Variography applied as a tool to monitor metallurgy. … · y Compañía Limitada, Consultores en Calidad, muestreo y Control de Procesos, Chile ... favour Merril Crowe over carbon,

VARIOGRAPHY APPLIED AS A TOOL TO MONITOR METALLURGY 73

IntroductionThe use of Variography in chronostatistics has been shownby Pitard2. When we look at the total estimation error wesummarize it as follows:

[1]

The first part of the equation is well known and used, atthe central limit theorem (CLT). Secondly, covariances, isused in chronostatistics studies or variographic analysis.There is strong evidence that covariances are not zero andthat is the main reason to take this tool to interpret andoptimize processes.

As a routine basis, data is collected at regular timeintervals in any industrial process. Usually, informationcollected represents an 8 or 12 hours period, or shifts. Wecan handle this data to evaluate our process, taking care thatthey are homogeneous, and no important changes have beenapplied to the process in the way it works.

Calculating a variogram Let us agree in a nomenclature to write our data: Each ofthe collected values is ai.

The natural way to compare two values of a variablemeasured at regular times in a process is to measure theirdifference d:

d = a1 – a2 [2]In a set of data we are interested in the average difference

between many measurements N a given interval j apart

[3]

It is well known that such difference converges towardzero. To avoid this inconvenience the squared differencesshould be used instead. The average squared difference isdivided by 2. The averaged squared differences representan absolute semi-variogram which is written as follows:

[4]

A relative, dimensionless semi variogram can becalculated as well, making it easier to compare variogramsfrom different experiments, simply dividing by the squaredaverage content of the lot a2

L:

[5]

In order to accomplish all calculations required, in aneasy way, an existing software was used: effectivemanagement of process variability (EMPV). This softwareis friendly to use, as no programming is required.

TELLO, A. Variography applied as a tool to monitor metallurgy. EMPV software application to gold and silver recovery. Fourth World Conference onSampling & Blending, The Southern African Institute of Mining and Metallurgy, 2009.

Variography applied as a tool to monitor metallurgy. EMPVsoftware application to gold and silver recovery

A. TELLO y Compañía Limitada, Consultores en Calidad, muestreo y Control de Procesos, Chile

Variography was introduced by Dr. Pierre Gy to monitor a process, in the sixties. Later on,Francis Pitard extended this concept, building a complete system of variographic controls fordifferent applications. Nevertheless, the existence of information about its use as a way toeffectively control plants has been limited. There are infinite areas where variography andchronostatistics can be used. In this paper, two different cases related to gold and silver recovery,through well known but complex metallurgical routes are studied. The use of effectivemanagement of process variability software (EMPV) has shown to be a suitable solution to clarifyproblems at the plant and, consequently, a solution to the encountered problems has beenproposed. Chronostatistics is like opening a new world to the metallurgist, making the processvariability speak in a more comprehensive and in depth way.

Once the ore has been extracted from the mine, sampling is necessary at each sequence of themetallurgical process involved. As a first example, leaching of the ore with cyanide in agitatedtanks is another case of a complex metallurgy. The aim of the process is to know about residualvalues in the tailings in order to optimize process.

As a second example, leaching of gold and silver in ore heaps, has to be optimized in terms oftime, reagents consumption and, of course, in predicting a reasonable recovery. This last issueappears to be crucial. After cyanide leaching at the heaps, a carbon in columns process isinvolved, where there are a series of carbon loaded columns that are submitted to a dynamicprocess of load and unload, to finally deliver an enriched solution to the precious metal electrowinning plant.

In both cases, variography has been a good approach to show metallurgists ways to improve theoperation.

Paper 02:text 10/7/09 1:33 PM Page 73

FOURTH WORLD CONFERENCE ON SAMPLING & BLENDING74

Gold and silver recoveryThe Zinc cementation process has been used extensively inthe gold mining industry for more than 100 years. Theprocess is very efficient and relatively low cost, and stillproduces favourable economics versus carbon basedprocess in a number of applications.

Carbon based processes ( CIP, CIL, CIC) have assumed adominant role in the last 30 years and account for more than70% of annual production today.

