This is an overview of various mass balancing techniques that can be used in the mineral processing environment. Some of these techniques can be incorporated into your online monitoring system as well as metallurgical accounting to highlight areas of production loss timeously.

1. MASS BALANCING –
MIDAS APPROACH
Metallurgical Accounting Course, South Africa 2015
MIDASTech International

2. THE ADVANTAGES OF
DETAILED MASS BALANCE
• Units process particles
• So understanding the complex response of particles to units
processes facilitates the basis of accurate simulation; rather
than fictional simulation which is all too common.
• Metallurgical accounting focuses on assays, and is therefore
a 1D Balance and inappropriate for simulation or
understanding metallurgical processing of the ore

3. MASS BALANCING LEVELS
• 0D Balance – Solid flows and Water flows
• 1D Balance - Size, OR bulk assays, OR elements OR density
classes OR Minerals
• 2D Balance i.e. Size/assay
• 3D Balance Size, Particle Types (i.e. density class), Properties
of particle types (i.e. multimineral composition)
MIDASTech International

4. DATA STRUCTURES FOR
MASS BALANCING

5. THE VARIOUS LEVELS OF
MASS BALANCING
• The diagram shows the general structure of ore
information. Measurement of information and
structure are not the same.
• A poorly constructed simulator will be based on
measurable information only rather than the actual ore
structure.
• An intelligent simulator will use the measured
information to identify the actual ore properties.

6. LEVELS OF MASS
BALANCING CONTINUED
• Hence it is not necessarily required to obtain the detail information
(3D); only to infer it from the 2D information. Hence there is a
hierarchical approach to mass balancing. Generally 1D first to
ensure solid flows are estimated; then 2D to ensure general mass
balance consistency.
• The 2D information can actually be used to infer the 3D, which is
also mass balanced, but not necessarily based on 3D
measurement. On the other hand a user can directly measure 3D
data via float-sink tests – and then elemental composition in each
density class, or mineralogical analysis.
• However the fundamental object remains – to identify the flow of
particles through the circuit

7. ACTUAL MINERAL
PROCESSING DATA
STRUCTURE
• Particles are multimineral

8. MULTIMINERAL PARTICLES
• The figure shows a multimineral particle.
• It is self-evident from examining ore particles that they
are indeed multimineral.
• The important concept is that one would think that if
we were to model multimineral particles in mineral
processing we would need billions of particles. But we
don’t!
• We are only seeking a representative set of
multimineral particles, say 200 per size-class which can
easily be handled by simple calculation software such as
Excel.

9. PARTICLE RECOVERY

10. BASED ON A FLOAT CELL
• Particles goes into a
flotation cell, and based on
their composition will have
a probability of going to the
concentrate.
• Hence high grade floatable
particles will be more likely
to go the concentrate than
low grade non-floatable
minerals.

11. PARTITION CURVES FOR
UNDERSTANDING EFFICIENCY
Mineral Composition
Probability of
particle going
to concentrate
Inefficient
Efficient

12. FROM THE PREVIOUS
DIAGRAM
• So if we know the information
about particle distributions
before and after a flotation
cell, we can plot the ‘partition
curve’ – the probability a
particle of a particular grade
will go to the concentrate.
• It is not enough to know
assays before and after a
float cell, as it can be
affected by the distribution
of mineral in the particles.
Hence the partition curve
helps us to distinguish
units that are performing
efficiently from those that
are performing
inefficiently.

13. COMPOSITION OF A MINERAL
IS INSUFFICIENT TO DEVELOP
A MODEL
Two particles both with the same composition of valuable mineral
(say chalcopyrite). In a simple model they would be presumed to
have the same properties

14. LOOKING AT MINERAL
PARTICLES…
• But looking at the mineral composition of just one mineral is
not good enough!
• Here we see two particles – both have the same grade of
valuable mineral interest. All other minerals are combined to
form the respective ‘gangue’ mineral. An inexperienced
metallurgist would think that the two particles have the same
properties and therefore should float the same.
• But if you think a little bit deeper, you might want to think
about the ‘gangue’ phase

15. LOOK A BIT DEEPER
The gangue mineral may be different i.e. quartz for particle 1 and
pyrite for particle 2. The belief the two particles will have the same
properties (particularly in flotation) is at best a work of fiction.
Clearly we need to recognise the existence of multiminerals

