steady state geochemical box model

8/20/2019 Steady State Geochemical Box Model

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STEADY STATE, GEOCHEMICAL BOXMODEL OF A TAILINGS IMPOUNDMENT:

Application to Impoundment 1, Kristineberg,

Sweden, and prediction of effect of remediation

S.U. Salmon and M. Malmström

Water Resources Engineering,Department of Civil and Environmental Engineering,Royal Institute of Technology,

Brinellvägen 32, S-100 44 Stockholm, Sweden

MiMi Report

March 2000


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Summary

The aim of these investigations was to develop a geochemical box model that could helpimprove understanding of the processes occurring in a tailings impoundment, to reproduce theimportant aspects of impoundment geochemistry and to predict the effect of remediation of the impoundment. Rate expressions for slow processes that are controlled by chemical

kinetics, such as sulphide oxidation and silicate dissolution, were selected from the literatureand compared. Using these rate expressions, regions of mechanism dominance for sulphideand ferrous iron oxidation were framed in terms of master variables.

Available field data from Impoundment 1, Kristineberg, was analysed and used to constrainas far as possible a general conceptual model. The slow rates expressions were coupled tofast, equilibrium processes, such as aqueous speciation and solubility equilibrium withsecondary minerals, in order to create a mathematical model of a generalised tailingsimpoundment. Modelling with field input data gave results that compared favourably with sitedata. The model was furthermore calibrated to the site using two scaling factors; model resultsafter calibration were even closer to field conditions. However, it should be noted that thecalibration factors were small; it is possible to account for the major deviations from the field

conditions by considering the uncertainty in parameters and constants in the expressions used.This implied that the field geochemistry could be explained with an essentially abiotic model.

The response of the impoundment geochemistry to changed conditions, such as can be caused by remediation, was modelled. Change in the partial pressure of oxygen had a much greater effect than individual variation in infiltration rate or water content; decreased partial pressureof oxygen led to decreased concentrations and fluxes of all modelled elements as well asincreased pH. Addition of lime led to increased pH but also increased sulphate concentrations,reflecting an increased sulphide oxidation rate.

The hypothesis that with decreasing partial pressure of oxygen, pyrite oxidation by ferric ironwould become increasingly important and maintain high pyrite oxidation rates was not

supported by the model results. A theoretical investigation showed that this process only becomes important when the pH decreases below four.


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Contents

1 Introduction............................................................................................................1

2 Modelling biogeochemical processes in mill tailings deposits .............................2

2.1 Geochemical databases - general................................................................................ 32.1.1 Equilibrium processes.........................................................................................................3

2.1.2 Empirical rate expressions ..................................................................................................4

2.2 Sulphide oxidation reactions....................................................................................... 52.2.1 Abiotic oxidation of pyrite ..................................................................................................52.2.2 Microbially mediated oxidation of pyrite............................................................................72.2.3 Mechanism predominance for pyrite oxidation.................................................................10

2.3 Ferrous iron oxidation...............................................................................................122.3.1 Abiotic homogeneous oxidation........................................................................................122.3.2 Surface mediated oxidation...............................................................................................132.3.3 Microbially mediated oxidation........................................................................................142.3.4 Mechanism predominance ................................................................................................15

2.4 pH buffering reactions............................................................................................... 16

2.4.1 Carbonate weathering .......................................................................................................162.4.2 (Hydr)oxide weathering ....................................................................................................172.4.3 Silicate weathering............................................................................................................18

3 Model description.................................................................................................19

3.1 The STEADYQL Code.............................................................................................. 193.1.1 Code description ...............................................................................................................193.1.2 Comments on the STEADYQL code................................................................................20

3.2 The model applied to Impoundment 1 at the Kristineberg site............................. 213.2.1 ”Base case” conceptual model ..........................................................................................213.2.2 Geochemical equilibrium and kinetic database used in the model....................................263.2.3 Input data ..........................................................................................................................26

3.3 Calibration..................................................................................................................283.3.1 Calibration factors and sensitivity.....................................................................................283.3.2 Calibration results .............................................................................................................30

4 Variations on the base case .................................................................................32

4.1 Absence of ferric hydroxide..................................................................................... 32

4.2 Equilibrium with gibbsite ......................................................................................... 33

4.3 CO2 partial pressures ................................................................................................ 34

4.4 Equilibrium with gypsum ......................................................................................... 344.4.1 Gypsum equilibrium..........................................................................................................34

4.4.2 Influx of calcium...............................................................................................................36

4.5 Presence of calcite ......................................................................................................374.5.1 Assumed equilibrium with calcite.....................................................................................374.5.2 Kinetic dissolution of calcite.............................................................................................384.5.3 Influx of a water in contact with calcite............................................................................38

4.6 Oxygen transport limitation on sulphide oxidation................................................ 404.6.1 Varying the effective diffusion coefficient .......................................................................424.6.2 Varying water content .......................................................................................................43

4.7 Heterogeneous ferrous iron oxidation......................................................................43

5 Base case results and modelling of remediation.................................................44

5.1 The base case: Modelling of Impoundment 1.......................................................... 445.1.1 Oxygen consumption ........................................................................................................44


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5.1.2 Iron....................................................................................................................................455.1.3 Proton balance...................................................................................................................455.1.4 Sulphide oxidation mechanism dominance.......................................................................46

5.2 Investigation of the effect of remediation ................................................................ 47

5.3 Results of investigations ............................................................................................485.3.1 Overall rate........................................................................................................................48

5.3.2 Pyrite oxidation mechanism dominance ...........................................................................51

6 Discussion ............................................................................................................53

7 Conclusions ..........................................................................................................54

8 References ............................................................................................................56

9 Appendices............................................................................................................59

Appendix A. Pyrite oxidation rate expressions...............................................................59

Appendix B. Pyrite oxidation mechanism predominance. ............................................. 60

Appendix C. Ferrous iron oxidation mechanism predominance...................................66

Appendix D. Geochemical database: Slow processes .....................................................73

Appendix E. Geochemical database: Equilibrium processes......................................... 77


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1 Introduction

Waste products from the mining of sulphidic, base metal ores are often in the form of finelyground mill tailings. Oxidation of metal sulphides in tailings impoundments, combined withother biogeochemical processes, can lead to the production of acidic, metal-laden drainagewater (acid mine drainage, or AMD) over extended periods of time. This can result in seriousconsequences for the environment receiving the AMD.

Processes occurring in a mill tailings impoundment take place over different time scales.Reactions such as precipitation, dissolution, and aqueous speciation often occur at asufficiently fast rate that equilibrium conditions can be assumed. Other processes are limited

by chemical or transport kinetics, such as homogeneous redox reactions, heterogeneousweathering of metal sulphides and diffusion of gases. The final geochemistry of theimpoundment is a result of the interactions between all processes and the master variables peand pH.

In this study we have investigated these phenomena through the construction of a steady state

box model, based on a conceptual model that includes both equilibrium reactions andreactions limited by slow chemical kinetics. To select appropriate rate laws for pyrite andferrous iron (Fe(II)) oxidation we have compared various empirical expressions reported inthe literature. Using the selected expressions we have framed regions in terms of master variables pH and Po2 where different reaction mechanisms dominate.

Model results have been compared with site data in order to investigate the possibility of prediction of impoundment geochemistry. In this part of the study, parameters such as physical dimensions, mineralogy and infiltration rates have been taken from pre-remediationdata from Impoundment 1, Kristineberg (see compilation by Malmström et al., 1999).

Remediation strategies to decrease AMD generation often involve attempts to decrease the

partial pressure of oxygen (Po2) in the impoundment. The water content and infiltration rateare also often manipulated either individually or at the same time, to help hinder the diffusionof oxygen or decrease the amount of leachate produced. The effect of remediation on animpoundment was investigated by varying these three parameters in the “base case” model.

Of particular interest to this study was the possibility that under certain conditions, thedominant oxidation process for metal sulphides may involve an oxidant other than oxygen,such as ferric iron, Fe(III). Such conditions may occur for example due to groundwater fluctuations, or remediation of an impoundment, where the intention is often to decreaseoxygen concentrations in the impoundment. In the latter case, the presence and action of other oxidants than oxygen may result in less effective remediation than expected.

Other aspects of the conceptual model investigated in this study include:• the presence or absence of secondary minerals ferrihydrite (Fe(OH)3(am)), gibbsite

(Al(OH)3(am)), calcite (CaCO3(s)) and gypsum (CaSO4.2H2O(s)), as solubility equilibrium

with these minerals can affect porewater geochemistry by controlling aqueousconcentrations of the associated ions,

• the possibility of biological catalysis of sulphide and ferrous iron oxidation reactions,• the effect of the input of oxygen being limited by transport kinetics (diffusion), rather

than being assumed to be at equilibrium, and• the possible significance of catalysis of oxidation of ferrous iron species adsorbed onto

mineral surfaces.


