2 4 Homo

7/30/2019 2 4 Homo

1/30

INTRODUCTION

In the following it is described how the requirement for homogenisation may be evaluated at thestrategic planning stage for a cement plant.

This evaluation is comprised by a number of computational steps, carried out in the order as

specified below:

1. Computation of a bench lay out in the mine.

2. Definition of raw blend components.

3. Definition of blending conditions for raw blend components.

4. Definition of a worst-case scenario for the evaluation.

5. Determining the overall requirement for homogenisation.

6. Determining the pre-homogenisation requirements.

7. Production of the raw blend in one pre-homogenisation stockpile.

When the evaluation of the homogenisation requirements is completed a basis has been created for

the selection of suitable pre-homogenisation stores, raw blend control procedures and raw mealhomogenisation silos. Further, since optimal bench levels have been defined operational block

models for the raw material deposits may be created for other optimisation and planning purposes.

7/30/2019 2 4 Homo

2/30

1.1 COMPUTATIONOFABENCHLAYOUTINAMINE.

The computation of a bench lay out may be carried out according to three methods:

The bench levels may be moved up and down, always separated by a constant relativedistance corresponding to the bench height, until the average grades of all benches have

achieved suitable values (fig 1).

The bench levels may be moved independently, giving rise to benches of variable height,until the average grades of all benches have achieved suitable values (fig 2).

The bench levels may be selected to coincide with geological boundary surfaces, if thegradient of these surfaces are smaller than 10%, so that average bench grades of suitable

values are achieved (fig 3).

The selection of the method obviously depends on: the geometrical constraints on the benches and

the geological structure of the deposit.

As a first objective for the design of a bench lay out it may be demanded, that the average bench

grades are as similar as possible. This will in the long run ensure the most uniform blending

conditions from bench to bench, and hence the smallest requirement for equipment, handling the

raw material streams.

If the average grade of the deposit is near to the blending set point, it has to be tested if the blending

of all benches is possible. If not, a different lay out may have to be computed. This may eventuallyresult in the average grades of the benches becoming most dissimilar. Such a situation may on the

other hand result in the minimum requirement for homogenising equipment.

7/30/2019 2 4 Homo

3/30

1.2 BRIEFRECAPITULATIONONTHEGEO-STATISTICALERRORESTIMATIONTECHNIQUE.

Fig 4 shows a number of drill holes, located in a grid of dimension hx hy. The holes are dividedinto intervals of length hz and a number of grades have been assigned to each interval.

Fig 5 shows the so-called covariance function for the X-direction of the drill grid. It demonstrates

how the covariance of a certain grade varies with the distance between two points. In this case the

covariance increases as the distance between observation points increases until a certain distance,

3 hx , where the covariance is constant. This type of covariance function is common in stratified

sedimentary rocks.

In a similar way the covariance function may be constructed for the Y and the Z direction of the

drill grid. Based on all three functions it is possible to construct a covariance function for any given

direction in space.

Fig 4 also shows a material block of dimension a1 a2 a3 , orientated along the X, Y and Z-axes,respectively. Assume that an average grade has been computed for this block, then it is possible to

compute the error on this average, using the formula in fig 6: Distances are computed between

points as follows: (1) within the block, (2) between the block and the DH intervals and (3) between

the individual DH intervals. Once all distances have been found the corresponding covariance value

is computed, using the covariance functions. Finally the estimation error is found by summing up

and inserting in the expression, fig 6.

The estimation error of a certain block depends on the geometry of the block, the size of the block

and the geometrical relationship between block and the analysed intervals (their position andnumber). The error is independent of the actual average grade of the block.

7/30/2019 2 4 Homo

4/30

2.1 DEFINITIONOFRAWBLENDCOMPONENTS.

Once the bench lay out have been defined the grade variation pattern in each bench must be

investigated in order to define suitable raw blend components.

Fig 7 shows the grade variation pattern for CaO in a bench, with a front direction orientated East-

West, across the strike*. Principally the bench comprises two groups of materials, a shale

component occupying the western part and a marl component occupying the eastern part. I.e.

working along the front from the western limit of the bench a sudden jump in CaO will be

experienced at a distance of 50 m from the limit.

Fig 8 shows another grade variation pattern for a bench. The materials are the same, but they are

now localised in North-South going bands with a width of 20 to 30 meters. When working along the

front jumps in the CaO occur with a frequency of 20 to 30 m.

