1.0 Introduction

Matthew Otwinowski

Scaling Analysis Of Acid Rock Drainage 

1.0 INTRODUCTION 

The purpose of this project is to provide a simple quantitative description of the interrelated nonlinear physical and chemical processes responsible for ARD. Accurate prediction and understanding of acid rock drainage may be based on the analysis of quantitative data from experiments and physico-chemical models, and potentially offers a cost-effective means of reducing the environmental impact of ARD.

It is believed that practical decisions should be based on the quantitative results of laboratory and field tests. Laboratory tests analyze various aspects of acid rock drainage by using a limited amount of waste rock, ranging from one to a thousand kilograms (meso-scale). Such tests concentrate on characterization of the chemical properties of waste rock. Because the processes involved are nonlinear, scaling up the meso-scale results to obtain macro-scale characteristics for millions of tons of waste rock is a difficult task which requires an extensive modelling effort. Tests for ARD prediction (e.g. humidity cells, column tests, small scale treatment systems) are used frequently to determine the optimum approach to minimizing the environmental impact and treatment cost. No researcher, however, has examined the size effects that may be significant for the prediction of macro-scale behaviour. Such efforts are often hindered by the long computation time required for parametric analysis of numerical models. Finding the appropriate scaling relations between physical, chemical and biological processes is one of the goals of this study. Knowledge of the scaling laws may allow one to improve interpretation of the existing experimental data, design better micro-scale and meso-scale experiments and reduce the cost of prediction techniques by using cheaper small scale experiments.

Prediction of long term environmental impact, based on the characterization of waste materials is not a simple task, however. Apart from chemical processes, ARD depends also on physical, biological and mineralogical factors. Chemical and biological aspects of acidic drainage were analyzed in our recent study [SyT]. It has been found that the interrelated elementary chemical and microbial reactions have to be described as coupled nonlinear processes which respond in a rather complex way to preventive measures like neutralization and oxygen depletion. Temperature is a very important factor. The rates of oxygen and water transport also are important factors to consider due to their effect on both oxidation and heat exchange with the surroundings.

Extensive computer models which have to be analyzed numerically, often require a very long computational time before one is able to gather quantitative information about the complexity of the coupled physical and chemical processes. Scaling relations based on the consideration of simplified reaction transport models often give good quantitative information about the relative importance of the factors involved, and allow one to translate laboratory data into large-scale estimates.

In this report we concentrate on the interplay between the chemical kinetics and transport of mass and energy. Mass and energy transport are physical factors which ultimately control reaction rates. The concentration of oxygen and the temperature distribution are non-homogeneous inside waste rock pile [PaR], [FeM], [BeR], [Ge], [NoD]. The quantitative analysis of the expected distribution of oxygen and temperature is important for the estimation of acid generation.

Previous waste rock models did not describe properly the process of pyrite oxidation in regions where oxygen concentration is low and temperature is high. In particular, to our knowledge, the temperature dependence of oxygen dissolved in water has not been included in previous models. [BeR], [BrC], [CdO], [Da], [DaR1], [DaR2], [DaR3], [FeE1], [Ge], [Res], [WhJ]. 

The report starts with an analysis of a kinetic chemical model which lays the ground for the quantitative physico-chemical model. In Chapter 2, we analyze the following coupled processes:

• pyrite oxidation by water and oxygen dissolved in water and the release ot Fe²⁺ (ferrous) ions and acid (reaction (Rl))

• oxidation of ferrous ions to ferric (Fe³⁺) ions by oxygen (reaction (R2))

• anaerobic oxidation of pyrite by ferric ions and water (reaction (R3))

• precipitation of ferric hydroxide, which eliminates ferric ions from the stream (reaction (R4))

• the neutralization process

Effective kinetic models for chemical reactions at high and low pH values are constructed and analyzed in Chapter 3. The temporal behaviour of the concentrations of chemical species is considered separately for pH values greater than four, and less than four. This distinction is necessary because of the dramatic changes in the nature of pyrite oxidation due to the precipitation of ferric hydroxide at pH values above four. Pyrite oxidation rates increase dramatically with temperature - for temperatures between 273K and 323K the rate of pyrite oxidation accelerates about ten times per 20K. Transport processes which control the supply of water and oxygen, are ultimately responsible for both the rate of acid generation and its release to the environment. The form of the effective kinetic equations derived in Chapter 3 is suitable for the scaling analysis of the reaction-diffusion equations in Chapter 4.

In Chapter 4 the mathematical scaling analysis of coupled chemical and physical processes is presented. We derive a dimensionless physico-chemical scaling parameter, δ, which describes the combined effects of chemical reactions and mass and energy transport. The dimensionless scaling parameter δ describes the relative effects of oxygen diffusion, thermal conductivity, pile porosity, ambient conditions, etc. The relative importance of the different factors involved in acid rock drainage is described quantitatively by the dimensionless scaling parameter which may become useful as a standard tool for predictive analysis of laboratory and field data. The strongly nonlinear properties of the combined physical and chemical processes are analyzed as a function of the parameters describing pile size, pile porosity, pyrite content and other quantities. It is found that there exist critical values of these parameters at which a discontinuous increase of chemical rates may take place together with a jump-wise increase of temperature and acid generation rates inside waste rock piles. We call this phenomenon a thermodynamic catastrophe. This aspect of ARD is very important for the prediction and control of acid rock drainage and to the best of our knowledge has not been discussed in previous studies.

In Chapter 5, different scenarios of acid generation for different sets of input data are analyzed in detail. The power of scaling analysis is demonstrated by showing how the results for one set of entry data can be obtained from results derived for a different set of entry data. Maximum allowed values of pile size and effective reactive surface area are calculated for two different realistic scenarios of ARD. Also, in Chapter 5, the required accuracy of experimental tests is analyzed.

The dimensionless scaling parameter, δ, presented in this report is more general and provides more information than the Thiele modulus typically used in literature [Ar], [DrA], The scaling analysis has been performed by analytical mathematical methods with a minimum use of numerical analysis. In the next step, the results presented in this report should be confronted with available experimental data on acid drainage. Data collected during field tests and laboratory thermokinetic experiments involving large samples of pyritic rocks should be used to calibrate the model.