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This report has been produced within the MiMi project, ”Mitigation of the environmentalimpact from mining waste” (MiMi, 1997), which is financed by the Swedish Foundation for Strategic Environmental Research (MISTRA).

2 Modelling biogeochemical processes in mill tailings

depositsOxidation of metal sulphides is generally considered to be one of the dominant processesaffecting the geochemistry of AMD-generating tailings impoundments. However, the finalleachate composition is a function of all physical and chemical processes occurring within animpoundment. The geochemistry in a tailings impoundment will also depend upon processessuch as:• other slow reactions controlled by chemical kinetics, such as the dissolution of silicate

minerals with the associated buffering effect, and the homogenous oxidation of ferrousiron to ferric iron;

• reactions that occur sufficiently fast to be considered to be at equilibrium, such asaqueous speciation in the porewater, and precipitation and/or dissolution of varioussecondary phases; and

• physical processes within and around the impoundment.

These processes can affect and be affected by the master variables pH and pe. A model thatsuccessfully represents the interactions between the main processes in an impoundment canassist in the understanding of the relative importance of the various processes, as well as inthe prediction of the outcome of changed conditions, for example, due to remediation.

The modelling process begins with a conceptual model, which is a qualitative description of the processes that are considered important in the generation of AMD. One means of thentesting whether the conceptual model is an accurate representation of the system is to

mathematically quantify the processes in such a way that the resulting system of mathematicalequations can be solved for state variables, usually using numerical computer-basedtechniques. If model results compare favourably with field data, the choice and representationof processes in the model is supported. If model results deviate significantly from fieldmeasurements, this may be an indication that the conceptual model or process representationis in some way incorrect. In such a way the model, and understanding of the processes atwork, is iteratively refined.

Mathematical descriptions of biogeochemical processes may be in the form of rate equationsfor reactions limited by kinetics, or mass action expressions with thermodynamic constantsfor processes assumed to be at equilibrium. Mathematical formulas and constants can beobtained by theoretical calculation, observations in the field, experimentation and/or data and

expressions reported in the literature. The collection of expressions and constants used in amodel is known as the geochemical database for that model (see Section 2.1). In the case of AMD, the most important processes are sulphide oxidation, ferrous iron oxidation, and pH-

buffering processes; these processes are described in Sections 2.2-2.4.


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2.1 Geochemical databases - general

2.1.1 Equilibrium processes

The general form of a reaction can be written:

dDcC bBaA +⇔+ (2-1)where A and B represent reactants, C and D represent products, and a, b, c and d arestoichiometric coefficients. The general mass action equation that describes the equilibriumcomposition is:

{ } { }

{ } { }ba

d c

B A

DC K =' (2-2a)

where K is the equilibrium constant (compare to Equation 3-1), and {A} denotes activity.Activity is related to concentration, [A], via an activity coefficient, f A, where f A= {A}/[A].Hence an equilibrium expression based on concentration,

[ ] [ ]

[ ] [ ]ba

d c

d

D

c

C

b

B

a

A

B A

DC

f f

f f K

K ==

' (2-2b)

can be defined. When Equation 2-2 is used to describe solubility equilibria, the activity of thesolid phases is set to 1.

Ionic strength, I, is defined by:

=i

ii zC I 2

2

1 (2-3)

where C is concentration and z is the charge of the ion. Equilibrium constants can becorrected for field ionic strength, for example, using the Davies equation (Stumm andMorgan, 1996, p103):

−+

⋅−= I I

I Az f ii 2.0

1log

2 (2-4)

where f is the activity coefficient as given above. A in this case is a parameter determined bythe expression 1.82 x 106(εT)-3/2, where ε is the dielectric constant and T the temperature. TheDavies equation is applicable for ionic strengths less than approximately 0.5 M. Geochemical

processes in mining wastes can lead to solutions with very high concentrations and high ionicstrengths.

Equilibrium constants can be corrected for field temperature using the Van’t Hoffs equation(Stumm and Morgan, 1996, p.52):

′′−°∆=

′′ T T R H

K K r 11ln (2-5)

where K” is the known equilibrium constant at temperature T”, K is the equilibrium constant

for the reaction at temperature T, °∆ r H is the reaction enthalpy and R is the gas constant.

Thermodynamic constants for the geochemical database can be obtained from literaturesources. Some examples of databases often used for AMD applications include Nordstrom etal. (1990), WATEQ (Ball and Nordstrom, 1991) and MINTEQ (Allison et al., 1991).


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2.1.2 Empirical rate expressions

For the general reaction given by Equation 2-1 above, an empirical rate expression may be of the form:

[ ] [ ]nm B Ak R = (2-6)where k is the rate constant and m and n are reaction orders that must be experimentally

determined. A general rate expression for kinetically controlled reactions is given in Section3.1.1 (Equation 3-2). Rate expressions for reactions limited by chemical kinetics can be foundin the literature, often as empirical expressions obtained from analysis of experimental resultsor field measurements.

Although the data available for equilibrium processes is not complete or necessarilyconsistent, there is still more data available for equilibrium processes than for processeslimited by chemical kinetic. It should be noted that rate constants and reaction ordersdetermined experimentally can be associated with considerable uncertainty, which can affectmodel results.

There is a shortage of quantitative rate expressions that agree with each other and areapplicable for field conditions, particularly in the case of AMD in cold climates, whereconditions of low temperature and high ionic strength prevail. This is particularly the case for metal sulphides other than pyrite; for example, no expressions were found in the literature for oxidation of chalcopyrite, galena, or sphalerite by oxygen. Also lacking is agreement betweenlaboratory-determined rate expressions and rates determined at field scale (Malmström et al.,1999a; see also Section 3.3).

Despite a number of experiments and publications discussing the effect of biological catalysisof sulphide weathering reactions, there is a particular shortage of quantitative biological rateexpressions. Most publications are concerned with the bacteria Thiobacillus ferrooxidans; for other species there are few publications (e.g. Schrenk et al., 1998) and no rate expressions that

we are aware of. Mixtures of different bacterial species are reported to have different effectsto pure cultures, but only qualitatively, and the effect of low temperature is often notexplored. Varying conditions, such as changing redox state and oxygen concentration, mayalso effect the type and activity of bacteria.

It has been reported in the literature that galvanic effects can exist between differentsulphides, accelerating the rate of oxidation of the sulphide with the lower potential in theelectromotive series by up to three orders of magnitude (e.g. Scharer et al., 1994, Kwong1995). Galvanic effects can also be accelerated or hindered in the presence of bacteria andvice versa, however, a systematic quantification of the effect on reaction rates is not given,only experimental results for a few conditions (e.g. see review in Herbert, 1999).

Most of the rate expressions reported in the literature are empirical rather than mechanistic innature, coming from equations fitted to experimental or field data. For example, most kineticexpressions for oxidation of sulphides by ferrous iron involve expressions with free Fe(III)concentration to some exponent, such as in Equation 2-11 below. This is in contradiction withat least one suggested mechanistic model for pyrite oxidation where it is the first hydrolysisspecies of Fe(III), Fe(H2O)5(OH)

2+ (often written FeOH2+) that interacts with the pyritesurface, rather than free Fe(III) (Moses et al., 1987).

Rate constants can be corrected for field temperature using the Arrhenius equation (Stummand Morgan, 1996, p.73):

RT

E a

Aek −

= (2-7)

where A is in this case the pre-exponential factor and Ea is the activation energy.


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Described in the sections below are the representations for some typical processes in tailingsimpoundments, namely abiotic and biologically mediated rate expressions for oxidation of sulphides and ferrous iron, and rate and/or equilibrium expressions for pH-buffering reactionssuch as dissolution of silicate minerals, carbonates and secondary hydroxides.

2.2 Sulphide oxidation reactions

Two parallel mechanisms have been considered for the weathering of metal sulphides, witheither aqueous oxygen or ferric iron as oxidant, here exemplified by oxidation of the ironsulphide pyrite:

+−+ ++→++ H SOFeO H OFeS aqs 222

7 24

22)(2)(2 (2-8)

+−++ ++→++ H SOFeO H FeFeS s

16215814 242

23

)(2 (2-9)

Under conditions where oxidant availability is not limiting, e.g. by slow transport, thesereactions are usually limited by chemical reaction kinetics. Abiotic rate expressions exist inthe literature for reaction of pyrite with both oxidants, and bacterial agents may also mediatethe reactions. For all reaction types, rate expressions from the literature are discussed below.

Focus in this section is on pyrite, as this mineral has been the subject of a greater number of investigations than any other sulphide and hence there is more information available.Furthermore, in the field data for the site which we have compared model results with, pyriteis reportedly the sulphide present in the largest quantities, such that oxidation of this mineralis the dominant process in that case.

