Roasting kinetics of high-arsenic copper concentrates: a review

Transcription

1 Roasting kinetics of high-arsenic copper concentrates: a review M. Devia Jacobs, Santiago, Chile I. Wilkomirsky and R. Parra Universidad de Concepción, Concepción, Chile Abstract The roasting process of copper concentrates containing variable quantities of arsenic in a fluidized bed regime was analyzed, considering the technical literature published on the topic in the last quarter century. Although emphasis has been given to the analysis in the fluidized bed regime, other processes have also been considered, under a reducing, neutral or oxidizing atmosphere. The kinetic mechanisms of roasting, as well as the models that have been applied or those likely to be used to explain the kinetics of arsenic removal, are analyzed. Regarding the kinetic mechanisms, those that have been applied to copper concentrates with both high and low arsenic content are included. The roasting kinetic model includes the kinetic data analysis techniques, general models, equations and an estimation of the conversion degree through dynamic, differential and integral methods, as well as particular models for mineralogical components, such as smelter dust and copper concentrates with low and high arsenic content. Minerals & Metallurgical Processing, 2012, Vol. 29, No. 2, pp An official publication of the Society for Mining, Metallurgy and Exploration, Inc. Key words: Arsenical copper concentrates, Fluidized bed roasting, Kinetics, Kinetic mechanisms and models Introduction In the roasting process in a fluidized bed regime under conditions of controlled oxidation, the variables of major relevance for arsenic and antimony removal, without excessive sulfur removal or mineralogical component oxidation, are: solid material particle size, oxygen potential of the fluidizing gas (that fixes the sulfur or SO 2 potentials), temperature and roasting time. This analysis considers the effect of reaction time on the phase transformations produced during roasting (i.e., the study of the kinetics of roasting) at low oxygen potential by copper concentrates with variable arsenic content in a certain range of temperatures. The oxygen potential can be estimated by thermodynamic analysis (p O2 ~ atm) in the temperature range of 600 to 700 C. The analysis describes the roasting kinetic mechanisms and the various kinetic models found in the literature, including (a) general models used in the copper concentrate roasting process, including the data processing techniques of gas-solid kinetics and (b) kinetic-specific models of the roasting of copper concentrates in fluidized beds. Kinetics of the roasting process Lindkvist and Holmström (1983), in order to obtain appropriate conditions for impurity removal, i.e., temperature, reaction time and sulfur potential, performed roasting tests of complex concentrates with high arsenic content in a fluidized bed roaster of special design. The roaster consisted of two beds with facilities for calcine recirculation, air preheating and oxygen enrichment to the fluidizing air. This design permits a better control of the reactions in the bed and reduces the amount of dust to cyclones. Copper concentrates tested ranged from 8% to 28% As, 28% Cu and a minimal Sb content. The calcine produced contained 0.3% As, with an Sb removal of 80% to 90%. Based on the phase diagram for the Cu-Fe-As system at 727 C, it was concluded that the p O2 for the roasting process ranges between to atm, whereas the S O2 potential ranges between 10-1 to atm. Results show that an increase of p O2 leads to the formation of Cu 3 As and Cu 2 O, compounds that can react in solid state to form sintering deposits that remain in the calcine, reducing the arsenic removal. Arsenic removal does not depend on the initial As content of the concentrate. Björkman et al. (1994) performed roasting laboratory tests for arsenic-bearing dusts from the Boliden plant, Sweden. Four types of dusts were tested: (a) roasting furnace electrostatic precipitator (ESP) dust (1.4% As), (b) smelting furnace ESP dust (1.88% As), (c) settling furnace dust (11.5% As) and (d) converter ventilation dust (4.5% As). The tests were performed in a vertical reaction tube reactor at 700 C, controlling the roasting time and the reaction gas flow rate to eliminate the dependency of the mass transfer. Arsenic removal from roasting furnace ESP dust reached 90% in 10 minutes, whereas arsenic removal was 19% for the smelting furnace ESP in 15 minutes. The adjustment of the data for roasting furnace ESP dust was obtained using the (a) pore obstruction model and Paper number MMP Original manuscript submitted August Manuscript accepted for publication November Discussion of this peer-reviewed and approved paper is invited and must be submitted to SME Publications Dept. prior to November 30, Copyright 2012, Society for Mining, Metallurgy, and Exploration, Inc. 121 Vol. 29 No. 2 May 2012