16. FAILURE TO RECOGNISE THE
EXISTENCE OF MULTIPLE
MINERALS
• Impractical models
• Fictional models
• Inordinate amount of laboratory analysis
• Lack of trust in simulation
• Invalid assay to mineral algorithms
• General confusion

17. BENEFITS OF DETAILED
MODELLING
• One can identify whether units are performing efficiently for a given
ore type
• Essential for plant trouble shooting
• Essential for plant simulation
• Essential for identifying how operational changes affect final grades
and recoveries
• Use of multiple mineral particles is essential for accuracy of models –
particularly separation of associated minerals such as pyrite,
chalcopyrite

18. THE SOLUTION!
• Recognise the existence of multiminerals (where they exist)
• Use software that incorporates modern mathematical methods to
deal with the real datastructure (Advanced simulation course,
inclusive of advanced mass balancing methods)
• Such methods are only available through MIDASTech

19. QUANTITATIVE
ADVANTAGES
• The MIDAS approach (Mass balancing together with simulation )
would target 5% operational improvement
• Leading to millions of dollars of savings per plant.

20. MIDAS TECH’S SET OF
MASS BALANCE SYSTEMS
• 1. MMVisioBal1D – 1D Mass Balance system,
• 2. MMVisioBal2D – 2D Mass Balance system,
• 3. MMVisioBal3D – 3D Mass Balance system
• 4. MMVisioBal2DPlus - inferring detailed 3D information
from 2D data (patented approach)

21. MASS BALANCING
METHODS
Two main approaches of mass balancing
• Conventional: Least squares – requires variances of
estimates; and is therefore a flawed approach if variances are
not known
• Modern: Information theory – appropriate when variances
are known; and can also be used when variances are known.
Fast, efficient and allows inference (MMVisioBalPlus)

22. MMVISIOBAL1D
• Entry point software (contact Stephen@MIDASTech.net)
• Uses Visio flowsheet system and Excel interface. System
largely automated. Once an Excel template is created and
data are inputted – press of a button yields mass balance
results

23. VISIO FLOWSHEET
Balanced
Variable
Stream
S1 S2 S3 S4 S8 S13 S11 S6 S17 S20 S23 S25 S27 S16 S19 S22 S5
TotalFlow
PercentSolids
SolidFlow 99695.00 105.01 74.85 99514.86 99315.01 99160.55 154.46 259.58 0.14 0.49 211.94 152.39 60.19 104.86 74.36 354.49 99575.05
WaterFlow
Assay
Au 1.21 26.90 32.17 1.15 1.06 1.03 19.28 38.04 19.28 20.23 13.99 18.19 3.43 26.90 32.25 35.71 1.16
Ag 33.97 1577.80 1752.46 31.04 27.60 26.21 915.26 1352.55 1288.41 1235.70 631.45 843.08 100.56 1577.61 1755.20 1374.14 31.08
Cu 1.30 17.50 15.15 1.27 1.24 1.22 12.82 13.01 21.73 14.14 9.97 12.73 3.05 17.49 15.16 14.63 1.27
Pb 1.21 4.81 4.52 1.20 1.19 1.18 4.82 5.25 5.20 4.02 2.43 3.00 1.01 4.81 4.52 5.78 1.20
F 779.56 1469.01 1520.43 778.20 777.52 777.14 1025.34 1101.44 1071.12 1402.03 1300.17 1313.65 1265.59 1469.47 1521.11 1040.69 778.49
Remainder 97.42 77.38 79.99 97.45 97.49 97.52 82.16 81.49 72.84 81.57 87.40 84.05 95.80 77.39 79.98 79.35 97.45

24. SIMPLE EXCEL INTERFACE
False Specification
Project Name MMMichaud
False SubProjectID 1
False False
False False
9. Options
Full 2D Full 2D
Water Balance FALSE
Start Experimental

