Effect of Coatings on Mineral Reaction Rates in Acid Mine ......Effect of Coatings on Mineral...

Effect of Coatings on Mineral Reaction Rates in Acid Mine Drainage

Danielle M. C. Huminicki

Dissertation submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

In Geosciences

Committee Members Advisor: Dr. J. Donald Rimstidt

Dr. Patricia Dove Dr. John Chermak

Dr. Madeline Schreiber

July 24, 2006 Blacksburg, Virginia

Keywords: gypsum coatings, calcite dissolution rates, acid mine drainage,

hydrodynamics, anoxic limestone drain, pyrite oxidation rates, iron oxyhydroxide coatings, limonite pseudomorphs, alkalinity

Effect of Coatings on Mineral Reaction Rates in Acid Mine Drainage

Danielle M. C. Huminicki

ABSTRACT

This dissertation includes theoretical and applied components that address the

effect of coatings on rates of mineral reactions that occur in acid mine drainage (AMD)

environments. The two major projects investigated how diffusion-limited transport of

reactants through pore spaces in coatings on mineral grains affects the reaction rate of

the underlying mineral. The first project considered the growth of gypsum coatings on

the surface of dissolving limestone in anoxic limestone drains (ALD), which reduces

the neutralization rate of the dissolving limestone and the subsequent effectiveness of

this treatment. The second project investigated the conditions where iron oxyhydroxide

coatings form on oxidizing pyrite and the potential strategies to prevent ‘runaway’

AMD by reducing the rate of acid production to the point that the acid can be

neutralized by the surrounding rocks.

In both studies, experiments were conducted to measure reaction rates for the

underlying minerals, as coatings grew thicker. These experimental data were fit to a

diffusion model to estimate diffusion coefficients of reactants through pore spaces in

coatings. These models are extrapolated to longer times to predict the behavior of the

coated grains under field conditions.

The experimental results indicate that management practices can be improved

for ALDs and mine waste piles. For example, supersaturation with respect to gypsum,

leading to coating formation, can be avoided by diluting the ALD feed solution or by

replacing limestone with dolomite. AMD can be prevented if the rate of alkalinity

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addition to mine waste piles is faster than acid is produced by pyrite oxidation. The

diffusion model developed in this study predicts when iron oxyhydroxide coatings will

become thick enough that alkalinity from the surroundings is sufficient to neutralize

acid produced by coated pyrite oxidation and additional alkalinity is no longer

required.

Dedication

I must dedicate this dissertation to Twin B, Michelle A. E. Huminicki. You are

my inspiration. I also want to thank my loving husband David Benson for his support

over the years and my parents Pat and Carol Huminicki, my sister Lisa Huminicki,

brother in-law Conrad Lauer, my beautiful nieces Paige and Cassidy Lauer, Roy and

Laura Benson, my sister in-law Allison Waskul and my dear nephew Andrew Waskul

with loving memory of my brother in-law Colin Waskul. And of course my Micky

dog!

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Acknowledgements

This research was funded by a grant number EAR-0003364 from the National

Science Foundation to Dr. J. Donald Rimstidt. I would like to thank Don for all his

advice and his cheery disposition to brighten the days. I would also like to thank him

for all his encouragement and support over the last four years. The author thanks

committee members Madeline Schreiber, John Chermak and Patricia Dove for

comments and suggestions for this dissertation, Chuck Cravotta and Jane

Hammarstrom for their in depth reviews of the manuscript ‘Neutralization of sulfuric

acid by calcite dissolution and the application to anoxic limestone drain design’

accepted by Applied Geochemistry and Sam Denning for help with laboratory work. I

would also like to thank Amanda Albright Olsen for her friendship and discussions

over the years and the geoscience graduate students at Virginia Tech.

Attributions

Dr. J. Donald Rimstidt, my primary advisor, is a secondary author on the

manuscripts included in this dissertation that were accepted to Applied Geochemistry

and prepared for submission to Environmental Science & Technology.

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Table of Contents

Title page ………………………………………………………………………………..i Abstract ………………………………………………………………………………...ii Dedication ……………………………………………………………………………..iii Acknowledgements ……………………………………………………………………iv Attributions ……………………………………………………………………………iv Table of Contents ………………………………………………………………………v List of Figures ……………………………………………………………………..….vii List of Tables …………………………………………………………….………....….ix

Chapter 1: Overview …………………………………………………………………..1 Chapter 2: Neutralization of sulfuric acid solutions by calcite dissolution and the

application to anoxic limestone drain design …………………………………………..5

Abstract ………………………………………………………………………………...5 Notation ………………………………………………………………………………...6

Introduction …………………………………………………………………………….8 Methods ……………………………………………………………………………….11 Results ………………………………………………………………………………...13

Rate determining variable …………………………………………………….15

Conversion from semi-batch to ideal BR conditions …………………………16

Rate determination ……………………………………………………………18

Filtering the rate data …………………………………………………………18

Rate law and regressor variables ……………………………………………...19 Discussion …………………………………………………………………………….21

vi

Effect of hydrodynamics on rates ……………………………………………..21

Effect of sulfate on rates ………………………………………………………23

Effect of gypsum coatings on rates …………………………………………...23

Applications ...………………………………………………………………...27

References …………………………………………………………………………….38 Appendix 2.1 Data from calcite dissolution batch reactor experiments...………….…40

Appendix 2.2 Calculation of +Hm and −

3HCOm in solution as a function of extent of

reaction………………………………………………………………………………...44 Chapter 3: Limiting pyrite oxidation and AMD generation by iron oxyhydroxide

coatings …………………..…………………………...………………………………47

Abstract ……………………………………………………………………………….47 Notation ……………………………………………………………………………….48

Introduction …………………………………………………………………………...49 Methods and Materials ………………………………………………………………..56 Results ………………………………………………………………………………...60 Discussion …………………………………………………………………………….67 Applications …………………………………………………………………………..77 References …………………………………………………………………………….82 Appendix 3.1 Tabulated data……………………….…………………………………84

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List of Figures

Chapter 2

Fig. 2.1 Log sulfate concentration versus pH for AMD solutions reported by Plumlee et al. (1999) (open circles). The solid line represents conditions of potential gypsum saturation for solutions neutralized to pH 7 by calcite. The heavy-dashed and light-dashed lines are the potential gypsum saturation curves for solutions that have been diluted 2x and 10x, respectively…...…………..…………………...………….10 Fig. 2.2 (a) SEM images of calcite grains reacted with solutions with the initial pH and sulfate concentrations indicated. Asterisks denote experiments where gypsum coatings formed. The scale bar at the bottom of each image is 10 micrometers. (b) Magnified SEM image of a calcite grain reacted with solutions with an initial pH of 1.5 and 1.0 molar sulfate concentration that shows gypsum crystals precipitated on the dissolving calcite surface. The scale bar is 10 micrometers.…………………….13-14 Fig. 2.3 Amount of H+ consumed by reaction with calcite as a function of time for a typical experiment (DHBy) with 0.3 M sodium sulfate and an initial pH of approximately 2……………………………….17 Fig. 2.4 Data (symbols) and linear regression of log r (mol/(m2·s) versus (a) pH or (b) log t for experiments where (a) no gypsum coatings formed and (b) gypsum coatings developed. Regression coefficients are reported in Table 2.……..………...…………………………………….………..……...20 Fig. 2.5 The measured (symbols) and predicted (line) calcite dissolution rates as a function of time for experiment DHBff where gypsum coatings formed. The decrease in rates with time is attributed to a growing armoring layer…………………………………………………………………………………..24 Fig. 2.6 (a) A/M as a function of particle radius. (b) Residence time as a function of Darcy velocity. (c) Effectiveness term, ((A/M)kt ), versus particle radius for a Darcy velocity of 0.01 m/s. (d) Effectiveness term, ((A/M)kt ), versus Darcy velocity for a particle radius of 0.01m……………………………….….30 Fig. 2.7 Predicted pH versus reactor length for the integrated rate law model for a reactor with a 1 m2 cross-sectional area. This model does not consider the release of H+ by the conversion of carbonic acid to bicarbonate. (a) pH versus length contoured in Darcy velocity for a bed packed with 0.01 m radius calcite grains. (b) pH versus length contoured in particle radius for a Darcy velocity of 0.1 m/s…….....31 Fig. 2.8 (a-d) pH as a function of reactor length predicted by the model that takes the conversion of carbonic acid to bicarbonate (Appendix 2) into account. (a) pH versus length contoured in Darcy velocity for a bed packed with 0.01 m radius calcite grains. (b) Alkalinity versus length contoured in Darcy velocity for a bed packed with 0.01 m radius calcite grains. (c) pH versus length contoured in particle radius for a Darcy velocity of 0.1 m/s. (d) Alkalinity versus length contoured in particle radius for a Darcy velocity of 0.1 m/s………..…………………………………………………..………….33-34 Fig. 2.9 Comparison of the rates of dolomite dissolution (Busenberg and Plummer, 1982) with the rates of gypsum coated calcite dissolution (this study)……………………………………………………….37

Chapter 3

Fig. 3.1 (a) Cross-section of a limonite pseudomorph from Bedford Co., VA that shows a porous center containing a small amount of unreacted pyrite surrounded by a dense outer coating. (b) Comparison of the reaction-limited pyrite oxidation rate by dissolved oxygen for the reaction py-DO in Table 1 (DO ~9 ppm) in air saturated solutions with the reaction-limited pyrite oxidation rates for reaction py-H2O2 in Table 3.1 for 0.3 m H2O2 solutions used in our experiments (solid lines). The dashed lines compare the oxidation rate of Fe(II)-DO in air saturated solutions (DO ~ 9 ppm) with the oxidation rate of Fe(II)-

viii

H2O2 in 0.3 m H2O2. The Fe(II) concentration was set at5101 −× molal…...………………..………….52

Fig. 3.2 Schematic design of the mixed flow reactor experiment. A 4 L carboy held 2 L of solution that was circulated using a peristaltic pump through a reactor with an inner diameter of 2 cm and a height of 1.3 cm. The reactor held 5 g of pyrite and 2.43 g of solution…...……………………………………….57 Fig. 3.3 Graph of r versus t-1/2 data from our MFR experiment. The slope of the line changed from

shallow 72/16 1042.3t1019.2r −−− ×+×= R2 = 0.58 to steep 82/15 1031.5t1072.7r −−− ×−×= R2 = 0.88

during the course of the experiment indicating that the coating became a more effective barrier to H2O2 transport. The chemical reaction-limited rate calculated for py-H2O2 from Table 3.1 for a 0.3 m H2O2

solution used in our experiments is 4.57×10-7 mol/(m2s). Inset of measured rate versus time data.…….61 Fig. 3.4 Graph of r versus t-1/2 from the Zhang and Evangelou (1996) data. The equation for the line is

112/17 1047.3t1060.2r −−− ×+×= R2 = 0.87. The chemical reaction-limited rate of pyrite oxidation

calculated for py-H2O2 from Table 3.1 by the 0.145 m H2O2 solution used in their experiments, 2.19×10-7 mol/(m2s), is about 2 orders of magnitude faster than their fastest rate because the coating of iron oxyhydroxide that formed on the pyrite surface by their pretreatment was a significant barrier to H2O2 transport to the pyrite surface. Inset shows rate versus time data……………………………………………………..…..…………………………………………….62 Fig. 3.5 (a-c). Graphs of r versus t-1/2 from the Nicholson et al. (1990) data for (a) 76, (b) 108 and (c) 215 micrometer grain sizes, respectively. The equations of the lines are (a)

102/17 1037.11091.8 −−− ×+×= tr R2 = 0.65, (b) 102/17 1042.31026.7 −−− ×+×= tr R2 = 0.65, and (c) 112/16 105.91007.1 −−− ×+×= tr R2 = 0.74. The chemical reaction-limited rate of pyrite oxidation

calculated for py-DO from Table 3.1 is 9.13×10-10 mol/(m2s). Insets show rate versus time data..….63-65 Fig. 3.6 Schematic diagram showing the steps leading to the replacement of pyrite by goethite. Stage 1a and b show the initial formation of a porous and permeable iron oxyhydroxide coating by the formation and attachment of colloidal iron oxyhydroxide. Stage 2 shows the densification and thickening of the coating leading to the transition from reaction-limited to diffusion-limited rates……………………….68 Fig. 3.7 Graph showing the predominance fields for kinetically favored species as a function of total iron concentration and pH. Lines 1, 2 and 3 separating these fields were calculated using the rate laws in Table 3.1 by solving for iron concentration as a function of pH (see text for explanation).……….…....74 Fig. 3.8 The modeled decrease in the rate of H+ production by the oxidation of pyrite coated by a growing layer of goethite (curve). The arrow shows the rate of H+ production for pyrite oxidation with no coatings. The tick marks on the right axis represent the bicarbonate concentration required to neutralize H+ produced at the corresponding rate shown on the left axis when bicarbonate is carried into the mine waste at an average infiltration rate of 10-10 m/s……………………………………………….79

ix

List of Tables

Chapter 2

Table 2.1 Coefficients for the equation +++ +=HHH

logMlogsalog γ correlating the concentration of

H+ to pH for sodium sulfate and sodium nitrate solutions……………………………………………….16

Table 2.2 Rate constants and reaction orders for the general rate law mn

Htkar +−= ….…………..….19

Table 2.3 Predicted diffusion coefficients for H+ through the pore spaces of a gypsum coating with 50% porosity. SO4 and Ca concentrations give the ratio of Ca reprecipitated as gypsum…..……………..….27 Table 2.4 Governing equations for the plug flow reactor model……………………………………..….28

Chapter 3

Table 3.1 Empirical rate laws for important chemical reactions discussed in this paper. For cases where the rate laws were expressed in terms of molar concentrations at ~25 degrees Celcius, it was assumed

that M ≈ m. We assume that AFO (Fe(OH)3(s)) rapidly converts to ferrihydrite (fh). The rate laws are referred to in the text in terms of the most important reactants, which are shown in bold….………..….51

1

Chapter 1

Overview

This dissertation consists of both theoretical and applied elements that focus on the

effect of coatings on mineral reaction rates associated with acid mine drainage (AMD).

The theoretical portion investigated the question of how coatings affect mineral

weathering rates. Laboratory experiments and diffusion models were used to address

this concept. Basic geochemical engineering principles were used to apply the

experimental results to environmental problems associated with AMD and develop

quantitative models to help improve current treatment and prevention methods. From

an applied point of view the goal is to eliminate the impact of AMD. From a theoretical

perspective the goal is to develop quantitative methods to model these complex

chemical systems.

The two major projects investigated how mineral reaction rates are affected by

diffusion-limited transport through pore spaces in coatings that developed on

dissolving or oxidizing mineral surfaces. The first project investigated the potential

formation of gypsum coatings in anoxic limestone drains (ALD) and the effect these

coatings have on limestone dissolution rates. The second project identified conditions

where iron oxyhydroxide coating form on oxidizing pyrite and how these coatings can

potentially eliminate AMD by reducing the rate of acid production by pyrite oxidation

to the point that it can be neutralized by the surrounding rocks.

Anoxic limestone drains (ALD) are passive treatment systems that consist of

crushed limestone that is used to neutralize the acidity and increase the net alkalinity of

AMD solutions. The precipitation of gypsum coatings on the surface of dissolving

2

limestone reduces the neutralization rate and the subsequent effectiveness of this

treatment. Hydrodynamic conditions in ALDs were also investigated in this study

because calcite dissolution rates are transport-limited at low pH and the neutralization

rate of AMD by limestone is affected by flow rates. The results from calcite dissolution

experiments in this study give insights to improve AMD treatment by ALDs.

The manuscript titled ‘Neutralization of sulfuric acid solutions by calcite

dissolution and the application to anoxic limestone drain design’ (accepted by Applied

Geochemistry) describes a laboratory study conducted to evaluate calcite dissolution

rates for a range of low-pH and high-sulfate solutions. Calcite particle size, surface

properties and flow rates had significant effects on dissolution rates and were included

in the development of two dissolution rate models for uncoated and gypsum-coated

calcite. This paper provides a geochemical engineering basis for improving the design

and operation of ALDs.

Prevention of AMD requires a method to sufficiently reduce pyrite oxidation rates

and H+ production so that naturally occurring alkalinity is sufficient to neutralize the

acid generated. The approach to prevent ‘runaway’ AMD is to significantly reduce the

oxidation rate of pyrite by cutting off the supply of oxidant. ‘Runaway’ AMD occurs at

low pH where pyrite oxidation rates become dominated by dissolved Fe(III), which are

extremely fast at low pH. One way to cut off the oxidant supply to the pyrite surface is

to coat the pyrite grains with iron oxyhydroxides. Limonite (iron oxyhydroxide)

pseudomorphs after pyrite are natural analogues of this process, which indicates that

coatings can provide long-term encapsulation of pyrite. Iron oxyhydroxides that

precipitate on the surface of pyrite act as a barrier to transport of oxygen from solution

3

to the pyrite surface. This process can slow the pyrite oxidation rate to the point that

the H+ generated by pyrite oxidation is neutralized by alkalinity supplied by infiltrating

groundwater. As a result, the pH remains unchanged and the iron oxyhydroxide

coatings are stable, thus ‘runaway’ AMD conditions are avoided. The dissolution rate

model for coated pyrite oxidation was used to identify management practices to

effectively reduce AMD.

The manuscript ‘Limiting pyrite oxidation and AMD generation by iron

oxyhydroxide coatings’ (in prep. for submission to Environmental Science &

Technology) describes experiments that were conducted to measure the rate of pyrite

oxidation at high pH and alkalinity conditions where iron oxyhydoxides developed on

the pyrite by processes analogous to the formation of limonite pseudomorphs after

pyrite. A mixture of 0.3 m hydrogen peroxide and 0.1 m sodium bicarbonate solution

was used as an oxidant and a source of alkalinity to maintain a pH of approximately 8.5

in order to induce iron oxyhydroxide coatings. Our experiments measured oxidation

rates as the coatings grew and the rate became limited by the diffusion of H2O2 through

the pore spaces in the coatings.

Once coatings develop there is a characteristic linear relationship of reaction rate

with time, r versus t-1/2, as the growing coatings continuously reduce the rate of oxidant

transport to the pyrite surface. A general model for this diffusion-limited behavior can

be derived from Fick’s first law of diffusion. Our experimental results were used to

calibrate this model and predict how long it takes for coatings to become thick enough

to reduce alkalinity demand effectively so that ‘runaway’ AMD does not develop. This

model predicts the rate at which coated pyrite oxidizes as a function of time. Taking

4

into consideration the stoichiometry of the oxidizing reaction the rate of hydrogen ion

production over time is 2/1)( )1(20002 −

−=+ t

Vf

ADmr

mppti

isol

H ν

φ, where m(sol) is the molal

concentration of the reactant in the bulk solution, Di, is the diffusion coefficient of the

reactant, A, is the surface area of the reacting mineral, φ, is the porosity in the coating,

vi, is the stoichiometric coefficient, fppt, is the fraction reacted that precipitated in the

coating, Vm, is the molar volume of the coating. This equation can be used to predict

the rate at which alkalinity must be added to mine waste piles to generate coating

growth and maintain neutral conditions.

Diffusion-limited reaction rates are very important in natural systems.

Therefore, the general concepts developed in this dissertation can be applied to other

situations. Some other coupled dissolution/precipitation reactions that are common in

nature are the development of clay coatings on weathering feldspars, manganese oxides

on quartz grains, aluminum and iron oxyhydroxide coatings on limestone and even

corrosion products re-precipitated on the surface of man-made materials. The reduced

transport of reactants and products to and from the mineral surface (i.e. hydrodynamics

of system) and the precipitation of secondary coatings on the surface of a reacting

mineral may be one reason that mineral reaction rates in nature are orders of magnitude

slower than rates measured in the laboratory. The findings of this research aid in the

management of AMD and the concepts presented lay out the foundation to model

mineral reaction kinetics in systems where transport and diffusion limits reaction rates

dominate.

