A Simulation-Based Geostatistical Approach to Real-Time Reconciliation of the Grade Control Model
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A Simulation-Based Geostatistical Approach to Real-Time Reconciliation of the Grade Control Model T. Wambeke1,2
· J. Benndorf3
Received: 21 April 2016 / Accepted: 24 September 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract One of the main challenges of the mining industry is to ensure that produced tonnages and grades are aligned with targets derived from model-based expectations. Unexpected deviations, resulting from large uncertainties in the grade control model, often occur and strongly impact resource recovery and process efficiency. During operation, local predictions can be significantly improved when deviations are monitored and integrated back into the grade control model. This contribution introduces a novel realization-based approach to real-time updating of the grade control model by utilizing online data from a production monitoring network. An algorithm is presented that specifically deals with the problems of an operating mining environment. Due to the complexity of the material handling process, it is very challenging to formulate an analytical approximation linking each sensor observation to the grade control model. Instead, an application-specific forward simulator is built, translating grade control realizations into observation realizations. The algorithm utilizes a Kalman filter-based approach to link forward propagated realizations with real process observations to locally improve the grade control model. Differences in the scale of support are automatically dealt with. A literature review, following a detailed problem description, presents an overview of the most recent approaches to solving some of the practical problems identified. The most relevant techniques are integrated and the resulting mathematical framework is outlined. The principles behind the self-learning algorithm are explained. A synthetic experiment demonstrates that the algorithm is capable
B
T. Wambeke [email protected]
1
Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands
2
IHC MTI, Delftechpark 13, 2628XJ Delft, The Netherlands
3
University of Technology Bergakademie Freiberg, Fuchsmühlenweg 9, 09599 Freiberg, Germany
123
Math Geosci
of improving the grade control model based on inaccurate observations on blended material streams originating from two extraction points. Keywords Grade control model · Reconciliation · Geostatistics · Ensemble Kalman filter
1 Introduction Traditionally, the mining industry has had mixed successes in achieving the production targets it has set out. Several projects have been identified where mineral grades are not as expected, schedules and plans are not met and recovery is lower than forecasted (McCarthy 1999; Vallee 2000; Tatman 2001; McCarthy 2003). The deviations of the produced tonnages and grades from model-based expectations result from a mismatch between the scale of the exploration data and the short-term production targets (Benndorf 2013). In other words, it is challenging to accurately defi
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