On fig 9 the width of the bands is narrowed down to 10 m, only, and the jumps in CaO occur with a

frequency of 10 m.

In this context 10 m along a front is defined as the smallest length over which materials can be

extracted selectively. If this length is made noticeably smaller blasted materials from adjacent

portions of the front start to slide into the extraction area, and it will no longer be possible to

forecast the average grade of the extracted material. Obviously, this distance depends on the actual

situation.

* In geology the intersection direction of layers with the horizontal. This direction is also the direction of smallest grade variation.

7/30/2019 2 4 Homo

5/30


Assume, that the covariance function has been constructed along the front direction for all three

cases in section 2.1. Then the respective covariance curves will appear as shown on fig 10, 11 and

12 above. In fig 10 the curve has a turning point at distance 50m. In fig 11 two turning points occur,

at 20m and 50 m, respectively. In fig 12 a turning point occurs at 10m, 20m, 30, etc.

Hence, for these ideal cases the covariance function directly shows the CaO variation frequency in

the front direction. In practice, though, the picture may be somewhat more complicated, but not

outside the limits of experienced interpretation.

It is also seen, that the covariance is practically zero at small distances and subsequently increases

to about 500. This maximum value of the covariance function is generally decisive for the

magnitude of the errors, which can be computed as described in section 1.2. When the maximumvalue is great so is the computed error and vice versa. The rate with which the covariance function

increases depends on the frequency of variation.

Fig 13 shows the covariance function for the direction perpendicular to the front (i.e. the direction

of the strike or smallest grade variation). The covariance is continuously small, since the material

for all distances in the strike direction is of the same type.

7/30/2019 2 4 Homo

6/30


Consider the first example of the CaO grade distribution in a bench, which was discussed in section

2.1, fig 7. This bench is shown on fig 14 above, containing the outlines of two blocks, 1and 2. The

blocks are containing both shale and marl. Assume that the average grades of the two blocks have

been computed, and that the error on these two averages has to be computed. This is done, applying

the error estimation procedure described in section 1.2 and a suitable covariance function.

The covariance function should obviously be the one comprising sample values from both the marl

and the shale. For this particular case this function corresponds to fig 10, section 2.2, which is

shown again on fig 15 above. The maximum value of the covariance function is high and the

computed errors for the two blocks in question are consequently great.

On fig 16 the same bench is shown, now with the outlines of two other blocks, 3 and 4. In this casethe blocks comprise either shale or marl. When computing the errors on the average grades of these

two blocks the suitable covariance functions to apply would obviously be the ones comprising

values from either the marl or the shale. Fig 17 is the covariance function in the direction of the

strike, as discussed in section 2.2. This would be the one to apply for this case since it always

represents the difference in grade within the same type of material. The maximum value of this

covariance function is low and consequently the computed errors for the blocks are small.

The considerations above suggest that two raw blend components should be selected for the bench:

shale and marl. Each of these components can be extracted selectively. Proportioning can easily

control the difference in grade between them, and any block extracted from them has a small error

with respect to CaO.

7/30/2019 2 4 Homo

7/30

The same principle applies to the two other bench examples, shown on fig 8 and 9 in section 2.1,

although increasingly more effort must be applied to keep the components separate as the frequency

of variation increases.

Also for the vertical direction in a bench the same principle applies. Only here, the frequency ofvariation may be much faster than for the two horizontal covariance functions. It will therefore be

more difficult to keep the components separate for this direction but this problem may be overcome

by changing the bench levels, to be discussed later.

7/30/2019 2 4 Homo

8/30

3.1 DEFINITIONOFBLENDINGCONDITIONSFORRAWBLENDCOMPONENTS.

With the selection of the raw blend components the general blending conditions can be defined. For

the sake of illustration a two-component blend and a single grade parameter, M, will be considered.

The following information is available for each raw blend component:

The average grade, Mi. The three covariance functions: (h)xi, (h)yi , (h)zi.

For the kiln feed the following is available:

The average grade of the kiln feed: Mkf The hourly kiln feed tonnage: HTkf The allowable standard-deviation on the hourly grade of the kiln feed: Hkf

The requirement on the uniformity of the kiln feed is stated so that: (1) the standard deviation on asuccession of hourly averages must not be greater than Hkf . These averages are themselvesdetermined with an error. To be sure that the succession of averages comply with (1) the error on

the hourly averages must not be greater than Hkf/2, which for convenience will be termed Mkf .

