Mini-series on material balance – Bonus: redundancy and data reconciliation

Discover a CASPEO mini-series dedicated to the material balance in mineral processing: The material balance, a key step between measurement and process control. Follow us and learn everything you ever wanted to know about material balance. No promotion, it will describe the topic from a neutral point. In this bonus and final part, review the objective of data reconciliation by material balance and why it is so important. 

Measurements performed around a processing operation allow the characterisation of material input or output streams, as well as stocks and work in progress at the beginning and end of the period. The material conservation laws give the relationships between the results of these measurements. Unmeasured parameters can be obtained from these relationships, provided that a minimum number of measurements are made to make the system observable. On the other hand, if there are more measurements than the minimum required, the results of the calculation and the measurement for the same parameter may have different values since any measurement is subject to error and is only an estimate of reality.

Data reconciliation by material balance

The objective of the algorithm of data reconciliation by material balance is to find a new set of estimates of reality, which are as close as possible to the measured values, relative to the measurement error (an accurate measurement will have an estimate closer to the measured value than a less accurate measurement) but verifying the material conservation laws. The estimates correspond to the maximum probability of getting the real values. They are also subject to error, but theory shows that this error is always less than the error of the parameter measurement. The good precision of some measurements benefits the estimates of parameters with less accurate measurements. The more redundancy there is, the better the improvement in accuracy.

Example: the material balance of a copper ore concentrator 

As an example, consider a copper ore concentrator with an ore feed stream, a concentrate stream, and a tailings stream. The residence time is short enough and the stocks low enough to consider the law of conservation: all the solid and copper that goes in comes out. The mass of solids and the copper content are measured on these three streams. The input minus output calculations on the solids and copper raw data are not zero, as the conservation laws would require, but give + 25 t and – 190 kg respectively:

This deviation from the laws is due to the measurement errors as indicated:

After reconciliation, the estimates are close to the measured values and their associated errors show the expected improvement from redundancy:

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