TW
T. Wambeke
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1
Data assimilation in the minerals industry
Real-time updating of spatial models using online production data
Declining ore grades, extraction at greater depths and longer hauling distances put pressure on maturing mines. Not enough new mines will be commissioned on time to compensate for the resulting shortages. Ore-body replacement rates are relatively low due to a reduced appetite for exploration. Development times are generally increasing and most new projects are remote, possibly pushing costs further upwards.
To reverse these trends, the industry must collect, analyse and act on information to extract and process material more productively (i.e. maximize resource efficiency). This paradigm shift, driven by digital innovations, aims to (partly) eliminate the external variability that has made mining unique. The external variability results from the nature of the resource being mined. This type of variability can only be controlled if the resource base is sufficiently characterized and understood.
Recent developments in sensor technology enable the online characterization of raw material characteristics and equipment performance. To date, such measurements are mainly utilized in forward loops for downstream process control. A backward integration of sensor information into the resource model does not yet occur. Obviously, such a backward integration would significantly contribute to the progressive characterization of the resource base.
This dissertation presents a practical updating algorithm to continuously assimilate recently acquired data into an already existing resource model. The updating algorithm addresses the following practical considerations. (a) At each point in time, the latest solution implicitly accounts for all previously integrated data (sequential approach). During the next update, the already existing resource model is further adjusted to honour the newly obtained observations as well. (b) Due to the nature of a mining operation, it is nearly impossible to formulate closed-form analytical expressions de- scribing the relationship between observations and resource blocks. Rather, the relevant relationships are merely inferred from the inputs (the resource model realizations) and outputs (distribution of predicted observations) of a forward simulator. (c) The updating algorithm is able to assimilate noisy observations made on a blend of material originating from multiple sources and locations. Differences in scale of support are dealt with automatically.
The developed algorithm integrates concepts from several existing (geo)statistical techniques. Co-Kriging approaches for example are designed to integrate both direct and indirect measurements and are well capable to handle differences in accuracy and sampling volume. However, they do fail to extract information from blended measurements and can not sequentially incorporate new observations into an already existing resource model. To overcome the latter issue, the co-Kriging equations are merged into a sequential linear estimator. Existing resource models can now be improved using a weighted sum of differences between observations and model-based predictions (forward simulator output). The covariances, necessary to compute the weights, are empirically derived from two sets of Monte Carlo samples (another sta- tistical technique); the resource model realizations (input forward simulator) and the observation realizations (output forward simulator). This approach removes the need to formulate analytical functions modelling spatial correlations, blending and difference in scale of support.
The resulting mathematical framework bears some resemblances to that of a dy- namic filter (Ensemble Kalman filter), used in other research areas, althoughthe under- lying philosophy differs significantly. Weather forecasting and reservoir modelling, for example, consider dynamic systems repetitively sampled at the same locations. Each observation characterizes a volume surrounding the sample locations. Mineral resource modelling, on the other hand, focuses on static systems gradually sampled at different locations. Each observation is characteristic for a blend of material originating from multiple sources and locations. Each part of the material stream is sampled only once, the moment it passes the sensor.
Various options are implemented around the mathematical framework to either reduce computation time, memory requirements or numerical inaccuracies. (a) A Gaussian anamorphosis is included to deal with suboptimal conditions related to non- Gaussian distributions. The algorithm structure ensures that the sensor precision (mea- surement error) can be defined on its original units and does not need to be translated into a normal score equivalent. (b) An interconnected parallel updating sequence (double helix) can be configured to avoid a covariance collapse (filter inbreeding). This occurs as degrees of freedom are lost over time due to the empirical calculation of the covariances. (c) A neighbourhood option is implemented to constrain computation time and memory requirements. Different neighborhoods need to be considered simul- taneously as material streams are blended. (d) Two covariance correction options are implemented to further inhibit the propagation of statistical sampling errors originating from the empirical computation of covariances.
