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The mixture velocity at intake 4 was set to 5.5 ft/s and the SF mass fraction was
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computed as 0.0001078 according to Equation (4-9). In the experiment, only SF was
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released from intake 4 but both air and SF were released in this model. If only SF was
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released in the model, it would take a long time for SF to be carried by the airflow
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coming from the upstream. However, if air was released together with SF from intake 4,
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SF would get a higher velocity at the beginning due to the high mixture velocity. At the
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same time, SF mass fraction was changed from 1 to 0.0001078 to match the
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experimental release rate. Then SF would be able to join the main flow stream quickly.
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The reason why the mixture velocity was set to 5.5 ft/s was that the amount of SF
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released from intake 4 was very small (200 SCCM, which is 4.53× 0−5 lb/s in the
experiment) and therefore, the velocity was also small compared to the average velocity
across a cross-sectional area in the upstream before the release point measured as 5.6 ft/s
in the model. The mixture velocity was smaller than 5.6 ft/s so the downstream flow
would not be affected by the injection of the mixture. Simple calculation was claimed
below to prove the injection of mixture did not change the flow behavior in the
downstream very much. The volumetric flow rate measured in the upstream before the
release point was 883.874 ft3/s and the volumetric flow rate at the intake 4 was 5.5 ft3/s.
So the ratio between these two flow rates was computed as 0.00618, which meant the
mixture released from the cube was negligible.
𝑚̇
𝑆𝐹6 𝑝
𝜑 = (4-9)
𝑚𝑎𝑠𝑠 ∗ ∗𝐴
𝑎 𝑟 𝑛𝑡𝑎 4 𝑛𝑡𝑎 4
where 𝜑 represents the SF mass fraction in the mixture, 𝑚̇ is the mass flow rate
𝑚𝑎𝑠𝑠 6 𝑆𝐹6
(lb/s) of SF measured in the experiment, is the air density, is the velocity
6 𝑎 𝑟 𝑛𝑡𝑎 4
for the mixture at the release plane, 𝐴 is the area of the release plane. Since the
𝑛𝑡𝑎 4
cube volume is 1 ft3(1ft×1ft×1ft), 𝐴 is 1 ft2.
𝑛𝑡𝑎 4
4.5.3 Assumptions
Several assumptions are made to save the time on establishing the model without
affecting the results significantly. There is no leakage between air passages. The gravity
of the air in the underground mine is neglected. Airflow in the underground is
incompressible and fully turbulent.
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4.5.4 Governing Equations
All the equations shown below were obtained directly from the theory guide of Ansys
Fluent (Ansys 2009a).
Species transport equations:
∂
(ρ𝑌)+∇∙(ρ𝑣 𝑌) = −∇∙𝐽⃗⃗ +𝑅 + (4-10)
∂t 𝑖
where ρ is the mixture density, 𝑌 is the local mass fraction of each species (in this model,
there are two species, which are SF and air), 𝑣 is the mixture velocity, 𝐽⃗⃗ is the diffusion
6 𝑖
flux of species i, 𝑅 is the net rate of production of species i by chemical reaction, is
the rate of creation by addition from the dispersed phase plus any user-defined sources. In
this case, both 𝑅 and equal to zero since there is no chemical reaction and user-
defined sources in the model mine.
In turbulent flows, mass diffusion is computed by using the following equation in
ANSYS Fluent:
∇𝑇
𝐽⃗⃗ = −(ρ𝐷 + 𝑡 )∇𝑌 −𝐷 (4-11)
𝑖 ,𝑚 𝑇, 𝑇
𝑡
where ρ is the mixture density, is the turbulent Schmidt number ( 𝑡 where is the
𝑡
𝑡
𝑡
turbulent viscosity and 𝐷 is the turbulent diffusivity). The default is 0.7. 𝐷 is the
𝑡 𝑡 ,𝑚
mass diffusion coefficient for species i in the mixture, 𝐷 is the thermal (Soret) diffusion
𝑇,
coefficient.
Momentum equations:
𝜕
( 𝑣 )+∇∙( 𝑣 𝑣 ) = −∇𝑝+∇∙(𝜏̿)+ 𝑔 +𝐹 (4-12)
𝜕𝑡
where p is the static pressure, 𝑣 is the mixture velocity, 𝜏̿ is the stress tensor, and 𝑔 and
𝐹 are the gravitational body force and external body forces, respectively. 𝐹 also contains
other model-dependent source terms such as porous-media and user-defined sources.
The tensor stress 𝜏̿ is given by
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4.5.5 Model Setup
As aforementioned, species transport model was applied to simulate both the airflow and
the SF flow in the underground. Obviously, the mixture species were air and SF . The
6 6
standard k-epsilon model was also used to take care of the turbulence. For near-wall
treatment, the standard wall functions were applied.
4.5.6 Mesh Independence Study
Mesh independence study was conducted to make sure the results from the species
transport model were mesh independent. It also meant that the modeling results were
constant with various mesh sizes. Three meshes, which were fine mesh, medium mesh,
and coarse mesh, were created for this study. A comparison of nodes number for the three
meshes were shown in Table 9. Plan view of the three meshes were provided in Figure
13.
4.5.6.1 Comparisons at the Monitor Points
Based on the three meshes, three species transport models were created. Transient solver
was chosen to complete the simulation in six hours for all the three models. For
comparison purposes, SF mass concentration were monitored at SP1, SP2, SP3, and
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SP9, respectively, in the three models. Monitor points were created in the center of the
planes where the sample points are located. An example of the monitor point location
was shown in Figure 50. Results for the sample points were shown from Figure 51 to
Figure 54.
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with time for the medium mesh and coarse mesh models. However, the final SF mass
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concentration after the six-hour simulation is nearly the same for the three models. The
range of the final SF mass concentration is from 650 PPB to 700 PPB, which is not a big
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difference in terms of the small unit (PPB).
Figure 52. SF mass concentration over time at SP2 for the three meshes.
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In Figure 52, the three curves represent the results from the three meshes, respectively.
SF mass concentration at SP2 almost reach a stable level (about 320 PPB) after six hours
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in the medium and coarse mesh models. The SF concentration still has an increasing
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trend after six-hour simulation in the fine mesh model. However, the final SF mass
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concentration in the fine mesh model was also 320 PPB in the ten-hour simulation as
shown in Figure 93. The reason why the three curves have not reached a stable level is
that SP2 is further away from the release point compared to SP1 and it takes longer for
SF to reach SP2.
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Additionally, the following simulations, which were steady-state simulation and transient
simulation, were performed in the fine mesh model.
4.5.7 Steady-State Simulation
The purpose for the steady-state simulation is to have an overall idea about the final SF
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flow and airflow status in the steady state flow domain. There were two steps to finish the
steady-state simulation. The first step was to let the species transport model run on a
steady solver to let the airflow reach its steady state. Boundary condition for intake 4 was
assigned as wall and no mixture was released in the steady state simulation. The second
step was to continue running the model on the steady solver and begin to release the
mixture from the intake 4. Boundary condition for intake 4 was changed to velocity inlet
in the second step. Convergence criteria was set to 0−3 in both the steps. It took 6900
iterations for the airflow in the first step of the steady-state simulation to get converged.
Results at the monitor points and planes were recorded right after the first step. After
16000 iterations of calculation in the model, SF mass concentration at the monitor points
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and planes reached their stable levels except return 1. Then the CFD model was kept
running to 36560 iterations when the SF mass concentration reached a stable level.
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Contours shown below were created at 16000 iterations. Contours and figures created at
36560 iterations would be specifically mentioned if they were shown below. A monitor
point was created for each sample point in the center of the plane where the sample point
was located. An example for the location of a monitor point was shown in Figure 50.
Results from the steady state simulation were shown in Table 19.
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4.5.7.1 Results Comparisons
Table 19. Results from the steady state simulation in the species transport model.
CFD
Air CFD Air SF
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Sample SF Results
6
quantity SF (kcfm) Results Error Error
6
points (cfm) Air
(kcfm) SF (kcfm) (%) (%)
6
(kcfm)
1 81.00 0.0129 1.29× 0−5 87.04 1.15× 0−5 7.45 10.49
2 19.60 0.0033 3.30× 0−6 19.68 1.31× 0−6 0.40 60.33
3 17.00 0.0028 2.80× 0−6 11.50 1.28× 0−6 32.35 54.42
7 53.74 53.04 1.31
9 63.00 0.0089 8.90× 0−6 64.05 5.31× 0−6 1.67 40.28
RP1 53.60 0.0088 8.80× 0−6 53.04 7.05× 0−6 1.05 19.93
In Table 19, the first four columns are the data obtained from the experiment. Column
five and six represent the CFD results of airflow quantity and SF flow quantity,
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respectively. The SF flow quantity was computed based on the SF mass concentration
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in the center of the cross-sectional area instead of the area-weighted concentration across
the area. The last two columns show the CFD errors of airflow quantity and SF flow
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quantity, respectively. The errors are calculated based on Equation (3-3). Figure 58 and
Figure 63 were made according to Table 19 to show the comparisons more
straightforwardly.
In Figure 16, there was no SF data at SP7 for both experiment and CFD. The reason was
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that SP7 was located far away from RP1 in the upstream and there was no SF detected in
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the field study. Obviously, there was also no SF found at SP7 in the CFD model.
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Both air and SF data were monitored at RP1 to make sure what was released in the CFD
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model matched that in the experiment. Results at RP1 in the model actually came from
the results at monitor plane A. The reason why the results at intake 4 were not used as the
results at RP1 was that the airflow quantity at intake 4 could not represent the airflow
quantity across the entry in the model mine. In addition, the airflow quantity at RP1,
which was shown in the second column in Table 19, was measured across the entry in the
experiment.
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Airflow Quantity (kcfm) Comparison
100.00
) 80.00
m
f
c
k
( 60.00
y
t
i
t
n Experiment Results
a 40.00
u
Q CFD Results
r
i 20.00
A
0.00
SP1 SP2 SP3 SP7 SP9 RP1
Points
Figure 58. Airflow quantity (kcfm) comparison.
As aforementioned, in the species transport model, a mixture of air and SF were released
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from intake 4. However, since the SF mass fraction is only 0.0001078 in the mixture, the
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following mixture velocity magnitude contours were treated as airflow velocity
magnitude contours to make the comparisons between the experiment and CFD model
more clearly.
It is clear that the airflow quantity at SP3 has the largest error, which is 32.35%, among
all the sample points. There are several reasons for this error. Firstly, SP3 is located right
next to the gob. It is very hard for the personnel to get access to and get the experimental
data. Secondly, the CFD model does not simulate everything in the underground. For
instance, there are people and machine moving around SP3 but CFD model does not
simulate it. Thirdly, the experiment itself is not accurate at SP3. There are falling rocks at
SP3 and it creates problems for the personnel to collect data. Finally, airflow at SP3 is
complex and the velocity contours at SP3 can be found in Figure 59 and Figure 60.
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Figure 60. Contour (XY plane) of velocity magnitude (ft/s) at SP3 in the CFD model.
From Figure 58, airflow quantity at SP1 simulated in the CFD is a little bit higher than
that measured in the experiment. The airflow magnitude contour in the cross-sectional
area where SP1 was located is shown Figure 61 and Figure 62. It is clear that velocity is
also not evenly distributed in the cross-sectional area as shown in Figure 61. The range of
velocity magnitude is from 0 to about 10 ft/s. Since the area of the plane where SP1 is
located was measured as 187.7 𝑡2 in the field study, the velocity magnitude at SP1 in
the experiment, which is computed by dividing the volumetric flow rate (81 kcfm) by
area, then becomes 7.19 ft/s. The experimental result, which is 7.19 ft/s, is actually within
the range obtained from the CFD model. Another velocity contour (in XY plane) is
shown in Figure 62 to have a better idea about the complexity of the airflow behavior at
around the SP1.
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In Figure 63, the SF flow quantity at the sample points obtained from the experiment and
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the CFD model are compared with each other. It is obvious that all the results from the
experiment are higher than that from the CFD model. It looks like there are big
differences between the results. However, the largest SF flow quantity is still smaller
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than 1.4× 0−6 kcfm in Figure 63. In other words, the differences between the
experimental and CFD results are not that big in terms of units of the SF flow quantity.
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There are several reasons for the higher SF mass concentration results in the experiment.
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The k-epsilon turbulence model is not perfect and does not represent turbulent flow in the
model very well due to the complex mine geometry. Additionally, there were people and
mining equipment (a huge chuck) moving when the experiment was conducted.
However, these factors were not simulated in the model. Besides, the injection of tracer
gas was not modeled exactly as what it was in the underground. In the species transport
model, SF was released from a cube but in reality, the tracer gas was released from a
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container held by an individual. Moreover, the airflow and SF flow might not be well-
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mixed when the sample points were taken in the experiment. Oppositely, the conditions
set in the 3D CFD model are perfect and flows of air and SF are mixed very well in the
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model.
The reason why the SF mass concentration measured in the experiment is higher than
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that in the CFD mode is that the results at RP1 actually come from the results at monitor
plane A as aforementioned. Due to the diffusion of SF across the monitor plane A, the
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SF mass concentration measured in the CFD model is lower than what is released from
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intake 4. However, the SF6 mass concentration at intake 4 is measured The contour of
SF mass concentration distribution near the RP1 can be found later in Figure 72.
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Contours of the SF mass concentration at SP1 and SP3 are shown below to illustrate the
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SF mass concentration distribution in the cross-sectional area, where the sample points
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are located. Contours of the SF mass concentration at SP2 and SP9 can be found in the
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Appendix.
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From Figure 68, there is no airflow in the gob area in the model mine. However, in
Figure 69, SF diffuses to the gob and the SF mass concentration is lower in the center of
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the gob and higher close to the walls. Additionally, Figure 69 shows that the diffusion of
SF is affected by the velocity magnitude, which agrees with Equation (4-10). According
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to Equation (4-10), as long as the mass fraction of the species (SF in this case) is
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constant, the sum of convection and diffusion of SF should also be constant. When the
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velocity magnitude is high, the convection term in the equation dominant the SF flow
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behavior. If the velocity magnitude is low, the effects from convection will be reduced
and diffusion will dominant the behavior of SF . For instance, SF diffuses less in the
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high velocity magnitude areas like the working face. The contour of velocity magnitude
and SF mass concentration near the working face were shown in Figure 70 and Figure
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71, respectively.
Figure 70. Visualization (in XY plane) of velocity magnitude (ft/s) near the working face
in the CFD model.
According to Figure 70, it is obvious that most of the airflow goes to the working face
and the rest of the airflow goes to the gob and the entry next to the gob. However, SF
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diffuses more to the entry next to the gob than to the working face.
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Figure 72. Visualization (in XY plane) of SF concentration distribution near the RP1 in
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the CFD model.
From Figure 72 and Figure 73, SF released from the intake 4 is concentrated in the
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centerline of the entry for a while and then slowly diffuses across the cross-sectional area.
The contour is more meaningful than that shown in Figure 24 and Figure 25, which are
obtained from the CFD models with and without turbulent viscosity. The reason is that
SF should not fully diffuse to the cross-sectional area right after the RP1 due to the
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effects from airflow convection. In addition, SF does not back diffusion in the upstream
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before RP1 in Figure 72. However, there is SF back diffusion in Figure 24 and Figure
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25, which does not make sense according to the governing equations.
The distance from RP1 to the place where SF is evenly distributed is 37 ft (measured in
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the CFD model). This 37 ft can be used as a reference for determining the locations of
sample points in future field study. If the sample points are located at the places where
SF mass concentration are evenly distributed, the error from experiment can be
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Figure 76. SF mass concentration over iterations at the monitor planes.
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Locations of the monitor planes are shown in Figure 48. Although they are called monitor
planes in Figure 77, a monitor point was created in the center of each monitor plane and
was used to record the changing of SF mass concentration with iterations. According to
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Figure 76, it is obvious that the SF mass concentration at the monitor plane A is the
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largest among the three monitor planes. The final SF mass concentration is about 19000
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PPB at the monitor plane A, while it is lower than 1000 PPB at monitor plane B and C. It
seems 19000 PPB (1.9× 0−5) at monitor plane A is unreasonable. However, it is still
smaller than the SF mass fraction at intake 4, which is 1.078× 0−4. The reason why the
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SF mass concentration at monitor plane A is different from that at intake 4 is due to the
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SF diffusion across the monitor plane A. The differences of SF mass concentration at
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the monitor planes are due to their locations in the model mine. For example, the SF
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mass concentration at monitor plane A is higher than that at monitor plane B because the
SF flow is separated before arriving at monitor plane B but it is not separated at monitor
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plane A. To better visualize the SF mass concentration at plane B and C, Figure 77 is
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created below. It is obvious that the final SF mass concentration at monitor plane B and
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C are about 500 PPB and 400 PPB, respectively.
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Figure 78. SF mass concentration over iterations at the sample points.
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According to Figure 78, the SF mass concentration at the four sample points reach a
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stable level after about 14000 iterations in the model. The final SF mass concentration at
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SP1 is the largest among the four sample points while it is the smallest at SP2. The reason
is that SP1 is located right next to RP1 and SP2 is located in the entry close to neutral 2
as shown in Figure 48. The SF flow, which is originally released form RP1, is separated
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several times before reaching SP2. However, it reaches SP1 without any separations or
obstacles.
4.5.8 Transient Simulation
Transient simulation was also processed in two steps. At first, the species transport model
was ran on a steady solver to let the airflow reach its steady state. Boundary condition for
intake 4 was changed to wall and no mixture was released in the steady state simulation.
Then the model continued to be ran on a transient solver and the mixture was released
from intake 4. Boundary condition for intake 4 was changed to velocity inlet.
Convergence criteria for both the steady state simulation and transient simulation were
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set to 0−3. The transient simulation, which was the second step, has been run for ten
hours. Compared to the six-hour experiment, it was longer. The reason was that the SF
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concentration has not reached a steady level in six hours for some returns and sample
points far from the release point in the CFD model. The ten-hour simulation made it
possible to visualize the final SF mass concentration at different locations.
6
4.5.8.1 Results from the Species Transport Model
The results from the transient simulation were made up of two parts. One was from the
six-hour simulation and the other was from the ten-hour simulation. Both the results were
compared to the results from the six-hour experiment. SF mass concentration was
6
monitored at various locations in the model mine.
4.5.8.1.1 Six-hour Simulation
The six-hour transient simulation was performed to make a comparison with the six-hour
experiment. SF mass concentration was monitored at two returns, one neutral, and three
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monitor planes. A monitor point was created for the returns and neutral, respectively. The
monitor point was located at the center of the returns, neutral, and monitor planes because
the sample points were located in the center of entries in the experiment. An example for
the location of the monitor point in return 3 was shown in Figure 50.
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Figure 80. SF mass concentration over time at all the monitor planes.
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The three monitor planes were created in the species transport model. Locations of the
monitor planes were shown in Figure 48. Monitor plane A was located right after the
release point 1. Monitor plane B was a plane created in the entry where the airflow was
about to enter the working face. The monitor plane C was a plane created in the working
face. Contours of velocity magnitude and SF mass concentration were created at the
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three monitor planes to have an idea about the distribution of the velocity magnitude and
SF mass concentration. Monitor points were also created at the three planes,
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respectively. All the monitor points were located in the center of the monitor planes like
the location of the monitor point in return 3 in Figure 50. SF mass concentration over
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time was monitored at the monitor points in the three monitor planes and was presented
in Figure 80.
Figure 80 shows the SF mass concentration over time at the monitor points located in the
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three monitor planes. It is clear that the SF mass concentration reach a stable level in a
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short period of time at monitor plane A because it is located right after the release point 1.
The final SF concentration at monitor plane A is about 19000 PPB (19 PPM), which is
6
much higher than that in the monitor plane B and C. There are two main reasons for the
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higher SF mass concentration in monitor plane A. One is SF flow has not been
6 6
separated because of turns or obstacles in the entry. The other one is no new airflow joins
the original mixture at monitor plane A. So the amount of SF originally released from
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the intake 4 is not reduced A while the airflow rate keeps the same at monitor plane. SF
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mass concentrations are much lower at monitor plane B and C due to the aforementioned
reasons. Figure 81 was created because the SF mass concentration values at monitor
6
plane B and C are hard to be read in Figure 80.
