Supervisor: Professor Supervisor: Professor HristopulosHristopulos D.T.D.T.
SPATIAL 3D ESTIMATION OF LIGNITE RESERVES AND DEVELOPMENT OF A
SPATIAL PROFITABILITY INDEX
ANDREW PAVLIDES
SCHOOL OF MINERAL RESOURCES ENGINEERINGSCHOOL OF MINERAL RESOURCES ENGINEERING
Technical University of CreteTechnical University of Crete
June 2014June 2014 ΕΡΕΥΝΕΡΕΥΝHHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ
PRESENTATIONPRESENTATION Quick overview of spatial analysis and kriging methodsQuick overview of spatial analysis and kriging methods
Multilayer deposits and challenges they presentMultilayer deposits and challenges they present
Spatial Profitability Index (S.P.I.) definitionSpatial Profitability Index (S.P.I.) definition
S.P.I. for lignite multilayer minesS.P.I. for lignite multilayer mines
Case study: Amyndaio mineCase study: Amyndaio mine
Graph for estimated change of profitable reserves using Graph for estimated change of profitable reserves using
S.P.I.S.P.I.
3D spatial estimation using I.K. 3D spatial estimation using I.K.
Conclusions and suggestionsConclusions and suggestions
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OVERVIEW OF SPATIAL OVERVIEW OF SPATIAL ANALYSIS - KRIGINGANALYSIS - KRIGING
Spatial analysis is a group of methods that attempt to determine Spatial analysis is a group of methods that attempt to determine
the spatial distribution of one or more random variables based the spatial distribution of one or more random variables based
on a set of dataon a set of data
Usually spatial analysis gives a grid map where the value of each Usually spatial analysis gives a grid map where the value of each
point of the grid is estimated from nearby datapoint of the grid is estimated from nearby data
Kriging is a category of linear methods using weighted Kriging is a category of linear methods using weighted
parameters parameters λλii to estimate the value of a random variable to estimate the value of a random variable XX((ss00))
at a point at a point ss00 from the values of the variable from the values of the variable XX((ss)) at n nearby at n nearby
points points
Kriging weights Kriging weights λλii are calculated by minimizing the prediction are calculated by minimizing the prediction
error of error of ee = = XX((ss) − ) − XX’(’(ss) using the covariance function ) using the covariance function CCXX ( (ss)) or or
the semivariogram the semivariogram γγXX ( (ss))..
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MULTILAYER DEPOSITS AND MULTILAYER DEPOSITS AND INTERMEDIATE LAYERSINTERMEDIATE LAYERS
In multilayer deposits, an ore layer could be so deep compared In multilayer deposits, an ore layer could be so deep compared
to above layers, that its exploitation would not be profitable to above layers, that its exploitation would not be profitable
The profitability of intermediate layers depends on both the The profitability of intermediate layers depends on both the
ore layers above as well as the ore layers underneathore layers above as well as the ore layers underneath
In this work, the profitability of the first layer is considered to In this work, the profitability of the first layer is considered to
be covered adequately by the stripping ratiobe covered adequately by the stripping ratio
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CHANGES IN PRICES AND CHANGES IN PRICES AND DEPOSITSDEPOSITS
An increase in the market price of the mineral extracted An increase in the market price of the mineral extracted
could potentially render former unprofitable parts of the could potentially render former unprofitable parts of the
mine as profitable increasing the reservesmine as profitable increasing the reserves
Environmental regulations or challenges could increase Environmental regulations or challenges could increase
the cost of processing the mined ore making the the cost of processing the mined ore making the
exploitation of deeper layers unprofitableexploitation of deeper layers unprofitable
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EXISTING INDEXESEXISTING INDEXES
Stripping ratio: Stripping ratio: δδs = P/Ws = P/W, , P P is the sum of the ore layers is the sum of the ore layers
thickness, thickness, WW is the overburden waste layer is the overburden waste layer
Discounted Cash Flow: Discounted Cash Flow:
PV: net present value, CPV: net present value, C00: investment, T: expected life of the : investment, T: expected life of the
mine (years), i the time period (years), Qmine (years), i the time period (years), Qii: annual production : annual production
volume, Pvolume, Pii: price per unit of product, C: price per unit of product, Cii: cost per unit of product: cost per unit of product
r accounts for the discount rate and risk factors.r accounts for the discount rate and risk factors.
