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Assessing profitability of mineral processing
Minerals Engineering, Vol. 6, No. 12, pp. 1203-1216, 1993
0892-6875/93 $6.00+0.00 © 1993 Pergamon Press Ltd
Printed in Great Britain
ASSESSING PROFITABILITY OF MINERAL PROCESSING
J. SEGOVIA and G. SCHENA Dept. of Naval, Ocean and Environment Engineering, Oeo-resources and Environment Section, University of Trieste, 34127 Italy (Received I0 May 1993; accepted 28 June 1993)
ABSTRACT
The rationale of a methodologyfor profitability analysis of integrated beneficiation systems is presented. Simple mathematical models are used to describe size reduction, preconcentration and concentration and simulate a process flowsheet. Based on a synthetic characterization of the plant feed a mass balance is calculated and the processing units scaled up. Capital and operating costs are expressed as a function of the equipment throughput. Metal quotations are used in connection to the mass balance for the calculation of the net smelter return to mine and the operation revenues. The system also permits the assessment of the benefits and cost consequences of including preconcentration in the integrated beneficiation process. When used for the analysis of a complex process flowsheet for low grade polymetaUic ores it compares costs and revenues related to the beneficiation of each value, indicating those deserving their own beneficiation route and those with not enough intrinsic value to repay the cost of treatment. The capacity of the method is demonstrated by means of an application example. Keywords Economics of mineral processing; costing; optimisation; pre-concentration.
ENGINEERING ECONOMICS A processing route is economically justified if its operating costs are lower than the operating revenues related to the sales of the process output i.e. when the operating margin is positive and exhibits profits. Initial investment in fixed assets should be included in the analysis as an appropriate 'quota' added to the operating cost. To make this simplified analysis more meaningful the allowable deductions for income tax calculation should be considered when computing the yearly cash flow. Dynamic methods such as the discount cash flow (DCF) procedure take the time value of money into account and permit the computation of synthetic indices of profitability. This analysis can show if the processing route for one mineral value is economical. Indeed treating polymetallic ores the analysis can show a negative operating margin for the route specifically concentrating a low grade value even if the overall margin of the beneficiation system is positive. This occurs because the treatment cost for one value is higher than the related revenues, while the other 1203
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J. SEGOVIAand G. SCHENA
mineral values cam be concentrated with related benefits. As an example for a plant treating a complex sulphide ore the concentration of pyrite may be uneconomical while benefits can be obtained from copper, zinc and lead. The overall positive operating margin can be increased by shutting down the pyrite concentration section. For project evaluation (that is e x - a n t e project analysis) revenues must be estimated. Metal quotations and price projections, treatment and refining charges and typical smelter contracts are available from specialised sources. Project specific capital and operating costs are available and a number of cost estimation procedures and databases with different degrees of accuracy have been proposed [1,2].
Preconcentration economics In mineral processing, preconcentration can be used to upgrade the mineral prior to further treatment. The upgrading can be accomplished by a number of separation techniques, which take advantage of the different physical properties of the mineral species to be processed. The aim of preconcentration is to reject a fraction of the ore which has insufficient intrinsic value to repay the cost of treatment, thereby enhancing the overall profitability of the system. The amount of material split by the preconcentrator can be varied by adjusting the value of the physical variable commanding the separation, that is the preconcentration cut-point. Depending on the process used, the cut-point, 8, can be a density, a flotation time, strength of an electric current, strength of a magnetic field, a radiation intensity, etc.. By adjusting the preconcentration cut-point, downstream processes may benefit from lower feed rates and, when overloaded, perform more efficiently. The overall plant recovery may drop because the fraction rejected by the preconcentrator also contains some valuable minerals. Often higher final concentrate grades are obtainable due to the higher feed grades to the concentrator. To obtain the same concentrate production, the plant feed rate may have to be increased and perhaps the sections ahead of the preconcentrator expanded. In order to compare the situation 'with' and 'without' a preconcentration stage it is necessary to consider the effect that this stage has on the overall plant performance. With the inclusion of preconcentration the overall recovery may be maintained at the same level as in the plant without preconcentration. This is achieved by adjusting the concentration scavenger and cleaner sections so that the grades of the final products (tail and concentrate) are the same as in the case without preconcentration and the rejected fraction does not have a grade greater than the concentration tails. If, while maintaining the grades of the final concentrate and tails, the preconcentrator reject has a grade lower than that of the concentration tails, the overall recovery can even be improved. This occurs, for example, when treating ores containing a substantial fraction of value-free material. The higher recovery of a final concentration process, following preconeentration, may compensate for the loss of values in the rejection of the preconeentrator. Often preconcentration also leads to indirect benefits. In the process of mine-block selection preconcentration allows the cut-off grade to be reduced, increasing the exploitable reserves with all the related benefits, such as economies of scale, longer project life etc.. The preconcentrator may also smooth fluctuations in the amount of value-free material going to the concentration stage. It reduces the unfavourable influence of the ore variability, allowing a steadier operation of the downstream units, which have the crucial duty of producing the final concentrate. Consider an hypothetical mineral occurrence in which the average assay value, in monetary terms per tonne at the feed to preconcentration, is known to be lower than the costs per tonne of subsequent treatments. Under this hypothesis the mineral cannot be economically treated as it is and a low-grade fraction has to be discarded. As this fraction increases, the value per tonne of the preconcentrate increases. Since concentration takes place, a point is reached at which the value of the preconceatrate per tonne is greater than the costs per tonne of subsequent treatment. From this point onward, the preconcentrate can be economically treated and a profit can be made. The fraction rejected can be
Assessing profitability of mineral processing
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increased by adjusting the separation cut-point of the preconcantration process. As the amount of low-grade material which does not repay further treatment increases the profit can be further improved. Eventually a point is reached at which the marginal value of the last rejected fraction is equal to its treatment cost. This is the point of maximum profit. If an extra fraction is rejected the overall profit decreases. This is because the value of the rejected extra fraction is greater than the treatment cost. By further increasing the cut-point, the profit per unit treated can be further increased, but the total profit decreases because marginally economic mineral has been rejected. In developing this simplified analysis it was assumed that treatment costs of the run-of-mine ore were greater than its total intrinsic value. This is not a necessary condition for the economic application of preconcentration. Preconcentration is justified as long as it increases the total profit of the overall beneficiation system. It appears evident from the discussion that the optimum cut-point must be selected according to economic criteria. A realistic solution is achieved if the cost of the preconcentration process and expected economies of scale are included in the analysis and any other simplifying hypothesis is removed for the development of the general optimisation procedure. The preconcentration should perform at the value of cut-point, 8, which maximises the operating margin (objective function), M, defined as the difference betwoen revenues, G, from concentrate sales and operating costs, E. Concentrate grades and recoveries of valuable species depend on the cut-point. Thus the revenues, G, are a function of the selected cut-point 8. Flowrates through the different sections of the plant depend on the cut-point. Economies of scale can be expected. Thus the operating costs, E, are a function of 8. The operating margin, M, can be expressed as: M(6) = (3(6) - E(8)
(1)
In the long-term the market price of input goods, services and production factors may change. The operating costs function, E, should be adjusted to the current set of market prices to ensure price time-stability. Indeed costs are time and site dependent. For the purpose of modelling and to demonstrate the application of the system, consider the plant shown in the flowsheet of Figure 1 which, after scalping the partially liberated ore, treats the oversize in a preconcentrator. The preconcentrate and the undersize scalped off are liberated by size reduction, and finally floated. Revenues Revenues depend on commodity market prices. For a plant treating a mineral with N valuable species ( j r 1...N) the base value per weight unit of concentrate of the jth valuable specie Vj is calculated deducting treatment and refining charges from metal paid. As an example for a metal 'me': Vine = (qme--qd).(Cme-Cd)-Tc-Sc.(Cme.-Cd)-Sh
where: Vine is the concentrate value per tonne qme is the metal world market quotation qd is the metal price deduction cd is the grade deduction %= is the concentrate grade T c is the treatment charge per tonne of concentrate
(2)
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J. SEC,OVIA and G. SCHENA t
Sc is the smelter refining charge per weight of metal paid Sh is the freight charge per dry toune shipped The value of the concentrate is likely to be penalised for undesirable elements or contaminants, for example iron in zinc concentrate or zinc in copper concentrate. Credits for valuable elements such as silver and gold and others are added to the base concentrate value.
