Process Design for Mineral Sem inar Process Design for Mineral - - PowerPoint PPT Presentation

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Luis A. Cisternas

Director – CICITEM Research Center for Mining and Department of Chemical Engineering Universidad de Antofagasta Antofagasta - Chile

Sem inar – Process Design for Mineral Operations

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Process Design for Mineral Operations

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Motivation General Strategy Crystallization Design Problem Flotation Circuit Design Problem Final Remark

Outline

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Motivation

• High price cycle

unprecedented

• Lowering the cost of

production

• Achieving the balance
• f 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 lover

Carlo Carrá Italian 1881-1966

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Problems: Process design has multiple dimensions

Roberto Matta Chilean 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 overview Fractional Crystallization Fractional Crystallization with Heat Integration & Cake Washing

Crystallization Design Problem

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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

• ther separation techniques. Leaching.

Various types

• f

crystallization exist: cooling, evaporation, reactions, and drowning-out The 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 Crystallization

Basic Crystallization Separation Relative Composition Diagram Feasible Pathway Diagram State Superstructure Connectivity Matrix Mathematical model Examples

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Basic Crystallization Separation

Isothermal Cut KCl+NaCl+H2O KNO3+NaNO3+H2O L serine acid + L aspartic acid + water

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Basic Crystallization Separation

Isothermal Cut KCl+NaCl+H2O KNO3+NaNO3+H2O L serine acid + L aspartic acid + water

p1 p2

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Basic Crystallization Separation

Basic Cycle

A S B

b

H C

a (a) c h Heat and Evaporate Cool and Dilute

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Relative Composition Diagram

RB RC RH RA= 0 S H F C a (a) 8

RB > RC > RH > RA

A

• f

n Compositio Weight B

• f

n Compositio Weight = R

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Feasible Pathway Diagram

RB RC RH RA= 0 S 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 10

10 9 6 H 7 8 5 C 4 3 S1 2 1 F B A S2 H C

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

S B A i w C x w x w x w x w x w x w x w x w x w x w x w x w x w x w w Min

l F i i i i i i i i i i i i i i i l l w

, , ;

, 1 , 2 2 , 1 1 , 10 10 , 9 9 , 6 6 , 5 5 , 4 4 , 2 2 , 8 8 , 7 7 , 5 5 , 6 6 , 3 3 , 1 1

= ≥ = + + + = + + + + = + +

∑

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

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Examples-Sylvinite

Equilibrium Data

KCl+NaCl 15.9 22.2 100 H1 KCl+NaCl 20.25 11.7 30 C1 NaCl KCl Solid Phase Weight Composition Temperatur e [°C ] key 0.0 0.58 1.40 ∞ RNaCl RC1 RH1 RKCl

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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 Feasible Pathway Diagram

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Examples-Sylvinite

State Diagram

Sylvinite H1 C1 NaCl K 1 2 5 6 7 8 Cl

Flow Sheet

LEACHING AT 100 ‘C LEACHING AT 30 ‘C Sylvinite NaCl KCl

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Saturated solution, % w

keys T 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-Astrakanite

Relative Composition Diagram Feasible Pathway Diagram

4

MgSO

R > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > RF3 >

4 2SO

Na

R

4

MgSO

R > RE1 > RF1 > RC > RD1 > RD2 > RDS1= RDS2 > RF2 > RE2 > RDS3 > >

4 2SO

Na

R

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Examples-Astrakanite

astrakanite.gms

REACTIVE CRYSTALLIZATION 18.7 ‘C COOLING CRYSTALLIZATION 25 ‘C Astrakanite EVAPORATIVE CRYSTALLIZATION 50 ‘C Astrakanite Water Water MgSO .6H O 2 4 Na SO .10H O 2 4 2

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Fractional Crystallization with Heat Integration & Cake Washing

State 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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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE wl (w + w h ) m m m G out t,m G in l,t Leaching Crystallization Evaporative Cooling Crystallization t i

Σ

n n,i (w + h x )