2 (b) power law model. Padilla et al. (1997) performed a thermogravimetric analysis to follow the decomposition and volatilization of As from enargite (Cu 3 AsS 4 ) in nitrogenous and slightly oxidizing atmospheres. Their results show that temperature has the larger effect on As volatilization, which reaches nearly 95% in less than 30 minutes at 650 C in a nitrogenous atmosphere, whereas in a slightly oxidizing atmosphere, the same volatilization was obtained in less than 20 minutes. They found that As volatilizes as sulfide in a nitrogenous atmosphere and as a mixture of sulfide and oxide in a 1% oxygen atmosphere. Fan et al. (1997) in laboratory tests of the roasting of enargite-bearing copper concentrates, concluded that As can be eliminated almost completely by thermal decomposition (99%), in 60 minutes under a neutral atmosphere at 650 C, or in 15 minutes at 700 C. The kinetics of enargite decomposition can be divided into two stages: below 600 C, the control mechanism is the diffusion of the gaseous products through the product layer, which can be represented by a pore obstruction model, whereas at temperatures higher than 600 C, the kinetic controlling step is the chemical reaction, which could be represented by a nucleation and growth of grains model. Padilla et al. (1999) studied the enargite decomposition in an inert atmosphere between 530 and 750 C for different particle sizes. These results indicated that enargite decomposition begins at around 500 C. Two different dependent zones for the decomposition were found: a low-temperature region between 550 and 650 C and a high-temperature region between 650 and 750 C. The kinetics of decomposition were represented by a topochemical reaction model for a spherical particle, with apparent activation energies of 12 kj/mol and kj/mol for the low- and high-temperature regions, respectively. Padilla et al. (2001) also performed laboratory tests in a fixed bed to investigate the enargite thermal decomposition by thermogravimetric analysis in the temperature range of 575 and 700 C. Enargite decomposition proceeded in two consecutive stages through tennantite (Cu 12 As 4 S 13 ) formation as an intermediate compound, both stages following a first order kinetic. Assuming chemical reaction control in both stages, Padilla et al. estimated the activation energies as 125 kj/mol (enargite decomposition) and 236 kj/mol (tennantite decomposition). The final product of enargite decomposition was a mixture of chalcocite (Cu 2 S) and nonstoichiometric copper sulfides (Cu1.8S, Cu1.96S). Kinetic and roasting mechanisms Mechanisms of roasting and mineralogical component formation. For enargite thermal decomposition, Padilla et al. (2001) found possible mechanisms between 575 and 700 C: Covellite (CuS) formation as an intermediate compound, following the reactions 4Cu 3 AsS 4 (s) = 12CuS(s) + As 4 S 4 (g) (1) 12CuS(s) = 6Cu 2 S(s) + 3S 2 (g) (2) According to this mechanism, the first stage accounts for 69% of the weight loss. Formation of tennantite as an intermediate compound: 4Cu 3 AsS 4 (s) = Cu 12 As 4 S a3 (s) + 1.5S 2 (g) (3) Cu 12 As 4 S 13 (s) = 6Cu 2 S(s) + As 4 S 4 (g) + 1.5S 2 (g) (4) In this second mechanism, the first stage represents only 15.5% of the total weight loss with respect to complete decomposition of the enargite to chalcosite (Cu 2 S). The formation of stable intermediate phases could be of importance in elucidating the mechanism and the controlling step of the enargite decomposition rate. The kinetics of enargite decomposition were determined using conventional thermogravimetry under a nitrogenous atmosphere. Results show that the decomposition of enargite to tennantite is very rapid at 700 C. Also, at 650 C, a mixture is formed of nonstoichiometric covellite and chalcosite for very short time. In all X-ray analysis, arsenic was present only in the form of enargite and/or tennantite and not as other sulfides, which suggests that enargite decomposition and arsenic volatilization is a rapid process. Padilla et al. (1999, 2001) concluded that these results were in agreement with the two-stage enargite decomposition model and confirmed the formation of tennantite as an intermediate compound and its further decomposition. On the