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Optimization of reactor volumes for gold cyanidation
Minerals Engineering 18 (2005) 671–679 This article is also available online at: www.elsevier.com/locate/mineng
Optimization of reactor volumes for gold cyanidation L.R.P. de Andrade Lima *, D. Hodouin Department of Mining, Metallurgy and Materials Engineering, Laval University, Quebec City, Canada G1K 7P4 Received 10 November 2004; accepted 9 December 2004
Abstract The mineral industry has been using cyanidation of aerated slurries to recover gold from ores for more than a century. However, the leaching plant is usually designed as a series of agitated tanks of the same size, without any attempt to find an optimal plant design for improving the circuit efficiency, either by decreasing the cyanide consumption, or increasing the gold recovery, or decreasing the total plant volume. The objective of the study is to test, by simulation, if it would be profitable to use plant designs differing from the usual ones. The focus is put on the selection of the volumes of the tanks in the cascade of leaching reactors. The methodology involves the use of gold dissolution and cyanide consumption kinetic models incorporated into a simulator, and the definition of a performance criterion for the plant optimization. The performance is characterized by a cost function containing a term representing the value of the unleached gold and a term accounting for the cyanide consumption costs. It is shown that, for the same total volume, using a sequence of increasing size reactors improves the performance of the plant. The results are produced for different size of the ore particles and different numbers of tanks in the leaching circuit. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Cyanidation; Gold ores; Leaching; Modelling; Process optimisation; Process synthesis
1. Introduction Leaching of ores by cyanide in aerated alkaline slurries has been the dominant process for gold extraction for more than one century. In order to accelerate the gold recovery, in most of the high-grade ore plants, the cyanidation process occurs continuously in a cascade of large agitated tanks. The reactor volume optimization is a relevant problem that has been studied for many chemical systems; however, hydrometallurgical reactors have received much less attention. This is particularly
* Corresponding author. Present address: Department of Chemical Engineering, M.H. Wong Building, McGill University, 3610 University Street, Montreal, Canada H3A 2B2. Tel.: +1 514 398 5170; fax: +1 514 398 6678. E-mail address: [email protected] (L.R.P. de Andrade Lima).
0892-6875/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2004.12.007
true for the leaching tanks that are of interest in this paper. It is widely accepted that pure gold cyanidation is an electrochemical process, where gold is oxidized and then complexed to the stable ion [Au(CN)2], and oxygen is reduced and hydrogen peroxide decomposed (Habashi, 1987; Yannopoulos, 1991; Marsden and House, 1992). A typical gold ore processing plant is composed of the following sequence of unit operations: ore comminution, size classification, gravity concentration, and slurry dewatering, followed by gold leaching and gold recovery on activated carbon or by zinc precipitation, and finally gold elution, electrolytic extraction, melting and casting. The major reactants in the gold leaching process are cyanide and oxygen, but also sodium hydroxide is used to control pH, and sometimes lead nitrate is used to control cyanide consumption by sulfides. In a conventional cyanidation process, high cyanide concentrations in large tanks are used to improve gold
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Nomenclature Ccn Cl Co Cs Cw Cs1 d J Ml Ms N PrCN PrAu Qcn Ql Qs
cyanide concentration in the liquid (mg/kg) gold concentration in the liquid (mg/kg) oxygen concentration in the liquid (mg/kg) gold concentration in the ore (mg/kg) solid concentration in the pulp (g/g) residual gold concentration in the ore (mg/ kg) average size of the ore particles (lm) cost function ($/h) liquid hold up (kg) ore hold up (kg) number of reactors in the cascade price of cyanide ($/kg) price of gold ($/g) cyanide flow rate added (kg/h) liquid flow rate (kg/h) ore flow rate (kg/h)
leaching rate and gold recovery, but at the same time this practice is responsible for high cyanide consumption and investment (Kondos et al., 1995; de Andrade Lima, 2001; de Andrade Lima and Hodouin, Submitted for publication). A compromise between these two antagonistic effects is required for gold leaching plant performance optimization. Optimal reactor design and optimal operating conditions tuning are attractive techniques for such a process, to improve profitability in a context of strongly competitive markets, tight product specifications and tough environmental regulations (Levenspiel, 1999; Edgar and Himmelblau, 1988; Chitra and Govind, 1985; Biegler et al., 1997). The determination of the minimum volume configuration of a cascade of continuous stirred tank reactors (CSTRs) is a particular problem, in the field reactor optimization, which was first pointed out by Denbigh (1944) and subsequently applied to various chemical systems (Leclerc, 1953; Aris, 1961; Kubota et al., 1961; Sze´pe and Levenspiel, 1964; Wood and Stevens, 1964; Luss, 1965; Crooks, 1966; Floquet et al., 1985; Lopes and Malcata, 1993). The problem of the optimum design of the reactor sizes in a cascade of CSTRs is mathematically defined as follows: 8 min f ðVÞ > > > V > > > < s:t: ð1Þ Vi P0 > > > N P > > > : Vi ¼VT i¼1
where f is an objective function, such as the conversion of a reactant or product, V is the vector of the net vol-
rAu rCN ro r0o Vi VT
dissolution rate of gold (mg/kg h) rate of cyanide consumption (mg/kg h) rate of oxygen consumption (mg/kg h) rate of oxygen feed (mg/kg h) net volume of the ith reactor in the cascade (m3) total net volume of the reactor cascade (m3)
Greek symbols qs ore density (g/cm3) ql liquid density (g/cm3) s average residence time (h) Subscripts 0 first reactor of the cascade i ith reactor of the cascade N last reactor of the cascade
umes of the tanks in the cascade Vi, and VT is the total net volume of the cascade. The minimization problem given by Eq. (1) can be solved using dynamic programming or direct optimization methods, such as the conjugate or the reduced gradient methods (see Bellman, 2003; Edgar and Himmelblau, 1988; Wang and Fan, 1964). Three systematic optimal design studies of the volumes in a cascade of leaching reactors are available. The first one (Henein and Biegler, 1988) minimizes the residence time for a given conversion degree, in a cascade of reactors for leaching reactions that follow a shrinking core kinetic model. In the case of leaching under surface-reaction control, the ideal volumes in the cascade of CSTRs depend on the targeted solid conversion, but always decrease from the first to the last reactor. For a conversion of approximately 99.5%, the ratios Vi/VT in the case of four CSTRs are 0.314, 0.269, 0.226, and 0.187, and for very low conversion the ratios are approximately 0.25. In the case of leaching under pore-diffusion control, the ideal volume ratios also depend on the solid conversion: for approximately 99.5% conversion the ratios Vi/VT for four CSTRs are 0.205, 0.295, 0.285, and 0.215, and for 80% conversion the ratios are 0.13, 0.23, 0.30 and 0.34. The second study (Papangelakis and Demopoulos, 1992; Papangelakis and Luus, 1993) deals with pressure oxidation. The performance index is the conversion multiplied by the ratio of the time for complete conversion to the mean residence time. This index tends to maximize the conversion while minimizing the plant volume, and, when the ore residence time in the reactor is sufficient for complete leaching, it reduces to the ore leaching conversion. The
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
results show that, for autothermal operations, the configuration of the autoclave that increases the reactor performance is that with a large first compartment followed by small ones. The third study (Crundwell, 2001) addresses the bacterial leaching of pyrite where Thiobacillus ferrooxidans is the only bacteria type that promotes the oxidation of the ferrous ions; the performance index is the conversion of pyrite. Using the same total residence time, the results show that the ideal configurations for a cascade of two to five reactors is a large first tank 1.5–2 times larger than the following small size tanks. Despite the economic importance of gold ore cyanidation, systematic studies of the optimal size design of the cascade of reactors are not available, especially due to the lack of reliable kinetic data for ore cyanidation. For a long time, the effort has been focused on the comprehension and quantification of pure gold cyanidation. However, gold ore cyanidation behaves very differently, because the gold grains are not completely liberated from the gangue, the galvanic interactions between the minerals, the effects of the foreigner ions in the solution, and the gold frequently occur in compounds or alloys. Recent studies by Nicol et al. (1984), Hodouin et al. (1990), Crundwell and Godorr (1997), Ling et al. (1996), and especially de Andrade Lima (2001) and de Andrade Lima and Hodouin (Submitted for publication) provided cyanidation kinetic equations that can be used in the optimization of this process.
