Seminar Process Design for Mineral Operationcepac.cheme.cmu.edu/pasi2008/slides/cisternas/... · Seminar – Process Design for Mineral Operations PASI 2008 Pan American Advanced

Luis A. CisternasDirector – CICITEM

Research Center for Miningand

Department of Chemical EngineeringUniversidad de Antofagasta

Antofagasta - Chile

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PASI 2008PASI 2008Pan American Advanced Studies Institute Program on Emerging Trends in PSE

Process Design for Mineral Operations

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MotivationGeneral StrategyCrystallization Design Problem Flotation Circuit Design ProblemFinal Remark

Outline

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Motivation

•High price cycle unprecedented•Lowering the cost of production•Achieving the balance of acceptable economic, environmental and social effects.•Improve energy efficiency

Copper Technology Roadmap Review 2006, AMIRA

Price of copper

Figure From:http://www.lanacion.cl/prontus_noticias/site/artic/20070802/pags/20070802215453.html

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The engineer`s loverCarlo Carrá

Italian 1881-1966

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Problems: Process design has multiple dimensions

Roberto MattaChilean 1911-2002

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Solution: Look as Picasso

Pablo Picasso Spanish 1881-1973

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The Onion Model

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Crystallization design problem overviewFractional CrystallizationFractional Crystallization with Heat Integration & Cake Washing

Crystallization DesignProblem

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Crystallization is extensively used in different industrial applications, including the production of a wide range of materials such as fertilizers, detergents, foods, and pharmaceutical products, as well as in the treatment of waste effluents

Crystallization design problem overview

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The crystallization stages are usually accompanied by other separation techniques. Leaching. Various types of crystallization exist: cooling, evaporation, reactions, and drowning-outThe characteristics of the product affects a series of other associated operations. filtration & washing. The separation is limited by multiple saturation points. Temperature changes & external chemical agents. Kinetic factors and metastability may affect the design.

Problems

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The greatest advantages obtained in the use of the phase diagram are the possibilities for the visualization of the behavior of phase equilibria, describing the processes, and obtaining mass balances with the help of the lever arms rule. The phase diagrams, however, also have a series of limitations as a design tool

Phase Diagram

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Phase Diagram

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Determine optimal stream configuration. Determine operational conditions & flowrates.Selection of equipment type.Determine solid-liquid separation. Washing & Filtration.Determine heat integration.

Goals

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Fractional CrystallizationBasic Crystallization SeparationRelative Composition DiagramFeasible Pathway DiagramState SuperstructureConnectivity MatrixMathematical modelExamples

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Basic Crystallization Separation

Isothermal CutKCl+NaCl+H2OKNO3+NaNO3+H2OL serine acid + L aspartic acid + water

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Isothermal CutKCl+NaCl+H2OKNO3+NaNO3+H2OL serine acid + L aspartic acid + water

p1

p2

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Basic Cycle

A S

B

bH

C

a

(a)

c

h

Heat and Evaporate

Cool and Dilute

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Relative Composition Diagram

RB

RC

RH

RA= 0S

H

F

C

a

(a)

8

RB > RC > RH > RA

A ofn CompositioWeight B ofn CompositioWeight

=R

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Feasible Pathway Diagram

RB

RC

RH

RA= 0S

H

F

C

a

(a)

8

RB > RC > RH > RA

RB > RC > RH > RA

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State Superstructure

F

S

C

H

A

S

B

RB > RC > RH > RA

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Connectivity Matrix

F

S

C

H

A

S

B

1

2

3

4

5 6

7

8

9

101096H

785C

43S1

21F

BAS2HC

RB > RC > RH > RA

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Mathematical model

F

S

C

H

A

S

B

1

2

3

4

5 6

7

8

9

10

SBAiwCxwxw

xwxwxwxwxwxwxwxwxwxwxwxw

wMin

l

Fiii

iiiiii

iiiiii

llw

,,;0,1,22,11

,1010,99,66,55,44,22

,88,77,55,66,33,11

=≥

=+

++=++

++=++

∑

General modelCisternas, L.A. (1999), Optimal design of crystallization-based separation schemes, AIChE J., 45, 1477-1487.

