A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects

Resources Policy ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects Esmaeil Rahimi a,n, Hasan Ghasemzadeh b a b

Department of Mining Engineering, Islamic Azad University, South Tehran Branch, Tehran 16396-64981, Iran K.N. Toosi University of Technology, Tehran, Iran

art ic l e i nf o

a b s t r a c t

Article history: Received 20 April 2014 Received in revised form 2 June 2015 Accepted 15 June 2015

Optimum cut-off grades with different types of objective functions are determined by optimization algorithms which recognized as the one of the basis of sustainable development indicators of mining. As different mineral processing methods are applied in mines, it is very essential to choose the most appropriate cut-off grades determination algorithm. The current paper is going to analyze the bioheap leaching method and their associated environmental considerations on optimum cut-off grades policy. Remarking the importance of capital costs, these costs are evaluated in the model. Since the recovery of processing methods are changed based upon copper content, the recovery is considered variable in determining optimum cut-off grades. Presented model is evaluated in Sungun Copper Mine where the hydrometallurgical tests confirm the possibility of using bioheap leaching method to extract copper from its sulfide ores. It is observed that using bio-heap leaching method for low grade copper ores is subjected not only to improve the NPV of copper mines but also to decrease the adverse environmental impacts and produce sustainable results from mining activities. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Bioheap leaching Cut-off grades Environmental considerations Capital costs Sungun Copper Mine Sustainable development

1. Introduction Sustainable development basis are being increasingly applied by mining companies and there is a balance between the cut-off grade determination and sustainable mining practice (Franks et al., 2011; Uqaili et al., 2012). In fact, to gain the optimal cut-off grades and maximum NPV, the environmental consideration social impacts must be integrated in the mine design and issues (Osanloo et al., 2008; Asad and Topal., 2011; Mansouri et al., 2014). Optimum cut-off grades determination is counted as one of the main challenges in sustainable development principles of mining and in the first researches it had no consideration about their requirements (Rashidinejad et al., 2008; Li and Chang, 2012; Khodayari and Jafarnejad, 2012). Environmental, cultural and social parameters are counted as the main factors of sustainable development (Quinn and Snell, 2008). However, these parameters have not been considered in most of the cut-off grades optimization algorithms. Some have just regarded environmental factors (Dagdelen and Kazuhiro, 2007; Gholamnejad, 2008). According to the fact that sustainable development from mining is very important, mine designing and planning should also measure parameters related to it. Thus, a novel optimum cut-off grade model not only relies on economical n

Fax: þ 98 2188536290. E-mail addresses: [email protected] (E. Rahimi), [email protected] (H. Ghasemzadeh).

and technical considerations but also reclamation, environmental and social parameters. This issue completes previous models on optimum cut-off grades. It is essential to come into consideration recovery variations caused by grade fluctuation in order to calculate optimum cut-off grades. This is led into a considerable reduction of final products because of average grade decrease. In fact; this issue is remarked as one of the specifications of the new algorithm in comparison to the previous algorithms. The recovery amount is always considered fixed in most of these algorithms (Bascetin and Nieto, 2007; He et al., 2009; Johnson et al., 2011). This is also true in capital costs (Fan et al., 2013). Capital costs can differently affect NPV. These costs include mine opening, plants constructions and production infrastructures. Different processing methods increase investment costs and change optimum cut-off grades. Moreover, investment costs positively affect the sustainable development from social points of view (Pearce et al., 2013). Science and technology development of ore production and the commodity price fluctuation lead to expanding various mineral processing methods. These processing methods have different technical applications in grade ranges. They also affect the optimum cutoff grades for the sake of various operation costs (Dehghani and Ataee-pour, 2012). Practicing different processing methods in cut-off grades algorithms haven’t been considered that much. There have been attempts to make optimum cut-off grades model applying different processing methods like hydrometallurgical ones

http://dx.doi.org/10.1016/j.resourpol.2015.06.004 0301-4207/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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2

(Rendu, 2008, 2009; Asad and Dimitrakopoulos, 2013). This is while, the sustainable development basis have been preserved. The particular benefits of hydrometallurgical methods have directed them to be exceedingly practiced in copper mines. Some of the specific characteristics of this method have made it be singled out as the main processing method of small mines such as low costs (Dreisinger, 2006; Rahimi et al., 2014) and producing sustainable development (Uqaili et al., 2012). In spite of the benefits, less pollution and the process simplicity of this method (Watling, 2006), its most outstanding weak point is the low production in comparison to pyrometallurgical methods (Schlesinger et al., 2011). As hydrometallurgical methods have lower recovery and low operating and capital costs, it is emphasized to treat low grades ores by them (Gupta, 2006). Holistically, hydrometallurgical methods are practiced along with pyrometallurgical ones in copper mines. Thus, it is very significant to determine optimum cut-off grades of hydrometallurgical and pyrometallurgical methods. One of the most applicable hydrometallurgical methods is heap leaching ones and there are some industrial applications of these methods for sulfide deposits (Sukla et al., 2009; Rahimi et al., 2015). In case several processing methods are put into practice in copper mines, determining optimum cut-off grades is important from economical, environmental and social aspects (Yang, 2014). Moreover, it is necessary to identify parameters influencing the profitability in mines in order to provide a model determining optimum cut-off grades. Thus, these factors are defined again. Consequently, capital and operating costs of mine and mineral processing methods are contemplated. Next, the modeling of optimum cut-off grades determination is developed with the objective function of NPV maximization. Since there are various mineral processing methods, associated environmental pollutants and social impacts of these methods are reassessed. The effects of grade variations on process recoveries are also profoundly remarked in order to complete modeling. Eventually, the optimum cut-off grades of leaching and concentration methods are calculated by a constrained optimization method and computer programming due to different constraints.

2. Effective parameters Cut-off grade is the criterion normally used in mining to discriminate between ore and waste (Lane, 1964; 1988). The complete cut-off grades modeling is a very complex engineering subject and requires engineering knowledge and a good understanding of the many issues. It address sustainable development requirements, average grades and process recoveries, marketable product, controlling capacities and project time , capital and operating expenditure in mine design and planning. So, these effective parameters on cut-off grades determination model are described as follow.

