A Computer Program To Assess Acid Generation in Pyritic Tailings

Chapter 11

A Computer Program To Assess Acid Generation in Pyritic Tailings 1

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Jeno M.Scharer ,Ronald V.Nicholson ,Bruce Halbert , and William J. Snodgrass 4

Downloaded by CORNELL UNIV on October 21, 2016 | http://pubs.acs.org Publication Date: December 20, 1993 | doi: 10.1021/bk-1994-0550.ch011

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Departments of Chemical Engineering and Earth Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada SENES Consultants Ltd., 52 West Beaver Creek Road, Richmond Hill, Ontario L4B 1L9, Canada Department of Civil Engineering, McMaster University, Hamilton, Ontario L8S 4M1, Canada 3

4

A computer program known as Reactive Tailings Assessment Program (RATAP) was developed to assist in predicting acid generation and major hydrogeochemical events brought about by the chemical and microbiological oxidation of sulfide minerals. The objective of the program is the application of fundamental kinetic and physical knowledge to field conditions for simulating the rate of acid production with time, simulating porewater quality in space and time. The kinetics of the abiotic and biological oxidations are key components of the program. The primary variables include the composition of the sulfide minerals, the specific surface area, the partial pressure of oxygen, the temperature, and the pH. In addition, biological reaction rates depend on the sorption equilibrium of the bacteria on the sulfide surface, the moisture content, and the availability of carbon dioxide (carbon source) and other macronutrients. The tailings soil profile is subdivided into layers comprising the unsaturated zone, the capillary fringe, and the saturated zone. Acid production occurs primarily in the unsaturated zone. A major control on the acid generation rate is the diffusive flux of oxygen in the pore space of the unsaturated zone. The diffusion coefficient, in turn, is related to the moisture content in a given zone. Computations are carried out at monthly time steps. The program can be run in a deterministic or probabilistic manner. For probabilistic assessment, an additional module known as RANSIM (random simulation), is utilized for the allocation of distributed parameter values. The program has been employed successfully to simulate field data at several tailings sites. 0097-6156/94/0550-0132$06.25/0 © 1994 American Chemical Society Alpers and Blowes; Environmental Geochemistry of Sulfide Oxidation ACS Symposium Series; American Chemical Society: Washington, DC, 1993.


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Acid Generation in Pyritic Tailings

SCHARER ET AL.

The control of acid mine drainage (AMD) from pyritic tailings is widely recognized as one of the most serious environmental issues facing many base metal, gold and uranium mine operations. While the collection and treatment of acidic drainage is common practice at operating mine sites, it is generally accepted that continued treatment after mine closure is neither desirable nor practical. Besides maintaining an effective treatment system indefinitely, the disposal of the large amount of chemical sludge produced after neutralization is a major operational problem Recognizing the magnitude of the problem, Canada Centre for Mineral and Energy Technology (CANMET) initiated several studies on the factors and processes which control mineral oxidation and on developing a predictive modelling tool to simulate acid generation in mine tailings. One of these early studies was a review of the mechanisms and kinetics of sulfide mineral oxidation (1). This study also documented the significance of chemolithotrophic bacteria in enhancing the oxidation rates. The first version of the RATAP model was completed by Beak Consultants Ltd. and SENES Consultants Ltd. in 1986. The objectives of the model development were: (1) the application of kinetic data to field conditions; and (2) evaluation of a coupled model to simulate AMD. Since its original conception, the RATAP model has undergone several modifications and has been calibrated extensively on several tailings sites in northern Ontario and in northeastern Quebec. The current version (version 3, released in March, 1992) may be run in a deterministic and probabilistic manner. It also allows the evaluation of a soil cover or underwater disposal options. Modelling Concepts In Table I, the reactive sulfide minerals in tailings and their more common oxidation products are shown. The RATAP model includes oxidation of five minerals : pyrite (FeSi), pyrrhotite (Fe^ S), chalcopyrite (CuFeS^, sphalerite (ZnS), and arsenopyrite (FeAsS). Based upon the review of the mineral composition of several tailings sites (1), calcite (CaC0 ), aluminum hydroxide (Al(OH) ), and ferric hydroxide (Fe(OH) ) are regarded as the principal buffering minerals. Depending on the reaction rate, solubility relationships, and pH, the oxidation may result in secondary mineral precipitation (2). The important secondary minerals considered in the program are gypsum (CaS0 -2H 0), ferric hydroxide (Fe(OH) ), jarosite (KFe3(S0 ) (OH) ), siderite (FeC0 ), aluminum hydroxide (Al(OH) ), covellite (CuS), malachite (Cu C0 (OH) ), anderite (Cu S0 (OH) ), smithsonite (ZnC0 ), and scorodite/ferric hydroxide coprecipitate (FeAs0 -2H 0/Fe(OH) ). Thermodynamic data for these solid phases have been compiled from published data (3-6). The physical concept employed in the RATAP model is summarized in Figure 1. The tailings soil profile is subdivided chemically and physically into 22 distinct layers comprising the hydraulically unsaturated zone, the capillary fringe and the saturated zone. Water movement from atmospheric precipitation is downward through the unsaturated zone and the capillaryfringe,while a portion of the flow may move horizontally out of the layer in the saturated zone to emerge as seepage passing through or below the perimeters of dams. The remaining portion moves downward into the subsurface aquifer. Exceptionally high mineral oxidation 3