A case specific forward simulator is built and run parallel to the more generally applicable updating code. The forward simulator is used to translate resource model realizations (input) into observation realizations (output). Empirical covariances are subsequently lifted from both realization sets and mathematically describe the link between sensor observations and individual blocks in the model. This numerical inference avoids the cumbersome task of formulating, linearising and inverting an analytical forward observation model. The application of a forward simulator further ensures that the distribution of the Monte Carlo samples already reflect the support of the concerned random values. As a result, the necessary covariances, derived from these Monte Carlo samples, inherently account for differences in scale of support.
A synthetic experiment is conducted to showcase that the algorithm is capable of assimilating inaccurate observations, made on blended material streams, into an already existing resource model. The experiment is executed in an artificial environment, representing a mining environment with two extraction points of unequal production rate. A visual inspection of cross-sections shows that the model converges towards the ”true but unknown reality”. Global assessment statistics quantitatively confirm this observation. Local assessment statistics further indicate that the global improvements mainly result from correcting local estimation biases.
Another 125 artificial experiments are conducted to study the effects of variations in measurement volume, blending ratio and sensor precision. The experiments investigate whether and how the resource model and the predicted observations improve over time. Based on the outcome, recommendations are formulated to optimally design and operate a monitoring system.
This work further describes the pilot testing of the updating algorithm at the Tropi- cana Gold Mine (Australia). The pilot aims to evaluate whether the updating algorithm can automatically reconcile ball mill performance data against the spatial Work Index estimates of the GeoMet model. The focus here lies on the ball mill since it usually is the single largest energy consumer at the mine site. The spatial Work Index estimates are used to predict a ball mill’s throughput. In order to maximize mill throughput and optimize energy utilization, it is important to get the Work Index estimates right. At the Tropicana Gold Mine, Work Index estimates, derived from X-Ray Fluorescence and Hyperspectral scanning of grade control samples, are used to construct spatial GeoMetallurgical models (GeoMet). Inaccuracies in the block estimates exist due to limited calibration between grade control derived and laboratory Work Index values. To improve the calibration, the updating algorithm was tested at the mine during a pilot study. Deviations between predicted and actual mill performance are monitored and used to locally improve the Work Index estimates in the GeoMet model. While assim- ilating about a week of mill performance data, the spatial GeoMet model converged towards a previously unknown reality. The updating algorithm improved the spatial Work Index estimates, resulting in a real-time reconciliation of already extracted blocks and a recalibration of future scheduled blocks. The case study shows that historic and future production estimates improve on average by about 72% and 26%.
...
Declining ore grades, extraction at greater depths and longer hauling distances put pressure on maturing mines. Not enough new mines will be commissioned on time to compensate for the resulting shortages. Ore-body replacement rates are relatively low due to a reduced appetite for exploration. Development times are generally increasing and most new projects are remote, possibly pushing costs further upwards.
To reverse these trends, the industry must collect, analyse and act on information to extract and process material more productively (i.e. maximize resource efficiency). This paradigm shift, driven by digital innovations, aims to (partly) eliminate the external variability that has made mining unique. The external variability results from the nature of the resource being mined. This type of variability can only be controlled if the resource base is sufficiently characterized and understood.
Recent developments in sensor technology enable the online characterization of raw material characteristics and equipment performance. To date, such measurements are mainly utilized in forward loops for downstream process control. A backward integration of sensor information into the resource model does not yet occur. Obviously, such a backward integration would significantly contribute to the progressive characterization of the resource base.
This dissertation presents a practical updating algorithm to continuously assimilate recently acquired data into an already existing resource model. The updating algorithm addresses the following practical considerations. (a) At each point in time, the latest solution implicitly accounts for all previously integrated data (sequential approach). During the next update, the already existing resource model is further adjusted to honour the newly obtained observations as well. (b) Due to the nature of a mining operation, it is nearly impossible to formulate closed-form analytical expressions de- scribing the relationship between observations and resource blocks. Rather, the relevant relationships are merely inferred from the inputs (the resource model realizations) and outputs (distribution of predicted observations) of a forward simulator. (c) The updating algorithm is able to assimilate noisy observations made on a blend of material originating from multiple sources and locations. Differences in scale of support are dealt with automatically.