2.2.1

Abiotic oxidation of pyrite

Experimentally determined empirical rate expressions can be found in the literature for processes limited by chemical kinetics, such as the following examples of expressions for theoxidation of pyrite:

By O2 (Williamson and Rimstidt, 1994):[ ]

[ ] 11.05.0

2 )(+

= H

aqOk Rate oxy (2-10)

By Fe(III) (Rimstidt and Newcomb, 1993): [ ] 62.03+= Fek Rate fer (2-11)

where k oxy and k fer are rate constants. Given in Appendix A are the expressions that wereselected from the literature as being relevant for the conditions of interest for thisinvestigation, namely sulphide oxidation occurring in a tailings impoundment with low pH,low temperature and high ionic strength. The expressions given by different authors vary inthe species they depend upon and the reaction orders for these species. For example, of theexpressions for oxidation of pyrite by oxygen, only one involves dependence on protonconcentration (Equation 2-10).

Figure 2-1 compares the values of the different rate expressions under the same conditions for oxidation of pyrite by oxygen. The figure shows that the reported rate laws predict surfacearea normalised rates of pyrite oxidation that differ by up to two orders of magnitude. Themajority of the rate laws, however, agree within one order of magnitude and predict a rate of

10-9-10-10 mol m-2s-1 at atmospheric conditions (log [O2(aq)] = -3.6 at 25°C).


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The expression reported by Williamson and Rimstidt (1994) (Equation 2-10) reputedlyapplies over a wider pH range (2-10) than the other expressions; for this reason thisexpression was chosen to represent pyrite oxidation by oxygen in this study.

-12

-11

-10

-9

-8

-7 -6 -5 -4 -3

log O2 (mol l-1

)

l o g r a t e ( m o l m - 2 s - 1 )

Williamson & Rimstidt,1994, at pH 2

Williamson & Rimstidt,1994, at pH 5

Nicholson et al., 1990,valid for pH 7.6-8.6

McKibben & Barnes, 1986,valid for pH 2-4

Nicholson et al., 1988,valid for pH 6.7-8.5

Figure 2-1. Rates of pyrite oxidation by oxygen as given in the literature; valid at the given pH and 25-30°C. The rate expression given by Williamson and Rimstidt (1994) is the onlyexpression with pH dependence. Rate expressions are given in Appendix A.

Figure 2-2 compares expressions for oxidation of pyrite by ferric iron at pH 4. For this studythe expression found in Rimstidt and Newcomb (1993) (Equation 2-11) was chosen torepresent pyrite oxidation by ferric iron, as it seemed closest to a mean rate value over a rangeof pH values and Fe(III) concentrations (e.g. at pH 4, Figure 2-2). The reported rate laws for ferric iron oxidation of pyrite predict surface area normalised rates that differ by many ordersof magnitude at low ferric iron concentrations. Note that the expressions tend to agree bestover the usual range of experimental conditions, e.g. for oxidation by Fe(III), for -5


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Figure 2-2. Pyrite oxidation by ferric iron at pH=4; log [Fe(II)]=2, 25-30°. Rates variedsomewhat with varying pH; experimental pH for the selected expressions was reported to be

between pH 0.5-3. Rate expressions are given in Appendix A.

Under appropriate conditions, the rate of oxidation of metal sulphides by either mechanismmay be accelerated by biological catalysis, either due to catalysis of the direct oxidation of

pyrite (see Section 2.2.2), or catalysis of the oxidation of Fe(II) to Fe(III) (see Section 2.3.3).Weathering of metal sulphides may also be accelerated by galvanic interactions betweensulphides, however, as mentioned in Section 2.1.2, no rate expressions which include thequantification of this effect were found in the literature.

2.2.2 Microbially mediated oxidation of pyrite

Microbial mediation is a potentially important path for sulphide oxidation and several authorsreport biotic oxidation rates that exceed reported abiotic rates (e.g. see review in Herbert,1999).

Although a catalytic effect of microbes has often been reported in the literature, systematic,quantitative studies of the oxidation rate are sparse. Additionally, in many studies of the bioticoxidation of pyrite the surface area has not been reported which hence limits the quantitativeuse of these data. In order to be able to include the effects of microbial action in models, theeffect of different microbes and cultures on different sulphides must be assessed. Data to basesuch models on are presently not available.

This section briefly reviews and compares two different approaches to modelling microbialsulphide oxidation that have been presented in the literature. The interactions betweenmicroorganisms and sulphides are complex and the magnitude of catalysis provided by thismechanism depends on many parameters, for only a few of which the effects have beenquantified. However, in the literature, the oxygen concentration, pH, and the temperature have

been recognised as key parameters for limiting the biotic oxidation rate.

Jaynes et al. (1984) suggested an empirical rate law for the pyrite oxidation rate:

2O pH T b X X kX R = 10 ≤≤ X (2-12)

where XT, X pH, XO2 give the temperature-, pH- and oxygen concentration-dependence of theoxidation rate, R b. Hence, k is the oxidation rate at optimal conditions, that is, whenXT=X pH=XO2=1. Jaynes et al. (1984) fitted empirical expressions to data reported in theliterature and derived the following expressions:

25.066.0104.4102.1 2435 −+×−×−= −− T T T X T (2-13)

7.23.235.0 2 −+−= pH pH X pH (2-14)

12 =O X for PO2>0.01 (2-15)

01.02

2

O

O

P X = for PO2


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In the RATAP-code, Scharer et al. (1994) used the rate law:

[ ][ ] 45.222

/ 10101

1−−

−

+++=

pH pH

o

RT

E

s x

mbio

OK

Oe

Y b R

aσ µ (2-17)

where b is a biological scaling factor, Ea is the activation energy, K o is the half saturationconstant for oxygen, YX/S is the growth yield, µm is the specific growth rate, and σ is thespecific surface coverage. Equation 2-17 explicitly accounts for the dependence of the biotic

oxidation rate on temperature, oxygen concentrations and pH through the terms RT E a

e

−

(the

Arrhenius equation), [ ][ ]22

OK

O

o + (Michaelis-Menten kinetics), and

45.2 10101

1−− ++ pH pH

,

respectively.

Scharer et al. (1994) suggested that the specific growth rate depends upon several parameterssuch as PCO2, water content, and the availability of nutrients. However, no reference is givenand no numerical value is suggested for this parameter, or for the growth yield or the specificsurface coverage. As these parameters are not available, it seems reasonable to simplifyEquation 2-17 to:

[ ][ ] 45.222

10101

1'

−− +++=

pH pH

o

BiobioOK

Ok b R (2-18)

where RT E

Bio Bio

a

ek k

−

= 0 , k 0Bio is a rate constant at a defined standard state, and b’ is a scaling

factor that accounts for the dependence of R bio on factors not explicitly handled by Equation2-18, i.e. deviation in microbial activity from the defined standard state. By defining theconditions of the experiments reported in the Table 2 in Scharer et al. (1994) as our standard

state (b’=1), their results can be used to estimate k Bio(T=30oC). For pyrite, chalcopyrite andsphalerite, we estimate k Bio to be 9.4 x 10

-8, 9.5 x 10-9 and 1.1 x 10-8 mol m-2s-1, respectively.

Figure 2-3 shows that in the temperature range 5


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a)

b)

c)

Figure 2-3. The dependence of the biotic pyrite oxidation rate on a) temperature; b) pH; and c) oxygen concentration according to models by Jaynes et al. (1984) andScharer et al. (1994) (see text).


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2.2.3 Mechanism predominance for pyrite oxidation

By combining the abiotic rate expressions for pyrite oxidation by O2 (Equation 2-10) and byFe(III) (Equation 2-11), a fraction diagram was generated for the different abiotic pyriteoxidation mechanisms (see Figure 2-4). This diagram shows that at low pH, oxidation of pyrite by Fe(III) contributes significantly to the overall pyrite oxidation rate, or even

dominates over the rate of oxidation by oxygen, depending on the partial pressure of oxygenand the ferric iron concentration.

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7pH

R a t e o f o x ' n o f p

y r i t e b y F e

3 +

/ O v e r a l l p y r i t e o x ' n r a t e

0.2 atm

0.02 atm

0.002 atm

Fe(OH)3 eqm

[Fe3+

]tot=1µµµµM

NB: Only hydrolysis

complexes accounted for.

Figure 2-4. Relative importance of the abiotic ferric iron oxidation mechanisms as a functionof pH for different ferric iron concentrations and partial pressures of oxygen (see Appendix Bfor details).

We have also attempted to frame regions of pH and oxygen concentration where the abioticand the biotic reaction paths dominate by comparing Equations 2-10, 2-11 and 2-18 (seeAppendix B). However, these calculations should be considered preliminary, as quantitativedata on the biotic kinetics, from which relevant rate laws and constants can be derived, aresparse in the literature. As noted in Section 2.2.1, abiotic rate laws from the literature predict process rates that differ over orders of magnitude, implying that the choice of the rate law iscritical for all model results. It should also be noted that kinetic expressions derived by

different methods may be inconsistent, which may flaw comparison.

Figure 2-5 shows the derived predominance areas of the various biotic and abioticmechanisms. Consistent with what has previously been reported in the literature, thiscomparison indicates that for a wide range of conditions, the microbially mediatedmechanism may dominate. Note, however, that the dominance area is strongly dependent on,for example, the scaling factor b’ and the assumed value of K o.