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Alpers and Blowes; Environmental Geochemistry of Sulfide Oxidation ACS Symposium Series; American Chemical Society: Washington, DC, 1993.

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ENVIRONMENTAL GEOCHEMISTRY OF SULFIDE OXIDATION

PRECIPITATION


TAILINGS SURFACE

OXIDATION ID

Ζ Ο Ν Ο

LU

< ce

CO CE LU

Equations (3) and (4) represent the overall stoichiometry of pyrite and pyrrhotite oxidation to ferrous ion and sulfate. Pyrrhotite is more reactive than pyrite. Pyrrhotite is reported to be highly reactive below at pH values less than 2 but kinetic data lack reproducibility (15). Both may be catalyzed by direct enzymatic oxidation of the sulfide moiety (16-18). Equation (5) is also catalyzed by bacteria, particularly Thiobacillus ferrooxidans. This enzymatic oxidation of iron results in indirect biological leaching mechanisms with ferric ion being the principal oxidant in acidic solution. Equations (7) and (8) are abiotic, but they are believed to be the most important acid forming reaction under anoxic conditions. The oxidation of pyrrhotite by ferric ion in Equation (8) is particularly fast and can result in the accumulation of significant amounts of elemental sulfur. The kinetics of the biological and abiotic oxidation of metal sulfides are key components of the RATAP program. A number of factors have been shown to affect the oxidation rates. The principal controlling factors are the specific surface area, the temperature, and the pH. The chemical oxidation of sulfide minerals is modelled by the following relationship (14): E

IKT

H

9

r = Ae- - [OJ10-*>

()

c

where: r = abiotic rate constant (mol τη V ) [ O J = dissolved oxygen concentration (mol τη" ) Ε = Arrhenius activation energy (Jmol ) 1

c

3

1

Λ


140


Τ

= temperature (K)

The activation energies for the abiotic reactions are reported to be ranging from 42 to 88 kJmol" (19-22). The value of the pH-dependent parameter, i.e. χ in Equation (9), depends on the sulfide mineral. For most minerals, the value of χ appears to be near 0.5 (22). In addition to the controlling factors affecting abiotic oxidation, biological reaction rates are dependent on the sorption of bacteria on the mineral surface, the availability of carbon dioxide as the carbon source, the availability of macronutrients (phosphate, for example), and the presence of inhibitors. Neglecting the secondary effects, the biological reaction rate can be expressed as follows (23): 1


1 ι+ιο^-^+ισ*-

[0 ] 2

-EafRT

κ +[0 ] 0

2

(10) 4

where: 1

= biological surficial oxidation rate (molm'V ) b = biological scaling factor = specific growth rate (s ) σ = specific surface coverage (gm* ) = growth yield (gmol ) Ko = half saturation constant for oxygen (molτη ) E , Γ, and [OJ are defined as in Equation (9) 1

