Multi-species Transport Research Articles

Modeling the transport and retention of nC60 nanoparticles in the subsurface under different release scenarios

The escalating production and consumption of engineered nanomaterials may lead to their increased release into groundwater. A number of studies have revealed the potential human health effects and aquatic toxicity of nanomaterials. Understanding the fate and transport of engineered nanomaterials is very important for evaluating their potential risks to human and ecological health. While there has been a great deal of research effort focused on the potential risks of nanomaterials, a limited amount of work has evaluated the transport of engineered nanomaterials under different release scenarios in a typical layered geological field setting. In this work, we simulated the transport of fullerene aggregates (nC60), a widely used engineered nanomaterial, in a multi-dimensional environment. A Modular Three-Dimensional Multispecies Transport Model (MT3DMS) was modified to evaluate the transport and retention of nC60 nanoparticles. Hypothetical scenarios for the introduction of nanomaterials into the subsurface environment were investigated, including the release from an injection well and the release from a waste site. Under the conditions evaluated, the mobility of nC60 nanoparticles was found to be very sensitive to the release scenario, release concentration, aggregate size, collision efficiency factor, and dispersivity of the nanomaterial.

MT3DMS: Model Use, Calibration, and Validation

MT3DMS is a three-dimensional multi-species solute transport model for solving advection, dispersion, and chemical reactions of contaminants in saturated groundwater flow systems. MT3DMS interfaces directly with the U.S. Geological Survey finite-difference groundwater flow model MODFLOW for the flow solution and supports the hydrologic and discretization features of MODFLOW. MT3DMS contains multiple transport solution techniques in one code, which can often be important, including in model calibration. Since its first release in 1990 as MT3D for single-species mass transport modeling, MT3DMS has been widely used in research projects and practical field applications. This article provides a brief introduction to MT3DMS and presents recommendations about calibration and validation procedures for field applications of MT3DMS. The examples presented suggest the need to consider alternative processes as models are calibrated and suggest opportunities and difficulties associated with using groundwater age in transport model calibration.

AMass Conservation AlgorithmFor Adaptive Unrefinement Meshes Used By Finite Element Methods

The AdaptiveHydraulics (ADH) model is an adaptivefinite element method to simulate three-dimensional Navier-Stokes flow, unsaturated and saturated groundwater flow, overland flow, and two-or three-dimensional shallow-water flow and transport. In the shallow-water flow and transport, especially involving multispecies transport, the water depth (h), the product of water depth and velocities (uh and vh), as well as water depth and chemical concentration (hc) are dependent variables of fluid-motion simulations and are often solved at various times. It is important for the numerical model to predict accurate water depth, velocity fields, and chemical distribution, as well as conserve mass, especially forwater quality applications. Solution accuracydepends highly on mesh resolution. Adaptive mesh refinement (AMR), particularly the h-refinement, is often used to add new nodes in the region where they are needed and to remove others where they are no longer required during the simulation. The AMR is proven to optimize the performance of a computed solution. However, mass withgain or loss can occur when elements are merged due to removing a node at mesh coarsening. Therefore, we develop and implement the mass-conservative unrefinement algorithm to ensure the mass conserved in a merged element in which a node has been removed. This study describes the use of the Galerkin finite element method to redistribute mass to nodes comprising a merged element. The algorithmwas incorporated into the ADH code. This algorithm minimizes mass error during the unrefinement process to conserve mass during the simulation for two-dimensional shallow-water flow and transport. The implementation neither significantly increases the computational time nor memory usage. The simulation was runwithvarious numbersof processors.The resultsshowedgoodscalingof solutiontimeasthenumberof processors increases.

