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Modeling
Predictive computer modeling is used to mathematically describe
the behavior of sulfide minerals under various conditions. These
models take into account chemical processes involved with weathering
of sulfide minerals such as oxidation of sulfide minerals, dissolution
of buffering minerals, oxidation/reduction reactions, ion exchange/adsorption,
secondary mineral precipitation and catalysis by bacteria. They
also take into account physical processes involved such as oxygen
diffusion, saturated/unsaturated water flow and diffusion of oxidation
products form reactive surfaces. The models can predict the migration
of impacted waters and predict future drainage quality, thereby
providing a basis for decision making regarding acid mine drainage
prevention and control measures.
Models can be empirical, deterministic, mechanistic or a combination.
Empirical models are based on statistical relationships between
parameters of interest (e.g. metal concentration) and other variables
such as time. The relationships are usually defined by regression
and correlation analyses. This method requires significant field
data collection in order to obtain accurate relationships between
parameters. Empirical models do not take into account geochemical
and physical processes in a mathematical sense rather, they directly
describe the result of all processes occurring simultaneously in
the field. Models that are based on statistical relationships for
a certain site are limited in their applicability to other sites,
therefore, empirical models are generally used on a site-to-site
basis.
Deterministic and mechanistic models rely on mathematical equations
to describe chemical and physical processes which, in turn, predict
acid generation potential, buffering potential and metal leaching
potential. Deterministic models apply scientific principles such
as the conservation of mass, momentum and energy. Mechanistic models
include kinetic, thermodynamic equilibrium and mass transport models.
Solving the theoretical equations in these models can be complex
and require that simplifying assumptions be made. These assumptions
include the use of simplified geometry, homogeneity and idealized
initial conditions and boundary conditions. Parameter estimates
(i.e. chemical reaction rates, mass transfer coefficients) have
a critical role in mechanistic modeling, and are often based on
laboratory studies, physical models and field experiments. The predictive
capability of mechanistic models can be significantly improved by
applying probabilistic uncertainty analyses to examine the sensitivity
of predicted values to one or more parameters or assumptions.
Models may be based partially on empirical models and partially
on deterministic models. Some parameters cannot be described well
by mathematical equations since some processes are not well understood,
therefore, empirical equations can be used. Modeling of drainage
from tailings can be described by empirical or deterministic/mechanistic
models. Mathematical models for drainage from tailings piles have
evolved significantly and for the most part, adequately predict
future drainage conditions. On the other hand, drainage prediction
for waste rock is largely described by empirical models since many
processes involved are not well understood and therefore, cannot
be explained mathematically.
A manual produced by the Mine Environment Neutral Drainage Program
(MEND) gives examples of different empirical and deterministic models
used for prediction of acid mine drainage generation (MEND,
2000).
Problem | Compliance
| Health & Safety | Sampling
| Analytical | Data
Quality
Site Assessment | Prediction
| Construction | GIS
| Monitoring & Assessment
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