2

1

3

a

In equation (10), the biological scaling factor is introduced to fit site-specific data. The specific growth rate of the indigenous bacterial population is evaluated at 30°C and pH = 3.0. The specific growth rate is modulated by taking into account the moisture content (24), the carbon dioxide partial pressure (25, 26), and the availability of nutrients (9). Typical biological and abiotic oxidation rates and Arrhenius activation energies expected in tailings are summarized in Table H. The reaction rates were obtained with excess oxygen. The specific surface reaction rate constants have been derived from experimental results of Nicholson (21), Mehta and Murr (27), Ahonen et al. (28), Ahonen and Tuovinen (19), and Scharer et αϊ. (23). The nominal surface area has been based on particle size distribution assuming spherical symmetry. The chemical and, to a lesser extent, biological oxidation rates of other sulfides are enhanced by the presence of pyrite (18, 28). This enhancement has been attributed to a galvanic interaction between pyrite and the other minerals. This enhancement was not accounted for explicitly in the RATAP model. Sulfide Oxidation Module. Sulfides are assumed to occur as distinct, homogeneous particles of relatively pure composition (1). As these particles oxidize, they shrink in size. The oxidizing surface either remainsfreeof secondary mineral precipitation (low-pH conditions) or the deposition is not rate limiting (20). To account for these laboratory and field observations, sulfide oxidation in tailings is based on a concept of "shrinking radius" kinetics. It can be easily shown that the


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141

Table Π. Comparison of Specific Reaction Rates of Sulfide Oxidation at 30°C, pH=3.0, 20 kPa P (adapted from 18,21.23127,28,36.37) 02

COMPONENT

ACTIVATION ENERGY

SPECIFIC REACTION RATE 1

(mol-mV )

1

(J-mol ) abiotic

with bacteria pyrite

8

6.64 χ 10"


pyrrhotite

52,700

8

44,700

12

20,000

9

47,000

1.10 χ 10"

8

9.20 χ 10"

9

1.34 χ 10

8

1.88 χ 10'

9

1.9 χ 10

chalcopyrite

6.67 χ 10"

chalcopyrite with pyrite

1.43 χ 10'

sphalerite

7.75 χ 10"

1 sphalerite with pyrite

9

4.25 χ 10"

6.92 χ 10

8

1.41 χ ΙΟ"

21,000

13

45,000

10

rate of radial shrinkage of a more-or-less spherical particle is as follows: k.(t) = IsïïïL

(11)

Pi

where: &i(0 r r j pi ci

b

= = = =

-1

rate of radial particle shrinkage (m-s ) chemical surficial oxidation rate (mol τη V ) biological surficial oxidation rate (mol τη V ) molar density of the i * sulfide (molτη ) 1

1

3

th

In Equation (11) the subscript ί refers to the I sulfide species. Since the reaction rates are evaluated at monthly intervals, the total shrinkage becomes the sum of the monthly time increments (At):

where: Xj

= total shrinkage of particle ; to time t (m)

The fraction of unreacted sulfide mineral concentration in any layer can be determined by the combination of Equation (11) with the Pareto size distribution density function, i.e. the differential form of Equation (1). It should be noted that


142


the Pareto distribution refers to an initial (time zero) distribution. It is self evident that no particle with an original radius of X or less can exist at any later time, since the particles with lesser radii have shrunk to zero size. Thus, the unreacted sulfide mineral concentration at any time t is given by the following integral expression: ï

where: Mj(0 = unreacted sulfide mineral concentration (molm" ) Mi = initial sulfide mineral concentration (mol τη" ) 3

