voller comminution: linking the blast furnace to the production of loess. vaughan r. voller what is...
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voller
Comminution: Linking the blast furnace to the production of loess.
Vaughan R. Voller
What is Comminution
From Wikipedia:Comminution is one of the four main groups of mechanical processing and describes the movement of the particle size distribution (grains, drops, bubbles) into a range of finer particle sizes (The other groups are agglomeration, separation and mixing).
•Explain Some Basic Comminution Processes and provide landscape examples•Show why it is important to the health and wealth of Minnesota •Develop some basic comminution laws•Describe the so called “population balance” model•Demonstrate two “toy” landscape models based on population balance concept
From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
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vollerModes of Comminution
Particle size
From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
Glacial abrasion
Debris FlowSaltation
Sklar and Dietrich
weathering
Comminution in Landscape Dynamics
x
Size Sorting
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Why is important to Minnesota
The US Steel Industry produces about 1/8th of World’s SteelThe Columbia Encyclopedia, Sixth Edition. Copyright © 2001-05 Columbia University Press.
On the order of ½ of the iron ore comes from Minnesota’s Iron Range
Ore has been shipped from Minnesota since the late 1890’s
Up until the 40’s this was high grade Hematite Ore Fe2O3
When supplies became exhausted switched to Taconite--LOW grade mixture of Silica and Magnetite Fe2O4
This required processing the ore to create suitable feed for The blast furnace
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The Taconite Process: Developed by E.W. Davis at the University of Minnesota
Run of mine ~25 % Fe-need to reduce to grain size of magnetite
http://www.aggdesigns.com/Cone-Crusher-info.htm#section1
Crushing
grinding
At grain sizeMagnetite canBe seperated
Product toosmall and wrongchemical compositionso agglomerated and indurated
Fe2O4 Fe2O3Product can be shippedand used Directly in BF
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Particle size
Two Things we would Like to Know
For a Given EnergyWhat is the Reduction in Particle Size—
The Comminution Laws
For a Given
“Communition Event”
How does size distribution change
From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
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voller
From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
The Comminution Laws
Consider a simplistic communtion operationthat for each event reduces the particle sizeby a factor of 1/2
Rittenger (1867): NewSurfaceE FP x4Nx4
FP x
1
x
1CE
xF After q events
21
ln
xx
ln
q2
1
x
x F
Pq
F
P
2P
2F
x
xN
Kick (1885): Energy for each event
E=Constant
After q events
E = qE
F
P
x
xlnCE
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voller
Rittenger (1867): NewSurfaceE
FP x
1
x
1CE
Kick (1885): Energy for each event
E=Constant
P
F
x
xlnCE
A general Law For general case x—an average part. size
Log Particle Size
Log E
nerg
y Inpu
t
Grind Limit Kick
Ritt
enge
r
CrushingAbrasion
After Hukki
Instructive to look at energy asA function of size reduction for quartz Rittenger works best at describing
Abrasion-Kick at describing crushing
Hukki suggested combined law
)Rittenger(2)x(f),Kick(1)x(f
,x
dxCdE
)x(f
Voller shows ifxln
)baxln(
xln
Cln1)x(f
FPP
F
x
1
x
1b
x
xlnaE
Linear combo of Kick and Rittenger
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Particle size
The comminution lawsSay how the “average” Particle sizes changes for a givenEnergy input
But how does the Particle size distribution change
For this we use
A Population Balance Model
From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
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From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
Assume that Size distribution afterA give time is characterized by Wj(t)
(j =1, --n) number if size intervalsWj(t) weight fraction in interval j
For a given grinding “event”We define a
A Selection Function k(j) ----fraction of particles broken out of interval j
A Breakage Function b(j,i) ---fraction of particles broken from interval i (<j) that end up in j
Think of grinding operation wherea feed is put into a batch ball mill
and worked on for a given length of time
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From Kelly and SpottiswoodIntro Min Proc, Wiley, 1982
Between two consecutive “events” we can construct a population balance
1j
1iijj )0(W)i(k)i,j(b)0(W))j(k1()1(W
Amount remaining in j Amount entering j
)p(W][)1p(W BKKI
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)p(W][)1p(W BKKI 1
y
x
e1
e1)y,x(b
Pop Bal Model Possible forms for Breakage and Selection functions
)5.0m,25.a(ax)x(k m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8 9 10 11 12
Derive form Comminution Laws
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voller
)p(W][)1p(W BKKI
Current version of the model is a BATCH model
In land scale dynamics-could relate ???? to “Cohort” Debris flow withNO breakage or erosion (saltation) due to contacts with basement
saltation
abrasion
imapct
No
No
Can We modify to accountfor abrasion-saltation ?
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Base Rock
Model Parameters for Debris Flow Mass Balance
=
K= selection
Fraction of selected particles that break by impact with basement
Assumption: Breakage productsthe same for particle-particle impacts and particle-basement impacts
= Volume of liberated from Base
=Volume Impacting Base
Related to Bitter erosionLaw ???
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voller
A proposed The Debris Flow Mass Balance
saltation
abrasion
imapct
1j
1ii
1j
1ii
1j
1iijj
)0(W)i(k)i,j(b)1()0(W)i(k)i,j(b)1(
)0(W)i(k)i,j(b)0(W))j(k1()1(W
Amount remaining in j amount entering j via particle-particle impacts
amount entering j via particle-bed impacts amount entering j liberated from bed
As written and are constant but could be functions of slope and particle size
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A size sorting Long-Profile population balance model
x5.Sx)x(k
1
y
x
e1
e1)y,x(b
Breakage: Particles beak by impacts and abrasion—selection a function ofSlope S
Equilibrium: Transport process are sufficient to maintain location of a given size interval between breaking events
Location: in size distribution an given size interval is associated With a location in the landscape
Fines: the smallest size intervalexits system (sub-marine deposit)
Uplift: Mass is maintained in system by adding fine mass created in an event to mass of largest particel size interval before next event
Profile: Depth of profile is proportional to weight fraction of size interval
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x
1j
1iijj )0(W)i(k)i,j(b)p(W))j(k1()1p(W
)1p(W)p(W))1(k1()1p(W n11
A size sorting Long-Profile population balance model
After repeated “events” an initial flat straight profile approaches A steady sate profile with an identified erosional and depositional component
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 3 4 5 6
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The breaking of particles isan important componentthe dynamics of the Earth’s surface.
Comminution: Linking the blast furnace to the production of loess.
Vaughan R. Voller
The breaking of ores is a criticalprocess in mineral processing---
The economic importance of this industry has led to extensive study of how rocks break (comminution)
The aim of this seminar has beento show how the work in mineralengineering could be appliedin understanding earth surfaceprocesses
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