documeA Cut-Off of Liberated and Selected Ore Minerals Optimisation Based on the Geometallurgy...

263THE FIRST AUSIMM INTERNATIONAL GEOMETALLURGY CONFERENCE / BRISBANE, QLD, 5 - 7 SEPTEMBER 2011

INTRODUCTIONThe most important objective of the strategic mine planning process consists in maximising the expected economic or net present value (Davis and Newman, 2008). This is achieved by mining and processing the ore reserves, and the marketing, smelting and refi ning of the concentrates or products over the projected mine life. The maximisation of the expected economic or net present value can be determined by applying current state-of-the-art cut-off grade optimisation methodologies (Lane, 1964, 1979, 1988; Rudenno, 1979; Lane et al, 1984; Dagdelen,1993). These methodologies are fundamentally based on the spatial distribution of orebody grades. In addition, account can be made of reasonable static and dynamic assumptions on some of the modifying factors in converting mineral resources to ore reserves (eg JORC, 2004; Napier, 1983; Baird and Satchwell, 2001; Asad, 2005).

However, a realistic expected economic value can be determined by considering the spatial variability of mineralogical and textural characteristics and associated liberation and selectivity properties (Turner-Saad, 2010). In addition, reliable static and dynamic assumptions can be made of the modifying factors over the projected mine life.

The straightforward principle of determining the expected economic value of mining, processing and marketing the concentrates or products of two independent discrete ore reserve blocks is described. The most important assumption is that the two ore reserve blocks with the same volume, bulk density, grade, dilution and static mineral processing recovery will produce the same recovered metal content. Nevertheless it is likely that the real recovered metal content of these two discrete blocks will be different. This is due to the

1. Executive Geometallurgical Consultant, CAE Mining, Level 23, 333 Ann Street, Brisbane Qld 4000. Email: [email protected]

A Cut-Off of Liberated and Selected Ore Minerals Optimisation Based on the Geometallurgy ConceptG Turner-Saad1

ABSTRACTAn improvement to cut-off grade optimisation theory based on geometallurgy has been completed. The improvement fundamentally consisted of taking into account mineralogical and textural characteristics instead of grades. These characteristics are related to the spatial variability of mineral abundance, association, particle size and liberation properties. Additionally, the improvement considered the spatial variability of mineral processing liberation and selectivity properties associated with mineralogy and texture. The enhanced optimisation enables estimation of the economic value of mining operations based on an optimum cut-off policy attributed to liberated and selected ore minerals.

The enhanced optimisation was developed as an essential component of a joint cut-and-fi ll mining and mineral processing methodology based on mixed integer mathematical programming. The formulation considers static and dynamic modifying factors that vary over the projected life of mining. The objective function of the mathematical formulation consists of maximising the realistic expected economic value of concentrates or products of liberated and selected ore minerals, whilst minimises liberated and selected gangue minerals. The optimal solution is obtained when the objective function is subject to geological, mining, processing, marketing, smelting, refi ning, environmental and fi nancial constraints. The methodology accesses geometallurgical multivariate resource models, which integrate the spatial variability of mineralogical and textural characteristics and mineral processing liberation and selectivity properties.

The geometallurgical process concurrently optimises stope geometries, ore reserves, mining sequences, and mining and mineral processing production based on the enhanced cut-off of liberated and selected ore minerals. In addition, the process considers additive and non-additive transfer functions associated to mutually exclusive geometallurgical spatial domains. The transfer functions also take into consideration the blending of mineralogical and textural characteristics with mineral processing liberation and selectivity properties.

This contribution presents an example of cut-off grade optimisation via mineralogical and textural characteristic, and liberation and selectivity processing parameter optimisation for a spatially variable orebody.

THE FIRST AUSIMM INTERNATIONAL GEOMETALLURGY CONFERENCE / BRISBANE, QLD, 5 - 7 SEPTEMBER 2011

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difference in the mineralogical and textural characteristics, and mineral processing performance of the two blocks. In general terms, the mineral processing recovery is a function of the abundance, association, grain size and liberation characteristics and product size properties of ore and gangue minerals. It is convenient to emphasise that concentrates or products are constituted by liberated and selected ore and gangue minerals.