3


0

The major advantage of employing a Pareto-type size distribution is that the resulting integral, i.e. Equation (13), is analytic. The integral is a polynomial expression of QCJR). The coefficients and the exponents of the polynomial series can be readily determined from the Pareto parameters. Oxygen Transport Module. In tailings and waste rock, the transport of oxygen through the pore space is regarded as the ultimate limit of the sulfate-generation flux (21, 30-32). The primary modes of oxygen transport in tailings are molecular diffusion through the pore space in the unsaturated zone and, to a much lesser extent, advective transport of dissolved oxygen in the percolating porewater: * dt

where: C De Ζ t

ν

+

Χ > * £ + ν * * - Ε ϊ ^ e

2

dz

"Hz

r

(14)

* dt 3

= = = = = =

concentration of oxygen in the air-filled pore space (mol τη" ) effective diffusion coefficient of oxygen (nrV) depth into tailings (m) time (s) water infiltration rate (nrs" ) modified Henry's law constant (molm oxygen in liquid per molm" oxygen in gas phase) = concentration of the I metal sulfide (mol τη" ) = stoichiometric coefficient relating oxygen uptake to sulfide mineral oxidation !

3

3

th

Ίι

3

The differential term on the right hand side of Equation (14) is the time differential of Equation (13). It can be shown (23), that the oxygen concentration approaches a steady-state condition within a few days for typical tailings conditions. Consequently, a "monthly steady state" approximation can be derived by neglecting the first term in Equation (14). Moreover, the oxygen dependence of the sulfide oxidation rate (see Equations (9) and (10) ) can be resolved as the sum of a zeroorder andfirst-orderoxygen-dependent terms, provided that the sulfide oxidation


11.

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143

rates approach zero as the oxygen concentration in the pore space becomes zero. A finite difference form of Equation (14) yields a tridiagonal matrix which is easily solved by decomposition followed by forward and backward substitution (11). Enthalpy (Temperature) Transport Module. The temperature has a profound effect on both the abiotic and the biological oxidation rates. To calculate the temperature in the tailings, a simple enthalpy balance is employed. Because it is difficult to construct a global enthalpy model, the monthly temperature at various depths in the tailings is calculated as a temperature rise resulting from enthalpies of sulfide oxidation reactions:


n

where: AT p k F C H E Ζ QRX C B

w

w v

w

p

= = = = = = = = = =

dAT

2

j d AT

π

dAT

n

„

*υ „

/1 c\

temperature rise in the tailings (K) tailings bulk density (kgτη ) thermal conductivity (Jm^K'V ) vertical water flux (molmV ) molar heat capacity of water (Jmol^K ) enthalpy of evaporation (J-mol ) evaporative water loss (mol τη Y ) depth into tailings (m) sulfide reaction enthalpy generation (Jm"V ) specific heat capacity of tailings (J kg" ) 3

1

1

1

1

1

1

1

As in case of oxygen transport, the temperature is calculated by assuming monthly steady-state conditions. In addition, the sulfide reaction enthalpy term is linearized by Taylor's expansion. The solution of the equation is iterative as shown in Figure 2. The baseline temperature is taken as the first estimate for the monthly steady-state temperature. Using this baseline, the temperature rise is calculated by employing afinite-elementmethod. The predicted tailings temperatures usually do not rise more than 5 Κ above the baseline which is consistent with field observations. Solute Transport Module. Calculations in the solute transport model are based on material balances for each component. Transport calculations include both kinetically controlled reactions (sulfate formation by sulfide oxidation, for example) and equilibrium-controlled reactions (sulfate formation due to gypsum dissolution, for example). Aqueous speciation and the determination of porewater pH are also performed in this module. The calculation procedure is similar to the methodology employed by Parkhurst et al (33). Rather than the Newton-Raphson method, the method of false position (11) is employed as a root-finding algorithm for estimating the pH. The latter method gives generally faster convergence.


