Advanced Open Pit Planning and Design 2014(for NICICo)FinalDraft
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5/11/2014
ADVANCED OPEN PIT MINE PLANNING AND DESIGN Presenter Prof Emmanuel Chanda The University of Adelaide, Australia
ADVANCED OPEN PIT MINE PLANNING AND DESIGN M1-Strategic mine planning M2-Open pit optimisation M3-Mine Production scheduling M4-Optimum Cut-off Grades M5-Mine Planning Software M6-Mine-to-Mill Optimisation M7-Equipment Selection M8-Financial Technical Modelling M9-Dewatering and Pumping Open Pit Mine Planning and Design
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Objectives Fundamentals of open pit mine design and current developments in planning and design methodology, Current industry practices to maximise economic return. Open pit mine planning and design process in theory and practice, Unit Operations – Drill-Blast-Load-Haul Apply this knowledge to plan/evaluate new open pit projects and/or existing mines. Open Pit Mine Planning and Design
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What do you expect to learn from this Course?
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Module 1 Strategic Mine Planning 1. What is strategic planning? 2. Mine planning process 3. Mining strategy 4. Feasibility Studies 5. Exercises Open Pit Mine Planning and Design
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Overview/scope • Big picture mine planning and design process • Big picture decision-making process • Applies to Greenfields as well operating mines • SP takes place at all levels of the company Corporate level: vision, mission, feasibility, etc Business unit level: expansion of production Mine level: medium/long term production strategy Analogy: military strategy Open Pit Mine Planning and Design
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What is Strategic Mine Planning? Strategic mine planning is concerned with those decisions that largely determine the value of the mining business whereas tactical mine planning deals with the tasks required to actually achieve that value. Both types of planning are necessary; they can be looked at separately, even discussed separately, but they cannot be separated in practice!
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Mine Planning
Types of planning and mine life cycle
Tactical Mine Planning Strategic Mine Planning
Prospecting
Exploration
Development
Production
Closure
Life cycle of an orebody Open Pit Mine Planning and Design
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Strategic mine planning focuses on those technical variables that affect the life of a mine and the value of the underneath mineral resource It starts with the discovery of the mineral resource and finishes when it is exhausted or abandoned. Go! List variables (factors) considered in SMP…
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Business Strategy
Strategic Planning
DecisionMaking Behaviour
Economic Evaluation
Mine Planning
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Decision-Making Behaviour: Risk Averse – seeks other business goals Risk Neutral – seeks maximise NPV
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Mine Planning Process Flowchart
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Mine Planning Process Four main stages of mine planning process: • Geology of resource • Value of resource • Long-Term planning (Strategic) – feasibility studies • Medium-term/Short-term planning - production Mine Planning Process*: Geology + Data Analysis
Resource Model
Mining Method Selection
Optimisation Mine Design Optimal Schedulling Financial Technical Model
* A dynamic and iterative process * Open Pit Mine Planning and Design
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Activity 1: Work in Groups of 2-4 To plan a new open pit mine in Kerman Province. List all the data required to perform a feasibility study and where these data would come from.
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Technical Aspects: Once the geological features are understood and the physical characteristics of the ore body are determined, the main technical decisions that follow are: Mining method selection Processing route Scale of operation (size) Mining sequence Selective cut-offs (e.g. cut-off grade at the mine)
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•All these variables are inextricably interrelated in the sense that they cannot be determined in isolation from each other •Moreover, they cannot be determined without taking into account the market variables and related data from the geologic, metallurgical, geotechnical, and environmental models……. •……….as shown on next slide…
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MARKET Metallurgical Model
Geological Model Mining Method Geotechnical Model
Processing Route
Scale of Operation
Mining Sequence
Environmental Model
Selective Cut-offs
MINE PLAN Open Pit Mine Planning and Design
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Mining Method Selection • The choice of the mining method depends on the shape, emplacement and properties of the orebody and host rock; again, beyond technical considerations, this is an economic decision • In general, there are two main mining methods: Surface mining (open pit, quarries) Underground mining (block caving, cut & fill)
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• However, depending on the emplacement of the orebody and its grade distribution, there are cases where both methods are feasible – e.g. open-pit followed by underground mining or the other way around • This is the classic case of sub-vertical deposits such as kimberlitic pipes containing diamonds and some porphyry copper deposits
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Economic considerations • Many decisions concerning the choice of the mining method are related to the "opportunity cost” concept • For example: In massive, disseminated deposits that are close to surface, open pit mining is more productive than an underground
Underground mining usually requires more development and preparation works
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Considerations in Mining Method Selection Finances: • Finance influences method selection: Length of pre-production development and phases Thoroughness of the ore body delineation program Scale of operations – bulk mining methods, eg., block caving Technology applications - automation
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Markets The mining method should be flexible enough to respond to market changes. When and how to high grade during peak commodity prices Changes to mine development schedule Focus on production of by-products (eg. cobalt in copper ore) Mining companies are price takers. What can be done about this? Open Pit Mine Planning and Design
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Technology and Human Resources Choice of particular mining method commits operation to certain type of technology, equipment, human resources and processes. Later change in method will be at a cost Must allow for possibility of introducing new technology Necessary skills must be available to operate selected mining system Lack of expertise may eliminate a particular mining method, though technically suitable. Consider specific training and supervision Open Pit Mine Planning and Design
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Processing route •
The selection of the processing route depends essentially on the characteristics of the ore; however, beyond technical considerations, this is a business decision
•
Essentially, there are basically two main routes: Physical methods (concentration) Chemical methods (hydrometallurgy)
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Mineral
Comminution
Liberation Unacceptable Classification
Acceptable
Concentration
Separation
Physical
Chemical
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Factors to consider
Products recovered Recoveries and achievable grades Environmental aspects Market considerations Capital and operating costs Cycle times Mine plan Cash flow and profitability
In short, technical and financial considerations Open Pit Mine Planning and Design
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Metallurgical tests •
Lab testing – for initial investigation Core samples and samples from outcrops (chip samples)
•
Pilot tests – to confirm lab tests and design Core samples and some bulk samples from underground workings
•
Industrial tests – to feasibility Bulk samples from underground workings and additional core samples
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Scale of the operation • The scale of the operation refers to production capacity, which in turn is related to the physical size of the installations at the mine and plants • This is directly related to the capital investment required to produce the final output deemed to put in the market • The larger the scale, the higher the investment and production Case Study: Olympic Dam Expansion Project in South Australia
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• From the point of view of a mining project, the scale of the operation is the dominant factor for establishing the mine life and business value • There is a compromise between the NPV of a project and its size – the optimum size exits, because a very large operation may shorten the mine life too much, making the marginal investment unworthy
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Size-profitability-risk relationship Scenario 500 kt/d
NPV (MUS$)
Scenario 300 kt/d Scenario 150 kt/d
Scenario 72 kt/d
Risk
3000
2700 2000
1000
Scale of operation Open Pit Mine Planning and Design
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Mining Sequence and Final Limits • It refers to the path or trajectory employed to exploit a mine – from an initial situation until reaching the final limits or exhausting the ore reserves • Usually, these two variables are treated separately but because of their co-dependency they should be handled together
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• The mining sequence is usually defined in terms of sequential “cuts” or "sectors“ in which a final mining envelope is split to guide the mining extraction • These sectors can be phases, cut-backs or push-backs as they are usually called in openpit mining; or blocks, panels, rooms or stopes as these are commonly referred to in underground mining
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• It is worth noting that the partition of a final mining envelope into cuts or sectors is done because the time value of money • In effect, the purpose is to postpone expenditures and bring forward revenue as much as possible from production sales
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The scheduling “saw graph” • To illustrate how the time value of money affects the economics of mining it is useful to introduce the “saw graph” tool • It assumes that mining activities always require some preparation works (development) prior to ore extraction:
Stripping in open pit mining (t, m3) Developments in underground (m3, m2, m, t) Open Pit Mine Planning and Design
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The scheduling “Saw Graph”
Minimum Ore Exposure yr-1
yr-2
yr-3
yr-4
yr-5
yr-6
Time
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Integral optimisation of the final pit Exploitation phases 500 t (ore)
1 2
100 t (waste)
3 4 5 6
Revenue 2.2 $/t Cost -1.0 $/t
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Partial and cumulative tonnage Phase 1 2 3 4 5 6 7
Partial tonnage Ore 500 500 500 500 500 500 500
Waste 100 300 500 700 900 1,100 1,300
O/W Ratio 0.2 0.6 1.0 1.4 1.8 2.2 2.6
Cumulative tonnage Ore 500 1,000 1,500 2,000 2,500 3,000 3,500
Waste 100 400 900 1,600 2,500 3,600 4,900
O/W Ratio 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Breakeven point Phase 6
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When neither the time value of money nor other operational factors such as mine and plant capacities are taken into account, the optimal final limit is reached at Phase 6 The implicit assumption is that ore is exposed simultaneously with waste and that ore revenue occurs at the same time as waste cost
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When accepting that ore and waste extraction have to consider certain physical restrictions in their programming (phase size and available equipment), then the time value of money becomes a relevant issue The programming can be done using the “saw graph” early described
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Case 1: Open pit plan with 6 phases • Plant ≤ 500 t/y • Mine ≤ 1,300 t/y 500
1
1
2
3
4
5
yr-1
yr-2
yr-3
yr-4
yr-5
6
yr-6
Time
2 500
3
Waste removal
4 1,000
5 6 Open Pit Mine Planning and Design
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Economic evaluation: Phase 6 +1,250 1,000
0
yr-1
yr-2
yr-3
yr-4
yr-5
yr-6
Time
- 300 - 800
- 1,000 -225
-546
+706
Present value(t=0, r=10%) = - 65 Open Pit Mine Planning and Design
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Economic evaluation: Phase 5 +1,250 1,000
0
yr-1
yr-2
yr-3
- 400
yr-4
yr-5
yr-6
Time - 500
- 1,000 -331
-376
+776
Present value(t=0, r=10%) = + 70 Open Pit Mine Planning and Design
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Case 2: Open pit plan with 5 Phases • Plant ≤ 500 t/y • Mine ≤ 1,300 t/y 500
1
1
2
3
4
5
yr-1
yr-2
yr-3
yr-4
yr-5
Time
2 500
3 4 5
1,000
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Economic evaluation: Phase 5 +1,250 1,000
0
yr-1
yr-2 yr-3 - 100
- 1,000
yr-4
yr-5
yr-6
Time
- 800 -83
-601
+776
Present value (t=0, r=10%) = + 92 Open Pit Mine Planning and Design
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Economic evaluation Net Present Value @ r = 10 % ($) Phase 1 2 3 4 5 6
Case 1 (6 Phases)
Case 2 (5 Phases)
Partial
Cum
Partial
Cum
1,036 733 485 250 70 -65
1,036 1,769 2,254 2,504 2,574 2,509
1,036 733 485 275 92 -
1,036 1,769 2,254 2,529 2,621 -
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Summary of results 1 2 3 4 5 6
Breakeven final limit (Phase 6) Open Pit Mine Planning and Design
Discounted final limit (Phase 5)
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Considering an underground alternative
1 2 3 4 5 6
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2 open pit phases, 4 underground lifts
1 2
NPV(1) 3
$ 800
4 5 6
(1) Net present value at the beginning of year 1 Open Pit Mine Planning and Design
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3 open pit phases, 3 underground lifts….