Figure 81. SF mass concentration over time at monitor plane B and C
6
From Figure 81, the SF mass concentration reaches a stable level after the six-hour
6
simulation for monitor plane B and C. The final SF mass concentration are 500 PPB and
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400 PPB for the monitor plane B and C, respectively. The difference in the SF mass
6
concentration between the two monitor planes is caused by the distribution of the amount
of SF at monitor plane B before arriving monitor plane C. In addition, the SF mass
6 6
concentration at monitor plane B shows up about half an hour earlier than that at monitor
plane C. It is because the monitor plane B is located closer to the release point 1
compared to the monitor plane C.
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directly from the VnetPC model used in the preliminary study (Zhang et al. 2014) for this
study. Trace element (PADT, 2014) (in this case, SF ) was created in the Flownex model
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to simulate the distribution of the SF concentration in the model mine.
6
Figure 101. Plan view of the Flownex model.
4.6.2 Results
Table 20. Results from the Flownex model with tracer gas.
Air Flownex Flownex Air SF
6
Sample SF SF
6 6
quantity Results Air Results SF Error Error
6
points (cfm) (kcfm)
(kcfm) (kcfm) (kcfm) (%) (%)
1 81.00 0.0129 1.29× 0−5 86.36 8.73× 0−6 6.62 32.36
2 19.60 0.0033 3.30× 0−6 19.59 1.98× 0−6 0.05 40.02
3 17.00 0.0028 2.80× 0−6 0.51 5.19× 0−8 96.98 98.15
7 53.74 53.70 0.07
9 63.00 0.0089 8.90× 0−6 63.07 6.37× 0−6 0.10 28.41
RP1 53.60 0.0088 8.80× 0−6 52.38 8.72× 0−6 2.28 0.85
From Table 20, sample point 3 has the largest error for both airflow quantity and SF
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concentration. Airflow quantity at sample point 3 is only 17 kcfm (1000 cubic feet per
minute). It is reasonable because network modeling is not significantly sensitive to the
areas with low airflow velocity. In addition, the gob was represented by four pathways
with high resistance values in the Flownex model. There was no accurate gob model in
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the Flownex model, which made the model less accurate compared with the 3D CFD
model. Since sample point 3 is located next to the gob, both the airflow quantity and the
SF concentration are certainly affected due to the lack of an accurate gob model in the
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Flownex model.
4.7 Hybrid Model
After taking the computing time into account, a hybrid model of Fluent and Flownex
become the idea to simulate both the airflow quantity and SF concentration for the
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model mine. Working face area in the model mine was determined to be the CFD
component in this case. However, according to the results from the Flownex model,
sample point 3 should be taken into account in the hybrid account since the airflow near
sample point 3 was complex and had the largest error compared to the experimental
results. The reason for not having the area close to sample point 3 as the CFD component
in this specific geometry was that the gob would be added to the CFD component
together with the area around sample point 3. It would increase both the complexity and
difficulty of the hybrid model, which was not the purpose of the study. The rest of the
model mine was simulated in Flownex. An overview of the link was shown in Figure
102. The working face CFD component and an enlarged view for part of the mesh in the
CFD model were presented in Figure 103.
Figure 102. Plan view of the hybrid model.
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In Figure 102, there were four data transfer links established between Flownex and Ansys
Fluent. An enlarged view of the data transfer links was shown in Figure 104. The data
transfer link 3 was used to check the error of mass flow rate between Fluent and
Flownex. The big yellow Ansys icon in this link acted as a Fluent controller. It passed the
updated boundary conditions and mass flow rate data between Fluent and Flownex back
and force. Behind the Ansys icon were large amounts of code that making this hybrid
model works.
Due to the requirements of Flownex, inlet and outlet boundary conditions in the CFD
model should be set as pressure-inlet and pressure-outlet separately. The inputs for inlet
and outlet in the CFD component were not important because Flownex would transfer the
two inputs to Fluent through data transfer link 1 and 4 (Figure 104) no matter what the
inputs were at the beginning. To get more stabilized results from the CFD model, the
standard k-omega model was used in this hybrid model after several tries with other
turbulent models.
Average total pressure values were used for both inlet and outlet boundary conditions.
The reason was that this hybrid model was made by a 1D Flownex model and a 3D CFD
model. Since the pressure distribution in the 3D model was not constant, average values
were taken to be filled in the 1D model.
Fluent was run 50 iterations per coupling iteration. The coupling simulation did not stop
until the error of mass flow rate values reached an acceptable convergence. Here, mass
flow rate values came from both Fluent and Flownex. To stabilize the coupling results,
Fluent was set to not stop running even if it reaches its convergence criteria. Fluent ran
much longer than it need to until the coupling converged. Flownex was converging very
well in this hybrid model.
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Figure 106. Convergence history for some parameters in the CFD model.
Table 21. Hybrid Model Results.
Air Hybrid Hybrid Air SF
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Sample SF SF
6 6
quantity Results Results SF Error Error
6
points (cfm) (kcfm)
(kcfm) Air (kcfm) (kcfm) (%) (%)
1 81.00 0.0129 1.29× 0−5 86.59 8.76× 0−6 6.90 32.08
2 19.60 0.0033 3.30× 0−6 19.59 1.98× 0−6 0.05 39.92
3 17.00 0.0028 2.80× 0−6 0.41 4.12× 0−8 97.60 98.53
7 53.74 53.70 0.07
9 63.00 0.0089 8.90× 0−6 63.01 6.37× 0−6 0.02 28.47
RP1 53.60 0.0088 8.80× 0−6 52.60 8.76× 0−6 1.87 0.43
From Table 21, airflow quantity at SP3 in the hybrid model is still inconsistent with the
experimental results. The reason is that gob area is not simulated in this hybrid model.
SP3 is right next to the gob and airflow at SP3 is affected by the gob. The ideal solution
for this case is to establish a hybrid model with gob taken into account. It means that the
CFD component in the hybrid model will contain the gob and several entries connected
with the gob. Then Flownex will be able to update the boundary conditions for the CFD
component. However, it will be too complex if including the gob in the hybrid model in
this study. The purpose of establishing this hybrid model in the study is to show that CFD
can be linked with other software to get an accurate solution.
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modeling results. However, the y axis in the figure represents the SF flow quantity and
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the largest SF flow quantity value is still less than 0.000014 kcfm. The comparison was
6
made in Figure 108 to show the fact that SF flow quantity from the experiment is higher
6
than that from the three models. One reason is that SF concentration was affected by the
6
airflow recirculation at the sample points. The other reason is that experimental data is
not recorded accurately due to human error and moving equipment.
Overall, the 3D CFD model are the most accurate model among the three models.
However, the long computing time make the CFD model time-consuming. In terms of the
results, the Flownex and hybrid model are almost the same for this mine geometry. On
one hand, the CFD component in the hybrid model does not affect the results very much
because the gob area was not simulated accurately. On the other hand, the hybrid model
works correctly in this paper, and it verifies the coupling capability of Flownex.
Moreover, the CFD component in the hybrid model will make a big difference for other
cases, such as a mine gob area, and areas with low airflow velocity. The reason is that
network modeling is not sensitive to the areas with low airflow velocity. If the CFD
component can be applied in this areas, network modeling will be as good as the CFD
model. Then the hybrid model will save both the time for building up and solving the
CFD model.
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5 Conclusions and Future Work
The purpose for this research was to figure out the best approach to simulate the flow
behaviors in an underground mine. Both the experiment and the models with different
software packages have been conducted in this research.
The field study was done in the underground mine for a six-hour period with the help of
releasing-sampling SF in different locations. The models created for the model mine
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basically consisted of network modeling and CFD modeling. Network modeling was built
at first. For the network modeling, a VetPC model and a Flownex model were made. In
terms of the CFD modeling, several 2D CFD models and 3D CFD models with various
settings were made. Finally, a hybrid model was made.
From Chapter 3, two models were created based on the mine geometry. One was the
VnetPC model provided by the mine. The other one was a 2D CFD model without the
mine gob. In examining the results from these two models, the 2D CFD model appeared
to be the better choice to simulate the underground mine. However, it did not take the gob
into account. Besides, distribution of the SF concentration was not simulated in both the
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VnetPC model and the 2D CFD model. Airflow quantity results from the two models
were compared with the results from experiment and then the results from the two models
were compared with each other. Several conclusions are made for Chapter 3. The
network modeling is not sensitive to the low airflow quantity areas. Besides, an
underground mine can be simulated with both a CFD model and a network model to
achieve a high accuracy on the results. The network model should be created at first and
the CFD model will be applied to the areas where there are large errors appearing in the
network model.
To improve these models, 3D CFD models with the gob included and a Flownex model
were built in Chapter 4. Since Flownex has the capability to model a trace element,
Flownex was used to represent network modeling instead of VnetPC. Several 2D CFD
models were created in Chapter 4 to verify the fact that the gob area had no need to be
divided into five zones for this specific model mine. All the 3D CFD models were then
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built up with the one-zone gob. At the same time, SF concentration was simulated in the
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3D CFD models. A mesh independence study and a sensitivity study on the porosity and
permeability values were generated for the 3D CFD model with and without turbulent
viscosity to make sure that mesh size, porosity and permeability values did not affect the
results from the 3D CFD model. Another mesh independence study was performed for
the 3D CFD model with species transport model. As a result. the fine mesh and the
porosity and permeability values from Lolon’s dissertation (Lolon 2008) were determined
to be applied in both the steady-state simulation and transient simulation in the two 3D
CFD models. In terms of the 3D CFD model using UDF approach, two cases (with and
without turbulent diffusivity) were created for the steady-state simulation to see the
effects of interpreting the turbulent diffusivity. Surprisingly, the turbulent diffusivity did
not affect the 3D CFD results for this mine geometry. Then a transient simulation was
established without turbulent diffusivity interpreted. Results from both the steady-state
simulation and the transient simulation were carefully analyzed in Chapter 4. Because the
SF mass concentration contours obtained from the 3D CFD model using UDF approach
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cannot be explained, the 3D CFD model with species transport model was created to
explore the correct results. Similar to the 3D CFD model using UDF approach, both
steady-state and transient simulation were conducted in the species transport model.
Results were analyzed in detail in Chapter 4.
The hybrid model was the last model built up in Chapter 4 and the purpose was to make
full use of the coupling capability of Flownex. It was much easier to establish the hybrid
model than the 3D CFD model for the model mine because both the Flownex part and the
CFD component part were not complex. Although the results from the hybrid model was
almost the same to that from the Flownex model without the CFD component, it still
proved the success of the hybrid model. Since working face in the 3D CFD model was
taken out and used as the CFD component in the hybrid model, it was correct to have no
difference between the Flownex model and the hybrid model. If the gob area was used as
the CFD component in the hybrid model, results from the hybrid model should be the
same as that from the 3D CFD model. However, it will increase the complexity for
building up the hybrid model, which is not the purpose of this research.
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To sum up, the goal of this research is to find an optimal method to simulate an
underground mine with an easy-setup and high-accuracy model. Obviously, the ideal
approach will be the 3D CFD model with species transport model. But it is impractical
and time consuming to simulate an entire underground mine only with the 3D CFD
model. Practically, the hybrid model is the best approach to achieve the goal. The hybrid
model represents a combination of network modeling and CFD model. It takes
advantages of both the two models. According to the findings in this research, there are
several suggestions on using this hybrid model for an underground mine.
The hybrid model is unique only when it is applied appropriately. For a large scale
underground longwall mine where a 3D CFD model is impractical to use, the hybrid
model will be a good fit. Areas with low airflow velocity should be simulated in the CFD
component. Gob area is also required to be modeled in the CFD component.
Computing time should be considered when using the hybrid model. The hybrid model is
time-saving but it also depends on how you assign the CFD component. It is not a good
idea to simulate the airways without any obstacles or areas where airflow is not complex
in the CFD component. The reason is that Flownex can also simulate these areas with less
time on establishing and solving the model. The CFD component should be used to
simulate the areas with complicated airflow, which cannot be simulated in the Flownex
model. It is always good to build up a model for the entire underground longwall mine
with only Flownex. Then the low airflow velocity areas can be determined.
There are also some limitations for the hybrid model. Like other modeling software, both
Ansys Fluent and Flownex have numerical errors. Then the hybrid model also has some
numerical errors. The hybrid model cannot simulate exactly what happens in the
underground, such as equipment moves in the underground while samples are taken.
Besides, turbulent models used in the CFD component in the hybrid model does not
perfectly represent turbulent flow when the model mine geometry is considerably
complex.
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References
Ansys. 2006. Fluent 6.3 User’s Guide.
Ansys. 2009a. Ansys Fluent 12.0 Theory Guide.
Ansys. 2009b. Ansys Fluent 12.0 UDF Manual.
Edwards, J C, and C C Hwang. 2006. “CFD Modeling of Fire Spread Along
Combustibles in A Mine Entry.” In SME Annual Meeting, St. Louis, Missouri, 1–5.
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Permeability Distributions and Its Application to Reservoir Modeling of Coal Mine
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Gerwin, H., W. Scherer, and E. Teuchert. 1989. “The TINTE Modular Code System for
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Bed High-Temperature Gas-Cooled Reactor.” Nuclear Science and Engineering 103:
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Heerden, Johan Van, and Peter Sullivan. 1993. “The Application of CFD for Evaluation
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Janse Van Rensburg, J. J., and M. Kleingeld. 2010. “A CFD Method to Evaluate the
Integrated Influence of Leakage and Bypass Flows on the PBMR Reactor Unit.”
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http://dx.doi.org/10.1016/j.nucengdes.2010.08.011.
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( PPRV ) for the Release of Perfluoromethylcyclohexane ( PMCH ) in Underground
Mine Tracer Gas Studies.” Virginia Polytechnic and State University.
Karacan, C Ö, T Ren, and R. Balusu. 2008. “Advances in Grid-Based Numerical
Modeling Techniques for Improving Gas Management in Coal Mines.” In 12th
U.S./North American Mine Ventilation Symposium, Pittsburgh, Pennsylvania, USA,
313–20.
Kelsey, Adrian et al. 2003. “CFD Modelling of Methane Movement in Mines Ian S
Lowndes David Whittles.” In Johannesburg, South Africa, 475–86.
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Lazzara, C.P., and F.J. Perzak. 1987. “Effect of Ventilation on Conveyor Belt Fires.” In
Symposium on Safety in Coal Mining, Pretoria, South Africa.
Lolon, S.A. 2008. “Computational Fluid Dynamics Simulation Study on Hot Spot
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Marais, D. 2007. “Validation of the Point Kinetic Neutronic Model of the PBMR.”
Potchefstroom Campus of the North-West University Supervisor:
Olivier, Jacobus C. 2005. “Network Modelling of Transient Heat Exchanger
Performance.” Potchefstroom University for Christian Higher Education.
PADT. 2013. Flownex–Fluent Link.
PADT. 2014. Flownex General User Manual.
Ren, T, and R Balusu. 2005. “CFD Modelling of Goaf Gas Migration to Improve the
Control of Spontaneous Combustion in Longwalls.” In Brisbane, QLD, 26–28.
Ren, T, R Balusu, and C Claassen. 2011. “Computational Fluid Dynamics Modelling of
Gas Flow Dynamics in Large Longwall Goaf Areas.” In Wollongong, NSW, 24–30.
Ren, T, R Balusu, and P Humphries. 2005. “Development of Innovative Goaf Inertisation
Practices to Improve Coal Mine Safety.” In COAL OPERATORS’ CONFERENCE,
Brisbane, QLD, 26–28.
Scheidegger, A.E. 1957. The Physics of Flow through Porous Media. New York: The
Macmillan Co.
Slabbert, Rohan. 2011. “Thermal-Hydraulics Simulation of a Benchmark Case for a
Typical Materials Test Reactor Using FLOWNEX.” North-West University.
Smith, A C, and L Yuan. 2008. “Simulation of Spontaneous Heating in Longwall Gob
Area with a Bleederless Ventilation System.” Mining Engineering (August): 61–66.
Walter, Ayelet, Alexander Schulz, and Günter Lohnert. 2004. “Comparison of Two
Models for a Pebble Bed Modular Reactor Core Coupled to a Brayton Cycle.” In
2nd International Topical Meeting on HIGH TEMPERATURE REACTOR
TECHNOLOGY, Beijing, China.
Xu, Guang. 2013. “Remote Characterization of Underground Ventilation Systems Using
Tracer Gas and CFD.” Virginia Polytechnic Institute & State University.
Yuan, L, and A C Smith. 2008a. Computational Fluid Dynamics Modeling of
Spontaneous Heating in Longwall Gob Areas.
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Applications of Queuing Theory for Open-Pit
Truck/Shovel Haulage Systems
Meredith Augusta May
Abstract
Surface mining is the most common mining method worldwide, and open pit mining accounts
for more than 60% of all surface output. Haulage costs account for as much as 60% of the total
operating cost for these types of mines, so it is desirable to maintain an efficient haulage system.
As the size of the haulage fleet being used increases, shovel productivity increases and truck
productivity decreases, so an effective fleet size must be chosen that will effectively utilize all
pieces of equipment. One method of fleet selection involves the application of queuing theory to
the haul cycle. Queuing theory was developed to model systems that provide service for
randomly arising demands and predict the behavior of such systems. A queuing system is one in
which customers arrive for service, wait for service if it is not immediately available, and move
on to the next server or exit the system once they have been serviced. Most mining haul routes
consist of four main components: loading, loaded hauling, dumping, and unloaded hauling to
return to the loader. These components can be modeled together as servers in one cyclic queuing
network, or independently as individual service channels. Data from a large open pit gold mine
are analyzed and applied to a multichannel queuing model representative of the loading process
of the haul cycle. The outputs of the model are compared against the actual truck data to
evaluate the validity of the queuing model developed.
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Chapter 1: Introduction
Surface mining is the most common mining method worldwide, and open pit mining accounts
for more than 60% of all surface output (Hartman & Mutmansky, 2002). Open pit mining
consists primarily of the removal of topsoil and overburden, drilling and blasting of ore, and the
transportation of material using a system of shovels or excavators and haul trucks. After the haul
trucks have been loaded, the trucks transport the material out of the mine to a dumping location
where the material will either be stored or further processed. The trucks then return into the mine
and the cycle repeats itself. For most surface mines, truck haulage represents as much as 60% of
their total operating cost, so it is desirable to maintain an efficient haulage system (Ercelebi &
Bascetin, 2009). As the size of the haulage fleet being used increases, shovel productivity
increases and truck productivity decreases, so an effective fleet size must be chosen that will
effectively utilize all pieces of equipment (Najor & Hagan, 2004).
When selecting earth-moving equipment for a particular mine site, shovels and trucks must be
matched based on their characteristics. The loader needs to be an appropriate size relative to the
height and width of the benches being mined, and the dumping height of the loader must be
sufficient to clear the side of the haul truck. The loader selected should also be able to fully load
a haul truck in three to six passes without using any partially filled buckets (Alkass, El-
Moslmani, & AlHussein, 2003). The number of trucks required to meet production requirements
and maximize efficiency is difficult to determine, and the number of trucks necessary will
change over time as mining advances and haul routes become longer.
One method of fleet selection involves the application of queuing theory to the haul cycle.
Queuing theory was developed to model systems that provide service for randomly arising
demands and predict the behavior of such systems. A queuing system is one in which customers
arrive for service, wait for service if it is not immediately available, and move on to the next
server once they have been serviced (Gross & Harris, 1998). For modeling truck-shovel systems
in a mine, haul trucks are the customers in the queuing system, and they might have to wait for
service to be loaded and at the dumping locations.
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Chapter 2: Literature Review
2.1 Methods of Fleet Selection
Before computer systems were readily available, estimates about haul cycles were made which
would approximate average times for specific activities such as loading, travelling, dumping, and
delay times. The reliability of this approach varies widely based on the analyst’s ability to obtain
accurate average times for the cycle. This conventional method assumes that trucks make each
round trip in exactly the same amount of time and that the productive capacity of a carrier is not
affected by the number of carriers in the system. This method is not able to analyze variations
between different cycles or different operating periods (Deshmukh, 1970).
Optimal fleet size can also be estimated based on production tonnage requirements and
individual truck productive capability. In this method a truck’s productive capacity is calculated
based on a truck’s effective payload and its estimated cycle time multiplied by a productivity
factor. The number of trucks that need to be operated is then calculated by dividing the hourly
tonnage required by the tons per truck per hour, based on the calculated productive capacity
(Burton, 1975). This method does not provide an accurate model of truck-shovel systems, but it
does provide a rough estimation of the number of trucks required to meet production needs.
