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
2
1
5/11/2014
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
3
What do you expect to learn from this
Course?
Open Pit Mine Planning and Design
4
2
5/11/2014
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
5
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
6
3
5/11/2014
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!
Open Pit Mine Planning and Design
7
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
8
4
5/11/2014
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…
Open Pit Mine Planning and Design
9
Business Strategy
Strategic
Planning
DecisionMaking
Behaviour
Economic
Evaluation
Mine Planning
Open Pit Mine Planning and Design
10
5
5/11/2014
Decision-Making Behaviour:
Risk Averse – seeks other business goals
Risk Neutral – seeks maximise NPV
Open Pit Mine Planning and Design
11
Mine Planning Process Flowchart
Open Pit Mine Planning and Design
12
6
5/11/2014
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
13
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.
Open Pit Mine Planning and Design
14
7
5/11/2014
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)
Open Pit Mine Planning and Design
15
•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…
Open Pit Mine Planning and Design
16
8
5/11/2014
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
17
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)
Open Pit Mine Planning and Design
18
9
5/11/2014
• 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
Open Pit Mine Planning and Design
19
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
Open Pit Mine Planning and Design
20
10
5/11/2014
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
Open Pit Mine Planning and Design
21
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
22
11
5/11/2014
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
23
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)
Open Pit Mine Planning and Design
24
12
5/11/2014
Mineral
Comminution
Liberation
Unacceptable
Classification
Acceptable
Concentration
Separation
Physical
Chemical
Open Pit Mine Planning and Design
25
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
26
13
5/11/2014
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
Open Pit Mine Planning and Design
27
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
Open Pit Mine Planning and Design
28
14
5/11/2014
• 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
Open Pit Mine Planning and Design
29
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
30
15
5/11/2014
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
Open Pit Mine Planning and Design
31
• 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
Open Pit Mine Planning and Design
32
16
5/11/2014
• 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
Open Pit Mine Planning and Design
33
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
34
17
5/11/2014
The scheduling “Saw Graph”
Minimum Ore
Exposure
yr-1
yr-2
yr-3
yr-4
yr-5
yr-6
Time
Open Pit Mine Planning and Design
35
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
Open Pit Mine Planning and Design
36
18
5/11/2014
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
Open Pit Mine Planning and Design
37
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
Open Pit Mine Planning and Design
38
19
5/11/2014
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
Open Pit Mine Planning and Design
39
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
40
20
5/11/2014
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
41
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
42
21
5/11/2014
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
Open Pit Mine Planning and Design
43
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
44
22
5/11/2014
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
-
Open Pit Mine Planning and Design
45
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)
46
23
5/11/2014
Considering an underground
alternative
1
2
3
4
5
6
Open Pit Mine Planning and Design
47
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
48
24
5/11/2014
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
49
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
50
25
5/11/2014
Economic evaluation
(Open Pit vs Underground)
Net Presente Value @ r = 10 % ($)
Phase
1
2
3
4
5
6
Case 3 (OP/UG)
Case 4 (Optimum)
Partial
Cum
Partial
Cum
1,036
733
485
275
92
50
1,036
1,769
2,254
2,529
2,621
2,671
1,036
733
485
275
150
50
1,036
1,769
2,254
2,529
2,679
2,729
Open Pit Mine Planning and Design
51
Optimum configuration
1
2
3
4
5
6
Open Pit Mine Planning and Design
52
26
5/11/2014
Summary of evaluations
Net Present Value @ r = 10 % ($)
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
Open Pit Mine Planning and Design
53
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
Open Pit Mine Planning and Design
54
27
5/11/2014
Role Of Feasibility Studies
• Why Feasibility Study
• Scoping Study
• Preliminary Study
• Bankable Feasibility Study
• Risks
Open Pit Mine Planning and Design
55
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
Open Pit Mine Planning and Design
56
28
5/11/2014
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
Open Pit Mine Planning and Design
57
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
Open Pit Mine Planning and Design
58
29
5/11/2014
Phases
• Scoping Study
• Pre-Feasibility Study
• Final Feasibility Study
Open Pit Mine Planning and Design
59
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.