Task Network

Multiple Saturation Points Product Intermed. Solvent Feed Product Solvent Product n l m

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k−1 k 1 K Rk−1 Rk

Multiple Saturation Points Product Intermed. Solvent Feed Product Solvent Product

Heat Integration

Papoulias S.A., & I.E. Grossmann (1983), A structural

• ptimization 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 Model

Mass balance for each component in multiple saturation nodes (SM): Mass balance for each component in intermediate product nodes (SI):

I i S s x w x w

I s S Lq l i l l s S Lq l i l l

• ut

in

∈ ∈ = ⋅ − ⋅

∑ ∑

∩ ∈ ∩ ∈

,

) ( , ) ( ,

I i S s x h w hx

I s S Lq l i l l l s S Lq l i l

in

• ut

∈ ∈ = −

∑ ∑

∩ ∈ ∩ ∈

,

) ( , ' ) ( ,

I

• ut

l l I i i l i l l

S s s S Lq l ym U hx x w ∈ ∩ ∈ ≤ − + ⋅

∑

∈

), ( ) (

, ,

I s S Lq l l

S s ym

• ut

∈ = −

∑

∩ ∈

1

) (

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

) ( ,

, ) ( ,

s I i S s C x w

F F F i s s S l i l l

• ut

∈ ∈ = ⋅

∑

∈

State Superstructure

I i S s x h w x w x w hx

M s S Lq Lw l i l l l s S l i l l s S l i l l s S Lq l i l

• ut
• ut

in in

∈ ∈ = − ⋅ − ⋅ +

∑ ∑ ∑ ∑

∩ ∪ ∈ ∈ ∈ ∩ ∈

,

) ( ) ( , ) ( , ) ( , ) ( ,

'

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Task Superstructure

Mass balance between the thermodynamic state network and task network

∑ ∑

∈ ∈

∈ ∈ = +

) ( , ,

), ( ,

s T t M in in t l I i i l l

S s s S l G hx w

∑

∈

∈ ∈ = +

) ( ,

), ( ,

s T t M

• ut
• ut

l t l l l

S s s S l G h w w

Mass balance in the task network:

∑ ∑

∈ ∈

∈ ∈ =

) ( , ) ( ,

, ,

s S l M

• ut

l t s S l in t l

• ut

in

S s T t G G

Task selection and energy balance:

True ) ( ) ( ), ( ) ( , ) ( 2 ), ( 1 ,

, , , , , , , , , , 2 , 1 , , , ) ( , , , , , ,

= ∈ ∈ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = = = = ¬ ∨ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ∈ = ∈ ∈ + = = =

∑

∈ s t M S s t C s t s t s t s t

• ut

s

• ut

l t s t S s t in d

• ut

d in t l D s t

• ut

l t C s t C s t s S l in t l s t s t s t s t s t

y g s S s s T t Q Q VC FC y s S l G HS Q s S l s S l G HQ G HQ Q G VC FC y

in

β α

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

14 , 3

≥ −

w t rc n

y y

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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:

I i Lw l Lw E e Cv Cf Qr Qw z zr zw ypw ymw ypr ymr y y yr yw Qr Cs Qr Cvf w Qr Cvr Cv Cff Cfr Cf w h nr Qr Qw z zr zw ypw ymw y ypr ymr y yr yw Qw Cs Qw Cvw Cv Cfw Cf Qr w h nw Qw zr z zw ypr ymr y ypw ymw y yr yw

e l e l e l e l i e l i e l i e l i e l i e l i e l i e l i e l i e l e l e l e l e l l e l e l e l l l e l e l e l i e l i e l i e l i e l i e l i e l i e l i e l i e l e l e l e l e l e l e l e l l l e l e l i e l i e l i e l i e l i e l i e l i e l i e l i e l e l e l

∈ ∈ ∈ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = = = = = = = = = = = ¬ ¬ ∨ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + = + = = = = = = = = = ¬ ∨ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + = = = = = = = = = = ¬