The following information is computed for each raw blend component:

The fractions of each blend component, Wi , in the kiln feed using the expressions:

W1 = (Mkf M2)/(M1 M2)

and subsequently that

W2 = 1 W1

The hourly tonnage requirement:

Covariance function, X direction: (h)x1Covariance function, Y direction: (h)y1

Covariance function, Z direction: (h)z1

Component 1 Component 2

Average grade of Kiln feed: Mkf

Hourly kiln feed requirement, ton: HTkf

Standard dev. on hourly kiln feed CaO: Hkf

FIG 18

Fraction in kiln feed: W1

Hourly tonnage requirement: HTM1

Allowable error on HTM1 grade: M1

Average grade: M1 Average grade: M2

Covariance function, X direction: (h)x2Covariance function, Y direction: (h)y2

Covariance function, Z direction: (h)z2

Fraction in kiln feed: W2

Hourly tonnage requirement: HTM2

Allowable error on HTM2 grade: M2

7/30/2019 2 4 Homo

9/30

HTMi = HTkf Wi

The allowable, hourly standard deviation on the average grade, Mi, of the succession of allquantities from component i, HTMi is determined from the expression:

Mkf= W12M12 + W22M22 (2)

(2) is an equation with two unknowns, M1 and M2. Suitable values may be found through iteration.For example, it might be advantageous to assign the smallest standard deviation to the component

with the apparently smallest grade variation and then compute the allowable standard deviation for

the other component, accordingly. One may also choose to disregard the effect of blending the

variances, altogether, and assign Mkfto both M1 and M2.

7/30/2019 2 4 Homo

10/30

4.1 DEFINITIONOFA WORST-CASE SCENARIOFORTHEEVALUATION.

In the subsequent sections it will be discussed how to evaluate the requirement for homogenisation

and pre-homogenisation. This will be done considering one raw blend component at a time. In

section 7 it will be discussed how to evaluate similar requirements for a combination of

components.

Since this evaluation often takes place at the strategic planning stage there will only be a limited

amount of data available. Under these circumstances a worst-case scenario is defined, which

specifies how to select data and define geometries as basis for the evaluation:

On fig 19 is shown two areas for the component in question, each defined by a number of drill hole

averages. For one of the areas, the low-grade area, the drill hole averages have the lowest possible

grade values in relation to the component average, M i; for the other area, the high-grade area, the

drill hole averages have the highest possible values in relation to M i. These two areas will provide

the drill hole information.

Subsequently, it is necessary to define the position of the unit block of material under consideration.This block should be positioned so that it represents a worst-case situation, i.e. a situation where the

error computed for its average grade is at its maximum. This position will obviously be at the centre

of the drill hole positions. Further, the orientation of the block must be so that one of its sides is

parallel to the actual front direction, the other being perpendicular to that direction (fig 19).

The above-mentioned establishment of a worst-case scenario has been made under the assumption

of the so-called proportionality effect, i.e. the average of a set of drill hole sample analyses and the

standard deviation of these sample analyses are proportional. This assumption holds true for many

situations, but not for all. In the last case it will be necessary to establish four worst-case situations:

two cases for the min and max drill hole averages (as described above) and two for the min and max

standard deviation on the drill hole averages.

COMPONENT i: Average grade = Mi

Drill Hole, average grade m i1

mi2

mi3mi4

mi5 mi6

mi8 mi7

mi1, mi2, mi3, mi4 < M1 < mi5, mi6, mi7, mi8

Front direction

High-grade areaLow-grade area

FIG 19

Unit block position andorientation

7/30/2019 2 4 Homo

11/30

5.1 DETERMININGTHEOVERALLREQUIREMENTFORHOMOGENISATION.

The hourly tonnage requirement from component i was defined as: HTMi. It is now necessary to

define the dimensions of the unit block of material, situated in the front, from where this quantity

derives. In doing so, there are certain dimensions, which are already fixed. These dimensions are

the height of the bench in question (h) and the total burden* of the hole-rows comprised by a single

blast (b). Further, the digging direction must also be defined, see fig 20.

Then, during the hour it takes to produce HTMi the digging operation advances l m along the front,

where l is computed as follows:

l = HTMi / h b banc density

The dimension of the unit block produced each hour from the front is consequently: h l b.