01
11
Ti i i
Ti
Q (P C )PV C , i , ,T
( r)
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SPATIAL PROFITABILITY INDEXSPATIAL PROFITABILITY INDEX The The spatial profitability index spatial profitability index δδ,, measured for each layer, is measured for each layer, is
calculated in order to assist in mid-term and long term mine calculated in order to assist in mid-term and long term mine
planning and estimates of reserves adjustments with planning and estimates of reserves adjustments with
changing economic situations changing economic situations
TheThe extractability indicatorextractability indicator II is calculated using the is calculated using the
profitability index profitability index δδ.. The extractability indicator The extractability indicator II equals one equals one
for layers that are considered economically profitable and for layers that are considered economically profitable and
zero for all other layerszero for all other layers
The algorithm that calculates the profitability index and the The algorithm that calculates the profitability index and the
extractability indicator can be used to quickly give an extractability indicator can be used to quickly give an
estimate of reserve changes in different economic situationsestimate of reserve changes in different economic situations
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SPATIAL PROFITABILITY INDEX SPATIAL PROFITABILITY INDEX CALCULATIONCALCULATION
The calculation starts from the The calculation starts from the bottombottom possibly profitablepossibly profitable ore ore
layer in a drill-hole and proceeds up to the second layer from layer in a drill-hole and proceeds up to the second layer from
the surface the surface
To calculate the profitability index for ore layer To calculate the profitability index for ore layer LLii in a given in a given
drill-hole, the sum of the expected profit of drill-hole, the sum of the expected profit of LLii and all of and all of
the economically profitable layers the economically profitable layers underneathunderneath LLii is estimated is estimated
The sum of the estimated expenses needed to exploit The sum of the estimated expenses needed to exploit
layer layer i i and all of the economically profitable layers and all of the economically profitable layers
underneathunderneath LLii is estimated is estimated
i
jj N
P
i
jj N
E
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SPATIAL PROFITABILITY INDEX SPATIAL PROFITABILITY INDEX CALCULATIONCALCULATION
The profitability indexThe profitability index is defined as is defined as
if if δδii ≥≥ 1, 1, then the indicator then the indicator II is set as 1 for layer is set as 1 for layer ii
if if δδii < 1, < 1, then the indicator then the indicator II is set as 0 for layer is set as 0 for layer ii and and all all
layers underneath itlayers underneath it and the last possibly profitable layer and the last possibly profitable layer
NN, changes accordingly, changes accordingly
, ,..., 2
i
jj N
i i
jj N
P
i NE
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S.P.I FOR LIGNITES.P.I FOR LIGNITE
The The profit profit PPii expected from lignite layer expected from lignite layer ii and all profitable and all profitable
layers underneath itlayers underneath it
nn: efficiency of the power station, : efficiency of the power station, TT: profit for each GCal, : profit for each GCal, ΣΣLLjj: :
sum of energy content for layer sum of energy content for layer i i and all profitable layers and all profitable layers
underneath itunderneath it
,...,i
i jJ N
P nT L j N i
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S.P.I FOR LIGNITES.P.I FOR LIGNITE
The The expenses expenses EEii expected from lignite layer expected from lignite layer ii and all and all
profitable layers underneath itprofitable layers underneath it
LwLwjj: Weight of the lignite layer : Weight of the lignite layer jj, W, Wjj: Weight of the waste : Weight of the waste
layer above lignite layer layer above lignite layer j j that should be removed,that should be removed, k kl l :cost :cost
per ton of lignite, per ton of lignite, kkww: cost per ton of waste material: cost per ton of waste material
ExExii: : extra costs for layer extra costs for layer ii. Can account for risk factor . Can account for risk factor r r for for
unpredicted costs.unpredicted costs.
