Application of Whittle Four-D to Risk Managementin Pit OptimisationT Tulp1

ABSTRACTNine case studies are presented to illustrate how risks can be: minimisedor quantified during pit optimisation, utilising Whittle Four-D software.Each case study covers a specific problem that has been encountered froma wide variety of pit optimisations.

Case A: Maximising profits when the tenement owner is paid a royaltyon tonnes processed.

Case B: Allocating product prices, rather than a single commodityprice during optimisation.

Case C: Quantifying processing costs that are affected by penaltyelements in the ore.

Case D: Exploration expenditures below current pits can be quantifiedthrough the use of simulation techniques.

Case E: Alternative strategies can be quantified when pits are restrictedby tenement boundaries.

Case F: Relocation of mine infrastructure that requires large capitalexpenditures, can be simulated by allocating costs to an area duringoptimisation.

Case G: Evaluating alternative corporate strategies during pitoptimisation.

Case H: Sensitivity analysis for price, processing cost and mining cost.Case I: Quantifying the advantages of using additional mining capacity

during the early periods of mining.

INTRODUCTIONWhittle Four-D consists of a suite of programs to optimise andanalyse open cut mines. The optimisation uses theLerchs-Grossmann algorithm, and the analysis takes time, miningand processing costs and the entire mining cycle intoconsideration.

Thoughtful application of the software can substantially assistin the analysis of risk factors associated with financial andmanagement decisions related to open cut mining.

Several case studies will be presented aimed at addressingvarious applications of 'pit optimisation' and its uses inidentifying and simulating risk factors.

Four-D is a modular set of programs that are used to set upinputs (FDUT, FDED, FDST), optirnise (FDOP), check (FDPR)and analyse (FDAN) the results from an ore model.

The optimisation process requires the following to beavailable:

1. Tom Tulp Geological Services, 100 Westview St,Scarborough WA 6019.

1. A block model, generated from a general mining package,which contains:

regular block sizes;waste and 'air' tonnes for each block;identification names for each ore or waste type;tonnes and metal units for each 'ore parcel'; andadjustment factors for mining and processing costs.

2. A financial model, which is generally set out in aspreadsheet and contains:

price of the metal unit;costs per tonne, for waste mining and ore mining andprocessing, at the reference block;cost adjustments, which vary from the 'unit costs' foreach rock type; andpositional cost adjustment for waste mining andprocessing.

3. Slope angles and directions required to maintain thegeotechnical integrity of the pit.

Pit optimisation and design is an iterative process that mayrequire many runs to learn the impact of each decision-makingstep. Forward planning, to define the problems or scenarios, andsubsequent implementation of each of the program modules, hasto be carefully considered in order to achieve the maximumbenefit. Within the model and parameter files used by Four-D,there are many criteria that can be applied to control theoptimisation and analysis.

Classifying the orebodyForethought in classifying the 'ore types' during the modellingstage allows control of the optirnisation and subsequent analysis.

Four-D can handle 25 combinations of processing methods and'ore types'. The following guide lines could be used to assist inclassifying the 'orebody' into 'ore types'.

Irregular metallurgical recoveries can be simulated by dividingthe orebody into types that have differing recoveries.

Penalty elements that affect reagent consumption or affect theprice can be used to distinguish the ore types.

Statutory requirements for measured, indicated and inferredcategories can be used.

Ore habits, such as oxidised/sulphide or vein/disseminated areproperties that can affect the metallurgical recoveries andsubsequent block values.

Each 'ore' or 'rock' type may have different miningcharacteristics that may uniquely affect the mining or processingcosts.

Product price for an ore/rock type (such as iron ore) can also beused to categorise the ore types.

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CASEA:An old mining claim is located within the proposed pit boundaryand agreements are in place to pay a tonnage royalty for alltonnes milled from the claim.

The risk in' establishing this agreement early, without furthernegotiations at the pit optimisation stage could result in the lossof revenue to the company and original tenement owner.

Processing costs are based on all costs associated with 'ore',consequently the area beneath the old claim has a higher

processing cost than the 'ore' outside the old tenement area. Sincethe 'ore' under the old claim is more expensive, the pit may beshallower, with less ore being mined and profits to the tenementowner and the company will consequently be less.