ROM 11tpd
CONCENTRATION
C: Concentrates T: Tails R: Yield
BULK FLOTATION
Rouu<
CRUSHING///---~~ _1 ........................
PRESCREENING
=
GRINDING CIRCUIT
I
T
GALENAFLOT. F~
C
R*P~= I -RscR+~.RP~E
I
P,Sc~.RmE
)[~-'] PRECONCENTRATION
]
/
R*PR=E.Rau.,K. (1-Rcu)
CHALCOPYRITEFLOT. 1 Rcu C
~ Float
R*PRE.Rcu+=R*t'~E.RBLCK.Rcu
RSCR.(I -RPRE)
Fig. 1 Sketch of a beneficiation system including preconcentration For example, for a copper concentrate, the minimum Cu grade for marketing is 26%. With Cme ---31%, °.me =2100 S/metal tonne, q,l -- 20 S/metal toune, cd = 1.1, T c = 85 $/tonne, SG = 170 S/metal tonne, Sh = 80 $/tonne Vine is 292 $/tonne. If an ore containing only one valuable mineral is treated, the revenues from processing one weight unit of run-of-mine ore can be expressed as follows:
C,(8) = V.r~(8).r~(8). f-
(3)
C
where r*pre(8 ) and r¢on(8) are respectively the value recovery in the preconcentrafion and the concentration processes. Thesuperscript '*' denotes the inclusion of the metal values contained in the scalped undersize. The variables f and c are the grades of the run of mine and the conc4mtrate respectively.
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If a multicompone~t ore containing M valuable components is treated, the revenues from processing one unit of run-of-mine ore can be expressed as: M
CK8) = ~
Vj.r~(8).r==j(8).~
(4)
where the variables r*prej(8) and r¢ond(8) are the value recovery of thejth species in the preconcentration and in the concentration processes respectively. The variablesI~ and cj are the grades of the run of mine and of the concentrates in the jth species respectively. The revenues from concentrate sales (Eq.(4)) can be calculated from the following expressions: M
C,(8 ) = ~_e ~" [ 1 -RscR(X) + Rsca(x). Rp~(8)]. R~
(5)
j-I
which can be rewritten as: --
j.l
Vj.R;R (8).R
(6)
where RSCR(X)is oversize recovery when scalping at size x. R * I ~ ( 8 ) is the yield of the pre-concentration inclusive of the fine fraction by-passing the preconcentration. R+¢j is the yield of the unit concentrating the value j referred to the total concentration plant feed. The superscript ' + ' is neglected when the yields are based on the feed to the jth concentration section. Thus R+o,1 ffi Re,I" Costs The total operating cost can be calculated by summing up the expenses to produce the run-of-mine ore and the processing costs. The cost of producing and processing a unit of run-of-mine ore can be derived using the following: E(8) = EROM +EcR + EpRE • RSCR(X) + EGR. [(1-RscR(X)+RscR(X).RpRE(8)] + E c. [ 1-RscR(x ) +R$cR(X).RPRE(8)] (7) where: EROM :cost for the production of one weight unit of run of mine ore ECR :cost for the coarse size reduction of one weight unit of run of mine ore. The cost should be inclusive of all the expenses from the first stage of reduction (crushing) up to the stage producing a size suitable for preconcentration. EpRE:
cost for the preconcentration of one weight unit of oversize from the scalping
RSCR(X):
oversize fraction when scalping at size x
EGR:
cost for grinding one weight unit of stream made up by the preconcentrate and the undersize from scalping
RpRE(8):
preconcentration yield
Ec:
cost for concentration of one weight unit of throughput
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J.
SEGOVI^and G. SCHENA
The basic Eq. (7) can be used when concentrating one valuable species only, or in the case of bulk-concentration of more species. The use of the equation can be extended to the case of differential concentration, providing that the costs of the two or more stages can be incorporated into a comprehensive global cost per unit of concentration feed. When dealing with differential concentration of two mineral values the last term of Eq. (7) can be rewritten as follows:
E C • [I-R$cR(X)+RscR(X).RpRE(6)] = Ec,t.[I-R$cR(X)+RscR(X).RpRE(8)] + E¢,2.[I-RscR(x)+RscR(x).RpRE(~)].[I-Rc,I(6)]
(8)
where the subscripts '1' and '2' indicate the first and the second concentration stage respectively. Ec.j is the operating cost for concentrating one weight unit of feed to the jth stage. The terms in parenthesis express the fraction of run-of-mine ore entering the jth concentration unit. Rc,j(8 ) is the yield of the jth concentration stage. The operating costs Eu's (U =generic treatment unit) are made up by items which contain fixed- and variable-cost elements. Fixed costs are not so much a function of the production level as a function of time and are incurred in order to maintain production facilities. Variable costs are related to the unit throughput. As an example, the electricity cost contains an element of both; there is a basic charge and a charge per unit of consumption. An appropriate accounting system can guide in the determinstion of Eu's. The operating costs depend o n the market prices of input goods (eg. energy, spare parts, etc.), services (e.g. banking, insurance, etc.) and primary factors (wages, capital, etc.). For a processing unit 'U' labour, supply and equipment operating costs items can be expressed as a function of its throughput [1,3] Yu = au" Xb
(9)
where: Yu X
is the operating cost item in dollars per day is the unit throughput in tonnes per day
a U and b are two appropriate constants, as an example for crushing labour costs au, L = aCR,L ----228.4 and bCR,L----0.279. The total operating cost for a mineral processing unit is the sum of direct and maintenance labour, supply of power, reagents etc. and equipment wear, repair parts, maintenance materials etc. ECR ffi YCR,L + YCR,SP + YCR,EQ
(10)
Similar formulae are used for capital costs, where according to USBM procedures, the cost is not the cost of the stand alone components; rather it is the cost of the equipment properly installed in the whole beneficiation system. For both plant-input and plant-output, prices are determined by the markets. In the short-term it can be assumed that the set of market prices for the input is constant. Prices of metals are very volatile and care should be taken in selecting the values for the analysis. Sensitivity analysis can help the final process selection. Eq. (7) can be modified to include costs of auxiliary operations, such as filtration and drying of concentrates, and the need to prepare the final marketable products. The practice of locating the preconcentrator away from the concentration plant, in the vicinity of the mine and crushing plant is not uncommon. In such a case preconcentrate transportation and handling costs must
Assessing profitability of mineral processing
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be included into Eq. (7). In terms of cost per weight unit of run-of-mine ore, the following item can be included in the right side of the equation: ETRA.[1- RSCR(X) + RScR(x).Rpp.E(8)]
(II)
where ETRA is the transportation cost per weight unit of preconc.entrate.