other hand, since it was not possible to establish which of the arsenic species, As 4 S 4 or As 2 S 3, was formed, they considered As 4 S 4 the thermodynamically stable species within the range of temperatures studied. Taking into account the RX analyses from the reaction products, the following enargite decomposition stages take place. First stage: 4Cu 3 AsS 4 (s) = Cu 12 As 4 S 13 (s) + 1.5S 2 (g) (5) Second stage: Cu 12 As 4 S 13 (s) = 6Cu 2 S 1+x (s) + As 4 S 4 (g) + (1.5-3x)S 2 (g) (6) where x varies between 0 and 0.11 when copper sulfide is the stoichiometric chalcosite (Cu 2 S) or digenite (Cu 2 S1-x), respectively. The addition of these two reactions gives a global reaction mechanism for the enargite decomposition as: 4Cu 3 AsS 4 (s) = 6Cu 2 S 1+x (s) + As 4 S 4 (g) + (3-3x)S 2 (g) (7) Kinetics and mechanisms of the roasting of arsenicbearing concentrates. Lindkvist and Holmström (1983) utilized a partial roasting system for arsenopyrite and enargite in a fluidized bed with two-stage recirculation and concluded that both As and Sb removal were almost complete. They suggest that if roasting is performed in two stages at a temperature near 725 C, results would be better due to the following reasons: The first stage, where most of the As and Sb removal takes place, can be performed at low oxygen potential, which enhances the removal of these impurities. In the second stage, calcine reacts with a gas with low As content, removing additional impurities. This fixes the final sulfur content of the calcine. Björkman et al. (1994) studied As removal from various materials on a laboratory scale at the Boliden plant, concluding that to achieve high As removal the following points are necessary: For a roasting furnace, 90% of the ESP dust can be removed in 10 minutes, while 10% is retained in the calcine as stable arsenates. For a smelting furnace, 19% of the ESP dust can be removed in 15 minutes. Most of the As reacts with wüstite (FeO), forming solid iron arsenate (FeAsO 4 ) as a stable phase. For settling furnace dusts, 40% of the arsenic is removed May 2012 Vol. 29 No

3 in 15 minutes. For converter ventilation dusts, 100% arsenic removal can be obtained in 15 minutes. Roasting kinetic models Research in the field of the kinetics of copper concentrate roasting has used differential thermal analysis (DTA), thermogravimetry (TG), differential thermogravimetry (DTG), X-ray diffraction analysis (RDA), X-ray fluorescence (XRF) and chemical analyses. The validity of these analyses can be verified by means of phase stability diagrams at different temperatures, using available software. Data processing analysis of gas-solid kinetics. Nikolaev et al. (1971) discussed the mathematical form of the compensation effect (log A = a + be), which refers to the changes that can take place in the conditions of a reaction (e.g., vaporization and changes in the partial pressure of a gaseous product) on the non-isothermal kinetics of solid phase reactions, where A is the pre-exponential parameter of the reaction rate constant, k, as defined by the Arrhenius relationship: where E is the activation energy, R the universal gas constant and T the reaction temperature. Next, the analytical expression of the compensation effect takes the following form: Nikolaev et al. (1971) have shown that this effect appears in a certain number of chemical reactions if the values of the temperature, T s, and k of the solid phase are similar. The experimental results confirmed the theoretical analysis. This suggests that the compensation effect can take place in isothermal decomposition of solid substances and catalytic reactions. A general analysis reveals the existence of an interrelation between the changes of the three quantities A, E and ΔT, in the range of temperatures at which the reaction in a solid state proceeds at a measurable rate. A linear relationship in the equation that describes the compensation effect (for dt/ dt = constant) appears when a change in the conditions of the decomposition of a given substance leads to a change in E, but only to a slight change in the T s temperature. The chemical transformation rate in a solid state under non-isothermal conditions could be applied to other process mechanisms, such as interface reaction, nuclei growth and diffusion in the form (10) where X is the conversion and n the reaction order. Combining this last equation with the Arrhenius expression will obtain: (8) (9) (11) The dependence of the conversion rate dx/dt on time can be expressed by a curve with a maximum temperature at T s (X = X s ): (12) where the solid