Once the block has been defined in space its average grade is computed, for the low-grade and

high-grade area of the raw blend component, respectively. Further, the estimation error on the

average grade of the block is computed. In both cases the drill hole average grades: m ij and the

covariance functions: (h)xi, (h)yi and (h)zi are used.

As a result one has:

Average grade of block for one hours production: Mij.

Estimation error (in terms of standard dev.) on the average grade: Mij

* In this context it is assumed that the material is blasted. However, the extraction geometry

can easily be adapted to a situation where the material is directly dug from the front.

COMPONENT i: Average grade = MiFIG 20

Burden (b)

Bench height (h)

Length of block (l)*

* the length the digging advances during one hour, given the diggingdirection and the hourly tonnage reclaimed from the component.

Digging direction

Average grade of block: Mij. Estimation error on the average grade: Mij

7/30/2019 2 4 Homo

12/30

5.2 DETERMININGTHEOVERALLREQUIREMENTFORHOMOGENISATION.

It can now be tested if the material blocks from the low- and high-grade areas need no

homogenisation. For this to be the case it must be demanded that:

Mij +/- Mij is situated within the interval Mi +/- Mi.

If this demand is not satisfied there are still a fairly simple remedy at the disposal, which may

reduce the variation with the smallest amount of efforts. It might be possible, through a strict

monitoring of the hourly production during the operational stage, to eliminate the hourly grade

variation of a component through stringent proportioning of the hourly production.

To test that possibility it is necessary to consider more raw blend components at a time (in this

context two components). The actual test is carried out as a simulation predicting the blending

fraction of the components, when the average grades, M ij, and the corresponding standard deviation,

Mij, have been determined for the components in question. Fig 21 and fig 22 above show thepossible result.

The abscissa of the curves is the blending fractions of the components (the red and blue component

on the figure) and the ordinate is the frequency with which the blending fractions occur. From

figure 21 it appears that a large amount of the blending fractions are either below zero or above 1,

impossible situations, which render this test unsuccessful. On figure 22, on the other hand, allblending fractions are between 0 and 1, meaning that the hourly variation can be controlled through

proportioning.

FIG 21: Unsuccessful test oncontrolling the hourly variationin grade through proportioning.

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

0 0,2 0,4 0,6 0,8 1 1,2

Raw Blend Fraction

Horz. bench #2

Horz. bench #3

0,00

0,50

1,00

1,50

2,00

2,50

3,00

0 0,2 0,4 0,6 0,8 1 1,2

Raw Blend Fraction

Inc. bench #3

Inc. bench #5

FIG 22: Successful test oncontrolling the hourly variation

in grade through proportioning.

7/30/2019 2 4 Homo

13/30

6.1 DETERMININGTHEPRE-HOMOGENISATIONREQUIREMENTS.

Suppose that homogenisation is required to bring down the grade-variation of the hourly tonnage,

HTMi, required from component i, the subsequent step will be to investigate if pre-homogenisationalone could bring about the required effect. For that purpose a worst-case scenario, with respect to

data and block geometries, are defined in a similar manner as described in section 4.1.

The detailed design of a pre-homogenisation system will be treated in the following lecture. For the

present discussion an idealised pre-homogenisation stockpile of horizontal layers will be assumed.

The geometry of such a stockpile is demonstrated on fig 23.

The total tonnage of the stockpile is defined as: T stck.

The tonnage reclaimed hourly from the stockpile: HTMi.

The number of layers in the stockpile is defined as: N l.

The tonnage of each such layer is: T li = Tstck/ Nl.

The contribution from each layer to HTMi is: HTli = HTMi / Nl.

La er 1

Layer2

Layer3

Tonnage reclaimed each hour from the pre-homogenisation stockpile: HTMi

Tonnage contribution to HTMi fromLayeri: HTli

FIG 23

7/30/2019 2 4 Homo

14/30


It is now necessary to define the dimensions of the unit blocks, corresponding to the total stockpiletonnage, Tstck, and the layer contribution to the hourly tonnage HTli, in their original positions in the

front (fig 24). Also in this case the digging direction has to be taken into consideration.

Tstck has the following geometry:

b h L, where L = Tstck / (b h density).

In order to compute the dimensions of HTli it is necessary first to compute the length in the digging

direction corresponding to one layer in the stockpile. This length is:

l = Tli / (b h density).

Consequently, HTli has the following geometry:

b l t, where t = HTli / (b l density).

