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Boletim Paranaense de Geocincias, n. 50, p. 69-80, 2002. Editora UFPR 71

LESKO, M. et al. Development of processing technology and mathematical model of modification of magsenite raw material

- thermic processing of magnesite concentrates,- modification of magnesite sinters,- production of magnesite fireproof materials.

The listed technological units are presented by

technological operations:- grinding and milling,- briquetting and pressing of fittings,- phase separations:

sorting on sieves,hydraulic sorting,sorting in dense suspensions,flotation sorting,magnetic sorting,

- interphase sorting:unwatering

dust sedimentation, filtration- thermal operations:

burning of magnesite sinters,burning of magnesite building materials,

- chemical operations:production of pure MgO,production of chemically fixed buildingmaterials and fireproof concretes.

Complex of these operations in mutual connectioncreates a technological scheme: the operations arerealized in corresponding machines and equipments. Theresult of the technological method of modification isdetermined by:

- properties of raw material,- structure of technological scheme,- control level of the technological process.

The content of the contribution is not the analysisof the level of control of the technological process, waterand sludge management, circulation of operating anddiluted suspension, thermic processes either theprocesses of briquetting and pressing.

The properties of raw material are always qualifiedaccording to that characteristic that is used in thetechnological operation and that reflects theperformance of the raw material in this operation.

Properties of the raw material

The properties of raw material are qualifiedfollowing the contents of harmful materials (Fe

2O

3, CaO,

SiO2

etc.), the way to outgrow the useful and harmfulcompounds are given by the genesis of the deposit. Fromthe technological position for sorting operations theyare characterised:

- by the function of separation of mass accordingto the separation characteristic (k) . Thesymbol krepresents the characteristics that areused at separation. For example at sorting onsieves it is the size of particle d, at sorting indense suspensions it is the density etc.,

- by the function of separation of useful andharmful compounds according to the separationcharacteristic (k).

If there are more arguments, functions with two orthree arguments can be created.

Functions representing the properties of rawmaterials are detected by technological analysisand they are presented:

- in numerical form tables,- in graphical form granularity curves,

modifiability curves,

- in analytical form.The structure of the technological scheme

determines the separation characteristic of the objectand it is determined by:

- characteristics of elements creating the object machines and equipments,

- relations between the elements of the object mutual connection of machines and equipments.

The characteristics of each machine used aredescribed by the separation capability that can bepresented:

- in the worst case by technological parameter,e.g. partial weight yield of particular product andpartial recovery of the studied compound,

- distribution function e.g. Tromps curve innumerical or analytical form (k).

}


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Boletim Paranaense de Geocincias, n. 50, p. 69-80, 2002. Editora UFPR72


In more complicated schemes the theory oftransmissive functions can be used for this purpose(Leko 1998).

Mathematical model of magnesite processing

Various modification processes are used whenprocessing magnesite from grinding to briquetting withconsequent thermal operations scheme in Fig.1. Wewill follow this scheme to discuss this problem.

Mathematical model of modification

of magnesite raw material

Vectorial expression will be used for themathematical description of the technological schemeof modification of magnesite because it enablescharacterization of technological relations respectingthe structure of technological process. The

technological scheme of modification is shown inFig.2. Mathematical models of particular operationswere presented before, e.g. models of sorting andgrinding (Leko 1996; Lynch 1981), models of sorting

(Leko 1998; Leko & Zelek 1994). Thecharacteristics of particular components of mathematicalmodels will be described in particular operations.Vectorial expression is characterised by brief expressionbecause each vectorial expression represents as manylinear equations as fractions or components we study.The following expression describes the flux of material solid state through a technological line. In similarway it is possible to create a model of flow of water,sludge, operating and diluted suspension.

Symbols used:Q

i vector representing material flux i in the system

column format (Kx1),i = 0, 1, ,I, whereI number of material fluxes

Fig. 1. Scheme of magnesite processing


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Fig. 2. Technological scheme of processing of magnesite raw material

in the system, the listed vector can also bemultidimensional. For simpler calculation it is useful toexpress the amount of particular components, e.g.fractions, fractions of different density etc. by weightof these components, k= 1, 2, , K number of studiedcomponents.

VectorQ0 presents the input batch to the finishing

plant.In general the vector Q

ican be expressed:

(2)

where qik

are the elements of the vector.The elements can be calculated from the expression

(3)

where ik

expresses the amount of the kfraction in thematerial flux i [weight fraction]. If it is possible todetermine the granular structure by certain type ofdistribution (normal, lognormal, Weibull, exponentialetc.) or certain distribution function, the content ofparticular fractions can be calculated fromcorresponding functions and it is enough to set just the

parameters of these functions. Batch to the mill fromthe point of granularity has various compositions. If thematerial is grinded in the 1st and 2nd stage, the granularityof the material fluxes changes thus the amount offractions decisive for technology is changing. They arethe fractions 0(3)5 mm, (3)512(15) mm, (12)1540(60) mm that are in given order to be modified byflotation (operations 11, 12, 13), sorting in dynamic


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Boletim Paranaense de Geocincias, n. 50, p. 69-80, 2002. Editora UFPR74


conditions (operation 8) and static conditions(operations 6, 7). If the batch is variable and it is grindedin existing grinders operations 1 and 2, if we havedifferent efficiency of wash and sorting operations 3,4, 5, portion of these fractions is different. Changeabilityof composition can be found out by simulation usingmathematical model of preparatory operations,

equations (1 to 9) from file 1.Operators:DR

j operator of grinding in operationj, represents

the principles of disintegration of existing and offormation of new fractions. Operator of grinding DR isrepresented as follows

DRj

= Bj

Sj

+ E Sj

The matrix Bj

presents disintegration (columns) andformation (rows) of fractions. It is a triangular matrix

format (KxK), its elements are determined by thestandard characteristics of the grinder.

The matrix Sj

(KxK) presents the conditions ofgrinding in gap in operationj.

E is a unit matrix with same format (KxK).The models of grinding and milling in further

technological operations are formed similarly (Leko

1998). Values of elements of matrix B and S are givenby the results of measurement.

PMj

operator of wash represents the distributionof solid state in consequence of wash. It is a diagonalmatrix format (KxK). Operator (E PM

j) represents

the transition of solid state to sludge.TR

j operator of sorting represents the distribution

of fractions to sifting products. It is a diagonal matrixformat (KxK). The element on the main diagonal tr

ii

(1)


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represents the distribution of fraction to sifting product.For sorting on sieves and grate is valid the conditionthat grains with diameter d< d

Rpass to the sifting

product in certain proportion depending on effectiveness

of sorting r< 1. Grainsd

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