5

Chapter 2

Neutralization of sulfuric acid solutions by calcite dissolution and the application

to anoxic limestone drain design

Abstract

Batch reactor (BR) experiments were conducted to measure the effect of

hydrodynamics and gypsum coatings on calcite neutralization rates. A factorial array of

BR experiments were conducted to measure the H+ concentration change caused by

calcite dissolution over a pH range of 1.5 to 3.5 and sodium sulfate concentrations of 0

to 1 molar. The rate of H+ concentration change with time was determined by

numerical differentiation of H+ concentration versus time data. Regression modeling

showed that for uncoated calcite, dissolution rates are significantly affected only by

pH, 76.032.210 +

−−=H

ar . For calcite coated with gypsum, only time had a significant

effect on calcite dissolution rates, 53.096.110 −−−= tr .

Because transport-limited dissolution rates for uncoated calcite are a function of

the pH and Reynolds number, a model was developed to express the effects of these

two variables on the rate of H+ consumption for a solution with a Darcy velocity, q,

through a porous medium with a particle radius, rp, such that

87.069.031.097.210 +

−−=′Hp mrqr . This equation was integrated numerically to simulate the

performance of an idealized anoxic limestone drain (ALD). This model predicts the pH

and alkalinity change along the length of the ALD. The model shows that the

efficiency of an ALD is greater when the Darcy velocity is low and the particle radius

is small.

6

In addition, the growth of gypsum coatings causes the rate of H+ neutralization

to decline as the square root of time as they form and block H+ transport to the calcite

surface. Supersaturation with respect to gypsum, leading to coating formation, can be

avoided by diluting the ALD feed solution or by replacing limestone with dolomite.

Notation

Symbol Definition, units

a rotating disc radius, m

ai activity of species, i

A surface area, m2

M

A surface area of pyrite to mass of solution, m2/kg

AR remaining surface area, m2

Asp specific surface area, m2/g (calcite grains, 0.015 m2/g)

CB H+ concentration in bulk solution, mol/m3

d hydraulic radius, m

D diffusion coefficient for H+, m2/s

fgyp fraction of Ca2+ precipitated as gypsum

FWcal formula weight of calcite, 100.008 g/mol

I ionic strength, mol/L

J flux of H+, mol/(m2·s)

k rate constant, mol/(m2·s)

1K ′ apparent dissociation constant for H2CO3

7

mi molal concentration of species i, mol/kg

mr amount of H+ reacted, mol/kg

M mass of solution, kg

Mi molar concentration of species i, mol/L

ncal,i initial amount of calcite

nCa,gyp amount of Ca2+ precipitated as gypsum, mol

nCa,L amount of Ca2+ in solution, mol

nCa,T total amount of Ca2+ released, mol

ni amount of species i, mol

tHn

,+ total amount of H+ reacted over an elapsed time period, mol

q Darcy velocity, m/s

r rate of H+ concentration change, mol/(m2·s)

r′ apparent rate of H+ concentration change, mol/(kg·s)

rp particle radius, m

Re Reynolds number, unitless

t time, s

3COT total amount of carbonate liberated from calcite, mol/kg

+HT concentration of H+ in the unreacted solution, mol/kg

V volume of solution in contact with calcite, L

Vs volume of solution in reactor at sample time, L

Vsp specific volume of water, 1 cm3/g

Vm molar volume of gypsum, 7.422×10-5 m3/mol

x thickness of gypsum layer, m

8

υ kinematic viscosity of water, 8.93 × 10-7 m2/s @ 25°C

ω angular velocity of rotating disc, rad/s

φ porosity, unitless ratio from 0 to 1

γi activity coefficient of species, i

Introduction

The estimated cost of cleanup and maintenance of acid mine drainage (AMD)

affected sites in the United States required to meet effluent limits recommended by the

U. S. Environmental Protection Agency is on the order of $1 million per day (Perry,

1992). Currently the best chemical technologies used to neutralize AMD include the

addition of hydrated lime (Ca(OH)2), which can be cost effective but requires mixing,

pebble quick lime (CaO), which is very reactive and requires monitoring equipment,

soda ash briquettes (Na2CO3), which are convenient to transport but relatively

expensive (Skousen et al., 1999), and caustic soda (NaOH), which is very soluble but

expensive. Reacting AMD with limestone is an inexpensive alternative to these

chemical treatments. AMD is typically channeled through a bed of crushed limestone,

and the calcite in the limestone dissolves to produce calcium ion and dissolved

carbonic acid and bicarbonate as described by the reactions:

CaCO3 (cal) + 2H+ = Ca2+ + H2CO3 pH < 6.3 (1)

CaCO3 (cal) + H+ = Ca2+ + HCO3

- pH > 6.3 (2)

Anoxic limestone drains (ALD) are essentially buried limestone-filled trenches

that are sealed off from oxygen in order to minimize the oxidation of ferrous iron and

9

hence, the precipitation of ferric iron oxyhydroxide coatings (Hedin et al., 1994). As

the pH of the solution increases, ferric iron and aluminum hydrolyze and precipitate as

oxyhydroxide coatings on the surface of limestone (Ziemkiewicz et al., 1997; Cravotta

and Trahan, 1999; Al et al., 2000; Hammarstrom et al., 2003). Gypsum can also

precipitate on the surface of dissolving calcite if the AMD solutions have high sulfate

concentrations (Booth et al., 1997; Wilkins et al., 2001; Hammarstrom et al., 2003).

Ca2+ + SO42- + 2H2O = CaSO4•2H2O (gyp) (3)

The accumulation of oxyhydroxide, sulfate, and other mineral coatings on the calcite

surface reduces the contact between the solution and calcite, leading to decreased

dissolution rates. Although ALDs help to prevent the formation of ferric iron

oxyhydroxide coatings, they are still vulnerable to reduced reactivity due to aluminum

oxyhydroxide or gypsum coatings.

The development of gypsum coatings on limestone can be examined by

considering the potential gypsum saturation for solutions neutralized by calcite,

described by 58.4log4

−= pHmSO , which is the line shown in Figure 2.1. Above this

line solutions neutralized by calcite would release enough Ca2+ by equation (2) to

become saturated with respect to gypsum. Typical sulfate concentrations and pH values

for metal AMD solutions (Plumlee et al., 1999), shown in Figure 2.1, suggest that a

significant fraction of AMD solutions have the potential to form gypsum in ALDs.

Even lower pH values and higher sulfate concentrations have been reported for AMD

produced by pyrite oxidation associated with coal (Cravotta and Bilger, 2001).

10

Fig. 2.1. Log sulfate concentration versus pH for AMD solutions reported by Plumlee et al. (1999) (open

circles). The solid line represents conditions of potential gypsum saturation for solutions neutralized to

pH 7 by calcite. The heavy-dashed and light-dashed lines are the potential gypsum saturation curves for

solutions that have been diluted 2x and 10x, respectively.

Iron and aluminum oxyhydroxide coatings are not strongly bonded to the

surface of calcite and can potentially be prevented from accumulating or removed from

surfaces by periodic flushing of limestone drains (Hammarstrom et al., 2003; Weaver

et al., 2004). However, the epitaxial nucleation of gypsum crystals onto calcite surfaces

makes gypsum strongly adherent and removal by flushing difficult.

Currently ALD design considers variables such as limestone grain size, porosity

of the drain, contact/residence time, initial 2COP , and initial acidity (Hedin et al., 1994;

11

Cravotta et al., 2004). However, experiments on calcite dissolution in acid solutions

(Pearson and McDonnell, 1974; Sjöberg, 1976; Plummer et al., 1979; Sjöberg and

Rickard, 1983; Alkattan et al., 1998; Arvidson et al., 2002) show that at low pH,

dissolution rates are transport-limited because calcite reacts with hydrogen ion much

faster than hydrogen ion can diffuse from the bulk solution to the surface. The rate of

hydrogen ion transport to the surface of calcite is controlled by the hydrodynamics of

the system. Therefore, improved design of ALD facilities must consider the effect of

hydrodynamics on the neutralization effectiveness of the solutions.

The purpose of this work is to use laboratory measurements of calcite

dissolution rates in sulfuric acid solutions and mathematical models to predict the

effects of both gypsum coatings and hydrodynamics on the effectiveness of ALD

treatment systems.

Methods

Batch reactor (BR) experiments were conducted to measure calcite dissolution

rates over a range of pH, ionic strength, and sulfate concentration. A subset of these

experiments determined the effect of gypsum coatings on calcite dissolution rates as a

function of sulfate concentration, ionic strength, pH, time, and degree of gypsum

saturation.

Crushed Iceland spar calcite crystals were used for the BR experiments. The

40-60 mesh (425-250 µm) size fractions, recovered by sieving, were washed with ethyl

alcohol and sonicated until the supernatant was clear. The crushed calcite was dried

12

over night at room temperature. The specific surface area, Asp, of these grains was

estimated to be 0.015 m2/g based on the relationship between surface area and grain

size reported by (Foust et al., 1980). BET surface area analysis was not performed on

these samples because of the small amount of surface area.

An array of 24 BR experiments was conducted. This array had a factorial

distribution of 0.0, 0.1, 0.3, or 1.0 M sodium sulfate solutions adjusted to pH values of

1.5, 2.0, 2.5, 3.0, or 3.5 using nitric acid. Four of these were duplicate experiments

conducted at pH 1.5 and sodium sulfate concentrations of 0.0, 0.1, 0.3, and 1.0 M. An

additional set of three BR experiments with solutions of 0.1, 0.3, or 1.0 M sodium

nitrate and a constant pH of 2.0 were conducted to determine the effect of ionic

strength on dissolution rates.

A 0.5 gram sample of calcite crystals was reacted in 200 mL of solution for

each experiment. The experiments were run at 22° C for 1 hour in a gyrotory shaker

water bath that stirred the flasks at a rate of 200 excursions per minute under conditions

open to the atmosphere. The reported rates represent the minimum dissolution rates in

an ALD because ALDs are closed systems, so CO2 gets trapped and the 2COP increase

enhances limestone dissolution. At evenly spaced time intervals the pH was measured

and a 2 mL sample was collected to determine the Ca concentration.

The Ca concentration of each sample was measured using atomic absorption

(AA) spectrophotometry. The precision of the AA analysis was 2.5%. The pH was

measured using an Ag/AgCl pH electrode calibrated using buffers at pH values of 7.00

±0.01 and 4.00 ± 0.01. Class A, 50.00 ± 0.05 and 100.00 ± 0.08 mL volumetric

Florence flasks and a 1 mL pipette with a precision of 1.93% were used to do the

13

analysis and prepare the solutions. Reacted grains recovered at the end of each

experiment were observed and characterized using scanning electron microscopy

(SEM) and visible light microscopy.

Results

The pH and Ca concentrations for each experiment are tabulated in Appendix

2.1. Figures 2.2(a) and (b) show SEM images of calcite surfaces after they were reacted

with each of the solutions in the factorial array of pH and42SONaM .

Fig. 2.2. (a) SEM images of calcite grains reacted with solutions with the initial pH and sulfate

concentrations indicated. Asterisks denote experiments where gypsum coatings formed. The scale bar at

the bottom of each image is 10 micrometers.

DHBbb DHBcc DHBs DHBt DHBu

DHBz* DHBp DHBaa DHBq DHBr

DHBx* DHBy DHBm DHBn DHBo

DHBv* DHBw* DHBj DHBk DHBl

pH

1.5 2.0 2.5 3.0 3.5

1.0

0.3

0.1

0.0

4 NaSO M 42SONaM

14

Fig. 2.2. (b) Magnified SEM image of a calcite grain reacted with solutions with an initial pH of 1.5 and

1.0 molar sulfate concentration that shows gypsum crystals precipitated on the dissolving calcite surface.

The scale bar is 10 micrometers.

10 µm

b

15

The results of the BR experiments show that after the 1 hour duration of these

experiments gypsum coatings encapsulated the calcite grains reacted at low pH (pH ≤

2) and high sulfate concentrations (0.1 to 1.0 M). Accordingly, data were separated into

two groups (1) no coatings and (2) gypsum coatings. Note that because of the greater

extent of reaction, calcite grains reacted at lower pH values are more rounded than

those reacted at higher pH values.

Rate determining variable

The rate of calcite dissolution by reactions (1) and (2) can be measured by the

change in H+ or Ca concentration in solution over time. However, the rate of Ca release

into solution is not representative of the real rate of dissolution in the low-pH, high-

sulfate experiments because some Ca reprecipitated as gypsum for this group of

samples. Therefore, rates were measured using the rate of H+ concentration change.

Choosing the rate of H+ concentration change as the rate-determining variable is

especially appropriate because these results are used to predict the acid neutralization

potential of calcite in sulfate-rich solutions.

In order to determine the rate of H+ concentration change, the measured pH was

converted to H+ concentration using calibration curves made by adding known amounts

of HNO3 to Na2SO4 or NaNO3 solutions and measuring the pH of those solutions.

These activity versus concentration data were determined over the pH interval 1.5 to

3.5 for 42SONaM = 0.0, 0.1, 0.3, and 1.0 M and for

3NaNOM = 0.1, 0.3, and 1.0 M. The log

transform of the equation

+++ = HHHMa γ (4)

16

is

+++ +=HHH

Ma logloglog γ . (5)

Therefore, the +Halog versus +H

Mlog data were fit to an equation of the form

+++ +=HHH

Msa γlogloglog (6)

where s = slope and pHaH

−=+log . The coefficients for these fits are listed in Table

2.1. The activity coefficients for hydrogen ion calculated by this method are

significantly smaller than those predicted by the Debye-Hückel model.

Table 2.1. Coefficients for the equation +++ +=HHH

Msa γlogloglog correlating the

concentration of H+ to pH for sodium sulfate and sodium nitrate solutions

s log γH+ R2

0.0 0.98 -0.24 0.98

0.1 1.13 -0.39 0.98

0.3 1.01 -0.77 1.00

1.0 1.02 -0.99 1.00

0.1 1.00 -0.17 0.93

0.3 0.91 -0.29 0.98

1.0 0.84 -0.37 0.97

Conversion from semi-batch to ideal BR conditions

The calcite dissolution experiments were performed in semi-batch reactors

(Hill, 1977) where a 2 mL sample was removed from the solution at each sampling

time. This changed the ratio of surface area of the calcite to the volume of solution over

the course of the experiment. In order to adjust the concentration versus time data to

ideal batch reactor conditions (constant A/V), the number of moles H+ consumed over

42SONaM

3NaNOM

17

each sample interval was calculated from the volume of solution present in the reactor

multiplied by the change in the concentration of H+ over one sample interval

)( ++ ∆=HsH

MVn . (7)

The total number of moles of H+ consumed is the sum of the moles consumed over the

1 hour elapsed time for a batch experiment

∑∑ +++ ∆== )(, HsHtH

MVnn . (8)

This method was used to create a table of +Hn and t. Then +H

n at each time was divided

by the initial volume of solution in the reactor to give the concentration of H+ that

corresponds to an equivalent unsampled ideal batch reactor. Figure 2.3 shows the result

of +Hn versus time for a typical experiment.

Fig. 2.3. Amount of H+ consumed by reaction with calcite as a function of time for a typical experiment

(DHBy) with 0.3 M sodium sulfate and an initial pH of approximately 2.

18

Rate determination

The rate of change of H+ concentration was determined by numerical

differentiation (Pollard, 1977) of the ideal batch reactor +Hn versus time data. This

numerical differentiation method is based on the computation of the slope of a

polynomial arc fit through five evenly spaced data points. Although this method uses

five data points at the ends of the data set, the computed rates are less robust because

the slopes are not constrained by data beyond these endpoints. Because the sample

interval was changed from 2 minutes at the beginning of each experiment to 5 minutes

after 30 minutes there is a break in the data around 1800 seconds that produces some

additional scatter.

All of the computed rates are reported in Appendix 2.1. The rate for 1 m2 of

calcite in contact with 1 L of solution was calculated by dividing the differentiated +Hn

versus time data by the surface area of calcite, which was estimated to be 0.0075 m2 for

each 0.5 g sample.

Filtering the rate data

Numerical differentiation magnifies analytical errors leading to a few highly

unreliable results. These were removed from the data set by standard filtering methods.

All negative rates were discarded and Chauvenet's criterion (Taylor, 1982) was applied

to the remaining data during a step in the regression modeling to reject extreme

outliers. In this case Chauvenet's criterion was applied by analyzing the distribution of

residuals for the fit. For a normally distributed error, the probability that a point should

19

fall outside of plus or minus three standard deviations is 0.27%. According to

Chauvenet's criterion, if the number of expected measurements at least as bad as the

suspect measurement is less than 0.5 then the suspect measurement should be rejected.

There are between 99 and 412 H+ data points in each of the data sets and any datum

that fell outside of three standard deviations was rejected. Data and excluded data are

reported in Appendix 2.1.

Rate law and regressor variables

Multiple linear regression of the rates versus pH, log t,

I1/2,

4SOM ,4SOa ,

4HSOM ,4HSOa , extent of reaction, and gypsum saturation showed that

only pH and time had any significant effect on calcite dissolution rates. Therefore, the

general rate law that was selected as the best fit for the calcite dissolution rate data was

mn

Htkar +−= . After initial regression and rejection of non-significant variables, the log

r was regressed as a function of pH and log t for the two groups of experiments without

coatings and with gypsum coatings, respectively. Table 2.2 summarizes the values of

the coefficients from the regression models for each group of experimental results.

Table 2.2. Rate constants and reaction orders for the general rate law mn

Htkar +−=

Data set log k n m R2 # Data

no gypsum coatings -2.32(0.07) 0.76(0.02) - 0.71 412

gypsum coatings -1.96(0.27) - -0.53(0.09) 0.27 99

The results from 20 calcite BR dissolution experiments where no gypsum coatings

formed are shown in Figure 2.4(a). The model for the regression of this set of 412 data

20

shows that only pH has a significant effect on dissolution rates. Figure 2.4(b) shows the

results of the regression models of the seven experiments where gypsum coatings

formed on the surface of the calcite. These 99 data were regressed as a function of log t

because the regression model showed that pH had no significant effect on the

dissolution rates.

Fig. 2.4. Data (symbols) and linear regression of log r (mol/(m2·s) versus (a) pH or (b) log t for

experiments where (a) no gypsum coatings formed and (b) gypsum coatings developed. Regression

coefficients are reported in Table 2.2.

21

Discussion

Effect of hydrodynamics on rates

For rapidly dissolving solids, dissolution rates are commonly controlled by the

rate of transport of species to or from the surface. This transport rate will be some

function of the stirring rate (Levich, 1962). It is generally agreed that the rates of

calcite dissolution are limited by the transport of H+ to the surface of calcite at pH less

than 4 and 25ºC (Rickard and Sjoberg, 1983; Sjöberg and Rickard, 1983). Transport-

limited calcite dissolution rates have been studied using rotating disc experiments

(Sjöberg and Rickard, 1983; Alkattan et al., 1998).

The mixing conditions in a rotating disc experiment can be expressed using the

Reynolds number (Re), a dimensionless number that describes hydrodynamic

conditions in terms of inertial versus viscous forces. The Re is related to the rotational

velocity of a rotating disc by

υω /Re 2a= . (9)

where ω = 2π (rpm)/60 (Herman and White, 1985). Because Re and the rates of

calcite dissolution under transport-limited conditions are both related to the rotational

velocity of the disc, rate data for calcite dissolution should also be related to Re.