Open Pit Mine Planning and Design
60
30
5/11/2014
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
Open Pit Mine Planning and Design
61
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
63
31
5/11/2014
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
64
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
Open Pit Mine Planning and Design
65
MCA – Project Management in Mine Planning and Design
32
5/11/2014
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
66
Open Pit Mine Planning and
Design
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
67
Open Pit Mine Planning and
Design
33
5/11/2014
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
69
Open Pit Mine Planning and
Design
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
Open Pit Mine Planning and
Design
34
5/11/2014
(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.
Open Pit Mine Planning and Design
71
MCA – Project Management in Mine Planning and Design
Requirements of a FS to be
bankable
• A FS must be;
– Credible
– Definitive
– Relevant
– Independent
Open Pit Mine Planning and Design
72
35
5/11/2014
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)
73
Open Pit Mine Planning and
Design
- 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.
74
Open Pit Mine Planning and
Design
36
5/11/2014
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
Open Pit Mine Planning and Design
76
37
5/11/2014
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
Open Pit Mine Planning and Design
78 of 10
38
5/11/2014
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
Open Pit Mine Planning and Design
79 of 10
Mining is a Business, but risky
Open Pit Mine Planning and Design
80
39
5/11/2014
MINING PROJECT RISKS
ECONOMIC / FINANCIAL
RISKS
TECHNICAL RISKS
OH&S RISKS
POLITICAL
RISKS
Participants discuss these elements of
Risk in Mining Projects.
81
Open Pit Mine Planning and Design
Conclusion
Strategic planning (SP) involves developing a range
of options, carrying out some form of evaluation,
assessing criteria and decision-making.
Open Pit Mine Planning and Design
82
40
5/11/2014
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!
Open Pit Mine Planning and Design
83
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
84
41
5/11/2014
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
86
42
5/11/2014
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
88
43
5/11/2014
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
Open Pit Mine Planning and Design
89
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)
Open Pit Mine Planning and Design
90
44
5/11/2014
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
91
Don’t Include
• Time costs which continue whether
you continue mining or not
• Up-front/sunk costs
Open Pit Mine Planning and Design
92
45
5/11/2014
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!
Open Pit Mine Planning and Design
93
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
Open Pit Mine Planning and Design
94
46
5/11/2014
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!
Open Pit Mine Planning and Design
95
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.
96
Open Pit Mine Planning and Design
47
5/11/2014
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
97
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
Open Pit Mine Planning and Design
98
48
5/11/2014
Floating Cone Method
Courtesy: Kores Corpration
Open Pit Mine Planning and Design
99
Floating Cone- Mining too little
-30
-80
+100
Open Pit Mine Planning and Design
-80
+100
100
49
5/11/2014
Floating Cone- Mining too much
Open Pit Mine Planning and Design
101
Lerchs-Grossman Algorithm
• Works with block values
• Works with block mining precedence
• Guarantees to find the three-dimensional
outline with the highest possible value
Open Pit Mine Planning and Design
102
50
5/11/2014
Lerchs-Grossman Algorithm
• Works with block values
• Works with block mining precedence
• Guarantees to find the three-dimensional
outline with the highest possible value
Open Pit Mine Planning and Design
103
Lerchs-Grossman Algorithm
Open Pit Mine Planning and Design
104
51
5/11/2014
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)
Open Pit Mine Planning and Design
105
Final Pit Design – composite plan
Open Pit Mine Planning and Design
106
52
5/11/2014
Activity 5 :
Individual learning
Refer to worksheet 3
Pit Optimisation – Task 2
Follow the example calculation of the LG pit optimisation
algorithm
Open Pit Mine Planning and Design
107
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
108
53
5/11/2014
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.
Open Pit Mine Planning and Design
109
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!
Open Pit Mine Planning and Design
110
54
5/11/2014
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!