, ,...,i i
i l j w j iJ N J N
E k Lw k W Ex j N i
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EXAMPLEEXAMPLE
kkww
€€/tn/tnkkll
€€/tn/tnnn%%
TT€€/GCal/GCal
ExEx%%
1.41.4 2.12.1 3535 4040 1010
In the examples that follow, the following values will be used.In the examples that follow, the following values will be used.
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EXAMPLEEXAMPLE 33rdrd layer: layer:
N=3. PN=3. P33=96 €/m=96 €/m22, ,
EE33=107 €/m=107 €/m22.. δδ33==0.9<10.9<1
So, ISo, I33=0 and N is set to 2=0 and N is set to 2
22ndnd layer: layer:
N=2. PN=2. P22=308 €/m=308 €/m22, ,
EE22=35.2 €/m=35.2 €/m22.. δδ22=8=8..8>8>11
So, ISo, I22=1=1
11stst layer: layer:
The first layer’s The first layer’s
profitability is profitability is
determined by the determined by the
stripping ratiostripping ratio
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CASE STUDY: AMYNDEO MINECASE STUDY: AMYNDEO MINE
Area 17 kmArea 17 km22 with extensive fault system. with extensive fault system.
The mine is in operation sinceThe mine is in operation since 1989 1989 and and
has producedhas produced 145145 Μ Μtt of lignite till the of lignite till the
end of 2013end of 2013..
Average lignite production:Average lignite production: 6 Mt/Y.6 Mt/Y.
Estimated mean calorific value:Estimated mean calorific value: 1 1,3,3
GCal/tn.GCal/tn.
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Satellite image (Google Earth)Satellite image (Google Earth)
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EVALUATION CRITERIAEVALUATION CRITERIAThe Criteria used to determine if a layer is considered a lignite The Criteria used to determine if a layer is considered a lignite
layer for this work are:layer for this work are:
Minimum Lower Calorific Value (LCV) = 900 MCal/tnMinimum Lower Calorific Value (LCV) = 900 MCal/tn
Maximum contents in ash and COMaximum contents in ash and CO22 up to 50% up to 50%
The criteria used are simplified in comparison with the PPC The criteria used are simplified in comparison with the PPC
criteria.criteria.
Using the profitability index and the extractability indicator, Using the profitability index and the extractability indicator,
the change of the estimated lignite reserves is investigatedthe change of the estimated lignite reserves is investigated
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DRILL-HOLE CORE DATADRILL-HOLE CORE DATA 6875 Drill-hole core data from 615 drill-holes6875 Drill-hole core data from 615 drill-holes
Data: Coordinates (X, Y, Depth), ash content, water Data: Coordinates (X, Y, Depth), ash content, water
content and in some cases COcontent and in some cases CO22 content and L.C.V. content and L.C.V.
L.C.V is estimated using linear regression for the core data L.C.V is estimated using linear regression for the core data
that miss itthat miss it
The 6875 drill-hole core data are evaluated and they are The 6875 drill-hole core data are evaluated and they are
signified as lignite or wastesignified as lignite or waste
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APPLYING THE S.P.I. APPLYING THE S.P.I.