On other hand, underground mine optimisation methodologies relate to stope geometries, mining sequences and mining production have been developed as isolated stages by a number of researchers as is shown in Figure 1 (Murray and Magri, 1978; Trout and Grice, 1993; Alford, 1995; Ovanic and Young, 1995; Ataee-pour and Baafi , 1998; Van Leuven, 1998; Thomas and Earl, 1999; Rahal et al, 2003; Smith, Sheppard and Karunatillake, 2003; Topal, Kuchta and Newman, 2003; Grieco, 2004; Smith and ORourke, 2005). These mathematical formulations did not take into account the combined relationship of the underground mining stages either for single or multiple commodity deposits. Additionally, there are no publications on the integration of the geometallurgical concept, and specifi cally for underground cut-and-fi ll mining.

A geometallurgically integrated and iterative underground cut-and-fi ll mining and mineral processing optimisation methodology based on a mixed integer mathematical programming has been developed. The methodology described is an extension and enhancement of the research previously published by Turner-Saad and Smith (2006) and Turner-Saad (2011), which integrates geometallurgical multivariate resources models of mineral deposits. This extended and enhanced methodology takes into consideration the spatial

variability of mineralogical and textural characteristics, and liberation and selectivity mineral processing properties of an orebody.

The purpose of the proposed methodology consists of assessing the realistic expected economic value of mining operations by defi ning what if strategic, tactical and operational scenarios. The assessment can be performed by defi ning and varying geological, mining, processing, marketing, smelting, refi ning, environmental and fi nancial scenarios and assumptions over the projected mine life.

METHODOLOGYIn this study, the objective of the geometallurgical optimisation process is to maximise the expected economic value of underground cut-and-fi ll mining and mineral processing operations. The estimation of expected economic value throughout this methodology is based a function of static and dynamic technical and fi nancial factors over the projected mine life. The essence of the methodology resides in defi ning optimum:

mining, blending, stockpiling and processing of reserves with different mineralogical and textural characteristics, and mineral processing liberation and selectivity properties; and

marketing, smelting and refi ning concentrates or products with different liberated and selected ore and gangue minerals,

where optimisation is in agreement with geological, mining, processing, marketing, smelting, refi ning, environmental and fi nancial constraints.

The development of the geometallurgical optimisation process is based on fi ve activities, inclusive of:

1. accessing geometallurgical multivariate resource models of a deposit;

2. defi ning the strategic, tactical and operational scenarios;3. defi ning the static and dynamic modifying factors over the

projected mine;4. optimising simultaneously stope geometries, ore reserves,

mining sequences, mining and mineral processing productions; and

5. assessing the realistic expected economic value.Optimisation is an iterative process due to the unlimited

number of what if strategic, tactical and operational scenarios that can be considered and because of the unlimited number of assumptions of the modifying factors.

The iterative optimisation process is based on concurrent integration of stope geometries, ore reserves, mining sequences, mining and mineral processing productions over the projected mine life as is shown in process diagram of Figure 1.

The methodology is based on a mixed integer mathematical programming formulation developed in AMPL A Mathematical Programming Language (Fourer, Gay and Kernigham, 1993) and using the IBM ILOG CPLEX Optimizer solver (IBM, 2011). A summary of the objective function and geological, mining, processing, marketing, smelting, refi ning, environmental and fi nancial constraints of the mathematical formulation are described in the next sections.

Objective functionThe objective function consists in maximising the realistic expected economic or net present value of concentrates or products of liberated and selected ore minerals whilst minimising liberated and selected gangue minerals.

MineralResources

MiningDesign

OreReserves

MiningSequence

SmeltingProduction

ProcessingProduction

MiningProduction

RefiningProduction

GeometallurgicalResources

MiningDesign

OreReserves

MiningSequence

SmeltingProduction

ProcessingProduction

MiningProduction

RefiningProduction

FIG 1 - Process diagrams of the isolated (left) and concurrent(right) mining and mineral processing optimisation.


