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Trace element source terms for mineral dissolution
Applied Geochemistry 37 (2013) 94–101
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Trace element source terms for mineral dissolution Madeline E. Schreiber ⇑, J. Donald Rimstidt Department of Geosciences, Virginia Tech, 4044 Derring Hall, Blacksburg, VA 24061, USA
a r t i c l e
i n f o
Article history: Received 19 March 2013 Accepted 15 July 2013 Available online 25 July 2013 Editorial handling by M. Kersten
a b s t r a c t We present an approach for determining source terms for modeling trace element release from minerals, using arsenic (As) as an example. The source term function uses laboratory-measured mineral dissolution rates to predict the time rate of change of As concentrations (mol/L s) released to water by the dissolving mineral. Application of this function to As-bearing minerals (realgar, orpiment, arsenopyrite, scorodite, pyrite, and jarosite) in air saturated water at 25 °C shows that mineralogy, grain size and pH are important factors affecting the As source term while DO concentration and temperature are relatively unimportant for conditions found in typical aquifers. The derived function shows that the source term decreases as a function of (1 t/tL)2, where tL is the grain lifetime, due to the shrinkage of the mineral grains as they dissolve. For some models, either a constant or an instantaneous term might be used, provided that certain time constraints are met. The methods outlined in this paper are intended to help bridge the gap between laboratory measurements and field-based models. Although this paper uses As as an example, the methods are general and can be used to predict source terms for other mineral-derived trace elements to groundwater. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Release of trace elements to groundwater is a potential cause for health concern worldwide. Elements such as arsenic, uranium, lead, cobalt, selenium, nickel and many others are present in both naturally-occurring minerals and human sources and can be released over time into groundwater as the source materials dissolve. A recent study by the USGS found that close to 20% of untreated water samples from public, private and monitoring wells in the US contain concentrations of at least one trace element above its drinking water standard (Ayotte et al., 2011). Precipitation contains only small amounts of trace elements dissolved from the atmospheric dust (Chilvers and Peterson, 1987). As the precipitation infiltrates and flows from surface to the saturated zone, dissolution of aquifer materials release trace elements into solution. Quantifying this rate of trace element release is a key step toward predicting if water sources may become contaminated. Arsenic is an example of a trace element of health concern. Arsenic (As) is both a toxin and a carcinogen, implicated in cardiovascular, pulmonary, immunological, neurological, and endocrine disorders, as well as skin, lung, bladder, and kidney cancers (NRC, 1999, 2001). Long-term exposure to contaminated drinking water has been cited as the most widespread threat to human health posed by As (Nordstrom, 2002; Smith et al., 1992). Contamination of groundwater by As is of particular concern, as it is linked to common naturally-occurring geochemical processes such as reduction ⇑ Corresponding author. Tel.: +1 540 231 3377; fax: +1 540 231 3386. E-mail address: [email protected] (M.E. Schreiber). 0883-2927/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apgeochem.2013.07.011
of Fe oxyhydroxides, oxidation of sulfides, and desorption from mineral surfaces (Mandal and Suzuki, 2002; Nordstrom, 2002; Smedley and Kinniburgh, 2002; Welch et al., 2000). Removal of As from groundwater can be a difficult and expensive process, because unlike organic compounds, As cannot be biotransformed to a less harmful species but instead must be either removed via ex situ processes (e.g., pump-and-treat) or immobilized via in situ processes (e.g., adsorption onto Fe-oxides or precipitation of As-bearing sulfides). Because groundwater is a primary pathway connecting As sources to target organisms, preventing As exposure from groundwater consumption requires an understanding of the factors that control As release from the source and transport to the target. Geochemical models that simulate As behavior in groundwater can range from simple inverse models to complex reactive transport models. Some of the more detailed models incorporate aquifer mineralogy (e.g., Zhu and Burden, 2001) surface complexation reactions to simulate retardation by adsorption–desorption processes (e.g., Parkhurst and Appelo, 1999; Wallis et al., 2011) and rate equations to simulate oxidation–reduction reactions (e.g., Decker et al., 2006; Radu et al., 2008; Wallis et al., 2010) and microbial growth (e.g., Wallis et al., 2010). One critical element that these models often lack is a source term that represents the rate of release of As from the solid matrix into groundwater. PHREEQC (Parkhurst and Appelo, 1999) and associated models PHAST (Parkhurst et al., 2010) and PHT3D (Prommer et al., 2003) include a source term module that can simulate mineral dissolution. However, even in models with source term modules, there are challenges in turning laboratory measured dissolution rates to ‘‘field
M.E. Schreiber, J.D. Rimstidt / Applied Geochemistry 37 (2013) 94–101
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Nomenclature A ABET Ageo Cm,i Cmx,i Cmx,m D(t) Ff Fsr k Mm
surface area, m2 BET specific surface area, m2/g geometric specific surface area, m2/g (assumes spherical particles) concentration of element i in mineral, ppm concentration of element i in the aquifer matrix, ppm concentration of mineral in the aquifer matrix, ppm diameter of mineral grains at time t, m field factor; adjusts for slower dissolution rates in field settings surface roughness factor (=ABET/Ageo) rate constant for zeroth order reaction = rgeo(pH, T), mol/m2 s mass of dissolving mineral in source region, g
effective’’ rates, and in simulating the release of elements that occur in trace concentrations in common minerals. To address these challenges, we derive general expressions that use laboratory-derived rate data to predict trace element source terms due to host mineral dissolution. To illustrate their implementation, we focus on the dissolution of common As-bearing minerals, including arsenopyrite (FeAsS), realgar (AsS), orpiment (As2S3), and pyrite (FeS2), and the secondary minerals scorodite (FeAsO42H2O) and jarosite (KFe3(SO4)2(OH)6). This method for transforming the laboratory rates into a usable form for models also incorporates a shrinking particle model that accounts for the decline in the source terms as the minerals dissolve away. The approach presented here does not introduce any novel equations but instead it provides a detailed accounting of the unit transformations that must be carried out (see Supplementary information). This approach cannot address rates of As release from minerals due to desorption. Although previous studies have documented that kinetics does play a role in desorption (O’Reilly et al., 2001; Raven et al., 1998; Smith and Naidu, 2009; Zhang and Selim, 2005), desorption kinetics are much faster than mineral dissolution kinetics and for the purposes of this paper are assumed to be close to equilibrium (see Bearup et al. (2012) for more discussion of this topic). We also do not consider As release from microbially-mediated reactions. Although it is well-recognized that microbiallymediated reduction of Fe oxyhydroxides can result in As release, our understanding of how As is released from mineral surfaces due to these processes is incomplete (Tufano and Fendorf, 2008) and there are currently no available rate data that can be transformed into source terms. Examples used in this paper are based on rates from experiments carried out under far from equilibrium conditions, so the resulting source terms are maximum values. However, the method is general and slower rates could be used if expressions for the dissolution rates as a function of chemical potential are known.
2. Methods 2.1. Selection of laboratory derived rates We selected from the literature experimentally-determined rates of dissolution for As-bearing minerals (see Table 1). When possible, data from several sources were compared and correlated in order to identify the most reliable values. We adjusted those values to find the rate expected for air-saturated, dilute groundwater, at 25 °C leaving pH as the only factor that remains as a variable. An underlying assumption is that mineral dissolution is irreversible
mi / rBET rgeo Rm(t)
qm qmx Si(t) t tL V Vm Wi Wm
stoichiometric factor, mol element i/mol mineral porosity of aquifer mineral dissolution rate, mol/m2 s (normalized to ABET) mineral dissolution rate, mol/m2 s (normalized to Ageo) mineral destruction rate at time t, mol/s density of mineral, g/cm3 density of matrix solids, g/cm3 source term for element i at time t, mol/L s time, s grain lifetime, s volume of source region, m3 molar volume, m3/mol molecular weight of element i, g/mol molecular weight of mineral, g/mol
and that the trace element is homogeneously distributed in the mineral. 2.2. Derivation of source term equation Four main steps are needed to convert laboratory-determined mineral dissolution rates to rates of release of element i contained in that mineral to groundwater in an aquifer. These adjustments simply express the mineral dissolution rate in different ways with appropriate unit transformations. Keeping track of these different rates is challenging and we refer the reader to the unit analyses shown in the Supplementary information. The source term for an element released from a dissolving mineral in an aquifer is linked to the laboratory determined dissolution rate of that mineral by the following transformations and adjustments: (1) The laboratory-determined mineral dissolution rates, rBET (mol/m2 s), are converted to rates based on geometric surface area and adjusted for the difference between laboratory and field rates to give rgeo (mol/m2 s). (2) rgeo (mol/m2 s) is converted to the mineral destruction rate, Rm(0) (mol/s), by multiplying by the specific surface area and the mass of mineral dissolving in the aquifer. (3) A shrinking particle model is used to predict the rate of mineral destruction as a function of time, Rm(t) (mol/s). (4) Rm(t) (mol/s) is divided by the volume of water in the aquifer pores to find the source term for constituent i, Si(t) (mol/L s). 2.2.1. Step 1: Converting laboratory-determined rates to field rates Most laboratory studies report mineral dissolution rates normalized to BET surface areas (ABET). Measurement of ABET is easily done for clean, monominerallic laboratory samples but is nearly impossible for natural materials because of the difficulty of obtaining pure representative mineral fractions and the challenge of separating minerals without changing the surface area of the minerals. Thus, it is necessary to recast the laboratory dissolution rates to a geometric surface area basis because Ageo can be computed using measured grain size. ABET is always larger than Ageo because of the roughness of the grain’s surfaces. This discrepancy is reported as the surface roughness factor (Fsr). The surface roughness factor accounts for all of the factors that cause the grains to differ from a perfect spherical shape, such as the grains’ cleavage and fracture geometry, surface etching patterns, and surface porosity. To adjust from a BET surface area to a geometric surface area, the rates are multiplied by Fsr. In this paper we will use a median value of 7 for Fsr (White and Peterson, 1990). Other studies comparing BET
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Table 1 Mineral dissolution rates (rgeo, mol/m2 s) based on Eq. (1) at 25 °C (298 K) of common As-bearing minerals normalized to geometric surface area. For DO oxidation reactions, the dissolution rate is based on a DO concentration of 103.6 mol (air-saturated water at 25 °C and 1 atm pressure). For Fe(III) oxidation reactions, we assume an Fe(III) concentration in equilibrium with ferrihydrite at 25 °C. Calculations assume Fsr = 7 and Ff = 1. Molar volume (Vm) data from the following sources: scorodite (Dove and Rimstidt, 1985); orpiment, realgar and pyrite (Robie and Hemmingway, 1995); arsenopyrite (Robie et al., 1967). Molar volume for jarosite calculated using average cell dimensions given in Desborough et al. (2010).