NaCN 1
673
The objective of this paper is to present an analysis of the volume design of cascade of reactors for gold ore cyanidation. For that purpose, a rate equation for gold leaching and another for cyanide consumption are used to model the steady state gold cyanidation, in conjunction to a cost function based on a metallurgical performance criterion. Initially the effect of the ore size fraction and the number of reactors in the cascade are studied, then the most appropriate reactor volume distribution is analyzed for this system. The primary leaching section of Doyon Mine (Cambior Inc., Canada) is used as a case study to illustrate the optimal design method (see Fig. 1). In this plant, leaching is conducted in a three-tank cascade of reactors, mechanically agitated and with a nominal volume of 412 m3 each. The ore flowrate is about 164.5 t/h, the solid content in the pulp is 48.8%, and the free cyanide concentration in the pulp feeding the leaching section is about 300 mg/L. The initial gold concentration, the ore density and the average size for each particle size fraction are presented in Table 1. The ore distribution in the leaching plant is presented in Fig. 2 and shows that more than 50% of the particles are finer than 30 lm. This paper is organized as follows. Section 2 presents the mathematical model of the gold cyanidation process, Section 3 presents the definition of the cost function, i.e. the plant performance index to be optimized, and Section 4 presents the simulated results of the tank design and the discussion of the effects of the particle size and
NaCN 1
Water 1
NaCN
1
1
Pb(NO3)2
NaCN
CaO
NaCN
To tailings disposal
Ore
1
2
3
O
To carbon--in-leach circuit
2
PRIMARY SEMI-AUTOGENEOUS GRINDING
GRINDING AND CLASSIFICATION
SOLID/LIQUID SEPARATION
PRIMARY LEACHING
Fig. 1. Gold extraction plant flowsheet showing comminution, classification, dewatering and primary leaching stages.
Table 1 Properties of the gold ore size fractions Size fraction
(lm)
210 + 149
149 + 105
105 + 74
74 + 53
53 + 37
37
d Cs0 qs
(lm) (mg/kg) (g/cm3)
177 1.7 2.84
125 2.2 2.79
88 2.3 2.78
63 1.5 2.78
44 1.9 2.80
30 2.2 2.80
Weight percentage, %
674
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679 60
Mass conservation of oxygen in the liquid phase:
50
Qli ðCoi1 Coi Þ þ r0o;i ro;i ¼ 0 Mli
ð7Þ
20
The assumptions of maximum mixedness, or negligible segregation in the reactor, and constant slurry volume hold-up in the tank lead to the following closure equations: 1 Qli ¼ Qsi 1 ð8Þ Cwi
10
Vi Mli ¼
40
30
Qsi Qli
0
20
30
40
50
60 70 80 90 100
200
Average particle diameter, µm
the number of reactors on the performance of the cyanidation process.
2. Gold cyanidation model Gold cyanidation takes place in agitated tanks where the slurry flow behavior exhibits some non-idealities (de Andrade Lima, 2001; de Andrade Lima and Hodouin, in press). In this study, without less of generality, the reactors are assumed as ideal CSTRs and the total cascade volume is assumed as the nominal volume of the three reactors of the actual cascade. The steady-state model of the leaching of gold ore particles, assumed to be mono-size, consists of the following material balances in the ith CSTR of a cascade: Conservation of the mass of the solid phase: Qsi ¼ Qsi1
ð2Þ
Conservation of the mass of the liquid phase: Qli ¼ Qli1
ð3Þ
Mass conservation of gold in the solid phase: Qsi ðCsi1 Csi Þ rAu;i ¼ 0 Msi
ð4Þ
ð5Þ
ð6Þ
ð10Þ
þ qs1
where Qs is the ore flow rate, Ql the liquid flow rate, Cw the weight concentration of solids in the pulp, Ml the liquid hold-up, V the net volume of the tank, qs the ore density, ql the liquid density, Ms the ore hold-up, Cs the ore gold concentration, rAu the gold dissolution rate, Cl the liquid phase gold concentration, Ccn the liquid phase cyanide concentration, Qcn the cyanide addition flow rate, rCN the rate of cyanide consumption, Co the liquid phase oxygen concentration, ro the oxygen consumption rate, and r0o the oxygen feed rate. Assuming that the segregation in the reactor is negligible, the solid particles, the liquid and the pulp have the same average residence time (s) given by: Vi Mli Msi ¼ ¼ Qli Qli Qsi þ ql qs
si ¼ Qsi
ð11Þ
The dissolution of gold from ores by cyanide is a heterogeneous reaction where cyanide, oxygen and gold play the major roles. Despite the fact that this three-phase reaction may have a complex path for both reactants and products, the use of the general pseudo-homogeneous assumption and a lumped kinetic model is justifiable in the context of industrial leaching, since the ore particle size is very small (see Fig. 2). Gold ore leaching and cyanide consumption kinetics can be described by the following equation (de Andrade Lima, 2001; de Andrade Lima and Hodouin, Submitted for publication): rAu ¼ ð1:13 103 4:37 1011 d 2:13
Mass conservation of cyanide in the liquid phase: Qli Qcni ðCcni1 Ccni Þ þ rCN;i ¼ 0 Mli Mli
1 ql
ð9Þ
þ ql1
Cs1 ðdÞÞ
Mass conservation of gold in the liquid phase: Qli Msi ðCli1 Cli Þ þ rAu;i ¼ 0 Mli Mli
Vi Msi ¼ Qli Qsi
Fig. 2. Ore particle size distribution at the entrance of the primary leaching tank.