heating rate is q s = (dt/dt)s, in C/s. Replacing Eq. (11) evaluated at X s in Eq. (12), and placing it in the Arrhenius equation, the following will be obtained: Since, (13) (14) This represents the analytical expression of the compensation effect for non-isothermal kinetics. This result permits the analysis of slight changes in the value of T s in non-isothermal kinetic reactions. Vyazovkin and Wright (1998) analyzed the state-of-the-art of thermally stimulated solid reaction kinetics, starting with the first isothermal kinetic analysis, by adjusting the data of reaction models. This method of adjustment does not permit the determination of the representative model of reaction nor the obtaining of definitive conclusions in relation to the reliable mechanism of isothermal kinetics. They showed that an alternative model based on the isoconversional method exists, which for isothermal and nonisothermal kinetics avoids the problems of ambiguous evaluation that reaction models create. This methodology permits the determination of the dependency of the activation energy with the extension of the conversion, and also permits reliable predictions of the reaction rate and enables one to draw conclusions about the reaction mechanism. Baitalow et al. (1999) discussed the application of a nonconventional approach in the formal kinetic analysis of solid state reactions, based on both the isoconversional methods and nonlinear regression analysis, to obtain reliable values of the kinetic parameters for the transition phases between the three polymorphic transformations of calcium carbonate. They compared two different mechanisms using calculated kinetic data. The isoconversional method of Friedman gives values of the activation energy that do not agree with the value calculated using the Flynn-Wall-Ozawa method. In addition, the apparent energy of reaction was dependent on the conversion degree. Vyazovkin and Wright (1999) applied the isoconversional method and an adjusted kinetic model for the isothermal and non-isothermal decomposition data of two chemical substances. They concluded that the approach using the kinetic model data provided an excellent fit for both isothermal and non-isothermal data, while the values derived from isothermal measurements cannot be used for a reasonable prediction of the isothermal kinetic. The isoconversional method provides similar dependencies of the activation energy on the extension of the conversion in isothermal and non-isothermal experiments. Derived dependency from non-isothermal data allowed 123 Vol. 29 No. 2 May 2012

4 Elimination of As, % Time, min Figure 1 Arsenic removal as a function of time and temperatures during enargite-bearing copper concentrate roasting in a fixed bed (Fan, 1997). reliable predictions of the isothermal kinetic. They conclude that the use of the isoconversional method is a trustworthy method to obtain reliable and consistent kinetic information for isothermal and non-isothermal data. Vyazovkin and Wright (2000) proposed a statistical procedure for the estimation of the confidence intervals for the activation energy using an advanced isoconversional method. By thermogravimetric measurements of the ammonium nitrate gasification process at five different heating rates, they proved that the proposed statistical procedure was able to determine the real uncertainty of the activation energy starting from a small number of measurements. The average relative errors resulting in the activation energy were 26%, 21% and 17% for three, four and five estimations of heating rates, respectively. Gao et al. (2001) established an iterative procedure to estimate the activation energy by eliminating the errors involved using ln β versus 1/T and ln (β/t 2 ) versus 1/T conventional isoconversional graphs due to the use of an approximated value of p(x), where β is the heating rate and x = E/RT. Since the p(x) function has no analytical solution, writing p(x) as an approximated expression permits the introduction of the functions H(x) and h(x) to determine the exact p(x) function instead of basing it on approximate values. They concluded that the iterative procedure would not have problems due to how small or large the E/RT values of the reaction were. The modified isoconversional graphs for the iterations are of the form Ln (β/h) versus 1/T and Ln (β/ht 2 ) versus 1/T. Torres-García (2003) analyzed some of the features that characterize the non-isothermal kinetics of heterogeneous reactions in solid state, both in formal and experimental terms. They suggest that these reactions could not be