Another common method for modeling fleet-loader systems involves stochastic simulation. In
stochastic simulation a random number selection technique such as Monte Carlo simulation
creates probability distributions from a stochastic variable based on data from time studies. This
is done to obtain a sequence of variable times that might occur during actual operations. This can
be used to find values for sections of the haul cycle such as loading time, dump time, or delay
time. A model of a haul cycle is created based on the loading, haulage, and waiting times
obtained through Monte Carlo simulation (Deshmukh, 1970). Computer simulation programs can
quickly perform these simulations and the optimum number of trucks can be found by comparing
models of a given haul route using different fleet sizes. Due to the stochastic and dynamic nature
of shovel-truck interactions, different simulation models used to calculate fleet requirements will
yield different fleet sizes for the same input parameters. This is largely due to the assumed
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probability distributions applied to variables in the cycle and the waiting times for haulers and
loaders calculated based on those assumptions (Krause & Musingwini, 2007).
Talpac is a commonly used computer simulation program designed for evaluating haulage fleets
that was developed by Runge. Users can input site specific parameters affecting fleet
productivity such as material characteristics, haul route, truck and loader types, work roster, and
operating limitations. Talpac can then calculate fleet productivity for long term and short term
planning, equipment evaluation, optimum loading techniques, haulage costs, and other
production values (Runge, 2011). Talpac is commonly used throughout the mining industry for
shovel-truck analysis even though it can only fit a maximum of five probability distributions for
cycle variables (Krause & Musingwini, 2007).
Another method of fleet selection involves the application of queuing theory to the haul cycle.
Queuing theory was developed to model systems that provide service for randomly arising
demands and predict the behavior of such systems. A queuing system is one in which customers
arrive for service, wait for service if it is not immediately available, and move on to the next
server once they have been serviced (Gross & Harris, 1998). For modeling truck-shovel systems
in a mine, haul trucks are the customers in the queuing system, and they might have to wait for
service at the loader and at the dumping location.
2.2 Applying Queuing Theory to Mining
Ernest Koenigsberg first applied queuing theory to mining practices in 1958. Koenigsberg
modeled conventional, mechanized room and pillar mining operations using closed loop queuing
systems with a finite number of customers based on the assumption of exponential service time
distributions. The mining system being considered consists of a set of specialized machines
which work in succession on a series of active mine faces. The entities involved in the cycle
include a cutting machine, drilling machine, blasting crew, loading machine group – a loader and
one or more shuttle car, and a roof bolting machine. Each machine proceeds to the next face
when it is done with its task. The time it takes for each machine to complete its task is non-
constant and subject to random time variations. Transit time and machine breakdowns also add
to random time variation. This setup was translated into queuing theory notation by considering
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the machines to be fixed in sequence with the mining faces queuing for service in cyclic, first
come-first served order. In queuing theory notation, this translates to a closed queue with N
customers receiving service in order of arrival from M machines. After the Mth stage, the
customer (mine face) rejoins the queue at stage one (Koenigsberg, 1958).
Koenigsberg adapts formulas to determine the probability that the system is in a given state, the
mean number of units waiting for service at a given stage, the delay at a given stage, mean cycle
time, probability that a stage is idle, and daily output. These equations can be recalculated for
different numbers of servers and customers so that the results for different machine
configurations can be compared. Koenigsberg finds that output increases as N, the number of
working faces is increased, and the rate of change of increase decreases with increasing N. He
also finds that the overall output is limited by the service rate of the slowest machine
(Koenigsberg, 1958).
Queuing theory gained popularity as a method of fleet selection and haul cycle analysis in the
1970s and 1980s. Simulation models were a commonly used technique for analysis of shovel-
truck systems during this time period because they could provide useful results that accounted
for the variability inherent in the system (Barnes, King, & Johnson, 1979). A major drawback of
computer simulation was the method’s requirement of computer memory and CPU time, which
was costly and time consuming. Analytical modeling methods with little to no computing
requirements, such as queuing theory, were a viable alternative to computer simulation models
(Billette, 1986).
In 1973 Maher and Cabrera applied cyclic queuing theory to civil engineering earthmoving
projects, similar to haulage systems found in open pit mining. Queuing theory is used here to
find the optimum number of trucks that should be used to minimize the cost per unit volume of
earth moved. The haulage system is analyzed with the option of considering loading and transit
times to be constant or variable, fitting a negative exponential distribution. This study also
recognizes that with more than one excavator in operation the system can have either two
separate queuing systems or one joint queue. The end result of this modeling is a set of charts for
choosing the most cost-effective number of trucks based on the ratio of the loading time and
haulage time and the ratio of the costs to operate the loader and the trucks (Maher & Cabrera,
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1973). These charts could be applied to any earthmoving or mining operation as long as the data
about cost and cycle time is known.
In 1977 Jorgen Elbrond developed a straightforward calculation technique based on queuing
theory to be used as an alternative to computer simulation for evaluating open pit operation
capacity. Elbrond’s technique is based on queuing theory’s formula for waiting time in a closed
circuit with added correction factors which reflect variability in loading, travel, and dumping
times. Waiting times at service stations are calculated as a function of the number of trucks in the
circuit by averaging the results found through simulations for three different cases: constant
travel time and constant service time, exponentially distributed travel time and exponentially
distributed service time, and exponentially distributed travel time and constant service time.
Correction factors are calculated using an interpolation procedure combining theoretical and
simulated cases. Other data relevant to the haul cycle such as dumping time and shift
composition is found using time studies. Once formulas had been completely developed, time
studies made at Hamersley Iron found a correlation coefficient of 0.865 between observed and
calculated wait time at shovels (Elbrond, 1977). This suggests that the technique used is a
reasonably accurate method of modeling haulage systems.
Barnes, King, and Johnson approach queuing theory as an alternative to costly computer
simulation and rough-estimate match factor and efficiency factor methods of approximating
production capacities of open-pit systems. In their paper Ernest Koenigsberg’s approach to mine
modeling using cyclic queues and Jorgen Elbrond’s work with finite queues are outlined and
compared to one another and to the results of stochastic simulation. The goal of this comparison
is to observe any systematic relationship between the estimates found using each method
(Barnes, King, & Johnson, 1979).
This comparison found that stochastic simulation is more flexible than the two queuing theory
methods and provides more accurate results. Unlike the methods relying on queuing theory,
simulation does not assume steady state conditions for the entirety of the cycle time; simulation
is able to account for startup time and end of shift activity. The main disadvantages associated
with stochastic simulation are the significant amount of time and manpower necessary to develop
the simulator and the considerable amount of computer time that is used to run the simulation.
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This study found that cyclic queuing as it existed at the time, such as Koenigsberg’s model, is
not an adequate method of estimating truck-shovel production. This is largely based on the
mathematical requirement that all segment times be exponentially distributed. This causes the
effects of bunching and mismatch to be greatly exaggerated, and for production to be
understated. It was concluded that this method does not produce a true representation of the
system’s productive capacity.
Elbrond’s finite queuing theory application can produce a fairly accurate estimate of production
values by applying a correction factor to account for the results found using exponentially
distributed activity times. Elbrond generates waiting times and subsequently production
predictions which closely approximate observed values by interpolating between his three cases,
which are: constant travel time and constant service time, exponentially distributed travel time
and exponentially distributed service time, and exponentially distributed travel time and constant
service time. Barnes, King, and Johnson conclude that while Elbrond’s finite queuing theory
method produces a more accurate model than Koenigsberg’s cyclic queues do, modifications are
needed either to the correction factors or to the method itself in order to more closely resemble
actual operations output (Barnes, King, & Johnson, 1979).
In the late 1970s nearly all applications of queuing theory to mine production used exponential
distributions. There were few alternatives available since the use of more-general distributions
such as normal or log-normal distributions involved prohibitively complex mathematics.
However, the Barnes, King, and Johnson study does address the possibility of using an Erlang K
distribution with finite queues, similar to Elbrond’s technique. For this proposed method only
two cases would need to be analyzed: exponential arrival with Erlang K service and deterministic
arrival with Erlang K service. The Erlang distribution parameters account for the effects of
variability in the service rate. Correction factors need only be applied as a function of arrival rate
variability. An extension of these models would be one with Erlang arrival and Erlang service
times to eliminate the need for interpolation or correction factors, but the math involved with
such a model would be exceptionally complex. At the time their paper was published, no
solution to an Erlang/Erlang finite queuing model had been developed, but it was determined that
developing such a model would provide a useful, inexpensive analytical alternative to simulation
methods for open pit production calculations (Barnes, King, & Johnson, 1979).
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Barbaro and Rosenshine presented a paper in 1986 which uses a cyclic queuing theory model to
evaluate the productivity of a truck-shovel system. A cyclic queuing model with exponentially
distributed service times is used to model an example problem and the results are compared to
those from simulation to demonstrate that the assumptions of exponentially distributed service
times and steady state behavior are not major problems. Barbaro and Rosenshine compare their
cyclic queuing model to the methods used in the 1979 Barnes, King, and Johnson study and
achieve results more favorable than those reached in the original paper. Barnes et al. consistently
reported results from queuing theory-based models that exceeded the theoretical maximum
capacity of the mine in question. The results of the Barbaro and Rosenshine study find that the
cyclic queuing model in question is correctly coded and provides valid results. In their study,
shovel utilization rates found using cyclic queuing models only differ from the results found
through simulation by 0.4% and productivity values differ by 0.9%. No explanation is offered to
explain the discrepancy between the different results found in the 1979 and 1986 studies
(Barbaro & Rosenshine, 1987).
Engineering Queues in Construction and Mining by D. G. Carmichael contains queuing theory
models based on assumptions applicable to mining and construction operations which have been
validated by reference to field data records comparing theory and practice. Models for many
different situations are provided, including queues with random arrivals and exponential service
times; queues with alternative distributions for arrivals and servicings; cyclic queues; serial
queues and storage; earthmoving, quarrying, and open-cut mining operations; and machine
maintenance and repair. While there are many formulas and equations supplied for each of these
topics that can easily be used as tools in scheduling, planning, productivity analysis, and cost
analysis, there is little information given about how closely these models follow actual
operations (Carmichael, 1987).
Muduli and Yegulalp’s 1996 paper presents an analytical method of modeling truck-shovel
systems as a multiple-chain closed queuing network. This allows the model to account for
haulage systems which do not necessarily contain identical trucks. Prior to this, nearly all
queuing theory-based models of haulage systems were based on the assumption that the fleet is
composed of only one truck type. Carmichael addresses heterogeneous cases where trucks are
not assumed to be identical in his book (Carmichael, 1987). Carmichael uses an approximation
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method to adapt the heterogeneous system into an equivalent homogeneous system, but this is
not a method based on queuing theory techniques. Muduli and Yegulalp address the problem
using a closed queuing network with multiple classes of customers. This allows for different
classes of trucks with different capacities and operating characteristics to be included (Muduli &
Yegulalp, 1996).
In queuing theory, a chain consists of a permanent categorization of jobs. As it applies to mining,
a job (truck) which is part of one chain cannot switch to another. Different types of trucks can be
sorted into different classes depending on their size and productivity. For this model, it is
assumed that there is a single class of trucks per chain. Different classes of trucks can be given
different characteristics by assigning different general service-time distributions to each one
(Muduli & Yegulalp, 1996).
Often in truck-shovel modeling all trucks within the system are assumed to be identical for
analytical purposes, even when it is recognized that multiple types and sizes of trucks are present
in the system. This is done to simplify calculations. To calculate performance characteristics of
these multiple chain queuing systems involving multiple classes of trucks a Mean Value
Analysis (MVA) approach is used for conditions when all trucks of different classes have
identical exponential service time distributions. For situations with generally distributed service
times a method called Extended MVA can be used for multiple classes of trucks and service
times (Muduli & Yegulalp, 1996).
This study compares results found using multiple chain queuing networks to the results of
evaluating a system with multiple classes of trucks by assuming all trucks are identical. It is
found that the maximum production rate calculated using an equivalent single-class model
underestimates the maximum production rate that is possible using multiple classes of trucks by
as much as 14% when two different classes of trucks are present. The relative error of maximum
truck production found using equivalent single-class models increases as the number of trucks
and the number of different classes of trucks involved increase. It is clear that a modeling system
that accounts for different classes of trucks is essential to determine the optimal number of
different sizes of trucks to maximize a mine’s production output (Muduli & Yegulalp, 1996).
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In 2002 Khalil El-Moslmani created a computer model based on queuing theory to model multi-
loader truck systems assuming trip times have a negative exponential distribution and service
times follow an Erlang distribution with three or fewer servers. For cases with multiple types of
haulers, unlike Muduli and Yegulalp’s method involving multiple chain queuing systems, an
approximation based on weighted averages is used to convert the heterogeneous system into a
homogeneous one. This is similar to Carmichael’s method of converting heterogeneous systems
into homogeneous ones (Carmichael, 1987).
El-Moslmani’s queuing model is solved to obtain values such as server utilization to be used in
the calculation of system production. The computer module, called FLSELECTOR, is used to
assist in choosing proper fleet size. FLSELECTOR is implemented using Visual Basic for
Application (VBA) and Microsoft Excel and allows for an optimum fleet to be selected based on
least cost, maximum production, or minimum project duration (El-Moslmani, 2002).
FLSELECTOR also allows the user to compare the different production outputs that would be
achieved using different haul routes from the loading area to the dumping area (Alkass, El-
Moslmani, & AlHussein, 2003). Charts for the ten best fleets for a particular set of requirements
can be viewed and printed. Arrival rate, service rate, utilization, production, cost, duration, and
cost per unit are calculated for each fleet. Calculation may take only a few seconds for situations
with one server and one type of truck or as long as ten minutes for more complex systems such
as those with three servers with more than two types of haulers (El-Moslmani, 2002).
The performance of FLSELECTOR is compared to the results of simulation and deterministic
methods. When comparing results to those from deterministic models, FLSELECTOR gives
smaller production values than the deterministic model does. This is consistent with studies
which have found that deterministic models tend to overestimate production values.
FLSELECTOR gives output relatively in line with that of the simulation system SimEarth.
Comparison indicates that the two methods’ outputs differ by an average of 14% (El-Moslmani,
2002).
Limitations of FLSELECTOR include the fact that it can only handle a maximum of three
servers and its assumption that no queues will form at the dumping point. Despite this,
FLSELECTOR provides a user-friendly method of applying queuing theory to fleet selection and
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offers multiple configurations of fleet components that can meet the needs of individual project
requirements. The paper does not specify whether predicted FLSELECTOR output has been
compared to the data obtained from actual fleet performances (El-Moslmani, 2002).
Najor and Hagan present an approach to mine scheduling that incorporates a heuristic model
based on queuing theory. The goal in developing this model is to reduce financial expenditure in
the mine production system by efficiently managing the fleet, maximizing the use of equipment
while minimizing the resources necessary to support this equipment, and ensuring that fleet size
matches targets for material movement. To develop this model, queuing theory is applied to a
capacity-constrained model based on truck productivity (Najor & Hagan, 2004).
Queuing formulas for values such as expected wait time and expected number of trucks being
serviced are incorporated into a spreadsheet which calculates production values and the
estimated cost per tonne of material moved. Comparison between the capacity constrained model
and a conventional, mechanistic approach shows that the capacity-constrained model offers more
conservative production values than the conventional approach, which tends to overestimate
mining capacity. On average, the conventional approach underestimates the amount of time it
would take to complete a project by 8% compared to the amount of time found using the
capacity-constrained method (Najor & Hagan, 2004).
It is recommended that the capacity constrained method be used in mines with relatively short
haul distances. As haul distance increases the productivity values found for haul trucks become
very similar regardless of what method is used to calculate them. In this study, the capacity-
constrained, queuing theory based model is applied to a situation requiring relatively few trucks
to meet production needs. The optimum fleet size found to minimize the cost per tonne of
material moved for the model in question consists of only three or four trucks (Najor & Hagan,
2004). This is significantly smaller than fleet sizes for large open-pit mines which can require
more than 100 trucks to meet production needs.
Krause and Musingwini demonstrate that a modified Machine Repair Model, an example of a
finite source queuing model, can be applied to mining projects to accurately estimate required
fleet size. Based on the Machine Repair Model, a truck is sent for loading (repair) every cycle
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and there is a set number of shovels (repair bays). Interarrival time and service time are both
assumed to be exponentially distributed. Since trucks are drawn from a finite population, their
arrival pattern depends on the state of the system. Equations for situations in the Machine Repair
Model are easily adjusted to fit loading and hauling situations. For example, the average time a
truck spends waiting for repair becomes the average amount of time a truck queues at the loading
unit or dump site (Krause & Musingwini, 2007).
The modified Machine Repair Model and four common methods of analyzing shovel-truck
systems are applied to a virtual mine. These common methods include Elbrond’s cyclic queuing
model, a regressive model developed by Caterpillar called Fleet Production and Cost model
(FPC), Talpac, and a stochastic simulation model called Arena. Loading cycle times of three,
four, and five minutes are simulated and dumping and maneuvering times are kept constant,
assuming consistent operator ability. Using these assumptions, the five models are run to
produce estimates of achievable shift production. The Arena model is used as a benchmark for
comparing the accuracy of the other estimation methods. The Arena model is used as a
benchmark because its ability to be programmed with any number of probability distribution
models fitted to an unlimited number of cycles makes it very flexible and capable of closely
imitating real mining systems (Krause & Musingwini, 2007).
All of the models used produce estimates of loads per shift that are within 97%-99.7% of the
Arena estimates. Arena reports slightly more loads per shift than the other models do, which can
indicate that the other models are slightly more conservative. Overall, the results indicate that the
modified Machine Repair Model is capable of producing productivity estimates that closely
resemble those of other common truck-shovel analysis methods. When used to calculate fleet
size necessary to meet increased production requirements at a surface coal mine in South Africa,
the modified Machine Repair Model again produces results that are comparable to the other
models. Arena, the modified Machine Repair Model, and Elbrond’s model all calculate an
optimum fleet size of nine trucks. FPC and Talpac calculate that an additional truck is necessary,
for a fleet size of ten trucks. Based on this, it is concluded that the modified Machine Repair
Method produces production values and fleet sizes that are comparable to other commonly used
models. The modified Machine Repair Model also has the advantage of being relatively
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inexpensive, since it can be modeled using Microsoft Excel, a program which most mining
companies already use (Krause & Musingwini, 2007).
Czaplicki’s goal in his 2009 book is to allow operations to get the maximum profit from their
loading and hauling systems by reducing losses in production time and having high utilization of
the machines involved. Czaplicki applies queuing theory to shovel-truck systems using a
modification of the Maryanovitch queuing model for truck reliability and repair. This involves
using cyclic queues with two phases, service and travel, where service consists of loading the
trucks and travel consists of haulage, dumping, and returning. Normal distributions are used to
represent service and travel times and it is assumed that no queuing occurs at the dump site.
Czaplicki presents formulas determining parameters such as truck fleet size, reserve fleet size,
probability distributions for numbers of trucks and shovels in work state, and system productivity
based on equipment reliability, the numbers of various pieces of equipment involved, and cycle
time distributions (Czaplicki, 2009).
Czaplicki applies his formulas to two case studies to see how accurately an example machinery
system can be modeled. One case study involves five loaders and trucks with a high availability,
and the other involves seven loaders and trucks with low availability that will require repair more
frequently and thus have less time available for haulage. For both system parameters, the
equations determine an appropriate number of trucks and repair stands. Both systems yield an
average queue length of approximately 1.4 trucks per loader. This means that the loader is able to
achieve near-continuous production and relatively little truck cycle time is lost due to waiting
(Czaplicki, 2009).
Ercelebi and Bascetin present a method of assigning trucks to shovels using closed queuing
network theory for systems using only one type of truck. For truck-shovel systems where
minimizing cost per amount of material moved is the primary goal, a balance must be achieved
between the cost of idle time for the shovel and the cost associated with providing extra trucks.
Loading, hauling, and dumping times are assumed to fit exponential distributions. Production
costs are determined by incorporating the hourly cost to run each piece of equipment into the
equations calculating the number of trucks to be used. Cost predictions for the system found
using queuing theory are compared to the results found using a linear programming model and a
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case study for overburden removal at an open pit coal mine. Queuing theory provides the
minimum loading and hauling costs for the system, along with an optimal number of trucks
assigned to the shovels. When this system is implemented on the mine in question, the
overburden removal target for the year is exceeded and average production costs are reduced
(Ercelebi & Bascetin, 2009).
