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Abubakary Salama
Haulage system optimization for underground mines
A discrete event simulation and mixed integer programming approach
Abubakary Salama
Division of Mining and Geotechnical Engineering
Department of Civil, Environment and Natural resources
Engineering
Cover picture: LKAB mine magazine No. 3, 2012
ISSN 1402-1544
ISBN 978-91-7583-051-3 (print)
ISBN 978-91-7583-052-0 (pdf)
Luleå 2014
www.ltu.se
PREFACE
This research was carried out between March 2010 and October 2014 within the research
subject Mining and Rock Engineering at the Division of Mining and Geotechnical Engineering,
Luleå University of Technology. The successful outcome of this work required the
considerable assistance and guidance I received from many people, and I am extremely
fortunate to have received this help towards completion of this thesis. Whatever I have done is
only due to their assistance and guidance, and I will not forget to thank them.
First and foremost, I thank Professor Håkan Schunnesson for his technical advice and support
in different aspects of underground mining, which played an important role in finalizing this
thesis. I am extremely grateful to him for providing such guidance. I also wish to express my
grateful appreciation to Dr. Jenny Greberg for her valuable materials, suggestions, and ideas
towards solving various problems. Her support, motivation, and close supervision contributed
tremendously to the success of this work. I owe my profound gratitude to the staff members at
Division of Mining and Geotechnical Engineering and to Dr. Micah Nehring of the University
of Queensland for their support, encouragement, and the recommendations that they provided
me with during the time of this study. Their help contributed a tremendous amount to the
content of this work.
I acknowledge and extend my deepest gratitude to the World Bank through the University of
Dar es Salaam, Tanzania, under project Code: CIA: 8.a.2: and I2 Mine project within the EU
7th framework program for financial support during this thesis work. I am also grateful to the
Kiirunavaara underground mine in Sweden for providing information helpful to development
of this work, and to the management of SimMine and Automod who provided training
opportunities.
Finally, I am fortunate to have received the constant encouragement and support of my family,
friends, and all those who in one way or another participated in preparation and compilation of
this thesis. I gratefully thank them for their consideration and patience.
Abubakary Salama
November, 2014
Luleå, Sweden
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ABSTRACT
In coming decades, many underground mines will operate at greater depths, which will affect
many operational factors such as increased rock stress, longer haulage distances, and higher
energy consumption, which potentially can generate lower production rates. The increased rock
stresses may lead to smaller sized openings, further restricting the size of loading and hauling
equipment that can be used. Longer hauling distances result in increased energy consumption
for loading and hauling equipment, and in turn, high energy consumption increases heat and
gas emissions for diesel equipment. Heat emission increases ventilation costs as large volumes
of air must be circulated to cool diesel engines and simultaneously maintain adequate air
quality for personnel.
The research presented in this thesis was carried out to evaluate and analyze different
haulage systems, including diesel and electric trucks, shafts, and belt conveyors. The aim was
to determine how these various material-handling equipment may produce the desired
production objectives and lead to lower energy costs. The net present value (NPV) of the mine
plan at increasing mining rates and altered commodity prices was also analyzed. The method
used was the combination of discrete event simulation and mixed integer programing. Discrete
event simulation was used to estimate mine production for different haulage systems, and the
results were used to compute appropriate mining costs for each hauling option. Mixed integer
programming (MIP) was then used to generate the optimal production schedule and mine plan.
The analysis showed that an increasing use of electric trucks will have positive effects on
production improvement because electric trucks have shorter cycle times than their diesel
counterparts. Therefore, electric trucks can make more cycles than diesel trucks in the same
period of time. The analysis also showed that low-profile equipment will remain viable for
haulage in high stress environments that result in smaller sized mine openings. In addition,
when friction hoist systems are used, rope speed and skip payload play important roles in
production improvement. With belt conveyors, production improvements can be obtained by
increasing surcharge angle and running the belt at a low speed. For long hauls, the troughing
angle should be increased and the belt operated at a higher speed.
Energy costs increase with depth and are higher for diesel trucks compared with other
haulage options. At 1000-meter depths and with current energy prices, energy costs for diesel
trucks, electric trucks, belt conveyor, and shaft account for 62%, 54%, 25%, and 14% of the
total haulage costs, respectively. These findings indicate that minimizing the usage of diesel
engine machines will have greater benefits towards cost reductions in an era of increasing
energy prices and greater mine depths. Diesel machines also have high heat and gas emissions,
which increases operating costs particularly for deeper mines where heat emissions increase
ventilation costs.
Changes in mine plans based on changing commodity prices at a fixed mining rate
resulted in an increase in the NPV from $96M to ultimately $755M for the studied case. An
increase in mining rate from 300,000 to 450,000 tonnes raised the NPV to $773M. This finding
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indicates that even though an increase in mining rates increases costs, companies may find that
pursuing such a course is beneficial at certain commodity prices, especially when the price is
elevated. When the price falls, increasing mining rate may need a detail evaluation of other
parameters such as grade, recovery, and investment changes.
The evaluation showed that the method of combining discrete event simulation and
mixed integer programming can yield a feasible solution and better understanding of the
operational systems and reduce risks in selecting a system before it is implemented. This study
provides mining companies an analysis of the use of underground haulage systems that can aid
decision making.
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LIST OF APPENDED PAPERS
PAPER I
Salama, A., Greberg, J., and Schunnesson, H. (2014). The use of discrete event simulation for
underground haulage mining equipment selection, International Journal of Mining and
Mineral Engineering, Vol. 5, No. 3, 256–271. doi: 10.1504/IJMME.2014.064486
PAPER II
Salama, A., Nehring, M. and Greberg, J. (2014). Operating value optimisation using simulation
and mixed integer programming, International Journal of Mining, Reclamation and
Environment, Vol. 28, No. 1, 25-46. doi: 10.1080/17480930.2013.768019
PAPER III
Salama, A., Nehring, M., Greberg, J., and Schunnesson, H. (2014). Evaluation of the impact of
commodity price change on the mine plan of underground mining, Accepted for publication
in International Journal of Mining Science and Technology.
PAPER IV
Salama, A., Nehring, M. and Greberg, J. (2014). Analysis of the impact of increasing mining
rate in underground mining using simulation and mixed integer programming. Submitted to
International Journal of Mining Science and Technology.
PAPER V
Salama, A., Greberg, J., Skawina, B., and Gustafson, A. (2014). Analysis of energy
consumption and gas emission for loading equipment in underground mining. Submitted to
Canadian Institute of Mining, Metallurgy, and Petroleum Journal.
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CONTENTS
PREFACE .................................................................................................................................. i
ABSTRACT .............................................................................................................................iii
CONTENTS............................................................................................................................ vii
1 INTRODUCTION................................................................................................................. 1
1.1 Background.................................................................................................................. 1
1.2 Problem statement ....................................................................................................... 2
1.3 Objectives .................................................................................................................... 3
1.4 Research questions ...................................................................................................... 3
1.5 Research scope and limitations.................................................................................... 4
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4.1 Production improvement of underground haulage systems ...................................... 33
4.2 Energy consumption and gas emission on loading and haulage equipment.............. 35
4.3 Mining rate and commodity price variations on NPV............................................... 42
REFERENCES ....................................................................................................................... 51
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1 INTRODUCTION
1.1 Background
The selection of haulage systems for underground hard rock mining operations has historically
focused on diesel trucks, shaft haulage, and belt conveyors (De La Vergne, 2003). Normally,
these systems work in combination with other ore-handling components, such as diesel or
electric load-haul-dump (LHD) machines and ore passes. Diesel truck haulage systems have
been widely used for material transportation in both open pit and underground mines. This
haulage equipment is highly flexible in travel routes and fleet size, has no electrical hazards,
and provides high productivity (Thomas et al., 1987). The disadvantages are the use of
flammable fuel, higher heat emissions and noise levels, and emission of toxic gases into the
mine environment (Chadwick, 1996; Haney & Saseen, 2000).
Shaft haulage is used to access large, steeply dipping ore bodies that are too deep to be
mined economically using open cut methods. Shaft haulage also can provide various services to
underground mines, such as ventilation, power, and water supply. For large flat-lying ore
bodies, a belt conveyor is typically the most economic method for material transportation. The
nature of the material to be conveyed, available tunnel space, and overall system economics
influence the choice of conveyor parameters. When a belt conveyor is used in ramps, the
material size distribution will be one of the major concerns to minimize damage to the belt and
restrict spillage. Since their introduction in the 1960s, diesel LHDs have commonly been used
in mining because this equipment is mobile, versatile, and its operational flexibility provides
high productivity. Electric LHDs also are used today in underground mines, but not as
commonly as diesel (Paraszczak et al., 2013). Finally, ore passes are used in material
transportation and can serve as ore storage in underground mines (Stacey et al., 2005).
However, to design a well-functioning ore pass, the entire ore handling system of the mine
from the production areas to the shaft points must be examined (Stacey & Swart, 1997).
Several factors must be considered when selecting hauling methods. Among these factors
are the mine method, production capacity, ground conditions, mine depth, dip and size of the
ore body, and planned mine life (McCarthy, 1999). Designing an optimal solution is not an
easy task because of the many variables involved, but a suboptimal selection can lead to high
production costs. Diesel units offer a low initial capital outlay, but have higher operating costs.
Shaft haulage systems usually have high capital costs, but low operational costs. Belt
conveyors have been demonstrated to be cost-effective relative to shaft systems in large
production operations (Pratt & Ellen, 2005). Electric units offer lower emissions and operating
costs, although the more infrastructures required increase installation costs (Chadwick, 1996).
In addition, since mines typically evolve over time, the options embedding in an ore-handling
system can enable managers to vary the operating strategy of a mine in response to these
changes. The value of the business could be reduced if the ore-handling system is not flexible
1
enough to respond to external influences such as technological developments and economic
changes. Shaft and conveyor systems may be inflexible because of their limited number of
fixed feed points, while trucking systems are more flexible because they generally can travel to
most locations in the underground mine (Atkinson, 1992). Economic measures such as net
present value (NPV), which is the summation of all discounted future cash flows over the life
of the operation, can have a large weight when selecting a haulage method. NPV takes into
account all positive and negative cash flows, including those associated with initial project
development and construction (Hall & Stewart, 2004).
As fewer near-surface deposits are found today, future mining frontiers will be deeper,
more remote, and hostile. In addition, mining operations will face more extreme climatic
conditions with an expected increase in energy price (Salama et al., 2014). Although these
conditions are great challenges in themselves, they will be presented against a backdrop of
more intensive public scrutiny of environmental issues and community relations. Today,
mining companies must be able to investigate the implications of increased mining operational
costs on their mine plan and be able to adapt. One important aspect of this adaptation is to
know which options are available and how their implementation may impact a mine plan.
Haulage is one of the most energy-intensive activities in mining, and thus, one of the main
contributors to energy costs. Therefore, the effective choice of a haulage system is an important
factor in optimizing production and minimizing energy costs in deep mines.
In this thesis, diesel and electric trucks, shaft, and belt conveyor systems have been
studied to evaluate their impact on the desired production objectives and energy costs. A
comparison of the NPV across haulage methods at an increasingly mining rate and altered
commodity prices also is included.
In coming decades, many underground mines will operate at greater depths, which will affect
many operational factors such as increased rock stress, longer haulage distances, and higher
energy consumption, which potentially can generate lower production rates. The increased rock
stresses may lead to smaller sized openings, further restricting the size of loading and hauling
equipment that can be used. Large openings are likely to be unsustainable at greater depths
based on both geotechnical and economic factors. Large openings increase the amount of rock
support needed to maintain stability, hence raising reinforcement costs. Longer hauling
distances result in increased energy consumption for loading and hauling equipment, and in
turn, high energy consumption increases heat and gas emissions for diesel equipment. Heat
emission increases ventilation costs as large volumes of air must be circulated to cool diesel
engines and simultaneously maintain adequate air quality for personnel.
Continuing increase in global energy demand, future increases in energy prices, and
environmental impact issues will force mining companies to review the implications of
increased costs of their operations. The use of haulage systems with lower energy consumption
for mining operations at great depths will be very important to reduce operating costs. While
these challenges continue, the mining industry will seek to optimize haulage systems such that
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desired production rates are achieved with minimum energy costs. An effective, low-cost
haulage system also will provide financial viability of future deeper operations.
1.3 Objectives
The main objective of this research was to evaluate how haulage systems for underground
mining can be optimized. The research work aims to fulfill the following specific objectives:
To fulfill the research objectives, the following research questions were addressed:
2) Are there any benefits of combining discrete event simulation and mixed integer
programming in the optimization of underground haulage systems?
3) What is the impact of increasing energy costs on different underground loading and
haulage systems?
4) What are the impacts of mining rate and commodity price variations on the net present
value (NPV) of an underground mining operation?
The contribution of each paper to these research questions (RQ) is shown in Table 1.
APPENDED PAPERS
I II III IV V
RQ1 X X
RQ2 X X X
RQ3 X X
RQ4 X X
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In paper I two different sized haulage units with the aim of improving production in an existing
mine was compared. In paper II the energy costs associated with diesel and electric trucks,
shaft, and belt conveyor haulage systems when hauling the required amount of ore at different
mine depths was evaluated. In Paper III the changes in NPV if there were changes in
commodity prices at constant mining rate during operations was explained, and in Paper IV the
changes in NPV at variable mining rates and commodity prices was described. In paper V
energy consumption and gas emissions by comparing diesel and electric loading equipment of
similar bucket sizes was analyzed.
The scope of this research was to evaluate the impact of various haulage systems on the desired
production objectives and energy costs. The NPVs across haulage systems at an increasing
mining rate and altered commodity prices were also compared. The haulage systems included
were diesel and electric trucks, shaft, and belt conveyors. The NPV was based on the cash flow
generated by each haulage system.
x There are several other low profile and energy-efficient mode of transportation systems
such as monorail and rail-veyor that can be used for the operations at great depth but
were not included in this research.
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2 THEORETICAL FRAME OF REFERENCE
Mine optimization is one of the important steps in the viability of a mining project. Approaches
to select hauling equipment in order to minimize haulage cost are one of the main parameters in
this optimization process. This thesis examines the optimization of haulage systems to
determine how these various material-handling equipment may produce the desired production
objectives and lead to lower energy costs. The load and haul systems analyzed were diesel and
electric LHDs, diesel and electric trucks, shafts, and belt conveyors. Discrete event simulation
was used to estimate mine production, and the results were used to compute appropriate mining
costs for each hauling option. The cost parameters considered in this thesis were energy
requirements on each haul method, and gas emissions for diesel units. Based on the simulation
results, mixed integer programming (MIP) was then used to generate the optimal production
schedule and mine plan. The impact of increasing mining rates and altered commodity prices
on the mine plan’s NPV were also evaluated. Although many techniques are available for
selecting equipment, the aim was to meet material handling needs at minimum cost under given
mining conditions.
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Equipment Selection
Figure 1 lists some of the techniques that can be applied in equipment selection
(Oberndorfer, 1992). Operations research, such as integer programming, uses mathematics to
arrive at optimal or near optimal solutions to complex decision-making problems. Genetic
algorithms involve selection or search algorithms based on the principals of natural selection.
They use techniques inspired by natural evolution such as mutation and past experience. Petri
nets are graphical and mathematical modeling tools that offer a graphical notation for stepwise
processes that include choice, iteration, and concurrent execution (Murata, 1989). Simulation,
which provides the ability to capture the dynamic and random nature of a system, can be
combined with animation and graphical representation to offer an increased understanding of a
proposed mining system (Banks, 2000). Analytical methods use mathematical principals to
fully predict a theory’s implications and can provide solutions without any estimation.
Analytical methods have been widely used for many years in both open pit and underground
mining operations to evaluate load and haul combinations, including production constraints
such as road conditions and rock characteristics (Atkinson, 1992; Ercelebi & Kirmanli, 2000).
6
Rubber-tired loaders, known as load-haul-dump (LHD), are commonly used in hard-rock
mines. The selected loader also must be able to reach and fill a truck’s flatbed efficiently. The
production rate of a loading unit depends on bucket size, tramming distance, the machine cycle
time, material characteristics, and machine operational parameters such as speed. When the
loading unit’s bucket size and the ore properties are known, the estimated production per cycle
can be calculated as shown in equation 1. When the tramming distance from the loading point
to the dumping point is defined, the theoretical cycle time and hourly production can be
obtained as shown in equations 2 and 3 respectively.
f୧୪୪
Pେ = Q כɀ כ (1)
fୱ୵ୣ୪୪୧୬
2D 60
Cycle time = כ + ݐ௫ (2)
ݒ1000
Pେ
P୦ = כj (3)
Cycle time
Where PC is the production in tonnes per cycle, Ph is the hourly production rate in tonnes/hour;
Q represents bucket size in m3; ffill stands for bucket filling factor; J is the ore density in t/ m3;
D is the one-way tramming distance in meters; fswelling is the swelling factor; v is the average
speed over the cycle in kilometers per hour; tfix represents fixed cycle time (load, damp, and
maneuver) in minutes; and j is the operating minutes per hour to account for delays in one hour
of operation.
In general, LHDs are effective for shorter tramming distances. For longer distances,
LHDs may be combined with other haulage equipment to transport the load to the desired
location effectively (Atkinson, 1992). Equation 3 is used to analytically estimate production
when the tramming distance is fixed; however, when tramming distances vary, equation 4 is
used to obtain the hourly production.
2
f୧୪୪ v 1000 ۍ1000 כD୫ୟ୶ + t ୧୶ ې
jכ כQ כɀ כ2 כ60
fୱ୵ୣ୪୪୧୬ ێv כ60 ۑ
Pୟ୴ୣ୰ୟୣ = כLn ێ ۑ (4)
D୫ୟ୶ െ D୫୧୬ 2
ێ1000 כD୫୧୬ + t ୧୶ ۑ
ۏv כ60 ے
In this equation, Paverage is the average hourly production rate in t/hour; Dmin is the lowest
tramming distance covered by LHD, Dmax is the highest tramming distance, and Ln is the
natural logarithm.
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2.1.1.2 Truck haulage system
Truck haulage systems are widely used in underground operations for long haul of material
from the loading areas to the shaft station or directly to the mine surface. A truck normally uses
development openings (declines) and main levels when hauling ore to the specified location.
The vehicle performance should be considered in designing dimensions of the declines (height,
width, and curve radius). Short curves will slow the vehicles, which may result in traffic
congestion. As shown in Figure 2, the width and grade of the decline road should enable
vehicles to safely negotiate curves at a given speed, taking into account sight distance and the
minimum vehicle turning radius.
The type and number of trucks are selected based on the loading equipment used. The
truck size selection depends on the number of cycles the loader needs to fill a truck. A high-
capacity truck and a lower-capacity loader will increase the number of loader cycles required,
which leads to an extended cycle time for the hauler and a lower production rate. The optimal
combination of loading and hauling units in an operation can be obtained based on the “match
factor” (Lizotte & Bonates, 1987), which the Caterpillar Company first formulated to quantify
the apparent balance between the numbers of loading units and hauling units. Equation 5
describes the match factor.
N୦ כLୡ୲୷
MF = (5)
N୪ כHୡ୲୷
8
Where MF stands for match factor, Nh represents number of haul units; Nl is the number of
loading units; and Lcty and Hcty are the load and hauls cycle times, respectively. When MF is
below 1, the system is under-trucked, and when MF is above 1, the system is over-trucked. An
MF of exactly 1 indicates a theoretical match between haulers and loaders, although these
calculations provide only an estimate of the optimal balance. The number of trucks also
depends on the other factors such as productivity estimate, available time in a shift, queuing of
trucks at loading and dumping points, traffic congestion, and so on.
Shaft haulage is used to access mineral resources that are too deep to be mined economically
using open-cut methods. A ramp entry also may be advisable to accelerate the preproduction
schedule and later to provide service access to the mine. Shafts provide various services to
underground mines such as ventilation, power, and water supply. According to Edward (1988),
a shaft consists of five main components: hoist, wind, conveyances, ropes, and headframe.
Edwards also identified an additional 277 subcomponents of a shaft system. The number of
main components and their interrelationship with subcomponents indicate the complexity of a
shaft-hoisting system. The selected hoisting equipment is normally intended for the entire life-
time of the mine and therefore it is important that the proper choice is made (Beerkircher,
1989). Shaft hoisting systems also are equipped with conveyances to transport material and
workers between the underground and mine surfaces. Conveyances consist of skips for ore or
waste transportation and cages for transporting workers and other materials suspended by
hoisting ropes.
The hoisting system consists of drum and friction hoists. The drum hoist is usually
located some distance from the shaft and requires a headframe and sheaves to center the
hoisting ropes in the shaft compartment. For this hoisting type, the ropes are stored on a drum.
The Koepe or friction hoist consists of a wheel with a groove lined with friction material to
resist slippage. The hoist ropes are not attached or stored on the wheel, but instead are wound
around the drum and over the head sheaves to the conveyances. In the friction hoist,
conveyance positions are fixed relative to each other with tail rope used to counterbalance the
rope loads throughout the hoisting cycle. This system lowers the starting torque and requires a
smaller motor to hoist the same load, reducing both capital and operational costs (Harmon,
1973). According to Schulz (1973), Tudhope (1973) and Brucker (1975), a friction hoist with
multiple ropes can carry a higher payload and have a higher output in tonnes per hour than a
drum hoist. Friction hoists also have lower pick demand than drum hoists with the same output
and can operate at lower light power supply.
The selection of a hoisting system starts with the cycle-time calculation, which is later
used to estimate skip payload for the system. The cycle time is the time the hoist system takes
to move a conveyance from the bottom to the top of its wind, and depends on the initial creep,
acceleration, full speed, deceleration, dumping, loading, and resting times. When the cycle time
and the estimated annual production rate are known, the skip production rate expressed in terms
of the average tonnage per hours hoisted can be determined using equation 6.
9
Pୖ
S = (6)
3600 כC
In this equation, SP stands for skip payload in tonnes; PR is the production rate in tonnes/hour,
and CT represents cycle time in seconds. Based on the skip size and production rate, the type
and size of the rope can be established. For both hoisting systems, rope selection is based on
safety factors, compatibility, rope life, and rope cost. Factors affecting rope life include the
number of trips it will make, hoist and sheave dimensions, and the type of loading. A friction
hoist system requires defining the number of ropes, while a single rope of high strength can be
selected for a drum hoist. Selection also is based on strength, resistance to failure, abrasion
resistance, and resistance to distortion to ensure safety in moving material, personnel, and other
operational services (Edward, 1988).
In mining operations, belt conveyors are the major tools used to transport material for long haul
distances. Conveyors have the advantages of high, continuous output, the ability to operate over
a range of grades, and low operating costs (Hartman, 1987). The disadvantages of belt
conveyors are their inflexibility, high initial investment costs, and limits in the ability to
transport oversized materials. As shown in Figure 3, a belt conveyor consists of five main
components: a head pulley with gear box and electric motors; a tail pulley; a rubber belt; carry
and return idlers; and a take-up pulley (Goodyear, 1976). The belt is propelled by a driving
pulley and returns through the end pulley. Material is loaded in the tail end and discharged at
the head end. A series of rollers called idlers support the belt and are mounted on the both the
carrying and return sides of the conveyor, arranged in terms of trough to increase the belt’s
carrying capacity. The return idlers support the return side of the conveyor belt. To increase
efficiency, conveying sticky materials should be avoided because cleaning increases delays and
costs (Swinderman, 1991). Considerations in selection of conveyor belts include belt width,
surcharge angle, belt speed, inclination angle, troughing angle, driving and take-up pulleys,
motors, and idler configuration.
10
Figure 3. Basic belt conveyor components, adapted from Yardley and Stace (2008)
These parameters, which influence the conveyor’s performance, are considered when
estimating the belt carrying capacity and power requirements. The surcharge angle is one of the
most important determinants of the carrying capacity because it governs the cross-section area
of the material on the belt. The nature of the material to be conveyed, available tunnel space,
and overall system economics influence the choice of width and speed. The belt capacity is
derived by simple geometry, as shown in Figure 4.
Figure 4. Cross section of conveyor belt with three equal idlers, adapted from Yardley and
Stace (2008)
All design methods assume that the belt is filled uniformly along its length and that the load
extends a small distance off the edge of the belt and forms an arc of the circle on the belt. The
material conveyed is assumed to have a surcharge angle, which is the angle between the tangent
to the outside edge of the load where it contacts the belt and the horizontal. Given the cross
section area of the belt, the belt capacity in tonnes per hour can be estimated using equation 7.
11
Where L is the load in tonnes per hour, A is the cross section area of the belt in m2ȖLVWKH
density in kg/m3; and S is the belt speed. Based on the calculated belt capacity, an estimate of
the initial belt width and speed can be made for conveying the required material.
Analytical methods using mathematical relationships between inputs and outputs can be used to
evaluate a system’s performance when there is little uncertainty and few random activities.
However, the methods are limited when modeling complex operations, have low flexibility,
and cannot predict future operations (Atkinson, 1992; Raj et al., 2009). Most analytical
methods require a small amount of data because the methods tend to be fairly simple
descriptions of the system. They use mathematical principals to fully predict the implications of
a theory and solve an equation without any degree of estimation (Banks et al., 2010). The use
of analytical methods can be successfully applied to small mining operations that have less
uncertainty, but most large mining operations need methods that can accommodate for
randomness and uncertainty.
