This report describes the results of a research project which has been initiated with the
purpose to provide a quantitative analysis of the interrelated elementary chemical and
biological processes which are responsible for pyrite oxidation and acid rock drainage
(ARD). The highly nonlinear nature of the kinetic equations describing coupled
chemical and microbial reactions involved in pyrite oxidation raised serious questions
about the predictability of the environmental impact of acid rock drainage.

The main objective of this project was to determine whether the coupled chemical
reactions involved in a multistage oxidation of pyrite lead to irregular or chaotic in time
changes of products of the chemical and microbial reactions responsible for acid rock
drainage. The main conclusion of the model analysis described in this report is the
absence of such an irregular temporal behaviour. The set of nonlinear kinetic
equations for the chemical reactions involved in pyrite oxidation does not produce a
chaotic behaviour or other types of chemical oscillations. The nonlinear nature of the
elementary nonequilibrium processes is responsible for the presence of the
quasi-equilibrium values of the concentrations of ferrous and ferric iron. This property is
a key to understanding the complexity of acidic drainage and should be helpful in
designing efficient ways of minimizing acidic drainage. The presence of the
quasi-equilibrium states increases our chances to formulate predictive ARD models.
This study does not exclude, however, physico-chemical oscillations when processes
of water and oxygen transport are included in a future model. (The analysis of transport
processes was outside the scope of the present project designed as a low-budget
preliminary analysis of the nonlinear chemical and biological kinetics.)

Several experimental results are reevaluated and, in some cases, values of rate
constants different than those previously published in the literature are determined. A
kinetic model in the form of coupled nonlinear ordinary differential equations is
constructed for the coupled chemical reactions responsible for acid rock drainage. The
equations describe the time dependence of the concentrations of the hydronium ions,
ferrous and ferric iron, sulphate and oxygen dissolved in water.

In our analysis a clear distinction is made between the chemical and bacterial reactions
which require the presence of dissolved oxygen and the chemical and bacterial
processes which do not require oxygen.

At pH values greater than four, the process of pyrite oxidation is mainly due to the
pyrite oxidation by oxygen dissolved in water:

FeS2(s) + 7/2 O2 + H2O = Fe2+ + 2SO4
2- + 2H+ (R1)

Ferrous iron is released to the water solution where it is oxidized to ferric iron:

Fe2+ + 1/402 + H+ = Fe3+ + 1/2 H20 (R2)

At pH values less than four the ferric iron reacts with pyrite

FeS2(s) + 14Fe3+ + 8H20 = 15Fe2+ + 2SO4
2- + 16H+ (R3)

At high pH values the ferric iron reacts further with oxygen and water, and forms ferric
hydroxide which precipitates:

Fe3+ + 3H20 = Fe(OH)3(s) + 3H+ (R4)

Reactions (Rl), (R3) and (R4) produce acid, which, if not neutralized, mobilizes the
metal ions, contained in the waste rock. High pH values can be maintained by
neutralizing minerals which often are present in the waste rock or by minerals (like
calcite) added to the waste rock. The process of neutralization by calcite is described
by two reactions

CaCO3 + 2 H+ + S04
2- + 2H20 = CaSO4· 2H20+ H2CO3
o (R5.1)
CaCO3 + H+ + S04
2- + H20 = CaSO4· 2H20+ HC03
– (R5.2)

The relative rates of the reactions (R5. 1) and (R5.2) depend on pH values and are
responsible for the efficiency of the neutralization process. The rate of oxidation of
ferrous iron increases with increasing pH values and the neutralizing potential of the
reactions (R5. 1) and (R5.2) decreases when pH increases. This leads to a
stoichiometric incompatibility between acid-generating and acid-neutralizing reactions.
Minimizing the stoichiometric incompatibility during the neutralization process should
reduce the amount of sludge generated and lower the cost of neutralization. Since the
analysis of the neutralization process is limited to equilibrium conditions for the
neutralizing species (pH is a control parameter), further analysis is required.

At pH less than four, ferric hydroxide is soluble and the reaction of pyrite oxidation by
ferric iron contributes to acidic drainage. The source of ferric iron may be reaction (R2)
(oxidation of ferrous iron) or the ferric hydroxide formed higher in the pile and washed
down to a region where pH is low. The reaction of pyrite oxidation by ferrous iron may
also be initiated if an insufficient amount of neutralizing minerals is used.

The kinetic model is analyzed for different regimes corresponding to possible different
situations at various sites. The rates of pyrite oxidation and oxygen depletion are
analyzed at different temperatures between 273K and 333K, and at concentrations of
dissolved oxygen corresponding to the concentration of oxygen in the gaseous phase
ranging from 21 % to 2 %. The ratio between the active surface area, S and the water
volume, V, varies between 0.1 m2/l and 100 m2/l. The nonlinear nature of the
elementary chemical processes involved is responsible for a dramatic increase in iron
concentration by increasing acidity. The competition between increasing temperature
and decreasing concentration of oxygen dissolved in water is analyzed in detail. The
increasing temperature, while accompanied by a lower concentration of dissolved
oxygen, leads to the oxidation rates increasing about ten times per a 20 K increase in
temperature. Computer simulations for the concentrations of hydronium ions, ferrous
iron, ferric iron and sulphate generated during time intervals ranging from a few hours
to several months have been performed for different values of the chemical and
physical parameters which control the process of acidic drainage. In some cases, the
nonlinear kinetic equations have been solved analytically and several useful
closed-form mathematical formulae have been obtained.

At low pH values and at temperatures about 303 K, Thiobacillus ferrooxidans at
concentrations on order of one gram of wet cells per litre, can accelerate the process
of pyrite dissolution by about a thousand times. Kinetic equations for the bacterial
processes of pyrite oxidation by dissolved oxygen and by ferric iron are proposed for
the first time. Bacterial processes accelerate each of the reactions (Rl), (R2) and (R4)
in a different way. The reaction (RI) is accelerated about three hundred times. The
reaction (R2) becomes about a million times faster. The reaction (R4) is accelerated by
bacteria about three times.

The reactions of the bacterial oxidation of ferrous iron to ferric iron and the pyrite
oxidation by ferric iron provide a nonlinear negative feedback mechanism which is
responsible for a smaller than desired effect of slowing-down pyrite oxidation by
reducing oxygen concentration. When oxygen partial pressure decreases from 0.21atm
to 0.04atm (i.e. by 75 %), the rate of pyrite oxidation by Thiobacillus ferrooxidans
decreases by only 30 %. This negative feedback mechanism is also responsible for a
chemistatic bacterial action and prolonged bacterial activity in an acidic environment.

Several problems which merit further experimental and modelling studies are identified.

Quantitative results presented in this study should be confronted with field data and,
after calibration, the kinetic model presented here can be used as a part of a
comprehensive physical waste rock model and an underwater disposal model.