Review No. 110

Review No. 110

¢ Bed blending homogenisation

¢ Reprint of article published in World CementBulk Materials Handling Review 1994

¢ By Ib Finn Petersen, F.L.Smidth & Co. A/S, Denmark

Bed blendinghomogenisation

By lb Finn PetersenF.L.Smidth & Co. A/S, Denmark

Bed blending homogenisationUsing statistical theories, Ib Finn Petersen,F.L. Smidth, Copenhagen, examines theblending effect that can be expected froman homogenizing store for raw materials.

IntroductionIt is commonly accepted that the number of layers in a blendingbed is the decisive factor for obtaining homog-enisation. Accord-ing to the so-called statistical theory of bed blending the reduc-tion in standard deviation from in-going to out-going material isrelated to the square root of the number of material layers simul-taneously reclaimed. However with stores that involve a movingaverage concept (typically a circular store operated according tothe continuous Chevron mode), the time series compositionalvariation of the in-going material plays an additional and signifi-cant role. This is analysed theoretically using general statisticsand the implications of particle size in relation to sample mass inconnection with blending tests are evaluated.

In a homogenising store for raw materials a stockpile is builtup of a large number of layers which afterwards are reclaimed insuch a way that material from all layers are present in the re-claimed material. In order to calculate the blending effect thattheoretically can be expected from such it is necessary to con-sider a little statistical theory.

Statistical background

The characteristic of a stochastic parameter is that its value isnever known exactly. A number of measurements can be per-formed, and from these measurements their distribution can beevaluated or characteristic quantities (such as the mean, the vari-ance etc.) calculated. In order to see how these quantities aredefined, consider a stochastic parameter X and assume that anumber of discrete measurements of the magnitude of this param-eter have been performed. The following values x1,x2,...,xn havebeen observed and they appear with the frequenciesf(x1),f(x2),...,f(xn,) where:

f(x1)+f(x2)+...+f(xn)=1

The expected value E[X] (i.e. the most likely value) of ourstochastic parameter X is defined as the mean:

E[X] = x1 f(x

1) + x

2 f(x

2 + ... + x

n f(x

n )

The expected value operator E [ ] will always involve weight-ing a parameter or an expression with the observed frequencies,as in the calculation of the mean value above. There exist a coupleof general calculation rules concerning the expected value op-erator, these are deduced by direct calculation:

• The expected value of the sum of a number of stochasticparameters is the sum of the expected value of eachstochastic parameter:

E[X1 + .... + X

n1 = E[X

11 + .... + E[X

n ]

• The expected value of the product of a constant and astochastic parameter is the product of the constant and theexpected value of the stochastic parameter:

E[aX] = a E[X]

Similarly, the variance Var[X] of a stochastic parameter is de-fined by means of the expected value operator as:

Var[X] = E[(X-E[X])2]

A few general calculation rules exist for the variance operator(a and b are constants and X and Y are stochasticparameters):

• The variance of the product of a constant and a stochasticparameter:

Var[a X] = a2 Var[X]

• The variance of the sum of a stochastic parameter and aconstant:

Var [X+b] = Var[X]

• The variance of the sum of two stochastic parameters in caseswhere these measurements are independent of each other:

Var [X+Y] = Var[X] + Var[Y]and in cases where these two stochastic parameters are notindependent of each other:

Var[X+Y] = Var[X] + Var[Y] + 2 Cov[X,Y]In the case where the parameters are not independent of eachother the so-called co-variation Cov[X,Y] appears in theexpression. The co-variance is a statistical quantity that measuresthe relationship between parameters X and Y. If thesemeasurements resemble each other to a large extent, theco-variance will be high. The co-variance between two stochasticparameters can be calculated according to:

Cov[X,Y] = E[(X-E[X])(Y-E[Y])]= E[X Y] - E[X]E[Y]

where E[ ] again represents the expected value operator.