144



Model Simulations Model calibration and validation studies have been carried out at several tailings areas. In this paper, model simulations are reported for the Nordic tailings management area near Elliott Lake, Ontario. The Nordic tailings cover approximately 100 hectares and contain 12 million metric tons of pyritic tailings. The deposition of tailings in this basin was halted in 1968. The reactive mineral content of the tailings at the cessation of mill operations is estimated to be 6% pyrite (10% in coarse tailings), 5% gypsum, 0.5% calcite, 0.4% ferric hydroxide, 0.2% aluminum hydroxide, and 13.6% sericite. Smyth (34) and Dubrovsky et al. (35) collected extensive field data on the site. The data selected for comparison are from two sampling sites (designated as T3 and T5) approximately 0.75 km apart. Location T5 comprises coarse tailings (sands) adjacent to the old tailings discharge pipe. The depth to the water table is 4.0 to 4.5 m. At location T3, the tailings consist of fine material (slimes) and the water table is 6.0 to 6.5 m below the surface. To simulate field conditions, the Pareto parameters for tailings samples at both sites were obtained. Conditions for 1968 were used as initial conditions and the simulation was run for 13 years. In Figures 4-11, the model output after 13 years of simulation is compared with field data collected in 1981. There was no parameter adjustment between year zero (1968) and year 13 (1981). The measured and predicted gaseous oxygen concentrations with depth are shown in Figure 4 (location T3) and Figure 5 (location T5). The oxygen profile is predicted to fall rapidly to zero at 1.3 m depth at location T3. This is consistent with the higher moisture content, hence lower effective diffusion rate coefficient, of fine tailings. The measured residual oxygen content of 2% persisting to a depth of 6 m represents the detection limit for the method. In contrast, the diffusion of oxygen in coarse tailings is higher and the oxygen concentration profile extends to a greater depth (see Figure 5). Predicted and observed dissolved calcium concentrations are shown in Figure 6 (location T3) and Figure 7 (location T5). The good agreement between measured and predicted values reflect the presence of gypsum as the controlling solid phase. Figure 8 and Figure 9 show the observed and predicted sulfate concentrations at location T3 and location T5, respectively. As in case of calcium, the simulated results agree fairly well with the observations. The pH simulations for the porewaters at T3 and T5 are shown in Figure 10 and Figure 11. The predicted pH values are within 1 pH unit of observations, which is reasonable in view of the ionic imbalance noted in the field data. The stepwise profile of the simulations reflect the presence of buffering minerals. Both the measured and simulated pH values are lower in coarse tailings (Figure 11) indicating greater depletion of solid buffers under higher acid flux. This is consistent with the higher gaseous porosity, hence higher rate of oxygen transport in coarse tailings. Infinetailings (Figure 10) the surface pH is slightly higher than at a depth of 1 m. This is due to the initially lower pyrite content and the depletion of pyrite from the upper 0.3 m. The residual pyrite content after 13 years of oxidation is shown in Figure 12. The oxidizing front (pyrite depletion) at T3 is sharper, which is consistent with the


11. SCHARER ET AL.

145


LEGEND: PREDICTED OBSERVED

ο > X Ο


LU Ο OC LU CL

x\ χ

Χ Χ Χ X XX

χ χ χ κ χ χ χ χ χ κ

DEPTH FROM TAILINGS SURFACE (m)

Figure 4.

Observed and simulated oxygen concentrations infinetailings, location T3.

21

18

LEGEND:

H

PREDICTED OBSERVED

15 H 2

LU Ο > Χ

12 H

ο I-

ζ

LU Ο DC LU CL

9

H

6

H

3 H

-τ—ι—ι—Γ 2.4

2.7


Figure 5.

Observed and simulated oxygen concentrations in coarse tailings, location T5.


3.0

146


Τ

5

Ε

ce

hZ ID Ο Ο Ο


2

2Η

D

LEGEND:

< ϋ

PREDICTED

H

OBSERVED

ο

3

ο• DEPTH FROM TAILINGS SURFACE (m)

Figure 6.

Observed and simulated calcium concentrations in fine tailings, location T3.

?

5

Ε

LEGEND: PREDICTED OBSERVED

< oc

3H

ο ζ ο Ο

2

Ο -J

< ο

ι

ο

6" 3

Τ" 0

1

2

3

4

οDEPTH FROM TAILINGS SURFACE (m)

Figure 7.

Observed and simulated calcium concentrations in coarse tailings, location T5.


