Science Blog: What will happen to a waste-rock dump in hundreds of years? A stochastic multicomponent reactive transport model can support this prediction

Daniele Pedretti, Research Professor

The management of waste-rock dumps is one of the most critical parts of mining activities. If not properly designed, these dumps can generate acid mine drainage (AMD), with consequent socio-environmental risks and economic losses. There are uncertainties in the prediction of whether a dump will generate AMD, particularly due to the physical and mineralogical heterogeneity of the waste rocks. A novel stochastic modeling approach provides a computationally efficient scale-independent solution to generate risk-based scenarios for predicting the probability of low-quality drainage over hundreds of years. More information on AMD risk prediction can be found through the references below.


The problem of mine waste management

Mining activities can generate large volumes of waste rocks (Figure 1) that are generally stored in large unsaturated dumps on the land surface at the mine site. Waste rocks are not tailings. Waste rocks comprise the overburden that overlies an ore or mineral body and is displaced during mining without being processed. The oxidation of sulfide minerals within waste-rock dumps can lead to poor-quality drainage called acid mine drainage (AMD), which presents an environmental risk and a financial liability for mining companies (Amos et al., 2014). AMD is highly toxic, and even short-term exposure to AMD can become fatal for any type of living organism. Sometimes, the conditions become so extreme that the resulting environments can eventually resemble a Martian landscape rather than a terrestrial one. This is the case, for instance, in the Rio Tinto area in southern Spain, in which the first “mines” could have started as early as 5000 years ago. This area is now considered an analog to replicate physicochemical (and biological) processes forming the Martian surface (Fernández-Remolar et al., 2005).

Figure 1: A typical landscape in which waste-rock dumps are formed on a previously flatter area near a mining site.

The problem of predicting AMD from waste-rock dumps

Rehabilitating a site where AMD has occurred means that millions of euros have to be spent by a mining company. It has been calculated that the total worldwide liability related to AMD is likely to be in excess of 10,000 million US dollars, while in the United States alone, the mining industry spends over US$1 million every day to treat AMD water (see e.g. Lottermoser, 2010). Therefore, a mining company wants to know if and when a waste-rock dump will produce AMD.

This prediction is severely complicated by the fact that sulfide oxidation and consequential AMD leaching is a rate-limited kinetic process controlled by a variety of possible well-known physical and biochemical mechanisms, summarized in books and review papers (e.g. Amos et al., 2014; Lottermoser, 2010; Nordstrom, 2011). Traditionally, predictions are made using small-scale kinetic cells or by means of static metrics, such as acid–base accounting. However, it has been widely shown that these methods are not reliable, being affected by so-called “scaling” effects, i.e. the departure of observed AMD production rates estimated in the laboratory using small-scale devices from those observed under field conditions (e.g. Malmström et al., 2000).

The reasons for this departure are partly linked to the ubiquitous physical and mineralogical heterogeneity of the waste rocks. Heterogeneity is not easily handled using small-scale experimental methods. Heterogeneity manifests itself by randomly varying the spatial distribution of the waste-rock properties determining the formation of AMD, including, for instance, the relative amount of non-acid-generating minerals (NAGs) versus potentially-acid-generating minerals (PAGs), the specific reactive surfaces of individual minerals, or their degree of liberation (e.g. Blaskovich, 2013; Malmström et al., 2000; Peterson, 2014; Strömberg and Banwart, 1999). The net effect of heterogeneity is that an observation performed at a local scale only provides information on the likelihood of AMD forming from that specific sample of waste rocks, but not of the expected behavior of the dump as a whole, which integrates the effects of all possible waste rocks in the dump.

A new solution based on statistical modeling

Integrating small-scale information into larger-scale predictive tools requires numerical modeling. Mathematical models have been adopted for a few decades now to support decision makers in predicting the weathering rates of waste rocks (Demers et al., 2013; Lefebvre et al., 2001; Malmström et al., 2004). Models allow for the explicit solution of the nonlinearly coupled mechanisms forming AMD, including the kinetic water–rock–gas–biosphere interaction (Figure 2). Heterogeneity can be included in these models (Fala et al., 2013; Lahmira and Lefebvre, 2015), but it can be highly computationally demanding to fully simulate a heterogeneous waste-rock dump using traditional methods.

