DYNAMIC MODELLING AND SIMULATION FROM...

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DYNAMIC MODELLING AND SIMULATION FROM FIRST PRINCIPLES FOR COAL PROCESSINGJONATHAN MEYER

AGENDA

• INTRODUCTION

• COAL PROCESSING

• DYNAMIC MODELS

• SYSTEM IDENTIFICATION PROCESS

• SIMULATION RESULTS

• SUMMARY

INTRODUCTION3

COAL BENEFICIATION

INTRODUCTION

COAL VALUE CHAIN:

• Selectively upgrade run-of-mine (ROM) coal to

produce:

• Power station coal

• Metallurgical coal

• Coking coal

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Mining Beneficiation

Coal product stockpile

Discard

COAL BENEFICIATION

INTRODUCTION

COAL ORE:

• Formation from plants that grew in marshes and swamps some 200 million years ago in South Africa.

Different materials form coal, shale and sand stone.

• Mixing of clay causes ash impurities in the coal.

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COAL BENEFICIATION

INTRODUCTION

TYPICAL COAL UNIT PROCESSES:

• Primary and secondary crushing and screening:

• Liberation:

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• Screening:

COAL BENEFICIATION

INTRODUCTION


• Dense medium separation

• Dense medium drums (+50mm)

• Dense medium cyclones (-50mm)

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“98% of the 53 coal‐preparation plants in South Africa are making use of the DMC”

COAL BENEFICIATION

INTRODUCTION


• Jigging

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GENERAL CONTROL PROBLEM

INTRODUCTION9

DYNAMIC MODELS10

DYNAMIC MODELS

STEADY-STATE VS DYNAMIC MODELS:

• Steady-state models typically have no time evolution of variables

• Example of steady-state models are metallurgical mathematical models

• Partition curves

• Each relative density (RD) fraction must settle (i.e. reach steady state)

• Sinks are dried and weighed

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Separation Cutpoint (

Écart Probable Moyen (EPM)

DYNAMIC MODELS


• Steady-state models typically have no time evolution of variables

• Example of steady-state models are metallurgical mathematical models

• Coal washability curves

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DYNAMIC MODELS


• Dynamic models incorporate the time evolution of variables

• Typically represented as state-space models

• First principles makes use of conservation of mass and mass of components

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, ,

, ,

DYNAMIC MODELS


• Motivation for dynamic models

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0%

5%

10%

15%

20%

25%

30%

35%

10%

11%

12%

13%

14%

15%

16%

17%

18%

19%

20%

21%

22%

23%

24%

25%

Freq

uency

% Ash

Peas Ash Results Distribution

May June July Fitted Normal Target Ash Current Mean

DYNAMIC MODELS

COAL UNIT PROCESS MODELS DEVELOPED:

• Primary and secondary crushing and screening:

• Liberation:

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, , ,

ρ , , , ,

cr

cricr

cr mWdt

dm

,

cr

crocr

mW

,

,

,Inputs:

, = Feed mass flow rate

Outputs:, = Product mass flow rate

= Crusher time constantParameters:

Inputs:

, = Feed mass flow rate

Outputs:, = Oversize mass flow rate, = Undersize mass flow rate

= Material velocity

, , = Screen dimensions

, = Material density

Parameters:

,

,

,

,

,

States:

= Crusher massStates:

= Screen mass

• Screening:

DYNAMIC MODELS


• Dense medium drum

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,

,

, , , , ,

, ,

, ,

, ,

, ,

, , ,

,

, ,

, ,

, ,

, ,

, , ,

,

, ,

, ,

, ,

, ,

,,

, = Product mass flow rate, , = Product medium density, , = Product ash percentage, = Discard mass flow rate, , = Discard ash content, , = Discard medium density

, = Feed mass flow rate, , = Feed medium density, , = Feed ash content, , = Feed fixed carbon content

, , = Feed medium content, = Product density, , = Product medium content, = Discard density, , = Discard medium content

, = Feed flow rate, , = Feed ash density, , = Feed medium flow rate, = Product volume, = Product flow rate, , = Product medium flow rate, = Discard volume, = Discard flow rate, , = Discard medium flow rate