− −

, ), ( ) (

, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 1 , , , , , , , , , , , , , , , , , , , , , , , , , , , 1 , , , , , , , , ,

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Heat Integration

K k T C w T C w Q Q R R

k k k k

C l C lk p l H l H lk p l U n U n V m V m k k

∈ Δ − Δ = + − −

∑ ∑ ∑ ∑

∈ ∈ ∈ ∈ −

) ( ) (

1

• bjective function minimizes the total venture cost:

∑∑ ∑ ∑ ∑ ∑

∈ ∈ ∈ ∈ ∈

+ + + + + + +

Lw l e e l e l U n U n n V m V m m S s t S s t C s t C s t s t s t S s s T t

Cv Cf Q c Q c Q c Q c VC FC

M

) ( ) ( min

, , , , , , , , ) (

Objective Function

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Example: Sylvinite

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

Sylvinite.gms Sylvinite_heat.gms Sylvinite_wash.gms Sylvinite_wash_heat.gms

Sylvinite cw Leaching at 30ºC Filtration Washing Wash solvent Washing NaCl Cake Water St Leaching at 100ºC Filtration Wash solvent KCl Cake

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Example: Astrakanite

Astrakanite Water Water Reactive crystallization at 18.7ºC Filtration Washing Wash solvent Wash solvent Na SO .10H O cake

2 4 2

MgSO .7H O cake

4 2

Washing Filtration Filtration Cooling crystallization at 25ºC R St Evaporative crystallization at 50ºC Astrakanite cake

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 Design Problem

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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

• rder 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=4 http://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

• ptimum

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 Final Flotation 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

( )

( ) ( ) (

)

( ) ( )

h u D 2 a a 1 h u D 2 a a 1 h u D 2 1 a 4 1 R

2 2 C

− − − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = exp exp exp

( )N

1 1 1 R ωτ + − =

Mechanical cell bank or column

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Grinding circuits

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∑∑ ∑∑γ

= Γ

K J j k P K J j k P j k

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 2 4 6 8 10 12

Milling time, minutes Floatability index for circuit product

Grinding without classification Grinding - classification Classification - grinding Classification - grinding - classification

Feed mass flow rate, tph Percentage feed composition

2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 2 4 6 8 10 12

Milling time, minutes Floatability index for circuit product

Grinding without classification Grinding - classification Classification - grinding Classification - grinding - classification

Feed mass flow rate, tph Percentage feed composition

242 244 246 248 250 252 254 2 4 6 8 10 12

Milling time, minutes Floatability index for circuit product

Grinding without classification Grinding - classification Classification - grinding Classification - grinding - classification

Feed mass flow rate, tph Percentage feed composition

242 244 246 248 250 252 254 2 4 6 8 10 12

Milling time, minutes Floatability index for circuit product

Grinding without classification Grinding - classification Classification - grinding Classification - grinding - classification

Feed mass flow rate, tph Percentage feed composition

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

Material Balances Feedstock flows Material Balances Flotation Steps

Mathematical Model

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

( )

1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 3 1 1

, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

1

b c s s f f f f s b s c V V b V V c s b s k s c s k k k b c s k s k s k s k b b c s k s k s k s k s k b b s 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

c s k c c s k s k s k

W WI T W ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = − ⎢ ⎥ ⎣ ⎦

• Equipment Selection

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

Objective Function

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

Example

The procedure was applied to the design

• f 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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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

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.

26.571 38.771 12.996 C-G G-C/C-G Case 12 26.571 38.771 12.996 C-G G/C-G Case 11 26.726 28.639 12.748 G-C G/G-C Case 10 26.421 37.627 11.964 NG NG Case 9 Costs Revenues Profit Selection Options Case

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

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Sem inar – Process Design for Mineral Operations

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Pan Am erican Advanced Studies I nstitute Program on Em erging Trends in PSE

Diffusion, Wick Combustion, Yerka Sublimation, Magritte Cycle Process, Magritte Radiation, Van Gogh fluids, Escher Compression, 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