Figure 2. The main processes occurring within a waste-rock dump (Amos et al. 2014).

In addition to the computational burden, the way heterogeneity is embedded in these models requires attention. Typically, the characterization of waste rocks is limited. Depending on the genetic origin of the ore type and the depositional mechanisms in the dumps,  the mean geometrical and mineralogical properties of a dump can be inferred. New tools such as automatic mineralogical analysis (e.g. using MLA) can be adopted to improve the amount of statistical information representing the mineralogical properties of the waste rock. However, complete mapping of the variability in rock composition and texture at all scales (particularly within the dumps) is nearly impossible. This lack of information is unfortunate, since the resulting dump-average geochemical behavior (and in particular the composition of the exfiltrating drainage) depends not only on the average mineralogical content and geometrical distribution of the dumps, but also on the non-linearly averaged interaction of water, gas and biotic content with each individual waste rock at each point of the dump, including the poorly accessible internal parts.

Geostatistics and stochastic modeling can partly resolve the headaches generated by the mathematical and physical complexity of the problem. Geostatistics generates maps of mineralogical variability that honor both the general (i.e. large scale) information available on the dump (such as the mean pyrite or calcite content, or the number of tipping phases and lifting levels from which the dump is built) and the existing local-scale information, such as the specific composition of the waste rock on a metric scale (e.g. what can be measured using a kinetic cell).

A stochastic multi-component reactive transport model has been developed in this sense and fully documented in Pedretti et al. (2017). The model is process based and allows for a quantitative estimation of the probability that a certain amount of aqueous byproducts will form as the water percolates through the waste-rock dump. For instance, it can be used to make predictions of the continuous temporal evolution of the polluted water pH from the dump as a whole. In other words, the stochastic method bypasses the scale limitation of small devices, which are not able to sample the entire variability of the rock contained in the dumps.  The stochastic framework is coded in MATLAB and relies on the multicomponent reactive transport model MIN3P (Mayer et al., 2002).

Figure 3 explains conceptually how the code works.  A dump is seen as a bundle of multiple streamlines that compose its internal drainage system. Along its movement from the recharge to the discharge zones, the water flowing along each streamline interacts with the biotic content, the gas and the matrix, which is characterized by a certain property, such as its pyrite and calcite content. Each variable can be treated as a random spatial field. For instance, the pyrite and calcite content of the rocks can randomly vary in the simulated dump, resulting in a specific distribution of zones characterized by a neutralizing potential ratio (NPR). The intensity of the interaction between flowing water and the matrix depends in this case on the relative NPR at each location.

The map shown in Figure 3 is, however, only one possible assemblage of minerals that can be built using a geostatistical simulator. For instance, another map with identical mean mineralogical properties (including the average mineral content and variability) can be created, but with a different distribution of the mineral content among the individual cells forming the simulated map.

Since one does not know a priori what the expected distribution of mineral is at each location of the dump, stochastic modeling intervenes.  A two-step approach is then followed:

  1. An ensemble of maps is created, each one characterized by the same mean properties but a different, random organization of minerals within each simulated dump.
  2. The multicomponent reactive transport model is run for each randomly generated dump, and the resulting drainage from each simulated dump is stored.

Once all the dumps are simulated, the results are statistically analyzed to evaluate the probability of occurrence of a specific geochemical characteristic of the drainage.

Figure 3. Conceptual model of the stochastic modeling tools developed to evaluate the probability of AMD in heterogeneous waste-rock dumps (WRPs). ST = streamtube; NST= number of streamtubes forming the drainage system; NPR= neutralizing potential ratio.

Figure 4 reports an example of results from this model. The plot represents the calculated pH resulting from an ensemble of 100 random waste-rock dumps characterized by the same mean mineralogical properties, but a random organization of minerals within the dump. The plot illustrates that, for the conditions analyzed in this example, a dump is very likely to become acidic (i.e. pH < 3) within 25 years from its creation (blue line). Indeed, 100% of the simulated dumps show a pH lying between 1.8 and 2.5. At 100 years after dump creation (yellow line), the majority of the dumps still display strongly acidic conditions. However, after 150 years, the pH starts to tend towards circumneutral values, although there is still a 60% chance that a dump will generate an acidic pH.

