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Resources Policy 33 (2008) 222– 229

Contents lists available at ScienceDirect

Resources Policy

0301-42

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/resourpol

Incorporating environmental issues into optimum cut-off gradesmodeling at porphyry copper deposits

M. Osanloo a,b, F. Rashidinejad b,�, B. Rezai a,b

a Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iranb Department of Mining Engineering, Science and Research Branch, Islamic Azad University, Hesarak, Pounak Sq., P.O. Box 14515-775, Tehran 14778-93855, Iran

a r t i c l e i n f o

Article history:

Received 7 December 2007

Received in revised form

3 June 2008

Accepted 6 June 2008

JEL classification:

Q32

Q52

Keywords:

Acid-generating rocks

Cut-off grade policy

Mine design and planning

Porphyry coppers

07/$ - see front matter & 2008 Elsevier Ltd. A

016/j.resourpol.2008.06.001

esponding author. Tel.: +98 (0) 912 213 1942;

ail address: frashidinejad@hotmail.com (F. Ra

a b s t r a c t

Cut-off grade is defined as the grade which discriminates between ore and waste within a given

orebody. Determination of a complete optimum cut-off grade policy is a very important function during

mine life. Using the modified optimum cut-off grade model presented in this paper not only the net

present value of a porphyry copper mining project is maximized, but also the adverse environmental

impacts of the project are minimized simultaneously. This methodology is more effective in long-range

planning. For showing the effectiveness of the model, two scenarios are considered in a hypothetical

deposit and the results show that incorporating the modified optimum cut-off grade policy, the net

present value will be increased by 3.6% in comparison with the Base Case.

& 2008 Elsevier Ltd. All rights reserved.

Introduction

Constrained by geology, mining engineering and environmen-tal aspects, mine design and planning is usually an exercise thatseeks an economic outcome. One of the most important aspects ofmining engineering is deciding which material in a deposit isworth mining and processing and which should be considered aswaste. This decision is summarized by the cut-off grade policy,which affects the size and the life of deposits (Camus, 2002).

Ores in general are defined operationally by a cut-off grade.Material with a mineral content above the cut-off is scheduled forfurther processing. Other material is left, or dumped as waste. Anessential preliminary to an analysis of cut-off grade strategy is anexamination of net present value (NPV) maximization for anoperation based upon a finite resource (Lane, 1964, 1988). Therelationship between the cut-off grade and NPV provides a meansby which the cut-off grades can be optimized, but because thecalculation of optimum cut-off grades can neither be determinednor measured precisely with a single parameter, the problem iscomplicated. Due to its complexities, the definition of a completeoptimum cut-off grade policy is as much ‘‘art’’ as ‘‘engineering’’.

ll rights reserved.

fax: +98 (0) 21 2285 5062.

shidinejad).

From the standpoint of exhaustible mineral resource manage-ment, the cut-off grade is the grade at which the resource materialwill meet all the costs associated with its depletion to amarketable product, according to a general plan that definesquantities, costs, and efficiencies over a defined period.

NPV is the standard and most commonly used criterion thatincorporates a means for dealing with unsteady and uncertaineconomic conditions. This criterion for any mining operation isthe sum of all future cash flows discounted by an appropriate rateof interest, which should at least be the cost of capital (Minnitt,2003).

The environmental protection has a high priority in modernmining. Mining environmental management tends to focus onconcerns over the impact of waste disposal on the surface,primarily in the form of tailings and waste material structuressuch as tailings dams and waste dumps. Mining systems need tobe re-engineered, based on a new paradigm that mining is abusiness whose success is fundamentally dependent upon wastemanagement—that ‘‘mining companies are waste managementcompanies’’, as proposed in the Agenda 21 program, by the WCEDand in many professional papers. This leads to the argumentthat mining design and planning which maximizes the NPVwithout environmental considerations during planning is notoptimal (Ramirez-Rodriguez and Rozgonyi, 2004). Actually, suchdesigns are mutually exclusive with the objectives of sustainable

ARTICLE IN PRESS

Sustainable Development Requirements

Best Mining Practice

Declining Head Grades

Increasing Demands of Society

Breakthrough Technologies

Fig. 1. Challenges of the best mining practice in mine of the future.

