.     

Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems

A time-space continuum model for transport of hydrothermal fluids in porous media is presented which provides for simultaneous, reversible and irreversible chemical reactions involving liquids, gases and minerals. Homogeneous and heterogeneous reactions are incorporated in the model in a similar fashion through source/sink terms added to the continuity equation. The model provides for moving reaction fronts through surfaces of discontinuity across which occur jump discontinuities in the various field variables satisfying generalized Rankine-Hugoniot relations. Reversible reactions including aqueous complexing, oxidation-reduction reactions, mineral precipitation and dissolution reactions and adsorption are explicitly accounted for by imposing chemical equilibrium constraints in the form of mass action equations on the transport equations. This is facilitated by partitioning the reacting species into primary and secondary species corresponding to a particular representation of the stoichiometric reaction matrix referred to as the canonical representation. The transport equations for the primary species combined with homogeneous and heterogeneous equilibria result in a system of coupled, nonlinear algebraic/partial differential equations which completely describe the evolution of the system in time. Spatially separated phase assemblages are accommodated in the model by altering the set of independent variables across surfaces of discontinuity. Constitutive relations for the fluid flux corresponding to primary species are obtained describing transport of both neutral and charged species by advection, dispersion and diffusion. Numerical implementation of the transport equations is considered and both explicit and implicit finite difference algorithms are discussed. Analytical expressions for the change in porosity and permeability with time are obtained for an assemblage of minerals reacting reversibly with a hydrothermal fluid under quasi-steady state conditions. Fluid flow is described by Darcy's law employing a phenomenological expression relating permeability and porosity. Finally an expression for the local retardation factor of solute species is derived for the case of advective transport in a single spatial dimension which accounts for the effects of homogeneous and heterogeneous equilibria including adsorption on the rate of advance of a reaction front. The condition for the formation of shock waves is given.     

多孔介质中含均相/非均相反应传质过程数值模拟

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。     

An improved description of the interactions between rare earth elements and humic acids by modeling: PHREEQC-Model VI coupling

The Humic Ion Binding Model VI (Model VI) - previously used to model the equilibrium binding of rare earth elements (REE) by humic acid (HA) - was modified to account for differences in the REE constant patterns of the HA carboxylic and phenolic groups, and introduced into PHREEQC to calculate the REE speciation on the HA binding sites. The modifications were shown to greatly improve the modeling. They allow for the first time to both satisfactorily and simultaneously model a large set of multi-REE experimental data with the same set of equations and parameters. The use of PHREEQC shows that the light rare earth elements (LREE) and heavy rare earth elements (HREE) do not bind to HA by the same functional groups. The LREE are preferentially bound to carboxylic groups, whereas the HREE are preferentially bound to carboxy-phenolic and phenolic groups. This binding differentiation might lead to a fractionation of REE-HA patterns when competition between REE and other metals occur during complexation. A survey of the available data shows that competition with Al³⁺ could lead to the development of HREE-depleted HA patterns. This new model should improve the hydrochemical modeling of the REE since PHREEQC takes into account chemical reactions such as mineral dissolution/precipitation equilibrium and redox reactions, but also models kinetically controlled reactions and one-dimensional transport.     

Modelling Zn(II) sorption onto clayey sediments using a multi-site ion-exchange model

In environmental studies, it is necessary to be able to predict the behaviour of contaminants in more or less complex physico-chemical contexts. The improvement of this prediction partly depends on establishing thermodynamic models that can describe the behaviour of these contaminants and, in particular, the sorption reactions on mineral surfaces. In this way, based on the mass action law, it is possible to use surface complexation models and ion exchange models. Therefore, the aim of this study is (i) to develop an ion-exchange model able to describe the sorption of transition metal onto pure clay minerals and (ii) to test the ability of this approach to predict the sorption of these elements onto natural materials containing clay minerals (i.e. soils/sediments) under various chemical conditions. This study is focused on the behaviour of Zn(II) in the presence of clayey sediments. Considering that clay minerals are cation exchangers containing multiple sorption sites, it is possible to interpret the sorption of Zn(II), as well as competitor cations, by ion-exchange equilibria with the clay minerals. This approach is applied with success to interpret the experimental data obtained previously in the Zn(II)–H⁺–Na⁺–montmorillonite system. The authors’ research team has already studied the behaviour of Na⁺, K⁺, Ca²⁺ and Mg²⁺ versus pH in terms of ion exchange onto pure montmorillonite, leading to the development of a thermodynamic database including the exchange site concentrations associated with montmorillonite and the selectivity coefficients of Na⁺, K⁺, Ca²⁺, Mg²⁺, and Zn²⁺ versus H⁺.     