Transport-limited calcite dissolution rates where no coatings formed are

described by

n

Hkar +−= (10)

where k is some function of Re. Alkattan et al. (1998) performed rotating disc

22

experiments to measure calcite dissolution rates of Iceland spar calcite as a function of

pH. In their experiments they attached a calcite crystal with a highly polished surface

to a disc and rotated the disc in acid solutions of pH between –1 and 3. They also did

rotating disc experiments where they measured dissolution rates as a function of disc

rotation speed at pH = 1. These data show that calcite dissolution rate increases with

increasing disc rotation speed verifying that the rates were transport-limited.

Because transport-limited rates are a function of both pH and Re, the data sets

for rates as a function of pH and Re from this study and Alkattan et al. (1998) were

combined and fit by multiple linear regression to give

87.031.061.2 Re10 +

−−=H

ar . (11)

The measured rates from our study are slower than those of Alkattan et al.

(1998) because they were not stirred as vigorously. A normal approximation Wilcoxon

rank sum test was done using SAS, which showed that these two data sets are

statistically significantly different from each other to a 99.99% probability. Based on

equation (11), the Re for our experiments was estimated to be about 60 whereas the

experiments that Alkattan et al. (1998) performed were conducted at Re values up to

7000.

In a packed bed, Re is a function of the Darcy velocity and hydraulic radius

(Bear, 1972; Scheidegger, 1974)

υqd

=Re . (12)

Equations (11) and (12) were combined to predict the dissolution rates as a function of

pH, Darcy velocity and hydraulic radius in a porous medium or packed bed

23

87.0

31.0

61.210 +

−= −H

aqd

rυ

. (13)

Effect of sulfate on rates

The rates of calcite dissolution for the experiments where sulfate was present

but no coatings formed are slightly higher than those rates where there was no sulfate

in solution. This may be due to sulfate enhancing the transport of hydrogen ion to the

surface of calcite via the formation of bisulfate ion

H+ + SO42- = HSO4

-. pK = 1.99 (14)

Another reaction that could enhance dissolution rates is the formation of calcium

sulfate complexes

Ca2+ + SO42- = CaSO4

0. pK = -2.30 (14b)

Although reaction (14b) is a less likely explanation for dissolution that is limited by H+

transport to the surface, it would reduce the Ca2+ activity at the surface of calcite and

lead to greater calcite undersaturation. This reaction would also drive reaction (14) to

the left and liberate H+ near the calcite surface. However, linear regression of log r as a

function of 4SOM showed no statistically significant effect of sulfate on calcite

dissolution rates and a Wilcoxon rank sum test (SAS) indicates that sulfate-present

and sulfate-absent rates are not significantly different from each other.

Effect of gypsum coatings on rates

In this study, gypsum coatings formed on the surface of calcite grains (Fig. 2.2)

24

at low pH (≤ 2) and high sulfate concentrations (≥ 0.1 M). The rates of calcite

dissolution for these experiments decreased with time because the growing gypsum

layer rapidly reduced the rate of hydrogen ion transport to the calcite surface (Fig. 2.5).

Fig. 2.5. The measured (symbols) and predicted (line) calcite dissolution rates as a function of time for

experiment DHBff where gypsum coatings formed. The decrease in rates with time is attributed to a

growing armoring layer.

Fick's first law of diffusion describes this physical behavior (Crank, 1975)

x

dCDJ −= (15)

where, J, is the flux of hydrogen ion to surface and x

dC is the concentration gradient of

H+ between the bulk solution and the calcite surface. Assuming that the H+

concentration at the calcite surface is zero allows (15) to be written as

25

x

CDJ B−= . (16)

The gypsum layer thickness is related to the extent of reaction by the total number of

moles of Ca released, the fraction of total Ca reacted that reprecipitated as gypsum, the

porosity of the layer, the molar volume of gypsum, and the remaining surface area of

calcite assuming that the specific surface area is constant.

)1(

,

φ−=

R

mgypTCa

A

Vfnx (17)

The flux of H+ to the surface of calcite can be converted to the rate of release of Ca

from the surface using equation (1) so thatdt

dn

dt

dnHTCa +

−=2

1,. This relationship and

equations (16) and (17) can be combined to give an equation that describes the rate of

Ca release,

mgypTCa

RBTCa

Vfn

ADC

dt

dn

,

,

2

)1( φ−= (18)

that can be integrated to

∫∫−

=t

tmgyp

RB

n

TCaTCa dtVf

ADCdnn

TCa

0

,

2

)1(

0

,,

φ, (19)

This evaluates to

tVf

ADCn

mgyp

RBTCa ∆−

=2

)1(

2

2

, φ. (20)

Solving for nCa,T, (t0 = 0, t = t) gives

2/1

,

)1(t

Vf

ADCn

mgyp

RBTCa

−=

φ. (21)

26

If we define

mgyp

RB

Vf

ADCc

)1( φ−= (22)

then the total amount of Ca released from the dissolving calcite is

2/1

, ctn TCa = (23)

but this Ca is partly in solution and partly in reprecipitated gypsum

qypCasolCaTCa nnn ,,, += (24)

so equations (23) and (24) can be combined.

gypCasolCa nctn ,

2/1

, −= (25)

Because the amount of Ca in solution was measured, c can be determined empirically

from the nCa,sol versus t1/2 data (Table 2.3).

The diffusion coefficient of H+ through the pore spaces in the gypsum coating

was estimated by rearranging equation (22) and substituting in the appropriate values.

The fraction of the solid that is gypsum coating can be estimated by analyzing the solid

material remaining at the end of the experiments. A fraction of the remaining material

will be gypsum and the rest will be calcite. To determine a ratio of gypsum to calcite in

the reacted solids, 0.1 gram of a reacted sample was powdered and dissolved

completely in nitric acid and the SO4 and Ca concentrations was determined by IC and

AA analyses.

−

=

ical

solCaical

meas

gypn

nn

Ca

SOf

,

,,4 (26)

and

27

AR = ncal ,i

ncal,i − nCa,sol

ncal,i

1−

SO4

Ca

meas

FWcal( ) Asp( ) (27)

The porosity of in the gypsum layer was estimated to be 50% so solving for D in

equation (22) yields approximate diffusion coefficients for H+ in solution through pores

in the gypsum layer (Table 2.3) ranging from approximately 4×10-15 to 1×10-13 m2/s,

which is five to six orders of magnitude slower than H+ diffusion through seawater (Li

and Gregory, 1974). Some of this difference may be the result of the tortuosity of the

gypsum layer. Some may be the result of variations in exposed surface area of calcite

or porosity of gypsum, which were assumed to be constant. The diffusion coefficient is

more sensitive to changes in porosity.

Table 2.3. Predicted diffusion coefficients for H+ through the pore spaces of a gypsum coating with 50% porosity. SO4 and Ca concentrations give the ratio of Ca reprecipitated as gypsum.

Applications

The goal of this project was to identify the factors that must be considered to

create an efficient design for ALDs. Our experimental results demonstrated that ionic

strength, extent of reaction,4SOM ,

4SOa ,4HSOM ,

4HSOa , gypsum saturation, and calcite

saturation do not significantly affect the rate at which calcite can neutralize acidity. Our

investigations showed that this rate is a function of exposed surface area, pH, and

SAMPLE SO4 (ppm) Ca (ppm) f gyp AR (m2) CB (mol/m

3) c D (m

2/sec)

DHBz 203.9 1255 0.09 3.62x10-3 31.6 6.32x10

-51.21x10

-13

DHBx 96.2 1477 0.05 5.72x10-3 31.6 2.26x10

-55.57x10

-15

DHBv 92 1447 0.05 5.89x10-3 31.6 2.00x10

-54.25x10

-15

DHBw 148.7 1325 0.09 5.11x10-3 10.0 3.44x10

-57.40x10

-14

28

Reynolds number. The results also showed that the neutralization rates are rapidly

reduced by the growth of gypsum coatings, while other studies (Ziemkiewicz et al.,

1997; Cravotta and Trahan, 1999; Al et al., 2000; Hammarstrom et al., 2003) have

shown that iron and aluminum oxyhydroxide coatings also reduce neutralization rates.

To develop a conceptual understanding of the factors that affect the

neutralization effectiveness of ALDs we will consider the neutralization effectiveness

of an ideal packed bed of spherical calcite grains with 47% porosity and no coatings. If

we assume that ai ~ mi (Kirby and Cravotta, 2005), then the rates of H+ concentration

change are expressed by the differential rate law shown in Table 2.4.

Table 2.4. Governing equations for the plug flow reactor model.

Description Equation Reference

Differential rate law 87.0+

+

−==′H

H kmM

A

dt

dmr

Derived from this

study

Integrated rate law 187.0

1

187.0

0)187.0(+−+−

++−

−=+ mktM

Am

H

Rimstidt and

Newcomb (1993)

Rate constant as a

function of Re 31.061.2 Re10−=k

Based on data

from Alkattan et

al. (1998)

Re as a function of q and d in a porous

medium υqd

=Re Scheidegger (1974)

Hydraulic radius in a

porous medium

−=

φφ

13

1prd

Graton and Fraser

(1935)

Surface area of solid to

mass of solution ratio p

sp

r

V

M

A

1000

55.8=

Derived from

Graton and Fraser

(1935)

Residence time q

lt

φ=

Rimstidt and

Newcomb (1993)

This rate law can be recast in terms of Darcy velocity q and particle radius rp such that

87.069.031.031008.1 +

−−×=′Hp mrqr . The integrated form of this rate law, shown in Table

29

2.4, expresses the concentration of hydrogen ions in solution at a given time in terms of

M

A, Re, and the residence time of the solution as a function of the length of the

packed bed. The ALD is most effective when ktM

A

from the integrated rate law is

large (Table 2.4). Since

M

Ais a function of particle radius (Graton and Fraser, 1935)

and it is large when rp is small (Fig. 2.6(a)), then decreasing particle size will lead to

faster rates of neutralization. Residence time is a function of Darcy velocity and

porosity (Rimstidt and Newcomb, 1993) and becomes large when q is small (Fig.

2.6(b)) because decreasing Darcy velocity provides a longer time for reaction and

therefore a greater amount of neutralization. The effectiveness term, ktM

A

, can be

rewritten in terms of q and rp using the relationships given in Table 2.4 to give

69.04 )(1008.5 −−×=

pqrkt

M

A. Note that the overall neutralization effectiveness is

greatest when values of rp and q are small (Figs. 2.6(c) and (d)).

If we consider an ALD to be an ideal plug flow reactor (Hill, 1977) with a cross

section of 1 m2 and cubic-packed spherical grains of limestone, the integrated rate law

can be used to predict the amount of hydrogen ions in solution as a function of extent

of reaction or the length of the reactor. For example, if the influent hydrogen ion

concentration, m0, is 0.01 mol/kg (pH ≈ 2) then the concentration of hydrogen ion at

any distance (l) down the drain is

( ) 7.769.05 55.0)(106.6 +×−= −−+ lqrm pH

. (28)

30

Fig. 6. (a) A/M as a function of particle radius. (b) Residence time as a function of Darcy velocity. (c)

Effectiveness term, ((A/M)kt ), versus particle radius for a Darcy velocity of 0.01 m/s. (d) Effectiveness

term, ((A/M)kt ), versus Darcy velocity for a particle radius of 0.01m.

31

Figure 2.7 shows the effluent pH versus the length of the ALD for various Darcy

velocities and particle radii. Figure 2.7(a) shows that for a given particle size the

effectiveness of the reactor increases with decreased Darcy velocity or increased

detention time. Figure 2.7(b) shows that for a given Darcy velocity the effectiveness of

the ALD increases as the particle size decreases.

Fig. 2.7. Predicted pH versus reactor length for the integrated rate law model for a reactor with a 1 m2

cross-sectional area. This model does not consider the release of H+ by the conversion of carbonic acid

to bicarbonate. (a) pH versus length contoured in Darcy velocity for a bed packed with 0.01 m radius

calcite grains. (b) pH versus length contoured in particle radius for a Darcy velocity of 0.1 m/s.

32

However, this model does not take into account the dissociation of H2CO3

produced by equation (1) to make bicarbonate alkalinity as the pH rises.

H2CO3 = H+ + HCO3

- (29)

As the pH approaches pK1 for carbonic acid, the rate of H+ concentration change

decreases because hydrogen ion becomes available from the dissociation of H2CO3 so

there is actually more hydrogen ion available to react than predicted by equation (27).

The amount of hydrogen ion available in solution to react is given by

( ) ( ) ( )

2

5.04 1

2

11 +++

+

−′++−′±+−′= HrrHrH

H

TmKmTKmTKm (30)

This equation is derived in Appendix 2.2. This relationship along with the differential

rate law (Table 2.4) can be used to create a numerical model that takes the hydrogen

ion produced from H2CO3 dissociation into account. This model also predicts the

amount of bicarbonate alkalinity produced by calcite dissolution. The differential rate

law (Table 2.4) can be rewritten to predict the amount of H+ consumed over a time

interval ∆t where +Hm is the amount of hydrogen ion available to react from equation

(29)

∆mr =A

M

k∆tm

H +

0.87

. (31)

The effectiveness factor tkM

A∆

can be substituted into equation (30) to give

∆mr = 5.08 ×10−4 (qrp )

−0.69 mH +

0.87( )∆l (32)

where rm∆ is the amount of hydrogen ion reacted with calcite over the distance ∆l.

Figure 2.8(a) shows that neutralization occurs over shorter distances as the

33

Darcy velocity decreases for a bed packed with 0.01 m radius particles. This figure also

shows that the rate of pH change declines as the solution pH approaches pK1. This

decline in the rate of pH change is accompanied by the conversion of carbonic acid to

bicarbonate. Figures 2.8(b) and (d) show that the carbonate alkalinity increases as the

pH rises. Figure 2.8(c) shows that neutralization occurs over shorter distances with

decreasing grain size.

34

Fig. 2.8. pH as a function of reactor length predicted by the model that takes the conversion of carbonic

acid to bicarbonate (Appendix 2.2) into account. (a) pH versus length contoured in Darcy velocity for a

bed packed with 0.01 m radius calcite grains. (b) Alkalinity versus length contoured in Darcy velocity

for a bed packed with 0.01 m radius calcite grains. (c) pH versus length contoured in particle radius for a

Darcy velocity of 0.1 m/s. (d) Alkalinity versus length contoured in particle radius for a Darcy velocity

35

of 0.1 m/s.

These models provide a conceptual framework that can be used to understand

the relationship between various ALD design parameters. They clearly show that there

are trade offs in ALD design. Figures 2.6, 2.7 and 2.8 show that the effectiveness of

ALD’s increases with decreasing particle size and flow rates. However, as the particle

size is reduced, the hydraulic radius of the pores becomes small, increasing their

potential to plug. If the Darcy velocity is low then the ALD must have a very large

cross-sectional area in order to treat a sufficient amount of AMD. Choosing the best

combination of q and rp will require field-scale experiments to investigate

systematically these trade offs. Although some field work has already been done to

improve ALD design (Hedin et al., 1994; Ziemkiewicz et al., 1997; Cravotta and

Trahan, 1999; Al et al., 2000; Hammarstrom et al., 2003; Cravotta, 2003; Cravotta et

al., 2004) guidelines for their construction and maintenance are incomplete. Our results

provide a complementary tool to help interpret these field tests and improve guidelines.

The effectiveness of ALD’s is further reduced by the formation of coatings on

the calcite grains. These coatings block access of H+ to the calcite surface and reduce

the rate of neutralization. The formation of gypsum coatings can be affected by Darcy

velocity. The Ca2+ concentrations near the surface of rapidly dissolving calcite can

become high because the diffusion of Ca2+ away from the surface is slower than H+

transport to the surface (Li and Gregory, 1974). If the Ca2+ concentration near the

surface becomes high enough that the activity product of gypsum is exceeded, gypsum

will precipitate even if the bulk solution is undersaturated. Increasing the Darcy

velocity will decrease the boundary layer thickness and increase the rate of Ca2+

transport away from the surface. However, the epitaxial nucleation of gypsum onto

36

calcite makes the physical removal of coatings by flushing unlikely (Booth et al.,

1997). Therefore, increasing flow rates will have only a limited beneficial effect on

decreasing gypsum formation.

The best strategy to control gypsum coating formation is to keep the Ca-SO4

activity product below the Ksp for gypsum. This can be done by either reducing the

SO42- concentration by diluting the influent solutions or by reducing the Ca2+

concentrations by using a carbonate mineral with a lower Ca/CO3 ratio. Dilution of

influent waters will decrease both the SO42- and Ca2+ concentrations in the neutralized

AMD. This means that the ALD will be able to treat AMD solutions with higher SO42-

concentrations and/or lower pH without forming gypsum coatings (Fig. 2.1). Another

strategy to keep the Ca2+ concentration in solution low is to use dolomite rather than

calcite. Typically calcite-rich limestone is used in ALD because it dissolves faster than

dolomite (Busenberg and Plummer, 1982). Because dolomite releases only 1 mole of

Ca2+ for every 4 moles of H+ consumed, twice as many hydrogen ions can be

neutralized before the solution become gypsum saturated

CaMg(CO3)2 + 4H+ = Ca2+ + Mg2+ + 2H2CO3. (33)

Our results show that uncoated dolomite reacts faster than gypsum-coated calcite after

only 1 month of gypsum growth (Fig. 2.9). Thus for high sulfate and low pH AMD

where gypsum coatings might develop, dolomite may be a cost effective alternative to

limestone.

37

Fig. 2.9. Comparison of the rates of dolomite dissolution (Busenberg and Plummer, 1982) with the rates

of gypsum coated calcite dissolution (this study).