There also exists a calculation rule concerning the co-vari-ance among linear expressions involving stochastic parameters:

Cov[a1 X + b

1 , a

2 Y + b

2 ]= a

1 a

2 Cov[X, Y]

Bed blendingAssume that the pile consists of N layers and that thecomposition of each layer 1..i..N can be represented by X1..Xi..XN.These layer compositions are to be considered as so-calledstochastic parameters.

The layers are represented in the reclaimed material by theweight fractions w1..wi,..wN. Accordingly, the composition of thereclaimed material is expected to become the weighted averageoperator i.e.:

Xout

= w1 X

1 = w

2 X

2 + ... + w

i X

i + ... + w

N X

N

However, in connection with bed blending the out-goingstandard deviation is of greater interest. From a statistical point ofview variances (squared standard deviations) are easier to handlethan the standard deviations themselves and it is always possibleto take the square root of a variance afterwards and therebyobtain the corresponding standard deviation.

BULK MATERIALS HANDLING REVIEW 1994

The variance in the reclaimed material can be calculateddirectly by applying the above calculation rules concerningthe variance operator on the expression for Xout’

In cases where the compositions of the layers in the pileare independent of each other, the variance in the reclaimedmaterial becomes:

Var[Xout ] = Var[w1 X1 + w2 X2 + ... + wi Xi + ... + wN XN ]

= w12 Var [X1] + w2

2 Var[X2] + ........... = wN2 Var (XN )

and in cases where the compositions of the layers in thepile are not independent of each other the variance in thereclaimed material becomes:

Var[Xout ] = Var[w1 X1 + w2 X2 + ... + wi Xi + ... + wN XN ]= w1

2 Var [X1 ] + w22 Var[X2 ] + ........... = wN

2 Var (XN )+2w1 w2 Cov[X1’ X2] +..... +2 wN-1 wN Cov[XN-1’ XN]

Or written as a general formula:

Var [Xout] = ∑ W1

2 Var [X

1] = ∑ ∑ 2.w

.w . Cov (X , X )

Pure statistical theory is one thing but how and where does itapply in practical bed blending situations? The additional co-variance terms in the above expressions for the out-going vari-ance originate from variation in the reclaimed composition fromindividual layers in the pile. This is important to remember whenapplying this expression.

Fixed averageIf the concern is the out-going variation during reclaiming of asingle pile in a longitudinal store stacked according to the Chev-ron method and reclaimed by a bridge reclaimer, the co-vari-ances does not play a significant role. Provided the pile hasbeen stacked in a large number of layers (200 - 400) no sig-nificant variation in the average composition reclaimed is tobe expected because of variation in composition among indi-vidual layers. When operating in the full cross-section of thepile, the reclaimed average composition will at any time be afixed average composition of the individual layers. The onlytime that variation in composition among individual layers playsa role is during reclaimation of the end cones.

Moving averageHowever, if the concern is a circular store operated accordingto the continuous Chevron mode, the situation is quite differ-ent. The reclaimed material will at any time have the averagecomposition of all layers represented in the reclaimer cut.However, the layers are inclined in the pile and as a conse-quence some layers will become fully reclaimed and new lay-ers will come into contact with the reclaimer as the reclaimermoves around in the store. Consequently, reclaimed materialwill become a moving average taken over the material quan-tity seen by the reclaimer. If the compositions of individuallayers vary, the reclaimed average composition also will vary.The resulting variation in the reclaimed average compositionis exactly as the above co-variance contributions describe.

A similar moving average situation occurs with Cone Shellstacking, both with a longitudinal and a circular store.