다양한 경계조건을 가진 일차 반응 네트워크로 결합된 다종 오염물 거동 해석해

In this study, analytical solution of multip-species transport equations coupled with a first-order reaction network under constant concentration boundary condition or total flux boundary condition is obtained using similarity transformation approach of Clement et al. (2000). The study shows the schematic process about how multi-species transport equations with first-order sequential reaction network is transformed through the similarity transformation approach into independent and uncoupled single species transport equations with first-order reaction. The analytical solution was verified through the comparison with popular commercial programs such as 2DFATMIC and RT3D. The analytical solution can be utilized in nuclear waste sites where radioactive contaminants and their daughter products occur and in industrial complex cities where chlorinated solvent such as PCE, TCE, and its biodegradation products produces. In addition, it can help the verification of the developed numerical code.

A novel method for analytically solving multi-species advective–dispersive transport equations sequentially coupled with first-order decay reactions

Analytical solutions for coupled multi-species solute transport problems are difficult to derive and relatively few in subsurface hydrology. Decomposition strategy such as linear transform format or matrix diagonalization method which decomposes the set of coupled advective–dispersive transport equations into a system of independent differential equations have been widely used to derive the analytical solution for coupled multi-species solute transport problem. These decomposition techniques are generally limited to derive the analytical solution for an infinite or a semi-infinite domain. In this study, we present a novel method for analytically solving multi-species advective–dispersive transport equations sequentially coupled by first-order decay reactions. The method first performs Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate to convert the set of partial differential equations into a system of algebraic equations. Subsequently, the system of algebraic equations is solved using simple algebraic manipulation, thus the concentrations in the transformed domain for each species can be independently obtained. Ultimately, the concentrations in the original domain for all species are obtained by successive application of Laplace and the corresponding generalized integral transform inversions. A coupled four-species transport problem in a finite domain is used to demonstrate the robustness of the proposed method for deriving the analytical solutions associated with sequentially coupled multi-species solute transport problem. The developed analytical solution is tested by comparing their results against those generated with the corresponding numerical solutions. Results show perfect agreements between the analytical and numerical solutions. Moreover, the developed analytical solution is compared with the analytical solutions for a semi-infinite domain available in literature to illustrate the impacts of the exit boundary conditions on coupled multi-species transport. It is observed that significant discrepancies exist between two solutions for small Peclet numbers, whereas two solutions deviate negligibly each other for medium Peclet numbers.

Numerical evaluation of voltage gradient constraints on electrokinetic injection of amendments

A new numerical model is presented that simulates groundwater flow and multi-species reactive transport under hydraulic and electrical gradients. Coupled into the existing, reactive transport model PHT3D, the model was verified against published analytical and experimental studies, and has applications in remediation cases where the geochemistry plays an important role.A promising method for remediation of low-permeability aquifers is the electrokinetic transport of amendments for in situ chemical oxidation. Numerical modelling showed that amendment injection resulted in the voltage gradient adjacent to the cathode decreasing below a linear gradient, producing a lower achievable concentration of the amendment in the medium. An analytical method is derived to estimate the achievable amendment concentration based on the inlet concentration. Even with low achievable concentrations, analysis showed that electrokinetic remediation is feasible due to its ability to deliver a significantly higher mass flux in low-permeability media than under a hydraulic gradient.

Two-dimensional numerical finite volume modeling of processes controlling distribution and natural attenuation of BTX in the saturated zone of a simulated semi-confined aquifer

This paper presents a two-dimensional finite volume model to predict multi-species reactive transport processes in the saturated zone of a simulated semi-confined aquifer. A multipurpose commercial software called PHOENICS was used to solve model equations numerically. Capability of the present model was first confirmed using experimental data and the results obtained by a published one-dimensional finite element reactive transport model by other researchers taking different scenarios into consideration. The model was then expanded to a two-dimensional case to simulate reactive transport of BTX compounds with discontinuous source in the saturated zone of the groundwater flow system. In addition to the physical transport processes, the two-dimensional model also incorporates linear and nonlinear adsorption isotherms, first order and Monod kinetics. The two-dimensional model considers both static and dynamics modes into account. The results show that considering chemical reactions during reactive transport of contaminants could successfully predict the contaminated zone. The results of such studies can be used for monitoring of contaminated areas, designing methods to control pollution transport, and minimize its harmful effects on aquifer systems.