1 2 3
NPV(1) 4
$ 450 $ 200 $ 50
5 6
(1)
Net present value at the beginning of year 1 Open Pit Mine Planning and Design
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NPV of underground lifts +800 +450
500
+200 +50 0 3
6
4
6
5
6
6
Lifts
NPV Lift 3 (t=0, r=10%) = + 350 NPV Lift 4 (t=0, r=10%) = + 250 NPV Lift 5 (t=0, r=10%) = + 150 NPV Lift 6 (t=0, r=10%) = + 50 Open Pit Mine Planning and Design
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Economic evaluation (Open Pit vs Underground) Net Presente Value @ r = 10 % ($) Phase 1 2 3 4 5 6
Case 3 (OP/UG)
Case 4 (Optimum)
Partial
Cum
Partial
Cum
1,036 733 485 275 92 50
1,036 1,769 2,254 2,529 2,621 2,671
1,036 733 485 275 150 50
1,036 1,769 2,254 2,529 2,679 2,729
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Optimum configuration
1 2 3 4 5 6
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Summary of evaluations Net Present Value @ r = 10 % ($) Phase 1 2 3 4 5 6
Case 1
Case 2
Case 3
Case 4
1,036 1,769 2,254 2,504 2,574 2,509
1,036 1,769 2,254 2,529 2,621 -
1,036 1,769 2,254 2,529 2,621 2,671
1,036 1,769 2,254 2,529 2,679 2,729
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NPV and Shareholder Value Firm's Information
Case 1 Case 2
Case 3 Case 4
Net present value ($)
2,509
2,621
2,671
2,729
Firm 's net debt ($)
1,000
1,000
1,000
1,000
Firm 's m arket value ($)
1,509
1,621
1,671
1,729
N° Shares
1,500
1,500
1,500
1,500
Share value ($/Sh)
1.01
1.08
1.11
1.15
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Role Of Feasibility Studies • Why Feasibility Study • Scoping Study • Preliminary Study • Bankable Feasibility Study • Risks
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Origin of the FS
• The Feasibility Study is a development of mine valuation reports. These had remained almost invariable from 1900 to 1960’s. • More complex and larger mining operations in 1960’s and 1970’s required sophisticated studies and reporting. The FS was developed which: – Brings together all aspects of an operation into one study – Looks at the inter-relationships and tries to solve any problems – Aims to determine technical and economic viability of a project
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Feasibility Studies • Demonstrate that the project is economically viable to the satisfaction of the Board, the shareholders and all other stakeholders. • The FS enable the financing of: – Preliminary earthworks – Engineering construction – Infrastructure
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Feasibility Studies • Provide a detailed analysis of all the factors affecting a project’s viability. • Enable determination of a “go” or “no go” decision • Have become an aid in obtaining financial backing
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Phases • Scoping Study • Pre-Feasibility Study • Final Feasibility Study
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Scoping Study
• The Scoping Study is a preliminary investigation into a project between a back of envelope and a pre-feasibility study, or an assessment of necessary size, grade of a target to explore. • It may also be called a ‘Concept(ual) Study.” • The study is normally undertaken with limited technical and other data being available. • There is high reliance on experience and knowledge of similar projects and it normally involves a basic level of literature search.
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Aim of A Scoping Study • Provide a document for decision-making. • Identify key factors that will influence the overall outcome of the project. • Identify and briefly assess possible options, identify risks • Give an indication of the potential financial worth of the project
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MCA – Project Management in Mine Planning and Design
Outcomes of Scoping Study • The outcomes will depend on the situation of the particular project and reasons for the study. The outcomes of a scoping study mayl include: – Information for decisions regarding the future of the project. – Identification of key factors and probably risk areas, requiring further early investigation. – Highlighting project activities or aspects which have the greatest influence (sensitivity) on the project value or return. – Highlighting project parameters that require more accurate measurement or definition. – A proposed plan to advance, or close, the project with schedules and estimated costs. Open Pit Mine Planning and Design
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Scoping Study- Case Study A scoping study for the Flying Fox T1 deposit as a stand-alone underground mine with offsite ore treatment was prepared by mining consultants Golder Associates Pty Ltd.
Main outcomes of the T1 scoping study were as follows: Mineable Resources at 196,000t @ 5.4% Ni* Contained nickel in concentrate 10,587 Ni tonnes Gross Revenue (after royalties) A$101 million Operating costs (mining, site, transport, treatment) A$201/tonne ore (A$1.70/lb Ni produced) • Capital costs - Establishment A$6.0 million - Mine development A$12.8 million • Undiscounted Net cash flow (before tax and D&A) A$37.2 million • • • •
* Note : Mineable Resources do not constitute a JORC compliant resource or reserve category. Open Pit Mine Planning and Design
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Preliminary Feasibility Study • Decisions: Abandon project, change or continue? • Planning: Focus continued investigations on projectcritical areas. – Justify detailed site investigation and resource definition. – Determine the optimum project scope. – Identify risks opportunities and potential “show stoppers/fatal flaws”. • Economic justification: Justify a full feasibility study. – Help sell the project. – Obtain private finance. • Development: Support permitting and stakeholder liaison
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MCA – Project Management in Mine Planning and Design
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Pre Feasibility – looking at alternate scenarios Andean Gold’s Cerro Negro project in Argentina • Open pit optimization for the Vein Zone was completed using Whittle 4x software and recovered gold block grades. A US$800/oz gold price was used as the base case and the remaining inputs are as shown below:
• • • • • •
Pit Optimization Parameters Bench Angle 85o Berm Width 9 metres every 20 metres Pit Slope 52o overall slope with ramps Mining Cost $1.50 per tonne mined Processing Cost $14.00 per tonne ore General & Administrative Cost $3.00 per tonne ore
Pit
Revenue Factor
Waste Tonnes ('000)
Ore Tonnes ('000)
Recovered Au (g/t)
0.30 0.38 0.48 0.58 0.68 0.78 0.84 0.86 0.88 1.00 1.14 1.28 1.42 1.60 1.72 2.00
9,763.1 11,922.4 14,631.9 15,704.0 16,357.2 16,697.4 16,765.5 25,403.2 25,370.3 25,725.8 26,977.6 27,120.3 27,163.4 29,865.5 29,983.6 30,555.8
2,083.3 2,580.3 3,111.4 3,580.2 3,941.0 4,143.1 4,247.6 4,547.3 4,581.3 4,750.5 5,016.1 5,110.1 5,199.4 5,363.9 5,422.6 5,536.6
5.30 4.84 4.43 4.06 3.81 3.68 3.61 3.56 3.54 3.45 3.31 3.26 3.22 3.15 3.12 3.07
1 5 10 15 20 25 28 29 30 36 40 45 50 55 60 67
Recovered Strip Ratio Ounces (W:O) ('000) 355.0 401.3 443.6 467.2 482.6 489.8 493.0 520.4 521.2 526.2 534.3 536.3 537.9 543.6 544.6 546.5
4.69 4.62 4.70 4.39 4.15 4.03 3.95 5.59 5.54 5.42 5.38 5.31 5.22 5.57 5.53 5.52
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Pre Feasibility – scheduling production Open pit schedule Period Pre-production Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Totals
Oxide "Ore" (000's Tonnes) 2.4 644.1 670.6 643.1 758.0 1,186.7 279.6 4182.1
Oxide "Ore" (g/t Au) 2.58 3.05 3.71 4.62 4.39 2.55 4.39 3.59
Mix "Ore" Mix "Ore" (000's (g/t Au) Tonnes) 28.2 4.7 31.7 89.3 163.3 130.4 447.7
4.00 2.18 3.65 3.45 2.76 2.52 2.96
Totals (000's Tonnes)
Totals (g/t Au)
672.3 675.3 674.9 847.3 1,350.0 410.0 4,629.8
3.09 3.7 4.58 4.29 2.58 3.8 3.53
Waste (000's Tonnes) 2,290.7 3,615.3 5,063.0 2,022.2 7,476.7 7,619.7 2,287.7 30,375.3
Strip Ratio
5.38 7.50 3.00 8.82 5.64 5.58 6.56
Open pit and underground schedule Vein Zone Period Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Totals
Portable Ore 000's Tonnes 672.3 675.3 674.9 847.3 1,350.0 410.0 4,629.8
Eureka
g/t Au 3.09 3.70 4.58 4.29 2.58 3.80 3.53
Portable Ore 000's Tonnes 677.7 674.7 675.1 502.7
2,530.2
Cerro Negro Total
g/t Au
g/t Ag
11.54 14.07 12.97 6.69
242.81 258.86 203.05 120.41
11.63
212.16
Portable Ore 000's Tonnes 1,350.0 1,350.0 1,350.0 1,350.0 1,350.0 410.0 7,160.0
g/t Au
g/t Ag
7.33 8.88 8.77 5.18 2.58 3.80 6.39
121.89 129.37 101.55 44.84 0.00 0.00 74.97
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Pre Feasibility – things will change over time Brisas Gold Mine Venezuela Key Economic Parameters and Results Mill Through-Put Range (tonnes per day)
2008
2006
75,000 - 68,000
70,000
83% 87% 82% 83%
83% 87% 81% 83%
8.35 1,156
8.41 1,113
457,000 63
456,000 60
Metallugy Recovery Plant Recovery - Gold Plant Recovery - Copper Net Payable Metal - Gold Net Payable Metal - Copper Life of Mine Production (payable metals) Gold (million ounces) Copper (million ounces) Average Annual Production Gold (ounces) Copper (ounces) Mine Life (years)
18.25
18.5
Initial Capital Cost ($million)
2008 $ 59.0 314.7 67.8 38.3 63.4 16.7 127.6 43.8 $731.3
2006 $ 76.6 241.5 65.8 23.8 55.6 18.3 97.0 59.4 $638.0
Mine Mill Infrastructure Tailings management facility Owner's Costs Pre-Stripping Indirect Costs (includes EPCM and Camp) Contingency Total Initial Capital
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Pre Feasibility – things will change over time Base Case Economics
2008 $
2006 $
Gold per ounce Copper per pound
$600 $2.25
$470 $1.80
Cash Operating Cost Per Ore Tonne Mining and Dewatering Processing General and Administrative Transport and Freight Smelting and Refining Total cash operating cost per tonne
$2.68 3.00 0.43 0.43 1.08 $7.62
$2.08 2.59 0.42 0.34 1.02 $6.45
Cash per Ounce of Gold Cash Operating Costs Exploitation Tax Capital Cost (initial, sustaining and sunk) Total Costs (including sunk costs) Total Cost (excluding sunk costs)
$120 22 135 $277 $268
$126 16 111 $253 $245
20.5%
15.4%
$2.77 $1.29
$1.91 $0.78
Metal Prices
Pre-Tax Internal Rate of Return Net Present Value (NPV) @ 0% discount (billions) @ 5% discount (billions)
70
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(Final) Feasibility Study (FFS) • The Feasibility Study Report is a decision-making document based on verified facts and minimum assumptions (criteria). The report may be used for several purposes: – Assemble a comprehensive framework of facts. – Present a detailed project description. – Forecast profitability. – Facilitate partners and/or sources of finance. – Basis for detailed engineering.
