February 12, 2012
Acid rock drainage (ARD) is attributed to the complex interaction of physical, hydrological, geochemical, and microbiological process (Wels et al). The model THA_Example_WastRockAnalysis, found in the WasteRock project of our example models library, presents the analysis of the water flow, heat flow and air flow in a waste rock pile using a triple coupling numerical model created with the SVAirFlow™, SVFlux™ and SVHeat™ software. Such triple coupling is typically referred to as Thermal-Hydrological-Air (THA) coupling. The purpose of this example is to demonstrate the application of SVOffice™ 2009 to understanding the dominant process in a waste rock pile.
The conceptual model for a waste rock pile is that heat is generated due to the oxidation of pyrite deep in the pile in the presence of oxygen and moisture. The heat source results in convective currents in the waste rock pile, which affects the flow of both air and water. This numerical example will result in a greater understanding of these flows.
Geometry and Boundary Conditions
The waste rock pile in this example is deposited on bedrock. The water is allowed to run off at the toe of the waste rock slope. The precipitation and evaporation drying process, air temperature and atmospheric air pressure are applied to the top surface of the rock pile.
When there is sufficient water and air within the waste rock pile, heat is generated due to the oxidation of pyrite. The released heat is simulated as a heat source. At the same time, air is consumed by the chemical reaction. The consumed air is simulated as an air sink in the model. The heat source generated in the chemical action is estimated according the following expression:
Heat source (J/day-m³) = exothermic (J/mol) / air molecular weight (kg/mol) x oxidation rate (kg/day-m³)
The air molecular weight = 0.0288 kg/mol, and the value of exothermic and oxidation rates were used as presented in the Wels et al paper, which is available on the following website:
The calculated heat source and air sink are given in the following table:
|Heat source||Exothermic||Oxidation rate||Air sink|
|1.43E+4||1.41E+6 (Wels et al)||9.04E-04 (Wels et al)||0.08|
Boundary and Initial Conditions
The bedrock is impermeable for water flow and air flow. The boundary conditions for waste rock piles are specified in the model.
Initial pore water pressure: -140 kPa. Initial pore air pressure: 0 kPa. Initial temperature: 15 °C. The model is set up to simulate a time period of one year.
Figure 1: Model Geometry
Results and Discussion
The temperature caused by the pyrite oxidation within the bottom of the waste rock pipe increases with time from the initial temperature 15 °C. At the same time, the cold air temperature is transferred down into the waste rock with time. It can be seen from Figures 2 to 4 that after one year the cold air temperature approaches the bottom of the waste rock pipe.
There are two processes driving air flow within the waste rock. The first one is the air sink due to the air consumption in the pyrite oxidation. The second is caused by the temperature gradient: the warming air rises from the bottom of waste rock to the surface, and the cold (or heavier) air drops down, causing a convective flow within the rock. Figures 5 to 7 illustrate the contour of pore air pressure and air flow at the time of 30, 180, and 365 days. The figures show that air flow is mostly driven by the oxidation process. The air flow due to the natural convection is not observed in this simulation, which may be related to the boundary conditions settings. The profile of air density within the waste rock is present in Figure 8.
Figures 9 and 10 illustrate the pore water pressure and water flow in the waste rock. The water flows out from the toe of the waste rock pile, and water is also evaporated from the surface.
This example has illustrated the capability of SVOffice 2009 to simulate the triple coupling model of air flow, heat flow, and water flow within a waste rock pile. The air flow driven by the air pressure gradient (due to the change in atmospheric air pressure), natural convection (due to the change in the temperature), and oxidation consumption can be simulated with SVAirFlow. The water flow driven by the water pressure, evaporation, and density dependent flow can be modeled using SVFlux. The heat transfer caused by the heat conduction and convection can be simulated with SVHeat. It is feasible to utilize the tripling coupling model of SVAirFlow, SVFlux and SVHeat for the analysis of the above complicated process in a waste rock pile.
Figure 2: Contour of temperature and air flow in waste rock piles at the time of 30 days
Figure 3: Contour of temperature and air flow in waste rock piles at the time of 180 days
Figure 4: Contour of temperature and air flow in waste rock piles at the time of 365 days
Figure 5: Contour of pore air pressure and air flow in waste rock piles at the time of 30 days
Figure 6: Contour of pore air pressure and air flow in waste rock piles at the time of 180 days
Figure 7: Contour of pore air pressure and air flow in waste rock piles at the time of 365 days
Figure 8: Contour of air density in waste rock piles at the time of 365 days
Figure 9: Contour of pore water pressure and water flow in waste rock piles at the time of 30 days
Figure 10: Contour of pore water pressure and water flow in waste rock piles at the time of 365 days