Co-variance and the variogramFor bed blending situations involving a moving average, acharacterisation of the in-going variation pattern is of interest.The in-going material enters on a belt, and by taking a numberof samples at constant time or tonnage intervals, the compo-sitional variation X(t) with respect to time or tonnage can bedisplayed. In order to characterise this variation pattern, thebasic idea is to consider not the time series X(t) itself but rather

the increment functionX(t)-X(t+h), where the lag h is a timeinterval. Obviously the mean value of this increment functionshould be zero i.e.:

E[X(t+h)-X(t)] = E[X(t+h)J - E[X(t)] = 0In addition the (semi) variogram Gam[h] is defined as half

of the variance of the increment function:

Gam[h] = Var[X(t+h)-X(t)]/2Evaluation of the variance of the increment function by

means of the general calculation rules above leads to thefollowing:

Var[X(t+h)-X(t)] = E[(X(t+h)-X(t) - E[X(t+h)-X(t)])2 ] = Var[X(t+h)] + Var[X(t)] - 2 Cov[X(t+h),X(t)]

= 2 Var[X(t)] - 2 Cov[X(t+h),X(t)]where Var[X(t)] is the overall variance of the input variation tothe store. Inserting this expression in the variogram gives:

Gam[h] = Var[X(t)] - Cov[X(t+h),X(t)]The variogram Gam[h] is only a function of the lag h, and theoverall variance Var[X(t)] is constant, so obviously the co-vari-ance Cov[X(t+h),X(t)] between sample with a time lag h is alsoonly a function of the lag. Accordingly the co-variance can bewritten as a function of the lag:

Gam[h] = Var[X(t)] - Cov[h]The variogram defined above is a practical tool for determiningthe co-variances in a time series of samples. If it is assumedthat sampling has been carried out at 1 hr intervals, thevariogram value corresponding to a lag of 1 hr is calculated asfollows. Compute differences between all pairs of samples witha lag of 1 hr and calculate the variance of these differencesand divide by 2, the value obtained is the variogram valuecorresponding to a lag of 1 hr. Then compute differencesbetween all pairs of samples with a lag of 2 hr, calculate thevariance of these differences and divide by 2, the valueobtained is the variogram value corresponding to a lag of 2 hr.This procedure is continued as long as a respectable numberof pairs corresponding to the still increased lag can be located.From a statistical point of view a respectable number of pairsis in the order of magnitude 20.

Finally, the variance of all samples is calculated. From aplot of the calculated variogram values versus lag, thevariogram value corresponding to a given lag can be inter-polated and the co-variance between two samples of the speci-fied lag can be calculated using the above expression relatingthe co-variance with the variogram. It should be noted that theco-variance can never become negative.

Variation patternsIn practice it is to be expected that a combination of threevariation patterns can appear in the material to be piled:• Random variations• Periodical variations• Variations where co-variance exists over a range of material quantity.

The homogenisation of these different variations patternsis considered below.

Random variationsThe blending of random variation is similar for both longitudinaland circular stores. In cases where compositional variationsin the stacked material are random, the composition of thelayers will be independent of each other and all co-variancesbetween layers will be zero. The variance in the reclaimedmaterial becomes:


1 j i j

Var[Xout ] = Var[W1 X1 + w2 X2 + ... + wi X i + ... + wNX N]= w1

2 Var[X1 ] + w22 Var[X2 ] +.......... + wN

2 Var[XN ]

and for the case of a Chevron pile reclaimed by a bridgescraper all the weight fractions (wi) will be identical andequal to 1/N, where N is the number of layers in the pile.Assuming the same variances in all layers:

Var[X1] = Var[X

2] = .......... = Var[X

N] = Var[X

in]

The variance of reclaimed material becomes:Var[X

out] = Var (X

in]/N

Remember that the blending effect is evaluated on the ba-sis of the standard deviation ratio. The above expression,corresponding to a blending effect equal to the square rootof the number of layers in the pile, is to be expected when arandom variation exists in the material stacked in the pile.

Periodical variationsFor blending beds involving a moving average - typically acircular store stacked according to the continuous Chevronmethod - special attention must be given to the blending ofperiodical variations.