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MCA – Project Management in Mine Planning and Design
Requirements of a FS to be bankable • A FS must be; – Credible – Definitive – Relevant – Independent
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Final Feasibility – high level issues • Geology and ore reserves - size, shape and depth of the ore, the grade of the ore and distribution, how homogeneous, any major faults or intrusions and hydrological reports. • Mining method and schedule – surface, open cut, underground, annual production rate vs life of mine, phasing of development, envisaged ROM grade, capital equipment and manning levels required. (High production rate, high capital expenditure, shorter mine life – what is the optimum?) • Infrastructure requirements - including ancillary buildings, roads, drainage, tailings disposal, general arrangement drawings of infrastructure layout. • Metallurgy/concentrator/washery design – recovery factor, concentrate grade, product quality. Recommendations for the process plant including: Flow diagram Material and water balances Equipment list (major items) together with budget quotations General arrangement plan and elections of process plant to scale 1:100 Electrical system (line diagram)
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- high level issues continued • • • • • • • • •
Infrastructure, water, power, accommodation and environmental issues – source, capital and operating cost, disposal of tailings. Permits – right to mine and discharge waste and make good. Construction schedule – timing, how long to first production – the quicker the better. Logistics - of supply materials, equipment and manpower to site including an investigation of transport modes. Identification of strategic decisions required - early ordering of long delivery items, early starts to opening of negotiations for right-of-way dispensation etc. Preliminary programme -for carrying-out the Project. Construction cost – minimum expenditure to get the project operating, which varies depending on type and size of mine. All costs to include transport and commissioning costs, fees and all management costs except for Client's own costs. Markets and marketing – transport to market (FOB or CIF), price for product quality sold, secondary processing costs, adequate demand for product. Financial analysis – put all of the above together to determine if the project is financially viable.
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Things can go wrong – Mt Todd gold mine • Combination of many errors in forecasting can be fatal for any project. • Project owner is Pegasus Gold Inc and wrote off US$353.5 million in November 1997 after closing down the project. • This write down of shareholders funds was of balance sheet items amounting to US$122.6 million of acquisition costs, US$49.4 million of deferred preproduction and development expenses and US$181.3 million for property and equipment.
Rudenno, 2008 Open Pit Mine Planning and Design 75
Case Study – Mt Told Gold Project • Commodity price overoptimism resulted in a forecast gold price of US$385 per ounce, including a hedging premium above expected spot prices. • Spot prices while the project was operating were about US$315 per ounce and the hedging premium was small.
MCA - Risk Assessment in Mine Planning and Design
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Case Study – Mt Told Gold Project Forecast
Actual
Change
1.07g/tAu 84% 8 Mt
0.96g/tAu 74% 6.7 Mt
-10% -12% - 16%
Crushing costs Contract mining Power costs
$1.36/t $1.00/t $0.058/kwh
$2.49/t $1.15/t $0.075/kwh
+83% +15% +29%
Cyanide usage Total cash costs Cash costs per ounce gold produced Gold price
0.68kg/t $11.86/t US$287/oz
0.86kg/t $13.58/t US$415/oz
+26% +15% +45%
US$385
US$315
-18%
0.7
0.74
+6%
Reserves grade Metallurgical recovery of gold Throughput per year
Exchange rate, A$1.00=US$
Open Pit MineinPlanning and Design MCA - Risk Assessment Mine Planning and Design 77
NATURE & PURPOSE OF FEASIBILITY STUDIES IN MINING Your Audience Type
Scoping
Preliminary
Feasibility
Audience
Internal Technical
Mixed Professional
External
Executives
Boards
Joint venture
Financiers
Extracts to stake holders
Investors
Exploration Business Development Executive
Their Interests
Consultants
Critical factors
Optimum project scope
Profitability
Potential
Profitability
Costs
Cost of next stage
Schedule Risks, etc
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Cost Accuracy Scoping
Preliminary
Feasibility
Study
Feasibility
Study
Project Control Estimate
Class 1
Class 2
Class 3
Class IV
(+/- 30% - 50%)
(+/- 25%)
(+/- 10% - 15%)
(+/- 5% - 10%)
Equipment factor estimate
Forced detail estimate
Order of magnitude Capacity factor estimate
Definitive; Fall out detail estimate
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Mining is a Business, but risky
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MINING PROJECT RISKS ECONOMIC / FINANCIAL RISKS
TECHNICAL RISKS
OH&S RISKS
POLITICAL RISKS
Participants discuss these elements of Risk in Mining Projects. 81
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Conclusion Strategic planning (SP) involves developing a range of options, carrying out some form of evaluation, assessing criteria and decision-making.
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Activity 2: Individual learning Refer to worksheet 1 – Development of a mining strategy: open pit and/or underground?
Complete the task and discuss the calculations with the person(s) sitting next to you!
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Module 2 OPEN PIT OPTIMIZATION What you will learn: • Block Values and Cost calculation • Pit Optimisation techniques • Pit Optimisation Software Open Pit Mine Planning and Design
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Block Grade to Block Value Dollar Value = Revenue - Costs
0.3%Cu
-$1.13/t
Some factors to consider: • Location of the block relative to the surface – effect on cost • Processing costs my depend on rock type
Dollar Value = Revenues - Costs • Revenues can be calculated from: – Ore tonnages – Grades – Recoveries – Product price
• Costs can be calculated from: – Mining cost – Milling cost – Overheads Open Pit Mine Planning and Design
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A Formula for a Block Value used in Whittle VALUE = (METAL*RECOVERY*PRICE - ORE*COSTP) - ROCK*COSTM
Calculate the value of ore block X: • 200 grams of metal X • 100 tonnes of rock/ore • Metallurgical recovery = 97% • Selling price of metal $10.00 per gram • Cost of processing $12.00 • Cost of mining $5.00 BV = [200x0.97x10 – 100x12 – 100x5] = $240
Calculating Costs • Must calculate values for: – Mining Cost per Tonne Mined – Processing Cost per Tonne Processed – Rehabilitation Cost per Tonne of Waste – Selling Cost per Unit of Product
• Some Time Costs must be included Open Pit Mine Planning and Design
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Include • Any cost which is directly proportional to the tonnes or units of product: • Fuel oil • Wages • Spare parts • Explosives • etc • Include with the appropriate activity
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Include • Time costs which would stop if mining stopped: • Site administration • Site infrastructure maintenance • Interest on working capital loan • Fall in resale value of equipment • Capital replacement • Truck purchase (long project)
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What to do with Time Costs • When mill limited – Divide annual time cost by annual mill throughput and add the result to the processing cost
• When mining limited – Divide annual time cost by annual mining capacity and add the result to the mining cost N.B. Even add the mill time costs!
• When selling limited ... Open Pit Mine Planning and Design
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Don’t Include • Time costs which continue whether you continue mining or not • Up-front/sunk costs
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Activity 3: Individual learning Refer to worksheet 2 – Block Values and Cost Calculation
Complete the task and discuss the calculations with the person(s) sitting next to you!
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Open Pit Optimisation Resource Model
Resource Classification
Resource estimate Measured Indicated Inferred
Beneficiation factors
position in mine planning flow sheet
Mine survey
Dilution & ore losses
Diluted Resource
Process Parameters
Economic Parameters
Operating Costs
Ore Reserve Model
Potential Ore Reserve
Reserve Classification
Open pit optimisation and design
Revenue, cost and slope parameters
Mining production schedule
Overburden & sub-grade
Ore Reserve estimate Proved and Probable
Beneficiation product
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Activity 4 : Individual learning Refer to worksheet 3 Pit Optimisation – Task 1
Complete the task and discuss the calculations with the person(s) sitting next to you!
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Definition of the Optimal Outline • Any
feasible outline has a Dollar Value. In this context “feasible” means that it obeys safe slope requirements •The optimal outline is defined as the one with the highest dollar value (Profit = Revenue – Costs) • Nothing can be added to an optimal outline which will increase the value without breaking the slope constraints. • Nothing can be removed from an optimal outline which will increase the value without breaking the slope constraints.
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Pit Optimisation Techniques • Moving/Floating/Dynamic Cone Algorithm • Lerchs-Grossmann 2-D Dynamic Programming Algorithm • LG 3-D Graph Theory Algorithm. •
Network Analysis Algorithm
•
Linear Programming (integer programming)
• etc Open Pit Mine Planning and Design
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Floating Cone Method • Position an inverted cone, with the required slopes, on each block with a positive value • If the total value of all blocks in the cone is positive, “mine” those blocks • Repeat these steps until no cone has a positive value • There are two problems
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Floating Cone Method
Courtesy: Kores Corpration Open Pit Mine Planning and Design
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Floating Cone- Mining too little
-30 -80
+100
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+100
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Floating Cone- Mining too much
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Lerchs-Grossman Algorithm • Works with block values • Works with block mining precedence • Guarantees to find the three-dimensional outline with the highest possible value
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Lerchs-Grossman Algorithm • Works with block values • Works with block mining precedence • Guarantees to find the three-dimensional outline with the highest possible value
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Lerchs-Grossman Algorithm
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LG 3d block and graph representation • Orthogonal set of blocks – 2 basic geometries to represent open pit • Arrows point to the blocks that first need to be removed to access the underlying block (at the base)
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Final Pit Design – composite plan
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Activity 5 : Individual learning Refer to worksheet 3 Pit Optimisation – Task 2
Follow the example calculation of the LG pit optimisation algorithm
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Precautions with the OP algorithms 1) Ascribing costs to blocks • The algorithms to determine the final pit limit assume that an economic value can be assigned to each block • However, many of the costs are time costs; it means that assigning them to blocks requires an assumption about what is the unitary operation that restricts production (to express these costs in terms of that activity) Open Pit Mine Planning and Design
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2) Assumption of a breakeven grade • To calculate the net value of a block one has to assume a breakeven cut-off grade • A common assumption is to classify as ore those blocks with a positive value and waste those blocks with a negative value. If the mine is the limiting operation, this misses the opportunity to create value.
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3) Time value of money • There are costs that can not be estimated without a mining plan. This is the case of waste material, which has to be placed in a dump and the cost will depend on the time that this happens – because of the haul distance • This can be solved by iterations!
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4) Blending requirements • There are cases where blocks should be blended with others to be classified as ore. But that again requires a mining plan in advance. • This can also be solved by iterations!
