Tom 24 2008 Zeszyt 4/3
WITOLD KAWALEC*
Modelling of transportation costs for alternative Life-Of-Mine plans of continuous surface lignite mines
Introduction
Geological modelling and mine design and scheduling have successfully adopted sophi- sticated computer methods not only for a comfortable digital replacement of a traditional
“paper” documentation but also for their powerful data processing capabilities with the extensive use of methods that were simply not available before. While any 3-D visualisation of geological data and mine developments (including enhanced surface rendering and the virtual reality tools) are of great value for both mining engineers and the public, the most important and highly specialised software tools have been developed for the purpose of mine optimisation. The opencast mining projects are now often based on the economic optimisation algorithms, dealing with the milestones of a project: ultimate pit design, pushbacks generation and life-of-mine plan. In general, the mine optimisation algorithms depend on the economic block model of a deposit – a set of cells each assigned with its mining cost and – in case of an “ore” block – calculated revenue from selling the contained ore.
The accuracy of the input data – an economic model – is crucial for any further processing and no result can be more reliable than the input data. Therefore the construction of the economic block model deserves a thorough data preparation, analysis and validation otherwise applying the advanced pit optimisation algorithms like ultimate pit design (Lerchs, Grossmann 1965; Underwood, Tolwiñski 1998) is pointless. The possible errors of a model depend on the geological modelling that has generated the quality block model, the proper assessment of the revenue from selling the contained ore (based on stock exchange data or
* Institute of Mining Engineering, Wroclaw University of Technology, Wroc³aw, Poland.
other price formula) and – often the most difficult – the accuracy of spatial distribution of mining costs.
The pit optimisation algorithms have been developed mostly for cyclical open cast operations, therefore the analysis of a truck haulage system has been implemented for accurate mining costs modelling. However, this is not suitable for continuous surface mining operations with a belt transportation system which reflects the localisation of waste dumping (external or in-pit) and the method of pit advancing (parallel or circular). For a given continuous surface mine, once the ultimate pit shell and the annual output have been fixed, the choice of an initial cut position together with the dump location and the resulting belt conveying arrangement have the biggest impact on mining costs. These have not been modelled yet for the purpose of pit optimisation algorithms therefore this paper deals with modelling the spatial distribution of mining costs with regard to alternative belt conveying costs.
1. Methods of local adjustment of mining costs
Pit optimisation algorithms have been developed mostly for ore mines with steep slope angle and relatively large depth. In such mines the increasing of pit depth is limited by rising costs of overburden removal and haulage. The size of surface mines with continuous mining operations (characterised usually by shallow slope angle and smaller depth) is more often constrained by costs of acquiring the land and costs of overburden removal and dumping. So, their mining cost distribution is subjected to different rules.
TABLE 1 Methods of mining costs adjustment (available in NPV Scheduler)
TABELA 1 Metody regulowania kosztów wydobycia (dostêpne w NPV Scheduler)
Mining cost factor Unit Description
averaged mining cost per mass
or volume unit (AMC) [PLN/t] or [PLN/m3] default value assigned to a cell if no CAF has been set
Cost Adjustment Factor (CAF)
as a function of depth [dimensionless] CAF proportional to depth; suitable for truck haulage and dewatering rising costs
CAF assigned to rock type [dimensionless] Independent from the above; represents different costs of exploitation (e.g. blasting versus cutting)
Optional cost of acquiring
the terrain [PLN]
Cost assigned to a given perimeter on the terrain surface rather than to cells; represents costs of purchasing land for mining activities Individual CAF computed
for each cell [dimensionless] Allows to distinguish changes of mining costs precisely with regard to any given criteria
Pit optimisation software (e.g. NPV Scheduler) allows a mining engineer to adjust mining costs (see table 1) with the use of so called Cost Adjustment Factor (CAF) which multiplies the average mining cost (AMC) to obtain the final mining cost (MC) that can be even individual for each cell in the economic block model.
There are several reasons for adjusting the MC (as described in Table 1) but the only specific one for continuous surface mining operations – the distribution of belt conveyor transportation costs – can be done with the use individual CAF. The proposed solution is described below.
