Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 64

2.10.5 An Example of Dynamic Reconciliation for a Simulated
Flotation Circuit
A Pb-Cu-Zn flotation plant is depicted in Figure 2.16. It produces four different
concentrates. On-stream analyzes (OSA) for lead, copper and zinc are available for
the main streams of the plant (all the streams of Figure 2.16), but only the plant
ore feedrate is measured. The plant is simulated using a phenomenological kinetic
model [40] and random variations of the process variables are imposed as well as
measurement errors. For data reconciliation a sub-model is considered that involves
an empirical transfer function to describe the feed-to-concentrate and feed-to-reject
dynamics for the ore and the three metals (only the ore flow model is given in Figure
2.17 but the flow models for the three metals have similar structures). However, the
separation coefficients for the ore and the three strategic metals are not modeled.
Consequently the model is incomplete.
Figure 2.16 Flowsheet of a lead-zinc-copper flotation plant
The reconciliation procedure has a hierarchical structure (see Figure 2.18). At the
upper level, metal assays are used to estimate flowrates in order to minimize model
equation residuals at time t (this is a one-step method using criterion J of Equation
2.127). Assuming that ore flowrates are set at their estimated values, metal assays are
reconciled at the lower level by minimizing squared residuals of the measurement
equations and squared residuals of metal flowrate dynamic models. This is again
a one-step method. There is also a possibility of refining flowrate estimation by
iterating between the two levels, but this is usually unnecessary since the process
variables do not vary much between two subsequent sampling times. Some results
are given in Figures 2.19 to 2.22. The first one shows the estimated values of the
unmeasured flowrates compared with the simulated values (“true values”). The other
figures show the reconciled values of the metal assays for selected streams.