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Major General Mine Design Systems Fully functional packages (with build-in CAD systems): • VULCAN • DATAMINE/CAE • SURPAC/GEMCOM • MineSight • Minex/Gemcom - WHITTLE • Micromine CAD overlaying packages: • AutoCAD • SurvCADD/Carlson • LKAB System
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Data Import
Import + 3D Borehole Processing
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Geological Interpretation
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Block Model + Grade Assessment
Block Model with Grade Open Pit Mine Planning and Design
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Economical Model - Grade >>> $Value Au [g/t]
>>>
Value $$$
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Optimisation/Design Major optimisation programs based on LerchsGrossman algorithm: • Whittle FX Optimiser (stand alone) • MineMax Planner (stand alone) • Pit Optimizer (Vulcan 3D) • NPV Scheduler (Datamine) • Pit Optimiser (Surpac) Open Pit Mine Planning and Design
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Whittle FX Strategic Mine Planning Software Pit by Pit Graph
Import Block Model
Constrains: • Economical • Geometrical • Operational
• No access constrains • No haul road/ramp
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Optimal Pit
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Mine Design
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Mine Design
Geomechanics/Geotechnical
Access constraints
Equipment selection
Ventilation network (underground)
Rehabilitation
Environmental constraints Open Pit Mine Planning and Design
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Final Optimal Pit
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Final Optimal Pit & Pushbacks
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Reporting & Evaluation
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Scheduling
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The Pushbacks Generation
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Optimizing Production Schedules
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Optimizing Production Schedules
+
=
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Activity 6 : Individual learning Review the following technical paper: Chanda, E.K., Spencer, E. (1999). Maximising Resource Utilisation in Open Pit Design, in Proc. 28th International
Symposium on Computer Applications in the Minerals Industry, 20-22 October, Colorado School of Mines, pp359-366, (SME-AIME, Littleton). 1) What is unique about the the approach used by the authors? Open Pit Mine Planning and Design
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waste dump planning
What you will learn: • Principles of dump design and • Dump optimisation
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Why waste dump planning? • A strip ratio of 10:1, say, implies that for every unit of ore mined, 10 times of waste rock is mined. • The waste rock ends up being stored in a waste dump • Traditionally little attention has been paid to dump design and planning, the focus being on planning of ore extraction • It has been recognised that dump design and planning is an integral part of pit design. •
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Rock flow in an open pit mine
Yu (2014) Open Pit Mine Planning and Design
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Waste Dump Design • Two main approaches: 1)
Top-down dumps – waste rock is dumped over an advancing face (angle of repose) – approx 38o from horizontal. After dumping is complete . The dump is reshaped to its intended configuration, usually using bulldozers.
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Waste Dump Design 2) Bottom-up storage – waste rock is dumped in series of piles , and then spread to form a relatively thin layer. Also known as paddock dumping.
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Waste Dump Design • Hybrid dumping– whereby top down used is used to produce relatively thick layers (10 or 15 m, say), which are then overlain by subsequent equally thick layers. This approach is safer and requires leas reshaping.
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Waste Dump Design
Dump progression with shortest haul first strategy
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Waste Dump Design
Dump design considering NAF PAF material (Yu 2013)
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Waste Dump Optimisation- how? MINEMAX Software Simultaneous pit and waste dump design Dump modelled as blocks WHITTLE Software Dump optimisation as mirror image of open pit optimisation XPAC – Advanced Destination Scheduler) Software Module schedules rock placement
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Waste Dump OptimisationRecent Developments
Integrated modelling of dumping system (Yu 2013)
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Module 3 PRODUCTION SCHEDULING What you will learn: • Principles of production scheduling • Scheduling Software
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Mine Scheduling (definition) • A mining schedule, which tell us when things occur, can be constructed by applying production constraints to the mining sequence • Basis for preparing and controlling the mine’s development and production • A schedule determines the cash flow ($$$) associated with mining.
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Typical Timeline
Year -2
-1
Pre-production (Development Construction)
+1
+2
Production
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Inputs • The scope of the work to be done from Mining Layout Designs • Rates at which this work is normally prepared, from Key Performance Indicators (KPI) • Labour working hours and rosters from Strategic Planning module • Plant capacities, from the Strategic Planning modules • Production schedules, Ore reserves, tonnes and grades, recoveries and dilutions
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Types of Mining Schedule • Production schedules – Long Term or Life of Mine (10+ years) – Medium Term (5 years approx.) – Short Term (3 months – 2 years) – Extremely Short Term (down to a shift, or for specific jobs) • Exploration drilling schedules • Development schedules • Production drilling schedules • Equipment schedules • Labour schedules • Filling schedules • Consumable schedules • Special project schedules Open Pit Mine Planning and Design
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Scheduling Packages • • • • • •
XPAC iGannt MS Project MS Excel Whittle 4D In-house
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XPAC • Developed by Runge Software • Business focussed mine scheduling application • Specifically developed for forecasting, reserve database and mine scheduling management of all types of mineral deposits and mining methods • Easy-to-use tools for the adaptation, analysis and scheduling of mineral resources • Designed for surface/underground coal mining • Has limitations in underground mining or in pits with complex geometries
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iGantt • Developed by MineMax • Tool for open-pit and underground production scheduling
• Integrates Gantt chart, 3D visualization and spreadsheet views of a production schedule • Used for scheduling a single operation or multiple operations across an enterprise Open Pit Mine Planning and Design
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Financial Technical Model • • • • • • • • • •
Plant design Infrastructure (road, power, water, village, etc.) Equipment selection Capitals Operating costs Royalty Tax Revenue … NCF NPV, IRR, PB, etc.
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Activity 8 : Individual learning Refer to worksheet 4 Production Scheduling Calculate the monthly production figures for a small gold mine
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Module 4 Cut-off grade optimization 1. 2. 3. 4.
Background The model Example 1: an hypothetical case Example 2: a copper open pit mine & mill 5. Conclusions 6. References
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1. Background • This model was developed in the early 1960s by Ken Lane, a mathematician who made his professional career in the Rio Tinto Group • At the time, the model was used in various mines of Rio Tinto – including Palabora mine in South Africa, and Bougainville mine in PNG. Open Pit Mine Planning and Design
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2. The model Final product
Qr
Concentrates Ore
R
Qc
C Cut-off gx
Slag
Qm
Tailings
Waste
M Open Pit Mine Planning and Design
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Variables used in Lane’s Model M = Mine capacity per period (t of material) C=
Plant capacity per period (t of ore)
R=
Refinery capacity per period (t of product)
Qm = Quantity of run-of-mine material (t of material) Qc = Quantity of ore (t of ore) Qr =
Quantity of final product (t of product) = Qc·g·y
T=
Time to mine, process or refine Qm
P=
Profit Open Pit Mine Planning and Design
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Model’s variables (cont’) d=
annual discount rate
m=
mining costs ($/t of material)
c=
concentrating costs ($/t of ore)
r=
refining and marketing costs ($/t of product)
f=
fixed costs, per period ($/period)
s=
selling price ($/t of final product)
y=
overall metallurgical recovery
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The profit equation for Qm
P s - r Qr c Qc m Qm f T As
(1)
Q r Q c· g · y
P s - r g y c Qc m Qm f T
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Profit from Qm and Present Value f
Qm Qc V W
gx
V = W=
Grade
Present value at the beginning of period T Remaining present value after mining Qm Open Pit Mine Planning and Design
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V
P
P2
P3
P4
Pn
•••••• Time
0
W
T
PW V (1 d)T Open Pit Mine Planning and Design
(2)
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If time T is small: (1 + d)T 1 + d·T
(3)
Replacing in (2): PW V (1 d T)
(4)
Re-arranging: V·(1 + d·T) = P + W
(5)
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Re-arranging: v = V - W = P - d·V·T
(6)
Where v is the contribution that the fraction Qm of the ore deposit makes to the present value of the business As such, v is the variable to maximise when choosing the optimum cut-off grade Open Pit Mine Planning and Design
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Replacing (1) in (6): v s r Qr c Qc m Qm f d V T
(7)
But the optimum present value V on the right side of equation (7) is unknown until the cut-off grade policy is optimised This “chicken and egg problem” is solved by iterations, using an arbitrary value of V in the first iteration and stoping when V converges Open Pit Mine Planning and Design
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Economic cut-off grades v s r Qr c Qc m Qm f d V T
(7)
In equation (7), time T depends on the stage that limits the pace at which ore is mined That is, the quantities Qm, Qc or Qr and their respective capacities M, C, or R This leads to three economic cut-off grades: Open Pit Mine Planning and Design
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a) When the mine imposes a limit (M) In this case,
T
Qm M
Replacing this in expression (7): m f d V v m s r Qr c Q c Qm M
Max vm
v m 0 g Open Pit Mine Planning and Design
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As Qm is given, g only affects Qc and Qr Then g must be chosen to make (s-r)·Qr - c·Qc as large as possible
s - r Qc g y c Qc Therefore:
gm
c s r y
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b) When the plant imposes a limit (M) T
In this case,
Qc C
Replacing this in expression (7): f d V v c s r Qr c Q c m Qm C
Max vc
v c 0 g Open Pit Mine Planning and Design
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In the same way, as Qm is given, g must be chosen to maximise:
s - r Qc g y c f d V Qc
Therefore: gc
c
C
f d V
C s r y
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c) When the refinery imposes a limit (R) In this case,
T
Qr R
Replacing this in expression (7):
f d V Q c Q m Q v r s r c m r R Max vr
v r 0 g Open Pit Mine Planning and Design
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In the same way, as Qm is given, g must be chosen to maximise:
f d V Q g y c Q s r c c R Therefore: gr
c f d V y s r R
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Balancing cut-off grades The operation is sometimes limited by two or eventually three stages simultaneously Then, three balancing cut-off grades can be introduced into the analysis gmc: Mine-Plant gmr: Mine-Refinery grc : Refinery-Plant Open Pit Mine Planning and Design
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Mine-mill example Qm
f
gm
gmc gc
Grade
gmc fully utilises mine and mill capacities; that is, maximum stripping ratio at the mine and throughput at the mill Open Pit Mine Planning and Design
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Mine capacity: 650,000 t/d Mill capacity: 150,000 t/d gm: 0.25 %Cu gc: 0.65 %Cu Possible throughputs: Cut-off % Cu
Mine t/d
Mill t/d
Grade % Cu
0.25
450,000
150,000
0.9
0.50
650,000
150,000
1.2
0.65
650,000
120,000
1.3
0.5 %Cu is a balancing cut-off Open Pit Mine Planning and Design
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In summary, Lane’s model considers six cut-off grades: • three economic cut-off grades, and • three balancing cut-off grades
The former depend on economic factors and capacities whereas the latter are determined by the grade distribution that can vary widely throughout irregular ore bodies None of these considers mining costs! Open Pit Mine Planning and Design
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Optimum cut-off grades The overall optimum is one of the six cutoff grades already defined: 1) 2) 3) 4) 5) 6)
gm gc gr gmc gmr grc
To assess which one is the optimum it is best to consider each pair of stages in turn Open Pit Mine Planning and Design
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To see which one is the optimum it is best to plot the value functions considering each pair of stages in turn Mine-Concentrator m f d V v m s r Qr c Q c Qm M f d V v c s r Qr c Q c m Qm C Open Pit Mine Planning and Design
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v
vm
vc
gm
gmc
Gmc = gmc
g
gc
v
vc
vm
gmc
gm
Gmc = gm
g
gc
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v
Gmc = gc vm gm gc
gmc
vc g
In a similar way, by considering the other pair of stages, it is possible to obtain Gmr and Grc Open Pit Mine Planning and Design
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The overall optimum cut-off grade is: G = Middle value (Gmc,Gmr,Grc)
v vr vm
vc
gm grc
gmr gmc
gc
gr
g
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3. Example 1: an hypothetical case • Mine capacity (M)
= 100
• Plant capacity (C)
= 50
• Refinery capacity (R) = 40 • Mining costs (m)
=1
• Concentrating costs (c)= 2 • Refining costs (r)
=5
• Fixed costs (f)
= 300
• Selling price (s)
= 25
• Overall recovery (y)
= 100 %
• Annual discount rate (d)= 15 % Open Pit Mine Planning and Design
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Grade-tonne relationship f(t) Grade interval
Quantity
0.0 – 0.1
100
0.1 – 0.2
100
0.2 – 0.3
100
.
