10.1.1.90.7867.pdf

4th International Mining Geology Conference Coolum, Qld, 14 17 May 2000 195

Mining Bench Height Evaluation for the Wallaby Resource A Conditional Simulation Case Study

I M Glacken1, M Nopp2 and M Titley3

ABSTRACT

A study on the feasibility of mining the recently discovered Wallaby gold deposit is due for completion by mid-2000. Open pit mining is the favoured method. Determination of the impact of mining bench height on the recovery of ore, including the estimation of dilution and ore loss, is critical to the economics of the operation.

Conditional simulation was used to derive a number of gold estimation scenarios within a typical volume of the deposit. These scenarios were interrogated for a selection of mining bench heights and ore block dimensions. The results were reported as a range of grade tonnage relationships and compared to the kriged resource model. This allowed the resource model to be calibrated to a specific mining bench height and ore block size. Once calibrated, more realistic dilution and ore loss values for a number of mining bench heights were calculated from the resource model. These values were then used to determine the economic sensitivity of particular mining methods.

The spread of results from the simulations also provided an indication of the confidence in the kriged grade estimates for the different zones of mineralisation within the deposit and highlighted areas of any significant uncertainty.

INTRODUCTION Wallaby is one of Australias largest gold discoveries in recent years. Two exploration tenements cover the deposit. The Granny Smith Joint Venture (Placer Dome Asia Pacific 60 per cent and Delta Gold Ltd 40 per cent) (GSJV) holds Wallaby, which is situated within the southern lease and includes the majority of the resource. Homestake Gold of Australia Ltd holds Just In Case which is in the northern lease. The Wallaby Mineral Resource (Indicated and Inferred) as at 31 December 1999 was 52 million tonnes at 2.7 g/t for 4.5 million ounces of gold at a 1.0 g/t cut-off. The GSJV is completing an open pit mining feasibility study that is due for completion around June 2000.

The nature of gold mineralisation in a deposit determines the dilution (waste mixed with ore) and ore loss (ore lost to waste) for different mining block sizes, referred to hereafter as the selective mining unit (SMU). A feasibility study must optimise the economic benefits gained from using larger ore mining equipment, hence larger SMUs, against the potential loss of revenue due to dilution and ore loss.

Conditional simulation is a tool which will generate a number of equally-likely images of the interpolated data. Importantly, simulation honours the statistical distribution of the input data. This differs to other estimation techniques which usually produce a single output image with a smoother statistical distribution than that of the input data, particularly when the spacing of the input data (drill holes) is much larger than the SMU. This smoothed model does not adequately represent the actual grade tonnage relationship of the deposit, and so cannot be used to determine the impact of different SMU sizes. By deriving a number of gold estimation scenarios using conditional simulation, a range of possible grade tonnage relationships for a given SMU can be

1. FAusIMM, Snowden Mining Industry Consultants, PO Box 77, West Perth WA 6872

2 MAusIMM, Snowden Mining Industry Consultants, PO Box 77, West Perth WA 6872

3 MAusIMM, Placer Granny Smith, PO Box 33, Laverton WA 6440

calculated. These simulated models can then be compared to the resource estimate and used to calculate more realistic dilution and ore loss values to assist in determining the economic sensitivity of a particular mining method.

Time constraints on the study meant that the entire model area could not be simulated, so a representative volume of the resource was selected. To ensure that the results can be used in the feasibility study, the kriged resource model was calibrated to a specific SMU, and adjustment factors provided for alternative SMUs.

The spread of results from the best, median and worst simulations also provide an indication of the confidence of the kriged grade estimates for the different zones of mineralisation within the deposit and highlights areas of significant uncertainty.

THE WALLABY DEPOSIT

Background

Wallaby is located in the North Eastern Goldfields region of Western Australia, approximately 27 km south-southwest of Laverton and 11 km southwest of the Granny Smith Mine, at latitude 2851S, longitude 12219E (Figure 1). The deposit lies on the northeastern shore of Lake Carey, which is a large salt lake. The discovery history is complex and has been published in Nielsen and Currie (1999).

FIG 1 Wallaby deposit location plan.

Recent exploration history

The GSJV commenced fieldwork at Wallaby during November 1997. The program comprised reconnaissance aircore drilling. Follow-up drilling in June 1998 confirmed continuity of grade between the initial anomalies. Reverse Circulation drilling began later that month but had difficulty penetrating the thick water-saturated lacustrine clays. A combination of aircore pre-collars with diamond tails proved to be the most cost

I M GLACKEN, M NOPP and M TITLEY

196 Coolum, Qld, 14 17 May 2000 4th International Mining Geology Conference

effective method of drilling. By December 1998, 65 holes for a total 22 500 m were completed on 100 m centres. This drilling broadly outlined the lateral limits of the deposit. An inferred resource of 30 Mt at 2.4 g/t for 2.3 Moz was reported at a cut-off of 1.0 g/t.

