The use of dimensionless numbers to characterise the feed to metallurgical reactors

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Pergamon PII:so8926875(%)oo132-x

&$mwit~~, Vol. IO, No. 1, pp. 69-80, 1997 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights resemd 0892-6875/97 $17.00+0.00

THE USE OF DIMENSIONLESS NUMRERS TO CHARACTERISE THE FEED TO METALLURGICAL REACTORS M.A. REUTERS*, C. WEST?, A. FOUR&, D.W. MOOLMAN* and C. ALDRICH* 0 Faculty of Applied Earth Sciences, Delft University of Technology, Delhi, The Netherlands t Measurement and Control Division, Mintek, Private Bag X3015, 2125 Randburg, South Africa $ Department of Chemical Engineering, University of Stellenbosch, Stellenbosch, South Africa * Previous address as t (Received 3 June 1996; accepted 23 September 1996)

ABSTRACT

Thefeed to metallurgicalreactors are often charactetisedby a varietyof different ores, and in pyrometallurgicalfurnaces additionallyby reductants. These feeds @ect the operation of the reactors in various ways. In for example@tation plants the feed and other streamsare characterised in termsof classes and sub-classes. Thispaper goes one step further in that it uses this class/sub-class classification to de$ne empirical dimensionlessfeed numbers, which may subsequently be applied to establish optimal reactor operating regimes as a function of thefeed material. Methodsused to determine optimaloperating regimes included neural nets, autoassociativeneural netsand Sammon nets as well as distance weightedleast squares smoothingof the data. This methodology was applied to metallurgicalfurnace data and the results clearly show that there exist functional relationshipsbetween the definedfeed numbers and vatious other pertinent operationalparameters. Therefore, thisapproachpermits a very concise representation possible. of industrialfeed data to reactorsat the same timemaking furnace optimization Thispaper also provides a practical comparisonbetween the mentionedempirical data representationmethodologies.It is also demonstratedwhere such an approachfits into a process control structureproviding real-timesupervisorycontrol. Copyright 0 1996 Elsevier Science Ltd Keywords

Process control; process optimisation; neural networks

INTRODUCTION

The characterisation of the streams of mineral benificiation plants into various classes and sub-classes or species, which group the physical and chemical properties, is standard technology [ 1,2]. However, some metallurgical reactors are difficult to model fundamentally, especially if the mineralogical, physical and chemical characteristics of the feed materials are to be included in the model in a meaningful way. Sometimes it is necessary to determine what the relative effect of each of the constituents of a feed is in order to optimize the metallurgy of the reactor. When it is difficult to characterise the feed and/or model the reactor or other metallurgical phases fundamentally, (semi-) empirical modelling approaches can be applied. For example, it is usual practice to define dimensionless basic@ numbers to characterise metallurgical slags rather than to characterise their properties in terms of the percentage composition of

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M. A. Reuteret

70

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the constituting compounds [3]. These dimensionless basic@ numbers can then be used in (semi-) empirical equations to model the slag chemistry. The feeds to pyrometallurgical reactors often consist out of a blend of numerous ores and reductants, and even secondary and recycling materials [4]. Due to the ensuing large dimensionality of such problems it would be rather unimaginative to use all the feed components quantified in terms of percentage or t/h and attempt to correlate these to various production and operational parameters. Although it is possible to follow this route the large dimensional&y could restrict the interpolative power of the resultant equation. Therefore, gleaning from the developments in minerals processing [ 1,2], the feed is classified into classes and sub-classes/species, which permits the creation of dimensionless feed numbers for the ore and reductants and other feed materials, so as to characterise the recipe of the feed to the furnace. In the same way that these dimensionless numbers are used for describing the feed to pyrometallurgical reactors, these numbers can be applied to characterise the feed to ill-defined minerals processing unit operations, hence consolidating the vast number of classes and sub-classes into a single number. This would simplify the modelling of these ill-defined processes as well as make the classification of data much more efficient. The examples show that these dimensionless feed numbers can be quite useful to establish optimal operating regimes of industrial reactors by the aid of a suitable statistical package [5] and/or neural nets [6]. These numbers can then be applied to change the recipe of the feed in the most optimum way so as to obtain the desired optimal reactor operation. Furthermore, two different classification neural nets i.e. autoassociative [7] and Sammon [8] neural nets are used to classify the data in terms of the feed numbers. The results show that this can be a very useful way for classifying data in real-time to predict as well as visualise reactor operation.