.
100
. 0.9 – 1.0
100 1000 0
0.5
g
1.0
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Balancing cut-off grades Cut-off
Tonnage
Ratios
Mine
Mill
Grade
Ref.
M/C
M/R
C/R
0.0
1000
1000
0.50
500
1.00
2.00
2.00
0.1
1000
900
0.55
495
1.11
2.02
1.82
0.2
1000
800
0.60
480
1.25
2.08
1.66
0.3
1000
700
0.65
455
1.43
2.20
1.54
0.4
1000
600
0.70
420
1.67
2.38
1.43
0.5
1000
500
0.75
375
2.00
2.67
1.33
0.6
1000
400
0.80
320
2.50
3.13
1.25
0.7
1000
300
0.85
255
3.33
3.92
1.18
0.8
1000
200
0.90
180
5.00
5.56
1.11
0.9
1000
100
0.95
95
10.00
10.53
1.05
M/C = 100/50 = 2.00
gmc = 0.50
M/R = 100/40 = 2.50
gmr = 0.45
C/R = 50/40 = 1.25
grc = 0.60
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Economic cut-off grades gm
gc
gr
c 0.10 s r y c
f d V
C s r y
For V = 0 0.40
c 0.16 f d V s r y R
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Optimum cut-off grades Gmc = Mid (0.10, 0.40, 0.50) = 0.40 Gmr = Mid (0.10, 0.16, 0.45) = 0.16
Grc = Mid (0.16, 0.40, 0.60) = 0.40 G = Mid (0.16, 0.40, 0.40) = 0.40
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Intermediate mine plan Year
Cut-off
Mine
Mill
Ref.
Profit
1
0.4
83.3
50
35
216.7
2
0.4
83.3
50
35
216.7
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
12
0.4
83.3
50
35
216.7
P = (25 - 5)·35 – 2·50 – 1·83.3 – 300·1 P = 216.7 PV@12y and 15% = 1174
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Second iteration gm
gc
gr
c 0.10 s r y d V C 0.58 s r y
c
f
For V = 1174
c 0.25 f d V s r y R
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Optimum cut-off grades Gmc = Mid (0.10, 0.50, 0.58) = 0.50 Gmr = Mid (0.10, 0.25, 0.45) = 0.25 Grc = Mid (0.25, 0.58, 0.60) = 0.58 G = Mid (0.25, 0.50, 0.58) = 0.50
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A new mine plan...
• With the new cut-off grade of 0.5, a new mine plan can be developed but this time changing the present value from year to year • If annual profits are discounted to time 0 and added up, it gives another estimate of V • If the difference of the initial and final value of V exceeds a defined tolerance threshold, the whole process is repeated
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Annual profit for the first year...
For a 0.5 cut-off grade, the annual profit and present value is as follow: P = (25 - 5)·37.5 – 2·50 – 1·100 – 300·1 P = 250 PV@ 10y and 15% = 1255
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Optimum mine plan and cut-off grades policy Year
Cut-off
Mine
Mill
Ref.
Profit
PV
1
0.50
100
50
37.5
250
1255
2
0.50
100
50
37.5
250
1194*
3
0.50
100
50
37.5
250
1123
4
0.50
100
50
37.5
250
1041
5
0.50
100
50
37.5
250
947
6
0.50
100
50
37.5
250
840
7
0.50
100
50
37.5
250
716
8
0.49
97
50
37.1
245
573
9
0.46
93
50
36.5
238
414
10
0.41
89
50
35.9
229
238
11
0.41
21
13
8.8
55
45
1000
513
380.8
2517
PV @ 11y and 15%= 1256
* W = V·(1+d) - P W = 1255 · 1.15 – 250 = 1194
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4. Example 2: a copper open pit mine & mill Relevant data: •
Mine capacity (M)
= 18.9 Mt/a
•
Plant capacity (C)
= 7.2 Mt/a
•
Mining costs (m)
= 0.85 $/t material
•
Milling costs (c)
= 3.7 $/t ore
•
Fixed costs (f)
= 3.5 M$/a
•
Copper price (s)
= 2205 $/t Cu ($1.0 /lb)
•
TC/RC & selling cost (r)
= 705 $/t Cu ($0.32 /lb)
•
Overall recovery (y) = 85 %
•
Annual discount rate (d)
= 10 %
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A set of four pushbacks
A
B C
D
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Input to the model: four scheduled, nested pits (periods) from a preliminary mine plan
2 PP
1
1
3 1
3
2
4
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Grade-tonnage relationship for the four pits Cut-off
Period 1
Period 2
Period 3
Period 4
% Cu
Mt
% Cu
Mt
% Cu
Mt
% Cu
Mt
% Cu
0.0
20.3
1.05
36.5
0.79
56.3
0.57
80.1
0.59
0.2
18.7
1.13
30.1
0.92
40.8
0.76
60.4
0.77
0.4
15.3
1.32
24.4
1.08
28.5
0.97
50.2
0.87
0.6
12.9
1.47
19.7
1.22
21.7
1.11
38.3
0.98
0.8
11.0
1.61
13.7
1.45
15.1
1.30
22.7
1.18
1.0
8.6
1.80
10.2
1.64
10.0
1.49
14.6
1.35
1.2
7.1
1.95
7.6
1.83
6.9
1.67
9.0
1.49
1.4
5.9
2.08
5.6
2.02
4.4
1.88
5.0
1.65
1.6
4.4
2.27
4.0
2.24
2.7
2.11
2.9
1.75
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Output for a “Base case” Year
Period 1
Cut-off
Mine
(% Cu)
(Mt)
Mill (Mt)
(% Cu)
Ratio
Profit
PV
(W/O)
(M$)
(M$)
1
1
0.85
14.2
7.2
1.67
0.97
110.3
475.5
2
1
0.78
6.1
3.4
1.59
0.82
49.6
412.8
2
2
0.78
9.8
3.8
1.43
1.56
44.8
412.8
3
2
0.72
16.8
7.2
1.37
1.34
81.3
359.6
4
2
0.67
9.9
4.7
1.31
1.13
50.4
314.2
4
3
0.61
6.7
2.5
1.12
1.62
19.4
314.2
5
3
0.61
18.9
7.2
1.12
1.62
56.3
275.8
6
3
0.60
18.6
7.2
1.11
1.58
55.8
247.0
7
3
0.56
12.1
4.9
1.08
1.45
36.5
215.9
7
4
0.56
4.5
2.3
0.96
0.98
14.9
215.9
8
4
0.53
13.6
7.2
0.94
0.89
44.5
186.1
9
4
0.50
13.1
7.2
0.92
0.82
43.3
160.3
10
4
0.47
12.6
7.2
0.91
0.75
42.4
132.9
11
4
0.44
12.1
7.2
0.89
0.68
41.4
103.9
12
4
0.41
11.6
7.2
0.87
0.61
40.2
72.9
13
4
0.37
11.2
7.2
0.86
0.55
38.9
39.9
14
4
0.33
1.5
1.0
0.84
0.50
5.1
5.0
94.6
1.11
1.04
193.2
PV = 475.5
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Output for an expanded case (Mill from 7.2 to 9.0 Mt/a) Year
Period 1
Cut-off
Mine
(% Cu)
(Mt)
Mill (Mt)
(% Cu)
Ratio
Profit
PV
(W/O)
(M$)
(M$)
1
1
0.78
16.3
9.0
1.59
0.81
131.8
521.2
2
1
0.71
4.0
2.3
1.53
0.71
33.1
441.6
2
2
0.67
14.0
6.7
1.30
1.10
71.3
441.6
3
2
0.65
18.5
9.0
1.29
1.05
95.4
381.3
4
2
0.60
4.1
2.2
1.22
0.86
22.1
324.0
4
3
0.45
14.2
6.8
1.00
1.10
46.6
324.0
5
3
0.45
18.9
9.0
1.00
1.10
62.0
287.7
6
3
0.45
18.9
9.0
1.00
1.10
62.0
254.4
7
3
0.45
4.2
2.0
1.00
1.10
13.7
217.9
7
4
0.51
12.9
7.0
0.93
0.84
43.2
217.9
8
4
0.48
15.9
9.0
0.91
0.76
54.1
182.8
9
4
0.45
15.2
9.0
0.89
0.69
52.9
146.9
10
4
0.42
14.6
9.0
0.88
0.62
51.5
108.8
11
4
0.38
14.1
9.0
0.86
0.56
50.0
68.1
12
4
0.34
7.4
4.9
0.84
0.51
26.4
25.0
103.9
1.06
0.86
193.2
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Conclusion for this case The “Base Case” produces a declining cut-off grade policy starting at 0.85 %Cu and yielding a PV of $ 475.5 million The “Expanded Case” lowers the initial cut-off from 0.85 to 0.78 %Cu and increases the PV by $46 million – from $475.5 to $521.2 million If the expansion capital investment is less than $46 million, then it is worth going ahead Open Pit Mine Planning and Design
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5. Concluding remarks Lane’s cut-off grade model is a first attempt to define economically what material is ore in a life-of-mine (LOM) plan It requires a holistic view of mining in that the optimisation needs a preliminary LOM plan. That is, a final pit limit, pushbacks design and scheduling based on a breakeven cut-off - the mine or plant cut-off grade, for instance Open Pit Mine Planning and Design
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Activity 8 : Individual learning Refer to worksheet 5 Cutoff Grade Optimisation Follow the calculations to the problems
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Lane’s model considers various variables as fixed input – capacities, and downstream cutoffs such as metallurgical recovery at the mill Most recent developments have expanded the model to include some of these variables and handle them simultaneously When the problem becomes too complex, it is solved using other mathematical tools, integer linear programming being one of them Open Pit Mine Planning and Design
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6. References Kenneth F. Lane - The economic definition of ore, Mining Journal Books, London 1988 Kenneth F. Lane - Choosing the optimum cut-off grade, Colorado School of Mines Quarterly. Vol. 59-4, 1964, pp. 811829 Blackwell, M. Some aspects of the evaluation and planning of the Bougainville copper project, Decision-Making in the Mineral Industry, CIM Special Vol 12, 1971 pp. 261-269
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Module 5 Mine Planning Software • • • •
Software Packages Categories Capabilities Providers
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Common Software Packages
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Categories of Mining Software
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Mapping Software
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Geological & Data managent
Source: (Sable, 2013) Open Pit Mine Planning and Design 206
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Geological Modelling/ Resource Estimation
Drill hole display (Source: Geovia, SUPARC) Open Pit Mine Planning and Design 207
Geological Modelling/ Resource Estimation
Ore body model(Source: CAE, STUDIO 3) Open Pit Mine Planning and Design 208
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Mine Design
Pit Design (Source: Maptek, VULCAN) Open Pit Mine Planning and Design 209
Planning and Scheduling
Pit Design (Source: Geovia, MineSched) Open Pit Mine Planning and Design 210
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Financial Evaluation
Financial Analysis Software (RungePincockMinarco) Open Pit Mine Planning and Design 211
Optimisation/Risk Analysis
Pit Optimisation (Geovia, WHITTLE) Open Pit Mine Planning and Design 212
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Monitoring & Control
Truck Dispatching (Modular Mining System; (DISPATCH) Open Pit Mine Planning and Design 213
Simulators
Coal Mining Simulator (Immersive Technologies) Open Pit Mine Planning and Design 214
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Virtual Reality
ViMine VR Software – 3D Ore body model Open Pit Mine Planning and Design 215
Summary
• Advances in Computer technology has made it possible to model complex mining environments • Most widely software is for Mine Design & Planning • Further developments in simulation and risk modelling • Mining software harmonisation by suppliers
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Module 6 mine to mill optimisation • Concept embraced and practiced by mining companies • The philosophy is base on: Characterise Track Measure Model • Potential to save mining companies thousands of Dollars
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Mine production system processes • Drilling • Blasting • Loading • Hauling • Milling (Crushing, grinding) Examine total “system” with regard to cost, productivity, product quality, optimisation...
