Dynamic structures in variance based data reconciliation adjustments for a chromite smelting furnace

The characterisation of furnace product materials is discussed in relation to their impact on the material balance reconciliation. It was found that the melts from open arc furnaces, as used in the chromite smelting industry, is not as homogenous as assumed. It was found that, for silicon in the ferrochrome melt, the spatial composition variance could be related to the degrees sub cooling relative to the alloy liquidus. The spatial variances in the furnaces were therefore incorporated in the variance-based reconciliation. The use of different data reconciliation techniques as a tool towards furnace control in the pyrometallurgical industry is discussed. Both the Lagrange multiplier, as well a direct method using the generalised reduced gradient method were evaluated. The adjustments to the measurements, which may be viewed as a combination of structural and random error in the measurements as well as systematic bias, were found to have dynamic structure. A comparison of time series models of the adjustments and their Fourier power spectra, has shown that any given adjustment is auto-correlated with previous historic values, even though the reconciliations were performed independently. Systematic biases were also apparent in the measured data, which were identified and subsequently confirmed.