The influence of Fe(II) competition on the sorption and migration of Ni(II) in MX-80 bentonite

► We model the diffusion of Ni(II) through bentonite using different sorption models. ► We examine sorption competition of Fe(II) and Ni(II) at different concentrations. ► Ni(II) breakthrough is 15 times earlier with Fe(II) sorption competition. ► Ni(II) sorption is non-linear and depends on the Fe(II) concentration levels. ► Sorption competition is important and has to be modelled by reactive transport codes. The results from batch sorption experiments on montmorillonite systems have demonstrated that bivalent transition metals compete with one another for sorption sites. For safety analysis studies of high level radioactive waste repositories with compacted bentonite near fields, the importance of competitive sorption on the migration of radionuclides needs to be evaluated. Under reducing conditions, the bentonite porewater chosen has a Fe(II) concentration of ∼5.3 × 10 −5 M through saturation with siderite. The purpose of this paper is to assess the influence of such high Fe(II) concentrations on the transport of Ni(II) through compacted bentonite, Ni(II) was chosen as an example of a bivalent transition metal. The one-dimensional calculations were carried out at different Ni(II) equilibrium concentrations at the boundary (Ni(II) EQBM ) with the reactive transport code MCOTAC incorporating the two site protolysis non electrostatic surface complexation/cation exchange sorption model, MCOTAC-sorb. At a Ni(II) EQBM level of 10 −7 M without Fe(II) competition, the reactive transport calculations using a constant K d approach and the MCOTAC-sorb calculation yielded the same breakthrough curves. At higher Ni(II) EQBM (10 −5 M), the model calculations with MCOTAC-sorb indicated a breakthrough which was shifted to later times by a factor of ∼5 compared with the use of the constant K d approach. When sorption competition was included in the calculations, the magnitude of the influence depended on the sorption characteristics of the two competing sorbates and their respective concentrations. At background Fe(II) concentrations of 5.3 × 10 −5 M, and a Ni(II) EQBM level of 10 −7 M, the Ni(II) breakthrough time was ∼15 times earlier than in the absence of competition. At such Fe(II) concentrations the Ni(II) breakthrough curves at all source concentrations less than 3.5 × 10 −5 M (fixed by the NiCO 3,S solubility limit) are the same i.e. Ni(II) exhibits linear (low) sorption. Competitive sorption effects can have significant influences on the transport of radionuclides through compacted bentonite i.e. reduce the migration rates. Since, for the case considered here, the Fe(II) concentration in the near field of a high-level radioactive waste repository may change in time and space, the transport of bivalent transition metal radionuclides can only be properly modelled using a multi-species reactive transport code which includes a sorption model.

Development of a multi-species mass transport model for concrete with account to thermodynamic phase equilibriums

In this study, a coupled multi-species transport and chemical equilibrium model has been established. The model is capable of predicting time dependent variation of pore solution and solid-phase composition in concrete. Multi-species transport approaches, based on the Poisson–Nernst–Planck (PNP) theory alone, not involving chemical processes, have no real practical interest since the chemical action is very dominant for cement based materials. Coupled mass transport and chemical equilibrium models can be used to calculate the variation in pore solution and solid-phase composition when using different types of cements. For example, the physicochemical evaluation of steel corrosion initiation can be studied by calculating the molar ratio of chloride ion to hydroxide ion in the pore solution. The model can, further, for example, calculate changes of solid-phase composition caused by the penetration of seawater into the concrete cover. The mass transport part of the model is solved using a non-linear finite element approach adopting a modified Newton–Raphson technique for minimizing the residual error at each time step of the calculation. The chemical equilibrium part of the problem is solved by using the PHREEQC program. The coupling between the transport part and chemical part of the problem is tackled by using a sequential operator splitting technique and the calculation results are verified by comparing the elemental spacial distribution in concrete measured by the electron probe microanalysis (EPMA).