A CUT-OFF OF LIBERATED AND SELECTED ORE MINERALS OPTIMISATION BASED ON THE GEOMETALLURGY CONCEPT

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The maximisation is controlled by a cut-off of liberated and selected ore minerals optimisation methodology, which it is an adaptation and enhancement of the original cut-off grade optimisation theory (Lane, 1964).

The estimated annual cash fl ows or profi ts are determined by means of a dynamic update of the net smelter return value that varies over the projected mine life. The dynamic net smelter return value is computed for concentrate or product types by applying the defi ned static and dynamic modifying factors (Liimatainen, 1998; Wellmer, 1989).

The formulation enables consideration of additive and non-additive transfer functions that correlate the mineralogical and textural characteristics with liberation and selectivity processing properties for each geometallurgical domain.

Geological constraintsThe aim of the geological constraints consists of selecting orebodies, domains and resource categories in a specifi c time period of the projected mine life. Consequently, a variety of scenarios can be analysed with this group of constraints.

Mining constraintsThe mining constrains simultaneously defi ne the stope geometry, reserves, mining sequence and production of ore and gangue minerals over the projected life of mining operations. It is performed by constraining the quantity and quality of ore and gangue minerals.

The mining constraints defi ne the level intervals, stope dimensions and locations, cut heights, pillar dimensions and locations for each orebody. The levels, stopes and cuts can be also selected in a specifi c time period to assess any particular mining scenario.

In addition, a number of mining constraints related to the underground cut-and-fi ll mining cycle (Hustrulid and Bullock, 2001) were established in the formulation. Furthermore, mine capacity, level, stope and cut productivities, mineralogical and textural characteristics, internal and wall dilution and cut-off of liberated and selected ore minerals are also considered. The stope geometry is then generated by differential cut-off of liberated and selected ore and gangue minerals that vary in both horizontally and vertically directions across levels, stopes and cuts.

The reserves consist of those blocks included in the mining production of ore and gangue minerals. The optimal solution defi nes the quantity and quality of the diluted and blended reserves blocks to be mined and processed for each time period and by orebody, domain, level, stope and cut.

Processing constraintsThe quantity and quality of liberated and selected ore and gangue minerals in concentrates or products is controlled by a group of constraints based on mineral processing liberation and selectivity parameters.

The additive and non-additive transfer functions defi ned for each domain calculate the quantity and quality of the concentrates or products according to the mineral processing capacity.

Normally, a static mineral processing recovery function is applied to determine the recovered metal content of specifi c commodity. However, dynamic mineral processing recovery transfer functions can be applied in the formulation based on the geometallurgical characteristics and properties of the ore minerals in each domain (Bojcevski, 2003). The expected net smelter return value could then vary signifi cantly depending

on whether the mineral processing recovery is treated as a static, dynamic additive or non-additive transfer function. In summary, the formulation uses transfer functions to determine the recovered metal content when the net smelter return value is computed for each concentrate or product.

Marketing constraintsThe quantity of liberated and selected ore and gangue minerals in concentrates or products are limited by this group of constraints and based on the market demand or smelters and refi neries short, medium- and long-term sales agreements.

Smelting constraintsThis group of constraints restricts the quality of liberated and selected ore minerals in concentrates. These constraints also limit the production capacity of the smelter.

Refi ning constraintsThe refi ning constraints group controls the quality of liberated and selected ore minerals in concentrates or products. In addition, this group of constraints limits the production capacity of the refi nery.

Environmental constraintsThe main purpose of this group of constraints consists limits the quality of liberated and selected gangue or deleterious minerals abundance in waste materials, tailings and concentrates or products, that in some way have an environmental impact.

Financial constraintsThis group of constraints controls the mining, processing, marketing, smelting, refi ning and environmental fi xed and variable operating costs for each time period over the projected mine life.