analyzed following a simple law rate similar to the established criteria for homogenous reactions. Also, the complexity of these reactions in many cases can cause both kinetic parameters (activation energy and frequency factor) to make the reaction mechanisms change with the advance of the reaction, a characteristic that gives global or apparent character to the evaluated kinetic parameters. They discussed the limited validity of the fit method of mathematical models to describe the essential characteristics of a thermally activated process and the importance of the use of a criterion of free kinetics, such as the isoconversion method, to describe the dependence of the activation energy as a function of the advance of the reaction. Khawan and Flanagan (2005a) analyzed different evaluation methods for the activation energy using an adjustment model and an isoconversional method under simulated isothermal data. They demonstrated that the activation energy is of two types: one from the true variation in accordance with the complex nature of the solid state processes and another artificial one resulting from the use of some isoconversional methods. Khawan and Flanagan (2005b) investigated the relation between the calculation methods, the apparent variation in the activation energy and non-isothermal experimental data using an adjustment model and an isoconversional method to analyze the non-isothermal data, both simulated and experimental. They show that the difference in the activation energy calculated for simple reactions could be the result of incorrect application of isoconversional methods. Farjas and Roura (2006) provided a quasi-exact analytical solution of the Avrami model when the transformation occurs under continuous heating. They obtained a solution with different activation energies for both the nucleation rate and the growth rate. The relation obtained was also a solution to the Kolmogorov-Johnson-Mehl-Avrami transformation rate equation (KJMA), suggesting that the corresponding non-isothermal KJMA transformation rate equation only differs from the one obtained under isothermal conditions by a constant parameter that depends on the ratio between the activation energies of the nucleation rate and the growth rate. They extended the KJMA transformation rate equation for continuous heating. Ebrahimi et al. (2007) studied the kinetics of molybdenite oxidation by non-isothermal TGA-DTA analysis for a heating rate of 5 C/min using the adjustment model of the kinetic approach applied to the TGA data. The Coats-Redfern model fit the experimental data well, giving a good adjustment for non-isothermal data for the chemical control regime. General models utilized in roasting processes. The experimental kinetic information allows the estimation of kinetic parameters, such as the constant reaction, activation energy and reaction entension (decomposition, vaporization, oxidation, etc.) and the selecting of the model that best represents the roasting process. The analysis methods permit the obtaining of particular information. For example, DRX analysis determines the mineralogical composition of both the feed material and the roasting products. In general, kinetic parameter calculations are based on the fact that the reaction rate can be described as the product between the kinetic constant k, which depends on temperature, and a reactant concentration function, which is temperatureindependent, in the form: (15) The dependency of the kinetic constant on the temperature can be expressed by the Arrhenius relationship: (16) where A is a constant (frequency factor), E a the activation energy, R the gas constant and T the absolute temperature. To determine the f(x) function, kinetic, mechanistic or phenomenological models can be used. In the first case, for the series of steps by which the reaction takes place for the species that participate, only the most remarkable are considered, without considering individual reactions; therefore, only limited information about the chemical reactions that take place during the roasting process can be obtained. May 2012 Vol. 29 No

