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Supervisor: Professor Hristopulos D.T. SPATIAL 3D ESTIMATION OF LIGNITE RESERVES AND DEVELOPMENT OF A SPATIAL PROFITABILITY INDEX ANDREW PAVLIDES SCHOOL.

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Presentation on theme: "Supervisor: Professor Hristopulos D.T. SPATIAL 3D ESTIMATION OF LIGNITE RESERVES AND DEVELOPMENT OF A SPATIAL PROFITABILITY INDEX ANDREW PAVLIDES SCHOOL."— Presentation transcript:

1 Supervisor: Professor Hristopulos D.T. SPATIAL 3D ESTIMATION OF LIGNITE RESERVES AND DEVELOPMENT OF A SPATIAL PROFITABILITY INDEX ANDREW PAVLIDES SCHOOL OF MINERAL RESOURCES ENGINEERING Technical University of Crete

2 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ PRESENTATION Quick overview of spatial analysis and kriging methods Quick overview of spatial analysis and kriging methods Multilayer deposits and challenges they present Multilayer deposits and challenges they present Spatial Profitability Index (S.P.I.) definition Spatial Profitability Index (S.P.I.) definition S.P.I. for lignite multilayer mines S.P.I. for lignite multilayer mines Case study: Amyndaio mine Case study: Amyndaio mine Graph for estimated change of profitable reserves using S.P.I. Graph for estimated change of profitable reserves using S.P.I. 3D spatial estimation using I.K. 3D spatial estimation using I.K. Conclusions and suggestions Conclusions and suggestions

3 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ OVERVIEW OF SPATIAL ANALYSIS - KRIGING Spatial analysis is a group of methods that attempt to determine the spatial distribution of one or more random variables based on a set of data Spatial analysis is a group of methods that attempt to determine the spatial distribution of one or more random variables based on a set of data Usually spatial analysis gives a grid map where the value of each point of the grid is estimated from nearby data Usually spatial analysis gives a grid map where the value of each point of the grid is estimated from nearby data Kriging is a category of linear methods using weighted parameters λ i to estimate the value of a random variable X(s 0 ) at a point s 0 from the values of the variable X(s) at n nearby points Kriging is a category of linear methods using weighted parameters λ i to estimate the value of a random variable X(s 0 ) at a point s 0 from the values of the variable X(s) at n nearby points Kriging weights λ i are calculated by minimizing the prediction error of e = X(s) − X’(s) using the covariance function C X (s) or the semivariogram γ X (s). Kriging weights λ i are calculated by minimizing the prediction error of e = X(s) − X’(s) using the covariance function C X (s) or the semivariogram γ X (s).

4 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ MULTILAYER DEPOSITS AND INTERMEDIATE LAYERS In multilayer deposits, an ore layer could be so deep compared to above layers, that its exploitation would not be profitable In multilayer deposits, an ore layer could be so deep compared to above layers, that its exploitation would not be profitable The profitability of intermediate layers depends on both the ore layers above as well as the ore layers underneath The profitability of intermediate layers depends on both the ore layers above as well as the ore layers underneath In this work, the profitability of the first layer is considered to be covered adequately by the stripping ratio In this work, the profitability of the first layer is considered to be covered adequately by the stripping ratio

5 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ CHANGES IN PRICES AND DEPOSITS An increase in the market price of the mineral extracted could potentially render former unprofitable parts of the mine as profitable increasing the reserves An increase in the market price of the mineral extracted could potentially render former unprofitable parts of the mine as profitable increasing the reserves Environmental regulations or challenges could increase the cost of processing the mined ore making the exploitation of deeper layers unprofitable Environmental regulations or challenges could increase the cost of processing the mined ore making the exploitation of deeper layers unprofitable

6 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ EXISTING INDEXES Stripping ratio: δs = P/W, P is the sum of the ore layers thickness, W is the overburden waste layer Stripping ratio: δs = P/W, P is the sum of the ore layers thickness, W is the overburden waste layer Discounted Cash Flow: Discounted Cash Flow: PV: net present value, C 0 : investment, T: expected life of the mine (years), i the time period (years), Q i : annual production volume, P i : price per unit of product, C i : cost per unit of product PV: net present value, C 0 : investment, T: expected life of the mine (years), i the time period (years), Q i : annual production volume, P i : price per unit of product, C i : cost per unit of product r accounts for the discount rate and risk factors. r accounts for the discount rate and risk factors.

