Process simulation using computer technology · Process Simulations Using Computer Technology Steve...
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Process Simulations Using Computer Technology
Steve Frankland Dargo Associates Ltd
What is a Process Simulations?
• Mathematical prediction of the outcome of a physical or chemical process
• Linking of several unit processes together
• Presentation of the results in an understandable form
What can be simulated?
• Any unit process that can be described mathematically – Separations – Phase Changes
Subjects for today
• Simulations/Models – Density – Size – Others – Crushers
• Flowsheeting – Link the processes together – Control of calculations
Density Separations
• Tromp Curves • Float/sink data
Tromp Curve
0
20
40
60
80
100
1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20
Density
Rec
ove
ry t
o S
inks
%
How do you use it?
Lower Density
Upper Density
Average Mass % Partition Coeff
Floats Mass
Sinks Mass
1.25 1.55 1.40 59.7 98.5 58.8 0.91.55 1.65 1.60 2.2 50.0 1.1 1.11.65 1.75 1.70 2.0 5.0 0.1 1.91.75 1.85 1.80 0.8 2.0 0.0 0.81.85 1.95 1.90 0.8 1.0 0.0 0.81.95 2.5 2.23 0.4 0.0 0.0 0.4
How do you generate the Tromp Curve
• Normalised Curve – Independent of Epm and Density
EpmPCDensityPartitionPC normalised *_ −=
• Equation
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−=−
Epme
PC DensityDensityPartition ))_(*098.1(
1
11
Assumptions
• There is one assumption – That the quality for each density
fraction is the same for floats and sinks – True enough if the density fractions are
closely spaced
UK Applications
• Largest UK mining activity is quarrying
• Most quarries classify rock • Large number have breakers/
crushers • Going to look more deeply at these
activities
Sizing
• Tromp Curve – Basically the same separation as density but
using size. • Equation
( )⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−+⎟⎠
⎞⎜⎝
⎛
−−
2_*
1*1α
α
α eSeparationSizeSizee
eRf
Rf = Amount of fines bypassing to O/Size α = efficiency factor
Crushing
• Crushing is a complex process • Depends on difficult to measure
parameters – Type of Comminution machine – Settings of machine – Throughput – Hardness of material
Types of Crusher Model
• Use known data of crusher product size distribution – This are often provided by manufacturers – Difficult to match for all rock types – Not always accurate
• Whiten method – Based on fundamental understanding of
crushing – Can be applied to any crusher and rock
combination
Schematic of a Breaker
Classification
Breakage
As described by Whiten and Anderson
Functions • Classification
– All particles less than a certain size (K1) pass directly to the undersize
– All particles above a certain size (K2) report to breakage
– All particles between K1 and K2 are partitioned (like sizing and density separations) between being broken and passing directly through
• Breakage – Broken particles are classified again
Maths again
If x < K1 then C(x) = 0.0
If x > K2 then C(x) = 1.0
If K1 < x < K2 then 3
1220.1)(
K
KKxKxC ⎥⎦
⎤⎢⎣
⎡−−
−=
Where x = size of particle C(x) = proportion reporting to breakage K1, K2 are as before K3 describes the shape of the classification function
THE CLASSIFICATION FUNCTION
Determining K1, K2 and K3
• K1 = A0 + A2*TPH + A3*F80 • K2 = B0 ± B1*CSS + B3*F80 – B4*LHR
+B5*ET • K3 = 2.3
Where CSS = Closed side Setting (mm) TPH = Feed Rate F80 = 80% passing size LHR = Liner age (hr) ET = Eccentric Throw (mm)
Meaning?
• K1 is very dependent on closed-side setting and throughput and a little on feed size
• K2 is very dependent on closed-side setting and throughput and a little on liner age and the crusher movement
• K3 is a constant
Use in practice
• For most applications, there are estimates of the constants Ax and Bx.
• For more accurate simulations, they can be determined by regression analysis.
The Breakage Function • For unusual rocks a detailed
examination may be required but for most rocks:
Where T10 = % passing 1/10th of original size 5-10 for primary crushing 10-15 for secondary crushing and 15-20 for tertiary crushing CSS = closed side setting TPH = dry throughput rate F80 = 80% passing size (mm)
80FDTPHDCSSDDT 321010 ×−×+×−=
Other simulations
• Froth Flotation – For coal use laboratory tests – Where good models exist they can be
incorporated • Magnetic Separations
– Simple mass balance based on recovery and RD of overdense
• Thickeners – Simple mass balance based on solids in O/flow
and underflow.
Linking the processes together
• Going to use LIMN as an example – Generalised flowsheeting package – Based on Microsoft’s Excel®
spreadsheet – Models are placed in Worksheets – Drawing on screen
• Other packages – JKSimMet – USBM
Dense Medium Bath
Case Study
• Consider a stone quarry • Flow diagram shown on next slide • Each crusher has a specific power
consumption • Plus 100mm has no value • 100mm x 40mm = £5.00/t • Minus 40mm = £3.00/t • What is the optimum setting to give
maximum revenue
Comminution Circuit
Scenarios
Proc ess Simula tions Using C omputer Tec hnolog y
Steve Frankla ndDa rg o Assoc ia tes Ltd
Optimisation Net Revenue
725.0
730.0
735.0
740.0
745.0
750.0
70.00 75.00 80.00
Secondary Crusher CSS
£
250.00150.00100.0050.00
Prim Scr Ap
Optimisation 2 Net Revenue
738.0739.0740.0741.0742.0743.0744.0745.0746.0
70.00 75.00 80.00
Secondary Crusher CSS
£
95.00100.00105.00110.00
Sec Scr Ap
Product Check Variables Results
Cell Address 77.50 110.00 125.415 870.0 744.5 20.7 5.15
Cell Description Sec CSS Sec Scr Cost Revenue Diff Prod <40 >10070.00 95.00 136.002 874.8 738.8 23.215 3.56872.50 95.00 137.150 881.6 744.5 21.439 3.56875.00 95.00 137.146 881.6 744.4 21.45 3.56877.50 95.00 137.141 881.5 744.4 21.46 3.56870.00 100.00 131.740 871.5 739.7 22.827 4.09772.50 100.00 132.698 877.8 745.1 21.181 4.09775.00 100.00 132.694 877.7 745.0 21.191 4.09777.50 100.00 132.690 877.7 745.0 21.202 4.09770.00 105.00 128.014 868.0 740.0 22.463 4.62772.50 105.00 128.825 873.9 745.1 20.928 4.62775.00 105.00 128.822 873.9 745.0 20.938 4.62777.50 105.00 128.818 873.8 745.0 20.948 4.62770.00 110.00 124.726 864.6 739.8 22.121 5.15172.50 110.00 125.422 870.0 744.6 20.682 5.15175.00 110.00 125.418 870.0 744.6 20.692 5.15177.50 110.00 125.415 870.0 744.5 20.701 5.151
Control
Summary Features
• Ease of use • Calculation of many different
configurations • Correctly balanced flowsheets • Optimisation • Training aid