Ta, Ingolfsson, and Doucette present a paper based on truck and shovel behavior in oil sands
mining. Their goal is to use queuing theory to capture the nonlinear relationship between average
mine throughput and the number of trucks in use and then develop this relationship into a
manageable optimization model. The model includes options for only a single truck size or
multiple truck sizes, and individual trucks are assigned a readiness parameter so that the model
can indicate both how many trucks are necessary and which individual trucks ought to be used.
Shovel service times and truck back-cycle times are represented with an Erlang distribution. The
probability that a shovel is idle is linearized so that shovel throughput can be expressed as a
linear function. This model is compared to simulation results and it is shown that the
optimization model accurately predicts shovel utilization and idle time. Information about truck
utilization and idle time is not calculated, but the optimization model provides valuable
information about how many trucks should be used to meet necessary production targets (Ta,
Ingolfsson, & Doucette, 2010).
2.3 Conclusion
Most surface mines use truck and shovel systems to transport ore and waste material. It can be
difficult to determine the proper number of trucks that should be used in these systems due to the
dynamic nature of fleets of equipment and the fact that the length of the haul road is continually
increasing as mining progresses. There are many different methods to model and simulate truck
and shovel behavior, and companies are constantly looking for ways to quickly and more
accurately predict equipment performance. Queuing theory presents a promising method to
account for idle time caused by trucks waiting to be serviced at either the loading or dumping
point. When trucks and shovels are represented as servers and customers in a queuing network,
the proper number of machines that should be implemented in a mine can be determined,
ensuring that production needs can be met while still maintaining efficient use of equipment.
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Chapter 3: Applications of Queuing
Theory for Open-Pit Truck/Shovel
Haulage Systems
3.1 Abstract
Surface mining is the most common mining method worldwide, and open pit mining accounts
for more than 60% of all surface output. Haulage costs account for as much as 60% of the total
operating cost for these types of mines, so it is desirable to maintain an efficient haulage system.
As the size of the haulage fleet being used increases, shovel productivity increases and truck
productivity decreases, so an effective fleet size must be chosen that will effectively utilize all
pieces of equipment. One method of fleet selection involves the application of queuing theory to
the haul cycle. Queuing theory was developed to model systems that provide service for
randomly arising demands and predict the behavior of such systems. A queuing system is one in
which customers arrive for service, wait for service if it is not immediately available, and move
on to the next server or exit the system once they have been serviced. Most mining haul routes
consist of four main components: loading, loaded hauling, dumping, and unloaded hauling to
return to the loader. These components can be modeled together as servers in one cyclic queuing
network, or independently as individual service channels. Data from a large open pit gold mine
are analyzed and applied to a multichannel queuing model representative of the loading process
of the haul cycle. The outputs of the model are compared against the actual truck data to
evaluate the validity of the queuing model developed.
3.2 Introduction
Surface mining is the most common mining method worldwide, and open pit mining accounts
for more than 60% of all surface output (Hartman & Mutmansky, 2002). For most surface mines,
truck haulage represents as much as 60% of their total operating cost, so it is desirable to
maintain an efficient haulage system (Ercelebi & Bascetin, 2009). As the size of the haulage fleet
being used increases, shovel productivity increases and truck productivity decreases, so an
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effective fleet size must be chosen that will efficiently utilize all pieces of equipment (Najor &
Hagan, 2004). Having more trucks in service than necessary wastes fuel, as trucks must spend
time idling while waiting for service, and the company must pay the vehicle operators to drive a
truck that is not actually needed. Alternately, having too few trucks causes idle time for the
loaders, which causes a drop in production.
By applying queuing theory to mining haulage systems, the inherent stochastic nature of haul
truck and loader behavior can be accounted for and the model created can be used to adjust fleet
sizes to better serve loading needs. In this project a queuing model was generated that can be
used to model truck and loader behavior in an open pit mine. The model is then applied to actual
haulage data from an active mining operation.
3.3 Queuing Theory Background
Queuing theory was developed to provide models capable of predicting the behavior of systems
that provide service for randomly arising demands. A queuing system is defined as one in which
customers arrive for service, wait for service if it is not immediately available, and move on to
the next server or exit the system once service is complete. Queuing theory was originally
developed to model telephone traffic. Randomly arising calls would arrive and need to be
handled by the switchboard, which had a finite maximum capacity. There are six basic
characteristics that are used to describe a queuing system: arrival distribution of customers,
service distribution of servers, queue discipline, system capacity, number of service channels,
and number of service stages (Gross & Harris, 1998).
3.3.1 Customer Arrivals
In most queuing situations the arrival process of new customers to the system is stochastic. In
these cases it is necessary to know the distribution of the times between successive customer
arrivals, or the interarrival times. It is also important to understand the behavior of customers
upon entering the system. Some customers may wait for service no matter how long the queue is,
while others may see that a queue is too long and decide not to enter the system. When this
happens the customer is described as having balked. Other customers may enter the system, but
lose patience after waiting in the queue and decide to leave the system. These customers are said
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to have reneged. In situations with two or more parallel waiting lines a customer who switches
from one line to the other is said to have jockeyed for position. Any or all of these behaviors may
be present when a queuing system has what are classified as impatient customers. Impatient
customers cause state-dependent arrival distributions, since the arrival pattern of new customers
depends on the amount of congestion in the system at the time of their entry.
3.3.2 Service Distributions
A probability distribution is also necessary to describe customer service times, since it will not
always take the same amount of time for each customer to receive service. Single service, where
one customer is serviced at a time, or batch service, where multiple customers receive
simultaneous service from a single server are both service options. A common example of a
queuing system utilizing batch service involves waiting in line for a roller coaster. In this
scenario, the people waiting in line are the customers and the roller coaster car is the server. A
single line is formed to wait, and when the roller coaster car arrives the first four people in line
who get into the car receive simultaneous batch service.
In some cases the service process may be dependent upon the number of customers waiting in
the queue. The server may work more quickly due to the lengthening queue, or alternately the
server may become flustered by the large number of customers waiting and the service rate may
slow as a result. Situations in which the service rate depends on the number of customers in the
queue for service are referred to as state-dependent services.
3.3.3 Queue Discipline
The manner in which customers in a queue are selected for service is referred to as the queue
discipline. The most common queue discipline is first come, first served, or FCFS, where
customers receive service in the order in which they arrived. This discipline is also commonly
referred to as FIFO, or first in, first out. Another common queue discipline is LCFS, or last
come, first served. This is commonly used in inventory situations where the most recently placed
items waiting to be used are the most easily reached to be selected. RSS is a service discipline in
which customers are selected for service in random order, independent of their order arriving to
the queue.
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There are a variety of different priority queue disciplines where different classes of customers are
given higher priorities than other classes. In these disciplines the customer with the highest
priority will be selected for service ahead of lower priority customers, regardless of how long
each customer has been in the queue. If the queue discipline is preemptive, a customer with the
highest priority is allowed to receive service immediately upon arrival at the server, even if a
lower priority customer is already in service. The lower priority customer whose service is
preempted resumes service after the higher priority customer has left. In nonpreemptive cases the
highest priority customer that arrives at the server moves to the head of the queue, but must wait
until the customer currently being serviced has left (Cooper, 1972).
3.3.4 System Capacity
If a queue has a physical limitation to the number of customers that can be waiting in the system
at one time, the maximum number of customers who can be receiving service and waiting is
referred to as the system capacity. These are called finite queues since there is a finite limit to the
maximum system size. If capacity is reached, no additional customers are allowed to enter the
system.
3.3.5 Number of Service Stations
The number of service stations in a queuing system refers to the number of servers operating in
parallel that can service customers simultaneously. In a single channel service station, there is
only one path that customers can take through the system. Figure 3.1 below shows the path
customers, represented by circles, take through a single service channel queuing network. The
customers arrive at the server, represented by the rectangle, and form a queue to wait for service
if it is not immediately available, and then proceed through the system once service has been
completed.
Figure 3.1: Single Channel Queuing System
When there are multiple servers available operating in parallel, incoming customers can either
wait for service by forming multiple queues at each server, as shown in (a) of Figure 3.2, or they
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can form a single queue where the first customer in line goes to the next available server,
depicted in (b). Both of these types of queues are commonly found in day-to-day life. At the
grocery store individual lines are formed at each cashier, but a single line is generally formed
when customers are waiting in line at the bank. The first customer in line then proceeds to the
next available teller. A single queue waiting for multiple servers is generally the preferred
method, as it is more efficient at providing service to the incoming customers.
Figure 3.2 Multichannel Queuing Systems
3.4 Notation
Queuing processes are frequently referred to by using a set of shorthand notation in the form of
(a/b/c/):(d/e/f) where the symbols a through f stand for the characteristics shown below in Table
3.1.
Table 3.1: Queuing Notation Abbreviations
Symbol Characteristic
a arrival distribution
b service distribution
c number of parallel servers
d service discipline
e maximum number of units that can be in the system at one time
f source population size
The symbols a through f will take different abbreviations depending on what type of queuing
process is being described. Symbols a and b both represent types of distributions, and may
contain codes representing any of the common distributions listed in Table 3.2.
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Table 3.2: Distribution Abbreviations
Symbol Explanation
M Markovian: exponentially distributed interarrival or service times
D Deterministic: constant distribution
E Erlang distribution with parameter l
l
G General Distribution
Symbols c, e, and f all represent discrete values and are represented with the appropriate number
or ∞ if there is no limit to the system size or population source. The service discipline, d, may be
represented by any of the abbreviations explained below in Table 3.3.
Table 3.3: Service Disciplines
Symbol Explanation
FCFS First come, first served
FIFO First in, first out (same as FCFS)
LCFS Last come, first served
RSS Random selection for service
PR Priority
SIRO Service in random order
The (d/e/f) term is often omitted, and in such cases the default assumptions are (FCFS/∞/∞). For
example, an (M/D/3) queue would have exponential interarrival times, deterministic service
rates, and three servers working in parallel. While not explicitly stated, a service discipline of
first come, first served and infinite queue capacity and an infinite calling population are
generally implied.
3.5 Queuing Systems in Mining
In mining operations, queues frequently form during the haulage process as trucks arrive at
loaders, crushers, and dump locations and have to wait their turn in line. This process can be
represented using queuing networks where the haul trucks represent the customers in the system
and the servers are the loaders or crushers that the trucks are waiting for. When representing
loading operations with queuing systems, the time a truck spends positioning and spotting at the
loader can be included either as part of the loading cycle time or as part of the time the truck was
waiting in the queue for service. Figure 3.3 below depicts a basic mining queuing system
composed of haul trucks and excavators.
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The above cyclic queuing model can be adjusted to include multiple loaders, operating in
parallel. Figure 3.5 below shows a possible configuration with three loaders with a single queue
formed for trucks to wait to be loaded, but any number of loaders could be used.
Figure 3.5: Cyclic Queuing System with Parallel Loaders
The cyclic queues represented above model the haulage systems for basic mine layouts. As the
complexity of mining operations increases more intricate queuing systems must be used to
represent operations. A network queue, such as the one depicted below in Figure 3.6 can be used
when there are multiple paths available to the haul trucks. For this type of queuing model to
work, metrics are necessary to determine the likelihood of each path being taken throughout the
haul cycle. This could depend on the congestion of part of the system, the characteristics of each
individual server, the contents of the truck’s load, or a myriad of other factors.
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Figure 3.7: Queuing Schematic with Multiple Pits
3.6 Recent Applications of Queuing Theory to Mining
One recent mining application of queuing theory involves a closed queuing theory network
assuming exponential distributions for loading, hauling, and dumping times. This model was
developed to minimize production costs per amount of material moved. Production costs are
incorporated by applying hourly costs to run each piece of equipment. Cost predictions for the
system found using queuing theory were compared to the results found using a linear
programming model and a case study for overburden removal at an open pit coal mine. Queuing
theory provides the minimum loading and hauling costs for the system, along with an optimal
number of trucks assigned to the shovels. When this system is implemented on the mine in
question, the overburden removal target for the year is exceeded and average production costs
are reduced (Ercelebi & Bascetin, 2009).
Another recent queuing mining project uses queuing theory to capture the nonlinear relationship
between average mine throughput and the number of trucks in use, and then develops this
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relationship into an optimization model. The model includes options for single truck sizes or
multiple truck sizes, and individual trucks are assigned a readiness parameter so that the model
can indicate both how many trucks are necessary and which individual trucks ought to be used.
Shovel service times and truck back-cycle times are represented with an Erlang distribution. The
probability that a shovel is idle is linearized so that shovel throughput can be expressed as a
linear function. This model is compared to simulation results and it is shown that the
optimization model accurately predicts shovel utilization and idle time. Information about truck
utilization and idle time is not calculated, but the optimization model provides valuable
information about how many trucks should be used to meet necessary production targets (Ta,
Ingolfsson, & Doucette, 2010).
3.7 Queuing Model
A model of a truck and shovel system for an open pit mine with multiple loaders operating
within the pit was constructed using Microsoft Excel. This was done with the goal of providing a
middle ground between very simplistic deterministic methods of analyzing haul truck fleet
performance and complex, full-blown simulations that incorporate every aspect of mine activity.
The rate of new haul truck arrivals and the loading rates of the excavators were both assumed to
be exponential. An (M/M/c) queuing model was selected to follow this assumption of
exponential service and interarrival times and to allow for various numbers of loaders to be
selected. An (M/M/c) model is one in which each server has an independent and identically
distributed exponential service-time distribution and an exponential arrival process. This model
of pit behavior is versatile and can be used to model pit behavior for a variety of different
haulage configurations and mine layouts. The service discipline used is first come first served,
with the assumption that there are no special classes of trucks.
3.7.1 Inputs
To use this model, the values for the number of loaders operating, the arrival rate of new trucks,
and the service rate per loader must be known to be used as inputs to the model. The necessary
inputs are outlined on the following page in Table 3.4.
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Table 3.4: Queuing Model Inputs
Symbol Explanation
λ Average arrival rate of new trucks
μ Average service rate per loader
c Number of loaders operating in parallel
The arrival rate, λ, is the average rate at which new trucks arrive at the loader. The service rate,
μ, is the service rate of an individual loader. In cases with more than one loader in operation, all
loaders are assumed to be equivalent, so μ would be the average service rate of the loaders. The
arrival rate, λ, and service rate, μ, should both be input in the form of trucks per hour. Both the
arrival rate and the service rate are independent of queue length. The queue will not have
impatient customers, since it would be unrealistic for haul trucks to not join the line to be loaded,
regardless of how many trucks are already waiting. There would also be no jockeying for
position since trucks form a single line to wait to be loaded, with the first truck going to the next
available loader. The model uses this information to calculate a variety of outputs about the truck
and shovel system.
3.7.2 Equations
Based on this queuing system and input variables, the variables r and ρ are defined as,
r = λ/μ Equation 3.1
and
ρ = r/c = λ/cμ Equation 3.2
Where r is the expected number of trucks in service, or the offered workload rate, and ρ is
defined as the traffic intensity or the service rate factor (Giffin, 1978). This is a measure of
traffic congestion. When ρ > 1, or alternately λ > cμ where c is the number of loaders, the
average number of truck arrivals into the system exceeds the maximum average service rate of
the system and traffic will continue back up. For situations when ρ > 1, , the probability that
there are zero trucks in the queuing system is defined as
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(∑ ) Equation 3.3
Where n is the number of trucks available in the haulage system. Even in situations with high
loading rates, it is extremely likely that trucks will be delayed by waiting in line to be loaded.
The queue length will have no definitive pattern when arrival and service rates are not
deterministic, so the probability distribution of queue length is based on both the arrival rate and
the loading rate (Gross & Harris, 1998). The expected number of trucks waiting to be loaded, ,
can be calculated based on using the following equation.
Equation 3.4
= ( )
The average number of trucks in the queuing system, L, and the average time a truck spends
waiting in line, , can be found by applying Little’s formula which states that the long term
average number of customers in a stable system, L, is equal to the long term average effective
arrival rate, λ, multiplied by the average time a customer spends in the system, W (Gross &
Harris, 1998). Algebraically, this is expressed as
L = λW Equation 3.5
and can also be applied in the form
= λ Equation 3.6
Using these equations, the average time a truck spends waiting to be loaded, can be
calculated as follows.
= = ( )
Equation 3.7
The average time a truck spends in the system, W, is defined as
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Equation 3.8
W = + = + ( )
The model currently supports up to seven loaders operating in parallel, but could easily be
adjusted to include more. There is no limit on haul truck fleet size, provided the arrival rate of
trucks to the loading system does not increase to the point of overwhelming the loading capacity.
This model is only valid for values of ρ, the traffic intensity per server, that are less than one. If ρ
were to increase above one, the system would back up indefinitely, as the arrival rate of empty
trucks would be greater than the loaders are capable of handling.
3.7.3 Outputs
When given the appropriate inputs, the model calculates and outputs values for various aspects
of pit activity. These include loader utilization, the average time a truck spends in the system, the
average time a truck spends waiting to be loaded, the average number of trucks waiting in line,
the average number of trucks in the system, and the system output in trucks per hour. Table 3.5
below lists the outputs created by the model and the appropriate units for each variable.
Table 3.5: Queuing Model Outputs
Variable Units Description
ρ % Loader Utilization
W hours Time spent in system
W hours Time spent in queue
q
L Number of trucks Number of trucks in system
L Number of trucks Number of trucks in queue
q
θ Trucks per hour System output
Figure 3.8 on the following page shows a screenshot of the model. The values the user inputs are
highlighted in yellow, and the intermediate calculations and final outputs are highlighted in
green.
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Figure 3.8: Screenshot of Model
3.8 Example Application
While this queuing model provides information about the system being modeled that is correct
based on the equations of queuing theory, it is necessary to see if the actual behavior of trucks in
a mine are consistent with the model. Haul truck data were obtained from a large surface gold
mine located outside of the United States. Information about the haul trucks in this mine was
obtained in the form of Global Positioning System (GPS) data. Each truck is equipped with a
GPS unit that records the easting, northing, elevation, and speed at regular time intervals. This
information, combined with the contour map of the mine, allows the complete haul route to be
examined.
3.8.1 Data
Haul truck GPS information was obtained in the form of .dat files containing thousands of data
points, each with a time stamp, truck number, truck speed, and location based on easting
northing and elevation. Truck speed is reported in kilometers per hour, and all of the time stamps
are in the format of seconds beginning January 1, 1970. When this information is imported into
AutoCad along with the mine map it is possible to determine information about loading
locations, haul routes, dumping locations, and areas where trucks are waiting. The data files were
formatted so that AutoCAD Civil 3D could plot each haul truck location on a contour map of the
mine property and store the truck ID number, time stamp, and corresponding velocity for each
point.
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3.8.3 Loading
Loading areas are identified based on the locations where haul trucks are stopped in the pit. This
was accomplished by importing the data from a particular shift into Microsoft Excel and filtering
the points based on truck velocity. Points where trucks had a velocity of zero were selected and
imported onto an AutoCAD contour drawing of the mine to show locations where vehicles were
stopped. The trucks could be stopped either to wait for service or while receiving service at the
loaders or dumping locations. As shown below in Figure 3.14 with points representing locations
where haul trucks are stopped, the locations where the three loaders were operating are clearly
identifiable by the clusters of points representing stopped trucks throughout the shift.
Figure 3.14: South Pit Loading Locations
The data points of haul trucks stopped in the loading areas were isolated from the rest of the data.
These points were sorted based on truck number, and for each truck the time stamp for when a
new loading cycle began was recorded. This was determined based on the amount of time that
had passed between data points for an individual truck. Since only data points located within the
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loading area were being considered, a large time gap meant that the truck had left the loading
area during that interval, so the next data point represents a new arrival.
Once the new arrival time stamps for all of the trucks active during this time period had been
recorded they were combined to form a list of all of the new truck arrivals for that shift. These
times were then used to calculate the distribution of arrival times of haul trucks to be loaded. The
amount of time between each new arrival was calculated by subtracting the difference between
each successive time stamp of arriving haul trucks. For these purposes, a new arrival is defined
as when the haul truck first comes to a stop within the pit limits. The times between arrivals were
sorted into bins and used to create a graph of frequency vs. time between new arrivals.
Frequency is represented as a percentage of the total number of arrivals that occurred during the
shift. Figure 3.15 below shows an example of this type of plot, created using data from twelve
hours of production in the south pit with twenty two trucks in operation.