By uniquely identifying the 'ore' beneath the claim, royaltyrates can be changed during optimisation and the differing profitscan be itemised (refer Figure 1). This will identify the optimumroyalty for the pit so that both the company and the tenementowner will make the maximum profit.

$1.50

............................................................................................................................. $.O.~ ........$40

$80

$60

$100 ..

Optimum profit/or companyanti claim own.r.

$140 -,-----------------------------------,

$120

~~E~._ c:.!!12U:I_0Ill:C: ...'Q-'l:o

Differing 'Ore Types' used to control$20 ore costs during optimisation and

an~ysis

$O..L..-+----1----f-----t----f----t-----+----lH4'l;OO9791652 9797985 9803929 9724384 9753150

Company Profit9783404 9813714 9848445

1-- Profits for various Royalty Rates]

FIG 1 - Case A: company vs claim profiL

184 Perth, 5 - 9 September 1994 4th Large Open Pit Mining Conference

CASED:

APPLICAnON OF WHITTI...E FOUR-D I PIT OPTIMISATION

CaseB

Dust was lost from the system and no processing methods wereallowed. The rest of the products had a 100 per cent metallurgicalrecovery.

To allow for the various product prices, recovery fractionsassociated with the process method were adjusted to reflect theprice ratio associated with each product.

Value = Metal * Recovery (= Price Ratio) * PriceThis method valued the block correctly during optimisation

and allowed further analysis from the results file.Obviously the recovered metal units reported in the analysis as

processed units were incorrect, and would have to be adjusted.

FIG 2 - Case B: ore block classification.

Whittle Four-D allows only one price to be used duringoptimisation and analysis with gross value of a block beingcalculated by using the standard formula:

Value =Metal * Recovery * Price

Iron ore and coal often have contract rates set for differentproducts produced from the processing of the 'ore'. The examplecomes from the iron ore industry where the ore is crushed andscreened, producing both a coarse and fme product.

Mined 'ore' was processed and resulted in the followingtonnages:

46% as a 'coarse' product,52% as a 'fme' product,2% as a 'dust' product.

Contract payments are made for;'coarse' at $0.50/unit'fme' at$OAO/unit

Royalties rates are;'high grade' at 10%'low grade' at 4%

Ore blocks were classified (refer Figure 2) as 'high' or 'low'grade by classifying on percentage Fe content and penaltyelements, such as P Si etc. present. Percentages of 'coarse', 'fme'and 'dust' were then applied to subdivide the total block tonnesinto 'product type' tonnes. This classified the 'ore' tonnes into'products types' and reflected the contract prices.

The following categories were set up:

Coarse Fine DustGrade High Low High Low High LowOretype Ore A OreB OreC Ore 0 OreE OreEPrice$/unit 0.50 0.50 0040 0040 - -RoYalty 10% 4% 10% 4% - -Finalprice 0045 0.48 0.36 0.38 - -Priceratio 0.938 1.000 0.750 0.792 - -

GradeClassltlcallon

Royalty

Product

Price

HighGrade

$O.SO/Unlt

Ore Block

$O.40/Unlt

lowGrade

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CASE C:Gold-eopper mineralisation is common and can havemetallurgical problems. Copper minerals react preferentially withcyanide instead of gold, consequently affecting the cost ofprocessing (refer Figure 3).

Optimisation of this type of deposit using a single 'ore type'increases the risk of including gold mineralisation which has ahigh copper content and is uneconomic.

Four-D allows 25 'ore'-'processing' combinations to beindividually considered during optimisation and analysis.

Correct classification of the 'ore' should be based on thecopper content, which allows accurate allocations of theprocessing costs to be applied.

Ore Type CuContent Process PriceOre A 100 ppm Cu $12.30/tOreB 200ppmCu $12.51/tOreC 300ppmCu $12.94/tOreE 400 ppm Cu $13.36/tOreF 500ppmCu $13.79/tOreG 800 ppm Cu $14.64/tOreH 1200ppmCu $16.13/tOre I 2000ppmCu $18.68/tOreJ 2500ppmCu $25.76/tOreK 5000ppmCu $33.11/t

$35.00 .,-------------------------------1

$30.00

ClC'iij $25.00III11

~Q,1ii0$20.00o

Cost ofProcess(ng increases as Coppercontent of'Ore' increases J

............. '-0',""" L~_;_~_:;_t_:.c_a_t_io_n_O_{_'o_re_TY_'P_e_S_'_ba_s_.e_d_o_n_c__u-J .. .. .....