25. EXPERIMENTAL DATA
(MMVISIOBAL1D)
Experimental
Variable
Stream
S1 S2 S3 S4 S8 S13 S11 S6 S17 S20 S23 S25 S27 S16 S19 S22 S5
TotalFlow
PercentSolids 28.60 19.85 16.09 28.12 23.96 24.14 10.65 11.51 4.77 4.01 4.21 19.38 3.65 5.28 7.73 18.00 19.22
SolidFlow 100000 104 74 172 288 142 47
WaterFlow
Assay
Au 1.37 33.78 25.07 1.16 0.59 0.54 6.20 6.85 8.58 14.23 13.90 18.26 6.93 19.33 37.36 53.85 3.43
Ag 60.00 1363.75 1118.75 30.00 22.50 13.75 312.50 377.50 507.50 646.25 557.50 952.50 320.00 1062.50 1601.25 1950.00 42.50
Cu 1.58 19.09 11.97 1.00 1.30 1.00 6.02 6.45 9.17 8.08 9.28 13.65 5.86 13.57 16.25 23.53 1.54
Pb 1.47 5.94 3.55 1.16 1.12 1.07 2.28 2.35 2.24 2.67 2.88 2.53 2.05 3.28 4.86 10.18 1.19
F 868.00 1189.20 1587.20 768.00 786.40 715.80 1190.80 1297.20 1514.60 1507.60 1256.20 1356.20 1223.00 1676.00 1346.00 762.40 759.20
Remainder 96.86 74.71 84.21 97.76 97.49 97.86 91.54 91.04 88.40 89.03 87.66 83.59 91.93 82.87 78.60 66.02 97.18536

26. CONFIDENCE
Confidence
Variable
Stream
S1 S2 S3 S4 S8 S13 S11 S6 S17 S20 S23 S25 S27 S16 S19 S22 S5
TotalFlow Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used
PercentSolids Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used
SolidFlow Standard Standard Standard Missing Missing Missing Standard Standard Missing Missing Missing Standard Standard Missing Missing Missing Missing
WaterFlow Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used Not Used
Assay
Au Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard
Ag Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard
Cu Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard
Pb Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard
F Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard
Remainder Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard Standard

27. BALANCED
Balanced
Variable
Stream
S1 S2 S3 S4 S8 S13 S11 S6 S17 S20 S23 S25 S27 S16 S19 S22 S5
TotalFlow
PercentSolids
SolidFlow 99695.00 105.01 74.85 99514.86 99315.01 99160.55 154.46 259.58 0.14 0.49 211.94 152.39 60.19 104.86 74.36 354.49 99575.05
WaterFlow
Assay
Au 1.21 26.90 32.17 1.15 1.06 1.03 19.28 38.04 19.28 20.23 13.99 18.19 3.43 26.90 32.25 35.71 1.16
Ag 33.97 1577.80 1752.46 31.04 27.60 26.21 915.26 1352.55 1288.41 1235.70 631.45 843.08 100.56 1577.61 1755.20 1374.14 31.08
Cu 1.30 17.50 15.15 1.27 1.24 1.22 12.82 13.01 21.73 14.14 9.97 12.73 3.05 17.49 15.16 14.63 1.27
Pb 1.21 4.81 4.52 1.20 1.19 1.18 4.82 5.25 5.20 4.02 2.43 3.00 1.01 4.81 4.52 5.78 1.20
F 779.56 1469.01 1520.43 778.20 777.52 777.14 1025.34 1101.44 1071.12 1402.03 1300.17 1313.65 1265.59 1469.47 1521.11 1040.69 778.49
Remainder 97.42 77.38 79.99 97.45 97.49 97.52 82.16 81.49 72.84 81.57 87.40 84.05 95.80 77.39 79.98 79.35 97.45

28. MMVISIOBAL3D
• Only used by sophisticated Mining Companies that are
focused on technically-enable profit strategies
Example:

29. EXPERIMENTAL
Experimental
SolidFlow 32.04
Size
Density
Class Mass%
Elements
Fe SiO2 Al2O3 P S TiO2 Mn CaO MgO LOI Remainder
-6+2 +4.05 13.93 66.33 1.27 0.86 0.07 0.01 0.04 0.02 0.02 0.03 2.36 28.99
+3.6-4.05 21.25 62.09 2.53 2.16 0.15 0.02 0.06 0.03 0.03 0.04 5.76 27.13
+3.3-3.6 16.32 56.05 4.24 4.13 0.21 0.03 0.11 0.05 0.04 0.07 9.84 25.23
+2.85-3.3 8.92 50.90 7.81 7.07 0.18 0.04 0.20 0.04 0.05 0.10 11.25 22.36
+2.6-2.85 2.10 38.39 16.98 14.59 0.11 0.03 0.33 0.04 0.07 0.12 12.22 17.12
-2.6 1.93 24.23 26.92 23.89 0.08 0.03 0.47 0.02 0.12 0.16 13.50 10.58
Average 64.45 58.42 4.36 4.04 0.15 0.02 0.10 0.04 0.04 0.06 7.15 25.62
-2+1 +4.05 10.20 66.21 1.41 0.91 0.07 0.01 0.04 0.02 0.02 0.03 2.39 28.89
+3.6-4.05 6.94 61.06 2.60 2.30 0.17 0.03 0.07 0.05 0.03 0.05 7.06 26.58
+3.3-3.6 11.81 56.71 4.30 4.12 0.20 0.03 0.13 0.05 0.05 0.07 9.67 24.67
+2.85-3.3 5.02 49.82 8.91 7.63 0.16 0.04 0.23 0.04 0.07 0.10 11.30 21.70
+2.6-2.85 1.15 29.80 24.09 19.46 0.10 0.04 0.37 0.02 0.12 0.16 12.67 13.17
-2.6 0.43 13.68 32.28 31.64 0.05 0.04 0.41 0.01 0.08 0.15 15.23 6.43
Average 35.55 58.32 4.54 4.13 0.14 0.02 0.11 0.04 0.04 0.06 7.25 25.33

30. BALANCED
Balanced
SolidFlow
Size
Density
Class Mass%
Elements
Fe SiO2 Al2O3 P S TiO2 Mn CaO MgO LOI Remainder
-6+2 +4.05 14.44 66.36 1.32 0.94 0.07 0.01 0.04 0.02 0.02 0.04 2.42 28.75
+3.6-4.05 20.34 62.18 2.40 2.16 0.15 0.02 0.05 0.03 0.03 0.04 5.81 27.14
+3.3-3.6 17.21 56.63 4.04 4.07 0.21 0.03 0.11 0.06 0.04 0.07 9.51 25.23
+2.85-3.3 8.58 51.56 7.35 6.87 0.18 0.04 0.18 0.04 0.06 0.10 10.99 22.64
+2.6-2.85 2.21 38.97 16.36 14.68 0.12 0.03 0.31 0.03 0.09 0.13 12.08 17.22
-2.6 1.66 23.48 26.56 24.95 0.07 0.03 0.44 0.03 0.10 0.16 13.75 10.44
Average 64.45 58.42 4.36 4.04 0.15 0.02 0.10 0.04 0.04 0.06 7.15 25.62
-2+1 +4.05 10.30 66.41 1.36 0.91 0.07 0.01 0.04 0.02 0.02 0.03 2.36 28.77
+3.6-4.05 7.83 61.37 2.50 2.30 0.17 0.02 0.07 0.04 0.03 0.05 6.82 26.63
+3.3-3.6 11.43 56.70 4.26 4.21 0.20 0.03 0.13 0.05 0.05 0.07 9.61 24.70
+2.85-3.3 4.51 50.01 8.81 7.77 0.16 0.03 0.22 0.04 0.07 0.11 11.13 21.65
+2.6-2.85 0.86 31.10 22.85 19.08 0.10 0.03 0.34 0.02 0.13 0.15 12.47 13.72
-2.6 0.62 13.51 32.02 32.29 0.05 0.03 0.41 0.01 0.09 0.16 15.11 6.31
Average 35.55 58.32 4.54 4.13 0.14 0.02 0.11 0.04 0.04 0.06 7.25 25.33
Bulk - - 58.39 4.42 4.07 0.15 0.02 0.10 0.04 0.04 0.06 7.19 25.52

31. INTEGRATED SOFTWARE
• All software, including simulation are integrated into a
system called MMPlantMonitor.
• A course (Advanced Simulation) is available. Next scheduled
course in South Africa in November via MEI (Flotation 15)
• Stephen Gay Stephen@MIDASTech.net
MIDASTech International