Consider the case where the composition in the materialfed to the store varies as a sinusoidal function with period Tand the amplitude A i.e.:

X(t) = A sin (2π t/T)

The variance of this periodical function over a full period,i.e. from t = 0 to t = 2πT is:

Var[X(t)] = A2/2

Similarly, the variogram can be calculated directly over afull period to:

Gam[h] = A2/2 (1 - cos(2π h/T))which corresponds to the co-variance function:

Cov[h] = Var[X(t)J - Gam[h]= A

2/2 - A

2/2 (1 - cos(2π h/T))

=A2/2cos(2π h/T)

Obviously, for the case of a periodical variation X(t) withperiod T, the co-variance is also a periodic function with thesame period simply because X(t)=X(t+T) .

Let the amount of material seen by the reclaimer be Ptons represented in N layers, and let the period Tand lag hbe measured in tons.

Each layer contains P/W tons of material. Although ev-ery layer is not represented with exactly the same weightfraction when a pile stacked according to the continuousChevron method is reclaimed, it is a good approximationand will be used below to simplify the analysis, i.e. all layersin the reclaimed material are represented with the weightfraction 1/N . The lag between each layer will then be P/Ntons. The co-variance contributions from all layers in thepile must be summarised in order to calculate the variancein the reclaimed material. The lag between all pairs of lay-ers can be summarised as follows:

When this is used in the expression for the variance of thereclaimed material, the following result is obtained:

Var(Xou t

) = A2/2N

+ (A2/N2) (N-1) cos(2π P/N/T)+ (A2/N2) (N-2) cos(2π2P/N/T)••+ (A2/N2) 2 cos(2π (N-2)P/N/T)+ (A2/N2) cos(2π (N-1)P/N/T)

or in the general form:

which corresponds to a blending effect of:

The quantity (P/T) is actually the number of periods repre-sented in the material seen by the reclaimer. Evaluations ofthis expression for 100, 200 and 400 layers seen by thereclaimer have demonstrated that the number of layers hasno significant influence on the blending effect. The resultsof these evaluations have therefore been represented by asingle curve in Figure 1. The ratio P/T (the number of peri-ods seen by the reclaimer) must be larger than 3 in order toobtain a blending effect of 10:1 of periodical variations in apile involving moving average.

Figure 1. Blending of periodical variations in a store Involvingmoving average.

Variations with a co-variation within a quantity rangeIn connection with blending beds involving a moving aver-age - typically a circular store stacked according to the con-tinuous Chevron method - special attention much be givento slow variations in the composition of the piled material.

Very often the material stacked in a pile originates fromthe same front in a quarry. It is therefore to be expected thatthere exists a similarity in composition within a quantity range.The composition of the stacked material will be very similarwhen samples with a small lag are considered, whereas thecomposition will be completely different when samples withlarger lags are considered. In other words, the co-variancewill decline from a large value to zero over a material quantity.

Various variogram functions have been introduced todescribe this phenomenon. In geostatistics the so-calledspherical variogram model is widely used.It has the following form:


Leg (t) Number of layer pairs

P/N (N-1)2 P/N (N-2)3 P/N (N-3)

- -- -

(N-2) P/N 2(N-1) P/N 1

In this summation only co-variance contributions greater than0 have to be summed, i.e. we only have to sum over thelayers N/a where:

andNa=N(a/P) When a < P andNa=N When a > P

The general formula becomes:

If we disregard the fundamental sampling error, i.e. theNugget effect, this corresponds to a blending effect of:

Figure 3 shows results from evaluating this expression for100,200 and 400 layers seen by the reclaimer. The number oflayers has no significant influence on the blending effect andthe results have been represented by a single curve. It can beconcluded that the range of co-variance to material seen byreclaimer ratio (a/P) has a strong decreasing influence on theblending obtained and clearly demonstrates that storesinvolving the moving average concept are susceptible to slowvariations in material composition.

Figure 3. Blending of material with a co-variation within aquantity range in store involving moving average.

The sample size effectFrom the above analysis it is obvious that the variation patternof the material to be blended plays a significant role inconnection with type selection of the store type.

