Acid volatile sulfides oxidation and metals (Mn, Zn) release upon sediment resuspension: Laboratory experiment and model development

1. Yong Seok Hong,
2. Kerry A. Kinney,
3. Danny D. Reible^*

Article first published online: 7 JAN 2011

DOI: 10.1002/etc.411

Copyright ? 2010 SETAC

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Environmental Toxicology and Chemistry

Volume 30, Issue 3, pages 564–575, March 2011

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1. Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas, USA

Email: Danny D. Reible (reible@mail.utexas.edu)

^*Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, Texas, USA.

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Keywords:

• Metals release;
• Resuspension;
• Mathematical model;
• Contaminated sediments

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

Abstract

Sediment from the Anacostia River (Washington, DC, USA) was suspended in aerobic artificial river water for 14 d to investigate the dynamics of dissolved metals release and related parameters including pH, acid volatile sulfides (AVS), and dissolved/solid phase Fe²⁺. To better understand and predict the underlying processes, a mathematical model is developed considering oxidation of reduced species, dissolution of minerals, pH changes, and pH-dependent metals' sorption to sediment. Oxidation rate constants of elemental sulfur and zinc sulfide, and a dissolution rate constant of carbonate minerals, were adjusted to fit observations. The proposed model and parameters were then applied, without further calibration, to literature-reported experimental observations of resuspension in an acid sulfate soil collected in a coastal flood plain. The model provided a good description of the dynamics of AVS, Fe²⁺, S⁰_(s), pH, dissolved carbonates concentrations, and the release of Ca_(aq), Mg_(aq), and Zn_(aq) in both sediments. Accurate predictions of Mn_(aq) release required adjustment of sorption partitioning coefficient, presumably due to the presence of Mn scavenging by phases not accounted for in the model. The oxidation of AVS (and the resulting release of sulfide-bound metals) was consistent with a two-step process, a relatively rapid AVS oxidation to elemental sulfur (S⁰_(s)) and a slow oxidation of S⁰_(s) to SO_(aq), with an associated decrease in pH from neutral to acidic conditions. This acidification was the dominant factor for the release of metals into the aqueous phase. Environ. Toxicol. Chem. 2011; 30:564–575. ? 2011 SETAC

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

INTRODUCTION

The toxicity of metals in anoxic sediments has been related to the balance between acid volatile sulfides (AVS) and simultaneously extracted metals (SEM), as operationally determined by 1?M HCl 1. The amorphous iron sulfide (FeS_(s)), one of the major metal sulfide species in AVS, is more soluble than other divalent metal sulfides, and other dissolved metals precipitate by displacing Fe²⁺2. Consequently, metals are often contained in low solubility forms in anoxic sediments where AVS are in excess of SEM. However, sediments are periodically subjected to oxic conditions, for example, during storm events or due to dredging activities. Moreover, surficial sediments are in contact with aerobic overlying water, and oxygen may penetrate from a few millimeters to centimeters by local sediment resuspension 3 and/or by enhanced oxygen diffusion from bioturbation 4. In aerobic environments, reduced metal sulfides are likely to be oxidized and phases other than sulfides, such as particulate organic carbon, can control the toxicity of metals 5, 6. Further, the kinetics of the oxidation and release processes are important to define the potential exposure and risk of the metals released into the aqueous phase.

Oxidation of AVS in aerobic sediments and the resulting pH decrease have been recognized as the primary factor influencing metal remobilization from sediments 7, because acidification affects the saturation state of minerals 8 and the characteristics of metal sorbing surfaces in sediments 9. Oxidation of metal sulfides 10, such as ZnS_(s) and CdS_(s), and biological transformation of metal-associated species 11 are important mechanisms for metal release. Complexation of metals with dissolved ligands, such as dissolved organic carbon (DOC) and inorganic anions, enhance metals remobilization 12. Resuspension energy and duration by tidal flow may also play an important role in phase partitioning of metals in sediments 13.

Sediment resuspension, however, does not necessarily lead to metal release and acidification of overlying water due to the buffering capacity of water and dilute sediment suspensions 14, 15. Metals release is the consequence of several interrelated biogeochemical processes; the degree of release can be dissimilar under different experimental or sediment conditions. To better understand and predict the degree of acidification and metals release, a resuspension experiment was conducted with sediments collected from the Anacostia River (Washington, DC, USA) where metals and organic contaminants are of potential concern 16, 17. A mathematical model was developed that simulates oxidation of reduced species, dissolution of minerals, pH changes, and pH-dependent metal sorption. The model was used to interpret the relative importance of individual processes on pH changes and metals release. As a test of the model's ability to describe resuspension in a system other than the test sediment, the model was also used to predict the metals release behavior upon resuspension of an acid sulfate soil 7.

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

MATERIALS AND EXPERIMENTAL PROCEDURES

General techniques

All solutions were prepared by dissolving analytical reagent grade or equivalent analytical purity chemicals in deionized water (18 MΩcm¹, Millipore). Deionized water was deaerated by bubbling N₂ gas (99.9%) for at least 12?h to make ferrous iron and sulfide stock solutions. All the experimental procedures regarding anoxic sediments and chemicals were conducted under 97% N_2(g) and 3% H_2(g) atmosphere in an anaerobic chamber (Coy Laboratory). All glass and plastic-ware were serially soaked in detergent and 1M HNO₃ for more than 1 d, respectively, rinsed several times with deionized water, and dried in an electric drying cabinet for 1 d at 70°C.

Resuspension experiments

Anacostia River sediment was passed through No. #?10 (2?mm) sieve to remove large debris and stored at 4°C. Two polypropylene bottles (3.5?L) were used as resuspension reactors for the duplicated experiments. Five hundred grams of wet sediments were suspended in 2.8 L of artificial river water (Na_(aq), 52.9?mg?L¹; Mg_(aq), 6.6?mg?L¹; Ca_(aq), 2.0?mg?L¹; K_(aq), 2.0?mg?L¹; Cl_(aq), 97.2?mg?L¹) and aerated/agitated with air at a flow rate of 5 L min¹. The flow rate was chosen to keep the slurry saturated with oxygen in ambient air, and to maintain the slurry homogeneously throughout the reactors. The flow rate was controlled by a flow meter (Cole Parmer), and the compressed air was filtered with a 0.2-μm glass fiber filter. The air was pre-bubbled into deionized water to supply humidity and to prevent any volatilization of water from the sediment slurry.

