effect of coatings on mineral reaction rates in acid mine ......effect of coatings on mineral...
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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
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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
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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+
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 1.99 -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
0.0 M Na2SO4 0.1 M Na2SO4 0.3 M Na2SO4 1.0 M Na2SO4
41
DHBs DHBp DHBm DHBj
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 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
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 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
0.0 M Na2SO4 0.1 M Na2SO4 0.3 M Na2SO4 1.0 M Na2SO4
0.0 M Na2SO4 0.1 M Na2SO4 0.3 M Na2SO4 1.0 M Na2SO4
42
DHBu DHBr DHBo DHBl
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 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+
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 1.54 -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 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
References
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Evangelou, V. P., 1995. Potential microencapsulation of pyrite by artificial inducement of ferric
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83
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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