M. Osanloo et al. / Resources Policy 33 (2008) 222–229 223

development.1 There is a balance between the cut-off grade andenvironmental strategies. In practice, achieving the balance is thereal challenge. Furthermore, mineralized bodies or potentially orebodies are becoming harder to find, more difficult in nature andtend to be deeper and of lower grade. They are becoming lessaccessible, more difficult to process, and thus more capitalintensive. Fig. 1 shows challenges of the best mining practice inmine of the future.

This paper addresses the characteristics of porphyry copperdeposits (PCDs) with special reference to their adverse environ-mental impacts in brief and argues that how incorporating theassociated environmental costs into the optimum cut-off grademodeling can add value to the mining projects and contribute tomove forward from the traditional to an environmentally friendlycut-off grade optimization. Finally, the new model applied to astandard hypothetical PCD and then the effectiveness of themodel evaluated.

Porphyry copper deposits

PCDs are categorized as multi-zone deposits. ‘‘All thesedeposits have similar characteristics. Their similarities are greaterthan their differences, even though they form in differentenvironments’’. PCDs are defined as large, low to medium-gradedisseminated copper deposits, in which hypogene sulfides areprimarily structurally controlled. This low grade of ore causes ahigh tonnage of extraction to be economically minable and thedominant processing technique of these low-grade depositsaround the world is flotation.

As Jensen and Bateman (1976) noted that the primary sulfidesconsist of pyrite, chalcopyrite, and bornite with minor sphaleriteand molybdenite. In capping these sulfides are largely or whollyremoved, leaving voids occupied by limonite of diagnostic colorsand patterns. Below the capping the yellow sulfides are coated, orpartially or wholly replaced by chalcocite and covellite. Pyrite isthe dominant sulfide mineral in porphyry coppers. The primarymineralogy of PCDs is generally similar and is accompanied byhydrothermal alteration of the host rocks and all have similarmodes of origin. The differences between them are in details of

1 The upward trend in restrictive environmental laws and regulations around

the world, demonstrate the truth of harder mining operation circumstances,

particularly for open-pit mines due to leaving a considerable number of remnant

materials on the surface. The success of a mining company without the

consideration of environmental issues seems very unlikely. On the other hand,

postponement of the environmental measures is not reasonable and causes much

more costs in future.

host rock, shape, size tenor, oxidation, and degree of supergeneenrichment.

Alteration patterns are among the most characteristic featuresof PCDs. The ‘‘idealized’’ or ‘‘model’’ spatial and temporalrelationships between various types of hydrothermal alterationare to a large extent well represented by most PCDs. Moreover,there is a close spatial and temporal relationship between thealteration patterns and the zonation of ore minerals. Thisrelationship suggests that PCD mineralization and wall-rockalteration are genetically related. Guilbert and Lowell (1974)presented mineralization and alteration zoning patterns for PCDs.

In general, from core to rim, alteration patterns for PCDs followthe zonal sequence potassic (K-silicate), phyllic (quartz-sericite orsericitic), propylitic, and argillic with the latter zone usuallyrestricted to shallow depths. The ore minerals occur in dissemi-nated form in the zone of potassic alteration, but in the phylliczones, they also occur in veinlets. Patterns of metal distributionalteration, and sulfide distribution, established in the Lowell–Guilbert model, are widely accepted and used in exploration. Thepatterns are also effectively used to select and plan drillholelocations and to interpret geophysical data (Nielsen, 1984). Fig. 2shows vertical cross-sections through Lowell–Guilbert model of atypical PCD along with alteration and mineralization zones.