Use of partial dissolution techniques in geochemical exploration

Application of partial dissolution techniques to geochemical exploration has advanced from an early empirical approach to an approach based on sound geochemical principles. This advance assures a prominent future position for the use of these techniques in geochemical exploration for concealed mineral deposits. Partial dissolution techniques are classified as single dissolution or sequential multiple dissolution depending on the number of steps taken in the procedure, or as “nonselective” extraction and as “selective” extraction in terms of the relative specificity of the extraction. The choice of dissolution techniques for use in geochemical exploration is dictated by the geology of the area, the type and degree of weathering, and the expected chemical forms of the ore and of the pathfinding elements. Case histories have illustrated many instances where partial dissolution techniques exhibit advantages over conventional methods of chemical analysis used in geochemical exploration.     

Non-equilibrium water/rock interactions—I. Model for interface-controlled reactions

The results of established crystal growth theory and silicate dissolution experiments are combined in developing a new model for mineral/water reactions controlled by surface processes. The overall reaction rate at steady-state is determined by coupling equations for the velocities of mass transport and interface detachment processes. Non-steady state processes can be successfully treated when interface reactions control the rate. For most sparingly soluble minerals, diffusion through the solution can be neglected as a rate-determining factor.Many surface processes are driven by the total interface under saturation, but only processes facilitating detachment contribute to dissolution. Other, non-detachment related, surface reactions result in lower dissolution rates. Slow rates of many mineral/solution reactions are attributed to the surface processes which consume the energy that would otherwise drive detachment.An analysis of the time dependence of interface reaction velocities indicates that linear rate laws apply when uniform detachment or layer-source generation mechanisms such as screw dislocations control the dissolution rate. At low interfacial undersaturations, first-order, logarithmic rate laws prevail. A parabolic time dependence occurs if surface detachment parameters vary as a function of (time)^{$\text{1}\text{2}$}.     

Coupled thermo-hydro-bio-geochemical reactive transport model of CERBERUS heating and radiation experiment in Boom clay

Final disposal of high-level radioactive waste in deep repositories in clay formations is being considered by several countries. Repository safety assessment requires the use of numerical models of groundwater flow, solute transport and chemical processes. These models are being developed from data and knowledge gained from in situ experiments such as the CERBERUS experiment carried out at the HADES facility excavated in the Boom clay formation at Mol (Belgium). This long-term experiment is aimed at evaluating the effect of heating and radiation in Boom clay. The test was performed in a cased well drilled at 223 m depth and lasted from 1989 to 1994. A ⁶⁰Co source of 400 TBq and two heaters were emplaced inside the well. Dose rate, temperature, porewater pressure and pH/Eh were measured in situ during the experiment and gas and porewater samples were taken for chemical analyses. Here a coupled thermo-hydro-geochemical (THC) model of the CERBERUS experiment is presented which accounts simultaneously for heating, radiation, solute diffusion and a suite of geochemical reactions including: aqueous complexation, acid–base, redox, mineral dissolution/precipitation, cation exchange and gas dissolution/ex-solution. Computed results indicate that heating and radiation causes a slight oxidation, a decrease in pH, slight changes in porewater chemistry and pyrite dissolution near the well. THC model results follow the general evolution of chemical data, but cannot fit SO₄ data. Model discrepancies are partly overcome when microbially-mediated Fe and SO₄ reduction are taken into account in a coupled thermo-hydro-bio-geochemical (THBC) model. This THBC model captures the trends of geochemical data, improves the fit to dissolved SO₄ and predicts pyrite precipitation, a process observed near the CERBERUS well. The ability of the THBC numerical model to reproduce the overall trends of geochemical data of the CERBERUS experiment provides confidence in such a model as a suitable tool for the long-term prediction of geochemistry in the near field of a HLW repository in clay. However, the small number of available chemical data throughout the experiment and the lack of DOC and microbial data allow only a partial validation of the THBC model.     

非连续变形分析（DDA）线性方程组的高效求解算法

非连续变形分析(DDA)方法对大规模工程问题的数值模拟耗时太长,其中线性方程组求解耗时可占总计算时间的70%以上,因此,高效的线性方程组解法是重要研究课题。首先,阐述了适用于DDA方法的基于块的行压缩法和基于试验-误差迭代格式的非0位置记录;然后,针对DDA的子矩阵技术,将块雅可比迭代法 (BJ)、预处理的块共轭梯度法 (PCG,包括Jacobi-PCG、SSOR-PCG) 引入DDA方法,重点研究了线性方程组求解过程中的关键运算;最后,通过两个洞室开挖算例,分析了各线性方程组求解算法在DDA中的计算效率。研究表明：与迭代法相比,直解法无法满足大规模工程计算需要;BJ迭代法与块超松弛迭代法(BSOR)的效率差别不大,但明显不如PCG迭代法。因此,建议采用PCG迭代法求解DDA线性方程组,特别是SSOR-PCG值得推广;如果开展并行计算研究,Jacobi-PCG是较好的选择,当刚度矩阵惯性优势明显时,BJ迭代法同样有效。     