The economics of treating high grade solutions(particularly those containing high silver concentration)favour Merril Crowe over carbon, because of the relativelyhigh capital and operating cost to elute and regeneratecarbon.

The economics of treating large volumes of low gradesolution or pulp strongly favor Carbon over Merril Crowebecause of the high cost of solid liquid separationclarification. This allowed lower cut off ore grades to beeconomically treated after the 1970s.

Overall, gold recovery is generally higher withcarbon/pulp based processes than MC because:

• Soluble gold and silver are lower, particularly with oresthat are difficult to filter or thicken

• There is additional leaching time in CIP• It is possible to overcome the weak preg-robbing

effects that occur in certain ore types.

Practical aspects of gold recovery at Kinross GoldCompanyKinross is an important and well known commercialCompany, which operates two plants for Gold recovery inChile. The first plant is Mantos de Oro, MDO and thesecond plant is Maricunga, CMM. Each of them applies oneof the two technologies presented above. It is interesting toknow that each of the processes has particular difficultiesand both of them can be optimized using a process controlcriteria, based on statistical studies by variography as thetool to show the key areas to improve.

Case Study #1: gold and silver recovery byagitated leaching followed by Merrill Crowe

cementationTypical flowsheet involves several stages:

• Ore stock pile coming from the mine• Crushing• Milling, sometimes cyanide addition starts here• Leaching in agitated tanks, air injection• Solid liquid Separation (CCD or Filtration). Tailings

collection after filter press process• Pregnant leach liquor goes to clarification • De-aeration in vacuum tower• Clarified solution is submitted to zinc addition (Merril

Crowe cementation)• Solid liquid separation by filtration. Liquid returned to

CCD stage• Solid goes to calcining• Smelting • Doré.

Process optimizationAs in any metallurgical process, the efficiency of the wholeprocess is measured by quantifying presence of values inthe tailings. In this case, after the stage where the pulp istreated in CCD; the solids undergo the filtration process infilter press, and tailings are sampled to check on the extent

of Gold and Silver dissolution by cyanide leaching.Sampling system actually used, consists of manual

sampling collecting grab samples from each of the filters,every 15 minutes to get a composite sample over the 12hours shift.

It is expected that tailings comply with specifications orwish list:

• US = Upper specification• TA = Targeted Average• LS = Lower Specification

Gold: statistical data analysis in tailingsThe following pages show information gathered in 2004 to2005, for grab sampling in tailings after filter press. Datacollected means 12 hours shifts. EMPV software allowsdisplaying data in graphics, showing histograms, controlcharts and Variograms.

Figure 1 shows data collected and wish list asspecifications.

Data distribution is important, as we can see real data andits behavior in terms of mode, on overall distribution.Figure 2 shows data distribution. We can see that mode(0.16) is different from average (0.19), probably becausethis average is affected by some extreme values, which iswhat usually happens when dealing with gold ores. It isimportant to note these extreme values and to evaluate howfrequently do they appear in the process.

A good explanation about the interpretation of avariogram can be found in a paper by A.G. Royle4, whoexplains this tool in a descriptive way. ‘In the Variogram,there is a range corresponding to the ‘range of influence’ ofthe variable, a well known concept that the variogram putson a rational and numerical basis. The variogram splits thetotal variance into two parts. One represents the spatialdifferences between the values of samples taken at pointsseparated by increasingly larger distances. The otherrepresents local or short range variances’.

In actual case, samples are taken a time-lag apart, but theconcept appearing in the variogram is the same as above:variance is split into two parts.

The local or random variance is called the ‘nugget’variance, while the larger scale one is the ‘spatial variance’.Thus, any assay measured in mineral deposits, or time-lagin a chronological study, exhibits a partly random variationand a partly spatial variation.

From variogram in Figure 3, we find the ‘spatialvariance’. Variance has a trend to increase reaching itsmaximum when J=14, or 7 days. Probably this is related tochange of shifts (people). We also detect a cycle with aboutsame period (6 days).

V(0) is the short range variance, or random variance,projected at J=0. Following Pitard5, this variance mainlyrepresents effects from sampling, sample preparation andchemical analysis. It is remarkable that if this variance isbig, there is no way of improving the process, as anymodification would be ‘masked’ by a high variance. In thiscase, V(0) is moderate, but even so, it should be minimized.

