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Reaction-kinetics of the vanadium roast process using steel slag as a secondary raw material
Minerals Engineering 17 (2004) 317–321 This article is also available online at: www.elsevier.com/locate/mineng
Reaction-kinetics of the vanadium roast process using steel slag as a secondary raw material B. Voglauer *, A. Grausam, H.P. J€ orgl Institute for Machine and Process Automation, Vienna University of Technology, Gußhausstr. 27-29, A-1040 Vienna, Austria Received 8 July 2003; accepted 15 October 2003
Abstract Secondary raw materials like steelworks slag or other vanadium bearing industry wastes like catalysts and oil burner ash can be used for the production of vanadium before their final disposal. Therefore, as in primary processing, alkaline roasting has to be carried out in a rotary kiln or multiple hearth furnace. This process transforms the vanadium, strongly embedded within the spinel mineral structure, into leachable vanadates. Mathematical modeling of this process for the establishment of simulation programs and for model based controller design requires accurate models of the chemical reaction kinetics. In this article a set of equations describing the reaction rate of the vanadium roast process and its derivation is presented. Validation showed good agreement between simulation and measurement data. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Reaction kinetics; Roasting; Modeling; Process control; Simulation
1. Introduction For the vanadium production a well known process can be applied to recover vanadium from steelworks slag or other vanadium bearing industrial wastes like catalysts and oil burner ash. The slag is roasted in a multiple hearth furnace or a rotary kiln under alkaline conditions, usually using NaCl or/and Na2 CO3 as additives. After a residence time of typically 1–2 h at 750–850 °C most of the mainly trivalent vanadium has reacted to vanadate, which is water-soluble. By subsequent leaching overall recovery gains for vanadium of 60–80% are reported by Dresher (1961), Hukkanen and Walden (1985) and Kanta Rao et al. (1979). Maintaining an oxidizing atmosphere during roasting is essential for an efficient conversion of vanadium. Furthermore, accurate temperature control in the roasting units is a necessity for a reasonable recovery of the vanadium and to avoid undesirable process behavior like hearth build up (Hukkanen and Walden, 1985; Rohrmann, 1985). Consequently, a well designed control scheme is vital for high process efficiency. For the controller design in case
* Corresponding author. Tel.: +43-1-58801-32817; fax: +43-1-5880132899. E-mail address: [email protected] (B. Voglauer).
0892-6875/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2003.10.032
of automated process control and for plain process simulation a physically based process model was established by Voglauer and J€ orgl (2003), which heavily depends on an appropriate reaction rate law. This article describes the derivation of a new reaction rate law for the vanadium roast process. Beginning with a literature survey, which did not reveal sufficient information for a suitable reaction kinetics rate law, a description of a laboratory scale roasting unit for practical experiments follows. By a series of well directed experiments a data base for the rate law derivation was provided. Finally a short summary of the rate law implementation within the formerly published roasting process model is presented.
2. Literature survey A literature survey was carried out to gather information about the vanadium roast process, especially concerning its reaction kinetics. The following gives a short summary of the most important facts revealed by the authors literature survey. It is a common assumption that vanadium within the slag is mainly trivalent (Winnacker and K€ uchler, 1986; Kanta Rao et al., 1979; Saha et al., 1969). It is also mentioned that the oxidation to a pentavalent state under oxidizing atmosphere is a
318
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
Nomenclature c c O2 cNa cV cVs E fa1 fa2 J k0 k1 –k6 kT