Evaluating MT3DMS for Heat Transport Simulation of Closed Geothermal Systems

Owing to the mathematical similarities between heat and mass transport, the multi-species transport model MT3DMS should be able to simulate heat transport if the effects of buoyancy and changes in viscosity are small. Although in several studies solute models have been successfully applied to simulate heat transport, these studies failed to provide any rigorous test of this approach. In the current study, we carefully evaluate simulations of a single borehole ground source heat pump (GSHP) system in three scenarios: a pure conduction situation, an intermediate case, and a convection-dominated case. Two evaluation approaches are employed: first, MT3DMS heat transport results are compared with analytical solutions. Second, simulations by MT3DMS, which is finite difference, are compared with those by the finite element code FEFLOW and the finite difference code SEAWAT. Both FEFLOW and SEAWAT are designed to simulate heat flow. For each comparison, the computed results are examined based on residual errors. MT3DMS and the analytical solutions compare satisfactorily. MT3DMS and SEAWAT results show very good agreement for all cases. MT3DMS and FEFLOW two-dimensional (2D) and three-dimensional (3D) results show good to very good agreement, except that in 3D there is somewhat deteriorated agreement close to the heat source where the difference in numerical methods is thought to influence the solution. The results suggest that MT3DMS can be successfully applied to simulate GSHP systems, and likely other systems with similar temperature ranges and gradients in saturated porous media.

A multi-species reactive transport model to estimate biogeochemical rates based on single-well push–pull test data

Push–pull tests are a popular technique to investigate various aquifer properties and microbial reaction kinetics in situ. Most previous studies have interpreted push–pull test data using approximate analytical solutions to estimate (generally first-order) reaction rate coefficients. Though useful, these analytical solutions may not be able to describe important complexities in rate data. This paper reports the development of a multi-species, radial coordinate numerical model (PPTEST) that includes the effects of sorption, reaction lag time and arbitrary reaction order kinetics to estimate rates in the presence of mixing interfaces such as those created between injected “push” water and native aquifer water. The model has the ability to describe an arbitrary number of species and user-defined reaction rate expressions including Monod/Michelis–Menten kinetics. The FORTRAN code uses a finite-difference numerical model based on the advection-dispersion-reaction equation and was developed to describe the radial flow and transport during a push–pull test. The accuracy of the numerical solutions was assessed by comparing numerical results with analytical solutions and field data available in the literature. The model described the observed breakthrough data for tracers (chloride and iodide-131) and reactive components (sulfate and strontium-85) well and was found to be useful for testing hypotheses related to the complex set of processes operating near mixing interfaces.

Analytical Solution for Multi-Species Contaminant Transport in Finite Media with Time-Varying Boundary Conditions

Most analytical solutions available for the equations governing the advective–dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this study, we present an analytical solution for a finite domain and a time-varying boundary condition. The solution was found using the Classic Integral Transform Technique (CITT) in combination with a filter function having separable space and time dependencies, implementation of the superposition principle, and using an algebraic transformation that changes the advection–dispersion equation for each species into a diffusion equation. The analytical solution was evaluated using a test case from the literature involving a four radionuclide decay chain. Results show that convergence is slower for advection-dominated transport problems. In all cases, the converged results were identical to those obtained with the previous solution for a semi-infinite domain, except near the exit boundary where differences were expected. Among other applications, the new solution should be useful for benchmarking numerical solutions because of the adoption of a finite spatial domain.

Development of a multi-species transport space theory and its application to permeation behavior in proton-conducting doped perovskites

This paper examines the multi-species (simultaneous proton, oxygen vacancy, and electron/electron hole) transport behavior of proton conducting oxides. Multi-species transport behavior broadens both the realm of applications and also the potential challenges for the technical use of these perovskite materials in devices such as fuel cells, separation membranes, and membrane reactors. In order to better understand the interplay between the various transporting species and their impact on macroscale conduction and permeation processes, a new conceptualization of multi-species transport is proposed. A general theoretical description of multi-species transport is presented in a graphical manner that is similar to a ternary phase diagram. When combined with data gathered from water isotope permeation experiments, we show that it is possible to specify the relative contributions from each mobile defect species in a yttria-doped barium zirconate multi-species perovskite transport membrane system under a variety of experimental conditions. This approach provides a unique method to obtain and analyze transport behavior on the basis of transference numbers, thereby providing information which is often difficult to determine by other means.