Samples were taken at 0, 1, 2, 4, 6, and 12?h, and at 1, 2, 4, 7, 10, and 14 d, to investigate both the short-term and long-term behavior of redox sensitive species. The frequency of sampling and experiment duration were selected to capture the primary processes of interest, sulfide oxidation, and the resulting metals release. The pH, O₂, and oxidation reduction potential (ORP) were determined directly in the sediment slurry by inserting individual electrodes. Thirty-milliliter sediment slurry samples were collected by polypropylene pipette and vacuum-filtered through 0.45-μm polypropylene membrane to separate the solid phase. Ten milliliters of filtrate were transferred to a 24-ml scintillation vial, and 14?ml of H₂O were added. The vial was sealed with a Teflon?-lined septum cap immediately, and dissolved inorganic and organic carbons were determined within 1?h after sampling. Another 5?ml of filtrate was transferred to a 15-ml centrifuge tube containing a phenanthroline solution to determine dissolved Fe²⁺ concentration 18. The rest of the filtrate (～10?ml) was acidified with 2% trace metal grade HNO₃ to determine dissolved metals (Ca, Mg, Zn, Mn) and anions (Cl, SO) concentrations. From the filter residue, 1?g of sediment was transferred to a scintillation vial to measure AVS. Another 1?g of sediment was transferred to a 50-ml polypropylene vial to determine solid phase Fe²⁺ by anoxic oxalate extraction 19. Anacostia River sediment contains a variety of trace metals 17. Zinc and Mn were chosen as the metals of interest in the present study because the two metals exhibited concentrations many times higher than other metals in sediments (see Supplemental Data, Table S1); preliminary experiments also showed that they were released in higher concentrations.

Sediment characterizations and analytical techniques

Pore water was generated by centrifugation of the sediment at 9,000?rpm for 20?min using J2-21 Beckman centrifuge (Beckman Coulter) and filtration with 0.45?μm polypropylene membrane. Ion chromatography (Metrohm) determined Cl and SO, and samples were filtered through OnGuard? II ion exchange cartridges (Dionex) to remove any cations that can cause precipitation in an ion chromatography column during anion analysis. Total dissolved inorganic carbon was determined by Apollo 9000 carbon analyzer (Tekmar Dohrmann), and DOC was determined by ultraviolet absorbance at 270?nm using a potassium hydrogen phthalate standard. The Fe²⁺ was measured by colorimetric method using 1,10-phenanthroline 18. Dissolved S^2? and NH concentrations were determined with Symphony silver sulfide (VWR) and Orion 9512 ammonium (Thermo Fisher Scientific) ion selective electrodes, respectively. The pH was determined by Symphony pH electrode (VWR) calibrated with standard 4.00, 7.02, and 10.05 pH buffers. The ORP was measured by platinum electrode in combination with Accumet? Ag/AgCl reference electrode (Fisher Scientific) calibrated with standard pH 4.00, 7.00 buffer solutions saturated with Quinhydrone. The oxygen concentrations were determined with an oxygen electrode (YSI). The concentration of metals, including Zn, Mn, Fe, Ca, Mg, Na, and K, were determined with inductively coupled plasma atomic emission spectrometer (Spectro Analytical Instruments) or graphite furnace atomic absorption spectroscopy (PerkinElmer).

The water content was determined by weight loss after water evaporation from bulk sediment in a 95°C oven. Total metals in sediment were extracted by MDS-2000 microwave (CEM, Matthews) digestion in concentrated HNO₃20. Solid phase Fe²⁺ and amorphous Fe³⁺ were recovered by anoxic oxalate extraction 19. Diffusion method 21 was used to determine AVS and SEM, with 0.05?M ascorbic acid addition to 1?M HCl to prevent any sulfide oxidation by Fe³⁺ during the analysis 22. Solid phase total organic carbon was determined by 50% of loss on ignition value at 550°C 23. All extracts were filtered with 0.45-μm polypropylene membrane. The extract concentrations were determined through the same analytical techniques for the pore-water analysis with proper dilutions. All the solid phase concentrations were calculated based on dry sediment weight unless otherwise noted.

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

MATHEMATICAL MODELING

Modeling oxidation kinetics of reduced sediments

A set of ordinary differential equations (ODE) were developed to describe the oxidation of reduced species upon anoxic sediment resuspension in aerobic water. Table 1 summarizes the stoichiometric reactions considered in the model. Due to the complexity and heterogeneity of biogeochemical processes in sediments 24, the proposed model is built to describe general biogeochemical processes affecting metal release, including both biotic and abiotic reactions 25, 26. The measured AVS oxidation and metals release kinetics, however, are expected to be dominated by abiotic processes due to speed and lack of an initiation period expected of microbial processes. The majority of the Zn release, for example, occurred within the first 100?h of an experiment.

Table 1. Biogeochemical kinetic reactions used for the proposed modelNo.Reaction stoichiometry12345678910

The oxidation kinetics of metal sulfides, S⁰_(s), and NH are assumed second order as follows

• (1)

where [R] represents the concentrations of any reduced species such as FeS, ZnS, MnS, S⁰, and NH, k_R represents the rate constant, and [O_2(aq)] is dissolved oxygen concentration. Although slower oxidation rates are likely for adsorbed phase 27, the oxidation of Fe²⁺ is assumed to occur at the same rates in both aqueous and adsorbed phases by the following base-catalyzed reaction 8, 28

• (2)

where [Fe²⁺] represents the aqueous and sorbed phase Fe²⁺ concentration, and and are rate constants. The first term of Equation 2 dominates ferrous iron oxidation when pH is between 3 and 5, and the second term is important when pH is greater than 5 28.