2004; Mansouri et al., 2014). As the mining and processing activities cause environmental pollutants, it is necessary to identify them. Hence, the environmental pollutants of mines, leaching and concentration methods are classified as below: (1) Mine waste disposal cost (t1), (2) Leached waste disposal cost (t2), (3) Solvent extraction (SX) and Electrowinning (EW) tailing disposal cost (t3), (4) Concentration tailing disposal cost (t4), (5) Smelter and Electrorefining tailing disposal cost (t5), (6) Environmental protection cost of hydrometallurgical processes (t6), (7) Environmental protection cost of pyrometallurgical processes (t7), (8) The amount of leached material remained on heap (a1%), (9) The amount of SX and EW tailing (a2%), (10) The amount of concentration tailing (a3%) and (11) The amount of smelter and electrorefining tailing (a4%). Every process of producing final product can individually produce environmental pollutants. Thus, it seems indispensable to examine environmental costs of these production processes to determine optimum cut-off grades. 2.1.2. Social impacts Mining is an economic short-term activity with long-term effects. The sustainable development requirements have extended social responsibility of mine stockholders (Mutti et al., 2012). Mining has had an important role in shaping human development not only from a technological perspective, but it has also significantly influenced on working arrangements, lack of safety, child labor, rivalry and internal strife (Laurence, 2011; Hajkowicz et al., 2011). All this is added to the hazardous and unhealthy working conditions of this type of activity and it makes unavoidable costs. There can be no doubt that when it takes place, cut-off grades policy will be changed. There for the social costs indicator in cut-off grades determination algorithm is shown by ts . 2.2. Average grades and process recoveries Mineral processing plants are designed based on average grades of feed. It is obvious that the average grades of ore sent to processing plants completely rely on optimum cut-off grades policy. As mines use several processing methods, this policy seems more significant. The average grade of ores sent to leaching (ā H ) and concentration (āC ) plants are obtained by Eq. (1), in continuous form of grades distribution. gc

G

ā C (g ) =

∫g c g × qi (g ) dg G

, ā H (g ) =

∫g c qi (g ) dg

∫g h g × qi (g ) dg gc

∫g h qi (g ) dg

These relations are defined in discounted form of grade distribution of mines based on ore tonnage as the following:

⎡⎛ ⎞ c 2 ⎢ g ζ (g ) − (g c )2 ⎟ 1 ⎢ ⎜⎜ up ⎟ ā C (g ) = ζ (g c ) ⎟ 2 ⎢ ⎜⎜ ζ (g c ) ⎟ g g − down up ⎢⎣ ⎝ ⎠

(

)

2.1. Sustainable development

( )+∑

ζ gc

Although some researchers have defined the concept differently, sustainable development, generally, is the combination of improved socioeconomic development, and enhanced environmental protection. Thus, two aspects of sustainability concept are considered in paper as follow: 2.1.1. Environmental impacts Sustainable development basis leads to applying the environmentally friendly mining activities. It is very essential to integrate the sustainable development requirements in mines’ profitability and optimum cut-off grades (Rodriguez and Rozgonyi,

(1)

× qi

ζG ζ =ζ g c + 1

⎡⎛ 2 ζ gh 2 ⎢ − gh 1 ⎢ ⎜⎜ gup = 2 ⎢ ⎜⎜ ζ g h ζ gh − gdown ⎢⎣ ⎝ gup

( ) ( )

ζ ζ qiζ (gup + gdown

( )

(g

ζ up

ζ + gdown

⎞ ⎟ ⎟ × qiζ (g h) + ⎟⎟ ⎠

)

⎤ ⎥ qiζ ⎥ , ā H (g ) ⎥ ⎥⎦ ζ =ζ c − 1

ζ ∑ ζ=ζ g h+1 (gupζ + gdown ) g

⎤ ⎛ c 2⎞ ⎥ c )2 − g ζ (g ) ⎟ ⎜ g ( down ζ (g c ) ⎥ q ) qiζ + ⎜ ⎟ i ⎥ ⎜ g ζ (g c ) − g ζ (g c ) ⎟ down ⎠ ⎝ up ⎥⎦

(2)

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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In relations (1) and (2), i is the year indicator, ζ is the grade category indicator, g shows the grade and q represents the material tonnage, G introduces the maximum ore grade. g h is leaching cut-off grades and g c introduces concentration cut-off grades. Also gup and gdown are the upper and lower limit of the grade category, respectively, in grades distribution table. Scientists have attempted a lot to recognize the relationship between the recovery of mineral processing plants and the average grades of feed (Neethling and Cilliers, 2012; Nakhaei et al., 2013). Obviously, concentration process recovery is specifically sensitive to average grades of feed (Cillingir and Sen, 2000). Hence, the relationship between average grades and process recovery should be regarded in order to precisely determine optimum cutoff grades. Although the influence of average grade of feed on concentration recovery has been evaluated (Nakhaei et al., 2012), no specific results have been obtained from the effect of average grade of feed on the heap leaching recovery. As there are several effective parameters on leaching recovery (Maley et al., 2009; Norris et al., 2010; Kodali et al., 2011), the effect of average grade of feed on leaching recovery hasn’t been clearly specified yet. However, this can be assessed by laboratory tests for a specific mine and it can be added to studies related to cut-off grades. 2.3. Marketable product The amount of marketable product is definitely depended on the feed average grades sent to processing plants and processes recovery. As a matter of fact, marketable product is influential on cut-off grades of mineral processing methods. In the continuous form of grade distribution, the annual final products made by smelting (σSi ) and EW (σ Xi ) plants are calculated as below:

σ Si (g ) = ηC η S . ā C (g ). σCi (g ) and σ Xi (g ) = η H η X . ā H (g ). σ Hi (g )

(3)

In this relation, ηC and ηS are the concentration and smelting recovery, respectively, ηH is the heap recovery,ηX is the SX and EW process recovery. σCi (g ) and σHi (g ) represent the amount of mined materials sent to concentration and heap, respectively, which are also calculated by Eqs. (4) and (5), in the continuous and discounted forms of grade distribution:

σCi (g ) =

∫g

⎛ ⎞ ζ gc c ⎜ gup( ) − g ⎟ ζ (g c ) + qi (g ) dg = ⎜ ⎟ × qi ⎜ g ζ (g c ) − g ζ (g c ) ⎟ down ⎠ ⎝ up

G c

ζG

∑ ζ=ζ g c+1

qiζ (4)