7 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ SPATIAL PROFITABILITY INDEX The spatial profitability index δ, measured for each layer, is calculated in order to assist in mid-term and long term mine planning and estimates of reserves adjustments with changing economic situations The spatial profitability index δ, measured for each layer, is calculated in order to assist in mid-term and long term mine planning and estimates of reserves adjustments with changing economic situations The extractability indicator I is calculated using the profitability index δ. The extractability indicator I equals one for layers that are considered economically profitable and zero for all other layers The extractability indicator I is calculated using the profitability index δ. The extractability indicator I equals one for layers that are considered economically profitable and zero for all other layers The algorithm that calculates the profitability index and the extractability indicator can be used to quickly give an estimate of reserve changes in different economic situations The algorithm that calculates the profitability index and the extractability indicator can be used to quickly give an estimate of reserve changes in different economic situations

8 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ SPATIAL PROFITABILITY INDEX CALCULATION The calculation starts from the bottom possibly profitable ore layer in a drill-hole and proceeds up to the second layer from the surface The calculation starts from the bottom possibly profitable ore layer in a drill-hole and proceeds up to the second layer from the surface To calculate the profitability index for ore layer L i in a given drill- hole, the sum of the expected profit of L i and all of the economically profitable layers underneath L i is estimated To calculate the profitability index for ore layer L i in a given drill- hole, the sum of the expected profit of L i and all of the economically profitable layers underneath L i is estimated The sum of the estimated expenses needed to exploit layer i and all of the economically profitable layers underneath L i is estimated The sum of the estimated expenses needed to exploit layer i and all of the economically profitable layers underneath L i is estimated

9 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ SPATIAL PROFITABILITY INDEX CALCULATION The profitability index is defined as The profitability index is defined as if δ i ≥ 1, then the indicator I is set as 1 for layer i if δ i ≥ 1, then the indicator I is set as 1 for layer i if δ i < 1, then the indicator I is set as 0 for layer i and all layers underneath it and the last possibly profitable layer N, changes accordingly if δ i < 1, then the indicator I is set as 0 for layer i and all layers underneath it and the last possibly profitable layer N, changes accordingly

10 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ S.P.I FOR LIGNITE The profit P i expected from lignite layer i and all profitable layers underneath it The profit P i expected from lignite layer i and all profitable layers underneath it n: efficiency of the power station, T: profit for each GCal, ΣL j : sum of energy content for layer i and all profitable layers underneath it

11 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ S.P.I FOR LIGNITE The expenses E i expected from lignite layer i and all profitable layers underneath it The expenses E i expected from lignite layer i and all profitable layers underneath it Lw j : Weight of the lignite layer j, W j : Weight of the waste layer above lignite layer j that should be removed, k l :cost per ton of lignite, k w : cost per ton of waste material Lw j : Weight of the lignite layer j, W j : Weight of the waste layer above lignite layer j that should be removed, k l :cost per ton of lignite, k w : cost per ton of waste material Ex i : extra costs for layer i. Can account for risk factor r for unpredicted costs. Ex i : extra costs for layer i. Can account for risk factor r for unpredicted costs.

12 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ EXAMPLE k w €/tn k l €/tnn%T€/GCalEx% In the examples that follow, the following values will be used. In the examples that follow, the following values will be used.

13 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑEXAMPLE 3 rd layer: 3 rd layer: N=3. P 3 =96 €/m 2, E 3 =107 €/m 2. δ 3 =0.9<1 N=3. P 3 =96 €/m 2, E 3 =107 €/m 2. δ 3 =0.9<1 So, I 3 =0 and N is set to 2 So, I 3 =0 and N is set to 2 2 nd layer: 2 nd layer: N=2. P 2 =308 €/m 2, E 2 =35.2 €/m 2. δ 2 =8.8>1 N=2. P 2 =308 €/m 2, E 2 =35.2 €/m 2. δ 2 =8.8>1 So, I 2 =1 So, I 2 =1 1 st layer: 1 st layer: The first layer’s profitability is determined by the stripping ratio The first layer’s profitability is determined by the stripping ratio

14 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ CASE STUDY: AMYNDEO MINE Area 17 km 2 with extensive fault system. Area 17 km 2 with extensive fault system. The mine is in operation since 1989 and has produced 145 Μt of lignite till the end of The mine is in operation since 1989 and has produced 145 Μt of lignite till the end of Average lignite production: 6 Mt/Y. Average lignite production: 6 Mt/Y. Estimated mean calorific value: 1,3 GCal/tn. Estimated mean calorific value: 1,3 GCal/tn.

