Matthew Otwinowski
Non-linear waste rock modelling
V. GEOSTATISTICAL FORMULAE FOR
WASTE ROCK REACTIVITY.
SCALING UP LABORATORY DATA:
FROM MICRO-SCALE TO MESO-SCALE
One of the crucial problems in ARD prediction is how to use the laboratory data obtained during leaching tests to estimate oxidation rates and acid generation rates in the field. Leaching tests are usually designed to generate information about the chemical composition of the leachate, often disregarding the physical aspects of rock reactivity. We analysed the physical effect of the variable particle size on oxidation rates and the consumption of oxygen per unit mass of waste rock in waste rock piles. These results are a very significant component of a large scale waste rock model. We adopt the approach in which the chemical properties of the waste rock can be characterized as quantities averaged over a volume of about 1m3. (Rock particles greater than 1m can be explicitly included in a large-scale model.) This type of physical and statistical characterization of waste rock leads to a relatively simple set of equations describing the oxygen consumption rates and transport of mass and energy in waste rock piles.
In order to calculate the oxidation rate for an ensemble of particles we have to combine information about the size-dependent oxidation rates for individual particles and the fractal distribution of particle size. Oxidation rates per particie scale with particle size R as Rα with α>0. Our calculations show that α=2 for surface dominated oxidation, and α=l for volume dominated oxidation1.
SURFACE DOMINATED OXIDATION RATES
VOLUME DOMINATED OXIDATION RATES
The geostatistical formulae2 allow one to estimate the reactivity of a unit mass of waste rock with a particle size between Rmin and Rmax based on results of leaching tests performed by using particles of size Rexp. (ρ is rock density; V is volume; C is a constant determined during leaching tests; C carries information about sulphide content, rock porosity and other geochemical and physical properties of waste rock). Ratevol and Ratesurf can be expressed in terms of a chemical rate constant α and effective reactive surface area per unit volume, σ.
The geostatistical formulae are very important for translating results of laboratory leaching tests into field situations.
Some of the previous models used Gaussian or Poisson particle size distribution. Such models should not be used for the interpretation of the laboratory leaching tests because they significantly underestimate the number of small rock particles and give unrealistic estimates for waste rock reactivity.
The geostatistical formulae give the oxidation rates per unit mass at the values of temperature and oxygen partial pressure for which a value of reaction constant C is measured during laboratory tests. A large-scale model evaluates the total sulphide oxidation and acid generation rates inside a waste rock pile with spatially nonhomogeneous distribution of oxygen and temperature.
ROCK FRAGMENTATION BY EQUIPMENT TRAFFIC
Equipment traffic during the different stages of pile construction is responsible for the formation of layers with small particles. The oxidation rates in the small particle layers are much greater than in the rest of the pile.
As an illustration of the application of the geostatistical formulae for rock activity we calculate a change in rock reactivity when the maximum size Rmax decreases from Rmax=50cm to Rmax=10cm, where df = 2.5 in both examples.
Volume dominated oxidation
Surface dominated oxidation
During the surface dominated oxidation the rates are faster than during the volume dominated oxidation (Csurf > Cvol). However, the particle size effect is stronger during the volume dominated stage than during the initial surface dominated stage.
During the volume dominated stage of oxidation, the release of contaminant is controlled, among other factors, by particle size and the rate of diffusion of reaction products from sulphide sites in the pores to the surface of porous rock (reaction products are temporarily stored in the rock particles and we call this phenomenon a storage tank effect).
---------------------
1 At the initial stage of ARD, acid is generated mostly due to the oxidation of sulphide minerals on the particle surface. When a large portion of the sulphide on the rock surface is oxidized, the oxidation of the sulphide inside the rock particles becomes increasingly important. These two stages are called surface dominated and volume dominated oxidation.
2 It is worthy of note that analogous results are impossible to obtain without referring to numerical integration when the Gaussian or Poisson distributions are used instead of fractal distribution for particle size. Apart from giving the correct description of fragmented rock, fractal distribution has an additional advantage of greatly simplifying the computer code used for a waste rock model.
No comments:
Post a Comment