2. The idea of modelling the distribution of belt conveying costs
2.1. G e n e r a l a s s u m p t i o n s
Following domestic (Bednarczyk 2007) and foreign (Petrich 2003) publications the belt conveyors share some 20% of the total investments and 40% of the total energy consumption of a lignite mine with continuous surface mining operations. The forecasted structure of mining costs for the planned “Legnica” continuous surface lignite mine repeats the 18%
share of all mining costs for belt conveying (including some 5.5% of energy consumption).
As almost 20% of total mining costs is distributed unequally over the pit which should have an impact on the overall spatial distribution of mining costs, which changes the cash flow over the mine life.
In order to identify the actual cost of transportation of a given cell in an economic block model it should be assigned with its own energy consumed by conveyors for delivering coal or overburden either to the final transfer point or to the dumping site (external or in-pit), respectively. Both only horizontal (in-pit dumping) and inclined transportation routes should be considered, therefore the energy required for horizontal transportation and for vertical transportation should be identified separately. The formula (1) contains all necessary factors for calculating the specific energy consumption factor (JKOP).
JKOP x y z( , , , )=(JEH×L x y z( , , , )+JE x y zv( , , , ))×CE×uE [PLN/m3] (1) where:
JEH – specific energy consumption factor horizontal transportation [KWh/(m3·m)],
JEV – specific energy consumption factor vertical transportation [KWh/(m3·m)], L(x,y,z) – horizontal length of a conveyor route from a point (x,y,z) [m], H(x,y,z) – height of rising of a conveyor route from a point (x,y,z)
to the surface [m],
CE – average electric energy price [PLN/KWh]; let CE= 0.16 z³/KWh, uE – multiplier of energy costs [dimensionless]; let uE = 3,2.
The specific energy consumption factor is identified per volume unit rather than mass unit in order to maintain the compatibility with volume units used by mines for overburden removal data. The factors should be individual for coal and overburden (in fact they can be individually calculated with regard to different rock type density).
Assuming that transportation costs are the only costs that distinguish blocks with one another, the CAFtransp can be calculated as a ratio (2) (Table 1):
CAF AMC JKOP
transp =( ×AMC0 82. + )
[PLN/m3] (2)
2.2. I d e n t i f i c a t i o n o f s p e c i f i c e n e r g y c o n s u m p t i o n o f b e l t c o n v e y o r s
The specific energy consumption of belt conveyors should be calculated for given types of conveyors that are planned for the pit. The specialised software for computations belt conveyors resistance to motion and their required drive power is necessary to give the exact data.
Assuming typical parameters of belt conveyors used in medium size lignite surface mines (belt width 1.8 m, belt speed 5.24 m/s, belt type St3150, idlers spacing: 1.2 and 6.0 m for top and bottom strand respectively, double pulley head drive, averaged ambient temperature 5°C and typical operating conditions, the specific energy consumption factors have been calculated1as shown in Table 2.
TABLE 2 Specific energy consumption by belt conveyors
TABELA 2 Zu¿ycie energii rozporz¹dzalnej wed³ug przenoœników
Specific energy consumption factor Unit Overburden Coal
JEH– horizontal transportation [kWh/(m3·m)] 0,315·10–3 0,2355·10–3 JEV– vertical transportation [kWh/(m3·m)] 6,93·10–3 4,08·10–3
2.3. M o d e l l i n g t h e l e n g t h o f b e l t c o n v e y o r r o u t e s
The exact identification of a transportation route is possible after the detailed mine design for each stage of a mine life. However, even at the stage of a pre-feasibility study it can be assessed on the basis of an ultimate pit outline and assumed variant of pit advance and waste dumping site (Fig. 1).
1 Calculations have been done with the use of the QNK-TT software (Kawalec, Kulinowski 2007).
For the preliminary assessment of transportation costs the following items should be set:
— type of advancing,
— positioning of an initial cut,
— transportation ramp location,
— range of external dumping for waste blocks (from the initial cut, beyond this range an in-pit dumping supersedes the external dumping).
In the case of circular pit advance the horizontal distance of the transportation route can be calculated with the use of Euclides distance (3) while for the parallel pit advance the “taxi”
distance (4) is appropriate.
distE( , )A B = (Ax-Bx)2+(Ay-By)2 (3)
distT( , )A B = Ax-Bx + Ay-By (4)
where: Ax, Ay, Bx, By are the plane coordinates of points A, B.
Some supplementary assumptions for identification of the transportation route from the ramp to the external dumping site should be set in accordance to the general mine design guidelines.