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a)

Figure 2-5. Mechanism predominance diagram for pyrite oxidation at T=1oC andK o=1 x 10

-6 M. The full and dotted lines denote b’=1 and b’=0.01, respectively. The arrowsindicate the response to an increase in the adjacent printed parameter. a) Ferric ironconcentration assumed to be controlled by an amorphous Fe(III)-hydroxide; b) [Fe(III)]tot=1 x 10

-6 M (only hydrolysis species accounted for). See Appendix B for details.


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2.3 Ferrous iron oxidation

In the presence of oxygen, ferrous iron produced by sulphide oxidation or other reactions can be oxidised to ferric iron in a process that is limited by chemical kinetics:

O H Fe H OFe aq 23

)(22

2

1

4

1+→++ +++ (2-19)

where hydrolysis of the iron ions is not shown in Equation 2-19. Oxidation may occur viathree different paths; abiotic homogeneous oxidation, microbial oxidation and surfacecatalysed oxidation. The Fe(III) produced may subsequently form complexes with other ionsin solution. If the resulting solution is oversaturated with respect to a secondary mineral, for example, amorphous ferric hydroxide, the ferric iron concentration in solution will becontrolled by the precipitation of this phase:

++ +↔+ H OH FeO H Fe am 3)(3 )(323 (2-20)

where this reaction is often assumed to be at equilibrium.

2.3.1 Abiotic homogeneous oxidation

The kinetics of the homogeneous oxidation of ferrous iron has been extensively studied in theliterature. Lowson (1982) reviewed the kinetics over a wide range of conditions and Millero(1985) summarised data valid for natural waters. As given by Millero (1985), the reaction rateis zero order with respect to hydroxyl ions and first order with respect to both ferrous iron andoxygen concentrations at pH


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Millero (1985) discussed how homogeneous reaction rates depend on the medium in whichthe reaction occurs. He showed that effects are due to either non-specific ion interactions,dependent on ionic strength, or on specific ion interactions, e.g. complex formation. Thisimplies that empirical rate laws should be expressed in terms of ion activities rather thanconcentrations. For ferrous iron oxidation in mine wastes in particular, this implies that therate of oxidation is slower at high ionic strength or in the presence of ligands that complex

ferrous iron, e.g. sulphate. On the other hand, Cu2+

, has been shown to have a catalytic effecton the reaction (see e.g. review by Pesic et al., 1989).

0

0.25

0.5

0.75

1

2 4 6 8

pH

0

1

2 4 6 8 pH

FeOH+

Fe2+ FeOH

+

Fe(OH)2 (aq)

-12

-10

-8

-6

-4

2 4 6 8 pH

Fe2+

Figure 2-6. Ferrous iron oxidation and speciation in solution as a function of pH. Left:Relative importance of the different species for the overall rate of reaction. Upper right: Thetotal rate of reaction as function of pH. Lower right: The speciation of ferrous iron in

absence of complexating ligands.

2.3.2 Surface mediated oxidation

Based on the observations of, for example, Tamura et al. (1976), that autocatalytic oxidationof ferrous iron occurs subsequent to ferric iron precipitation (see also Sung and Morgan,1980), Wehrli (1990) pointed out that surface-mediated oxidation may be an important pathfor oxidation. Such oxidation is assumed to occur via a three-step mechanism:

Adsorption: >FeIIIOH + Fe2+ → >FeIII-O-FeII + + H+ (2-25)

Electron transfer: >FeIII-O-FeII + → >FeII-O-FeIII + (2-26)

Desorption: >FeII-O-FeIII + +H+ +H2O → >FeIIOH + FeIII(OH)2+ (2-27)

where the catalytic effect is due to the fast electron transfer in the surface complex (Wehrli,1990). Adsorbed Fe(II) oxidation competes with homogeneous oxidation as a parallelmechanism, where the total rate of reaction is determined by the amount of Fe(II) adsorbed aswell as by the rate constant for the heterogeneous reaction. The adsorption of Fe(II) can besimplistically described by the equilibrium expression:

{ }

{ }[ ]+

++

−

−−=

2

FeOH Fe

H FeOFeK

III

II III

(2-28)


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where curved brackets refer to surface concentrations. The adsorption of ferrous iron onminerals has not been extensively studied in the literature. However, Zhang et al. (1992)report experimental results and a surface complexation model for the adsorption of ferrousiron onto lepidocrocite (γ -FeOOH(s)).

Based on the results of Tamura et al. (1976), Wehrli (1990) suggested the rate expression

{ }[ ])(2 aqOFeOFek r II III Surf Surf +−−= (2-29)

and gave a tentative rate constant.

For a heterogeneous system with a solid phase concentration of A/V [m2 l-1], Equation 2-29can be converted to:

{ }[ ])(2 aqOFeOFek V

A R II III Surf Surf

+−−= (2-30)

where A refers to surface area (m2) and V to solution volume (l).

2.3.3 Microbially mediated oxidation

The third mechanism for ferrous iron oxidation involves microbial mediation (see e.g. reviews by Evangelou and Zhang, 1995, Nordstrom and Southam, 1997; and Nemati et al., 1998).

Although several bacteria have been reported to be active ferrous iron oxidisers, Thiobacillus ferrooxidans has been most extensively studied. For fully aerated conditions at pH of about 2and temperature between 20 and 35 oC, several authors have suggested a modified Michaelis-Menton-type rate expression for the ferrous iron oxidation (e.g. Lacey and Lawson, 1970; Nyavor et al., 1996; Nemati and Webb, 1997). Nyavor et al., (1996) report a switch to

pseudo-first-order kinetics at high cell concentrations and an inhibiting effect of ferric iron.Pesic et al. (1989) quantified the ferrous iron oxidation rate in the presence of variousconcentrations of bacteria in sulphate media and reported empirical rate laws that can bewritten as:

[ ][ ][ ]++= H aqOFeC k R bact biobio )(22. for pH>2 (2-31)

[ ][ ])(22.' aqOFeC k R bact bio bio+= for pH


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2.3.4 Mechanism predominance

Equation 2-24 can be combined with Equation 2-30 and used to compare the surface mediatedferrous iron oxidation rate with the homogeneous reaction at abiotic conditions. Such acomparison (Figure 2-7, solid lines) shows that in the pH range 4


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2.4 pH buffering reactions

Oxidation of iron sulphides can lead to the release of protons, as indicated by Equation 2-8. Ina tailings impoundment a series of pH-buffering reactions occur with the gangue materials present, which can include carbonate, hydroxide and silicate minerals (Blowes and Ptacek,1994). First to dissolve are carbonates, which react at a greater rate than sulphides, as shown

in Figure 2-8. Carbonates react at a great enough rate that solubility equilibrium with aqueoussolution can often be assumed. Dissolution of carbonate minerals buffers pH around neutral,where many metal hydroxides can precipitate due to low solubility, with the associatedremoval of heavy metals from solution and production of protons (for example, see Equation2-20, ferric hydroxide solubility equilibrium).

With continued acid production, depletion of carbonates leads to a drop in pH, after which thehydroxides begin to dissolve and buffer pH; these are also eventually depleted. Remaining aresilicate minerals, which usually have a greater buffering capacity but react more slowly thancarbonates, hydroxides and sulphides. The solution is thus still buffered, but at a lower pH.

-14

-12

-10

-8

-6

-4

-2

2 4 6 8 10

pH

l o g ( r a t e ) m o l m - 2 s - 1

albite (1)

anorthite (2)

biot ite (3)

chlor ite (4)

K-feldspar (5)

muscovi te (6)

calcite (atmospheric Pco2)*

calcite (Pco2=30%)*

pyrite (Po2

=0.1 atm)**

Figure 2-8. Weathering rates of silicates, pyrite and calcite at 5°C. Anorthite and K-feldspar have almost identical rates for the pH range shown. References:1) Wollast &Chou, 19852) Amrhein & Suarez, 19883) Malmström & Banwart, 19974) Malmström et al., 1995

5) Helgeson et al., 19846) Knauss & Wolery, 1989* Chou et al., 1989** Williamson & Rimstidt, 1994

2.4.1 Carbonate weathering

Carbonate weathering can be exemplified by the dissolution of calcite as given below, hereshown at equilibrium:

−+ +⇔ 232

)(3 COCaCaCO

s (2-33)

Protonation of the carbonate ion at pH ≤ 10 leads to increase in solution pH.


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As can be seen in Figure 2-9, dissolution rates of the carbonates calcite, dolomite(CaMg(CO3)2(s)) and magnesite (MgCO3(s)) increase with decreasing pH, becoming thentransport limited. At the pH of natural waters, dissolution and precipitation are surface-controlled; however, at the lower pH of a typical tailings impoundment, solubility equilibriummay be a reasonable assumption, until the available carbonate is consumed.