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Examples-Sylvinite

Equilibrium Data

KCl+NaCl15.922.2100H1KCl+NaCl20.2511.730C1

NaClKClSolid Phase

WeightComposition

Temperature

[°C ]key

0.00.581.40∞

RNaClRC1RH1RKCl

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Examples-Sylvinite

Relative Composition Diagram

RKCl > RH1 > RC1 > RNaCl RKCl > RH1 > RC1 > RNaCl

Sylvinite

H2O

H1

C1

NaCl

H2O

Kcl

1

2

3

4

5 6

7

8

10

8

State Diagram


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Examples-Sylvinite

State Diagram

Sylvinite

H1

C1

NaCl

K

1

2

5 6

7

8Cl

Flow Sheet

LEACHING AT100 ‘C

LEACHING AT30 ‘C

Sylvinite

NaCl KCl

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0.377.9822.02SD3

0.854.1445.86SD2

0.842.4835.99SD1

0.2SD3 + Na26.95.88F397

0.8SD2 + SD319.1514.4F297

5.8Mg1 + SD25.5532.2F197

0.5SD1 + Na23.2511.98E250

6.6Mg6 + SD14.7431.32E150

0.9SD1 + Na1017.816.6D225

1.6Mg7 + SD11321.15D125

1.7Mg7 + Na1011.820.57C18.7

Na2SO4MgSO4RSolid phase

Saturated solution, % wkeysT ºC

Mg7=MgSO4.7H2O; Mg1=MgSO4.1H2O; Mg6=MgSO4.6H2O; Na10=Na2SO4.10H2O; Na=Na2SO4; SD1= Na2SO4.MgSO4.4H2O; SD2= Na2SO4.MgSO4; SD3= MgSO4.3Na2SO4

Examples-Astrakanite Equilibrium data for MgSO4+Na2SO4+H2O system.

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Examples-AstrakaniteRelative Composition Diagram


4MgSOR > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > RF3 > 42SONaR

4MgSOR > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > > 42SONaR

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Examples-Astrakanite

astrakanite.gms

REACTIVECRYSTALLIZATION

18.7 ‘C

COOLING CRYSTALLIZATION

25 ‘C

Astrakanite

EVAPORATIVE CRYSTALLIZATION

50 ‘C

Astrakanite

Water Water

MgSO .6H O24Na SO .10H O2 4 2

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Fractional Crystallization with Heat Integration & Cake WashingState Superstructure Task superstructure.Heat integration.Cake Washing•Cisternas L.A., J.Y. Cueto and R.E. Swaney, “Flowsheet Synthesis of Fractional Crystallization Process with Cake Washing”, Computer and Chemical Engineering, 28, 613-623 ( 2004)• Cisternas L.A., C. Guerrero and R. Swaney,, “Separation System Synthesis of Fractional Crystallization Processes with Heat Integration”, Computer and Chemical Engineering, 25, 595-602 2001

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Task Superstructure

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wl (w + w h )m m mG

outt,mG

inl,t

Leaching

CrystallizationEvaporative

CoolingCrystallization

t

iΣn n,i(w + h x )

Task Network

MultipleSaturation

Points

ProductIntermed.

Solvent

Feed

Product

Solvent

Product

n

l m

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k−1

k

1

K

Rk−1

Rk

MultipleSaturation

Points

ProductIntermed.

Solvent

Feed

Product

Solvent

Product

Heat Integration

Papoulias S.A., & I.E. Grossmann (1983), A structural optimization approach to process synthesis-II. Heat recovery networks. Comp. and Chem. Engng., 7, 707

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Cake Washing

Parallel Options

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Mathematical ModelMass balance for each component in multiple saturation nodes (SM):

Mass balance for each component in intermediate product nodes (SI):IiSsxwxw I

sSLqlill

sSLqlill

outin

∈∈=⋅−⋅ ∑∑∩∈∩∈

,0)(

,)(

,

IiSsxhwhx IsSLql

illlsSLql

ilinout

∈∈=− ∑∑∩∈∩∈

,0)(

,')(

,

Iout

llIi

ilill SssSLqlymUhxxw ∈∩∈≤−+⋅∑∈

),(0)( ,,

IsSLql

l Ssymout

∈=−∑∩∈

01)(

Specification for feeds flow rates in feed nodes (SF):)(,,

)(, sIiSsCxw FF

Fis

sSlill

out

∈∈=⋅∑∈

State Superstructure

IiSsxhwxwxwhx MsSLqLwl

illlsSl

illsSl

illsSLql

iloutoutinin

∈∈=−⋅−⋅+ ∑∑∑∑∩∪∈∈∈∩∈

,0)()(

,)(

,)(

,)(

, '