APPLICATIONA case study was considered to demonstrate the capability of integrating the cut-off of liberated and selected ore minerals and the joint cut-and-fi ll mining and mineral processing optimisations. The assessment of the integrated optimisation was performed throughout the defi nition of several scenarios. Each scenario included the combinations of static and dynamic modifying factors over the projected mine life.

The geologic setting of the case study consists of several mesothermal and pyrometasomatic replacement orebodies in a thick limestone sequence. The mineralisation is composed of mainly massive galena and sphalerite with amounts of chalcopyrite associated with pyrrhotite, arsenopyrite, silicates, sulfates and carbonates.

Two structural and geometric types of orebodies have been identifi ed within the project:

1. a gently dipping sheet, and2. steeply plunging chimneys.

The sheet orebodies comprise a combination of silicates and sulfi des, whilst the chimneys are dominated by sulfi des with or without silicates. One of the irregular sheet orebodies was used as the case study, which represents a metasomatic replacement system. A long-section model of the orebody is shown in Figure 2.

A geometallurgical multivariate resource model of the orebody was previously generated and accessed as fundamental to the optimisation process. The resource model comprised the spatial variability of mineralogical and


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textural characteristics and mineral processing liberation parameters. These parameters, in turn, were constrained by several mutually exclusive geometallurgical liberation and selectivity spatial domains within the orebody by applying and combining implicit modelling and multivariate statistical analysis.

The spatial models of mineralogical characteristics used in the optimisation process included: abundance (per cent), association (per cent), particle size (microns) and liberation (per cent) of the galena, sphalerite, chalcopyrite, pyrrhotite and arsenopyrite. An example of the galena model is shown in Figure 3.

The mineral processing liberation and comminution information was also accessed and specifi cally associated with the spatial models of feed size F80 (mm), product size P80 (microns), throughput (t/h) and energy consumption (kWh/t) as are shown in Figure 4. The processing recoveries of galena, sphalerite, chalcopyrite, pyrrhotite and arsenopyrite were

considered in the optimisation process. The processing selectivity or fl otation information was related to the recovery of ore and gangue minerals. The recovery information was defi ned as transfer functions based on the relationship of the abundance (per cent), association (per cent), particle size (microns), liberation (per cent) and product size P80 (per cent) of each ore mineral, in each domain.

The integrated and iterative optimisation process consisted of assessing the impact of using static and dynamic modifying factors over the projected mine life, including:

cut-off and average of liberated and selected ore minerals; stope geometries; reserves; ore and waste mining sequences; expected mining, processing, smelting and refi ning

productions; and expected profi ts.The optimisation was constrained by geological, mining,

processing, marketing, smelting, refi ning, environmental and fi nancial constraints. Four scenarios were considered.

Scenario 1:

geological constraints: static orebody and domains; and static measured and indicated mineral resources;

mining constraints: static limits of level intervals; static limits of stope dimensions and locations; static limits of cut heights; static limits of pillar dimensions and locations; static limits of levels, stopes and cuts dilution rates; static limits of levels, stopes and cuts productivities; and static limits of ore and waste production capacities;

FIG 2 - Explicit spatial model of the case study orebody.

Abundance [%] Association [%]

Grain Size [microns] Liberation [%]

FIG 3 - The galena abundance (per cent), association (per cent), particle size (microns) and liberation (per cent) spatial models of the case study orebody.



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processing constraints: static limits of ore production capacity; static limits of ore minerals abundance; dynamic limits of liberation or comminution

properties; and dynamic limits of selectivity or fl otation properties;

marketing constraints: static limits of marketing costs; static limits of shipping costs; and static limits of treatment costs;

smelting constraints: static limits of concentrates production capacity; and dynamic limits of ore minerals abundance.

refi ning constraints: static limits of products production capacity; and dynamic limits of ore minerals abundance.

environmental constraints: static limits of deleterious minerals abundances in

waste; static limits of deleterious minerals abundances in

tailings; and static limits of deleterious minerals abundances in

concentrates or products; fi nancial constraints:

static limits of mining, processing, smelting and refi ning fi xed and variable operating costs;

static limits of discount rate; and dynamic limits of metal prices.