38

References

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40

Appendix 2.1

Data from calcite dissolution batch reactor experiments. Asterisks are negative rates and strikethroughs are

outliers that were deleted from the regression analyses. + denotes formation of gypsum coatings

DHBbb DHBz+ DHBx+

DHBv+

time (sec) Ca (ppm) pH log r Ca (ppm) pH log r Ca (ppm) pH log r Ca (ppm) pH log r

0 0.00 1.49 -2.596 0.00 1.52 * 0.00 1.41 -1.620 0.00 1.50 *

120 9.77 1.50 -3.269 78.55 1.52 -3.523 103.22 1.43 -2.483 86.02 1.49 *

240 16.29 1.51 -3.776 107.25 1.53 -3.295 158.18 1.44 -3.081 107.53 1.47 *

360 22.80 1.52 -3.603 169.18 1.54 -3.748 151.47 1.46 -2.762 123.66 1.46 *

480 29.32 1.53 -3.618 199.40 1.54 -3.767 179.62 1.47 -3.478 134.41 1.45 *

600 32.57 1.54 -3.667 228.10 1.55 -3.356 194.37 1.47 -3.396 142.47 1.44 *

720 42.35 1.55 -3.454 261.33 1.56 -3.406 201.07 1.48 -2.955 147.85 1.44 *

840 52.12 1.57 -3.488 282.48 1.57 -3.419 207.77 1.49 -3.332 153.23 1.43 *

960 58.63 1.58 -3.788 314.20 1.58 -3.433 210.46 1.49 * 158.60 1.43 -3.142

1080 68.40 1.60 -3.072 344.41 1.59 -3.447 207.77 1.49 -3.112 163.98 1.43 *

1200 81.43 1.62 -3.701 365.56 1.60 * 210.46 1.49 -3.137 172.04 1.42 *

1320 91.21 1.64 -3.932 401.81 1.61 -3.726 214.48 1.5 -4.058 174.73 1.42 -3.549

1440 97.72 1.66 -3.792 413.90 1.62 -4.258 227.88 1.5 * 182.80 1.42 *

1560 104.23 1.69 -3.731 468.28 1.62 -4.202 239.95 1.5 * 185.48 1.41 *

1680 114.01 1.72 -3.801 468.28 1.63 -4.269 234.58 1.5 * 185.48 1.41 -4.248

1800 120.52 1.75 -3.699 498.49 1.63 -3.957 237.27 1.5 -3.724 190.86 1.41 -4.259

2100 146.58 1.80 -3.633 513.60 1.65 -3.579 246.65 1.51 -3.724 204.30 1.41 *

2400 162.87 1.85 -3.713 581.57 1.67 -3.775 252.01 1.51 * 212.37 1.40 *

2700 169.38 1.90 -3.726 604.23 1.68 -4.010 261.39 1.51 * 220.43 1.40 *

3000 175.90 1.96 -3.748 611.78 1.69 -3.983 266.76 1.51 * 231.18 1.39 *

3300 192.18 2.02 -3.812 611.78 1.70 -3.997 278.82 1.51 -18.289 241.94 1.39 -3.560

3600 205.21 2.09 -3.732 664.65 1.71 -4.012 288.20 1.51 * 252.69 1.39 *

DHBcc DHBaa DHBy DHBw+


0 0.00 1.99 -3.064 0.00 1.92 -2.775 0.00 1.99 -2.492 0.00 1.88 *

120 9.06 2.00 -3.874 11.40 1.93 -3.282 28.13 2.00 -3.303 40.32 1.88 -3.117

240 13.60 2.01 -4.017 19.54 1.95 -3.474 59.38 2.01 -3.445 61.83 1.89 -3.481

360 21.15 2.03 -3.941 27.69 1.97 -3.598 78.13 2.03 -3.369 87.37 1.89 -3.583

480 28.70 2.04 -3.950 37.46 1.98 -3.646 100.00 2.04 -3.422 110.22 1.90 -3.142

600 37.76 2.06 -4.305 47.23 2.00 -3.368 134.38 2.06 -3.271 141.13 1.91 -3.596

720 51.36 2.06 -3.773 57.00 2.03 -3.404 143.75 2.08 -3.315 153.23 1.91 -3.539

840 61.93 2.11 -3.668 66.78 2.05 -3.580 184.38 2.10 -3.323 166.67 1.92 -3.606

960 64.95 2.12 * 79.80 2.07 -3.498 190.63 2.12 -3.419 181.45 1.92 -4.484

1080 67.98 2.13 -3.456 91.21 2.10 -3.312 209.38 2.13 * 189.52 1.94 -2.534

1200 75.53 2.16 -4.034 104.23 2.13 -3.634 228.13 2.14 * 202.96 1.93 -2.826

1320 80.06 2.18 -4.912 110.75 2.16 -4.082 243.75 2.15 -3.795 219.09 1.95 *

1440 89.12 2.19 -4.456 104.23 2.18 -3.989 259.38 2.17 -3.926 233.87 1.94 *

1560 98.19 2.22 -4.261 117.26 2.21 -4.007 281.25 2.18 -4.187 244.62 1.95 -3.922

1680 105.74 2.25 -4.354 135.18 2.23 -4.110 287.50 2.19 -4.273 254.03 1.95 -4.016

1800 111.78 2.28 -4.194 133.55 2.26 -3.765 309.38 2.20 -3.789 271.51 1.96 -4.082

2100 129.91 2.34 -4.106 159.61 2.33 -3.689 343.75 2.24 -3.581 291.67 1.96 -3.703

2400 143.50 2.40 -4.160 175.90 2.39 -3.825 365.63 2.28 -3.718 307.80 1.98 -3.731

2700 154.08 2.47 -4.190 190.55 2.45 -3.831 393.75 2.31 -3.848 314.52 1.98 -3.808

3000 166.16 2.54 -4.311 195.44 2.52 -3.929 421.88 2.34 -3.786 337.37 2.00 -3.550

3300 172.21 2.60 -4.427 206.84 2.57 -4.131 446.88 2.38 -3.762 348.12 2.01 -4.131

3600 179.76 2.67 -4.290 218.24 2.63 -3.829 468.75 2.41 -4.510 364.25 2.02 -3.413

0.0 M Na2SO4 0.1 M Na2SO4 0.3 M Na2SO4 1.0 M Na2SO4


41

DHBs DHBp DHBm DHBj


0 0.00 2.54 -3.179 0.00 2.51 * 0.00 2.50 -2.753 0.00 2.49 *

120 1.95 2.57 -3.957 4.17 2.51 -4.397 23.74 2.52 -3.448 13.77 2.49 -3.951

240 3.91 2.59 -4.611 6.94 2.52 -4.169 33.52 2.53 * 42.70 2.50 -3.724

360 4.89 2.62 -4.168 8.33 2.53 -4.622 50.28 2.54 -3.374 57.85 2.51 -4.178

480 6.51 2.66 -4.223 9.72 2.53 -4.564 62.85 2.62 -3.476 73.00 2.51 -4.121

600 7.82 2.69 -4.282 12.50 2.54 -4.558 82.40 2.61 * 89.53 2.52 -4.115

720 9.12 2.73 -4.257 16.67 2.54 -4.582 104.75 2.59 * 104.68 2.52 -4.217

840 10.42 2.77 -4.192 15.28 2.55 -4.576 111.73 2.60 -3.875 118.46 2.53 -3.807

960 13.36 2.83 -4.178 18.06 2.55 * 122.91 2.62 -3.893 133.61 2.54 -3.899

1080 13.36 2.86 * 20.83 2.56 -3.789 135.47 2.63 * 148.76 2.55 -3.765

1200 14.66 2.90 -4.618 25.00 2.56 * 145.25 2.64 -4.587 168.04 2.57 -4.295

1320 15.96 2.95 -4.907 27.78 2.57 -4.574 149.44 2.65 -4.601 181.82 2.58 -4.310

1440 17.26 2.99 -4.902 29.17 2.58 -5.106 167.60 2.66 -4.616 192.84 2.59 -4.324

1560 17.26 3.04 -4.937 31.94 2.58 -5.126 175.98 2.67 -4.631 201.10 2.60 -4.339

1680 19.22 3.08 -5.089 33.33 2.59 -4.748 187.15 2.68 -4.758 214.88 2.61 -4.389

1800 19.54 3.12 -4.932 37.50 2.60 -4.593 187.15 2.69 -4.262 220.39 2.62 -4.197

2100 20.85 3.20 -4.855 41.67 2.62 -4.468 206.70 2.73 -4.123 239.67 2.64 -4.073

2400 21.82 3.28 -4.970 50.00 2.64 -4.510 220.67 2.76 -4.278 269.97 2.66 -4.118

2700 23.45 3.36 -5.031 58.33 2.66 -4.550 245.81 2.79 -4.298 292.01 2.68 -4.142

3000 23.45 3.45 -5.097 63.89 2.68 -4.450 243.02 2.82 -4.333 311.29 2.70 -4.167

3300 25.08 3.54 -5.196 72.22 2.71 -4.393 254.19 2.85 -4.368 325.07 2.72 -4.193

3600 24.76 3.64 -5.183 80.56 2.73 * 270.95 2.88 -4.403 341.60 2.74 -4.218

DHBt DHBq DHBn DHBk


0 0.00 3.02 -3.846 0.00 2.99 -3.340 0.00 2.95 -3.486 0.00 2.98 -3.204

120 1.88 3.04 -4.620 4.17 3.01 -4.188 8.38 2.96 -4.160 8.24 2.99 -4.333

240 3.13 3.05 -6.074 6.94 3.02 -4.836 15.36 2.97 -4.666 10.99 2.99 -5.110

360 2.19 3.06 -5.007 9.72 3.04 -4.379 20.95 2.98 -4.528 13.74 3.00 -4.579

480 2.81 3.08 -4.884 12.50 3.06 -4.404 26.54 2.99 -4.313 19.23 3.00 -4.681

600 3.13 3.10 -4.912 13.89 3.08 -4.587 32.12 3.01 -4.348 21.98 3.01 -4.271

720 4.06 3.12 -5.097 16.67 3.09 -4.635 37.71 3.02 -4.378 28.85 3.02 -4.322

840 5.00 3.13 -5.148 19.44 3.11 -4.345 43.30 3.04 -4.409 31.59 3.03 -4.371

960 5.63 3.15 -4.865 22.22 3.14 -4.365 46.09 3.05 -4.573 38.46 3.04 -4.257

1080 6.56 3.18 -4.870 23.61 3.15 * 54.47 3.08 -3.801 42.58 3.06 -3.878

1200 7.81 3.21 -5.496 26.39 3.17 -5.847 57.26 3.10 -4.741 43.96 3.07 -4.491

1320 8.75 3.23 -5.413 29.17 3.19 -4.785 64.25 3.12 -4.766 50.82 3.08 -5.016

1440 9.38 3.26 -5.264 31.94 3.22 -4.881 68.44 3.14 -4.790 56.32 3.09 -4.623

1560 10.00 3.30 -5.310 31.94 3.24 -5.058 72.63 3.16 -4.815 60.44 3.11 -4.636

1680 10.94 3.33 -5.497 34.72 3.26 -4.988 79.61 3.18 -4.873 64.56 3.12 -4.977

1800 11.56 3.36 -5.224 36.11 3.29 -4.722 81.01 3.20 -4.696 67.31 3.13 -4.578

2100 14.06 3.44 -5.074 40.28 3.35 -4.629 87.99 3.24 -4.587 76.92 3.16 -4.392

2400 15.63 3.53 -5.168 43.06 3.41 -4.753 92.18 3.28 -4.653 85.16 3.19 -4.565

2700 16.25 3.62 -5.251 47.22 3.46 -4.812 99.16 3.32 -4.705 93.41 3.21 -4.499

3000 16.88 3.72 -5.308 50.00 3.52 -4.818 103.35 3.36 -4.689 94.78 3.25 -4.439

3300 18.44 3.83 -5.395 54.17 3.58 -4.873 106.15 3.41 -4.686 108.52 3.28 -4.664

3600 19.69 3.94 -5.561 56.94 3.65 -4.787 115.92 3.45 -5.208 116.76 3.31 -4.407



42

DHBu DHBr DHBo DHBl


0 0.00 3.48 -4.052 0.00 3.47 -3.760 0.00 3.49 * 0.00 3.48 -3.784

120 0.31 3.52 -4.712 2.15 3.49 -4.623 3.41 3.49 -5.116 2.91 3.49 -4.458

240 0.31 3.56 -5.393 3.49 3.50 -5.214 3.98 3.50 -4.967 4.36 3.50 -4.964

360 0.31 3.59 -5.270 3.49 3.52 -4.940 3.98 3.51 -5.018 5.81 3.51 -4.758

480 0.31 3.62 -5.182 5.91 3.53 -4.991 5.97 3.52 -5.032 5.81 3.52 -5.177

600 0.31 3.66 -5.534 5.38 3.55 -4.823 6.53 3.53 -5.081 8.72 3.52 -5.198

720 0.31 3.66 -5.610 6.18 3.57 -5.024 9.09 3.54 -4.867 10.17 3.53 -4.788

840 0.63 3.70 -5.210 7.26 3.58 -5.049 7.95 3.56 -4.901 11.63 3.54 -4.838

960 1.56 3.74 -5.346 8.06 3.60 -4.828 9.66 3.57 -5.200 11.63 3.55 -4.853

1080 1.56 3.78 -5.208 8.87 3.62 -5.354 10.51 3.59 -4.484 14.53 3.56 -4.868

1200 1.88 3.82 -5.676 9.41 3.65 -6.954 10.80 3.60 -4.960 15.99 3.57 -4.703

1320 1.88 3.87 -5.750 10.48 3.67 -5.199 11.93 3.62 -5.586 17.44 3.59 -5.330

1440 1.88 3.92 -5.795 11.29 3.70 -5.318 13.64 3.63 -5.431 18.90 3.60 -5.174

1560 1.88 3.97 -5.912 12.37 3.72 -5.354 14.20 3.65 -5.281 20.35 3.62 -5.008

1680 2.19 4.01 -5.962 13.17 3.75 -5.410 15.63 3.67 -5.392 23.26 3.64 -5.259

1800 2.19 4.07 -5.685 13.71 3.77 -5.220 15.63 3.69 -5.056 24.71 3.65 -5.013

2100 2.19 4.21 -5.648 14.78 3.83 -5.050 19.89 3.75 -4.949 27.62 3.69 -4.788

2400 2.19 4.34 -5.836 16.67 3.89 -5.142 21.31 3.80 -5.007 30.52 3.73 -4.925

2700 2.50 4.48 -5.929 18.01 3.95 -5.160 22.73 3.87 -4.989 34.88 3.76 -5.056

3000 2.81 4.64 -6.074 19.62 4.02 -5.226 25.57 3.94 -5.044 36.34 3.79 -4.993

3300 3.13 4.79 -6.266 19.89 4.08 -5.328 28.41 4.02 -5.088 39.24 3.83 -4.969

3600 3.44 4.98 -6.160 20.70 4.16 -5.090 29.83 4.09 -5.427 42.15 3.86 -5.716

DHBgg DHBee+

DHBff+

DHBdd+


0 0.00 1.54 -3.701 0.00 1.43 * 0.00 1.52 -1.983 0.00 1.56 *

120 22.04 1.54 * 23.60 1.43 -3.396 151.52 1.53 -3.112 73.33 1.56 -2.833

240 38.57 1.54 -3.925 41.30 1.44 -3.246 132.23 1.53 -3.889 93.33 1.57 -3.102

360 55.10 1.55 -3.597 70.80 1.45 -3.295 99.17 1.54 -3.358 104.00 1.57 *

480 68.87 1.56 -3.648 79.65 1.46 -3.309 121.21 1.54 -3.383 112.00 1.57 *

600 85.40 1.57 -3.630 103.24 1.47 -3.322 126.72 1.55 -3.377 120.00 1.57 *

720 93.66 1.58 -4.140 129.79 1.48 -3.371 134.99 1.55 -3.402 130.67 1.57 *

840 126.72 1.58 -3.696 176.99 1.49 -3.154 154.27 1.56 -3.396 557.33 1.57 *

960 148.76 1.60 -3.298 179.94 1.51 -3.046 165.29 1.56 * 140.00 1.57 -18.794

1080 151.52 1.61 * 209.44 1.52 * 162.53 1.57 -2.610 148.00 1.57 -18.493

1200 176.31 1.62 -4.136 244.84 1.54 -3.507 179.06 1.57 * 162.67 1.56 -20.095

1320 195.59 1.63 -4.151 258.11 1.55 -4.034 181.82 1.57 -3.474 160.00 1.56 *

1440 206.61 1.64 -4.166 250.74 1.56 -3.638 223.14 1.58 -3.837 168.00 1.56 *

1560 258.95 1.65 -4.216 294.99 1.58 -3.672 203.86 1.58 -3.864 160.00 1.56 *

1680 269.97 1.66 -4.046 361.36 1.59 -3.747 206.61 1.59 -3.857 176.00 1.56 *

1800 250.69 1.68 -3.812 346.61 1.61 -3.481 225.90 1.59 -3.961 184.00 1.56 *

2100 292.01 1.71 -3.767 390.86 1.64 -3.433 236.91 1.60 -3.520 208.00 1.56 -4.412

2400 548.21 1.74 -3.816 442.48 1.67 -3.488 247.93 1.61 -3.974 218.67 1.56 *

2700 347.11 1.77 -3.852 471.98 1.70 -3.437 261.71 1.61 -3.919 226.67 1.55 *

3000 385.67 1.80 -3.899 508.85 1.74 -3.477 269.97 1.62 -3.849 840.00 1.55 -4.412

3300 410.47 1.83 -3.893 538.35 1.77 -3.619 275.48 1.62 * 246.67 1.55 *

3600 443.53 1.87 -3.732 567.85 1.81 -3.284 283.75 1.62 -3.580 266.67 1.55 -3.935

1.0 M Na2SO4


0.0 M Na2SO4 0.1 M Na2SO4 0.3 M Na2SO4

43

DHBIa DHBIb DHBIc

time (sec) Ca (ppm) pH log r Ca (ppm) pH log r Ca (ppm) pH log r

0 0.00 1.92 -2.588 0.00 2.12 -2.696 0.00 1.79 -2.328

120 43.48 1.95 -3.339 21.74 2.16 -3.401 12.58 1.83 -3.120

240 68.32 1.97 -4.189 32.61 2.19 -4.424 25.16 1.85 -4.510

360 80.75 1.99 -3.802 47.10 2.21 -3.970 31.45 1.87 -3.723

480 99.38 2.01 -3.986 65.22 2.24 -3.992 47.17 1.89 -3.630

600 118.01 2.02 -4.013 76.09 2.26 -4.034 56.60 1.92 -3.658

720 133.54 2.04 -3.862 86.96 2.29 -4.055 40.88 1.94 -3.842

840 158.39 2.06 -3.906 94.20 2.31 -4.111 78.62 1.96 -3.727

960 173.91 2.08 -3.931 108.70 2.34 -3.984 91.19 1.99 -3.675

1080 186.34 2.10 -3.955 123.19 2.37 -4.347 94.34 2.01 *

1200 204.97 2.12 * 166.67 2.40 -4.669 103.77 2.04 -4.339

1320 214.29 2.13 -4.453 141.30 2.43 -4.510 106.92 2.06 -4.368

1440 232.92 2.15 -4.398 141.30 2.46 -4.685 113.21 2.08 -4.396

1560 254.66 2.17 -4.442 155.80 2.48 -4.711 122.64 2.10 -4.425

1680 263.98 2.19 -4.500 163.04 2.51 -4.757 132.08 2.12 -4.486

1800 270.19 2.21 -4.334 137.68 2.53 -4.646 132.08 2.14 -4.324

2100 304.35 2.25 -4.164 177.54 2.58 -4.500 144.65 2.18 -4.167

2400 313.66 2.30 -4.227 170.29 2.63 -4.586 150.94 2.23 -4.192

2700 338.51 2.34 -4.348 210.14 2.68 -4.646 169.81 2.28 -4.261

3000 350.93 2.38 -4.382 210.14 2.73 -4.712 182.39 2.33 -4.385

3300 378.88 2.42 -4.427 224.64 2.78 -4.748 182.39 2.37 -4.476

3600 388.20 2.46 -4.472 289.86 2.84 -4.676 182.39 2.43 -4.172

0.1 M NaNO3 0.3 M NaNO3 1.0 M NaNO3

44

Appendix 2.2

Calculation of +Hm and −

3HCOm in solution as a function of extent of reaction

The purpose of this section is to derive a relationship that predicts the pH of an

acidic solution that has reacted with calcite and consumed mr moles of H+. For this

model if we assume that there in no initial dissolved CO2 that contributes to acidity

then the amount of H+ in the solution is controlled by two competing reactions.

Dissolution of 1 mole of calcite consumes 2 moles of H+ and produces 1 mole of

carbonic acid.

CaCO3 (cal) + 2H+ = Ca2+ + H2CO3 (1)

In addition as the pH rises toward the first dissociation constant of carbonic acid some

of the H2CO3 dissociates and releases hydrogen ion back into solution.