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Task Superstructure

Mass balance between the thermodynamic state network and task network

∑∑∈∈

∈∈=+)(

,, ),(,sTt

Minin

tlIi

ill SssSlGhxw

∑∈

∈∈=+)(

, ),(,sTt

Moutout

ltlll SssSlGhww

Mass balance in the task network:

∑∑∈∈

∈∈=)(

,)(

, ,,sSl

Moutlt

sSl

intl

outin

SsTtGG

Task selection and energy balance:

True)(

)(),(

0000

)(,)(2),(1,

,

,

,

,

,

,

,,,

,2,1,,,

)(,,,

,,

,

=

∈∈

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

====

¬

∨

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

∈=∈∈+=

==

∑∈

st

M

Sst

Cst

st

st

st

outs

outltst

Sst

ind

outd

intl

Dst

outlt

Cst

Cst

sSl

intlstst

stst

st

yg

sSssTt

QQ

VCFC

y

sSlGHSQsSlsSlGHQGHQQ

GVCFC

y

in

βα

IF carnallite is fed to node 3 (stream 14) THEN the task is reactive crystallization

014,3 ≥− wtrcn yy

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Cake Washing

Mass balance for each component in wash/reslurry stage:

Efficiency constraint for wash/reslurry stage:Degree of impurity:Wash or reslurry/filter selection:

IiLwlLwEe

CvCfQrQw

zzrzwypwymwyprymr

yyyryw

QrCsQrCvfwQrCvrCv

CffCfrCfwhnrQr

Qwzzr

zwypwymw

yyprymry

yryw

QwCsQwCvwCv

CfwCfQr

whnwQw

zrzzw

yprymr

yypwymwy

yryw

el

el

el

el

ieliel

iel

iel

iel

iel

iel

ieliel

el

el

elel

lelel

el

llelel

el

ieliel

iel

iel

iel

ieliel

ieliel

el

el

el

elel

el

el

llelel

iel

ieliel

iel

iel

ieliel

ieliel

el

el

∈∈∈

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

=

=

=

=

=

=

=

=

=

=

¬

¬

∨

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+

+=

+=

=

=

=

=

=

=

=

=

¬

∨

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+=

=

=

=

=

=

=

=

=

=

¬

−−

,),(

0000

000

00

)(

0

000

0

0

00

,

,

,

,

,,,,

,,

,,

,,

,,

,,

,,,,

,

,

,,

0,,

,

0,,

,

,,,,

,,

,,

,,

,1,,,

,,,,

,

,

,

,,

,

,

0,,

,,

,,,,

,,

,,

,1,,,

,,,,

,

,

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Heat Integration

KkTCwTCwQQRRkkkk Cl

Clkpl

Hl

Hlkpl

Un

Un

Vm

Vmkk ∈Δ−Δ=+−− ∑∑∑∑

∈∈∈∈− )()(1

objective function minimizes the total venture cost:

∑∑∑∑∑ ∑∈∈∈∈ ∈

+++++++Lwl e

elelUn

Unn

Vm

Vmm

Sst

Sst

Cst

Cststst

Ss sTtCvCfQcQcQcQcVCFC

M

)()(min ,,,,,,,,)(

Objective Function

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Example: Sylvinite

The MILP formulation contains 299 equations, 218 continuous variables, and 27 binary variables.

Sylvinite.gmsSylvinite_heat.gmsSylvinite_wash.gmsSylvinite_wash_heat.gms

Sylvinite

cw

Leachingat 30ºC

Filtration

WashingWashsolvent

Washing

NaClCake

Water

St

Leachingat 100ºC

Filtration

Washsolvent

KClCake

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Example: Astrakanite

Astrakanite

Water Water

Reactivecrystallization

at 18.7ºC

Filtration

WashingWashsolvent

Washsolvent

Na SO .10H Ocake

2 4 2 MgSO .7H Ocake

4 2

Washing

Filtration Filtration

Coolingcrystallization

at 25ºC

R

StEvaporative

crystallizationat 50ºC

Astrakanitecake

The MILP formulation contains 1209 equations, 1201 continuous variables, and 145 binary variables. Solution time was 84 s for OSLv2 (GAMS) with a 1.7 GHz Pentium 4 processor.