Applying the drill hole information and the covariance functions for the x, y and z-direction the

following is now computed:

The average grade of the stockpile: Mstckij, meaning the average stockpile grade for rawblend component i in the area j (high- or low- grade area) of component i.

Digging direction

Burden (b)

Bench height (h)

Length of layeri (l)

Thickness of HTli (t)

FIG 24

Length (L) corresponding to one

The average grade of the stockpile: Mstckij The error on the average grades of all HTli: HTij The total error on the hourly tonnage, HTMi: Mij = (1/Nl)2 HTij2

7/30/2019 2 4 Homo

15/30

Assume, that the number of layers in the stockpile, N l, has been decided upon already. Thenthe computed error on the average grades of all HT li is HTij, meaning the error on the layercontribution to the hourly tonnage from component i in the area j.

The total error on the hourly tonnage, HTMi , reclaimed from the stockpile will consequentlybe:

Mij = (1/Nl)2HTij2

The number of layers may also be decided at this stage. Iterating the above-mentionedprocedure can do this, so that one finds the number of layers for which the error on the

hourly tonnage just corresponds to the allowable Mi.

How to proceed from this stage depends on the frequency on the grade variation along the front,which will be discussed in the subsequent sections.

7/30/2019 2 4 Homo

16/30


Case 1: There is a pronounced grade variation in the vertical direction of the working face (fig 25).

Thin layers of maximum-grade material are alternating with thin layers of minimum-grade

materials. In this case any block, HTli, extracted from the front may comprise both minimum-

grade material and maximum-grade material. Therefore, the maximum value of the vertical

covariance function, (h)z, computed based on all sample values in the vertical direction, willbe high. As a consequence the error, HTji, on the quantity, HTli, will always be high.

In order to compute the average grade, M ij, of the hourly tonnage to be reclaimed from the

stockpile, HTMi, it is necessary to consider the sequence in which the quantities, HTli, are entered

into the stockpile. This sequence is dependent on: how the corresponding unit blocks are positioned

in the in the blasted pile to be dug, the exact sequence of digging and the sequence in which theyare dumped into the crusher hopper (fig 26). Obviously, the entry sequence of these blocks into the

stockpile is practically impossible to predict.

Assume that the blocks in a layer are randomly distributed along the length of the layer. Then, if

there are a sufficiently large number of layers in the stockpile the quantity, HTMi, should comprise

more or less the same combination of maximum- and minimum grade blocks from hour to hour (fig

27). In that case the average grade, Mij, of all HTMi should converge towards the average grade of

the stockpile, Mstckij. The hourly variation of the material being reclaimed from the store could

therefore reasonably be set to:

Mij (= Mstckij) +/- Mij [1]

(where j indicates that this computation has to be carried out for both the high-grade and the low-

grade area of component i and where Mij is computed as described in section 6.2 )

7/30/2019 2 4 Homo

17/30

Assume then that the blocks,HTli, are placed in the same repetitive manner from layer to layer.Then the quantity, HTMi, would for one hour comprise only maximum-grade blocks, the next hour

only minimum-grade blocks (fig 28) etc. In fact the variation seen in the layers entering the store

would also be seen in the tonnage reclaimed from hour to hour.

To quantify this situation one should then for the low-grade area of component i select the lowest

value for the minimum-grade material as representative for the hourly average, Milmin, and similarly

for the high-grade area the highest value for the maximum-grade material as representative for the

hourly average, Mihmax. Each of these grades would then be subject to the errorMji, i.e.:

Milmin +/- Mji and Mihmax +/- Mji. [2]

Depending on which situation is at hand it can now be concluded that if:

Mij (=Mstckij) +/- Mji is within the interval Mi +/- Mi

or

Milmin +/- Mji and Mihmax +/- Mji are within the interval Mi +/- Mi

then pre-homogenisation is sufficient to reduce the hourly grade variation of HTMi to an acceptable

level. It should be mentioned, though, that the second set of the above-mentioned conditions only

has an insignificant chance of being satisfied.

If none of the conditions are satisfied, then the proportioning simulation, as described in section 5.2,may be carried out. If the result of this test is negative as well all indications are that raw meal

homogenisation is required.

7/30/2019 2 4 Homo

18/30


As was demonstrated in the last section, the error on the hourly tonnage being reclaimed from the

pre-homogenisation stockpile depended on whether the materials in the layers of the stockpile were

distributed in a random or repetitive manner.

