Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 27

Figure 2.4 Multi-level representation of stream matter for a generic gold ore processing plant

2.3.5 Additional Constraints

In addition to the above basic mass conservation constraints, one may have to add
equations that represent either additional structural constraints, or stoichiometric
constraints, or process behavior modeling assumptions (mass or energy transfer and
rate equations). In the first case, the most frequent constraint arises when an ex-
haustive species analysis is available. Then the species mass fractions must sum to
1,

∑ i

c i = 1 (2.18)

for i values corresponding to exhaustive analyses. Alternatively, the constraint may
be expressed by writing that the sum of some component flowrates must be equal to
the total flowrate:

∑ i

f 0 = f i . (2.19)

In the above example, these constraints are valid for carbon, water and ore com-
ponents, and also for particle size classes.
A stoichiometric constraint may arise for instance when minerals are assumed
to have fixed composition, such as FeS 2 or CuFeS 2 . When both sulfides are present
and are the only sulfur, copper, and iron carriers, there is a relationship between
sulfur, copper, and iron contents that must be verified. Another possible constraint
arises when there are stream splitting systems where an equal share of the streams is
assumed. Another possibility is that a species production rate has a prior estimated
value that must be obeyed with some level of uncertainty.
Other constraints may arise in multi-phase systems, when a species transfers
from one phase to another one. This is obviously the case in leaching, elution, ad-