2.4. D e s c r i p t i o n o f t h e p r o c e d u r e
The multi-step procedure of creating the ultimate pit together with its Optimal Extraction Sequence (OES) – the sequence of mining blocks in an ultimate pit that delivers the highest NPV for a given economic model and general slope angles – necessary for further
Fig. 1. Generalised schemes of overburden (white arrows) and coal (grey arrows) transportation routes on an ultimate pit outline background; circles denote transportation ramps; from left to right: parallel pit advancing
(external and in-pit waste dumping), circular pit advancing (external and in-pit waste dumping) Rys. 1. Ogólne schematy nadk³adu (strza³ki bia³e) i wêgla (strza³ki szare) tras transportu na planie koñcowego obrysu odkrywki; ko³a symbolizuj¹ rampy transportowe; od lewej do prawej: równoleg³e poszerzanie odkrywki (sk³adowanie odpadów zewnêtrzne i w odkrywce), poszerzanie odkrywki po kole
(sk³adowanie odpadów zewnêtrzne i w odkrywce)
optimisation mine planning has been described below (Fig. 3) with the use of IDEF0 scheme (Fig. 2).
Next steps of generating the Life-of-Mine plan are standard for the Tolwinski’s long-term optimisation algorithm available in the NPV Scheduler software (Jurdziak, Kawalec 2000):
— pushbacks generation (with regard to assumed pit advancing method),
— scheduling upon the given pushbacks scenario.
These steps are presented in the following case study.
3. Case study
The case study of a Life-Of-Mine plan with regard to alternative transportation costs has been done for a small lignite deposit “Morzyczyn” of the opencast lignite mine “Konin” in
Fig. 2. Box and arrows positions and roles in a typical IDEF0 scheme Rys. 2. Po³o¿enia i role prostok¹tów i strza³ek w typowym schemacie IDEF0
Fig. 3. The scheme of ultimate pit generation with regard to alrenative transportation costs Rys. 3. Schemat tworzenia odkrywki ostatecznej w odniesieniu do alternatywnych kosztów transportu
central Poland. Due to geological documentation the deposit contains some 9.2 million tonnes of mineable reserves, average thickness of lignite seam is 5.7 m and of overburden is 48 m. The lignite seam is split with interlayers. The coal quality parameters are below the power plant requirements:
a) Calorific value: avg. QRi= 7000 kJ/kg (required minimum: 7800 or 8300 kJ/kg).
b) Sulphur content: avg. SR= 0,94% ((allowed maximum: 0,96%).
c) Ash content: avg. AR= 18% ((allowed maximum: 12%).
High stripping ratio as well as the close neighbourhood of the protected landscape are the strong arguments against the exploitation of this deposit. However it can be used for the study.
The orebody modeling has been done in the Datamine Studio geological, mining software. The structural wireframe models of the terrain, top and bottom lignite seam surfaces and waste interlayer zones have been interpreted from the raw drillhole data. Then the structural block model has been built with the cells sizes of 120´120´4 m. The model contains three main zones: coal, overburden and interlayers.
Due to relatively low density of drillhole grid (350´ 350 m over the area of some 30 km2) interpolation of quality parameters has been done with the use the simplest “nearest neighbour”
method. The total tonnage of the rocks within the “coal” zone has reached 85 million tonnes (regardless of actual coal seam thickness, stripping ratio and quality parameters). The average values of the calorific value, ash and sulphur content were very similar to those from geological documentation.
For the economic model the base price2of coal has been set to 57.65 PLN/Mg, the base mining cost (AMC) to 5,25 PLN/cum (upon the analysis of mining costs in the “Konin” mine).
Fig. 4. The visualisation of the entry ultimate pit shell (Lerch’s-Grossmann’ algorithm, NVP Scheduler) Rys. 4. Wizualizacja wejœcia ostatecznego otoczenia odkrywki (algorytm Lercha-Grossmanna, NVP
Scheduler)
2 Based on coal quality parameters (calorific value, ash and sulphur content) price formula has been used.
This economic model has been used for generation of the ultimate pit with the use of Lerch’s-Grossmann’ algorithm. The average slope angle has been set to 15°, the annual lignite output to 2 million tonnes and the discount rate to 10%.
The generated entry ultimate pit contains 19.6 million tonnes of coal (avg. calorific value 7720 kcal/kg, avg. ash content 16.5% and avg. sulphur content 0.85%) and 113 million m3of overburden. The shape of the pit shell is presented below.