A surface complexation and ion exchange model of Pb and Cd competitive sorption on natural soils

The bioavailability and fate of heavy metals in the environment are often controlled by sorption reactions on the reactive surfaces of soil minerals. We have developed a non-electrostatic equilibrium model (NEM) with both surface complexation and ion exchange reactions to describe the sorption of Pb and Cd in single- and binary-metal systems over a range of pH and metal concentration. Mineralogical and exchange properties of three different acidic soils were used to constrain surface reactions in the model and to estimate surface densities for sorption sites, rather than treating them as adjustable parameters. Soil heterogeneity was modeled with >FeOH and >SOH functional groups, representing Fe- and Al-oxyhydroxide minerals and phyllosilicate clay mineral edge sites, and two ion exchange sites (X⁻ and Y⁻), representing clay mineral exchange. An optimization process was carried out using the entire experimental sorption data set to determine the binding constants for Pb and Cd surface complexation and ion exchange reactions.Modeling results showed that the adsorption of Pb and Cd was distributed between ion exchange sites at low pH values and specific adsorption sites at higher pH values, mainly associated with >FeOH sites. Modeling results confirmed the greater tendency of Cd to be retained on exchange sites compared to Pb, which had a higher affinity than Cd for specific adsorption on >FeOH sites. Lead retention on >FeOH occurred at lower pH than for Cd, suggesting that Pb sorbs to surface hydroxyl groups at pH values at which Cd interacts only with exchange sites. The results from the binary system (both Pb and Cd present) showed that Cd retained in >FeOH sites decreased significantly in the presence of Pb, while the occupancy of Pb in these sites did not change in the presence of Cd. As a consequence of this competition, Cd was shifted to ion exchange sites, where it competes with Pb and possibly Ca (from the background electrolyte). Sorption on >SOH functional groups increased with increasing pH but was small compared to >FeOH sites, with little difference between single- and binary-metal systems. Model reactions and conditional sorption constants for Pb and Cd sorption were tested on a fourth soil that was not used for model optimization. The same reactions and constants were used successfully without adjustment by estimating surface site concentrations from soil mineralogy. The model formulation developed in this study is applicable to acidic mineral soils with low organic matter content. Extension of the model to soils of different composition may require selection of surface reactions that account for differences in clay and oxide mineral composition and organic matter content.     

Sorption of silica by clay minerals

Clay minerals were reacted with silica-spiked solutions of unbuffered distilled water; water buffered at pH 5.5, 8 and 10; alkali chloride solutions; natural and artificial sea water to assess the influence of pH, silica and cation activities. The data are plotted as silica produced by dissolution or sorption of silica by clay surface as a function of initial silica concentration at a given pH and solution composition. This allows the determination of the dissolved silica value at which the clay mineral surface neither dissolves nor sorbs silica. The values of the various activities in different solutions are used to infer the phase equilibria between solution, clay mineral and the surface phase produced either by dissolution or sorption. Most intensively investigated were sorption reactions of kaolinite in sea water and other ionic solutions to form silica-rich, cation-rich surface phases in cationic solutions and silica-rich phases in cation-free solutions.Inferred equilibrium constants imply that silicate reconstitution is doubtful as a mechanism for partial control of silica and cation composition of sea water but is reasonable in silica-rich interstitial waters.     

A hydrogeochemical transport model for an oxidation experiment with pyrite/calcite/exchangers/organic matter containing sand

We report the hydrogeochemical modeling of a complicated suite of reactions that take place during the oxidation of pyrite in a marine sediment. The sediment was equilibrated in a column with MgCl₂ solution and subsequently oxidized with H₂O₂. The oxidation of pyrite triggers dissolution of calcite, cation and proton exchange, and CO₂ sorption. The composition of the column effluent was modeled with PHREEQC, a hydrogeochemical transport model. The model was extended with a formal ID transport module which includes dispersion and diffusion. The algorithm solves the advection-reaction-dispersion equation with explicit finite differences in a split-operator scheme. Also, kinetic reactions for pyrite oxidation, calcite dissolution and precipitation, and organic C oxidation were included. Kinetic relations for pyrite oxidation and calcite dissolution were taken from the literature, and a coefficient equivalent to the ratio A/V (surface over volume), was adjusted to fit the experimental data. The comparison of model and experiment shows that ion exchange and sorption are dominant chemical processes in regulating and buffering water quality changes upon the oxidation of pyrite. Cation exchange was assigned to the colloidal fraction ( < 2 μm) and deprotonated organic matter, proton buffering to organic matter, and CO₂ sorption to amorphous Fe-oxyhydroxide. These processes have been neglected in earlier modeling studies of pyrite oxidation in natural sediments.     