20
) s 18
l
a y = 13.057e-0.007x
v 16
i
r R² = 0.8759
r
a 14
l
a
t 12
o
t
f 10
o
%
8
(
y
c 6
n
e
u 4
q
e
r 2
F
0
0 100 200 300 400 500 600
Time Between Truck Arrivals (sec)
Figure 3.15: South Pit Arrival Distribution
Various equations were applied to the data and it was found that the exponential equation is an
adequate fit for the interarrival times of haul trucks in the south pit. The same process was
applied to trucks operating in the north pit, but there were not enough trucks operating in that pit
to yield any discernible distribution of arrival times. Figure 3.16 on the following page shows the
frequency of interarrival times for that pit over a full shift. It is clear that the data do not form a
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distribution. Haulage operations such as this one cannot be modeled using queuing theory, since
a distribution could not adequately represent interarrival times in the system.
10
)
s
l 9
a
v
i r 8
r
A
7
l
a
t 6
o
T
f 5
o
% 4
(
y 3
c
n
e 2
u
q
e 1
r
F
0
0 200 400 600 800 1000
Time Between Truck Arrivals (sec)
Figure 3.16: North Pit Interarrival Times
3.8.4 Service Times
The loading service time distributions were more difficult to obtain, since the GPS information
does not differentiate between times when a truck is stopped because it is waiting to be loaded
and times when a truck is stopped while being loaded. The service times for individual loaders
were determined by isolating the data points corresponding to each loader operating in the pit
and identifying the time stamp that corresponds to each time the truck left that specific loading
area. Similar to how arrival times were determined, the departure times were identified as the last
time a particular truck was in the loading area before a large time gap.
Once all of the time stamps corresponding to trucks departing from the loader had been recorded,
they were combined to form a list of all of the truck departures for that loader during that work
shift. These times were then used to calculate the distribution of service times for the loader. The
amount of time between each departure was calculated by subtracting the difference between
each successive time stamp of departing loaded haul trucks. This difference in times between
successive truck departures represents the amount of time it takes for a loader to service one haul
truck. This method includes the truck’s spotting time as part of the service time. The times
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between departures were sorted into bins and used to create a graph of frequency vs. time
between new arrivals. Frequency is represented as a percentage of the total number of departure
times calculated for the shift. Figure 3.17 below shows an example of this type of plot for one
loader, created using data from twelve hours of production in the south pit with twenty two
trucks in operation.
25
)
s
e
m
20
i
T
l
y = 34.43e-0.007x
a
t R² = 0.839
o T 15
f
o
%
10
(
y
c
n
e
u 5
q
e
r
F
0
0 100 200 300 400 500 600
Time Between Departures (sec)
Figure 3.17: Service Distribution for a Single Loader
3.8.5 Validation of Model and Results
The mining operations in the north pit do not fit any distribution, and cannot be represented
using mathematical equations. In the south pit, both the interarrival times of new trucks to the pit
and the service rates of the loaders fit exponential distributions. Data from the mining operations
in the south pit can be used as inputs for the queuing model created, since it fulfills the
requirements of exponential arrival distributions and service rates. Not all mining operations will
be able to be applied to the model, since they will not all have similarly distributed loading and
interarrival rates, as evidenced by the north pit, which clearly does not meet these requirements.
The south pit of the mine described operates with either two or three loaders in the pit depending
on the shift and the haul trucks dump ore at the crusher and waste material at the dump site as
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previously described. Figure 3.18 below is a queuing schematic of the haulage operations for the
south pit.
Figure 3.18: Queuing Schematic of Mine Haulage Route
The queuing model developed can be applied to the pit operations of this mine, represented by
the top half of the above schematic. The arrival and service distributions for the south pit
operations have been confirmed to fit exponential distributions, so an (M/M/3) queuing model is
appropriate for this application. Loaded haul trucks exiting the queuing system of the pit will
either travel to the crusher or the waste dump before returning to the pit to be loaded again.
Which dumping location a truck will utilize is dependent upon whether the loader filled the truck
with ore or waste material, and varies according to the geology of the ore body in the pit and the
cutoff grade the mine is using. A metric that includes this information would be necessary to
expand the current queuing model to apply to the entire haulage system, and is beyond the scope
of this project.
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The loading rate and average arrival rates for each hour segment were entered into the queuing
model, using an (M/M/3) model for the first five hours of the shift and an (M/M/2) model for the
remainder, since the number of loaders in operation changed during the shift. Table 3.7 below
contains the outputs generated by the queuing model, based on the inputs from Table 3.6. The
model calculated the average number of trucks in the pit system (L), the number of trucks
waiting for service (L ), the average amount of time trucks spent in the pit system (W), the
q
average amount of time trucks spent waiting for service (W ), and server utilization (ρ).
q
Table 3.7: Queuing Model Outputs for Hourly Data
W W
q
Hour L L (hours) (hours) ρ (%)
q
1 3.187 0.888 0.103 0.029 76.6
2 3.187 0.888 0.103 0.029 76.6
3 2.201 0.348 0.088 0.014 61.8
4 2.474 0.472 0.091 0.018 66.7
5 2.793 0.643 0.096 0.022 71.7
6 3.5 1.869 0.159 0.085 81.6
7 3.5 1.869 0.159 0.085 81.6
8 4.248 2.543 0.185 0.111 85.3
9 14.87 12.94 0.572 0.498 96.4
10 4.248 2.543 0.185 0.111 85.3
11 4.248 2.543 0.185 0.111 85.3
The shift was also analyzed as a whole, broken down into the segments with 3 and 2 loaders. The
average arrival rates and service rates were calculated and used as inputs for the model. These
results are shown below in Table 3.8.
Table 3.8: Queuing Model Outputs for Entire Shift
L L W W ρ θ
q q
3 loaders 2.724 0.604 0.095 0.021 70.7 39
2 loaders 4.408 2.69 0.19 0.116 85.9 26.4
To see if the model’s outputs match the actual results, the expected number of trucks in the
system, L, was compared to the actual number of trucks in the system for these timeframes. The
predicted results were plotted vs. the actual results, as shown in Figure 3.19.
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The line of best fit created in the previous graph was modified to force the line through the
origin, since there can never be a negative number of trucks in the system. The resulting
modified graph is shown below in Figure 3.21.
6
n y = 1.0177x
i
s k
5
R² = 0.6035
c
u
rr
Tu 4
o
f oH
r r
e be
p
3
m
m
u
Ne
t
ds
y
2
eS
t
c
i
d
1
e
r
P
0
0 1 2 3 4 5 6
Actual Number of Trucks in System per Hour
Figure 3.21: Predicted vs. Actual Number of Trucks in System, Modified
The relationship between the predicted number of trucks in the system and the actual number of
trucks in the system is very close to 1 to 1, indicating that the outputs of the (M/M/3) queuing
model can accurately describe the state of the haulage system being modeled.
3.9 Analysis
This queuing model is useful for analyzing the efficiency of mining haulage and loading
operations for the configurations in which they are currently operating. The amount of time
trucks spend waiting to be loaded, W , and the server utilization, ρ, are both indicators of how
q
efficiently the system is operating. The larger the values of W , the longer trucks are spending
q
idling waiting at the loaders, burning fuel without contributing to the haulage process. The server
utilization indicates what proportion of operational time loaders are actually in use. Both of these
values can be combined with costing data for the equipment in use to find out how much money
is being spent on idling equipment.
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For example, a pit system operating with two loaders, an arrival rate of 16 trucks per hour, and a
service rate of 12 trucks per hour per loader is found to have a loader utilization of 66.7%, a
system output of 23.5 trucks per hour, and an average of 0.0435 hours spent waiting in the queue
per truck for each loading cycle. Since each truck passing through the system would potentially
have to spend time waiting at the loader, the system output multiplied by the average time spent
waiting in the queue is the average amount of time trucks are idling in the pit per hour. Over an
eight hour shift, this comes to a combined total of 8.18 hours of truck idling time. Based on the
loader utilization, each loader was not in use for 33.3% of the shift. This comes to a total of 5.34
hours of idle time between the two loaders for the eight hour period. This mine could be
operating a pair of EX2600 hydraulic shovels with a fleet of CAT 793D haul trucks, which cost
$421 per hour and $356 per hour respectively to operate (InfoMine). This comes to a total of
$5,158.54 spent on idling equipment during one eight-hour shift. If the haulage operations were
adjusted, either by changing the number of loaders operating or adjusting the fleet size, the new
arrival rate that results can be used to run the model again, and see whether the changes made
would be valuable to the system in terms of the cost to operate unnecessary equipment.
If there are usually multiple trucks waiting for the loaders, as indicated by L , it would likely be
q
beneficial to decrease the fleet size to reduce the amount of time trucks are spending waiting to
be loaded. Changes to the queuing model can be made by adjusting the arrival rate of new trucks
to the system to see how the system would react to trucks arriving more or less frequently. While
this is similar to comparing the effects of adding or removing trucks to the system, the amount of
change in arrival rate caused by changing the fleet size will vary depending on the specific
characteristics and layout of each mine.
As the model currently exists, the effects of changes to fleet size can only be examined if the
changes are actually made in the pit, the new inputs are determined, and the model is run again.
This is due to the fact that the arrival rate, which is a necessary queuing input, is dependent upon
more than just the number of trucks in the system. To determine an optimal fleet size for a given
mine layout and loading configuration without running a full simulation, it may be more useful
to use models involving stochastic simulation, such as Monte Carlo simulation to incorporate
haul routes, travel times, and fleet sizes. This would allow various fleet sizes and configurations
to be compared without having to make real world changes to acquire additional inputs for the
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Chapter 4: Summary and Conclusion
4.1 Summary
The haulage process undertaken by haul trucks in open pit mines can be represented as cyclic or
network queues, or broken down into individual components which can each be treated as single
or multichannel queues. In queuing notation, trucks are treated as customers in a system where
loaders are the servers. Trucks arrive to be loaded and form a queue if the loaders are busy.
An (M/M/c) queuing model was developed to model truck and shovel interactions within the pit.
This model makes the assumption of exponentially distributed truck interarrival times and
service times, and can be applied to operations with seven or fewer loaders. To apply this model
the user must know the average arrival rate of new trucks to the system, λ, the number of loaders,
and the average service rate per loader, μ. Based on these inputs, the model calculates several
outputs describing system behavior. Table 4.1 below lists the outputs created by the model along
with their associated units and descriptions.
Table 4.1: Model Outputs
Variable Units Description
ρ % Loader Utilization
W hours Time spent in system
W hours Time spent in queue
q
L Number of trucks Number of trucks in system
L Number of trucks Number of trucks in queue
q
θ Trucks per hour System output
These outputs can be used to measure the efficiency of haulage operations based on their current
configurations. If changes are made to the system, new values for the average interarrival times
and service rates would need to be calculated so that the model could be run again to compare
the efficiency of the new system to the values before changes were made.
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4.2 Conclusion
Queuing theory can be used to model truck and shovel behavior in open pit mines. The (M/M/c)
model developed is consistent with the data from one open pit operation. Exponential interarrival
times and exponential service times are consistent with the data from this mine, so the
assumptions of the model are valid for some operations.
The (M/M/c) model is capable of analyzing haulage systems as they currently exist and can be
used to evaluate the efficiency of operations based on their current fleet sizes. This can also be
combined with costing data for the equipment in use to find out how much money is being spent
to operate idling equipment that is not directly contributing to production.
As the model currently exists, the effects of changes to fleet size can only be examined if the
changes are actually made in the pit, and the model is run again using new inputs, calculated
after the changes had been made. This is due to the fact that the arrival rate, which is a necessary
queuing input, is dependent upon more factors than just the number of trucks in the system.
While queuing theory can be used to model haulage operations at some mine sites, it may not be
the best or the easiest method to use for fleet analysis. Queuing theory can only be applied to
mining operations where the arrival times of trucks to the pit and service times of the loaders can
be fit to distributions. For operations that meet these requirements, inputs for the model must be
obtained from active mining operations, and changes to the system can only be run through the
model after these changes have been implemented in the field and used to obtain new inputs for
the model.
To determine an optimal fleet size for a given mine layout and loading configuration without
running a full simulation, it may be more useful to use models involving stochastic simulation,
such as Monte Carlo simulation, to incorporate haul routes, travel times, and fleet sizes. This
would allow various fleet sizes and configurations to be compared without having to make real
world changes to acquire additional inputs for the model, as would be necessary for the queuing
model. This type of stochastic model could also be used in situations when queuing theory is not
applicable, for example in mines where the loading operations do not fit the distributions
necessary for queuing theory to be applied. The queuing model can analyze the efficiency of
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Table A-5: Number of Trucks in System
1343073693 4 1343080167 5
Number 1343073843 1 1343080289 3
Time of Trucks
1343074143 3 1343080418 1
Stamp in System
1343074273 7 1343080590 2
1343067870 2
1343074408 4 1343080737 2
1343068012 5
1343074529 4 1343080887 3
1343068208 5
1343074663 3 1343081015 2
1343068337 5
1343074798 3 1343081045 4
1343068460 4
1343074927 4 1343081171 3
1343068587 4
1343075064 2 1343081309 4
1343068726 3
1343075187 3 1343081454 3
1343068872 2
1343075319 3 1343081591 3
1343069035 1
1343075448 2 1343081634 0
1343069181 3
1343075854 1 1343081907 3
1343069306 2
1343076032 3 1343082038 4
1343069451 4
1343076163 2 1343082180 3
1343069617 1
1343076299 2 1343082270 0
1343069762 1
1343076448 3 1343082300 0
1343069912 4
1343076598 3 1343082598 2
1343070038 4
1343076748 3 1343082721 2
1343070167 5
1343076888 4 1343082868 1
1343070297 4
1343077013 4 1343083011 3
1343070437 4
1343077136 3 1343083139 6
1343070568 3
1343077270 3 1343083263 6
1343070691 2
1343077339 0 1343083392 5
1343070956 2
1343077564 1 1343083524 5
1343071077 2
1343077654 0 1343083648 2
1343071307 2
1343077910 2 1343083780 2
1343071432 4
1343078043 3 1343083920 2
1343071555 4
1343078168 4 1343084049 2
1343071718 4
1343078309 4 1343084207 1
1343071839 4
1343078430 3 1343084357 1
1343071967 4
1343078699 2 1343084507 2
1343072103 2
1343078848 5 1343084641 2
1343072232 3
1343078969 5 1343084782 2
1343072358 3
1343079095 4 1343084996 5
1343072508 4
1343079239 2 1343085118 8
1343072637 3
1343079365 3 1343085243 5
1343072817 2
1343079490 1 1343085371 4
1343072938 2
1343079620 1 1343085498 5
1343073296 3
1343079770 2 1343085629 5
1343073429 3
1343079897 2 1343085751 3
1343073558 3 1343085880 2
1343080020 2
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1343086007 3 1343091841 3
1343097553 5
1343086157 2 1343091965 4
1343097675 5
1343086300 1 1343092087 6
1343097801 5
1343086450 1 1343092227 4
1343097933 3
1343086600 2 1343092348 4
1343098063 2
1343086748 2 1343092472 1
1343098191 2
1343086888 5 1343092603 5
1343098333 1
1343087011 7 1343092729 5
1343098477 2
1343087142 7 1343092860 4
1343098558 3
1343087263 7 1343092982 3
1343098686 3
1343087385 7 1343093114 5
1343098817 3
1343087515 5 1343093250 3
1343098952 1
1343087636 5 1343093373 3
1343099078 3
1343087759 4 1343093504 4
1343099168 4
1343087905 3 1343093643 4
1343099289 3
1343088029 4 1343093767 4
1343099415 2
1343088158 7 1343093895 2
1343099538 2
1343088308 3 1343094045 2
1343099688 2
1343088438 4 1343094185 3
1343099782 2
1343088569 4 1343094387 3
1343099893 3
1343088699 5 1343094619 3
1343100019 3
1343088820 4 1343094766 4
1343100199 1
1343088959 4 1343094889 5
1343100289 3
1343089086 5 1343095011 6
1343100389 7
1343089212 3 1343095141 7
1343100509 7
1343089336 2 1343095263 6
1343100632 5
1343089486 1 1343095394 5
1343100768 6
1343089677 1 1343095514 4
1343100899 5
1343089814 3 1343095637 3
1343101022 2
1343089984 4 1343095761 2
1343101143 4
1343090126 4 1343095911 2
1343101264 5
1343090247 4 1343095955 0
1343101389 5
1343090396 5 1343096115 1
1343101516 4
1343090517 3 1343096247 2
1343101639 5
1343090679 4 1343096398 2
1343101762 3
1343090801 3 1343096535 3
1343101904 3
1343090981 1 1343096668 4
1343102002 2
1343091131 3 1343096807 3
1343102122 3
1343091260 2 1343096947 4
1343102270 4
1343091320 0 1343097077 4
1343102377 4
1343091452 1 1343097211 3
1343102498 4
1343091577 3 1343097301 3
1343102609 4
1343091704 4 1343097423 5
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1343102870 5 1343102870 5 1343102738 4
1343102990 5 1343102990 5 1343108191 7
1343103110 4 1343103110 4 1343108315 6
1343103230 3 1343103230 3 1343108435 6
1343103359 2 1343103359 2 1343108561 5
1343103500 4 1343103500 4 1343108675 6
1343103603 4 1343103603 4 1343108801 5
1343103724 4 1343103724 4 1343108926 6
1343103843 5 1343103843 5 1343109047 5
1343103975 5 1343103975 5 1343109174 6
1343104084 4 1343104084 4 1343109294 5
1343104204 4 1343104204 4 1343109429 4
1343104330 3 1343104330 3 1343109550 4
1343104455 3 1343104455 3 1343109740 2
1343104576 3 1343104576 3
1343104696 3 1343104696 3
1343104817 3 1343104817 3
1343104927 3 1343104927 3
1343105047 4 1343105047 4
1343105178 3 1343105178 3
1343105294 5 1343105294 5
1343105414 4 1343105414 4
1343105571 2 1343105571 2
1343105684 5 1343105684 5
1343105794 4 1343105794 4
1343105915 4 1343105915 4
1343106040 5 1343106040 5
1343106165 5 1343106165 5
1343106305 4 1343106305 4
1343106433 4 1343106433 4
1343106564 4 1343106564 4
1343106701 3 1343106701 3
1343106834 3 1343106834 3
1343106969 2 1343106969 2
1343107089 1 1343107089 1
1343107220 2 1343107220 2
1343107329 2 1343107329 2
1343107449 5 1343107449 5
1343107564 6 1343107564 6
1343107688 6 1343107688 6
1343107818 4 1343107818 4
1343107938 5 1343107938 5
1343108071 5
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DPM Monitoring in Underground Metal/Nonmetal Mines
E. McCullough !, L. Rojas-Mendoza !, E. Sarver !,∗
! Virginia Polytechnic Institute and State University, Department of Mining and Minerals, Blacksburg, VA 24060,
USA
The metal and nonmetal mining industries face increasingly stringent regulations regarding worker exposures to
airborne particulates, including diesel particulate matter (DPM). Although significant progress has been achieved in
reducing DPM exposures, mine operators still struggle to comply under a variety of conditions – particularly in
large-opening mines where ventilation is challenging. One major issue in such environments is the inability to
easily monitor DPM trends over long periods of time to determine factors influencing its buildup in areas of
interest, as well as its response to mitigation strategies. At present, DPM measurements are limited to the NIOSH
5040 method (i.e., filter collection and external analysis) and the handheld Airtec DPM monitor (FLIR Systems,
Inc., Albuquerque, NM), which provides quasi-real time data over relatively short time periods.
To transform the Airtec device to an autonomous area-monitoring unit, its basic components were modified by
Nomadics, Inc. under NIOSH contract number 200-2010-36901. This resulted in a prototyped unit called the
Airwatch DPM monitor, which does not require frequent filter replacement or battery re-charging; networking
capabilities to connect multiple monitors were also achieved. While the prototyped monitor was successfully lab
tested, field-testing was limited to just a few days underground. Further testing is needed to fully evaluate the
monitor and ready it for commercial availability. Under a new Capacity Building in Ventilation project at Virginia
Tech (CDC/NIOSH contract no. 200-2014-59646), we aim to demonstrate the capability of the Airwatch DPM
monitor in high-priority areas of a stone mine over relatively long-term periods – and then use the monitors to
investigate DPM response to ventilation conditions.