Discrete event simulation has in this work been chosen as the operations research technique for
evaluating the mine operations, due to its ability to capture the dynamic and random nature of
the systems. Simulation combined with animation and graphical representation offers a direct
approach to increased understanding of a proposed mining system. The random and dynamic
nature of the mining operations makes it very difficult to model the operations using analytical
models. When simulation is employed, model input can be based on appropriate probability
distributions that characterize the input variables.
There are two ways to study a system: conduct an experiment on the actual system or create a
model to represent the system. Designing a model of a real system usually requires the set of
assumptions for the operating system (Sturgul, 1999). These assumptions are expressed in
mathematical, logical, and symbolic relationships among the objects of interest in the system,
and they can be solved analytically or using simulation. When simulation is employed, the
models can be analyzed using computational procedures that are “run” to generate results.
12
Figure 5. System model taxonomy, based on Law and Kelton (1991)
Discrete event simulation has been applied in the mining industry since the 1960s to simulate
various problems, especially in transport systems (Zhao & Suboleski, 1987). Operational issues
such as fleet requirements, the flow of hauling machines, and mine planning (aimed at
optimizing, improving, analyzing, and planning existing and future systems) can be modeled
using simulations. Sturgul provided a comprehensive review of mine system simulation
literature covering the period 1961–1995 (Sturgul, 1996).
The United States mining industry was among the first to recognize the importance of
simulation in mine planning and design (Sturgul, 1999). At the first symposium on the use of
computers in mining, Rist (1961) presented a paper on computer simulation of a mine operation
in which a model was built to determine the optimum number of trains for a haulage level.
Since then, simulation has progressed to include several mining aspects, such as queuing
theory, scheduling, decision making, and location models (Panagiotou, 1999).
In Europe, the first mine simulations appeared in the 1950s in northern Sweden to model
train transportation at the Kiirunavaara underground iron mine. This model was done by hand
13
(Elbrond, 1964). Thereafter, the use of discrete simulation became more widespread in several
countries. Mutagwaba and Durucan (1993) reported a simulation model for a mine
transportation system developed in the United Kingdom. Other example includes a simulation
model to study train transportation in German underground coal mines (Wilke, 1970).
Recently, the use of discrete event simulation has become even more popular in European
mining operations, with studies in Sweden, Germany, and Turkey (Panagiotou, 1999).
In South African mines, simulation has become a useful means to explore the impact of
new capital investments in proposed mining method, and also been used in existing mines for
planning, optimization, and selection of equipment (Turner, 1999). One example is the Ingwe
Douglas Piller project in which a simulation was conducted to determine the truck-shovel
combinations suitable for a proposed mining operation.
Xu and Dong (1974) presented a discrete event simulation used to develop a computer
model of a shovel and truck transportation system for an open pit mine in China. The technique
has spread to both coal and hard rock mines for analysis of haulage systems.
Since the 1980s in Russia, computer simulation has been used to develop the best
correlations of haul unit capacities in underground mining (Konyukh et al., 1999).
In Australia, simulation has been used in various mining applications, including an early
project using computer simulation to develop ore handling operations for the Mt. Newman
Mining Company in Port Hedland, which was published in 1989 (Basu & Baafi, 1999).
Subsequently, several projects for both surface and underground mining in coal and hard rock
areas have been conducted, including simulation modeling to optimize underground ore
handling at the Cadia East Mine, (Greberg & Sundqvist, 2011).
The earliest use of discrete event mine simulation in South America is difficult to
ascertain because there is no established science or engineering citation service in that location;
however, Nogueira (1984), one of the earlier papers on simulation modeling in South America,
described a simulation model to improve truck-shovel operations at the CVRD Mine in Brazil.
The model was designed to assess the best truck/shovel combinations in order to determine
mine operation’s capacity.
Generally, discrete event simulation modeling is useful for mine planning and design,
machine selection, and designing haulage systems in order to optimize mine operations and
production throughputs. Early studies focused mainly on certain parts of the mining process,
such as equipment selection for the development stage, although more recent studies have
sought to cover more parts of the system and even to simulate an entire mine.
Verification ensures that a conceptual model design is translated accurately into a computer
model. Validation ensures that the model is sufficiently accurate for a certain purpose (Muller,
2011). Verification and validation of a model ensure that it accurately represents the real
system. Several techniques can be used for verification, including testing the model logic, using
debugging techniques, running the model under varying conditions, making logic flow
diagrams, and building diagnostics into the model. Validation can be accomplished using a
degenerate test, testing internal validity, using an extreme condition test, comparing to historic
data, test face validity, comparing output results with actual system, and a Turing test (Banks et
14
al., 2010). A verified and validated simulation model can provide results that are very close to
those in the actual operating system.
In this thesis, model verification was done by using debugging techniques, animations
check, model inspection from the specialists, and running the model under varying conditions.
The debugging features were used to make sure that everything was running correctly before
resuming execution. Simulation runs were initially conducted with conceptual estimated size of
equipment, storage facilities, and haulage systems structures. Initial results allowed these
parameters to be redefined and radically changed. The changes involved extra programming,
but enhanced the program’s versatility to conform with the proposed mine logistics. Validation
was accomplished with internal validity and a comparison of the model’s output with that of
the real system.
Discrete event simulation tools can be divided into three categories (Banks et al., 2010). The
first is general purpose programming language, such as C, C++, FORTRAN, and Java, which
offer a high degree of flexibility at a low cost, but require sophisticated programming skills
(Sturgul & Jacobson, 1994). Programs written in general purpose simulation languages can be
applied to develop other discrete event simulation software packages (Sturgul, 1999). The
second category is simulation programming language, such as GPSS/H, SIMAN, and
AUTOMOD. These types of software are object-oriented simulation languages that have high
flexibility and require good programming skills. The third category is simulation language
environment, a special computer language containing features that can be applied to various
applications. A program using elements with little or no coding is written to create models,
which may use graphics and built-in modeling elements. The most popular simulation language
environments in the mining industry include SLAM, SIMUL 8, and SimMine.
Based on the type of problem to be simulated, careful selection should be made among
the large number of simulation software options. According to Yuriy and Vayenas (2008),
many features may be considered when selecting simulation software, such as ease of use,
availability of adequate debugging and error diagnostics, ability to import data from other
software such as computer designs and spreadsheets, availability of animation for easy
visualization of operations, quality of the output report, statistical tools, and graphs for
interpretation. These features enable the modeled simulation to be verified and validated and
promote understanding of the operational systems. For this thesis, SimMine, General Purpose
Simulation System (GPSS/H), and AutoMod software were used for the discrete event
simulation models.
SimMine software was chosen due to its capability to evaluate the production facilities
design and production equipment selection. This software is based on discrete event simulation
principles and uses a full graphical user interface to set up the model; no coding is required. It
utilizes statistical distribution functions to model variations in process times. For verification
purposes and to increase understanding, the tool has a three-dimensional environment that
offers animated visual feedback of the model, which allows the user to view the dynamic
system as it operates (SimMine, 2012).
15
General Purpose Simulation System (GPSS) is a versatile computer programming
language originally developed in 1961 to solve various simulation problems that exhibit a
discrete character of events during operation (Schriber, 1989). According to Schriber (1989),
GPSS comprises several modern versions – GPSS/H, GPSS V/S, GPSS/PC, GPSS/VX and
GPSSR/PC – that can be used to model various operations. In this research GPSS/H version
was used, which is widely applied in both open-pit and underground mining operations because
of its ability to capture the dynamic and random nature of the systems (Sturgul & Singhal,
1988; Harrison & Sturgul, 1989; Sturgul, 1999). The tool includes built-in files, expanded
control statements, ordinary variables and arrays, a floating-point clock, built-in mathematical
functions, and built-in random generators that help in writing arithmetic expressions and
programming coding. It also is equipped with an interactive debugger to trace errors and
mistakes. GPSS/H includes what is called a proof animation, which provides two-dimensional
animation usually based on a scale drawing. It can run in post processed mode (after the
simulation has finished running) or concurrently. This animation feature offers a direct way to
understand a proposed mining system.
AutoMod consists of material movement systems that allow users to model both manual
and automated equipment such as LHDs with high degree of accuracy (Muller, 2011). When
system elements such as paths and stations are known, operating parameters such as speeds,
turning speed, acceleration, and deceleration can be defined in the movement system (Banks,
2004). Statistically performance reports and three-dimensional animation are created
automatically, providing a realistic and statistically accurate view of the system, which helps to
verify and validate models of complex systems. AutoMod provides advanced debugging and
trace facilities that enable errors and flaws to be easily traced. The tool is equipped with an
Autostat feature that greatly reduces the time required for experimentation and analysis.
Autostat’s evolutionary strategies algorithm is well suited for finding near-optimal solutions in
systems.
Discrete event simulation has the ability to model complex systems in great detail and to
provide results very close to those in the actual operating system. The method’s main drawback
is the effort and costs required to collect and process the input data from different sources to
ensure valid simulation results. Developing a detailed, accurate simulation model for a large
and complex system requires collecting a large amount of data, fitting the data to statistical
distributions, and selecting simulation software carefully. Failure in any of these tasks may
result in an inaccurate estimation of the system performance. Therefore, the simulation model
must be run many times, allowing events to occur many times, to represent the system’s typical
behavior and to obtain performance measure estimates with high confidence levels.
16
Figure 6. Deterministic modelling taxonomy, based on Pochet & Laurence (2006)
The MIP is recognized within mathematics as a tool to model and find the optimal solution to
large, complex, and highly constrained problems. The application of MIP models varies
extensively from transportation scheduling and distribution of goods to production planning in
manufacturing (Winston & Goldberg, 2004). MIP uses a combination of linear programming
and integer programming to define all feasible solutions before applying a number of solution
techniques, including the simplex method, branch-and-bound, and cutting planes, to obtain the
optimal solution.
Rigorous and heuristic operations research (OR) techniques such as mixed integer
programming (MIP) have long been used to model and solve numerous mining related
problems with the aim to optimize planning and production scheduling in both the open-pit and
underground mining environments. Numerous authors have advanced the state of the art in the
broad topic of mining optimization. Dimitrakopoulos and Ramazan (2008) used stochastic
integer programming to provide a framework for optimizing mine production schedules,
considering uncertainty with a focus on geologic risk. For gold and copper deposits, the authors
claimed to use the stochastic integer programming approach to increase the production
schedule’s NPV for gold and copper deposits by 10% and 25% respectively over traditional
single-fixed orebody estimates. Epstein et al. (2012) solved the relaxation of a tight linear
formulation to optimize underground and open-pit ore deposits sharing multiple downstream
processing plants over a long-term planning horizon. Application of their solution at Codelco
operations since 2001 indicates NPV of single mine production plans has increased by 5% with
an additional 3% increase occurring when integrating multiple mines. Newman and Kuchta
(2007) aggregated time periods as part of a heuristic approach to provide basic solutions to the
iron ore blending problem at Kiirunavaara underground iron mine. The results generated under
17
the heuristic approach were then used to create a rigorous integer programming model to
produce good quality solutions in a much shorter time. Salama et al. (2014) used simulation
combined with mixed integer programming to investigate the impact of changing energy prices
on underground mining operations across multiple depths, using a number of haulage options.
For the particular case study used, their findings indicated that shaft and conveyor haulage
systems are most beneficial at increased energy prices.
In the past, the use of MIP in the mining industry has been somewhat confined to open-
pit applications (Lerchs & Grossman, 1965). But since the 1990s, MIP has been more
extensively used in the underground environment (Almgren, 1994; Trout, 1995; Newman et al.,
2007). Trout (1995) scheduled production within the Mount Isa Mine, Australia, to emphasize
stope development and backfilling processes; however, he was unable to apply MIP optimally
because of the large number of binary variables. Almgren (1994) used MIP as an aid in
scheduling development and production at the Kiirunavaara Mine and also ran into difficulties
in solving the large-scale MIP because of the time-dynamic nature of his initial problem
formulation. In the past, use of MIP has been hindered because models of real-world problems
often must incorporate a large number of decision variables, many of which must assume
integer values. With a large number of integer variables, solution times may be unacceptably
long for practical planning purposes. Model formulation using MIP is currently created by
processing the production data and then formulating the model formulation, which reduces the
number of binary and integer variables in a multi-period production model. Thus, solution
times are greatly reduced and optimal results are reached (Newman et al., 2007).
Mixed integer programming (MIP) can be applied to generate the optimal production schedule
and mine plan. Among the several mathematical languages available to formulate mixed
integer programing problems are an integer matrix library (IML), a mathematical language
(AMPL), and GNU linear programming (GLPK). Optimization tools can be used to solve the
formulated models, including XA, CPLEX, GUROBI, and MOSEK. In this thesis, A
Mathematical Language (AMPL) tool was used for mathematical formulation and then applied
CPLEX software to reach the solution. The tools were chosen for their capability to formulate
and solve a variety of different optimization problems in a variety of computing environments
(Epstein et al., 2012; Nehring et al., 2012). They can solve linearly or quadratically constrained
optimization problems in which the objective of optimization can be expressed as a linear
function or a convex quadratic function. CPLEX is equipped with a pre-solver tool that can
reduce the size of the problem, and thus, save time required to run the model. The MIP model
will generate the optimal or near optimal solution, but requires considerable time to run the
complex models.
The discrete event simulation was combined with MIP to increase the efficiency of the
analyzed systems, to improve the understanding of the behavior of various systems, and reduce
risk when selecting the operational systems. Previously, simulation and MIP have been
combined with simultaneous execution to achieve feasible solutions for operational systems
18
(White & Olson, 1986; Chanda, 1990; Fiorini et al., 2008). Fiorini et al. (2008) proposed
concurrent simulation and optimization models to achieve a feasible, reliable, and accurate
analysis and generate a short-term planning schedule; Chanda (1990) used the combined tools
to model the problem of scheduling the draw point for mine production optimization. The
combined methodology produces a more realistic model than a single technique (Chanda,
1990). In this research, the tools were not employed simultaneously, but rather, used a discrete
event simulation for production estimates for different haulage options. The simulation results
were used to compute appropriate mining costs for each hauling operation. Mixed integer
programming (MIP) then generated the optimal production schedule and mine plan.
Discrete event simulation was used to estimate mine production for different haulage methods,
and the results were used to compute appropriate mining costs for each hauling option. The cost
parameters considered in this thesis were energy requirements on each haul method and gas
emissions for diesel units.
Energy consumption plays a significant role in the selection and management of loading and
hauling equipment. Diesel fuel is the most common energy source for mining operations
(Kecojevic & Komljenovic, 2010), although electricity is gaining attention in various
underground mines (Paraszczak et al., 2013). As shown in Figure 7, the price of crude oil was
below $90 per barrel in the world market during 2011 when the reference case was considered.
The reference case represents current judgment regarding exploration and development costs
and accessibility of oil resources.
19
Under the assumption that the Organization of the Petroleum Exporting Countries (OPEC)
producers will maintain their market share and schedule investments in incremental production
capacity, oil prices are projected to reach $106 per barrel in 2020 and $163 per barrel in 2040
(AEO, 2013). Mining companies must take into account the many factors that will continue to
hike their operational costs, such as increases in global energy demands and energy prices,
increased mine depths and longer haul distances, and environmental impacts. As a result of
these financial pressures, haulage methods that help companies reach their desired production
objectives at the lowest cost will be very significant (Kecojevic & Komljenovic, 2010).
Electric LHDs may use overhead electric lines, batteries, or trailing cables. Batteries offer the
highest flexibility, but battery vehicles are heavy and must be regularly recharged. Overhead
power lines may be feasible where routes remain constant for an extended period of time, but
are impractical for LHDs that require a high maneuverability. The most viable way to power
electric LHDs is with a trailing cable plugged into the mine’s electrical infrastructure. Electric
units have low noise levels, no exhaust gases, and low demand for ventilation because they
generate less heat. But powering with electric cable has the disadvantages of the LHD’s
reduced versatility, cable faults and relocation issues, limited haul range, restricted movement,
and cable wear (Chadwick, 1996; Paraszczak et al., 2013; Paterson & Knights, 2013;
Paraszczak et al., 2014a). On the other hand, diesel LHDs are versatile and can easily move
from one location to another. During loading and dumping, the fuel consumed by diesel LHDs
can be estimated based on equation 8 (Kecojevic & Komljenovic, 2010). For electric LHDs, the
energy consumed during loading and dumping is estimated based on the motor input power and
time the equipment is utilized. The energy consumption in kWh per loading cycle from loading
point to dumping point and back to loading point can be estimated using equation 10 for both
diesel and electric LHD machines.
For many years diesel trucks have been utilized for material transportation in open-pit and
underground mining operations, although electric trucks are gaining attention in various deep
underground mines. Examples of mine companies operating electric trucks are Kidd Creek and
Hope Brook Gold in Canada, Mount Isa in Australia, and Stillwater mine in the United States
(Paraszczak et al., 2014a). In comparison to diesel trucks, electric trucks are faster, cheaper to
operate, need minimal ventilation, and do not require the risk of underground diesel storage. On
the other hand, electric trucks have higher initial costs as more infrastructures are needed, and
have less flexibility than trackless vehicles (Anon, 2009).
Electric trucks can be powered from trailing electric cables, batteries, or electric trolley
lines mounted at the back of the drift. However, when trucks must travel long distances, neither
trailing electric cables nor batteries are feasible; both lithium-iron and lithium-iron-phosphate
batteries have a specific energy in the range of 0.4 MJ/Kg to 0.9 MJ/Kg, which means they
must be recharged after a few hours of operations. The Swedish truck company, Kiruna,
originally developed the system to power electric trucks with an overhead electric trolley line
mounted at the back of the drift. The company’s EMT-35 and EMT-50 truck models are 35-
20
tonne and 50-tonne units respectively. Figure 8 shows a Kiruna truck in the Zinkgruvan mine,
one of the first underground mines to use the technology. Electrics trucks operate on a three-
phase AC, 690V overhead trolley line secured to the back of the ramp drift. During loading and
dumping, the electric trucks leave the overhead power and rely on a small diesel engine, which
produces minimal particulate emissions (Chadwick, 2011).
K כGHP כLF
F = (8)
KPL
FC כ38.6
Eୈ = (9)
3.6
21
In these formulas, FC is the energy consumed in liters per machine hour; K stands for the
kilograms of fuel used per brake horsepower per hour; GHP represents the gross engine
horsepower at governed engine revolution per minute; KPL is the weight of fuel in Kg/liter;
and LF is the load factor in percentage. ED is the energy consumed by diesel equipment in
kWh; the calorific value of 38.6 MJ/L is the amount of heat released by a fuel when combusted
and 3.6 MJ is the heat used to produce 1 kWh. Equation 10 is used to estimate the energy
consumption (E) in kWh per cycle as diesel or electric trucks transport material for dumping
and return to the loading point.
TR is the total resistance in tonnes; g is the acceleration due to gravity in m/s2; VW is the gross
vehicle weight in tonnes; BC represents bucket capacity in tonnes; t is the time taken to
transport material for dumping and return to the loading point in hours; VL is the vehicle speed
in m/s when loaded; and VE is the vehicle speed in m/s when empty.
For purposes of this thesis, a friction or Koepe hoisting system with two swing-out body skips
in balance and four flattened-strand ropes was selected. A friction hoist has the ability to handle
heavy loads with comparatively smaller mechanical equipment configurations, resulting in
smaller energy consumption compared to a drum hoist. The duty cycle of the hoist is the main
determinant of the required hoisting energy of the shaft system. The duty cycle is the
relationship between hoist powers and hoisting cycle time.
Figure 9 depicts the plot of the duty cycle for a friction sheave hoist. This diagram shows
the horsepower (HP) needed to drive the hoisting system depending on the skip speed,
acceleration and deceleration rates, creep speeds and distances, each indicated as HP1 to HP6
(Harmon, 1973). The hoisting cycle time consists of three major activities: skip loading, skip
travel, and skip unloading. The skip load is estimated based on calculated cycles and is used to
determine the rope strength needed to ensure safe working conditions. The energy estimation
for the hoisting system at different mine depths was determined after integrating the area under
the curves, as shown in equation 11 (Harmon, 1973).
E is the energy consumption for the duty cycle in kWh/trip; Wo is the skip live load; V stands
for the hoisting velocity; AT is the acceleration time; TFS is the constant-YHORFLW\WLPHDQG
is the hoisting efficiency in decimal.
22
Figure 9. Power estimation for friction hoist (Bise, 2003)
AC induction motors normally drive conveyors because these motors have low operating costs.
When material is moved by the belts, electrical energy is converted into various forms of
energy such as movement energy, potential energy, noise energy, and heat energy. The energy
conversion model shows the relationship between the energy needed to drive the conveyor and
the conveyor parameters (Hiltermann et al., 2011). Three types of energy is required to drive
the conveyor: the energy needed to run the empty conveyor, the energy required for moving the
material horizontally over a certain distance, and the energy needed to lift the material to a
certain elevation. Assumptions include the introduction of an artificial friction coefficient to
evaluate the main resistance and the introduction of a length coefficient to calculate the
secondary resistances. Various models available to estimate the energy to drive the conveyor
system include CEMA (Conveyor Equipment Manufacturers Association), Goodyear, FDA
(Fenner Dunlop Australia), and others. This thesis used the Goodyear model because it is
capable of estimating the size of the drive more accurately and takes into account all three
energy types needed to estimate the conveying energy (Hiltermann et al., 2011).
Equation 12 (Hager & Hintz, 1993) describes the energy required to move the conveyor’s
various parts and run the empty belt. Pec is the energy required to run the empty belt in
kilowatts (kW), g is the acceleration due to gravity in m/s2; C is the friction factor; Q is the
mass of moving parts of the conveyor in kg/m; L stands for the distance of incline and decline
belt; L0 is the horizontal center to center distance: S is the belt speed; and t represents the hours
in which the belt is in operation.
23
Equation 13 (Hager & Hintz, 1993) calculates the energy required to move the material
horizontally over a certain distance where Ph is the energy to move the material horizontally
and T stands for the transfer rate in tons per hour.
gכTכH
P୪ = ± כt (14)
3600
The summation of equations 12, 13, and 14 is used to obtain the total energy consumed by the
conveyor belt (Pt), as shown in equation 15 (Hager & Hintz, 1993).
P୲ = Pୣୡ + P୦ + P୪ (15)
The exhaust gases discharged from diesel engines contain several components harmful to
human health and to the environment, including particulate matters and carbon (Pallegrino et
al., 2005; Paraszczak et al., 2014b). In addition, heat and gas emissions from a diesel engine
increase operating costs, particularly in deep mines where heat emissions necessitate increasing
costs to ventilate the mine (Paraszczak et al., 2013). As a result, energy efficiency and cost
reduction in mining operations has gained worldwide attention (Johnson, 2005).
The South African Department of Minerals set a goal for the mining industry to reduce
energy demand by 15% by 2015 (Merwe, 2007). The European Commission is expected to
lower emissions levels to <0.01g/kWh particulate matters, the same as those of the US and
Japan (Johnson, 2005). Australia has introduced sweeping new taxes on coal and iron ore
producers through the mineral resources rent tax and a broader carbon tax aimed at
environmental protectionism (Salama et al., 2014).
Continuing global energy demands and emissions challenges will force mining
companies to study lower-emissions power sources. For this study, the carbon dioxide emission
from diesel engines was estimated. The amount of CO2 emitted depends on the particular
equipment’s fuel consumption, which is most accurately determined through onsite
measurements. However, this method is very expensive because it requires continuously
monitoring of the emissions from every piece of equipment working. A less expensive, though
less accurate method is to use CO2 calculation. This calculation is based on the combustion
process of fixed carbon restrained in a volume of diesel fuel. The diesel engine emits gases
because of incomplete combustion and the impurities in the fuel (Pellegrino et al., 2005).
To calculate emissions, the diesel conversion factors published by the Environmental
Protection Agency (EPA, 2005), was applied. Equation 16 expresses the amount of CO2
emitted in tonnes by diesel equipment (Bogunovic & Kecojevic, 2009).
24
44
COଶ = FC כCC כ10ି כ0.99 כ ൨ (16)
12
In this equation, CC stands for carbon content for the fuel (g/l), and 0.99 is the oxidation factor,
meaning that 99% of fuel burns out while 1% remains un-oxidized. According to the EPA
(2005), the carbon content for diesel fuel is 738.2g/l; 44/12 stands for the ratio of molecular
weight of CO2 to the molecular weight of carbon.
Mine planners traditionally plan and design mine production at a fixed commodity price, or at
least a commodity price that does not change rapidly. In most operations, a change in the
commodity price does not prompt a revaluation of the mine plan, and the plan generated at the
feasibility stage remains in place. As a result, although the profitability of an operation may
increase with an increase in commodity price, it does not gain the additional value that it could
if the mine plan is re-evaluated (McIsaac, 2008).
For example, Figure 10 shows copper prices over a 20-year period from 1993 to 2013. Copper
was trading at $US 1647/t in October 1993, and then rose and fell until reaching a price of $US
10,000/t in February 2011. Since then copper prices gradually declined to the current price of
$US 6500/t. Most feasibility studies on undeveloped copper projects conducted over recent
years generally have used a price range between $US 5000/t and $US 5500/t over the long term
even though the copper price at the time of the studies was about $US6500/t (Salama et al.,
2014; McIsaac, 2008). A short-term change in commodity price will add only as much value as
the increased margin of the new price will provide (Newman & Kuchta, 2007). However, if the
price change occurs over a longer term, then the mine plan should be adjusted to capture fully
the additional value offered in the new market conditions. Adjustments to the mine plan could
25
be changes to the production sequencing of a particular pushback, to the point at which the
open pit transitions to an underground operation, or to the point when existing ore handling
systems are modified (Hall & Stewart, 2004).