The fact that the dominant PCDs are potentially acid generat-ing (AG) leads to more attention to the issue of waste manage-ment at PCDs. A prediction on acid generation should begin wellbefore sulfide wastes are produced at mine sites. Preliminaryevaluations can be performed as early as the exploration drillingand early mining of an ore body. Fundamental basic data for wastecharacterization and acid-generation characteristic include: ex-isting lithologies, structural features, ore and gaunge textures andmineralogy, particle size distribution, depth of oxidation, andwhole-rock geochemistry. Geological data such as pyrite content,geochemical analysis and static test data can be used to constructa three-dimensional block model of different waste material unitsprior to mining. Alteration assemblages and zonation patterns inPCDs can be used as a guide for sampling and estimation of theore and waste acid-generation potential. Unfortunately, during thedevelopment of waste material characterization while ore body ismodeled is not a common practice and despite undesirableoutcomes in the past, the mining design process continues tofocus on technical mining and financial considerations with theenvironmental and social objectives considered later in the designsequence, unfortunately more often in the form of impactmitigation (Odell and Scoble, 2005).

To have a mining plan for a PCD provides the basis ofsustainable development requirements and acid-generation char-acteristics of the deposit need to be available. With such data, it is

ARTICLE IN PRESS

Fig. 2. Vertical cross-sections through Lowell–Guilbert model of a typical PCD (Guilbert and Lowell, 1974).

M. Osanloo et al. / Resources Policy 33 (2008) 222–229224

possible to design an eliminative or reducer system in detail andapply the associated costs in the mining plan elements such ascut-off grades.

Traditional optimum cut-off grades model for open-pit mines

Work undertaken in the field of cut-off grades optimization hasnot advanced much beyond the work undertaken by Lane (1988).His heuristic trial and error technique for optimum cut-off gradescalculation is the basis of the approach that takes into account theopportunity cost associated to the remaining finite resourceswhich leads to the extraction of high-grade materials as early aspossible constrained by mining, processing, and marketingconsiderations. Opportunity cost is a key concept in Lane’s theory.Every action has an opportunity cost. This is not restricted tomonetary or financial costs; the real cost of output foregone, losttime, pleasure or any other benefit that provides utility shouldalso be considered.

The structure of opportunity cost in Lane’s theory is on thebasis of two separate components: one is the corporation’s cost ofcapital and the other is the decline/incline in value as aconsequence of changing economic conditions. The procedurefor Lane’s calculation of optimum cut-off grades not only relies onthe economic factors such as revenue and costs but also on mineequipment, crushers, mills, and smelter facilities. The capacities ofthis equipment do not often permit much flexibility and, there-

fore, cut-off grades can only be varied within narrow limits. Incontrast when expansion schemes are being designed, and evenmore so when totally new mines are being developed, thetechnique can indicate cut-off grades quite different from break-even cut-off grade strategies, with substantial correspondingimprovements in the overall returns.

Several writers have endeavored to modify and improve theeffectiveness of the original Lane’s technique during the last twodecades. They include Dagdelen (1992, 1993), Dagdelen andMohammad (1997), Osanloo and Ataei (2003), Asad (2005),Bascetin and Nieto (2006), Dagdelen and Kawahata (2007). Thesecontributions emphasize the techno-economic aspects of amining project but not the environmental issues.

In theory, the problem of cut-off grade optimization must becompatible with the optimization of total mining process asshown in Fig. 3, but practically this cannot be solved by a rigorousmethod and practitioners use heuristic trial and error techniques.

The cut-off grade optimization in each mining operationtypically implies definition of a cut-off grade strategy that yieldsthe maximum expected NPV of the mining project. The term‘‘expected’’ is important because mining companies do not alwaysknow how much they will be able to sell in the future. In dealingwith these uncertainties mining professions must estimate,calculate, and consider contingencies. This process includesestimating cost functions for both short and long term. Toestimate these functions, production costs must be classified aseither fixed or variable. In the short run, both variable and fixed

ARTICLE IN PRESS

Commodity Price

Ore Reserve Estimation

Start

Production Costs

Ultimate Pit Limit

Production Profiles

Cut-off Grade

Design of Increments

Fig. 3. Steps in traditional mining design and planning by circular and interdependent analysis.