CLASSIFICATION OF FEED DATA TO METALLURGICAL REACTORS Using a similar definition as presented by King [ 11, the feed to metallurgical reactors are classified into classes g (physical characteristics of feed e.g. particle size, type of feed, etc.) and sub-classes t (chemical characteristics e.g. mineralogy, source of feed, etc.). This classification of the feed can be consolidated into a dimensionless number of the following form: m-l

Dimensionless Feed Number = M mgt g,t

’

n-l

== t=o g=o Total feed mass (tomes) Mass of class g and sub-class t Class and sub-class

(109 -2’*mgJ M

,

(1)

/

Essentially this empirical number weights each mass fraction of each sub-class t of a class g according to the given exponential factors. The exponential bases are selected to ensure a continuous spread of data, but at the same time that each sub-class in a class occupies a unique cluster. Therefore, if for example there are up to four sub-classes of reductants in each class a large weighting i.e. 10 was selected to distinguish classes in order to ensure that the sub-classes in a particular class do not overlap into another class. These concepts, that have their origin in minerals engineering, have up to now not been transferred to defining feeds to pyrometallurgical unit operations and it will be the objective of this paper to demonstrated these concepts using plant data for submerged-arc fmnaces. Metallurgical furnaces The feed material to furnaces consist primarily of the ore, fluxes and the reductant. ‘Often the ores and the reductants are taken from a variety of sources comprising of various sixes and sub-classes. Table 1 gives a classification of reductants and ores for furnaces in terms of classes i.e. its physical properties such as

Chamcterising the feed to metallurgical

reactors

71

particle size or it,s physical form (e.g. pellets), and the sub-class i.e. its mined origin reflecting its mineralogy or in other words its mineral and gangue contents. The ore classes could typically be pellets, concentrate, pebbles, lumpy, flux (flux was included as part of the ore). Reductant classes may be classified into large, cobbles, nuts, char for example. The sub-classes in this instance are the mined origin of the ores and their metal contents, and the origin of the reductants and their contents of S, P etc. In order to render the real industrial data used in this paper anonymous, the classes and sub-classes were labelled by alphanumeric symbols as indicated in Table 1. For clarification, however, class R2 could for example be reductants with a size classification cobbles originating from mines/seams D, E and F respectively. Similarly C2 could be lumpy ore originating from mines H and I. TABLE 1 A classification of the raw materiais feed to furnaces

There are numerous ways in which the classification of the feed according to Table 1 may be used to relate ore and reductant classes and sub-classes data to production data. It is obviously possible to relate each class and sub-class of the reductant and ore respectively to corresponding production data. However, the drawback of this approach is its large dimensionality i.e. the data set is characterised by a large number of variables (21 for the feed represented in Table 1). In order to minimise the dimensionality of the data i.e. minimise the number of variables characterising the data set, two further possible approaches will be discussed below. Class percentage number: This is probably one of the simplest and most trivial approaches that can be used i.e. the percentage of each class in the reductant and ore respectively cau be defined as indicated by eq. 2, in this instance for the Rl class of the reductant. %

Rl=

TotalmassofW,CD Total mass of reductant

,loo

(2)

These respective percentages are related to corresponding production data in order to determine their relative effects on various output variables such as product quality, energy efficiency etc. A drawback of this approach is that the dimensionality of the data is as large as the number of classes. Dimensionless Feed numbers: Since the percentage number does not distinguish between the various subclasses of ores and reductants within the classes, empirical dimensionless Feed Numbers were created to characterise the quantity, shape/size and type of the feed materials to a furnace. From eq. 1 a Re&ctant Feed Number and an Ore Feed Number were detined as given by eqs. 3 and 4 respectively. These numbers have the added advantage that they characterise the reductant and the ore by one number respectively hence reducing the dimensionality of the data considerably. M”E 10:1-c

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M. A. Reuter etal.

m-l n-l (108 -2’*r& Reductant Feed Number = c c R g=o t=o Total reductant mass (t&es) R g and sub-class mgt Mass of reductant of class g,t’ Class and sub-class

m-l

Ore

Feed Number = c

(3) I

n-l

c

(4g ‘iae@)

g=o t=o

E e g:i

(4)

Total ore mass (tonnes) 1 Mass of ore of &ss g and sub-class t Class and sub-class

The classes and sub-classes in eqs. 3 and 4 refer to the definitions given in Table 1. For example sub-class F of the reductant class R2 has the indices for class g= 1 and for sub-class t =2. Similarly for the ore the ore sub-class K for C3 has the indices g =2 and t = 1. ANALYSIS OF DATA FOR A SUBMERGED-ARC FURNACE By the

application of the standard classification of the feed material as reflected by Table 1 and the appropriate numbers defined by eqs. 2 to 4, it is possible to proceed to perform statistical and neural net analysis on 5 months of industrial data in order to establish the relationships that exist between the feed and the product quality for a submerged-arc furnace.