On fig 29 is shown a very fast grade variation of maximum- and minimum-grade material. The

chance of placing the material types in a repetitive manner in the store is practically zero. The

hourly grade variation of the tonnage, HTMi, can therefore be determined according to expression [1]of section 6.3.

On fig 30 is shown a very slow grade variation, deriving from a thicker layer of maximum-grade

material being placed on top of a thicker layer of minimum-grade material in the front. In this casethere is a real danger of a repetitive placement of the two material types in the stockpile. The

resulting hourly variation has to be determined based on [2] of section 6.3 and it will probablyprove, that the effect of the pre-homogenisation becomes insignificant.

The second situation can be remedied in two ways:

1. The digging direction could be changed 90 degrees, whereby one of the two layers, by and

large, would be placed on top of the other in the pre-homogenisation stockpile.

2. The bench levels could be changed, so that one of the materials were extracted from one

bench, the other material from another bench, thus minimising the blending of materials

before they are entered into the stockpile.

The consequence of applying either of the remedies appears from the discussion in the subsequent

sections.

7/30/2019 2 4 Homo

19/30


Case 2: There is a pronounced grade variation in the lateral direction of the front. Larger front

sections of maximum grade material alternate with larger front sections of minimum grade

material (fig 31). In this case any block, HT li, extracted from the front comprises either

maximum-grade material or minimum-grade material. The vertical covariance function, (h)z,has to be computed for each of the materials individually and the maximum value of this

function will therefore be low. Consequently, the error, HTij, on the quantity, HTli, will besmall.

Under the assumption of a random distribution of the quantities HT li along the length of thestockpile layers the average grade, Mij, of the hourly tonnage reclaimed from the stockpile, HTMi,

can be expected to converge towards the average of the stockpile, M stckij. Therefore, as in case 1, the

hourly variation in the material being reclaimed from the stockpile can reasonably be set to:

Mij (= Mstckij) +/- Mij.Compared to case 1, the average grade of the quantity HTMi will show a smaller variation for case 2

due to the small value ofMij.

A repetitive placement of the quantities HTli in the layers will never occur in the same way as in

case 1 due to the entry sequence of the different material types. However, worst case situationsmay also arise for this case.

7/30/2019 2 4 Homo

20/30

Assume that all the blocks, HTli, from the low-grade area of component i attain their minimum

grade, then the average grade of the hourly tonnage, HTMi, attain its minimum value. In order to

compute this average grade first compute the number of layers, N lmin ,which can be extracted along

the front section containing minimum-grade blocks. Then compute the number of layers, Nlmax ,

which can be extracted along the front section containing maximum-grade blocks. Select the lowestgrade value from the minimum-grade blocks, Milmin, and the lowest grade value from the maximum-

grade blocks, Milmax. The minimum average grade of HTMi for the low-grade area of component i

then becomes:

Mimin = (Nlmin/Nl) Milmin + (Nlmax/Nl) Milmax, [3]

where Nl is the total number of layers in the stockpile.

Similarly, the maximum average grade Mimax of the hourly tonnage, HTMi , can be computed for the

high-grade area of component i, by substituting Milmin and Milmax in expression [3] with Mihmin andMihmax, the two latter being the highest value of the minimum-grade blocks and the highest value of

the maximum-grade blocks for the high-grade area of component i, respectively, i.e.:

Mimax = (Nlmin/Nl) Mihmin + (Nlmax/Nl) Mihmax.

Altogether, the following expressions determine the errors on the hourly tonnage, HTMi:

Mij (= Mstckij) +/- Mij., Mimin +/-Mij and Mimax +/-Mij

If the variation intervals above lie within the interval Mi +/- Mi then pre-homogenisation issufficient. If not, the proportioning simulation will show if raw meal homogenisation is required,too.

7/30/2019 2 4 Homo

21/30


Case 2 offers much better possibilities for the pre-homogenisation to smooth variations efficiently

than case 1.

Due to the way the layers are entered into the stockpile in case 2, the repetitive pattern in theindividual layers, as may arise for case 1, will not be possible. Thereby there will be no

situations where the tonnage reclaimed during one hour consists of either maximum-grade

or minimum-grade material.

Since the blocks, HTli , for case 2 are always dug from either maximum-grade or minimum-grade material the error adhering to their averages will always be small in contrast to case 1,

where this error may be significant.