The S.P.I. is applied to each of the 615 drill holes of the The S.P.I. is applied to each of the 615 drill holes of the
data set to remove non profitable layers from the data setdata set to remove non profitable layers from the data set
After applying the S.P.I. the total After applying the S.P.I. the total Energy Content DensityEnergy Content Density
(GCal/m(GCal/m22) is calculated for each of the 615 drill-holes) is calculated for each of the 615 drill-holes
A linear trend is removed from the modified dataA linear trend is removed from the modified data
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VARIOGRAMVARIOGRAM The omnidirectional variogram is estimatedThe omnidirectional variogram is estimated
The exponential variogram model’s parameters are The exponential variogram model’s parameters are
calculated to better fit the experimental variogramcalculated to better fit the experimental variogram
γ: γ: variogram, variogram, ss: location, : location, σσ22: : variance, variance, ξ: ξ: correlation correlation
length, Clength, C00: nugget effect: nugget effect
σ σ 22
(GCal/(GCal/mm22))22
ξξ CC00
(GCal/(GCal/mm22))22
126.6126.6 0.880.88 33.933.9
2 /0( ) (1 )r
X X e C s
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KRIGING LEC DENSITY MAPKRIGING LEC DENSITY MAP Energy content Energy content
reserves using reserves using
the S.P.I. are 293 the S.P.I. are 293
PCalPCal
Without using the Without using the
S.P.I. the reserves S.P.I. the reserves
are 299 PCalare 299 PCal
Cells are 30m x Cells are 30m x
30m30m
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DIFFERENCE IN LEC DENSITY %DIFFERENCE IN LEC DENSITY %
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CHANGE OF RESERVES USING CHANGE OF RESERVES USING S.P.IS.P.I
In order to investigate the change of profitable energy In order to investigate the change of profitable energy
reserves for different economic situations, different cut-off reserves for different economic situations, different cut-off
levels (instead of 1) were investigated for the S.P.I. levels (instead of 1) were investigated for the S.P.I.
The different cut-off levels that a layer will be considered The different cut-off levels that a layer will be considered
profitable, correspond to different economic situations profitable, correspond to different economic situations
compared to the values given in the examplecompared to the values given in the example
The range of the cut-off level investigated was 0.5 – 4.7 The range of the cut-off level investigated was 0.5 – 4.7
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Estimated difference of Estimated difference of Reserves by using the S.P.I.Reserves by using the S.P.I.
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Estimated difference of Estimated difference of Reserves by using the S.P.I.Reserves by using the S.P.I.
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THEORETICAL MODEL FOR THE THEORETICAL MODEL FOR THE CHANGE OF RESERVESCHANGE OF RESERVES
A sigmoid function model describes the estimated A sigmoid function model describes the estimated
difference of reserves difference of reserves
ERD: Estimated difference of reservesERD: Estimated difference of reserves
2 3
1( )1 cb b
bERD
e
bb11
PCal (or %)PCal (or %)bb22 bb33
94.894.8 (31.7)(31.7) 0.940.94 4.04.0
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USES OF THE S.P.I. USES OF THE S.P.I.
The S.P.I. graph can give good estimations of the reserve The S.P.I. graph can give good estimations of the reserve
changes for different economic situations very fastchanges for different economic situations very fast
In mid-term planning, the S.P.I. can be used to adjust the In mid-term planning, the S.P.I. can be used to adjust the
technical bottom of the mine rejecting unprofitable benchestechnical bottom of the mine rejecting unprofitable benches
The S.P.I. can be used to signify subsectors of the mine that The S.P.I. can be used to signify subsectors of the mine that
should be exploited using non-continuous mining methodsshould be exploited using non-continuous mining methods
In mid-term lignite planning, the S.P.I. can be used to give In mid-term lignite planning, the S.P.I. can be used to give
preference to subsectors that hold more energy when the preference to subsectors that hold more energy when the
company needs profits (to buy equipment or entice company needs profits (to buy equipment or entice
investors) or in times when energy consumption is expected investors) or in times when energy consumption is expected
to increaseto increase
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3D SPATIAL ESTIMATION OF 3D SPATIAL ESTIMATION OF LIGNITE LAYERSLIGNITE LAYERS
Mine planning becomes easier and more efficient if an Mine planning becomes easier and more efficient if an
estimation of where lignite layers are located exists, as the estimation of where lignite layers are located exists, as the