Drilling continued through 1999, concentrating on; infill to increase grade confidence, determination of open pit mining limits, improving geological understanding, collection of core for metallurgical testwork, de-watering pump tests and geotechnical evaluation.

Project status An open pit mining feasibility study is due for completion around June 2000. The current combined Indicated and Inferred Mineral Resource is 52 Mt at 2.7 g/t for 4.5 Moz gold at a 1.0 g/t cut-off. The potential open pit mine covers an area of 1300 m/NS x 100 mMEW x 300 m vertical.

A program of diamond drill holes is being completed to test extensions to the Wallaby mineralisation at depths down to 1000 m below the surface. Preliminary exploration of possible southern extensions of the mineralisation system beneath the Lake Carey sediments is on-going.

Regional geology of Wallaby

The Wallaby deposit is located within the Eastern Goldfields Province of the Archaean Yilgarn granite-greenstone terrain of Western Australia. The geology within this zone has been divided into two associations; association 1, comprising mafics, ultramafics and banded iron formations, and association 2, comprising andesitic volcanics and volcaniclastics interbedded with mafic volcanics and overlain by clastic and chemical sediments. Association 2 occurs in the western and eastern parts of the district, while association 1 occurs in a north-south corridor through the central part of the Laverton area. Wallaby occurs within association 1 and is located on the eastern flank of the Mt Margaret Anticline. Figure 2 shows the location of Wallaby and the regional geology around the Laverton area.

Deposit geology

The Wallaby deposit is covered by 1 to 20 m of aeolian dune sands and between 24 to 120 m of Tertiary lake clays and sands. This transported cover is shallowest on the eastern margin and steadily thickens to the west. A deep regional palaeochannel trending south-southeast runs through the western side of the Wallaby deposit. No economic gold mineralisation is hosted in the transported cover.

Oxide saprolitic material occurs mainly in the eastern part of the deposit. Saprolitic material in the west has been mostly stripped by the palaeochannel. Approximately ten per cent of the gold in the wallaby deposit is in oxide material.

The host rock at Wallaby is an Archaean matrix-supported polymict conglomerate. The dominant clast type is mafic volcanics. Other clast types include felsic porphyries, sediments (mostly banded iron formations and cherts), and carbonate and quartz clasts. The conglomerate is predominantly massive, although occasional graded bedding, grit beds and clast alignment indicate the unit is upright and has a dip of around 45 to the south east. The conglomerate has been metamorphosed to upper greenschist facies.

Two north-south trending subvertical dyke swarms have intruded the conglomerate. The dykes represent a fractionated alkali syenite suite and range in composition from various monzonites through syenites, to carbonatitic syenites and a carbonatite. A number of the more alkali-rich fractionates have been emplaced as sills within the shear structures. These generally have an east-west orientation and southerly dip.

FIG 2 Wallaby deposit regional geology.

Mineralisation occurred after the emplacement of the felsic and alkali intrusives but prior to the emplacement of the carbonatitic fractionate. Figure 3 shows the geology in schematic section.

Structure, mineralisation and alteration

Mineralisation occurs along shears formed during a dominant top block north to north east thrust regime. The shear zones display limited shear foliation. This is due to the ability of the host conglomerate to absorb large amounts of strain with limited physical deformation. The main shears are relatively flat lying, with a gross gentle dip towards the south east. Lower grade mineralisation is associated with steeper on echelon linkage structures, with a dominant dip to the north east. The shear zones are defined more by alteration than foliation, and range in size from 1 to 40 m.

The alteration at Wallaby can be classified as an inner, intermediate, or outer halo.

The inner halo defines the dominant ore-zones and is a dolomite-albite-pyrite-chalcopyrite and gold assemblage. It is bleached, lacks a significant magnetic response, and primary textures are often obliterated. Small amounts of visible gold occur in small, late-stage quartz/carbonate veins. Gold is closely related to pyrite content. The highest grades tend to be related to abundant fine pyrite. Mineralisation behaves differently in the intrusives than in the conglomerate, with the grades tending to be lower in the intrusives.