H2CO3 = H+ + HCO3

- (2)

The apparent equilibrium constant for the dissociation of carbonic acid is

32

3

1

COH

HCOH

m

mmK

−+

=′ (3)

The stoichiometry of reaction (1) requires that the total amount of carbonate in solution

is

rCO mT2

13= (4)

but the carbonate is distributed between carbonic acid and bicarbonate so

−+=3323 HCOCOHCO mmT (5)

Equation (3) can be rearranged and substituted into equation (5) to express the total

45

dissolved carbonate concentration in terms of bicarbonate concentration

−

−+

+′

=3

3

3 HCO

HCOH

CO mK

mmT (6)

+

′=

+

− 133 K

mmT H

HCOCO (7)

+

′

=+

−

11

3

3

K

m

Tm

H

CO

HCO (8)

so the bicarbonate concentration is

( )11 3

3 Km

TKm

H

CO

HCO ′+

′=

+

− (9)

The amount of hydrogen ion remaining in solution after mr moles of H+ have reacted

with calcite and some of the carbonic acid has dissociated to release additional

hydrogen ions is:

−++ +−=3HCOrHH

mmTm (10)

substituting equation (9) into (10) gives

( )11 3

Km

TKmTm

H

CO

rHH ′+

′+−=

+

++ (11)

and then substituting equation (3) into (11) gives

1

15.0

Km

KmmTm

H

rrHH ′+

′+−=

+

++ (12)

If we let rHmTC −= +1 and 12 5.0 KmC r

′= then

46

1

21

Km

CCm

H

H ′+=−

+

+ (13)

and

( )( ) 211 CKmCmHH

=′+− ++ (14)

which is a quadratic equation in terms of +Hm

( ) 021111

2 =−′−−′+ ++ CKCmCKmHH

(15)

that can be solved using the quadratic formula where

( )+

+

−′=

+−′=

=

Hr

rH

TmKc

mTKb

a

5.0

1

1

1

to give

( ) ( ) ( )

2

5.04 1

2

11 +++

+

−′++−′±+−′= HrrHrH

H

TmKmTKmTKm (16)

Once +Hm is known the bicarbonate concentration can be found from equation (9).

47

Chapter 3

Limiting pyrite oxidation and AMD generation by iron oxyhydroxide coatings

Abstract

Acid mine drainage (AMD) can be reduced or ultimately prevented if alkalinity is

added to mine wastes faster than acid is produced by pyrite oxidation. When excess

alkalinity is added to oxidizing pyrite, the pyrite will eventually be replaced by iron

oxyhydroxides. A natural analogue of this process is the formation of limonite

pseudomorphs after pyrite. Fast rates of alkalinity addition encourage the formation of

the iron oxyhydroxide coatings that block dissolved oxygen transport to the pyrite and

reduce the rate acid generation by pyrite oxidation so that ‘runaway’ AMD does not

develop. ‘Runaway’ AMD occurs at low pH mainly because pyrite oxidation is

dominated by dissolved Fe(III) oxidation, which is extremely fast at low pH. Also at

low pH microbes becomes available that rapidly regenerate Fe(III) by Fe(II) oxidation.

We measured the rate of pyrite oxidation in solutions with high pH and alkalinity

where iron oxyhydoxide coatings developed on pyrite. Experiments were performed in

H2O2 solutions with added bicarbonate alkalinity. The experiments conducted

measured oxidation rates that were considered to represent two stages of iron

oxyhydroxide coating formation, (1) the initial coating development and (2) the

densification and inward propagation of the coating. The data supports the idea that

during the first stage of coating formation of a thin, highly porous and permeable layer

of colloidal iron oxyhydroxide particles attach to the pyrite surface. The data also

48

supports the idea that during the second stage of coating formation there is a transition

from reaction-limited to diffusion-limited rates as coatings grow inward and become

thicker and denser.

Our experimental results and those reported in the literature show when iron

oxyhydroxide coatings grow on pyrite the rate of pyrite oxidation declines as a function

of t-1/2. A general model based on Fick’s first law and our results predicts how long it

takes for coatings to become thick enough to effectively reduce alkalinity demand

required to neutralize acid produced by pyrite oxidation so that AMD does not occur.

This model predicts the rate of hydrogen ion production over

time 2/1)( )1(20002 −

−=+ t

Vf

ADmr

mppti

isol

H ν

φ and provides a useful guide to determine the

amount of alkalinity that must be added to mine wastes to avoid AMD development.

Notation

Symbol Definition, units

A surface area, m2

Asp specific surface area, m2/g

b surface area constant, unitless

Ci concentration of species i, mol/m3

Di diffusion coefficient, m2/s

Ir groundwater infiltration rate, m/s

Ji flux, mol/(m2s)

ki rate constant

mi concentration of species i, molal

49

Mi concentration of species i, molar

ni amount of species i, mol

rf flow rate, kg/s (1 kg H2O ~ 0.001 m3)

ri specific rate of reaction of species i, mol/(m2s)

ri′ apparent rate of reaction of species i, mol/s

t time, s

tR response time, s

VR volume of reactor, m3

Vm molar volume, m3/mol

x thickness of coating, m

φ porosity, unitless ratio from 0 to 1

Introduction

Acid mine drainage (AMD) occurs when acid is generated by sulfide mineral

oxidation faster than it is neutralized by the surroundings. Because of its abundance,

pyrite is a dominant source of acidity. In low pH AMD, Fe(III) is the most important

oxidant of pyrite (Williamson and Rimstidt, 1994) (py-Fe(III) reaction in Table 3.1)

because Fe(III) is rapidly regenerated from Fe(II) by microbes (Williamson et al.,

2006). These rates are very fast and facilitate ‘runaway’ AMD. However, at higher pH

(> 4), Fe(III) solubility is so low that dissolved oxygen (DO) is the main oxidant

(Williamson and Rimstidt, 1994) (py-DO reaction in Table 3.1) and pyrite oxidation

rates by DO are much slower than Fe(III) oxidation rates (Williamson et al., 2006). If

50

pyrite oxidation by DO produces hydrogen ions slow enough that the pH is neutralized

by alkalinity from the surroundings then the pH will remain high, iron released from

the pyrite will oxidize and precipitate locally as iron oxyhydroxides, and runaway

AMD will not occur. Therefore, the problem of controlling AMD reduces to finding

some combination of methods to increase the rate of alkalinity delivery to the pyrite

surfaces while decreasing the rate of acid production by pyrite oxidation.

Much can be learned about how to control AMD by considering the natural

formation of limonite pseudomorphs after pyrite (Fig. 3.1(a)) where pyrite has oxidized

but acidic conditions did not develop. These natural analogues are typically found in

limestone where large amounts of bicarbonate ions are available to neutralize acid.

51

TABLE 3.1. Empirical rate laws for important chemical reactions discussed in this paper. For cases where the rate laws were expressed in terms of molar

concentrations at ~25 degrees Celcius, it was assumed that M ≈ m. We assume that AFO (Fe(OH)3(s)) rapidly converts to ferrihydrite (fh). The rate laws are referred to in the text in terms of the most important reactants, which are shown in bold.

Reaction 2FeSr (mol/m2sec) pH Source

py-H2O2

FeS2 + 7H2O2 → Fe2+ + 2SO42- + 2H+ + 6H2O

93.082.5

22

2 10OH

Mdt

dM FeS −−= 1-4 McKibben & Barnes (1986)

py-DO FeS2 + 7/2 O2 + H2O → Fe2+ + 2SO4

2- + 2H+ 11.0

5.019.8102

+

−−=H

DOFeS

m

m

dt

dm 2-10

Williamson & Rimstidt (1994)

py-Fe(III)

FeS2 + 14Fe3+ + 8H2O → 15Fe2+ + 2SO4

2- + 16H+ 32.047.0

)(

3.0

)(58.8102

+

−−=HIIIFe

IIFeFeS

mm

m

dt

dm 0.5-3

Williamson & Rimstidt (1994)

Fe(II)-H2O2 Fe2+ + 0.5H2O2 + H

+ → Fe3+ + H2O

+

−=H

OHIIFeIIFe

m

mmk

dt

dm22)(

2

)(

log k2 = 11.72 – 2.14I1/2 + 1.38I

6-8 Millero (1989)

Fe(II)-DO

Fe2+ + 1/4 O2 + H+ → Fe3+ + 1/2H2O 2

)(96.12)(10

+

−−=H

DOIIFeIIFe

m

mm

dt

dm 4-8 Stumm (1961)

Fe(III)-Fe(OH)3(s)

FeD + FeT →AFO + nH+

FeD – dissolved inorganic Fe(III), FeT – dissolved and precipitated inorganic Fe(III), AFO – amorphous iron oxyhydroxide (Fe(OH)3)

TD FeFef

OHFeMMk

dt

dM=3)(

6-9 Ninh Pham et al.

(2006)

fh-goe Fe5O3(OH)9 (fh) → 5FeOOH (goe) + 2H2O

@ T=21˚C 55.15 )3384(1041 −×− −

−= teα α is the extent of reaction (0-1)

6-8 Yee et al. (2006)

Fe(II)-fh

5Fe2+ + 5/4 O2 + 7H2O → Fe5O3(OH)9 (fh) + 4H+

DOsorbedIIFeIIFe

IIFemmm

dt

dm)()(

3.7)(10−=

6.8-7.0 Park & Dempsey

(2005)

52

Figure 3.1. (a) Cross-section of a limonite pseudomorph from Bedford Co., VA that shows a porous

center containing a small amount of unreacted pyrite surrounded by a dense outer coating. (b)

Comparison of the reaction-limited pyrite oxidation rate by dissolved oxygen for the reaction py-DO in

Table 3.1 (DO ~9 ppm) in air saturated solutions with the reaction-limited pyrite oxidation rates for

reaction py-H2O2 in Table 3.1 for 0.3 m H2O2 solutions used in our experiments (solid lines). The dashed

lines compare the oxidation rate of Fe(II)-DO in air saturated solutions (DO ~ 9 ppm) with the oxidation

rate of Fe(II)-H2O2 in 0.3 m H2O2. The Fe(II) concentration was set at5101 −× molal.

dense outer coating

pyrite porosity

1 cm

a

-15

-10

-5

0

5

10

15

4 5 6 7 8 9 10

py-H2O2

py-DO

Fe(II)-H2O2

Fe(II)-DO

b

pH

10-15

10-10

10-5

100

105

1010

1015

r, m

ol/(m

2s)

53

In nature, under high pH conditions, abiotic oxidation of Fe(II) (Stumm and Lee, 1961)

(reaction Fe(II)-DO in Table 3.1) is much faster than pyrite oxidation by dissolved

oxygen (Williamson and Rimstidt, 1994) (reaction py-DO in Table 3.1) as shown in

Fig. 3.1(b) so that Fe(II) released from the pyrite quickly oxidizes to Fe(III). Since

Fe(III) has low solubility at near neutral pH it quickly precipitates as a ferric iron

oxyhydroxide coating on the pyrite before it is transported away from the surface. This

contrasts with ‘runway’ AMD conditions below pH of 4 where Fe(III) is soluble and

migrates away from pyrite so the physical and chemical kinetic conditions do not allow

the formation of limonite pseudomorphs. In the presence of bicarbonate alkalinity,

hydrogen ion is neutralized to produce water and carbon dioxide so that the overall

reaction is

FeS2(py) + 3.75O2 + 4HCO3- = Fe(OH)3(s) + 2SO4

2- + 0.5H2O + 4CO2. (1)

This reaction does not produce hydrogen ions so the pH is not affected and Fe(III)

rapidly precipitates as iron oxyhydroxide coatings by reaction Fe(III)-Fe(OH)3(s) in

Table 3.1 (Ninh Pham et al., 2006). The coating ultimately converts to goethite because

the transformation rate of poorly crystalline iron oxyhydroxide to goethite is fast in the

presence of ferrous iron (Yee et al., 2006) (reaction fh-goe in Table 3.1). This means

that there is an approximately 1 to 1 volume replacement of pyrite (23.94 cm3/mol) by

goethite (20.82 cm3/mol) creating a pseudomorph with only about 13% porosity.

Additional pore filling by the oxidation of Fe(II) diffusing out followed by the

precipitation of Fe(III) in the near neutral solutions in pores of the outer coating creates

a dense outer rim. This texture is commonly observed in limonite pseudomorphs (Fig.

3.1(a)) and suggests that as coatings become denser and thicker they become a very

54

effective barrier to DO transport. This allows pyrite in the interior of the pseudomorph

to persist, unreacted for long periods of time even though the exterior is exposed to

oxidizing conditions. Thus limonite pseudomorphs after pyrite demonstrate that iron

oxyhydoxide coatings on pyrite can reduce the rate of pyrite oxidation and acid

generation so that ‘runaway’ AMD does not develop.

Based on the foregoing discussion a reasonable strategy to control AMD is to coat

the pyrite grains with a substance that is a barrier to oxygen transport. A number of

types of coatings have been proposed including ferric phosphate (Evangelou, 1995),

phospho-silicates (Fytas and Evangelou, 1998; Fytas et al., 1999; Fytas and Bousquet,

2002), ferric hydroxide-silica (Zhang and Evangelou, 1998), phospholipids (Kargbo,

2004), and iron-8 hydroxyquinoline (Lan, 2002). These coatings have been shown to

reduce oxidation rates in the laboratory. However, they all require the addition of

relatively expensive reagents. In addition, most of these reagents do not specifically

target the pyrite so that excess reagent is required to effectively react with the pyrite

along with the surrounding minerals. In contrast Nicholson et al. (1990) have shown

experimentally that the addition of relatively inexpensive bicarbonate alkalinity to

oxidizing pyrite produces iron oxyhydroxide coatings that slow pyrite oxidation rates.

In addition, Zhang and Evangelou (1996) reported iron oxyhydroxide coatings that

were formed on pyrite in solutions buffered at pH of 6 by sodium acetate reduced the

rate of pyrite oxidation by hydrogen peroxide.

Our approach was to investigate the rate of pyrite oxidation at pH between 6 and 9

and high alkalinity conditions where iron oxyhydoxide overgrowths develop on pyrite

by processes analogous to the formation of limonite pseudomorphs. Hydrogen peroxide

55

and sodium bicarbonate were used in our laboratory simulations to establish the

principles that control the stages of coating development. Hydrogen peroxide was used

as the oxidant because pyrite oxidation by oxygen is very slow and requires

substantially longer experiments (Nicholson et al., 1990). This is a reasonable

approach because the rate of Fe(II) oxidation is greater than pyrite oxidation for both

hydrogen peroxide (McKibben and Barnes, 1986; Millero and Sotolongo, 1989)

(reactions Fe(II)-H2O2 and py-H2O2 in Table 3.1) and oxygen (Stumm and Lee, 1961;

Williamson and Rimstidt, 1994) (reactions Fe(II)-DO and py-DO in Table 3.1) (Fig.

3.1(b)) above pH 6 so that the relative rates of the various reaction steps are the same

for both oxidants. Zhang and Evangelou (1996) conducted similar coating experiments

under comparable conditions as those done in this study except they used precoated

pyrite grains whereas we have investigated the oxidation behavior as coatings form.

Thus, our experiments span the entire process of coating formation between Zhang and

Evangelou (1996) and Nicholson et al. (1990), which allowed us to develop a model

that predicts how coatings form, and how long it takes for coatings to become thick

enough to effectively reduce alkalinity demand required to neutralize acid produced by

pyrite oxidation. To do this we determined the diffusion coefficient of oxygen through

the pore spaces in the iron oxyhydroxide coating and used that value to calculate the

rate of acid production by coated pyrite as a function of time. With this model we can

predict how fast alkalinity must be delivered to the pyrite to avoid development of

‘runaway’ AMD.

56

Methods and Materials

Pyrite used in the experiments was the same Peruvian pyrite used in the

experiments done by Jerz and Rimstidt (2004) and Williamson and Rimstidt (1994).

The pyrite was prepared in the manner described by Jerz and Rimstidt (2004) where the

pyrite was crushed and sieved to recover a grain size between 250 and 420 micrometers

with an average estimated specific surface area (Foust et al., 1980) of 1.13×10-2 m2/g.

The grains were sonicated in a 0.1 m HCl solution then rinsed with ethyl alcohol until

the supernatant was clear and the grains showed no visible oxidation product layer.

Grains were dried and stored in glass vials until used.

A mixture of 0.3 m hydrogen peroxide and 0.1 m sodium bicarbonate solution was

used as an oxidant and a source of alkalinity to maintain a pH of approximately 8.5 to

induce iron oxyhydroxide coatings.

Experiments were conducted by circulating this solution through a mixed flow

reactor (MFR) (Fig. 3.2). In the reactor two plastic mesh screens with openings of

approximately 80 µm held 5 g of pyrite in a packed bed. Samples were collected at

evenly spaced time intervals of 594 seconds using a fraction collector (Fig. 3.2). Tygon

1/16 inch (1.6 mm) inner diameter tubing was used to carry solutions. The mass of the

solution in the reactor during the experiment was 2.43 ± 0.2 g. Experiments were run

for 24 hours at 23 ± 1 °C and atmospheric 2OP . The flow rate was determined by

weighing each sample container before and after sample collection. The average flow

rate was approximately 0.5 g/sec.

57

Figure 3.2. Schematic design of the mixed flow reactor experiment. A 4 L carboy held 2 L of solution

that was circulated using a peristaltic pump through a reactor with an inner diameter of 2 cm and a

height of 1.3 cm. The reactor held 5 g of pyrite and 2.43 g of solution.

Iron and sulfate concentrations were measured for each sample collected. Samples

were acidified allowing us to measure total iron concentration using an atomic

absorption spectrophotometer (AA). Sulfate concentrations were determined from

another set of filtered samples using an ion chromatograph (IC). To confirm that all

sulfur was oxidized to sulfate we compared total sulfur concentration values from

several ICP-AES sample analyses with sulfate concentration values measured by IC

analyses. Concentration values measured from both analytical techniques were

comparable so we assumed that all sulfur was in the form of sulfate. Reacted grains

were observed and characterized using a scanning electron microscope (SEM) and

visible light microscopy.

Iron that precipitated in the reactor over the course of the experiment was

recovered by leaching the entire reactor by immersing it in 500 mL of a 0.04 M

NH2OH •HCl in 25% (v/v) CH3COOH solution and heated to 100˚C for 1 hour. The

Feed

solution

Reactor

Peristaltic

pump

Fraction collector

Pyrite

58

concentration of iron in the leachate was measured using AA.

The volume of solution in the reactor was small so that the time it took to reach

steady state was on the order of minutes. The reactor response time,f

RR

r

Vt = , is

approximately 3 minutes such that after 5tR has elapsed the effluent solution has

achieved 99% of the steady state concentration. Since steady state was reached before

the second sample was collected the rates were not corrected for non-steady state

conditions.

Rates of release of both iron and sulfate were calculated (mol/(m2s)). The rate

of species release was calculated from the solution flow rate multiplied by the change

in species concentration

( )mrr fi ∆=′ . (2)

The rates of pyrite oxidation by hydrogen peroxide and oxygen were calculated from

our experimental data as well as from those of Zhang and Evangelou (1996) and

Nicholson et al. (1990) from the rate of sulfate release based on the stoichiometry of

the reactions py-H2O2 and py-DO (Table 3.1). These rates would equal the release rate

of iron to solution if no iron reprecipitated as coatings. Using sulfate, as the rate-

determining variable is reasonable since sulfur is oxidized to sulfate at the pyrite

surface very fast (Williamson and Rimstidt, 1994). The rate of sulfate release was also

used to determine the rate of pyrite destruction over time because some of the iron re-

precipitated as ferric oxyhydroxide coatings.

The change in pyrite surface area over the course of the experiment was estimated

using the relationship

59

3/23/2

mVbnA = (3)

The b constant was calculated from the initial estimated pyrite surface area, A, the

initial amount of moles of pyrite reacted and the molar volume of pyrite for our

experiments to be 590.2. This constant was then used to calculate the change in surface

area as a function of the amount of pyrite reacted. The rates were adjusted to account

for this change in surface area.