$15.00

300200100$10.00 ..L--+.------t---f---+---t---+------j---+---+---t-

400 500 800 1200 2000 2S00 SOOOCopper content (ppm)

E Cost of processi~l

FIG 3 - Case C: processing costs based on Cu content.

186 Perth,S - 9 September 1994 4th Large Open Pit Mining Conference

APPLICAnON OF WHITILE FOUR-D IN PIT OPTIMISAnON

CASED:Exploration risks below eXlstmg pits can be minimised byapplying simulation techniques.

Extrapolation of the 'orebody' below the current pit using there-blocking facility in Four-D can quickly add ore zones belowthe CWTent orebody, which have similar plunge/dip characteristicsand similar tonnage and metal distributions as the knownmineralisation. Refer to Figures 4'and 5.

Optimisation of the simulated orebody will allow: Identification of limits for the future expansion of the cWTent

pit. Definition of the maximum perimeter of mining, to allow

rational relocation of surface infrastructure. Preliminary identification of the surface-underground

interface.With the aid of sensitivity analysis the minimum and maximum

extent of the exploration target can be estimated.Using this type of approach to exploration, drilling targets can

be defmed and exploration can be staged to allow the minimumrisk of capital expenditure.

Simulatingexploration targets

RopresenfatlvesecI10n 01 the

'erOllcx!'(~Icotod

Extondlng the bIodc modoIlo*nJkJle

explOronon 'orgets01 dOplh.

FIG 5 - Case D: simulating exploration targets.

II!

----------------------------------

Data Extracted via FDUT

--t---- - - t- -- - - -+-. - ---j _. ---- -1000 1500 2000

Tonnes Ore & Metal units(Thousandsl

i :. .

~ ~

l__T_O_Po_'_m_o_de_1o_c_cu_p_le_d.bY oldPI~~----. "---

-- .--. ""'l"Io-__ ,.,... __

----~~ -~-~J.~/~ .,.x:X-- .

----- J 1:'~ -CRepresentative Zone forJ_____/ _ __~ Extrapolation

- f---r ~

\ '[ Bu-e-o-rM--;;dcll-im-it;d bY~la-C~k-o-r-d-ataJ~ I due to limited drlIl:g inrormation.

o1=-----"---+---+1-- -

SQO

7

13

ss

49

43.~c'ij37'821... 31

~iD.:25

t~19

FIG 4 . Case D: depth distribution of tonnes and metal.

4th Large Open Pit Mining Conference Perth, 5 - 9 September 1994 187

TTULP

CASEE:Being able to optimise selected regions within the total model hasgreat advantages when there are several alternatives to a decision.Each alternative can be evaluated, thereby defining the riskfactors, and a logical course of action can be implemented.

When pit perimeters encroach or extend beyond definedboundaries, such as tenements or townships, Four-D can be madeto work within selected regions of the total model. This situationcan occur when the orebody is parallel to the boundary whichconstrain the pit perimeter and consequently limits the depthextension of the pit (refer Figure 6).

Using the reblocking facility a set of high cost blocks can beincluded in the model. This will restrict the limits of theoptimisation, and financial difference can then be quantified(refer Figure 7).

When the company is well informed before negotiationscommence, financial risks can be defined and can be used to limitfinal settlements.

FIG 6 - Case E: pit optimisation with and withoutrestictions at the Tenement boundary.

o

~.............

..\ .,~

11 13 15 17 19 21Pit Shell Number

9753

Diffuence in opuating profit could be used to negotiaterthu mining on the adjacent tenement

- - ' __ .__ - .