The above-mentioned advantages of case 2 are under the provision, however, that the frequency of

the lateral variation is slow compared to the dimension on the layers in their position in the front. If

this frequency becomes so fast, that both maximum- and minimum grade material occur within the

individual blocks delineating the layers in the front (fig 32) the situation is in fact back to that of

case 1. The pre-homogenisation requirements now have to be determined as described for this case.

The case 2 conditions can be generalised to comprise more than the rather simple situations

illustrated in the previous sections. Hence, the objective for the planning of a pre-homogenisation

operation should be to apply an entry sequence so that each distinct type of material is entered

individually in so many layers as possible. Apart from offering the best possibilities for an efficientpre-homogenisation it also presents the most suitable conditions for controlling the current average

of the materials entered into the stockpile.

7/30/2019 2 4 Homo

22/30

7.1 PRODUCTIONOFTHERAWBLENDINONEPRE-HOMOGENISATIONSTOCKPILE.

So far the pre-homogenisation requirements have been evaluated for each raw blend component,

individually. There are, however, no hindrances for evaluating the pre-homogenisation

requirements for a combination of such components, i.e. for a finished raw blend produced in the

pre-homogenisation stockpile. Exactly the same procedure, as described in the previous sections,

may be applied. This procedure is not influenced by the individual blend components being situated

at different localities. What matters are how they are extracted and how they are entered into the

stockpile.

Under these circumstances the tonnage for which the evaluation is carried out is the hourly kiln

feed, HTkf , and the computed variation intervals for this quantity should of course be tested against

the allowable variation in the kiln feed, Mkf+/- Mkf. Obviously, there is no reason to carry out theproportioning simulation, since no proportioning will take place after the pre-homogenisation.

With respect to the entry sequence of the components great care must be taken to investigate the

relationship between entry frequency and store geometry before any decision is taken. It is often

believed that truck blending will be beneficial for the overall homogeneity of a stockpile. For

example 2 trucks from one component and 1 truck from another component may be entered in that

sequence etc.

Assume a stockpile tonnage of 30000 ton, entered in 200 layers. The layer tonnage is then 150.

Then assume a truck payload of 30 ton; that is 5 trucks a layer. Entering 2 truck loads from one

component and 1 from the other etc. the layers will be brought to consist of 5 sections of differentmaterial (fig 33), i.e. a situation similar to the previously discussed CASE 1 has been created, with

all the corresponding disadvantages. Obviously, the purer the grade of the material components is

the worse the result of the pre-homogenisation.

7/30/2019 2 4 Homo

23/30

When entering different material components into a single stockpile one should aim at a CASE 2

situation, i.e. as many layers as possible are build up in the stockpile from one component before

the entry of another component is initiated.

7/30/2019 2 4 Homo

24/30

SUMMARY

The overall evaluation of the homogenisation requirements on a plant should be carried out on thestrategic planning level. It is important that a suitable concept, corresponding to the material and

operational conditions on the plant in question is implemented from the commencement of

operation. Further, evaluating the requirements at the strategic level means that optimal bench

levels can be defined and thus the most suitable block model of the raw material deposits can be

constructed for subsequent optimisation and planning.

The homogenisation requirements are dependent on:

The geochemical variation pattern of the raw material components. The bench lay out. The extraction geometry. The pre-homogenisation stockpile geometry. The allowable kiln feed variation. The hourly kiln feed tonnage.

Any subsequent modification must take the mutual dependency between these factors into

consideration.

The amount of data available at the strategic planning level may be relatively scarce. Therefore, it

might be advantageous to localise some areas, typical with respect to geochemistry and structure,

and for these areas to produce a sufficiently representative set of data, whereupon a more safeevaluation of the homogenisation requirements could be based.

Factors influencing thehomogenisation requirements on aplant.

The geochemical variation pattern of the rawmaterial components.

The bench lay out. The extraction geometry.

The pre-homogenisation stockpile geometry. The allowable kiln feed variation. The hourly kiln feed tonnage.

7/30/2019 2 4 Homo

25/30

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

0 0,2 0,4 0,6 0,8 1 1,2

Raw Blend Fraction

Horz. bench #2

Horz. bench #3

FIG 21: Unsuccessful test oncontrolling the hourly variationin grade through proportioning.