concentration concentration of oxygen concentration of sodium concentration of insoluble vanadium concentration of soluble vanadium energy of activation factor for adaption to large-scale factor for adaption to large-scale performance quantity coefficient in Arrhenius law parameters for adaption temperature dependent factor
mB m_ B;in m_ B;out nDS r r0 rNa rV rV s R t T
fast reaction (Saha et al., 1969) and therefore not dominant for the overall reaction speed. Most investigations were carried out using NaCl or Na2 CO3 as the sodium source for the reaction but never both at the same time. According to Dresher (1961) the NaCl reaction is described by Eqs. (1) and (2). 1 V2 O5 þ 2NaCl þ O2 ! Na2 O V2 O5 þ Cl2 2 V2 O5 þ 2NaCl þ H2 O ! Na2 O V2 O5 þ 2HCl
ð1Þ ð2Þ
Dresher (1961) describes details of the reaction kinetics within a mechanism study of the NaCl reaction, however having validity only for a synthetic mixture of V2 O5 and NaCl in a quartz matrix. In case of Na2 CO3 the reaction is described to proceed according to Eq. (3). (e.g. by Goddard and Fox, 1981). Na2 CO3 þ V2 O5 ! 2NaVO3 þ CO2
ð3Þ
Many authors report better recovery yields for the Na2 CO3 reaction, but also of lower selectivity for vanadium. Therefore, mixtures of NaCl and Na2 CO3 are used in practice (Goddard and Fox, 1981). Due to the bad selectivity of Na2 CO3 and subsequent side reactions there is a higher sodium consumption, which has a strong influence on the reaction kinetics of the vanadium reaction. Furthermore, if the sodium educt becomes rare, the formation of insoluble bronze type compounds is reported by Goddard and Fox (1981). The influence of water as a reactant is reported to be high especially at the beginning of the NaCl reaction (e.g. by Dresher, 1961). Summarizing the literature survey it can be stated that many influences on the reactions exist, but since the general conditions of the individual investigations are very different and partly not known in detail, the available knowledge cannot be combined to form a reaction kinetics law with sufficient accuracy for the authors purposes. Therefore, practical
mass of bulk in a floor incoming mass-flow of bulk outgoing mass-flow of bulk rotation speed of drive-shaft reaction rate initial reaction rate spec. reaction rate of sodium spec. reaction rate of insoluble vanadium spec. reaction rate of soluble vanadium universal gas constant time temperature
experiments on a laboratory scale had to be carried out. 3. Practical experiments For the practical experiments a laboratory scale roasting unit was developed. A muffle furnace was modified containing a continuously stirred batch reactor, where it was possible to adjust the process conditions according to the requirements (see flowchart in Fig. 1). In particular, maintaining a well defined composition of the gas atmosphere in the reactor (O2 , N2 and H2 O) and the controllability of the reaction temperature were required. Several different bulk mixtures were used as initial conditions of the bulk concentrations to cover the range of interest. The initial concentrations of vanadium were kept constant at a typical value, but the initial concentrations of sodium were varied around an operating point. For these initial conditions roasting experiments were carried out at three different oxygen concentrations of the reactive gas, all at constant reaction temperatures. The influence of the temperature was investigated by experiments at four different temperatures but constant initial bulk conditions. For chemical analysis the experiment was stopped at the desired time by pouring the complete sample in a cooled tray. The cooled and grinded material was then analyzed by taking a random sample for the standard analyzing routine. Thus, for recording one complete process progression the experiment had to be started from the beginning several times with remaining initial conditions. Since starting each reaction needed some handling time (preparation of the reactor, waiting for constant temperature, etc.) it is obvious that this routine for recording the progress of reaction is highly time consuming but at the same time very precise.
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
319
Fig. 1. Flowchart of the experimental set up.
