Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 55

of the V X variance and covariance terms is considerable in the drastic increase of the
precision when using reconciled data.

Cu circuit Bulk circuit

Cu-Pb
concentrates
from 3 Cu-Pb
flotation
circuits

Pb concentrate

Cu concentrate Zn-Pb bulk concentrate

Figure 2.12 Copper-lead-zinc flotation plant

Tabl e 2. 5 Recoveries R and their reliabilities (standard deviations σ R ) as calculated with reconciled
and raw data

Method Steady-state

reconcilation

Raw data and
(2.112)

Raw data and
(2.113)

Recovery of R ( % ) σ R (%) R ( % ) σ R (%) R ( % ) σ R (%)

Copper in copper concentrate
of copper circuit

78.0 4.0 59.4 31 79.8 7.2

Lead in lead concentrate of
bulk circuit

95.3 3.0 89.3 13 79.0 38

Zinc in bulk concentrate of
bulk circuit

56.0 7.0 29.6 13 77.8 10

Example 4. Another use of reconciled data is the estimation of model parameters
[91] such as grinding, leaching, and flotation rate constants [58], and hydrocyclone
selectivity. For example, the confidence intervals of the estimated rates of breakage
in an industrial ball mill of a closed circuit are presented in Figure 2.13 as func-
tions of particle size [90]. Using reconciled values instead of raw data drastically
improves the model reliability, particularly in the fine size range where the sensitiv-
ity of the rate of breakage is extremely high, because of the typical structure of the
breakage phenomena, which involves chain reactions.

2.10 An Overview of Dynamic Reconciliation Methods

Steady-state data reconciliation is frequently used to enhance process information
quality. However steady-state operating conditions do not exist in practice and cor-
responding methods cannot fulfill the need for reliable dynamic state estimation,