Uniqueness of the solution Maximizing the objective function M(8) with respect to 8 can produce two different situations: a) There is a range of densities in which the values of M(8) are greater than the operating margin relative to the plant without preconcentration. In such a range M increases with the density, reaches a maximum and then decreases as the density increases. Thus preconcentration can improve the overall profitability of the beneficiation system. The point where the partial derivative of M(8) with respect to the density 8 is zero represent the optimum cut point 8opt. The cut density should be set at 8opt. Here marginal revenues equal marginal costs. To ensure that profits are maximised, the second derivative of the cost must be greater than the second derivative of the revenues. In other words, at 8opt the slope of the marginal cost must exceed the value of the slope of the marginal revenues. This translates into the geometric statement that the marginal cost curve should cut the marginal revenue curve from below. b) For any value of the cut-point of the preconcentration unit, the value of the margin, M(8), is lower than the margin related to the plant without preconcentration and tends to this value as the cut-point decreases. The preconcentration cannot enhance the profitability of the beueficiation system. For example this may be the case with a very disseminated mineral occurrence: also, cutting at low density rejects a float material deserving treatment. The decision procedure Integrated processes which include preconcentration in their flowsheet often need to be compared with a flowsheet which does not include preconcentration and is usually considered simpler. Profitability principles can be applied in decision-making between alternatives (integrated processes), that is when a choice is necessary between two or more policies (alternatives) to be followed for a projected time period of selected duration -i.e. when an integrated process that includes preconcentration is compared with competitors that do not. The decision procedure is based on the concept of present worth. The present worth, PV, can be expressed as: p v __ %
÷
N
(12)
k=l
where Io is plant capital cost (cash outflow) encountered at year 0, i is the discount rate expressed as a decimal, Mk are the margins of the considered alternative during the kth year. Thus the two alternatives having different investments and margins may be compared by determining their respective present worth. The alternative with the higher PV is the more favourable. The internal rate of return, IRR, is the discount rate which equates PV to zero. IRR can be used as a decision criterion. It eliminates the need for an external discount rate supplied for calculation. The alternative with the higher IRR is the one tobe promoted.
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J. SEGOVIA and G. SCHENA
INCORPORATING PROCESS MODELS For the calculation of the weight recovery of the preconcentration, RpRE, use can be made of mathematical expressions of partition curves. A number of models have been suggested to approximate a separation process by mean of partition functions [4,5]. Originally, many of these models were suggested primarily for classification but they can be confidently used for separation systems. For the description of concentration units as flotation circuits kinetic models originally developed for chemical reactors, can be used.
Preconcentration by dense medium separation A simple exponential partition function [4] can be used to describe separation by dense medium:
oxlo 9 / ]
(13)
where: re
6 m
isthe partition number calculated at the density d i is the density cut point also referred to as 650 is a partition curve sharpness parameter midpoint of the ith density range.
For an ideal separation m - . ,o and Ep =,. O. To simulate the preconcentration, Ep -probable error- is used as a measure of separation sharpness and kept constant and the parameter 'm' has to be calculated for each density cut-point, 6, examined. The values of Ep depend upon the separation vessel. For a dynamic DMS Ep=O.04 g.m1-1 is an appropriate value. The approximate relationship: m = 0.79.--8
e
(14)
can be used [4]. Use can be made of more complex models for the actual partition function a a and take into account the by-pass of low density particles to the sink and maximum possible recovery of heavies. The preconcentrate yield is: d~
(15)
--
d~ where f(di)'s are values taken from the histogram of the intra-demity distribution of the preexmcentration feed and d i is the range midpoint and eta are the actual partition coefficients. The preconcentrate grade, P, can be calculated as a function of the density:
Assessing profitability of mineral processing
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(16) /'(8)
-
RpRE(8 )
where g(di) is the value of the intra-density feed grade distribution function at di. Concentration by a process matching the perfect m i x ~ model The concentrator unit can be modelled as a perfect mixer. An ordinary model resulting from coupling first order kinetics with residence time distribution in single perfect mixers is used. In general terms: T(8) -
F(8)
(17)
(1 +/~x)~ where: F(8) and T(8) are respectively the grades of the feed and the tails of the concentrator, K¢ is the concentration rate constant and • the average residence time, 'n' is the number of mixers in series. ~ may result from equalling the metal recovery in a batch laboratory cell with the recovery in a bank of 'n' cells in series. Since metal recovery in a single reactor modelled as a perfect mixer is : p ffi 1- T/F, Eq. (17) can be expressed as: Pc = Pc-"[1-(1 +Kc~)-~]
(18)
where: Pc: Pc®:
is the recovery of the bank of 'n' PM cells each with a mean retention time ~. is the recovery that is approached asymptotically as ~ . ,
Integrated plant simulation By coupling the model for preconcentration with the kinetic model for flotation the integrated plant reported in Figure 1 was simulated. The number of process dependent constants necessary for such an approach is very low : the value of Ep is adequate to describe the DMS preconcentrator, the kinetic constant/s and the average cell retention time for the flotation of each species are suitable for the concentrator model. Grades and recoveries were calculated for each process stream. Capital and operating costs were calculated for the alternatives with and without preconcentrator.
APPLICATION EXAMPLE In this section the capacity of the system is demonstrated with a case study. The flowsheet of the plant undergoing analysis is shown in Figure 1. It treats a complex low grade polymetallic ore. On the site of the ore body a mine and a processing plant have been operating for considerable time with the same flowsheet. Some years ago, due to low metal prices and low grades, the project became sub-economicel and after a period of state subsidy the operation was shut down. The model is used to re,assess the economic profitability of the project in the light of the new economic scenario. The minerals are chalcopyrite, sphalerite, galena, marmatite and pyrite. Grades: Cuffi0.24%; Znffi3.55%; Pbffi0.61%; Feffi7.8%; S=6%. The preconcentration feed was characterised by its weight/density and grsde/density distributions (Figure 2). The generation of these sets of data requires heavy liquid tests and chemical analyses. Mass balances
1212
J. SEGOV1Aand G. SCHENA
calculated for controlling the efficiency of the flotation plant were used for establishing the rate constants. They were supplemented by batch flotation tests. The sets were taken from historical data collected during the last period of plant operation. Concentrates values were based on average metal quotations for last the quarter 1992. The processing plant treats 500 tonnes per day.