A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem

In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method.

Steady and unsteady 3D non-isothermal modeling of PEM fuel cells with the effect of non-equilibrium phase transfer

A 3D model that fully couples multi-species and multi-phase transport, electrochemical kinetics, and heat transfer processes has been developed. The non-equilibrium membrane water absorption/desorption processes along with non-equilibrium condensation/evaporation processes have been investigated utilizing this comprehensive model. In addition, the fallacious assumption that water is produced in vapor phase during the half cell electrochemical reaction is addressed for the first time. The difference and relationship of the cell output current density among three water production mechanisms are exhibited to show the potential error induced by vapor or liquid production assumptions. The present model is capable of predicting transient phenomena within the cell as well. Our results show that compared to the liquid production modeling the dynamic response of PEM fuel cells in vapor production modeling is significantly overestimated owing to the sluggish condensation process.

Decomposition method for solving multi-species reactive transport problems coupled with first-order kinetics applicable to a chain with identical reaction rates

A new method for decomposing of multiple solute transport equations, coupled by first-order reactions, is developed. The approach is based on the semigroup theory and reduces the multi-species problem to single-species equations with various initial and boundary conditions. Analytical formulas are derived for all reactants. This new method overcomes some of the limitations that were implicit in previously published algorithms. More exactly, the derivation of closed formulas for a reaction chain with identical reaction rates is possible. The proposed approach is flexible for solving one-, two- or three-dimensional advection–dispersion systems. The methodology is demonstrated on the reductive biodegradation of chlorinated solvents, such as tetrachloroethene (PCE) and trichloroethene (TCE).

Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

Transport equations governing the movement of multiple solutes undergoing sequential first-order decay reactions have relevance in analyzing a variety of subsurface contaminant transport problems. In this study, a one-dimensional analytical solution for multi-species transport is obtained for finite porous media and constant boundary conditions. The solution permits different retardation factors for the various species. The solution procedure involves a classic algebraic substitution that transforms the advection-dispersion partial differential equation for each species into an equation that is purely diffusive. The new system of partial differential equations is solved analytically using the Classic Integral Transform Technique (CITT). Results for a classic test case involving a three-species nitrification chain are shown to agree with previously reported literature values. Because the new solution was obtained for a finite domain, it should be especially useful for testing numerical solution procedures.

Effects of sorption competition on caesium diffusion through compacted argillaceous rock

We carried out a small-scale laboratory diffusion experiment on a disk-like sample of Opalinus clay from the Mont Terri underground laboratory (Switzerland) using 134Cs as tracer. A through-diffusion phase was followed by an out-diffusion phase where the tracer taken up by the sample was released again. Since the tracer concentration at both boundaries was monitored, careful mass-balance considerations were feasible. A first analysis of the experimental data was done in the frame of a single-species model accounting only for transport and non-linear sorption of caesium. The model could match the data of the through-diffusion phase, however only, when strongly reducing the sorption data based on batch sorption experiments. Yet, such a procedure was in strong contradiction with sorption measurements performed on dispersed and compacted systems. In addition, predictions concerning tracer out-diffusion and mass-balance considerations clearly revealed the shortcomings of this type of model. In a second attempt we applied a multi-species transport model where now the whole water chemistry and a sorption model for caesium were considered. First, the value for the diffusion coefficient was fixed to the best-fit value of the single-species model. But again, the sorption site densities had to be reduced strongly albeit the reduction factor was smaller. Only when fixing the sorption site densities to those values of the sorption model and letting the effective diffusion coefficient D e free for the adjustment, could through-diffusion data be reasonably well fitted and out-diffusion as well as mass-balances be predicted in a satisfying manner. The main results are: (1) The best-fit could be achieved with a value for D e of 1.8 × 10 −10 m 2 s −1 which is rather high but corroborated by results of a molecular modelling study. (2) If caesium arrives in the Opalinus clay sample potassium and sodium (calcium etc.) ions are released and caesium ions are sorbed. The released cations diffuse to lower concentration regions according to their individual concentration gradients. Since locally the cation concentration for potassium, (sodium and calcium) is increased, sorption of these cations is also locally enhanced, affecting in return the sorption behaviour of migrating caesium. Consequently, the sorption process of caesium in such diffusion experiments cannot be addressed by a non-linear isotherm formalism any longer. (3) A reasonable analysis of such single tracer diffusion experiments therefore requires the combined description of transport (diffusion) and sorption of many cations and the whole complex water chemistry of the system. Thus, single-species models can only be applied with care in the considered concentration ranges.