qm
Mineral
Realgar (real, DO) Orpiment (orp, DO) Arsenopyrite (aspy, Fe) Arsenopyrite (aspy, DO) Pyrite (py, Fe) Pyrite (py, DO) Scorodite (scor) Jarosite (jar)
Wm (g/mol)
Vm (m3/mol) (105)
Reaction
Rate equation for mineral dissolution
pH range
Rate data source
(g/cm3) 3.56 3.52 6.07 6.07 5.01 5.01 3.20 3.09
107.0 246.0 162.8 162.8 120.0 120.0 230.8 500.8
7.05 2.98 2.6 2.6 2.39 2.39 6.99 15.96
DO oxidation DO oxidation Fe(III) oxidation DO oxidation Fe(III) oxidation DO oxidation Incongruent dissolution Dissolution
Log rgeo = 9.48 + 0.13pH Log rgeo = 10.02 + 0.18pH Log rgeo = 2.9 2.94pH Log rgeo = 8.19 Log rgeo = 0.49 2.79pH Log rgeo = 9.145 + 0.11pH Log rgeo = 9.68 0.14pH Log rgeo = 10.02 + 0.392pH
2.3–8.7 2.3–8.2 <4 1.8–12.6 <4 >4 3–8 >3.5
Lengke et al. (2009) Lengke et al. (2009) Rimstidt et al. (1994) Yu et al. (2007) Williamson and Rimstidt (1994) Williamson and Rimstidt (1994) Harvey et al. (2006) Madden et al. (2012)
to geometric surface areas report roughness factors ranging from 2 to 11 (Anbeek, 1992; Brantley and Mellott, 2000). Many studies have shown mineral dissolution rates measured in field settings are slower than laboratory measured rates by field factors (Ff) ranging from 0.1 to 0.001 (e.g., Malmström et al., 2000; Paces, 1983; Swoboda-Colberg and Drever, 1993; Velbel, 1985, 1993). At the present time the cause of this effect is not fully understood and therefore values of Ff are not predictable. We include this field factor effect in our equations as a calibration variable and set the value of Ff = 1 for subsequent examples. Combining these adjustments gives
Integrating (7) with the requirement that the diameter is D(0) when t = 0 gives
r geo ¼ F sr F f r BET
DðtÞ ¼ Dð0Þ 2kV m t
ð1Þ
The rate of volume loss of the particle is also given by the time derivative of the volume formula for a sphere
dV pD2 dD ¼ dt 2 dt
ð6Þ
Setting (5) equal to (6) gives
dD ¼ 2kV m dt
ð7Þ
ð8Þ
so the lifetime for a particle (tL) with an initial diameter of D(0) is 2.2.2. Step 2: Converting rgeo to rate of element release from mineral, Rm(0) Next rgeo is multiplied by the geometric surface area of the grains, assuming spherical particles, and the mass of mineral in the source region (Mm) to find the rate of mineral destruction:
Rm ð0Þ ¼ Ageo M m r geo
ð2Þ
Note that although we assume spherical particles in our model, the model could be altered to accommodate other geometries, such as euhedral crystals. The geometric surface area of a spherical particle is (Lowell and Shields, 1991)
Ageo ¼
6 106 qm D
! ð3Þ
2.2.3. Step 3: Predicting the rate of mineral destruction over time, Rm(t) With continual flushing, the mineral grains will dissolve and the release rate of element i will decrease. Although more sophisticated models may be appropriate when detailed information about the mineral dissolution behavior is known, a simple ‘‘shrinking particle’’ model provides a good first approximation of this behavior. To simplify this derivation and to make it consistent with previous derivations (Lasaga, 1998) we define k = rgeo at fixed pH and temperature. This model is an extension of the particle lifetime model derived by Lasaga (1981). Assuming that mineral particles are spherical, the mineral destruction rate is
Rm ¼ Ak ¼ pD2 k
ð4Þ
and the rate of volume loss for the particle is
dV ¼ Rm V m ¼ pD2 kV m dt
ð5Þ
tL ¼
Dð0Þ 2kV m
ð9Þ
In addition to predicting particle lifetime, the shrinking particle model predicts how the rate of mineral destruction decreases as the mineral dissolves. Eq. (9) can be rearranged to
2kV m ¼
Dð0Þ tL
ð10Þ
and substituted into (8) to yield
DðtÞ t ¼ 1 Dð0Þ tL
ð11Þ
Rearranging (4) to
D¼
1=2 Rm pk
ð12Þ
and substituting into (11) gives
2 Rm ðtÞ t ¼ 1 Rm ð0Þ tL
ð13Þ
This convenient formulation gives the dimensionless rate as a function of dimensionless time so Rm(t) can be calculated for any time based on Rm(0) and tL. 2.2.4. Step 4: Derivation of source term Combining Eqs. (2) and (13) gives the rate of mineral destruction over time as a function of the mineral properties (density, grain size, dissolution rate), the mass of the mineral in the aquifer (Mm), and the particle lifetime:
Rm ðtÞ ¼
! 2 6 106 t r geo Mm 1 tL qm D
ð14Þ
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where the mass of mineral per m3 aquifer is
Mm ¼ C mx;m qmx ð1 /Þ V
ð15Þ
The source term (Si(t), mol/L s) is found by multiplying Rm(t) by the stoichiometric factor for i and dividing by the volume of solution in the aquifer pores.
! 6 106 Si ðtÞ ¼ qm D /103 2 t ðF sr F f r BET Þ ðC mx;m qmx ð1 /ÞÞ 1 tL
mi
!
log rBET ðreal; DOÞ ¼ 8:78 þ 0:43 log mDO þ 0:13 pH
ð16Þ
Eq. (16) can be simplified to: 9
Si ðtÞ ¼
6 10
mi F sr F f C mx;m
2 qmx ð1 /Þ t 1 rBET / tL qm
Note that mi for minerals in which i is an essential element is simply the stoichiometric coefficient for i in the mineral formula. In the case where i is a trace constituent in the mineral,
CmW m
ð18Þ
106 W i
ð23Þ
The rate equation for orpiment oxidation by DO (Lengke and Tempel, 2003) is
ð17Þ
mi ¼
ð22Þ
Using a DO concentration of air-saturated water at 25 °C and 1 atm pressure (103.6 mol, or 8.5 mg/L), and adjusting for BET to geometric surface area by adding log (7), or 0.845, to the log rate gives:
log rgeo ðreal; DOÞ ¼ 9:48 þ 0:13 pH
!
D
3.1.1. Realgar and orpiment Realgar (AsS) and orpiment (As2S3) are often associated with hydrothermal gold deposits, volcanic deposits, and geothermal hot springs (Lengke and Tempel, 2002, 2003). Lengke et al. (2009) conducted linear regression analysis of rate data from several studies and report the following rate expression for realgar oxidation by dissolved oxygen (DO):
log rBET ðorp; DOÞ ¼ 10:32 þ 0:15 log mDO þ 0:18 pH
ð24Þ
Using the DO for air-saturated water and the BET to geometric surface area conversion, the rate of orpiment dissolution normalized to geometric surface area is:
log rgeo ðorp; DOÞ ¼ 10:02 þ 0:18 pH
ð25Þ
Eq. (17) would be used when the concentration of the mineral (g-mineral/106 g-aquifer matrix) has been quantified by point count analysis or some similar means. If the aquifer matrix has been analyzed to determine the concentration of element i, the concentration of the element-bearing mineral can be estimated from
3.1.2. Arsenopyrite When arsenopyrite (FeAsS) oxidizes in solutions with pH < 4, Fe(III) concentrations are high enough to make Fe(III) the predominant oxidant of arsenopyrite. At 25 °C and pH 1.8, the rate of oxidation of arsenopyrite by Fe(III) under oxic conditions (Rimstidt et al., 1994) is:
Mm C mx;i qmx W m ð1 /Þ ¼ V mi W i
log rBET ðaspy; FeÞ ¼ 2:84 þ 0:98 log mFeðIIIÞ
ð19Þ
When this method of determining Mm is used to calculate Si, the source term equation becomes
Si ðtÞ ¼
! 6 106 C mx;i qmx W m qm D mi W i /103 2 t F sr F f r BET ð1 /Þ 1 tL
mi
!