1 qs
Ccn0:961 Co0:228
ÞðCsðdÞ
ðmg=kg hÞ
ð12Þ
rCN ¼
1:69 108 Ccn3:71 0:547 6:40 d
2:93
ðmg=kg hÞ
¼ 0:357½1 1:49 expð1:76 102 dÞ Cs1 ðdÞ
ð13Þ ðmg=kgÞ ð14Þ
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
where d is the average diameter of the ore particles, and Cs1 the residual gold concentration in the solid phase. The non-linear system of equations given by Eqs. (2)– (14) for each tank of the cascade of N tanks is simultaneously solved using the classical NewtonÕs method, and leads to the values of the concentrations of free cyanide, gold and oxygen in the solution, and to the ore gold content at the outlet of each leaching tank. This model is used together with the conjugate directions optimization method (see Edgar and Himmelblau, 1988) to find the pulp residence time in the cascade of leaching tanks that minimizes a cost function.
675
tios, as functions of the ore particle size, are presented for a three-tank cascade. Finally, the effect of increasing the number of reactors on the optimal volume distribution and the cost savings is discussed. The objective of the first simulation test is to characterize the variation of the gold loss and cyanide consumption as a function of the number of equally sized tanks in a cascade of constant total volume. The total volume of the cascade (VT) is assumed to be equal to the nominal one of the three-tank cascade of the Doyon Mine (1236 m3), and the ore is assumed to be mono-size 1900
3. Cost function
1600
1500
1300
ð15Þ
where Ccn0 is the cyanide concentration at the first tank entrance (since it is assumed that the cyanide might have been added in the grinding stage or in the first tank), Ql the liquid flow rate, PrCN the price of the free cyanide, Qs the ore flow rate, CsN the ore gold concentration at the last tank exit, and PrAu the gold price. In the following simulations the cost function (J) is expressed in US dollars per time unit, and the reference values for the purchase prices of cyanide and gold are 1.35 $/kg and 10 $/g respectively. When the amount of cyanide added to the circuit increases, the plant operating cost increases, but the gold recovery increases. On the other hand, if the amount of cyanide added to the circuit is insufficient, the gold loss rises but the cost of processing diminishes. There is, consequently, an equilibrium operating regime, well expressed in the criterion, which is a function of the design of the cascade of reactors, i.e., their number and sizes.
1700
1400
1
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade 54
52
Cost due to cyanide consumption, $/h
J ¼ QlðCcn0 CcnN ÞPrCN þ QsCsN PrAu
Cost due to gold loss, $/h
1800
An objective function (see f(V) in Eq. (1)), based on a performance index of the plant, is required for optimizing the reactor volumes of the gold leaching cascade. As previously mentioned, the gold recovery increases with the concentration of free cyanide; however, the cyanide consumption increases with the free cyanide concentration (see Eqs. (12) and (13)). These effects are antagonistic and indicate that a compromise between them can be searched for the optimization of the plant design. A suitable objective function should account for the economic aspect of the process, including the cost of the cyanide and a penalty for the loss of non-dissolved gold, as follows:
50
48
46
44
42 1
2
3
4
5
6
7
8
4. Results and discussion
(b)
The effect of increasing the number of reactors in the cascade of cyanidation tanks on the cost function is first discussed in this section. Then the optimum volume ra-
Fig. 3. Values of the two terms of the cost function of Eq. (15) as a function of the number of reactors in a cascade of equally sized reactors, for the ore size fraction 37 lm, at constant total cascade volume.
Number of reactors in the cascade
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
around an average diameter of 30 lm (see Table 1). Fig. 3a shows the effect of the number of tanks on the gold loss (second term in Eq. (15)). Fig. 3b shows the corresponding cost due to cyanide consumption (first term in Eq. (15)). The use of a cascade of small reactors reduces the gold losses, due to a more effective gold dissolution, but the cyanide consumption increases with the number of reactors in the cascade. The values of the cyanide cost lie between 0.2 and 4% of the value of the lost gold. Although the marginal cyanidation cost is small, compared to the lost gold value, the fact that the cyanide cost minimization requires a large tank, while maximization of gold recovery requires a series of small tanks, will necessarily be reflected in the subsequent study of optimal design. The next simulation test aims at characterizing the optimal size distribution of the tanks in a constant total volume cascade of reactors. Fig. 4 shows the volume ratios that minimize the criterion of Eq. (15), for various average particle sizes of the ore to be leached, but for a fixed number of reactors of three. The optimal volume ratios are dependent upon the ore particle size, but the ideal values of V2/V1 and V3/V1 are approximately 1.25 and 1.5 respectively. This cascade of reactors of increasing volumes is in agreement with results obtained for other processes exhibiting second order kinetics, since the residence time must increase in the last tanks to allow a complete conversion of the reactants. For instance, Wood and Stevens (1964) studied a three-reactor cascade, where a second order irreversible reaction with rate constant of a thousand times faster than that of gold leaching takes place. Using a cost function given by the concentration of one of the reactants at the last tank exit, they showed that, for a conversion of 95%, the ideal values of the ratios V2/V1 and V3/V1 were 1.4 and 1.9 respectively. Despite the fact that the reaction
order for gold is approximately two, in the present case, the cost due to the cyanide consumption has a non-negligible effect on the total cost function (see Fig. 3) and this component of the criterion (see Eq. (15)) causes the reduction of the optimal volume ratios. The same simulation tests for determining the optimal size distribution of the tanks at constant overall volume are performed for a varying number of reactors in the cascade plant (from 1 to 10). Fig. 5a, Fig. 6a, and Fig. 7a shows the optimal tank volume distribution, for various ore size fractions (149/+105, 53/+37 and 37 lm (see Table 1)). All the optimal volume 1250 V1
1125
V2 V3
1000
V4
Volume of the reactors, m 3
676
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
375
250
125
0 1
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade 35000
30000
1.75 V2/V1
25000
Saving cost, $/year
Optimal volume ratio
V3/V1
1.50
20000
15000
10000
1.25 5000
0 1
1.00 20
30
40
50
60 70 80 90 100
20 0
Average particle diameter, µm Fig. 4. Optimum volume ratios (V2/V1 and V3/V1) as a function of the average particle size for a three-tank cascade.