4. Reaction kinetics
rate r into parts depending on the temperature f ðT Þ and on the concentrations f ðcÞ (see Eq. (6))
In order to derive an appropriate reaction rate law investigations were carried out to find a rate law structure that could be fitted to the measurement data. To accomplish this task information from the literature survey was taken into account. Finally a rate law according to Eq. (4) was determined: " # cNa fa1 k4 rVs ¼ kT k1 k2 cV k6 cVs fa2 ðcNa þ k3 Þ " # cNa 1 k4 cV þ k5 cNa rNa ¼ kT k1 k2 ð4Þ fa2 ðcNa þ k3 Þ " # cNa 1 ck4 rV ¼ kT k1 k2 V f ðcNa þ k3 Þ a2
r ¼ f ðT Þ f ðcÞ
ð6Þ
The temperature dependent part f ðT Þ was assumed to comply with the Arrhenius law according to Eq. (7). By deducing the Arrhenius diagram lnðr0 Þ 1=T (natural logarithm of the initial reaction rate r0 over the inverse of the temperature T ) it was possible to verify the Arrhenius law as a good approximation for f ðT Þ. E
f ðT Þ ¼ kT ¼ k0 eRT
ð7Þ
For better illustration of the resulting reaction kinetics Fig. 2 shows the reaction rate of soluble vanadium rVs plotted versus the concentrations of sodium cNa and insoluble vanadium cV , calculated according to Eq. (4). Since three different concentrations of oxygen were
Here cVs represents the concentration of soluble vanadium, cV the concentration of the insoluble vanadium and cNa the concentration of sodium. kT is a temperature dependent factor and will be discussed later. The adaptation factors fa1 and fa2 had to be introduced as corrective terms due to an expected difference between the roasting results of the laboratory roasting device and the large scale industry application. k1 to k6 represent the free parameters for fitting the reaction rate law to the laboratory measurement data. Therefore, for each oxygen concentration a set of parameters k1 to k6 was calculated by applying the performance criterion according to Eq. (5), which minimizes the sum of squared errors between measured and simulated concentrations of soluble vanadium cVs . X 2 J¼ ðcVs jmeas: cVs jsim: Þ jk1 k6 ! MIN: ð5Þ The dependency of the reaction rate on the temperature was considered by assuming separability of the reaction
Fig. 2. Graphical illustration of the reaction rate of soluble vanadium rVs over the cNa –cV -plane, three surfaces for the individual oxygen concentrations cO2 .
320
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
investigated, three surfaces of the reaction rate rVs versus the concentrations can be seen. The highest reaction rate was found for the highest concentration of oxygen cO2 jlarge , upmost surface). For the medium concentration of oxygen cO2 jmedium the surface has a very similar shape only at a lower level, and for the smallest concentration of oxygen cO2 jsmall the shape changes slightly, thus indicating different reaction mechanisms. For arbitrary oxygen concentrations the reaction rate is calculated by linear interpolation.
5. The process-model A dynamic model of the vanadium roast process has been derived by Voglauer and J€ orgl (2003), assuming homogenous gas- and bulk-layers in every floor of an idealized multiple hearth furnace (see Fig. 3). The nonlinear state space model is capable of calculating mean values for mass mGi ðtÞ and mBi ðtÞ, temperatures TGi ðtÞ and TBi ðtÞ and concentrations cji ðtÞ for the j components on the ith floor (B––bulk, G––gas). Validation showed good consistency of the transport- and the thermodynamic behavior, for validation of the chemical behavior the newly derived rate law was implemented. Due to chemical reactions a source-/drain term rj has to be introduced in the mole-balance (see Eq. (8)), representing the specific reaction rate of component j. dcj cj dmB m_ B;in cj;in m_ B;out cj þ ¼ þ rj dt mB dt mB
ð8Þ
Assuming no further reactions of the j components besides the above mentioned conversion of vanadium, the reaction rates rj can be calculated according to Eq. (4).
6. Results and discussion Fig. 4 shows the stationary concentration profiles over the multiple hearth furnace after adjustment of the adaptation parameters fa1 and fa2 . A good agreement of the concentration profile of cVs (soluble vanadium) can be achieved between simulation (diamond) and measurement (circ), especially for the second (lower) half of the furnace. For the concentrations of cV (insoluble vanadium) the agreement is acceptable as well. It has to be considered that the measurement profile represents the results only of a random sample without the knowledge of a confidence interval. The consistency check, therefore, can be made only qualitatively with a good indication of the quantitative aspect. Nevertheless, it can be stated, that the new reaction rate law seems capable of describing the stationary concentrations of soluble and insoluble vanadium in the furnace. The main interest concerning the roast process is usually focused on the overall rate of recovery. Hence, it is of importance to validate the dynamic behavior of the model for the lowest floor of the furnace. Therefore, an experiment was carried out at the multiple hearth furnace, where the composition of the bulk input was changed resulting in a decrease of the overall rate of recovery. Fig. 5 shows the deviation of the overall rate of recovery from an operating point over time for the experiment with the input being changed stepwise at time t ¼ 0. Both, measurement and simulation decrease by about 1.5%. It can be observed, that the measurement decrease starts earlier, while in the simulation the
1.2
and cV
s
1
cV
s
Concentrations cV
0.8
0.6
0.4
cV
0.2
0 1
2
3
4
5
6
7
8
Floor-number
Fig. 3. Scheme of a multiple hearth roaster.