This equation can be simplified by combining terms to yield
Si ðtÞ ¼
6 109 F sr F f C mx;i D
!
qmx qm
Wm Wi
To convert to geometric surface area, we add log (7), or 0.845, to the log rate. We can also simplify the rate equation by estimating the dissolved Fe(III) concentration by assuming that it is controlled by ferrihydrite (fh) solubility:
FeðOHÞ3 ðfhÞ þ 3Hþ ¼ Fe3þ þ 3H2 O; ð20Þ
2 ð1 /Þ t 1 rBET / tL ð21Þ
Note that this approach assumes that i is contained in only one mineral. If i is present in more than one mineral, the equation can be expanded to distribute i among those minerals. In this way, the release of the trace element from multiple minerals with differing dissolution rates can be predicted. 3. Results and discussion 3.1. Determining rgeo for selected As-bearing minerals The functions for rgeo in Table 1 were calculated assuming a surface roughness factor (Fsr) of 7 and a field factor (Ff) of 1. For minerals undergoing oxidation by DO, we use a DO concentration of air-saturated water at 25 °C and 1 atm pressure (103.6 mol, or 8.5 mg/L). Rates for other DO concentrations at different temperatures and pressures can be easily calculated and incorporated by the user, as needed.
ð26Þ
log K ¼ 5:0
ð27Þ
Ferrihydrite was chosen here to illustrate how this calculation is performed. When constructing a model for a real case the equilibrium constant for the iron oxyhydroxide that is present in the source region should be used. Approximating the molarity of Fe(III) to be equivalent to the activity:
mFeðIIIÞ aFeðIIIÞ ¼ 105:0 a3Hþ
ð28Þ
The Fe(III) concentration as a function of pH can be combined with Eq. (26) to predict the dissolution rate of arsenopyrite via Fe(III) oxidation:
log rgeo ðaspy; FeÞ ¼ 2:9 2:94 pH
ð29Þ
If the arsenopyrite occurs in wastes that generate little or no acid, the ambient pH remains near neutral so the iron released from oxidizing arsenopyrite rapidly oxidizes to Fe(III) and becomes incorporated into iron oxyhydroxides or scorodite. Under these conditions DO is the predominant oxidant. Several papers report rates of arsenopyrite oxidation by DO (McKibben et al., 2008; Walker et al., 2006; Yu et al., 2007) but the experimental conditions (pH, DO concentrations) vary widely, as do the resulting rate expressions. Comparison of the arsenic release rates from DO oxidation of arsenopyrite from these studies reveals several apparent inconsistencies. For example, Walker et al. (2006) show no significant effect of DO concentrations (0.3–17 mg/L) on arsenopyrite oxidation while the rate laws reported in McKibben et al. (2008) and Yu et al. (2007) show DO dependence (reaction orders
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of 0.33 and 0.45, respectively). The discrepancies in these results likely reflect the very complicated chemistry that underlies this oxidation process, but could be due to a number of assumptions (e.g., which species to use for the reaction progress variable) or experimental conditions (e.g., temperature, pH, stirring rates, preparation of solids, and analytical methods). More research needs to be done on arsenopyrite oxidation by DO to settle some of these unresolved discrepancies. Because arsenopyrite oxidation by oxygen will be most important at pH > 4, the relevant datasets are from Yu et al. (2007) and Walker et al. (2006). Both these datasets indicate no significant pH dependence of the oxidation rate and yield rates within the same order of magnitude, but as the dataset from Yu et al. (2007) was generated under a wider range of pH values, we will use the rate generated from that dataset:
1 log r geo ðaspy; DOÞ ¼ 2211 þ 0:45 log mDO T
ð30Þ
Converting the BET to geometric surface area by adding log (7), or 0.845 to the log rate, and assuming a temperature of 25 °C (298 K) and DO for air-saturated water, the dissolution rate of arsenopyrite by DO oxidation normalized to geometric surface area is:
log r geo ðaspy; DOÞ ¼ 8:19
ð31Þ
As noted above, arsenopyrite oxidation by DO at circumneutral pH will result in precipitation of iron oxyhydroxides, which may armor the arsenopyrite from further oxidation (see Huminicki and Rimstidt, 2009). The model developed in this paper does not account for armoring, but the user could add additional terms to include this effect. 3.1.3. Pyrite The widespread occurrence of As-bearing pyrite makes it a potentially significant source of As. Pyrite with As contents of up to several percent are not unusual (Kolker and Nordstrom, 2001; Savage et al., 2000). Fe(III) is the most important oxidant under acid conditions (pH < 4) and dissolved oxygen is the most important oxidant at pH > 4 (Williamson et al., 2006). The rate of pyrite dissolution by Fe(III) oxidation (Williamson and Rimstidt, 1994) is:
log r BET ðpy; FeÞ ¼ 6:07 þ 0:93 log mFeðIIIÞ 0:40m log mFeðIIÞ
ð32Þ
To convert to geometric surface area, we add log (7), or 0.845, to log rate. As described above, we can also estimate the dissolved Fe(III) concentration by assuming that it is controlled by ferrihydrite solubility. The Fe(II) concentration in typical AMD is around 250 ppm (4.5 103 m) (Williamson et al., 2006). The resulting rate of pyrite oxidation by Fe(III) normalized to geometric surface area is:
log r geo ðpy; FeÞ ¼ 0:49 2:79 pH
ð33Þ
For pH > 4, pyrite oxidation rates are a function of DO and pH (Williamson and Rimstidt, 1994):
log r BET ðpy; DOÞ ¼ 8:19 þ 0:5 log mDO þ 0:11 pH
ð34Þ
Assuming DO saturation and adjusting BET to geometric surface area gives:
log r geo ðpy; DOÞ ¼ 9:145 þ 0:11 pH
ð35Þ
Note that we have assumed that the pyrite oxidation rates are not significantly affected by the pyrite trace element content. This assumption is justified by previous studies of the oxidation rates of pyrite samples from multiple sources (Lehner and Savage, 2008; Manaka, 2006; Wiersma and Rimstidt, 1984) that reported that rates vary by no more than 0.5 log units from sample to sample. The equations also assume a homogeneous As distribution in the pyrite although we realize that there can be significant zoning of
the As (Craig et al., 1998). This means that an analysis of a bulk pyrite sample should be used to assess the As content rather than microanalyses of a few spots. Finally, a significant amount of As can be taken up by Fe(III) minerals that might form as the pyrite oxidizes at high pH; this uptake should be accounted for in any geochemical model of As behavior. 3.1.4. Scorodite Scorodite (FeAsO42H2O) is a common weathering product of arsenopyrite and is often found in mine settings (Demopoulos, 2005; Dove and Rimstidt, 1985; Harvey et al., 2006; Langmuir et al., 2006; Zhu and Merkel, 2001). Congruent dissolution of scorodite, which occurs at low pH, releases equimolar concentrations of As and Fe. At higher pH, scorodite dissolves incongruently, forming iron hydroxide and arsenate oxyanions (Zhu and Merkel, 2001). Harvey et al. (2006) determined the scorodite dissolution rate as a function of temperature and pH. Results of experiments conducted between pH 2 and 6 reveal that the transition from congruent to incongruent dissolution, assuming that ferrihydrite is the iron oxyhydroxide that forms, occurs at approximately pH 3, which produces a shift in the pH dependence of the dissolution rate. The rate for incongruent scorodite dissolution as a function of temperature and pH from 3 to 6 is (Harvey et al., 2006):
log r BET ðscorÞ ¼ 6:2 0:14 pH 1290
1 T
ð36Þ
Adjusting for the conversion from BET to geometric surface area and assuming a temperature of 25 °C (298 K) results in:
log r geo ðscorÞ ¼ 9:68 0:14 pH
ð37Þ
3.1.5. Jarosite Arsenate can substitute for sulfate in jarosite, KFe3(SO4)2(OH)6, by various coupled substitutions that maintain charge balance (Savage et al., 2005) to produce jarosite that contains up to 9.9 wt% As(V) (Paktunc and Dutrizac, 2003). Jarosite dissolution rates have been measured for a range of pH by Madden et al. (2012). For pH greater than 3.5, the rate is
log r BET ðjarÞ ¼ 2:073 þ 0:392 pH 3858:9
1 T
ð38Þ
Adjusting this rate to get the rate of jarosite dissolution in terms of a geometric surface area at a temperature of 25 °C (298 K) gives
log r geo ðjarÞ ¼ 10:02 þ 0:392 pH
ð39Þ
3.2. Mineral dissolution rates versus pH Graphs of the mineral dissolution rates (rgeo) of these As-bearing minerals versus pH show several interesting trends (Fig. 1). For pH values typical of natural waters (4–8), there is a maximum of four orders of magnitude difference in dissolution rates of As-bearing minerals (107 to 1011 mol/m2 s). Dissolution rates of arsenopyrite, pyrite, orpiment and realgar are within one order of magnitude of each other, while the rate of scorodite dissolution is two orders of magnitude slower. Contrasting with patterns in acid waters, rates show less pH dependence within the pH range of natural waters. 3.3. Predicting the lifetime of As-bearing minerals The rgeo values from Table 1 can be used with the shrinking particle model (Eq. (9)) to find particle lifetimes. Fig. 2 compares particle lifetimes for 100 lm diameter grains of As-bearing minerals over the pH range of natural waters. The particle lifetime is directly proportional to the particle diameter (see Eq. (9)) so that
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M.E. Schreiber, J.D. Rimstidt / Applied Geochemistry 37 (2013) 94–101 Table 2 Parameters used in calculation of the As source term for scorodite example. Parameter
Symbol
Scorodite
Porosity of aquifer Stoichiometric factor Surface roughness factor Field factor Mineral density, g/cm3 Particle diameter, m Lifetime of particle, s Mineral dissolution rate, mol/m2 s Mass of mineral in aquifer, ppm
/
0.3 1 7 1 3.3 1.0 104 3.27 1010 3.09 1012 –
m Fsr Ff
qm D tL rBET Cmx,m
Additional parameters needed if Cmx,m is not known (Eq. (21)) Matrix density, g/cm3 qmx Mineral molecular weight, g/mol Wm Arsenic molecular weight, g/mol Wi Arsenic concentration in matrix, ppm Cmx,i
2.8 230.8 74.92 50,000
Fig. 1. Log mineral dissolution rate (rgeo, mol/m2 s) versus pH based on equations from Table 1. ‘‘Fe’’ = oxidation by Fe(III), ‘‘DO’’ = oxidation by dissolved oxygen.