To compare our experimental results with the other data sets (Nicholson et al.,

1990; Zhang and Evangelou, 1996) we adjusted all data to normalize the units, surface

area, and the effect of different reactor conditions on the measured rates. Zhang and

Evangelou (1996) performed similar experiments as ours except they precoated their

pyrite grains to produce iron oxyhydroxide coatings using the same solution that they

used to measure the effect of coatings on pyrite oxidation rates. This solution had a

composition of 0.145 M H2O2, 0.1 M NaCl and 0.01 M NaOAc adjusted to pH of 6.

We calculated rates by numerical differentiation (Pollard, 1977) of their iron

concentration (mol) versus time data (Appendix 3.1(b)). Their sample interval was

1800 seconds. They used 0.05 g samples of ~ 0.1µm grain size pyrite that we estimated

to have a specific surface area (Foust et al., 1980) of 6 m2/g. Their rates were adjusted

to account for the reduced surface area caused by the dissolution of about 5% of the

pyrite over the course of their experiment leading to a small but significant effect on

rates. The b constant was estimated to be 68800.

Nicholson et al. (1990) reported rate data for pyrite oxidation by DO for average

grains sizes of 76, 108 and 215 µm where iron oxyhydroxide coatings formed. The DO

concentration was maintained by equilibrium with air (21% O2 and 1 atm total

60

pressure) and the solution was buffered by 0.005 N NaHCO3 to a pH ~ 8.5. Each

experiment had a one-year duration and used a 20 g sample of pyrite. We converted

their rates from (mol/g-pyrite/h×109) to mol/(m2s) using estimated specific surfaces

areas of 3.25×10-2, 2.15×10-2 and 1.20×10-2 m2/g, respectively (Appendix 3.1(c)). The

b constants were estimated to be 2693, 1784, and 996 respectively. The rates at the

beginning of their experiments increased with time because the reactor had not reached

steady state conditions. The calculated time to reach steady state was approximately

4.25 days so these data were discarded from our analysis.

Results

Our experimental results were used to determine the rate of pyrite oxidation by

H2O2 where iron oxyhydroxide coatings formed and limited the H2O2 transport to the

surface. The rates of pyrite oxidation from our experiments are reported in Appendix

3.1(a). Duplicate EXP J was conducted at the same experimental conditions as EXP K,

however, data was not collected over night during the 24 hr run so this data was not

included in the model even though initial and final measured rates are comparable to

those of EXP K. Rates that have been extracted from Zhang and Evangelou (1996) and

Nicholson et al. (1990) are listed with the same units as our rates in Appendix 3.1(b)

and 3.1(c). All rate data are displayed in Figures 3.3, 3.4, and 3.5. The r versus t-1/2

graph of our data (Fig. 3.3) shows a linear decrease in rates that is attributed to the

development of an initial iron oxyhydroxide coating. The transition from a shallow

slope of r versus t-1/2 to a steeper one is interpreted as a result of the coating becoming

a more effective barrier to hydrogen peroxide transport to the pyrite surface.

61

4.5E-074.5×10-7 2 20

1

1.5E-07

2.5E-07

3.5E-07

0.003 0.013 0.023 0.033

1.5×10-7

2.5×10-7

3.5×10-7

10

Figure 3.3. Graph of r versus t-1/2 data from our MFR experiment. The slope of the line changed from

shallow 72/16 1042.3t1019.2r −−− ×+×= R2 = 0.58 to steep 82/15 1031.5t1072.7r −−− ×−×= R2 = 0.88

during the course of the experiment indicating that the coating became a more effective barrier to H2O2

transport. The chemical reaction-limited rate calculated for py-H2O2 from Table 3.1 for a 0.3 m H2O2

solution used in our experiments is 4.57×10-7 mol/(m2s). Inset of measured rate versus time data.

The oxidation rate for pyrite precoated with iron oxyhydroxide (Zhang and Evangelou,

1996) by hydrogen peroxide also showed a linear decrease as a function of t-1/2 (Fig.

3.4), however, because the initial stage of coating formation had already occurred there

was no shallow slope of the r versus t-1/2 to represent the initial coating formation stage.

The r versus t-1/2 fits for pyrite oxidation by dissolved oxygen (Nicholson et al., 1990)

Elapsed time (hours)

t-1/2

r, m

ol/(m

2s) Stage 1

Stage 2

1.5E-07

2.5E-07

3.5E-07

4.5E-07

0 50000 100000

1.5×10-7

2.5×10-7

3.5×10-7

4.5×10-7

r, m

ol/(m

2s)

time (s)

62

also showed similar linear relationships for each of the data sets (Fig. 3.5). We

attributed the initial increase in rates with time (up to 11 days) for their experiments to

non-steady state conditions in the reactor and did not use these data in the r versus t-1/2

Figure 3.4. Graph of r versus t-1/2 from the Zhang and Evangelou (1996) data. The equation for the line is

112/17 1047.3t1060.2r −−− ×+×= R2 = 0.87. The chemical reaction-limited rate of pyrite oxidation

calculated for py-H2O2 from Table 3.1 by the 0.145 m H2O2 solution used in their experiments, 2.19×10-7

mol/(m2s), is about 2 orders of magnitude faster than their fastest rate because the coating of iron

oxyhydroxide that formed on the pyrite surface by their pretreatment was a significant barrier to H2O2

transport to the pyrite surface. Inset shows rate versus time data.

0.0E+00

1.0E-09

2.0E-09

3.0E-09

4.0E-09

5.0E-09

6.0E-09

0.00410.00910.01410.0191

1×10-9

10

1

2

2×10-9

3×10-9

4×10-9

5×10-9

6×10-9

0

Elapsed time

r, m

ol/(m

2s)

t-1/2

0.E+00

2.E-09

4.E-09

0 20000 40000 60000

time (s)

r, m

ol/(m

2s)

0

2×10-9

4×10-9

63

0.0E+00

4.0E-10

8.0E-10

1.2E-09

0.000150.000350.000550.000750.00095

0

8×10-10

1.2×10-9

4×10-10

50

100

300

Elapsed time (days) r, m

ol/(m

2s)

t-1/2

a

0

4E-10

8E-10

1E-09

0.E+00 2.E+07 4.E+07

10-9.4

10-9.1

10-8.9

107.3 10

7.6 0

0 r,

mol/(m

2s)

time (s)

64

0.0E+00

4.0E-10

8.0E-10

1.2E-09

0.000150.000650.00115

0

8×10-10

1.2×10-9

4×10-10

10 100

300

Elapsed time (days)

r, m

ol/(m

2s)

t-1/2

0

4E-10

8E-10

1.2E-09

0.E+00 2.E+07 4.E+07

10-9.4

10-9.1

10-8.9

107.3 10

7.6 0

0

r, m

ol/(m

2s)

time (s)

b

65

Figure 3.5(a-c). Graphs of r versus t-1/2 from the Nicholson et al. (1990) data for (a) 76, (b) 108 and (c)

215 micrometer grain sizes, respectively. The equations of the lines are (a) 102/17 1037.11091.8 −−− ×+×= tr R2 = 0.65, (b) 102/17 1042.31026.7 −−− ×+×= tr R2 = 0.65, and (c)

112/16 105.91007.1 −−− ×+×= tr R2 = 0.74. The chemical reaction-limited rate of pyrite oxidation

calculated for py-DO from Table 1 is 9.13×10-10 mol/(m2s). Insets show rate versus time data.

0.0E+00

4.0E-10

8.0E-10

1.2E-09

1.6E-09

0.000150.000650.00115

0

1.2×10-10

1.6×10-9

8×10-10

10

100 300

Elapsed time (days)

r, m

ol/(m

2s)

t-1/2

4×10-10

0

4E-10

8E-10

1.2E-09

1.6E-09

0.E+00 2.E+07 4.E+07

10-9.4

10-9.1

10-8.9

107.3

107.6 0

0

r, m

ol/(m

2s)

time (s)

10-8.8

c

66

fits. We will show that these linear relationships between r and t-1/2 can be explained by

the accumulation of a layer of iron oxyhydroxide on the pyrite surface.

In our experiments some of the iron reprecipitated as coatings on the pyrite surface

and some reprecipitated on the reactor walls and tubing. The rate of sulfate release was

used to determine the rate of pyrite oxidation and that information was used to

determine the total amount of iron released )( )(calFen . This iron was quickly oxidized to

Fe(III) and either reprecipitated onto the pyrite grains )( )( pyFen , precipitated onto the

reactor walls and tubing )( )(wallsFen , or carried out of the reactor by solution )( )(solFen so

that

)()()()( solFereactFepypptFecalFe nnnn ++= − . (4)

The rate of pyrite oxidation and the rate that iron was carried out of the reactor by the

solution were both measured (Appendix 3.1(a)) and the total amount of iron released

from pyrite oxidation and the amount of iron released to solution was determined from

these rates to be 2.5×10-4 and 1.5×10-4 moles, respectively. The difference between

these amounts is the total amount of iron that was reprecipitated onto either the reactor

and tubing or the pyrite. This was about 40% of the total iron released. Of this, 37% of

the precipitated iron was recovered by leaching the reactor and tubing (9.12×10-5

moles) and we infer that the rest (3%) had precipitated on the pyrite surfaces.

Coating thicknesses were calculated from the fraction of iron reprecipitated on the

pyrite surface, the molar volume of the coating, the surface area of pyrite, and the

porosity of the coating

67

)1( φ−=

A

Vfnx

mpptFe . (5)

We estimated the coating thickness as a function of time for all of the experiments

assuming that in each case only 3% of the iron released reprecipitated as a coating (fppt

= 0.03), the coatings had 10% porosity (φ = 0.1), and the coatings consisted of goethite.

These thickness values are tabulated in Appendix 3.1(a-c).

Discussion

In our conceptual model iron oxyhydroxide coating formation on oxidizing pyrite

occurs in two stages: (1) the initial coating development and (2) the densification and

inward propagation of the coating (Fig. 3.6). Our data supports the idea that in the first

stage of coating formation a thin, highly porous and permeable layer of colloidal iron

oxyhydroxide particles develops on the pyrite surface (Calderia et al. ,2003). Until it

grows thicker and denser this layer provides a weak barrier to DO transport to the

pyrite surface as is shown by the line with a relatively low slope in Fig. 3.3. In the

second stage, iron oxyhydroxide forms in the pores of this layer so that the layer

becomes a more effective barrier to DO transport. This causes the pyrite oxidation rate

to decrease more rapidly with time, which is interpreted to be represented by the line

with the steeper slope in Fig. 3.3.

The first stage of coating formation begins when pyrite is oxidized by the py-DO

reaction. H+ produced by this reaction is neutralized by HCO3- near the pyrite surface

so that the pH remains unchanged. At near neutral pH, Fe(II) rapidly oxidizes to Fe(III)

(Fig. 3.1(b)). Because Fe(III) has low solubility at neutral pH, it rapidly precipitates to

form a colloid of poorly crystalline iron oxyhydroxide by the Fe(III)-Fe(OH)3(s)

68

STAGE 1

O2

Fe(II)+O2

+ + +

Fe(III)+HCO3- 1a

1b Fe(OH)3 colloid

Reaction-limited oxidation rates

Colloid formation and attachment

STAGE 2

O2

Fe(II)+O2

Fe(III)+HCO3-

overgrowth

2a

2b

porosity

Colloid cementation and overgrowth

Diffusion-limited rates

inward growth of coating

reaction. We assume that this initially precipitated iron oxyhydroxide quickly converts

to ferrihydrite (fh) (Caldeira, 2003) and we have used fh in all subsequent reactions.

Figure 3.6. Schematic diagram showing the steps leading to the replacement of pyrite by goethite. Stage

1a and b show the initial formation of a porous and permeable iron oxyhydroxide coating by the

formation and attachment of colloidal iron oxyhydroxide. Stage 2 shows the densification and thickening

of the coating leading to the transition from reaction-limited to diffusion-limited rates.

H+ produced by this reaction is also neutralized by HCO3-. Because the point of zero

charge (PZC) for the iron oxyhydroxide colloid is between pH 8 and 9 (Schick, 2001)

this colloid has a very slight positive charge and the pyrite, which has a PZC near pH

69

1.4 (Bebie et al., 1998) has a strong negative charge at a pH of about 8 so some of the

iron oxyhydroxide colloid is attracted to and attaches to the surface forming a thin,

porous and permeable layer (Stage 1b in Fig. 3.6). During this initial stage it is

assumed that the pyrite oxidation rate is at first reaction-limited and because the colloid

layer is composed of particles, it is porous and permeable making it a relatively

ineffective barrier to DO transport. This results in mixed kinetics where there is a

transition from a reaction-limited to a diffusion-limited rate (Stage 2a in Fig. 3.6). This

initial stage of coating formation was also observed under similar conditions by

Calderia et al. (2003).

In the second stage of coating development the reactions from the initial stage

continue while the coating becomes denser and thicker (Fig. 3.6). Once the transition to

diffusion-limited rates occurs, Fe(II) that is released from the pyrite core diffuses

outward. The Fe(II) encounters DO diffusing inward so it oxidizes to Fe(III) and

precipitates as iron oxyhydroxides. This decreases the porosity of the outer rim and

further lowers the rate of DO transport inward. In the presence of Fe(II) the initially

precipitated poorly crystalline iron oxyhydroxide (fh) rapidly transforms to goethite

(Yee et al., 2006), which persists because goethite is the stable iron oxyhydroxide

phase under these conditions. Once the conditions of Stage 2b (Fig. 3.6) are

established, pyrite oxidation rates decline more rapidly with time, as the coating grows

both denser and thicker. This process leads to the characteristic linear relationship of r

versus t-1/2 shown in Figures 3.3, 3.4, and 3.5.

Graphs of r versus t-1/2 all show that pyrite oxidation rates decreased over time

because the growing coating reduced the rate of oxidant transport to the pyrite surface.

70

We fit the experimental data for coating formation to an equation of this form because

a relationship between r versus t-1/2 can be derived from Fick’s first law of diffusion

x

CDJ i

i

∆= . (6)

From this relationship we can also determine a diffusion coefficient, Di, for the oxidant

through the iron oxyhydroxide coating where C∆ is the difference in the concentration

of the oxidant (mol/m3) between the bulk solution and the pyrite surface, iJ , is the flux

of the oxidant to the pyrite surface and x is the effective coating thickness. The

concentration, C∆ , is defined as

)(1000 )()( sfcsol mmC −=∆ (7)

where 1000 is a conversion factor that recasts the molal concentrations (∆C) into units

of mol/m3. We can reasonably assume that C∆ approaches m(sol) as m(sfc) becomes small

and that C∆ becomes nearly constant as soon as a dense coating develops.

The flux of oxidant, Ji, to the surface of pyrite can be converted to the rate of

release of Fe from the surface using 2

1FeS

oxid

i

Fe rdt

dn

dt

dn=−=

ν, where, iν , is the

stoichiometric coefficient that relates the rate of oxidant consumption to Fe release

from the reactions

FeS2 + 7.5H2O2 = Fe3+ + 2SO4

2- + 7H2O + H+ so 5.7

22=OHν (8)

and

FeS2 + 3.75O2 + 0.5H2O = Fe3+ + 2SO4

2- + H+ so 75.3=DOν . (9)

A general model that describes the decrease in the rate of pyrite oxidation over time as

71

a coating forms can be developed by combining these relationships and substituting in

2FeSii rJ ν= , C∆ ≈ m(sol), and equation (5) for x into equation (6), to give

mpptFei

isolFeFeS

Vfn

ADm

dt

dn

dt

dn

ν

φ)1(1000 )(2−

== (10)

which can be rearranged and integrated

∫∫

−=

t

tmppti

isol

n

FeFe dtVf

ADmdnn

Fe

0

)1(1000 )(

0ν

φ. (11)

If 0=Fen when t = 0,

tVf

ADmn

mppti

isolFe

ν

φ)1(1000

2

)(2 −= . (12)

and solving for Fen gives

2/1)( )1(2000t

Vf

ADmn

mppti

isol

Fe

−=

ν

φ, (13)

which can be simplified by defining

mppti

isol

Vf

ADmc

ν

φ)1(2000 )( −= (14)

so the total amount of Fe released from pyrite at time, t, is

2/1ctnFe = . (15)

The time derivative of this equation yields the rate of pyrite oxidation as a function of

time,

2/1)( )1(2000

2

12

−

−= t

Vf

ADmr

mppti

isol

FeS ν

φ. (16)

Therefore we expect that because of the growth of the iron oxyhydroxide coatings, the

72

rate of pyrite oxidation will decline as a function of t-1/2. The slope of the linear

regression fit of r versus t-1/2 is ½ c so that we can solve for the diffusion coefficient

from the relationship

−=

mppti

isol

Vf

ADmc

ν

φ)1(2000

2

1

2

1 )( (17)

to find

2

)( )1(2000

1c

Am

VfD

sol

mppti

i φ

ν

−= . (18)

Using values from the slopes of the lines in Figures 3.3, 3.4, and 3.5 and substituting in

the appropriate values for the constants into equation (18) yields diffusion coefficients

for hydrogen peroxide and DO through a goethite coating. The diffusion coefficients

for hydrogen peroxide were determined from our experimental data to be 3.6×10-15

m2/s and 1.7×10-20 m2/s for the denser coatings from Zhang and Evangelou’s (1996)

experiments. These values are much lower than 1.4×10-9 m2/s, the diffusion coefficient

of hydrogen peroxide in aqueous solution (Stewart, 2003). Similarly, the diffusion

coefficients for oxygen calculated from the Nicholson et al. data were 2.38×10-17,

2.36×10-17, and 9.04×10-17 m2/s for 76, 108, 215 µm grain sizes, respectively, which is

much lower than 2.0×10-9 m2/s, the diffusion coefficient of DO through water (Han and

Bartels, 1996). Nicholson et al. (1990) assumed different values for fppt and φ and

reported slightly higher values of 3.19×10-16, 3.64×10-16, and 2.17×10-16 m2/s for 76,

108, 215 µm grain sizes, respectively. In any case, we can conclude the diffusion

coefficients of both hydrogen peroxide and DO in iron oxyhydroxide coatings are

lower than in water by more than five orders of magnitude. This means that if coatings

73

form they will drastically limit pyrite oxidation rates.

Equation (18) shows that the porosity of the coating and the fraction of iron

reprecipitated as coatings affects the magnitude of the calculated diffusion coefficient.

The diffusion coefficient for the initial stage of coating formation in our experiments

was calculated to be lower (7.21×10-19 m2/s) than during the second stage of coating

formation partially because we did not account for the high initial porosity of the

coating in the model. Also if we assume a greater fraction of iron reprecipitated on the

pyrite as coatings in stage 2 then the diffusion coefficient for that stage will appear

greater. For example the diffusion coefficient increases by one order of magnitude for

every 10 order of magnitude increase in the fraction of iron reprecipitated as coatings.

The conditions where the rates of the governing reactions favor iron oxyhydroxide

coating formation on pyrite can be mapped out in a kinetic predominance diagram

using the empirical rate laws in Table 3.1. In order for coatings to form on pyrite the

rate of iron oxidation and precipitation must be greater than the rate of pyrite oxidation

so that Fe(II) oxidizes on or near the pyrite surface and does not escape to solution

before it precipitates. Based on the empirical rate laws in Table 3.1 these conditions are

met when pH, DO concentration and iron concentration fall within a certain range. To

find this range we set the rate laws for the reactions of interest equal to each other and

solved for the iron concentration as a function of pH for solutions with a DO

concentration in equilibrium with air. These relationships determine the location of the

lines that separate the fields of the predominant species that should accumulate (Fig.