However, where a blending guarantee is to be fulfilled onthe basis of sampling prior to and after the store, variation inchemical composition within the particles also plays a role. Thiscan be demonstrated by two different sampling methods of theout-going material from a store. The material had a particle topsize of approximately 30 mm. In the first sampling every sampleof reclaimed material consisted of 5 increments of 50 kg each,giving a total sample size of 250 kg. This sample method gavean out-going standard deviation of 1.04 % CaO. In the secondmethod every sample of the reclaimed material consisted of 3increments of 135 kg giving a total sample size of 405 kg. Thisgave an out-going standard deviation of 0.56 % CaO, wherethe standard deviations have been corrected for analytical andpreparational errors. The difference in results demonstrates theimportance of sample size on standard deviation.

This effect of sample size on the resultant standarddeviation is analysed comprehensively by means of the

Figure 2. General spherical variogram function.

Gam[h] = C ( 3h/2a - h3/2a3 ) + C0 when h < a andGam[h] = C + C0 when h > a

The parameters involved have names:

C + C0 is the Sill which corresponds to the overall variance.C0 is the Nugget effect. It corresponds to the variance

that can be found among samples taken at the samespot. It contains the fundamental sampling error orthe composition heterogeneity discussed later.

a is the composition range from a high degree ofsimilarity to none at all.

The corresponding co-variance function becomes:Cov[h] = C (1 - 3h/2a - h3/2a3) when h<a andCov[h] = 0 when h>a

This also demonstrates that the range in the sphericalvariogram corresponds to the material quantity where theco-variance drops from full value to zero.

In order to calculate the variance for the reclaimed materialfor the case where the compositional variation of stacked ma-terial corresponds to a spherical variogram, a similar exerciseto that for evaluating periodical variation has to be carried out.

Let the amount of material seen by the reclaimer be P tonsrepresented in N layers, and let the range a and lag h be mea-sured in tons. Every layer contains P/N tons of material. Alllayers are represented in the reclaimed material by the weightfraction 1/N. The lag between each layer will then be P/N tons.

The co-variance contributions between all layers seen bythe reclaimer must be summarised in order to calculate thevariance in the reclaimed material. The lag between all pairsof layers can be summarised as follows:

When this is used in the expression for the variance of thereclaimed material, the following result is obtained:Var[X

out] = C/N

+ 2C/N2 ( N-1) (1-3 P/2N/a - P3W/a3 )

+ 2C/N2 (N-2) ( 1 - 3 P 2/2N/a - 2 P3/W/a3 )

+ 2C/N2 ( 1 - 3 P (N-1)/2N/a - (N-1) P3/W/a3 )

Leg (t) Number of layer pairs

P/N (N-1)2 P/N (N-2)3 P/N (N-3)

- -- -

(N-2) P/N 2(N-1) P/N 1


Gam

(a/h

)

(a/h)

Ble

ndin

g ef

fect

H

a/p ratio

Visman sampling model. This model involves splitting upthe total variance obtained in a sampling scheme into thefollowing contributions:

Where :var(t) = total variancevar(c) = compositional variance of 1 kg incrementvar(d) = distribution variancevar(pa) = variance of analysis and preparation∆m = mass of increments in sampling schemen = number of increments per sample

The Visman sampling model thus divides the total varianceinto three terms:1. Variance due to the composition heterogeneity which is

caused by the difference in composition within particles.This contribution cannot be reduced by mixing but it is ofcourse affected by grinding. Composition heterogeneityis dependent on sample mass.

2. Variance due to the distribution heterogeneity caused bythe manner in which the particles of all compositions aredistributed. This contribution is independent of samplemass. Mixing reduces distribution heterogeneity.

3. Variance due to analysis and preparation errors.The variance due to analysis and preparation errors can bedetermined from the results of double determinations inanalysis and preparation; this leaves the two first terms to bedetermined - composition homogeneity and distributionheterogeneity.