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• Loading: increased fragmentation => higher rate of shovel productivity, hence lower costs per BCM. • Hauling: Truck production per hour will increase with greater fragmentation due to faster shovel loading rates. Reduced cycle time. • Crushing: Lower crushing costs result from increased fragmentation as more material pass through as under size. • Drilling and blasting costs are harder to relate to fragmentation).
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Optimum Fragmentation Curves •
Unit costs as a function of the degree of fragmentation
•
Systems optimisation:
Overall Cost Curve
Degree of fragmentation Open Pit Mine Planning and Design
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Exploration Drilling Intact rock data Crushing/grinding Energy data Bond's Work Index Settings
Mineralogy data
Ore body modeling and pit design
Fracture frequency data
Hauling Payload data Voids ratio* LCM TKPM rating Autonomy Routing data
Process Optimization Blast design, Load-Haul
Excavation/Loading Digability* Dig rate* Dipper design Power consumption Swing analysis Autonomy
Blast Design Pattern layout VOID Powder factor Explosive
S01U264007
Percentage Passing (%)
120 100 80 S01U264007 35.2Mtpa ROM Target
60 40 20 0 1
10
100
1000
Size (mm)
Muckpile properties Size distribution* Voids ratio* LCM Visualization Density
Blasthole Drilling Bore diameter Hole deviation monitor Geophysical data Real time drilling data
Blast Modelling Displacement model Fly rock Heave mechanics
Optimum Fragmentation • Examine individual components and the whole system • Goal: “achieving a prescribed level of fragmentation at minimum cost” • In-situ ore with particle size considered to be very large and reducing to size in the order microns (eg -80 mesh). • Measuring Fragmentation, how?
Diggability (BCM/HR) Size distribution of muckpile (WIPFrag Software), Split-Desktop software Photographs are taken from muck pile, digging face, moving truck, etc. Open Pit Mine Planning and Design
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Drilling and Blasting SubSystem
Fragmentation evaluation •
Measurement of parameters- correlate with fragmentation
Photographs are taken from muck pile, digging face, moving truck, etc. Crusher monitoring - energy, feed, product size, throuputghput Shovel monitoring- load, wait, down time, swing, power
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Case Study
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Case Study Modeling Muck Pile Fragment Size to Optimize Excavator Productivity in Open Pit Mining Prominent Hill Copper Mine, South Australia
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Prominent Hill
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Prominent Hill Muckpile Image Analysis using SPLIT DESKTOP: • The split desktop system uses digital image analysis technology to convert an image captured from a digital camera to a distribution of defined areas within the photograph. • The software was developed from a system of manual image analysis where a photographic image was manually delineated and the diameter of each particle measured
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Prominent Hill Camera
Photo of muckpile
Photo collection and scale placement on flitch face.
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Prominent Hill
Blast master 10040RL Open Pit Mine Planning and Design
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Prominent Hill
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Prominent Hill
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Prominent Hill • Our modelling of the excavator production rates has suggested that P80 of 800 mm would be the optimal size to maximise excavator productivity at 6300 t/hr. • However due to mine machinery and crusher constraints we believe a revised figure of 600 mm would be more appropriate
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Module 7 Equipment Selection • Simulation modelling using GPSS/H – Case Study • Cost Estimation (Capital & Operating)
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Simulation and Animation of an Australian Surface Mine • • • • • •
Study Background Methodology Results Discussion Conclusion Recommendations
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Wilcherry Hill Iron Ore Mine • The Wilcherry Hill project is located 30 km north of the township of Kimba in South Australia. • The Wilcherry Hill project comprises of four tenements and covers an area of 976 square kilometres. • The tenements are EL4162Wilcherry Hill, EL4286-Valley Dam, EL4421- Peterlumbo, EL3981-Eurilla Dam.
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Project Development • Development at Wilcherry Hill is proposed in three phases; stage 1, 2 and 3. • Stage 1 will be the focus of this project • Comprises mining, crushing and export of Direct Shipping Ore (DSO) • Ore sourced from the upper parts of the mining pits.
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Methodology Aim • Simulation and animation model using the Stage 1 layout of the mine • Determine the optimum number of shovels and trucks required for this mining scenario • Provide the company with a model they can use for many “what if?” scenarios.
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Programming in GPSS/H • Approximately 1,200 lines of computer code were used to model this mining scenario • Over 60,000 command lines were used to generate this animation
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Methodology GPSS/H Simulation Main Commands
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Methodology Variables, User Information and Generate •
•
•
Variables: REAL
&X,&Y,&Z,&A,&B,&C,&D,&E,&F,&G,&H,&I
User Information: PUTSTRING PUTSTRING PUTSTRING INTEGER GETLIST
(' ') ('HOW MANY TRUCKS?') (' ') &TRUCKS &TRUCKS
Generate: GENERATE
3,,0,&TRUCKS,,12PH,12PL
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Methodology Animation
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Methodology Mine Layout (Draw, Class and Paths)
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Methodology Run
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Methodology Animation
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Methodology Animation
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Results Assumptions HD 785 EMPTY: LOADED: LOADED SF: ORE WEIGHT: STRUCK BODY CAPACITY: ORE SPECIFIC GRAVITY: FULL STRUCK LOAD ORE WEIGHT: HOURS PER SHIFT:
72 164 147.6 75.6 40 4 160 8
t t t t m3 t
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Results Ore Results
TRUCKS: ORE DUMPS PER SHIFT: STOCKPILE DEPOSITION PER SHIFT: STOCKPILE WITHDRAWAL RATE: COMPARISON (IRONCLAD):
3 9 1440 180
4 13 2080 260
5 17 2720 340 291
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6 20 3200 400
7 23 DUMPS 3680 T 460 T/HR T/HR
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Results Ore Results
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Results Waste Results TRUCKS: WASTE DUMPS PER SHIFT: DUMP DEPOSITION PER SHIFT: DUMP RATE: COMPARISON (IRONCLAD):
3 68 5140.8 642.6
4 87 6577.2 822.15
5 104 7862.4 982.8 885
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6 123 9298.8 1162.35
7 142 DUMPS 10735.2 T 1341.9 T/HR T/HR
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Results Waste Results
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Conclusion • GPSS/H Simulation and Animation – Number of shovels: one shovel – Number of trucks: five trucks and possibly an extra standby truck
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Acknowledgements Postgraduate Students: • Sophie Mellor • Jian Liu
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Cost Estimation • Capital Costs • Operating Costs
Capital cost estimation: general considerations • Indicative capital cost estimates – Based on empirical data from other projects – Estimates are within +/- 30% accuracy – Suitable for scoping or pre-feasibility studies – Often use “rules-of-thumb” to estimate costs
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Capital cost estimation: general considerations: • Indicative capital cost estimates (cont.) – The sixth-tenths rule (Mular, 1978): • Cost 1 / Cost 2 = (Capacity 1 / Capacity 2)0.6 • Capacity 2 and Cost 2 relate to a known similar operation in a similar environment • Capacity 1 relates to the operation being studied • Cost 1 is then estimated – Annualised cost per tonne rule: • Annualised cost per tonne of a known operation = {Total capital cost} ÷ {tonnes per year} • Use this factor directly to estimate capex for another, similar operation. Open Pit Mine Planning and Design
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Capital cost estimation: general considerations • Cost indices – Most cost estimations are based on historical data available to the estimator. – These data date and cost indices can be used to update them: Cost now = {cost then}{cost index now/cost index then} – Indices available from Cost Guides
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Capital cost estimation: general considerations • Working capital – This is the capital component of operating costs needed to support the operation prior to substantial revenue inflows. – Often underestimated and can result in project failure. – Sometimes a factor (such as 10% of fixed capital cost) is applied. However a more detailed analysis is usually good practice. Open Pit Mine Planning and Design
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Capital cost estimation: general considerations • Options for capital equipment – Contract mining • capital not available; • short duration; • specialist skills required; and/or • specialist equipment required. – Hired equipment – machine only and hirer responsible for fuel, oil, servicing and operation (dry hire); or – full hire (all inclusive), usually hourly rate with standby rate. Open Pit Mine 258 Planning of 10 and Design
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Capital cost estimation: general considerations • Ownership cost – Fixed cost per hour irrespective of whether the machine is working or not – It is a function of: • purchase price • cost of any extras • freight charges • tyre costs • resale value • depreciation period
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Capital cost estimation: general considerations
• Ownership cost (cont.) – Straight-line depreciation formula: – D = (P - R) / (N.H) where D is depreciation per hour, P is purchase price, R is residual value, N is useful life in years, H is hours of service per year. – Interest component of the cost: – I = P(r + i)(N + 1) / 200 N.H where I is interest cost per hour, r is interest rate on capital (%), i is insurance rate (%). – Total hourly ownership charge in $/hour, C = D + I
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Capital cost estimation: general considerations • Ownership cost example: – Assume: • Cost $400,000; • Life 10,000 hours over seven years; • residual value 35% of capital cost; and • interest and insurance is 12% per year. – D = (400,000 - 140,000) / 10,000 = $26.00/hour – I = (400,000 x 12 x 8) / (200 x 10,000) = $19.20/hour – C = 26 + 19.20 = $45.20/hour
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Capital cost estimation: general considerations •
Equipment replacement – Equipment becomes uneconomic when actual owning and operating cost exceeds that of a new unit – Overhaul or replace? • Cost of overhaul? • Time to overhaul and requirement for temporary replacement? • How long will economic life be extended? • Other work required during the extension of life? • Rate charged to mining operation to cover cost compared with cost of new equipment and economics of mine? • Will overhauled equipment have acceptable availability?
