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Experimental and Numerical Studies on a One-Step Method for the Production of Mg in the Silicothermic Reduction Process Chao Zhang, Chao Wang, Shaojun Zhang, and Liejin Guo* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China S Supporting Information *

ABSTRACT: In this paper, a new efficient one-step technical method was first developed for the production of magnesium in the industry. The one-step method could combine the two processes of dolomite decomposition and magnesium reduction in the magnesium reduction retort. Thus, the high-temperature carbon dioxide produced by the dolomite decomposition process could be collected in a timely manner instead of being emitted into the atmosphere, and excessive heat loss caused by the two separate processes also could be almost completely avoided. This paper presents an experimental study on the intrinsic chemical kinetics mechanisms of this new efficient one-step technology. By applying each of the most likely solid-state kinetic models, the kinetic parameters of the two reactions that reacted during the dolomite decomposition stage and magnesium reduction stage were evaluated, and the kinetic models that best verify the experimental data were attempted. For the dolomite decomposition stage of the one-step technology, the equation of the chemical kinetic model can be represented by α2/2 = kD1τ in the temperature range of 1173−1473 K, and the apparent activation energy was determined to be 160.6 kJ mol−1. For the magnesium reduction stage of the one-step technology, the surface reaction chemical kinetic model 1 − (1 − β)1/3= kSτ described very satisfactorily the experimental values for the different reduction temperature. Then, a one-step model incorporating the chemical reaction kinetics of the dolomite decomposition stage and the magnesium reduction stage and heat conduction was first developed. The simulations of the impact of heating temperature on the dolomite decomposition stage and magnesium reduction stage were carried out in the reduction retorts of the furnace utilizing this model. The distribution of dolomite decomposition extent in the retorts, the total extent of dolomite decomposition with time, the distribution of magnesium reduction extent in the retorts, and the total extent of magnesium reduction with time were studied in detail. The analysis showed that the one-step technology is effective in not only reducing the cycle time of dolomite decomposition stage and magnesium reduction stage but also saving energy. stage, the raw material dolomite is calcined in a rotary kiln24 that has a high temperature of about 1200 °C. When the temperature of the dolomite is over the decomposition temperature, the dolomite starts to break down into calcined dolomite while releasing carbon dioxide. The thermal decomposition of dolomite proceeds in a single step, according to the scheme

1. INTRODUCTION In recent years, with the fast development of the automotive and industries, the world demand for magnesium has also increased very quickly.1−3Magnesium could be produced through either the electrolysis of magnesium chloride melts from seawater or the silicothermic reduction of magnesium oxide under a high-vacuum environment and at a high temperature using ferrosilicon as a reducing agent. The Pidgeon process is the most employed thermal reduction process in industry, and it could produce over 90% of the primary magnesium output of China, which currently supplies more than three-quarters of the world demand for magnesium.4 Because of its low investment cost and simple industrial operations, the Pidgeon process is anticipated to be the major industrial production technology for producing high-purity magnesium in recent decades.5 However, the high energy consumption and serious air pollution problems caused by this process become an increasingly serious concern.4,6−9 Though a lot of research10−23 has been carried out to investigate this process, no advanced innovative technologies were invented to solve these thorny issues in the past few decades. Thus, it is necessary to develop a low-energy, high-efficiency, lowemission technology to produce magnesium in industry. In general, the traditional silicothermic reduction process comprises two stages: the dolomite decomposition stage and the magnesium reduction stage. In the dolomite decomposition © 2015 American Chemical Society

1473 K

(CaCO3 ·MgCO3)(s) ⎯⎯⎯⎯⎯⎯→ (CaO·MgO)(s) + 2CO2(g)↑ (1)

In this stage, high-temperature carbon dioxide, which accounts for approximately 48% of the total mass of the dolomite, is released into the atmosphere. The temperature of the calcined dolomite produced by this process is also about 1200 °C, and it must be cooled down to room temperature in order to move on to the magnesium reduction stage. The room-temperature calcined dolomite is mixed with ferrosilicon and fluorite, and the mixture is then smashed to 200 mesh and briquetted by the dry powder pigeonhole ball machine apparatus under a certain pressure to produce briquettes with a shape of walnut. Briquettes were placed inside the retorts and Received: Revised: Accepted: Published: 8883

