Analysis,delineation
and evaluation of separation
processes
Separation
(for instance flotation) FEED
PRODUCT B
PRODUCT A
device and its fields
splitting forces
components and their features
separation
main feature
analysis
evaluation
delineation
parameter
Elements of separation process: Delineation, Analysis, Evaluation
ph
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s
mec
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delineation x1
c
x2
x3 x4
mechanicstermodynamic probability
Quantity and quality of products
Delineation
Main feature and its building parameters
Vmax
W
VA,VR,VS
A, ,, x, , H
ni, , ,cs,pH,
.....
xc /x
jV
* maxH, c
s
CpCu
Cm
hd
Material main feature
Other factors (fluctuations)
Fields, space time provided by separator
Delineation
feed
(ordering disorderingother forces)
splitting forces
separating forces
outer forces
product B
product A
components
particle analytical fraction
inner forces
separation
mineral
chemical element
real fraction
group
variable rest material
features
content (upgrading)value (classification)group number (sorting)price (economics) others (entropy) (others) none (splitting)
ANALYSIS
separation
particle trajectory
forces
component-feature
component
splitting
space
fields
feature
+
+
+
+
Structure of separation by flotation
Components: typeANALYSIS
(feed)initial component
main component
primary component
secondary component
elemental component
(product)
(real fraction)
(analytical fraction)
(group)
(mineral) (mineral particle)
(chemical element)
-name
-quantity
-quality
-economical value
-main feature providing separation
-features forming main feature
-time of components displacement
-separating forces acting on components
-ordering and other forces acting on components
-other (temperature, pressure, etc.)
Components: featuresANALYSIS
Components: types and feaures
fractal-like structure
ANALYSIS
feature
type
component
quantity
main parameter
neutral p.other p.
sub-component ( quality)
chemicalelements
type
quantity main parameter
neutral p.other p. sub-component ( quality)
Features can be grouped into families
ANALYSIS
main feature*
numerical value ascribed number other
volume massweight populationother
type
namesymbolother
component features
* based on other features
quantity quality (amount of subcomponent)
other (time, money,forces, etc.)
content %mass fraction other
Taking into account four families
Their combination provides different
ANALYSIS
Ways of analysis of separation results
upgrading classification sorting
quality=f(quantity)
quantity= f(main feature)
quality=f(main feature)
quantity=f(name)
quality= f(name)
feature= f(name)
producting(sampling
portioning)distribution descriptive
quantity
quality
feature
name
value
SEPARATION
Sorting
Product separation
Ways of analysis of separtion processes
Analys
ANALYSIS
Flotation, as a rule, is analyzed as upgrading
YIELD ()
(Analysis of separation taking into account content (mass or similar paremeters of the system))
UPGRADING AND ITS BALANCE
N megagrams of feed = K megagrams concentrate + O megagrams of tailing
N = K + O.
Let us devide it by N and express it in %:
%100%100%100N
O
N
K
N
N .
All three terms are yields:
%100%100 N
N, %100
N
K= K, %100
N
O = O
Thus:K + O = N = 100%
ANALYSIS
UPGRADING AND ITS BALANCE
CONTENT
Amount of a component (fraction, type of grain, etc.) in a product, usually in %
– content of a component in feed %, – content of a component in concentrate, %, – content of a component in combined products, %,
– content of a component in tailing, %.
Used symbols
ANALYSIS
Infinitive number of upgrading parameters can be derived from
, and Most popular are:
Recovery:
Upgrading ratio
Cumulative recovery
k=/ K=/
ANALYSIS
c
ba
Other parameters, for instance
ANALYSIS
Typical upgrading balance
(for feed and final products)
way of calculating content of considered component in feed
(%) ()/100%
ANALYSIS
Product Yield
Mg/day
Yield
%
Content %
(%) × (%) Upgrading
ratio k = /
Recovery
(%) /
Concentrate K
172 20.14 60.40 (= ) 1216.456 3.92 79.0
Tailing O 682 79.86 4.045 (= ) 323.034 0.26 21.0
Feed N 854 100.00 15.395 (= ) 1539.490
(1216.456+323.034) 1 100.0
Upgrading balance
ANALYSIS
Product
Amount of
product (Mg)
Yield of product (%)
Yield of products (cumul.)