MgSO4·Na2SO4·4H2O

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•Flotation Circuit problem overview•Superstructures for task, state and equipment selection •Mathematical model•Examples

Flotation Circuit DesignProblem

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Flotation design problem overview

Mineral flotation processes consist of several units that are grouped into banks and interconnected in a predefined manner in order to divide the feed into concentrate and tailing. The behavior of these processes depends on the configuration of the circuit and the physical and chemical nature of the slurry treated

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Figures From http://cache.eb.com/eb/image?id=1534&rendTypeId=4http://cape.uwaterloo.ca/images/pal1.gif

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The design of these circuits is carried out based on the experience of the designer, with the help of laboratory tests and simulations. Some attempts have been described in the literature on automated methods for the design of these types of circuits. However, methods for the design of flotation circuits have not yet progressed to the stage where an optimum circuit configuration can be completely derived automatically.

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Superstructures for task, state & equipment

Superstructures are developed in a hierarchical form:•First level: separation task superstructure •Second level: processing systems are presented which must carry out rougher, cleaner, and scavenger operations and define states. •Third level: equipment selection (column versus mechanical bank; grinding-classification circuit)

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Tasks

Rougher

Feed

Concentrate

Tail Scavenger

Tail

Concentrate

Final Flotation

Tail

Cleaner

Concentrate

FinalFlotation

Concentrate

Tails

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Task Superstructure

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State Superstructures

Mixing with/without grinding

Mixing without grinding

Mechanical cell bank or column

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Equipment Superstructures

Grinding-classification circuits

( ) ( )( ) ( ) ( )( )huD2aa1huD2aa1huD2

1a41R 22C −−−+

⎟⎟⎠

⎞⎜⎜⎝

⎛

−=expexp

exp

( )N111Rωτ+

−=

Mechanical cell bank or column

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Grinding circuits

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∑∑∑∑γ

=Γ

K JjkP

K JjkPjk

W

W

,,

,,,

Floatability Index

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2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3

0 2 4 6 8 10 12Milling time, minutes

Floa

tabi

lity

inde

x fo

r circ

uit p

rodu

ct

Grinding without classification

Grinding - classification

Classification - grinding

Classification - grinding - classification

Feed mass flow rate, tphPercentage feed composition

2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3


Floa

tabi

lity

inde

x fo

r circ

uit p

rodu

ct






242

244

246

248

250

252

254


Floa

tabi

lity

inde

x fo

r circ

uit p

rodu

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Material Balances

Feedstock flows

Material Balances Flotation Steps

Mathematical Model

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( )

1 1

1 1

1 1 1 1

1 1 1 1

2 1 1 2 1

3 1 1

, ,

, ,

, , , , , ,

, , , , , , , ,

, , , , , , , , , ,

, , , , , ,1

b cs s

f f f fs b s c

V V b V V cs b s k s c s k

k kb c

s k s k s k s k

b b cs k s k s k s k s k

b bs k s k s k

y y

C C C C

C C W C C W

W WI W WI

WI T W WI T

WI T W

⎡ ⎤⎢ ⎥

= =⎢ ⎥⎢ ⎥

= ∑ = ∑⎢ ⎥∨⎢ ⎥

= =⎢ ⎥⎢ ⎥

= =⎢ ⎥⎢ ⎥

= −⎢ ⎥⎣ ⎦ ( )1

3 1 1

, ,

, , , , , ,1

cs k

c cs k s k s k

W

WI T W

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥

= −⎢ ⎥⎣ ⎦

Equipment Selection

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Objective Function

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Example

The procedure was applied to the design of a copper concentration plant, whose species are: k=1 (100% chalcopyrite), k=2 (50% silica, 50% chalcopyrite) and k=3 (100% silica).

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Economic results in millions of US$ for a metal price of 1.00 US$/lb where the k=3 recovery is comparable to the k=2 recovery.(NG)= no grinding, (G)= grinding w/o classification, (G-C)= grinding – classification, (C-G)= classification – grinding.

26.57138.77112.996C-GG-C/C-GCase 1226.57138.77112.996C-GG/C-GCase 1126.72628.63912.748G-CG/G-CCase 1026.42137.62711.964NGNGCase 9

CostsRevenuesProfitSelectionOptionsCase

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Diffusion, WickCombustion, Yerka Sublimation, Magritte

Cycle Process, Magritte Radiation, Van Gogh fluids, EscherCompression, Baldaccini

Final Remark

Complete list of references on design of separation based on crystallization, design of flotation circuits, design of leaching process, and design of solvent extraction circuits

Can be found on http:/www.uantof.cl/d2p

Seminar Process Design for Mineral Operationcepac.cheme.cmu.edu/pasi2008/slides/cisternas/... · Seminar – Process Design for Mineral Operations PASI 2008 Pan American Advanced

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