And:

σ Hi (g ) =

∫g

gc h

qi (g ) dg

⎛ ζ gh ⎜ gup − gh =⎜ h ζ gh ⎜ ζ g − gdown ⎝ gup

( ) ( )

( )

⎞ ⎟ h ⎟ × qiζ (g ) + ⎟ ⎠

⎛ ⎞ ζ (g c ) ⎜ g c − gdown ⎟ c +⎜ × qiζ (g ) c ⎟ c ζ g ( ) ⎜ g ζ (g ) − g ⎟ ⎝ up down ⎠

ζ=ζ g c−1

∑

qiζ

ζ = ζ g h+ 1

3

hydrometallurgical methods (Bioheap, SX and EW) indicates the usability of hydrometallurgical methods to low grade ores treatment. Capital costs in optimum cut-off grades determination include the costs related to heap (CH ), SX and EW (C X ), concentration (CC ), smelter and refinery plants (CS ). The capital costs added to modeling are considered based upon production capacity of processing plants. Clearly, when there are not any investments on constructing some plants, associated treatment costs can be added annually to production costs. In this paper assume that the capital cost of mineral processing plants is invested at time zero. Thus, total investments are calculated simply by dividing the discounted capital cost per operation life. 2.5. Operating costs Optimum cut-off grades determination depends upon the operating costs beside capital costs. Thus, the operating costs of leaching process should be considered in order to complete cut-off grades determination algorithm. The operating costs of the leaching process (h) include all costs of bacteria's growth and development, cultivation, nutrition and the consumed chemical materials in chemical leaching applied in copper sulfide ores and indicated as hb . c , Costs of material hauling by different methods (hT ), Utility and energy costs (hU , F ), Labor costs ( h L ). The SX and EW costs are shown by x sx and x ew , respectively. In addition, concentration operating costs (c), mining costs (e ) and leaching costs (h) as the percentage of operating costs are important parameters in optimum cut-off grades determination. 2.6. Controlling capacities and project time Mine and plants capacity are the maximum amount of materials (ore, waste, intermediate and final product) mined or produced in a given time period. These limiting capacities have influence upon the cut-off grades. Thus, the time of project can be also controlled by them. Limiting capacities of applying heap leaching and concentration methods are including: Mining capacity (Cap, ) is limited by the restriction on drilling, blasting operations, hauling, loading equipment’s capacities and etc. Concentration plant capacity (Cap* ), is therefore governed by the maximum rate of crushing, milling, flotation, etc. Smelting, refining and marketing capacities (Cap: ) which is restricted by dryer, flash furnace, Anode furnace, convertor furnace and electrorefining cells capacities. Heap capacity (Cap/ ), is the maximum amount of ore which can be embanked on the heap that relies on crushing and stacking capacities, Acid irrigation rate, safety equipment, safe pad loading, liners, aeration rate, inoculums, heap heating, ionic liquid solution (ILS) and Raffinate irrigation rate and etc. SX and EW capacities (Cap? ), is dependent upon settlers’ capacities, mixer capacities, extracting materials, EW cells capacities and etc.

3. Method

(5)

2.4. Capital expenditure The effect of capital costs has not been considered in optimum cut-off grades calculations. Determining accurate optimum cut-off grades needs to consider capital costs of mine and mineral processing plants. A comparison between the capital costs of pyrometallurgical (concentration, smelter and electrorefining) and

3.1. Material destination Economic criteria and technical aspects are applied to assign destinations for mined material (waste dumps, stockpiles, heap or concentration) based on their value. Mineral and metallurgical characteristics of the ore consider as one of the most important part of technical aspects beside size and shape of the pit. Other technical parameters influencing the determination of mined material destination consist of grade, processing methods re-

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Determination of economic deposit size, composition, shape and grad e-tonnage distribution; block model construction Hydrometallurgical environmental considerations

Mine Environmental Considerations Option 1 The mined material comprises the mainly copper oxide ores

No

The mined material comprises only copper sulfide ores

Yes

Implementation of new algorithm No

Option 3 Determination of optimum cut-off grades by proposed method

Option 2 Sulfide part Hydrometallurgical and Pyrometallurgical environmental considerations

Yes

Oxide and sulfide copper ores

Oxide part

Pyrometallurgical environmental considerations Ores treats only by pyrometalurgical methods

Scenario 2

Yes Scenario 1

Input data: the associated costs, Capital costs, Price, Capacities, Quantities and process recoveries

Input data: the associated costs, Capital costs, Price, Capacities, Quantities and process recoveries

Mined material grades< leaching cut-off grades

No Destination: Heap leaching

Stockpiling policy

Yes

No

Input data: the associated costs, Capital costs, Price, Capacities, Quantities and process recoveries

Destination: Stockpile

Destination: WRD

Implementation of new algorithm Implementation of new algorithm Determination of optimum cut-off grades by proposed method

Determination of optimum cut-off grades by proposed method

Mined material grades< Concentration cutoff grades

Yes

Destination: Stockpile No

Destination: WRD

Destination: Concentration Concentration cutoff grades < Mined Material grades

Yes Destination: Concentration process

Stockpiling policy

No

Mined material grades < CL or BL cut-off grades

Yes

Stockpiling policy

Destination: Stockpile

No Destination: CL or BL processes

Destination: WRD

Fig. 1. Flowchart to determine mined material destinations (BL: Bacteria Leaching, CL: Chemical Leaching, WRD: Waste Rock Dump).

covery, grade variation, plants production capacity, plant life time and their availability. On the other hand, economic criteria are also applied to cut-off grades determination. The most significant economical factors determining mined materials destination include commodity price, capital and operation costs and discounted rate. On the other hand, parameters related to sustainable development are composed of environmental and social. Fig. 1 illustrates the mined material destinations considering economical, technical and environmental aspects.

As shown in the Fig. 1, it is necessary to access to ore exploration information like deposit and grade-tonnage distribution and etc. After completing this information, information related to costs accessing to sustainable development is taken from mine and the surrounding. Ore mineralogy determination is essential for determining the final destination. Based on the oxide ore content, two different treatment directions are analyzed. Three options are also defined in Fig. 1 to calculate the cut-off grades of copper mines. The first case option is described an oxide copper mine which usually recognize as the small mines.