$6

$2

$14

$12

$4

11 $10::Iii_>1/1DIg~i $8 "'"s.-o

$16 1--------;=::::===============~T------T5IOptimisation without restrictions

-- Unrestricted Pit Discounted Cash

Unrestricted Pit Mill Tonnes

--- Restricted Pit Discounted Cash Flow

-0-- Restricted Pit Mill Tonnes

--------------------

FIG 7 - Case E: optimisation confined by tenements.

188 Perth, 5 - 9 September 1994 4th Large Open Pit Mining Conference

CASEF:Mills, railway lines and old tailings dams, are all major structuresthat may have to be re-located to allow for pit expansions. Theyall represent large expenditures of capital and have a spatialrelationship to the pit and orebody.

Utilising Four-D's capacity to link areas together as additional'arcs' the appropriate areas can be linked to the 'orebody' modelmaking them an integral part of the model which is to beoptimised (refer Figure 8).

Costs to relocate each feature can then be added to a singlewaste block by giving it a very high tonnage which represents therelocation costs.

Tonnage = Cost / unit cost of mining waste

The optimisation will determine if proposed mining operationsgenerate enough cash to move the 'obstruction'. Four-D producesmany 'pit shells' which can be used to determine the timing andstaging of moving the structure. Period analysis of the results fIlewill also indicate when the expenditure is to occur and what theoperation's cash flow will be during the transition periods.

APPLICATION OF WHITTLE FOUR-D IN PIT OPTIMISATION

CaseF

Capital ..pendln..to r.locat. the M11

_'4"":,~:~-----:=r'-r"-oL110 ,.,cx:at. ",. MII

Opllmuml'lt""'.~.

Diagram showsthe nested structure of the pit shells

generated from the optimlsationof the block model.

FIG 8 - Case F: capital expenditure to relocate the Mill.

4th large Open Pit Mining Conference Perth, 5 - 9 September 1994 189

TTULP

CASEG:The Lerchs-Grossman algorithm produces a pit with themaximum profit.

Corporate strategies and risks may incorporate alternativeobjectives which do not demand a maximum profit from themining operation. To achieve the alternative objectives howeversome of the optimum profit has to sacrificed.

During the analysis of an operation it is worthwhile to examineand quantify these alternative strategies. Output from the Four-Danalysis module can easily be imported into a spreadsheet forfurther evaluation of the project.

The following have been cited as alternative objectives: Maintain a rate of return. Keep production costs below a ceiling. Maximise metal throughput. Maximise tonnage throughput. Maintain an economy of scale. Maintain a metallurgical blend. Minimise risk.

Graphic presentation of the required criteria can quicklydemonstrate the alternatives, refer to Figures 9,10 and 11.

200

~..u

400 o

i~

300 c~~

~CL

500

~-'"T'600

/.... Ifcorporate objectives are to produce below

$450/0% then optimum profit can be sacri.fU:edto obtain additional mill tonnes from a huger7 '-P_it_S_he_u_-,.- _

500 ..

3500 1--------~=======;---1

2500

3000 .

1000

o 1004 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73

Pit Shell Number~ Optimum Value ($)~ Cost $/oz

FIG 9 - Case G: optimum value and cost/oz.

190 Perth, 5 - 9 September 1994 4th Large Open Pit Mining Conference

AI'Pl.ICATIO . OF WHITTl.E 1'0 R-D I PIT OPTIMISATIO

300 ------ ----------------- 600

250

~um pit produc~sgold b~low S40010Z200

--- ..=~cCC ::11500::1~o=~::e-

100

50

Significantly mor~milllonnts can b~achitv~d iflht production cost art tob~low S45010z although optimumprofils would bt sacrifictd

400 ~..uC::Io

i300 ~

()

200

o 1004 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73

Pit Shell Numbers

Mill Tonnes ~ Cost per Ounce ($Ioz)L-- . __

FIG 10 - Case G: mill tonnes and cost per ounce.

---------------------------------------------,

0.2

0.4

0.8

or

exttnding tlte mint liftcan all bt qua"tifitd

E::IE "I. variation from the optimum1i value can us.d to assist In denning

~ alternative corporat. objectives ..,g 0 ~==================::::;~_:J~~'_=_=_'~~~~.------_1_ 0.6 ~g lil:

~it-

50

475449315200

-100 ~~~~~~-H++++H_Hf+++++++++_~~~f+H+t_+-t++H_H+H++++++_J0181 248 346 382 442 468 537

368 432Production Costs ($Ioz)

Optimum Value Mill Tonnes (t) Recovered Gold -- Mine Life (Periods)._------------------------- - ------- -----

FIG 11 - Case G: percentage variation from optimum value.