Fig. 3. Arsenic source term (mol As/L s) from 10, 100 and 1000 lm diameter particles of scorodite using Eq. (21) and data from Table 2. The lifetimes for the 10, 100 and 1000 lm particles are 103, 1037, and 10,367 years, respectively. For other minerals, the shape of the curves will be the same but the times will be different.
Fig. 2. Particle lifetimes (years) for selected As-bearing minerals with 100 lm diameter grain size. The particle lifetime is directly proportional to grain size so that a 10 times increase in diameter will result in 10-fold increase in lifetime, and vice versa.
increasing the particle diameter by 10 times causes the lifetime to increase by 10 times.
shows that grain size has an important influence on the source term. Small grains dissolve quickly, and thus have a high initial As source term, but that term declines rapidly with time. In comparison, larger particles release As more slowly but persist over longer times. One simple way of examining how a source term changes over the lifetime of a mineral is to determine a characteristic time over which the source term at time t is within a certain % of the initial source term. To do this, we can rearrange Eq. (13) to solve for t:
t ¼ tL 3.4. Calculating the arsenic source term Calculating the source term, Si(t), requires additional information about the As-bearing mineral and the aquifer. If the mass of mineral in the aquifer matrix (Cmx,m) is known, Eq. (17) can be used to calculate the source term, with the parameters listed in the top of Table 2. In the more common case where the mass of mineral in the aquifer is not known, but an As concentration of the aquifer matrix (Cmx,i) is, and the As-bearing mineral(s) are identified, Eq. (21) can be used with the additional parameters at the bottom of Table 2. As an example, the As source term for an aquifer matrix containing 5 wt% As in the form of 100 lm diameter scorodite particles was calculated using the parameters in Table 2. Fig. 3 shows how the As source term for scorodite (10, 100 and 1000 lm grains) declines over time. Similar to the lifetime diagram (Fig. 2), Fig. 3
sffiffiffiffiffiffiffiffiffiffiffiffiffi! Rm ðtÞ 1 Rm ð0Þ
ð40Þ
This equation shows that for any mineral, the source term declines to 50% of the initial value when t = 0.29 tL. Thus, the source term will decline by 50% for 10 lm scorodite grains after 30 years; for 1000 lm scorodite grains, it will take almost 3000 years. In nature, As-bearing primary minerals, such as arsenopyrite, dissolve over time, forming secondary and tertiary As-bearing phases. The co-occurrence of primary and secondary/tertiary minerals complicate modeling efforts, as each of these minerals has different dissolution rates and particle lifetimes, resulting in differences in As source terms and changes in the source term over time. For example, arsenopyrite dissolves quickly (100 lm particle lifetime 10 years) and releases high concentrations of As to groundwater during that short time. If conditions are favorable for the formation of scorodite, this secondary mineral will persist in the aquifer for a much longer period of time (in this case,
100
M.E. Schreiber, J.D. Rimstidt / Applied Geochemistry 37 (2013) 94–101
1000 years for 100 lm particle) but will release As to the aquifer much more slowly, resulting in lower As concentrations in groundwater. Incongruent dissolution of scorodite to form Fe oxyhydroxides, to which As can adsorb, will result in a tertiary source of As to groundwater systems, if conditions later shift to favor dissolution of the Fe oxyhydroxides.
3.5. End-member source term cases For some models either a constant or an instantaneous/pulse source term might be used, provided that certain conditions are met. A constant source term is justified if the simulation time is considerably shorter than the particle lifetime and an instantaneous source is justified only when the simulation time is much longer than the particle lifetime. Eq. (40) can be used to determine how short or long a simulation time must be for these end-member cases. For example, in order for the source term to remain above 90% of the initial value, the simulation time must be less than 5% of the particle lifetime. For As release from 100 lm diameter scorodite grains (pH 7; lifetime 1037 years) shown in Fig. 3, the simulation time must be less than 52 years to justify a constant source term in the model. If we can assume that source term is ‘‘spent’’ once it reaches 10% of the initial value, the simulation time must be longer than 68% of the lifetime of the mineral for the dissolution to be considered instantaneous. For example, a simulation of As release from 1 lm grains of scorodite (pH 7; lifetime 10.7 years) as an instantaneous event would require a minimum simulation time of 7 years.
3.6. Caveats for source terms application The examples in this paper use rate equations based on experiments performed far from equilibrium conditions. Rates that have been adjusted using either a (C Ceq) or a (1 Q/K) term could be used for models where minerals are dissolving under near equilibrium conditions. We estimate the precision of the rates selected here to be no better than ±0.3 orders of magnitude (± a factor of 2) with in some cases much larger uncertainties related to accuracy. Adjustments for the effect of temperature on rate using the Q10 rule (rate increases 2 per 10 °C) are on the same order as the precision of the rates. The largest effect of DO concentration reported for sulfide minerals involves a reaction order for oxygen of 0.5. Based on this, if DO were reduced from air saturation to 10% of air saturation the dissolution rate would decrease by a factor of three. Laboratory studies of mineral dissolution rates continue to produce more and improved data. Extensive efforts to compile and correlated mineral dissolution rate data have already produced easily accessible and more reliable rate equations that can be used to construct source terms for many minerals (see Marini, 2007; Palandri and Kharaka, 2004; Rimstidt et al., 2012). Inclusion of in situ coupled geochemical data over longer time frames would be especially useful to test theoretical models for simulating As release to groundwater. The purpose of this paper is not to supply definitive release rate values but rather to show how the laboratory data can be used in models of field situations. We suggest that any application of this approach should begin by updating and reevaluating the laboratory data.
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apgeochem.2013. 07.011.