Calcite is an efficient buffer of pH in the neutral pH range, buffering the pH around 6.5 - 7.5(Blowes and Ptacek, 1994). The related increase in pH can lead to the precipitation of hydroxides and carbonates with lower solubility than calcite, for example siderite, FeCO3(s),the dissolution of which in turn buffers solution pH around 4.8-6.3 once the calcite isconsumed.

Figure 2-9. Rates of carbonate dissolution, 25°C (modified from Wollast, 1990).

If the assumption of equilibrium is applicable, the solubility of calcite will depend on the

solubility product, K sp =[Ca2+

][CO32-

]. Aqueous speciation and the precipitation of secondaryminerals such as gypsum, CaSO4⋅2H2O(s), can affect free calcium concentrations; free CO3

2-

concentrations are dependent upon the partial pressure of CO2(g) and pH. If these factors aretaken into account, the relationship between field pH and Ca2+ concentrations, as well as themeasured (or estimated “reasonable”) Pco2, can be used as a rough guide as to whether calciteis at equilibrium with porewater concentrations.

If equilibrium cannot be assumed, rate expressions for calcite dissolution are available. Chouet al. (1989) gave an expression for the surface area normalised rate of dissolution:

−++ −−++= 23

22

*32

3321 COCaO H CO H H aak ak ak ak rate (2-34)

where k i are rate constants and a j are activities (see also Appendix E). The first three terms

represent the forward rate of Equation 2-33, that is, dissolution; the fourth term represents therate of the reverse reaction, precipitation, where the reverse reaction only becomes significantfor pH > 8.

2.4.2 (Hydr)oxide weathering

High concentrations of many metals are often found in tailings impoundments, for example,iron as a result of iron sulphide oxidation, and Al due to weathering of aluminosilicates.Suitable conditions of pH and concentration can lead to the precipitation of secondaryhydroxides such as amorphous Al(OH)3(s), amorphous Fe(OH)3(s), ferrihydrite (poorlycrystalline form of hydrous ferric oxide/hydroxide), gibbsite (Al(OH)3(c)) and goethite(FeO(OH)(s)), as well as less soluble hydroxysulphate minerals such as jarosite(KFe3(SO4)2(OH)6(s)) and alunite (KAl3(SO4)2(OH)6(s)). After depletion of carbonate minerals


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and the subsequent drop in pH, dissolution of amorphous Al(OH)3(s) can buffer solution pHaround 4.0-4.3. Consumption of aluminium hydroxide leads to a drop in solution pH to below3.5 and dissolution of ferric hydroxide (Blowes and Ptacek, 1994).

As indicated by Equation 2-20, dissolution and precipitation of amorphous hydroxides isoften considered sufficiently fast that solubility equilibrium control over aqueous

concentrations can be assumed, according to the following equation:

[ ][ ]3

3

+

+

= H

FeK (2-35)

This equilibrium affects and is affected by the pH of solution. Solubility of secondaryminerals is increased by complex formation in the aqueous phase; in particular free ferric ironconcentrations are strongly affected by hydrolysis of the Fe(III) ion.

2.4.3 Silicate weathering

The reaction for chlorite dissolution is given below as an example of silicate weathering:

( ) →+ + H sOH O AlSi AlFeFe Mg III II 5

77)()( 81032.02.05.4

)(32)()(2.02.05.4 23

322

sSiO AlsOH FeFe Mg ++++ +++ O H 25

57+ (2-36)

As shown, weathering of silicates leads to the consumption of protons and release of metalcations. As shown in Figure 2-8, most silicates display pH-dependent weathering with aminimum rate around neutral pH. The rate of reaction is often expressed as the sum of three

terms

[ ] [ ]mn OH k k H k R −+ ++= 321 (2-37)

where the first and last term represent acid and base catalysis of the reaction, respectively. Asmentioned above, silicate minerals tend to have a greater buffering capacity than carbonatesand hydroxides, but weather at a slower rate due to reaction kinetic limitations.

See Appendix D for rate expressions obtained from the literature and utilised in the currentmodel, including those for silicate weathering.


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3 Model description

The current model for the Kristineberg tailings impoundment is based on modelling byStrömberg and Banwart (1994), where the steady state, box model code STEADYQL wasapplied to waste rock heaps at the Aitik site in northern Sweden. In Section 3.1 the code is briefly described and discussed; Section 3.2 covers how the conceptual model for Impoundment 1 in Kristineberg was formed and the mathematical expressions and databaseused; Section 3.3 describes calibration to field data.

3.1 The STEADYQL Code

3.1.1 Code description

STEADYQL (Furrer et al., 1989, 1990) is a code for box models where the system beingmodelled is treated as a completely mixed flow-through reactor. Processes can occur over

three time-scales: i) fast processes, controlled by chemical equilibrium, ii) slow processes,limited by kinetics, and iii) relatively very slow processes, such as movement of fronts andconsumption of minerals, which are considered not to occur over the time period that themodelled steady state applies for.

Equilibrium processes are accounted for by the mass action equation:

( ) ( ) ( )),( jia

j

jC iK iC ∏= (3-1)

where C(i) is the free concentration of specie i [mol dm-3], K(i) is the conditional stability

constant of specie i, and a(i,j) is the stoichiometric coefficient of component j in species i(compare with Equations 2-1 and 2-2). Adsorption reactions are accounted for by a simplesurface complexation model, by including an immobile component in Equation 3-1. Solubilityequilibria can be expressed by a modified version of Equation 3-1, where activity of the solid phase(s) is fixed, forcing the affected free aqueous concentrations into equilibrium with the phase(s). If the system without the solubility restriction would have been over- or undersaturated, this approach conceptually corresponds to precipitation or dissolution,respectively, of the solid phase.

The rate of any slow process is expressed as a power law of a number of parameters and freeconcentrations of chemical species:

∏ ∏=m i

ilnmlw iC mPl R ),(),( )()()( (3-2)

where R(l) [mol dm-2s-1] is the rate of the process, P(m) is the value of parameter m, w(l,m) isthe exponent of parameter m in process l, and n(l,i) is the reaction order the chemical species iin the rate expression for process l.

For any component the total flux J [mol dm-2s-1] is given by the equation:

−=' '

)'()','(),()()(l i

iC jiav jlsl Rtot J (3-3)

where l’ represents all processes but the outflow, i’ and j’ denotes mobile components, s(l,j)denotes the stoichiometric coefficient of component j in process l, and v is the outflow


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velocity [dm s-1] (referred to as infiltration rate q by Strömberg and Banwart, 1994, and in thefollowing sections). In Equation 3-3 the second term represents the outflow. Note that themodel mathematically describes flows in terms of area normalised fluxes.

The model runs to steady state, such that for all components Equation 3-3 equals zero. TheSTEADYQL program is dimensioned for up to 60 species, 20 components, 30 processes and

33 kinetic parameters. Figure 3-1 shows a schematic example of how the code can be applied;the model shown is of Impoundment 1 at the Kristineberg site, as described in the followingsections.

Figure 3-1. Steady state box model of a tailings impoundment.

3.1.2 Comments on the STEADYQL code

Although real systems are rarely at steady-state, this may be a more accurate approach thanthe common assumption of full equilibrium, which also lacks time resolution but makes noallowance for reactions limited by chemical kinetics. In order to account for changingconditions over a long time, such as consumption of minerals, it is possible to compare steadystates representing time periods where different processes or conditions dominate. For example, in order to model the effect of the consumption of amorphous Fe(OH) 3(s) in a system

where dissolution of this specie is buffering pH, the progression can be considered as twosubsequent steady states, a) in the presence of, and then b) in the absence of, the hydroxide.

In many computer codes, reactions are chosen automatically by the code from anaccompanying database after the input of desired components by the user. In STEADYQL,the reactions to be represented must be specifically chosen, as does the entire database,leaving it up to the user to ensure that the dominant reactions are accurately entered andrepresented. For example, unless an equilibrium is assumed and specifically included in thedatabase, precipitation of secondary minerals will not occur, even if the solution isoversaturated with respect to the mineral(s). On the other hand, this aspect of the code givesthe user full control over which reaction will occur in each simulation, and which rateexpression is used.


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Models based on the STEADYQL code can represent advective transport; however, there isno possibility to represent diffusive transport. As a box model the system is assumed to be acontinuously stirred tank reactor (CSTR). There is thus no time or space resolution; it is not possible to simulate movement of fronts. One possibility, for example to represent diffusionof a gas into the box, is to simulate the kinetic addition of the gas to the box; however, there isno coupling between the rate of diffusion into the box and the oxygen concentration gradient

created by the consumption of oxygen below the box (see Section 4.6). A possiblerepresentation of zones with different characteristics could be via linking inflow and outflowof sequential boxes, and repeated calculation of steady state (e.g. Berg, 1997). Such anapproach has also been used to represent the movement of fronts in the commercial tailingsimpoundment model RATAP (Scharer et al., 1994).