-30,0 -25,0 -20,0 -15,0
=. -10,0 -5,0
~ •-r"
78 Cu
2
~ 2,7
2,4 ,
density
Fig.2 Preconcentration feed characterisation The mining cost indexation system [3] was used to update operating costs calculated with the USBM method [1]. Indices relevant to 1992 were used. The indices reflect the costs of inputs to the mining industry. They include wages, equipment, power, supply and others considered to represent the most important items of capital and operating costs. When a cost is updated it is assumed that the mix of cost component remain unchanged. The total cost for the production of one tonne of run-of-mine ore was taken as 155. Figure 3 shows the operating margin as a function of the preconcemration cut density, the margin for the plant without preconcentration is also reported, The diagram shows that both process alternatives have positive, but low, operating margins and that preconcentration does not increase the profitability of the whole beneficiation system. This is due to the dissemination of the copper values in the ore; also at relatively low cut densities, where high metal recovery is expected in the sink product, regretfully valuable ore disseminated in the gangue is rejected with the float product. It is interesting to note that the old plant included the preconcentrator in its flowsheet. A breakdown of the operating costs is shown in Figures 4a and 4b. The contribution of the single mineral values to the revenues are given in Figure 5a and 5b. It can be concluded that an existing operating plant can be operated with (low) profits and the preconcentrator shut down and that Zn is the only value concentrated with profit. This suggests that the Pb and Cu flotation sections do not contribute to the overall profit. Capital costs were also calculated for both a new plant which includes preconcentration and a plant that does not (Figures 6a and 6b). Total capital cost was $ 4.5 m for the plant with preconcentration and very much the same for the alternative without dense medium separation. The extra capital required for the preconcentrator is partially compensated for by a smaller and cheaper flotation plant.
Assessing profitability of mineral processing
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35 REVENUES
30 COSTS
. . . . . . . . . . . . . . . . .
25
II II o
20
a
om
15
10
Ma~ Margin
OPERATING MARGIN
I
I 2,65
2,70
2,75
2,80
2,85
2,90
Cut density, g/ml
Fig.3 Operating margins, revenues and costs as a function of the preconcentration cut density The decision system was also applied to an hypothetical green field scenario. The following data were considered suitable: 15 years of production, 0.14 discount rate. The analysis shows that for both alternatives the operating margins are not sufficient to recovery the cost of the plants. However the plant without preconcentration, because of the higher operating margin, is the one ranking first according to the PV and IRR criteria. This is an obvious conclusion in the specific application but cases exist in which the most expensive alternative is the most economic in the long term because the higher yearly operating margins repay the extra capital costs. The analysis suggests that the project is not profitable! The IRR so calculated should be used only as a comparative index of profitability among process alternatives. Indeed mine related capital costs were not included in the analysis and the value cannot be compared to internal rates of return above 20~ required for integrated mineral projects.
J. SEGOVIA and G. SCHENA
1214
Operating cost with preconcentration
Mining
Operating cost without preconcentration
Mining
Crashing
54%
Crushing
55%
~.%
3%
DMS 8%
Grindin[ 13%
Grinding 10% Zn, Ca, Pb Filth 2%
Cu Flotation 5%
Pb Flotation 5%
Zn, Pb, Cu Filtl 2%
. . . . . . . . . tation Zn Flotation 7% 7%
~ Flotatior Cu Flotation 5%
Pb flotation 5%
Zn Flotation 8%
9%
Fig.4 Operating cost breakdowns Revenues with preconcentration
Revenues without preconcentration gn
Zn 94%
95%
Cu 5%
Pb 1%
Ou
4,5%
Pb 0,5%
Fig.5 Revenues from metal concentrates Capital cost with preconcentration
Capital cost without preconcentration
Filtration
Filtration
2%
Mill Building
2% ill Building 35%
Flotation
Flotation
37%
38%
dng Grinding 14%
DMS 9%
3%
ing Grinding 21%
Fig.6 Capital cost breakdowns
4%
Assessing profitability of mineral processing
1215
CONCLUSIONS Processing plays a key role in the economics of the overall mineral production system. The mine may deliver at the lowest cost and provide potential for a profitable operation, but the processing plant has the responsibility of making profits, and not losses, out of such a potential. The target may be achieved by reducing costs and increasing revenues. In a properly run plant, the costs must always be kept to their minimum value and efforts have to be made to increase the revenues, maximising recoveries and grades of the concentrates. A rational and consistent procedure for maximising profit should be based on financial principles, and lead to the maximisation of the operating margin, rather than on the sole effort of minimising costs or maximising revenues of an operation. The commercial profitability is only a measure of the difference between the total capital received and at expended in running the plant. This is of interest for a private company precisely because the capital receipts represent the benefits and the capital expenditures constitute the costs. The greater the excess of receipts over expenditures, the more profitable the business. Economic profitability criteria for state owned mines can be more complex. The decision support system presented here can be used as a tool for the economic analysis of the preconcentration. When well tuned with current prices it can be used for off-line optimisation. It can indicate the preconcentrator cut-point which maximises the plant operating margin. It can also indicate that the preconcentrator has to be shut down. In a green field scenario it can be used in the early stages of the feasibility study to check if the preconcentration section should to be included in the integrated beneficiation plant. Once the integrated process has been selected using this system then the technical issues become more important and a more accurate description of the processing units is required, the use of a modular simulator becoming desirable.
NOTATIONS n~ 4~a au
b c
d 8
di E
Ep Eu f F G g
i
I0 IRR M m n
P PV q Peo
partition number actual partition coefficients constants for operating cost function exponent for operating cost function concentrate grade density cut-point density midpoint of the ith density range total operating cost probable error operating cost for processing unit U grade of the run of mine grades of the concentrator feed total revenues preconcentrator feed grade interest rate expressed as a decimal plant capital cost at year 0 internal rate of return concentration rate constant operating margin sharpness parameter number of mixers in series preconcentrate grade present worth metal world market quotation metal recovery at
1216
rU
1% Sc Sh T
% V x
X Yu
J. SEGOVIA and G. SCHENA
recovery in the processing unit U yield of processing unit U smelter refining charge freight charge per dry tonne shipped grades of the concentrator tails average residence time treatment charge per tonne of concentrate concentrate value size unit throughput operating cost item
ACKNOWLEDGEMENTS This work was partially supported by the CEC grant BR E 2 CT 92 0301.
REFERENCES °
2. 3. 4. 5.
United Sates Department of the Interior., Bureau of Mines cost estimating system handbook. Part 2. Mineral processing. Information Circular No. 9143. (1987). Ruhmer, W.T., Handbook on the Estimation of Metallurgical Process Cost. Second edition, MINTEK, Special Publication No. 14. (1992). United Sates Department of the Interior., International Mining Cost Indexation System. Information Circular No. 9170. (1987b). Tarjan, G., Application of distribution function to partition curves. Inter. J. Miner. Process., 1: 261-265 (1974). Trawinski, H., The mathematical simulation of Tromp curves. Int. Ceramic Review. 27 (1), 21-24 (1978).