The intermediate halo comprises biotite, pyrite, magnetite and chalcopyrite. It is dark green to brownish grey and may have a significant magnetic response. This alteration is derived from the same fluids as the inner zone but with a lower fluid to rock ratio. A petrological study of the magnetite shows magnetite and pyrite are in textural equilibrium throughout the deposit at all scales. This implies they formed at the same time.

MINING BENCH HEIGHT EVALUATION FOR THE WALLABY RESOURCE


FIG 3 Wallaby deposit: schematic east-west section regolith and geology.

The outer halo is generally unmineralised conglomerate. It is split into a chlorite-albite assemblage and an actinolite-magnetite-pyrite alteration. The actinolite assemblage has a significant magnetic response and is the distal alteration from the mineralising fluid. The chlorite-albite assemblage is from the regional upper greenschist facies metamorphism.

Description of mineralisation zones

There are two main flat lying ore-zones, termed 50 and 60, which are separated by about 100 to 150 m. These zones range in thickness from 5 to 35 m. Ore-zone 40 is thought to be a flat lying above ore-zone 50, but is almost entirely in oxide and is not as well constrained as the other ore-zones.

The north east dipping ore-zones, 240 and 250, lie above and below ore-zone 50 respectively. Ore-zone 240 is well constrained, is very strongly mineralised, and ranges in thickness from 3 to 25 m. Ore-zone 250 comprises a series of stacked northeast dipping structures which cannot be easily correlated between holes. There is structural evidence indicating that parts of ore-zone 250 flatten, and in some cases dip to the south. Ore-zone 250 is not well constrained and has the lowest grades. The individual ore-zone 250 structures range in thickness from 2 to 7 m.

Ore-zone 70 lies directly below ore-zone 60 and being the deepest, is not well defined by drilling. The current interpretation ore ore-zone 70 is a series of gently northeast dipping stacked planar zones. The stacking suggests it may be similar to ore-zone 250 but with areas of better grade continuity.

The ore-zones cross intrusive/conglomerate boundaries with little change in geometry. There is a subtle increase in gold dispersion through the felsic intrusives, especially for the very low gold values. Figures 4 and 5 show the ore-zones in schematic north-south and east-west section.

RESOURCE ESTIMATION Solid 3D triangulations representing the major mineralised ore-zones were created. Mineralised ore-zones were based on a structural model and defined by alteration, depleted magnetic susceptibility and a gold grade cut-off around 0.2 g/t. Ore-zone 250 consists of a number of small, poorly defined mineralisation zones that could not be adequately linked to form a homogeneous interpretation. The ore-zone lies between the base of ore-zone 50 and the top of ore-zone 60 and there is a relatively high proportion of unmineralised material included within this profile.

The geometry of the intrusives could not be interpreted in enough detail to create a solid wireframe, as it is not uncommon for a drill hole to intersect intrusives having a thickness greater than 100 m while surrounding holes may not contain any intrusives greater than 1 m thick. Also, the majority of the intrusives are unrooted, ie drilling continued through them and back into conglomerate. The geometry of the intrusives is an important issue as the intrusives have a different gold grade distribution. An intrusive lithology code was assigned to samples from the geology logs. This code was initially used for statistical analysis and then later, during block model construction, to estimate the proportion of intrusive material in a model block.

Drill hole samples were assigned weathering, lithology and ore-zone codes, by using the wireframe models and logging codes. The three codes were combined into a single unique open pit ore-zone code (OPDOM) representing the different combinations of codes. Two metre downhole composites were created for statistical analysis, variography and grade estimation. The 2 m composite length was selected as it provides the best resolution of the ore-zones geometry while minimising the mix of short and long composites. All composites were terminated on changes within the OPDOM code to ensure different materials were not mixed.



FIG 4 Wallaby deposit ore-zone geometry, east-west section.

FIG 5 Wallaby deposit ore-zone geometry, north-south section.



Statistical analysis and variographic analysis of the composites was completed, with the following significant conclusions: The grade of felsic intrusive hosted mineralisation needed to

be estimated independently of the conglomerate-hosted mineralisation, as it has a different grade distribution and different variogram parameters.

The alkali intrusive samples could be combined with the conglomerate samples for the following reasons: 1. The number of alkali intrusive samples within some

ore-zones is insignificant. 2. Where significant number of samples are available the

grade distribution is similar to the conglomerate. 3. The alkali intrusive geometry was difficult to model

separately and too few samples were available to use proportional indicator modelling. Thus, the conglomerate and alkali intrusive material were combined, and are referred to as conglomerate in the rest of the paper.

Hard mineralisation boundaries must be used to constrain the mineralisation within ore-zones. However, ore-zones that intersect each other (such as 240 and 50) may use samples from either ore-zone.