(%)
Content of MeSO4
(%) ()
= ()/
%
Upgrading ratio
K = /
Recovery of MeSO4
=/, %
Recovery of MeSO4
= K, %
Concentrate K1 103 12.06 12.06 81.7 985.30 985.30 81.70 5.305 63.98 63.98 Concentrate K2 69 8.08 20.14 28.6 231.09 1216.39 60.40 3.922 15.01 78.99 Semiproduct P1 189 22.13 42.27 7.0 154.91 1371.30 32.44 2.106 10.06 89.05 Semiproduct P2 238 27.87 70.14 5.48 152.73 1524.03 21.73 1.411 9.92 98.97
Tailing O 255 29.86 29.86 0.52 15.53 15.53 0.52 0.0338 1.01 1.01
Feed N
(calculated) 854 100.00 100.00
= = 15.40
1539.56 1539.56 15.40 1 100.00 99.98 ~100
Feed (analytical): = for instance 15.65
= stałe
Principle upgrading curves
Henry’s: = f()
Halbich’s: = f ()
Mayer’s = f()
constant
Fuerstenau’s: 1 = f (2)
ANALYSIS
0 20 40 60 80 100, %
0
20
40
60
80
100
, %
ideal mixing n
o u
pg
rad
ing
real upgrading
ideal upgrading
EVALUATIONHenry’s
Mayer’s
0 20 40 60 80 100
cumulative yield , %
0
20
40
60
80
100
cum
ula
tive
rec
over
y,
, %
no upgra
ding
ideal upgrading
*
Mayer
EVALUATION
Halbich’s
0 20 40 60 80 100
content of a component in concentrate
0
20
40
60
80
100
cum
ula
tive
rec
ove
ry, ,
%
ideal upgrading
, %
line
of n
o up
grad
ing
EVALUATION
Fuerstenau’s
0 20 40 60 80 100
componet 2 in product 2, %
0
20
40
60
80
100
(co
mp
on
en
t 1
in p
rod
uc
t 1
)%
ideal upgrading
F = (89/89)
no upgrading
EVALUATION
Iideal (number)
two numbers
function
;
curves
indices
UPGRADING
degree
ph
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mec
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cs
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= f () lub = f ) lub f)
delineation
analysis
x1
c
x2
x3 x4
evaluation
ph
ysic
s
mec
hani
cs
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r app
roac
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delineation
analysis
x1
c
x2
x3 x4
evaluation
total theoretical delineation
total empirical delineation
splitting force
other forces
ordering force
feature
mechanism
results
parameters, balance, elements (variable, plot, equation)
etc. vs. no and ideal separation E, P, I, .......
ph
ysic
s
mec
hani
cs
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hes
analysis
x1
c
x2
x3 x4
evaluation
splitting force
other forces
ordering force
feature
etc. vs. no and ideal separation E, P, I, .......
comparison
*
Comparison
Upgrading (quality versus quantity)
Henry 3D plot
0 20 40 60 80 100
content,, %
0
20
40
60
80
100
yiel
d,
, %
idea
l up
grad
ing
no s
epar
atio
n
ideal upgrading
(remixing)
Henry 2D plot
real upgrading ( 1)
0 20 40 60 80 100
recovery, (remaining components in tailing), %
0
20
40
60
80
100
reco
very
, (c
on
sid
ere
d c
om
po
ne
nt
in c
on
ce
ntr
ate
), %
ideal upgrading (remixing)
variable
no upgrading
ide
al u
pg
rad
ing
Fuerstenau 2D plot real upgrading
-insensitive upgrading curve)
e.g. Fuerstenaua upgrading curve)
why Fuerstenau’s upgrading curve?
0 20 40 60 80 100
recovery, (remaining components in tailing), %
0
20
40
60
80
100
reco
very
,(c
on
sid
ere
d c
om
po
ne
nt
in c
on
ce
ntr
ate
), %
ideal upgrading (remixing)
variable
ide
al u
pg
rad
ing
Fuerstenau 2D plot
-universal
- insensitive
-easy to use mathematical eqs
-low self-similarity (provide real R2)
-allows comparison of different comp.
-and more
Fuerstenau’s (recovery-recovery or -) vs Halbich’s (grade-recovery or β- ) upgrading curves
)(
)100(
r
r
aa
a
a
100)100(100
)(1002
Fuerstenau’s is α-insensitive equivalent to Halbich’ upgrading curve
Fuerstenau’s and Halbich’s upgrading curves
(two in one)
0 20 40 60 80 100Cci, %
0
20
40
60
80
100
C
ci,
%
0 20 40 60 80 100
cumulative yield, , %
0
20
40
60
80
100
cum
ula
tive
rec
over
y,
,
%
no upgra
ding
no upgradingidea
l a
b
upgrading
ideal upgrading
0 20 40 60 80 100rci, %
0
20
40
60
80
100
r ci
, %
no upgrading
idea
l c
up-
grad
ing
idea
l up
gra
din
g
Mayer’s vs MDTW’s upgrading curves
α-sensitive α-insensitive