4th Large Open Pit Mining Conference Penh. 5 . 9 September 1994 191

TTULP

CASEH:Sensitivity analysis or 'What happens ifl', requires manypermutations of the 'base case' with variations in many of thevariables. Conventionally a Monte Carlo system would be used toevaluate the many permutations that are possible.

An approximation can be achieved, however, through multipleruns with the analysis module (FDAN) in Four-D.

Setting reasonable ranges for each of the three economicvariables (price. mining costs and process costs), multiplevaluations of a pit or pits, can be achieved (refer Table 1).Similarly mining factors (dilution, recovery and rates) or milling(recovery and rate) can be altered to simulate minimum andmaximum levels of achievement.

Results can be imported into spreadsheets for graphicalpresentation (refer Figure 12) that will highlight the variability ofthe anticipated results.

TABLE 1. Sensitivity analysis for Case H.

Cost M -5% Base +5% +10% +15%CostP $1.19 $1.25 $1.31 $1.37 $1.44

-5% $17.81 Al B1 Cl D1 ElBase $18.75 A2 B2 C2 D2 E2

+5% $19.69 A3 B3 C3 D3 E3+100/0 $20.63 A4 B4 C4 D4 E4+15% $21.57 A5 B5 C5 D5 E5

Price -100/0 -5% Base +5% +100/0$/oz $333.00 $351.50 $370.00 $388.50 $407.00

16.,----------------------------------.

14

12 .

10

~!r 8~

6

4

2

................./..../'

.../ .MulJiple lIIIalysis/0' various pr/ca, miJlln, IIIId,ocasln, costs, wItltln /I sln,1L pit slldl CIIII be

. simply summarised usln, ~ frequency 0'cumultl/ive frefUency dJstrlbulions.

2500000O100000oo 1500000O 200000OOOperating Value (S)

500000Ooo-'--~=--t--t_-+--+--r--+---+-_____1I_-+__-_+_-_____1--+__....J...O

300000OO

--- % Frequency Wast Case -- % Frequency Best Case

-- Cum. % Frequency Best Case -w-- Cum % Frequency Wast Case

'----------------------------------_._--

FIG 12 - Case H: sensitivity analysis.

192 Perth, 59 September 1994 4th Large Open Pit Mining Conference

APPLICATIO OF WHIT11..E FOUR-D IN PIT OPTIMISAnON

CASEI: CONCLUSIONDuring analysis with Four-D, mining and milling rates aremutually exclusive of each other when either one reaches its totalcapacity.

This situation is often reached when a pre-strip is required onan orebody. Additional mining capacity will be required to utilisethe latent mill capacity available during the initial periods. Toevaluate when and what additional capacity is required, a periodanalysis of the results flle will rapidly indicate when the mill is atfull capacity and what 'normal mining rate' is required tomaintain that tJuoughput. The additional initial mining capacitythat is required can then be readily determined and evaluated(refer Figure 13).

Simulating the mining fleet's capacity, through changingmining rates and costs during analysis, minimises the financialimpact of having a mill running below capacity.

Thoughtful application of the Whittle Four-D software, canquantify or simulate a variety of risk factors encountered duringpit optimisation.

Price, processing and mining costs can all be controlled duringoptimisation with the correct classification of 'ore types' in theblock model. Large capital expenditures can be allocated to areas,to simulate relocation of mine infrastructures. Simulation of orezones below current pits allows exploration targets to be definedand quantified.

Boundaries confining the pit expansions can be used duringoptimisation or used to define alternative strategies. Corporateobjectives and cost, orebody or mining sensitivities can bequantified from the results of the optimisation.

8 - ---- --- $16

Additional J.Jm lonn.._______.. mined dUring PI results In

Sl.2mll proOt for project

6

\ -J --=::--

194 Perth, 5 - 9 September 1994 4th Large Open Pit Mining Conference

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