Ordinary Kriging with cutting would be suitable for grade estimation for the following reasons: 1. The variography study showed no spatial grade

anisotropy. That is, high-grades were not oriented differently to the lower grades.

2. The distributions within each ore-zone and lithology have a relatively low degree of skewness.

3. Only 0.1 per cent of high-grade composites required trimming.

4. Lack of geological evidence for the alignment of grades either high or low, in veins, shoots or any structures within the ore-zones.

The ore-zones have considerable local variation, so the average orientation does not give the best result for variography and grade estimation. This is especially relevant for ore-zones 50, 60 and 240 as their orientations are not consistent throughout the deposit. To avoid having to split these ore-zones into numerous smaller zones, the samples were unfolded for variography and an in-house anisotropic modelling package was used for the grade estimation. The Placer Open Pit software allows construction of an anisotropy model. The anisotropy model is a block model containing local azimuth, dip and plunges for each block. This local information is used as directions for the search and variogram calculations when performing grade estimations.

A geology block model was constructed using a constant 10 mN x 10 mE x 5 mRL block size. An OPDOM code was assigned from the relevant wireframe models. As an accurate geology model of the felsic intrusives could not be created, an indicator method was used. The proportion of felsic intrusive within each block was calculated using ordinary kriging of conditional 0 (absence of felsics in a sample) and 1 (felsic sample) indicators.

Both the conglomerate and felsic intrusive grades were estimated for each model block using ordinary kriging. A final average tonnage-weighted gold grade was calculated for each model block, based on the proportions of conglomerate and felsic intrusive within each block.

CONDITIONAL SIMULATION

Objectives of conditional simulation Conditional simulation is a technique which has developed as an alternative to estimation techniques such as polygons, inverse distance weighting, ordinary kriging or indicator kriging.

Simulation generates many equally likely scenarios, in contrast to estimation which provides one only. As the name implies, it uses the principles of Monte Carlo simulation, random number drawing from a specific distribution, while ensuring that the outcome is conditional to the input data and the geological model. In particular, each simulation honours the statistical distribution of input grades (the grade returned at any point where a data value exists is that data value) including the variability, as typified by the range, variance, or coefficient of variation. Each simulation also honours the spatial continuity of the raw data as represented in the variogram, and any other features of the geological model which have been built in.

Kriging, which is theoretically the most optimal estimation technique, also uses the spatial variability of the data to derive the weighting scheme for each unknown point to be informed, but the output kriged map does not preserve the variogram. In contrast to simulation, a single kriged estimate provides the minimum variance set of values. Each individual simulation, taken in isolation, is more variable than any one kriging estimate, but the ensemble of simulations (typically between 20 and 100 are generated), treated together, provide more information than kriging. Simulation preserves more characteristics of the input data than other estimation techniques; it also has the benefit of providing the risk dimension to resource evaluation studies that kriging cannot readily provide.

Although the principles of simulation in other fields have been known for decades, conditional simulation in the mining and petroleum fields has been practised for only 20 to 25 years, and it is only with the advent of fast, affordable computers and memory that practical simulation has been available to the mining industry. Good descriptions of simulation are provided in Goovaerts (1997), by Srivastava (1994), and in Chil and Delfiner (1999).

Applications of conditional simulation

The applications of conditional simulation in the mining industry fall into four broad categories:

Probability and confidence interval analysis In this field of application, the suite of simulations generated are used to provide indications of the range of likely outcomes. This involves ranking each individual simulation in some way average grade above a cut-off, maximum tonnage, or maximum metal and then tabulating or processing the extreme values. It is possible to generate a true probability or confidence interval around a median, mean, or any value using simulations for example, the 95 per cent grade and tonnage confidence interval around the cut-off at 1 g/t in a gold deposit, or the range of tonnage expected to be delivered to a plant from one bench of a nickel laterite deposit. Using this approach, the extreme cases can be further processed to yield best and worst outcomes, using such techniques as pit optimisation, underground stope optimisation, schedule analysis or cashflow forecasting. It is also possible using the suite of simulations to derive the probability of exceeding any particular key value, such as a cut-off grade or minimum level of contaminants. A case study of this type of approach is presented in Coombes et al (1998).

Optimisation

Optimisation of simulations takes the entire range of outcomes and produces a best result, which is optimal for a given set of known criteria. These criteria are often presented as a loss function, or more generally an economic function combining profit and loss components (Srivastava, 1987; Glacken, 1996). The typical application of optimisation of conditional simulation output is in grade control applications, whereby an optimal



dig-line is generated according to the balance of economic criteria applied in designating a block to either ore, waste, or one of a number of stockpiles. This approach has been explored by Shaw and Khosrowshahi (1997) and by Schofield (1998), and has been adopted in a number of available proprietary software systems.