The selection of a mining rate, which has a great influence on optimization, may be based on an
empirical formula or economic measures (Tatman, 2001). Taylor’s Rule (1986) is an equation
for estimating production rate that is still used today; however the rule is limited with several
factors such as hoisting capacity, mine depth, and geometry of the deposit. Tatman (2001)
developed an empirical equation used for mines with steeply dipping underground deposits that
takes into account the orebody’s geometry rather than size.
Economic measures such as NPV should ultimately carry great weight when establishing
a mining rate. NPV is the summation of all discounted future cash flows over the life of the
operation. Smith (1997) discussed the economic characteristics affecting the optimum mining
rate from investors’ viewpoint. He suggested that the mining rate can be selected by
maximizing the NPV and discounting cash flow return on investment. Once the production rate
is determined and the operations starts, the production rate is difficult to change significantly
unless new capital investment is planned (Smith, 1997).
Production capacity may be expanded for several reasons, such as geological information
and economic changes. At the early stage, the mining rate is defined based on the orebody
delineated with very limited geological information and the assumption that all materials inside
the orebody are accessible. Later, the grade distribution within the orebody may change the
production sequence because some material considered waste might be mineable if it is
extracted with neighbouring high-grade material. For example, if the price of the contained
mineral falls, part of the reserve may become unprofitable to mine. But if the price is rises, the
lower grade areas may be considered for extractions. For existing an operation with a flexible
hauling system, the decision to increase production will result in higher mining costs. In
operation environments fixated on cost reduction, a proposal that increases costs may be very
difficult to implement. Such a proposal may need to be justified financially because the cost
increase may not be recuperated in production gains.
26
3 RESEARCH METHOD
Research can be defined as a scientific and systematic search for pertinent information on a
specific topic (Kothari, 2004). The research approach may include either quantitative or
qualitative methods or both. The quantitative approach, which generates data in the form of
numbers, measurements, and counts (Ghosh, 1982), may be subdivided into three categories:
inferential, experimental, and simulation. The aim of an inferential approach is to form a
database to study a system’s characteristics. An experimental approach includes a controlled
research environment to observe and analyze the effect variables have on other variables. A
simulation approach is used to build models to which initial conditions and variables are
applied to understand future conditions. A qualitative approach uses an assessment of attitudes,
opinions, and behaviors through questioning and verbal analysis. This research uses the
quantitative approach and the following methodology to present the results:
x Literature review
x Data collection
x Data analysis
x Discrete event simulation model
x Mixed integer programming model
The literature review included research on underground haulage system optimizations, energy
and gas estimation methods, mining rate, and commodity price. Sources included conference
proceedings, abstracting and indexing journals, published and unpublished bibliographies,
books, and technical reports.
Data collection is the process of gathering information with which to answer the stated research
questions and evaluate outcomes (Alavi et al., 2001). To ensure valid simulation results, data
from various sources is required before a model can be built. Data also are needed for model
validation, performing experiments with the validated model, and for developing mathematical
and logical relationships that adequately represent the problem entity and its intended purpose.
In this case, collected data were used to create the discrete event simulation models to estimate
mine production for different haulage methods. The simulation results were used to compute
appropriate mining cost per tonne for each hauling operation. Mixed integer programming
27
(MIP) was applied to generate the optimal production schedule and mine plan that maximized
the net present value (NPV) of all activities under consideration.
Data used in this research were obtained from three different underground mines. The
first, located in East Africa, consisted of pyrite and chalcopyrite ore. The mine use four mining
methods: sublevel open stoping with backfill, drift and fill mining, narrow vein mining, and
Alimak mining. This research focused on the sublevel open stoping method with an aim to
improve production using different sized diesel trucks. Among the collected observational data
were loading and dump times, empty and loaded travel times, and production data.
The second underground mine, located in Australia, extract copper-bearing ore using
sublevel open stoping with backfill. For this research, the analyzed orebodies were at depths of
1000, 2000, and 3000 meters. The aim was to compare the energy costs for hauling 100,000
tonnes per month from each depth using diesel trucks, electric trucks, shaft, and belt conveyors.
Two additional orebodies in this mine (the Eastern and Western) were analyzed to determine
the feasibility of increasing quarterly underground ore production from 300,000 to 450,000
tonnes from each orebody. In these two orebodies, LHDs were used to transport the ore to the
shaft points. Data obtained from this mine included stope extraction data, production planning
and scheduling, trucks, LHDs, and hoisting shaft system data. Data used for the belt conveyor
were from the Fenner Dunlop (2009) conveyor handbook.
The third underground mine was located in Sweden and consisted of a high-grade
magnetite deposit approximately four kilometers long with an average thickness of 80 to 100
meters in the northeasterly direction. The mine was divided into 10 main production areas
called blocks and uses a sublevel caving method to exploit the ore. At the time, the mine
produced approximately 27 Mt of crude ore annually and was expected to reach 37 Mt from all
10 blocks by 2015. To reach this production level, the mining company planned to increase the
loading capacity from each block. This research analyzed the energy consumption and gas
emissions for various loading equipment. Energy consumption (energy to drive the machine)
was estimated using simulation and analytical calculations. Energy required to operate fans and
hydraulic system were outside the scope of this investigation. The data collected included
kinematics for the machines, machine loading rates, vehicle efficiency, haul road surface
features, and load factors. Other data such as machine operating weight, and motor power
capacity was obtained from equipment manufacturers.
Data used for optimization included mining cost per tonne, mine life, commodity prices,
and a discount rate per year. The capital costs for each haulage method, taxation, and
depreciation were outside the scope of this investigation and were not included.
Data analysis techniques vary depending on the amount of data, if the data set is too small, if
data is missing, or if data is unavailable. With a large amount of data available, probability
distributions can be used to characterize the uncertainty and randomness of the operation. In
this research, some data in this category include the loading and hauling equipment
specifications such as speeds, loading and dump times, and empty and loaded travel times.
In some cases, when only a small amount of data is available, an attempt to fit data into
distributions may be inappropriate. In this case, empirical distributions (actual data values) can
28
be applied. Data that fall in this category include energy consumption and gas emission
estimations. As discussed, the most accurate method to determine energy consumption and gas
emissions is through on-site measurements, but this method is expensive and requires constant
monitoring. Instead, consumption rate can be estimated based on the machine loading rate,
vehicle efficiency, haul road gradient and surface features, load factors, and utilization time.
Gas emissions can be estimated based on the combustion process of fixed carbon restrained in a
volume of diesel fuel. These methods are less expensive, although is less accurate compared
with measurement method.
When no data are available, experts can apply their best guesses and assumptions to make
a subjective estimate. This method applies to some new equipment or systems that may be still
in the development phase and not yet on the market. When data becomes available, the
parameters and distributions can be updated.
The mine layout was imported into SimMine software to develop the model for the first
underground mine. The layout included a 5.5-meter wide ramp, loading bays, 3.5-meter high
production drifts, and 100-meter long crosscuts. Seven production drifts, each between 250
meters and 400 meters in length and with an average floor-to-roof vertical distance of 17
meters, were connected by a ramp. In this part of the mine, the general mine sequence allowed
three stopes to be mined simultaneously. Because of the limited size of the drifts, only one
LHD could be used in each production drift. During the simulation, the number of trucks was
changed from three to nine. Therefore, each LHD served one to three trucks. The LHD
tramming distance depended on the length of the production drift. The cycle time was longer
for vehicles working at the far end of the drift than for those in the middle or near the access.
Therefore, the simulation was run separately for the stopes located at the end, center, and near
the loading point of the drift. The haul road included a ramp, a main level, and one crosscut. To
reach the dumping points, the trucks from the lower levels traveled from loading points through
crosscuts, the ramp, and the main level; those at the upper drifts traveled a small portion of the
ramp before entering the main level. To check for the effect of haulage distance to the dumping
point, the simulation considered the upper drifts in the first run, the middle drifts in the second
run, and the bottom drifts in the third run. The aim was to optimize the number of trucks to
increase mine output and evaluate the potential to reach the production targets. In each location,
the system was simulated for a month, which consisted of seven working days with two shifts
of 10 hours each.
For the second underground mine, discrete event simulation and mixed integer
programming was applied to optimize four haulage systems based on each method’s energy
costs as the mine depth increased. Two separate models were created for the material flow at
depths of 1000, 2000, and 3000 meters. The first model involved 40-tonne diesel and 38-tonne
electric trucks, and the second model involved the shaft and belt conveyor.
The shaft modeling utilized a 15-tonne skip weight maintained for all mine depths with
the rope speed varied based on required production rate. Shaft stages at 2000 and 3000 meters
deep were used to connect the upper and lower shafts. Four 26-milimeter flattened strand hoist
ropes with sheave diameter of 3.4 meters were used, and the friction hoist efficiency was an
29
estimated 90%. Energy consumption was calculated based on the horsepower required to move
the shaft up and down. For the belt conveyor, three equal roll idlers placed at different
troughing angles were used on the carry and return side of the belt. At 1000 meters, the idlers
were placed at a 20-degree troughing angle. To reduce the elevation of the belt at deeper mine
depths, this angle was increased to 30 degrees for operation at 2000- and 3000-meter depths.
The system was simulated for a month, which consisted of seven working days for two shifts of
10 hours each day for both models. The simulation results were used as input in the MIP model
for NPV calculation and mine planning optimization.
Also for the second underground mine, two additional orebodies (Eastern and Western)
located at different depth levels were analyzed. The Eastern orebody was located at deeper
levels and considered high grade, while the Western orebody was at a shallow depth and was
low grade. The aim was to assess the feasibility of increasing quarterly underground ore
production from 300,000 to 450,000 tonnes from each orebody. To determine if production
capacity of 450,000 tonnes was feasible, simulation was used to calculate the number of LHD
units needed to achieve this volume. The simulation results was used to calculate the
discounted cash flows generated by each stope, which could in turn be used to adjust
production scheduling to achieve the optimal NPV.
For the third underground mine, the mine block modeled in the simulation consisted of 17
production drifts and four ore passes close to the main drift. Seven diesel and seven electric
LHDs with similar bucket size capacities were simulated in order to estimate the productivity
performance for each. The simulation results were used to calculate the energy consumption for
both equipment types and the gas emissions for the diesel units. The simulation was run for two
eight-hour day shifts and one six-hour night shift. The simulation ended when working LHDs
completed removing all the available ore in the block.
For the second underground mine, the optimal mine production scheduling was obtained using
an MIP model. All extraction-related activities are presented in full, along with all formulations
and constraints across the long-term scheduling horizon. Construction of all Mixed Integer
Programming (MIP) models for the purpose of optimal production scheduling (maximize NPV)
took place using A Mathematical Programming Language (AMPL), and then solved using
CPLEX version 10.3. The solution process for each haulage system was run for approximately
10 hours and was cut short even if convergence to the optimal solution had not yet been
achieved. In all cases however, a gap of less than 5% was achieved. Production scheduling took
place at monthly intervals and was limited to 180 periods (15 years). The following describe
the model formulation for the orebodies at depths of 1000, 2000, and 3000 meters using diesel
trucks, electric trucks, shaft, and belt conveyors haulage systems.
Indices
The MIP model was defined in general terms using the following subscript notation:
t long-term schedule time period: t = 1, 2, 3…. T
s long-term stope identification: s = 1, 2, 3…. S
f fill mass identification: f = 1, 2, 3…. F
30
Sets
Several sets were defined to aid in formulation of constraints:
ȕs set of eligible long-term time periods in which the stope s can be in production
ȕt set of eligible stopes that can be in production in long term time period t
adjs set of all stopes that are adjacent to and share a boundary with a stope s
badjf set of stopes that are adjacent to and share a boundary with existing fill mass f
tpbt set of time periods that include all periods up to the current period t
mbm number of stopes to be mined
Parameters
These parameter items represent the numeric inputs and conditions:
nt present value discount factor for time period t
cfs undiscounted cash flow ($) from each stope s
es earliest start time for stope s
ls latest start time for stope s
rs extraction reserve (t) for each stope s
sct truck/shaft/conveyor fleet movement capacity (t) for each time period t
Decision variables
One binary variable was required to reflect operating conditions and ultimately perform the
scheduling task:
wst 1 if production from stope s is scheduled for time period t,
0 otherwise
The objective function (equation 17) seeks to maximize the NPV of all activities under
consideration by determining the optimal schedule. The production-scheduling model
comprises numerous constraints that reflect practical limitations imposed by the sublevel
stoping method across the long-term scheduling horizon. These constraints can be classified
according to the limitations they impose on resources, sequencing, and timing. The resource
constraints (18) and (19) applicable across the long-term horizon include those for the truck,
shaft, conveyor, the ore capacity, and non-negativity and integer values. These constraints limit
the production of all development and stope extraction ore from exceeding the fleet capacity in
any long-term time period, and enforce non-negativity and integer values of the appropriate
variables. The sequencing constraints applicable across the long-term horizon are stope
production precedence sequencing constraint (20), non-concurrent stope sequencing constraint
(21); stope adjacency constraint (22); fill mass adjacency constraint (23); and existing fill mass
adjacency constraint (24). These constraints respectively ensure that simultaneous production
between stopes with a common boundary does not occur. The geotechnical stability ensures
stoping activities by limiting simultaneous adjacent production to two common boundaries
before commencing production, and to a single adjacent side once production is completed
production to become a fill mass. It also ensures fill mass stability of all existing fill masses by
limiting exposure to a single common boundary in each long-term time period. The timing
constraints applicable across the long-term horizon are “may mine” (25) and “must mine” (26)
31
constraints. These constraints ensure that commencement of stope production is initiated no
more than once during the long-term scheduling horizon if their late start date occurs beyond
the scheduling horizon. The mathematical formulation was done using A Mathematical
Language (AMPL) tool and then solved using CPLEX software.
Objective Function
Subject to
rୱ × wୱ୲ sc୲ t (18)
ୱאஒ౪
w ୱᇲ ୲ 1 f, t (24)
ୱᇲ אୠୟୢ୨
32
4 RESULTS AND DISCUSSIONS
Papers I and II presented the issue of productivity related to different haulage systems. Using
the simulation method, Paper I analyzed the feasibility of production targets for an underground
mine to identify possible improvements through proper hauling fleet selections. Two truck
types of different sizes were compared: a TH430 with a theoretical capacity of 30 tonnes and a
TH660 with a theoretical capacity of 60 tonnes. At the time of the study, the mine operated
with three LHDs and three TH430 trucks (one assigned to each LHD). Based on the mine
design and overall mine plan, the three LHDs and three TH430 produced 52% of the planned
monthly production. The haulage system was simulated to optimize the number of trucks
needed to increase output and to reach the assigned production targets.
60
50 end of drift
40 drift center
30 near access
20
10
-
3 4 5 6 7 8 9 3 4 5 6 7 8 9
TH430 TH660
No. of Trucks
Figure 11 shows the results when both trucks types worked at the upper drifts. The
amount of ore produced at the end, center, and near the loading bay seemed slightly higher for
the TH660 than the TH430 even though the payload for the TH660 was twice as high as for the
TH430. In all cases, the amount of ore produced sharply increased when the number of trucks
33
was increased from three to six. Beyond this point, the amount of ore produced only slightly
increased because additional trucks increased traffic (the percentage of time lost when trucks
meet in the haul ways, or the main drift and the ramp). The results for trucks in the middle and
lower drifts showed the same trend observed in the upper drifts. When comparing the
performance of trucks in all locations, production was greater for trucks working on the stopes
in the upper drifts than on those in the middle and lower drifts because trucks in the latter two
cases had a longer cycle to complete than those in the upper drifts. When combining all
simulated locations, the results showed that a combination of two trucks and one LHD for the
upper drifts and three trucks and one LHD for the lower or middle drifts improved the average
production from 52% to 75% of the goal when the TH430 was used, and from 52% to 83%
when the TH660 was used. This finding indicates that production would rise only 8% if the
TH430s were replaces with TH660s. This solution would have to be justified financially
because the costs associated with changing truck size might not be recuperated in extra
production.
In Paper II the fleet required to achieve a monthly production target of 100,000 tonnes for
a deep underground mine using the sublevel stoping mining method was analyzed. Four
different hauling systems were analyzed, diesel and electric trucks, shaft, and belt conveyor
haulage systems at three different mine depths. Table 2 presents the study results. At the 1000-
meter depth, seven diesel and five electric trucks were required to achieve the production target
although the electric truck was two tonnes smaller. This is because the cycle time for electric
trucks was shorter than the diesel trucks, which allowed it to complete more cycles in the same
time period. Thus, an electric truck had higher productivity compared with a diesel unit of
similar tramming capacity. The results also indicated that at 2000- and 3000-meter depths, 9
and 13 electric trucks, more than 15 and 25 diesel trucks, respectively were required to achieve
the production target. The model showed that using diesel trucks to haul materials directly to
the mine surface was not economically feasible.
For shaft haulage, the design characteristic was based on the maximum rope speed of 19
meters per second, a safety factor of seven, and a maximum skip size of 70 tonnes to reduce
slippage and avoid exceeding the rope strength. Based on rope strength and the required
production rate, a skip weight of 15 tonne was considered. This skip weight is maintained for
all mine depths with the variation of rope speed. As the results in Table 2 show, at the 1000-
meter depth, 100,000 tonnes of ore could be hauled at a speed of 8.5 meters per second. The
rope speeds were increased to 10 and 14 meters per second for 1000- to 2000-meter depths and
2000- to 3000-meter depths, respectively. The results indicated that rope speed and skip size
play important roles in production improvement for existing mine operations using a friction
hoist system.
34
Table 2. Simulation results
For a belt conveyor, the initial design included a 600-milimeter belt with a speed of one
meter per second and idlers placed at a 20-degree troughing angle. The belt speeds, width, and
idlers, were selected based on the total expected belt length, number of transfer points, capital
costs, and operating costs. During simulation, the belt width, troughing angle, and speed were
raised to accommodate the planned production. The troughing angle was increased to 30
degrees when the belt operated at 2000- and 3000-meter depths. As the results in Table 2 show,
at 1000 meters the production target was achieved when the speed was increased to 1.3 meters
per second. For lower levels, the speed was raised to 1.6 meters per second to haul the required
amount of ore. At all three depths, the amount of ore was achieved when the belt width was
increased to 900 millimeters. The analysis showed that the belt’s production capacity depended
greatly on surcharge angle, belt width, troughing angle, and belt speed.
4.2 Energy consumption and gas emission on loading and haulage equipment
This section describes the operational performance and the analysis of the energy consumption
and gas emissions of different loading equipment. It also describes the optimization of haulage
equipment based on energy requirements. Simulation was used to obtain the equipment
operational performance, and mixed integer programming for optimization purpose.
Paper V presented an analysis of the energy consumption and gas emissions of different sizes
of loading equipment. The analysis consists of fourteen types of LHD machines (seven diesels
named 1D to 7D, and seven electrics named 1E to 7E) with similar bucket capacities. The
results showed that with current prices of diesel and electricity, the hourly fuel cost for diesel
was higher than the hourly cost for electricity. For example, in one hour of operation, the diesel
LHD 7D consumed 38.6 liters of fuel while its electric counterpart consumed 306 kWh of
electricity. Assuming a fuel price of $2.1 per liter and electricity price of $0.12 per kWh (WES,
2014), the diesel LHD would have an hourly fuel cost of $81.1 and the electric LHD an hourly
35
cost of $36.8. The cost increased as the bucket size increased for both machine types. On
average and for the current price, the study showed that the hourly energy cost for the electric
LHD was 47 % less compared with the diesel LHD with a similar bucket size. For comparison
purposes, the diesel fuel units were converted to kWh (see Paper V, p. 4). The results are
shown in Figure 12.
Energy consumption was higher for diesel machines compared with electric machines.
The lower consumption for electric LHDs was because these machines were equipped with
low-power motors. A diesel truck with a bucket capacity of 4.6 m3 had a power of 220 kW,
while an electric truck of the same capacity had a power of 132 kW. The energy required to
drive equipment is proportional to its speed. On average, diesel LHDs travel faster than electric
LHDs at the same gear because the diesel LHD engine has a torque converter with lower offset
ratio compared to electric engines (Sandvik, 2013). This enables the diesel LHDs to have
higher speed and hence higher consumption compared with electric counterparts. The
difference in consumption increased with the increase in bucket size because larger buckets
weight more. For example, a diesel machine with a 1.5 m3 bucket weighs 8.7 tonnes when the
bucket is empty, compared with a vehicle with a 9 m3, which weighs 56.8 tonnes. When these
two machines move in a similar gear, the heavier machine will consume more drive power than
the lighter one.
400
Energy consumption (kWh/Hour)
350
300
250
100
50
0
1D 1E 2D 2E 3D 3E 4D 4E 5D 5E 6D 6E 7D 7E
Types of LHDs
Figure 12. Comparison of energy consumption for diesel and electric LHDs
Next, the CO2 gas emissions for diesel LHDs were estimated. Actual gas emissions are
measured while the LHDs are operating, but this method is time-consuming and requires close
monitoring of the working equipment, which increases costs. Instead of field measurements,
emissions can be estimated based on the combustion process of fixed carbon restrained in a
volume of diesel fuel (C12H23). Figure 13 shows the results for the estimated hourly CO2
emissions with hourly fuel consumption for each diesel unit. For example, a diesel LHD 1D
36
consumed 6.9 liters of diesel and emitted 18.6 Kg of CO2 in one hour, while the diesel LHD 7D
consumed 38.6 liters and emitted 103.5 Kg of CO2. According to this estimate, the increase in
energy consumption resulted in higher levels of CO2 emissions. The high emissions expose the
diesel operators to noxious gases, which have negative impacts on human health and may
increase operator’s fatigue. Another result may be operator inefficiency, which increases
production delays. Ventilation costs also rise in an effort to mitigate the high heat and gas
emissions. In an environment of increasing energy prices and the need to mine at greater
depths, mining companies should minimize usage of diesel machines and increase usage of
electric ones to achieve greater cost reductions.
35
80
30
70
25
60
20
50
15
40
30 10
20 5
10 0
1D 2D 3D 4D 5D 6D 7D
Diesel LHDs
Figure 13. Comparison of fuel consumption and gas emissions for diesel LHDs
Paper II also analyzed energy consumption associated with diesel and electric trucks, shaft, and
belt conveyor haulage systems with current and predicted future energy prices. In this analysis,
the future energy price was assumed to be three times the current energy price. To reach these
estimations, simulation results was used to calculate the energy cost components of the total
operating costs for each haulage option. The operating costs (OPEX) for both energy price
scenarios are presented in Tables 3 and 4. The energy costs were subtracted from the revenues
to calculate the undiscounted cash flows, which in turn were the basis for the production
scheduling optimization process used to calculate the net present values (NPV). The NPVs
from each haulage option at depth levels of 1000, 2000, and 3000 meters, based on current and
future energy price scenarios, were compared.
37
Table 3. Operating cost ($/t) structure at current energy prices
38
As shown in Figure 14, diesel trucks had higher energy costs as depths increased
compared with other haulage options for both price scenarios. At the current energy price, the
energy costs for diesel trucks accounted for 38.2%, 46.8%, and 63.1% of the operating costs at
1000-, 2000-, and 3000-meter depths, respectively. At three times the current energy price, the
energy costs at each depth for diesel truck haulage increased significantly to 64.9%, 72.5%, and
83.7% of the operating costs. While diesel truck haulage generally offers greater operational
flexibility, its high energy costs resulted in rapid reduction in its financial viability as depths
increased.
80%
Percentage of Operating Cost (%)
80%
70%
70%
60%
60%
50%
50%
40% 40%
30% 30%
20% 20%
10% 10%
0% 0%
Electric Truck (1000m)
Electric Truck (2000m)
Electric Truck (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Figure 14. Energy costs as a percentage of operating costs at current price and
three times the current price
The lowest energy cost component increase was the shaft haulage system. At the depths
of 1000, 2000, and 3000 meters, energy costs accounted for 10.8%, 13.0%, and 15.4% of
operating costs at the current energy price. At three times the current energy price, energy costs
at each depth for shaft haulage accounted for 26.6%, 30.9%, and 35.4% of operating costs
39
respectively. Ore haulage is one of the most energy-intensive activities in a mining operation,
and energy is a main contributor to haulage costs; therefore, the energy cost as a percentage of
the total haulage cost was analyzed. As shown in Figure 15, an increasing trend of energy costs
occurred across all cases in combination with the increase in depth; diesel trucks showed higher
costs and the shaft system lower ones.
90% 90%
80% 80%
70% 70%
60% 60%
50% 50%
40% 40%
30% 30%
20% 20%
10% 10%
0% 0%
Electric Truck (1000m)
Electric Truck (2000m)
Electric Truck (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Diesel Truck (1000m)
Diesel Truck (2000m)
Diesel Truck (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Diesel Truck (1000m)
Diesel Truck (2000m)
Diesel Truck (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Figure 15. Energy cost as a percentage of haulage costs at the current and three times the
current energy prices
For further analysis, the calculated energy costs were used for all haulage options in a
cash flow analysis for NPV calculations. Mixed integer programming (MIP) was then used to
generate the optimal production schedule and mine plan at each energy price scenario.