Sediment usually contains carbonate minerals such as CaCO_3(s), MgCO_3(s), and FeCO_3(s) that buffer the pH of pore water in sediment 29. The dissolution kinetics of CaCO_3(s) and MgCO_3(s) have been investigated with well-characterized minerals 30; however, it is difficult to generalize the kinetics due to the lack of sufficient data under wide environmental conditions 8. Hence, the following kinetic expression 31 is used to describe the dissolution kinetics of three different carbonate minerals:

• (3)

where [MeCO₃] represents the concentrations of carbonate-bearing minerals, such as CaCO_3(s), MgCO_3(s), and FeCO_3(s), represents the dissolution rate constant, represents the solubility products of minerals, {Me²⁺} means the activity of dissolved metals, such as Ca²⁺, Mg²⁺, and Fe²⁺, and {CO} is the activity of dissolved carbonate. Once the carbonate is dissolved, it will be redistributed to bicarbonate and carbonic acid. The carbonate species and protons are considered to be in equilibrium, because acid-base reactions are relatively fast compared to the oxidation of reduced species or the dissolution of minerals 32.

Due to the continuous aeration of sediment slurry, the dissolved CO_2(aq) was continuously stripped from the slurry. The CO_2(aq) stripping disturbs the equilibrium of dissolved carbonate species and increases the pH. This was an artifact of aerating sediments and rarely happens in natural environments; however, including this reaction is important in modeling pH in the laboratory system. This reaction is included as a first-order ODE as follows:

• (4)

where [CO_2(aq)] represents the concentration of dissolved carbon dioxide in sediment slurry, [CO_{2(aq), atm}] represents the concentration of dissolved carbon dioxide that is in equilibrium with atmospheric CO_2(g), and represents the gas transfer rate.

Modeling pH

The model for pH includes the buffering capacities of both carbonate species and surface functional groups of organics and oxides. Please refer to the Supplemental Data for a more detailed derivation; only a brief description is included here. The carbonate species follows the equilibrium reactions

• (5)

• (6)

where {CO_2(aq)} is the activity of dissolved carbon dioxide or carbonic acid, {H⁺} is the activity of protons, {HCO} is the activity of dissolved bicarbonate, {CO} is the activity of dissolved carbonate concentrations, and K_CO,a1 and K_CO,a2 represent the first and second proton dissociation constant for carbonic acid.

The solid phase organic carbon is modeled as humic acids composed of carboxylic and phenolic functional groups, which are further divided into four sites with different proton-binding strengths 33. The following reaction represents the proton binding to the j^th site

• (7)

where [OC_jH] represents the concentration of neutralized j^th humic acid, [OC] represents the concentration of deprotonated j^th site, and K_OC,j represents proton dissociation constants for the j^th site. K_OC,j can be estimated by

• (8)

• (9)

where pK_cb and pK_ph represent intrinsic proton dissociation constants for carboxylic and phenolic functional groups, respectively, and ΔpK_cb and ΔpK_ph represent distribution terms that modify Pk_OC,j.

The oxides have amphoteric surface hydroxyl groups that can both associate and dissociate protons 34. The proton will be associated with oxides surface as follows:

• (10)

• (11)

where [] represents the concentrations of protonated i oxide molecule, [OX_iOH] represents the concentrations of neutralized i oxide molecule, [OX_iO] represents the concentrations of deprotonated i oxide molecule, and K_OX,_al,i and K_OX,_a2,i represent the first and second proton dissociation constants for oxide i.

The temporal behavior of proton and total carbonate concentrations can be expressed as follows:

• (12)

• (13)

where represents total dissolved carbonate species concentration, ₀, ₁, ₂ are fractions of {CO_2(aq)}, {}, {} among total carbonate activities 35, respectively, and , , , represent the summation of CO_2(aq), , , H⁺ production rates as listed in Table 1 and which appear to dominate in these sediments. Γ and Λ represent the coefficient for protons and dissolved total carbonates that are defined as follows:

• (14)

• (15)

where β_0,i, β_1,i, β₂,_i are fractions of [], [OX_iH], [] among total i oxide surface. χ_0,j, χ_1,j are fractions of [OC_jH], [] among total j^th surface of humic acid. [C_t,OX] is the total surface hydroxyl functional group concentration for oxide, [C_t,OC] is the total surface functional group concentration for organics, /?H, β/?H, /?H represent the derivative of fractions for carbonate, oxide, and organics with respect to proton concentration.

Modeling metals complexation

The oxides and organic carbon surfaces that are part of the pH model are also considered to participate in metal sorption. The freely dissolved metals are assumed to complex with the surface functional groups of organics and oxides monodentately as follows:

• (16)

• (17)

where {Me²⁺} represents the activity of freely dissolved metals, K_me,OC,j represents the metal sorption constants for the j^th site of organic carbon, and K_me,OX,i represents the metal sorption constants for i oxide. The surface complexation sites are considered to be of eight types which are described in the pH model. The K_m,OC,j for these organic sites can be calculated as 33

• (18)

• (19)

where K_Me represents the intrinsic sorption constant of a metal for carboxylic function group, and ΔLK₁ is fixed at 2.8 33.

Inorganic ligands, such as SO and Cl, have been known to increase the solubility of metals concentration by complexation, and their role was calculated through relationships of the form

• (20)

where {L^z} represents the activity of dissolved anion ligands with charge z, and K_L represents the stability constants for inorganic ligands. The metal complexation reactions with inorganic ligands and stability constants are summarized in Supplemental Data, Table S2.

Davies equation was used to correct the activity of monoprotic and biprotic dissolved ionic species as follows 8:

• (21)

• (22)

• (23)

where represents activity coefficient, I represents ionic strength, and C_i and Z_i are the concentration and the charge of the ionic species i. The electrostatic interactions at the surface are neglected due to the uncertainties of electric double layer in a complex sediment system 36. This assumption was also employed by Carbonaro et al. 37.

Solution techniques

The equations compose a set of coupled ODEs constrained by equilibrium conditions. The ODEs are integrated implicitly using a noble ODEs solver DVODE, an updated version of “VODE” 38, with time step of 10⁴ d and tolerances of 10¹². The ODEs constitute a stiff system of equations because the coupled system exhibits extremely different relaxation times 39 and a sparse Jacobian matrix. In between the integration time step, the equilibrium equations are solved to calculate the metals partitioning to sediment surface and aqueous ligands. The metal sorption model is a set of nonlinear algebraic equations, and Fixed Point Iteration is used to solve the equations 40. By repeating this procedure, the governing equation is solved for the time period of interest.