The parameters var(c) and var(d) can be determined byusing two sampling schemes with different increment massand, eventually, a different number of increments per sample,giving the following data:

Which gives the following simultaneous equations:

With the solution:

The two tests above exactly fit this concept. The data obtainedis as follows:

Sampling Increment Number of Correctedmethod mass increments total

(kg) variance

1 ∆m1 n1 Var1 (t)2 ∆m2 n2 Var2 (t)

Sampling Increment Number of Corrected totalmethod mass increments variance

(kg) (% CaO)2

1 50 5 1.042=1.082 135 3 1.562=0.32

This gives the following results when the above equations aresolved:Composition heterogeneity : var(c) = 354.7 [ (%CaO)2 kg ]Distribution heterogeneity : var(d)=-1.67 [(%CaO)2 ]Obviously the composition heterogeneity which actuallyoriginates from the differences in composition within theparticles dominates. This term represents an effect that thestore cannot, and is not supposed to do anything about. Thesmall negative value for the distribution heterogeneity is merelyan indication that this term has been completely eliminated (itmight as well have been zero but for numerical reasons theexact value zero is not obtained). The distributionheterogeneity is an effect that the store should certainly beable to reduce and this has actually been achieved.

It is worthwhile considering what composition heterogeneityinvolves. This is easily done using P. Gy’s analysis of thefundamental sampling error.

The following quantities for the material in question aredefined:g = size range factor (normally 0.25 according to Gy)f = particle shape factor (normally 0.5 according to

Gy)λ = particle density [kg/m3]var(par) = compositional variance within particles [%CaO2]d = particle top size [m]The following quantities can then be expressed as follows:fd 3 = volume of one top size particle [m3]gfd 3 = volume of one average size particle [m3]λgfd 3 = mass of one average size particle [kg]

A sample of masszim ∆m n [kg] will then contain thenumber (∆m n)/(λ g f d3) particles. From very basic statisticalconcepts it is obvious that when a sample that comprises asingle particle has the variance var(par), the variance of asample that contains (∆m n)/(λgfd3) particles will have thevariance ( λ g f d3 var(par))/(∆m n) i.e.:

This demonstrates that composition heterogeneity will be directlyproportional to material density and to particle top size raised tothe 3rd power (i.e. the top size particle volume). The consequenceof this relationship is that sample mass should be chosen suchthat it is proportional to the particle top size raised to the 3rd power.The test results above indicate that a sample mass of the order of400 kg is necessary with a material of top size 30 mm. However,with material for vertical mill feed where a top size of 100 mm iscommon, a sample mass of the order of 14 000 kg would beneeded, which is obviously totally impractical for a test. Althoughthis effect of particle size will vanish in the subsequent grindingprocess, it does indicate that there is no need to run a stockpilewith an extremely high number of layers.

BibliographyCONRADSEN, K. En Introduktion til Statistic IMSOR 1976, Chap. 0(Danish text).DAVIES, O.L. Statistical Methods in Research and Production, OliverBoyd,London,1961DAVID, M. Geostatical Ore Reserve Estimation, Elsevier, Amsterdam,1979.MERKS, J.W. Sampling and Weighing of Bulk Solids, Series onBulkMaterials Handling, Vol.4 (1985), Chap. 5.


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TURKEYF.L.Smidth & Co. A/S.Liaison Officec/o TrakmakTraktörve Makine Ticaret Ltd. SirketiIsmet Inönü Cad.Mithat Pasa Han. 92-9480090 Gümüssuyu, IstanbulTelephone: +90-212-251-13-31Direct line: +90-212-251-51-65Telefax: +90-212-251-62-82

UNITED KINGDOMF.L.SMIDTH - FULLER LTD.17, Lansdowne RoadCroydon, CR9 2JTTelegrams: folasmidthTelex: 264021 fiscro gTelephone: +44-81-686-2422Telefax: +44-81-681-7229

LICENSEES/JOINT VENTURES:FRANCEAMECO S.A.Rue Gutenberg - Z.I.F-68170 RixheimTelex: 881892 ameco fTelephone: +33-89 65 5211Telefax: +33-89 65 56 24

USAAMECO North AmericaP.O. Box 200183869 Griffin RoadCartersville, GA 30120Telex: 881-892Telephone: +1-404-336-5030Telefax: +1-404-336-5400