Linear statistical analysis Using the simple definition represented by eq. 2, it is possible to relate the percentage of each class to various outputs such as recovery, power consumption and metal quality. Table 2 below shows the Pearson correlation coefficients [5] between the input and the output variables. TABLE 2 Pearson correlation coefficients Sulphur content in the metal

0.044 -0.175 0.212 0.033 -0.145 - . 0.275 -0.204 0.173

Sillcon content in the metal 0.030. -0.007 -0.223 -0.377 0.490 0 160 -6.247 0.252 -0.247

Power consumption -0.225 0.126 0.237 -0.048 0.021 4 0.055 0.200 0.050

Chromium recovery -0.093 0.123 -0.012 -0.176 0.19 7 -0:281 0.133 0.229

By considering the linear correlation coefficients in Table 2, various aspects regarding the positive or negative effect of the various ore and reductant classes on the output variables may be derived. However, none of the coefficients are large enough to place too much confidence in them. It is therefore clear, that these data can not really be modelled on a linear statistical way.

Characterising the feed to metallurgical reactors

73

If the relative effects of the ore and reductant sub-classes within each class is of interest i.e. if for instance it is necessary to determine which of the reductant sub-classes in every class are most beneficial to the operation, the linear modelling approach based on just classes summarised in Table 2 is of little help. For this reason the dimensionless feed numbers were defined, which will be discussed below. Figures 1 and 2 show the percentages of the different classes in the reductant or ore respectively as well as the corresponding changes in the Reductant and Ore Feed Numbers as defined by eqs. 3 and 4 respectively. These figures are arranged such that the classes with the higher weighting occupy the upper parts of the space in the graph area and the classes with the smaller weighting are in the lower parts of the graph, This will make it easier to interpret the fluctuations in either the Ore or the Reductant Feed Numbers. 400

350

300 L

d

100 50

Fig.1 The percentage of the different classes of reductauts used for a furnace and the corresponding change in the reductant number From Figure 1 it scanbe observed that the change in the reductaut recipe changes fairly often for this data set, and this explains the sharp jumps and changes in The Reductant Feed Number. The relatively large Reductant Feed Number during the last 40 or so days of these particular data is explained by the introduction of R4, R3 and R2 which all have a relatively high weighting in the reductant feed number as compared to the Rl reductant class. From Figure 2 it can be seen that the Ore Feed Number remains fairly constant, as the change in the relative amounts of ore sub-classes does not vary greatly. It is possible to relate the defined Feed Numbers for the reductant and the ores to important production variables such as metal quality and energy consumption. Figures 3 to 5 show the combined effect of the Ore and Reductant Feed Numbers on the indicated output variables. The three dimensional surfaces were created by distance weighted least squares (DWLS) smoothing as per SYSTAT [5]. For the DWLS smoothing the original data points are also plotted. From Figures 3 to 5 it is clearly evident that optimal operating regimes exist and that they can be extracted by the application the dimensionless feed numbers. Therefore, it is possible to establish from the Ore and Reductant numbe.rs which ores are most suited for a particular type of operation i.e. (i) Figure 3 indicates an operating point at which the sulphur content is minimised or in other words the feed mix can be

14

M. A. Reuter et al.

determined that minimizes the sulphur content in the ferrochrome, (ii) Figure 4 indicates for what ore and reductant combination the silicon content of the ferrochrome alloy can be minimised and (iii) Figure 5 indicates for what feed materials the power consumption is a minimum. 300

250

200

b 2

z' 150 v :: Lr. 100

Fig.2 The percentages of the different classes of ores used for a furnace and the corresponding change in the ore number

Fig.3 The effect of the Reductant at&Ore Numbers on the sulphur (96s) content in the ferrochrome (DWLS smoothing of data)

6

Characterisingthe feed to metallurgicalreactors

Fig.4 The effect of the Reductant and Ore Numbers on the silicon (%Si) content in the ferrochrome (DWLS smoothing of data)

Fig.5 The effect of the Reductant and Ore Numbers on the power consumption (MWh/t) for ferrochrome production (DWLS smoothing of data)

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M. A. Reuter et al.