(b)
2
3
4
5
6
7
8
Number of reactors in the cascade
Fig. 5. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade, for the ore size fraction 149 + 105 lm.
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
677
1250
1250 V1
1125
V1
1125
V2
V2 V3
1000
V3
1000
V4
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
Volume of the reactors, m 3
Volume of the reactors, m 3
V4
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
375
375
250
250
125
125 0
0
1
1
2
(a)
3
4
5
6
7
8
9
10
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade
Number of reactors in the cascade 18000
42000 15000
Saving cost, $/year
Saving cost, $/year
35000
28000
21000
12000
9000
6000
14000 3000
7000 0 1
0
(b) 1
(b)
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
Number of reactors in the cascade
10
Number of reactors in the cascade
Fig. 6. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade for the ore size fraction 53 + 37 lm.
distributions exhibit the same patterns for the various particle sizes. Almost all ideal configurations have a distribution that increases from the first to the last reactor. For the same number of reactors in the cascade the ideal distribution depends on the size fraction studied, especially due the fact that, in addition to the kinetics effect of the size fraction given in Eqs. (12)–(14), the gold content and the ore density change from a size fraction to another (see Table 1). The finer size fraction (see Fig. 7a) presents a slightly different pattern form the other
Fig. 7. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade for the ore size fraction 37 lm.
size fractions. When the number of reactors in the cascade increases, the ideal volume of the first reactor decreases, but above N = 5 this value starts increasing again. The same happens with the volume of the second reactor above N = 9. This effect occurs because, for this size fraction, the gold dissolution is very fast and the cyanide consumption is strong. As a result, to reduce the cyanide consumption the ideal configuration corresponds to only one large reactor, but to reduce the gold losses the ideal configuration requires a volume distribution that increases from the first to the last reactor.
678
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Thus, for a large number of reactors, the ideal cascade needs a large reactor followed by a cascade of tanks of increasing volumes from the first to the last reactor. Figs. 5b, 6b and 7b give the cost function reduction of the optimal configuration in comparison to the cost function of an equally sized cascade of reactors, as a function of the number of reactors. These results show that the plant performance improvement in comparison to equally sized reactors increases up to four reactors in the cascade. After this point, the saved cost starts decreasing, which is indicating that, for a large number of reactors, the optimal volumes are not very different from a cascade of equal size reactors (see dashed line in Fig. 5a, Fig. 6a, and Fig. 7a), because, for a large number of reactors, both the optimal or the equal size cascade behave close to a plug flow reactor. For the finer size fraction (Fig. 7) the maximum value of the saved cost is modest in comparison with the larger particles, because the fast gold dissolution kinetics promotes a quick recovery of gold either in the optimal or equal size reactor cascades.
5. Conclusions The objective of the paper was to determine whether the usual practice of using equal size reactors in series for gold ore cyanidation is efficient or could be improved. A steady-state simulator of a leaching plant composed of a cascade of tanks was used to calculate an economic loss function. Simulated results, for various particle sizes and numbers of reactors, show that there is an optimal reactor volume distribution for the gold leaching cyanidation circuit, which makes a trade off between the gold recovery and the reagent cost. The main conclusion is that for most of the cases the series of cyanidation tanks must be of increasing volumes from the first one to the last one.
Acknowledgement This research was supported by the Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq, Brazil), Federal University of Bahia (UFBa, Brazil), and the Ministry of Education of Quebec (Canada). The support of Doyon Mine (Cambior, Inc.) during the experiments is gratefully acknowledged.
References Aris, R., 1961. The Optimal Design of Chemical Reactors. Academic Press, New York. Bellman, R., 2003. Dynamic Programming. Dover Publications, New York.
Biegler, L.T., Westerberg, A.W., Grossmann, I.E., 1997. Systematic Methods for Chemical Process Design. Prentice Hill, NJ. Chitra, S.P., Govind, R., 1985. Synthesis of optimal serial reactor structures for homogeneous reactions. AIChE Journal 31, 177–184. Crooks, W.M., 1966. DenbighÕs 2-tank CSTR system. British Chemical Engineering 2, 710–712. Crundwell, F.K., Godorr, S.A., 1997. A mathematical model of the leaching of gold in cyanide solutions. Hydrometallurgy 44 (1–2), 147–162. Crundwell, F.K., 2001. Modeling, simulation, and optimization of bacterial leaching reactors. Biotechnology and Bioengineering 71 (4), 255–265. de Andrade Lima, L.R.P., 2001. Modeling, control, and optimization applied to the gold hydrometallurgy, Ph.D. Thesis, Laval University, (in French). de Andrade Lima, L.R.P., Hodouin, D., submitted for publication. A lumped kinetic model for gold ore cyanidation, Hydrometallurgy. de Andrade Lima, L.R.P., Hodouin, D., in press. Residence time distribution of an industrial mechanically agitated cyanidation tank, Minerals Engineering, doi:10.1016/j.mineng.2004.10.006. Denbigh, K.G., 1944. Velocity and yield in continuous reaction systems. Transaction of Faraday Society 40, 352–373. Edgar, T., Himmelblau, D., 1988. Optimization of Chemical Process. McGraw-Hill. Floquet, P., Pibouleau, L., Domenech, S., 1985. Proce´dures dÕoptimisation de cascads de re´acteurs avec ou sans recyclage. The Chemical Engineering Journal 30, 11–21. Habashi, F., 1987. One hundred years of cyanidation. CIM Bulletin 80, 108–114. Henein, H., Biegler, L.T., 1988. Optimization of reactor volumes for topochemical reactions. Transaction of the Institute of Mining and Metallurgy C 97, C215–C223. Hodouin, D., Bissonnette, B., Kane, M., 1990. An instrumented laboratory cell for gold cyanidation modelling. In: Proceedings of the 22th Annual Meeting of the Canadian Mineral Processors, Ed. CIM, pp. 562–574. Kondos, P.D., Descheˆnes, G., Morrison, R.M., 1995. Process optimization studies in gold cyanidation. Hydrometallurgy 39, 235–250. Kubota, H., Namkoong, S., Akehata, T., Shindo, M., 1961. Optimum process conditions for a completely Mixed multistage reactor. Canadian Journal of Chemical Engineering 39, 64–66. Leclerc, V.R., 1953. Le re´acteur e´tage´-outile fondamental de ge´nie chimique. Chemical Engineering Science 2, 213–219. Levenspiel, O., 1999. Chemical Reaction Engineering, third ed. John Wiley & Sons, NY. Ling, P., Papangelakis, V.G., Argyropoulos, S.A., Kondos, P.D., 1996. An improved rate equation for cyanidation of a gold ore. Canadian Metallurgical Quarterly 35 (3), 225–234. Lopes, T.I., Malcata, F.X, 1993. Optimal design of a series of CSTRÕs for biochemical reactions in the presence of enzyme desactivation. Journal of Chemical Engineering of Japan 26 (1), 94–98. Luss, D., 1965. Optimum volume ratios for minimum residence time in stirred-tank reactor sequences. Chemical Engineering Science 20, 171. Marsden, J., House, I., 1992. The Chemistry of Gold Extraction. Ellis Horwood. Nicol, M.J., Fleming, C.A., Cromberge, G., 1984. The adsorption of gold cyanide onto activated carbon. II: Applications of the kinetic model to multistage absorption circuits. Journal of the South African Institute of Mining and Metallurgy 84, 50–54. Papangelakis, V.G., Demopoulos, G.P., 1992. On the attainment of stable autothermal operation in continuous pressure leaching reactors. Hydrometallurgy 29, 297–318. Papangelakis, V.G., Luus, R., 1993. Reactor optimization in the pressure oxidation process. In: Papangelakis, V.G., Demopoulos, G.P., (Eds.) Proceedings of the Modeling, Simulation & Control of Hydrometallurgical Processes, CIM, pp. 159–171.