The developed algorithm integrates concepts from several existing (geo)statistical techniques. Co-Kriging approaches for example are designed to integrate both direct and indirect measurements and are well capable to handle differences in accuracy and sampling volume. However, they do fail to extract information from blended measurements and can not sequentially incorporate new observations into an already existing resource model. To overcome the latter issue, the co-Kriging equations are merged into a sequential linear estimator. Existing resource models can now be improved using a weighted sum of differences between observations and model-based predictions (forward simulator output). The covariances, necessary to compute the weights, are empirically derived from two sets of Monte Carlo samples (another sta- tistical technique); the resource model realizations (input forward simulator) and the observation realizations (output forward simulator). This approach removes the need to formulate analytical functions modelling spatial correlations, blending and difference in scale of support.
The resulting mathematical framework bears some resemblances to that of a dy- namic filter (Ensemble Kalman filter), used in other research areas, althoughthe under- lying philosophy differs significantly. Weather forecasting and reservoir modelling, for example, consider dynamic systems repetitively sampled at the same locations. Each observation characterizes a volume surrounding the sample locations. Mineral resource modelling, on the other hand, focuses on static systems gradually sampled at different locations. Each observation is characteristic for a blend of material originating from multiple sources and locations. Each part of the material stream is sampled only once, the moment it passes the sensor.
Various options are implemented around the mathematical framework to either reduce computation time, memory requirements or numerical inaccuracies. (a) A Gaussian anamorphosis is included to deal with suboptimal conditions related to non- Gaussian distributions. The algorithm structure ensures that the sensor precision (mea- surement error) can be defined on its original units and does not need to be translated into a normal score equivalent. (b) An interconnected parallel updating sequence (double helix) can be configured to avoid a covariance collapse (filter inbreeding). This occurs as degrees of freedom are lost over time due to the empirical calculation of the covariances. (c) A neighbourhood option is implemented to constrain computation time and memory requirements. Different neighborhoods need to be considered simul- taneously as material streams are blended. (d) Two covariance correction options are implemented to further inhibit the propagation of statistical sampling errors originating from the empirical computation of covariances.
A case specific forward simulator is built and run parallel to the more generally applicable updating code. The forward simulator is used to translate resource model realizations (input) into observation realizations (output). Empirical covariances are subsequently lifted from both realization sets and mathematically describe the link between sensor observations and individual blocks in the model. This numerical inference avoids the cumbersome task of formulating, linearising and inverting an analytical forward observation model. The application of a forward simulator further ensures that the distribution of the Monte Carlo samples already reflect the support of the concerned random values. As a result, the necessary covariances, derived from these Monte Carlo samples, inherently account for differences in scale of support.
A synthetic experiment is conducted to showcase that the algorithm is capable of assimilating inaccurate observations, made on blended material streams, into an already existing resource model. The experiment is executed in an artificial environment, representing a mining environment with two extraction points of unequal production rate. A visual inspection of cross-sections shows that the model converges towards the ”true but unknown reality”. Global assessment statistics quantitatively confirm this observation. Local assessment statistics further indicate that the global improvements mainly result from correcting local estimation biases.
Another 125 artificial experiments are conducted to study the effects of variations in measurement volume, blending ratio and sensor precision. The experiments investigate whether and how the resource model and the predicted observations improve over time. Based on the outcome, recommendations are formulated to optimally design and operate a monitoring system.
This work further describes the pilot testing of the updating algorithm at the Tropi- cana Gold Mine (Australia). The pilot aims to evaluate whether the updating algorithm can automatically reconcile ball mill performance data against the spatial Work Index estimates of the GeoMet model. The focus here lies on the ball mill since it usually is the single largest energy consumer at the mine site. The spatial Work Index estimates are used to predict a ball mill’s throughput. In order to maximize mill throughput and optimize energy utilization, it is important to get the Work Index estimates right. At the Tropicana Gold Mine, Work Index estimates, derived from X-Ray Fluorescence and Hyperspectral scanning of grade control samples, are used to construct spatial GeoMetallurgical models (GeoMet). Inaccuracies in the block estimates exist due to limited calibration between grade control derived and laboratory Work Index values. To improve the calibration, the updating algorithm was tested at the mine during a pilot study. Deviations between predicted and actual mill performance are monitored and used to locally improve the Work Index estimates in the GeoMet model. While assim- ilating about a week of mill performance data, the spatial GeoMet model converged towards a previously unknown reality. The updating algorithm improved the spatial Work Index estimates, resulting in a real-time reconciliation of already extracted blocks and a recalibration of future scheduled blocks. The case study shows that historic and future production estimates improve on average by about 72% and 26%.