The exact mix for each of the reductant and ore feed numbers can be determined from Figures 1 and 2 respectively. For example a minimum Si content in the metal is produced for reductant numbers around 30 (Figure 4) which corresponds to the feeds of the first thirty days (Figure 1). Similarly, the ore number that minimizes power consumption is ca. 190 (Figure 5). From Figure 2 it is clear that this mix was fed on various days. Neural net modelling and classification of data It is also possible to model the data by a neural net [6]. In this example the raw data depicted by Figure 4 are modelled by the application of a multi-layer perceptron neural net having two linear input nodes (feed numbers), three sigmoidal hidden nodes and one linear output node (Si content in ferrochrome). The training statistics [6] for training the 121 data sets are R2=0.43 for 109 degrees of freedom. The resulting neural net function is depicted by Figure 6. Note that the neural net function as plotted in Figure 6 is very similar to the functional relationship between the depicted variables as given by the interpolation of Figure 4.

Fig.6 The effect of the Reductant and Ore Numbers on the silicon (%Si) content in the ferrochrome (regression neural net model)

Self-organising-maps (SOM) or Sammon maps can be used for data visualisation. A self-organising neural net creates twodimensional feature maps from input data in such as way that the order of the data is preserved [9]. The Sammon net [8] for instance maps points from a higher dimensional space to a lower dimensional space. Figure 7, for example maps the three dimensional data set i.e. feed and reductant numbers, and the corresponding Si content in the ferrochrome onto a two dimensional map. Each point on this Figure is determined by the (x,y) vector produced by the Sammon net after training. Note, therefore, that the axes in Figure 7 are (x,y) co-ordinates produced by the Sammon net of the physical parameters and do not represent the physical parameters themselves. From this mapping the following observations

Characterisingthe feed to metallurgical reactors

can be

0 .

17

made: the data can be classified into low to high Si contents from left to right, indicating that there is a functional relationship between the feed numbers and the Si-content in the metal, and the cluster to the right hand side corresponds to a low Si content in the metal for reductant numbers >300 (see Figure 1).

The last point suggests that low Si metal can also be produced by using the reductants represented by a large reductant number.

.

.

. 9 %si:297-3.34

I

?? %Si:3.35-3.7l ?? Wi:3.73-4.11

.

.

. .

Fi,g. 7 Two dimensional Sammon map of the dimensionless feed numbers and (% Si) content in the ferrochrome Figure 8 depicts a map created by an autoassociative neural net [7]. The same trends as reflected by Figure 7 are depicted even more clearly by Figure 8. Figure 9 depicts a two dimensional mapping of the feed numbers and the MWh/t by an autoassociative neural net, also producing a logical clustering of the data i.e. the clustering of the increasing MWhlt from bottom left to top right.

m%Si:297-3.34

L-_---l . Y&:3.35-3.72

??t&%:3.73-4.11

Fig.8 Two dimensional mapping of feed numbers and XSi in metal by an autoassociative neural net

M. A. Reuter et al.

78

Fig.9 Two dimensional mapping of feed numbers and MWh/t by an autoassociative neural net As a summary the total data set was used and mapped by an autoassociative neural net onto two dimensions. As may be observed from Figure 10 even these data could be classified well. Note once again that the Si content increases from the bottom left to the top right comer, with a low Si cluster at the top.

.

4-

. .

8%.Si:2.97-3.34 b %Si:3.35-3.72 j %Si.3.73-4.llj ??

I

u0.040

l.ooo

20&l

3.ooa

..ooo

i_ mcm

6.000

7.ooa

8.ow

Fig.10 Two dimensional mapping of feed numbers, MWh/t, %S and %Si in ferrochrome by an autoassociative neural net

It would be evident from the results depicted by Figures 7 to 10 that the dimensionless feed numbers could be instrumental in mapping the operation of reactors effectively onto two dimensions. As summarised by Laine et al. [lo] these maps could be very useful for following gradual shifts in the operation and hence be able to act as an expert advisor to the operator.

Characterisingthe feed to metallurgical reactors

79

PRACTICAL IMPLEMENTATION OF THE METHODOLOGY Mintek has developed FumStar, a commercial intelligent control system for submerged-arc furnaces [ 111. As can be obsierved from the hierarchical structure of the control system (Figure ll), the metallurgical/electrical SQL relational database plays an important part in this system in that it organizes the metallurgical and the electrical data in such a way that the engineer can extract meaningful data from it. The philosophy that was followed during the design of the database was to render as much as possible of the data visual to the operator or engineer i.e. (i) fundamental simulation models were developed and linked to the database, (ii) phase diagrams were constructed and linked to the current operating point, (iii) statistical packages were interfaced to the database to perform various statistical modelling, and (iv) neural net modelling and 3D plotting of results are modules that permit the investigation of the inter-relationships between process variables. Currently R&D is focusing on the real-time data visualisation of data in the database by the alpplication of among others self organizing maps i.e. neural nets used for the classification of data.