Moreover, it is not possible to represent Monod-type kinetics, such as the Michaelis-Mentenexpressions often used to represent biological kinetics (see e.g. Equation 2-17). Instead, suchexpressions have to be approximated by a fractional dependence on the variable parameter, or simple scaling factors applied to the reactions affected by the biological catalysis.Additionally, surface speciation reactions can be represented, but only with simple massaction expressions.

The advantage of this type of steady-state model, for example over a pure geochemicalequilibrium model, is the simple coupling of porewater geochemistry with slow, kineticallylimited processes, showing the interdependence between these processes, and in particular theeffects of and on the system master variable pH.

3.2 The model applied to Impoundment 1 at theKristineberg site

Based on the general concepts of the processes mentioned in Section 2, as well as field data, a

model was built up of a tailings impoundment. Field data was obtained from Impoundment 1at the Kristineberg site, Sweden, before remediation, which occurred in 1996 (Lindvall et al.,1999). The model represents the top 1 m of the impoundment, which is approximately theextent of the pre-remediation weathered zone. The main aim of the modelling was to explainthe main ion composition of the groundwater, in order to then use the model for the predictionof the effect of remediation. Described in the sections below is the “base case” conceptualmodel, as well as the geochemical database and input parameters that make up themathematical formalisation of the conceptual model. In Section 3.3, the process in which themodel was calibrated to site data using two scaling factors is described. Variations on the“base case” conceptual model, tested by the addition or removal of various processes, aredescribed in Section 4.

3.2.1 ”Base case” conceptual model

The conceptual model for the site was created through consideration of sources and possiblesinks for the aqueous ions. The processes represented in the “base case” model were selectedas described below. The model was developed through an iterative process, in whichcomparisons between variations on the base case were used to refine the conceptual model.Variations tested in the conceptual model are described in the Section 4.

Pre-remediation field data has been taken from Malmström et al. (1999b) who summarisedand compared data from du Rietz (1953), Qvarfort (1983, 1989), Ekstav and Qvarfort (1989),

Axelsson et al. (1986, 1991) and others. Available data from pre-remediation studies of theimpoundment includes analysis of the chemical composition of a few solid phase profiles,


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mineralogical determination of the gangue material, mineralogy of the Kristineberg mine2,and groundwater analyses from within the impoundment.

The 1 m weathered zone at the top of the impoundment has been modelled, where the averagegroundwater level was 1 m with an annual variation of 1 m (Axelsson et al., 1986). The totaldepth of the impoundment ranged from a few meters up to 11 m. The average depth of the

weathered zone in Impoundment 1 was also 1 m (see compilation in Malmström et al. 1999b).As concentrations in the saturated zone did not vary greatly with depth (Ekstav and Qvarfort,1989), the unsaturated zone is conceptualised as the major source of ions in solution (Banwartand Malmström, 1999). The volume fraction of minerals in the modelled box were calculated by combining the reported mineralogy with the average of the solid phase compositions at thetop and bottom of the 1 m weathered zone. According to the aqueous phase analyses, themajor ions in solution in the field were SO4

2-, Fe, Zn, Ca and Mg (Figure 3-2).

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

SO42- Fe Mg Ca Zn Al Na Cu K

C o n c e n t r a t i o n ( m o l / l )

average

3.5

4

4.5

5

5.5

6

6.5

pH

p H

Figure 3-2. Groundwater composition in Impoundment 1, Kristineberg showing minimum,maximum and average values. Data are taken from Ekstav and Qvarfort (1989), and areaverages from a time series of measurements over 5 years, 1989-1983, from Piezometers 3, 4,and 4H. The depth of sampling was 1.5m below the groundwater table, which lay on average1m below the surface of the impoundment (see Malmström et al., 1999b).

Preliminary geochemical modelling with the program PHREEQC (Parkhurst, 1995) using theMINTEQ database (see Section 2.1.1) was carried out on groundwater analyses fromImpoundment 1, in order to obtain an indication of which primary and secondary mineralsmay have been close to thermodynamic equilibrium with porewaters, and thus controllingaqueous concentrations. However, care must be taken in interpretation of geochemicalequilibrium modelling, due to conditions of high ionic strength and incomplete chemicalanalysis; for example, no anion analyses other than sulphate are available. Moreover, pre-remediation aqueous concentrations were reported only as average, minimum and maximumvalues for each specie; no entire analysis was reported. Geochemical equilibrium modellingwith average values may not represent the groundwater geochemistry accurately; for example,

2 Tailings in Impoundment 1 came not only from the Kristineberg mine but also mines in thesurrounding region.


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average values of the sulphate concentration and pH may be used, but the sulphateconcentration may have been low in analyses with high pH, or vice versa.

3.2.1.1 Sulphate, Zinc and Copper

The main ore minerals of the Kristineberg mine are reported to be pyrite, chalcopyrite andsphalerite (du Rietz, 1953). Oxidation of these minerals was thus considered to be the sourceof the aqueous ions SO4

2-, Zn2+ and Cu2+. The Kristineberg mine itself was reported to be poor in pyrrhotite, however the tailings in Impoundment 1 come from surrounding mines as well,so it is possible that pyrrhotite is present. Comparison of aqueous Fe(tot) and SO 4

2-

concentrations from field data indicated that the SO42- to Fe(tot) ratio was too low to be due to

the stoichiometric oxidative dissolution of pyrite by oxygen alone. One possibility was a portion of the iron sulphide is present as pyrrhotite, however, as mentioned, pyrrhotite wasnot named in the original mineralogical assay. Additionally, analysis of solid phasecompositions showed that the ratio of iron to sulphur bound in iron sulphides is 0.92, which isgreater than the theoretical ratio of 0.87 for pyrite, but lower than the expected >1.7 for pyrrhotite (Malmström et al., 1999b). In lieu of other information, this suggested that the

majority of the iron sulphide is in the form of pyrite rather than pyrrhotite.

Two other possibilities to explain the low aqueous SO42- to Fe(tot) ratio were a) the

immobilisation of sulphate through, for example, precipitation of gypsum, and/or b) thedissolution of a solid Fe-bearing minerals, such as chlorite and/or amorphous ferric hydroxide(see Section 3.2.1.2 below). Geochemical modelling indicated that gypsum was close tosolubility equilibrium in the porewaters, and hence may have affected Ca2+ and SO4

2-

concentrations (see Sections 4.4 and 4.5 for testing of the model with gypsum present).However, as the presence of gypsum could not be confirmed, it was not included in the basecase.

3.2.1.2

Iron

According to the reported mineralogy and the analysis of the solid phase chemicalcomposition, possible sources of the very high iron concentrations in the aqueous phase wereoxidation of iron sulphides pyrite and chalcopyrite, as well as dissolution of the silicatemineral chlorite. Other possible sources included the dissolution of secondary minerals.Possible sinks of ferrous iron considered were precipitation of secondary minerals, for example via oxidation of ferrous to ferric iron and subsequent precipitation of amorphousFe(OH)3(s).

As no redox measurements were made in the impoundment before remediation, thedistribution of iron between ferric and ferrous forms is unknown. Ferric iron is the morethermodynamically stable redox form of aqueous iron at the oxygen concentrations assumedfor the modelling, Po2=0.1atm. However, the high iron concentration at the high pH found inthe impoundment (up to pH 6.15) suggested that most iron is in the form of ferrous iron, asferric hydroxide becomes highly insoluble as pH approaches neutral. High iron concentrationsthus indicate that there may be a kinetic barrier to oxidation of Fe(II) to Fe(III) due to slowreaction kinetics, hence the importance of representing this process in the model by a kineticexpression. Additionally, it has been reported in the literature that the rate of abiotic oxidationof aqueous ferrous iron to ferric iron by oxygen decreases greatly with decreasing pH, but thatat low pH the reaction can be accelerated by bacterial catalysis, if conditions are otherwisesuitable; however, this catalytic effect was tested in the model and found to be unlikely in thefield (see Section 2.3).


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Although redox values f or the impoundment are not reported, the modelling showed thatwithin pe values of 4-7 3 amorphous ferric hydroxide may be at solubility equilibrium, andhence exerting control on aqueous ferric iron concentrations. According to pre-remediationfield reports (Qvarfort, 1983), the upper layers of the impoundment displayed thecharacteristic colour of ferric (oxy-)hydroxides, supporting the theory that some form of secondary Fe(III) mineral was present. For the base case, it was assumed that ferric hydroxide

was present and exerting solubility control on the ferric iron concentration. The model wasalso tested without the hydroxide present, see Section 4.1.

3.2.1.3 Base cations

High aqueous concentrations of Ca2+ and Mg2+, as well as an average pH of 4.87, suggestedthat some form of buffering reaction was occurring in the impoundment. As shown in Table3-1, mineralogical reports indicate that calcite and dolomite constitute 10 vol-% of the ganguematerial at Kristineberg, and these were the only reported minerals containing calcium.However, the chemical composition of the tailings indicated that the carbonate content waslower than this, and that at least half the calcium present was bound in non-carbonate minerals(Malmström et al., 1999b). Additionally, investigations with the model showed that

equilibrium with calcite could not result in field pH and calcium concentrations, even withelevated CO2(g) partial pressures (see Section 4.5.1). Possible reservoirs of Ca

2+ other thancarbonates could be an unreported Ca-bearing silicate such as plagioclase((Na,Ca)Al(Al,Si)Si2O8(s)), or secondary gypsum, where gypsum could act as either source or sink for calcium, depending on the over-/undersaturation of solution with respect to thismineral.