Reblocking/Resampling

This application of conditional simulation takes one or several of a suite of simulations and treats that simulation as reality; in other words, a model of the phenomenon under study. This can be readily achieved as simulations do not smooth the data as with kriging, and also by the fact that it is possible to simulate into very small volumes (essentially nodes or points) without encountering conditional bias. The fine-scale simulations can be sampled to represent various grade control or drilling pattern, or also to represent production over a range of timeframes or production intervals. Another typical application is the analysis of a range of mining unit (SMU) sizes, which can easily be generated by reblocking or averaging of a fine-scale simulation, providing that the variable under study can be linearly averaged (which is certainly the case for most mining applications). It is this application of simulation which was used to investigate the range of bench heights at Wallaby; by simulating at a fine-scale, it was possible to aggregate the node values over a range of bench heights and then to investigate the ore loss and/or dilution relative to the kriged model. This was particularly important given the strong ore-zone control on mineralisation at Wallaby and the potential for more or less dilution at various mining scales.

Instead of reblocking a single simulation, a best and worst case scenario (actually the 5th and the 95th percentile of the simulations when ranked by average grade) were considered in order to assess the extra dimension of the uncertainty due to the risk in the overall grade.

Calibration of a resource model By comparing the selectivity of a resource model with that

of a similar kriged model, it is possible to assess the effective selectivity of the kriged model. This assumes that the simulation is a more accurate representation of reality than the kriged model, and given the accurate reproduction of statistical and spatial characteristics, coupled with the optimal change of support for simulation and lack of conditional bias, this should be the case. By comparing the simulation tonnage-grade curve with the kriging curve on a similar block size, it is possible to calibrate the kriged model (effectively increase or decrease the selectivity) to more accurately represent the likely mining conditions. This approach was also adopted in the Wallaby study.

DETAILS OF STUDY

Selection of test area

One downside of simulation is that it can be a fairly time-intensive technique as multiple realisations of very small blocks are required. Validation of the results can also be a lengthy exercise. It was therefore decided that the simulation should be carried out within a representative volume of the Wallaby orebody which was large enough to allow meaningful analysis of results, but also small enough to be completed in a reasonable time frame. The test volume was selected to include representative areas through the main ore zones in terms of grade and thickness, and also to allow sufficient vertical extent for the effects of dilution and ore loss to be modelled over a range of bench heights. A typical cross-section through the test area is shown in Figure 6.

FIG 6 East-west cross-section of the test area at 808 200 mN showing the arrangement of grade ore-zones.

Generation of conditional simulations The variography study established that the degree of rotation of anisotropy between the high- and low-grades was small. In other words, the continuity of the high-grades was not oriented particularly differently to the low-grades within any or all of the ore-zones. This information, together with the low degrees of skewness displayed by the data, led to the choice of sequential Gaussian as the simulation algorithm. This approach was further supported by the lack of geological evidence for strong connectivity of high-grades or low-grades; in other words, neither the high-grades nor the low-grades appear to be aligned in veins, shoots, or structures to any significant degree.

The use of sequential Gaussian necessitated the generation of normal scores variograms for the gold grades for both the conglomerate samples and the intrusive samples within each of the five ore-zones represented in the study area. The global data sets for the entire resource, composited to 2 m, were used for the variography. Care was taken to ensure that the directions of maximum continuity coincided both with the known structural directions and with those directions previously modelled in the traditional variography used for the kriged resource estimate. The variograms are characterised by low to moderate nugget variances (25 to 40 per cent of total variability) and overall ranges up to 100 m. The flat structures (ore-zones 50 and 60 show southerly strikes on the mineralisation, but the link structures (ore-zones 240 and 250) have primary directions of continuity which dip shallowly to the northeast.

Since the style of mineralisation in the intrusive suite is different to the conglomerate, these units were treated independently within each ore-zone. The grades within the conglomerate and intrusive suites were simulated separately and twenty simulations were produced for each of the five ore-zones within each suite, with the grades simulated into a fine grid of 2.5 mN x 2.5 mE x 2.5 mRL.

A block model of the spatial occurrence of the intrusive and conglomerate suites was created from the proportion of intrusive determined using categorical kriging (indicator kriging of the presence of absence of a single variable). To this end all composites within the extended area were coded to either one or zero depending on whether they were felsic intrusive or conglomerate. A variogram model based upon these indicator

FILTER Category

Background Rcode 50 Rcode 60 Rcode 240 Rcode 250



codes was modelled and used to estimate the proportion of intrusive material for each block using ordinary kriging, with a steeply orientated sample search.