Construction of all MIP models for the purpose of optimal production scheduling (maximize
NPV) was performed using a Mathematical Programming Language (AMPL) then solved using
CPLEX 10.3. Production scheduling was made at monthly intervals and was limited to 180
periods (15 years).
40
NPV Comparison between haulage methods at current energy prices
700
600
500
NPV ($M)
100
0
1 000 2 000 3 000
Depth (meters)
Figures 16 and 17 shows the NPVs achieved for all haulage options. Diesel trucks
generated lower NPVs compared with other haulage systems at 1000- and 2000-meter depths.
At 3000 meters, diesel and electric trucks generated negative cash flow (not seen in the Figure
as only positive values displayed). Therefore, as the mine depth increased, trucks were
economically not feasible for hauling material directly to the mine surface.
600
500
NPV ($M)
0
1 000 2 000 3 000
Depth (meters)
41
Figure 17 shows that when the energy price increased to three times the current price, the shaft
haulage system became a viable option for hauling material from deeper levels. At this price,
diesel and electric trucks and the belt conveyor produced negative NPVs. An analysis of these
results showed that in an era of increasing energy prices and increased need to mine at greater
depths, only haulage methods with lower energy requirements will remain feasible.
Papers III and IV described changes to the NPV for the Eastern and Western orebodies located
at different depths. The aim of the study was to evaluate the feasibility of increasing
underground ore production from 300,000 to 450,000 tonnes from each orebody in each quarter
at altered copper prices. The copper price at the time of this study was approximately $6,500/t.
The analysis used a range of copper prices starting at $5,250 and increasing by $500 increments
up to $9,750. The price of $5,250 was used because most feasibility studies on copper projects
conducted during recent years generally used price between $5,000/t and $5,500/t over the long
term even though the price at the time of this study was approximately $6,500/t. During the
copper price boom of 2011, copper prices reached almost $10,000/t and therefore, the final
price investigated for mine planning purposes was $9,750/t. Discrete event simulation was used
to determine the number of LHD machines required to achieve both mining rates; results are
shown in Figure 18.
Simulation results
500000 100
450000 95
400000 90
Amount of ore mined (t)
350000 85
Utilization (%)
300000 80
250000 75
200000 70
150000 65
100000 60
50000 55
0 50
1 2 3 4 5
Number of LHDs
42
As Figure 18 shows, three LHDs would be required to achieve the mining rate of 300,000
tonnes. At this rate, the average machine utilization was 89%. The term utilization means the
proportion of available working time (expressed as a percentage) that equipment is operating.
Five LHD units would be required to mine 450,000 tonnes. With five machines in operation,
the average machine utilization fell to 73% for each machine because LHDs must be queued at
the loading and dumping points. The results from both mining rates were used to compute the
appropriate mining costs for the operation, which then were used as input to the MIP to
generate the NPVs.
Table 5 compares the NPVs at each copper price for both mining rates. The copper price
of $5,250 per tonne at the 300,000-tonne mining rate was used as the base case. The increase in
copper price from $5,250 to $5,750 per tonne raised the NPV by 3.52% for each mining rate.
There was no difference in the NPVs for the two mining rates when copper prices were $6,250,
$6,750, and $7,250 per tonne. As the price increased to $7,750 per tonne, the two mining rates
generated different NPVs. At the price of $9,750 per tonne, the NPV rose to $773.45M, a
9.69% increase for the higher mining rate; at the lower rate, NPV rose to $755.65M, a 7.25%
increase. According to this analysis, increasing mining rates lead to higher mining costs, but
increased rates may be beneficial under certain market conditions.
The analysis of these results indicated that adjusting mining rates is sensitive to commodity
price. A short-term change in commodity price will add only the value provided by the
increased margin associated with the new price. If the price change is longer term, mining
operations should continually update and adjust their mine plans to capture additional value
under new market conditions. When the price falls, maintaining or increasing mining rate may
43
need a detail evaluation of other parameters such as grade, recovery, and investment changes.
In this study, the capital costs of the working equipment were not included, and therefore, the
evaluation was based on the development and operating costs. Future research should include
sensitivity analysis to measure the changes in the NPVs by including the flexibility of the
quantifiable parameters, such as ore grade, metal price uncertainty, and capital costs.
44
5 CONCLUSIONS AND FURTHER RESEARCH
The studies described in the previous chapters aimed to answer the stated research questions.
Following are the research questions and the conclusions from the performed studies.
x The increase in mine depth lead to increase haul distances from the working faces to the
mine surface. This in turn will increase cycle time for the loading and hauling
equipment and can also generate lower production rates. For many years diesel trucks
has become increasingly utilized in material transportation in mining. Paper II showed
that electric trucks have higher productivity compared to diesel trucks of similar
tramming capacity because electric trucks have shorter cycle times, which allows
electric trucks to complete more cycles than diesel trucks in the same time period.
Therefore, an increasing use of electric trucks will have positive effects on production.
The study excluded the impact of additional initial costs for electric trucks due to
additional infrastructure, and also excluded the fact that the infrastructure related to
electric equipment can be of hindrance for other operations.
x The increase in mining depth in many cases leads into higher rock stresses. The
increased rock stresses can lead to need for smaller size of the openings, adding
restrictions to the size of loading and hauling equipment to be used. Paper I showed that
because of the limited size of the mine openings, replacing the current system by bigger
trucks had little effect on production gains as the smaller trucks increases the production
from 52% to 75%, and the larger ones increases to 83% of planned production. This
indicates that there is no high impact on production improvement as production will fall
only by 8%. This solution needs to be justified financially as the costs associated with
changing the truck size might not be recuperated by extra production. The future
operations in the highly increased stress environment which lead into smaller size of the
openings, low profile equipment will remain viable to increase production.
x As described in paper II the shaft design was based on the maximum rope speed of 19
m/s, a safety factor of 7 and a maximum skip size of 70 tonnes. The study in paper II
shows that in order to achieve the required 100,000 tonnes per month, shaft can either
be operated at higher speed with small skip size or at a relatively low speed with the
large skip size. When a belt conveyor is used, the study indicated that increasing
surcharge angle and running the belt at a low speed would reach the production goal. To
45
achieve a similar production improvement, for a long haul, the troughing angle must be
increased and the belt operated at a higher speed. The literature review shows that shaft
and conveyor have high capital cost, and once installed they can be operated at low
cost. Operating shaft and conveyor at high speed will increase the energy consumption
and therefore high operating costs.
RQ 2: Are there any benefits of combining discrete event simulation and mixed integer
programming in the optimization of underground haulage systems?
For many years, analytical methods have been widely used in haulage selection for both open
pit and underground operations. As seen in the literature review, the existence of many
uncertainties and the random behavior of the system make haulage selection less accurate when
using analytical methods. Analytical methods can still be successfully used in small mining
operations which have less uncertainty, but most large mining operations need methods which
will involve randomness and can handle complexity.
When the systems involve random behavior, methods such as discrete event simulation
(DES) have advantage of more accurate accounting for real-world uncertainty and diversity in
operations. In Papers II, III, and IV, DES was used to study the behavior of mining operations
and make predictions before a new system was implemented. The investigation provides
mining operations with a preliminary assessment of the production rates and energy costs
associated with various haulage methods as mine depth increases for the purpose of aiding the
decision-making process in regard to future deeper underground mining. As seen in Paper II
when mine depth increases to 3000m, the simulation results shows that 13 electric trucks are
required to achieve the planned production. However, discrete event simulation is not suitable
for directly solving optimization problems like mine planning and scheduling and therefore
cannot provide the full picture with economic benefit or loss of the analyzed system. Mixed
Integer Programming (MIP) is used to optimize a system (Maximize profit or minimize loss).
The two techniques in those cases can be combined. Paper II also shows that when combining
MIP and DES, at 3000m depth for the current energy price, 13 trucks generate a negative cash
flow. This mean that at this depth, haul the material direct to the mine surface using electric
trucks become not feasible. The studies show that the benefits of the combined tool of DES and
MIP are:
x The combined tools give more information both on operational and optimizing the
performance of the system. Increased efficiency and a more feasible solution for
optimization problems, and therefore, increased potential to improve both the
productivity and the flexibility of the production operations and to reduce risks when
selecting equipment
x Support in decision making on optimization problems that includes both operational
performance and economic objectives such as cost minimization or maximization of
contribution to profits.
x Increasing the viability of the mine plans prior to execution, and enabling the analysis
of several scenarios within a short time interval.
46
RQ 3: What is the impact of increasing energy costs on different underground loading
and haulage systems?
x Paper V showed that when comparing loading equipment of similar bucket sizes, diesel
units have higher fuel consumption compared with electricity consumption for electric
units thus, the fuel costs of diesel machines are higher than the electricity costs for
electric units of similar size. In an environment of increasing energy costs, electric
loading equipment will have a positive effect on cost reduction.
x Paper II showed that, as mine depth increase, energy costs increase more when diesel
trucks are used, compared with other haulage options. At 1000 meters depth and at the
current energy price, the costs of diesel trucks, electric trucks, belt conveyors, and shaft
systems account for 62%, 54%, 25%, and 14% of the total haulage costs, respectively.
This finding indicates that minimizing usage of diesel trucks will have the greatest
benefit in cost reductions. Diesel machines also emit more heat and gases, which can
raise operating costs, particularly for ventilation systems in deep mines.
RQ 4: What are the impacts of mining rate and commodity price variations to the net
present value (NPV) of an underground mine operation?
The traditional notion in mine planning and design is that, mine production is planned at a fixed
commodity price, and a fixed mining rate. This means that although the profitability of an
operation may increase with an increase in commodity price, it may not gain the full additional
value that it might if the mine plan were re-evaluated. Paper III indicated that the change in
mine plans associated with changes in commodity prices at a fixed mining rate resulted in an
increase in the NPV from $96M to ultimately $755M for the mine studied. Therefore, if the
price change is long term, the mine plan should be changed to capture the additional value
offered under the new market conditions. Paper IV showed that the increase in mining rate
from 300,000 to 450,000 tonnes resulted in increased mining costs. With inclusion of the
additional costs, the change in production raised the NPV to $773M. Although increasing
production rates beyond traditional limits will increase costs, pursuing this course may be
beneficial when commodity prices are elevated to a certain level. When the price falls,
maintaining or increasing mining rate may need a detailed evaluation of other parameters such
as grade, recovery, and investment changes.
The research presented in this thesis was carried out to evaluate and analyze different haulage
systems. The studied haulage systems are diesel and electric trucks, shaft, and belt conveyor.
The comparison of the net present value (NPV) of the mine plan at an increasingly mining rate
and altered commodity prices were also analyzed. Based on the conducted research, further
study in this field may include the following:
47
x Energy consumption for other haulage options: A comprehensive study could be
conducted on the available low profile, energy-efficient transportation systems, such as
monorail and rail-veyor. The monorail system is mounted on a roof that allows
flexibility of trackless arrangements suitable for smaller drifts. A rail-veyor, which uses
a light rail track, can be installed more quickly than a conventional rail system. Rail-
veyor has a low profile feature allowing for small drifts and can travel on up to 20%
grades.
x Capital costs: In the analysis presented in this research, the NPVs were estimated
without including the capital costs of the haulage systems. The economic success of a
mining project in a competitive market depends on financial decisions regarding the
investment. For the decision regarding the investment, because of the long period of
construction and investment recovery, it is important to evaluate if the investment can
yield an expected return (ROI) given the presence of various uncertainties. It is
suggested that future research should include the investment costs of the analyzed
haulage systems. This would generate more knowledge on present value of the future
investment, how long it will take for the investment to yield returns, and if the
investment is profitable in the long run.
x Sensitivity analysis: The most widely used investment appraisal method is the
discounted cash flow net present value (NPV). The main drawback of the NPV is that it
cannot deal with flexibility. The NPV method advice decisions with positive cash flows
and rejects those with negative cash flows. Since market conditions are highly
uncertain, flexibility options can add significant value to a project’s viability.
Sensitivity analysis is one of several methods that can account for project uncertainty.
Sensitivity analysis explains the extent that variations in quantifiable parameters
influence a system’s viability. Some of these parameters may include ore grade, the
option to defer the investment, the option to expand capacity, costs, and metal price
uncertainty. The values of these parameters are estimated based on the probable
forecasts over a long time period. The actual values may differ from the forecasted
values. Sensitivity analysis considers how changes to these parameters could impact the
expected NPV, and would add value to future analysis.
x Combining discrete event simulation (DES) and mixed integer programming
(MIP): In this thesis, SimMine, GPSS/H, and AutoMod tools were used for creating
DES models. For optimization purpose, AMPL was used for mathematical formulation
and then CPLEX was applied to reach the solution. Due to large number of DES and
MIP tools options, future research may use the combining approach by studying the
other tools to evaluate the transportation problems. The solution time of MIP models
depends on number of binary variables and constraints, and tightness of the model (the
data set used, the constraints and the objective function). In this thesis, the solution time
was reduced by decreasing the number of binary variables and the solution was cut
short even if convergence to the optimal had not yet been achieved, and a small gap of
<5% was observed. To reduce the effect of the gap, further study may consider both
binary variables reduction and tightness of the model and transform the network by
considering the relaxed production capacity constraints.
48
x The combined use of other tools for process analysis and optimization of mining
systems: The combined use of other existing tools for process analysis and optimization
applied to mining systems needs further evaluation. The studies would aim at both
improving decision making regarding system investments but also at creating a tool that
in real time can aid the mine planners and operators in optimizing the processes,
production and use of resources.
49
50
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58
APPENDED PAPERS
PAPER I
Salama, A., Greberg, J., and Schunnesson, H. (2014). The use of discrete event simulation for
underground haulage mining equipment selection, International Journal of Mining and
Mineral Engineering, Vol. 5, No. 3, 256–271. doi: 10.1504/IJMME.2014.064486
256 Int. J. Mining and Mineral Engineering, Vol. 5, No. 3, 2014
Reference to this paper should be made as follows: Salama, A., Greberg, J. and
Schunnesson, H. (2014) ‘The use of discrete event simulation for underground
haulage mining equipment selection’, Int. J. Mining and Mineral Engineering,
Vol. 5, No. 3, pp.256–271.
1 Introduction
event simulation was used to compare the performance of two different hauling units of
different sizes. The comparison was based on the amount of ore produced, average
machine utilisations, and average traffic. The ore was transported by load-haul-dump
(LHD) from the production faces to the loading bays. At the loading bays trucks are
loaded and move the material to the bottom point of the shaft.
2 Equipment selection
simulation concerns the modelling of a system over time by representing the system
changes as separate events. A separate event means that time progresses until the next
event occurs. Monte-Carlo techniques which involve the use of random numbers to
simulate the actual statistical distributions that represent the entities of the system are
utilised. Examples of discrete event systems that can be simulated are transportation
systems, business processes, mining operations, emergency response systems, etc.
Discrete event simulation also applies to different types of rules and procedures which
increase the understanding of the interaction between variables and their importance in
the system performance and provides suggestions on modifications availabilities in the
system (Banks, 2000).
transportation in underground coal mines in Germany (Wilke, 1970). Recently, the use of
discrete event simulation has become popular in mining operations in Europe with studies
in Sweden, Germany, Turkey (Panagiotou, 1999). In Australia, simulation has been used
for various mining applications. An early project using computer simulation for
developing ore handling operations at Mt. Newman Mining in Port Hedland, Western
Australia was published in 1989 (Basu and Baafi, 1999). After that, several projects in
both surface and underground mining in coal and hard rock have been carried out.
Simulation modelling was used to optimise the underground ore handling at the
Northparkes E26 Mine, and mine planning in the Newcrest Cadia East project (Greberg
and Sundqvist, 2011).
In South America, there are several large copper, iron and bauxite mines in operation
in various countries. Examples of these are the Chuquicamata, Teniente and Escondida
operations in Chile, the Carajas mine of Brazil which operates the largest iron ore open
pit in the world, and the Cerrejon coal mine which operates the largest truck fleet in the
world (Knights and Bonates, 1999). The starting point for the use of discrete even mine
simulation in South America is unclear as there is a lack of adequate scientific or
engineering records. Knight and Bonates reported that several simulations models were
developed in South America in the 1980s. One of the earliest papers relating to
simulation modelling in South America is by Nogueira (1984), which describes the
application of a simulation model to improve truck-shovel operations at the CVRD Mine
in Brazil. The model was designed to assess the best truck/shovel combinations to
determine the capacity of the mine operation. Another model was developed at Codelco
Chile’s Teniente mine using GPSS/H (Sturgul, 1999). The model uses discrete simulation
to simulate a system with continuous state variables. The t-test was performed to test the
simulated results.
Generally, discrete simulation modelling has been used in mine planning and design,
machine selection and the haulage system with the aim of optimising the mine operations
and production throughputs. Early studies focused mainly on limited parts of the mining
process, such as for instance, equipment selection for the development stage, while more
recent studies have aimed to cover more parts of the system and even to simulate a
complete mine.
visualisation of the operations, quality of the output report and graphs for interpretation
(Yuriy and Vayenas, 2008).
SimMine software was selected for this analysis. SimMine is a mining simulation and
evaluation software designed for underground and development modelling with the
ability to import a mine layout. It also has capability to evaluate the design of the
production facilities and the selection of production equipment such as trucks and
loaders. It is based on discrete event simulation principles and uses a full graphical user
interface to set up the model; no coding is required. It utilises statistical distribution
functions to model variations in process times. For validation purposes and to increase
the understanding, the tool has a three dimensional environment which offers animated
visual feedback of the model allowing to view the dynamic system as it operates.
4 Case study
Figure 1 Schematic layout for sub level open stoping method (see online version for colours)
262 A. Salama et al.
The mine uses paste fill which consists of a mixture of granite aggregate, tails, and 2.5%
or 6.5% cement content. The 2.5% recipe are used to backfill stopes in the area where
mining operations will not continue to the level above, while the 6.5% recipe is used
when the mining operations will take place on the level above the stope. The required
strength is 90 kPa for the 2.5% recipe and 350 kPa for the 6.5%. To minimise dilution,
mining of adjacent stopes can start only when the required strength is achieved. In the
mining area considered in this paper (zone A), the major production occurs at mine drifts
below the lowest point of the main shaft. Here, the lowest level of production is about
300 m vertical distance from the shaft’s lowest loading point. Below these levels, mine
development is in progress.
The haulage system is simulated to optimise the number of trucks for the studied mine
production system, to increase the mine output and to evaluate the possibilities to reach
the assigned production targets. Furthermore, order to optimise production a productivity
comparison is also made between two different types of trucks. Truck type one is a
TH430 which has a theoretical capacity of 25–30 tonne. Truck type two is a TH660 with
a payload of 50–55 tonne.
Figure 3 Mine layout of zone A area (see online version for colours)
The LHD tramming distance depends on the length of the production drift. The tramming
distance is defined as the distance from the active face to the loading bay. The cycle time
will be longer for equipment working at the far end of the drift than for equipment in the
middle or near the loading bay. Therefore, the simulation was run separately for the
stopes located at the end, centre, and near the loading point of the drift. The total length
of the haul road includes 800 m ramp, 800 m main level and 100 m cross cuts. To reach
the dumping points, a truck from the lower levels travels from loading points through
cross cuts, ramp and main level, while those from the upper drifts also travel a small
portion of the ramp before entering the main level. To check for the effect of haulage
distance to the dumping point, the simulation was repeated by changing the stope
locations. Figure 4 shows the stopes selected from the top drifts in the first run, the
middle drifts in the second and the bottom drifts in the third. As shown in Figure 4,
stopes located from drifts 1 to 3 are termed as upper drift stopes, those in drifts 3 to 5 are
classified as mid-drift stopes, and those in drifts 5 to 7 are called lower drift stopes. The
simulation was run for three stopes at a time; two stopes were chosen from the same drift
but on opposite sides, and the third was taken from the two drifts down or up for stability
reasons. For example, for the upper drift stopes, if two stopes are chosen from drift 1, the
third will be chosen from drift 3. The simulation was run for a period of 24 days in a
month. During operations cycle, ~6 days not used for loading and hauling due to other
activities such as drilling and backfilling.
The simulation analysis aimed to assess the performance of two different types of haul
units. The comparison was based on amount of ore produced, average machine
utilisations and average traffic. As shown in Figure 5, the simulation was first run on the
stopes located at the upper levels to compare with the real mine case. During this run, the
results shows that the set up with three LHDs and three TH430 trucks (one assigned to
266 A. Salama et al.
each LHD) produces 53% of the planned production. In a real mine case, when
considering TH430 for three trucks served with three LHDs, the amount of ore produced
is 52% which indicates that the simulated result is close to the real operation in the mine.
The simulation was then repeated by increasing number of trucks in each location.
In comparison with both truck types, the amount of ore produced at the end, centre
and near the loading bay seems to be slightly higher for the TH660 than that of TH430
even though the pay load for the TH660 is twice as high as for the TH430. Despite that
trucks in upper levels have less cycle time compared with the ones in lower levels, but it
is noted that the difference in production is not higher due to the fact that trucks working
at upper levels have a longer waiting time at a loading point compared with those
working in lower levels. The waiting time increases when operations are going on at the
far end of the drift. In this case, the LHDs spend more time loading and hauling material
from the face to the loading point because of the longer tramming distance. With four and
five trucks in operation each LHD will serve one predetermined truck, while the extra
trucks will be directed from dispatch to move to the LHD that has no queue.
As depicted in Figure 5 for three trucks in operation, the amount of ore produced of
53% and 60% is achieved when trucks TH430 utilised for 83%, while TH660 should
work for 75% of the available time, respectively. The increased number of trucks leads to
a reduction in average truck utilisation for both truck types. The term utilisation is
defined as the proportional of the available time (expressed as a percentage) that
equipment is operating. As can be seen in Figure 6, trucks TH430 have higher average
utilisations compared with trucks TH660. This is because TH430 has higher speed, less
idle time when waiting for loading, less lost time when meet with each other and
therefore making them to work more time compared with trucks TH660.
Figure 5 Percentage of ore produced for the TH430 and TH660 trucks (see online version
for colours)
The use of discrete event simulation for underground haulage 267
The analysis is also made based on average truck traffic. The term traffic refers to the
percentage of time lost when trucks meet in the haul ways (the main drift and the ramp).
Figure 7 shows that the traffic is minimal when three trucks are in operation, and
increases when more trucks are working. The average traffic is high for trucks TH660
than for trucks TH430. Owing to the long box size of TH660 trucks, a great time
is consumed when waiting to give way to each other, when they meet at the intersection
points between ramp and crosscuts, and when they meet at the corner points.
This indicates that the ramp will be one of the main causes of production delay when
more production drifts are in operation for deeper levels.
It is observed that among all the simulated scenarios, a combination of two trucks and
a single LHD for the upper drifts and three trucks and one LHD for the lower or mid
drifts improves the average production from 52% to 75% of planned production when
TH430 is used, and to 83% when TH660 is used. Reaching a production target of 100%
proves infeasible under the given circumstances, as it during the simulation study was
found that the maximum level of production could neither be attained using the current
haulage system nor when the bigger size truck was used. This result provides the
management with a detailed insight into the future system and help in making decisions
and understanding variety of issues about the behaviour of the system before being
implemented. If it is desired to further increase the simulation model accuracy, collection
of an increased amount of data and correctly fitting them to statistical distributions has to
be performed. To increase analysis efficiency, discrete event simulation can be combined
with economic analysis models to improve understanding of the behaviour of various
systems, and reduce risk when selecting the operational systems.
268 A. Salama et al.
Figure 7 Traffic comparisons of the trucks (see online version for colours)
6 Conclusion
The application of discrete event simulation for comparison of the production rate of two
different types of hauling units has been discussed. Various scenarios for fleet equipment
in terms of production, utilisation and traffic were simulated. The results show
that, among all the simulated scenarios, a combination of 2 trucks and a single LHD
for the upper drifts and 3 trucks and 1 LHD for the lower or mid drifts improves the
average production from 52% to 75% of planned production when the TH430 is used,
and 52–83% when the TH660 is used. This indicates that there is no high impact on
production improvement when TH430 is replaced by TH660 as production will rise only
by 8%. This solution needs to be justified financially as the costs associated with
changing the truck size might not be recuperated by extra production. Reaching a
production target of 100% seems to be infeasible under the given circumstances. Possible
alternative for production improvement could be the additions of another ramp to
minimise truck traffic, extension of the existing shaft or adding another shaft to reduce
hauling distances to the existing shaft point, changing the mine plan and scheduling, or
considering a different haulage method especially when the mine depth is increased.
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PAPER II
Salama, A., Nehring, M. and Greberg, J. (2014). Operating value optimisation using
simulation and mixed integer programming, International Journal of Mining, Reclamation
and Environment, Vol. 28, No. 1, 25-46. doi: 10.1080/17480930.2013.768019
International Journal of Mining, Reclamation and Environment, 2014
Vol. 28, No. 1, 25–46, http://dx.doi.org/10.1080/17480930.2013.768019
Mining operations around the world will increasingly need to operate at greater
depths. This significantly influences the complexity of ore extraction and ore trans-
portation to the surface. The increase in mine depth leads to increases in haulage dis-
tance from mine areas to the mine surface. This results in an increase in energy
costs to haul material further. Due to the increasing cost of future operations, the
choice of the haulage method becomes an important factor in the optimisation of the
mine plan. The haulage process is one of the most energy intensive activities in a
mining operation, and thus, one of the main contributors to energy cost. This paper
presents the comparison of the operating values of the mine plans at depth levels of
1000, 2000 and 3000 m for diesel and electric trucks, shaft and belt conveyor haul-
age systems for the current and a predicted future energy price scenario. The aim is
to analyse the impact of energy requirements associated with each haulage method,
as well as the use of alternative sequencing techniques as mine depth increases. This
study is carried out using a combination of discrete event simulation and mixed
integer programming (MIP) as a tool to improve decision-making in the process of
generating and optimising the mine plans. Results show that energy cost increases
across each haulage method at both current and future energy prices, with increasing
depth. This study thus provides a broad and up to date analysis of the impact on
operating values that may be experienced with the use of the main haulage systems
available at present. Also, the study shows how the combination of discrete event
simulation and MIP generates a good tool for decision support.