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Furthermore, hydrometallurgical tests demonstrated that heap leaching method is useful. As can be seen in Fig. 1, the heap leaching optimum cut-off grades determination is mandatory to assign mined material destinations including waste dumps, stockpiles, heap for oxide minerals. The second case option indicates a copper mine containing hypogene and supergene sulfide ores. As can be seen in Fig. 1, there are more scenarios to assign material destinations. In this case, to exactly calculate optimum cut-off grades, an economical model with an objective function is needed. As observed in Fig. 1 in this scenario, in case the mined material grades are more than calculated cut-off grades of concentration, the material will be definitely sent to the concentration. So, this material is sent to the Bacteria leaching plants or chemical leaching ones if the ore grade exceeds the cut-off grade calculated through hydrometallurgical method by the novel algorithm. Otherwise, the mineral is sent to the stockpiles and WRD based on their grade and hope to prices increase in the future. Selecting ore destination depends on ore production policy and sustainable development of countries. The third case option introduces a mine embracing copper oxide and sulfide ores. In this option, the cut-off grades of these methods are considered as a factor to ascertain ore destinations. Finally, the cut-off grades of oxide and sulfide deposits calculate individually. According to the grade, the algorithm choosing the final direction for each one of the sulfide or oxide deposits in transition zones is similar to the previous one. Only separated blocks will follow different directions for the sake of mineralogy and environmental factors.

function in the discounted form of grades distribution can be written as Tlife

NPV = max :

− hi . σ Hi (g ) −

CS . f (ā C ). η S . ā C (g ). σCi (g ). (1 + ∂)t Tlife

−

CX . f (ā H ). η X . ā H (g ). σ Hi (g ). (1 + ∂)t − ei . σ Ei (g ) Tlife

− t1γi (w , s ) − t2 a1 (σ Hi (g ) − σ Xi (g ) ) − t3 a2 (σ Hi (g ) − σ Xi (g ) ) − t4 a 3 (σCi (g ) − σ Si (g ) ) − t5 a 4 (σCi (g ) − σ Si (g ) ) − t6. σ Xi (g ) ⎤ − t7. σ Si (g ) − t s.(σ Xi (g ) + σ Si (g )) − (f ic + f ih + ∂. NPVi ) ⎥ ⎥⎦ . (1+∂)−t

It is also expressed in the continuous series of cash flows by Eq. (7).

NPV =

∫t

Tlife

Cash Flow . e−∂t dt

o

(7)

In expressions (6) and (7), to is the beginning time of project operation phase,Tlife is the project life and ∂ is the discount rate. From the other point of view, the heap leaching and concentration processes recovery will be assumed to vary directly with the ore average grades sent to plants. It is possible to find equations of the form of below (Equation.8) relating recoveries of heap leaching (ηH ) and concentration (ηC ) to their average grades. These equations can be assigned by mineral processing tests or prediction methods.

ηC = f (aC ) and η H = f (a H )

(8)

However the SX, EW, Smelter and electrorefining processes recovery are assumed independent of the mined material average grades. One can now calculate the cash flow function considering capital and operating costs, environmental considerations as well as the grade-recoveries relations under the various constraints. Considering relation 6 and 7, the NPV of mentioned cash flows

(9)

P represents commodity price and s indicates the smelting costs. γi (w, s)is the annual mined materials sent to stockpiles or waste dumps. f c is the fixed costs of concentration and smelting methods and f h indicates the fixed costs of heap leaching method. NPV is also expressed in continues series of cash flows by Eq. (10): Tlife

⎡

o

⎣

∫t=t ⎢⎢ (Pi − si ). f (āC ). ηS . āC (g ). σCi (g )

+ (Pi−x sxi − x ewi ). f (ā H ). η X . ā H (g ). σ Hi (g ) − ci. σCi (g ) − hi . σ Hi (g ) −

CC CH . σCi (g ). e ∂i − . σ Hi (g ). e ∂i Tlife Tlife

−

CS . f (ā C ). η S . ā C (g ). σCi (g ). e ∂i Tlife

−

CX . f (ā H ). η X . ā H (g ). σ Hi (g ). e ∂i − ei . σ Ei (g ) − t1γi (w , s ) Tlife

(6)

t = to

CC CH . σCi (g ). (1 + ∂)t − . σ Hi (g ). (1 + ∂)t Tlife Tlife

−

Tlife

∑ Cash Flowt × (1 + ∂)−t

⎣

+ (Pi − x sxi − x ewi ). f (ā H ). η X . ā H (g ). σ Hi (g ) − ci. σCi (g )

NPV = max :

NPV =

⎡

∑ ⎢ (Pi − si ). f (ā C ). ηS . ā C (g ). σCi (g ) ⎢

t = to

3.2. Objective function The NPV maximization is considered as the objective function in optimum cu-off grades modeling. The maximum amount is calculated in the form of discounted series of annual cash flows as follow:

5

− t2 a1 (σ Hi (g ) − σ Xi (g ) ) − t3 a2 (σ Hi (g ) − σ Xi (g ) ) − t4 a 3 (σCi (g ) − σ Si (g ) ) − t5 a 4 (σCi (g ) − σ Si (g ) ) − t6. σ Xi (g ) ⎤ − t7. σ Si (g ) − t s. (σ Xi (g ) + σ Si (g ) )−(f ic + f ih + ∂. NPVi ) ⎥ ⎥⎦ . e−∂i di

(10)

3.3. Optimum cut-off grades As mentioned, the maximum amount of NPV can be obtained by relations (9) and (10). On the other hand, the mine and plants capacity are considered as governing constraints which the time of project can be controlled by them. Thus, the annual cash flows would be defined as constrained optimization problem. Hence, the Lagrangian multiplier optimization method is used to determine leaching and concentration optimum cut-off grades as well as maximum annual cash flows. The lagrangian function of continuous annual cash flows considering governing constraints is presented in Eq. (11).