All of the simulations for each ore type were validated by comparing the input data histograms with the output simulated values by ore-zone. Q-Q plots indicated very good correlation between the input data and the simulated values per ore-zone. In addition, spot checks on the variography showed good reproduction of variogram models, which are constrained by the wide spaced data.

The ordinary kriged proportion model was then used to weight the relative grades of conglomerate and intrusive when the simulations were merged using the following formula:

Simulated grade in block = proportion of intrusive x simulated intrusive grade + (1 proportion of intrusive) x

simulated conglomerate grade The densities are similar between the rock types (three per

cent difference) and, given the variability generated by the simulations, tonnage weighting of the grades was not considered to be necessary.

Each of the 20 simulations was merged in this way, and the average of all simulations after merging was also generated.

The merged density was allocated using the proportion of intrusive in a block and the density for pure intrusive and for pure conglomerate.

The simulation models were ranked according to the grade at zero cut-off, and the second lowest and second highest simulation models (effectively the 5th and the 95th percentile models) were selected to represent worst and best case scenarios respectively. The middle, or median, model was selected as a middle case scenario. Note that the ranking is based on the average grade at zero cu-toff over the entire test area, and not for any particular ore-zone, since ranking of individual ore-zones could cause unrealistically conservative worst case and overly optimistic upper case models, particularly when benches span boundaries between ore-zones.

As an additional validation, the mean grades and coefficient of variation (COV) per ore-zone for the input data and the median simulation, together with the means from the kriged resource model, are compared in Table 1. The median simulation data clearly honours the input data, while some of the kriged model results display more significant differences. Three 25 m spaced east-west sections through the test volume for the overall median simulation are shown in Figure 7. The simulation has been reblocked to 10 mE x 10 mN x 5 mRL.

FIG 7- Diagram of three 25 m spaced east-west cross-sections through the median simulation, reblocked to 10 mN x 10 mE x 5 mRL.

TABLE 1 Comparison of gold statistics: composites, simulation and kriged model.

2 m composites Median simulation Wallaby kriged model Ore-zone Mean COV Mean COV Mean

Ore-zone 0 0.11 2.609 0.11 2.609 0.25 Ore-zone 50 2.11 2.607 2.10 2.514 2.03 Ore-zone 60 1.66 1.325 1.66 1.316 1.53 Ore zone 240 2.69 1.284 2.69 1.269 2.83 Ore-zone 250 0.45 2.039 0.45 2.039 0.48



CALIBRATING THE RESOURCE MODEL One of the desirable outcomes from the simulation study was

the ability to investigate the selectivity of the kriged resource estimate. Because the simulations were generated at a fine-scale, and honoured both the statistical and spatial variability of the input composite data, when reblocked to the dimensions of the kriged estimate (ie 10 mN x 10 mE x 5 mRL) they provide a range of outcomes, each of which is free of conditional bias, and which can be used to look at the smoothness of the kriging.

The results for the overall study area, including all ore-zones, are shown in Figure 8. This shows that, overall, the kriged model sits within the range of the 10 mN x 10 mE x 5 mRL reblocked simulations.

However, when individual ore-zones within the simulations are compared with similar blocks in the kriged model, the results are different. Figure 9 shows the results for ore-zone 50, and Figure 10 shows the results for ore-zone 250. The ore-zone 50 results show that the grades for the reblocked simulation (10 mN x 10 mE x 5 mRL) and the kriged model at 0 g/t, respectively. However, the slopes and positions of the curves indicate that the kriged model for ore-zone 50 is oversmoothed, and probably represents the selectivity to be expected from blocks of at least 20 m x 20 m x 15 m. An explanation for the lower grade of the simulations reblocked to larger block sizes compared to the kriged model is that the reblocking includes the effect of boundary dilution with increasing bench height, whereas the kriged model does not.

The comparison of kriging results and various reblocked (median) simulations for ore-zone 250 show a different result (Figure 10). The grades for the reblocked simulation (10 mN z 10 mE x 5 mRL) and the kriged model at 0 g/t COG are similar, at 0.45 g/t and 0.48 g/t, respectively. As expected, an increase in simulation block size results in a general increase in tonnes and a decrease in grade. The decrease in grade is most dramatic for higher cut-offs in ore-zone 250. The implication is that it may be

difficult to achieve high-grades if large selective mining units are used. A large increase in tonnes with increasing block size is evident in ore-zone 250 for low cut-offs. This is to be expected form the volume-variance effect, and contrasts with a larger change in grade for increasing block size at the higher cut-offs. The slope and nature of the curves suggest that the kriged model for ore-zone 250 is insufficiently smoothed and represents the selectivity to be expected from blocks of less than 5 m x 5 m x 5 m. This is not generally expected from a kriged model, and an explanation may be found in the search and sample selection applied during the kriging.