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679 Sze´pe, S., Levenspiel, O., 1964. Optimization of backmix reactors in series for a single reaction. Industrial & Engineering Chemistry Process Design and Development 3, 214–217. Wang, C.S., Fan, L.-T., 1964. Optimization of some multistage chemical processes. Industrial & Engineering Chemistry Fundamentals 3, 38–42.
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Wood, R.K., Stevens, W.F., 1964. Optimum volume ratios for minimum residence time in stirred-tank reactor sequences. Chemical Engineering Science 19, 426–428. Yannopoulos, J.C., 1991. The Extractive Metallurgy of Gold. Van Nostrand Reinhold.
Optimization of reactor volumes for gold cyanidation L.R.P. de Andrade Lima *, D. Hodouin Department of Mining, Metallurgy and Materials Engineering, Laval University, Quebec City, Canada G1K 7P4 Received 10 November 2004; accepted 9 December 2004
Abstract The mineral industry has been using cyanidation of aerated slurries to recover gold from ores for more than a century. However, the leaching plant is usually designed as a series of agitated tanks of the same size, without any attempt to find an optimal plant design for improving the circuit efficiency, either by decreasing the cyanide consumption, or increasing the gold recovery, or decreasing the total plant volume. The objective of the study is to test, by simulation, if it would be profitable to use plant designs differing from the usual ones. The focus is put on the selection of the volumes of the tanks in the cascade of leaching reactors. The methodology involves the use of gold dissolution and cyanide consumption kinetic models incorporated into a simulator, and the definition of a performance criterion for the plant optimization. The performance is characterized by a cost function containing a term representing the value of the unleached gold and a term accounting for the cyanide consumption costs. It is shown that, for the same total volume, using a sequence of increasing size reactors improves the performance of the plant. The results are produced for different size of the ore particles and different numbers of tanks in the leaching circuit. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Cyanidation; Gold ores; Leaching; Modelling; Process optimisation; Process synthesis
1. Introduction Leaching of ores by cyanide in aerated alkaline slurries has been the dominant process for gold extraction for more than one century. In order to accelerate the gold recovery, in most of the high-grade ore plants, the cyanidation process occurs continuously in a cascade of large agitated tanks. The reactor volume optimization is a relevant problem that has been studied for many chemical systems; however, hydrometallurgical reactors have received much less attention. This is particularly
* Corresponding author. Present address: Department of Chemical Engineering, M.H. Wong Building, McGill University, 3610 University Street, Montreal, Canada H3A 2B2. Tel.: +1 514 398 5170; fax: +1 514 398 6678. E-mail address: [email protected] (L.R.P. de Andrade Lima).
0892-6875/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2004.12.007
true for the leaching tanks that are of interest in this paper. It is widely accepted that pure gold cyanidation is an electrochemical process, where gold is oxidized and then complexed to the stable ion [Au(CN)2], and oxygen is reduced and hydrogen peroxide decomposed (Habashi, 1987; Yannopoulos, 1991; Marsden and House, 1992). A typical gold ore processing plant is composed of the following sequence of unit operations: ore comminution, size classification, gravity concentration, and slurry dewatering, followed by gold leaching and gold recovery on activated carbon or by zinc precipitation, and finally gold elution, electrolytic extraction, melting and casting. The major reactants in the gold leaching process are cyanide and oxygen, but also sodium hydroxide is used to control pH, and sometimes lead nitrate is used to control cyanide consumption by sulfides. In a conventional cyanidation process, high cyanide concentrations in large tanks are used to improve gold
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Nomenclature Ccn Cl Co Cs Cw Cs1 d J Ml Ms N PrCN PrAu Qcn Ql Qs
cyanide concentration in the liquid (mg/kg) gold concentration in the liquid (mg/kg) oxygen concentration in the liquid (mg/kg) gold concentration in the ore (mg/kg) solid concentration in the pulp (g/g) residual gold concentration in the ore (mg/ kg) average size of the ore particles (lm) cost function ($/h) liquid hold up (kg) ore hold up (kg) number of reactors in the cascade price of cyanide ($/kg) price of gold ($/g) cyanide flow rate added (kg/h) liquid flow rate (kg/h) ore flow rate (kg/h)
leaching rate and gold recovery, but at the same time this practice is responsible for high cyanide consumption and investment (Kondos et al., 1995; de Andrade Lima, 2001; de Andrade Lima and Hodouin, Submitted for publication). A compromise between these two antagonistic effects is required for gold leaching plant performance optimization. Optimal reactor design and optimal operating conditions tuning are attractive techniques for such a process, to improve profitability in a context of strongly competitive markets, tight product specifications and tough environmental regulations (Levenspiel, 1999; Edgar and Himmelblau, 1988; Chitra and Govind, 1985; Biegler et al., 1997). The determination of the minimum volume configuration of a cascade of continuous stirred tank reactors (CSTRs) is a particular problem, in the field reactor optimization, which was first pointed out by Denbigh (1944) and subsequently applied to various chemical systems (Leclerc, 1953; Aris, 1961; Kubota et al., 1961; Sze´pe and Levenspiel, 1964; Wood and Stevens, 1964; Luss, 1965; Crooks, 1966; Floquet et al., 1985; Lopes and Malcata, 1993). The problem of the optimum design of the reactor sizes in a cascade of CSTRs is mathematically defined as follows: 8 min f ðVÞ > > > V > > > < s:t: ð1Þ Vi P0 > > > N P > > > : Vi ¼VT i¼1
where f is an objective function, such as the conversion of a reactant or product, V is the vector of the net vol-
rAu rCN ro r0o Vi VT