On the basis of the optimised ultimate pit analysis, including the location of its phases – nested ultimate pits generated for a series of discounted base lignite price (Jurdziak, Kawalec 2000), the alternative circular and parallel pit advancing have been proposed for evaluation (Fig. 5). The transportation costs have been then calculated and embedded into the modified economic block model as an additional CAF field to be utilised by the NPV Scheduler software.
For these costs calculations the range of external dumping and the common length of the conveyor route from the transportation ramp to the dumping site have been assumed.
The two ultimate pits based on two, alternative CAFs have been then generated exactly within the entry ultimate pit shell (no new pit optimisation). Though the ultimate pit (and the lignite reserves) is then common, the consecutive phases are different both in terms of size (phases 7–9 on Fig. 6) and expected profit (Fig. 7).
Two sets of alternative pushbacks series have been generated within digitised boundaries of their global limits:
— trapezes rotated clockwise around the point of transportation ramp from the initial cut boundary for the circular pit advancing,
— rectangles parallel with each other moved to the north from the initial cut boundary for the parallel pit advancing – compare Figure 5).
These pushbacks control the sequencing of mined blocks that follows the geometrical constraints of continuous surface mining operations. The differences between size (Fig. 8), shape and value of pushbacks (Fig. 9) alternative scenarios are much bigger then of phases,
Fig. 5. The schemes of positioning the initial cut (grey rectangular), transportation ramp (white ring) and the direction of pit advancing: circular clockwise (left) and parallel (right)
Rys. 5. Schematy pozycjonowania wrêbu pocz¹tkowego (szary prostok¹t), rampy transportowej (bia³y pierœcieñ) i kierunek poszerzania odkrywki: ko³owym zgodnie z kierunkiem ruchu wskazówek zegara
(z lewej) i równoleg³y (z prawej)
Fig. 6. Coal reserves (Mg) and overburden volume (m3) of cumulated ultimate pit phases generated for two mining Cost Adjustment Factors (1 – denotes circular advancing, 2 – denotes parallel advancing) Rys. 6. Rezerwy wêgla (Mg) i objêtoœæ nadk³adu (m3) skumulowanych ostatecznych faz odkrywki
generowane dla dwóch Czynników Regulacji Kosztów Wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
Fig. 7. Cash flow and top assessment of the NPV of cumulated phases of the ultimate pit generated for two mining Cost Adjustment Factors (1 – denotes circular advancing, 2 – denotes parallel advancing) Rys. 7. Przep³yw pieniê¿ny i najlepsza ocena NPV skumulowanych ostatecznych faz odkrywki generowanych
dla dwóch Czynników Regulacji Kosztów Wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
Fig. 9. Cash flow and NPV of cumulated pushbacks generated for two alternative mining scenario (1 – denotes circular advancing, 2 – denotes parallel advancing)
Rys. 9. Przep³yw pieniê¿ny i najlepsza ocena NPV materia³ów skumulowanych generowanych dla dwóch alternatywnych scenariuszy wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
Fig. 8. Coal reserves (Mg) and overburden volume (m3) of cumulated pushbacks generated for two alternative mining scenario (1 – denotes circular advancing, 2 – denotes parallel advancing) Rys. 8. Rezerwy wêgla (Mg) i objêtoœæ nadk³adu (m3) materia³ów skumulowanych generowane dla dwóch alternatywnych scenariuszy wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
generated regardless on any mining constraints but the pit slope angle. The NPV of the last cumulated pushback is some 25% lower than the top assessment made for ultimate pit (Figures 7 and 9).
Fig. 10. Mining cost (MCOST) and annual profit throughout the mine life for two alternative mining scenarios (1 – circular advancing, 2 – parallel advancing)
Rys. 10. Koszty wydobycia (MCOST) i zysk roczny przez ca³y czas u¿ytkowania kopalni dla dwóch alternatywnych scenariuszy wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
Fig. 11. Cash flow (cumulated) and NPV of the mine throughout its life for two alternative mining scenarios (1 – circular advancing, 2 – parallel advancing)
Rys. 11. Przep³yw pieniê¿ny (skumulowany) i NPV kopalni przez ca³y czas jej u¿ytkowania dla dwóch alternatywnych scenariuszy wydobycia (1 – dla poszerzania ko³owego, 2 – dla poszerzania równoleg³ego)
The Life-Of-Mine plans have been generated for both scenarios with the same settings:
— target: stripping ratio (target: 5.8, bounds: from 4.5 to 6.5, relaxed for first 3 years),
— lignite output: 2 million tonnes, maintained for years 4–11, with 3 beginning years for opening the pit (temporary output limited to 10, 50 and 70% of the target value, respectively) and one year for closing mining operations,
— the prestripping period allowed (year labelled “0” on charts) – the development of the initial cut before any coal is reached.