Table IWish List: gold and silver specifications in tailings

US TA LSAu (g/T) 0.3 0.2 0.1Ag(g/T) 25 15 9



In relative terms V(0) is 19.7% of the average content.From the variogram, we get control limits to be applied in

the chart. V(0) is a Variance; square root of V(0) is a

standard deviation, showing variability in the measurementstep. Control Limits are:

UCL = Average +3 times Square root of [V(0)]LCL = Average - 3 times Square root of [ V(0)]

Silver: statistical data analysis in tailingsFrom Figure 4 to Figure 7 we can see data analysis forsilver in tailings.

• Control chart is built by using square root of [V(0)]determined from variogram. This chart shows someevents where Ag goes higher, meaning that leachingwas not effective for the ore at that time

• Distribution chart shows that average and mode are alittle different also.

• Variogram shows the range where it is possible to find.

Figure 3. Absolute variogram, gold in tailings

Figure 2. Data distribution gold in tailings

Figure 1. Data control chart for gold in tailings

Table IIEMPV Report: Agitated Leaching Tailings Au

Relative AbsoluteV(0) 3,88E-02 1,38E-03 * (Au (ppm))^2V(0)^.5 1,97E-01 3,72E-02 * (Au (ppm))V[process j=1] 1,97E-02 7,02E-04 * (Au (ppm))^2V[process j=1]^.5 1,40E-01 2,65E-02 * (Au (ppm)) V[cyclic] 3,23E-02 1,15E-03 * (Au (ppm))^2V[cyclic]^.5 1,80E-01 3,39E-02 * (Au (ppm))



some correlation between samples, which appears to be18 shifts or 9 days.

V(0) is lower in comparison to V(J=1) considered asvariance of the process. This fact means that samplingvariance is relatively low in comparison to processvariability.

Overall conclusion to improve the processThe sampling system for gold and silver in tailings is thesame.

However, sampling variance for gold is higher thansampling variance for silver. This is a remarkableconclusion. Probably, gold distribution in the ore is moreheterogeneous than silver. Sampling variance for Gold can

be diminished if sample increments are bigger, andsampling system is flawless by design.

If the plant manager wants to increase gold recovery, heshould consider different heterogeneity for gold and silver.Variograms for gold and silver are able to determine V(0)separated from each other, allowing a clear screening ofsampling effect.

On the other hand, if sampling for gold is more difficult,due to heterogeneity in the ore, it is clear that a manualsystem will not allow a good control of tailings due toprobable segregation happening on the belt where manualsampling is performed.

As a recommendation, a complete automatic, samplingsystem should be installed.

Figure 6. Absolute variogram for Ag in tailings

Figure 5. Distribution of Ag in tailings

Figure 4. Data control chart for silver in tailings



Case Study #2: gold and silver recovery byactivated carbon in columns, followed by

electrowiningTypical flowsheet involves several stages:

• Ore stock pile coming from the mine• Crushing–(primary and secondary)• Crushing (tertiary, up to particle size suitable for heap

leaching) • Conditioning with lime• Heap Leaching by adding cyanide in solution• Solution pumping to absorption desorption refining

plant (ADR plant)• Valuable metals (Au and silver) are adsorbed in Carbon

in columns. Solution goes in counter current withcarbon in the columns.

• Loaded carbon is advanced to elution column• Loaded carbon is eluted. Downloaded carbon goes to

regeneration step.• Solution goes to EW cells

• Smelting • Doré

Mass Balance: Au in PLS transferred to adsorptiontrainsTo get a mass balance some concepts should be defined

Fixed parameters(Au)s0 = Gold concentration in feed (PLS)Fs = Flow of solutionFC = Flow of Carbon(Au)C0 = Gold concentration in eluted carbon

Design parameters(Au)sn = Gold concentration in barren alter stage n(Au)C1 = Gold concentration in loaded carbon

Variable parameters N = Number of stages(C) = Carbon tonnage in each stage

We may establish a mass balance equationMass balance Fs ([Au]s0 -[Au]s1) = FC ([Au]C1 - [Au]C2) [6]Equation [6] simply states that there should be a balance

for the gold transferred from solution (left side) into carbonin columns (right side).

