Proceedings of Fourth Australan Compter Conference Adelaide, South Australia, 1969

The Simulation of Mineral Processing Machinery By W. J. Whiten Department of Mining and Metallurgical Engineering University of Queensland, Brisbane

ABSTRACT: The use of computers by a University of Queensland research project for steady state and unsteady state simulation of mineral treatment processes is descbed. Several systems of Fortran programmes have been used for this work. The design, advantages and dis-advantages of these programmes are discussed.

WORDS: Mineral dressing, mineral processing, continuous simulation, digital simulation, steady state simulation, simulation languages. COMPUTING REVIEWS CATEGORIES: 3.22, 3.29.

INTRODUCTION research group at the Uiversity of Queeslad supported by the Australia Mineral Idustries Research Associatio ad

Mout Isa Mies Limited, has bee workig for several years the simulatio ad cotrol of mieral treatmet processes. The object of the research work is to develop techniques for the optimisatio ad automatic cotrol of these processes. Up

the ed of 1967 the work was mainly griding (the breaking of ore to a fine powder) ad classificatio ( the separ-

atio of ore into fine and coarse size fractions) . This work has w bee exteded to iclude froth flotatio ( the cocentration of valuable mieral grains using surface iteraction with bubbles). Simulatio of both steady state ad usteady state is being studied. Post-graduate studets associated with the pro-ject are workig the crushig of ore, flow through storage bins, ad wet cocetratio of beach sands.

The followig equipmet has either bee simulated a digital computer or is being aalysed for simulatio:

1. Commiutio (i.e. size reduction of ore lumps) Rod mills Ball mills Coe Crushers

2. Classificatio (i.e. separatig coarse particles from fie) Hydrocycloes Rake Classifiers Sieve Beds

Vibratig Screes 3. Cocetratio (i.e. removal of waste from ore)

Flotatio Cells Tray Gravity Cocetrators

Up to the preset time the Unversity of Queeslad's GE 225 computer has bee used.

DEVELOPMENT OF MODELS The models are developed ad verified wheever possible with data from full scale idustrial equipment usually supplemeted by data from pilot plat equipment. We have foud that the most satisfactory models are developed from theory with para-meters being calculated to fit the experimental data.

Ofte it has t bee possible to develop a suitable model from theory ad these cases empirical relations are derived from experimetal data. Stepwise multiple liear regressio has

bee used extesively for the reductio of data but it has t proved very satisfactory. Some other methods of data reductio are to be evaluated.

MODELS USED idicate the type of models being used for simulatio, the two most used steady state models are described briefly:

1. The Ball Mill (this machine breaks the ore particles). The discharge p (a vector cotaiing percets a rage of size fractios) is calculated from

= c/r = ( S + I - S)nf

where fs the feed size distributio vector r is the feed rate is the breakage matrix, i.e. a descriptio of the average

size dstrbutio produced by the breakage of each size fractio

S is a diagoal matrix gg selectio rates for the breakage of each size fraction

c is the ball mill costat. The toage ad water fed to the mill are assumed the same the product. Whe is o-itegral p s calculated by

lear iterpolatio from the itegers earest to . 2. The Hydrocycloe (a separator of fie ad coarse sizes of

ore particles). The beha viour of the hydrocyclone is described by a

reduced efficiecy curve, a split size d 50, ad the amout of water goig with the fie ad coarse products.

The reduced efficiecy curve is calculated from e1130 - () =

also Loge (d50) = .886- .719u + .219 - .0443W0 + b3 W = 1.1 W 1 + b2 - lOu p = Q,2/(k z1 vz(l-S,). 24)

Where is the diameter of the overflow (the fie size exit) u is the diameter of the uderflow (the coarse size exit) W 1 the toage of water the feed W 0 the toage of water the overflow S1 the fractio solids the feed Q, the volume of the feed

the operatig pressure k1 k 2 k3 are parameters.

The refereces give the models greater detail ad also worked examples.

USAGE OF MODELS The models allow the calculatio of the complete descriptio of the product provided the feed description ad the properties of the machie (i.e. the model parameters) are kw. The simu-

latio of simple processig plats without closed circuits is doe by following the flow of .ore through the plat calculat-

ig the product of each uit tur.

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In the case of closed circuits which are the more usual, an iterative procedure is used. An initial approximate description ( often zero) of the circulating or returned load ( or loads) is used to allow the calculation to proceed until better ( we hope) values are obtained to replace the initial approximation. The physical background to the iterations indicates that they will converge. Normally 4 to 20 iterations are required for convergence.