0892-6875/93 $6.00+0.00 © 1993 Pergamon Press Ltd
Printed in Great Britain
ASSESSING PROFITABILITY OF MINERAL PROCESSING
J. SEGOVIA and G. SCHENA Dept. of Naval, Ocean and Environment Engineering, Oeo-resources and Environment Section, University of Trieste, 34127 Italy (Received I0 May 1993; accepted 28 June 1993)
ABSTRACT
The rationale of a methodologyfor profitability analysis of integrated beneficiation systems is presented. Simple mathematical models are used to describe size reduction, preconcentration and concentration and simulate a process flowsheet. Based on a synthetic characterization of the plant feed a mass balance is calculated and the processing units scaled up. Capital and operating costs are expressed as a function of the equipment throughput. Metal quotations are used in connection to the mass balance for the calculation of the net smelter return to mine and the operation revenues. The system also permits the assessment of the benefits and cost consequences of including preconcentration in the integrated beneficiation process. When used for the analysis of a complex process flowsheet for low grade polymetaUic ores it compares costs and revenues related to the beneficiation of each value, indicating those deserving their own beneficiation route and those with not enough intrinsic value to repay the cost of treatment. The capacity of the method is demonstrated by means of an application example. Keywords Economics of mineral processing; costing; optimisation; pre-concentration.
ENGINEERING ECONOMICS A processing route is economically justified if its operating costs are lower than the operating revenues related to the sales of the process output i.e. when the operating margin is positive and exhibits profits. Initial investment in fixed assets should be included in the analysis as an appropriate 'quota' added to the operating cost. To make this simplified analysis more meaningful the allowable deductions for income tax calculation should be considered when computing the yearly cash flow. Dynamic methods such as the discount cash flow (DCF) procedure take the time value of money into account and permit the computation of synthetic indices of profitability. This analysis can show if the processing route for one mineral value is economical. Indeed treating polymetallic ores the analysis can show a negative operating margin for the route specifically concentrating a low grade value even if the overall margin of the beneficiation system is positive. This occurs because the treatment cost for one value is higher than the related revenues, while the other 1203
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J. SEGOVIAand G. SCHENA
mineral values cam be concentrated with related benefits. As an example for a plant treating a complex sulphide ore the concentration of pyrite may be uneconomical while benefits can be obtained from copper, zinc and lead. The overall positive operating margin can be increased by shutting down the pyrite concentration section. For project evaluation (that is e x - a n t e project analysis) revenues must be estimated. Metal quotations and price projections, treatment and refining charges and typical smelter contracts are available from specialised sources. Project specific capital and operating costs are available and a number of cost estimation procedures and databases with different degrees of accuracy have been proposed [1,2].
Preconcentration economics In mineral processing, preconcentration can be used to upgrade the mineral prior to further treatment. The upgrading can be accomplished by a number of separation techniques, which take advantage of the different physical properties of the mineral species to be processed. The aim of preconcentration is to reject a fraction of the ore which has insufficient intrinsic value to repay the cost of treatment, thereby enhancing the overall profitability of the system. The amount of material split by the preconcentrator can be varied by adjusting the value of the physical variable commanding the separation, that is the preconcentration cut-point. Depending on the process used, the cut-point, 8, can be a density, a flotation time, strength of an electric current, strength of a magnetic field, a radiation intensity, etc.. By adjusting the preconcentration cut-point, downstream processes may benefit from lower feed rates and, when overloaded, perform more efficiently. The overall plant recovery may drop because the fraction rejected by the preconcentrator also contains some valuable minerals. Often higher final concentrate grades are obtainable due to the higher feed grades to the concentrator. To obtain the same concentrate production, the plant feed rate may have to be increased and perhaps the sections ahead of the preconcentrator expanded. In order to compare the situation 'with' and 'without' a preconcentration stage it is necessary to consider the effect that this stage has on the overall plant performance. With the inclusion of preconcentration the overall recovery may be maintained at the same level as in the plant without preconcentration. This is achieved by adjusting the concentration scavenger and cleaner sections so that the grades of the final products (tail and concentrate) are the same as in the case without preconcentration and the rejected fraction does not have a grade greater than the concentration tails. If, while maintaining the grades of the final concentrate and tails, the preconcentrator reject has a grade lower than that of the concentration tails, the overall recovery can even be improved. This occurs, for example, when treating ores containing a substantial fraction of value-free material. The higher recovery of a final concentration process, following preconeentration, may compensate for the loss of values in the rejection of the preconeentrator. Often preconcentration also leads to indirect benefits. In the process of mine-block selection preconcentration allows the cut-off grade to be reduced, increasing the exploitable reserves with all the related benefits, such as economies of scale, longer project life etc.. The preconcentrator may also smooth fluctuations in the amount of value-free material going to the concentration stage. It reduces the unfavourable influence of the ore variability, allowing a steadier operation of the downstream units, which have the crucial duty of producing the final concentrate. Consider an hypothetical mineral occurrence in which the average assay value, in monetary terms per tonne at the feed to preconcentration, is known to be lower than the costs per tonne of subsequent treatments. Under this hypothesis the mineral cannot be economically treated as it is and a low-grade fraction has to be discarded. As this fraction increases, the value per tonne of the preconcentrate increases. Since concentration takes place, a point is reached at which the value of the preconceatrate per tonne is greater than the costs per tonne of subsequent treatment. From this point onward, the preconcentrate can be economically treated and a profit can be made. The fraction rejected can be
Assessing profitability of mineral processing
1205
increased by adjusting the separation cut-point of the preconcantration process. As the amount of low-grade material which does not repay further treatment increases the profit can be further improved. Eventually a point is reached at which the marginal value of the last rejected fraction is equal to its treatment cost. This is the point of maximum profit. If an extra fraction is rejected the overall profit decreases. This is because the value of the rejected extra fraction is greater than the treatment cost. By further increasing the cut-point, the profit per unit treated can be further increased, but the total profit decreases because marginally economic mineral has been rejected. In developing this simplified analysis it was assumed that treatment costs of the run-of-mine ore were greater than its total intrinsic value. This is not a necessary condition for the economic application of preconcentration. Preconcentration is justified as long as it increases the total profit of the overall beneficiation system. It appears evident from the discussion that the optimum cut-point must be selected according to economic criteria. A realistic solution is achieved if the cost of the preconcentration process and expected economies of scale are included in the analysis and any other simplifying hypothesis is removed for the development of the general optimisation procedure. The preconcentration should perform at the value of cut-point, 8, which maximises the operating margin (objective function), M, defined as the difference betwoen revenues, G, from concentrate sales and operating costs, E. Concentrate grades and recoveries of valuable species depend on the cut-point. Thus the revenues, G, are a function of the selected cut-point 8. Flowrates through the different sections of the plant depend on the cut-point. Economies of scale can be expected. Thus the operating costs, E, are a function of 8. The operating margin, M, can be expressed as: M(6) = (3(6) - E(8)
(1)
In the long-term the market price of input goods, services and production factors may change. The operating costs function, E, should be adjusted to the current set of market prices to ensure price time-stability. Indeed costs are time and site dependent. For the purpose of modelling and to demonstrate the application of the system, consider the plant shown in the flowsheet of Figure 1 which, after scalping the partially liberated ore, treats the oversize in a preconcentrator. The preconcentrate and the undersize scalped off are liberated by size reduction, and finally floated. Revenues Revenues depend on commodity market prices. For a plant treating a mineral with N valuable species ( j r 1...N) the base value per weight unit of concentrate of the jth valuable specie Vj is calculated deducting treatment and refining charges from metal paid. As an example for a metal 'me': Vine = (qme--qd).(Cme-Cd)-Tc-Sc.(Cme.-Cd)-Sh
where: Vine is the concentrate value per tonne qme is the metal world market quotation qd is the metal price deduction cd is the grade deduction %= is the concentrate grade T c is the treatment charge per tonne of concentrate
(2)
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J. SEC,OVIA and G. SCHENA t
Sc is the smelter refining charge per weight of metal paid Sh is the freight charge per dry toune shipped The value of the concentrate is likely to be penalised for undesirable elements or contaminants, for example iron in zinc concentrate or zinc in copper concentrate. Credits for valuable elements such as silver and gold and others are added to the base concentrate value.