Fig. 4. Stationary concentrations of soluble vanadium cVs and insoluble vanadium cV over the floor numbers of the furnace, simulation (}) and measurement ( ).
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
setting up a rate law structure, the parameters of the rate law can be adjusted and the rate law can be implemented into the dynamic model of the process. A process model can be used advantageously for investigating process variations or parameter sensibilities by process simulation and for optimal design of a control algorithm for automatic process control (e.g. in Geyrhofer et al., 2003).
1.0
0.5
∆ Rate of recovery,%
321
0
–0.5
–1.0
–1.5
–2.0
–2.5 0
Acknowledgements 50
100
150
200
250
Time, min Fig. 5. Deviation of the overall rate of recovery from an operating point over time t after a change of the input composition, simulation (continuous) and measurement ( ).
rate of recovery remains constant at the beginning of the experiment due to the transportation lag. Again it has to be considered that the measurement represents the results of a random sample and no confidence interval can be given. Furthermore, it is known that a short circuit flow through the furnace exists, which is not considered in the simulation model. Under these conditions it may be derived, that the reaction rate model used in the simulation can be used to achieve a satisfactory approximation of the dynamic behavior of the overall rate of recovery and hence of the concentration of soluble vanadium.
7. Conclusions A physically based dynamic model of a multiple hearth furnace, which can be used for roasting of primary and secondary raw materials, was derived. In order to model the chemical aspect of the roasting process a new reaction rate law based on systematic experiments on laboratory scale was set up and implemented into the dynamic model. Validation showed that a satisfactory approximation of the concentrations of interest can be achieved. Generally, the presented approach for the derivation of a roasting process rate law seems suitable for common roasting processes. It is of great importance to find a proper rate law for the very special application and therefore, practical experiments will usually be necessary. By identifying the major influencing quantities and
This project was supported within the scope of the Industrial Competence Center for Mechatronics and Automation (IKMA) by the Austrian Ministry for Economic Affairs (BMWA) and the Provincial Government of Upper-Austria. The authors would like to thank VOEST-ALPINE MECHATRONICS GmbH. and all other cooperating industry partners and supporting institutions.
References Dresher, W.H., 1961. A mechanism study of the formation of sodium vanadate compounds under the conditions of the salt-roast process. In: Proceedings of the Annual Meeting of the Society of Mining Engineers of AIME, St. Louis, USA. Geyrhofer, W., Voglauer, B., J€ orgl, H.P., 2003. Control of a roasting process for the recovery of vanadium. In: Proceedings of Conference on Control Applications 2003 (CCA 2003), Istanbul, Turkey, pp. 614–617. Goddard, J.B., Fox, J.S., 1981. Salt roasting of vanadium ores. In: Proceedings of 110th AIME Meeting, Chicago, USA, 22–26 February, pp. 127–145. Hukkanen, E., Walden, H., 1985. The production of vanadium and steel from Titanomagnetites. International Journal of Mineral Processing 15, 89–102. Kanta Rao, P., Bhaskara Sarma, P.V.R., Tripathy, A.K., Jena, P.K., 1979. Extraction of vanadium as highpurity vanadium pentoxide from vanadium-bearing titaniferous magnetites, Transactions–– Institute of Mining and Metallurgy Mining, Section C, vol. 88, pp. 187–190. Rohrmann, B., 1985. Vanadium in South Africa. Journal of the South African Institute of Mining and Metallurgy 85, 141–150. Saha, A.K., Misra, R.N., Bhatnagar, P.P., 1969. Studies on the extraction of vanadium by fluo-solid salt roasting. NML Technical Journal, 6–11. Voglauer, B., J€ orgl, H.P., 2003. Dynamic model of a rotary kiln for process simulation and control, In: Proceedings of 4th Conference on Mathematical Modelling (4th MATHMOD), Vienna, Austria, pp. 1051–1056. Winnacker, K., K€ uchler, L., 1986. Chemische Technologie-Band 4 (Metalle), fourth ed. Carl Hanser Verlag.