Model initial conditions and parameters

The model initial conditions for Anacostia sediment and acid sulfate soil are summarized in Table 2, determined from the measured values shown in Supplemental Data, Table S3. The experimental procedures are similar, but the biogeochemical characteristics of the two sediments are different. Anacostia River sediment was collected from a freshwater environment, whereas acid sulfate soil was collected from a saline environment that was enriched with sulfate and iron. Hence, acid sulfate soil contained higher Fe²⁺ and AVS than Anacostia River sediments. The solid density in the reactor was calculated by dividing dry sediment mass by total liquid volume. For modeling purposes, the solid phase concentrations (mole?g¹) were converted to molar concentrations (M) by multiplying by the solid density in the slurry (g?L¹). All the kinetic parameters were shown based on the solid phase molar concentrations. The ZnS_(s) and MnS_(s) were determined by the metals extracted during AVS/SEM measurement assuming that the metals were initially presented as monosulfides 41. The FeS_(s) was calculated by subtracting the ZnS_(s) and MnS_(s) from AVS. The Fe²⁺_available (total dissolved and sorbed Fe²⁺) was estimated to satisfy the measured dissolved Fe²⁺. The FeCO_3(s) was calculated by subtracting FeS_(s), Fe²⁺_available, and Fe²⁺_nonavailable from Fe²⁺_total which was oxalic acid extractable Fe²⁺. The S⁰_(s) was assigned to zero assuming the sediment was initially fully reduced. The NH_(aq) was calculated from pore-water NH_(aq) concentration by mixing pore water with artificial river water assuming mass conservation. The Ca_available, Mg_available, and anions were estimated from the measured initial dissolved concentrations.

Table 2. Proposed model initial conditions that were estimated from measured values in the Supplemental Data, Table S3ParametersUnitAnacostiaaAcid sulfate soilb

• a

  Anacostia River, Washington, DC, USA.

• b

  Burton et al. 7.

• c

  Fe²⁺ phases that were extractable by oxalate acid, but were not affected by aeration in sediments.

• d

  CaCO_3(s) and MgCO_3(s) concentrations were estimated by calibrating the model to measured pH and dissolved Ca and Mg concentrations.

• e

  Fifty percent of oxalate extractable Fe³⁺ was used.

• f

  Twelve percent of total organic carbon was used.

Water content%53.470.0Solid densityg L¹76.852.6Fe²⁺_{(s), nonavailable}cμmol g¹10.810.8FeS_(s)μmol g¹42.3215Fe²⁺_availableμmol g¹5.2176.1Fe²⁺_{(s) sorbed}μmol g¹5.2119.0FeCO_3(s)μmol g¹0.0057.0S⁰_(s)μmol g¹0.0011.3ZnS_(s)μmol g¹8.471.20MnS_(s)μmol g¹3.913.48CaCO_3(s)dμmol g¹23.570.3MgCO_3(s)dμmol g¹13.081.8FeOOH_(s)emg g¹10.016.5Humic acidfmg g¹8.45.6Ca²⁺_availableμmol g¹30.00.00Mg²⁺_availableμmol g¹13.026.6Na⁺_availableμmol g¹157342NHmM0.160.16ClmM0.2711.8SOmM0.000632.4HCOmM0.700.70pH 6.506.30

To describe proton and metals binding to sediment particle, only two parameters, active fraction of iron oxide and organics, are calibrated. Active fractions of iron oxides and organics vary in the literature, i.e., 2 to 100% of total iron 25, 42 and 30 to 100% of total organic carbon 43. In the present study, the anoxic oxalate extractable iron was considered to be the dominant iron oxide phase 34. Fifty percent of the measured extractible iron was assumed to be active in metals sorption by calibrating the model to be consistent with the initial metals distribution. Similarly, 12% of the measured total organic carbon was considered to be active as humic acid to be consistent with the final total metals partitioning between sediment and water. The active fraction may not hold any physical significance but simply reflect an empirical relationship offsetting neglected processes, such as multidentate sorption and electrostatic interactions. It is important to know that metal release behavior is sensitive to this fraction (see Sensitivity analysis section) and it need to be reevaluated when the present model is applied to other sediments.

Initial conditions for the acid sulfate soil were inferred from Burton et al. 7, and are included in Table 2. Total metal concentrations were used to estimate ZnS_(s) and MnS_(s) instead of SEM. Chromium reducible S⁰_(s) was used for the elemental sulfur. Initial conditions from the Anacostia River sediment were used for Fe²⁺_nonavailable and NH_(aq), which were not reported in Burton et al. 7.

Efforts have been taken to minimize calibrated parameters. Model parameter values were collected from the literature where possible, and the remainders were estimated by calibrating the model with experimental results. The parameters that were calibrated to experimental results include the elemental sulfur oxidation rate constant and active iron and carbon fractions. Because simplified models were used to describe metals' sorption to sediment particle, the calibrated parameters may not be applicable to other sediments and conditions. However, the model provided a reasonable description of the two sediments studied. Only data from the Anacostia River experiments were used for calibration, and the calibrated parameters were held constant for estimating biogeochemical reactions and metals release behaviors in acid sulfate soil 7. Table 3 summarizes the rate constants related to the kinetic reactions, and Table 4 shows constants related to proton and metal binding to organics and oxides.

Table 3. List of parameters associated with biogeochemical kinetic reactionsParameterValueUnitsDescriptionReference

• a

  The rate constant for carbon dioxide exchange between water and air was fitted to dissolved carbonate concentrations.

• b

  The oxidation rate constant of FeS_(s) was used to describe MnS_(s) oxidation because the two species were oxidized rapidly with a similar rate in aerobic condition 10.

• c

  The elemental sulfur oxidation rate constant was estimated to fit SO experimental data in Anacostia River (Washington, DC, USA) sediment resuspension experiments.

• d

  Carbonaro et al. 37 reported 320?M¹ d¹ for ZnS_(s) oxidation rate constant, but the constant was increased to 600?M¹ d¹ to better describe the acid volatile sulfides oxidation in Anacostia River sediments.

• e

  The dissolution rate constant was estimated by calibrating the model to measured pH as well as dissolved Ca, Mg, and Fe concentrations.