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Tufano, K.J., Fendorf, S., 2008. Confounding impacts of iron reduction on arsenic retention. Environ. Sci. Technol. 42, 4777–4783. Velbel, M., 1985. Geochemical mass balances and weathering rates in forested watersheds of the southern Blue Ridge. Am. J. Sci. 285, 904–930. Velbel, M.A., 1993. Constancy of silicate-mineral weathering-rate ratios between natural and experimental weathering: implications for hydrologic control differences in absolute rates. Chem. Geol. 105, 89–99. Walker, F.P., Schreiber, M.E., Rimstidt, J.D., 2006. Kinetics of arsenopyrite oxidative dissolution by oxygen. Geochim. Cosmochim. Acta 70, 1668–1676. Wallis, I., Prommer, H., Pichler, T., Post, V., Norton, S.B., Annable, M.D., Simmons, C.T., 2011. Process-based reactive transport model to quantify arsenic mobility during aquifer storage and recovery of potable water. Environ. Sci. Technol. 45, 6924–6931. Wallis, I., Prommer, H., Simmons, C.T., Post, V., Stuyfzand, P.J., 2010. Evaluation of conceptual and numerical models for arsenic mobilization and attenuation during managed aquifer recharge. Environ. Sci. Technol. 44, 5035–5041. Welch, A.H., Westjohn, D.B., Helsel, D.R., Wanty, R.B., 2000. Arsenic in ground water of the United States: occurrence and geochemistry. Ground Water 38, 589–604. White, A.F., Peterson, M.L., 1990. Role of reactive-surface-area characterization in geochemical kinetic models. In: Melchior, D.C., Bassett, R.L. (Eds.), ACS Symposium Series 416. Chemical Modeling of Aqueous Systems II. American Chemical Society, Los Angeles, California, pp. 461–475. Wiersma, C.L., Rimstidt, J.D., 1984. Rates of reaction of pyrite and maracasite with ferric iron at pH 2. Geochim. Cosmochim. Acta 48, 85–92. Williamson, M.A., Kirby, C.S., Rimstidt, J.D., 2006. Iron dynamics in acid mine drainage. In: 7th International Conference on Acid Rock Drainage (ICARD). American Society of Mining and Reclamation (AMSR), Lexington, KY, pp. 2411– 2423. Williamson, M.A., Rimstidt, J.D., 1994. The kinetics and electrochemical ratedetermining step of aqueous pyrite oxidation. Geochim. Cosmochim. Acta 58, 5443–5454. Yu, Y.M., Zhu, Y.X., Gao, Z.M., Gammons, C.H., Li, D.X., 2007. Rates of arsenopyrite oxidation by oxygen and Fe(III) at pH 1.8–12.6 and 15–45 degrees C. Environ. Sci. Technol. 41, 6460–6464. Zhang, H., Selim, H.M., 2005. Kinetics of arsenate adsorption–desorption in soils. Environ. Sci. Technol. 39, 6101–6108. Zhu, C., Burden, D.S., 2001. Mineralogical compositions of aquifer matrix as necessary initial conditions in reactive contaminant transport models. J. Contam. Hydrol. 51, 145–161. Zhu, Y., Merkel, B.J., 2001. The Dissolution and Solubility of Scorodite, FeAsO42H2O: Evaluation and Simulation with PHREEQC2. Wiss. Mitt. Inst. für Geologie, TU Bergakedemie Freiberg, Germany.
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Applied Geochemistry journal homepage: www.elsevier.com/locate/apgeochem
Trace element source terms for mineral dissolution Madeline E. Schreiber ⇑, J. Donald Rimstidt Department of Geosciences, Virginia Tech, 4044 Derring Hall, Blacksburg, VA 24061, USA
a r t i c l e
i n f o
Article history: Received 19 March 2013 Accepted 15 July 2013 Available online 25 July 2013 Editorial handling by M. Kersten
a b s t r a c t We present an approach for determining source terms for modeling trace element release from minerals, using arsenic (As) as an example. The source term function uses laboratory-measured mineral dissolution rates to predict the time rate of change of As concentrations (mol/L s) released to water by the dissolving mineral. Application of this function to As-bearing minerals (realgar, orpiment, arsenopyrite, scorodite, pyrite, and jarosite) in air saturated water at 25 °C shows that mineralogy, grain size and pH are important factors affecting the As source term while DO concentration and temperature are relatively unimportant for conditions found in typical aquifers. The derived function shows that the source term decreases as a function of (1 t/tL)2, where tL is the grain lifetime, due to the shrinkage of the mineral grains as they dissolve. For some models, either a constant or an instantaneous term might be used, provided that certain time constraints are met. The methods outlined in this paper are intended to help bridge the gap between laboratory measurements and field-based models. Although this paper uses As as an example, the methods are general and can be used to predict source terms for other mineral-derived trace elements to groundwater. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Release of trace elements to groundwater is a potential cause for health concern worldwide. Elements such as arsenic, uranium, lead, cobalt, selenium, nickel and many others are present in both naturally-occurring minerals and human sources and can be released over time into groundwater as the source materials dissolve. A recent study by the USGS found that close to 20% of untreated water samples from public, private and monitoring wells in the US contain concentrations of at least one trace element above its drinking water standard (Ayotte et al., 2011). Precipitation contains only small amounts of trace elements dissolved from the atmospheric dust (Chilvers and Peterson, 1987). As the precipitation infiltrates and flows from surface to the saturated zone, dissolution of aquifer materials release trace elements into solution. Quantifying this rate of trace element release is a key step toward predicting if water sources may become contaminated. Arsenic is an example of a trace element of health concern. Arsenic (As) is both a toxin and a carcinogen, implicated in cardiovascular, pulmonary, immunological, neurological, and endocrine disorders, as well as skin, lung, bladder, and kidney cancers (NRC, 1999, 2001). Long-term exposure to contaminated drinking water has been cited as the most widespread threat to human health posed by As (Nordstrom, 2002; Smith et al., 1992). Contamination of groundwater by As is of particular concern, as it is linked to common naturally-occurring geochemical processes such as reduction ⇑ Corresponding author. Tel.: +1 540 231 3377; fax: +1 540 231 3386. E-mail address: [email protected] (M.E. Schreiber). 0883-2927/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apgeochem.2013.07.011
of Fe oxyhydroxides, oxidation of sulfides, and desorption from mineral surfaces (Mandal and Suzuki, 2002; Nordstrom, 2002; Smedley and Kinniburgh, 2002; Welch et al., 2000). Removal of As from groundwater can be a difficult and expensive process, because unlike organic compounds, As cannot be biotransformed to a less harmful species but instead must be either removed via ex situ processes (e.g., pump-and-treat) or immobilized via in situ processes (e.g., adsorption onto Fe-oxides or precipitation of As-bearing sulfides). Because groundwater is a primary pathway connecting As sources to target organisms, preventing As exposure from groundwater consumption requires an understanding of the factors that control As release from the source and transport to the target. Geochemical models that simulate As behavior in groundwater can range from simple inverse models to complex reactive transport models. Some of the more detailed models incorporate aquifer mineralogy (e.g., Zhu and Burden, 2001) surface complexation reactions to simulate retardation by adsorption–desorption processes (e.g., Parkhurst and Appelo, 1999; Wallis et al., 2011) and rate equations to simulate oxidation–reduction reactions (e.g., Decker et al., 2006; Radu et al., 2008; Wallis et al., 2010) and microbial growth (e.g., Wallis et al., 2010). One critical element that these models often lack is a source term that represents the rate of release of As from the solid matrix into groundwater. PHREEQC (Parkhurst and Appelo, 1999) and associated models PHAST (Parkhurst et al., 2010) and PHT3D (Prommer et al., 2003) include a source term module that can simulate mineral dissolution. However, even in models with source term modules, there are challenges in turning laboratory measured dissolution rates to ‘‘field
M.E. Schreiber, J.D. Rimstidt / Applied Geochemistry 37 (2013) 94–101
95
Nomenclature A ABET Ageo Cm,i Cmx,i Cmx,m D(t) Ff Fsr k Mm
surface area, m2 BET specific surface area, m2/g geometric specific surface area, m2/g (assumes spherical particles) concentration of element i in mineral, ppm concentration of element i in the aquifer matrix, ppm concentration of mineral in the aquifer matrix, ppm diameter of mineral grains at time t, m field factor; adjusts for slower dissolution rates in field settings surface roughness factor (=ABET/Ageo) rate constant for zeroth order reaction = rgeo(pH, T), mol/m2 s mass of dissolving mineral in source region, g
effective’’ rates, and in simulating the release of elements that occur in trace concentrations in common minerals. To address these challenges, we derive general expressions that use laboratory-derived rate data to predict trace element source terms due to host mineral dissolution. To illustrate their implementation, we focus on the dissolution of common As-bearing minerals, including arsenopyrite (FeAsS), realgar (AsS), orpiment (As2S3), and pyrite (FeS2), and the secondary minerals scorodite (FeAsO42H2O) and jarosite (KFe3(SO4)2(OH)6). This method for transforming the laboratory rates into a usable form for models also incorporates a shrinking particle model that accounts for the decline in the source terms as the minerals dissolve away. The approach presented here does not introduce any novel equations but instead it provides a detailed accounting of the unit transformations that must be carried out (see Supplementary information). This approach cannot address rates of As release from minerals due to desorption. Although previous studies have documented that kinetics does play a role in desorption (O’Reilly et al., 2001; Raven et al., 1998; Smith and Naidu, 2009; Zhang and Selim, 2005), desorption kinetics are much faster than mineral dissolution kinetics and for the purposes of this paper are assumed to be close to equilibrium (see Bearup et al. (2012) for more discussion of this topic). We also do not consider As release from microbially-mediated reactions. Although it is well-recognized that microbiallymediated reduction of Fe oxyhydroxides can result in As release, our understanding of how As is released from mineral surfaces due to these processes is incomplete (Tufano and Fendorf, 2008) and there are currently no available rate data that can be transformed into source terms. Examples used in this paper are based on rates from experiments carried out under far from equilibrium conditions, so the resulting source terms are maximum values. However, the method is general and slower rates could be used if expressions for the dissolution rates as a function of chemical potential are known.