Reaction-kinetics of the vanadium roast process using steel slag as a secondary raw material B. Voglauer *, A. Grausam, H.P. J€ orgl Institute for Machine and Process Automation, Vienna University of Technology, Gußhausstr. 27-29, A-1040 Vienna, Austria Received 8 July 2003; accepted 15 October 2003
Abstract Secondary raw materials like steelworks slag or other vanadium bearing industry wastes like catalysts and oil burner ash can be used for the production of vanadium before their final disposal. Therefore, as in primary processing, alkaline roasting has to be carried out in a rotary kiln or multiple hearth furnace. This process transforms the vanadium, strongly embedded within the spinel mineral structure, into leachable vanadates. Mathematical modeling of this process for the establishment of simulation programs and for model based controller design requires accurate models of the chemical reaction kinetics. In this article a set of equations describing the reaction rate of the vanadium roast process and its derivation is presented. Validation showed good agreement between simulation and measurement data. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Reaction kinetics; Roasting; Modeling; Process control; Simulation
1. Introduction For the vanadium production a well known process can be applied to recover vanadium from steelworks slag or other vanadium bearing industrial wastes like catalysts and oil burner ash. The slag is roasted in a multiple hearth furnace or a rotary kiln under alkaline conditions, usually using NaCl or/and Na2 CO3 as additives. After a residence time of typically 1–2 h at 750–850 °C most of the mainly trivalent vanadium has reacted to vanadate, which is water-soluble. By subsequent leaching overall recovery gains for vanadium of 60–80% are reported by Dresher (1961), Hukkanen and Walden (1985) and Kanta Rao et al. (1979). Maintaining an oxidizing atmosphere during roasting is essential for an efficient conversion of vanadium. Furthermore, accurate temperature control in the roasting units is a necessity for a reasonable recovery of the vanadium and to avoid undesirable process behavior like hearth build up (Hukkanen and Walden, 1985; Rohrmann, 1985). Consequently, a well designed control scheme is vital for high process efficiency. For the controller design in case
* Corresponding author. Tel.: +43-1-58801-32817; fax: +43-1-5880132899. E-mail address: [email protected] (B. Voglauer).
0892-6875/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2003.10.032
of automated process control and for plain process simulation a physically based process model was established by Voglauer and J€ orgl (2003), which heavily depends on an appropriate reaction rate law. This article describes the derivation of a new reaction rate law for the vanadium roast process. Beginning with a literature survey, which did not reveal sufficient information for a suitable reaction kinetics rate law, a description of a laboratory scale roasting unit for practical experiments follows. By a series of well directed experiments a data base for the rate law derivation was provided. Finally a short summary of the rate law implementation within the formerly published roasting process model is presented.
2. Literature survey A literature survey was carried out to gather information about the vanadium roast process, especially concerning its reaction kinetics. The following gives a short summary of the most important facts revealed by the authors literature survey. It is a common assumption that vanadium within the slag is mainly trivalent (Winnacker and K€ uchler, 1986; Kanta Rao et al., 1979; Saha et al., 1969). It is also mentioned that the oxidation to a pentavalent state under oxidizing atmosphere is a
318
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
Nomenclature c c O2 cNa cV cVs E fa1 fa2 J k0 k1 –k6 kT
concentration concentration of oxygen concentration of sodium concentration of insoluble vanadium concentration of soluble vanadium energy of activation factor for adaption to large-scale factor for adaption to large-scale performance quantity coefficient in Arrhenius law parameters for adaption temperature dependent factor