5.0E?+?1d¹Carbon dioxide transfer rate constantCalibratedak_FeS9.9E?+?4M¹ d¹FeS_(s) oxidation rate constant37k_MnS9.9E?+?4M¹ d¹MnS_(s) oxidation rate constant

10

bk_S09.0E?+?2M¹ d¹S oxidation rate constantCalibratedc0.103M¹ d¹Fe²⁺ oxidation rate constant (3?4.3E-9M d¹Fe²⁺ oxidation rate constant (5?k_ZnS6.0E?+?2M¹ d¹ZnS_(s) oxidation rate constantCalibratedd1.4E?+?4M¹ d¹NH oxidation rate constant250.25d¹Carbonate minerals dissolution rate constantCalibratede4.5E-9M²Solubility product of CaCO₃82.0E-11M²Solubility product of FeCO₃83.6E-8M²Solubility product of MgCO₃8K_CO,a15.0E-7MCarbonic acid protonation constant8K_CO,a25.0E-11MBicarbonate protonation constant8Table 4. List of parameters for proton and metal sorptions to particulate organic carbon and iron oxide 33, 34ParametersHumic acidFeOOH_(s)Description

• a

  Specific site density of phenolic functional group can be calculated by 0.5 · n_cb.

• b

  Specific site densities of oxides (mol?g¹) were calculated by multiplying Γ_max by specific surface area (SSA). Available sorption sites (M) for organics and oxides in the system were calculated by multiplying specific site densities (mol?g¹) by bulk density (g?L¹) and oxide/organic contents (g?g¹).

• c

  Dimensionless variables shown without units.

• d

  Estimated from the first hydrolysis reaction constant of Fe²⁺.

• e

  Modified with ΔpK_Zn to describe strong Zn sorption to 9.0% of total sorption site.

n_cb (mmol g¹)a3.3—Specific site density of carboxylic functional groupΓ_max (μmol m²)—8.33Site density for oxidesSSA (m² g¹)b—600Oxides specific surface areapK_cbc4.1—Proton dissociation constant for carboxylic grouppK_ph8.8—Proton dissociation constant for phenolic groupΔpK_cb2.1—Distribution term that modifies pK_cbΔpK_ph3.6—Distribution term that modifies pK_phPk_OX,a1—6.26First protonation constant for oxidesPk_OX,a2—9.66Second protonation constant for oxidespK_Mg0.75.3Mg²⁺ sorption constantpK_Ca0.77.3Ca²⁺ sorption constantpK_Mn0.64.6Mn²⁺ sorption constant1.33.75dFe²⁺ sorption constantpK_Zn1.51.8eZn²⁺ sorption constantΔpK_Zn—2.0Distribution term that modifies pK_Zn for oxidesΔLK₁2.8—Distribution term that modifies pK_Zn for organics

Model accuracy

To characterize model accuracy, the standard error (SE) and relative standard error (RSE) of the model is calculated from the experimental observations as follows:

• (24)

• (25)

where N is the number of data points from experiment, Y_E is the mean of duplicated experimental observations, and Y_M is the value of model prediction. The SE, RSE, and median of Y_E are summarized in the Supplemental Data, Table S4, and the values are used in the Results and Discussion section.

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

RESULTS AND DISCUSSION

From the Anacostia River sediment resuspension experiment, the following time-dependent parameters were measured: AVS, O_2(aq), DOC, ORP, Fe²⁺_(aq), Fe²⁺_(s), HCO_(aq), pH, SO_(aq), Cl_(aq), Ca_(aq), Mg_(aq), Mn_(aq), and Zn_(aq). The O_2(aq), DOC, and Cl_(aq) concentrations, and ORP are available in the Supplemental Data (Figs. S1 to S4), and the others are shown and discussed below.

Oxidation of sulfur species

Sulfur species are the most important factors controlling metals availability and redox status of sediments. Experimental and modeling results for the sulfur species in Anacostia sediment are shown in Figure 1a. Initially, the sediment contained 54?μmol?g¹ of AVS, however, the AVS rapidly decreased to 10?μmol?g¹ after 4?h, and the residual AVS was slowly reduced to 2?μmol?g¹ after 200?h. The decrease of AVS did not directly increase SO, suggesting production of intermediate sulfur species in the sediments.

Figure 1. Transient acid volatile sulfides (AVS) (□), S⁰ (Δ), and SO (?) dynamics in (a) Anacostia River sediment (Washington, DC, USA) and (b) acid sulfate soil 7 resuspension experiments. Symbols and error bars are the mean and standard deviations of duplicate resuspension experiments, and lines are modeling results. S⁰ concentrations in Anacostia River sediment are not measured, but modeled from sulfur species mass balance. RSE?=?relative standard error of the model fit.

The rapid decrease of AVS at the beginning of the experiments was likely due to the oxidation of FeS_(s) which composes 90% of AVS in this sediment. The slow oxidation of ZnS_(s) explained the slow oxidation of residual AVS. The literature-reported rate constants for ZnS_(s) oxidation were 320?M¹ d¹37 and 820?M¹ d¹44. Initial simulation using the lower value slightly underestimated ZnS_(s) oxidation at longer times, and a value of 600?M¹ d¹ that fell into the range of the reported rate constants was used subsequently. All reported results employ the latter oxidation rate. The biphasic AVS oxidation was also consistent with other experimental observations 45. The dynamics of AVS oxidation to SO_(aq) was modeled as a two-step process which closed the sulfur mass balance successfully. The S⁰_(s) was considered to be the dominant byproduct of AVS oxidation, which slowly oxidized to SO, producing significant acidity.

Similar dynamics of sulfur species were observed in acid sulfate soils 7, whereas no significant residual AVS was observed due to lower metal sulfides (i.e., ZnS_(s)) concentrations compared to Anacostia sediment. The RSE were generally higher than those of Anacostia River sediment, however, the values indicated that the proposed model simulated the sulfur species behavior well, using same parameters from Anacostia River sediment but with the experiment-specific initial conditions. Figure 1b shows the experimental and modeling results.