Implications for kriging

The comparison of the reblocked simulations and the kriged model indicates that the kriged model performs reasonably well overall, with the degree of smoothing commensurate with blocks in the order of 5 mN x 5 mE x 5 mRL to 10 mN x 10 mE x 5 mRL. Based on this overall comparison, tonnage and grade factors were prepared relative to the 10 mN x 10 mE x 5 mRL reblocked simulation so as to report the grades and tonnages expected for a range of block size and bench height scenarios at a range of cut-off grades.

However, it is clear from the comparison of grade-tonnage curves for ore-zones 50 and 250 that there are differing degrees of smoothing per ore-zone in the kriged model, with the comparison for ore-zone 50 suggesting a moderate degree of smoothing and ore-zone 250, in contrast, very little smoothing. These differences are important since they highlight where the kriged model may be expected to under- or over-perform relative to the actual selectivity of the modelled block size. While it would be possible to factor the model to reflect the differing degrees of smoothing, a better approach would be that the kriging parameters first be examined to identify whether the necessary modifications can be effected by changing certain kriging parameters.

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FIG 10 Ore-zone 250 kriged model (in bold) and median simulations at various block sizes.



BENCH HEIGHT STUDY Tonnage and grade factors

The reblocked simulations were used to investigate the effects of using different bench heights for the proposed Wallaby pit. The results from the various reblocking exercises were presented relative to the 10 mN x 10 mE x 5 mRL reblocked simulation which has been compared to the kriged results above. The other simulations were presented as tonnage and grade factors for a range of cut-off grades. The results for ore-zones 50 and 250 are presented in Figures 11 to 14.

0.80

0.90

1.00

1.10

1.20

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6Cut-off Grade g/t

Fac

tor

5x5x5 5x5x10 10x10x7.5 10x10x1010x10x12.5 10x10x15 15x15x15

FIG 11 Tonnage factors for ore-zone 50 relative to 10 mN x 10 mE x 5 mRL blocks.

0.80

0.90

1.00

1.10

1.20

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6Cut-off Grade g/t

Fac

tor

5x5x5 5x5x10 10x10x7.5 10x10x10 10x10x12.510x10x15 15x15x15

FIG 12 Grade factors for ore-zone 50 relative to 10 mN x 10 mE 5 mRL blocks.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6Cut-off Grade g/t

Fac

tor

5x5x5 5x5x10 10x10x7.5 10x10x10 10x10x12.510x10x15 15x15x15

FIG 13 Tonnage factors for ore-zone 250 relative to 10 mN x 10 mE 5 mRL blocks.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6

Cut-off Grade g/t

Fact

or

5x5x5 5x5x10 10x10x7.5 10x10x10 10x10x12.5 10x10x15 15x15x15

FIG 14 Grade factors for ore-zone 250 relative to 10 mN x 10 mE x 5 mRL blocks.

The results show generally that block sizes larger than the base case generate more tonnage for any given cut-off grade, but at lower grades than the base case. For ore-zone 50 the tonnage increases with increasing cut-off grade up to a point, beyond which the tonnage relative to the base case remains constant. The tonnage curves for ore-zone 250 show that the larger blocks show a drop-off in tonnage as the cut-off grade increases, suggesting that the homogenisation of the higher grade and lower grade portions of the mixed ore-zone 250 occurs more quickly at larger bench heights. The grade factors for ore-zone 250 are also fairly insensitive to changes in cut-off grade, reflecting the dilution shown in the tonnage factor chart. The results show that the choice of bench height may be more consequential for ore-zone 250 than for ore-zone 50, and that the cut-off grade in this ore-zone has relatively little effect on the tonnage and grade factors relative to the base case. In contrast, the choice of bench height for ore-zone 50 appears to be less important that the cut-off grade.

The tonnage and grade factor curves were each modelled by a polynomial regression method so that the tonnage and grade relative to the base case could be determined for any intermediate cut-off. This enabled the factors to be built directly into the pit optimisation.