ROM 11tpd
CONCENTRATION
C: Concentrates T: Tails R: Yield
BULK FLOTATION
Rouu<
CRUSHING///---~~ _1 ........................
PRESCREENING
=
GRINDING CIRCUIT
I
T
GALENAFLOT. F~
C
R*P~= I -RscR+~.RP~E
I
P,Sc~.RmE
)[~-'] PRECONCENTRATION
]
/
R*PR=E.Rau.,K. (1-Rcu)
CHALCOPYRITEFLOT. 1 Rcu C
~ Float
R*PRE.Rcu+=R*t'~E.RBLCK.Rcu
RSCR.(I -RPRE)
Fig. 1 Sketch of a beneficiation system including preconcentration For example, for a copper concentrate, the minimum Cu grade for marketing is 26%. With Cme ---31%, °.me =2100 S/metal tonne, q,l -- 20 S/metal toune, cd = 1.1, T c = 85 $/tonne, SG = 170 S/metal tonne, Sh = 80 $/tonne Vine is 292 $/tonne. If an ore containing only one valuable mineral is treated, the revenues from processing one weight unit of run-of-mine ore can be expressed as follows:
C,(8) = V.r~(8).r~(8). f-
(3)
C
where r*pre(8 ) and r¢on(8) are respectively the value recovery in the preconcentrafion and the concentration processes. Thesuperscript '*' denotes the inclusion of the metal values contained in the scalped undersize. The variables f and c are the grades of the run of mine and the conc4mtrate respectively.
Assessing profitability of mineral processing
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If a multicompone~t ore containing M valuable components is treated, the revenues from processing one unit of run-of-mine ore can be expressed as: M
CK8) = ~
Vj.r~(8).r==j(8).~
(4)
where the variables r*prej(8) and r¢ond(8) are the value recovery of thejth species in the preconcentration and in the concentration processes respectively. The variablesI~ and cj are the grades of the run of mine and of the concentrates in the jth species respectively. The revenues from concentrate sales (Eq.(4)) can be calculated from the following expressions: M
C,(8 ) = ~_e ~" [ 1 -RscR(X) + Rsca(x). Rp~(8)]. R~
(5)
j-I
which can be rewritten as: --
j.l
Vj.R;R (8).R
(6)
where RSCR(X)is oversize recovery when scalping at size x. R * I ~ ( 8 ) is the yield of the pre-concentration inclusive of the fine fraction by-passing the preconcentration. R+¢j is the yield of the unit concentrating the value j referred to the total concentration plant feed. The superscript ' + ' is neglected when the yields are based on the feed to the jth concentration section. Thus R+o,1 ffi Re,I" Costs The total operating cost can be calculated by summing up the expenses to produce the run-of-mine ore and the processing costs. The cost of producing and processing a unit of run-of-mine ore can be derived using the following: E(8) = EROM +EcR + EpRE • RSCR(X) + EGR. [(1-RscR(X)+RscR(X).RpRE(8)] + E c. [ 1-RscR(x ) +R$cR(X).RPRE(8)] (7) where: EROM :cost for the production of one weight unit of run of mine ore ECR :cost for the coarse size reduction of one weight unit of run of mine ore. The cost should be inclusive of all the expenses from the first stage of reduction (crushing) up to the stage producing a size suitable for preconcentration. EpRE:
cost for the preconcentration of one weight unit of oversize from the scalping
RSCR(X):
oversize fraction when scalping at size x
EGR:
cost for grinding one weight unit of stream made up by the preconcentrate and the undersize from scalping
RpRE(8):
preconcentration yield
Ec:
cost for concentration of one weight unit of throughput
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SEGOVI^and G. SCHENA
The basic Eq. (7) can be used when concentrating one valuable species only, or in the case of bulk-concentration of more species. The use of the equation can be extended to the case of differential concentration, providing that the costs of the two or more stages can be incorporated into a comprehensive global cost per unit of concentration feed. When dealing with differential concentration of two mineral values the last term of Eq. (7) can be rewritten as follows:
E C • [I-R$cR(X)+RscR(X).RpRE(6)] = Ec,t.[I-R$cR(X)+RscR(X).RpRE(8)] + E¢,2.[I-RscR(x)+RscR(x).RpRE(~)].[I-Rc,I(6)]
(8)
where the subscripts '1' and '2' indicate the first and the second concentration stage respectively. Ec.j is the operating cost for concentrating one weight unit of feed to the jth stage. The terms in parenthesis express the fraction of run-of-mine ore entering the jth concentration unit. Rc,j(8 ) is the yield of the jth concentration stage. The operating costs Eu's (U =generic treatment unit) are made up by items which contain fixed- and variable-cost elements. Fixed costs are not so much a function of the production level as a function of time and are incurred in order to maintain production facilities. Variable costs are related to the unit throughput. As an example, the electricity cost contains an element of both; there is a basic charge and a charge per unit of consumption. An appropriate accounting system can guide in the determinstion of Eu's. The operating costs depend o n the market prices of input goods (eg. energy, spare parts, etc.), services (e.g. banking, insurance, etc.) and primary factors (wages, capital, etc.). For a processing unit 'U' labour, supply and equipment operating costs items can be expressed as a function of its throughput [1,3] Yu = au" Xb
(9)
where: Yu X
is the operating cost item in dollars per day is the unit throughput in tonnes per day
a U and b are two appropriate constants, as an example for crushing labour costs au, L = aCR,L ----228.4 and bCR,L----0.279. The total operating cost for a mineral processing unit is the sum of direct and maintenance labour, supply of power, reagents etc. and equipment wear, repair parts, maintenance materials etc. ECR ffi YCR,L + YCR,SP + YCR,EQ
(10)
Similar formulae are used for capital costs, where according to USBM procedures, the cost is not the cost of the stand alone components; rather it is the cost of the equipment properly installed in the whole beneficiation system. For both plant-input and plant-output, prices are determined by the markets. In the short-term it can be assumed that the set of market prices for the input is constant. Prices of metals are very volatile and care should be taken in selecting the values for the analysis. Sensitivity analysis can help the final process selection. Eq. (7) can be modified to include costs of auxiliary operations, such as filtration and drying of concentrates, and the need to prepare the final marketable products. The practice of locating the preconcentrator away from the concentration plant, in the vicinity of the mine and crushing plant is not uncommon. In such a case preconcentrate transportation and handling costs must
Assessing profitability of mineral processing
1209
be included into Eq. (7). In terms of cost per weight unit of run-of-mine ore, the following item can be included in the right side of the equation: ETRA.[1- RSCR(X) + RScR(x).Rpp.E(8)]
(II)
where ETRA is the transportation cost per weight unit of preconc.entrate.