dissolution rate of gold (mg/kg h) rate of cyanide consumption (mg/kg h) rate of oxygen consumption (mg/kg h) rate of oxygen feed (mg/kg h) net volume of the ith reactor in the cascade (m3) total net volume of the reactor cascade (m3)
Greek symbols qs ore density (g/cm3) ql liquid density (g/cm3) s average residence time (h) Subscripts 0 first reactor of the cascade i ith reactor of the cascade N last reactor of the cascade
umes of the tanks in the cascade Vi, and VT is the total net volume of the cascade. The minimization problem given by Eq. (1) can be solved using dynamic programming or direct optimization methods, such as the conjugate or the reduced gradient methods (see Bellman, 2003; Edgar and Himmelblau, 1988; Wang and Fan, 1964). Three systematic optimal design studies of the volumes in a cascade of leaching reactors are available. The first one (Henein and Biegler, 1988) minimizes the residence time for a given conversion degree, in a cascade of reactors for leaching reactions that follow a shrinking core kinetic model. In the case of leaching under surface-reaction control, the ideal volumes in the cascade of CSTRs depend on the targeted solid conversion, but always decrease from the first to the last reactor. For a conversion of approximately 99.5%, the ratios Vi/VT in the case of four CSTRs are 0.314, 0.269, 0.226, and 0.187, and for very low conversion the ratios are approximately 0.25. In the case of leaching under pore-diffusion control, the ideal volume ratios also depend on the solid conversion: for approximately 99.5% conversion the ratios Vi/VT for four CSTRs are 0.205, 0.295, 0.285, and 0.215, and for 80% conversion the ratios are 0.13, 0.23, 0.30 and 0.34. The second study (Papangelakis and Demopoulos, 1992; Papangelakis and Luus, 1993) deals with pressure oxidation. The performance index is the conversion multiplied by the ratio of the time for complete conversion to the mean residence time. This index tends to maximize the conversion while minimizing the plant volume, and, when the ore residence time in the reactor is sufficient for complete leaching, it reduces to the ore leaching conversion. The
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
results show that, for autothermal operations, the configuration of the autoclave that increases the reactor performance is that with a large first compartment followed by small ones. The third study (Crundwell, 2001) addresses the bacterial leaching of pyrite where Thiobacillus ferrooxidans is the only bacteria type that promotes the oxidation of the ferrous ions; the performance index is the conversion of pyrite. Using the same total residence time, the results show that the ideal configurations for a cascade of two to five reactors is a large first tank 1.5–2 times larger than the following small size tanks. Despite the economic importance of gold ore cyanidation, systematic studies of the optimal size design of the cascade of reactors are not available, especially due to the lack of reliable kinetic data for ore cyanidation. For a long time, the effort has been focused on the comprehension and quantification of pure gold cyanidation. However, gold ore cyanidation behaves very differently, because the gold grains are not completely liberated from the gangue, the galvanic interactions between the minerals, the effects of the foreigner ions in the solution, and the gold frequently occur in compounds or alloys. Recent studies by Nicol et al. (1984), Hodouin et al. (1990), Crundwell and Godorr (1997), Ling et al. (1996), and especially de Andrade Lima (2001) and de Andrade Lima and Hodouin (Submitted for publication) provided cyanidation kinetic equations that can be used in the optimization of this process.
NaCN 1
673
The objective of this paper is to present an analysis of the volume design of cascade of reactors for gold ore cyanidation. For that purpose, a rate equation for gold leaching and another for cyanide consumption are used to model the steady state gold cyanidation, in conjunction to a cost function based on a metallurgical performance criterion. Initially the effect of the ore size fraction and the number of reactors in the cascade are studied, then the most appropriate reactor volume distribution is analyzed for this system. The primary leaching section of Doyon Mine (Cambior Inc., Canada) is used as a case study to illustrate the optimal design method (see Fig. 1). In this plant, leaching is conducted in a three-tank cascade of reactors, mechanically agitated and with a nominal volume of 412 m3 each. The ore flowrate is about 164.5 t/h, the solid content in the pulp is 48.8%, and the free cyanide concentration in the pulp feeding the leaching section is about 300 mg/L. The initial gold concentration, the ore density and the average size for each particle size fraction are presented in Table 1. The ore distribution in the leaching plant is presented in Fig. 2 and shows that more than 50% of the particles are finer than 30 lm. This paper is organized as follows. Section 2 presents the mathematical model of the gold cyanidation process, Section 3 presents the definition of the cost function, i.e. the plant performance index to be optimized, and Section 4 presents the simulated results of the tank design and the discussion of the effects of the particle size and
NaCN 1
Water 1
NaCN
1
1
Pb(NO3)2
NaCN
CaO
NaCN
To tailings disposal
Ore
1
2
3
O
To carbon--in-leach circuit
2
PRIMARY SEMI-AUTOGENEOUS GRINDING
GRINDING AND CLASSIFICATION
SOLID/LIQUID SEPARATION
PRIMARY LEACHING
Fig. 1. Gold extraction plant flowsheet showing comminution, classification, dewatering and primary leaching stages.
Table 1 Properties of the gold ore size fractions Size fraction
(lm)
210 + 149
149 + 105
105 + 74
74 + 53
53 + 37
37
d Cs0 qs
(lm) (mg/kg) (g/cm3)
177 1.7 2.84
125 2.2 2.79
88 2.3 2.78
63 1.5 2.78
44 1.9 2.80
30 2.2 2.80
Weight percentage, %
674
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679 60
Mass conservation of oxygen in the liquid phase:
50
Qli ðCoi1 Coi Þ þ r0o;i ro;i ¼ 0 Mli
ð7Þ
20
The assumptions of maximum mixedness, or negligible segregation in the reactor, and constant slurry volume hold-up in the tank lead to the following closure equations: 1 Qli ¼ Qsi 1 ð8Þ Cwi
10
Vi Mli ¼
40
30
Qsi Qli
0
20
30
40
50
60 70 80 90 100
200
Average particle diameter, µm
the number of reactors on the performance of the cyanidation process.