Mining Operating Cost /t (Ore + Waste)

Mining Cost of Attributable Capital /t (Ore + Waste)

Processing Operating Cost /t (Ore)

Processing Cost of Attributable Capital /t (Ore)

Marketing (Smelting, Refining, Selling, Overhead) Costs /t

Ore Revenue

Infrastructure, Concentrator, Land, Mineral Rights, etc., Divided by Estimated Tonnage Ore

Waste Block

Ore Block

Cut-off Grade Optimisation Software

(CGOS)

Cut-off grade Total Tons

(Ore + Waste) Tons (Ore)

Total tonsassumed output ≠CGOS output →Repeat using output tonsore & waste (adjust manually)

Total tonsassumed output =CGOS output →Use as base for pit design

Fig. 4. Illustration of the traditional cut-off grade analysis.

M. Osanloo et al. / Resources Policy 33 (2008) 222–229 225

costs are often incurred; in the long run, all costs are variable.A sharp distinction between fixed and variable costs is not alwayspossible or realistic. The optimum determination of the cut-offgrade policy is itself a function of the production profile andextraction sequence of the blocks in the block model. Fig. 4 showsthe traditional cut-off grade analysis for a single-mineral deposit.

The current practice of mine design and planning beginswith a geologic block model. The traditional approach for minedesign and planning of a single-mineral deposit is to estimate therevenues per percent quantity of contained mineral in a block.One then compares a total production costs against this value.This total cost is the sum of all costs to point of the sale including

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M. Osanloo et al. / Resources Policy 33 (2008) 222–229226

the cost of capital and an element of profit. Any block withrevenue less than this cost qualifies as waste and the percentagecontained mineral is the cut-off grade value.

This constant break-even cut-off grade is based on an operatingcost and takes no account of capital costs or replacement capitalrequirements. This factor defines the destination of the minedmaterial. It is valid to use to determine the ultimate pit limitinside which no construction or non-mining activity may takeplace in order to ensure no sterilization of potential ore should thecommodity price escalates. Within the ultimate pit limit, mineplanners design intermediate shells (pushbacks) so that thedeposit is divided into nested pits going from the smallest pitwith highest value per ton of ore to the largest pit with the lowestvalue per ton of ore. Mine planners design these pushbacks toinclude haul road access and they act as a guide during thescheduling of yearly production from different benches.

Table 1A list of variables in the modified optimum cut-off grade model

Notation Explanation Unit Remarks

i Year indicator – –

N Mine life Years –

Modified optimum cut-off grades model for open-pit mines

To produce sustainable results of mining projects, comprehen-sive design criteria must be integrated in the design process.Present cut-off grade models address operating cost, commodityprice, capacities and grade-tonnage distribution in each mineplanning increment, without considering the environmentalissues. A missing part of these calculations is the cost relevantto the environmental considerations.

The most significant environmental impact in exploiting PCDsrelates to acid mine drainage (AMD) from the mine, its wastedumps, and tailings dams. The modified optimum cut-off gradesmodel presented in this paper complies with the Lane’s theory inregard to incorporating the environmental impacts of PCDs in theoptimum cut-off grade policy.

The best practice is to consider environmental mine-wastemanagement requirements to eliminate or reduce acid minedrainage in the original place. Open-pit mining, froth flotation,and smelting are the most commonly practiced in copperproduction from PCDs. This process is associated with land andsurface disturbance material pollution on the mine site andgroundwater contamination in the vicinity by the waste materialand tailings.