5 Table 1 Kinetic model (Strbac et al., 2006). Equation Kinetic mechanism X 2 = kt Lineal diffusion (1 - X)Ln(1 - X) + X = kt Bidimensional diffusion (cylindrical symmetry). [1 - (1X) 1/3-2 ] = kt Tri-dimensional diffusion (spherical symmetry), Jander equation. (1-2/3X) - (1 - X) 2/3 = kt Tri-dimensional diffusion (spherical symmetry), Ginstling-Braunstein equation. -Ln(1 - X) = kt Random nuclei formation of the new phase, one nuclei per particle. [- Ln (1- X)] 1/2 = kt Random nuclei formation of the new phase Avrami equation I. [- Ln (1- X)] 1/3 = kt Random nuclei formation of the new phase Avrami equation II. 1 - (1 - X) 1/2 = kt Edge reaction (cylindrical symmetry). 2 - (1 - X) 1/3 = kt Edge reaction (spherical symmetry). Kinetic equations. For the pyritic decomposition of the mineralogical components by inert roasting of copper concentrates, the results obtained under isothermal conditions can be described in terms of the desulfurization degree based on the roasting time at different temperatures. In this form, for a given temperature, the desulfurization degree can be related by a mathematical function such as X = f (t), where X is the desulfurization degree and t is the roasting time. In other cases, X can be the oxidation degree, decomposition degree, conversion degree or the particle-reacted fraction. Figure 1 shows a typical graph representing the reaction degree as a function of roasting time for an enargite-contaminated copper concentrate (Fan, 1997). There is a model catalog that allows the relation of X and t in a way that corresponds to the Sharp classification method (Strbac et al., 2006). The Sharp method, also known as the average reaction time method and frequently used for calculations of kinetic parameters, requires some specific characteristics of the experimental information for the kinetic analysis. The method is based on the determination of the reaction mechanism from X = f (t) experimental data, using the half-time reduced diagram in the form: (17) where t 0.5 is the half reaction time and X the extent of the reaction. In order to determine the F(X) kinetic function that best fits the experimental results, several models can be used (Table 1). Thermal decomposition is a phenomena that occurs when a substance is heated. The mass convertion then can be defined as (18) where m i and m f are the initial and final masses at a given time, respectively. The mass change can be evaluated as a function of the temperature (dynamic method) or as a function of time at constant temperature (isothermal method). In the dynamic methods, the temperature increases generally in linear form, in accordance with a heating program. A. Conversion degree determination by the dynamic method. The dynamic method makes use of TGA, either as a dynamic or an isothermal method, to relate the conversion to temperature or time. Therefore, a kinetic model to describe the thermal decomposition can be expressed in the form of an equation such as: (19) where X is the conversion degree, k(t) is the constant rate, which depends on the temperature and f(x) a function of the kinetic mechanism. Since the mass change is a function of the temperature, then: (20) Combining these last two equations, the reaction rate can be expressed as: (21) In the dynamic method, the temperature varies at a constant heating rate β; therefore, the conversion can be expressed as a function of the temperature. In this manner, the rate equation takes the form: where β is the heating rate, equal to β = dt/dt. From Eqs. (21) and (22), it can be determined that (22) (23) Separating variables and integrating from an initial temperature T 0 (which corresponds to a X 0 conversion) up to T p for a X p conversion yields (24) If T 0 is low enough, it is reasonable to suppose that X 0 = 0 and, assuming that there is no reaction between 0 and T 0, the integral conversion function g(x) can be defined as: (25) where A, E and f(x) can be determined experimentally. The integral conversion function g(x) needs to be determined 125 Vol. 29 No. 2 May 2012

6 experimentally. The dynamic method can be classified as a differential or an integral method, according to the general rate equation or its integrated form, respectively. B. Differential methods. The analysis of the mass variation generated by changes in the heating rate is the basis of the most powerful differential methods for the determination of kinetic parameters. The Kissinger method makes use of the inflexion point of the thermogram diagram to estimate the activation energy value. By differentiating the general rate equation, the following can be obtained: To determine E, n must be known, since dx/dt m, X m and T m are experimental values obtained from TG tests. Combining Eqs. (30) and (32) for X m obtains: (34) Since for a given value of n the value (1 X m ) is constant, it follows that: (35) (26) By generalizing this equation for the inflexion point at T m (maximum reaction rate), the following is obtained: Therefore, Rearranging Eq. (28) takes the form: (27) (28) (29) The Kissinger method can