A Hybrid Approach for Joint Simulation of Geometallurgical Variables with Inequality Constraint

Abstract

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.

Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms: A Case Study from an Iron Ore Deposit

“…The negative sign also corrobo-rates that the global variability of Fe in the region is highly controlled by Al 2 O 3 ; thus, an increase in the Fe grade in the region corresponds to a decrease in the amount of Al 2 O 3 . This type of good correlation advocates the use of co-simulation methods rather than independent simulation methods because cosimulation takes into account the intrinsic correlation between covariables (Eze et al 2019;Abildin et al 2019).…”

“…Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms ables in the multi-element deposits (Madani and Ortiz 2017;Maleki and Madani 2017;Eze et al 2019;Abildin et al 2019). The TBCOSIM methodology presents a better result with an average correlation coefficient of almost 0.57, although it is not considered as a reliable result.…”

“…Regarding this issue, many approaches have been proposed and developed to improve stochastic 3D spatial modeling of regionalized variables. For cross-correlated variables, co-simulation approaches are highly advocated over independent simulation approaches because the spatial cross-dependency can be taken into account (Wackernagel 2003;Chilè s and Delfiner 2012;Paravarzar et al 2015;Madani and Ortiz 2017;Eze et al 2019;Abildin et al 2019). In some special circumstances, for example, the variables behave differently and show some complex interrelationship characteristics, and Battalgazy and Madani the use of conventional approaches is restricted (Boisvert et al 2013;Deutsch 2013).…”

Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships

“…One solution is to employ one more decorrelation steps, such as minimum/maximum autocorrelation factor (MAF) or principal component analysis (PCA), to make sure the correlation at lag 0 and other arbitrary lag is substantially removed. However, these methods do not guarantee that the correlation will be entirely eliminated through all other lags [35]. A way around this impediment is to co-simulate the PPMT factors even with small correlation that are left after forward transformation of the original variables to factors by inference of cross-dependency functions using the linear model of co-regionalization [25].…”

Co-simulated Size Number: An Elegant Novel Algorithm for Identification of Multivariate Geochemical Anomalies

“…The existence of cross-correlation among certain variables motivates one to use Gaussian cosimulation approaches rather than independent simulation (Wackernagel 2003;Chilè s and Delfiner 2012;Eze et al 2019;Abildin et al 2019). The reason relates to taking into account the inter-dependency characteristic among certain variables, for which it leads to generate results that reproduce the local and global multivariate statistical parameters of data in the area of study.…”