Keywords: discrete event simulation; mixed integer programming; deep mining;
haulage energy
1. Introduction
As mining companies rapidly exploit the near surface deposits, the mining frontiers of
the future will be deeper, more remote and more hostile. In addition, mining operations
will face more extreme climatic conditions, and they will occur in unstable ground, with
less water and less energy availability. While these conditions present huge challenges
in themselves, all this will be against a backdrop of more intensive public scrutiny over
environmental issues and community relations. Whether true or not, politicians will
increasingly use public perceptions in policy-making decisions which in Australia has
recently resulted in the introduction of sweeping new taxes on coal and iron ore
producers through the mineral resources rent tax as well as the introduction of a broader
carbon tax in the name of environmental protectionism.
More so now than ever, mining companies must be able to investigate the implica-
tions of the increased cost of energy, water and other resources on their mine plan, and
be able to adapt. One important aspect in being able to adapt is to firstly know what
options are available and how a mine plan may be impacted through their implementa-
tion. With this in mind, this paper presents a case study of an underground ore body
amenable to sub-level stoping. An analysis takes place which compares operating values
of the mine plans generated for the ore-body at depth levels of 1000, 2000 and 3000 m,
using diesel and electric trucks, shafts and conveyors as haulage systems at current, and
three times the current energy prices, using discrete event simulation combined with
mixed integer programming (MIP).
This paper thus investigates and discusses, from an operating value and mine planning
perspective, the implications of mining in an environment of increasing energy costs,
increased environmental scrutiny and the requirement to perform larger scale mining
activity at increasing depths. There is no doubt that this is the reality facing the mining
industry worldwide, and it would appear that much of the mining academic and research
community has also shifted its focus in a large way to reflect this reality. At a recent
research retreat, the division of Mining Engineering at The University of Queensland
decided to form the Centre for Deep Mining for the purpose of focusing its broad research
activities on a central key theme. Another example of this has been the launch of the I2
Mine (Innovative Technologies and Concepts for the Intelligent Deep Mine of the Future)
project by the European Commission involving a consortium of 26 industry and research
organisations from 10 European countries. This project is stated by the funders as mark-
ing the start of a series of activities designed to realise the concept of an invisible, zero-
impact mine and ‘will concentrate on the development of technologies suitable for deep
mining activities [14]. The division of Mining and Geotechnical Engineering at Luleå
University of Technology, Sweden is part of this research project which is one of the
numerous projects aimed at improving mining operations at great depth. This paper pre-
sents the results of a study carried out to realise the stated objective.
2. Haulage systems
The haulage system is one of the most intensive users of energy in a mining operation
and is thus one of the main contributors to the total energy cost. As the number of
underground mines operating at greater depth increases, the haulage method is among
one of the most important factors in optimising mine production. Therefore, hauling ore
from deeper levels needs to be evaluated in order to account for energy costs associated
with hauling options. In this paper, four haulage systems are analysed using discrete
event simulation and MIP to aid the mine planning process.
1960s with significant subsequent efforts to improve productivity and safety. The main
advantages associated with the use of diesel equipment include: flexibility in travel
routes, flexibility in the size of the fleet, absence of electrical hazards, high productivity,
rapid haulage speed, generally good reliability and low operating cost [3]. Disadvan-
tages of these vehicles are the use of flammable fuel, higher capital cost, higher heat
emission, higher noise level and emission of toxic gases and particulates [4]. This study
uses diesel and electric trucks to compare energy consumption at various mine depths.
Both types of trucks were simulated based on similar working conditions. Loading and
hauling properties are described based on information from the manufacturer and data
from mine site. Both truck types are loaded at the storage bin located beneath the
crusher station. During loading and dumping, electric trucks leave the trolley line and
use a diesel driven motor.
K GPH LF
LMPH ¼ ð1Þ
KPL
Where LMPH is the litres used per machine hour, K stands for the kilogramme of fuel
used per brake horsepower per hour, GHP represents the gross engine horsepower at
governed engine revolution per minute, KPL is the weight of fuel in kg/litre and LF is
the load factor in percentage. The load factor is defined as the portion of full power
required by the truck. According to [13], the engine load factors are termed as Low:
20–30%, low load factor, excellent haul road condition, no overloading; Medium: 30–
40%, moderate road factor, good haul road condition, minimal overloading; High: 40–
50%, high load factor, poor haul road condition, overloading. The energy consumption
of the electric truck depends on the engine size, operator efficiency, condition of the
equipment, and was estimated based on a load factor, condition of the equipment and
gross engine horsepower. In modelling, engine load factors of 35% for empty, 50% for
full diesel and electric trucks and diesel oil density of 0.85 kg/l [2] were used.
Shaft hoisting systems are generally equipped with conveyances to transport material
and workers from the underground to the surface. Conveyances are the skips for ore or
waste transportation and cages for transporting workers and other materials which are
suspended by the rope. The hoisting system consists of two types of hoists which are
drum hoist and friction hoist. In drum hoist systems, the rope is stored in a drum, and in
friction hoist systems, the rope passes over the wheel during the hoisting cycle. Friction
hoist conveyance positions are fixed relative to each other with tail rope used to counter
balance the rope loads throughout the hoisting cycle. This requires a lower starting tor-
que and therefore requires a smaller motor to hoist the same load while reducing both
capital and operational cost [9]. In this paper, a friction hoist system with two swing-out
body skips in balance and four flattened-strand ropes is used.
0:7457 Wo V ðta þ tv Þ
E¼ ð2Þ
19:8 105 g2
where E is the power consumption for duty cycle in KWh/trip, Wo is the skip live load,
V stands for the hoisting velocity, ta is the acceleration time, tv is the constant-velocity
time and η is the hoisting efficiency as a decimal.
the system. When working with unfavourable terrain, conventional conveyor systems
have higher flexibility in horizontal and vertical elevations which give a greater varia-
tion of centre to centre distance of the belt, flexible belt speed and belt width [12].
Choice of the type of conveying method depends on production requirement, length,
terrain, environment, geotechnical properties, etc. In this study, a conventional conveyor
is used at different inclination depending on the mine depth. The belt inclination of 20°
was used when mine depth is at 1000 m and at 30° when the mine depth increased to
2000 m and 3000 m. During conveyor system design, the choice of width and speed
will be influenced by the nature of the material to be conveyed, available tunnel space
and the overall economics of the system. An increase in belt speed can permit a reduc-
tion in belt width for mined material to be conveyed [12]. Other factors that need to be
considered in the design include the ability of the belt to conform properly to the trough
formed by the idlers and the effect on the belt of forming the trough. The trough angle
which the conveyor can adopt relative to the horizontal is limited by the tendency of
the material to slide down the belt or to move internally relative to itself [32]. Conveyor
design can be much more complicated and include loading at various points, changes in
slope, downhill sections and multiple drive factors such as the design of idlers and
structure, belt characteristics and the environment can affect the power requirement and
belt tensions.
g C Q ðL þ L0 Þ S
Pec ¼ t ð3Þ
1000
where Pec is the power required to run the empty belt in kilowatt (kW), g is the acceler-
ation due to gravity in m/s2, C is the friction factor, Q is the mass of moving parts of
the conveyor in kg/m, L stands for the distance of incline and decline belt, L0 is the
horizontal centre to centre distance, S is the belt speed and t is the hours where the belt
is in operation. The power required to move the material horizontally over a certain
distance is shown in Equation (4) [11].
30 A. Salama et al.
g C Q ðL þ L0 Þ T
Ph ¼ t ð4Þ
3600
where Ph is the power to move the material horizontally and T stands for the transfer
rate in tons per hour. When the belt is moving material at an inclined section or lower
the material at a decline section, the power consumption can be obtained as shown in
Equation (5) [11].
gT H
Pl ¼ t ð5Þ
3600
where Pl is the power to raise or lower the load and H is the change in elevation, a
positive and negative sign means that the belt is rising up or lowering down the mate-
rial, respectively. The total power consumed by a conveyor belt can be obtained by the
summation of Equations (3)–(5), and can be given as shown in Equation (6) [11].
As it can be seen in the power consumption equations, the power required to run the
empty conveyor is dependent on the speed of the belt. This illustrates that the conveyor
belt is energy efficient when it is running under full load conditions which should be
taken into consideration when the electricity cost of the belt conveyor is investigated.
4. Optimisation in Mining
A lack of tools and software for improved decision-making in underground mine plan-
ning and scheduling in particular has meant that these tasks are largely carried out via
manual processes. Extensive and time consuming evaluation of various options in most
cases will therefore generally be carried out by experienced engineers with sound judge-
ment. Even so, there is no guarantee that the optimal outcome will be achieved. While
a sound feasible solution may be achieved, it is still most likely to be a sub-optimal
outcome. This is especially the case for large and highly constrained operations. The
challenges that exist are both short (tactical) and long term (strategic) in nature and
require careful consideration in order to improve mine performance, increase profitabil-
ity and ultimately make best use of the finite mineral resource.
Optimisation of strategic mine plans for the purpose of maximising net present
value (NPV) using operations research techniques can be categorised into three main
areas [15] including: production schedule optimisation, stoping/pit limit optimisation
and infrastructure placement optimisation. These three core areas themselves incorporate
numerous other sub-factors (cut-off grade policy, mill throughput/recovery relationship,
environmental factors), which are currently largely predetermined or dealt with in a
sequential manner such that the solution for one forms the starting point to solve the
next [23]. While these processes are largely treated as separate individual components
in the overall system, future research must focus on combining these areas into one
common model in order to achieve truly optimal integrated results.
Optimisation of production schedules is considered the most advanced of the
three main areas in mine planning. Numerous works by various authors, [24], [16–
18], [25]. have shown that with clever and efficient modelling, the production sched-
uling problem can be solved for increasingly larger datasets. The increased ability to
solve far more complex problems also allows further integration of other key sub-fac-
tors including key environmental cost factors affecting mine sites such as the con-
sumption of water and energy and release of carbon. The development of further
efficiencies in modelling these complex problems will in time also advance the abil-
ity to integrate the three main areas mentioned above in the development of an inte-
grated and comprehensive mine planning optimisation tool. One recent development
of particular interest has been a MIP model that integrates short- and long-term pro-
duction plans by combining the short-term objective of minimising deviation from
targeted mill feed grade with the long-term objective of maximising NPV into a sin-
gle mathematical optimisation model [22]. The development of short- and long-term
mine production schedules in isolation from each other had previously meant that
only a local optimum could be achieved when each scheduling phase is carried out.
The globally optimal solution, however, can be achieved when integrating scheduling
phases and accounting for the interaction between short-term and long-term activities
simultaneously.
Another recent development of interest is an integrated production scheduling and
stope boundary optimisation model for underground sub-level stoping operations [20].
This model, based on MIP, takes the very first steps in generating the globally optimal
integrated production schedule/stoping boundary definition problem for the purpose of
maximising NPV. As acknowledged by the author of this research, this model still has
many improvements to be made and ultimately needs to also incorporate infrastructure
placement in order to integrate and capture all three key areas simultaneously.
32 A. Salama et al.
5. Case Study
A case study on an underground ore-body amenable to sub-level stoping is used for the
purpose of investigating the impact of various operational scenarios on operating value.
The scenarios being investigated include mining of the ore-body at various depths using
a number of haulage options across various energy prices. While some data for this
particular case study are conceptual in nature, it is, however, based on real operational
scenarios with stope tonnages, grades, resource limitations and sequencing interactions
reflective of real sub-level stoping operations, thus making it useful for investigation
purposes. The setting of this mine is a typical remote mining region within Australia.
As such, all figures are quoted in Australian Dollars (AUD).
Present values in this case will solely be based on the operating cash flows gener-
ated by each scenario whereby the operating costs (OPEX) are subtracted from the
operating revenues generated by each scenario. Capital costs (CAPEX) required to
implement each scenario in this case are outside the scope of this investigation, and are
therefore not included. The operation under investigation extracts copper bearing ore
from an ore-body striking east-west and dipping at 70 to 75° in the southerly direction.
For the purposes of this investigation, the exact same ore-body will be mined at three
underground depth levels including:
(1) 1000 m,
(2) 2000 m and
(3) 3000 m.
For each depth level, four haulage options will be investigated. Each haulage sce-
nario will take effect from just below the crushing horizon which will be located at
each of the three depth levels under investigation. As such, all hauled ore will have
already undertaken a primary crush via the underground crushing station. The method
of loading and haulage of ore to transport it from the drawpoint of each stope to the
crusher will be carried out via LHD unit which will be the same for each haulage
option across each depth level. The four haulage options under consideration are:
International Journal of Mining, Reclamation and Environment 33
Personnel and machinery access for both trucking options will be via the same
decline on which trucks will be operating. A separate decline will be used for personnel
and machinery for the vertical shaft and conveyor haulage option. For each depth level
across each haulage, option two energy prices will be used to evaluate its impact on
operating value as follows:
In order to maintain consistency in the evaluation process, the same ore-body will
be evaluated at each of the three depth levels across each haulage and energy price sce-
nario. A sub-level stoping method is used to fully exploit the ore-body in all scenarios.
The sub-level stoping method is generally modelled according to four phases. This gen-
erally starts with internal development, followed by production drilling, followed by
extraction and finally the backfilling and consolidation phase. In this case, it is assumed
that all external development activities required to access all areas of the ore-body have
been completed. This thus leaves each stope available to commence production from
the first time period with the internal development phase. The ore-body at all three
depth levels is at the same stage of production with 3.4 Mt already having been mined
from a total initial reserve of 20 Mt grading 2.19% Cu for 438,375 tons of Cu metal.
The remaining reserve in each case is 16.2 Mt, which will vary slightly in grade
between each of the three depth levels depending on which stopes have been removed.
The targeted total production rate for this operation is 100,000 tons per month or
1.2 Mtpa. At these production rates, this operation is therefore expected to have a
remaining mine life of 13.5 years.
The differing operating conditions that are required as a result of increased stress
due to increased depth is reflected in altered stope size and sequencing. Optimised pro-
duction scheduling in each case will therefore incorporate and continue on from the
existing schedule by including stopes that are already in production, and by continuing
to adhere to particular stress management sequencing constraints. Figures 1 and 2 show
the plan views of the ore-body being investigated at the 1000 and 2000 m depth levels.
A total of 100 equally sized stopes using the maximum allowable size of
25 m 25 m 100 m in order to maintain geotechnical stability were required to fully
exploit the ore-body at the 1000 and 2000 m depth levels as depicted in Figures 1 and
2. Each stope in both cases contains 200,000 tons of ore grading between 1.80% Cu
and 2.6% Cu. Of the initial 100 stopes, 17 have already completed the entire production
process to become a fully consolidated fillmass (green). A total of five stopes (blue) are
currently in some phase of production. This therefore leaves the remaining 78 stopes
available for the commencement of production with the internal development phase.
Stoping conditions at a depth of 1000 m are generally good with stresses able to be well
managed using standard bolting practises for both the roof and walls. This, therefore,
allows an open sequencing regime to be used. Stoping conditions at the 2000 m depth
level are such that the implementation of the stress shadowing sequence due to high
34 A. Salama et al.
stresses that run in the north-south direction is required. This involves the extraction of
an initial slot perpendicular to the principle stress resulting in a redistribution of stresses
around the slot causing stopes on either side to be partly shadowed from the stress.
Stopes are then sequentially mined out from this slot toward the outer limits of the ore-
body. To allow for greater scheduling alternatives later in the mine’s life, the initial slot
is placed centrally within the ore-body to gain the greatest effect from the shadowing
process over as many stopes as possible. Each stope in both the 1000 and 2000 m sce-
nario requires a total of 10 months to fully complete production. This starts with one
month of internal development, followed by one month of production drilling, followed
by six months of extraction and finally two months of backfilling and consolidation.
The six month extraction phase draws 25,000t, 25,000t, 50,000t, 50,000t, 25,000t and
25,000t of ore from months three through to eight, respectively.
International Journal of Mining, Reclamation and Environment 35
A total of 200 equally sized stopes using the maximum allowable size of
25 m 12.5 m 100 m (half the size of stopes at the 1000 and 2000 m level) in order
to maintain geotechnical stability were required to fully exploit the ore-body at the
3000 m depth level as depicted in Figure 3 subject to the implementation of the stress
shadowing sequence (as described earlier) due to extreme stresses that run in the north-
south direction. Each stope in this case contains 100,000 tons of ore grading between
1.80% Cu and 2.6% Cu. Of the initial 200 stopes, 34 have already completed the entire
production process to become a fully consolidated fillmass (green). A total of 10 stopes
(blue) are currently in some phase of production. This therefore leaves the remaining
156 stopes available for the commencement of production with the internal develop-
ment phase. Each stope in this case requires a total of eight months to fully complete
production. This starts with one month of internal development, followed by one month
of production drilling, followed by four months of extraction and finally two months of
backfilling and consolidation. The four month extraction phase draws 16,666t, 33,333t,
33,333t and 16,666t of ore for months three through to six, respectively.
Long-term production scheduling will be carried out at monthly intervals over the
life of the operation. A copper price of $5000/t is used and a discount rate of 10% pa
is applied. An operating cost per tonne of ore ($/t) is estimated for each scenario. These
estimations were carried out by analysing simulation results and adjusting and extrapo-
lating a set of actual operating costs. The total operating costs (OPEX), the operating
cost from haulage options (Haulage OPEX) and the costs from other operations (OPEX
Ex. Haulage) are presented in Tables 1 and 2 for the current and three times energy
prices, respectively.
These operating costs are subtracted from the operating revenues to calculate the
undiscounted cash flows associated with the extraction phase of each stope which in
turn forms the basis for the production scheduling optimisation process. The only
resource constraint that is applicable in this case is related to the targeted ore tonnage
to be produced from the operation. Monthly production is therefore limited to be less
than or equal to 100,000 tons. The main sequencing constraints typically associated
with sub-level stoping which are also applicable in this case are:
The other constraint which will require compliance relates to the implementation of
the stress shadowing sequence for the 2000 and 3000 m depth levels. This therefore
International Journal of Mining, Reclamation and Environment 37
limits when stopes can enter production due to the respective stope on the outer side of
each stope needing to be mined first.
(1) Simulation will be used to aid in determining the expected operating costs asso-
ciated with each haulage option at each depth level across energy price scenario.
GPSS/H was used for all simulation.
(2) Once costs have been established, these will be used to calculate operating cash
flows associated with each stope. A MIP production scheduling model which is
solved using CPLEX will then be used to carry out optimised production sched-
uling in order to generate an operating NPV for each scenario.
Figure 4. Part of GPSS/H simulation programme for diesel and electric trucks.
integer and the floating point data, and can be read using The GETLIST statement and
the BGETLIST blocks. Blocks describe how a transaction moves through the system
and is processed. A value to the block is assigned by BLET, LET and SAVEVALUE
blocks. Several other GPSS/H blocks were used during modelling. In GPSS/H, there
are over 50 different types of blocks available which can be used to model complex
problems [27]. Complete programming codes were created and the simulation output
was generated. Part of the GPSS/H simulation programme for diesel and electric trucks
is shown in Figure 4. The system was simulated for a month which consists of seven
working days for two shifts of 10 h in each day.
Subscript notation. The model is defined in general terms using the following subscript
notation.
t, long-term schedule time period: t = 1, 2, 3… T.
s, long-term stope identification: s = 1, 2, 3… S.
f, fillmass identification: f = 1, 2, 3… F.
International Journal of Mining, Reclamation and Environment 39
Sets. Several sets are defined which aid in the formulation of constraints.
βs, set of eligible long-term time periods in which stopes can be in production.
βt, set of eligible stopes that can be in production in long-term time period t.
adjs, set of all stopes that are adjacent to and share a boundary with stopes.
badjf, set of all stopes that are adjacent to and share a boundary with each existing
fillmass f.
tpbt, set of time periods that include all periods up to the current period t.
Parameters. These parameter items represent the numeric inputs and conditions.
nt, present value discount factor for time period t.
cfs, undiscounted cashflow ($) from each stopes.
es, earliest start time for stopes.
ls, latest start time for stopes.
rs, extraction reserve (t) for each stopes.
sct, shaft/LHD/truck fleet movement capacity (t) for each time period t.
Decision variables. One binary variable was required to reflect operating conditions and
ultimately perform the scheduling task.
wst, 1, if production from stopes is scheduled for time period t,
0 otherwise.
Objective function. The objective function seeks to maximise the NPV of all activities
under consideration by determining the optimal schedule within which to progress each
stope through production.
X
Max : nt cfs wst ð7Þ
s;t
It should be noted that taxation and depreciation are not included in this formula-
tion. However, these should be incorporated if necessary.
Constraint (8) limits production of all development and stope extraction ore from
exceeding the shaft/LHD/truck fleet capacity in any long-term time period. Constraint
(9) enforces non-negativity and integer values of the appropriate variables.
40 A. Salama et al.
All proceeding production sequencing between stopes are also enforced by con-
straints (10) and (11). Constraint (12) ensures that simultaneous production between
stopes that share a common boundary does not occur. Constraint (13) provides some
geotechnical stability to stoping activities by limiting simultaneous adjacent production
to two common boundaries before itself commencing production, and to a single
adjacent side once having completed production to become a fillmass. Constraint (14)
ensures fillmass stability of all existing fillmasses by limiting exposure to a single
common boundary in each long term time period.
Timing constraints. The following formulations display the mathematical timing con-
straints that are applicable across the long-term horizon.
May mine constraint
X
wst 6 1 8sjls[T ð15Þ
t2bs
Diesel truck
Electric truck
Shaft
Conveyor
Depth (meters)
the costs and parameters mentioned earlier, and they were then solved using CPLEX
version 10.3. The solution process for each of the 24 scenarios was left to run for
approximately 10 h and was cut short even if convergence to the optimal solution had
Operating NPV Comparison Between Main Haulage Methods at
Operating NPV ($M) Increasing Depth at Three Times Current Energy Prices
Diesel truck
Electric truck
Shaft
Conveyor
Depth (meters)
90% 90%
80% 80%
70% 70%
60% 60%
50% 50%
40% 40%
30% 30%
20% 20%
10% 10%
0% 0%
Diesel Truck (1000m)
Diesel Truck (2000m)
Diesel Truck (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Shaft (1000m)
Shaft (2000m)
Shaft (3000m)
Conveyor (1000m)
Conveyor (2000m)
Conveyor (3000m)
Figure 7. Energy and non-energy cost components of the operating cost as a percentage of total
operating costs at current and three times current energy prices.
International Journal of Mining, Reclamation and Environment 43
not yet been achieved. In all cases, however, a gap of less than 5% was achieved. Pro-
duction scheduling took place at monthly intervals and was limited to 180 periods
(15 years). In some cases, especially in the open sequencing regime at the 1000 m level,
full extraction was completed earlier than the 180 month limit, while in the highly con-
strained cases, this did not result in the full extraction of all stopes.
The operating NPVs that were achieved from each of the 24 scenarios are shown in
Figures 5 and 6. As shown, the operating costs for diesel trucks together with increas-
ing sequencing constraints with increasing depth, result in lower operating NPVs and
an unfeasible operation at current and three times current energy prices compared to
electric truck, shaft and conveyor belt haulage systems for all depth levels. While diesel
truck haulage generally offers greater operational flexibility, its high energy intensity
results in a rapid reduction in its financial viability with increasing depth. Regardless of
the haulage option being deployed, an analysis and extrapolation of these results would
indicate a break-even operating cost of about $115.0/t, $112.0/t and $103.0/t for the
current energy prices and $105.0/t, $98.0/t and $84.0/t for three times current energy
prices at 1000, 2000 and 3000 m depths, respectively.
It is worthwhile analysing the energy cost component of the operating cost as a per-
centage of the total operating cost of each haulage method and how these change with
increasing depth. Figure 7 shows the energy and non-energy cost components of the
operating cost as a percentage of the total operating cost at current and three times
Figure 8. Energy and non-energy cost components of the haulage cost as a percentage of total
haulage costs at current and three times current energy prices.
44 A. Salama et al.
current energy prices. As expected, energy costs increase with increasing depth for both
energy prices scenarios. As shown in Figure 7, the energy cost for diesel trucks is
observed to have higher increase for both energy prices at the 1000, 2000 and 3000 m
depth levels, respectively, compared to other haulage options. The lowest energy cost
component increase is observed to be for the shaft haulage system.
Since it is recognised that the ore haulage process is one of the most energy inten-
sive activities in a mining operation and is thus one of main contributors to operating
cost; it is therefore appropriate to analyse the energy cost component of the haulage
cost as a percentage of the total haulage cost as shown in Figure 8. Across all cases,
the results show an increasing trend with depth in the energy cost with greater increases
for the diesel truck, and lower increases for shaft haulage at the 1000, 2000 and 3000 m
depth levels for both energy prices scenarios.