2. Gold cyanidation model Gold cyanidation takes place in agitated tanks where the slurry flow behavior exhibits some non-idealities (de Andrade Lima, 2001; de Andrade Lima and Hodouin, in press). In this study, without less of generality, the reactors are assumed as ideal CSTRs and the total cascade volume is assumed as the nominal volume of the three reactors of the actual cascade. The steady-state model of the leaching of gold ore particles, assumed to be mono-size, consists of the following material balances in the ith CSTR of a cascade: Conservation of the mass of the solid phase: Qsi ¼ Qsi1
ð2Þ
Conservation of the mass of the liquid phase: Qli ¼ Qli1
ð3Þ
Mass conservation of gold in the solid phase: Qsi ðCsi1 Csi Þ rAu;i ¼ 0 Msi
ð4Þ
ð5Þ
ð6Þ
ð10Þ
þ qs1
where Qs is the ore flow rate, Ql the liquid flow rate, Cw the weight concentration of solids in the pulp, Ml the liquid hold-up, V the net volume of the tank, qs the ore density, ql the liquid density, Ms the ore hold-up, Cs the ore gold concentration, rAu the gold dissolution rate, Cl the liquid phase gold concentration, Ccn the liquid phase cyanide concentration, Qcn the cyanide addition flow rate, rCN the rate of cyanide consumption, Co the liquid phase oxygen concentration, ro the oxygen consumption rate, and r0o the oxygen feed rate. Assuming that the segregation in the reactor is negligible, the solid particles, the liquid and the pulp have the same average residence time (s) given by: Vi Mli Msi ¼ ¼ Qli Qli Qsi þ ql qs
si ¼ Qsi
ð11Þ
The dissolution of gold from ores by cyanide is a heterogeneous reaction where cyanide, oxygen and gold play the major roles. Despite the fact that this three-phase reaction may have a complex path for both reactants and products, the use of the general pseudo-homogeneous assumption and a lumped kinetic model is justifiable in the context of industrial leaching, since the ore particle size is very small (see Fig. 2). Gold ore leaching and cyanide consumption kinetics can be described by the following equation (de Andrade Lima, 2001; de Andrade Lima and Hodouin, Submitted for publication): rAu ¼ ð1:13 103 4:37 1011 d 2:13
Mass conservation of cyanide in the liquid phase: Qli Qcni ðCcni1 Ccni Þ þ rCN;i ¼ 0 Mli Mli
1 ql
ð9Þ
þ ql1
Cs1 ðdÞÞ
Mass conservation of gold in the liquid phase: Qli Msi ðCli1 Cli Þ þ rAu;i ¼ 0 Mli Mli
Vi Msi ¼ Qli Qsi
Fig. 2. Ore particle size distribution at the entrance of the primary leaching tank.
1 qs
Ccn0:961 Co0:228
ÞðCsðdÞ
ðmg=kg hÞ
ð12Þ
rCN ¼
1:69 108 Ccn3:71 0:547 6:40 d
2:93
ðmg=kg hÞ
¼ 0:357½1 1:49 expð1:76 102 dÞ Cs1 ðdÞ
ð13Þ ðmg=kgÞ ð14Þ
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
where d is the average diameter of the ore particles, and Cs1 the residual gold concentration in the solid phase. The non-linear system of equations given by Eqs. (2)– (14) for each tank of the cascade of N tanks is simultaneously solved using the classical NewtonÕs method, and leads to the values of the concentrations of free cyanide, gold and oxygen in the solution, and to the ore gold content at the outlet of each leaching tank. This model is used together with the conjugate directions optimization method (see Edgar and Himmelblau, 1988) to find the pulp residence time in the cascade of leaching tanks that minimizes a cost function.
675
tios, as functions of the ore particle size, are presented for a three-tank cascade. Finally, the effect of increasing the number of reactors on the optimal volume distribution and the cost savings is discussed. The objective of the first simulation test is to characterize the variation of the gold loss and cyanide consumption as a function of the number of equally sized tanks in a cascade of constant total volume. The total volume of the cascade (VT) is assumed to be equal to the nominal one of the three-tank cascade of the Doyon Mine (1236 m3), and the ore is assumed to be mono-size 1900
3. Cost function
1600
1500
1300
ð15Þ
where Ccn0 is the cyanide concentration at the first tank entrance (since it is assumed that the cyanide might have been added in the grinding stage or in the first tank), Ql the liquid flow rate, PrCN the price of the free cyanide, Qs the ore flow rate, CsN the ore gold concentration at the last tank exit, and PrAu the gold price. In the following simulations the cost function (J) is expressed in US dollars per time unit, and the reference values for the purchase prices of cyanide and gold are 1.35 $/kg and 10 $/g respectively. When the amount of cyanide added to the circuit increases, the plant operating cost increases, but the gold recovery increases. On the other hand, if the amount of cyanide added to the circuit is insufficient, the gold loss rises but the cost of processing diminishes. There is, consequently, an equilibrium operating regime, well expressed in the criterion, which is a function of the design of the cascade of reactors, i.e., their number and sizes.
1700
1400
1
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade 54
52
Cost due to cyanide consumption, $/h
J ¼ QlðCcn0 CcnN ÞPrCN þ QsCsN PrAu
Cost due to gold loss, $/h
1800
An objective function (see f(V) in Eq. (1)), based on a performance index of the plant, is required for optimizing the reactor volumes of the gold leaching cascade. As previously mentioned, the gold recovery increases with the concentration of free cyanide; however, the cyanide consumption increases with the free cyanide concentration (see Eqs. (12) and (13)). These effects are antagonistic and indicate that a compromise between them can be searched for the optimization of the plant design. A suitable objective function should account for the economic aspect of the process, including the cost of the cyanide and a penalty for the loss of non-dissolved gold, as follows:
50
48
46
44
42 1
2
3
4
5
6
7
8
4. Results and discussion
(b)
The effect of increasing the number of reactors in the cascade of cyanidation tanks on the cost function is first discussed in this section. Then the optimum volume ra-
Fig. 3. Values of the two terms of the cost function of Eq. (15) as a function of the number of reactors in a cascade of equally sized reactors, for the ore size fraction 37 lm, at constant total cascade volume.