Data analysis. Carbon columns at ADR plantTo calculate a balance, it is needed to know precision ofsampling systems at each of the trains existing in ADRplant.

ADR plant consists of three trains of carbon in column.Trains A and B are fed by same PLS solution, but samplingsystem at each train is independent. Train C is fed withintermediate solution. Barren solution is independent foreach train also.

As we do not have replicate sampling in an industrialplant, we need to know the effect of random variablesaffecting average content determined at each compositesample taken at each sampling point. The only way toaccomplish this is to run variograms with existing data,which give us a good picture of what is happening at thesampling point, and what is the contribution to total

Table III EMPV report agitated leaching tailings: Ag

Relative AbsoluteV(0) 5,62E-03 1,68 * (Ag (ppm))^2V(0)^.5 7,49E-02 1,30 * (Ag (ppm)) V[process j=1] 1,31E-02 3,93 * (Ag (ppm))^2V[process j=1]^.5 1,15E-01 1,98 * (Ag (ppm)) V[cyclic] 2,33E-02 6,96 * (Ag (ppm))^2V[cyclic]^.5 1,52E-01 2,64 * (Ag (ppm))

Figure 8. Relative variogram: feed train A

Figure 7. Diagram of different flows in balance



variance.If we run classic statistics of the data, calculating

averages, standard deviation and number of samples, wewill never know the effect of sampling in our data. Standarddeviations taken from traditional analysis account for thetotal variability and do not decompose variability into itscomponents.

Variability when feeding trains with rich solutionSampling systems at each of the trains is ‘almost’automatic. Solution is taken by introducing a wire at theflow exiting the column; each of the collected drops by thewire is received in an open recipient, that sometimesoverflows. If the system is controlled and supervised,avoiding overflow, the sample is good enough for processcontrol purposes. Variograms show this relatively goodsampling system, with low values for V(0).

Figures 8, 9 and 10 show the variograms obtained fromoperational data. It is remarkable that the shape ofvariograms in Trains A and B are very similar, because theyare fed with the same PLS solution.

Train C (Figure 10) shows a different shape. Each of thefigures is a relative variogram because it is easier tocompare relative results when looking at operational data.Anyway, the shape of the variograms is exactly the same

when dealing with absolute variograms. Table IV shows a summary of absolute and relative

parameters obtained from variographic analysis. In TableIV there is also a column explaining the term rV(0) whichis used in graphs in the next page. rV(0) is Square root ofV(0) or V(0)^.5.

Table V shows a global summary of classic statistics andvariographic statistics. We can see absolute parameters asaverage and standard deviation. We also find relativeparameters such as coefficient of variation. In the sametable, appears data obtained from variograms. Coefficientof variation is a relative measurement expressed as:

CV = Standard deviation / AverageIn Figures 11 and 12, we can see graphs of the

information presented in Tables IV and V. It is evident thatstandard deviation is considering total variances of thewhole set of data, while rV(0) is showing just the variabilityat the sampling point. In the same graph, we can comparethe three trains. The conclusion is that train C has morevariability at the sampling point than trains A and B.

Figure 12 shows relative comparisons, where coefficientof variation is used instead of standard deviation. As aconclusion in this analysis, we find that biggest samplingvariability in columns is given by Train C. Reducing thisvariability is an important task to perform, to get accurate

Figure 10. Relative variogram: feed train C

Figure 9. Relative variogram: feed train B



results from the balance of solutions, as final the result, isthe addition of the three trains.

Variability for Barren solution from trainsFigures 13, 14, and 15 show variograms from Barrensolutions, in trains A, B and C. Cyclic behaviour in train Ais evident. Every 2 shifts there is a change at the plant,where handling solutions increase recovery in each train.This situation is well known at the plant but is much moreevident when looking at the variograms. Train B is a little

different from A, but handling is the same. Train C has alonger cycle and every 6 shifts or three days solutions arehandled.

Data in Tables VI and VII show the data obtained fromV(0) at each of the variograms.