Keywords: Diesel Particular Matter, Metal/non-Metal, Monitoring
1. Introduction create synergies that are harmful to human health. DPM
exposure in U.S. underground mines is regulated by the
Diesel exhaust represents a ubiquitous occupational
Mine Safety and Health Administration (MSHA).
hazard in underground mine environments. The exhaust
MSHA issued its Final Rule on DPM metal and
is a highly complex mixture of diesel particulate matter
nonmetal mine environments under 30 CFR Part 57 in
(DPM) and hydrocarbon gasses [1]. Since there is no
2008, mandating that a miner’s personal exposure limit
technologically proven way to measure DPM directly, it
(PEL) to DPM cannot exceed 160 μg/m3 of TC during an
is often quantified using elemental carbon (EC)
eight-hour work shift. MSHA requires that the standard
measurements. [2]. Elemental carbon accounts for 23-
National Institute for Occupational Safety and Health
100% of DPM, and is not generally affected by
(NIOSH) 5040 Method be used to measure DPM
environmental interferences [3,4]. Historically, total
exposures to determine compliance [4]. This method
carbon (TC) analysis was used which typically
employs a thermo-optical technique to analyze carbon
comprises over 80% of DPM [1]. TC is defined as the
particles in air samples collected on a 37 mm quartz
summation of elemental carbon and organic carbon
fiber filter. It should be noted that this technique
(OC). However, cigarette smoke and mineral dust can
quantitates TC (by direct quantitation of EC and OC) or
interfere with TC readings, which has sometimes caused
requires a site-specific conversion factor to convert EC
DPM measurements to report artificially high values [3].
into a TC equivalent [6,7]. These values should then be
DPM has a variable particulate size distribution. adjusted to an eight-hour time-weighted average.
Particles are created within the micron and sub-micron
scales [5]. Idealized size distribution is trimodal and
related lognormally [1]. The smallest particulate mode is 1.1 DPM and Human Health
called the nuclei mode, which has particles diameters
Underground miners are disproportionally exposed
ranging from about 0.005 to 0.05μm. This mode
to DPM-related occupational hazards because heavy
represents less than 20% of DPM by mass, but greater
diesel-powered equipment runs regularly in tight spaces,
than 90% of DPM by particle count [1]. Most DPM
with variable ventilation conditions. In spaces where
particulate mass is represented in the accumulation
airflow is limited, DPM does not disperse well, and due
mode, with particle diameters on the order of about 0.05
to its size can remain suspended in the air. Reported
to 1.0μm. The coarse mode represents particles with
DPM concentrations in underground mine settings can
diameters greater than 1μm. All particles sizes are
be on the order of ten times higher than levels found in
capable of suspension in air, and DPM is prone to
some other industrial settings, and more than 100 times
clustering and reacting with other atmospheric
higher than levels observed in urban areas [1]. NIOSH
components while suspended [1]. Such reactions may
_______________________________________________________________________________
1
*Corresponding author: [email protected]
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estimated in 2008 that 34,000 underground miners were carbon dioxide is reduced to methane, which is measured
at risk of exposure to DPM [1].Human exposure to DPM by FID. Since some char is produced by the OC during
presents many potential health complications. NIOSH the first phase, which will oxidize in the second phase,
estimated in 2008 that 34,000 underground miners were the analyzer must also determine how much methane in
at risk of exposure to DPM [1]. Approximately 60,000 the second phase is attributable to OC vs. EC. For this, it
deaths in the United States per year are attributed to fine contains a pulsed diode laser and photodetector to
particulate exposure. Of these deaths, 21,000 are monitor the sample for transmission of light. Effectively,
believed to be from DPM in particular [5]. The Clean once the transmittance is seen to increase (i.e., char
Air Task Force reports that the estimated annual production in first phase) and then decrease back to its
economic cost of particulate-related illness and death in original value (i.e., char oxidation in the second phase),
the USA was $139 billion [8]. Clearly, the social and all subsequent methane production is attributed to EC.
economic impact caused by particulate-related illnesses For this optical analysis, the instrument requires a
should not go unaddressed. portion of the sample filter wider than the diameter of
the laser [10,11].
To collect DPM samples for analysis by the 5040
2. DPM Monitoring
method, a field sampling apparatus is used which
As noted above, for demonstrating compliance with consists of a small air pump, and a 37 mm quartz fiber
DPM exposure limits in underground metal and filter that is held inside a plastic cassette. Often a device
nonmetal mines, the NIOSH 5040 method must be used. for removing relatively large particles from the DPM-
While this method provides an accurate measurement of laden airflow is also placed inline before the sample
EC and OC concentrations (which can be translated into filter; generally, the oversized particles (i.e., > 0.8μm)
TC as proxy for DPM) over the short duration of sample are removed via an impactor filter. By using a size-
collection, it is intended for determining personal selective sampler, airborne dust (i.e., which may include
exposures. Thus, it does not provide the ability to easily carbon-containing particles) is prevented from collecting
monitor DPM over long periods of time. For on the DPM filter and creating a sample matrix
understanding DPM trends in the context of mine interference for the analytical method [2]. When the
operation, and therefore mitigating exposure risks, impactor becomes full, DPM capture is no longer
monitoring capabilities are indeed critical. Recognizing efficient and the impactor must be replaced. SKC
this fact, a handheld, quasi real-time DPM monitor manufactures an all-in-one DPM cassette, which
called the Airtec (FLIR Systems, Inc., Albuquerque, contains an impactor and quartz fiber DPM filter [12]. In
NM) was developed in collaboration with NIOSH. The very dusty environments, a cyclone may also be placed
Airtec is now commercially available as an engineering inline before the sampling cassette to exclude relatively
tool for mine operators. Another device, the Airwatch, large (i.e., > 5μm) particles before air reaches the
has recently been prototyped. It is intended to meet the impactor.
need for autonomous area monitoring, but is not yet
In an earlier design, the SKC DPM cassette was
ready for commercialization.
observed by Noll et al. to be problematic [2].
The following sections describe these three DPM Specifically, DPM deposition on the filters was not
monitoring options for underground metal and nonmetal uniform in regards to the surface area (i.e., surface areas
mines, and their key characteristics are summarized in over which DPM deposited were irregular and varied
Table 1. between cassettes.) Uniform deposition is critical for
accurate calculation of aerosol EC, and then TC,
concentrations since only a fraction of the filter is
analyzed and must be assumed representative: the 5040-
2.1 NIOSH 5040 Method
quantitated EC and TC masses are effectively converted
The most up to date version of the NIOSH 5040 to concentration values based on the fraction of sample
method was published in 2003 [6]. The method surface area analyzed, the sampling time and the
incorporates thermo-optical analysis because of its flowrate [2]. Once modification was made to improve
selectivity and flexibility (e.g. can run manually and is the cassette design, they were determined to provide
programmable). The instrument was specifically reliable measurements in laboratory and field
developed for analysis of carbon-based aerosols (e.g., environments [2].
DPM) and is manufactured by Sunset Laboratories, Inc.
Following promulgation of DPM rules in
(Tigard, OR). In general, the thermal analysis is
underground mines, the NIOSH 5040 method has
completed in two phases. First, the sample is placed in
provided a means for gathering a wealth of information,
an oven and heated to 850°C in inert atmosphere,
particularly about personal exposures; and improvements
causing the OC to become catalytically oxidized. This
in the mine environment have undoubtedly resulted.
forms carbon dioxide, which can then be reduced to
However, this method, it is not a particularly practical
methane. The methane is then measured using a flame
engineering tool for mine operators aiming to conduct
ionization detector (FID) [9]. Next, the sample is re-
routine monitoring of DPM. Collected samples must be
heated up to about 900°C in an oxygen-rich atmosphere,
mailed to only a handful of equipped laboratories to
such that the EC is also oxidized; again, the resulting
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perform the required analysis, which makes collecting Functionally, the Airtec monitor has three main
results quite time consuming [5] – not to mention parts: a small air pump, a plastic cassette that holds a
expensive. One test costs approximately $100 for filter onto which DPM is collected, and a laser and
supplies and analysis, and this figure does not include sensor pair. As the DPM is collected, the laser is directed
mine labor [5]. Moreover, the lag period between sample toward the filter and the sensor detects how much of the
collection and analysis makes it difficult to both laser becomes blocked by EC (a primary component of
recognize the conditions leading to overexposures and to DPM). The laser becomes increasingly “extinct” as more
gage the effectiveness of attempted DPM control DPM is collected, and thus an effective measurement of
mechanisms. EC is obtained. As is often the case with filter samples
collected for the 5040 method, the Airtec can also use an
Beyond the issue with significant lag time between
impactor to keep dust from entering the device and
sample collection and result reporting, 5040 method
depositing on the filter. (Previously, a “sharp cut”
results are also limited because they are associated with
cyclone was also commercially available that could
bulk samples (i.e., the final result is a time-weighted
effectively remove particles > 0.8μm, but this model of
average concentration). This means that particular time
cyclone is not being manufactured anymore.)
segments within the sampling period cannot be isolated
[5]. It would be helpful for mine operators to determine While the Airtec has afforded significant monitoring
when peak exposures of DPM occur, ideally in real time, capabilities to mine operators, a new device developed
so that they can adjust ventilation controls accordingly. under NIOSH contract number 200-2010-36901 called
the Airwatch DPM Monitor may provide even more
utility in the way of long-term area monitoring. The
2.2 In-mine DPM Monitoring Airwatch is currently in the prototype and demonstration
phases. It is technologically similar to the Airtec, but
To address the need for in-mine monitoring, the
includes several modifications that allow the device to
Airtec DPM Monitor was developed. It is a handheld
operate autonomously over long periods of time. Most
device and displays EC concentrations on a running 15-
importantly, it can run on mine power (i.e., instead of
minute average – quasi real-time. The instrument meets
batteries) and does not require frequent user attention or
NIOSH accuracy criteria and provides results with no
maintenance. The latter is possible because the Airwatch
statistical difference from the 5040 method [13]. It
uses a self-advancing filter tape on which the DPM is
measures EC using a laser extinction technique, which
collected [14]. The tape is similar in form to an audio or
works because EC concentrations are related to laser
VHS cassette tape, wherein the clean filter media is
absorption [13]. The laser extinction is measured directly
rolled around one cylinder from one end and attached to
on a filter as it collects DPM, which is ideal for a small,
another cylinder on the other end. DPM is collected via
portable device.
an air pump and deposited on a small area of tape
Mine operators may use the Airtec to “spot” check between the two cylinders. Here, a laser and sensor pair
areas of interest in order to identify high DPM similar to those used in the Airtec units is employed to
contributing sources, and also to evaluate personal track laser extinction, which can again be related to EC
exposures to DPM. It has proven particularly useful for collected on the filter tape. When a given filter area is
monitoring DPM in equipment cabs because it is not completely used (i.e., laser extinction is sufficiently
influenced by instantaneous pressure changes, such as high), the tape progresses forward to expose a clean area
those caused by opening and closing doors [7]. of filter to the laser and sensor. The exact life of this
Researchers at NIOSH have observed that the Airtec is filter tape depends on the sampling environment and
sensitive to cigarette smoke and will register it as a DPM monitoring setup (i.e., concentration of DPM in the air,
reading [7], and so users should be aware of this and frequency at which the Airwatch is programmed to
potential for false-positive readings and not smoke while collect data.) To avoid interference in laser extinction
the monitor is being used. Being able to monitor DPM in from dust particles, a sharp-cut cyclone is employed to
near real-time allows mine operators to identify when prevent dust particles from depositing on the filter. As
levels are nearing compliance limits, as well as evaluate opposed to an impactor for this purpose, the cyclone
the effectiveness of engineering controls to abate it. does not need frequent replacement
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Table 1. DPM Monitoring Options
Method Analytical Primary Availability Sampling Unit
Technique Applications of Results
5040 Method Thermo-optical Personal Lag time Portable
with FID exposures (days to
(quantitates EC (required for weeks)
and OC) compliance),
short-term area
monitoring
Airtec Monitor Laser extinction Personal Quasi real- Portable
exposures, time
(quantitates EC)
short-term area
monitoring,
spot-checking
Airwatch Laser extinction Long-term, Quasi real- Stationary
Monitor (quantitates EC) autonomous time
area
monitoring,
networking
capabilities
In its current design, the Airwatch can be DPM control – certainly far from ideal. Some mines do
programmed to transmit data to remote monitoring not even have forced-ventilation systems in place.
cations via hardwires (i.e., Ethernet or 4-20mA). Since a Rather, they depend on natural ventilation, which is
current-based signal is used, the signal transmitted does uncontrolled and unreliable due to seasonal variations in
not degrade over distance. Where available, mining temperatures that drive the movement of air [16]. Only a
operations could certainly benefit from real-time DPM few research studies have been conducted regarding
information that can be transferred quickly over wireless DPM in large-opening mines (e.g., see 16-18), but it is
networks, and this capability is also envisioned for the clear that effective, data-driven ventilation
Airwatch monitor. Long-term, operators might be able to improvements require enhanced DPM monitoring
centrally process data and automatically incorporate networks.
them into other systems or decision-making schemes to
alter mine parameters, such as ventilation [15]. Although
the Airwatch has been successfully tested in the 3.1 Project and Task Description
laboratory, extensive field testing has not been
Two main objectives related to DPM monitoring
conducted to date
and ventilation have been established for this project: 1)
to demonstrate the capability of the prototyped Airwatch
devices to autonomously monitor DPM in high-priority
3. Research Approach
areas of a study mine and 2) to determine DPM response
Under a new Capacity Building in Ventilation to ventilation conditions in various areas of the mine.
project sponsored by CDC/NIOSH through the Office of Work began during late 2014 and will be developed over
Mine Safety and Health Research (contract no. 200- the remainder of the five-year project. Table 2 displays
2014-59646), the Airwatch technology will be the tasks that will be undertaken in order to fulfill the
demonstrated in an underground mining environment, project objectives.
and ultimately employed to monitor DPM under
3.3 Progress to Date
different ventilation scenarios.
Work is proceeding in cooperation with an industry
The focus environment for this project is the large-
partner (an underground stone mine) and to date, there
opening mine. These mines experience airflow quantities
has been progress towards Tasks 1 and 2. For Task 1,
so low that they are sometimes immeasurable with
due to the very low air velocities in the study mine, it
conventional equipment. In many, ventilation techniques
will be necessary to use an ultrasonic anemometer to
are currently being employed to control DPM but they
collect accurate data. A UA6 (TSI Incorporated,
are still highly experimental, using trial-and-error
Shoreview, MN) is currently being lab-tested and will be
approaches to gage effectiveness [16]. These are notably
employed for spot ventilation surveys. The ventilation
costly, time-consuming, and less than optimal in terms of
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data will be collected in concert with DPM data using 4. Impact
the Airtec monitor. Survey points will be chosen
Despite significant improvements over the past
together with the mine operator. A customized DPM
couple of decades, DPM is still a significant health
cassette, designed and 3D-printed by NIOSH, will be
concern for underground mine workers. Efforts to further
used to reduce the DPM deposition area on the filters.
reduce exposure risks require enhanced monitoring tools.
This will effectively reduce the total surface area of the
Demonstration of the efficacy and utility of the Airwatch
DPM filter so that the Airtec unit is much more sensitive
DPM monitor is expected to aid in progress toward its
and can provide faster EC readings (versus the 15-
commercial availability. Ultimately, this tool should
minute minimum sampling time that is normally
provide mine operators a means of tracking DPM with
required).
other environmental and operational conditions (e.g.,
For Task 2, upgraded Airwatch monitors have been ventilation) such that worker health can be adequately
built (on a separate NIOSH contract). The new units protected while optimizing other factors (e.g., energy
have been modified to make them more rugged and user usage, production, maintenance schedules, etc.).
friendly. Comparative measurements are planned
Beyond theses expected research outcomes of the
whereby the Airwatch and Airtec units will be employed
Capacity Building in Ventilation project described here,
simultaneously. Moreover, work is currently underway
development of expertise in the areas of mining
to design self-contained monitoring stations that couple a
engineering and occupational health is a primary
2-axis ultrasonic anemometer that logs data
objective. The project team includes multiple student
cooperatively with an Airwatch unit to track air velocity.
researchers. Their current work will add to the scientific
This future work will help determine how DPM responds
literature surrounding DPM monitoring and control; and
to ventilation controls. Due to environmental conditions,
the knowledge and experience they gain during this
the datalogger should be stowed inside some type of
project will soon contribute to the broader mining
moisture-proof enclosure to protect it from atmospheric
community.
conditions.
Table 2: Work tasks related to DPM monitoring and ventilation response
Task Description
Initial Collection of Mine data • Become familiar with operation and environmental conditions at the mine of
(Year 1) study.
• Conduct ventilation and DPM surveys by using:
o Airtec real Time Monitors
o Ultrasonic Anemometers
Receipt and lab resting of • Receipt of prototyped autonomous DPM monitoring units from NIOSH
prototyped autonomous DPM • Becoming familiar with the units’ design and operational requirements.
monitors (Years 1-2) • Units will be lab tested to confirm they are functioning properly
o Capability to measure continually
o Capability to log data
o Accuracy and consistency amongst all units output.
• Verification of autonomous DPM monitors’ readiness for use underground.
Field-testing of autonomous • Determining installation locations together with the mine operator.
DPM monitors (Years 2-4) o High priority areas for monitoring of DPM
o Safe and reliable for the operation of the testing equipment.
• Installation of the prototyped monitors at the field site
• Ensuring proper functioning in the mine environment and capability to record
DPM data for long periods of time
Monitoring DPM responses to • Tracking DPM response to different ventilation scenarios.
specific ventilation (Years 4-5) • Scenarios will be determined in conjunction with the mine operator
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A M E A
ETHOD FOR VALUATING THE PPLICATION
V F D C
OF ARIABLE REQUENCY RIVES WITH OAL
M V F
INE ENTILATION ANS
Tyson M. Murphy
ABSTRACT
The adjustable-pitch setting on an axial-flow fan is the most common method of
controlling airflow for primary coal mine ventilation. With this method, the fan operates
at a constant speed dictated by its motor design. The angles of the blades are adjusted to
change the amount of airflow and pressure to meet ventilation requirements. Typically,
the fan does not operate at its optimum efficiency, which only occurs in a narrow band of
air pressures and quantities. The use of variable frequency drives (VFDs), which control
fan speed, provides a solution to this problem. VFDs are already used in various similar
applications such as pumping and building ventilation. New technology now enables
efficient VFD operation in medium voltage (2,300 – 6,900 V) fan applications. The
primary benefit of a variable frequency drive is that it allows motors to operate at reduced
speeds, and thus at a lower power, without a loss of torque. VFDs also allow for efficient
operation over the entire life of the fan. The technical considerations of using a VFD are
presented in this work, along with a method for choosing and modeling a variable speed
fan to achieve maximum energy savings. As a part of this research, a spreadsheet
program was developed that will calculate the optimum fan operating speed based on
given fan data and specified operating conditions. A representative room and pillar coal
mine is modeled to illustrate the selection and modeling process and as an example of the
economic implications of using a VFD. The use of VFDs is shown to potentially yield
large energy savings by increasing the fan efficiency over the life of the mine. Although
there are definite power savings while using variable speed fans, the magnitude of these
savings is specific to an individual mine and the operating conditions encountered. The
determination of whether the use of VFDs is economically feasible requires analysis for
the specific mine and its operating conditions. This work provides the background and a
method for such an evaluation.
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CHAPTER 1: INTRODUCTION
1.1 Problem Statement
Primary mine ventilation fans provide necessary airflow and pressure to properly
circulate air in the working areas of the mine. During mining, as the size of the mine and
mine resistance changes, ventilation requirements will vary as changing airflows are
required to maintain a safe mining environment. Usually, the requirements are calculated
for different points over the projected mine life, and a fan is chosen that is capable of
operating at all of these points over the 15-20 year life of the fan. Missing in this process
is a method for dealing with the decrease in fan efficiency at operating requirements that
are lower than what the fan is optimally designed for.
The most common primary mine fan is the axial flow type. This type of fan traditionally
operates at a fixed speed based on motor design and power supplied to the fan. The
power and speed are generally constant for a given fan design. Currently, the most
common method of varying the airflow and head of an axial flow fan, in response to the
changing conditions of the mine, is to change the pitch of the fan blades (Hartman, et al.,
1997). Fan curves are created based on multiple pitch angles for each fan, and a fan is
selected that allows for the highest efficiency at changing pitches for the life of the fan.
This method of fan operation results in inefficiencies during the life of the mine. Most
often, a mine will operate a fan at a higher airflow than necessary during early mining,
simply because it is more efficient than operating the fan at a lower airflow. Nearing the
end of mining operations, the fan may be operated near 100% of its capabilities to meet
the requirements. In all but a narrow range of airflows and pressures, the fan does not
operate at its optimum efficiency.
In addition to the inefficiencies associated with providing adequate airflow, changing the
airflow can be an inconvenience to mine operators. Older fans need to be shut down to
perform pitch adjustments, while more modern fans can be changed during operation.