INDIALarsen &Toubro Ltd.(Licensee)Cement Machinery DivisionPowai WorksP.O. Box 8901Bombay 400072Telegrams: powaiworksTelex: 117-1698 Itgw in 117-1693 Itpw inTelephone: +91-22-5781401Telefax:+91-22-5783437

FULLER-K.C.P. LTD.(Joint Venture)Ramakrishna BuildingVictoria Crescent RoadMadras 600105Telex: fkay in 41-7596Telephone: +91-44-8276030 +91-44-8276343 +91-44-8272121Telefax: +91-44-8279393

FLS AUTOMATION:

DENMARKFLS Automation A/SHøffdingsvej 77DK-2500ValbyCopenhagenTelex: 16416 fisad dkTelephone: +45-3618 2700Telefax:+45-3618 27 99

Jawo Handling ApSEgelund A 20P.O. Box 46DK-6200 AabenraaTelephone: +45-74 62 64 36Telefax:+45-74 62 0136

FRANCEFLS Automation S.A.2/4 rue Vincent van GoghF-93364 Neuilly-Plaisance CédexTelex: 233597Telephone: +33-1-4944-6800Telefax: +33-1-4308-5099

+33-1-4308-5188

SPAINFLS Automation España, S.A.Edificio F. L.SmidthCarretera de la Coruña, km. 17,8E-28230 Las Rozas (Madrid)Telephone: +34-1-636-03-70Telefax: +34-1-636-02-45

USAFLS Automation Inc.309 International CircleSuite 140Hunt ValleyMD 21030Telephone: +1-410-771-0850Telefax: +1-410-771-9062

FLS-FULLER BULK HANDLING:

USAFuller-Kovako Corporation2158 Avenue CBethlehem, Pennsylvania18017-2188Telex: 173189Telephone: +1-610-264-6055Telefax: +1-610-264-6735

Kemutec Inc. (USA)130 Wharton RoadKeystone Industrial ParkBristol, PA 19007Telephone: +1-215-788-8013Telefax: +1-215-788-5113

HONG KONGFuller-Kovako Asia Limited 15A, Towerl.Tern Centre 237 Queen’s Roda CentralHong KongTelephone: +852 8051119Telefax:+852 8540858

NETHERLANDSFuller-Kovako BVP.O. Box 22396 HG Koudekerk aan den RijnTelephone: +311714-19101Telefax: +311714-15851

SWEDENH.W. Carlsen ABCarl Gustafs vag 46S-21421 MalrnoTelex: 33380 Carlsen STelephone: +46-40-922230Telefax:+46-40-922231

UNITED KINGDOMKemutec Group Ltd.Hulley RoadHurdsfield Industrial EstateMacclesfieldCheshire SK10 2NDTelephone: +44 625 42 87 33Telefax:+44 625 42 7319

Braby-Fuller Ltd.Hulley RoadHurdsfield Industrial EstateMacclesfieldCheshire SK10 2NDTelephone: +44 625 50 39 06Telefax:+44 625 42 7319

Kemutec Group Ltd.Manufacturing FacilityCumberland House,Marsh RoadBristol BS3 2NATelephone: +44 272 66 40 41Telefax:+44 272 2314 45

Kemutec Group Ltd.Manufacturing FacilityMiddlewaySt BlazeyParCornwall PL24 2JUTelephone:+44 726 8122 01Telefax:+44 726 8129 22

VENTOMATIC:

Export sales office SWITZERLANDVentomatic SAVia Carlo Pasta 3/aPal. CesarinoCH-6850 MendrisioTelephone: +4191-46 88 58 / 59Telefax:+4191-46 59 81

ITALYCAR-Ventomatic SpAViaG.Marconi.20Valbrembo BergamoPostal address:P.O.Box 1431-24100 BergamoTelex: 300578Telephone: +3935-468311Telefax:+39 35-460 838

Documents

Review No. 110