When comparing precision data it is evident trains A andB are with higher V(0) than train C. However, despite thisrelative high variation, absolute values are very low, with aminor incidence in the overall balance at the plant. As arecommendation, sampling system at trains A and B, should

Table IVVariogram data summary: gold fed to carbon columns

TRAIN EMPV report names Graph names Relative AbsoluteA V(0) 1,79E-03 3,22E-04 * (G/T AU)^2

V(0)^.5 rV(0) 4,23E-02 1,79E-02 * (G/T AU) Average 0,419(G/T AU)

B V(0) 1,35E-03 2,30E-04 * (G/T AU)^2V(0)^.5 rV(0) 3,67E-02 1,51E-02 * (G/T AU)

Average 0,416(G/T AU) C V(0) 3,07E-03 1,00E-04 * (G/T AU)^2

V(0)^.5 rV(0) 5,54E-02 1,00E-02 * (G/T AU) Average 0,172(G/T AU)

Table VComplete statistics summary. Gold fed to carbon columns

Au Au Au (PLS) (PLS) (Intermediate. solution.)

Train A B C Absolute Data parametersAverage (mg/L) 0,419 0,416 0,172Std. Deviation (mg/L) 0,041 0,037 0,024Absolute rV(0) 1,79E-02 1,51E-02 1,00E-02Absolute rV(p) 8,01E-03 8,07E-03 5,45E-03Absolute rV(res) 1,67E-02 1,63E-02 9,22E-03Relative Data ParametersCoefficient of Variation (CV) 0,10 0,09 0,14Relative rV(0) 4,23E-02 3,67E-02 5,54E-02Relative rV(p) 2,02E-02 1,88E-02 3,65E-02

Figure 11. Absolute dispersion: feed to trains of activated carbon in columns



Figure 12. Relative dispersion: feed to trains of activated carbon in columns

Figure 13. Variogram, barren solution train A

Figure 14. Variogram, barren solution train B



be improved as V(0) accounts for 26 and 24% of totalvariability at the sampling point.

Variability from loaded and downloaded carbonAs we already mentioned, a mass balance can be calculatedwith Equation [6]:

Fs ([Au]s0 -[Au]s1) = FC ([Au]C1 - [Au]C2) [6]Now it is the time to look at the right side of the equation:

balance with loaded and downloaded carbon.

Figure 16 shows absolute variogran for loaded carbon. Itis evident there is no splitting of variability between shortrange or random variability and long term or spatialvariability; this variogram is completely random, and V(0)is equal to total variability found. Table VIII is a summaryof classic and variographic statistics. In this table, it is seenthat coefficient of variation and relative rV(0) are about the

Figure 15. Variogram, barren solution train C

Table VIISummary statistics Barren solutions trains A, B, C

Au Barren Au Barren Au Barren Train A B C Absolute data parametersaAverage (mg/L) 0,025 0,022 0,029Std. Dev. (mg/L) 0,009 0,008 0,007Absolute rV(0) 6,57E-03 5,28E-03 2,20E-03Absolute rV(p) 2,70E-03 2,01E-03 3,59E-03Absolute rV(res) 2,88E-03 1,18E-03 4,73E-03Relative Data parametersCoefficient of Variation (CV) 0,36 0,35 0,24Relative rV(0) 2,58E-01 2,40E-01 7,59E-02Relative rV(p) 1,06E-01 9,14E-02 1,24E-01Relative rV(res) 1,13E-01 5,34E-02 1,63E-01

Table VIVariogram data summary: gold in barren from carbon columns

Relative AbsoluteTrain A V(0) 6,64E-02 4,31E-05 * (G/T AU)^2

V(0)^.5 2,58E-01 6,57E-03 * (G/T AU) Au Average Train 0,0255(G/T AU)

Train B V(0) 5,75E-02 2,78E-05 * (G/T AU)^2V(0)^.5 2,40E-01 5,28E-03 * (G/T AU)

Au Average Train 0,0220(G/T AU) Train C V(0) 5,77E-03 4,84E-06 * (G/T AU)^2

V(0)^.5 7,59E-02 2,20E-03 * (G/T AU) Au Average Train 0,029(G/T AU)

Figure 16. Variogram loaded carbon



same, showing that 100% of relative variability is random.The fact that variability in loaded carbon is completely

random, does not allow a good balance because of lack ofprecision.