Fig. 5 shows the schematic representation of various materialdestinations from ‘‘w’’ mines to ‘‘x’’ processing plants and ‘‘y’’waste dumps. The produced tailings go to ‘‘z’’ tailings dams. It ispossible to consider a more complicated case with the co-disposal

Mine 1

Mine 2

Mine w

PP 1

PP 2

PP x

TD 1

TD 2

TD z

WD 1

WD 2

WD y

Fig. 5. Schematic representation of various material destinations.

concept. To simplify the modeling one mine with two wastedumps, and one processing plant with two tailings disposalfacilities are considered. WD1 and WD2 are designated fordumping of non-AG and AG material, respectively. Some pre-ventive measures is required for WD2 and the related capital andoperating cost must be determined based upon the detaileddesign.

Separation of the AG portion of tailings is not well establishedin the mining industry, but it is in compliance with sustainablemining practice and is a cost-effective and reasonable solution.The notations established for explanation of the modifiedoptimum cut-off grade model, are shown in Table 1.

The objective function of the model is to maximize the NPV ofoperation in compliance with the Lane technique. This can berepresented mathematically as follows:

Max NPV ¼XN

i¼0

CFi

1þ dð Þi

!(1)

where

CFi ¼ ðSi � riÞ � Qri�mi � Qmi

� ai � Ai

� ðQmi� Qci

Þ � bi � Bi � ðQmi� Qci

Þ

� ci � Qci� ui � Ui � ðQci

� QriÞ � vi � Vi

� ðQci� Qri

Þ � ðf þ d� NPViÞ � T (2)

or

CFi ¼ ðSi � ri þ uiUi þ viViÞ

� Qri� ðmi þ aiAi þ biBiÞ � Qmi

� ðci � aiAi � biBi þ uiUi þ viViÞ

� Qci� ðf þ d� NPViÞ � T (3)

The following constraints are evident:

QmipM for i ¼ 1; . . . ;N

QcipC for i ¼ 1; . . . ;N

QripR for i ¼ 1; . . . ;N

Qri¼ g � y� Qci

Ai þ Bi ¼ 1 and Ui þ Vi ¼ 1

S Copper price $/ton of product –

M Mining throughput Ton/year –

C Processing throughput Ton/year –

R Marketing throughput Ton/year –

m Mining operating cost $/ton of material Ore+waste

a NA waste disposal operating cost $/ton of waste WD1

b AG waste disposal operating cost $/ton of waste WD2

c Processing operating cost $/ton of ore –

u NA tailings disposal cost $/ton of tailings TD1

v AG tailings disposal cost $/ton of tailings TD2

r Marketing costs $/ton of product –

f Fixed or time cost $/year –

g Average grade %–% –

y Metallurgical recovery % –

d Discount rate % –

CF Cash flow $ –

Qm Material mined Ton/year –

A NA material mined and send to WD1 – –

B AG material mined and send to WD2 – –

Qc Material processed Ton/year –

U NA tailings send to TD1 – –

V AG tailings send to TD2 – –

Qr Marketable material Ton/year –

AG: acid generating, NA: non-acid generating.

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M. Osanloo et al. / Resources Policy 33 (2008) 222–229 227

The cut-off grades designate the material mined, materialprocessed, as well as marketable material in a given period ‘‘i’’and they directly affect profitability of the project. Therefore, thesolution of the problem is the determination of an optimum cut-off grade in a given period, which ultimately maximizes theobjective function. According to the Lane’s theory, the compo-nents of a mining operation either individually limit the miningoperation or mutually. The limitation of the capacity of anindividual stage leads to the determination of the limitingeconomic cut-off grades. However, if stages are limiting thethroughput mutually, the capacities of these stages are balancedto use the maximum capacity of each stage by considering grade-tonnage distribution of mining increments. This leads to thedetermination of balancing cut-off grades.