Open Pit Mine Planning and Design
111
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
Open Pit Mine Planning and Design
112
55
5/11/2014
Data Import
Import
+
3D Borehole
Processing
Open Pit Mine Planning and Design
113
Geological Interpretation
Open Pit Mine Planning and Design
114
56
5/11/2014
Block Model + Grade Assessment
Block Model with Grade
Open Pit Mine Planning and Design
115
Economical Model - Grade
>>> $Value
Au
[g/t]
>>>
Value
$$$
Open Pit Mine Planning and Design
116
57
5/11/2014
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
117
Whittle FX
Strategic Mine Planning Software
Pit by Pit Graph
Import Block Model
Constrains:
• Economical
• Geometrical
• Operational
• No access constrains
• No haul road/ramp
Open Pit Mine Planning and Design
118
58
5/11/2014
Optimal Pit
Open Pit Mine Planning and Design
119
Mine Design
Open Pit Mine Planning and Design
120
59
5/11/2014
Mine Design
Geomechanics/Geotechnical
Access constraints
Equipment selection
Ventilation network (underground)
Rehabilitation
Environmental constraints
Open Pit Mine Planning and Design
121
Final Optimal Pit
Open Pit Mine Planning and Design
122
60
5/11/2014
Final Optimal Pit & Pushbacks
Open Pit Mine Planning and Design
123
Reporting & Evaluation
Open Pit Mine Planning and Design
124
61
5/11/2014
Scheduling
Open Pit Mine Planning and Design
125
The Pushbacks Generation
Open Pit Mine Planning and Design
126
62
5/11/2014
Optimizing Production
Schedules
Open Pit Mine Planning and Design
127 of 26
Optimizing Production Schedules
+
=
Open Pit Mine Planning and Design
128
63
5/11/2014
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
129
waste dump planning
What you will learn:
• Principles of dump design and
• Dump optimisation
Open Pit Mine Planning and Design
130
64
5/11/2014
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.
•
Open Pit Mine Planning and Design
131
Rock flow in an open pit mine
Yu (2014)
Open Pit Mine Planning and Design
132
65
5/11/2014
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.
Open Pit Mine Planning and Design
133 of 10
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.
Open Pit Mine Planning and Design
134 of 10
66
5/11/2014
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.
Open Pit Mine Planning and Design
135 of 10
Waste Dump Design
Dump progression with shortest haul first strategy
Open Pit Mine Planning and Design
136 of 10
67
5/11/2014
Waste Dump Design
Dump design considering NAF PAF material (Yu 2013)
Open Pit Mine Planning and Design
137 of 10
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
Open Pit Mine Planning and Design
138 of 10
68
5/11/2014
Waste Dump OptimisationRecent Developments
Integrated modelling of dumping system (Yu 2013)
Open Pit Mine Planning and Design
139 of 10
Module 3
PRODUCTION SCHEDULING
What you will learn:
• Principles of production scheduling
• Scheduling Software
Open Pit Mine Planning and Design
140
69
5/11/2014
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.
Open Pit Mine Planning and Design
141
Typical Timeline
Year
-2
-1
Pre-production
(Development
Construction)
+1
+2
Production
Open Pit Mine Planning and Design
142
70
5/11/2014
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
Open Pit Mine Planning and Design
143
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
144
71
5/11/2014
Scheduling Packages
•
•
•
•
•
•
XPAC
iGannt
MS Project
MS Excel
Whittle 4D
In-house
Open Pit Mine Planning and Design
145
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
Open Pit Mine Planning and Design
146
72
5/11/2014
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
147
Open Pit Mine Planning and Design
148
73
5/11/2014
Open Pit Mine Planning and Design
149
Open Pit Mine Planning and Design
150
74
5/11/2014
Financial Technical Model
•
•
•
•
•
•
•
•
•
•
Plant design
Infrastructure (road, power, water, village, etc.)
Equipment selection
Capitals
Operating costs
Royalty
Tax
Revenue
…
NCF NPV, IRR, PB, etc.