15 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ Satellite image (Google Earth)

16 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ EVALUATION CRITERIA The Criteria used to determine if a layer is considered a lignite layer for this work are: Minimum Lower Calorific Value (LCV) = 900 MCal/tn Minimum Lower Calorific Value (LCV) = 900 MCal/tn Maximum contents in ash and CO 2 up to 50% Maximum contents in ash and CO 2 up to 50% The criteria used are simplified in comparison with the PPC criteria. The criteria used are simplified in comparison with the PPC criteria. Using the profitability index and the extractability indicator, the change of the estimated lignite reserves is investigated Using the profitability index and the extractability indicator, the change of the estimated lignite reserves is investigated

17 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ DRILL-HOLE CORE DATA 6875 Drill-hole core data from 615 drill-holes 6875 Drill-hole core data from 615 drill-holes Data: Coordinates (X, Y, Depth), ash content, water content and in some cases CO 2 content and L.C.V. Data: Coordinates (X, Y, Depth), ash content, water content and in some cases CO 2 content and L.C.V. L.C.V is estimated using linear regression for the core data that miss it L.C.V is estimated using linear regression for the core data that miss it The 6875 drill-hole core data are evaluated and they are signified as lignite or waste The 6875 drill-hole core data are evaluated and they are signified as lignite or waste

18 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ APPLYING THE S.P.I. 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 set 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 set After applying the S.P.I. the total Energy Content Density (GCal/m 2 ) is calculated for each of the 615 drill-holes After applying the S.P.I. the total Energy Content Density (GCal/m 2 ) is calculated for each of the 615 drill-holes A linear trend is removed from the modified data A linear trend is removed from the modified data

19 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ VARIOGRAM The omnidirectional variogram is estimated The omnidirectional variogram is estimated The exponential variogram model’s parameters are calculated to better fit the experimental variogram The exponential variogram model’s parameters are calculated to better fit the experimental variogram γ: variogram, s: location, σ 2 : variance, ξ: correlation length, C 0 : nugget effect γ: variogram, s: location, σ 2 : variance, ξ: correlation length, C 0 : nugget effect σ 2 (GCal/m 2 ) 2 ξ C 0 (GCal/m 2 )

20 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ KRIGING LEC DENSITY MAP Energy content reserves using the S.P.I. are 293 PCal Energy content reserves using the S.P.I. are 293 PCal Without using the S.P.I. the reserves are 299 PCal Without using the S.P.I. the reserves are 299 PCal Cells are 30m x 30m Cells are 30m x 30m

21 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ DIFFERENCE IN LEC DENSITY %

22 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ CHANGE OF RESERVES USING S.P.I In order to investigate the change of profitable energy reserves for different economic situations, different cut-off levels (instead of 1) were investigated for the S.P.I. In order to investigate the change of profitable energy reserves for different economic situations, different cut-off levels (instead of 1) were investigated for the S.P.I. The different cut-off levels that a layer will be considered profitable, correspond to different economic situations compared to the values given in the example The different cut-off levels that a layer will be considered profitable, correspond to different economic situations compared 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

23 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ Estimated difference of Reserves by using the S.P.I.

24 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ Estimated difference of Reserves by using the S.P.I.

25 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ THEORETICAL MODEL FOR THE CHANGE OF RESERVES A sigmoid function model describes the estimated difference of reserves A sigmoid function model describes the estimated difference of reserves ERD: Estimated difference of reserves ERD: Estimated difference of reserves b 1 PCal (or %) b2b2b2b2 b3b3b3b (31.7)

26 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ USES OF THE S.P.I. The S.P.I. graph can give good estimations of the reserve changes for different economic situations very fast The S.P.I. graph can give good estimations of the reserve changes for different economic situations very fast In mid-term planning, the S.P.I. can be used to adjust the technical bottom of the mine rejecting unprofitable benches In mid-term planning, the S.P.I. can be used to adjust the technical bottom of the mine rejecting unprofitable benches The S.P.I. can be used to signify subsectors of the mine that should be exploited using non-continuous mining methods The S.P.I. can be used to signify subsectors of the mine that should be exploited using non-continuous mining methods In mid-term lignite planning, the S.P.I. can be used to give preference to subsectors that hold more energy when the company needs profits (to buy equipment or entice investors) or in times when energy consumption is expected to increase In mid-term lignite planning, the S.P.I. can be used to give preference to subsectors that hold more energy when the company needs profits (to buy equipment or entice investors) or in times when energy consumption is expected to increase