2. Methods 2.1. Selection of laboratory derived rates We selected from the literature experimentally-determined rates of dissolution for As-bearing minerals (see Table 1). When possible, data from several sources were compared and correlated in order to identify the most reliable values. We adjusted those values to find the rate expected for air-saturated, dilute groundwater, at 25 °C leaving pH as the only factor that remains as a variable. An underlying assumption is that mineral dissolution is irreversible
mi / rBET rgeo Rm(t)
qm qmx Si(t) t tL V Vm Wi Wm
stoichiometric factor, mol element i/mol mineral porosity of aquifer mineral dissolution rate, mol/m2 s (normalized to ABET) mineral dissolution rate, mol/m2 s (normalized to Ageo) mineral destruction rate at time t, mol/s density of mineral, g/cm3 density of matrix solids, g/cm3 source term for element i at time t, mol/L s time, s grain lifetime, s volume of source region, m3 molar volume, m3/mol molecular weight of element i, g/mol molecular weight of mineral, g/mol
and that the trace element is homogeneously distributed in the mineral. 2.2. Derivation of source term equation Four main steps are needed to convert laboratory-determined mineral dissolution rates to rates of release of element i contained in that mineral to groundwater in an aquifer. These adjustments simply express the mineral dissolution rate in different ways with appropriate unit transformations. Keeping track of these different rates is challenging and we refer the reader to the unit analyses shown in the Supplementary information. The source term for an element released from a dissolving mineral in an aquifer is linked to the laboratory determined dissolution rate of that mineral by the following transformations and adjustments: (1) The laboratory-determined mineral dissolution rates, rBET (mol/m2 s), are converted to rates based on geometric surface area and adjusted for the difference between laboratory and field rates to give rgeo (mol/m2 s). (2) rgeo (mol/m2 s) is converted to the mineral destruction rate, Rm(0) (mol/s), by multiplying by the specific surface area and the mass of mineral dissolving in the aquifer. (3) A shrinking particle model is used to predict the rate of mineral destruction as a function of time, Rm(t) (mol/s). (4) Rm(t) (mol/s) is divided by the volume of water in the aquifer pores to find the source term for constituent i, Si(t) (mol/L s). 2.2.1. Step 1: Converting laboratory-determined rates to field rates Most laboratory studies report mineral dissolution rates normalized to BET surface areas (ABET). Measurement of ABET is easily done for clean, monominerallic laboratory samples but is nearly impossible for natural materials because of the difficulty of obtaining pure representative mineral fractions and the challenge of separating minerals without changing the surface area of the minerals. Thus, it is necessary to recast the laboratory dissolution rates to a geometric surface area basis because Ageo can be computed using measured grain size. ABET is always larger than Ageo because of the roughness of the grain’s surfaces. This discrepancy is reported as the surface roughness factor (Fsr). The surface roughness factor accounts for all of the factors that cause the grains to differ from a perfect spherical shape, such as the grains’ cleavage and fracture geometry, surface etching patterns, and surface porosity. To adjust from a BET surface area to a geometric surface area, the rates are multiplied by Fsr. In this paper we will use a median value of 7 for Fsr (White and Peterson, 1990). Other studies comparing BET
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Table 1 Mineral dissolution rates (rgeo, mol/m2 s) based on Eq. (1) at 25 °C (298 K) of common As-bearing minerals normalized to geometric surface area. For DO oxidation reactions, the dissolution rate is based on a DO concentration of 103.6 mol (air-saturated water at 25 °C and 1 atm pressure). For Fe(III) oxidation reactions, we assume an Fe(III) concentration in equilibrium with ferrihydrite at 25 °C. Calculations assume Fsr = 7 and Ff = 1. Molar volume (Vm) data from the following sources: scorodite (Dove and Rimstidt, 1985); orpiment, realgar and pyrite (Robie and Hemmingway, 1995); arsenopyrite (Robie et al., 1967). Molar volume for jarosite calculated using average cell dimensions given in Desborough et al. (2010).
qm
Mineral
Realgar (real, DO) Orpiment (orp, DO) Arsenopyrite (aspy, Fe) Arsenopyrite (aspy, DO) Pyrite (py, Fe) Pyrite (py, DO) Scorodite (scor) Jarosite (jar)
Wm (g/mol)
Vm (m3/mol) (105)
Reaction
Rate equation for mineral dissolution
pH range
Rate data source
(g/cm3) 3.56 3.52 6.07 6.07 5.01 5.01 3.20 3.09
107.0 246.0 162.8 162.8 120.0 120.0 230.8 500.8
7.05 2.98 2.6 2.6 2.39 2.39 6.99 15.96
DO oxidation DO oxidation Fe(III) oxidation DO oxidation Fe(III) oxidation DO oxidation Incongruent dissolution Dissolution
Log rgeo = 9.48 + 0.13pH Log rgeo = 10.02 + 0.18pH Log rgeo = 2.9 2.94pH Log rgeo = 8.19 Log rgeo = 0.49 2.79pH Log rgeo = 9.145 + 0.11pH Log rgeo = 9.68 0.14pH Log rgeo = 10.02 + 0.392pH
2.3–8.7 2.3–8.2 <4 1.8–12.6 <4 >4 3–8 >3.5
Lengke et al. (2009) Lengke et al. (2009) Rimstidt et al. (1994) Yu et al. (2007) Williamson and Rimstidt (1994) Williamson and Rimstidt (1994) Harvey et al. (2006) Madden et al. (2012)
to geometric surface areas report roughness factors ranging from 2 to 11 (Anbeek, 1992; Brantley and Mellott, 2000). Many studies have shown mineral dissolution rates measured in field settings are slower than laboratory measured rates by field factors (Ff) ranging from 0.1 to 0.001 (e.g., Malmström et al., 2000; Paces, 1983; Swoboda-Colberg and Drever, 1993; Velbel, 1985, 1993). At the present time the cause of this effect is not fully understood and therefore values of Ff are not predictable. We include this field factor effect in our equations as a calibration variable and set the value of Ff = 1 for subsequent examples. Combining these adjustments gives
Integrating (7) with the requirement that the diameter is D(0) when t = 0 gives
r geo ¼ F sr F f r BET
DðtÞ ¼ Dð0Þ 2kV m t
ð1Þ
The rate of volume loss of the particle is also given by the time derivative of the volume formula for a sphere
dV pD2 dD ¼ dt 2 dt
ð6Þ
Setting (5) equal to (6) gives
dD ¼ 2kV m dt
ð7Þ
ð8Þ
so the lifetime for a particle (tL) with an initial diameter of D(0) is 2.2.2. Step 2: Converting rgeo to rate of element release from mineral, Rm(0) Next rgeo is multiplied by the geometric surface area of the grains, assuming spherical particles, and the mass of mineral in the source region (Mm) to find the rate of mineral destruction:
Rm ð0Þ ¼ Ageo M m r geo
ð2Þ
Note that although we assume spherical particles in our model, the model could be altered to accommodate other geometries, such as euhedral crystals. The geometric surface area of a spherical particle is (Lowell and Shields, 1991)
Ageo ¼
6 106 qm D
! ð3Þ
2.2.3. Step 3: Predicting the rate of mineral destruction over time, Rm(t) With continual flushing, the mineral grains will dissolve and the release rate of element i will decrease. Although more sophisticated models may be appropriate when detailed information about the mineral dissolution behavior is known, a simple ‘‘shrinking particle’’ model provides a good first approximation of this behavior. To simplify this derivation and to make it consistent with previous derivations (Lasaga, 1998) we define k = rgeo at fixed pH and temperature. This model is an extension of the particle lifetime model derived by Lasaga (1981). Assuming that mineral particles are spherical, the mineral destruction rate is
Rm ¼ Ak ¼ pD2 k
ð4Þ
and the rate of volume loss for the particle is
dV ¼ Rm V m ¼ pD2 kV m dt
ð5Þ
tL ¼
Dð0Þ 2kV m
ð9Þ
In addition to predicting particle lifetime, the shrinking particle model predicts how the rate of mineral destruction decreases as the mineral dissolves. Eq. (9) can be rearranged to
2kV m ¼
Dð0Þ tL
ð10Þ
and substituted into (8) to yield
DðtÞ t ¼ 1 Dð0Þ tL
ð11Þ
Rearranging (4) to
D¼
1=2 Rm pk
ð12Þ
and substituting into (11) gives
2 Rm ðtÞ t ¼ 1 Rm ð0Þ tL
ð13Þ
This convenient formulation gives the dimensionless rate as a function of dimensionless time so Rm(t) can be calculated for any time based on Rm(0) and tL. 2.2.4. Step 4: Derivation of source term Combining Eqs. (2) and (13) gives the rate of mineral destruction over time as a function of the mineral properties (density, grain size, dissolution rate), the mass of the mineral in the aquifer (Mm), and the particle lifetime:
Rm ðtÞ ¼
! 2 6 106 t r geo Mm 1 tL qm D
ð14Þ
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where the mass of mineral per m3 aquifer is
Mm ¼ C mx;m qmx ð1 /Þ V
ð15Þ
The source term (Si(t), mol/L s) is found by multiplying Rm(t) by the stoichiometric factor for i and dividing by the volume of solution in the aquifer pores.