mB m_ B;in m_ B;out nDS r r0 rNa rV rV s R t T
fast reaction (Saha et al., 1969) and therefore not dominant for the overall reaction speed. Most investigations were carried out using NaCl or Na2 CO3 as the sodium source for the reaction but never both at the same time. According to Dresher (1961) the NaCl reaction is described by Eqs. (1) and (2). 1 V2 O5 þ 2NaCl þ O2 ! Na2 O V2 O5 þ Cl2 2 V2 O5 þ 2NaCl þ H2 O ! Na2 O V2 O5 þ 2HCl
ð1Þ ð2Þ
Dresher (1961) describes details of the reaction kinetics within a mechanism study of the NaCl reaction, however having validity only for a synthetic mixture of V2 O5 and NaCl in a quartz matrix. In case of Na2 CO3 the reaction is described to proceed according to Eq. (3). (e.g. by Goddard and Fox, 1981). Na2 CO3 þ V2 O5 ! 2NaVO3 þ CO2
ð3Þ
Many authors report better recovery yields for the Na2 CO3 reaction, but also of lower selectivity for vanadium. Therefore, mixtures of NaCl and Na2 CO3 are used in practice (Goddard and Fox, 1981). Due to the bad selectivity of Na2 CO3 and subsequent side reactions there is a higher sodium consumption, which has a strong influence on the reaction kinetics of the vanadium reaction. Furthermore, if the sodium educt becomes rare, the formation of insoluble bronze type compounds is reported by Goddard and Fox (1981). The influence of water as a reactant is reported to be high especially at the beginning of the NaCl reaction (e.g. by Dresher, 1961). Summarizing the literature survey it can be stated that many influences on the reactions exist, but since the general conditions of the individual investigations are very different and partly not known in detail, the available knowledge cannot be combined to form a reaction kinetics law with sufficient accuracy for the authors purposes. Therefore, practical
mass of bulk in a floor incoming mass-flow of bulk outgoing mass-flow of bulk rotation speed of drive-shaft reaction rate initial reaction rate spec. reaction rate of sodium spec. reaction rate of insoluble vanadium spec. reaction rate of soluble vanadium universal gas constant time temperature
experiments on a laboratory scale had to be carried out. 3. Practical experiments For the practical experiments a laboratory scale roasting unit was developed. A muffle furnace was modified containing a continuously stirred batch reactor, where it was possible to adjust the process conditions according to the requirements (see flowchart in Fig. 1). In particular, maintaining a well defined composition of the gas atmosphere in the reactor (O2 , N2 and H2 O) and the controllability of the reaction temperature were required. Several different bulk mixtures were used as initial conditions of the bulk concentrations to cover the range of interest. The initial concentrations of vanadium were kept constant at a typical value, but the initial concentrations of sodium were varied around an operating point. For these initial conditions roasting experiments were carried out at three different oxygen concentrations of the reactive gas, all at constant reaction temperatures. The influence of the temperature was investigated by experiments at four different temperatures but constant initial bulk conditions. For chemical analysis the experiment was stopped at the desired time by pouring the complete sample in a cooled tray. The cooled and grinded material was then analyzed by taking a random sample for the standard analyzing routine. Thus, for recording one complete process progression the experiment had to be started from the beginning several times with remaining initial conditions. Since starting each reaction needed some handling time (preparation of the reactor, waiting for constant temperature, etc.) it is obvious that this routine for recording the progress of reaction is highly time consuming but at the same time very precise.
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
319
Fig. 1. Flowchart of the experimental set up.