3.7). Note that Figure 3.7 is not a thermodynamic phase diagram but rather it shows the

reaction products that accumulate at various iron and pH conditions because of the

74

-12

-10

-8

-6

-4

6.5 7.5 8.5 9.5

Fe5O3(OH)9 (fh)

Fe(III) (aq) Fe(II) (aq)

1

2

3

10-12

10-10

10-8

10-6

10-4

pH

mFe

relative rates of iron production and consumption. This diagram was constructed by

first assuming that Fe(II) is constantly being produced by the py-DO reaction (Table

3.1) where the DO concentration is 2.7×10-4 m (air saturation). As long as the Fe(II)

concentration and pH lie in the field labeled Fe(II), Fe(II) is produced by the py-DO

reaction faster than it is consumed by any other reaction so Fe(II) accumulates.

Figure 3.7. Graph showing the predominance fields for kinetically favored species as a function of total

iron concentration and pH. Lines 1, 2 and 3 separating these fields were calculated using the rate laws in

Table 3.1 by solving for iron concentration as a function of pH (see text for explanation).

However, for a given pH, once the Fe(II) concentration rises to the level of either line 1

or 3 (Fig. 3.7), Fe(II) is converted to either Fe(III)(aq) or ferrihydrite as fast as it is

produced by pyrite oxidation and the Fe(II) concentration becomes constant. The

75

equation for line 1 (Fig. 3.7) distinguishes between the conditions where the rate of

Fe(II) oxidation (Fe(II)-DO reaction) predominates over the rate of pyrite oxidation

(py-DO reaction) and was determined from the empirical rate laws in Table 3.1 by

setting

2

)(96.12

11.0

5.019.8 1010

+

−− −=−+ H

DOIIFe

H

DO

m

mm

m

m. (19)

and solving for )( IIFem as a function of pH where DOm = 2.7×10-4 m

89.155.6

)( 10 +=HIIFe mm . (20)

Line 2 separates the conditions where the rate of iron oxyhydroxide precipitation

(reaction Fe(III)-Fe(OH)3(s) in Table 3.1) predominates over the rate of Fe(II)

oxidation (reaction Fe(II)-DO in Table 3.1) and was determined by setting

TD FeFef

H

DOIIFemmk

m

mm=−

+

−2

)(96.1210 . (21)

and then solving for total iron, TFem , as a function of pH, where DOm is 2.7×10-4 m,

DFem is the solubility of Fe(III) for ferrihydrite and )( IIFem is fixed by equation (20) so

that

D

T

FefH

DOIIFe

Femkm

mmm

2

)(

963.1210

+

−

= . (22)

The values from Pham et al. (2006) were used for the rate constant, kf, as a function of

pH between 6 and 9.5. The concentration of dissolved Fe(III), FeDm , as a function of

pH for ferrihydrite was estimated from the solubility curves in Langmuir (1997) and

substituted into equation (22) to obtain line 2 in Figure 3.7. Line 3 (Fig. 3.7)

differentiates between the conditions where the rate of iron oxyhydroxide precipitation

76

by reaction Fe(II)-fh (Park and Dempsey, 2005) predominates over the rate of Fe(II)

production by reaction py-DO. This line was determined by setting

11.0

5.019.8

)()(

3.7 1010

+

−

=H

DODOsorbedIIFeIIFe

m

mmmm (23)

and solving for

11.0

)(

5.0

49.15

)(

10

+

−

=HsorbedIIFeDO

IIFemmm

m . (24)

This reaction is dependent on the amount of iron sorbed, sorbedIIFem )( , to the surface of

pyrite. We used a value of 2×10-3 M to plot line 3 shown in Figure 3.7. This diagram

shows that the Fe(II) concentration at the surface of the pyrite must accumulate to the

levels indicated by lines 1 or 3 before any significant amounts of Fe(III) are produced

and the total iron concentration must exceed the amounts indicated by lines 1 and 2

before significant amounts of fh will form. Such levels might not be achieved if

flowing solutions sweep the dissolved iron away from the pyrite surface. This would

lower the fraction of iron precipitated on the pyrite surface, fppt, in stage 1 of coating

formation.

We could extend this diagram (Fig. 3.7) to lower pH, however, because the

solubility of fh increases very rapidly below pH of 6, coatings are unlikely to form

unless iron concentrations are extraordinarily high.

The effectiveness of coatings for reducing pyrite oxidation rates depends on the

properties of the coating. Ostwalds' step rule predicts that the more soluble amorphous

iron oxyhydroxides will precipitate first and then convert to poorly crystalline

ferrihydrite. Then, goethite, which is the most stable phase, will grow at the expense of

77

ferrihydrite. The rate of transition to goethite at high pH depends upon the ferrous iron

concentration (Yee et al., 2006). In low pH AMD, Fe(II) is rapidly oxidized to ferric

iron by microbes. Similarly, in the hydrogen peroxide experiments ferrous iron is

oxidized very rapidly. However, DO oxidation of Fe(II) is much slower so that a

significant amount of Fe(II) is likely to exist in the pores of the coating, which will

enhance the rate of the ferrihydrite to goethite transformation by reaction Fe(OH)3-goe.

Powder X-ray diffraction verified that the mineralogy of the ‘limonite’ pseudomorphs

after pyrite (Fig. 3.1) was entirely goethite.

Applications

To assess the efficacy of iron oxyhydroxide coatings as a means to control pyrite

oxidation rates we need a model that compares the rate of H+ generation by coated

pyrite grains with the rate at which alkalinity must be delivered to the pyrite in order to

maintain coating stability. Our conceptual model assumes that the initial stage (Stage 1,

Fig. 3.6) of coating development is so fast compared to the long-term coating behavior

that it can be ignored. At pH > 3.2, abiotic oxidation of Fe(II) and iron oxyhydroxide

precipitation is much faster than pyrite oxidation so pyrite oxidation is the rate limiting

reaction (Williamson et al., 2006). When sufficient bicarbonate alkalinity exists, pyrite

oxidation produces iron oxyhydroxide coatings (equation 1). We used our experimental

results in combination with the results of Zhang and Evangelou (1996) and Nicholson

et al. (1990) to develop a general diffusion model that describes the rate at which

coated pyrite is oxidized as a function time as coatings grow. This model predicts the

rate at which hydrogen ion must be neutralized in order to keep the pH high enough to

78

stabilize the coatings. We can use this information to find the rate at which alkalinity

must be added to a mine waste pile to maintain neutral to slightly alkaline conditions,

which leads to coating formation on the pyrite grains.

To provide an example of how much bicarbonate alkalinity addition is

necessary to maintain coating generation, we investigated the following scenario. We

considered a 1 m3 volume of mine waste at the surface of a mine waste pile with a 1 m2

cross-sectional area and 1 m depth. We assume that this mine waste consisted of coarse

sand containing 10% pyrite and 1 kg of solution in contact with 1 m2 of exposed pyrite

surface area. This is equated to saturated conditions.

Because the rate of pyrite oxidation is stoichiometrically related to the rate of

hydrogen ion production by the overall reaction

FeS2 + 3.75O2 + 3.5H2O = Fe(OH)3 + 2SO42- + 4H+ (25)

We combined our model for the rate of pyrite oxidation for pyrite grains with a

growing iron oxyhydroxide coating (equation (16)) with the stoichiometry of (25) to

find the rate of H+ generation

2/1)( )1(20002 −

−=+ t

Vf

ADmr

mppti

isol

H ν

φ . (26)

We can plot this rate as a function of time (Fig. 3.8) using a model system where the

DO concentration, m(sol) , is 2.7×10-4 m (air saturated water), the diffusion coefficient,

DOD , is 1×10-17 m2/s, the porosity of the coating was set at 0.1, 2Oν , from equation (25)

is 3.75, the fraction of iron that precipitated as coatings, fppt, as measured from our

experiments is 0.03 and Vm (goethite) is 2.02×10-5 m3/mol. A layer of iron

oxyhydroxide will form on the pyrite grains as long as the solution remains alkaline so

79

-12

-11

-10

-9

-8

0 20 40 60 80 100

10-12

reaction-limited rate

200

100

50

25

10-11

10-10

10-9

10-8

2215

time (years)

r, m

ol/(m

2s)

bicarbonate (p

pm)

the pH is high and goethite is stable. This means that the rate of H+ production initially

from the reaction-limited oxidation rate calculated using the rate law for py-DO and the

stoichiometric relationship in equation (25) for a pH of 8.5 is 10-8.4 mol/s. In order to

neutralize this H+, HCO3- must be added by infiltrating water at least at this rate. For

simplicity, we assume all alkalinity comes from bicarbonate ion.

Figure 3.8. The modeled decrease in the rate of H+ production by the oxidation of pyrite coated by a

growing layer of goethite (curve). The arrow shows the rate of H+ production for pyrite oxidation with

no coatings. The tick marks on the right axis represent the bicarbonate concentration required to

neutralize H+ produced at the corresponding rate shown on the left axis when bicarbonate is carried into

the mine waste at an average infiltration rate of 10-10 m/s.

If we assume for example an average groundwater infiltration rate (Gleisner, 2005), Ir,

of 10-10 m/s with a bicarbonate concentration of 0.41 mol/m3 (25 ppm), which is on the

minimum end of the range for typical groundwaters (Langmuir, 1997) then we can

80

determine the rate at which alkalinity is added to the mine waste by infiltrating

groundwater

4.10103

−==− −+ HCOrHCAIr mol/s. (27)

As illustrated in Figure 8 this rate plots well below the initial rate of H+ production (10-

8.4 mol/(m2s)) by reaction-limited pyrite oxidation so that additional alkalinity must be

added to neutralize the acid produced, otherwise ‘runaway’ AMD conditions will

develop.

To determine how much additional alkalinity must be added and for how long in

order to avoid AMD development, we can consider that as coatings grow the rate of

pyrite oxidation declines so the rate of H+ production rate also declines from 10-8.4

mol/s initially to 10-9.8 mol/s after 10 years and to 10-10.2 mol/s after 50 years (Fig. 3.8).

Therefore, the concentration of HCO3- in the infiltrating solutions, which would have

to be 2215 ppm, initially could be reduced to 95 ppm after 10 years and to 35 ppm after

50 years (Fig. 3.8). Because the range of concentration for bicarbonate in natural

waters is typically between 25 and 200 ppm (Langmuir, 1997) this means that if

bicarbonate alkalinity is added at a high rate over the first decade so that coatings are

produced, the rate of H+ generation from pyrite oxidation would decline sufficiently

to a point where the rates of alkalinity delivery by groundwater recharge could be

substantially reduced to neutralize any acid produced. To effectively reduce AMD by

coatings by using appropriate bicarbonate addition rates requires available bicarbonate.

We suggest that sufficient alkalinity be added to the recharge waters to maintain

alkaline conditions after initial excess alkalinity addition and coating generation.

This model is an instructive example that shows AMD can be effectively reduced

81

by providing extra alkalinity to the mine wastes soon after they are disposed. Field

implementation of this scheme will be effective if other factors are taken into

consideration. Any acid generated prior to treatment will require additional alkalinity.

We consider bicarbonate alkalinity because it buffers the pH between 8 and 8.5, which

is required for coatings to form and be attracted to the surface of pyrite.

The PZC for iron oxyhydroxides (Langmuir, 1997) is between pH of 8 and 9.

Below the PZC iron oxyhydroxide colloids will have a net positive charge and be

attracted to the negatively charged pyrite surface. Above the PZC for iron

oxyhydroxides the colloid will have a net negative charge and will be less likely to be

attracted to the pyrite. Therefore, keeping the pH below 8 or so may be important

during the first stage of coating development. Also, careful control of infiltration rates

will likely be required. If the infiltration rate is too low alkalinity will not be delivered

fast enough but if the infiltration rate is too fast dissolved iron will be flushed away

before it can build up to the concentration necessary for coating growth (Fig. 3.7).

Finally, pyrite oxidation rates below the air saturated zone are substantially slower

and any infiltration front that develops should bring with it excess alkalinity that will

neutralize acid that is generated deeper in the pile. If the coatings cement the pile then

potentially no transport of oxidizing material will take place and hence acid production

by pyrite oxidation will not occur. Any excess alkalinity from the oxidizing solutions

that infiltrate out of the pile post treatment could potentially be recycled through the

pile to further enhance this treatment.

82

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transition metal sulfides: An electrokinetic study. Geochem. Cosmochim. Acta 62, 633-642. Caldeira, C. L., Ciminelli, V. S. T., Dias, A., and Osseo-Asare, K., 2003. Pyrite oxidation in alkaline

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Evangelou, V. P., 1995. Potential microencapsulation of pyrite by artificial inducement of ferric

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Fytas, K., Evangelou, B., 1998. Phosphate coating on pyrite to prevent acid mine drainage. International

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saturated conditions. Thesis submitted to the Department of Geology and Geochemistry,

Stockholm University, Stockholm, Sweden.

Han, P., Bartels, D. M., 1996. Temperature dependence of oxygen diffusion in H2O and D2O. Journal of

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Park, B., Dempsey, B. A., 2005. Heterogeneous oxidation of Fe(II) on ferric oxide at neutral pH and a

low partial pressure of O2. Environmental Science and Technology 39, 6494-6500.

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Soil Science 161, 852-864.

83

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oxidation behavior. Soil Science 163, 53-62.

84

Appendix 3.1. Tabulated data.

a) MFR experimental data from this study. The outlier rate (bold) was discarded in the r versus t-1/2

fit. To estimate

the amount of moles of Fe released at that interval the average of the rate before and after that interval was used.

Both experiments EXP K and duplicate EXP J were conducted at pH ~ 8.5 and room temperature using 0.3 m H2O2

and 0.1 m NaHCO3

MFR EXP K

t (s) SO4 (ppm) Fe (ppm) r f (kg/s) (mol/m2s) Σn Fe A (m

2) x (m)

0

594 164.28 36.89 1.34E-05 4.08E-07 1.36E-05 0.05624 1.63E-10

2376 192.61 50.45 1.16E-05 4.15E-07 2.75E-05 0.05624 3.29E-10

4158 189.86 45.03 1.17E-05 4.10E-07 4.12E-05 0.05623 4.93E-10

5940 188.07 43.94 1.09E-05 3.80E-07 5.38E-05 0.05623 6.45E-10

7722 189.58 41.23 1.07E-05 3.77E-07 6.64E-05 0.05622 7.96E-10

9504 188.16 42.86 1.04E-05 3.64E-07 7.86E-05 0.05621 9.41E-10

11286 187.03 45.03 1.11E-05 3.83E-07 9.14E-05 0.05621 1.09E-09

13068 185.35 46.11 1.04E-05 3.57E-07 1.03E-04 0.05620 1.24E-09

14850 186.71 46.65 1.05E-05 3.62E-07 1.15E-04 0.05620 1.38E-09

16632 191.04 46.65 1.00E-05 3.55E-07 1.27E-04 0.05619 1.52E-09

18414 193.25 46.65 9.30E-06 3.33E-07 1.38E-04 0.05619 1.66E-09

20196 296.90 47.20 1.01E-05 5.58E-07 1.50E-04 0.05618 1.79E-09

21978 192.41 47.20 9.82E-06 3.50E-07 1.61E-04 0.05618 1.93E-09

23760 189.19 46.65 9.84E-06 3.45E-07 1.73E-04 0.05617 2.07E-09

25542 189.99 47.20 1.02E-05 3.59E-07 1.85E-04 0.05617 2.22E-09

27324 199.34 46.65 9.59E-06 3.54E-07 1.97E-04 0.05616 2.36E-09

29106 189.41 46.65 9.80E-06 3.44E-07 2.08E-04 0.05616 2.50E-09

30888 193.00 46.65 9.80E-06 3.51E-07 2.20E-04 0.05615 2.64E-09

32670 192.33 46.11 9.91E-06 3.54E-07 2.32E-04 0.05615 2.78E-09

34452 191.00 45.03 9.54E-06 3.38E-07 2.43E-04 0.05614 2.91E-09

36234 194.77 45.03 9.20E-06 3.32E-07 2.54E-04 0.05614 3.05E-09

38016 195.58 43.94 9.05E-06 3.28E-07 2.65E-04 0.05613 3.18E-09

39798 194.27 42.86 8.59E-06 3.09E-07 2.75E-04 0.05613 3.30E-09

41580 196.49 42.86 9.00E-06 3.28E-07 2.86E-04 0.05612 3.43E-09

43362 186.77 41.77 8.78E-06 3.04E-07 2.96E-04 0.05612 3.56E-09

45144 191.07 41.23 8.76E-06 3.10E-07 3.07E-04 0.05611 3.68E-09

46926 195.59 35.80 9.02E-06 3.27E-07 3.18E-04 0.05611 3.81E-09

48708 184.11 25.50 9.28E-06 3.17E-07 3.28E-04 0.05610 3.94E-09

50490 180.90 21.70 9.14E-06 3.07E-07 3.38E-04 0.05610 4.06E-09

52866 184.91 21.70 9.01E-06 3.09E-07 3.49E-04 0.05609 4.19E-09

54054 179.83 20.61 8.85E-06 2.95E-07 3.59E-04 0.05609 4.30E-09

55836 168.21 21.16 9.34E-06 2.92E-07 3.68E-04 0.05608 4.42E-09

57618 174.09 24.41 8.79E-06 2.84E-07 3.78E-04 0.05608 4.54E-09

59400 171.23 25.50 8.84E-06 2.81E-07 3.87E-04 0.05608 4.65E-09

61182 167.14 23.33 8.79E-06 2.73E-07 3.96E-04 0.05607 4.76E-09

62964 161.09 19.53 9.03E-06 2.70E-07 4.05E-04 0.05607 4.87E-09

64746 156.13 16.82 8.75E-06 2.54E-07 4.14E-04 0.05606 4.97E-09

66528 158.70 13.56 8.73E-06 2.57E-07 4.22E-04 0.05606 5.07E-09

68310 151.93 10.85 8.83E-06 2.49E-07 4.30E-04 0.05606 5.17E-09

70092 146.25 8.68 8.86E-06 2.41E-07 4.39E-04 0.05605 5.27E-09

71874 139.43 8.14 8.86E-06 2.29E-07 4.46E-04 0.05605 5.36E-09

73656 138.35 6.51 8.79E-06 2.26E-07 4.54E-04 0.05604 5.45E-09

75438 136.98 5.97 8.57E-06 2.18E-07 4.61E-04 0.05604 5.54E-09

77220 134.20 5.42 8.67E-06 2.16E-07 4.68E-04 0.05604 5.62E-09

79002 130.79 4.88 8.92E-06 2.17E-07 4.75E-04 0.05604 5.71E-09

80784 129.23 3.80 8.53E-06 2.05E-07 4.82E-04 0.05603 5.79E-09

82566 112.76 3.25 8.49E-06 1.78E-07 4.88E-04 0.05603 5.87E-09

84348 121.95 4.88 8.56E-06 1.94E-07 4.95E-04 0.05603 5.94E-09

86130 122.93 3.80 8.67E-06 1.98E-07 5.01E-04 0.05602 6.02E-09

2FeSr

85

MFR EXP J

t (s) SO4 (ppm) Fe (ppm) r f (kg/s) (mol/m2s) Σn Fe A (m

2) x (m)