This mechanistically based approach is therefore useful to provide quantitative information on the likelihood that a dump will generate AMD with a specific geochemical fingerprint. The model can be used to any type of deposit, independently from a specific geochemical or physical configuration. As such, the model can be used for financial risk assessment or for environmental hazard predictions.

Figure 4. Probability of AMD pH from a simulated dump at different times after the beginning of dump weathering (in years).


Amos, R.T., Blowes, D.W., Bailey, B.L., Sego, D.C., Smith, L., and Ritchie, A.I.M. (2014). Waste-rock hydrogeology and geochemistry. Appl. Geochem.

Blaskovich, R.J. (2013). Characterizing waste rock using automated quantitative electron microscopy.

Demers, I., Molson, J., Bussière, B., and Laflamme, D. (2013). Numerical modeling of contaminated neutral drainage from a waste-rock field test cell. Appl. Geochem. 33, 346–356.

Fala, O., Molson, J., Aubertin, M., Dawood, I., Bussière, B., and Chapuis, R.P. (2013). A numerical modelling approach to assess long-term unsaturated flow and geochemical transport in a waste-rock pile. Int. J. Min. Reclam. Environ. 27, 38–55.

Fernández-Remolar, D.C., Morris, R.V., Gruener, J.E., Amils, R., and Knoll, A.H. (2005). The Río Tinto Basin, Spain: Mineralogy, sedimentary geobiology, and implications for interpretation of outcrop rocks at Meridiani Planum, Mars. Earth Planet. Sci. Lett. 240, 149–167.

Lahmira, B., and Lefebvre, R. (2015). Numerical modelling of transfer processes in a waste-rock pile undergoing the temporal evolution of its heterogeneous material properties. Int. J. Min. Reclam. Environ. 29, 499–520.

Lefebvre, R., Hockley, D., Smolensky, J., and Lamontagne, A. (2001). Multiphase transfer processes in waste-rock piles producing acid mine drainage: 2. Applications of numerical simulation. J. Contam. Hydrol. 52, 165–186.

Lottermoser, B. (2010). Mine Wastes (Springer-Verlag Berlin Heidelberg).

Malmström, M.E., Destouni, G., Banwart, S.A., and Strömberg, B.H.E. (2000). Resolving the Scale-Dependence of Mineral Weathering Rates. Environ. Sci. Technol. 34, 1375–1378.

Malmström, M.E., Destouni, G., and Martinet, P. (2004). Modeling Expected Solute Concentration in Randomly Heterogeneous Flow Systems with Multicomponent Reactions. Environ. Sci. Technol. 38, 2673–2679.

Mayer, K.U., Frind, E.O., and Blowes, D.W. (2002). Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resour. Res. 38, 13–1–13–21.

Nordstrom, D.K. (2011). Hydrogeochemical processes governing the origin, transport and fate of major and trace elements from mine wastes and mineralized rock to surface waters. Appl. Geochem. 26, 1777–1791.

Pedretti, D., Mayer, K.U., and Beckie, R.D. (2017). Stochastic multicomponent reactive transport analysis of low quality drainage release from waste-rock piles: Controls of the spatial distribution of acid generating and neutralizing minerals. J. Contam. Hydrol. 201, 30–38.

Peterson, H.E. (2014). Unsaturated hydrology, evaporation, and geochemistry of neutral and acid rock drainage in highly heterogeneous mine waste-rock at the Antamina Mine, Peru.

Strömberg, B., and Banwart, S. (1999). Weathering kinetics of waste rock from the Aitik copper mine, Sweden: scale dependent rate factors and pH controls in large column experiments. J. Contam. Hydrol. 39, 59–89.


Daniele Pedretti

Text: Daniele Pedretti

Daniele works as a research professor in hydrogeology at the Geological Survey of Finland. He holds a doctoral degree in geosciences and hydrogeology from the Technical University of Catalonia, with emphasis on the stochastic modeling of flow and conservative/reactive transport in porous and fractured media. He worked for three years on a mining-related waste-rock project during his postdoctoral period at the University of British Columbia. Daniele can be contacted at daniele.pedretti@gtk.fi.