11.

SCHARER ET AL.


147

4 -J

3H


2 H

LEGEND: PREDICTED

1

H

OBSERVED

DEPTH FROM TAILINGS S U R F A C E (m)

Figure 8.

Observed and simulated sulfate concentrations in fine tailings, location T3.

cn Ε < ce ο Ο

ϋ LU

2H

LEGEND:

< Χ

PREDICTED

CL -J

OBSERVED

ZD

CO ο

ϋ~

Ο

DEPTH FROM TAILINGS S U R F A C E (m)

Figure 9.

Observed and simulated sulfate concentrations in coarse tailings, location T5.

American Chemical Society Library

ίΐ 55 ϊϋΐίί Si. it W. Alpers and Blowes; Environmental Geochemistry of Sulfide Oxidation ACS Symposium Series; American Chemical Society: Washington, DC, 1993.


6 -

5 "


4 3

LEGEND: PREDICTED

2 -

OBSERVED

1 -

0

2

4

6


Figure 10. Observed and simulated pH in fine tailings, location T3.

β LEGEND: PREDICTED

6 *

OBSERVED

5 4 X

3 -

X

X

X

2 1 -

0

1

2

3

4


Figure 11. Observed and simulated pH in coarse tailings, location T5.


11.


SCHARER ΈΤ AL.

149

20 LEGEND: 18 H PREDICTED (LOCATION T3) PREDICTED (LOCATION T5)

16 • «

14 12

ID ce

OBSERVED (LOCATION T3) OBSERVED (LOCATION Τ5)

-i

10 8 H


Q.

6 4 2

"i

DEPTH FROM TAILINGS SURFACE

(m)

Figure 12. Pyrite depletion in fine (location T3) and coarse (location T5) tailings. higher moisture content and higher oxygen gradient in the fine-grained tailings. The oxidizing zone after 13 years is approximately 1.5 m deep at T3 and 2.5 m deep at T5. The greater depth of the oxidizing zone in coarse tailings reflects higher oxygen transport Random Simulation Module As with any predictive assessment, probabilistic analysis involves mathematical expressions (models) of some physical system, in the present case, sulfide tailings. Many variables are not known with certainty. The uncertainty arises from natural heterogeneity, normal experimental or measurement errors, or simply the lack of sufficient database. Consequently, it is impossible to describe the input variables by a single value. Rather, the state of knowledge (or ignorance) about any input variable can be described by a subjective probability distribution. Hie module allows the selection of a number of known statistical distributions ranging from simple triangular distribution to gaussian, log-normal, and beta frequency functions. In the probabilistic assessment mode, several input parameters are specified as distributions. The distributed parameters are sampled by statistical sampling procedure (either Monte Carlo or latin hypercube sampling techniques) and the values drawn are entered into the component models. The process, which is referred as a trial, is repeated as often as desired. At least 100 trials are required to obtain reasonable outputs for up to 100-year simulations. Figure 13 is an example of probabilistic assessment of pH in tailings porewater. The output variable (sulfate concentration with depth at a given time, for example) from such an analysis is treated as a sample of a collection of output


150


variables. For these, the statistical mean, the variance, the probability density function, or the cumulativefrequencyfunction may be estimated as desired. The information may be interpreted as describing the output in terms of subjective probability. As an example, it may be used to evaluate the probability that the pH drops below a threshold limit in the porewater at a given time and depth.


Conclusions The goal of the RATAP program is the application of fundamental kinetic and transport data from the laboratory to tailings in the field. In tailings, the predominant reactive minerals are pyrite and pyrrhotite. The mechanism and the kinetics of pyrite oxidation are fairly well known. Although most studies have examined the biological oxidation phenomena from a bioleach processing perspective, the more significant fundamental studies of microbial pyrite oxidation kinetics (28,29, 36,37) are relevant to the assessment of biological action on pyrite in tailings. In contrast to the voluminous literature on the oxidation of pyrite, kinetic studies on pyrrhotite, either as a sole reactant or in mixture, are scarce. Although the importance of galvanic interactions between pyrrhotite and other sulfide minerals has been recognized (29, 38, 39), only a single recent work (19) has focussed on the comparative kinetics of pyrrhotite oxidation in sufficient detail to be of any value in estimating biological activity in pyrrhotite containing tailings. Pyrrhotite oxidation kinetics have been a subject of recent laboratory studies by Nicholson and Scharer in this volume.