27 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ 3D SPATIAL ESTIMATION OF LIGNITE LAYERS Mine planning becomes easier and more efficient if an estimation of where lignite layers are located exists, as the reserves held in each bench can be estimated independently Mine planning becomes easier and more efficient if an estimation of where lignite layers are located exists, as the reserves held in each bench can be estimated independently 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 take the value 0 for waste material and 1 for lignite material 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 take the value 0 for waste material and 1 for lignite material Coordinates are normalized vertically to address anisotropy, based on the correlation lengths of the directional variograms Coordinates are normalized vertically to address anisotropy, based on the correlation lengths of the directional variograms

28 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ 3D SPATIAL ESTIMATION OF LIGNITE LAYERS 3D Indicator Kriging is applied on this data set 3D Indicator Kriging is applied on this data set Indicator Kriging estimates the value of an indicator in [0,1] for each cell in a 30m x 30m x 1.5m grid Indicator Kriging estimates the value of an indicator in [0,1] for each cell in a 30m x 30m x 1.5m grid Based on a threshold for this indicator, each cell takes the value 1 (Lignite) or 0 (Waste) Based on a threshold for this indicator, each cell takes the value 1 (Lignite) or 0 (Waste) The value of the threshold in the suggested method, is set in each column of the grid (30x30 m) so that the total lignite thickness in the column to equal the lignite thickness given by a 2D Kriging in the same coordinates The value of the threshold in the suggested method, is set in each column of the grid (30x30 m) so that the total lignite thickness in the column to equal the lignite thickness given by a 2D Kriging in the same coordinates

29 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ SLICE Y=41925

30 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ SLICE Y=40727

31 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑVALIDATION Using leave one out cross-validation the misclassified points are 33.1% of the total Using leave one out cross-validation the misclassified points are 33.1% of the total This is an improvement over using IK without a 2D estimation (38.5% misclassified points) This is an improvement over using IK without a 2D estimation (38.5% misclassified points) When used in the total mire area, both IK using the 2D estimation and IK using a uniform threshold, estimate the reserves at 244 MT of lignite When used in the total mire area, both IK using the 2D estimation and IK using a uniform threshold, estimate the reserves at 244 MT of lignite When used in an exploited mine area, that had about 145MT of lignite, the IK using a uniform threshold estimation of the reserves deviates by -7.5MT while IK using the 2D estimation deviates by +7.5 MT When used in an exploited mine area, that had about 145MT of lignite, the IK using a uniform threshold estimation of the reserves deviates by -7.5MT while IK using the 2D estimation deviates by +7.5 MT

32 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ CONCLUSIONS - SUGGESTIONS The S.P.I. takes into account each layer’s economic profile instead of using means to find a ratio of waste to lignite The S.P.I. takes into account each layer’s economic profile instead of using means to find a ratio of waste to lignite The S.P.I. assists in long term and in mid-term mine planning The S.P.I. assists in long term and in mid-term mine planning The S.P.I. can easily be incorporated in algorithms of reserves estimation and mine design algorithms or algorithms of pit optimization The S.P.I. can easily be incorporated in algorithms of reserves estimation and mine design algorithms or algorithms of pit optimization Reduction of estimated reserves for different economic situations can be modeled using the S.P.I. This model could be used to quickly give estimations of reserve changes Reduction of estimated reserves for different economic situations can be modeled using the S.P.I. This model could be used to quickly give estimations of reserve changes

33 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ CONCLUSIONS - SUGGESTIONS Using 3D analysis to identify the location of individual lignite layers can be used to estimate the energy content or the lignite mass in subsector or benches Using 3D analysis to identify the location of individual lignite layers can be used to estimate the energy content or the lignite mass in subsector or benches 3D spatial estimation of the lignite content of individual mine benches in combination with S.P.I. can locate benches that become unprofitable as prices change 3D spatial estimation of the lignite content of individual mine benches in combination with S.P.I. can locate benches that become unprofitable as prices change

34 June 2014 ΕΡΕΥΝHΤΙΚΗ ΜΕΘΟΔΟΛΟΓΙΑ THANK YOU ! ! !


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