Dilution and ore loss factors

The results of the reblocking were also presented as percentage dilution and ore loss. The dilution was defined at a given cut-off as the difference between the tonnage from larger blocks and the base case (10 mN x 10 mE x 5 mRL) blocks, relative to the base case blocks. This is effectively the relative change in tonnage above a given cut-off. Ore loss was defined as the change in grade between the larger blocks and the base case blocks relative to those base case blocks. This ore loss is directly proportional to the percentage change in revenue per tonne with changing block size.

The dilution and ore loss factors were tabulated for a range of cut-off grades and the issue of risk was introduced by examining the differences between the low, median, and high-grade scenarios. Overall, dilution rates vary between ten and 25 per cent relative to the base case block size, with larger block sizes incurring more dilution. For tightly constrained ore-zones such as 50, the change in dilution and ore loss is relatively small moving from smaller blocks to larger blocks. However, for ore-zone 250, larger block sizes incur proportionally more dilution. The spread of outcomes between the high and low simulations is much greater for ore-zone 250 than for ore-zone 50, reflecting the much greater uncertainty in the definition of the 250 ore-zone. The dilution and ore loss results show that recovery from ore-zone 250 would be maximised with smaller benches.



OUTCOMES OF THE STUDY The use of simulation at Wallaby has provided a number of benefits for the mine planning and feasibility study activities. Firstly the resource estimate has been validated, and areas of potential under- and oversmoothing highlighted. Secondly, the analysis of different bench heights as provided by the reblocked simulations has led to the generation of a range of tonnage and grade correction factors which can be used in reserve optimisation scenarios and over the range of expected cut-off grades. The calculation of dilution and ore loss percentages for various ore-zones, cut-off grades, and simulation scenarios has shown the sensitivity of the ore-zones to bench heights and cut-off grade combinations. Upon the input of mining costs based on the predicted equipment and blasting scenarios for the various bench heights it will be possible to generate actual forecast revenue figures. Finally, the analysis of high, low, and median scenario simulations has highlighted those areas which are very robust (low range of outcomes) and those areas which are high risk (high range of outcomes). The optimisation of end-member simulations, ranked on those critical areas (such as the grade and tonnage of ore-zone 250) will reveal the robustness of any pit design.

A further application of conditional simulation, not yet used at Wallaby, would be to sample a chosen simulation or simulations on various grade control grids. This could be used as a first pass analysis of the implications and costs of different grade control patterns and could be used to optimise drilling costs.

Overall, the application of conditional simulation has lent an extra dimension to the feasibility study through the quantification of risk, the validation and calibration of the resource, and the important information for the economic and mining evaluation of suitable bench heights.

ACKNOWLEDGEMENTS

The management of Placer (Granny Smith) and Delta Gold have given permission to publish these findings. Tim Keleman and Mathew Matheson at Granny Smith assisted with geological and grade control aspects of the study, and Elizabeth Haren completed the variography, geological modelling and data preparation. Jacqui Coombes, Steve Potter, and Craig MacDonald of Snowden helped generate and post-process the simulations. Vivienne Snowden acted as project review.

REFERENCES

Chils, J-P and Delfiner, P, 1999. Geostastics, Modelling Spatial Uncertainty, 696 p (John Wiley and Sons).

Coombes, J, Thomas, G S, Gifford, M and Jepsen, L, 1998. Assessing the risk of incorrect prediction a nickel/cobalt case study, in Proceedings Mine to Mill 1998, pp 63-68 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Glacken, I M, 1996. Change of support and use of economic parameters in block selection, in Geostatistics Wollongong 96 (Eds: E Y Baafi and N A Schofield) 1997 pp 811-821 (Kluwer: The Netherlands).

Goovaerts, P, 1997. Geostatistics for Natural Resources, 483 p (Oxford University Press: New York).

Nielsen, K I and Currie, D A, 1999. The discovery of the Just in Case/Wallaby gold deposit, Laverton District, Western Australia, in Proceedings New Generation Gold Mines 99 Conference, November 1999, pp 1-13.

Shaw, W J and Khosrowshahi, S, 1997. Grade control sampling and ore blocking: Optimisation based on conditional simulation, in Proceedings Third International Mining Geology Conference, pp 131-134 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Schofield, N A, 1998. The myth of mine reconciliation, in Proceedings Mine to Mill 1998, pp 87-92 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Srivastava, R M, 1987. Minimum variance of maximum profitability? CIM Bulletin, 80(901):63:68.

Srivastava, R M, 1994. The visualisation of spatial uncertainty, in Stochastic Modelling and Geostastics. Principles, Methods, and Case Studies, Volume 3 of AAPG Computer Applications in Geology, (Eds: J M Yarus and RL Chambers) pp 339-345.

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