0,00

0,50

1,00

1,50

2,00

2,50

3,00

0 0,2 0,4 0,6 0,8 1 1,2

Raw Blend Fraction

Inc. bench #3

Inc. bench #5

7/30/2019 2 4 Homo

26/30

Experimental, spherical variogram, direction 1

0,0

100,0

200,0

300,0

400,0

500,0

600,0

1 2 3 4 5 6 7

h (in drill grid units)

gamma(h)

Experimental, spherical variogram, direction 1

0,0

100,0

200,0

300,0

400,0

500,0

600,0

1 2 3 4 5 6 7

h (in drill grid units)

ga

mma(h)

7/30/2019 2 4 Homo

27/30

1 2 1 35 34 1 2 35 36 32

1 2 2 34 33 1 2 36 33 30

4 1 2 32 35 4 1 34 33 34

3 3 3 33 32 3 3 33 32 37

2 4 5 37 33 2 4 37 37 39

1 2 1 2 4 35 36 32 35 34

1 2 2 3 2 36 33 30 34 33

4 1 2 3 5 34 33 34 32 35

3 3 3 5 3 33 32 37 33 32

2 4 5 7 3 37 37 39 37 33

7/30/2019 2 4 Homo

28/30

1 35 1 35 1 36 2 35 2 32

1 34 2 34 2 33 2 36 2 30

4 32 2 32 2 33 1 34 1 34

3 33 3 33 3 32 3 33 3 37

2 37 5 37 5 37 4 37 4 39

Figure texts:

Figure 1: Bench lay out selection for constant bench height.

Figure 2: Bench lay out selection for variable bench height.

Figure 3: Bench lay out selection according to geology.

Figure 4: Drill hole grid with outline of block a1 x a2 x a3.

Figure 5: Covariance function in the X-direction. Abscissa: distance between points,ordinate: covariance for the corresponding point distance.

Fig 6: Expression for computation of the estimation error on the average grade of a block.

Fig 7: Average drill hole values showing the CaO distribution in a bench. The grey areacomprises shale; the white area comprises marl.

Fig 8: Average drill hole values showing the CaO distribution in a bench. The grey bandscomprises shale; the white bands comprises marl.

Fig 9: Average drill hole values showing the CaO distribution in a bench. The thin greybands comprises shale; the thin white bands comprises marl.

Fig10: Covariance function for the front direction (X-direction) of the bench shown in fig 7.



7/30/2019 2 4 Homo

29/30

Fig13: Covariance function for the strike direction (Y-direction) of all benches.

Fig 14: Selection of two blocks, 1 and 2, containing both shale and marl.

Fig 15: Covariance function required to compute the error on the average grade of block 1and block 2.

Fig16: Selection of two blocks, 3 and 4, containing either shale or marl.

Fig 17: Covariance function required to compute the error on the average grade of block 3and block 4.

Fig 18: Required blending parameters to be defined as basis for the evaluation.

Fig 19: Positioning of the unit block under investigation in relation to the drill hole grid in

the low-grade and high-grade areas of component i.

Fig 20: Extraction geometry for one hours production and the average and error on thecorresponding block grade.

Fig 21: Unsuccessful test on controlling the hourly variation in grade through proportioning.Fig 22: Successful test on controlling the hourly variation in grade through proportioning.

Fig 23: Geometrical arrangement of layers and quantities in a horizontal pre-homogenisation stockpile.

Fig 24: Geometrical arrangement of layers and quantities in the front, from where they areextracted.

Fig 25: layer i as positioned in the front before digging.

Fig 26: Layer i positioned in the pre-homogenisation stockpile.

Fig 27: The grade variation of the tonnage reclaimed from the stockpile each hour, whenthe material in the layers is randomly distributed.

Fig 28: The grade variation of the tonnage reclaimed from the stockpile each hour, whenthe material is placed in a repetitive manner from layer to layer.

Fig 29: : The grade variation of the tonnage reclaimed from the stockpile each hour, whenthere is a very fast vertical variation frequency in the front.

Fig 30: The grade variation of the tonnage reclaimed from the stockpile each hour, whenthere is a very slow vertical variation frequency in the front.

Fig 31: The grade variation of the tonnage reclaimed from the stockpile each hour, whenthere is a slow lateral variation frequency in the front.

Fig 32: The grade variation of the tonnage reclaimed from the stockpile each hour, whenthere is a very fast lateral variation frequency in the front.

7/30/2019 2 4 Homo

30/30

Fig 33: Effect of truck blending on pre-homogenisation result.

Documents

2 4 Homo