Abstract
Multivariate analytical models are quite successful in explaining one or more response variables, based on one or more independent variables. However, they do not reflect the connections of conditional dependence between the variables that explain the model. Otherwise, due to their qualitative and quantitative nature, Bayesian networks allow us to easily visualize the probabilistic relationships between variables of interest, as well as make inferences as a prediction of specific evidence (partial or impartial), diagnosis and decision-making. The current work develops stochastic modeling of the leaching phase in piles by generating a Bayesian network that describes the ore recovery with independent variables, after analyzing the uncertainty of the response to the sensitization of the input variables. These models allow us to recognize the relations of dependence and causality between the sampled variables and can estimate the output against the lack of evidence. The network setting shows that the variables that have the most significant impact on recovery are the time, the heap height and the superficial velocity of the leaching flow, while the validation is given by the low measurements of the error statistics and the normality test of residuals. Finally, probabilistic networks are unique tools to determine and internalize the risk or uncertainty present in the input variables, due to their ability to generate estimates of recovery based upon partial knowledge of the operational variables.
Highlights
Copper mining is a constantly growing industry [1], and in countries like Chile, this industry represents 10% of the gross national product (GNP) [2], while approximately 19.7 million tons are produced annually worldwide [3]
The results are ordered into three subsections: The results of the uncertainty analysis (UA), which address the UA in the response variable at 30, 60 and 90 days of leaching; the modeling results of the copper recovery from the heap leaching process through the Bayesian networks, in addition to the conditional relationships between the independent variables and the recovery, and the conditional dependence between the independent variables, together with the degree of strength of the dependencies
The effectiveness of the Bayesian network is studied as a tool to model the productive process of heap leaching, by calculating the indicators of goodness of adjustment mean absolute deviation (MAD), mean squared error (MSE) and mean absolute percentage error (MAPE), together with tests of the normality of the residues when evaluating the value expected response to changes in input variables and ignorance of one or more independent variables
Summary
Copper mining is a constantly growing industry [1], and in countries like Chile, this industry represents 10% of the gross national product (GNP) [2], while approximately 19.7 million tons are produced annually worldwide [3]. During the last 50 years, heap leaching processes were a very attractive technological option for the treatment of low grade minerals, allowing the economic exploitation of marginal deposits, often in remote locations in many parts of the world [9]. They are applied to previously crushed minerals in crushers, where the copper (Cu) present in the mineralized rock is extracted by the mixture between water and leaching agents [10]. Larger sizes generally range between 10 and 40 mm, where sizes less than 6 mm are unacceptable, because they affect the permeability of the pile, especially if there are clayey minerals that result in a greater obstruction of heaps over time, due to swelling and gradual decrepitation
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