The mining industry continuously struggles to keep produced tonnages and grades aligned with targets derived from model-based expectations. Deviations often result from the inability to characterise short-term production units accurately based on sparsely distributed exploration data. During operation, the characterisation of short-term production units can be significantly improved when deviations are monitored and integrated back into the underlying grade control model. A previous contribution introduced a novel simulation-based geostatistical approach to repeatedly update the grade control model based on online data from a production monitoring system. The added value of the presented algorithm results from its ability to handle inaccurate observations made on blended material streams originating from two or more extraction points. This contribution further extends previous work studying the relation between system control parameters and algorithm performance. A total of 125 experiments are conducted to quantify the effects of variations in measurement volume, blending ratio and sensor precision. Based on the outcome of the experiments, recommendations are formulated for optimal operation of the monitoring system, guaranteeing the best possible algorithm performance.
...
The mining industry continuously struggles to keep produced tonnages and grades aligned with targets derived from model-based expectations. Deviations often result from the inability to characterise short-term production units accurately based on sparsely distributed exploration data. During operation, the characterisation of short-term production units can be significantly improved when deviations are monitored and integrated back into the underlying grade control model. A previous contribution introduced a novel simulation-based geostatistical approach to repeatedly update the grade control model based on online data from a production monitoring system. The added value of the presented algorithm results from its ability to handle inaccurate observations made on blended material streams originating from two or more extraction points. This contribution further extends previous work studying the relation between system control parameters and algorithm performance. A total of 125 experiments are conducted to quantify the effects of variations in measurement volume, blending ratio and sensor precision. Based on the outcome of the experiments, recommendations are formulated for optimal operation of the monitoring system, guaranteeing the best possible algorithm performance.
The ball mill is usually the largest energy consumer at a mine site and significantly affects operational expenditures. Given a target particle size, Bond Mill Work Index estimates are used to predict a ball mill’s throughput. In order to maximize ball mill throughput and optimize energy utilization, it is important to get these estimates right. At the Tropicana Gold Mine, Work Index estimates, derived from X-Ray Fluorescence and Hyperspectral scanning of Grade Control samples, are used to construct spatial GeoMetallurgical models (GeoMet). Inaccuracies in block estimates exist due to limited calibration between grade control derived and laboratory Work Index values. To improve the calibration, an updating algorithm has been tested at the Tropicana Gold Mine. The aim of the study was to demonstrate a new process for updating block estimates using actual mill performance data. Deviations between predicted and actual mill performance are monitored and used to locally improve the Work Index estimates in the GeoMet model. The updating algorithm improves the spatial Work Index estimates, resulting in a real-time reconciliation of already extracted blocks and a recalibration of future scheduled blocks. The case study shows that historic and future production estimates improve on average by about 72 and 26%.
...
The ball mill is usually the largest energy consumer at a mine site and significantly affects operational expenditures. Given a target particle size, Bond Mill Work Index estimates are used to predict a ball mill’s throughput. In order to maximize ball mill throughput and optimize energy utilization, it is important to get these estimates right. At the Tropicana Gold Mine, Work Index estimates, derived from X-Ray Fluorescence and Hyperspectral scanning of Grade Control samples, are used to construct spatial GeoMetallurgical models (GeoMet). Inaccuracies in block estimates exist due to limited calibration between grade control derived and laboratory Work Index values. To improve the calibration, an updating algorithm has been tested at the Tropicana Gold Mine. The aim of the study was to demonstrate a new process for updating block estimates using actual mill performance data. Deviations between predicted and actual mill performance are monitored and used to locally improve the Work Index estimates in the GeoMet model. The updating algorithm improves the spatial Work Index estimates, resulting in a real-time reconciliation of already extracted blocks and a recalibration of future scheduled blocks. The case study shows that historic and future production estimates improve on average by about 72 and 26%.