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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(

σEi is the total deposit. Heap leaching limiting cut-off grade is also calculated as relation (13), when the mine production capacity is the governing constraint:

)

3 g h, g c , λ = G

∫g= g (Pi − si). f (āC). ηS . g . qi(g )dg c

gc

∫g= g (Pi − xsxi −

+

∫g

G

ci. qi(g )dg −

c

CH ∂i .e . Tlife

−

∫g

∫g

g h

gc h

CC ∂i .e . Tlife

∫g

G c

qi(g )dg

. η X . Pi − f (ā H ). η X . (x sxi + x ewi )−f (ā H ). η X .(t6 + t s ) ⎛ σ Ei ⎞ 0.5 ⎜ ⎟ ⎝ Cap E ⎠

c

−C X . f (ā H ). η X . (1 + ∂)

qi(g )dg −

+ t2 a1. f (ā H ). η X

+ t 3 a 2 . f (ā H ) . η X ]

∫g f (āC). ηS . g . qi(g )dg c

C − X . e ∂i Tlife

gc

∫g f (āH). ηX . g . qi(g )dg − ∫0

t1. qi(g )dg − t2a1(

∫g

ei . qi(g )dg

gc h

qi(g )dg

gc

gc

h

h

∫g f (āH). ηX . g . qi(g )dg ) − t3a2( ∫g

gc

G

h

c

∫g f (āH). ηX . g . qi(g )dg ) − t4a3( ∫g

(13)

Other limiting cut-off grades are determined with concentration, smelter, heap, SX and EX limiting capacities. In the previous step, the only one of the operations is assumed as the limiting factor. As controlling capacities are placed in pair in balance, 10 balancing cut-off grades will be determined which are named dual balancing cut-off grades (DBG). The dual balancing cut-off grades come from the following relations:

G

h

gh

−

hi . qi(g )dg −

G

CS ∂i .e . Tlife

∫0

⎡ ⎤ ⎛ σ Ei ⎞ 0.5 ⎜ ⎟ g Eh = ⎢hi − t1 + CH (1 + ∂) ⎝ Cap E ⎠ + t2 a1 + t3 a2 ⎥/[f (ā H ) ⎢⎣ ⎥⎦

xewi ). f (āH). ηX . g . qi(g )dg −

h

qi(g )dg −

⎧ σCi Cap* σ Hi Cap/ ⎨ , , = = Cap, ⎩ σ Ei Cap, σ Ei

qi(g )dg

,

Cap: σ Si = Cap? σ Xi

(14)

G

−

∫g f (āC). ηS . g . qi(g )dg ) c

t5a4(

∫g

qi(g )dg −

c

In case three controlling capacities be in balance, 10 others balancing cut-off grades are calculated. They are named triple balancing cut-off grades (TBG) come from the following relations.

G

G

∫g f (āC). ηS . g . qi(g )dg ) c

gc

− t6.

∫g f (āH). ηX . g . qi(g )dg−

⎧ ⎪ σ Ci σ Hi σ Ei σ Si σ Ci σ Ei σ Si σ Hi σ Xi ⎨ , , , = = = = = = ⎪ Cap , Cap: Cap* Cap , Cap: Cap/ Cap ? (15) ⎩ Cap* Cap/

h

G

∫g f (āC). ηS . g . qi(g )dg

t7.

c

⎛ − ts. ⎜ ⎝

gc

∫g f (āH). ηX . g . qi(g )dg h

⎞

G

+

(f

c i

∫g f (āC). ηS . g . qi(g )dg ⎟⎠− c

)

+ fih + ∂. NPVi . T +

m

∑ λkTk(g )

(11)

k=1

In Eq. (11), “3 ” is the Lagrangian indicator, “λ ” is the Lagrange multiplier, “m” is the number of constraint, “k” indicates the constraint number and “G” represents the maximum ore grade. “T” is the project time which can be controlled by mine and plants capacity. On the other hand, leaching and concentration optimum cut-off grades are calculated under governing constraints described in Section 2.6. These grades are named limiting cut-off grades (LG). Hence, if mine throughput is the limiting factors, the concentration limiting cut-off grade is achieved by Eq. (12).

⎡ ⎛ σ Ei ⎞ ⎛ σ Ei ⎞ 0.5 ⎜ 0.5 ⎜ ⎟ ⎟ g Ec = − ⎢ − ci − hi + CC (1 + ∂) ⎝ Cap E ⎠ − CH (1 + ∂) ⎝ Cap E ⎠ ⎢⎣ ⎤ − t2 a1 − t3 a2 + t4 a 3 + t5 a 4 ⎥/[f (ā H ). η X . Pi − Pi. f (ā C ). η S ⎥⎦ − f (ā H ). η X . (x sxi + x ewi ) + si . f (ā C ). η S − f (ā H ). η X . (t6 ⎛ σ Ei ⎞ 0.5 ⎜ ⎟ ⎝ Cap E ⎠

+ t s )+(t7 + t s ).f (ā C ). η S − C X . f (ā H ). η X . (1 + ∂) ⎛ σ Ei ⎞ 0.5 ⎜ ⎟ ⎝ Cap E ⎠

+ CS . f (ā C ). η S . (1 + ∂)

+ t2 a1. f (ā H ). η X

+ t3 a2. f (ā H ). η X − t4 a 3. f (ā C ). η S − t5 a 4 . f (ā C ). η S ]

(12)

The annual cash flows surfaces are depend on concentration and leaching cut-off grades. The illustration of cash flows surfaces is also so useful to clarify the cut-off grades concept. Therefore, considering the mine and plants capacity as the constraints, three cash flow surfaces are shown in Fig. 2. Two cash flow surfaces are also eliminated to simplify the figure. The surfaces configuration can be recognized as a function of capacities and economical parameters. In addition, the limiting, dual and triple balancing cutoff grades are denoted. The initial assumption of optimum cut-off grades applied in optimization algorithm can be considered as limiting, duals balancing or triples balancing are geometrically located in maximum point of the surface, passing through the minimum of all cash flow surfaces. It is also denoted in Fig. 2. In Fig. 2, the maximum points of the cash flow surfaces show the limiting cut-off grades. The maximum points of two cash flow surfaces intersecting curves indicate dual balancing cut-off grades. Finally, triple balancing cut-off grade is denoted on three cash flow surfaces intersecting points. In this paper, the initial assumption of optimum cut-off grades is determined by lagrangian multiplier method. Then, final optimum cut-off grades and NPV maximum can be calculated by iterative process and Matlab programming. The iterative process must be used since an unknown NPV is appeared in the NPV maximization function. The unknown NPV is related to opportunity cost and the opportunity cost is inevitable when there are constraints in cash flow function. This cost occurs when the materials was not previously scheduled to be mined or processed. This cost is also demonstrated by “∂. NPV.i T ” as is shown in relations (9)–(11). Obviously, the opportunity cost reduces when the deposit is exhausted during mine life.