Open Pit Mine Planning and Design
151
Activity 8 :
Individual learning
Refer to worksheet 4
Production Scheduling
Calculate the monthly production figures for a small gold
mine
Open Pit Mine Planning and Design
152
75
5/11/2014
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
Open Pit Mine Planning and Design
153
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
154
76
5/11/2014
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
155
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
156
77
5/11/2014
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
Open Pit Mine Planning and Design
157
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
Open Pit Mine Planning and Design
(1a)
158
78
5/11/2014
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
159
V
P
P2
P3
P4
Pn
••••••
Time
0
W
T
PW
V
(1 d)T
Open Pit Mine Planning and Design
(2)
160
79
5/11/2014
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)
Open Pit Mine Planning and Design
161
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
162
80
5/11/2014
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
163
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
164
81
5/11/2014
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
165
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
Open Pit Mine Planning and Design
166
82
5/11/2014
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
167
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
Open Pit Mine Planning and Design
168
83
5/11/2014
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
169
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
Open Pit Mine Planning and Design
170
84
5/11/2014
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
171
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
172
85
5/11/2014
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
173
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
174
86
5/11/2014
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
175
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
176
87
5/11/2014
v
vm
vc
gm
gmc
Gmc = gmc
g
gc
v
vc
vm
gmc
gm
Gmc = gm
g
gc
Open Pit Mine Planning and Design
177
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
178
88
5/11/2014
The overall optimum cut-off grade is:
G = Middle value (Gmc,Gmr,Grc)
v
vr
vm
vc
gm grc
gmr gmc
gc
gr
g
Open Pit Mine Planning and Design
179
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
180
89
5/11/2014
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
Open Pit Mine Planning and Design
181
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
Open Pit Mine Planning and Design
Balancing
cut-off grades
182
90
5/11/2014
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
Open Pit Mine Planning and Design
183
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
Open Pit Mine Planning and Design
184
91
5/11/2014
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
Open Pit Mine Planning and Design
185
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
Open Pit Mine Planning and Design
186
92
5/11/2014
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
Open Pit Mine Planning and Design
187
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
Open Pit Mine Planning and Design
188
93
5/11/2014
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
Open Pit Mine Planning and Design
189
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
Open Pit Mine Planning and Design
190
94
5/11/2014
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 ($0.32 /lb)
•
Overall recovery (y) = 85 %
•
Annual discount rate (d)
= 10 %
Open Pit Mine Planning and Design
191
A set of four pushbacks
A
B
C
D
Open Pit Mine Planning and Design
192
95
5/11/2014
Input to the model: four scheduled, nested pits
(periods) from a preliminary mine plan
2
PP
1
1
3
1
3
2
4
3
4
Open Pit Mine Planning and Design
193
Grade-tonnage relationship for the four pits
Cut-off
Period 1
Period 2
Period 3
Period 4
% Cu
Mt
% Cu
Mt
% Cu
Mt
% Cu
Mt
% Cu
0.0