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 of improving the grade control model based on inaccurate observations on blended material streams originating from two extraction points.
...
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 of improving the grade control model based on inaccurate observations on blended material streams originating from two extraction points.
In recent years a real-time resource model updating concept has proven to increase the material quality control and process efficiency in geostatistics. The real-time resource model updating concept integrates online-sensor data, measured fromthe production line, into the resourcemodel. This integration quickly improves the accuracy of the resource model. The aim of this contribution is to adapt this concept into coal production and to apply the developed framework on an industrial case. The result of this study will provide an additional improvement to coal quality management, by mainly focusing on the ash content in the deposit. This includes high ash values in coal seams, which are caused by sand intrusions and are greatly affecting the operational process. A tailored Ensemble Kalman Filter approach, specifically applicable in coal production, is presented after a detailed literature review. For validation, a 2D case study is performed in a fully controllable environment. Further, the approach is benchmarked against an alternative proven approach. To demonstrate the value added a full scale industrial application is performed focusing on improving the lignite quality control in the production process. The results of integrating online measurement data into the resource model indicate a significant improvement (in the order of 70%) in coal quality production.
...
In recent years a real-time resource model updating concept has proven to increase the material quality control and process efficiency in geostatistics. The real-time resource model updating concept integrates online-sensor data, measured fromthe production line, into the resourcemodel. This integration quickly improves the accuracy of the resource model. The aim of this contribution is to adapt this concept into coal production and to apply the developed framework on an industrial case. The result of this study will provide an additional improvement to coal quality management, by mainly focusing on the ash content in the deposit. This includes high ash values in coal seams, which are caused by sand intrusions and are greatly affecting the operational process. A tailored Ensemble Kalman Filter approach, specifically applicable in coal production, is presented after a detailed literature review. For validation, a 2D case study is performed in a fully controllable environment. Further, the approach is benchmarked against an alternative proven approach. To demonstrate the value added a full scale industrial application is performed focusing on improving the lignite quality control in the production process. The results of integrating online measurement data into the resource model indicate a significant improvement (in the order of 70%) in coal quality production.
An integrated approach to simulate and validate orebody realizations with complex trends
A case study in heavy mineral sands
Characterization of spatial variability in earth science commonly requires random fields which are stationary within delineated domains. This contribution presents an alternative approach for simulating attributes in combination with a non-stationary first-order moment. A new procedure is presented to unambiguously decompose the observed behaviour into a deterministic trend and a stochastic residual, while explicitly controlling the modelled uncertainty. The practicality of the approach resides in a straightforward and objective inference of the variogram model and neighborhood parameters. This method does not require a prior removal of the trend. The inference principle is based on minimizing the deviation between empirical and theoretical errors calculated for increasingly distant neighborhood shells. Further, the inference is integrated into a systematic simulation framework and accompanying validation guidelines are formulated. The effort results in a characterization of the resource uncertainty of an existing heavy mineral sand deposit.
...
Characterization of spatial variability in earth science commonly requires random fields which are stationary within delineated domains. This contribution presents an alternative approach for simulating attributes in combination with a non-stationary first-order moment. A new procedure is presented to unambiguously decompose the observed behaviour into a deterministic trend and a stochastic residual, while explicitly controlling the modelled uncertainty. The practicality of the approach resides in a straightforward and objective inference of the variogram model and neighborhood parameters. This method does not require a prior removal of the trend. The inference principle is based on minimizing the deviation between empirical and theoretical errors calculated for increasingly distant neighborhood shells. Further, the inference is integrated into a systematic simulation framework and accompanying validation guidelines are formulated. The effort results in a characterization of the resource uncertainty of an existing heavy mineral sand deposit.