Regulators are also used to restrict airflow by diverting intake air into exhaust airways
before it reaches the faces. Invariably, this results in unused fresh air that is exhausted
from the mine.
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1.2 Proposed Solution
Variable frequency drives (VFDs) are one solution to the inefficiencies of current fan
operation. VFDs are already used in various similar applications such as pumping and
building ventilation. In mining, VFDs have been used in belt haulage systems,
continuous miners, and trams. The benefit of a variable frequency drive is that it can
allow motors to run at various speeds, without a loss of torque.
The speed of a motor is based on the frequency of the power supplied and the design of
the motor. To change the speed, either a physical change in the motor construction or a
change in electrical frequency is required. The torque of a motor is determined by both
its voltage and frequency, and a motor is rated based on a fixed ratio of these two factors.
A VFD can supply power with the proper frequency and voltage/frequency ratio to
produce different speeds while maintaining a constant torque in the motor.
The ability to change the speed of ventilation fans is advantageous in controlling the
airflow and pressure in a mine. There are many advantages to this approach of
controlling airflow. If a VFD is used to control fan speed, energy savings can be realized
by operating a fan at a point that meets the ventilation requirements while maintaining
high fan efficiency throughout the life of the fan. The use of VFDs also provides
flexibility in mine operations by potentially allowing the fan to be adjusted as needed or
“on the fly” during mining.
1.3 Scope of Research
This research shows the possible benefits of using variable frequency drives in mine fan
applications. Technical requirements of ventilation, VFDs, motors, and fans are
reviewed to determine the feasibility of installing and using VFDs for mine fan
applications. A simple coal mine was designed and modeled to perform a ventilation
analysis that incorporates variable speed fans. It is then used to develop and illustrate a
method for determining the appropriate reduced speed fan settings to achieve optimum
operating conditions. Also of importance are the economic benefits of using a VFD to
control fan speed. Although the economics are specific to a single mining operation and
its operating conditions, the example mine is used to illustrate some of the trends and
issues that are likely to be present.
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CHAPTER 2: LITERATURE REVIEW
2.1 AC Motors and Drives
2.1.1 Induction Motor Principles
AC squirrel-cage induction motors are the most commonly used motors in industry today
because of their simple construction, durability, and low cost. As with all induction
motors, the basic components of a squirrel-cage induction motor are the stator (stationary
winding) and rotor (rotating winding). Instead of an actual winding, a squirrel-cage rotor
is simply constructed of longitudinal copper bars connected at their ends by copper
shorting rings, as shown in Figure 2.1, hence the name “squirrel-cage.” The entire copper
cage is imbedded in a cylindrical magnetic core.
Figure 2.1 – Simple Squirrel Cage Induction Rotor (Luttrell 2005)
When balanced three phase voltages are applied to the windings of the stator, the
resulting currents in the windings produce a magnetic field. The speed of this rotating
field is referred to as the synchronous speed, n (rpm), and is a function of the electrical
sync
frequency of the applied voltage, f (Hz), and the number of poles in the stator, p, as
e
given by the following equation:
120f
n = e (1)
sync p
Lines of flux, produced by the rotating magnetic field, cut the copper bars of the rotor,
thus inducing current in the rotor bars. The interaction between the stator’s magnetic
field and the rotor’s currents results in rotational torque. The rotor then accelerates, with
its terminal speed approaching that of the magnetic field. However, the rotor speed can
never reach the synchronous speed. If this occurred, the rotor would be traveling at the
same speed as the magnetic field and the flux from the magnetic field would not cut the
rotor bars. Therefore, no currents would be induced in the rotor, and no rotational torque
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would be developed. Because of these effects, the mechanical (rotor) speed of the motor
must always be less than the synchronous speed of the magnetic field to maintain
rotational torque.
The speed differential between the synchronous speed, n , and the mechanical speed,
sync
n , is defined as a percentage of the synchronous speed, and is referred to as slip, s, given
m
by the following equation:
n −n
s = sync m ×100% (2)
n
sysc
As an example, consider an eight-pole motor operating with a rated slip of 2%.
Assuming a power line frequency of 60 Hz, the synchronous speed of the motor is
120f 120×60
n = e = =900rpm
sync P 8
The mechanical speed of this motor is
n = n (1−s)=900(1−0.02)=882rpm
m sync
An induction motor operates at relatively constant speed. A typical speed-torque
characteristic for an induction motor, along with the load torque for a mine ventilation
fan is shown in Figure 2.2(a). As long as the motor torque exceeds the load torque of the
fan, the fan will accelerate until the two curves intersect. This point of intersection
becomes the operating point of the motor. Induction motors operate at a relatively
constant speed with slight variations depending on the load torque, which is a desirable
characteristic for a ventilation fan.
A significant increase in torque will result in increased slip, and thus a small change in
speed (Figure 2.2(b)). If for some reason the load increases, the motor only slows
slightly. Since the synchronous speed of the magnetic field remains constant, more lines
of flux cut the rotor bars and increase the motor current to accommodate the required
increase in torque. An increase in slip thus causes increased current as well as increased
torque. It is because of this relationship that high startup currents are present when
starting a large motor, from zero rpm to rated speed, and are sometimes as high as 6 to 10
times the operating current (Beaty and Fink 1987).
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Motor Profile
Fan Load Profile
euqroT
Motor Profile
Operating Torque
Speed n m n sync
euqroT
ΔT
Speed Δn
(a) (b)
Figure 2.2 – Speed-Torque Profiles
In order to change the speed of an induction motor, it is necessary to either change the
electrical frequency or the number of poles in the motor (Equation 1). Motors require
special types of windings with a set of external relays for changing poles. Also, only
discrete changes in speed can be achieved with this method. For example, a motor with a
synchronous speed of 1200 rpm can be slowed to 900 rpm if the number of poles is
increased from six to eight, but speeds between these values can not be achieved. As a
result, the technique of changing the number of poles (and thus how the motor is wound)
is now obsolete (Chapman 2002), and changing the electrical frequency is the preferred
method for varying speed.
An important consideration when varying the speed of a motor is to maintain the same
torque characteristics of the motor. Torque is proportional to the magnetic flux density in
the motor air gap, which is proportional to the ratio of voltage and frequency, and is
determined by the motor design. To maintain a constant flux, and thus constant torque
characteristics at varying speed, voltage must also be varied to maintain a constant ratio
of voltage and frequency. If the voltage is not de-rated as frequency drops, the steel in
the core of the motor will saturate, and the magnetization current in the motor will
increase and become excessive (Chapman 2002). Equation 3 describes this relationship
where V is in Volts, and f is in Hz. Figure 2.3 shows the voltage and frequency ratios for
different motor voltage ratings.
V
=c (3)
f
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2.1.2 Variable Frequency Drive Principles
Variable frequency drives (VFDs), also referred to as variable speed drives and
adjustable speed drives, input line power and output a reduced voltage and frequency
supply to the motor. VFDs consist of three major components, as shown in Figure 2.4 – a
rectifier/converter to convert AC to DC voltage, an intermediate DC link, and an inverter
that outputs a simulated sinusoidal AC voltage from the controlled DC voltage. VFDs
use a non-alternating DC voltage internally because it is easier to generate an output
waveform (Turkel 1995). Additional input transformers and output filters can be
included depending on the drive configuration and design. There are a variety of
different ways that these functions are accomplished, but the same basic configuration is
used.
M
DC Link
Rectifier Inverter
Figure 2.4 – VFD Components
The technology used in VFDs has changed greatly over the past 30-40 years, and is now
at a point where the advantages outweigh the disadvantages for use in medium voltage
applications. High cost and reliability problems, as well as issues of input and output
power quality that have prevented the widespread use of medium voltage drives have
been resolved (Giesecke and Osman 1999). Giesecke and Osman (1999) also provide
what they refer to as the systematic evolution of VFDs and the changing technology that
has made VFDs feasible. Advances in the areas of semiconductor switching devices
have, in particular, made the use of these drives possible in medium voltage applications.
Manufacturers have also embraced this technology, evolving from the approach in the
early 1990’s that the drive had to be perfectly matched to the motor by the same
manufacturer (Huffman 1990) to manufacturers that will now make VFDs that are
capable of retrofit on any AC motor.
A listing of VFD topologies is shown below (Morris and Armitage), with a brief listing of
advantages and disadvantages with regard to medium voltage applications. The topology
of a VFD is the electrical configuration of the drive, which ultimately determines the
overall function of the drive. Motor control platforms, which are a part of the converter
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section of the drive, determine how energy is delivered to the motor, and control the
speed and torque delivered (Morris and Armitage). Emphasis is placed on topologies
and motor control of medium voltage systems for fan and pump applications, since that is
the focus of this research.
Examples of Drive Topologies:
- Voltage Source Inverter (VSI) – Advantages: Can retrofit on existing motors
without derating, full torque at low speeds, input power factor near unity, low
network harmonics, and high efficiency.
- Current Source Inverter (CSI) – Advantages: Cost effective, four quadrant
operation. Disadvantages: Continuous low speed operation not possible,
inconsistent power factor over operating range, higher cost, larger drive, and
additional losses.
- Load Commutated Inverter (LCI) – Advantages: Single Motor Drive for
medium and high power ratings, wide speed and power range, inherent 4-
quadrant operation. Disadvantages: Not for use on squirrel cage induction
motors.
There are two primary motor control platforms used in VFD applications. The first is
Pulse Width Modulation (PWM). This platform uses a pulse width modulator to simulate
a sine wave, with the voltage and frequency determining the torque and speed. The
output is a series of pulses of varying widths. The width of each pulse controls the
magnitude of the voltage and the frequency of the changing polarity of the pulses control
the frequency of the power delivered (Yaskawa Electric America). Figure 2.5 shows a
PWM line diagram with the corresponding desired waveform. The ongoing
development of power devices and increased use has made PWM VSI converters
relatively inexpensive (Shakweh 2000).
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time
egatloV
Desired waveform
PWM waveform
Figure 2.5 – PWM waveform
A few semi-conductor switching technologies that exist in VFD applications are:
- GTO – Gate Turn Off Thyristor
- IGBT – Insulated Gate Bipolar Transistor
- SGCT – Symmetrical Gate Commutated Thyristor
- IGCT – Integrated Gate Commutated Thyristor
GTOs were initially used in VFDs, but were not successful due to their expense and
complexity. IGBT technology has been significantly improved for use in medium
voltage applications and is a popular choice of technology for VFD manufacturers.
According to ABB, who pioneered the IGCT, their technology is ideal for medium
voltage drives primarily due to faster switching and lower power dissipation, resulting in
its high efficiency and reliability, and reduced size and cost compared to IGBTs (ABB).
Regardless of manufacturers’ claims that their technology is superior to the competition,
both IGBTs and IGCTs are viable technologies and are both being continually improved.
Direct torque control (DTC) is a more recently developed motor control platform,
especially for medium voltage drives. DTC controls speed and torque directly, without
the use of a modulator. DTC can catch a load already in motion, providing the ability to
resume fan operation after an interruption in power without waiting for the fan to come to
a stop (Morris and Armitage). DTC accomplishes this by using motor flux and torque as
primary control variables that are compared to values from an internal motor model.
Adjustments are made to the voltage and frequency accordingly. This process does not
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require an actual speed measurement to be taken, thus requiring no feedback and
eliminating any feedback encoder failure (ABB). The actual operation of DTC is
beyond the scope of this research, but Buja and Kazmierkowski present a review of DTC
techniques and their operation (Buja and Kazmierkowski 2004).
VFDs that are based on the VSI PWM technology inherently have four disadvantages
that require additional motor considerations – internal temperature increases, breakdown
of the insulation in the windings, bearing currents, and harmonics and electromagnetic
interference (deAlmeida et al. 2004). A solution to these problems is to use a sine wave
output filter. The filter is located between the drive and the motor, and has the following
benefits: no extra motor stress, no insulation stresses or cable resonances, minimal
currents to ground or bearings, minimal noise, and can utilize standard motors (Shakweh
2000). This last point is especially important, as it allows VFDs to be installed on
existing motors without modifications or additional costs.
Another option is a VFD incorporating IGCT technologies with output filters, which
offers nearly sinusoidal output and a rapid response to torque variations, resulting in no
motor derating, and no additional winding insulation (Steinke et al. 1999). By utilizing
DTC, the starting torque is maximized and fluctuations in load are compensated for with
a quick response. These features also allow the drive to be used on nearly any motor,
including retrofitting motors in existing applications.
An example of the topology of a modern VFD is shown in Figure 2.6 below, and a
photograph of the same drive is pictured in Figure 2.7. This drive is ABB’s ACS1000
medium voltage drive.
© 2005 ABB MV Drives
Figure 2.6 - ABB’s ACS 1000 Variable Frequency Drive topology (ABB)
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© 2005 ABB MV Drives
Figure 2.7 – Photograph of ABB’s ACS 1000 Drive (ABB)
2.1.3 Applications of VFDs
Variable frequency drives are common in many different industries today. The benefits
of a VFD are widely utilized in various applications. In the mining and mineral
processing industry, VFDs are used for operating belt conveyors, mills, and pumping, as
well as trams and continuous miners.
There are three basic categories of motor load which are classified based on how torque
requirements vary with speed (Allen-Bradley).
1) Constant torque load – The torque is constant at all speed ranges, and the
horsepower is directly proportional to speed. These applications are essentially
friction loads, such as conveyors and extruders, high inertia loads, and positive
displacement pumps.
2) Variable torque load – The torque is low at low speeds, and high at high speeds.
Usually the torque is a function of speed squared. Applications with this load
profile are fans, pumps, and blowers.
3) Constant horsepower load – Speed and torque are inversely proportional: high
torque at low speeds and low torque at high speeds. This load is a function of the
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2.2 Mine Ventilation
2.2.1 Introduction
The purpose of mine ventilation is to help maintain a safe and healthy environment
underground that provides a reasonable comfort level (McPherson 1993). Adequate
airflow is necessary to provide fresh air for miners to breathe and to remove harmful
gases and dust. In coal mines especially, there are many federal and state regulations that
govern exactly how this is to be accomplished. There are maximum dust and gas
concentrations that must be maintained in the mine, thereby creating specific airflow
requirements in certain areas. Fans located in either the mine or on the surface, provide
this necessary airflow and are an essential part of this ventilation system. As the mine is
developed and the expanses underground increase, the ventilation system must also be
able to adapt over time to the changing conditions. A great deal of engineering goes into
developing a mine ventilation system to incorporate all of these factors. Behind meeting
all safety and regulatory standards, economics also play a large role in how a ventilation
system is created. There has been much research on the principles and methods of mine
ventilation. Below is a brief overview of the components of a simple room and pillar
mine ventilation system, and how one is developed.
2.2.2 Components
Airflow is generated by large mine fans and travels through the mine workings, usually
from an intake shaft to an exhaust shaft. In the mine, air direction and quantity are
controlled by a variety of devices. Permanent and temporary stoppings are used to block
passages, regulators reduce the flow of air by partially blocking an airway and creating a
shock loss, and over- or under-casts allow air to cross at intersections without mixing.
These devices are used below in a description of a simple room and pillar coal mine.
In room and pillar mining, the mains and panels are separated into parallel airways by the
placement of stoppings. These stoppings are physical barriers used to prevent mixing of
air, and are either temporary or permanent (Hartman et al. 1997). These airways are used
for intake, return, or neutral airflow, depending on the number of entries in the section.
An example is illustrated with further detail in the Chapter 3.
Air flows from the intake shaft into the mains. From the mains the air is split to travel
through each panel to the working face. In Figure 2.4, the layout employs a double split
method where the intake air flows through the center entries, is split at the face, and is
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2 2
H ⎛n ⎞ ⎛D ⎞ w
H ∝n2D2w, or 2 = ⎜ 2 ⎟ ⎜ 2 ⎟ 2 (5)
⎜ ⎟ ⎜ ⎟
H n D w
⎝ ⎠ ⎝ ⎠
1 1 1 1
3 5
P ⎛n ⎞ ⎛D ⎞ w
P∝n3D5w, or 2 = ⎜ 2 ⎟ ⎜ 2 ⎟ 2 (6)
⎜ ⎟ ⎜ ⎟
P n D w
⎝ ⎠ ⎝ ⎠
1 1 1 1
where, Q = airflow
H = head/pressure
P = motor power
D = fan diameter
n = fan speed
w = air specific weight
subscript 1 = values with initial parameters/conditions
subscript 2 = values at changed parameters/conditions
Measuring fan performance as a function of power results in an expression of fan
efficiency. The mechanical efficiency, η, is expressed as Equation 7, where P is the air
a
power, and P is the brake power.
m
P
η= a ×100% (7)
P
m
Air power can be calculated from the head, H, and quantity, Q. In English units (H in in.
WG and Q in cfm), the formula is Equation 8. Brake power is the power that must be
supplied to the fan, and is found by multiplying the fan efficiency by the air power.
Brake power can also be simply read from the manufacturer’s fan curves or calculated
from the fan laws (Equation 6).
HQ
P = hp (8)
a 6346
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2.2.4 Ventilation Analysis
In order to provide the necessary airflow, the fan must generate a high enough pressure to
overcome the resistance of the mine airways. This pressure, or head loss, is a function of
the airflow and the size, length, and friction factor of each airway section in the mine.
Head loss can be related to airflow and these airway parameters by Atkinson’s equation,
Equation 9. The total head loss for the mine is found by combining (in parallel or in
series) all individual airway losses based on Kirchhoff’s laws. Hartman (1997) and
McPherson (1993) describe this process in detail in their books.
KO(L+ L )Q2
H = e (9)
l 5.2A3
Where, H = Head loss, in. WG
l
K = Friction factor, lb·min2/ft4
O = Perimeter, ft
L = Length, ft
L = Equivalent length of shock losses, ft
e
Q = Airflow, ft3/min
A = Area, ft2
Values for friction factors vary depending on the type of mine, how the airways are
supported, and the airway condition.
The head loss is directly proportional to the square of the quantity of air (Equation 9). If
K, O, L, L , and A are held constant, they can be combined to form one single constant,
e
R, or the resistance of the airway (Hartman et al. 1997). Equation 9 can then be rewritten
as:
H = RQ2 (10)
l
Since the resistance is constant at given operating conditions, this equation can be used to
define the characteristics of the mine over a range of pressures and airflows. The
resulting graph of such a calculation (Figure 2.8) is known as the system or mine
characteristic curve, which describes the head loss at any quantity of airflow.
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3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0 50 100 150 200 250 300 350
Airflow, kcfm
GW
.ni
,daeH
100
90
80
70
60
50
40
30
20
10
0
PH
,rewoP
ekarB
Power Curve
Operating
power
Operating point
System Curve Fan Curve
Figure 2.9 – Determining the Fan Operating Point and Power
2.2.5 VnetPC Modeling
VnetPC is a ventilation modeling program developed by Mine Ventilation Services, Inc.
This software takes data that describes the mine airways (length, friction factor,
geometry) and fan properties (H-Q characteristic) to generate a ventilation model that
includes fan operating points, regulator/booster requirements, airway quantities and
resistances, and power requirements.
The branch data entered into the program is based on a ventilation network representation
of the mine that consists of branches (mine airways) and nodes (intersections of airways).
Branches are defined by their respective node endpoints. This topology represents a
simplified layout of the actual mine. Each branch has properties associated with it,
including length, resistance per unit length, parallel airway factor, type of airway, and
surface state. Figure 2.10 shows a segment of mains and a panel from a mine plan.
Figure 2.11 illustrates the corresponding ventilation network. The ventilation layout
combines parallel airways into a single flow path and only includes nodes where airways
combine or split. Stoppings are modeled as sets of parallel airway leakage paths, with a
single high resistance corresponding to the number of stoppings modeled per path (Bruce
and Koenning 1987). The ventilation network is not to scale because the lengths of
branches between nodes are a property of each branch.
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CHAPTER 3: MINE AND VENTILATION MODELING
3.1 Mine Model Development
To simulate the effects of varying fan speed, a simple room and pillar coal mine was
designed to serve as the basis for the ventilation analysis. The actual design is not critical
to this research because only comparisons of fan configurations are studied. The design
used for this model can be replaced with any mine plan, and the results should have
similar trends. The mine design is simple and straightforward so that the changes in
ventilation requirements are due to mine development and distance from the fan over
time. Since the objective of this study is to simulate the effects of changing the fan
speed, special configurations, multiple ventilation shafts, and multiple fans are avoided.
