VII. Thermodynamic Catastrophes And Their Effect On Acid Generation Rates In Waste Rock Piles

     

Matthew Otwinowski

Non-linear waste rock modelling

VII. THERMODYNAMIC CATASTROPHES AND 
THEIR EFFECT ON ACID GENERATION RATES 
IN WASTE ROCK PILES

The numerical results show that at certain critical parameter values, the thermodynamic system may exhibit a sharp transition to a high energy state characterized by dramatically faster oxidation rates. We call this transition a thermodynamic catastrophe. Thermodynamic catastrophes are associated with the bifurcation properties of the nonlinear reaction-transport problems.

The total sulphate generation rates, the average sulphate generation rates and the maximum sulphate generation rates increase significantly with pile height. In Table III, piles which are 6 m and 8 m high have very similar sulphate acid generation rates. This happens because at low temperatures the decrease in oxygen concentration in larger piles is sufficient to counteract the effect a small increase of temperature has on the oxidation rates.

By increasing the height of above ten metres one observes a strongly nonlinear increase in temperature, accompanied by a very dramatic increase in the acid generation rates. At a height of L*=14.5 metres a thermodynamic catastrophe takes place¹. The average acid generation rates in piles A15.0 and A15.1 are more than 300% faster than in pile A12.0 which is only 25% smaller. By increasing the pile height from 12 m to 15 m, the maximum temperature increases by about 10°C. This is sufficient to increase the oxidation rates very dramatically. Piles A15.0 and 15.1 are in a critical thermodynamic state and generate much more acid than the lower piles. The maximum acid generation rate in pile A15.1 is about 50% greater than in pile A15.0 which is only 0.1 m lower. This is a direct result of a thermodynamic instability. In large piles, the energy dissipation rates are insufficient to counteract the energy generation rates. The maximum energy generation rate in pile A15.5 is about 5 times greater than in the smaller piles. Energy is generated very rapidly in warm spots which are formed when the thermodynamic dissipative structure of temperature and oxygen concentration becomes unstable. This process is illustrated by the three-dimensional plots in Figs. 7.1-7.2.

Fig. 7.1. Sulphate generation rates in piles A15.0 (left) and A15.1 (right). Note that in the critical region associated with thermodynamic catastrophes, large horizontal gradients of acid generation rates develop. (The regular pattem results from the regular trapezoidal pile shape - irregular piles show irregular spatial distribution of temperature, oxygen and acid generation rates).

Fig. 7.2. Temperature and oxygen concentration profiles in pile A15.1. (Large horizontal Temperature gradients trigger fast convective flow in the whole volume of the pile).

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¹ We chose the pile height as a critical parameter as an example only. Other combined geochemical and physical effects also lead to the critical thermodynamic behaviour.