An analysis of these results clearly shows that in an era of increasing energy prices
and the increased need to mine at greater depths, only those haulage methods with
lower energy requirements will remain viable. The implementation of lower energy
intensive haulage methods often means a greater initial capital cost is required. In addi-
tion to this, they generally offer less flexibility. This in turn makes the mine planning
process with the aid of simulation and MIP to help guide decision-making and make it
all the more important.
7. Conclusions
Energy cost is one of the largest components of the operating costs in underground
mining operations. Haulage methods which contribute low energy costs will be of great
value to mining operations. The methodology presented in this paper combines discrete
event simulation and MIP in analysing the operating values of the mine plans using var-
ious energy cost at increasing depth. The operating costs were validated after simulation
of four haulage options and were used to obtain the cash flows associated with each
stope for input into the MIP. A relationship was established showing how energy costs
increase with increasing mine depth for both current and three times energy prices. It
was shown that the increase in energy cost associated with diesel truck is substantially
higher compared to other haulage options. The investigation provides mining operations
with a preliminary assessment of the energy costs associated with various haulage meth-
ods as mine depth increases for the purpose of aiding the decision-making process in
regard to future deeper underground mining. Deposits are analysed by using metal
grades to establish revenues with each resource block based on an assumed metal price.
Uncertainties associated with metal prices and grade block model will occur over the
life of any operation. This leads to a new block value which results in generating a new
mine plan. The uncertainty related to metal price and grade was not included in this
study. Future work may therefore involve conditional simulation to measure the sensi-
tivity to some of these uncertainties.
Acknowledgements
The authors would like to acknowledge the efforts of personnel from the Division of Mining and
Geotechnical Engineering at Luleå University of Technology, and the School of Mechanical and
Mining Engineering at The University of Queensland whose collaborating efforts made this
project possible. Also the authors would like to thank I2Mine project within the EU 7th
framework programme for funding parts of the work.
International Journal of Mining, Reclamation and Environment 45
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PAPER III
Salama, A., Nehring, M., Greberg, J., and Schunnesson, H. (2014). Evaluation of the impact
of commodity price change on the mine plan of underground mining, Accepted for
publication in International Journal of Mining Science and Technology.
Evaluation of the impact of commodity price change on mine plan of underground
mining
a
Division of Mining and Geotechnical Engineering, Department of Civil, Mining and
Environmental Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden;
b
School of Mechanical and Mining Engineering, The University of Queensland, St Lucia,
QLD, Australia, 4072
Abstract
The fluctuations in commodity prices influences mining operations to continually update and
adjust their mine plans in order to capture additional value under the new market condition.
Some of the adjustments could include changes to the production sequencing, changes to the
point at which the open pit transitions to the underground, and the time for changing or
modifying the existing ore handling systems as a result of an increase in mine depth. This
paper seeks to present a method for quantifying the net present value component of optimal
mine plans that may be directly attributed to the change in commodity prices. The evaluation
is conducted on an underground copper deposit whereby optimal mine plans were generated
across a total of ten copper price scenarios ranging between $5250/t Cu and $9750/t Cu.
Discrete event simulation combined with mixed integer programming was used to attain a
viable production strategy and to generate optimal mine plans. The analysis indicates that the
increase in prices results in an increase in net present value from $96.57M to ultimately reach
$755.65M. In an environment where mining operations must be looking to gain as much
value as possible from the rights to exploiting a finite resource, it is simply not appropriate to
keep operating under the same mine plan if commodity prices have altered during the course
of operation.
1
1. Introduction
Mine planners traditionally plan and design mine production at a fixed commodity price
(at least a commodity price that does not change too rapidly). Most of the feasibility studies
on undeveloped copper projects conducted over recent years generally uses a price range
between $5000/t and $5500/t over the long term even though the copper price at the time of
the studies was about $7500/t Cu. The constant fluctuations in commodity prices should be
influencing mining operations to continually change and adjust their mine plans in order to
capture additional value to the business. Unfortunately in most cases, a change in the
commodity price often does not prompt a revaluation of the mine plan and the plan that was
generated at the feasibility stage continues to be used. This means that while the profitability
of an operation may increase with an increase in commodity price, it is not gaining the full
additional value that it could be if the mine plan is not re-evaluated. Some of the adjustments
could include changes to the production sequencing of a particular pushback, changes to the
point at which the open pit transitions to the underground operation, and the appropriate time
for changing or modifying the existing ore handling systems as a result of an increase in mine
depth.
2. Background
The ore handling systems for most underground hard rock mining operations have
historically focused on shaft haulage, trucks, and conveyors [9]. These systems contain other
ore-handling components such as Load-Haul-Dump (LHD) machines, ore passes, and
crushers. The availability of other haulage options such as monorail systems, electric units,
and rail transportation, makes the decision on the selection of the ore handling system vital
towards the cost reduction and improved mining rate. Shaft and conveyor systems can be
inflexible because of the limited number of fixed feed points, diesel truck systems are flexible
because they can travel to most locations in the underground mine but they are characterized
by higher energy consumption and higher emissions. Ore passes are used in conjunction with
other haulage systems such as shaft or haul trucks. Ore passes transportation systems are
flexible depending on the level of production and can also serve as ore storage in the mine [1].
Prior to designing an ore pass system it is essential to examine the ore handling system of the
entire mine from the production areas to the shaft points [15]. Monorail systems are used to
transport material on a widely branched rail system over long distance. This system is
independent of the quality of the floor since it is mounted from the roof which allows
flexibility of trackless arrangements [10]. Electric units offer less emissions, although more
infrastructures may be required which limit the flexibility of some other operations. Because
mines typically evolve over time, the ability of a mine to vary its operating strategy in order to
optimize production in response to commodity price changes can often be a function of the
optionality embedded within the ore-handling system. A short term change in commodity
price will only add as much value as provided by the increased margin associated with the
new price [7]. However if the price change is longer term in nature, then the mine plan should
be altered in order to fully capture the additional value that is offered under the new market
conditions.
2
In this study, LHD machines are used to load and haul ore from two different ore bodies
and dump to two different ore passes located 250m from each ore body. The materials
dumped into each ore pass falls under gravity to the lower level where it is then taken to the
shaft loading facility. The aim is to quantify the net present value (NPV) component that can
be directly attributed to the change of the mine plan generated across a total of ten copper
price scenarios ranging between $5250/t Cu and $9750/t Cu. Simulation was firstly used to
attain the number of LHD machines required to haul 300,000 tonnes of ore from each
orebody. This in turn provided the basis from which to compute appropriate mining costs for
the operation. Mixed integer programming (MIP) was then used to generate the optimal
production schedule and mine plan at each commodity price scenario.
Fig.1 shows copper prices over a twenty year period from 1993 to 2013. As shown,
copper was trading at $US1647/t in October 1993 and then raising and falling until reaches a
price of $US10000/t in February 2011. Since then a gradual decline in the copper price has
resulted in a current price of $US7159/t. Thus this study focuses on evaluating the changes of
the optimal mine plan at a range of copper prices starting at $5250 increments by $500 until
$9750 is reached. The mine operation involves the material transportation by LHD machines
from the draw points to ore passes: The material is then hoisted to the mine surface through
shafts. Other haulage methods can be considered in order to evaluate the changes on the NPV
of the mine plan. However, the evaluation and analysis of these possible methods are out of
scope of this study.
3
2.2. Simulation
Discrete event simulation is increasingly gaining attention as one of the tools used to
predict and evaluate the performance of mining systems. It has been used for various
applications such as fleet optimization in underground mining, comparison of timing and
efficiency between drills, mine to mill production systems, and maintenance scheduling [12].
Most simulation tools are equipped with graphics, animations, and capability to import
information from other software such as computer aided design and spreadsheets. Also, they
include debugging and error diagnostics which make simulation feasible to use when
analyzing complex operations like mining operations [14]. Simulation involves the generation
of a model to represent a real operating system. Data used in the model creation can be
statistically analyzed and fitted into various probabilistic distributions to increase the
understanding of the behavior of the operated system. The model verification is done by
transforming the conceptual model to a real model through testing the model logic, making
flowcharts of the simulated model, and running the model under varying conditions.
Validation is then performed to compare the simulation output with real system characteristics
to ensure that the model is sufficiently accurate. In this study, the General Purpose Simulation
System/Henrikson (GPSS/H) was used to evaluate the performance of the orepass system.
The simulation analysis considered the operational cycle from the working faces where LHDs
are used to load material from the working faces and dump them to ore passes.
The use of rigorous and heuristic Operations Research (OR) techniques such Mixed
Integer Programming (MIP) and Genetic Algorithms (GA) have long been used to model and
solve numerous mining related problems. The largest and most prevalent of these problems
has arguably been the mine planning and production scheduling problem in both the open pit
and underground mine environment. Numerous authors have advanced the state of the art on
the broad topic of optimization in mining. [5] Use stochastic integer programming to provide
a framework for optimizing mine production schedules considering uncertainty with a focus
on geologic risk. For gold and copper deposit the authors claim to have increased the NPV of
the production schedule using the stochastic integer programming approach by 10 and 25%
respectively over traditional single fixed orebody estimate. [6] Solve the relaxation of a tight
linear formulation to address the problem of optimizing underground and open-pit ore
deposits sharing multiple downstream processing plants over a long-term planning horizon.
Since its application at Codelco operations since 2001 the NPV of single mine production
4
plans are stated as increasing by 5% with an additional 3% increase occurring when
integrating multiple mines. [7] Aggregate time periods as part of a heuristic approach in order
to provide basic solutions to the iron ore blending problem at Kiirunavaara underground iron
mine. The results generated under the heuristic approach are then used as input to solve a
rigorous integer programming model to produce good quality solutions in a much shorter
time. [8] Use simulation and mixed integer programming to investigate the impact of a
changing energy price on underground mining operations across multiple depths using a
number of primary ore haulage options including conveyor, shaft hoist as well as diesel and
electric trucks. For the particular case study that was used their findings indicate that shaft and
conveyor haulage systems are most beneficial at increased energy prices.
3. Case study
A case study on an underground orebody amenable to sublevel stoping is used for the
purpose of investigating the change in NPV that can be attributed to a new mine plan when it
is revised to take into account an amended commodity price. While some data for this
particular case study is conceptual in nature, it is however based on real operational scenarios
with stope tonnages, grades, resource limitations and sequencing interactions reflective of real
sublevel stoping operations, thus making it useful for investigation purposes. The setting of
this mine is a typical remote mining region within Australia. As such, all figures are quoted in
Australian Dollars (AUD). The value that can be attributed to each stope in this case will
solely be based on the operating cash flows that are generated whereby the operating costs are
subtracted from the operating revenues associated with each scenario. Capital costs are
outside the scope of this investigation and are therefore not included. The operation under
investigation extracts copper bearing ore from a deep underground mine orebodies striking
east-west and dipping at 70 to 75 degrees in the southerly direction.
Sublevel stoping production is modelled according to 4 phases. This generally starts with
internal development, followed by production drilling, followed by extraction and finally the
backfilling and consolidation phase which makes each stope to fully complete production for
nine months. In this case, it is assumed that all external development activities required to
access all areas of the orebody have been completed. This thus leaves all stopes within both
orebodies available to commence production from the first time period with the internal
development phase. No prior production of any kind has yet taken place from any stope.
Overall reserves are calculated to be 15 Mt at an average grade of 2.50% Cu for 375,000
tonne of copper metal. The steady state production rate for this operation is 450,000 tonne per
quarter, or 1.8Mtpa. At these production rates, this operation is therefore expected to have a
mine life of at least 8.5 years, or 34 quarters. The production capacity for each orebody is
300,000 tonne per quarter. Production scheduling will incorporate all stopes from two
orebodies in order to generate a life of mine plan at quarterly intervals. Fig. 2 shows the plan
view of the operation being investigated (with stope numbers indicated). The operation
comprises of two orebodies containing 50 equally sized stopes each at the maximum
allowable size of 25m x 25m x 100m in order to maintain geotechnical stability. Each stope
contains 150,000 tonnes of ore. The Western orebody is considered low grade with average
5
grade of 1.20% Cu. The Eastern orebody however is high grade with average grade of 3.80%
Cu.
In order to determine if the production capacity of 300,000 tonne from each orebody is
feasible and to then determine an appropriate operating cost, the size and number of LHD
units to achieve this is required. This then allows the calculation of discounted cash flows
generated by each stope across all ten copper prices which in turn enables production
scheduling optimization to take place to achieve the optimal NPV.
Stoping conditions at this depth within the Western orebody are considered reasonable
with stresses able to be well managed using standard bolting practises for both the roof and
walls. This allows an open sequencing regime to be used within this orebody. Stoping
conditions in the Eastern orebody are significantly poorer and thus require additional ground
support at a significantly increased cost in order to maintain an open sequencing regime
within this orebody. Long term production scheduling will be carried out at quarterly intervals
over the life of the operation for a number of copper price scenarios. Due to the perceived
risks associated with this project a discount rate of 25% per annum is applied. For the purpose
of this study, LHDs are used to load and haul ore from eastern and western ore bodies at
stockpile bays and dump to two different ore passes located at 250m from each orebody. The
LHDs from eastern orebody are dumping material to an eastern ore pass, and those from the
western orebody dumps into the western ore pass. Materials are collected in the chutes on the
lower levels of the ore passes and are further transported to the shaft point. Both ore passes
comprises of two sections of different length and are inclined at 70º in the west direction of
the orebodies. The ore pass has diameter of 3.2m and the dimension of grizzly bars is 0.94m
by 1.6m.
6
4. Model Formulation
The system consists of discrete event simulation and mixed integer programming models.
The simulation model involves hauling the mined material by LHDs and moving it into ore
passes where the materials drops to the lower level and then is taken to the shaft point. A
GPSS/H was used in determining the number of LHDs required to move the planned amount
of tonnes. The simulation results were then used to calculate operating cash flows associated
with each stope using Mixed Integer Programming (MIP). The MIP model was created using
a Mathematical Programming Language (AMPL) and then solved using CPLEX and the
results are then used to carry out optimised production scheduling in order to generate an
operating NPV for each commodity price.
7
Fig. 3. Part of GPSS/H simulation program codes
x The amount of ore in a bucket was assumed to follow normal distribution with a
standard deviation of 10% of the mean load. The bucket fill factor was
assumed as 95%
x During simulation it was assumed that there is no machine failure. This is
because no reliability data was available.
8
pass structures. Initial results allow these parameters to be redefined and radically changed.
The changes involve extra programming but enhance the versatility of the program to
conform with proposed mine logistics. Input data are examined and then fitted to probabilistic
distributions before being applied to the software. The loading and dumping times were
observed to follow exponential and uniform distributions respectively, while travelling times
follow normal distribution as shown in Table 1. These data were obtained from a remote
mining region within Australia. The validation was done using internal validity system where
the reaction of the model was checked due to variation of the random numbers.
The model is defined in general terms using the following subscript notation.
4.2.2. Sets
ȕs set of eligible long term time periods in which stope s can commence production
(between es to ls).
ȕt set of eligible stopes that can be in production in long term time period t.
adjs set of all stopes that are adjacent to and share a boundary with stope s.
tpbt set of time periods that include all periods up to the current period t.
4.2.3. Parameters
One binary variable was required to reflect operating conditions and ultimately perform
the scheduling task.
The objective function (1) seeks to maximize the NPV of all activities under
consideration by determining the optimal schedule within which to progress each stope
through production.
It should be noted that taxation and depreciation are not included in this formulation however
should be incorporated if necessary.
4.2.6. Constraints
The production scheduling model comprises numerous constraints which reflect the
practical limitations imposed by the sublevel stoping method over the long term scheduling
horizon. These constraints can be classified according to the limitations they impose on
resources, sequencing and timing.
The following formulations display the mathematical resource constraints that are
applicable across the long term horizon.
¦r * w
sE t
s st d SCt t (2)
10
Constraint (2) limits production of stope ore extraction from exceeding the shaft/LHD/truck
fleet capacity for the overall mining operation or a specific part including a particular orebody
in any long term time period. Constraint (3) enforces non-negativity and integer values of the
appropriate variables.
The following formulations display the mathematical sequencing constraints that are
applicable across the long term horizon.
¦w
t 'tpbt
st ' ¦ ws' t d 2
s 'adj s
s, t (5)
Constraint (4) ensures that simultaneous production between stopes that share a common
boundary does not occur. Constraint (5) provides some geotechnical stability to stoping
activities by limiting simultaneous adjacent production to two common boundaries before
itself commencing production, and to a single adjacent side once having completed
production to become a fillmass.
The following formulations display the mathematical timing constraints that are
applicable across the long term horizon.
May mine constraint
¦w
t E s
st d1 s / ls ! T (6)
Constraint (6) ensures that commencement of stope production is initiated no more than once
during the long term scheduling horizon if their late start date occurs beyond the scheduling
horizon. Constraint (7) requires stope production commences at some point during the long
term scheduling horizon if their late start date falls within the long term scheduling horizon.
The simulation analysis was firstly carried out to provide data relating to the equipment
type and number of units required to meet the predetermined production targets. The obtained
number of LHD units was used to establish the mine cost per tonne which in turn, provide the
input for the mixed integer programming computation.
11
5.1. Simulation results and discussion
The simulation analysis aiming to assess the number of LHD machines to haul 300,000
tonne of ore for a period of three months was performed. The simulation was first run for the
Western orebody and the results are shown in Fig. 4. It shows that, when a single LHD is in
operation, the amount of ore produced is 129,000 tonnes and that the LHD machines are
achieving full utilization. The term utilization is defined as the proportion of the available
working time (expressed as a percentage) that equipment is operating. During model
development, input data was coded to allow for the interactive input of various variables at
the start of the simulation run. The number of LHDs were then increased and revealed that the
production target of 300,000 tonnes of ore was achieved when three LHDs are working on the
production stopes. At this production rate, the average machine utilization was 89%. This
indicates that 11% of the working time is lost due to the queuing of LHDs at the loading and
dumping points. As depicted in Fig. 4, with three LHDs working, the amount of ore hauled is
around 344,000 tonnes which is more than the production target of 300,000 tonne. As stated
earlier that the maintenance and repair were not included during analysis which may result
into lower production than the one obtained in the simulation runs.
The simulation was then run for the Eastern orebody and similar trend as western deposit
were observed. The results from both deposits were used to to compute appropriate mining
costs for the operation. The MIP was then used to generate the optimal production schedule
and mine plan at each commodity price scenario and the results shown in Fig. 5.
Construction of all Mixed Integer Programming (MIP) models for the purpose of optimal
production scheduling (maximizing NPV) took place using A Mathematical Programming
Language (AMPL). Based on the mine costs obtained from the simulation results, the
12
undiscounted cash flows associated with the extraction phase were computed for each stope.
These cash flows form the basis from which the mixed integer programming model is used to
generate optimal production schedule and mine plan at each commodity price scenario. The
computation was solved using CPLEX 10.3. The solution process for each of the 10 price
scenarios being evaluated were left to run over night (approximately 8 hours) and was cut
short even if convergence to the optimal solution had not yet been achieved. In all cases
however, a gap of less than 3.00% was achieved (this refers to the value from the potential
optimal solution). It was determined that a range of copper prices, starting at $5250,
increments by $500 until $9750 is reached will be used to investigate the impact of a
changing commodity price on the mine plan. As mentioned earlier, at the peak of the copper
price boom of 2011, copper prices almost reached $10000/t and thus the final price to be
investigated for mine planning purposes will be $9750/t Cu to reflect this.
Production scheduling took place at quarterly intervals and was limited to 60 periods (15
years). Under each price scenario, full extraction from both orebodies was completed within
the 60 quarter limit. Full extraction was expected since the respective cut-off grades for the
lowest copper price of $5250/t Cu in each case can be calculated to be 0.89% Cu and 3.55%
Cu. The lowest grade stope contained 0.96% Cu and 3.56% Cu for the Western and Eastern
orebodies respectively. The operating NPVs that were achieved from each of the 10 copper
price scenarios are shown in Fig. 5. As expected, the $5250/t copper price produced the
lowest NPV of $96.57M. This climbs with each incremental $500/t rise in the price of copper
to ultimately reach $755.65M at the final copper price of $9750/t.
Fig. 5. NPV comparison of optimal mine plans across various copper price scenarios.
Further analysis then took place to see changes in the commencement period in the
optimal mine plan of each stope as the copper price changes. Table 2 presents the quarter in
which each stope within each orebody commences its three quarter production phase at
copper prices of $5250/t, $6260/t, $7750/t, $8750/t and $9750/t respectively. Table 2 shows
that, there are fluctuations in the commencement period for each stope under each price
13
scenario. For example, Stope H236 in the Western orebody is selected for production in the
9th quarter at the $5250/t copper price scenario. The same stope is then selected for the 28th,
31st, 14th and 22nd quarter at the $6250/t, $7750/t, $8750/t and $9750/t copper price scenarios
respectively. It seen that, Stope N247 in the Eastern orebody is the only stope that maintains
the same commencement quarter across all selected scenarios.
14
It was then analyzed to determine the average commencement quarter for stopes
contained in the Western and Eastern orebodies across each copper price scenario. As shown,
the average commencement quarter at the copper price of $5250/t is 17.50 and 17.52 for
stopes in the Western and Eastern orebodies respectively. This means that stopes in the
Western orebody are slightly favored over stopes in the Eastern orebody at this price. With
each subsequent price increase the average commencement period for stopes in the Western
orebody shows an increasing trend while those of Eastern orebody show a decreasing trend.
Stopes in the Western orebody have lower grade and lower cost, and stopes in the Eastern
orebody have higher grade and higher cost. This evident that as the copper price increases the
higher grade and higher cost stopes are favored to a greater extent.
It was also evaluated by comparing the changes of the value of the optimal mine plans
with the value of mine plan from the base case scenario at each price scenarios. The base case
scenario is the optimal mine plan value generated at a copper price of $5250/t. As shown in
Table 3, when the copper price increases from $5250/t to $5750/t, the NPV value of optimal
mine plan rise by $70.40M and that $2.48M from this increase is due to changes in the mine
plan itself. This represents 3.52% gain due to changes of the mine plan, with the remaining of
96.48% attributable to the change in copper price.
Table 3. Attributable value to change in mine plans across various copper prices
It can further seen that, the percentage NPV values attributed to a change in mine plan
from the value of the base case increases steadily to account for 7.25% of the total change at
the final copper price of $9750/t Cu. This shows that the variable copper price have greater
impact on the scheduling activities. This can be used to estimate at what time a stope
commences a production based on the added value at a particular price. It can be noted that if
other haulage methods used for the analysis, the value of NPV will vary depend on which
15
method is employed. Therefore the study may help for decision makers in knowing
appropriate time to updates or modify the existing ore handling systems.
6. Conclusions
In this study, the simulation was first carried out and shows that, three LHDs are
required to meet the predetermined production targets. This in turn provided the basis from
which to compute appropriate mining costs for the operation. The MIP model was then used
to generate the optimal production schedule and mine plan at each commodity price scenario.
It is therefore concluded that:
x An analysis of the change in the mine plans associated with changes of prices
from $5250/t to $9750/t Cu indicates that the increase in prices results in a
substantial increase in the NPV from $96.57M to ultimately reach $755.65M.
x A change in the mine plan reflected through a change in the commencement
period of each stope across each price scenario. This indicates that as the copper
price increases the higher grade and higher cost stopes are favored to a greater
extent.
x In an environment where mining operations must be looking to gain as much
value as possible from the rights to exploiting a finite resource, it is simply not
appropriate to keep operating under the same mine plan if commodity prices
have altered during the course of operations.
x Further, it can be concluded that the method of using discrete event simulation
combined with mixed integer programming is very beneficial for investigating
and solving operational issues like the one presented in this study. Especially
for deep mines or low grade mines operating with small margins. The use of the
described methods can be a way of maximizing NPV and thus securing a
profitable and optimized operation.
x It would appear beneficial from an economic perspective to investigate the
possibility of allowing a fluctuating mining at the variable commodity price
environment rate rather than operating at a fixed mining rate. The increase in
mining rate will result in addition of more equipment which may lead to a
higher operating cost.
Acknowledgements
The authors would like to acknowledge the I2Mine project within the EU 7th framework
programme for funding parts of the work.
16
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[4] Schriber T. Perspectives on simulation using GPSS. In: Proceedings of winter simulation,
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[9] Vergne JN De La. The hard rock miner’s handbook. Edition 3 2003.
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17
PAPER IV
Salama, A., Nehring, M. and Greberg, J. (2014). Analysis of the impact of increasing mining
rate in underground mining using simulation and mixed integer programming. Submitted to
International Journal of Mining Science and Technology.
Analysis of the impact of increasing mining rate in underground mine using simulation
and mixed integer programming
1
Division of Mining and Rock Engineering, Department of Civil, Mining and Environmental
Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden;
2
School of Mechanical and Mining Engineering, The University of Queensland, St Lucia,
QLD, Australia, 4072
Abstract
This paper challenges the traditional notion that mine planners need to plan production at
mining rates that result in a low mining cost. For a given mine configuration, a mine that
considers increases to its mining rate most often increases mining costs. In an environment in
which operations are fixated on cost reduction, a proposal to increase costs may be very
difficult to implement. Such a proposal may need to be justified financially because the
increase in costs might not be recuperated by the extra production gained. This paper
evaluates the net present value (NPV) of the selected range of copper prices for two
underground orebodies located at different depths using a production rate of 300,000 tonnes
and one that introduces additional costs at 450,000 tonnes per quarter. Discrete event
simulation combined with mixed integer programming was used for the analysis. The results
shows that, for the low mining rate at the final copper price, an NPV of $755.65M is
achieved, whereas an NPV of $773.45M is achieved at a high mining rate. Therefore, even
though pushing mining rates beyond traditional limits increases mining costs, pursuing this
option at certain commodity prices may be beneficial, particularly when prices are elevated.