Uniqueness of the solution Maximizing the objective function M(8) with respect to 8 can produce two different situations: a) There is a range of densities in which the values of M(8) are greater than the operating margin relative to the plant without preconcentration. In such a range M increases with the density, reaches a maximum and then decreases as the density increases. Thus preconcentration can improve the overall profitability of the beneficiation system. The point where the partial derivative of M(8) with respect to the density 8 is zero represent the optimum cut point 8opt. The cut density should be set at 8opt. Here marginal revenues equal marginal costs. To ensure that profits are maximised, the second derivative of the cost must be greater than the second derivative of the revenues. In other words, at 8opt the slope of the marginal cost must exceed the value of the slope of the marginal revenues. This translates into the geometric statement that the marginal cost curve should cut the marginal revenue curve from below. b) For any value of the cut-point of the preconcentration unit, the value of the margin, M(8), is lower than the margin related to the plant without preconcentration and tends to this value as the cut-point decreases. The preconcentration cannot enhance the profitability of the beueficiation system. For example this may be the case with a very disseminated mineral occurrence: also, cutting at low density rejects a float material deserving treatment. The decision procedure Integrated processes which include preconcentration in their flowsheet often need to be compared with a flowsheet which does not include preconcentration and is usually considered simpler. Profitability principles can be applied in decision-making between alternatives (integrated processes), that is when a choice is necessary between two or more policies (alternatives) to be followed for a projected time period of selected duration -i.e. when an integrated process that includes preconcentration is compared with competitors that do not. The decision procedure is based on the concept of present worth. The present worth, PV, can be expressed as: p v __ %
÷
N
(12)
k=l
where Io is plant capital cost (cash outflow) encountered at year 0, i is the discount rate expressed as a decimal, Mk are the margins of the considered alternative during the kth year. Thus the two alternatives having different investments and margins may be compared by determining their respective present worth. The alternative with the higher PV is the more favourable. The internal rate of return, IRR, is the discount rate which equates PV to zero. IRR can be used as a decision criterion. It eliminates the need for an external discount rate supplied for calculation. The alternative with the higher IRR is the one tobe promoted.
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J. SEGOVIA and G. SCHENA
INCORPORATING PROCESS MODELS For the calculation of the weight recovery of the preconcentration, RpRE, use can be made of mathematical expressions of partition curves. A number of models have been suggested to approximate a separation process by mean of partition functions [4,5]. Originally, many of these models were suggested primarily for classification but they can be confidently used for separation systems. For the description of concentration units as flotation circuits kinetic models originally developed for chemical reactors, can be used.
Preconcentration by dense medium separation A simple exponential partition function [4] can be used to describe separation by dense medium:
oxlo 9 / ]
(13)
where: re
6 m
isthe partition number calculated at the density d i is the density cut point also referred to as 650 is a partition curve sharpness parameter midpoint of the ith density range.
For an ideal separation m - . ,o and Ep =,. O. To simulate the preconcentration, Ep -probable error- is used as a measure of separation sharpness and kept constant and the parameter 'm' has to be calculated for each density cut-point, 6, examined. The values of Ep depend upon the separation vessel. For a dynamic DMS Ep=O.04 g.m1-1 is an appropriate value. The approximate relationship: m = 0.79.--8
e
(14)
can be used [4]. Use can be made of more complex models for the actual partition function a a and take into account the by-pass of low density particles to the sink and maximum possible recovery of heavies. The preconcentrate yield is: d~
(15)
--
d~ where f(di)'s are values taken from the histogram of the intra-demity distribution of the preexmcentration feed and d i is the range midpoint and eta are the actual partition coefficients. The preconcentrate grade, P, can be calculated as a function of the density:
Assessing profitability of mineral processing
1211
(16) /'(8)
-
RpRE(8 )
where g(di) is the value of the intra-density feed grade distribution function at di. Concentration by a process matching the perfect m i x ~ model The concentrator unit can be modelled as a perfect mixer. An ordinary model resulting from coupling first order kinetics with residence time distribution in single perfect mixers is used. In general terms: T(8) -
F(8)
(17)
(1 +/~x)~ where: F(8) and T(8) are respectively the grades of the feed and the tails of the concentrator, K¢ is the concentration rate constant and • the average residence time, 'n' is the number of mixers in series. ~ may result from equalling the metal recovery in a batch laboratory cell with the recovery in a bank of 'n' cells in series. Since metal recovery in a single reactor modelled as a perfect mixer is : p ffi 1- T/F, Eq. (17) can be expressed as: Pc = Pc-"[1-(1 +Kc~)-~]
(18)
where: Pc: Pc®:
is the recovery of the bank of 'n' PM cells each with a mean retention time ~. is the recovery that is approached asymptotically as ~ . ,
Integrated plant simulation By coupling the model for preconcentration with the kinetic model for flotation the integrated plant reported in Figure 1 was simulated. The number of process dependent constants necessary for such an approach is very low : the value of Ep is adequate to describe the DMS preconcentrator, the kinetic constant/s and the average cell retention time for the flotation of each species are suitable for the concentrator model. Grades and recoveries were calculated for each process stream. Capital and operating costs were calculated for the alternatives with and without preconcentrator.
APPLICATION EXAMPLE In this section the capacity of the system is demonstrated with a case study. The flowsheet of the plant undergoing analysis is shown in Figure 1. It treats a complex low grade polymetallic ore. On the site of the ore body a mine and a processing plant have been operating for considerable time with the same flowsheet. Some years ago, due to low metal prices and low grades, the project became sub-economicel and after a period of state subsidy the operation was shut down. The model is used to re,assess the economic profitability of the project in the light of the new economic scenario. The minerals are chalcopyrite, sphalerite, galena, marmatite and pyrite. Grades: Cuffi0.24%; Znffi3.55%; Pbffi0.61%; Feffi7.8%; S=6%. The preconcentration feed was characterised by its weight/density and grsde/density distributions (Figure 2). The generation of these sets of data requires heavy liquid tests and chemical analyses. Mass balances
1212
J. SEGOV1Aand G. SCHENA
calculated for controlling the efficiency of the flotation plant were used for establishing the rate constants. They were supplemented by batch flotation tests. The sets were taken from historical data collected during the last period of plant operation. Concentrates values were based on average metal quotations for last the quarter 1992. The processing plant treats 500 tonnes per day.