The mine design results in ventilation requirements that increase with mine development
over time.
Although the coal mine modeled is not based on an actual mine, typical data were used
for describing the ventilation characteristics. It is assumed that the coal seam is 6 ft thick
and extends over a large area, at a depth of approximately 800 ft. An average coal
density of 80 lb/ft3 was also assumed. The mine plan developed for this seam is a
standard room and pillar layout. Pillar dimensions are 80 ft x 80 ft developed on 100 ft
centers, with a 5 entry panel and 8 entry mains, illustrated in Figure 3.1. An 80 ft barrier
between panels is maintained. Access to the mine will consist of 18 ft diameter intake
and return shafts, as well as a 14 ft x 14 ft dual compartment slope at an angle of 17º.
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Figure 3.1 – Pillar layout and dimensions
To develop a reasonable timeline for mining this seam while simplifying the ventilation
model, a few basic operating parameters had to be determined. For this room and pillar
mine, two continuous miners will be used, each with an average production capability of
1,100 tons per shift. At two shifts per day, and 300 operating days per year, production
totaled 1.3 M tons per year. Panel length was determined by an increment of the distance
a continuous miner could cover in one year, including time for development of the mains
ahead of the panels. Excluding the 1000 ft of mains ahead of the panels, each miner can
cover approximately 15,600 linear feet of mining in a year. By using a panel length of
7,800 ft, each miner will mine two full panels per year. For simplicity, pillar extraction is
not used, and after each panel is mined out, it is then sealed.
The average operating life for a primary mine fan is between 15 and 20 years, therefore,
the objective was to study the mine over a 15 year life. A portion of the resulting mine
plan is shown below in Figure 3.2.
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3.2 Ventilation Model Development
Because of the simplicity of the mine layout, only one intake and one return shaft were
used in this model. For the ventilation modeling, it was assumed that there would only be
one continuous miner operating per panel, resulting in the design of two panels mined
simultaneously. From a ventilation standpoint, the worst conditions result from having a
miner at the end of each panel at the same time. At this point in time, the air must travel
the farthest distance from the shaft to the last open crosscut in each active panel. The
conditions at this point were the conditions assumed for the development of the
ventilation model.
Ventilation requirements in the model include:
• Maintain a minimum airflow of 50,000 cfm at the last open crosscut at each panel.
• Maintain a minimum airflow of 3,000 cfm at the tailpiece of each belt.
• Maintain an average airflow of 5,000 cfm at the last open crosscut at the end of
the mains when development is not occurring.
• Velocity in the intake airways must fall within the recommended range of 600-
1150 fpm (Mutmansky and Greer 1984).
Regulators are placed in the returns of each panel to control the airflow at the last open
crosscut. Control devices are also placed at the belt tailpieces to limit the airflow. In
VnetPC, these locations are modeled as branches with a fixed quantity, where regulators
or booster fans are added as necessary to maintain the specified airflow.
Values for the friction factor in each airway vary widely based on the conditions at each
mine. These values have been researched by a number of people, and a recent study by
Prosser and Wallace (1999) provided the values for coal mine airways, listed in Table 3.1
below, used in this research. The authors identify average values and standard deviations
from a series of measurements, but to be conservative, the values used in this research
represent their average values plus one half of the standard deviation, as is recommended
by the authors.
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Table 3.1 – Friction factors for coal mine airways (from Prosser and Wallace)
Friction Factor
Airway
(lb·min2/ft x10-10)
4
Intake 46
Return 52
Belt 74
A dual split configuration is used in both the mains and the panels (Figure 3.3).
Equalizers are located every 2000 ft along the mains to connect the returns along each
side of the mains. This practice allows the airflows to balance in each return and offers
an alternative path for airflow if a return becomes blocked. The belt is isolated from the
intake and returns, and is considered a neutral airway. Since the panels are sealed after
they are mined out, only the farthest panels along the mains have an effect on ventilation
requirements.
Figure 3.3 – General mine ventilation layout (Novak 2003)
To compare and contrast fan and VFD configurations over the life of the mine, a yearly
time interval was modeled. Any time increment could have been used, but since each
time interval required separate models, a yearly increment was deemed sufficient to allow
the effects of using VFDs to be perceptible. A separate ventilation model was created for
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3.3 Determining the Optimum Operating Point
To provide a standard for comparison, the optimum operating point was required for each
model. This ‘optimum’ can be defined as the operating point which results in the lowest
head and quantity produced by the fan to adequately supply each face with the required
air quantity. There has been much research into determining this optimum point, and
devising ways to calculate it. For example, there are methods that favor linear modeling
and others that prefer using non-linear models to solve the ventilation network and
determine the losses at each regulator and find the fan operating point to balance a
network (Jacques 1991; Zhuyun and Yingmin 1991). Most of this research does not
consider actual power costs though, and only attempts to optimize the ventilation network
and fan conditions with regulator settings.
A succinct explanation of how to find the optimum operating point is to “minimize the
work performed by all fans in the ventilation network while minimizing energy losses at
all regulators,” (Krzystanek and Wasilewski 1995). Although Krzystanek and
Wasilewski do not propose a method to determine this, their process leads to the
conclusion that reducing the overall amount of regulation results in an increase in the
efficiency of the ventilation system, accompanied by a decrease in the required head and
quantity of the fan. This increase in efficiency can be directly related to energy savings,
as operating a fan at a lower head and quantity results in lower power consumption.
For this research, it was not practical to develop a computer program that would account
for variable speed fans or even to redesign current computer programs for the same
effect, but it was feasible to use VnetPC to solve this problem in a slightly different
manner. The program solves the ventilation model based on either a given fixed fan
pressure or a fan curve, and sizes the regulators to ensure adequate ventilation. By
iteratively varying the fan pressure and calculating the solution, the fixed quantity
branches can be monitored, and the optimum operating point determined when a fan
pressure yields a minimum sum of regulator resistance in these branches. Three
iterations of this process can be seen in Figure 3.5. VnetPC replaces regulators with
booster fans in the fixed quantity branches if the overall fan pressure is too low to supply
the required airflow, shown in iteration 1. Thus, ideally, the fan pressure can be reduced
until the regulators furthest from the intake shafts will behave like a free split, and have
zero regulation.
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CHAPTER 4: REDUCED SPEED FANS
Once the ventilation model was created and the optimum operating points were found,
the next stage of the research was to determine the speed at which to operate the fan to
meet the ventilation requirements while maximizing the fan and motor efficiency. This
was accomplished by first choosing an appropriate fan, and then creating reduced speed
head-quantity, power, and efficiency curves. The following sections detail each of these
steps.
4.1 Selecting an Appropriate Fan
The choice of an appropriate fan is based on the manufacturer’s fan curve data. A fan is
selected based on an available pitch setting that will satisfy the mine’s most extreme
operating condition at an acceptable efficiency. In practice there is no single optimum
fan for a given mine, but rather, many fans constructed by different manufacturers will
meet the specifications determined by the mine. The definition of ‘optimum’ is also
specific to the mining operation, but below are additional points to consider when
choosing a fan for use with a VFD. Comments on fixed pitch fans are included, and refer
to fans that can be manufactured without any provisions for adjusting the pitch setting of
the fan blades. Although at this point in time, the cost of a fixed pitch fan is the same as
an adjustable pitch fan (Spendrup 2005), there is the prospect that an increased demand
for fixed pitch fans might be incentive for manufacturers to produce them for a lower
cost.
For fixed pitch fans:
• The maximum efficiency that can be obtained at this fan setting will be the
maximum efficiency achievable at any operating point while using a VFD as well.
For fans with similar costs, choose the one that provides the highest efficiency.
• In most cases, the best fan will meet the most extreme operating condition while
operating near its maximum capabilities at an acceptable efficiency.
• Depending on the lifetime operating conditions, it might be more economical to
use a fan that will meet the maximum operating conditions at the center of its
efficiency “bubble” (resulting in operation at a point well below its maximum
capabilities), rather than one that meets the operating conditions at a lower
efficiency. Choosing a fan that is larger than necessary to provide adequate
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airflow might require higher capital expenses, but maintaining a high efficiency in
each year will result in savings that might offset the additional expense.
For adjustable pitch fans:
• A fan that will meet the requirements for a fixed pitch fan can be the best option
for adjustable pitch fans.
• The limitations of the maximum achievable efficiency in each year are reduced,
providing a greater range of operating conditions that fall within the larger
efficiency zones.
• Using the same size fan as with fixed pitch, it is usually possible to increase the
fan efficiency for each operating point by adjusting the pitch. Ultimately,
economics (capital costs) will determine whether an adjustable pitch or fixed
pitch fan should be used.
For the mine modeled in this research, a Spendrup Series 274-165-880 fan was found to
provide adequate ventilation capabilities at an acceptable efficiency. This is a 108 in.
diameter fan that operates at 880 rpm. The yearly operating points are shown with the
manufacturer’s fan curves in Figure 4.1.
16
5 6
4
14 3
2
12 16
15
10
14
1500
8 13
12 1200
6 11
10 900
9
4 8
7 600
6
5
2 4 23 300
0 0
0 100 200 300 400 500 600 700
.g.w
.ni
,erusserP
latoT
naF
1
85% 75%
80%
70%
6
5
4
3 2
1
Fan Flow Rate, kcfm
PH
,rewopesroH
ekarB
Figure 4.1 – Spendrup 274-165-880 fan with yearly operating points
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An additional Spendrup fan, model 305-183-880, also provides adequate ventilation, but
at a lower overall fan utilization. This is evident from Figure 4.2 which shows that the
maximum operating conditions only occur at approximately 50% of the fan’s capabilities.
As noted in the suggestions for fan selection, above, this larger 120 in. fan meets the
maximum ventilation requirements at a higher efficiency than the smaller Spendrup 274-
165-880 fan (84% vs. 78%).
20
6
5
18 4
3
16 2
14
12 16 3000
15
10 2500
14
8 13 2000
12
6 11 1500
10
9
4 8 1000
7
6
5
2 234 500
0 0
0 100 200 300 400 500 600 700 800 900 1000
.g.w
.ni
,erusserP
latoT
naF
1
84% 80%
75%
70%
6
5
4
3
2
Fan Flow Rate, kcfm
PH
,rewopesroH
ekarB
1
Figure 4.2 – Spendrup 305-183-880 fan with yearly operating points
4.2 VFD and Fan Combinations Modeled
To determine whether the size/capacity of the fan has an overall effect on the
performance of fans with VFDs, multiple scenarios were modeled for the mine plan
described in Chapter 3. For this analysis, six different fan and VFD scenarios were
modeled. They will be referred to as options 1 through 6, and are described below.
These options attempt to illustrate the performance results of using VFDs and/or
adjustable pitch fans on the mine modeled in the previous sections. Even though actual
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performance results are specific to the mine, trends and patterns can be illustrated by
comparing the options relative to each other with this example.
Options Modeled:
1. Use the Spendrup 274-165-880 fan as a standard adjustable pitch fan
operating in a conventional manner. This option is likely to be similar to the
typical choice of fan to meet the requirements of the example mine.
2. Use a larger Spendrup 305-183-880 fan as a standard adjustable pitch fan in a
conventional manner. This option would not likely be chosen, as the fan is
not fully utilized and costs are unnecessarily higher.
3. Use the Spendrup 274-165-880 as a fixed pitch fan with a VFD. This option
was modeled to show performance differences if a fan were manufactured that
had one fixed blade pitch setting. Costs could be lower if the fan did not
require adjustable pitch settings. It was assumed that the pitch was fixed at
setting number 6.
4. Use the Spendrup 305-183-880 as a fixed pitch fan with a VFD. This option
is modeled for the same reasons described in option 3. This fan was assumed
to be fixed at pitch setting number 4.
5. Use the Spendrup 274-165-880 fan as manufactured as an adjustable pitch fan
and operating at reduced speeds with a VFD.
6. Use the Spendrup 305-183-880 fan as manufactured as an adjustable pitch fan
and operating at reduced speeds with a VFD.
4.3 Methodology for Modeling Reduced Speed Fans
4.3.1 Fixed Pitch Fans
For the analysis and plotting, tables of data points (or equivalent equations) of the fan
curves are required. If standard manufacturer’s hard copy or digital (i.e. PDF) graphs are
used, scanning and then digitizing the curves is necessary. Resulting data tables should
include points along each of the fan curves, power curves, and any intersections of the
fan curves and efficiency lines. If the fan has a fixed pitch, then only the curve for that
pitch setting is useful.
The general process for creating these reduced speed fan curves follows. The Spendrup
series 274-165-880 fan was used in the example to describe the process throughout this
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section. The same process was used for the Spendrup series 305-183-880 fan, with the
values of fan performance changed. All of the results are presented collectively after the
process is described.
From the original fan curves, Figure 4.1, it was determined that pitch setting number 6 is
required to meet the maximum operating conditions with a resulting efficiency between
75 and 80%. Using the fan laws for quantity, head, and power (Equations 4 through 6), a
new fan curve and power curve can be calculated in a spreadsheet for any new speed
from each data point on the original curve and the original design speed. Finding this
appropriate speed for each operating point is an iterative process, requiring the equation
of the mine resistance, and the equation of the fan curve.
The mine resistance at the optimum operating point can be calculated from the mine head
and total quantity by Equation 10. Using this resistance, an equation (of the same form)
for the mine resistance can be created for head as a function of quantity. For example, if
R = 0.354x10-10 in·min2/ft6, the resulting equation for mine head is:
H = 0.354×10−10×Q2
The process to obtain the approximate equation of the fan curve involves general curve
fitting. The data points along the curve are known from the digitized fan curve, and the
form is approximately quadratic. The equation relating head, H, to quantity, Q, is:
H = cQ2 +c Q+c (11)
fit 1 2 3
Where, c , c , and c are constants
1 2 3
This curve fitting is performed using Microsoft’s Excel Solver add-in. The constants are
adjusted automatically by the Solver algorithm until the sum of squares difference
between the fit values of head and actual values of head is minimized. Using the
previous two equations relating the head and quantity of the mine and the fan, an
intersection point can be found by solving both equations simultaneously within the range
of the fan’s operating quantity. This point indicates the operating point of the fan for the
given mine resistance at the specified speed.
The process of curve creation to finding the operating point was repeated iteratively using
a binary search method until a speed was found that resulted in a difference between the
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Table 4.1 – Yearly Speed Requirements
Year Speed, rpm
1 350
2 350
3 375
4 400
5 425
6 450
7 480
8 515
9 550
10 590
11 625
12 670
13 715
14 765
15 815
16 875
It was also important to check the ventilation model’s branch results to verify the
spreadsheet calculations are correct and ensure that the minimum airflow requirements
are being met at the designated branches. At lower pressures, the fixed quantities of the
regulators required only small adjustments to accomplish this. The process involved
inputting the new reduced speed fan curve into VnetPC, and executing the model. If the
quantities at the faces were inadequate, the regulators were adjusted and the model re-
executed. The fan results were recorded, and the process repeated at each yearly interval.
The significant results from this modeling were the fan quantity and head, as well as the
air power required, and are summarized in Table 4.2 in the next section.
4.3.2 Calculating Power and Efficiency
After the required speeds and resulting fan curves were determined, the brake power for
each operating point was then found. There are two methods to find this value. First, the
yearly operating points were plotted on a graph that included each reduced speed power
curve. The value of power was then read from the graph at each yearly quantity. For
example, at year 14, the brake power is approximately 875 hp, as read from the graph in
Figure 4.4. However, this reading is only as accurate as the scale on the graph. For
better accuracy, an equation was found for each reduced speed power curve by fitting a
curve to the data points with power as a function of quantity. A second order polynomial
of the form in Equation 12 is adequate to describe these curves.
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P = cQ2 +c Q+c (12)
fit 1 2 3
Where, c , c , and c are constants
1 2 3
The fitting process was done using Microsoft Excel’s Solver function, using the same
methods described above to fit the fan curves, except measured and fit power values were
used. From these equations, the quantity at the operating point can be used to calculate
power.
16 1600
14 1400
16
12 1200
15
10 1000
14
8 13 800
12
6 11 600
10
9
4 8 400
7
6
5
4 2 3 200
2
0 0
0 100 200 300 400 500 600 700
.g.w
.ni
,erusserP
latoT
naF
875
815
765
715
670
625
590
550
515
480
450
425
400
375
Fan Speed, RPM350
Fan Flow Rate, kcfm
PH
,rewopesroH
ekarB
Figure 4.4 – Reading power from the reduced speed power curves
Efficiency at each operating point was then found by dividing the air power resulting
from the model by the brake power calculated above. It is also helpful to represent this
information graphically to see the possible efficiency ranges of the fan at different speeds
and pitch settings. The process used to illustrate the approximate efficiencies and
possible efficiency ranges on a fan curve plot is described below.
Head and quantity are read from the point of intersection of the fan curve and each
efficiency line on the fan curve plot. For example, in Figure 4.5, points A, B, C, and D
are the intersections of pitch setting number 6 fan curve with each efficiency line. Only
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Table 4.3 – Results from adjustable pitch, reduced speed fan
Fan Pitch Quantity, Head, in. Air Power, Brake Power, Calculated
Year Speed, rpm Setting kcfm WG HP HP Efficiency, %
1 350 6 219 1.70 59 77 77
2 350 6 219 1.70 59 77 77
3 375 6 231 2.02 74 96 77
4 400 6 244 2.37 91 118 77
5 425 6 257 2.72 110 143 77
6 495 5 271 3.11 133 168 79
7 525 5 286 3.55 160 202 79
8 565 5 306 4.17 201 254 79
9 600 5 324 4.74 242 306 79
10 645 5 347 5.54 303 381 79
11 690 5 370 6.37 371 469 79
12 730 5 391 7.17 442 557 79
13 780 5 417 8.22 540 680 79
14 835 5 446 9.46 665 836 80
15 815 6 474 10.74 803 1046 77
16 875 6 509 12.41 994 1294 77
4.4 Summary of Modeling Results
Considering the adjustable pitch- fixed speed fan of option 1 (Figure 4.1) the highest
ventilation requirements occur at the higher end of the fan’s capabilities. Since this is an
adjustable pitch fan, the fan can operate on all of the curves indicated (pitch settings 1 to
6) as well as at an infinite number of points between the specified curves at 880 rpm. In
practice though, it is unlikely that the fan will be adjusted precisely between labeled
settings. Limiting operation to the labeled pitch settings will result in the best case
scenario of operation shown in Figure 4.9. For operation in years 1 through 9 the fan is
far below 70% efficiency, and in practice, would not likely be operated at these points.
If the fan of option 1 were operated at the points in Figure 4.9, the power consumption
and calculated efficiencies are listed in Table 4.4 for each operating point. These
calculated values are based on the air power requirement obtained from VnetPC
simulations, and the brake power values as read from the fan curve graphs. These data
are the result of what can be considered operating with current practices assuming the
“best case scenario” ventilation requirements, and serve as the basis for comparison of
the remaining options. In this situation, fan efficiency is not a factor in determining the
operating point, only air power. For example, at point number 2, to draw a minimum 257
kcfm of air through the mine, the fan can be operated at curve number 1 at 38%
efficiency, resulting in a brake power of 241 hp. Operating at curve number 2 will also
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meet the minimum requirements, but achieving operation at 70% fan efficiency requires
operation at 310 kcfm and 5.8 in. w.g., which results in an approximate brake power of
400 hp. Thus, the operating point which yielded the lowest power consumption was
chosen regardless of fan efficiency.
Figure 4.9 – Operating points at pitch settings
Table 4.4 – Operating parameters for Spendrup 274-165-880 fan
Fan Speed, Pitch Quantity, Head, in. Air Power, Brake Power, HP Calculated
Year rpm Setting kcfm WG HP (Vnet) (from fan curves) Efficiency
1 880 1 257 2.28 92 241 38%
2 880 1 257 2.28 92 241 38%
3 880 1 256 2.39 96 246 39%
4 880 1 255 2.61 105 260 40%
5 880 2 323 3.70 189 331 57%
6 880 2 321 3.99 202 346 58%
7 880 2 318 4.29 215 356 60%
8 880 2 316 4.58 228 359 64%
9 880 3 377 5.84 347 494 70%
10 880 3 374 6.15 363 511 71%
11 880 3 372 6.33 372 516 72%
12 880 4 432 7.93 540 693 78%
13 880 4 428 8.38 563 707 80%
14 880 5 477 10.10 759 945 80%
15 880 6 526 11.90 986 1284 77%
16 880 6 514 12.43 1006 1310 77%
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