! 6 106 Si ðtÞ ¼ qm D /103 2 t ðF sr F f r BET Þ ðC mx;m qmx ð1 /ÞÞ 1 tL
mi
!
log rBET ðreal; DOÞ ¼ 8:78 þ 0:43 log mDO þ 0:13 pH
ð16Þ
Eq. (16) can be simplified to: 9
Si ðtÞ ¼
6 10
mi F sr F f C mx;m
2 qmx ð1 /Þ t 1 rBET / tL qm
Note that mi for minerals in which i is an essential element is simply the stoichiometric coefficient for i in the mineral formula. In the case where i is a trace constituent in the mineral,
CmW m
ð18Þ
106 W i
ð23Þ
The rate equation for orpiment oxidation by DO (Lengke and Tempel, 2003) is
ð17Þ
mi ¼
ð22Þ
Using a DO concentration of air-saturated water at 25 °C and 1 atm pressure (103.6 mol, or 8.5 mg/L), and adjusting for BET to geometric surface area by adding log (7), or 0.845, to the log rate gives:
log rgeo ðreal; DOÞ ¼ 9:48 þ 0:13 pH
!
D
3.1.1. Realgar and orpiment Realgar (AsS) and orpiment (As2S3) are often associated with hydrothermal gold deposits, volcanic deposits, and geothermal hot springs (Lengke and Tempel, 2002, 2003). Lengke et al. (2009) conducted linear regression analysis of rate data from several studies and report the following rate expression for realgar oxidation by dissolved oxygen (DO):
log rBET ðorp; DOÞ ¼ 10:32 þ 0:15 log mDO þ 0:18 pH
ð24Þ
Using the DO for air-saturated water and the BET to geometric surface area conversion, the rate of orpiment dissolution normalized to geometric surface area is:
log rgeo ðorp; DOÞ ¼ 10:02 þ 0:18 pH
ð25Þ
Eq. (17) would be used when the concentration of the mineral (g-mineral/106 g-aquifer matrix) has been quantified by point count analysis or some similar means. If the aquifer matrix has been analyzed to determine the concentration of element i, the concentration of the element-bearing mineral can be estimated from
3.1.2. Arsenopyrite When arsenopyrite (FeAsS) oxidizes in solutions with pH < 4, Fe(III) concentrations are high enough to make Fe(III) the predominant oxidant of arsenopyrite. At 25 °C and pH 1.8, the rate of oxidation of arsenopyrite by Fe(III) under oxic conditions (Rimstidt et al., 1994) is:
Mm C mx;i qmx W m ð1 /Þ ¼ V mi W i
log rBET ðaspy; FeÞ ¼ 2:84 þ 0:98 log mFeðIIIÞ
ð19Þ
When this method of determining Mm is used to calculate Si, the source term equation becomes
Si ðtÞ ¼
! 6 106 C mx;i qmx W m qm D mi W i /103 2 t F sr F f r BET ð1 /Þ 1 tL
mi
!
This equation can be simplified by combining terms to yield
Si ðtÞ ¼
6 109 F sr F f C mx;i D
!
qmx qm
Wm Wi
To convert to geometric surface area, we add log (7), or 0.845, to the log rate. We can also simplify the rate equation by estimating the dissolved Fe(III) concentration by assuming that it is controlled by ferrihydrite (fh) solubility:
FeðOHÞ3 ðfhÞ þ 3Hþ ¼ Fe3þ þ 3H2 O; ð20Þ
2 ð1 /Þ t 1 rBET / tL ð21Þ
Note that this approach assumes that i is contained in only one mineral. If i is present in more than one mineral, the equation can be expanded to distribute i among those minerals. In this way, the release of the trace element from multiple minerals with differing dissolution rates can be predicted. 3. Results and discussion 3.1. Determining rgeo for selected As-bearing minerals The functions for rgeo in Table 1 were calculated assuming a surface roughness factor (Fsr) of 7 and a field factor (Ff) of 1. For minerals undergoing oxidation by DO, we use a DO concentration of air-saturated water at 25 °C and 1 atm pressure (103.6 mol, or 8.5 mg/L). Rates for other DO concentrations at different temperatures and pressures can be easily calculated and incorporated by the user, as needed.
ð26Þ
log K ¼ 5:0
ð27Þ
Ferrihydrite was chosen here to illustrate how this calculation is performed. When constructing a model for a real case the equilibrium constant for the iron oxyhydroxide that is present in the source region should be used. Approximating the molarity of Fe(III) to be equivalent to the activity:
mFeðIIIÞ aFeðIIIÞ ¼ 105:0 a3Hþ
ð28Þ
The Fe(III) concentration as a function of pH can be combined with Eq. (26) to predict the dissolution rate of arsenopyrite via Fe(III) oxidation:
log rgeo ðaspy; FeÞ ¼ 2:9 2:94 pH
ð29Þ
If the arsenopyrite occurs in wastes that generate little or no acid, the ambient pH remains near neutral so the iron released from oxidizing arsenopyrite rapidly oxidizes to Fe(III) and becomes incorporated into iron oxyhydroxides or scorodite. Under these conditions DO is the predominant oxidant. Several papers report rates of arsenopyrite oxidation by DO (McKibben et al., 2008; Walker et al., 2006; Yu et al., 2007) but the experimental conditions (pH, DO concentrations) vary widely, as do the resulting rate expressions. Comparison of the arsenic release rates from DO oxidation of arsenopyrite from these studies reveals several apparent inconsistencies. For example, Walker et al. (2006) show no significant effect of DO concentrations (0.3–17 mg/L) on arsenopyrite oxidation while the rate laws reported in McKibben et al. (2008) and Yu et al. (2007) show DO dependence (reaction orders
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of 0.33 and 0.45, respectively). The discrepancies in these results likely reflect the very complicated chemistry that underlies this oxidation process, but could be due to a number of assumptions (e.g., which species to use for the reaction progress variable) or experimental conditions (e.g., temperature, pH, stirring rates, preparation of solids, and analytical methods). More research needs to be done on arsenopyrite oxidation by DO to settle some of these unresolved discrepancies. Because arsenopyrite oxidation by oxygen will be most important at pH > 4, the relevant datasets are from Yu et al. (2007) and Walker et al. (2006). Both these datasets indicate no significant pH dependence of the oxidation rate and yield rates within the same order of magnitude, but as the dataset from Yu et al. (2007) was generated under a wider range of pH values, we will use the rate generated from that dataset:
1 log r geo ðaspy; DOÞ ¼ 2211 þ 0:45 log mDO T
ð30Þ
Converting the BET to geometric surface area by adding log (7), or 0.845 to the log rate, and assuming a temperature of 25 °C (298 K) and DO for air-saturated water, the dissolution rate of arsenopyrite by DO oxidation normalized to geometric surface area is:
log r geo ðaspy; DOÞ ¼ 8:19
ð31Þ
As noted above, arsenopyrite oxidation by DO at circumneutral pH will result in precipitation of iron oxyhydroxides, which may armor the arsenopyrite from further oxidation (see Huminicki and Rimstidt, 2009). The model developed in this paper does not account for armoring, but the user could add additional terms to include this effect. 3.1.3. Pyrite The widespread occurrence of As-bearing pyrite makes it a potentially significant source of As. Pyrite with As contents of up to several percent are not unusual (Kolker and Nordstrom, 2001; Savage et al., 2000). Fe(III) is the most important oxidant under acid conditions (pH < 4) and dissolved oxygen is the most important oxidant at pH > 4 (Williamson et al., 2006). The rate of pyrite dissolution by Fe(III) oxidation (Williamson and Rimstidt, 1994) is:
log r BET ðpy; FeÞ ¼ 6:07 þ 0:93 log mFeðIIIÞ 0:40m log mFeðIIÞ
ð32Þ
To convert to geometric surface area, we add log (7), or 0.845, to log rate. As described above, we can also estimate the dissolved Fe(III) concentration by assuming that it is controlled by ferrihydrite solubility. The Fe(II) concentration in typical AMD is around 250 ppm (4.5 103 m) (Williamson et al., 2006). The resulting rate of pyrite oxidation by Fe(III) normalized to geometric surface area is:
log r geo ðpy; FeÞ ¼ 0:49 2:79 pH
ð33Þ
For pH > 4, pyrite oxidation rates are a function of DO and pH (Williamson and Rimstidt, 1994):
log r BET ðpy; DOÞ ¼ 8:19 þ 0:5 log mDO þ 0:11 pH
ð34Þ
Assuming DO saturation and adjusting BET to geometric surface area gives:
log r geo ðpy; DOÞ ¼ 9:145 þ 0:11 pH
ð35Þ
Note that we have assumed that the pyrite oxidation rates are not significantly affected by the pyrite trace element content. This assumption is justified by previous studies of the oxidation rates of pyrite samples from multiple sources (Lehner and Savage, 2008; Manaka, 2006; Wiersma and Rimstidt, 1984) that reported that rates vary by no more than 0.5 log units from sample to sample. The equations also assume a homogeneous As distribution in the pyrite although we realize that there can be significant zoning of
the As (Craig et al., 1998). This means that an analysis of a bulk pyrite sample should be used to assess the As content rather than microanalyses of a few spots. Finally, a significant amount of As can be taken up by Fe(III) minerals that might form as the pyrite oxidizes at high pH; this uptake should be accounted for in any geochemical model of As behavior. 3.1.4. Scorodite Scorodite (FeAsO42H2O) is a common weathering product of arsenopyrite and is often found in mine settings (Demopoulos, 2005; Dove and Rimstidt, 1985; Harvey et al., 2006; Langmuir et al., 2006; Zhu and Merkel, 2001). Congruent dissolution of scorodite, which occurs at low pH, releases equimolar concentrations of As and Fe. At higher pH, scorodite dissolves incongruently, forming iron hydroxide and arsenate oxyanions (Zhu and Merkel, 2001). Harvey et al. (2006) determined the scorodite dissolution rate as a function of temperature and pH. Results of experiments conducted between pH 2 and 6 reveal that the transition from congruent to incongruent dissolution, assuming that ferrihydrite is the iron oxyhydroxide that forms, occurs at approximately pH 3, which produces a shift in the pH dependence of the dissolution rate. The rate for incongruent scorodite dissolution as a function of temperature and pH from 3 to 6 is (Harvey et al., 2006):