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Fig. 2. The geometric locations of optimum, limiting, dual and triple balancing cut-off grades.

4. Results and discussion 4.1. Case study The Sungun Copper Mine is the second largest porphyry copper deposit of Iran which is mostly contained Leached, Supergene, Hypogene and Skarn zones. Copper mineralization in the mentioned Zones comprises Chalcopyrite, Chalcocite, covellite, Bornite, malachite and azurite. The copper mineralization is mainly hosted by a hydrothermally altered monzonite-quartz porphyry intrusion. The geological map of Sungun area is shown in Fig. 3. Exploration in Sungun copper mine is composed of 240 core which most of them are vertical (83%) with the length of more than 80,000 m. The dimensions of block model are designed in 25 m  25 m  12.5 m. This means that the one quarter the average drill hole spacing and the planned bench height. The blocks are encrypted with a coding system to enable litho logical

limitations to be used in the interpolation of grades. This is based upon interpolation into a block model applying litho logical and zone criteria as based on the parameters calculated from statistical analysis. Kriging method has been used for the Supergene and Hypogene Zones and inverse distance method performed for the Skarn Zones. The resource used for pit design and mine planning is the Measured and Indicated resources of 807 Mt with 0.62% average grade at the cut-off grade of 0.25%. The copper ore production is planned to extract in two phases. In phase 1, the ore production capacity is considered 7 million tons per year for the first six years of production and after that 14 million tons per year (Phase 2) for the rest of mine life. Floatation plant produces 150,000 tons concentrate with 30% copper grade in Phase 1. Three development plans are also considered to produce copper concentrate with grade of 28%. It is designed to treat about 58 Mt by bioheap leaching and concentrator plants of plan 3 containing hypogene

Fig. 3. The geological map of Sungun copper mine (National Iranian copper industrial company (NICICO), 2002).

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Table 1 Grade distribution of third development plan of Sungun Copper Deposit sent to plants. Grade (%)

Pushback1

Pushback2

0–0.1 0.1–0.2 0.2–0.3 0.3–0.4 0.4–0.5 0.5–0.6 0.6–0.7 0.7–0.8 0.8–0.9 0.9 o

2,392,080 5,624,321 6,838,790 6,170,450 4,034,890 2,216,795 1,212,608 412,308 193,675 113,490

1,216,120 3,916,979 5,516,210 5,674,550 5,158,110 3,761,305 2,100,492 1,167,792 458,735 219,880

and supergene sulfide minerals. The grade distribution of this plan is also outlined in Table 1. Determination of sulfide ore destinations, bioleaching and concentration cut-off grades are crucial considering two applicable processing methods. The selection of heap location and associated costs were the main problems considering the Sungun mountainous area. In contrary, the Sungun native bacteria were so helpful in bioleaching process. The recovery of concentration process (plan 1) was calculated about 85% considering average grade of feed (0.75%). 4.2. Sampling The representative samples of Sungun hypogene and supergene sulfide minerals were divided into some sub samples by conequartering method to determine the bioleaching recovery (Fig. 4a). The sub samples were crushed less than 1 in. by a laboratory jaw crusher (Fig. 4b). Chemical composition of Sungun hypogene and supergene sulfide ores is presented in Table 2. 4.3. Acid consumption The Roll Bottle test has performed to determine the net acid consumption of every Sample. Test conditions included a pulp of pulverized ore sized to below 0.5 in. in acidic Solution (pH ¼ 1.5). The test period is 120 h (Fig. 5). The results of tests are presented in Table 3. 4.4. Shake-flask test Shake-flask tests are conducted on Sungun native bacteria (mesophilic, moderately thermophilic and extremely thermophilic) to specify bioleaching recovery of Sungun hypogene and supergene sulfide samples. The results of test are shown in Table 4.

4.5. Column tests The Sungun Hypogene and supergene ore samples were prepared for the four mini column tests after crushing less than 1 inch. The columns with 1 m height and 132 mm diameter were filled by crushed ore samples (Fig. 6). The concentration of curing acidic solution was 6 gr/l and rate of irrigation was 12 l/m2 per h. The total recovery of copper was more than 80% at ambient temperature. To complete the test results, the samples were used for the four large columns test after crushing less than 1 in. The columns with 2 m height and 35.5 cm diameter were filled by crushed and agglomerated ore samples. The total ore weight in every column was about 480 kg. The concentration of curing acidic solution was firstly 6 gr/l and consequently 12 gr/l which rate of irrigation was 8 l/m2 per h. The copper concentration variations, acid consumption and total recovery of copper for the four samples of Sungun hypogene (H) and supergene (S) ores during leaching time are depicted in Figs. 7–9. As can be seen, the maximum copper recoveries of hypogene and supergene sulfide minerals are 66% and 69.49%, respectively, in the columns with 2 m height. The copper recovery variations of bioleaching method versus average grades are also evaluated by experimental tests based on four grades. As can be seen in Fig. 10, a relation between average grade and leaching recovery is obtained. The relation of copper recovery of concentration method versus average grades was also achieved in Sungun flotation laboratory depicted in Fig. 10. The maximum amounts of NPV and optimum cut-off grades are affected by obtained equations of ηC and ηH (Fig. 10). Thus, these equations are added to Eq. (9)–(13) as f (aC ) and f (a H ). To calculate optimum cut-off grades of Sungun Copper Mine, two scenarios are considered to treat hypogene and supergene copper ores. These scenarios are also shown in Fig. 1. In the first case scenario, it is assumed that hypogene and supergene copper ores are simultaneously processed by concentration and bioheap leaching methods. In the second scenario, only the concentration method is used. The assumed costs of processing methods, technical and environmental parameters are summarized in Table 5. The concentration cut-off grades are determined using presented algorithm when the leaching parameters are equal zero. The results are outlined in Table 6. The bioheap leaching and concentration cut-off grades are determined by lagrangian method and iterative process. In addition, Annual cash flows and maximum NPV are presented in Table 7. The overall NPV of Sungun Copper Mine in first case scenario is obtained T$147,072 (Table 6) which can be compared to the NPV of the new presented algorithm in Table 7 (T$164,696). Moreover, the

Fig. 4. Hypogene and supergene ores of Sungun Copper Mine (A); The laboratory jaw crusher used for Sungun copper samples (B).

