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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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

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= f () lub = f ) lub f)

delineation

analysis

x1

c

x2

x3 x4

evaluation

ph

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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

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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