log r BET ðscorÞ ¼ 6:2 0:14 pH 1290
1 T
ð36Þ
Adjusting for the conversion from BET to geometric surface area and assuming a temperature of 25 °C (298 K) results in:
log r geo ðscorÞ ¼ 9:68 0:14 pH
ð37Þ
3.1.5. Jarosite Arsenate can substitute for sulfate in jarosite, KFe3(SO4)2(OH)6, by various coupled substitutions that maintain charge balance (Savage et al., 2005) to produce jarosite that contains up to 9.9 wt% As(V) (Paktunc and Dutrizac, 2003). Jarosite dissolution rates have been measured for a range of pH by Madden et al. (2012). For pH greater than 3.5, the rate is
log r BET ðjarÞ ¼ 2:073 þ 0:392 pH 3858:9
1 T
ð38Þ
Adjusting this rate to get the rate of jarosite dissolution in terms of a geometric surface area at a temperature of 25 °C (298 K) gives
log r geo ðjarÞ ¼ 10:02 þ 0:392 pH
ð39Þ
3.2. Mineral dissolution rates versus pH Graphs of the mineral dissolution rates (rgeo) of these As-bearing minerals versus pH show several interesting trends (Fig. 1). For pH values typical of natural waters (4–8), there is a maximum of four orders of magnitude difference in dissolution rates of As-bearing minerals (107 to 1011 mol/m2 s). Dissolution rates of arsenopyrite, pyrite, orpiment and realgar are within one order of magnitude of each other, while the rate of scorodite dissolution is two orders of magnitude slower. Contrasting with patterns in acid waters, rates show less pH dependence within the pH range of natural waters. 3.3. Predicting the lifetime of As-bearing minerals The rgeo values from Table 1 can be used with the shrinking particle model (Eq. (9)) to find particle lifetimes. Fig. 2 compares particle lifetimes for 100 lm diameter grains of As-bearing minerals over the pH range of natural waters. The particle lifetime is directly proportional to the particle diameter (see Eq. (9)) so that
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M.E. Schreiber, J.D. Rimstidt / Applied Geochemistry 37 (2013) 94–101 Table 2 Parameters used in calculation of the As source term for scorodite example. Parameter
Symbol
Scorodite
Porosity of aquifer Stoichiometric factor Surface roughness factor Field factor Mineral density, g/cm3 Particle diameter, m Lifetime of particle, s Mineral dissolution rate, mol/m2 s Mass of mineral in aquifer, ppm
/
0.3 1 7 1 3.3 1.0 104 3.27 1010 3.09 1012 –
m Fsr Ff
qm D tL rBET Cmx,m
Additional parameters needed if Cmx,m is not known (Eq. (21)) Matrix density, g/cm3 qmx Mineral molecular weight, g/mol Wm Arsenic molecular weight, g/mol Wi Arsenic concentration in matrix, ppm Cmx,i
2.8 230.8 74.92 50,000
Fig. 1. Log mineral dissolution rate (rgeo, mol/m2 s) versus pH based on equations from Table 1. ‘‘Fe’’ = oxidation by Fe(III), ‘‘DO’’ = oxidation by dissolved oxygen.
Fig. 3. Arsenic source term (mol As/L s) from 10, 100 and 1000 lm diameter particles of scorodite using Eq. (21) and data from Table 2. The lifetimes for the 10, 100 and 1000 lm particles are 103, 1037, and 10,367 years, respectively. For other minerals, the shape of the curves will be the same but the times will be different.
Fig. 2. Particle lifetimes (years) for selected As-bearing minerals with 100 lm diameter grain size. The particle lifetime is directly proportional to grain size so that a 10 times increase in diameter will result in 10-fold increase in lifetime, and vice versa.
increasing the particle diameter by 10 times causes the lifetime to increase by 10 times.
shows that grain size has an important influence on the source term. Small grains dissolve quickly, and thus have a high initial As source term, but that term declines rapidly with time. In comparison, larger particles release As more slowly but persist over longer times. One simple way of examining how a source term changes over the lifetime of a mineral is to determine a characteristic time over which the source term at time t is within a certain % of the initial source term. To do this, we can rearrange Eq. (13) to solve for t:
t ¼ tL 3.4. Calculating the arsenic source term Calculating the source term, Si(t), requires additional information about the As-bearing mineral and the aquifer. If the mass of mineral in the aquifer matrix (Cmx,m) is known, Eq. (17) can be used to calculate the source term, with the parameters listed in the top of Table 2. In the more common case where the mass of mineral in the aquifer is not known, but an As concentration of the aquifer matrix (Cmx,i) is, and the As-bearing mineral(s) are identified, Eq. (21) can be used with the additional parameters at the bottom of Table 2. As an example, the As source term for an aquifer matrix containing 5 wt% As in the form of 100 lm diameter scorodite particles was calculated using the parameters in Table 2. Fig. 3 shows how the As source term for scorodite (10, 100 and 1000 lm grains) declines over time. Similar to the lifetime diagram (Fig. 2), Fig. 3
sffiffiffiffiffiffiffiffiffiffiffiffiffi! Rm ðtÞ 1 Rm ð0Þ
ð40Þ
This equation shows that for any mineral, the source term declines to 50% of the initial value when t = 0.29 tL. Thus, the source term will decline by 50% for 10 lm scorodite grains after 30 years; for 1000 lm scorodite grains, it will take almost 3000 years. In nature, As-bearing primary minerals, such as arsenopyrite, dissolve over time, forming secondary and tertiary As-bearing phases. The co-occurrence of primary and secondary/tertiary minerals complicate modeling efforts, as each of these minerals has different dissolution rates and particle lifetimes, resulting in differences in As source terms and changes in the source term over time. For example, arsenopyrite dissolves quickly (100 lm particle lifetime 10 years) and releases high concentrations of As to groundwater during that short time. If conditions are favorable for the formation of scorodite, this secondary mineral will persist in the aquifer for a much longer period of time (in this case,
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1000 years for 100 lm particle) but will release As to the aquifer much more slowly, resulting in lower As concentrations in groundwater. Incongruent dissolution of scorodite to form Fe oxyhydroxides, to which As can adsorb, will result in a tertiary source of As to groundwater systems, if conditions later shift to favor dissolution of the Fe oxyhydroxides.
3.5. End-member source term cases For some models either a constant or an instantaneous/pulse source term might be used, provided that certain conditions are met. A constant source term is justified if the simulation time is considerably shorter than the particle lifetime and an instantaneous source is justified only when the simulation time is much longer than the particle lifetime. Eq. (40) can be used to determine how short or long a simulation time must be for these end-member cases. For example, in order for the source term to remain above 90% of the initial value, the simulation time must be less than 5% of the particle lifetime. For As release from 100 lm diameter scorodite grains (pH 7; lifetime 1037 years) shown in Fig. 3, the simulation time must be less than 52 years to justify a constant source term in the model. If we can assume that source term is ‘‘spent’’ once it reaches 10% of the initial value, the simulation time must be longer than 68% of the lifetime of the mineral for the dissolution to be considered instantaneous. For example, a simulation of As release from 1 lm grains of scorodite (pH 7; lifetime 10.7 years) as an instantaneous event would require a minimum simulation time of 7 years.
3.6. Caveats for source terms application The examples in this paper use rate equations based on experiments performed far from equilibrium conditions. Rates that have been adjusted using either a (C Ceq) or a (1 Q/K) term could be used for models where minerals are dissolving under near equilibrium conditions. We estimate the precision of the rates selected here to be no better than ±0.3 orders of magnitude (± a factor of 2) with in some cases much larger uncertainties related to accuracy. Adjustments for the effect of temperature on rate using the Q10 rule (rate increases 2 per 10 °C) are on the same order as the precision of the rates. The largest effect of DO concentration reported for sulfide minerals involves a reaction order for oxygen of 0.5. Based on this, if DO were reduced from air saturation to 10% of air saturation the dissolution rate would decrease by a factor of three. Laboratory studies of mineral dissolution rates continue to produce more and improved data. Extensive efforts to compile and correlated mineral dissolution rate data have already produced easily accessible and more reliable rate equations that can be used to construct source terms for many minerals (see Marini, 2007; Palandri and Kharaka, 2004; Rimstidt et al., 2012). Inclusion of in situ coupled geochemical data over longer time frames would be especially useful to test theoretical models for simulating As release to groundwater. The purpose of this paper is not to supply definitive release rate values but rather to show how the laboratory data can be used in models of field situations. We suggest that any application of this approach should begin by updating and reevaluating the laboratory data.
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apgeochem.2013. 07.011.
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