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Table 2 Chemical composition of Sungun hypogene and supergene sulfide ores.

Supergene zone (%) Hypogene zone (%)

Cu

CuO

Fe

CuFeS2

Cu2S

CuS

Fe2O3

Fe3O4

FeS2

FeOOH

0.53 0.36

0.2 0.06

3.36 3.93

12.01 74.92

55.24 6

9.99 0.94

0.138 0.029

0.068 0.01

6.42 8.5

0.134 0.001

Fig. 5. The Roll Bottle test of Sungun copper ore. Table 3 The results of acid consumption tests.

Supergene zone (%) Hypogene zone (%)

Acid consumption (kg/ Cu recovery ton) (%)

Fe Recovery (%)

42.1

49.7

10

34.5

29

4

concentration optimum cut-off grades of the first and second scenarios are dropped to 0.26% and 0.275%, respectively, at the end of mine life (Tables 6 and 7). Clearly, obtained concentration cutoff grade of the first scenario (0.26%) is slightly higher than bioheap leaching cut-off grade of the second scenario (0.229%). From environmental point of view, it is indicated that The TEC per unit of final product in second case scenario is increased to $288.3 which is slightly smaller than the TEC of first case one ($302.1). It means that the total environmental costs related to its mine and plants are less while applying both leaching and concentration methods for mineral processing. In case these two

Fig. 6. The illustration of columns with 1 m height and 132 mm diameter.

Table 4 The results of Shake-flask test. Sample

Bacteria

pH

Inoculation (%)

Recovery (%)

Sample

Bacteria

pH

Inoculation (%)

Recovery (%)

H H H H H H H H H

Me Me MT MT MT MT W W ET

1.8 2 1.8 2 1.8 2 1.8 2 1.8

10 15 10 10 15 15 0 0 10

42 45 60 61 64 70 33 28 31

S S S S S S S S S

Me Me Me Me MT MT W W ET

1.8 2 1.8 2 2 1.8 1.8 2 1.8

10 10 15 15 10 15 0 0 10

71 75 74 75 77 80 51 47 56

H: Hypogene ore, S: Supergene ore, Me: Mesophilic bacteria, MT: Moderately Thermophilic bacteria, ET: Extremely Thermophilic, W: Without bacteria.

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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10

4

2.5

3.5

Cu (gr/L)

2.5

S1

S2

S3

S4

Cu (gr/L)

2

3

2 1.5 1

1.5

H1

H2

H3

H4

1 0.5

0.5 0

0

1

10

25

40

55

70

85

100

1

10

25

40

55

Time (day)

70

85

100

70

85

100

85

100

Time (day)

Fig. 7. Cu concentration versus leaching time: supergene ores (A), hypogene ores (B).

25

30 S2

S3

S4

20

Acid Consumption (Kg/ton)

Acid Consumption (Kg/ton)

25

S1

20 15 10

H1

H2

H3

H4

15 10 5

5 0

0

1

10

25

40

55

70

85

100

1

10

25

40

55

Time (day)

Time (day)

Fig. 8. Acid consumption versus leaching time: supergene ores (A), hypogene ores (B).

80 S1

S2

S3

S4

70 60

60 Cu recovery (%)

Cu recovery (%)

70

50 40 30 20

H1

H2

H3

H4

50 40 30 20 10

10

0

0

1

10

25

40

55

70

85

1

100

10

25

40

55

70

Time (day)

Time (day)

Fig. 9. Cu recovery versus leaching time: supergene ores (A), hypogene ores (B).

C

Concentration

100

= (0.94).exp ((0.06).aC) + (-0.93).exp ((-388.1).aC) R2=0.98

Leaching

80

60

1.4

1.3

1.2

1.1

1

0.9

0.8

0.7

0.4

0.3

0.2

0.1

0.05

0

= (0.59).exp ((0.076)* aH) + (-0.59).exp ((-3985). aH) R2=0.99

0.5

H

20

0.6

40

0

Copper recovery (%)

120

Average grade (%) Fig. 10. Bioheap leaching and concentration methods recovery versus average grades.

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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Table 5 Economical and environmental parameters, operational capacities and plants recovery of Sungun Copper Mine. Component

Value

Unit

Component

Value

Unit

Component

Value

Unit

∂

6

%

t7

0.65

$/Tp

P

7.05

T$/Tp

Cap*

6.900

TT/year

e

2.2

$/Tm

hB.C

0.2

$/To

Cap/

1.110

TT/year

s

1.13

T$/Tp

hS

0.9

$/To

Cap,

8.500

TT/year

c

4.3

$/To

hT

0.5

$/To

Cap:

30

TT/year

fc

8.505

T$/year

hL

0.4

$/To

Cap?

3.5

TT/year

1.100

T$/year

hU , F

0.3

$/To

t1

0.2

fh ηX

0.95

%

x sx

142

$/Tp

t2

0.4

ηS

0.97

%

xew

88

$/Tp

t3

0.7

$/Tt* $/Tt

97

%

0.9

$/Tt

3

%

CC CH

1.3

t4

a1 a2

0.7

$/To $/To

$/Tw*

t5

1

$/Tt

a3

95

%

CS

260

$/Tp

t6

0.35

$/Tp

a4

5

%

CX

160

$/Tp

ts

0.15

$/Tp

Note: *(T$: Thousand dollars, TT: Thousand tons, Tp : Tons of product, To : Tons of ore, Tm : Tons of material, Tw : Tons of waste, Tt : Tons of tailings)

Table 6 The optimum concentration cut-off grades policy of the Sungun Copper Mine (Scenario 1). Year

Pushbacks

Total material (TT)

* ) σ Ei (TT m

σ Si (T p* )

g c (%)

CECi ($/Tpi )

TECi* ($/Tpi )

1 2 3 4 4 5 6 7

1 1 1 1 2 2 2 2

58,400 49,900 41,400 32,900 29,191 24,400 15,900 7,400

8500 8500 8500 3709 4791 8500 8500 7400

17,252 17,450 17,705 7807 10,083 18,038 18,238 16,112

0.302 0.296 0.288 0.282 0.294 0.277 0.270 0.260

249.1 252.0 255.9 258.8 258.8 261.3 264.9 270.0

292.6 293.7 295.3 296.6 296.6 297.8 299.5 302.1

Life (year)