4. Reaction kinetics
rate r into parts depending on the temperature f ðT Þ and on the concentrations f ðcÞ (see Eq. (6))
In order to derive an appropriate reaction rate law investigations were carried out to find a rate law structure that could be fitted to the measurement data. To accomplish this task information from the literature survey was taken into account. Finally a rate law according to Eq. (4) was determined: " # cNa fa1 k4 rVs ¼ kT k1 k2 cV k6 cVs fa2 ðcNa þ k3 Þ " # cNa 1 k4 cV þ k5 cNa rNa ¼ kT k1 k2 ð4Þ fa2 ðcNa þ k3 Þ " # cNa 1 ck4 rV ¼ kT k1 k2 V f ðcNa þ k3 Þ a2
r ¼ f ðT Þ f ðcÞ
ð6Þ
The temperature dependent part f ðT Þ was assumed to comply with the Arrhenius law according to Eq. (7). By deducing the Arrhenius diagram lnðr0 Þ 1=T (natural logarithm of the initial reaction rate r0 over the inverse of the temperature T ) it was possible to verify the Arrhenius law as a good approximation for f ðT Þ. E
f ðT Þ ¼ kT ¼ k0 eRT
ð7Þ
For better illustration of the resulting reaction kinetics Fig. 2 shows the reaction rate of soluble vanadium rVs plotted versus the concentrations of sodium cNa and insoluble vanadium cV , calculated according to Eq. (4). Since three different concentrations of oxygen were
Here cVs represents the concentration of soluble vanadium, cV the concentration of the insoluble vanadium and cNa the concentration of sodium. kT is a temperature dependent factor and will be discussed later. The adaptation factors fa1 and fa2 had to be introduced as corrective terms due to an expected difference between the roasting results of the laboratory roasting device and the large scale industry application. k1 to k6 represent the free parameters for fitting the reaction rate law to the laboratory measurement data. Therefore, for each oxygen concentration a set of parameters k1 to k6 was calculated by applying the performance criterion according to Eq. (5), which minimizes the sum of squared errors between measured and simulated concentrations of soluble vanadium cVs . X 2 J¼ ðcVs jmeas: cVs jsim: Þ jk1 k6 ! MIN: ð5Þ The dependency of the reaction rate on the temperature was considered by assuming separability of the reaction
Fig. 2. Graphical illustration of the reaction rate of soluble vanadium rVs over the cNa –cV -plane, three surfaces for the individual oxygen concentrations cO2 .
320
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
investigated, three surfaces of the reaction rate rVs versus the concentrations can be seen. The highest reaction rate was found for the highest concentration of oxygen cO2 jlarge , upmost surface). For the medium concentration of oxygen cO2 jmedium the surface has a very similar shape only at a lower level, and for the smallest concentration of oxygen cO2 jsmall the shape changes slightly, thus indicating different reaction mechanisms. For arbitrary oxygen concentrations the reaction rate is calculated by linear interpolation.
5. The process-model A dynamic model of the vanadium roast process has been derived by Voglauer and J€ orgl (2003), assuming homogenous gas- and bulk-layers in every floor of an idealized multiple hearth furnace (see Fig. 3). The nonlinear state space model is capable of calculating mean values for mass mGi ðtÞ and mBi ðtÞ, temperatures TGi ðtÞ and TBi ðtÞ and concentrations cji ðtÞ for the j components on the ith floor (B––bulk, G––gas). Validation showed good consistency of the transport- and the thermodynamic behavior, for validation of the chemical behavior the newly derived rate law was implemented. Due to chemical reactions a source-/drain term rj has to be introduced in the mole-balance (see Eq. (8)), representing the specific reaction rate of component j. dcj cj dmB m_ B;in cj;in m_ B;out cj þ ¼ þ rj dt mB dt mB
ð8Þ
Assuming no further reactions of the j components besides the above mentioned conversion of vanadium, the reaction rates rj can be calculated according to Eq. (4).
6. Results and discussion Fig. 4 shows the stationary concentration profiles over the multiple hearth furnace after adjustment of the adaptation parameters fa1 and fa2 . A good agreement of the concentration profile of cVs (soluble vanadium) can be achieved between simulation (diamond) and measurement (circ), especially for the second (lower) half of the furnace. For the concentrations of cV (insoluble vanadium) the agreement is acceptable as well. It has to be considered that the measurement profile represents the results only of a random sample without the knowledge of a confidence interval. The consistency check, therefore, can be made only qualitatively with a good indication of the quantitative aspect. Nevertheless, it can be stated, that the new reaction rate law seems capable of describing the stationary concentrations of soluble and insoluble vanadium in the furnace. The main interest concerning the roast process is usually focused on the overall rate of recovery. Hence, it is of importance to validate the dynamic behavior of the model for the lowest floor of the furnace. Therefore, an experiment was carried out at the multiple hearth furnace, where the composition of the bulk input was changed resulting in a decrease of the overall rate of recovery. Fig. 5 shows the deviation of the overall rate of recovery from an operating point over time for the experiment with the input being changed stepwise at time t ¼ 0. Both, measurement and simulation decrease by about 1.5%. It can be observed, that the measurement decrease starts earlier, while in the simulation the
1.2
and cV
s
1
cV
s
Concentrations cV
0.8
0.6
0.4
cV
0.2
0 1
2
3
4
5
6
7
8
Floor-number
Fig. 3. Scheme of a multiple hearth roaster.