20.3
1.05
36.5
0.79
56.3
0.57
80.1
0.59
0.2
18.7
1.13
30.1
0.92
40.8
0.76
60.4
0.77
0.4
15.3
1.32
24.4
1.08
28.5
0.97
50.2
0.87
0.6
12.9
1.47
19.7
1.22
21.7
1.11
38.3
0.98
0.8
11.0
1.61
13.7
1.45
15.1
1.30
22.7
1.18
1.0
8.6
1.80
10.2
1.64
10.0
1.49
14.6
1.35
1.2
7.1
1.95
7.6
1.83
6.9
1.67
9.0
1.49
1.4
5.9
2.08
5.6
2.02
4.4
1.88
5.0
1.65
1.6
4.4
2.27
4.0
2.24
2.7
2.11
2.9
1.75
Open Pit Mine Planning and Design
194
96
5/11/2014
Output for a “Base case”
Year
Period 1
Cut-off
Mine
(% Cu)
(Mt)
Mill
(Mt)
(% Cu)
Ratio
Profit
PV
(W/O)
(M$)
(M$)
1
1
0.85
14.2
7.2
1.67
0.97
110.3
475.5
2
1
0.78
6.1
3.4
1.59
0.82
49.6
412.8
2
2
0.78
9.8
3.8
1.43
1.56
44.8
412.8
3
2
0.72
16.8
7.2
1.37
1.34
81.3
359.6
4
2
0.67
9.9
4.7
1.31
1.13
50.4
314.2
4
3
0.61
6.7
2.5
1.12
1.62
19.4
314.2
5
3
0.61
18.9
7.2
1.12
1.62
56.3
275.8
6
3
0.60
18.6
7.2
1.11
1.58
55.8
247.0
7
3
0.56
12.1
4.9
1.08
1.45
36.5
215.9
7
4
0.56
4.5
2.3
0.96
0.98
14.9
215.9
8
4
0.53
13.6
7.2
0.94
0.89
44.5
186.1
9
4
0.50
13.1
7.2
0.92
0.82
43.3
160.3
10
4
0.47
12.6
7.2
0.91
0.75
42.4
132.9
11
4
0.44
12.1
7.2
0.89
0.68
41.4
103.9
12
4
0.41
11.6
7.2
0.87
0.61
40.2
72.9
13
4
0.37
11.2
7.2
0.86
0.55
38.9
39.9
14
4
0.33
1.5
1.0
0.84
0.50
5.1
5.0
94.6
1.11
1.04
193.2
PV = 475.5
Open Pit Mine Planning and Design
195
Output for an expanded case (Mill from 7.2 to 9.0 Mt/a)
Year
Period 1
Cut-off
Mine
(% Cu)
(Mt)
Mill
(Mt)
(% Cu)
Ratio
Profit
PV
(W/O)
(M$)
(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
Open Pit Mine Planning and Design
PV = 521.2
196
97
5/11/2014
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
197
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
198
98
5/11/2014
Activity 8 :
Individual learning
Refer to worksheet 5
Cutoff Grade Optimisation
Follow the calculations to the problems
Open Pit Mine Planning and Design
199
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
200
99
5/11/2014
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
Open Pit Mine Planning and Design
201
Module 5
Mine Planning Software
•
•
•
•
Software Packages
Categories
Capabilities
Providers
Open Pit Mine Planning and Design
202
100
5/11/2014
Common Software Packages
Open Pit Mine Planning and Design
203
Categories of Mining Software
Open Pit Mine Planning and Design
204
101
5/11/2014
Mapping Software
Open Pit Mine Planning and Design
205
Geological & Data managent
Source: (Sable, 2013)
Open Pit Mine Planning and Design
206
102
5/11/2014
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
103
5/11/2014
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
104
5/11/2014
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
105
5/11/2014
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
106
5/11/2014
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
Open Pit Mine Planning and Design
216
107
5/11/2014
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
Open Pit Mine Planning and Design
217
Mine production system processes
• Drilling
• Blasting
• Loading
• Hauling
• Milling (Crushing, grinding)
Examine total “system” with regard to cost,
productivity, product quality, optimisation...
Open Pit Mine Planning and Design
218
108
5/11/2014
• 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).
Open Pit Mine Planning and Design
219
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
220
109
5/11/2014
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
222
110
5/11/2014
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
Open Pit Mine Planning and Design
223
Case Study
Open Pit Mine Planning and Design
224
111
5/11/2014
Case Study
Modeling Muck Pile Fragment Size to Optimize
Excavator Productivity in Open Pit Mining
Prominent Hill Copper Mine, South Australia
Open Pit Mine Planning and Design
225
Prominent Hill
Open Pit Mine Planning and Design
226
112
5/11/2014
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
Open Pit Mine Planning and Design
227
Prominent Hill
Camera
Photo of muckpile
Photo collection and scale placement on flitch face.