reserves held in each bench can be estimated independentlyreserves held in each bench can be estimated independently
Using the evaluated drill core data, a new data set is made for Using the evaluated drill core data, a new data set is made for
each drill hole. At each 30 cm of depth in the drill-hole the data each drill hole. At each 30 cm of depth in the drill-hole the data
take the value 0 for waste material and 1 for lignite materialtake the value 0 for waste material and 1 for lignite material
Coordinates are normalized vertically to address anisotropy, Coordinates are normalized vertically to address anisotropy,
based on the correlation lengths of the directional variogramsbased on the correlation lengths of the directional variograms
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3D SPATIAL ESTIMATION OF 3D SPATIAL ESTIMATION OF LIGNITE LAYERSLIGNITE LAYERS
3D Indicator Kriging is applied on this data set3D Indicator Kriging is applied on this data set
Indicator Kriging estimates the value of an indicator in [0,1] Indicator Kriging estimates the value of an indicator in [0,1]
for each cell in a 30m x 30m x 1.5m gridfor each cell in a 30m x 30m x 1.5m grid
Based on a threshold for this indicator, each cell takes the Based on a threshold for this indicator, each cell takes the
value 1 (Lignite) or 0 (Waste)value 1 (Lignite) or 0 (Waste)
The value of the threshold in the suggested method, is set The value of the threshold in the suggested method, is set
in each column of the grid (30x30 m) so that the total in each column of the grid (30x30 m) so that the total
lignite thickness in the column to equal the lignite lignite thickness in the column to equal the lignite
thickness given by a 2D Kriging in the same coordinates thickness given by a 2D Kriging in the same coordinates
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SLICE Y=41925SLICE Y=41925
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SLICE Y=40727SLICE Y=40727
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VALIDATIONVALIDATION
Using leave one out cross-validation the misclassified Using leave one out cross-validation the misclassified
points are 33.1% of the totalpoints are 33.1% of the total
This is an improvement over using IK without a 2D This is an improvement over using IK without a 2D
estimation (38.5% misclassified points)estimation (38.5% misclassified points)
When used in the total mire area, both IK using the 2D When used in the total mire area, both IK using the 2D
estimation and IK using a uniform threshold, estimate the estimation and IK using a uniform threshold, estimate the
reserves at 244 MT of lignitereserves at 244 MT of lignite
When used in an exploited mine area, that had about When used in an exploited mine area, that had about
145MT of lignite, the IK using a uniform threshold 145MT of lignite, the IK using a uniform threshold
estimation of the reserves deviates by -7.5MT while IK estimation of the reserves deviates by -7.5MT while IK
using the 2D estimation deviates by +7.5 MTusing the 2D estimation deviates by +7.5 MT
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CONCLUSIONS - SUGGESTIONSCONCLUSIONS - SUGGESTIONS
The S.P.I. takes into account each layer’s economic profile The S.P.I. takes into account each layer’s economic profile
instead of using means to find a ratio of waste to ligniteinstead of using means to find a ratio of waste to lignite
The S.P.I. assists in long term and in mid-term mine The S.P.I. assists in long term and in mid-term mine
planningplanning
The S.P.I. can easily be incorporated in algorithms of The S.P.I. can easily be incorporated in algorithms of
reserves estimationreserves estimation and mine design algorithms or and mine design algorithms or
algorithms of pit optimizationalgorithms of pit optimization
Reduction of estimated reserves for different economic Reduction of estimated reserves for different economic
situations can be modeled using the S.P.I. This model could situations can be modeled using the S.P.I. This model could
be used to quickly give estimations of reserve changesbe used to quickly give estimations of reserve changes
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CONCLUSIONS - SUGGESTIONSCONCLUSIONS - SUGGESTIONS
Using 3D analysis to identify the location of individual Using 3D analysis to identify the location of individual
lignite layers can be used to estimate the energy content lignite layers can be used to estimate the energy content
or the lignite mass in subsector or benchesor the lignite mass in subsector or benches
3D spatial estimation of the lignite content of individual 3D spatial estimation of the lignite content of individual
mine benches in combination with S.P.I. can locate mine benches in combination with S.P.I. can locate
benches that become unprofitable as prices change benches that become unprofitable as prices change
June 2014June 2014 ΕΡΕΥΝΕΡΕΥΝHHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ
THANK YOU ! ! !THANK YOU ! ! !