Non-isothermal multi-phase modeling of PEM fuel cell cathode

In this study, numerical simulation has been carried out for the heat transfer and temperature distribution in the cathode of polymer electrolyte membrane fuel cells along with the multi-phase and multi-species transport under the steady-state condition. The commercial software, COMSOL Multiphysics, is used to solve the conservation equations for momentum, mass, species, charge and energy numerically. The conservation equations are applied to the solid, liquid and vapor phases in the bipolar plate and gas diffusion (GDL) and catalyst layers of a two-dimensional cross section of the cathode. The catalyst layer is assumed to be a finite domain and the water production in the catalyst layer is considered to be in the liquid form. The temperature distribution in the cathode is simulated and then the effects of the relative humidity of the air stream, the permeability of the cathode and the flow channel shoulder to channel width ratio are investigated. It is shown that the highest temperature change, both in the in-plane and across-the-plane directions, occurs in the GDL, while the highest temperature is reached in the catalyst layer. The distribution of temperature in the bipolar plate is shown to be relatively uniform due to the high thermal conductivity of the plate. A decrease in the inlet relative humidity of the air stream results in the decrease of the maximum temperature due to the absorption of heat during the evaporation of liquid water in the GDL and catalyst layer. The non-uniformity of the temperature distribution, especially in the catalyst layer, is observed with the increase of the permeability of the cathode. Similarly, the decrease of the channel shoulder to channel width ratio leads to a non-uniform distribution of temperature especially under the channel areas. Copyright © 2009 John Wiley & Sons, Ltd.

Tidal influence on BTEX biodegradation in sandy coastal aquifers

A numerical study was conducted to investigate the influence of tides on the fate of terrestrially derived BTEX discharging through an unconfined aquifer to coastal waters. Previous studies have revealed that tide-induced seawater circulations create an active salt–freshwater mixing zone in the near-shore aquifer and alter the specific subsurface pathway for contaminants discharging to the coastal environment. Here the coupled density-dependent flow and multi-species reactive transport code PHWAT was used to examine the impact of these tidal effects on the aerobic biodegradation of BTEX released in a coastal aquifer and its subsequent loading to coastal waters. Simulations indicated that tides significantly enhance BTEX attenuation in the near-shore aquifer. They also reduce the rate of chemical transfer from the aquifer to the ocean and exit concentrations at the beach face. For the base case consisting of toluene transport and biodegradation, 79% of toluene initially released in the aquifer was attenuated prior to discharge with tides present, compared to only 1.8% for the non-tidal case. The magnitude of tidal forcing relative to the fresh groundwater flow rate was shown to influence significantly the extent of biodegradation as it controls the intensity of salt–freshwater mixing, period of exposure of the contaminant to the mixing zone and rate of oxygen delivery to the aquifer. The oxygen available for biodegradation also depends on the rate at which oxygen is consumed by natural processes such as organic matter decomposition. While simulations conducted with heterogeneous conductivity fields highlighted the uncertainties associated with predicting contaminant loadings, the study revealed overall that BTEX may undergo significant attenuation in tidally influenced aquifers prior to discharge.