TIME (years) Figure 13. Probabilistic assessment of porewater pH.


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RATAP has proven to be a useful analytical tool in assessing acid generation in pyritic tailings. The model has been successfully applied to establish the extent and duration of AMD, at several tailings sites. Comparisons of simulated porewater quality and solids concentrations with field data in the Elliot Lake area have shown excellent agreement. The application of the model at other sites may require scaling of the kinetic parameters. The scale factors can be easily established from laboratory tailings oxidation studies. We acknowledge the invaluable editorial suggestions and comments by Dr. C. Alpers, of the USGS.


Literature Cited 1.

2.

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Senes Consultants Ltd., Estimation of the Limits of Acid Generation by Bacterially Assisted Oxidation in Uranium Mill Tailings; CANMET DSS File # 15SQ 23241-5-1712; 1984. Nordstrom, D. K., Aqueous Pyrite Oxidation and the Consequent Formation of Secondary Iron Minerals in Acid Sulphate Weathering, Kittrick, J.A., Fenning, D.S., and Hossner, L.R., Eds. Soils Sci. Soc. Am.: 1982, 37-56. Sillen, L. G., Martell, A. E. Stability Constants of Metal Ion Complexes. Special Publication No. 17. The Chemical Society, London, U.K.: 1964. Smith, R. M . ; Martell, A. E. Critical Stability Constants. Inorganic Complexes. Plenum Press, New York and London 1976, Vol. 4, 257 pp. Boorman, R. S.; Watson, D. M. CIM Bulletin 1976, 69, 86-96. Motekaitis, R. J.; and Martell, A. E. The Determination and Use of Stability Constants. VCH Publishers, New York, NY: 1988, 216 pp. Blowes, D. W.; Reardon, E. J.; Jambor, J. L.; Cherry, J. A. Geochim. Cosmochim. Acta 1991, 55, 965-978. Steger, H. F.; Desjardins, L. E. Chem. Geol. 1978, 23, 225-233. Hoffmann, M. R.; Faust, B. C.; Panda, F. Α.; Koo Η. Α.; Tsuchiya, Η. M . Appl. Environ. Microbiol. 1981, 42, 259-271. Kendall, M.; Stuart, A. The Advanced Theory of Statistics, Griffin and Co., London, U.K.: 1977, Vol. 2, pp 176-178. Press, W. H.; Flannery, B. P.; Teukolsky, S. Α.; VeHerling, W. T. Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, U.K.: 1986, 818 pp. Hillel, D. Fundamentals of Soil Physics, Academic Press, New York, NY: 1980, 282 pp. Reardon, E. J.; Moddle, P. M. Uranium 1985, 2, 111-131. Lowson, R. T. Chemical Reviews 1982, 82, No. 5, 461-497. Pearse, M . J. Mineral Processing and Extractive Metallurgy 1980, 89, C26C36. Lundgren, D. D.; Silver, M . Ann. Rev. Microbiol. 1980, 34, 262-283. Torma, A. E. Biotechnology Advances 1983, 1, 73-80 Torma, A. E.; Banhegyi, I. G. Trends in Biotechnol. 1984, 2, 13-15. Ahonen, L.; Tuovinen, Ο. H. Appl. Environ. Microbiol. 1991, 57, 138-175. Morth, A. H.; Smith, Ε. E. Kinetics of the Sulfide-to-Sulphate Reaction. Proc. 151st National Meeting, Am. Chem. Soc., Pittsburgh, PA: 1966.


152 21.

22.

23.


24. 25. 26.

27. 28.

29. 30.

31. 32.

33.

34.

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1993


A Computer Program To Assess Acid Generation in Pyritic Tailings

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