Onlineopl~miwtion

model bard

fundamental. semi-cmpiricrl,

cm

empirical,

kJ

Online tinancial and management model

-

1 linguistic & Al models e.g. expert systems 1

1 ?

...................................1..

. . . . .. .. .. . .. . . . .. . . . . . .. . . . . . .. . . . . .. . . . . . . .. .

LEVEL 5

Rehttonal database for collating met~llurgksl nod elatrtc~l data 1nulflxe

IO variw

IO&

Metallurgistl/Labontory

*....................................*...... Real ttme databases w SCADA nodes situated on I network Inlqface

lo mriour

toolr e.g.

-baking 6 electrical

model

-operororguidance

sysren

PLANT-WIDE

NETWORK

LEVEL 3

Fig. 11 The hierarchical levels of a commercial supervisory control system for submerged-arc furnaces

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M. A. Reuter et al.

The structure depicted by Figure 11 makes it possible to provide the operator with a real-time operating point, which is superimposed onto the two dimensional map indicating to the operator where he is currently operating his metallurgy, where he has moved from and hence where he is possibly moving to. An expert system (already a part of FumStar [ 111) would provide additional information as a function of the current operating point. To assist in this, the map will be divided into quadrants (A, B, etc.), each quadrant symbolizing an operating mode of the furnace (see Figure lo), which is linked to the expert system.

CONCLUSIONS By the use of the definition of classes and sub-classes, empirical feed numbers could be defined for metallurgical furnaces. The examples of the defined feed numbers clearly show that they are a valid method for characterising the feed data, albeit an empirical approach. In addition these numbers also decreases the dimensionality of the variables that characterise the feed. For furnaces the feed is characterised in terms of only two numbers viz. the Reductant Feed Number and the Ore Feed Number. As may be seen from the results, useful operating information can be inferred from these numbers. The mapping of the data demonstrated that the feed numbers contain sufficient information to map these onto two dimensions. This can be very useful for tracking the operation of a reactor and hence providing expert real-time operator guidance in a well defined control structure. Note, however, such an approach becomes less powerful if it cannot be implemented in real-time in a control structure as depicted in this paper. This approach has its roots in minerals engineering and could, in the authors ’ opinion, also be applied to characterise any feed to unit operations that accept feeds that are rather ill-defined containing a wide variety of materials. Similarly, the generic nature of the depicted control system makes equally applicable to any other metallurgical process. ACKNOWLEDGEMENT This paper is published with the permission of Mintek.

REFERENCES 1. 2.

3. 4. 5. 6.

7. 8. 9. 10. 11.

King, R.P., The use of simulation in the design and modification of flotation plants. Flotation-Gaudin Memorial Volume, ed. Fuerstenau, M. C., 937-962 ( 1976). Reuter, M.A. & Van Deventer, J.S.J., The Use of Linear Programming in the Optimal Design of Flotation Circuits Incorporating Regrind Mills. InternationalJournal of Mineral Processing, 28, 15-43 (1990). Turkdogan, E.T., Physical Chemistryof High TemperatureTechnology. Academic Press, New York, 447 (1980). Reuter, M.A., Sudhiilter, S.C., Kruger, J. & Koller, S., Synthesis of processes for the production of environmentally clean zinc, Minerals Engineering, 8(1/2), 201-219 (1995). SYSTAT for Windows: Statistics,Version 5 Edition. Evanston, IL. Systat, Inc., 750 (1992). Reuter, M.A., Hybrid neural net modelling in metallurgy, Metallurgical Processes for EarZy Twenty-FirstCentury, Ed. H.Y. Sohn, The Minerals, Metals and Materials Society, 907-927 (1994). Kramer, M.A., Associative neural networks, Computersand ChemicalEngineering, 16(4), 13-32 (1992). Tattersall, G.D. & Limb, P.R., Visualisation techniques for data mining, BT Technol. J., 12(4), 23-30 (1994). Kohonen, T., The self-organizing map, Proceedings of the IEEE, 78(g), 1464-1480 (1990). Lame, S., Lappalainen, H. dc J&n&t-Jounela, S.-L., On-line determination of ore types using cluster analysis and neural networks, Minerals Engineeting, 8(6), 637-648 (1995). Reuter, M.A., Pretorius, C., West, C., Dixon, P. 8c Gosthuizen, M:, Intelligent control of submerged-arc furnaces for ferroalloys, presented atMineralsEngineering 1996, Brisbane (1996).