The geological, mining, marketing, smelting, refi ning, environmental and fi nancial constraints of scenarios 2, 3 and 4 were similar to scenario 1. The only difference was in the processing constraints and specifi cally in defi ning the static

limits of the mineral processing liberation or comminution properties.

Scenario 2:

processing constraints: static limits production capacity of ore, static limits of ore minerals abundance, static limits of liberation or comminution properties

energy consumption (kWh/t), and dynamic limits of selectivity or fl otation properties.

Scenario 3:


energy consumption (kWh/t), static limits of liberation or comminution properties

throughput (t/h), and dynamic limits of selectivity or fl otation properties.

Scenario 4:


energy consumption (kWh/t), static limits of liberation or comminution properties

throughput (t/h), static limits of liberation or comminution properties

product size P80 (microns), and dynamic limits of selectivity or fl otation properties.

In summary, the objectives of the four scenarios consisted of assessing the impact of relaxing and constraining the energy consumption (kWh/t), throughput (t/h) and product size P80 (microns).

Feed Size F80 [mm] Product Size P80 [microns]

Throughput [tph] Energy Consumption [kWh/t]

FIG 4 - The feed size F80 (mm), product size P80 (microns), throughput (t/h) and energy consumption (kWh/t) spatial models of the case study orebody.


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RESULTS AND DISCUSSIONThe probability density function (per cent) and cumulative distribution function (per cent) of the galena abundance (per cent) in the resource model is shown in Figure 5. As expected, both functions were dynamic in the sense that new functions are computed for every time period. The new functions rep- resent the statistical distribution of the remaining resources of the orebody. This means that the quantity of material mined in a specifi c time period is removed from the resource model. The statistical distribution of the updated resource model has a direct impact on the defi nition of the balancing cut-offs of liberated and selected ore minerals of the following time periods. The maximisation of the expected economic value requires mining of high values in each time period as can be seen in both functions of Figure 5.

The quantity (t) quality (per cent) cut-off of liberated and selected ore minerals (per cent) plot in Figure 6, also confi rm that the resource model was updated dynamically in each time period. This means that the quantity and quality of the galena is decreasing in every time period and subsequently the cut-off of liberated and selected ore minerals as well.

The dynamic and decreasing balancing cut-offs of liberated and selected ore minerals is illustrated in Figure 7. The balancing cut-offs are decreasing due to the updated resource model having higher values. Also, in Figure 7, the static mine, concentrator and refi nery production capacities over the projected mine life can be seen.

The dynamic mine, concentrator and refi nery productions, profi ts and present value plots are illustrated in Figure 8.

The behaviour of the information represents the depletion of the resources in each time period due to mining, processing, smelting and refi ning.

The optimum cut-off of liberated and selected galena (per cent) and average of galena abundance (per cent) over the projected life of the mining operation and by scenario is shown in Figure 9. The differences in cut-offs among scenarios is due to the limits defi ned for the energy consumption (kWh/t), throughput (t/h) and product size P80 (microns). The average galena abundance (per cent) decreases over mine life as a result of the maximisation process.

Figure 10 describes the material, ore, product productions (t) and profi ts ($) of each scenario. The differences among scenarios is due to the static limits defi ned in some of the mineral processing liberation properties. However, from these plots can be seen that the refi nery capacity is the bottleneck of production.

The energy consumption (kWh/t), throughput (t/h) and product size P80 (microns) over the projected life of the

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cut-Off [%]

Liberated and Selected Galena

Ore:Material Ratio Concentrator:Mine Capacities Ratio

0.0 0.5 1.0 1.5 2.0 2.5 3.0Cut-Off [%]


Product:Material Ratio Refinery:Mine Capacities Ratio

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cut-Off [%]


Product:Ore Ratio Refinery:Concentrator Capacities Ratio

FIG 7 - The dynamic concentrator-mine (top), refi nery-mine (middle) and refi nery-concentrator (bottom) balancing cut-off s of liberated and selected galena (per cent) of each time period with a static mine, concentrator and

refi nery production capacities over the projected mine life.