Number of reactors in the cascade
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
around an average diameter of 30 lm (see Table 1). Fig. 3a shows the effect of the number of tanks on the gold loss (second term in Eq. (15)). Fig. 3b shows the corresponding cost due to cyanide consumption (first term in Eq. (15)). The use of a cascade of small reactors reduces the gold losses, due to a more effective gold dissolution, but the cyanide consumption increases with the number of reactors in the cascade. The values of the cyanide cost lie between 0.2 and 4% of the value of the lost gold. Although the marginal cyanidation cost is small, compared to the lost gold value, the fact that the cyanide cost minimization requires a large tank, while maximization of gold recovery requires a series of small tanks, will necessarily be reflected in the subsequent study of optimal design. The next simulation test aims at characterizing the optimal size distribution of the tanks in a constant total volume cascade of reactors. Fig. 4 shows the volume ratios that minimize the criterion of Eq. (15), for various average particle sizes of the ore to be leached, but for a fixed number of reactors of three. The optimal volume ratios are dependent upon the ore particle size, but the ideal values of V2/V1 and V3/V1 are approximately 1.25 and 1.5 respectively. This cascade of reactors of increasing volumes is in agreement with results obtained for other processes exhibiting second order kinetics, since the residence time must increase in the last tanks to allow a complete conversion of the reactants. For instance, Wood and Stevens (1964) studied a three-reactor cascade, where a second order irreversible reaction with rate constant of a thousand times faster than that of gold leaching takes place. Using a cost function given by the concentration of one of the reactants at the last tank exit, they showed that, for a conversion of 95%, the ideal values of the ratios V2/V1 and V3/V1 were 1.4 and 1.9 respectively. Despite the fact that the reaction
order for gold is approximately two, in the present case, the cost due to the cyanide consumption has a non-negligible effect on the total cost function (see Fig. 3) and this component of the criterion (see Eq. (15)) causes the reduction of the optimal volume ratios. The same simulation tests for determining the optimal size distribution of the tanks at constant overall volume are performed for a varying number of reactors in the cascade plant (from 1 to 10). Fig. 5a, Fig. 6a, and Fig. 7a shows the optimal tank volume distribution, for various ore size fractions (149/+105, 53/+37 and 37 lm (see Table 1)). All the optimal volume 1250 V1
1125
V2 V3
1000
V4
Volume of the reactors, m 3
676
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
375
250
125
0 1
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade 35000
30000
1.75 V2/V1
25000
Saving cost, $/year
Optimal volume ratio
V3/V1
1.50
20000
15000
10000
1.25 5000
0 1
1.00 20
30
40
50
60 70 80 90 100
20 0
Average particle diameter, µm Fig. 4. Optimum volume ratios (V2/V1 and V3/V1) as a function of the average particle size for a three-tank cascade.
(b)
2
3
4
5
6
7
8
Number of reactors in the cascade
Fig. 5. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade, for the ore size fraction 149 + 105 lm.
L.R.P. de Andrade Lima, D. Hodouin / Minerals Engineering 18 (2005) 671–679
677
1250
1250 V1
1125
V1
1125
V2
V2 V3
1000
V3
1000
V4
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
Volume of the reactors, m 3
Volume of the reactors, m 3
V4
V5
875
V6 V7
750
V8 V9
625
V10 Equal-sized
500
375
375
250
250
125
125 0
0
1
1
2
(a)
3
4
5
6
7
8
9
10
2
(a)
3
4
5
6
7
8
9
10
9
10
Number of reactors in the cascade
Number of reactors in the cascade 18000
42000 15000
Saving cost, $/year
Saving cost, $/year
35000
28000
21000
12000
9000
6000
14000 3000
7000 0 1
0
(b) 1
(b)
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
Number of reactors in the cascade
10
Number of reactors in the cascade
Fig. 6. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade for the ore size fraction 53 + 37 lm.
distributions exhibit the same patterns for the various particle sizes. Almost all ideal configurations have a distribution that increases from the first to the last reactor. For the same number of reactors in the cascade the ideal distribution depends on the size fraction studied, especially due the fact that, in addition to the kinetics effect of the size fraction given in Eqs. (12)–(14), the gold content and the ore density change from a size fraction to another (see Table 1). The finer size fraction (see Fig. 7a) presents a slightly different pattern form the other
Fig. 7. Optimal reactor volumes in the cascade (a) and cost saving due to the use of the optimal configuration (b) as a function of the number of reactors in the cascade for the ore size fraction 37 lm.
size fractions. When the number of reactors in the cascade increases, the ideal volume of the first reactor decreases, but above N = 5 this value starts increasing again. The same happens with the volume of the second reactor above N = 9. This effect occurs because, for this size fraction, the gold dissolution is very fast and the cyanide consumption is strong. As a result, to reduce the cyanide consumption the ideal configuration corresponds to only one large reactor, but to reduce the gold losses the ideal configuration requires a volume distribution that increases from the first to the last reactor.
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Thus, for a large number of reactors, the ideal cascade needs a large reactor followed by a cascade of tanks of increasing volumes from the first to the last reactor. Figs. 5b, 6b and 7b give the cost function reduction of the optimal configuration in comparison to the cost function of an equally sized cascade of reactors, as a function of the number of reactors. These results show that the plant performance improvement in comparison to equally sized reactors increases up to four reactors in the cascade. After this point, the saved cost starts decreasing, which is indicating that, for a large number of reactors, the optimal volumes are not very different from a cascade of equal size reactors (see dashed line in Fig. 5a, Fig. 6a, and Fig. 7a), because, for a large number of reactors, both the optimal or the equal size cascade behave close to a plug flow reactor. For the finer size fraction (Fig. 7) the maximum value of the saved cost is modest in comparison with the larger particles, because the fast gold dissolution kinetics promotes a quick recovery of gold either in the optimal or equal size reactor cascades.
5. Conclusions The objective of the paper was to determine whether the usual practice of using equal size reactors in series for gold ore cyanidation is efficient or could be improved. A steady-state simulator of a leaching plant composed of a cascade of tanks was used to calculate an economic loss function. Simulated results, for various particle sizes and numbers of reactors, show that there is an optimal reactor volume distribution for the gold leaching cyanidation circuit, which makes a trade off between the gold recovery and the reagent cost. The main conclusion is that for most of the cases the series of cyanidation tanks must be of increasing volumes from the first one to the last one.
Acknowledgement This research was supported by the Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq, Brazil), Federal University of Bahia (UFBa, Brazil), and the Ministry of Education of Quebec (Canada). The support of Doyon Mine (Cambior, Inc.) during the experiments is gratefully acknowledged.
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