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Infrastructure capital (cont.) • Access and site works – location and logistics – access and service roads ($65,000 to $230,000/km depending on purpose) – port facilities – airstrips ($700,000 to $4.5 million) – site works (highly variable; $65,000 to $400,000/ha). – drainage – fencing and security Open Pit Mine 263 Planning of 10 and Design
Infrastructure capital (cont.) • Industrial facilities – workshops and servicing facilities – warehouses – materials handling – mobile equipment • Utilities – power generation, transmission, distribution – water supply (source, quantities, storage, distribution) – fuel storage and distribution – sewerage and solid waste disposal Open Pit Mine Planning and Design
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Infrastructure capital (cont.) • Communications – external – internal • Port and marine facilities • Waste disposal systems – overburden dumps – water management – tailings handling and storage – solid wastes Open Pit Mine Planning and Design
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Infrastructure capital (cont.) • Administration facilities – – – – – – – – –
administration building laboratories training facilities change rooms crib/lunch rooms safety and medical facilities fire station core storage security
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Infrastructure capital (cont.) • Transportation – road transport – rail transport – slurry pipeline – overland conveyors – sea or river transport – cableways (aerial ropeways)
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Infrastructure capital (cont.) • Townships – housing – roads – services – recreation facilities – shopping facilities – medical facilities – educational facilities – service industries • Construction facilities Open Pit Mine Planning and Design
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Estimating of Operation Costs • Before any economic analysis or decision-making can be undertaken the operating and capital costs of equipment must be estimated. • Equipment operating costs vary between mine sites and there is no cost which can be applied universally. • Equipment costs are generally derived from mine statistics, from suppliers or estimated from first principles. • The standard presentation of costs is Dollars per Operating Hour or Dollars per Tonne • Make sure to cross-check your estimated costs with currently prevailing mine sites.
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Major Mine Equipment Operating Costs
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Cost Calculation Steps Daily Production Rate
Select Equipment
Production Rate for each equipment
Capital and Owning Costs for the equipment
ore and waste
Shovels, trucks, drills, excavators etc.
# of machines required
Mine buildings and costs associated with the mine development period
Some equipment needs to be replaced. Equipments have lifetime as 5, 10, 20 yrs. Ownership Costs consists depreciation and average annual investment cost. AAI=(n+1)Capital Cost / 2n AAI should include tax, interest, insurance. So AAIC with a percent
Other capital expenditures
Milling Costs (ownership and capital costs)
AAIC=P x AAI Ownership Cost = Depreciation + AAIC
Direct operating costs, total operating costs, direct operating costs + maintenance Ore and Waste
Mining Costs # of production & support employees salaries
Other Costs
Operating Costs
Productivity (tonnes/manshift) Materials, supplies, power Total and labour costs ($/hr or $/m or $/tonnes) Ore and waste separation will be Open Pit Mine madePlanning and Design
Total Mining Cost = Total Operating Cost + ownership Cost
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Module 8 Financial Technical Modelling • • • • • • •
What is Financial Technical Modeling? Revenue Assumptions Project Financing Evaluation Guidelines The Frame Work of Evaluation Project Cost of Capital Conclusions
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WHAT IS A FINANCIAL TECHNICAL MODEL (FTM)? • Financial/technical models of mining projects are spreadsheets in which the technical processes of ore and waste mining, ore processing and production of salable product are incorporated as quantities mined, processed and sold and, in turn, as generating the revenues earned and costs incurred in such processes. • The revenues earned depend on forecasts of product prices, generally supplied by sources external to the mining operation. • The costs are determined by technical analysis of the project by project staff.
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• Other financial inputs, such as interest rates, debt raisings and repayments and depreciation schedules will normally be supplied by head office corporate staff. • Forecasts of future inflation rates and exchange rates may well be supplied by external sources. • Example 1 of Financial Technical Model
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REVENUE ASSUMPTIONS - 1 • World market prices dominant but hard to predict • World economic conditions are volatile • Uneven outlook throughout the world • Supply and demand dominates - excess supply is usual but not now (China!) • Potential for major economic disruptions, e.g. oil price shocks, Soviet collapse, GFC, war, China effect, etc.
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PROJECT FINANCE
• Money lent for developing a project • Secured against assets and cash flow of project • Repayable from earnings of project • Limited recourse (sometimes no recourse) to other assets of project owners
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SOURCES OF FINANCE • EQUITY: – New Issues (shares, options, hybrids, units) – Asset sales – Retained earnings – Term loans – Securities (bills, bonds, notes, debentures) – Commodity loans-Leases – Project finance • DEBT: security, recourse to borrowing
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ADVANTAGES OF EQUITY FINANCING • It's less risky than a loan because you don't have to pay it back, and it's a good option if you can't afford to take on debt. • You tap into the investor's network, which may add more credibility to your business. • Investors take a long-term view, and most don't expect a return on their investment immediately. • You won't have to channel profits into loan repayment. • You'll have more cash on hand for expanding the business. • There's no requirement to pay back the investment if the business fails.
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DISADVANTAGES OF EQUITY FINANCING • It may require returns that could be more than the rate you would pay for a bank loan. • The investor will require some ownership of your company and a percentage of the profits. You may not want to give up this kind of control. • You will have to consult with investors before making big (or even routine) decisions -- and you may disagree with your investors. • In the case of irreconcilable disagreements with investors, you may need to cash in your portion of the business and allow the investors to run the company without you. • It takes time and effort to find the right investor for your company. Open Pit Mine Planning and Design
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ADVANTAGES OF DEBT FINANCING • The bank or lending institution has no say in the way you run your company and does not have any ownership in your business. • The business relationship ends once the money is paid back. • The interest on the loan is tax deductible. • Loans can be short term or long term. • Principal and interest are known figures you can plan in a budget (provided that you don't take a variable rate loan).
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DISADVANTAGES OF DEBT FINANCING • Money must paid back within a fixed amount of time. • If you rely too much on debt and have cash flow problems, you will have trouble paying the loan back. • If you carry too much debt you will be seen as "high risk" by potential investors – which will limit your ability to raise capital by equity financing in the future. • Debt financing can leave the business vulnerable during hard times when sales take a dip. • Debt can make it difficult for a business to grow because of the high cost of repaying the loan. • Assets of the business can be held as collateral to the lender. Open Pit Mine Planning and Design
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EQUITY/DEBT FINANCING MIX • Most businesses opt for a blend of both equity and debt financing to meet their needs when expanding a business. • The two forms of financing together can work well to reduce the downsides of each. • The right ratio will vary according to your type of business, cash flow, profits and the amount of money you need to expand your business (50:50; 30:70, etc) Open Pit Mine Planning and Design
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EVALUATION GUIDELINES Made at a point in time Sunk costs (don’t worry!) Constant $ or current $ For comparing alternatives, make sure techniques used permit fair comparisons • Computer financial models (spreadsheet modeling) • Investment decision versus sale/purchase evaluation • • • •
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FRAMEWORK OF EVALUATION • A construction of cash flows - in and out • Express every aspect in terms of cash • Express uncertainty in ranges of values, creating multiple models of the one project • Cash flows not accounting profits • Evaluate on a stand alone basis • Ignore side issues unless the side issue is the purpose of the project
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MAJOR ITEMS IN FTM CASH ($): • Cash is the lifeblood of the enterprise • “Cash flows” are actual $ spent or received • Non-cash items (e.g. depreciation) are important as far as they affect cash flows • Project cash flows for a period are inflows minus outflows - may be +ve or -ve • Periods are usually years; may be quarters or months, depending on the size of the project
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INFLOWS AND OUTFLOWS* • Inflows: sales revenue; may include other minor items • Outflows: Initial capital expenditure, working capital, maintaining capital, operating costs, taxes, royalties, rehabilitation costs, etc • Royalties: ?Treat as reductions in revenue • Off site costs, such as realisation costs, ? Treat as reductions in revenue
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WORKING CAPITAL • Component of initial Cap. ex. - to fund op. costs until sales revenues arrive - in theory recovered at end of mine life • Required throughout project life but generally supplied by sales revenues • Itemised on a period by period basis in detailed financial models • Avoid double counting in financial model but must be counted in initial funding requirement Open Pit Mine Planning and Design
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CURRENCY Local currency (A$ for Australian projects in Australia) Because costs in local currency Convert revenues to local currency Forecast exchange rates can dominate the evaluation Foreign projects in host country currency - limited conversion to A$ needed • In cases of foreign country hyperinflation, use a stable currency, e.g. US$, if sales revenues in US$ • • • • •
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EXCHANGE RATES • $ EXCHANGE RATE IS QUITE VOLATILE • Moves with commodity prices but affected by other influences as well. • Forex turnover in all currencies in Australian market represents 4.3% of global turnover, 7th largest forex market in the world. • A$/US$ pair ~45% of total turnover. Euro/US$ pair ~14%. A$/JPY only 1% • Aust. forex market grew with world market. Also, helped by carry trade and hedge fund activity, plus growing funds under management in Australia seeking to invest overseas. Bulk of trades with overseas FIs • Aust. banks hedge ~ 100% of forex deals.
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CONSTANT VS CURRENT $ • $ change in value over time • Constant $ - generally average value of $ of the day at time of evaluation, preserved throughout project life. • Current $ - $ of the day for each period in the future - requires calculation of the change in value from period to period, i.e. usually inflation rates • Costs affected by local inflation, revenues by world inflation, up to a point. Mineral commodity revenues controlled by supply and demand most of the time.
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MORE CONSTANT VS CURRENT $ • Constant $ evaluation easier • Present day costs known but not future revenues • Current $ evaluation both costs and revenues based on forecasts of future events • But current $ are the real world - constant $ is artificial simplification • Constant $ evaluations can be misleading by ignoring inflation but can be very effective in choosing between alternatives • Constant $ cost of funds different from current $ cost of funds
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INTEREST RATES • A function of the time value of money • On debt, represent low risk return • Therefore, risky investments offer higher return • Diversified equity investments offer about 6% above the risk free rate • Government bonds represent risk free rate • Interest rates and discount rates closely linked Open Pit Mine Planning and Design
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PROJECT COST OF CAPITAL • Invested funds are recovered from future returns with interest • What rate of interest is appropriate for using funds in this project? • Must be above the risk free rate but how much above? • Individual resource projects generally have a slightly higher cost of capital than the company as a whole • Function of project risk, diminishing reserves and need for exploration • The appropriate cost of capital should be the discount rate for project evaluation purposes.
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COMPANY COST OF CAPITAL • Co funds - equity plus debt • Cost of equity - empirical measures • Cost of debt - average after tax interest rate on debt - factual • Cost of funds = weighted average cost of equity and debt • Current $ cost of capital - includes allowance for inflation -can be converted to constant $
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CURRENT $ TO CONSTANT $
1 + CONSTANT $ COST OF CAPITAL = (1+ CURRENT $ COST OF CAP)/(1+ INFLATION RATE)
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MORE ON COST OF CAPITAL • Cost of equity capital applies for 100% equity funding • Debt lowers the cost of capital but increases risk • What is the minimum acceptable return on equity? • Historically, 8% real on all equities - therefore, higher in current $ terms • Should it be higher for “risky” mining investments?
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CAPITAL ASSET PRICING MODEL Developed from long term studies of equity markets in USA:
R = Rf + B(Rm -Rf) Where: • R = required rate of return • Rf = risk free interest rate • B =relative risk of particular stock • Rm = average market return
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MARKET RISK PREMIUM • Rm-Rf = market risk premium • Expected premium, but based on historical data as proxy • Australian data over 100 years indicates 5% to 6% arithmetic average - 6% geometric average • US data indicates 5% to 6% geometric average • Volatility of returns means (Rm-Rf) geometric average is 2% to 10% with 95% confidence. A pretty big range.