Open Pit Mine Planning and Design
228
113
5/11/2014
Prominent Hill
Blast master 10040RL
Open Pit Mine Planning and Design
229
Prominent Hill
Open Pit Mine Planning and Design
230
114
5/11/2014
Prominent Hill
Open Pit Mine Planning and Design
231
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
Open Pit Mine Planning and Design
232
115
5/11/2014
Module 7
Equipment Selection
• Simulation modelling using GPSS/H – Case Study
• Cost Estimation (Capital & Operating)
Open Pit Mine Planning and Design
233
Simulation and Animation of an
Australian Surface Mine
•
•
•
•
•
•
Study Background
Methodology
Results
Discussion
Conclusion
Recommendations
Open Pit Mine Planning and Design
234
116
5/11/2014
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.
Open Pit Mine Planning and Design
235
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.
Open Pit Mine Planning and Design
236
117
5/11/2014
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.
Open Pit Mine Planning and Design
237
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
Open Pit Mine Planning and Design
238
118
5/11/2014
Methodology
GPSS/H Simulation Main Commands
Open Pit Mine Planning and Design
239
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
Open Pit Mine Planning and Design
240
119
5/11/2014
Methodology
Animation
Open Pit Mine Planning and Design
241
Methodology
Mine Layout (Draw, Class and Paths)
Open Pit Mine Planning and Design
242
120
5/11/2014
Methodology
Run
Open Pit Mine Planning and Design
243
Methodology
Animation
Open Pit Mine Planning and Design
244
121
5/11/2014
Methodology
Animation
Open Pit Mine Planning and Design
245
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
Open Pit Mine Planning and Design
246
122
5/11/2014
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
Open Pit Mine Planning and Design
6
20
3200
400
7
23 DUMPS
3680 T
460 T/HR
T/HR
247
Results
Ore Results
Open Pit Mine Planning and Design
248
123
5/11/2014
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
Open Pit Mine Planning and Design
6
123
9298.8
1162.35
7
142 DUMPS
10735.2 T
1341.9 T/HR
T/HR
249
Results
Waste Results
Open Pit Mine Planning and Design
250
124
5/11/2014
Conclusion
• GPSS/H Simulation and Animation
– Number of shovels: one shovel
– Number of trucks: five trucks and possibly an
extra standby truck
• TALPAC simulations
– Number of shovels: one shovel
– Number of trucks: six trucks
Open Pit Mine Planning and Design
251
Acknowledgements
Postgraduate Students:
• Sophie Mellor
• Jian Liu
Open Pit Mine Planning and Design
252
125
5/11/2014
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
Open Pit Mine Planning and
Design
254 of 10
126
5/11/2014
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
255
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
Open Pit Mine Planning and Design
256
127
5/11/2014
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
257 of 10
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
128
5/11/2014
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
Open Pit Mine Planning and Design
259
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
Open Pit Mine Planning and Design
260
129
5/11/2014
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
Open Pit Mine Planning and Design
261
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?
Open Pit Mine Planning and
Design
262 of 10
130
5/11/2014
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
264
131
5/11/2014
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
265
Infrastructure capital (cont.)
• Administration facilities
–
–
–
–
–
–
–
–
–
administration building
laboratories
training facilities
change rooms
crib/lunch rooms
safety and medical facilities
fire station
core storage
security
Open Pit Mine Planning and
Design
266 of 10
132
5/11/2014
Infrastructure capital (cont.)
• Transportation
– road transport
– rail transport
– slurry pipeline
– overland conveyors
– sea or river transport
– cableways (aerial ropeways)
Open Pit Mine Planning and Design
267
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
268
133
5/11/2014
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.
Open Pit Mine Planning and Design
269
Major Mine Equipment Operating Costs
Open Pit Mine Planning and Design
270
134
5/11/2014
Open Pit Mine Planning and Design
271
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
Mining Cost
272
135
5/11/2014
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
Open Pit Mine Planning and Design
273
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.
Open Pit Mine Planning and Design
274
136
5/11/2014
• 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
Open Pit Mine Planning and Design
275
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.
Open Pit Mine Planning and Design
276
137
5/11/2014
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
Open Pit Mine Planning and Design
277
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
Open Pit Mine Planning and Design
278
138
5/11/2014
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.
Open Pit Mine Planning and Design
279
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
280
139
5/11/2014
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).