Optimisation and design of control systems have up to now been done by working from the printed results of simulation. Manual procedures had been adopted here due to the limited amount of core available, the difficult nature of some restraints and the requirement to produce results quickly. This has pro-vided some useful jnsight into the behaviour of the models but now that a larger computer is available automatic optimisation appears more economic.

SIMULATION PROGRAMMES Firstly we look at some of the factors affecting the design of the simulation programmes. These are:

1. Data describing one machine or ore flow may have a complicated structure. e.g. The description of an ore flow may require the

following: The amount in each size fraction. The sizes dividing the size fractions. The percents of the vaous ore components in each

size fraction. The specific gravities of the ore components. The amount of water in the ore. Also the amounts of various reagents and composite

particles may be required. 2. Between simulation runs usually only a few of the values

describing the plant are changed. Which values change is usually unpredictable. Thus an input system that accepts changes to the data is desirable.

3. Turn around times of 2-3 runs per day have been found not unsatisfactory. This is somewhat faster (at present) than the University of Queensland's punching service hence it has been required that the preparation of simu-lation runs involves a minimum of data preparation.

4. Modification and alterations to programmes are often required as new models are developed.

5. The programmes should be simple enough for use by industry and students. When the simulation programmes have been 'tested and vefied they are made available to the companies supporting the research and are used for teaching in the niversity.

The following criteria-. have been used as a guide for the design of programmes:

1. Detail should be required only in the sections of pro-gramme where it is used.

This ensures that programmes do not contain un-necessary complication and changes can be made easily.

2. change to one part of the system should not affect unrelated parts.

i.e. the programmes should consist as much as possible of completely independent subsections.

3. Programmes should be of general purpose design. provide greater system utilisation and reliability. reliability.

4. The data should be simple to prepare and check. provide greater system utilisation and reliability. one system of programmes has been written (nor appears

feasible) to satisfy all of the above. The choice of program-ming languages was between assembly language (GE 225 GAP) and Fortran 11 with Fortran IV coming available later. Fortran has been used except for a few assembly language subroutines for list handling. The compromises that have been developed are descbed in A-D below.

. Fortran Subroutines Initially a sees of subroutines for simulating the various

machines were wtten in Fortran 11. lnput, circuit description, convergence tests, and output were all coded into the Fortran main programme.

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These programmes were quite efficient in their use of storage and machine time.

The disadvantages were: 1. The data decks were long and rather sensitive to errors. 2. The main programmes contained too much information

and thus were not sufficiently easy to change. 3. Maintaining the programmes and subprogrammes proved

a problem. Main programmes were required for several trivially different simulations. For each of these pro-grammes instructions for data preparation had to be kept and also when subprogrammes were updated many card decks had to be altered.

. General!sed Simulation Programme increase the efficiency of the simulation system a pro-

gramme was written to read the circuit descption and accept changes to the circuit description and the data. This pro-gramme was written in Fortran 11 with the exception of a sub-programme to preread characters from the card input. The simulation subprogrammes written previously were incor-porated into this system. The features of this system are:

1. The circuit to be simulated is described by a series of simulation commands, e.g. *01 BALL MILL 10FTX12F FEED PRODUCT This description is converted to an integer code and then interpreted.

2. Twelve character data names are defined by their use in the circuit descriptions. These names are used to identify input and output. The internal data areas are defined dynamically their types being found from implicit infor-mation in the circuit descption.

3. The input data is checked for errors. U an error is found it is noted then the programme continues if possible.

4. Each simulation is started by a *EXECUTE data card. After each simulation any parts of the data, the circuit descption and dimensioning information may be changed.

5. The output is completely automatic and follows the order given in the circuit description.

6. Iterative loops are abandoned should any of the machines being simulated become grossly overloaded.

This programme has proved very efficient and convenient to use. The simplicity of the circuit descption and the lack of a fixed order for the data means that a sees of simulation runs can be made quickly with little chance of error. The extra flex-

bility provided by this programme rapidly paid for the extra development costs. The main deficiencies of this system are:

1. The main programme is at present too long for easy and cheap alteration the GE 225.

2. V ery little core storage ( G 225) is left for any expan-sion of the system.

3. Facilities beyond predicting output given input are not available.

C. Experfmental List Structure Simulation Next it became necessary to provide for more complex data

and unsteady state simulation. An experimental system was written to evaluate the use of data structures. Fortran IV was used as the basic language with several assembly language sub-programmes to give efficient handling of the data structures and subroutines with a variable number of arguments.

The basic data structure consists of homogeneous vectors containing one of real values, integer values, or pointers to other vectors. Each vector has a header element containing a type code and number of elements.

The main features of this system are: 1. Each data structure

( a) ls referenced by a single integer pointer (b) Cares an alphabetic name used for input and

output ( c) Cares input and output directions including for-

mats (d) ls on the list of all data structures.