Oxidation of FeS_(s) has been proposed to occur through dissociation of FeS_(s) to Fe²⁺ and S^2?, and subsequent oxidation of Fe²⁺ to Fe³⁺ at the particle surface. The Fe³⁺ then catalyzes the transformation of S^2? to S⁰_(s) under neutral to acidic conditions 46. Although S⁰_(s) is chemically inert in natural environments, it can be oxidized by microbial reactions 11, 47. The oxidation rates are strongly dependent upon the bioavailability of S⁰_(s), and this bioavailability is mainly determined by the specific surface area of S⁰_(s)48. Hence, the literature-reported oxidation rates of S⁰_(s) varies widely depending on the type of S⁰_(s) and experimental media (water, soil, or sediments), and also the presence and species of S⁰_(s) oxidizing microorganisms, i.e., Acidithiobacillus thiooxidans11. From the literature that had the closest experimental conditions to the present study, the reported half-life of chemically synthesized S⁰_(s) (<45 μm diameter) was 7 d, whereas the half-life of biogenic S⁰_(s), which had smaller diameter and larger specific surface area, was 5 d in aerobic riverine sediments 49. In the present study, the calculated half-life of S⁰_(s) was 4 d that was close to the half-life of biogenic S⁰_(s)49.

Although the proposed model has combined these complex oxidation mechanisms for both FeS_(s) and S⁰_(s) into the second-order reaction constant, the dynamics of sulfur species in the two sediments were well described by identical model kinetic parameters.

Oxidation of ferrous iron

The time-dependent concentration changes of Fe²⁺ in the aqueous phase and the solid phase for both experiments are shown in Figure 2a and b. It should be noted that aqueous phase Fe²⁺ dynamics were different in the two experiments. In the Anacostia sediment slurry, dissolved Fe²⁺ was detected only for the first couple of hours, which was consistent with other investigations 14. The rapid decrease of dissolved Fe²⁺ seemed to be caused by the rapid oxidation of Fe²⁺ in both aqueous and sorbed phase. In the solid phase, residual oxalate extractable Fe²⁺ was observed even after 250-h aeration. The RSE were 44.8% and 22.8% for Fe²⁺_(aq) and Fe²⁺_(s), respectively, indicating the experimental observations were modeled well by the base-catalyzed chemical Fe²⁺ oxidation model 8.

Figure 2. Transient Fe²⁺_(aq) (Δ) and Fe²⁺_(s) (□) dynamics in (a) Anacostia River sediment (Washington, DC, USA) and (b) acid sulfate soil 7 resuspension experiments. Symbols and error bars are the mean and standard deviations of duplicated resuspension experiments, and lines are modeling results. Fe²⁺_(s) concentrations in acid sulfate soil 7 are not measured, but modeled from ferrous iron species mass balance. Dotted line in (b) is modeled using a first-order kinetic reaction with a rate constant of 0.25 d¹ in addition to Equation 2. RSE?=?relative standard error of the model fit.

In acid sulfate soil 7, initial dissolved Fe²⁺ behavior was similar to that of the Anacostia River sediment slurry, although the concentrations were 10 times greater. Dissolved Fe²⁺ concentration increased to 80?mg?L¹ between 100 and 200?h, which was modeled as a result of the dissolution of siderite (FeCO_3(s)), and also the pH-dependent desorption of Fe²⁺ from oxides and organics. The model described the general Fe²⁺_(aq) release behavior but could not capture the time of Fe²⁺ release, probably due to slower dissolution of siderite after acidification of the slurry. Dissolved Fe²⁺ decreased again after 200?h, and the model does not describe this decrease at longer times through processes that are not included in the model, e.g., microbially mediated iron oxidation.

At the surface of minerals, such as iron oxides and clay, Fe²⁺ becomes more reactive and is easily oxidized, playing an important role in the reductive transformation of organic and inorganic chemicals in subsurface 50, 51. In acid sulfate soil slurry at 200?h, however, Fe²⁺ would not be associated with solid surfaces due to low pH 52. Iron oxidizing microorganisms (i.e., acidophilic chemolithotroph) grow rapidly in acidic environments, and a small population of the organisms metabolize a large amount of Fe²⁺, because only a small amount of energy is available from the oxidation of Fe²⁺ to Fe³⁺53. It is likely that the prolonged aerobic and acidic conditions evolved and activated iron-oxidizing bacteria and oxidize Fe²⁺_(aq). This behavior was not observed in Anacostia River sediment because the concentration of Fe²⁺ was much lower than acid sulfate soil. The Fe²⁺_(aq) oxidation after 180?h can be better simulated by a first-order kinetic reaction with a rate constant of 0.25 d¹, which is an approximation of the microbial processes likely occurring. This longer-time behavior of Fe²⁺_(aq) did not affect metal release, however, and was not included in the short-term model simulations.

Dissolved carbonate concentration and pH changes

The oxidation of reduced species produced protons and decreased pH. Figure 3a and b show the pH and dissolved carbonate concentrations in both experiments. The dissolved carbonate concentration was initially 0.7?mM in both experiments and decreased to below the instrument detection limit (～0.02?mM) within 10?h, reducing the buffering capacity of the aqueous phase for the next 14 d. The pH in the Anacostia sediment slurry was initially 6.5, then decreased to 5.8, and increased to 6.5 again during the first hour by processes not captured by the model. The rapid pH decrease is likely caused by the fast oxidation of Fe²⁺ followed by production of acidity that is not fully buffered by the carbonate in aqueous phase. The later increase of pH may come from carbon dioxide stripping or dissolution of carbonate from carbonate-bearing minerals from the sediment slurry. Carbon dioxide stripping from the aqueous phase increases pH because the carbonic acid that is in equilibrium with carbon dioxide is continuously produced from bicarbonate or carbonate-consuming protons. Similar carbonate species and pH behavior was observed in acid sulfate soil 7 after the first hour.

Figure 3. Transient pH (□) and total dissolved carbonate species (Δ) dynamics in (a) Anacostia River sediment (Washington, DC, USA) and (b) acid sulfate soil 7 resuspension experiments. Symbols and error bars are the mean and standard deviations of duplicate resuspension experiments, and lines are modeling results. RSE?=?relative standard error of the model fit.