放射性废物处置研究进展

放射性废物的处置是制约核能可持续发展的关键因素,目前已成为国际社会关注的热点问题之一.针对处置场地核素运移污染的风险问题,对放射性废物的处置及其选址、核素运移试验和核素运移模型进行了回顾和论述.指出采用多重屏障系统进行放射性废物的处置,其安全性是可以得到保障的;处置场的选址应遵循就近原则,并应从环境水文地质的角度来构建...     

Modelling the sorption of Zn and Ni on Ca-montmorillonite

In some previous work titration and Ni/Zn sorption edge/isotherm measurements carried out under a wide variety of experimental conditions on purified Na-montmorillonite were modelled in terms of cation exchange and surface complexation mass action equations. A major objective of the experimental/modelling programme is to understand and predict sorption in commercial bentonite systems. Since montmorillonite is the dominant clay mineral in bentonite and is often present in a mixed Na/Ca form, a natural extension to the previous investigations was to study Ni/Zn sorption on a conditioned Ca-montmorillonite. An important open question was whether the same basic parameters such as site types, site capacities, and acidity constants could be used for both materials and to see to what extent the Ni and Zn surface complexation constants were influenced by the form of the montmorillonite. Sorption edges for Ni and Zn at different Ca(NO₃)₂ background electrolyte concentrations, together with sorption isotherms measured over a range of pH values, are presented and modelled using the MINSORB code. The parameters characterising the sorption of Ni and Zn on Na- and Ca-montmorillonite systems are compared. Finally, examples are given that illustrate how the modelling can provide insight into the sorption processes.     

Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes

The kinetics of chemical reactions at mineral surfaces and the rates of diffusion of species in an aqueous phase are coupled in many geochemical systems. Analytical solutions to equations describing coupled mineral dissolution/growth and solute transport in both transient and steady-state systems are used to delimit regimes of pure reaction control, pure transport control and mixed kinetic control of mass-transfer rates. The relative significance of the two processes depends on the magnitudes of the diffusion coefficients and rate constants as functions of temperature, and the degree of disequilibrium in the system. In addition, the system geometry, the ratio of mineral surface area to diffusion cross-section, and the porosity and tortuosity of the medium through which aqueous species diffuse affect reaction vs. diffusion control. In general, diffusion control increases with increasing temperature and increasing distance over which diffusion occurs. Calculations for the mixed kinetic regime in transient systems demonstrate that the relative significance of diffusion and surface reaction varies with reaction progress, and approaches a limiting value as equilibrium is approached. This limiting value may be appropriate to natural water-rock interactions that occur at conditions that are close to equilibrium. This result permits extension of simple models for irreversible mass transfer in homogeneous systems to systems in which mass-transfer kinetics are controlled by coupled surface reactions and mass transport. Criteria are established for time and length scales and fluid velocity limits on the validity of the continuum hypothesis and the local equilibrium assumption in mass-transport modeling.     

Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation

The transport of chemically reactive solutes (e.g. surfactants, CO₂ or dissolved minerals) is of fundamental importance to a wide range of applications in oil and gas reservoirs such as enhanced oil recovery and mineral scale formation. In this work, we investigate exponential time integrators, in conjunction with an upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs. We model sub-grid fluctuations in transport velocities and uncertainty in the reaction term by writing the advection–dispersion–reaction equation as a stochastic partial differential equation with multiplicative noise. The exponential integrators are based on the variation of constants solution and solve the linear system exactly. While this is at the expense of computing the exponential of the stiff matrix representing the finite volume discretisation, the use of real Léja point or the Krylov subspace technique to approximate the exponential makes these methods competitive compared to standard finite difference-based time integrators. For the deterministic system, we investigate two exponential time integrators, the second-order accurate exponential Euler midpoint (EEM) scheme and exponential time differencing of order one (ETD1). All our numerical examples demonstrate that our methods can compete in terms of efficiency and accuracy compared with standard first-order semi-implicit time integrators when solving (stochastic) partial differential equations that model mixing and chemical reactions in 3D heterogeneous porous media. Our results suggest that exponential time integrators such as the ETD1 and EEM schemes could be applied to typical 3D reservoir models comprising tens to hundreds of thousands unknowns.