0.0 0.5 1.0 1.5 2.0 2.5 3.0C

DF [%

]PDF

[%]

Abundance [%]


Probability Density Function Cumulative Distribution Function

FIG 5 - The dynamic probability density function (per cent) and cumulative distribution function (per cent) of the galena abundance (per cent) of each

time period over the projected mine life.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Quality [%

]Qua

ntity

[t]

Cut-Off [%]


Material Average of Galena Abundance

FIG 6 - The dynamic quantity (t) (material) - quality (per cent) (average of galena abundance) - cut-off of liberated and selected galena (per cent) of

each time period over the projected mine life.



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mining operations is shown in Figure 11. The differences between each scenario is due to the static limits defi ned for each mineral processing liberation parameter.

The spatial distribution of the stope geometries and mining sequences of the four scenarios and the cut-off of liberated and selected galena are shown respectively in Figures 12 and 13. The spatial differences among the four scenarios is mainly due to the impact of the defi ned static mineral processing liberation or comminution parameters used during the optimisation process. Defi nitively, any change of static or dynamic parameters involved in the modifying factors has a specifi c impact in the stope geometry, reserves, mining sequence, mine and processing productions and subsequently the economics.

CONCLUSIONSThe main conclusions of this study are:

the realistic expected maximum economic or net present value of mining operations is reached when the mining and mineral processing stages are optimised concurrently instead of isolated;

the joint mining and mineral processing methodology enables maximising the depletion of the resources;

the fundamental information of the optimisation process is the geometallurgical multivariate resource models, which integrate the spatial variability of mineralogical and textural characteristics and mineral processing liberation and selectivity properties;

the additive and non-additive transfer functions also need to take into consideration the capability of blending the ore from mutually exclusive geometallurgical spatial domains, which contain different mineralogical and textural characteristics and mineral processing liberation and selectivity properties;

the realistic economic assessment of what if strategic, tactical and operational scenarios is obtained when dynamic modifying factors are applied over the projected mine life; and

further research and development is required to enhance and apply the methodology to other underground and open pit mining methods.

ACKNOWLEDGEMENTSSpecial thanks to Dr Simon C Dominy for his support and help in reviewing, commenting on and editing this paper.

REFERENCESAlford, C, 1995. Optimisation in underground mine design, in

Proceedings APCOM XXV, pp 213-218 (The Australasian Institute of Mining and Metallurgy: Melbourne).

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cut-Off [%]


Mine Production Concentrator Production Refinery Production

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cut-Off [%]


Mine Value Concentrator Value Refinery Value

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cut-Off [%]


Mine Profit Concentrator Profit Refinery Profit

FIG 8 - The dynamic mine, concentrator and refi nery productions (t) (top), profi ts ($) (middle) and present value ($) (bottom) by cut-off of liberated and selected galena (per cent) for each time period over the projected mine life.

0 5 10 15 20

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Optimum Cut-Off of Liberated and Selected Galena [%]

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0 5 10 15 20

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FIG 9 - The dynamic optimum cut-off of liberated and selected galena (per cent) (left) and average of galena abundance (per cent) (right)over the projected mine life.


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0 5 10 15 20

Time Period [y]

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0 5 10 15 20

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0 5 10 15 20

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Product Size P80 of the Liberation Process [microns]


FIG 11 - The energy consumption (kWh/t) (top), throughput (t/h) (middle) and product size P80 (microns) (bottom) of the liberation process over the projected mine life.

0 5 10 15 20

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0 5 10 15 20

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0 5 10 15 20

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Scenario 4


FIG 10 - The dynamic material (t), ore (t), concentrate or product (t) productions and profi ts ($) over the projected mine life.



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Scenario 1 Scenario 2


FIG 13 - The spatial distribution of the cut-off of liberated and selected galena (per cent) of a cut-and-fi ll mining over the projected mine life.



FIG 12 - The stope geometries and mining sequences of a cut-and-fi ll mining over the projected mine life.


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