Figure 4a and b shows the comparison of acidity (proton concentrations) production rates from the oxidation of AVS, Fe²⁺, and NH_(aq). The acidity production rates for Fe²⁺ were the highest for the first couple of hours, which were 0.004?M d¹ and 0.014?M d¹ for Anacostia River sediment and for acid sulfate soil 7, respectively. The initial pH changes must be more affected by the oxidation of ferrous iron than any other species due to its rapid oxidation kinetics under neutral pH. After the rapid oxidation of Fe²⁺, acidity production from sulfur species oxidation dominated for the rest of the experimental period.

Figure 4. Modeling results of proton production rates (mM d¹) and cumulative proton production (mM) from (a, c) Anacostia River sediment (Washington, DC, USA) and (b, d) acid sulfate soil 7 resuspension experiments.

After the initial changes, the pH slowly decreased to 5.5 and 3.7 for Anacostia River sediment and acid sulfate soil 7, respectively, during 14 d of aeration. The acid sulfate soil 7 had four times more AVS than the Anacostia River sediment that would produce four times more acidity from the oxidation. Figure 4c and d shows the cumulative produced acidity from the oxidation of AVS, Fe²⁺, and NH_(aq). Approximately, 0.006?M of acidity is produced from sulfide in Anacostia sediment, and 0.023?M of acidity is produced from sulfide in acid sulfate soil 7. The acidity produced from ferrous iron or ammonium is not significant compared to sulfide, suggesting the importance of sulfide in controlling the long-term pH changes in the event of sediment resuspension.

Metals release from sediment

The dissolved metal concentrations and modeling results are shown in Figure 5. Most of the aqueous phase metals (Mg, Ca, Mn, Zn) concentrations were gradually elevated with different orders of magnitude by the sediment resuspension. The aqueous phase concentrations of Ca, Mg, and Mn were confined within an order of magnitude, whereas those of Zn showed two orders of magnitude difference upon sediment resuspension.

Figure 5. Dissolved Mg (?), Ca (Δ) , Mn (□), and Zn (○) release from (a) Anacostia River sediment (Washington, DC, USA) and (b) acid sulfate soil 7 resuspension experiments. Symbols and error bars are the mean and standard deviations of duplicated resuspension experiments, and lines are modeling results. pK_Mn for humic acid is adjusted to ?1.3 and ?1.5 for Anacostia River sediment and acid sulfate soil 6, respectively. RSE (%) for Anacostia River sediment are RSE_Mg?=?21.8, RSE_Ca?=?22.5, RSE_Mn?=?24.9, RSE_Zn?=?39.6. RSE (%) for acid sulfate soil 7 are RSE_Mg?=?16.2, RSE_Ca?=?27.6, RSE_Mn?=?34.7, RSE_Zn?=?32.5. RSE?=?relative standard error of the model fit.

The metal release was the result of many interrelated reactions, such as metal sulfide oxidation and dissolution of minerals, followed by pH decrease and pH-dependent sorption to oxides and organics. The model included these underlying processes and described the metals release behavior well (RSE of 16–40%) with the exception of Mn. Manganese is chemically closely related to Fe and can be coprecipitated with iron oxides and other oxides (Al, Si) from sediment diagenesis 54, 55. Moreover, microwave digestion and 1?M HCl probably overestimate the initial Mn concentrations in sediments by including residual phases 56 that are resistant to oxidation. These uncertainties may lead to improper estimation of Mn release behavior in the proposed model. For the Mn, the RSE decreased from 596 to 24.9% in Anacostia River sediments and from 268 to 34.7% in acid sulfate soil 7 (Supplemental Data, Fig. S5), when pK_Mn of humic acid was increased from ?0.6 to ?1.3 and ?1.5, respectively, which were close to those of Fe²⁺ and Zn²⁺.

The phase distribution of metals in solid, adsorbed to organics/oxides, and aqueous phase is shown in Figure 6. The modeling results explain the metal behaviors upon anoxic sediment resuspension in aerobic overlying water. The Mg and Ca were initially precipitated as MgCO_3(s) and CaCO_3(s) that dissolved buffering the acidity produced by the oxidation of reduced species. Once Mg and Ca were released, they were mainly associated with organic carbon. Note that no significant mass of metals are adsorbed to oxides due to the low pH.

Figure 6. Modeling results of temporal metals phase distribution (%) in dissolved (Me_(aq)), adsorbed to organics (Me-OC), adsorbed to oxides (Me-OX), and solid phases (MgCO₃, CaCO₃, MnS, ZnS) from (a–d) Anacostia River sediment and (e–h) acid sulfate soil 7 resuspension experiments.

The Mn and Zn existed as MnS_(s) and ZnS_(s) initially, and were released by oxidation of the metal sulfides. The MnS_(s) was oxidized rapidly, whereas ZnS_(s) was resistant to oxidation, leaving 15% unoxidized sulfide phase after 14-d aeration. Unlike other metals in the present study, Zn was strongly associated with sediments, especially in organic phases even in acidic conditions. In Anacostia River sediment and acid sulfate soil, 1.4 and 19% of Zn and 6.9 and 24% of Mn were released, respectively, as shown by the solid lines in Figure 6.

The release of these metals as a result of sediment oxidation during resuspension events could be cause for concern 57. The National Recommended Water Quality Criteria acute and chronic guideline for Zn is 0.12?mg?L¹58, and the measured maximum concentration was 0.59?mg?L¹. The maximum allowable Mn concentration in water for human consumption is 0.05?mg?L¹, and the maximum measured was 2.01?mg?L¹. Note that these high concentrations were observed in the closed resuspension experiments and are not likely to be observed in the environment, due to dispersion, dilution, and buffering by the overlying water. The effects of these different conditions were evaluated with a sensitivity analysis.

Sensitivity analysis

Metals releases are the consequence of many interrelated biogeochemical reactions, and identification of the most important processes and parameters are critical in evaluating the metals release upon sediment resuspension. A sensitivity study was conducted using the Anacostia River sediment resuspension experiments for baseline or reference conditions. The sensitivity with respect to a specific parameter in the present study is defined as the ratio of change in response variable to the change in input variable as follows 59

• (26)

where X_base is the baseline input value, X is the changed input value, Y_base is the baseline response value, and Y is the resulting response value. During the sensitivity analysis, only one input parameter was changed, while all other parameters were fixed. The simulation considers Zn as the metal species of interest, because Zn was the dominant metal in the Anacostia River sediment. Hence, Y is the dissolved metal (Zn_(aq)) concentrations after 15-d sediment resuspension, and X is the Zn speciation-related input parameters and initial conditions of sediments. Table 5 summarizes the sensitivity of X to Y and detailed values of the parameters and sensitivities are available in Supplemental Data, Table S5.