Figure 17 shows a variogram of downloaded carbon. Thisvariogram presents marked cycles, and it is different fromloaded Carbon. V(0) is very high and implies that resultsare highly imprecise, and this situation confirms that carbonbalance is much more variable than solutions balance,where precision is in of the order of 4,5%.

As a Global conclusion, it can be recommended to trust inthe balance of solutions instead of using carbon in columnsto reach a balance.

ConclusionsThe two case studies, show the tremendous capability ofvariographic analysis to find areas of process optimization

Variographic analysis is an easy and well developedtechnique which, used in conjunction with a suitablesoftware such as EMPV, allows quick understanding of thekey points in a metallurgical process.

It is the author’s experience that variographic studieshave no limit to be used as an optimizing technique. Careshould be taken to respect natural limits of variogramsalready published by other authors. However, main featuresallow identification of at least two kind of variances;namely, short range variance or random variance, usuallyassociated to nugget effect, and long term or spatialvariability associated with the process itself and which isthe main variance to consider to learn from the process.

The advantage of chronostatistics is clear whenconsidering time as an important part of process control.

AcknowledgementThe author wishes to acknowledge the support andpermission to publish the results shown here to KINROSSCompany. This publication wouldn’t be a reality without itssupport.

References1. TELLO, A. y Compañía Ltda., Consultores en

Calidad, muestreo y Control de Procesos, VitalApoquindo 1380, Santiago, Chile, e-mail:[email protected]

2. PITARD, F. Chronostatistics, wcsb2

3. FLEMING, C., and WYSLOUZIL, B.W Workshop ofGold Ores, Lakefield Research 2000.

4. ROYLE, A.G. Why Statistics?, Geostatistics,McGraw-Hill, Inc., New York 1980, pp. 1–16.

5. PITARD, F. The in situ nugget effect: a majorcomponent of the random term of a Variogram, wcsb3Porto Alegre, 2007, pp. 91–110.

Figure 17. Absolute variogram: downloaded carbon

Table VIIISummary statistics, loaded and downloaded carbon

Loaded DownloadedCuenta 102 95promedio 1920 66desv std 454 73Absolute rV(0) 4,29E+02 3,98E+01Coefficient of Variation (CV) 2,36E-01 1,10E+00Relative rV(0) 2,18E-01 6,37E-01

Findings:Loaded

Relative AbsoluteV(0) 4,76E-02 1,84E+05 * (Au G/T)^2V(0)^.5 2,18E-01 4,29E+02 * (Au G/T) V[process j=1] 7,64E-03 1,98E+04 * (Au G/T)^2V[process j=1]^.5 8,74E-02 1,41E+02 * (Au G/T) V[resid] 8,83E-03 3,68E+04 * (Au G/T)^2V[resid]^.5 9,40E-02 1,92E+02 * (Au G/T)

Findings:Downloaded

Relative AbsoluteV(0) 4,05E-01 1,59E+03 * (Au G/T)^2V(0)^.5 6,37E-01 3,98E+01 * (Au G/T) V[process j=1] 8,83E-02 5,88E+02 * (Au G/T)^2V[process j=1]^.5 2,97E-01 2,42E+01 * (Au G/T) V[cyclic] 4,53E-01 2,04E+03 * (Au G/T)^2V[cyclic]^.5 6,73E-01 4,52E+01 * (Au G/T)



Alberto TelloManager, Alberto Tello, y Compa~nia Limitada

20 years at Mining and Metallurgy Research Center (CIMM in spanish), Chile.6 years as General manager at Cognis chemical products in South America (Solvent extraction formining purposes in South America).10 years as Consultant on sampling and process control. This work has been developed to mainmining Companies working in Chile, Peru and Venezuela. Among Others: Codelco, BHPB, AngloAmerica, Kinross, SQM, Antofagasta Minerals, Freeport Mac Moran, Aur Resources, etc.




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Variography applied as a tool to monitor metallurgy. … · y Compañía Limitada, Consultores en Calidad, muestreo y Control de Procesos, Chile ... favour Merril Crowe over carbon,