-30,0 -25,0 -20,0 -15,0
=. -10,0 -5,0
~ •-r"
78 Cu
2
~ 2,7
2,4 ,
density
Fig.2 Preconcentration feed characterisation The mining cost indexation system [3] was used to update operating costs calculated with the USBM method [1]. Indices relevant to 1992 were used. The indices reflect the costs of inputs to the mining industry. They include wages, equipment, power, supply and others considered to represent the most important items of capital and operating costs. When a cost is updated it is assumed that the mix of cost component remain unchanged. The total cost for the production of one tonne of run-of-mine ore was taken as 155. Figure 3 shows the operating margin as a function of the preconcemration cut density, the margin for the plant without preconcentration is also reported, The diagram shows that both process alternatives have positive, but low, operating margins and that preconcentration does not increase the profitability of the whole beneficiation system. This is due to the dissemination of the copper values in the ore; also at relatively low cut densities, where high metal recovery is expected in the sink product, regretfully valuable ore disseminated in the gangue is rejected with the float product. It is interesting to note that the old plant included the preconcentrator in its flowsheet. A breakdown of the operating costs is shown in Figures 4a and 4b. The contribution of the single mineral values to the revenues are given in Figure 5a and 5b. It can be concluded that an existing operating plant can be operated with (low) profits and the preconcentrator shut down and that Zn is the only value concentrated with profit. This suggests that the Pb and Cu flotation sections do not contribute to the overall profit. Capital costs were also calculated for both a new plant which includes preconcentration and a plant that does not (Figures 6a and 6b). Total capital cost was $ 4.5 m for the plant with preconcentration and very much the same for the alternative without dense medium separation. The extra capital required for the preconcentrator is partially compensated for by a smaller and cheaper flotation plant.
Assessing profitability of mineral processing
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35 REVENUES
30 COSTS
. . . . . . . . . . . . . . . . .
25
II II o
20
a
om
15
10
Ma~ Margin
OPERATING MARGIN
I
I 2,65
2,70
2,75
2,80
2,85
2,90
Cut density, g/ml
Fig.3 Operating margins, revenues and costs as a function of the preconcentration cut density The decision system was also applied to an hypothetical green field scenario. The following data were considered suitable: 15 years of production, 0.14 discount rate. The analysis shows that for both alternatives the operating margins are not sufficient to recovery the cost of the plants. However the plant without preconcentration, because of the higher operating margin, is the one ranking first according to the PV and IRR criteria. This is an obvious conclusion in the specific application but cases exist in which the most expensive alternative is the most economic in the long term because the higher yearly operating margins repay the extra capital costs. The analysis suggests that the project is not profitable! The IRR so calculated should be used only as a comparative index of profitability among process alternatives. Indeed mine related capital costs were not included in the analysis and the value cannot be compared to internal rates of return above 20~ required for integrated mineral projects.
J. SEGOVIA and G. SCHENA
1214
Operating cost with preconcentration
Mining
Operating cost without preconcentration
Mining
Crashing
54%
Crushing
55%
~.%
3%
DMS 8%
Grindin[ 13%
Grinding 10% Zn, Ca, Pb Filth 2%
Cu Flotation 5%
Pb Flotation 5%
Zn, Pb, Cu Filtl 2%
. . . . . . . . . tation Zn Flotation 7% 7%
~ Flotatior Cu Flotation 5%
Pb flotation 5%
Zn Flotation 8%
9%
Fig.4 Operating cost breakdowns Revenues with preconcentration
Revenues without preconcentration gn
Zn 94%
95%
Cu 5%
Pb 1%
Ou
4,5%
Pb 0,5%
Fig.5 Revenues from metal concentrates Capital cost with preconcentration
Capital cost without preconcentration
Filtration
Filtration
2%
Mill Building
2% ill Building 35%
Flotation
Flotation
37%
38%
dng Grinding 14%
DMS 9%
3%
ing Grinding 21%
Fig.6 Capital cost breakdowns
4%
Assessing profitability of mineral processing
1215
CONCLUSIONS Processing plays a key role in the economics of the overall mineral production system. The mine may deliver at the lowest cost and provide potential for a profitable operation, but the processing plant has the responsibility of making profits, and not losses, out of such a potential. The target may be achieved by reducing costs and increasing revenues. In a properly run plant, the costs must always be kept to their minimum value and efforts have to be made to increase the revenues, maximising recoveries and grades of the concentrates. A rational and consistent procedure for maximising profit should be based on financial principles, and lead to the maximisation of the operating margin, rather than on the sole effort of minimising costs or maximising revenues of an operation. The commercial profitability is only a measure of the difference between the total capital received and at expended in running the plant. This is of interest for a private company precisely because the capital receipts represent the benefits and the capital expenditures constitute the costs. The greater the excess of receipts over expenditures, the more profitable the business. Economic profitability criteria for state owned mines can be more complex. The decision support system presented here can be used as a tool for the economic analysis of the preconcentration. When well tuned with current prices it can be used for off-line optimisation. It can indicate the preconcentrator cut-point which maximises the plant operating margin. It can also indicate that the preconcentrator has to be shut down. In a green field scenario it can be used in the early stages of the feasibility study to check if the preconcentration section should to be included in the integrated beneficiation plant. Once the integrated process has been selected using this system then the technical issues become more important and a more accurate description of the processing units is required, the use of a modular simulator becoming desirable.
NOTATIONS n~ 4~a au
b c
d 8
di E
Ep Eu f F G g
i
I0 IRR M m n
P PV q Peo
partition number actual partition coefficients constants for operating cost function exponent for operating cost function concentrate grade density cut-point density midpoint of the ith density range total operating cost probable error operating cost for processing unit U grade of the run of mine grades of the concentrator feed total revenues preconcentrator feed grade interest rate expressed as a decimal plant capital cost at year 0 internal rate of return concentration rate constant operating margin sharpness parameter number of mixers in series preconcentrate grade present worth metal world market quotation metal recovery at
1216
rU
1% Sc Sh T
% V x
X Yu
J. SEGOVIA and G. SCHENA
recovery in the processing unit U yield of processing unit U smelter refining charge freight charge per dry tonne shipped grades of the concentrator tails average residence time treatment charge per tonne of concentrate concentrate value size unit throughput operating cost item
ACKNOWLEDGEMENTS This work was partially supported by the CEC grant BR E 2 CT 92 0301.
REFERENCES °
2. 3. 4. 5.
United Sates Department of the Interior., Bureau of Mines cost estimating system handbook. Part 2. Mineral processing. Information Circular No. 9143. (1987). Ruhmer, W.T., Handbook on the Estimation of Metallurgical Process Cost. Second edition, MINTEK, Special Publication No. 14. (1992). United Sates Department of the Interior., International Mining Cost Indexation System. Information Circular No. 9170. (1987b). Tarjan, G., Application of distribution function to partition curves. Inter. J. Miner. Process., 1: 261-265 (1974). Trawinski, H., The mathematical simulation of Tromp curves. Int. Ceramic Review. 27 (1), 21-24 (1978).