Table 3Scenarios of a hypothetical deposit

Notation Unit Base Case Scenario 2

S $/lb 25.00 25.00

M Ton/year 100.00 100.00

C Ton/year 50.00 50.00

R lb/year 40.00 40.00

m $/ton of material 1.00 1.00

a $/ton of waste 0.00 0.15

b $/ton of waste 0.00 0.50

c $/ton of ore 2.00 2.00

u $/ton of tailings 0.00 0.25

v $/ton of tailings 0.00 0.80

r $/lb of product 5.00 5.00

f $/year 300.00 300.00

y % 100.00 100.00

d % 15.00 15.00

A – 0.92 0.92

B – 0.08 0.08

U – 0.85 0.85

V – 0.15 0.15

Table 2Grade-tonnage distribution of hypothetical ore body

Grade (lb/ton) Quantity (ton)

0.0–0.1 100

0.1–0.2 100

0.2–0.3 100

0.3–0.4 100

0.4–0.5 100

0.5–0.6 100

0.6–0.7 100

0.7–0.8 100

0.8–0.9 100

0.9–1.0 100

Total 1000

Limiting economic cut-off grades

Limiting economic cut-off grades may be determined indivi-dually by mine, processing plant or marketing throughputs. Ifmine throughput is the governing limitation, the optimum cut-offgrade is given by

gm ¼ci � aiAi � biBi þ uiUi þ viVi

ðSi � ri þ uiUi þ viViÞ � y(4)

If processing plant throughput is the governing limitation, theoptimum cut-off grade is given by

gc ¼ci � aiAi � biBi þ uiUi þ viVi þ ðf þ d� NPViÞ=C

ðSi � ri þ uiUi þ viViÞ � y(5)

If marketing throughput is the governing limitation, theoptimum cut-off grade is given by

gr ¼ci � aiAi � biBi þ uiUi þ viVi

ðSi � ri þ uiUi þ viVi � ðf þ d� NPViÞ=RÞ � y(6)

where overall present value is obtained from the followingequation:

NPVi ¼CFi � ðð1þ dÞN � 1Þ

d� ð1þ dÞN(7)

One can see that two of the limiting economic cut-off grades areunknown initially since they depend upon knowing the overallpresent value. This in turn depends upon the cut-off grade. Theeffect of changing economic conditions has been ignored in theeconomic model and the term ‘‘d�NPVi’’ considered as anopportunity cost. Since the unknown NPVi appears in theequations, an iterative process must be used. In practice, initiallevels are assumed, a policy calculated, and the present values ontermination compared with the specified terminal value. Depend-ing upon the difference, the initial levels are modified and a newpolicy is calculated. This iterative process is repeated until onlyminor improvements can be achieved; i.e. the mathematicalgunnery practice is utilized.

The optimum cut-off grade will never be less than gm, since it isthe break-even cut-off grade. Also, the optimum cut-off grade willnever be higher than gc, since this will lead to throwing some ofthe valuable ore in waste dumps. Hence, the following relation-ship holds:

gmpgrpgc (8)

Therefore, the overall effective optimum cut-off grade (Gopt)that maximizes the objective function is the any value between gm

and gc. This can be presented as:

gmpGoptpgc (9)

Balancing cut-off grades

If two components are simultaneously to be in balance, i.e.operating at full capacity, three cases are raised. To be able tocalculate this, one needs to know the distribution of grades of themined material. The first balancing cut-off grade (gmc) is the cut-off grade that from the following:

Qmi

M¼

Qci

C(10)

The effective optimum cut-off grade satisfying mine andprocessing plant (Gmc) is,

Gmc ¼ gm if gmcpgm

Gmc ¼ gc if gmcXgc

Gmc ¼ gmc otherwise

or Gmc ¼ middle value among gm; gc and gmc

The second balancing cut-off grade (gcr) is the cut-off grade thatcomes from the following:

Qci

C¼

Qri

R(11)

ARTICLE IN PRESS

Table 4Optimum cut-off grade policy for Scenario 1—Base Case

Year Total mined (ton) Gopt (lb/ton) G (lb/ton) Qm (ton) Qc (ton) Qr (ton) Life (year) CF ($) Overall NPV ($) Cum. NPV ($)