1
1. Introduction
A traditional notion among mine planners is that mining rates should be planned in such a
way as to reduce production costs [1]. This concept generally relates to the mining rate that
results in the highest machine utilization for the selected equipment. Whereas an existing
mine may consider increases to its mining rate by adding additional equipment to a given
mine configuration, doing so typically increases mining costs. In an environment in which
operations are fixated on cost reduction, a proposal to increase costs may be very difficult to
argue for. The value of the mine plan is well recognized as varying with the mining rate for a
given orebody [9]. Changes to the mining rate are sensitive to the current price and are usually
not constant for the life of an operation. Research focusing on determining the optimal mine
plan and, simultaneously, allowing a variable mining rate and varying the commodity price
over the life of the operation is distinctly lacking. Most mine planning adopts a traditional
single rate at a fixed commodity price. [12] developed a mine plan using variations in metal
without changing the mining rate. The authors propose that a mine can continue its operations
only if the metal price is high enough to maintain a positive cash flow. [25] and [24]
developed methods to determine the optimal cut-off grade and mining rate to yield the
maximum net present value. In both cases, the metal price was fixed for the life of the deposit
and little discussion ensued on the degree to which the system will change considering metal
price variations. [10] developed a mine plan model with dynamic programming using Lane’s
cutoff grade theory for a fixed mining rate. An approach was later developed to allow variable
mining rates at a fixed price in the value optimization of the mine plan. [23] employed golden
search optimization using simulation-based models that consider metal price uncertainty to
determine a robust fixed cut-off grade. However, his evaluation showed that the mining rate
was fixed for the entire life of the underground mining operation. [3] presented an
optimization of the value of the mine plan across a range of metal prices without considering
a variable mining rate. The authors suggest that, when mining operations seek to gain as much
value as possible, continuing to operate under the same mine plan is inappropriate if
commodity prices change during the course of operation. In addition, the authors suggest that
a mining rate that can be altered during the life of the mine attributable to a reconfiguration in
the number of pieces of equipment – even if mining costs increase – should be explored as a
means to further maximize the value of the mine plan. Much of the literature shows the
validity in generating new mine plans when commodity prices change under fixed mining rate
conditions and the same general equipment configuration. The aim of this paper is to
investigate the validity of mine plan value maximization across a range of commodity prices
(from $5,250/t Cu, increasing incrementally by $500/t to $9,750/t) while allowing a variable
mining rate (from 300,000 tonnes to 450,000 tonnes per quarter) during the life of an
underground sublevel stoping copper operation. The analysis was performed using discrete
event simulation combined with mixed integer programming. Simulation was first used to
compute the appropriate mining costs at the current and increased mining rates for the
operation. Mixed integer programming (MIP) was then used to generate optimal schedules
and mine plans for the selected range of copper prices.
2
The mining rate selected significantly influences the optimization process. The selection
may be based on an empirical formula or economic measures [7]. [8] produced an equation to
estimate the mining rate on the basis of the size of the deposit, known as Taylor’s Rule, which
is still used today. However Taylor’s rule has limitations with several factors, such as hoisting
capacity, mine depth, and geometry of the deposit. [7] developed an empirical equation for
steeply dipping underground deposits by taking into account the geometry, rather than the
size, of the orebody. Economic measures such as NPV should ultimately have a large
weighting when considering one mining rate over another. NPV is the summation of all
discounted future cash flows over the life of the operation. [9] discussed the economic
characteristics affecting the selection of the optimum mining rate from an investor’s point of
view. He suggested that the mining rate can be selected by maximizing the NPV and
discounted cash flow return on investment. Once the mining rate is determined and the
operations start, to significantly change the mining rate is difficult unless an expansion with
new capital investment is planned [24]. An expansion of mining capacity may occur for
several reasons, such as geological information and economic changes. In the early stage, the
mining rate is defined on the basis of the orebody delineated with very limited geological
information and all materials inside the orebody are assumed to be accessible. At a later stage,
the grade distribution within the orebody may change the production sequence because some
of the material considered as waste may become mineable if being extracted with the
neighboring high-grade material. For example, if the price of the contained mineral falls, part
of the reserve may become unprofitable to mine. If a price is elevated from the one that was
initially used, then a modification should occur to reflect the new economic circumstances [6].
For existing operations that have a flexible hauling system, the mining rate can be increased
by adding more equipment, although doing so decreases the equipment utilization more than
when less equipment is used in operations. Increases in equipment also result into higher
mining costs. In an environment in which operations are fixated on cost reductions, a proposal
to increase cost may be very difficult to implement and may require financial justification
because the increase in costs might not be recuperated through the added production gained.
Equipment productivity is very important when planning and designing a mining
operation. Some of the factors that affect equipment productivity include: mine schedule,
number of cycles per hour, location of dig and dump sites (travel time), operator proficiency,
digging conditions, and bucket capacity [20]. The mine design and layout is heavily
influenced by the equipment used to carry out the extraction, and the final equipment
selection can only be completed after completion of the mine configuration. The mine
planning team always selects equipment and designs the mine in such a way as to maximize
equipment utilization [19]. This process includes but is not limited to designing pushback
widths (in the case of an open pit) or the size and location of underground drives (in the case
of underground) to be large enough to allow easy loading and haulage without excessive
interaction with other equipment. This study investigates whether an increase in mining rates
from employing more equipment that results in an increase in mining cost is appropriate to
pursue under existing mine configurations at altered commodity price scenarios.
3
This study was performed using a combined iterative approach with discrete event
simulation and mixed integer programming. Discrete event simulation is the modeling of
stochastic dynamic systems in which the state variables change only at discrete points in time,
making it very fit for modeling complex systems such as, for instance, mining operations.
Lately, the use of discrete event simulation for mining applications increased, and research
showed wide applicability of simulation studies in various operations for both underground
and open-pit mines [22]. For instance, the method was used for fleet optimization in
underground mining, comparison of timing and efficiency between drills, mine to mill
production systems, and maintenance scheduling [21]. A number of simulation software
packages are available on the market, such as GPSS/H, AutoMod, and SLAM. In this
analysis, the General Purpose Simulation System/Henrikson (GPSS/H) was used. The
operational cycles from the working faces at which LHDs load material and dump them to ore
passes is modeled. The simulation showed the number of LHD machines required to haul
450,000 tonnes of ore to each respective orepass. The simulation results are further used to
compute the associated mining costs. Mixed integer programming (MIP) is then used on the
basis of the results from the discrete event simulation model and generates optimal schedules
and mine plans for the selected range of copper prices. Discrete event simulation combined
with mixed integer programming was successfully used in prior studies that proved the
benefits of combining the two tools [3].
Arguably, MIP is the most common optimization technique used to solve highly complex
and constrained problems within the mining industry. MIP combines linear programming
(LP) with the additional constraint that some variables must take on an integer value. This
integer variable is typically represented as a binary “1” or “0” value to reflect a “yes” or “no”
decision [13]. Reverting from LP to MIP in the mining context is most common when
assigning equipment and resources to various operations within the mine is necessary. These
resources can only be allocated in their entirety and, as such, the decision of whether or not to
allocate the full resource across a number of working areas must be made. Similar to LP, the
constraints in an MIP form a multi-dimensional volume encompassed by linear functions. A
number of solution processes, including the Simplex Method, the Branch and Bound Method,
and Cutting Planes, are generally in-built in commercially available solvers to exact the
optimal solution from this multi-dimensional volume [14]. Authors including [15-18], and [3]
generated and extensively used MIP models to successfully solve a number of mining-related
problems.
2. Case study
4
mining region within Australia. As such, all figures are quoted in Australian dollars (AUD).
The value attributed to each stope was based on the operating cash flows generated. The cash
flows were obtained by subtracting the revenues from the operating costs in each scenario.
The operation under investigation extracts copper bearing ore from a deep underground mine
that exploits two copper bearing orebodies striking east–west and dipping at 70 to 75 degrees
in the southerly direction.
The sublevel stoping production was modeled according to four phases. This process
starts with internal development, followed by a production drilling (three months), extraction
(three months), and backfilling and consolidation phase (three months) that takes each stope
nine months to fully complete. Overall reserves were calculated at 15 Mt at an average grade
of 2.50% Cu for 375,000 tonnes of copper metal. The steady-state production rate for this
operation was 450,000 tonnes per quarter (or 1.8 Mtpa). At these production rates, this
operation is expected to have a mine life of at least 8.5 years, or 34 quarters. The production
capacity for each orebody was 300,000 tonnes per quarter. Production scheduling incorporates
all stopes from both orebodies to generate a life of mine plan at quarterly intervals. Therefore,
this process requires both orebodies to be in production in each scheduling period to achieve
the overall mining rate of 450,000 t. Table 1 shows some of the parameters for Eastern and
Western orebody. Each stopes had a size of 25 m x 25 m x 100 m to maintain geotechnical
stability. The Western orebody was considered low grade and the Eastern orebody was
considered high grade.
Stoping conditions at this depth within the Western orebody are considered reasonable, with
stresses that can be well managed using standard bolting practices for both the roof and the
walls. This situation allows an open sequencing regime to be used within this orebody.
Stoping conditions in the Eastern orebody are significantly poorer and, thus, require
additional ground support at a much higher cost to maintain an open sequencing regime
within this orebody. Long-term production scheduling is carried out at quarterly intervals over
the life of the operation for a number of copper price scenarios. For the purpose of this study,
LHDs were used to load and haul ore from the draw points of each stope to the ore passes
located 250 m from the Western orebody. The ore was collected in chutes on the lower level
of the orepass and further transported to the shaft point. The Eastern orebody is located at
deeper levels. The LHDs were used to haul the material and transport them up to the shaft
point for further transporting to the surface. This study assesses the feasibility of increasing
underground ore production from 300,000 to 450,000 tonnes from each orebody in each
quarter, while maintaining a maximum allowable extraction rate of 450,000 tonnes from the
overall operation in each period. To determine whether the production capacity of 450,000
tonnes from each orebody was feasible and to calculate an appropriate corresponding
operating cost, the number of LHD units to achieve this volume was required. This
5
information then allowed the calculation of the discounted cash flows generated by each stope
across all ten copper prices, which in turn enabled production scheduling optimization to take
place to achieve the optimal NPV.
The cost analysis was conducted on operating a 10-tonne capacity LHD unit together
with the preparation and production work required to keep ore material available to these
units during an entire quarter. Details of this costing exercise are beyond the scope of this
paper. For a mining rate of 300,000 tonnes per quarter, a mining cost of $32 per tonne was
determined for the Western orebody. Because the Eastern orebody is located in highly
stressed environments, the additional ground support and other features required to maintain
an open sequencing regime is predicted to increase mining costs to $158/t. The increase in the
mining rate to 450,000 tonnes added $6/t to the previously established mining costs, which
increased the costs to $38/t and $164/t for the Western and Eastern orebodies, respectively.
Table 2 provides a summary of mining costs and LHD requirements that formed the basis for
this investigation. These operating costs (OPEX) included all mining activities (for example,
development, drilling/blasting, backfilling) within each orebody and the activities needed to
haul this material to the surface for processing. Capital costs were not included in this
investigation.
Table 2. Mining cost for mining rates of 300,000 tonnes and 450,000 tonnes from each
orebody
2.2 Assumptions
The following assumptions were made to model production from this operation.
x During simulation, the availability of 87% was used for all LHDs. This figure was
based on the Mean Time Between Failure (MTBF) of 55.6 hours and Mean Time To
Repair (MTTR) of 8.56 hours.
x A discount rate of 25% was applied because the mine was not in production for a long
time and the capital, operating costs, and reserve are not well understood. If these
factors are well defined in a later stage, then the discount rate can be lowered.
x The copper price at the time of this study was approximately $6,500/t Cu. For the
purpose of this analysis, a range of copper prices starting at $5,250 and increasing by
$500 increments until $9,750 was used for the analysis. The price of $5,250 was used
6
because most feasibility studies on copper projects conducted during recent years
generally used price between $5,000/t and $5,500/t over the long term even though the
price at the time of this study was approximately $6,500/t Cu. The copper price boom
of 2011 witnessed copper prices reaching almost $10,000/t and, thus, the final price to
be investigated for mine planning purposes was $9,750/t Cu to reflect the price during
the boom.
x All internal development activities required to access all areas of the orebody were
completed, and no prior production of any kind occurred from any stope. However,
the development cost was included in the analysis.
x This study was completed solely on the basis of operating costs (OPEX). Capital costs
are outside the scope of this investigation and were not included.
3. Model Formulation
The formulation was comprised of simulation and mixed integer programming models.
The simulation model involved moving the mined material by LHDs and dumping them into
ore passes, whereby materials at the lower level were taken to the shaft point. A General
Purpose Simulation System/Henrikson (GPSS/H) was used to determine the number of LHDs.
The simulation results were then used to calculate operating cash flows associated with each
stope using MIP. The MIP model was created with mathematical language tools and then
solved using CPLEX; the results were then used to carry out optimized production scheduling
to generate an operating NPV for each commodity price.
The model consists of Eastern and Western orebodies located at different depth from the
surface with the aim to simulate the number of LHDs that can haul 450,000 tonnes per
quarter. LHDs load and haul ore and dump to the ore passes located 250 m from the orebody.
The ore pass drops material to the lower level, where they are conveyed to the shaft point. In
this paper, the simulation model considered the movement of the material from the production
areas to the ore passes. The time needed to load a bucket, travel to the ore pass, dump, and
return to the loading point were all used as input variables. Only a single LHD can load at a
loading point and other LHDs arriving wait until the loading point is free. After dumping,
only a single LHD is allowed to dump and no interaction occurs during dumping for LHDs
from both sides of the orebodies.
A GPSS/H consists of multiple processes operating at the same time and provides the
capability for these processes to automatically interact with one another. Objects may be sent
between processes that share common resources and influence the operation of all processes.
The representation of the object is called transactions. Transactions compete for the use of
system resources. As transactions flow, they automatically queue when the resources are not
free for used. A transaction represents the real-world system and is executed by moving from
one block to another block. Blocks are the basic structural element of the GPSS/H simulation
language. In GPSS/H, more than fifty different types of blocks are available for use in
modeling complex problems [5]. Complete programming codes were created and the
7
simulation was run with four times replications. A replication is a simulation that uses the
experiment’s model logic and data but its own unique set of random numbers; thus, it
produces unique statistical results that are analyzed in a set of such replications [4]. The
execution of a run takes the actions at the current simulated time and then advances the
simulated clock. These two phases repeat continuously until the end of the program. The
written program used macros to code repetitive type events, such as loading, tramming, and
dumping, to reduce the size of blocks in the model. The simulation was run for three months
and consisted of two shifts of eight hours each in a day for five days in a week.
The MIP model is presented that was created to generate the optimal quarterly life of
mine production schedules for each commodity price and equipment utilization scenario and
to comply with all constraints.
Subscript notation: The following subscript notation was used to define the model in general
terms.
Decision variables: One binary variable reflected whether or not a stope enters products in a
certain period.
8
Objective function: The optimal schedule was determined by maximizing the NPV of all
activities/stopes under consideration.
Note that taxation and depreciation were not included in this formulation but should be
incorporated if necessary.
Constraints: The practical limitations imposed by the sublevel stoping method over the long-
term scheduling horizon were reflected through a series of constraints. Constraints (2) to (6)
are considered resource constraints because they reflect the natural restriction of resource
allocation throughout the mine during each scheduling period. Constraint (2) limits the
production of stope ore extraction from exceeding the shaft/LHD/truck fleet capacity for the
overall mining operation or a specific part, including a particular part such as an orebody, in
any long-term period. Constraint (3) enforces non-negativity and integer values of the
appropriate variables. That a single mining rate was selected in each period was vital, as
ensured by constraint (4). Constraint (5) restricts each stope to be allocated to a single mining
rate in each period that it is in production. The rate of extraction of all stopes in any given
period must match the extraction rate selected for that particular period, as enforced by
constraint (6).
Shaft / machine fleet ore capacity constraint ݎ௦ ൈ ݓ௦௧ ܿݏ௧ ݐ (2)
௦אఉ
Non-negativity and integer value constraint ݓ௦௧ ൌ ܾ݅݊ܽݎ݁݃݁ݐ݊݅ ݕݎ (3)
Single mining rate in each period ݃௧ ͳ ݐ (4)
אఈ
Single mining rate for each stope in each period ݃௧ ͳ ݏǡ ݐ (5)
אఊೞ
Mining rate match on all stopes in each period ݓ௦௧ ൈ ௦ െ ݃௧ Ͳ ݐ (6)
௦ǡ
Stope adjacency constraint ݓ௦௧ ݓ௦ᇲ ௧ ͳ ݏ ǡ ݐȁ ݏᇱ ݆݀ܽ א௦ (7)
Fillmass adjacency constraint ݓ௦௧ ᇲ ݓ௦ᇲ ௧ ʹݏǡ ݐ (8)
௧ ᇲ א௧ ௦ ᇲ אௗೞ
9
Constraints (7) to (8) are considered sequencing constraints because they reflect the safe and
effective natural sequences inherent to the sublevel stoping method across the scheduling
horizon. Constraint (7) ensures that simultaneous production between stopes that share a
common boundary does not occur. Constraint (8) provides some geotechnical stability to
stoping activities by limiting simultaneous adjacent production to two common boundaries
before itself commencing production, and to a single adjacent side once having completed
production to become a fillmass. Finally, constraints (9) to (10) are categorized as timing
constraints because they reflect timing related issues associated with each stope across the
scheduling horizon. Constraint (9) ensures that the commencement of stope production is
initiated no more than once during the long-term scheduling horizon if the late start date
occurs beyond the scheduling horizon. Constraint (10) requires stope production to commence
at some point during the long-term scheduling horizon if the late start date falls within the
long-term scheduling horizon. Note that this mathematical optimization model was used to
carry the evaluation when allowing for a variable mining rate. When a constant mining rate is
maintained, constraints (4), (5) and (6) are not required.
During model development, the model was coded to allow for the interactive input of
variables at the start of the simulation run. As shown in Fig. 1, a single 10 t LHD operating in
either orebody experiences full utilization and is expected to move 118,000 tonnes of ore each
quarter. The addition of another LHD to the same orebody reduces total utilization to 96%,
moving a combined 230,000 tonnes in each period. Adding another LHD reduces the
utilization of each machine to 89% with a total movement capacity of 320,000 tonnes and an
excess of 20,000 tonnes. Increasing each orebody mining rate from the current rate of 300,000
tonnes to the targeted rate of 450,000 tones indicates that overall targeted mining from the
entire operation could theoretically be sourced entirely from one of the two orebodies in each
scheduling period. Moving an LHD from one orebody to the other for part of the quarter
causes a production delay; however, this delay was assumed to have a negligible effect on the
simulation.
10
Simulationresultsforwesternorebody
500000 100
450000 95
Amountoforemined(t)
400000 90
350000 85
Utilization(%)
300000 80
250000 75
Theoremined
200000 70
150000 65 LHDUtilization
100000 60
50000 55
0 50
1 2 3 4 5
NumberofLHDs
As shown in Fig. 1, four LHDs to the same orebody reduced total utilization to 83% and
moved a combined 380,000 tonnes in each period. With five working LHDs, the total amount
of ore moved was 432,000 tonnes and the average machine utilization fell to 73%. The
20,000-tonne excess LHD fleet capacity from the initial orebody was assumed to be able to
compensate for the 20,000-tonne shortfall from the other orebody. Therefore, three LHDs are
required within one orebody to achieve the 300,000-tonne mining rate, and two more LHDs
are required to be in operation (a total of five LHDs) to achieve a mining rate of 450,000
tonnes.
The MIP models for the purpose of optimal production scheduling (maximizing NPV)
were written using A Mathematical Programming Language (AMPL). Based on the input
costs and parameters previously mentioned, these models were solved using CPLEX 10.3.
The solution process for each of the 10 price scenarios being evaluated was left to run
overnight (approximately eight hours) and was cut short even if convergence to the optimal
solution was not yet achieved. However, in all cases, a gap of less than 3.00% was achieved.
In this case, production scheduling occurred in quarterly intervals and was limited to 60
periods (15 years). Under each price scenario, full extraction from both orebodies was
completed within the 60-quarter limit. Full extraction was expected because the respective
cut-off grades for the lowest copper price of $5,250/t was higher than the grade of the lowest
grade stope for the Western and Eastern orebodies, respectively. Figure 2 shows and
compares the operating NPVs achieved when limiting mining rates to 300,000 tonnes and
450,000 tonnes in each orebody across each of the 10 copper price scenarios.
11
800,00 773,45
694,50
700,00
615
600,00
536,47
NPV ($M)
500,00 462,52
385,36
400,00
755,65
311,92 680,16
300,00 606,32
239,60 532,46
459,56
200,00 166,97 385,36
311,92
96,57 239,60
100,00
166,97
96,57
0,00
5 250 5 750 6 250 6 750 7 250 7 750 8 250 8 750 9 250 9 750
Copper Price ($/t)
300,000t Mining Rate Limit for each Orebody 450,000t Mining Rate Limit for each Orebody
*Base case scenario refers to the optimal mine plan at a copper price of $5,250/t for both full and reduced
machine utilization
Fig. 2. NPV comparison of optimal mine plans across various copper price scenarios
As shown in Fig. 2, for the 300,000-tonne mining rate, the $5,250/t copper price produces
the lowest NPV of $96.57M. This NPV increased and ultimately reached $755.65M at the
final copper price of $9,750/t. For the 450,000-tonne mining rate, which had a higher mining
cost, a similar trend was initially observed, whereby the lowest NPV of $96.57M was
produced at the copper price of $5,250. No differences were seen in the NPV between
300,000 tonnes, and 450,000 tonnes was observed for copper price scenarios of $5,250/t,
$5,750/t, $6,250/t, $6,750/t, and $7,250/t. A slight increase of $2.96M, or 0.65%, in the NPV
for the two mining rates emerged at the $7,750/t copper price. From this point, the difference
in NPVs between the 450,000-tonne and 300,000-tonne mining rates increased as the copper
price increased.
12
Table 3
Attributable value to change in mine plans for 300,000-tonne and 450,000-tonne mining rates
Table 3 compares the NPVs at each copper price for both mining rate scenarios. The
copper price of $5,250/t under the 300,000-tonne mining rate was used as a base case and
shows that the copper price increase from $5,250/t to $5,750/t results in an increase in NPV of
3.52% for both mining rates. This copper price also shows that no difference exists in the
NPVs for both mining rates at the $6,250/t, $6,750/t, and $7,250/t copper prices from the base
case scenario. As the price increased to $7,750/t, the differences in the NPVs for the two
mining rates began to be observed. As is shown, the value attributed to the change in the mine
plan at 450,000 tonnes increased to 7.20% from the base case scenario as opposed to 6.44%
under the 300,000-tonne mining rate. This result indicates that increasing the mining rate is
worth 0.76% to the value of an operation from the base case scenario compared with
maintaining mining at this copper price. As the copper price increased further to $9,750/t, the
NPV increased to 9.69% for the higher mining rate compared with 7.25% for the lower rate.
Therefore, at the final copper price, the increased mining rate was worth 2.44% to the value of
an operation from the base case scenario compared with maintaining the same mining rate.
The changes to the NPV of the mine plan for the orebody located at a shallow depth with
the orebody located at a deeper depth were analyzed. The aim is to evaluate the possibility of
maintaining or increasing the mining rate when the mine depth increases. The analysis of
these results shows that a short-term change in commodity prices only added as much value
provided by the increased margin associated with the new price. A longer-term price change
should influence mining operations to continually update and adjust their mine plans to
capture additional value under new market conditions. Some of these adjustments may
include an increase in the mining rate. In this analysis, the capital costs of the working
equipment were not included and, therefore, the evaluation was based on development and
13
operating costs. For the lower mining rate at the final copper price, an NPV of $755.65M was
achieved, whereas at a higher mining rate, the NPV was $773.45M. If the capital costs of
purchasing the equipment to achieve these mining rates are included, the final NPVs in both
cases decreased. Therefore, even though pushing mining rates beyond traditional limits may
increase mining costs, at certain market conditions doing so may be beneficial.
5. Conclusions
This paper presented the NPV component that can be directly attributed to changes in
mine plans as commodity prices vary under traditional mining rates with low cost in
comparison to more aggressive higher mining rates with higher costs. The results for the case
study show the following points.
x For the 300,000-tonne mining rate at the final copper price, the NPV was observed to
increase to $755.65M, whereas for the 450,000-tonne mining rate, the NPV increased
to $773.45M.
x As mining operations proceed at great depth, increasing or maintaining mining rates
may be beneficial, particularly in the case of increasing commodity prices even if
doing so results in a higher operating cost.
x The analysis of these results from an economic perspective shows that commodity
price variations play an important role in the optimality of mining planning and
design. A short-term change in commodity prices only adds as much value provided
by the increased margin associated with the new price. A longer-term price change
should influences mining operations to continually update and adjust their mine plans
to capture additional value under the new market condition.
x The combination of discrete event simulation and mixed integer programming can be
used to provide a feasible solution and a better understanding of the operational
systems and to reduce the risk associated with selecting a system before being
implemented.