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WEIGHTED AVERAGE COST OF CAPITAL WACC* = (E/A)R +(D/A)Rd(1-tc) Where; • E = market value of equity • D = debt • A =debt + equity • R = cost of capital, from CAPM • Rd = interest rate on debt • and tc = corporate tax rate • R is after tax, Rd is pre-tax *used where a mix of DEBT & EQUITY applies
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PROJECT PERIODS • Equal length periods cover entire life of project • Permits use of standard compound interest relationships and rules • Periods = years, generally • May be quarters or months for small projects • Project commences with the first period of investment • Evaluation relates to beginning of first period
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SUNK COSTS: • Past expenditures have no bearing on the evaluation,e.g., exploration expenditure. • The evaluation is considering future expenditures and revenues resulting from a decision yet to be made. • True of cost of evaluation and confirmatory work except for tax benefits
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END OF PERIOD CONVENTION • Expenditures and receipts occur irregularly through time - but, for purposes of evaluation, all cash flows are deemed to take place at the end of the period • Generally conservative • Midpoint of period can be used
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PAUSE – REFLECT!
• Cost of Capital •WACC • Project periods • Sunk Costs • Lagged revenue
• Working Capital • Constant vs Current $ • Currency, Exchange rates
• Revenue assumptions • Sources of finance • Cash • In- Outflow $
• CAPM • Interest rates • Equity vs Debt Financing • Royalties • End of period convention Open Pit Mine Planning and Design
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DEPRECIATION • Depreciation is the means of recovering capital expenditure • Depreciation deducted from cash flow to determine taxable income, and thus tax payable • Depreciation then added back to after tax profit to determine period cash flow • Dividend payments are not part of the project evaluation. • Positive NPV of cash flows mean capital has been serviced at the discount rate while invested, has been recovered and excess return has been received Open Pit Mine Planning and Design
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Capital Expenditure • Expenditure providing for mine operations for longer than one year • Expenditure for operations within the year are expensed, not capitalised • Depreciation schedules – straight line over life of asset, life of mine or 10 years; declining balance depreciation can defer tax but eventually returns to straight line.
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Tax payable calculations • Taxable income = sales revenue for year minus all operating costs, overhead costs, interest payments and depreciation • Tax rate 30% at present (Australia) • Negative taxable income, no tax paid and no tax refund except where group taxation makes immediate use of tax losses possible • Usually, tax losses carried forward to reduce taxable income in later years
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Period cash flows • Project cash flows for each year (or shorter period) made up of: After tax profit or loss Plus any depreciation added back Plus adjustments for any after tax items such as capital expenditures, loan drawdowns or loan repayments made or received during the year.
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ROYALTIES • Charge levied by State or Federal Government in return for permission to mine • Reflects “Crown” ownership of minerals • Various forms of royalty: ad valorem, pro rata, profit share, resource rent taxation in different jurisdictions • Check what applies to specific project and treat as a reduction in revenues
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LAGGED REVENUE • Example: Smelter pays to the company based on the waiting period to produce the expected amount of product depending to the shipping capacity. • For gold it is not much time to produce gold from ore/concentrate to gold bullion, say1 week, but base metals may take more time, say 2-3 months lagged.
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Module 9 Dewatering and Pump Selection • Case Study • Pump & Pipe Selection • Pumping Costs
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Introduction • Proposed mine is in the Mudgee area of NSW – Populated towns nearby in every direction – Long history of coal mining in the Central West NSW with several active coal mines nearby; deposits of high-grade coking coal are endemic • The old abandoned open cut mine had 4 identical pits. Water has filled these pits to an average depth of 50m • Coking coal prices are expected to rise, thus prompting a review of the feasibility of recommissioning and extending the abandoned mine pits
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Dogweed Coking Coal Mine
Mudgee
Sydney
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Objectives • Design a suitable system to dewater the pits ahead of the mining operation – Determine capital costs and pump operating costs per year
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Methodology • 3 methods of water volume estimation: – Volume by Integration – Volume by Parts – Volume by using a modelling program eg AutoDesk Inventor Dewatering times, depth of water with time Calculation of required pump head over water depth at different velocities/pipe diameters Pipe system selection and costing
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Geometry of the Pit Dimension 70m wide, 75o highwall, 36 lowwall of spoil 80m high, 9m thick, dipping at 6 Depth of water – 50m
Infrastructure setting In – situ density Waste 2.3t/BCM
Top Overburden
lowwall highwall
89 m Bottom Overburden
α=36⁰
β=75⁰
Coal 1.4t/BCM
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Volume of water estimation
Dimensions of the water in pit
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Method#1 Estimate volume by parts • The dimension of the water in the pit can be considered as different parts adding together: Volume/m3
Formula
Rectangle
𝑥×𝑦×ℎ
Low Wall Edge
𝑎×ℎ×𝑦 2 𝑏×ℎ×𝑦 2 2×𝑏×ℎ×𝑥 2 2 × ℎ × 𝑏2 3 2×ℎ×𝑎×𝑏 3
High Wall Edge Sides Corners 1 Corners 2
Paramete Formula r x y 1km-2b h a b
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ℎ tan 36𝑜 ℎ tan 75𝑜
Value 70 973.21 50 68.82 13.40 318
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Method #2 Estimate volume by integration • Looking at the model from top, we can evaluate width X and length Y in terms of the incremental height Z: 𝑋=
𝑎(ℎ−𝑍) 𝑏(ℎ−𝑍) + ℎ ℎ 2𝑏(ℎ−𝑍) +𝑦 ℎ
+𝑥
𝑌= Therefore, the volume is calculated by integrating the area of the cross section over the height of the model: ℎ
𝑉𝑜𝑙𝑢𝑚𝑒 =
ℎ
𝐴𝑟𝑒𝑎 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑑𝑍 = 0 2𝑎𝑏ℎ 3
2𝑏2 ℎ
𝑋𝑌 . 𝑑𝑍 0
𝑎𝑦ℎ
𝑏𝑦ℎ
That is, 𝑉𝑜𝑙𝑢𝑚𝑒 = + 3 + 2 + 2 + 𝑏𝑥ℎ + 𝑥𝑦ℎ This confirms the volume by parts. By inputting known variables, volume of the water in the pit is 5.49x106 m3 Open Pit Mine Planning and Design
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Method #3 Estimate volume by using Inventor
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Method #3 Estimate volume by using Inventor
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Dewatering time • The disposal flow rate limit is 200 L/s, therefore the dewatering time can be calculated: Volume of water per pit (m3)
Rate of dewatering (m3/s)
V
Q
5490065
0.2
Time to Number of Total time dewater pits taken for one pit dewatered dewatering (days) per year (years) T=V/(Qx24x N=365/T TT=Nx4 60) 317.7 1.15 3.48
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Depth of Water Over Time Depth Of Water In Pit Over Time 60.00
50.00
Depth of Water
40.00 y = -0.0001837707x2 - 0.0958277546x + 49.5843902089 R² = 0.9996479452 30.00 Depth 20.00
10.00
0.00 0
50
100
150
200
250
300
350
Days Since Dewatering Commenced
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Calculating Pump Head • Pressure drop: Bernoulli’s Equation 𝑝1 𝑉12 𝑝2 𝑉22 + 𝛼1 + 𝑧1 = + 𝛼2 + 𝑧2 + Σℎ𝐿 𝛾 2𝑔 𝛾 2𝑔 • Major head loss: 𝐿 𝑉2 ℎ𝐿𝑚𝑎𝑗𝑜𝑟 = 𝑓 𝐷 2𝑔 • Minor head loss: 𝑉2 ℎ𝐿𝑚𝑖𝑛𝑜𝑟 = 𝐾𝐿 2𝑔 • Friction factor: Reynold’s number and Moody Chart Open Pit Mine Planning and Design
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Pipe System Model
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Calculation Example Dept h 30
0 1 2 3 4 5 6
Target Velocity 2
hZ 30 30.5 30.5 30.5 30.5 80 80
hV 0 0.20408 0.20408 0.20408 0.20408 0.20408 0.20408
Pipe Diameter (m) 0.356825
hP 0 -0.70408 61.75476 61.74711 60.66451 10.08396 0
Pipe Length (m) 76.25
hLM 0 0 0 0 1.082598 1.070343 10.06611
hLm 0 0 0 0.007653 0 0.010204 0.017857
TOTAL PUMP PRESSURE HEAD (m) Open Pit Mine Planning and Design
Reynolds Number 71364.96
Friction Factor 0.022
V (m/s) L (m) (0 if negligible) 0 0 2 2 0 2 0 2 86.039 2 85.065 2 800 62.46 326
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Variation of Pump Head with Depth Pump Pressure Head wrt Velocity (V)/Pipe Diameter (D) 115 105
Required Pump Pressure Head
95 85 2.829421211 0.3 75
0.439714514 0.761 1.123896216 0.476
65 y = -x + 109.53 55
1.390120911 0.428 1.763489674 0.38 2.228982782 0.338
45
y = -x + 96.312
35
y = -x + 89.115 y = -x + 85.056 y = -x + 82.993 y = -x + 80.325
25 0
10
20
30
40
50
60
Water Depth
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Pump selection • Must be capable of meeting largest flow rate • Must be capable of pumping largest pressure head • Relatively acceptable costs
– ALLIGHT SYKES-HH220I
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Pump Power Curve HH220i Power Curve at 200 L/s 400
350
300
250 kW
y = -0.0003x3 + 0.0837x2 - 4.411x + 187.66 200
150
100
50
0 20
40
60
80
100
120
140
Total Head (m)
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Pump selection • Features: Diesel, electric or hydraulic drive Low fuel usage, reduced engine size Lower maintenance costs
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Pipe system selection • Pipe type: HDPE – Suited to butt welding – Corrosion, abrasion, weathering and chemical resistant – Relatively low item cost – Easy installation – Flexible and resilient • Keep in mind: – Velocity must be high enough to prevent too much settling Open Pit Mine Planning and Design
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Electricity Consumed by Pump kW-Hours Consumed by Pump During Dewatering of a Pit for Different Pipe Diameters 330
kW Required by Pump
280
0.761
230
0.476 0.428 0.38
180
0.338 0.3 130
80 0
50
100
150
200
250
300
350
Time (Days)
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System Costs Change in Costs per System with Increasing Pipe Diameter 700000
600000
Cost ($)
500000
400000 Cap cost of pipes Op cost of system
300000
Total 200000
100000
0 0.25
0.35
0.45
0.55
0.65
0.75
0.85
Pipe Diameter (m)
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Optimised System Costs • Optimal pipe diameter = 380mm – Costs from R2, Australian suppliers, PIPE DIAMETER
380mm
Capital cost of pipe
$115697.7
Pipe, transport, installation
Capital cost of pump
$81960
Installation costs required
Electricity costs
$174935.6
At 10.2 c/kWh
TOTAL
$303301.5
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What Have We Achieved? Fundamentals of open pit mine design and current developments in planning and design methodology, Current industry practices to maximise economic return (technology, operations). Open pit mine planning and design process in theory and practice, Unit Operations – Drill-Blast-Load-Haul Mining Economics Apply this knowledge to plan/evaluate new open pit projects and/or existing mines. Open Pit Mine Planning and Design
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Bottom Line is…..
We mine for profit !!!
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