1 1000.00 0.50 0.75 100.00 50.00 37.50 10.00 250.00 1254.69 217.39

2 900.00 0.50 0.75 100.00 50.00 37.50 9.00 250.00 1192.90 406.43

3 800.00 0.50 0.75 100.00 50.00 37.50 8.00 250.00 1121.83 570.81

4 700.00 0.50 0.75 100.00 50.00 37.50 7.00 250.00 1040.10 713.74

5 600.00 0.50 0.75 100.00 50.00 37.50 6.00 250.00 946.12 838.04

6 500.00 0.50 0.75 100.00 50.00 37.50 5.00 250.00 838.04 946.12

7 400.00 0.50 0.75 100.00 50.00 37.50 4.00 250.00 713.74 1040.10

8 300.00 0.49 0.74 97.15 50.00 37.03 3.09 243.40 568.81 1119.67

9 202.85 0.46 0.73 92.84 50.00 36.44 2.15 236.04 409.12 1186.77

10 110.02 0.40 0.70 83.33 50.00 34.94 1.32 215.53 242.07 1240.05

11 26.68 0.40 0.70 26.68 16.01 11.19 0.31 71.48 20.33 1255.41

12 – – – – – – – �105.87 – 1149.54

Total – – – 1000.00 516.01 382.10 – – – –

Table 5Optimum cut-off grade policy for Scenario 2

Year Total mined (ton) Gopt (lb/ton) G (lb/ton) Qm (ton) Qc (ton) Qr (ton) Life (year) CF ($) Overall NPV ($) Cum. NPV ($)

1 1000.00 0.50 0.75 100.00 50.00 37.50 10.00 236.94 1189.17 206.04

2 900.00 0.50 0.75 100.00 50.00 37.50 9.00 236.94 1130.60 385.20

3 800.00 0.50 0.75 100.00 50.00 37.50 8.00 236.94 1063.24 541.00

4 700.00 0.50 0.75 100.00 50.00 37.50 7.00 236.94 985.79 676.47

5 600.00 0.50 0.75 100.00 50.00 37.50 6.00 236.94 896.71 794.27

6 500.00 0.50 0.75 100.00 50.00 37.50 5.00 236.94 794.27 896.71

7 400.00 0.50 0.75 100.00 50.00 37.50 4.00 236.94 676.47 985.79

8 300.00 0.48 0.74 96.29 50.00 36.92 3.12 229.43 539.97 1060.79

9 203.71 0.46 0.73 92.32 50.00 36.37 2.17 223.02 388.40 1124.18

10 111.39 0.40 0.70 83.48 50.00 34.97 1.32 204.94 229.81 1174.84

11 27.91 0.40 0.70 27.91 16.72 11.69 0.31 75.38 21.41 1191.04

12 – – – – – – – 0.00 – 1191.04

Total – – – 1000.00 516.72 382.45 – – – –

M. Osanloo et al. / Resources Policy 33 (2008) 222–229228

The effective optimum cut-off grade satisfying processing plantand market (Gcr) is

Gcr ¼ gr if gcrpgr

Gcr ¼ gc if gcrXgc

Gcr ¼ gcr otherwise

or Gcr ¼middle value among gc; gr and gcr

The third balancing cut-off grade (gmr) is the cut-off grade thatcomes from the following:

Qmi

M¼

Qri

R(12)

The effective optimum cut-off grade satisfying mine and market(Gmr) is

Gmr ¼ gm if gmrpgm

Gmr ¼ gr if gmrXgr

Gmr ¼ gmr otherwise

or Gmr ¼ middle value among gm; gr and gmr

Gopt is the middle value among Gmc, Gcr, and Gmr andsubsequently Qm, Qc, Qr, and the NPV can be computed.

2 Note: The calculations sheet addressed in the hypothetical example is

available and can be requested from the corresponding author.