Open Pit Mine Planning and Design
281
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
282
140
5/11/2014
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
283
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
•
•
•
•
Open Pit Mine Planning and Design
284
141
5/11/2014
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
Open Pit Mine Planning and Design
285
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
Open Pit Mine Planning and Design
286
142
5/11/2014
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
Open Pit Mine Planning and Design
* Very important!
287
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
288
143
5/11/2014
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$, if sales revenues in US$
•
•
•
•
•
Open Pit Mine Planning and Design
289
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.
Open Pit Mine Planning and Design
290
144
5/11/2014
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.
Open Pit Mine Planning and Design
291
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
Open Pit Mine Planning and Design
292
145
5/11/2014
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
293
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.
Open Pit Mine Planning and Design
294
146
5/11/2014
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 $
Open Pit Mine Planning and Design
295
CURRENT $ TO CONSTANT $
1 + CONSTANT $ COST OF CAPITAL
= (1+ CURRENT $ COST OF CAP)/(1+ INFLATION
RATE)
Open Pit Mine Planning and Design
296
147
5/11/2014
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?
Open Pit Mine Planning and Design
297
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
Open Pit Mine Planning and Design
298
148
5/11/2014
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.
Open Pit Mine Planning and Design
299
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
Open Pit Mine Planning and Design
300
149
5/11/2014
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
Open Pit Mine Planning and Design
301
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
Open Pit Mine Planning and Design
302
150
5/11/2014
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
Open Pit Mine Planning and Design
303
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
304
151
5/11/2014
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
305
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.
Open Pit Mine Planning and Design
306
152
5/11/2014
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
Open Pit Mine Planning and Design
307
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.
Open Pit Mine Planning and Design
308
153
5/11/2014
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
Open Pit Mine Planning and Design
309
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.
Open Pit Mine Planning and Design
310
154
5/11/2014
Module 9
Dewatering and Pump
Selection
• Case Study
• Pump & Pipe Selection
• Pumping Costs
Open Pit Mine Planning and Design
311
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
Open Pit Mine Planning and Design
312
155
5/11/2014
Dogweed Coking Coal Mine
Mudgee
Sydney
Open Pit Mine Planning and Design
313
Objectives
• Design a suitable
system to dewater the
pits ahead of the
mining operation
– Determine capital
costs and pump
operating costs per
year
Open Pit Mine Planning and Design
314
156
5/11/2014
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
Open Pit Mine Planning and Design
315
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
Open Pit Mine Planning and Design
316
157
5/11/2014
Volume of water estimation
Dimensions of the water in pit
Open Pit Mine Planning and Design
317
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
Open Pit Mine Planning and Design
ℎ
tan 36𝑜
ℎ
tan 75𝑜
Value
70
973.21
50
68.82
13.40
318
158
5/11/2014
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
319
Method #3
Estimate volume by using Inventor
Open Pit Mine Planning and Design
320
159
5/11/2014
Method #3
Estimate volume by using
Inventor
Open Pit Mine Planning and Design
321
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
Open Pit Mine Planning and Design
322
160
5/11/2014
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
Open Pit Mine Planning and Design
323
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
324
161
5/11/2014
Pipe System Model
Open Pit Mine Planning and Design
325
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
162
5/11/2014
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
Open Pit Mine Planning and Design
327
Pump selection
• Must be capable of meeting largest flow rate
• Must be capable of pumping largest pressure head
• Relatively acceptable costs
– ALLIGHT SYKES-HH220I
Open Pit Mine Planning and Design
328
163
5/11/2014
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)
Open Pit Mine Planning and Design
329
Pump selection
• Features:
Diesel, electric or hydraulic drive
Low fuel usage, reduced engine size
Lower maintenance costs
Open Pit Mine Planning and Design
330
164
5/11/2014
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
331
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)
Open Pit Mine Planning and Design
332
165
5/11/2014
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)
Open Pit Mine Planning and Design
333
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
Open Pit Mine Planning and Design
334
166
5/11/2014
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
335
Bottom Line is…..
We mine for profit !!!
Open Pit Mine Planning and Design
336
167