Acknowledgments
The authors would like to acknowledge the I2Mine project within the EU 7th framework
program for funding this research, as it significantly helped with the completion of this work.
References
14
15
20. Barabady J, and Kumar U. Reliability analysis of mining equipment: A case study of a
crushing plant at Jajarm Bauxite Mine in Iran. Reliability Engineering and System
Safety, 2008, 93, 647–653
21. Banks J, Carson JS, Nelson BL, and Nicol DM. Discrete event System simulation,”
Pearson Education, New Jersey, 2010.
22. Govinda Raj M, Vardhan H, Rao, YV. Production optimisation using simulation
models in mines: a critical review, International Journal of Operational research, 2009;
6(3), 350-359.
23. McIsaac G. Strategic design of an underground mine under conditions of metal price
uncertainity. Queen’s University, Kingston, Ontario, Canada, 2008.
24. Baqun Ding. Examining the planning stages in underground metal mines. PhD thesis,
Queen’s University, 2001.
25. Yearn Park. Economic optimization of mineral development and extraction. PhD
thesis, McGill University, 1992.
16
PAPER V
Salama, A., Greberg, J., Skawina, B., and Gustafson, A. (2014). Analysis of energy
consumption and gas emission for loading equipment in underground mining. Submitted to
Canadian Institute of Mining, Metallurgy, and Petroleum Journal.
ANALYSIS OF ENERGY CONSUMPTION AND GAS EMISSIONS FOR LOADING
EQUIPMENT IN UNDERGROUND MINING
ABSTRACT
The equipment used for loading and hauling in underground hard-rock mining operations has
historically been dominated by Load-Haul-Dump (LHD) machines. These machines can be
powered by diesel or electricity. Diesel LHDs have commonly been used in mining because
the equipment is mobile, versatile, and its operational flexibility provides high productivity,
but they also have higher operating costs. Factors contributing to higher operating costs are
energy consumption and ventilation. Electric LHDs are also used, but are not as common as
diesel. Electric LHDs have lower energy consumption and lower ventilation demands
compared with diesel LHDs of the same size. However, electric LHD are less versatile
because the use of electric cables have a limited haul range and may introduce cable faults
and relocation issues. As operating costs for deeper mines and energy costs are expected to
increase in the future, cost-efficient loading and hauling equipment is essential. This study,
conducted at an underground mining operation to analyze the energy consumption and gas
emissions of diesel and electric LHDs with similar bucket capacities. The method used is
discrete event simulation. Based on current energy prices, the results showed that the hourly
energy costs generated by electric LHDs was 47 percent less compared than diesel LHDs of
the same size. In addition, diesel LHDs emitted 2.68 Kg of CO2 gas for every liter of diesel
fuel. Therefore, in an environment of increasing energy prices and the increased need to mine
at greater depths, minimizing the use of diesel-engine machines and increasing the use of
electric machines can greatly benefit cost reductions.
KEYWORDS
1
INTRODUCTION
Loading equipment for underground hard-rock mining operations has historically been
dominated by LHDs (De La Vergne, 2003). These machines can be powered by diesel or
electricity. Diesel LHDs have been utilized in material transportation in mining since the
1960s. These machines are versatile and can easily move from one location to another, but
have higher operating costs because of fuel consumption, consumables and regular checks,
and the ventilation required to mitigate the heat and emissions they generate (Thomas et al.,
1987; Chadwick, 1996; Miller, 2002). Electric LHDs, which are not commonly utilized in
underground mines (Paraszczak et al., 2013), have the advantages of being quieter and
producing no exhaust gases and less heat (Chadwick, 1996; Paraszczak et al., 2013; Paterson
& Knights, 2013; Paraszczak et al., 2014). They may be powered with batteries, overhead
electric lines, or trailing cables. Batteries offer the highest flexibility, but battery-powered
vehicles are heavy and must be regularly recharged. Overhead power lines may be feasible for
haul trucks when routes remain constant for an extended time, but are impractical when a high
degree of maneuverability is necessary. The currently most viable way to power electric
LHDs is with a trailing cable plugged into the mine’s electrical infrastructure. Powering with
electric cable reduces the LHDs’ versatility because of limited haul range, relocation issues,
and restricted movement, and may present problems with cable faults and wear. But electric
LHDs have obvious advantages in mass mining methods such as block and sublevel caving
where relocation delays are less critical because operations are along a similar path for an
extended time (Paterson & Knights, 2013).
In coming decades, underground mines can be expected to operate at greater depths,
which will increase costs because of additional energy needed for longer haul distances and
additional ventilation to mitigate geothermal heat and exhaust gas emissions from working
equipment. These expected increased costs make the choice of loading and hauling equipment
an essential factor in cost reduction. The demand for electric LHDs also can be expected to
increase as mining companies seek to address high ventilation costs, higher fuel prices, and
strict regulations on emissions (Miller, 2002; Salama et al., 2014).
This study, conducted at an existing underground mine, compared the operational
performance of diesel and electric LHD machines and analyzed their energy and gas
emissions using the AutoMod discrete event simulation tool. Simulation was used to obtain
the equipment productivity and operating times. Simulation results were used in combination
with empirical calculations to estimate energy and gas emissions. The study analyzed seven
diesels and seven electrics LHDs with similar bucket capacities.
2
Energy consumption and gas emissions
Energy consumption is the amount of fuel used during a specific period of time, and is most
accurately measured onsite. However, onsite measurement is very expensive because it
requires continuously monitoring of every piece of equipment in operation. In the absence of
field measurements, consumption can be estimated based on available energy models such as
Energy Savings Measurement Guide, Energy Efficiency Opportunities, Energy Mass Balance,
and Mining Industry Energy Bandwidth (Bise, 2003). Most of these models use simplified
methods for estimating diesel fuel and electricity consumption (Tatiya, 2013), and although
less expensive, they also are less accurate compared with on-site measurement. The methods
3
depend on load factor, engine capacity, road conditions, and the time the equipment is utilized
(Caterpillar, 2009). Equation 1 can be used to estimate diesel fuel consumption during loading
and dumping (Kecojevic & Komljenovic, 2010). For electric LHDs, the energy consumed
during loading and dumping is estimated based on the motor input power and time the
equipment is utilized.
כ
כ
ൌ ሺͳሻ
In this equation, FC is the fuel consumed in liters per machine hour; K stands for the
kilograms of fuel used per brake horsepower per hour; GHP represents the gross engine
horsepower at governed engine revolution per minute; KPL is the weight of fuel in Kg/liter;
and LF is the load factor in percentage. Equation 2 is used to convert the fuel consumed (FC)
by diesel LHDs into kWh for comparison with electric LHDs.
͵ כͺǤ
ୈ ൌ ሺʹሻ
͵Ǥ
In this equation, ED is the energy consumed by diesel equipment in kWh; the calorific value
of 38.6 MJ/L is the amount of heat released by a fuel when combusted and 3.6 MJ is the heat
used to produce 1 kWh. Equation 3 is used to estimate the energy consumption in kWh per
loading cycle (E) from loading point to dumping point and back to loading point for both
diesel and electric LHDs.
In this equation, TR is the total resistance in tonnes; g is the acceleration due to gravity in
m/s2; VW is the gross vehicle weight; BC represents bucket capacity in tonnes; VL is the
vehicle speed in m/s when loaded; t is the time taken to transport material for dumping and
return to the loading point in hours; and VE is the vehicle speed in m/s when empty. The CO2
emissions are estimated based on the combustion process of fixed carbon restrained in a
volume of diesel fuel. These emissions occur because of incomplete combustion in the diesel
engine and impurities in the fuel (Pellegrino et al., 2005). The emissions are calculated based
on the diesel conversion factors published by the Environmental Protection Agency (EPA,
2005). Equation 4 is used to express the amount of CO2 emitted in tonnes from diesel
equipment (Bogunovic and Kecojevic, 2009).
ͶͶ
ଶ ൌ Ͳ כ ିͲͳ כ כǤͻͻ כ ൨ሺͶሻ
ͳʹ
4
In this equation, CC stands for carbon content of the fuel (g/l); 0.99 is the oxidation factor,
meaning that 99 percent of fuel burns out and 1 percent is unoxidized; 44/12 is the ratio of the
molecular weight of CO2 to the molecular weight of carbon.
In this study, discrete event simulation was used to estimate the LHD machines’
operating times, which was used as input for the fuel consumption estimation. Discrete event
simulation is a technique used to model stochastic, dynamic systems in which changes in the
state of the variables in the events occur at discrete points in time. The technique is very
suitable for modeling complex systems (Law & Kelton, 1991) and has been used increasingly
for various systems in both open-pit and underground mining operations (Banks et al., 2010).
Simulation can model operations in order to analyze, optimize, improve, and plan systems
with regard to for instance fleet requirements, the flow of hauling machines, and mine
planning. Among the various simulation tools available on the market, AutoMod was selected
for this study. AutoMod is used to create discrete event simulation models of various
applications such as assembly lines, manufacturing systems, and mining operations. It is used
to analyze and optimize alternative system designs, and can predict results for existing and
future systems. AutoMod provides advanced debugging and trace facilities that enable errors
and flaws to be easily traced. In addition, the tool is equipped with concurrent 3D graphics
and a comprehensive set of templates and objects for modeling different applications (Muller,
2011).
CASE STUDY
The analyzed mine uses sublevel caving mining method. In this method,
development drifts are initially made. Next the ore passes are drilled, which extend vertically
from the current mining area to the bottom of a new mining area where transportation levels
exist. Horizontal sublevels are created, and access routes over the length of the orebody
within a sublevel are developed. The self-supported horizontal crosscuts are drilled through
the orebody perpendicular to the access routes.
In this mine, spaces between sublevels are about 28.5 meters and the spaces between
crosscuts are 25 meters apart. At the crosscuts, near-vertical rings of holes are drilled in a fan-
shaped pattern. Each ring contained around 10,000 tonnes of ore and waste. The ore is
recovered on each sublevel starting with overlying sublevels and proceeding downwards. In
each sublevel, the ore is removed from the hanging wall to the forefront of the footwall. As
the ore is recovered from a sublevel, the hanging wall will collapse, according to design, and
will cover the mining area with broken waste rock.
5
Figure 2 A section of the mine used in the analysis
As shown in Figure 2, the mine is divided into 10 main production areas, called blocks,
extending from the uppermost mining level down to the current main level. Each block
consists of several sublevels. Each block is about 400 to 500 meters long, and each has its
own group of orepasses located at the center of the production area and extending down to the
main haulage level. At the time of the study, the mine was producing approximately 27 Mt of
crude ore per year. By 2015, it is estimated to produce 37 Mt per year from all 10 blocks. To
reach this target, the mining company plan to increase the loading capacity from each block to
10,000 tonnes per day.
Figure 3 shows the block we analyzed. In this part of the mine, one 25-tonne-capacity
electric LHD operates from 6:00 a.m. until 10:00 p.m. and one 21-tonne-capacity diesel LHD
(called 7D in this study) operates from 10:00 p.m. to 6:00 a.m. The average daily production
of these machines is 60 percent of the future planned production. These LHDs load the ore
from draw points within each production drift and transport it to the orepasses. Large trains
operating on the main level transport the ore from orepasses to a crusher, which crushes the
ore for hoisting to the surface through a series of vertical shafts. Once mining has begun in a
block, continuous production must be maintained until all available ore is removed (according
to the mine restrictions).
For this study, the energy consumption and gas emissions for the LHD 7D and the
diesel LHDs shown in Table 1 were compared with electric LHDs of similar bucket sizes. The
25-tonne electric LHD was not considered for this analysis because there is available diesel
counterpart with similar bucket size. The data for LHD 7D was collected from the mine, while
data for all other LHDs were obtained from the manufacturers. The energy consumption was
estimated based on simulation results and empirical formulas. Simulation was used to
estimate the LHDs’ operating times and then the simulation result was as input to estimate the
energy consumption and gas emissions.
The combined use of simulation and analytical calculations enables a more accurate estimate
of energy consumption and emissions than a single analytical method, which is the traditional
6
method for this type of estimates. The single use of analytical methods can be successfully
applied when a system involves less random activities. During loading operations randomness
is present in many situations, such as variability in loading and dump times, in tramming
distances, and in times to clear boulders at the orepasses. When a system contains uncertainty
and random behavior, the discrete event simulation approach offers the advantage of more
accurate accounting for real world uncertainty and diversity of operations.
The simulation model was developed using AutoMod software, which consists of
material movement systems that allow users to model both manual and automated equipment
such as LHDs with high degree of accuracy (Muller, 2011). When system elements such as
paths and stations are known, then operating parameters such as speed, turning speed,
acceleration, and deceleration can be defined in the movement system (Banks, 2004). The
software creates performance reports with statistics and 3-D animation, providing a realistic
and statistically accurate view of the system. AutoMod also provides advanced debugging
features to easily trace errors and flaws and is equipped with the Autostat feature to reduce
time required for experimentation and analysis.
Input data
Table 1 shows the kinematics data for the diesel and electric LHDs. 14 types of LHD
machines was analyzed (seven diesel-powered and seven electric-powered) with similar
bucket capacities. The electric LHD 7E was not yet on the market, and therefore, the data for
this machine was estimated based on assumptions from the manufacturer’s experts. The
average speed for all LHDs at gear three was used for the analysis. Table 2 shows the
technical parameters used for energy consumption calculations. The calculated energy was the
energy required to drive the machine, and energy required to run machines’ installed fans and
hydraulic systems were excluded in this study.
Table 1 – Kinematics parameters
As shown in Table 2, the operating weight of both types of LHDs increased with
increased machine size. The diesel LHDs had higher drive power compared to the electric
LHDs with similar bucket sizes. Normally, the fuel or electricity consumption rate of a
7
vehicle is determined based on the machine loading rate, vehicle efficiency, road gradient and
surface features, load factors, and the LHD operating time. The load factor was obtained by
taking the ratio of the power the LHD was using (input power) to the power required when the
LHD operates at its rated capacity. A strip chart recorder was used to measure the average
input power for diesel LHD 7D in the mine, which was 274 kW. As Table 2 indicates, this
LHD had a drive power capacity of 350 kW, which gives a load factor of 78 percent. The
same value of load factor was assumed for all analyzed diesel and electric LHDs.
The resisting force was estimated based on the tire rolling resistance because the
LHDs were hauling material from the production drifts to the orepasses near the main drift, a
grade resistance of zero. The simulation results was used to obtain the LHDs’ operating times,
after excluding time lost for maintenance, production area availability, meal breaks, shift
changes, and interference with other mining activities, such as drilling, charging and orepass
maintenance. The production area availability due to other mining activities was 80 percent,
which was applied for all LHDs. For this study, data for breakdown, scheduled maintenance,
and equipment downtime was available for the diesel LHD 7D. No operating characteristics
data were available for the other analyzed diesel and electric LHDs, which to the exclusion of
a comparison of availability and utilization for diesel and electric machines. In the simulation,
a machine availability of 80 percent was used for all LHDs. The value was based on the mean
time between failure (MTBF) of 59.9 hours and mean time to repair (MTTR) of 14.3 hours
for the diesel LHD 7D (Gustafson et al., 2013). The machine efficiency was 85 percent and 95
percent for all diesel and electric machines respectively. Using equations 1, 2, 3, and 4, we
calculated the energy consumption and gas emissions.
Model logic
Figure 3 below shows the mine block used for the analysis. The block consists of17
production drifts, each approximately 100 meters long, and four orepasses located close to the
main drift. A three-meter blasting round on each production drift begin in sequence at the
hanging wall, using an upward rise to provide free face and then retreat toward the footwall.
Mucking out by LHDs continue until the waste dilution reach the set limit. Approximately
10,000 tonnes of ore is excavated from one blasted ring, which mean the total ore to be mined
from this block is approximately 6.17 metric tonnes. Loading is assumed to start from the first
8
drift on the left side of the block and to continue to the next drift until the last drift is finished.
This procedure is repeated until the entire production area is mined out.
As shown in Figure 3, two parking areas are included as waiting places for LHD
machines during breaks. In this case, only one machine is operating at a time. The machine
uses two orepasses when operating on the left side of the production area and the remaining
two orepasses when operating on the right. Which orepass is used depends on the buffer
capacity and boulder frequency. If the buffer capacity limit is reached, then the LHD moves to
the next orepass. If a boulder enters the orepass, the LHD waits for clearance; for this study,
we triangularly distributed this waiting time as a minimum of one minute, an average of five
minutes, and maximum of 30 minutes. If the boulder clearance is not finished during this
time, the LHD moves to the next orepass. If the rock breaker is working to clear boulders
when the next orepass buffer capacity is reached, the LHD waits for the rock breaker to finish
removing the boulders. The initial simulation model consist of the diesel LHD 7D machine,
which is currently in operation in the mine. The simulation model was adjusted and all
analyzed LHDs was simulated. The machines’ productivity, energy consumption, and gas
emissions was then compared. Figure 4 shows the logic for the LHD loading operations.
9
Figure 3 The mine block considered in this study
10
Figure 4 Flow chart of LHD loading operation
Verification ensures that a conceptual model design has been transformed into a
computer model with sufficient accuracy and validation ensures the model is sufficiently
accurate for a certain purpose (Sargent, 2003). Both processes ensure that a created model is
accurate and represents the real system. Techniques used for verification may include testing
the model logic, using debugging techniques, running the model under varying conditions,
making logic flow diagrams, and building diagnostics into the model (Muller, 2011). Ways to
achieve validation may include a degenerate test, testing internal validity, using an extreme
condition test, comparison with historical data, testing face validity, comparing output results
with the actual system, or using a Turing test (Banks et al., 2010). A verified and validated
simulation model could provide results very close to those in the actual operating system.
For this study, verification was achieved using debugging techniques, an animations
check, model inspection from the specialists, and running the model under varying conditions.
11
The debugging features were used to make sure that everything was running correctly before
resuming execution. Simulation runs were initially conducted with conceptual estimated size
of equipment, storage facilities, and haulage systems structures. Initial results allowed these
parameters to be redefined and radically changed, which involved extra programming that
enhanced the program’s versatility to conform with proposed mine logistics. To achieve
validation, internal validity was used and compared the model’s output with output of the real
system.
Productivity comparison
The simulation was first conducted for the diesel LHD 7D, which was currently
operating in the mine. After the first simulation, we adjusted the model and applied it to the
other LHD machines to obtain a comparison of the hourly production rates, hourly energy
consumption, and CO2 gas emissions.
350
300
250
200 Diesel LHDs
150 Electric LHDs
100
50
0
1D 1E 2D 2E 3D 3E 4D 4E 5D 5E 6D 6E 7D 7E
Type of LHDs
Figure 5 shows the hourly productivity (tonnes per hour) of the analyzed LHDs. The diesels
LHDs moved more tonnes per hour than the electric LHDs of similar bucket size because
diesel LHDs travel faster and have higher versatility, resulting in shorter cycle times than
electric LHDs. The hourly production rose with increases in bucket capacity for both diesel
and electric LHDs. Despite the smaller-bucket machines’ greater maneuverability and thus
shorter cycle times, the larger-bucket machines were able to dump more ore. Based on the
productivity results for all analyzed machines, a single unit would not be enough to achieve
the future daily target of 10,000 tonnes; therefore, increased production capacity will demand
an additional electric or diesel LHD to be in operation, and in turn, multiple drifting and
stoping operations. The production area used for the analysis can accommodate up to two
12
LHDs operating simultaneously. During dumping, the machine operating on the left side of
the mine block would use the first two orepasses, and the LHD operating on the right would
dump material in the orepasses on the right side. If more than two machines were employed,
the performance evaluations include delays for queuing and traffic. The option to add more
equipment would need to be justified financially because the cost of additional equipment
might not be recuperated by extra production.
Recognizing that moving ore is one of mining’s most energy-intensive activities and
that energy and ventilation are large contributors to operation costs, the energy consumption
and CO2 emissions were analyzed. Energy consumption of the diesel LHD 7D in the mine
during its operation was measured, and simulation and the empirical formulas were used to
estimate energy consumption of the other analyzed machines. Simulation was used to obtain
each LHD’s operating time, which was then used to calculate the utilization. In all cases, the
LHD machines’ utilizations were calculated using equation 5.
ൌ ͲͲͳ כΨሺͷሻ
Table 3 shows the fuel or electricity consumption for the diesel and electric LHDs.
Based on current prices, the diesel LHDs’ hourly fuel costs were higher than the hourly cost
of electricity. For example, in one hour of operation, diesel LHD 7D consumed 38.6 liters of
fuel while its electric counterpart consumed 306 kWh of electricity. Based on an assumed a
fuel price of $2.1/L and electricity price of $0.12/kWh (WES, 2014), this consumption
equates to an hourly fuel cost of $81.1 and an electricity cost of $36.8. The cost increased
with an increase in the bucket size for both machine types. The diesel fuel consumption was
converted into kWh for comparison purposes with electric units; these results are shown in
Figure 6.
Energy consumption was higher for diesel machines. For example, in one hour of
operations, the diesel LHD 7D consumed 405kWh of energy while its electric counterpart
consumed 306 kWh. Electric LHDs use less energy because they are equipped with lower
powered motors compared with diesel machines. The diesel LHD with a bucket capacity of
4.6m3 had 220 kW of power, while the electric LHD of the same capacity only 132 kW.
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Table 3 Comparison of diesel fuel and electricity consumption
The energy required to drive LHDs is proportional to its speed. On average, diesel machines
travel faster than electric ones at the same gear because the diesel engine has a torque
converter with low offset ratio. This feature enables diesel machines to have higher speed and
higher energy consumption compared with their electric counterparts. The difference in
consumption rates increases with an increase in bucket size because larger buckets weigh
more. For example, a diesel machine with 1.5m3 bucket weighs 8.7 tonnes with an empty
bucket and one with a 9m3 bucket weighs of 56.8 tonnes. When operated in the same gear, the
heavier machine will consume more fuel than the lighter one.
400
350
300
250
200 Diesel LHDs
150 Electric LHDs
100
50
0
1D 1E 2D 2E 3D 3E 4D 4E 5D 5E 6D 6E 7D 7E
Types of LHDs
14
Next, the CO2 gas emissions for diesel LHDs estimated. Figure 7 shows the hourly
CO2 emissions with respective hourly fuel consumption for each LHD. For example, diesel
LHD 1D consumed 6.9 liters of diesel and emitted 18.6 Kg of CO2 in one hour, while diesel
LHD 7D consumed 38.6 liters and emitted 103.5 Kg of CO2, which indicates that an increase
in energy consumption results in higher CO2 emissions and the higher related costs of
necessary ventilation.
100 40
90 35
30
70
25
60
20 Co2 emission
50 Fuel consumption
15
40
30 10
20 5
10 0
1D 2D 3D 4D 5D 6D 7D
Diesel LHDs
Figure 7 Comparison of fuel consumption and gas emissions for diesel LHDs
The analysis of these results indicated that the energy costs were higher for the diesel
LHDs than their electric counterparts. On average and based on current prices, the hourly
energy costs for an electric LHD was 47 percent less compared than the diesel of the same
size. Diesel quipment also had higher heat and gas emissions. Based on the ratio of emissions
and the amount of fuel used, the diesel LHDs emitted 2.68 Kg of CO2 gas for every liter of
diesel fuel. In comparison, electric LHDs have zero emission, low energy consumption, and
they emit less heat, although electric machines have higher initial costs because of the
additional infrastructure (transformer boxes and substations) they require. This additional
infrastructure also requires time to relocate when electric machines must be moved from one
production area to another, causing potential production delays. These research results
indicate that utilizing electric rather than diesel machines can result in cost reductions,
especially in an environment of increasing energy prices and deep mining with sublevel
caving methods. When other mining methods are used, a detailed analysis may be required for
the operational performance of electric LHDs.
15
The use of simulation method
The simulation method for this research was chosen because the mining system
includes many uncertain operational elements and random behaviors. The discrete event
simulation approach was considered as the most appropriate technique for studying such
operations and can accurately account for the real-world uncertainty and diverse variables of
the interdependent components within mining operations. A verified and validated simulation
model provided results very close to those seen in an actual operating system. A detailed,
accurate simulation model for large, complex systems requires a large data set, statistical
distributions of the data, and a careful choice of simulation software. Sampling from the
probabilistic distribution behavior of the data can be used to evaluate possible factors such as
speed and machine failure.
CONCLUSION
In this study conducted at an existing underground mine the energy consumption and
gas emissions of seven diesel and seven electric LHDs with similar bucket capacities were
analyzed and compared. The results indicated the following:
x Diesel LHDs are mobile, versatile, and their operational flexibility makes them more
productivity than electric LHDs of similar bucket size. On average, diesels LHDs have
a daily production rate 15 to 20 percent higher than electric LHDs of the same size.
x Based on current energy prices, the hourly energy cost for an electric LHD is 47
percent less than a diesel LHD of the same size.
x Diesel LHDs emit 2.68 Kg of CO2 gas for every liter of fuel. Emissions from diesel
LHDs require large volumes of air for ventilation, which generates additional costs.
Electric LHDs have zero emissions and emit less heat than diesel units.
x With increasing energy prices and the need to mine at greater depths, minimizing use
of diesel machines and increasing electric machines reduce energy costs.
ACKNOWLEDGMENT
The authors are grateful to the I2Mine project within the EU 7th framework program
for funding this research.
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