Table 3-1. The average composition of the waste rock fraction in theKristineberg ore (data from Qvarfort , 1983).

Mineral Chemical composition vol-%Chlorite

Talc(Fe,Mg,Al)4-6(Si,Al)4O10(OH)8(s)

Mg3Si4O10(OH)2(s)50

Quarts SiO2(s) 25Sericite KAl2(AlSi3)O10(OH)2(s)

# 15Calcite

DolomiteCaCO3(s)

CaMg(CO3)2(s)10

#Different definitions given in the literature; resembles an Fe(III)-substitutedmuscovite (Malmström et al., 1999b, interpreting data from du Rietz, 1953)

Investigations with the model showed that three of the potential sources of Ca2+ were feasible;kinetic dissolution of a small volumetric fraction of calcite (see Section 4.5); gypsumdissolution (see Section 4.4), or dissolution of an unreported Ca-bearing silicate (see Section4.5). Thus release of Ca2+ in the field could be the result of one or a combination of the above

possibilities. However, the prevailing source could not be identified. To allow for aconservative buffering capacity of the weathering of the unknown calcium source, totalmagnesium concentrations, originating from chlorite weathering in the model, were allowedto be equal to the sum of Mg2+ and Ca2+ concentrations in the field.

High concentrations of Mg2+ in the aqueous phase indicated weathering of dolomite and/or Mg-bearing silicate minerals. However, in the mineralogical analysis of gangue material,separate volumetric fractions were not given for calcite and dolomite (see Table 3-1), andcalculations indicated that solubility equilibrium with dolomite was not feasible. It wasassumed that the source of Mg2+ was silicate weathering.

3

Typical conditions encountered within the mid-upper layers of an impoundment, e.g.Appleyard and Blowes (1994); pe can vary between 1-14 for an entire impoundment. Theresulting pe in our model varied from 8 at atmospheric Po2, to below one at 0.001atm.


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Mg2+-bearing silicate minerals in the gangue material were reported to be talc and chlorite(see Table 3-1). However, separate volumetric fractions were not given. Given that only onetracer (Mg2+) was available for both minerals, that the stoichiometric ratio of H+ consumptionto Mg2+ release for both minerals is similar (see also discussion of aluminium below), and thatthere is no rate expression for talc weathering available, the weathering of talc and chlorite

was represented by a single process. This process was assumed to be the weathering of achlorite with a composition corresponding to that of chlinochlore, found in the mineralogy of the mine.

Pre-remediation solid phase analyses of K + or Na+ are not available; however K +

concentrations in the aqueous phase and the reported mineralogy suggested the weathering of e.g. muscovite. As no source for Na+ was given in the mineralogy and explanation of therelatively low Na+ concentrations was not the main aim of the investigation, no process toaccount for Na+ release was included in the model.

3.2.1.4 Si and Al

Pre-remediation solid phase analyses of Al or Si were not available. However, high aqueousAl concentrations suggest considerable aluminosilicate weathering; in the model Al isreleased by the weathering of muscovite and chlorite, as given in Table 3-1. Aluminiumconcentrations in the model are actually higher than the field concentrations; this may be dueto the representation of the reported talc-chlorite mixture entirely by chlorite, for reasonsdiscussed in Section 3.2.1.3, as talc does not contain aluminium. In a quick test with talc andno chlorite, assuming the same weathering rate as for chlorite, the results were the same for pH and all components other than aluminium, which was too low. As other model resultswere insensitive to the assumption of either talc or chlorite as the source of Mg 2+, and no ratelaw is available in the literature for talc weathering, Mg-aluminosilicate weathering wasrepresented by chlorite dissolution for the base case.

Equilibrium with the secondary mineral gibbsite was tested as a variation upon the base case,as gibbsite was close to solubility equilibrium in the preliminary geochemical modelling; onthe basis of this testing and lack of field data, gibbsite was not included in the base case (seeSection 4.2).

Aqueous Si concentrations were not measured prior to remediation, but high aluminium and base cation concentrations indicated silicate weathering. Dissolved silicon concentrationswere taken from post-remediation measurements (H. Holmström, personal communication). Itwas assumed that concentrations had not changed greatly since remediation, given the pHdependency of silicate weathering and that the pH has not changed significantly. Geochemicalmodelling, including these Si concentrations, suggested equilibrium with a SiO2 secondarymineral such as chalcedony, SiO

2(am) or quartz. In the model, equilibrium with SiO

2(am) is

assumed. However, this assumption is not as significant as other secondary phaseassumptions, as equilibrium with a SiO2-phase does not affect pH or alkalinity.

3.2.1.5 Equilibrium with gas phase

Consistent with a gradientless, steady state formulation, fixed oxygen and carbon dioxide partial pressures in the gas phase were conceptualised as being in equilibrium with theaqueous phase. Tested variations on the base case included the absence of CO 2 equilibrium,which had little effect on results (see Section 4.3), and the slow addition of oxygen toapproximate diffusion (see Section 4.6). The test with oxygen diffusion, using the base casewater content of 0.15, resulted in aqueous oxygen concentrations that were similar to those in

equilibrium with the base case partial pressure of oxygen (see Table 4-3), which supported thechosen representation for the base case.


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3.2.1.6 Aqueous speciation model

The reactions representing the aqueous speciation of the reported main ions in solution weretaken from literature sources (see Section 3.2.2, and Appendix E for the aqueous speciationmodel used).

3.2.1.7 The final “base case” conceptual model

Figure 3-1 above is a representation of the conceptual geochemical model for the Kristinebergsite. Slow kinetic processes are the weathering of sulphides and silicates and the oxidation of aqueous ferrous iron; aqueous speciation is assumed to be at equilibrium, and solubilityequilibrium is assumed for secondary minerals SiO2(am) and Fe(III)(hydr)oxide. Variations onthe base case that were tested are summarised in Section 4 below. The reactions, rate andequilibrium expressions and constants used in the model are given in Appendices D and E.

3.2.2 Geochemical equilibrium and kinetic database used in the model

For reactions limited by chemical reaction kinetics, empirical rate expressions were chosenfrom literature where available, or where not available, expressions were assumed by analogywith similar minerals. The latter was the case for oxidation of chalcopyrite and sphalerite byoxygen, where analogy was made with oxidation of pyrite (see Appendix D for theexpressions used). Rate constants were corrected to field temperature by the Arrheniusequation (Equation 2.7) using activation energies reported in the literature (see Appendix D).

Thermodynamic constants for the geochemical database in the Kristineberg model wereobtained from, in order of descending preference, Nordstrom et al. (1990) and the WATEQand MINTEQ databases (see Section 2.1.1, and Appendix E for the aqueous speciation modelused). Constants were corrected for field temperature using the Van’t Hoffs equation

(Equation 2-5) and for ionic strength using the Davies equation (Equation 2-4), where theionic strength was taken as an average value from preliminary geochemical equilibriumcalculations using field data and the model PHREEQC, I=0.27.

3.2.3 Input data

Values and sources of some of the parameters used in the model are given in Table 3-2 (seealso Appendix D). Parameters 1-4 were obtained from pre-remediation field reports.Parameters 5-7 were estimated based on information in the pre-remediation field reports. Thecompact density was compiled from the estimated mineralogy of the impoundment, as given

by Malmström et al. (1999b). The water content (θ = volume water/total volume) wasestimated from the porosity of the impoundment to be 0.1-0.25 for the unsaturated zone(Malmström et al., 1999b). A middle value of 0.15 was used for θ in the base case. For impoundment temperature, the average air temperature of 1°C was used, as no measurementswere available.

Oxygen concentrations before remediation were not reported. Atmospheric conditions existedat the surface (0.21 atm) and probably anoxic conditions at the groundwater table, which layat a depth of approximately 1 m, at the bottom of the weathered zone. As the base casemineralogy was taken as the average composition of the oxidised zone, the base case oxygen partial pressure assumed to be at equilibrium with the aqueous phase was 0.1 atm.Replacement of the assumed equilibrium with kinetic addition of oxygen to the box,

approximating diffusion, was tested as a variation upon the base case (see Section 4.6).


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Equilibrium was assumed with carbon dioxide, for which there also were no fieldmeasurements. The partial pressure taken as the base case value was atmospheric partial pressure. The base case was also tested without this equilibrium, and with higher partial pressures of carbon dioxide (see Section 4.3).

Table 3-2: Model parameters. See also text for explanation.