Each plan has been based on its own mining costs distribution (CAF) and sequence of pushbacks. As expected, the 1stscenario provides higher cumulated cash flow and NPV than the 2nd one due to lower transportation costs.
The comparison of the results of two alternative long-term mine plans provides valuable data for a mine planner for further studies before the optimal mining solution can be found.
Conclusions and remarks
The presented method of modelling belt conveyor transportation costs for alternative mining scenarios allows to build more accurate economic block model of deposits that are planned to be mined with the use of continuous surface operations. This economic block model is suitable for the generation and analysis of the ultimate pit and – after creating the
Fig. 12. Strip ratio and averaged calorific value of lignite throughout the life-of-mine for two alternative mining scenarios (1 – circular advancing, 2 – parallel advancing);
note: no data for period 0 (prestripping), strip ratio for period 1 omitted (prestripping continued) Rys. 12. Szybkoœæ wykonywania odkrywki i uœredniona wartoœæ kaloryczna lignitu przez ca³y czas u¿ytkowania kopalni dla dwóch alternatywnych scenariuszy wydobycia (1 – dla poszerzania ko³owego,
2 – dla poszerzania równoleg³ego); uwaga: brak danych dla okresu 0 (przed rozpoczêciem odkrywki), szybkoœæ wykonywania odkrywki dla okresu 1 pominiêta (ci¹g dalszy przed rozpoczêciem odkrywki)
appropriate set of pushbacks – for building and investigation alternative Life-of-Mine plans.
The method seems to be a suitable supplement to the general purpose pit optimisation software which has not been adjusted for continuous surface mining requirements that are less flexible than those of cyclical mining.
The original data for the presented case study have been used upon the permission of the
“Konin” lignite mine. The obtained results are illustrative only.
The computations have been made with the use of the Datamine Studio and NPV Scheduler mining software licensed for the Wroclaw University of Technology by Datamine Corporation.
REFERENCES
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MODELOWANIE KOSZTÓW TRANSPORTU W PLANACH ALTERNATYWNEGO U¯YTKOWANIA KOPALNI DLA KOPALNI LIGNITU O POWIERZCHNI CI¥G£EJ
S ³ o w a k l u c z o w e Z³o¿e lignitu, kopalnia odkrywkowa, analiza finansowa
S t r e s z c z e n i e
Analiza finansowa planu u¿ytkowania kopalni w przypadku zoptymalizowanej odkrywki zale¿y od do- k³adnoœci modelu ekonomicznego z³o¿a. Formu³a cenowa lignitu wynika z jego parametrów jakoœciowych i analizy rynku energii, ale koszty górnicze zale¿¹ od systemu wydobycia. Gdy ustalone zostan¹ ostateczna wielkoœæ odkrywki i roczny uzysk, alternatywna rozbudowa odkrywki z odpowiednim systemem transportu mog¹ generowaæ ró¿ne lokalnie koszty górnicze. Przedstawiono modelowanie rozk³adu tych kosztów w modelu bloku ekonomicznego z³o¿a lignitu i ich wp³yw na przep³ywy pieniê¿ne kopalni w czasie jej u¿ytkowania.
MODELLING OF TRANSPORTATION COSTS FOR ALTERNATIVE LIFE-OF-MINE PLANS OF CONTINUOUS SURFACE LIGNITE MINES
K e y w o r d s Lignite deposit, open pit, financial analysis
A b s t r a c t
The financial analysis of a Life-Of-Mine plan of an optimised open pit depends on accuracy of its deposit economic model. The price formula of lignite can be built of its quality parameters and energy market analysis but mining costs depend on a mining system. Once the ultimate pit size and its annual output are set the alternative pit advancing with suitable conveying system can generate locally various mining costs. Modelling the distribution of these costs in an economic block model of a lignite deposit and their influence on mine’s cash flow over its lifetime have been presented.