Table 5. Sensitivity of Zn speciation-related parameters to final Zn_(aq) concentrations [10⁶ M] after 15-d sediment resuspensionParametersDescriptionSensitivitypHFinal pH after 15 d7.8pK_OC,ZnZn sorption constant to humic acid3.0pK_Fe,ZnZn sorption constant to ferric iron2.7ZnS_(s)Initial ZnS_(s) concentration1.5Humic acidActive humic acid content0.9k_ZnSZnS_(s) oxidation rate0.7FeOOHActive ferric oxide content0.5

Positive values of sensitivity imply that an increase in the parameter will lead to an increase in dissolved Zn concentration, and negative sensitivity implies that an increase in the parameter will decrease dissolved Zn. These results are specific to the Anacostia River sediments because all the parameters were derived from the site; however, the relative importance of individual parameters may be more general and be site-independent. The most obvious result is that dissolved Zn_(aq) concentration is strongly dependent on pH.

Accurate prediction or measurement of pH would be critical in evaluating metals release upon sediment resuspension. The more detailed sensitivities of pH to Zn release, i.e., under wider pH conditions, are available in Supplemental Data, Table S6. In particular, the pH changes around neutral conditions had a dramatic impact on metals release because the residual surface charge of oxides is sensitive to pH at neutral pH. This was not noted experimentally, however, in that pH in the resuspension experiments were quite low and metal sorption to oxides was not significant. Besides pH, parameters related with Zn partitioning, active humic fractions, and ZnS_(s) oxidation rate constant, were important in determining dissolved Zn concentrations after 15-d aeration.

Model assessment and application

The present study is currently limited to the tested sediments and two metals, Zn and Mn, however, the approach and model framework may be potentially useful to other similar AVS-rich sediments. More studies are necessary with other sediments and metals to increase the proposed model's predictability of metals release behavior upon sediment resuspension. Furthermore, application of the model to other sediments and conditions may require a more complete form of WHAM 33 and SCAMP 34 as opposed to the simplified forms used in the present study.

In the natural environment, sediment resuspension and metals release would be much more complicated than the simulated batch condition in the present study. The resupply of air may not be enough to saturate the water with oxygen in ambient air. The suspension of particles will be affected by the hydrodynamic conditions of the sites. The initial forms of metals would be strongly dependent on the site-specific biogeochemical conditions in sediments. Hence, in the real environment, the simulation of metals release upon sediment resuspension needs to include both the microscale biogeochemical reactions processes, in addition to macroscale water and sediment transport processes. The proposed model could be incorporated within a larger-scale sediment transport model framework 60, and used to study the transport of metals upon sediment resuspension in complex natural systems, and to better assess the risk associated with metals release.

Jump to…Top of pageAbstractINTRODUCTIONMATERIALS AND EXPERIMENTAL PROCEDURESMATHEMATICAL MODELINGRESULTS AND DISCUSSIONCONCLUSIONSSUPPLEMENTAL DATAAcknowledgementsREFERENCESSupporting Information

CONCLUSIONS

The present research focused on identifying the individual biogeochemical processes important to metal release during sediment resuspension. The oxidation of Fe²⁺ produces the most acidity for the first few hours, but the acidity was buffered by both the dissolved carbonate species and sediment surface. Acid volatile sulfide is rapidly oxidized to S⁰_(s) without producing acidity, then S⁰_(s) is further oxidized more slowly to sulfate with the production of acidity. The longer-term Fe²⁺ and S⁰_(s) oxidation processes are likely mediated by microorganisms, and more research should be conducted to better understand the biogeochemical processes upon anoxic sediment resuspension. The pH-dependent Ca_(aq), Mg_(aq), and Zn_(aq) release from sediment was well described by the mathematical model, except Mn_(aq), which was presumably scavenged by sorption to a phase not included in the model. Adjustment of Mn²⁺ sorption to fit Anacostia sediment observations led to good predictions of Mn release from the acid sulfate soil. Sensitivity analysis showed that pH was the most important parameter for metals release. Further simulations have shown that the oxidation kinetics of metals sulfides and the affinity of metals to either organics or oxides are the controlling factors for the solubility of metals in solution. The model does not consider the electrostatic interactions between metals and sediment surface, possible multidentate sorptions, and other buffering species, and therefore the calibrated values of the parameters may reflect the influence of these neglected processes. Despite these shortcomings, the model captures the major oxidation process of reduced species, followed by pH decrease and metals release, and was able to predict observed behavior in acid sulfate soil to which the model was not calibrated. The proposed model can be used to assess the risk associated with metal release upon anoxic sediment resuspension, although some calibration may be required for other sediments.

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SUPPLEMENTAL DATA

Supplemental Data. pH Model derivation.

Figure S1. Dissolved oxygen concentration (M) changes in Anacostia sediment resuspension experiment.

Figure S2. Redox potential changes in Anacostia sediment resuspension experiment.

Figure S3. Dissolved organic carbon concentration changes in Anacostia sediment resuspension experiment.

Figure S4. Dissolved chloride concentration changes in Anacostia sediment resuspension experiment.

Figure S5. Experimental and modeling results of Mn_{(aq) in} Anacostia River sediment and acid sulfate soil resuspension experiments.

Table S1. Total metals loading in Anacostia River sediment.

Table S2. Complexation reactions of metals with inorganic ligands in aqueous phase.

Table S3. Basic characteristics of sediments.

Table S4. Statistical analysis of the model fit.

Table S5. Sensitivity of Zn speciation-related parameters.

Table S6. pH-Dependent sensitivity of Zn_(aq) concentrations after 15 d. (448 KB PDF)

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Acknowledgements

The authors appreciate the helpful suggestions of Lynn Katz, Chris Shank, and Mary Jo Kirisits, all of the University of Texas, and valuable comments from four anonymous reviewers.

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