Fig. 4. Stationary concentrations of soluble vanadium cVs and insoluble vanadium cV over the floor numbers of the furnace, simulation (}) and measurement ( ).
B. Voglauer et al. / Minerals Engineering 17 (2004) 317–321
setting up a rate law structure, the parameters of the rate law can be adjusted and the rate law can be implemented into the dynamic model of the process. A process model can be used advantageously for investigating process variations or parameter sensibilities by process simulation and for optimal design of a control algorithm for automatic process control (e.g. in Geyrhofer et al., 2003).
1.0
0.5
∆ Rate of recovery,%
321
0
–0.5
–1.0
–1.5
–2.0
–2.5 0
Acknowledgements 50
100
150
200
250
Time, min Fig. 5. Deviation of the overall rate of recovery from an operating point over time t after a change of the input composition, simulation (continuous) and measurement ( ).
rate of recovery remains constant at the beginning of the experiment due to the transportation lag. Again it has to be considered that the measurement represents the results of a random sample and no confidence interval can be given. Furthermore, it is known that a short circuit flow through the furnace exists, which is not considered in the simulation model. Under these conditions it may be derived, that the reaction rate model used in the simulation can be used to achieve a satisfactory approximation of the dynamic behavior of the overall rate of recovery and hence of the concentration of soluble vanadium.
7. Conclusions A physically based dynamic model of a multiple hearth furnace, which can be used for roasting of primary and secondary raw materials, was derived. In order to model the chemical aspect of the roasting process a new reaction rate law based on systematic experiments on laboratory scale was set up and implemented into the dynamic model. Validation showed that a satisfactory approximation of the concentrations of interest can be achieved. Generally, the presented approach for the derivation of a roasting process rate law seems suitable for common roasting processes. It is of great importance to find a proper rate law for the very special application and therefore, practical experiments will usually be necessary. By identifying the major influencing quantities and
This project was supported within the scope of the Industrial Competence Center for Mechatronics and Automation (IKMA) by the Austrian Ministry for Economic Affairs (BMWA) and the Provincial Government of Upper-Austria. The authors would like to thank VOEST-ALPINE MECHATRONICS GmbH. and all other cooperating industry partners and supporting institutions.
References Dresher, W.H., 1961. A mechanism study of the formation of sodium vanadate compounds under the conditions of the salt-roast process. In: Proceedings of the Annual Meeting of the Society of Mining Engineers of AIME, St. Louis, USA. Geyrhofer, W., Voglauer, B., J€ orgl, H.P., 2003. Control of a roasting process for the recovery of vanadium. In: Proceedings of Conference on Control Applications 2003 (CCA 2003), Istanbul, Turkey, pp. 614–617. Goddard, J.B., Fox, J.S., 1981. Salt roasting of vanadium ores. In: Proceedings of 110th AIME Meeting, Chicago, USA, 22–26 February, pp. 127–145. Hukkanen, E., Walden, H., 1985. The production of vanadium and steel from Titanomagnetites. International Journal of Mineral Processing 15, 89–102. Kanta Rao, P., Bhaskara Sarma, P.V.R., Tripathy, A.K., Jena, P.K., 1979. Extraction of vanadium as highpurity vanadium pentoxide from vanadium-bearing titaniferous magnetites, Transactions–– Institute of Mining and Metallurgy Mining, Section C, vol. 88, pp. 187–190. Rohrmann, B., 1985. Vanadium in South Africa. Journal of the South African Institute of Mining and Metallurgy 85, 141–150. Saha, A.K., Misra, R.N., Bhatnagar, P.P., 1969. Studies on the extraction of vanadium by fluo-solid salt roasting. NML Technical Journal, 6–11. Voglauer, B., J€ orgl, H.P., 2003. Dynamic model of a rotary kiln for process simulation and control, In: Proceedings of 4th Conference on Mathematical Modelling (4th MATHMOD), Vienna, Austria, pp. 1051–1056. Winnacker, K., K€ uchler, L., 1986. Chemische Technologie-Band 4 (Metalle), fourth ed. Carl Hanser Verlag.