Cash flows (T$)

Overall NPV (T$)

4.7 4.1 3.5 1.3 1.6 2.2 1.4 0.7

48,347 48,969 49,747 21,944 28,340 50,701 51,239 45,197

147,072 130,357 111,137 89,546 89,546 65,940 40,529 9644

Note: *(CEC: Concentration Environmental Cost, TEC: Total Environmental Cost), TTm : Thousand Tons of material

Table 7 The optimum concentration and leaching cut-off grades policy of the Sungun Copper Mine (Scenario 2). Year

Push backs

Total material (TT)

1 2 3 4 4 5 6 7

1 1 1 1 2 2 2 2

58,400 49,900 41,400 32,900 29,191 24,400 15,900 7400

σ Si (Tp*)

σ Xi (Tp*)

g h (%)

g c (%)

LECi

CECi ($/Tpi )

TECi* ($/Tpi )

Life (year)

Cash flows (T$)

Overall NPV (T$)

16,852 17,104 17,306 7639 9866 17,703 17,898 15,747

1244 1247 1247 544 702 1244 1240 1075

0.271 0.265 0.259 0.251 0.251 0.244 0.237 0.229

0.311 0.306 0.300 0.294 0.294 0.288 0.282 0.275

240.0 246.6 252.2 258.3 258.3 264.8 271.9 279.5

243.7 247.1 249.9 252.8 252.8 255.9 259.0 262.2

279.2 280.6 281.9 283.3 283.3 284.8 286.5 288.3

4.5 4.0 3.4 1.2 1.5 2.1 1.4 0.7

53,689 54,486 55,093 24,293 31,374 56,202 56,696 49,748

164,696 145,926 123,987 100,035 100,035 73,978 45,733 11,563

Note: *(LEC: Leaching Environmental Cost, TT: Thousand Tons)

methods are simultaneously applied, there will be a reduction in the environmental costs of the mine. In consequence, the optimum cut-off grades are diminished, the benefits will increase and it is easier to access to mining sustainable development. These findings are logical because the pollutants of hydrometallurgical methods are less than the concentration ones. This result is repeatedly observed in various researches. Since the simultaneous effect of practicing pyrometallurgical and hydrometallurgical methods hasn’t been evaluated in calculating optimum cut-off grades, mine planning and accessing to sustainable development, the current research carries out new facts.

5. Discussion on finding A comparison between the current research to others reveals the conclusion that mining was beneficial in case of applying both

the hydrometallurgical and concentration methods for mineral processing. This problem is determined through assessing the calculated cash flows in this research to other research. Similar results have been obtained in NPV increase and environmental unit costs decrease. As expected, NPV and environmental costs variations decreases the total cut-off grades of this mine in different years of production comparing to similar research. In addition, the decrease of cut-off grades increases the net copper production than other similar modeling. This research has a remarkable novelty because the outcomes and its modeling embrace capital cost and processing recovery variation for changing the optimum cut-off grades. This research considers environmental parameters and accessibility to sustainable development besides technical and economical problems. This increases the novelty of the current research subject. A comparison between the current research results to similar one is led to the idea that the investment costs plays a key role in determining optimum cut-off grades

Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i

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and accessibility to sustainable development from mining. This subject has been ignored in previous researches. Furthermore, the effect of recovery changes has reflected similar results. Comparing this algorithm to the similar ones, it is concluded that this new one is the most complete one for the sake of considering several technical parameters (capacity limitations, ore tonnages and by products, grade-recovery variations), economical parameters (capital costs, investment costs, operation costs and opportunity costs) and sustainable development parameters (social costs and environmental costs of different processing methods). The main limits of the current research include not simple accessing to technical and economical information of the mine like total operation costs, investment costs, final plant recovery and eventually commodity price condition. On the other hand, the most difficult parts of this research are calculating and determining the sustainable development factors including social and environmental issues and their not being quantative. From practical aspects, calculating the recovery of different processing methods and determining grade-recovery curve are identified as the time and cost consuming part of the research. There might be few errors because of sampling and laboratory conditions. Analyzing the changes of commodity price on cut-off grade policy and accessing to sustainable development are regarded as important issues supplying this algorithm in future. The effect of reprocessing other by products such as Molybdenum, gold, copper slag and, etc on optimum cut-off grades can be essential to complete this algorithm. The results of the research will be more exact if the discount rate is contemplated in construction phase and investment costs. This requires a new algorithm expansion.

6. Conclusions This novel algorithm is simply applied to specify optimum cutoff grades in Sungun copper mine and it ends to reviewing mined materials destination in this mine. The results obtained from developing the new algorithm indicate that this is best fit with the needs of a sustainable development. The algorithm is also able to calculate leaching and concentration optimum cut-off grades considering environmental parameters, social aspects, capital costs and grades-processes recovery relations. Minding these factors can be directed into solving the most significant failures of traditional approaches of optimum cut-off grades determination. The outcomes of the new algorithm and its comparison to other research imply that it is essential to remark investment costs in optimum cut-off grades calculations so that it is directed to real NPV determination. While studying Sungun copper mine, this issue indicates 16% reduction in NPV in comparison to research which hasn’t obtained any investment costs. The presented algorithm regards the effect of average grade variations on processes recoveries and optimum cut-off grades. Thus, grade reduction on Sungun copper mine leads to the recovery decrease of concentration method up to 9% and also NPV to 13% which directly affects the amount of optimum cut-off grades. Holistically, this study proved that the environmental cost of mines practicing leaching and concentration methods is less than mines using only concentration method. This problem is for the sake of less adverse environmental and social impacts of hydrometallurgical methods than pyrometallurgical ones. So, applying hydrometallurgical processes for processing low grades copper ores pave the way to access sustainable development by performing novel algorithm. Moreover, it is remarkable that the production economical value and NPV process are preserved.

Acknowledgment The authors are grateful to Mr. Rezai as the Bioleaching project manager of Sungun Copper Mine for providing samples.

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Please cite this article as: Rahimi, E., Ghasemzadeh, H., A new algorithm to determine optimum cut-off grades considering technical, economical, environmental and social aspects. Resources Policy (2015), http://dx.doi.org/10.1016/j.resourpol.2015.06.004i