Parameter Base case value Source1) Annual effective infiltration rate, q 7.7 x 10-9 ms-1 Axelsson et al., 19862) Average depth of unsaturated zone, h 1m Axelsson et al., 19863) Porosity, ν 0.25 Axelsson et al., 19864) Total specific surface area of thetailings material, As,tot

0.1 m2g-1 Qvarfort, 1983(0.1-0.25 m2g-1)

5) Compact density, δ 3.3 x 106 gm-3 Malmström et al., 1999b

6) Water content, θ 0.15 Malmström et al., 1999b(0.1-0.25)

7) Impoundment temperature, T 1°C estimated from Axelssonet al., 1986 in Malmströmet al., 1999b

8) Partial pressure of oxygen, Po2 0.1 atm estimated by the authors9) Partial pressure of CO2, Pco2 10

-3.5 atm (atmospheric) estimated by the authors10) Surface site concentration onsecondary ferric minerals, [>FeOH]§

10-9 M Zhang et al., 1992

§ Uncertain parameter; see Section 4.7

The surface area for each mineral, Amin, was calculated by the authors from:Amin = γ min x As,tot x specific density (3-4)

where the volumetric fraction of each mineral, γ min, was taken to be the values estimated inTable 3-3, As,tot was as given in Table 3-2 and the specific density is (1- ν)δ = 2.48 x 10

6 gm-3.

Table 3-3. Minerals included in the model. Mineralogy corresponding to the average of reported chemical compositions at the highest and lowest levels in the weathered zone (depthsof approximately 0 and 1 m, respectively). The remaining material is considered to beunreactive quartz.

Sulphides vol.% Silicates vol.%Pyrite 4 Chlorite 53

Chalcopyrite 0.2

Sphalerite 0.1

Muscovite(sericite)

16

Investigations of the sensitivity of the model to variations in the infiltration rate (q), the water content (θ) and the partial pressure of oxygen (Po2), as well as variability in the mineralogicalcomposition (γ i), are detailed in Section 5. Variations in the partial pressure of carbon dioxide(Pco2) and the surface site concentration of secondary ferric minerals ([>FeOH]) are discussedin Sections 4.4 and 4.7, respectively.


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3.3 Calibration

Model results were compared to the average of monthly averages of the field groundwater analyses taken from November 1983 to September 1988 from three piezometers (Piezometers3, 4H and 4, see Table 3-4). Model results were in general remarkably similar to fieldmeasurements. A notable exception to this is that the predicted concentration of Zn2+ deviated

considerably from field values.

Table 3-4. Comparison of field measurements 4 with uncalibrated and calibrated modelresults. All concentrations in mol l-1. Field data from Ekstav and Qvarfort (1989) (see alsoFigure 3-2).

Range of fieldvalues

Field monthlyaverage

Uncalibrated model, base case

Calibrated model, base case

pH 4.05-6.15 4.87 5.41 4.53

SO42- 0.07-0.14 0.1 0.12 0.1

Fe(tot) 0.06-0.09 0.08 0.06 0.07Cu2+ 8 x 10-6- 2 x 10-4 6 x 10-5 3 x 10-5 6 x 10-5

Zn2+

0.004 - 0.007 0.006 5 x 10-6

5 x 10-5

Ca2+ 0.002 - 0.012 0.005§

Mg2+ 0.007 - 0.017 0.011§ 0.04§ 0.017§

Mg2++Ca2+§ 0.009-0.029 0.016§

K + 3 x 10-6 – 2 x 10-4 6 x 10-5 3 x 10-4 1 x 10-4

Al 9 x 10-4 – 0.003 0.002 0.02 0.008§As no sources of Ca2+ were included in the model, we allowed Mg2+model = ( Mg

2+ + Ca2+)fieldto allow for a conservative buffering capacity of minerals that release Ca2+ in the field.

For pH, SO42-, Fe(tot), Cu2+ and K +, the uncalibrated model gave concentrations within the

range of the field values; Mg2+model was higher than the average (Mg2+ + Ca2+)field by a factor

of 2.5 and Al was an order of magnitude greater than the field average. In general these

deviations between model results and field observations are small and can be well accountedfor by the uncertainties in the empirical rate laws employed.

The model was calibrated to average field results. Following the approach outlined byStrömberg and Banwart (1994), three factors were considered for scaling of kinetic processes:Xreact, α and β.

3.3.1 Calibration factors and sensitivity

3.3.1.1 Calibration factors

The scaling factor Xreact was used to allow for the commonly observed scale dependence of mineral weathering rates. Field rates are commonly up to three orders of magnitude lower than rates measured in the laboratory, where empirical rate laws are normally determined; thismay be due to, for example, differences in temperature, particle size distribution, porewater pH, mineral content and water flow patterns between the scales (Malmström et al., 1999a).

In the current model we have attempted to explicitly account for some of the parameters thathave been identified as contributing to such scale dependence. The rate equations taken fromthe literature were from laboratory experiments with conditions as similar as possible to the 4 Note that the top 0-1 m of the impoundment, that is, the average depth of the weathered zone, has

been modelled, where the groundwater lay on average at a depth of 1 m. However, the only availablegroundwater analyses, shown in Table 3-4 and Figure 3-2, were taken 1.5 m below the groundwater surface, that is, approximately 2.5 m below the tailings surface.


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acidic AMD environment. Rate and equilibrium constants were corrected for temperature;mineralogy was also taken into account, and the resulting pH from the uncalibrated modelwas within the range of field values recorded. Xreact is intended to calibrate the model for additional discrepancies between the scales.

The scaling factor α was included to account for direct microbial catalysis of sulphide

oxidation, which has been reported to accelerate the rate of oxidation by up to an order of magnitude (e.g. see review in Herbert, 1999). In Section 2.2.2 we showed how specific ratelaws can account for microbial kinetics. However, the STEADYQL code does not allow for such formulations, hence the use of a simple scaling factor.

In a similar fashion as for α, and for the same reasons, we have accounted for microbialmediation of ferrous iron oxidation with another scaling factor, β. Microbial mediation isreported to have the potential to increase the rate of oxidation of Fe(II) by more six orders of magnitude (Singer and Stumm, 1970; see also Section 2.3.3). However, the base case valuescould be brought close to average field values without the use of this factor, and in fact wereonly taken further from average field values when this factor was anything other than unity,hence the value of 1 in the base case.

3.3.1.2 Sensitivity to calibration factors

Model results were quite sensitive to the calibration factors; Figure 3-3 shows the results of variation of Xreact and α,. It can be seen that change in these scaling factors by less than anorder of magnitude gave concentrations that were outside the range of field values. That wedid not find another solution to the model for field conditions with other values of the scalingfactors suggests that the scaling factors used in the base case are unique within the testedintervals, where the tested intervals varied by several orders of magnitude above and belowthe values shown in Figure 3-3.

0.00

0.10

0.20

0.30

0 0.2 0.4 0.6 0.8 1Xreact

T o t .

C o n c e n t r a t i o n ( M ) , F r a c t . F e

4

4.5

5

5.5

pH

Mg2+

Fe2+

SO42-

Fract.Fe

pH

0.00

0.10

0.20

0.30

0 2 4 6αααα

T o t

c o n c e n t r a t i o n ( M ) , F r a c t . F e

4

4.5

5

5.5

pH

A) B)

Figure 3-3. Effect of variation in a) Xreact and b) α, separately, within the base case. In eachcase, one factor is varied and the other factor has been held constant at the base case value,namely Xreact=0.4 and α=2.5. “Fract.Fe” indicates the contribution of pyrite oxidation byferric iron to the overall pyrite oxidation rate; compare with Figure 3-4, and see Sections 2.2.3and 5.3.2.


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For increase in β by three orders of magnitude (from 1 to 1000), concentrations similar to the4base case could be obtained (Figure 3-4). However, with increasing β from 1 to 1000, pHdecreased by over half a pH unit and was then less than the minimum value found in the field. Noteworthy is that at β=1000, the rate of oxidation of pyrite by ferric iron is 30% of theoverall pyrite oxidation rate, compared to 5% when β=1, as in the base case (see Section 5.3.2for discussion of mechanism predominance results). For β = 10000, that is, when the rate of

ferrous iron oxidation was increased by a factor of more than 104, concentrations greatlyincreased above field conditions, pH dropped to 3, and oxidation was dominated by the ferriciron mechanism.

Possible conclusions from this include that if conditions changed to favour acceleration of ferrous iron oxidation in Impoundment 1, for example, due to biological mediation, the effectcould be of a magnitude of up to 1000 and still not affect concentrations of dissolved ions.This would, however, lead to a slightly lower pH than the field value. Additionally, catalysisincreasing ferrous iron oxidation by more than 2 orders of magnitude would increase thesignificance of the oxidation of pyrite by ferric iron compared to the base case; themechanisms are equally important when β=2000. In the base case, pyrite oxidation by oxygendominated at all times (see Section 5.3.2).

0.0

0.5

1.0

1.5

2.0

2.5

1 10 100 1000 10000

ββββ

T o t . c o

n c e

steady state geochemical box model

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