2. Data structures are defined by calling fortran functions giving the structures alphabetic name as an argument. These functions build the structure and provide a pointer to it as the function value.

3. Input is preceded by either the data structure name or codes for forming a vector referenced from a COMMON pointer region.

4. Fortran subroutines are used for the simulation. Only one argument is required for each data structure used by the subprogramme.

5. Convergence tests are performed with the aid of a func-ton that calculates the relative change in its argument dung the last iteration.

6. Output is effected by giving one or more data pointers to the ouput subroutine. New pages are automatically pro-vided, headed and numbered at suitable points in the output. The single line calling for output may cause the

pnting of several pages using perhaps 20 different for-mats th~ order of which may vary with the size of the data.

7. Continuous (unsteady state) simulation is accomplished with the aid of a function that gives a eode to determine the next operation and advances time as necessary.

8. Debug facilities provided with the data structures are: (a) trace of vector storage allocation and retrieval

operations. (b) trace of the data structure addressing operation. (c) dump routine for the data structure memory.

The following is an example of a main programme to simu-late the behaviour of a ball mill:

CALL IFEED = LPULP ( 12 FEED IPROD = LPULP ( 12 PRODUCT

= LBALLM (12 BALL MILL 10 CALL READ

CALL BALLM (IBM, IFEED, IPROD CALL PRINT (, IFEED, IPROD ao END

Not much more than the basic description of the problem is required in the main programme. Detail not required here is kept within the appropriate subprograms.

This system provides a simple method of describing the simulation problem and still allows the full generality of for-tran to be used when required. The data can take a far more complicated form than can be used with any degree of ease with the more usual techniques in fortran. The amount of stor-age used to implement this system is considered to be quite reasonable.

Due to the amount of core (5) available for programmes, segmentation is usually required. The use of a COMMON system for data communication is now not considered satisfac-tory. Some penalty is paid in the running times required for simulation.

Further development requires a larger computer.

D. Fortran IV Subprogrammes provide programmes for student use, use outside of the

University and rapid utilisation of the new PDP 10 computer a system of Fortran IV subroutines has recently been written.

The Griffin Press, Adelaide

These programmes have the following characteristics: 1. provide a uniform system, subprogrammes for all

normal simulation operations have been written. These include simulation of each process, the compason for convergence tests, and also input and output of each data type.

2. The programmes have been designed for use as il sub-system in other programmes such as optimisation.

3. lnput is identified by order only. Output is identified by a 12 character name provided as an argument in the output subroutine calling sequence.

4. COMMON store has not been used for communication between the basic subprogrammes. Instead greater fiexi-bility is obtained by transmitting an aay of often required information as an argument.

While this system has the advantage of using only simple programming techniques, it has the following deficiencies:

1. Often several subprogramme arguments are required to describe one piece of equipment. When more complex data is required the number of arguments becomes excessive.

2. The data are not named thus making checking of and alterations to data harder. Further the order of data is predetermined by programme.

3. The wting of input and output sections requires one line for each machine of pulp stream which is long compared with c.

4. Although the use of optimsaton routines is relatively simple the process is not as tidy as would be desired.

5. Care has to be taken in accounting for system changes.

CONCLUSION Fortran has been used as a simulation language. Various methods of overcoming the deficiencies in fortran for this usage have been described. The programmes described in this paper have proved of practical use for the optimisation and control of mineral processing machinery. The simulation of a grinding section at Mount lsa Mines lead to the reaangement of the section which in increased the throughput from 115 tph to 125 tph. An automatic control system designed by simulation further increased throughput to 130 tph. These techniques are now being applied to several other plants.

ACNOWLEDGEMENTS Are due to the Australian Mineral Industries Research Associ-ation, Mount Isa Mines, the staff of the University of Queens-land Computer Centre, and in particular Dr. . J. Lynch.

REFERENCES DRAPER, ., LYNCH, . J., W, W. J. (1967): "Developing

the Optirnum Performance of a Mti-stage Grinding Circuit." Transactions of the lnstitution of Mining and Metallurgy, Vol. 76, p. C169.

DREDGE, ., LYNCH, . J. (1968): "Course Notes-Second Residential School of Mineral Processing." ELLY, J. R., LYNCH, . J., RAO, . C., W, W. J. (1967):

" Analysis of the Performance of a Ball Mill-Rake Classifier Cornminution Circuit." Aust. ... Proceedings, . 224, p. 9.

LYNCH, . J., RAO, . C., W, W. J. (1967): "Technica1 Note on On-Stream Sizing Analysis in Closed Grinding Circuits", Aust.

... Proceedings, . 223, p. 71.

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