be used independently of the conversion; therefore, it is not necessary to know the order reaction n to determine the decomposition activation energy. Since it is known that the general behavior of particles follows a function of the type f(x) = (1 X) n, in the same form the following can be obtained: Differentiating: (30) Thus, by ploting β/t m 2 versus 1000/T m, E can be determined without previous knowledge of the reaction mechanism, for n 0. C. Integral methods. This type of method uses the weight change data directly to provide an estimation of Eq. (25). These methods are known as the integral methods of Flynn-Wall- Ozawa, Coats-Redfern, Horowitz-Metzger and Van Krevelen. a) Integral method of Flynn-Wall-Ozawa. This method estimates the integral by introducing a new variable, z = E/RT, with the boundary conditions Then, where:. and (25) (36) (37) (38) This new integral can be evaluated for different values of z. One of the series that can be used for the polynomial estimation is the Schlömilch expansion: (31) Therefore, (32) At the inflexion point (maximum decomposition temperature), the second derivative is nil, then: (33) (39) Then: (40) For x > 20, p(z) can be expressed as (41) A method that provides an approximation of Eq. (41) to May 2012 Vol. 29 No

7 estimate the activation energy without knowing the order of reaction was developed independently by Flynn and Wall and by Ozawa. According to this method, Eq. (37) can be transformed into (42) Using logarithm and reordering, the following can be obtained: (43) b) Integral method of Coats-Redfern. This method uses an asymptotic expansion to solve the equation (44) In this form, the integral equation is transformed into: Using logarithms, the following is obtained: However, for z > 20, ln (1-2RT/E) 0, then (45) (46) (47) c) Integral methods of Van Krevelen and Horowitz-Metzger. Both methods consider an arbitrary temperature T r. After a series of mathematical transformations and simplifications of the p(z) function, the following can be obtained: with and i) In the case of Van Krevelen, ii) In the case of Horowitz-Metzger, Both methods permit the expression (48) (49) (50) (50a) (51) where (51a) In these methods, the reference temperature is arbitrary. Another alternative is to select the temperature at which the reaction rate is maximum. These two methods permit the estimation of the activation energy from the slope of log g(x) versus log T. There is an apparent contradiction between both methods, because log g(x) cannot simultaneously be a linear function of T and of log T. In this respect, the Coats-Redfern method shows a similar linearity and has better adjustment. Roasting models applied to mineralogical components. Heterogeneous reactions involving solid-gas or thermal decomposition are considered first order with respect to the gas and zero order with respect to the solid. Padilla et al. (2001) used the following first order equations to determine the enargite decomposition, which takes place in two stages: (52) (53) where W en and W tn are the enargite and tennantite mass weights, and k 1 and k 2 the kinetic constants, respectively, for the reactions 4Cu 3 AsS 4 (s) = Cu 12 As 4 S 13 (s) + 1.5S 2 (54) Cu 12 As 4 S 13 (s) = 6Cu 2 S 1+x (s) + As 4 S 4 (g) + (1.5-3x)S 2 (g) (55) The global fractional conversion of enargite decomposition then can be expressed as (56) Padilla et al. (1999) adjusted the experimental data of the kinetic decomposition of enargite by means of a topochemical reaction model for spherical particles (Padilla et al., 1999) in the form (57) Roasting models applied to arsenic-bearing copper concentrates. Björkman et al. (1994) performed roasting laboratory tests for arsenic-bearing dusts and adjusted the results to two models: (a) the pore obstruction model and (b) the power law model, which obey the following relationships: Pore obstruction model: (58) where t is the roasting time (min), k the rate constant (min -1 ), λ a constant and X the fraction reacted. Power law model: (59) where t is the roasting time (min), k the rate constant (min -1 ) and m a constant. Conclusions For the Cu-Fe-As-Sb-S-O system at 727 C, p O2 varies from to atm and p SO2 from 10-1 to atm. An increase of p O2 leads to Cu 3 As and Cu 2 O formation, which can induce sintering, while some of the arsenic remains in the calcine. Arsenic removal from enargite in a N 2 atmosphere is affected by the temperature, with 95% As removal obtained after 127 Vol. 29 No. 2 May 2012

