supervisor: professor hristopulos d.t. spatial 3d estimation of lignite reserves and development of...

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


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))..


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


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


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)


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


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


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


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


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


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.


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


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.


Satellite image (Google Earth)Satellite image (Google Earth)


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


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


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


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


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


DIFFERENCE IN LEC DENSITY %DIFFERENCE IN LEC DENSITY %


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


Estimated difference of Estimated difference of Reserves by using the S.P.I.Reserves by using the S.P.I.


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


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


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


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


SLICE Y=41925SLICE Y=41925


SLICE Y=40727SLICE Y=40727


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


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


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


THANK YOU ! ! !THANK YOU ! ! !

supervisor: professor hristopulos d.t. spatial 3d estimation of lignite reserves and development of...

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