0

1200 208.76 45.02 8.46E-06 3.27E-07 1.10E-05 0.05624 1.32E-10

2400 189.23 43.80 8.35E-06 1.46E-06 2.09E-05 0.05623 2.50E-10

3600 183.09 42.99 8.41E-06 1.42E-06 3.05E-05 0.05622 3.65E-10

4800 181.82 42.99 8.56E-06 1.44E-06 4.02E-05 0.05621 4.82E-10

6000 175.80 40.55 8.25E-06 1.34E-06 4.93E-05 0.05621 5.90E-10

7200 168.28 38.92 8.41E-06 1.31E-06 5.81E-05 0.05620 6.96E-10

8400 159.32 36.08 8.18E-06 1.21E-06 6.63E-05 0.05619 7.94E-10

9600 152.37 32.82 8.09E-06 1.14E-06 7.40E-05 0.05618 8.86E-10

10800 147.77 34.04 8.17E-06 1.12E-06 8.15E-05 0.05618 9.77E-10

12000 146.23 32.01 8.37E-06 1.13E-06 8.92E-05 0.05617 1.07E-09

13200 150.20 34.04 8.25E-06 1.15E-06 9.69E-05 0.05616 1.16E-09

14400 156.42 36.08 7.92E-06 1.15E-06 1.05E-04 0.05616 1.25E-09

15600 155.02 39.33 8.07E-06 1.16E-06 1.12E-04 0.05615 1.35E-09

16800 144.18 40.14 7.92E-06 1.06E-06 1.20E-04 0.05614 1.43E-09

18000 152.70 40.55 8.02E-06 1.13E-06 1.27E-04 0.05614 1.53E-09

19200 150.23 40.55 7.43E-06 1.03E-06 1.34E-04 0.05613 1.61E-09

20700 149.73 42.99 8.06E-06 1.12E-06 1.44E-04 0.05612 1.72E-09

21600 151.69 41.36 9.74E-06 1.37E-06 1.51E-04 0.05611 1.81E-09

79200 101.98 3.95 8.78E-06 8.28E-07 1.56E-04 0.05611 1.87E-09

80400 101.27 4.76 8.92E-06 8.36E-07 1.62E-04 0.05610 1.94E-09

81600 101.79 2.32 9.23E-06 8.69E-07 1.68E-04 0.05610 2.01E-09

83100 104.23 3.95 8.04E-06 7.76E-07 1.74E-04 0.05609 2.09E-09

84000 105.78 3.54 8.42E-06 8.24E-07 1.78E-04 0.05609 2.14E-09

85200 103.86 3.13 8.12E-06 7.81E-07 1.84E-04 0.05608 2.20E-09

86400 103.52 3.13 8.28E-06 7.93E-07 1.89E-04 0.05608 2.27E-09

2FeSr

86

b) Data from Zhang and Evangelou (1996) pyrite coating experiment. The iron concentration

data, n Fe, was retrieved using digitizing software from their graph of Fe released versus time

The experiment was conducted at pH ~ 6 and room temperature using 0.145 M H2O2,

0.1 M NaCl and 0.01 M NaOAc

t (s) Σn Fe (mol/m2s) A (m

2) x (m)

0 0.00E+00 2.44E-09 0.29987 2.79E-09

2324 2.19E-06 4.87E-09 0.29881 2.79E-09

4183 4.66E-06 4.07E-09 0.29762 2.80E-09

5926 6.57E-06 4.04E-09 0.29669 2.80E-09

7669 8.91E-06 3.53E-09 0.29556 2.81E-09

9877 1.03E-05 2.69E-09 0.29488 2.81E-09

11736 1.19E-05 3.04E-09 0.29410 2.82E-09

13246 1.34E-05 2.30E-09 0.29337 2.82E-09

15222 1.44E-05 2.15E-09 0.29288 2.82E-09

16732 1.57E-05 2.27E-09 0.29225 2.83E-09

18475 1.67E-05 1.71E-09 0.29176 2.83E-09

20451 1.75E-05 1.13E-09 0.29137 2.83E-09

22426 1.80E-05 1.45E-09 0.29112 2.83E-09

24169 1.90E-05 1.53E-09 0.29064 2.83E-09

25912 1.96E-05 1.64E-09 0.29034 2.84E-09

27539 2.07E-05 1.73E-09 0.28980 2.84E-09

29514 2.13E-05 8.64E-10 0.28951 2.84E-09

31373 2.18E-05 1.74E-09 0.28926 2.84E-09

32884 2.30E-05 1.56E-09 0.28867 2.84E-09

34627 2.34E-05 1.28E-09 0.28848 2.84E-09

36718 2.44E-05 1.61E-09 0.28799 2.85E-09

38461 2.50E-05 1.30E-09 0.28769 2.85E-09

40088 2.58E-05 1.42E-09 0.28730 2.85E-09

42412 2.65E-05 1.84E-09 0.28695 2.85E-09

43574 2.76E-05 1.54E-09 0.28641 2.85E-09

45782 2.80E-05 4.69E-10 0.28621 2.86E-09

47176 2.83E-05 1.18E-09 0.28606 2.86E-09

49151 2.92E-05 1.70E-09 0.28562 2.86E-09

50778 2.99E-05 1.02E-09 0.28527 2.86E-09

52870 3.03E-05 8.28E-10 0.28508 2.86E-09

54613 3.08E-05 9.59E-10 0.28483 2.86E-09

56472 3.13E-05 1.17E-09 0.28458 2.86E-09

58447 3.20E-05 1.50E-09 0.28424 2.87E-09

59958 3.27E-05 1.04E-09 0.28389 2.87E-09

2FeSr

87

c) Data from Nicholson et al. (1990) pyrite coating experiments. The rate data was retrieved

using digitizing software from their graphs of rate versus time and converted into mol/(m2s).

Entries in bold were not included in the r versus t-1/2

fits. These experiments were conducted at pH ~ 8.5 and room temperature under air saturated conditions using 0.005 N NaHCO3.

t (s) (mol/m2s) Σn Fe A (m

2) x (m)

113795 4.00E-10 2.96E-05 0.6499 3.07E-11

241211 4.82E-10 1.05E-04 0.6497 1.09E-10

74918 3.71E-10 1.23E-04 0.6497 1.28E-10

110800 9.30E-10 1.90E-04 0.6495 1.97E-10

107673 3.72E-10 2.16E-04 0.6494 2.24E-10

82868 1.12E-09 2.77E-04 0.6493 2.87E-10

212908 1.35E-10 2.95E-04 0.6492 3.06E-10

125508 1.20E-09 3.93E-04 0.6490 4.08E-10

49133 1.17E-09 4.30E-04 0.6489 4.47E-10

51252 1.03E-09 4.65E-04 0.6488 4.82E-10

193775 1.05E-09 5.97E-04 0.6484 6.19E-10

152168 7.06E-10 6.66E-04 0.6483 6.92E-10

98583 6.27E-10 7.06E-04 0.6482 7.34E-10

141674 8.38E-10 7.83E-04 0.6480 8.14E-10

99325 7.20E-10 8.30E-04 0.6478 8.62E-10

388874 6.96E-10 1.00E-03 0.6474 1.04E-09

143317 8.20E-10 1.08E-03 0.6472 1.12E-09

342974 6.55E-10 1.23E-03 0.6468 1.28E-09

289972 7.25E-10 1.36E-03 0.6464 1.42E-09

482369 8.93E-10 1.64E-03 0.6457 1.71E-09

288382 1.05E-09 1.84E-03 0.6452 1.92E-09

252394 5.36E-10 1.92E-03 0.6450 2.01E-09

218632 5.28E-10 2.00E-03 0.6448 2.09E-09

487245 4.35E-10 2.13E-03 0.6444 2.23E-09

245796 2.73E-10 2.18E-03 0.6443 2.27E-09

289283 3.81E-10 2.25E-03 0.6441 2.35E-09

269302 2.60E-10 2.29E-03 0.6440 2.40E-09

263790 4.32E-10 2.37E-03 0.6438 2.47E-09

315307 4.47E-10 2.46E-03 0.6436 2.57E-09

661011 1.49E-10 2.52E-03 0.6434 2.64E-09

285388 4.65E-10 2.61E-03 0.6432 2.73E-09

268931 3.63E-10 2.67E-03 0.6430 2.79E-09

338655 4.27E-10 2.76E-03 0.6428 2.89E-09

247412 1.78E-10 2.79E-03 0.6427 2.92E-09

310140 4.69E-10 2.88E-03 0.6424 3.02E-09

269673 3.28E-10 2.94E-03 0.6423 3.08E-09

438272 2.57E-10 3.01E-03 0.6421 3.16E-09

264849 3.74E-10 3.08E-03 0.6419 3.23E-09

314459 4.33E-10 3.16E-03 0.6417 3.32E-09

195921 3.42E-10 3.21E-03 0.6416 3.36E-09

583443 2.97E-10 3.32E-03 0.6413 3.48E-09

728297 2.95E-10 3.45E-03 0.6409 3.63E-09

583231 2.61E-10 3.55E-03 0.6407 3.73E-09

1795937 2.84E-10 3.88E-03 0.6398 4.08E-09

583178 2.53E-10 3.97E-03 0.6396 4.18E-09

606923 2.51E-10 4.07E-03 0.6393 4.29E-09

2423107 4.89E-10 4.83E-03 0.6373 5.10E-09

3060135 4.11E-10 5.62E-03 0.6352 5.96E-09

3883384 4.47E-10 6.72E-03 0.6323 7.16E-09

630164 5.02E-10 6.92E-03 0.6318 7.38E-09

313823 5.97E-10 7.04E-03 0.6315 7.51E-09

902143 3.82E-10 7.26E-03 0.6309 7.75E-09

778622 2.83E-10 7.40E-03 0.6305 7.90E-09

1623046 4.69E-10 7.88E-03 0.6293 8.43E-09

656956 3.85E-10 8.04E-03 0.6288 8.60E-09

608354 3.05E-10 8.15E-03 0.6285 8.73E-09

436390 3.36E-10 8.24E-03 0.6283 8.84E-09

2013457 4.12E-10 8.76E-03 0.6269 9.41E-09

608142 3.43E-10 8.90E-03 0.6266 9.56E-09

243093 3.24E-10 8.94E-03 0.6264 9.61E-09

556572 4.21E-10 9.09E-03 0.6260 9.78E-09

510910 3.59E-10 9.21E-03 0.6257 9.91E-09

291563 3.45E-10 9.27E-03 0.6256 9.98E-09

437344 3.23E-10 9.36E-03 0.6253 1.01E-08

604909 4.32E-10 9.52E-03 0.6249 1.03E-08

342391 2.92E-10 9.58E-03 0.6247 1.03E-08

76 micrometer grain size 2FeSr

88

101469 3.59E-10 1.57E-05 0.4307 2.45E-11

25804 4.84E-10 2.11E-05 0.4306 3.29E-11

217865 4.59E-10 6.41E-05 0.4306 1.00E-10

124256 7.02E-10 1.02E-04 0.4305 1.59E-10

77862 1.11E-09 1.39E-04 0.4304 2.17E-10

191955 9.54E-10 2.18E-04 0.4303 3.41E-10

239011 6.81E-10 2.88E-04 0.4302 4.50E-10

125712 1.04E-09 3.44E-04 0.4301 5.39E-10

72225 1.00E-09 3.75E-04 0.4300 5.87E-10

144714 9.42E-10 4.34E-04 0.4299 6.79E-10

25195 1.02E-09 4.45E-04 0.4299 6.97E-10

189494 6.63E-10 4.99E-04 0.4298 7.81E-10

145031 6.29E-10 5.38E-04 0.4297 8.43E-10

99802 8.56E-10 5.75E-04 0.4297 9.00E-10

25857 9.85E-10 5.86E-04 0.4297 9.18E-10

96017 9.09E-10 6.23E-04 0.4296 9.77E-10

317825 1.12E-09 7.76E-04 0.4293 1.22E-09

191585 9.35E-10 8.53E-04 0.4292 1.34E-09

384836 6.92E-10 9.68E-04 0.4290 1.52E-09

290195 6.35E-10 1.05E-03 0.4289 1.64E-09

439620 8.97E-10 1.22E-03 0.4286 1.91E-09

217865 8.71E-10 1.30E-03 0.4284 2.04E-09

312162 6.32E-10 1.38E-03 0.4283 2.17E-09

291916 7.13E-10 1.47E-03 0.4281 2.31E-09

411249 6.43E-10 1.58E-03 0.4279 2.49E-09

169538 6.31E-10 1.63E-03 0.4279 2.56E-09

335928 3.52E-10 1.68E-03 0.4278 2.64E-09

318963 6.59E-10 1.77E-03 0.4276 2.79E-09

289666 5.59E-10 1.84E-03 0.4275 2.90E-09

217124 4.74E-10 1.88E-03 0.4274 2.97E-09

675296 1.93E-10 1.94E-03 0.4273 3.05E-09

365570 3.49E-10 1.99E-03 0.4272 3.14E-09

269182 5.51E-10 2.06E-03 0.4271 3.24E-09

267805 6.43E-10 2.13E-03 0.4270 3.36E-09

310759 2.90E-10 2.17E-03 0.4269 3.42E-09

245151 5.09E-10 2.22E-03 0.4268 3.51E-09

313723 3.94E-10 2.27E-03 0.4267 3.59E-09

461534 4.69E-10 2.37E-03 0.4266 3.74E-09

270717 7.96E-10 2.46E-03 0.4264 3.88E-09

285908 3.93E-10 2.51E-03 0.4263 3.96E-09

243246 4.59E-10 2.55E-03 0.4262 4.04E-09

507901 3.63E-10 2.63E-03 0.4261 4.16E-09

730239 6.03E-10 2.82E-03 0.4258 4.46E-09

602966 3.53E-10 2.91E-03 0.4256 4.61E-09

1770232 3.97E-10 3.21E-03 0.4251 5.08E-09

556148 2.82E-10 3.28E-03 0.4250 5.19E-09

3034017 5.84E-10 4.03E-03 0.4237 6.40E-09

3077553 4.85E-10 4.66E-03 0.4226 7.42E-09

3829282 4.03E-10 5.31E-03 0.4214 8.48E-09

681780 6.48E-10 5.49E-03 0.4211 8.78E-09

214504 3.47E-10 5.52E-03 0.4211 8.84E-09

1066114 3.02E-10 5.66E-03 0.4208 9.06E-09

633401 5.56E-10 5.81E-03 0.4206 9.30E-09

1673235 5.98E-10 6.23E-03 0.4198 9.99E-09

626361 2.76E-10 6.30E-03 0.4197 1.01E-08

582032 2.93E-10 6.37E-03 0.4196 1.02E-08

461481 3.65E-10 6.44E-03 0.4195 1.03E-08

1939797 3.99E-10 6.77E-03 0.4189 1.09E-08

580417 2.84E-10 6.84E-03 0.4188 1.10E-08

363849 3.01E-10 6.88E-03 0.4187 1.11E-08

557260 2.75E-10 6.95E-03 0.4186 1.12E-08

486755 4.32E-10 7.03E-03 0.4184 1.13E-08

217177 3.50E-10 7.07E-03 0.4184 1.14E-08

581079 2.89E-10 7.14E-03 0.4182 1.15E-08

388674 3.54E-10 7.19E-03 0.4181 1.16E-08

461640 4.40E-10 7.28E-03 0.4180 1.17E-08

108 micrometer grain size

89

104157 1.03E-09 2.57E-05 0.2404 7.21E-11

45885 6.56E-10 3.30E-05 0.2404 9.24E-11

266957 6.98E-10 7.77E-05 0.2403 2.18E-10

74345 9.29E-10 9.43E-05 0.2403 2.64E-10

99516 1.29E-09 1.25E-04 0.2403 3.51E-10

71003 1.05E-09 1.43E-04 0.2403 4.01E-10

96226 9.41E-10 1.65E-04 0.2402 4.62E-10

283388 1.60E-09 2.74E-04 0.2401 7.67E-10

33194 1.15E-09 2.83E-04 0.2401 7.93E-10

75273 1.51E-09 3.10E-04 0.2401 8.70E-10

95325 1.28E-09 3.39E-04 0.2401 9.52E-10

145268 1.25E-09 3.83E-04 0.2400 1.07E-09

191604 9.14E-10 4.25E-04 0.2400 1.19E-09

124102 1.33E-09 4.64E-04 0.2399 1.30E-09

95059 1.05E-09 4.89E-04 0.2399 1.37E-09

23685 9.75E-10 4.94E-04 0.2399 1.39E-09

120840 9.22E-10 5.21E-04 0.2399 1.46E-09

316104 1.06E-09 6.01E-04 0.2398 1.69E-09

216960 8.84E-10 6.47E-04 0.2398 1.82E-09

338198 7.13E-10 7.05E-04 0.2397 1.98E-09

291226 7.58E-10 7.58E-04 0.2397 2.13E-09

412411 8.00E-10 8.37E-04 0.2396 2.35E-09

289979 6.67E-10 8.83E-04 0.2395 2.48E-09

265260 4.65E-10 9.13E-04 0.2395 2.57E-09

291517 5.52E-10 9.51E-04 0.2395 2.67E-09

386391 3.39E-10 9.82E-04 0.2394 2.76E-09

218499 3.84E-10 1.00E-03 0.2394 2.82E-09

315999 5.06E-10 1.04E-03 0.2394 2.93E-09

290271 4.14E-10 1.07E-03 0.2394 3.01E-09

363660 4.18E-10 1.11E-03 0.2393 3.11E-09

144631 3.00E-10 1.12E-03 0.2393 3.14E-09

701886 1.35E-10 1.14E-03 0.2393 3.21E-09

267859 3.06E-10 1.16E-03 0.2393 3.26E-09

315521 3.60E-10 1.19E-03 0.2392 3.34E-09

339153 3.25E-10 1.21E-03 0.2392 3.41E-09

218419 3.59E-10 1.23E-03 0.2392 3.47E-09

339816 4.20E-10 1.27E-03 0.2392 3.56E-09

266082 3.36E-10 1.29E-03 0.2392 3.62E-09

363926 3.78E-10 1.32E-03 0.2391 3.72E-09

291332 4.38E-10 1.35E-03 0.2391 3.80E-09

411695 3.77E-10 1.39E-03 0.2391 3.91E-09

145586 3.96E-10 1.40E-03 0.2390 3.95E-09

531951 1.97E-10 1.43E-03 0.2390 4.02E-09

801427 4.03E-10 1.50E-03 0.2389 4.24E-09

580542 2.19E-10 1.53E-03 0.2389 4.32E-09

1770191 2.90E-10 1.66E-03 0.2388 4.67E-09

534046 3.93E-10 1.71E-03 0.2387 4.81E-09

629477 2.74E-10 1.75E-03 0.2387 4.93E-09

2328665 4.75E-10 2.01E-03 0.2384 5.68E-09

3102933 4.62E-10 2.35E-03 0.2381 6.65E-09

3852109 1.10E-10 2.45E-03 0.2380 6.94E-09

704353 3.01E-10 2.50E-03 0.2380 7.08E-09

266904 3.35E-10 2.52E-03 0.2379 7.14E-09

920994 3.04E-10 2.59E-03 0.2379 7.33E-09

752068 3.84E-10 2.66E-03 0.2378 7.53E-09

1647547 2.48E-10 2.76E-03 0.2377 7.81E-09

679977 4.20E-10 2.83E-03 0.2377 8.00E-09

532110 2.44E-10 2.86E-03 0.2376 8.09E-09

535744 5.92E-10 2.93E-03 0.2376 8.31E-09

1937924 3.80E-10 3.11E-03 0.2374 8.81E-09

606004 3.72E-10 3.16E-03 0.2373 8.96E-09

266877 4.02E-10 3.18E-03 0.2373 9.04E-09

630379 4.13E-10 3.25E-03 0.2372 9.21E-09

411138 2.71E-10 3.27E-03 0.2372 9.29E-09

266612 2.63E-10 3.29E-03 0.2372 9.34E-09

461107 3.36E-10 3.33E-03 0.2372 9.44E-09

535770 6.89E-10 3.41E-03 0.2371 9.70E-09

459436 5.20E-10 3.47E-03 0.2370 9.86E-09

215 micrometer grain size

Effect of Coatings on Mineral Reaction Rates in Acid Mine ......Effect of Coatings on Mineral...

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