Inputs:

Outputs:

Parameters:

States:

DYNAMIC MODELS


• Dense medium drum

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DYNAMIC MODELS



• Dense medium cyclones

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,

,

, , , , ,

, ,

, ,

, ,

, ,

, , ,

,

, ,

, ,

, ,

, ,,

,

, , ,

,

, ,

, ,

, ,

, ,

, = Overflow mass flow rate, , = Overflow medium

density, , = Overflow ash percentage, = Underflow mass flow rate, , = Underflow ash content, , = Underflow medium

density

, = Feed mass flow rate, , = Feed medium density, , = Feed ash content, , = Feed fixed carbon

content

Inputs:

Outputs:

, = Feed flow rate, , = Feed ash density, , = Feed medium flow

rate, = Overflow volume, = Overflow flow

rate, , = Overflow medium

flow rate, = Underflow volume, = Underflow flow

rate, , = Underflow

medium flow rate

Parameters:

, , = Feed medium content, = Overflow density, , = Overflow medium content, = Underflow density, , = Underflow medium content

States:

DYNAMIC MODELS



• Dense medium cyclones

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DYNAMIC MODELS

PUBLISHED LITERATURE FOR FURTHER DETAILS:

• E. J. Meyer and I. K. Craig. The development of dynamic models for a dense medium separation circuit in

coal beneficiation. Minerals Engineering, 23(10):791-805, 2010.

• E. J. Meyer and I. K. Craig. Development of a steady-state partition curve from a dense medium cyclone

dynamic model in coal beneficiation. In Proceedings of the 18th IFAC World Congress, Milano, Italy, volume

18, pages 10523-10528. IFAC, IFAC, 2011. doi: 10.3182/20110828-6-IT-1002.02846.

• E. J. Meyer and I. K. Craig. Coal dense medium separation dynamic and steady-state modelling for process

control. Minerals Engineering, 65:98-108, 2014.

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SYSTEM IDENTIFICATION PROCESS21

SYSTEM IDENTIFICATION PROCESS

SOLVE PARAMETERS FOR DYNAMIC SYSTEM:

• State-space representation

• Input/output data

• Compute norm

• Minimise norm solving for parameters

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, ,

, ,

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SIMULATION RESULTS

BENEFICIATION PROCESS

SIMULATION RESULTS24

Drum screen model

Cyclone screen model

Drum model

Cyclone model

DENSE MEDIUM SEPARATION PLANT MODEL INPUT DATA


Plant feed mass flow rate

Drum medium density

Cyclone medium density

PLANT MODEL INPUT DATA - ASH


RECONSTITUTE FEED ASH USING COAL WASHABILITY AND PARTITION CURVE:

• M-Curve fit (product ash vs yield) from coal washability

• Obtain partition curve by reducing dynamic model to steady-state model

• Calculate feed ash

, ,

, ,

DRUM SCREEN MODEL


Fit (%) 98.9

Corr. 1.00

DRUM MODEL


Fit product(%)

69.2

Corr. product 0.95

Fit discard(%)

39.3

Corr. discard 0.81

DRUM MODEL ASH


Fit product ash (%)

41.2

Corr. Product ash

0.87

Fit discard ash (%)

13.3

Corr. Discard ash

0.60

CYCLONE SCREEN MODEL


Fit (%) 96.2

Corr. 1.00

CYCLONE MODEL


Fit product(%)

44.8

Corr. product 0.86

Fit discard(%)

25.0

Corr. discard 0.82

CYCLONE MODEL ASH


Fit product ash (%)

25.0

Corr. Product ash

0.72

Fit discard ash (%)

1.5

Corr. Discard ash

0.46

SUMMARY33

SUMMARY34

MODEL FIT RESULTS SUMMARY:

Model measure Fit (%) Correlation

Drum screen 98.9 1.00

Drum product 69.2 0.95

Drum discard 39.3 0.81

Drum product ash 41.2 0.87

Drum discard ash 13.3 0.60

Cyclone screen 96.2 1.00

Cyclone product 44.8 0.86

Cyclone discard 25.0 0.82

Cyclone product ash 25.0 0.72

Cyclone discard ash 1.5 0.46

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