8 30 minutes at 650 C. In a slightly oxidizing atmosphere, the same level of removal can be obtained in less than 20 minutes. A near complete removal of arsenic from copper concentrates containing enargite can be obtained in an inert atmosphere at 700 C in 15 minutes. Below 600 C, the controlling step is the diffusion through the product layer (pore obstruction model). Above 600 C, the controlling step is the chemical reaction (grain nucleation and growth model). Roasting kinetic mechanisms. The enargite decomposition involves two possible mechanisms between 575 and 700 C: (a) formation of covellite as an intermediate compound and (b) formation of tennantite as an intermediate compound. During enargite decomposition, arsenic vaporizes at two temperatures, according to TGA analysis: a small part at 579 C and the main vaporization at 630 C. Roasting kinetic models kinetic data analysis techniques. The isoconversional method establishes the dependency of the activation energy with the conversion, permitting a reliable prediction of the reaction rate and the reaction mechanism. There is an iterative procedure to calculate the activation energy and avoid errors when using Ln β versus 1/T and Ln (β/t 2 ) versus 1/T isoconversional graphs. Roasting kinetic models general models. There is a model catalog that permits the relation of X and t that corresponds to the Sharp classification method. This method, also known as the average reaction time, is often used for kinetic parameter calculations. There are two kinds of models to determine the conversion degree: (a) dynamic or non-isothermal models (differentials: Kissinger method; integrals: Flynn-Wall-Ozawa, Coats-Redfern and the de Van Krevelen and Horowitz-Metzger methods) and (b) isothermal models. Roasting kinetic models models for mineralogical components. For the analysis of enargite decomposition defined in two stages, two first-order rate equations represent the phenomena: (52) (53) For the global decomposition of enargite, the following expression can be applied: (56) Experimental data fit well to the enargite decomposition kinetics given by the topochemical model for spherical particles: (57). References Baitalow, F., Schmidt, H.D., and Wolf, G., 1999, Formal kinetic analysis in the solid state, Thermochimica Acta, Volume 337, pp Björkman, B., Gegerstedt, U., Lindblom, B. and Samuelsson, C., 1994, Kinetics of impurity elimination during roasting, Extraction and Processing for Treatment and Minimization of Wastes, J. Hager et al., eds., Warrendale, PA, The Minerals, Metals and Materials Society, p Ebrahimi, R., Habashi, M.H., and Hasan, A., 2007, Model-fitting approach to kinetic analysis of non-isothermal oxidation of molybdenite, Iranian Journal of Chemical Chemistry Engineers, Vol. 26, No. 2, pp Fan, Y., 1997, Cinética y Mecanismos de Vaporización de Sulfuros de Arsénico desde Concentrados de Cobre, Tesis de Magíster en Ciencias de la Ingeniería, Mención Metalurgia Extractiva, Universidad de Concepción, Concepción, Chile. Farjas, J., and Roura, P., 2006, Modification of the Kolmogorov-Johnson-Mehl- Avrami rate equation for non-isothermal experiments and its analytical solution, Acta Materialia, Vol. 54, pp Gao, Z., Nakada, M., and Amasaki, I., 2001, A consideration of errors and accuracy in the isoconversional methods, Thermochimica Acta, Volume 369, pp Khawan, A., and Flanagan, D.R., 2005a, Role of isothermal methods in varying activation energies of solid-state kinetics I. 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Mishra, ed., Warrendale, PA, The Minerals, Metals and Materials Society, p Padilla, R., Fan, Y. and Wilkomirsky, I., 2001, Decomposition of enargite in nitrogen atmosphere, Canadian Metallurgical Quarterly, Vol. 40, No. 3, pp Strbac, N., Mihajlovic, I., Zivkovic, D., Zivkovic, Z., and Andelic, B., 2006, Thermodynamic and Kinetic Analysis of the Cu-Fe-S System Oxidation Process, Journal of the University of Chemical Technology and Metallurgy, Vol. 41, 2, pp Torres-García, E., 2003, Cinética de reacciones térmicamente activadas en sólidos: Un acercamiento, Instituto Mexicano del Petróleo, México D.F., México. Vyazovkin, S., and Wright, C.A., 1998, Isothermal and non-isothermal kinetics of thermally stimulated reactions of solids, International Review in Physical Chemistry, Vol. 17, pp Vyazovkin, S., and Wright, C.A., 1999, Model-free and model-fitting approaches to kinetic analysis of isothermal and non-isothermal data, Thermochimica Acta, Vol , pp Vyazovkin, S., and Wright, C.A., 2000, Estimating realistic confidence intervals for the activation energy determined from thermoanalytical measurements, Analytical Chemistry, Vol. 72, No. 14, pp May 2012 Vol. 29 No