Application of the model to a hypothetical porphyry copperdeposit

To show the effect of the modified optimum cut-off grademodel on the profitability of potentially AG PCDs, consider two

scenarios in a hypothetical deposit. Assume that grades of the orebody are equally distributed throughout the pit and a grade blockmodel is constructed (Table 2). Eight percent of material minedthat is sent to waste dumps and 15% of tailings sent to tailingsdam is AG.

The associated capacities, commodity price, costs, recovery(yield), discount rate, and proportion of AG material aresummarized in Table 3. The first scenario is the Base Case. It isthe same example addressed by Hustrulid and Kuchta (1995) inwhich no environmental cost is considered. Scenario 2 is the sameas the Base Case but with consideration of all associated costsintroduced in Table 1.

An Excel spreadsheet2 was developed to facilitate doing thecalculations. Tables 4 and 5 show the results of the scenarios 1 and2, respectively.

A discussion of results from the model

To simplify the interpretation of the calculations and show theeconomic robustness of the scenarios, only results of the firstiteration appear in the above tables. The overall NPV obtainedusing the annual CF should be the same as that shown in thetables for year 1. The cumulative NPV of the scenario 1 withoutconsideration of the environmental cost is $1255.41 but it is not

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M. Osanloo et al. / Resources Policy 33 (2008) 222–229 229

realistic and on the basis of sustainable development concept,because based upon the assumption in this case, a part of themineralized body is estimated to be AG and this should be takeninto account in the early stages of mine design and planning.

If all remedial measures are moved to the end of the mine life,the reclamation cost for neutralization of AG material is estimatedto be $105.87. This adversely affects the NPV, decreasing it to$1149.54. The cumulative NPVs of scenario 2 are $1191.04, which is3.6% higher than the Base Case. All costs are considered in theoptimum cut-off grade policy during the mine life.3

Summary and conclusions

Any mining operation should be economic and have acceptableenvironmental impacts. Declining head grades, increasing de-mands of society, sustainable development requirements andbreakthrough technologies are the facts and challenges of mineralresource management and the best mining practice in mine of thefuture. PCDs are the major source of copper and some otherelements as by-product. However, these deposits have had themost adverse environmental impacts in the past. The adverseenvironmental impacts of mining projects are one of the mostserious concerns of government and society in the world today.Environmental protection has high priority in modified miningand the optimum mine designs excluding environmental criteriaare typically non-optimum or utmost semi-optimum designs.

The most significant aspect of mining porphyry coppers isproducing a vast amount and variety of waste material andtailings that claims attention and must be properly managed tominimize the adverse environmental impacts. Economic andenvironmental thoughts coalesced in this paper to form a usefulmethodology that maximizes the profitability of a mining projectand minimizes its adverse environmental impacts simultaneously.

The AG potential of waste materials and tailings in eachalteration zone can be estimated by laboratory and in-situ tests.A modified optimum cut-off grade model was developed in thispaper with the concept of elimination or reduction of the AMD inthe original place. Four coefficients that discriminate between AGand non-AG waste material and tailings incorporated into theLane’s model to ensure optimality of cut-off grades. As cut-offgrade calculation is very intricate, an Excel spreadsheet wasdeveloped to facilitate the determination of a complete optimumcut-off grade policy for long range.

Application of the model to the hypothetical PCD yielded a3.6% improvement on NPV of the project with given assumptions.This improvement is meaningful from the standpoint of a mineoptimization, because mining companies typically are satisfied by2–3% increase of their investment returns and this amount is asignificant gain especially for mines worth billions of dollars. Ofcourse, this long-standing area of study still demands more

3 The amounts of Qm, Qc, and Qr in these scenarios by utilizing the modified

optimum cut-off grade model are more or less the same, but it is expected that

applying it to actual mines causes more significant alterations into these amounts.

research to meet the challenges of the best mining practice inmine of the future.

Acknowledgments

The authors hereby acknowledge the Editor and the twoanonymous reviewers of this journal for their constructivecriticisms and valuable comments.

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