TY - JOUR
T1 - A hybrid approach for joint simulation of geometallurgical variables with inequality constraint
AU - Abildin, Yerniyaz
AU - Madani, Nasser
AU - Topal, Erkan
N1 - Funding Information:
The first and second authors acknowledge the Nazarbayev University for supporting this work via “Faculty Development Competitive Research Grants for 2018–2020” under Grant Contract No. 090118FD5336. The corresponding author is thankful to the University of Chile for providing the dataset. The two anonymous reviewers and the Editor are also thanked for their constructive comments which substantially improved the overall quality of the paper.
Publisher Copyright:
© 2019 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Geometallurgical variables have a significant impact on downstream activities of mining projects. Reliable 3D spatial modelling of these variables plays an important role in mine planning and mineral processing, in which it can improve the overall viability of the mining projects. This interdisciplinary paradigm involves geology, geostatistics, mineral processing and metallurgy that creates a need for enhanced techniques of modelling. In some circumstances, the geometallurgical responses demonstrate a decent intrinsic correlation that motivates one to use co-estimation or co-simulation approaches rather than independent estimation or simulation. The latter approach allows us to reproduce that dependency characteristic in the final model. In this paper, two problems have been addressed, one is concerning the inequality constraint that might exist among geometallurgical variables, and the second is dealing with difficulty in variogram analysis. To alleviate the first problem, the variables can be converted to new variables free of inequality constraint. The second problem can also be solved by taking into account the minimum/maximum autocorrelation factors (MAF) transformation technique which allows defining a hybrid approach of joint simulation rather than conventional method of co-simulation. A case study was carried out for the total and acid soluble copper grades obtained from an oxide copper deposit. Firstly, these two geometallurgical variables are transferred to the new variables without inequality constraint and then MAF analysis is used for joint simulation and modelling. After back transformation of the results, they are compared with traditional approaches of co-simulation, for which they showed that the MAF methodology is able to reproduce the spatial correlation between the variables without loss of generality while the inequality constraint is honored. The results are then post processed to support probabilistic domaining of geometallurgical zones.
AB - Geometallurgical variables have a significant impact on downstream activities of mining projects. Reliable 3D spatial modelling of these variables plays an important role in mine planning and mineral processing, in which it can improve the overall viability of the mining projects. This interdisciplinary paradigm involves geology, geostatistics, mineral processing and metallurgy that creates a need for enhanced techniques of modelling. In some circumstances, the geometallurgical responses demonstrate a decent intrinsic correlation that motivates one to use co-estimation or co-simulation approaches rather than independent estimation or simulation. The latter approach allows us to reproduce that dependency characteristic in the final model. In this paper, two problems have been addressed, one is concerning the inequality constraint that might exist among geometallurgical variables, and the second is dealing with difficulty in variogram analysis. To alleviate the first problem, the variables can be converted to new variables free of inequality constraint. The second problem can also be solved by taking into account the minimum/maximum autocorrelation factors (MAF) transformation technique which allows defining a hybrid approach of joint simulation rather than conventional method of co-simulation. A case study was carried out for the total and acid soluble copper grades obtained from an oxide copper deposit. Firstly, these two geometallurgical variables are transferred to the new variables without inequality constraint and then MAF analysis is used for joint simulation and modelling. After back transformation of the results, they are compared with traditional approaches of co-simulation, for which they showed that the MAF methodology is able to reproduce the spatial correlation between the variables without loss of generality while the inequality constraint is honored. The results are then post processed to support probabilistic domaining of geometallurgical zones.
KW - Geometallurgy
KW - Inequality constraint
KW - Joint simulation
KW - MAF
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U2 - 10.3390/min9010024
DO - 10.3390/min9010024
M3 - Article
AN - SCOPUS:85059805491
SN - 2075-163X
VL - 9
JO - Minerals
JF - Minerals
IS - 1
M1 - 24
ER -