May 18, 2015 July 28, 2015 August 31, 2015 August 31, 2015 DOI: 10.1021/acs.iecr.5b01830 Ind. Eng. Chem. Res. 2015, 54, 8883−8892

Article

Industrial & Engineering Chemistry Research

in a specific ratio. The mixture is pelletized to make briquettes for decomposition and reduction in the retorts externally heated in a magnesium reduction furnace. In the dolomite decomposition stage, the briquettes are heated to a temperature greater than 900 °C and release high-temperature carbon dioxide, which will be pumped out, cooled, collected, and recycled by the magnesium manufacturers. When all of the briquettes complete the decomposition, the temperature of the furnace is heated to at least 1150 °C and a vacuum of 1−10 Pa is maintained in the retorts in order to extract the magnesium vapor from the briquettes. The comparison of the flowcharts of the traditional Pidgeon process and the new one-step technology is shown schematically in Figure 1. It is evident that the carbon dioxide could be recovered in the new one-step method, and there is also no need to purchase the rotary kiln, which costs over 1 million dollars.

were heated to the optimal reaction temperature to proceed to the magnesium reduction stage.18 In this stage, a tremendous amount of heat is used for heating the briquettes and meeting heat demand for this endothermic reaction, and a high-vacuum environment that could protect the magnesium vapor from oxidation during this process must be also provided by the retorts. Magnesium is released in vapor form that is transported from the reduction section to the crystallization area and then condenses and forms the crown in the cooled end of the retort.20 The overall reaction of this process taking place in the retorts could be expressed as follows: 1373 − 1473 K, ∼ 10 Pa

2(CaO·MgO)(s) + Si(Fe)(s) ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ CaF2

2Mg(g) ↑ + 2CaO·SiO2(s) + Fe(s)

(2)

It is clear from the reactions that a large amount of carbon dioxide is emitted from the dolomite decomposition stage. The calculations suggest that in this stage, the greenhouse gas emissions is about 3.7 tons for each ton of magnesium produced by traditional Pidgeon process, and this value is calculated when considering merely carbon dioxide inside the dolomite material. Besides that, a great deal of energy is wasted and dissipates into the air as heat in the dolomite decomposition stage and the calcined dolomite cooling process, which is followed by the dolomite decomposition stage. This is because the dolomite decomposition stage is a high-temperature heating process, and the temperature of the carbon dioxide and calcined dolomite produced by this process is over 1200 °C. The high-temperature carbon dioxide is exhausted directly to atmosphere, and the calcined dolomite is cooled to room temperature in the air in order to be processed in the next stage. The energy, dissipated in this way, is about 7.55 MJ for each kilogram of magnesium produced by traditional Pidgeon process. If the carbon dioxide can be recovered and the lost heat can be saved, then the value of impact for the magnesium produced in China will be obviously decreased, and good economic benefits will be achieved in this process. Throughout the past couple of decades, people have done a great deal of experimental research on the chemical kinetics of the dolomite decomposition stage25−44 and the magnesium reduction stage,23,45−49 and some solid−solid reaction models50 were applied to describe these two processes. The phase boundary reaction model of zero order was found by Halikia et al.51 to best represent the dolomite decomposition stage, and the shrinking nonreacted core model was used to describe the intrinsic kinetics of the magnesium reduction stage. Although the experimental data they obtained is useful and the chemical kinetics models are better used in the numerical simulation process, their work plays a minor role in reducing greenhouse gas emissions and preventing additional heat loss in the traditional Pidgeon process. Therefore, a new one-step technology used for producing primary magnesium is presented in this paper. Some of the best features of this method are the combination of the two processes of dolomite decomposition and magnesium reduction in the magnesium reduction retort. It not only can collect the high-temperature carbon dioxide produced by the dolomite decomposition process but also can save the excessive heat loss caused by the two separate processes. This new one-step technology simply adopts finely ground dolomite instead of dolime to mix with ground ferrosilicon containing 75% of silicon as the reducing agent and calcium fluoride as a catalyst

Figure 1. Comparison of the flowcharts of the Pidgeon process and the one-step method.

To obtain the optimum process conditions of the new onestep technology, this paper presents an experimental study on the intrinsic chemical kinetics mechanisms of the processes. By applying each of the most likely solid-state kinetic models, the kinetic parameters of the two reactions that reacted during the dolomite decomposition stage and magnesium reduction stage were evaluated, and the kinetic models that best verify the experimental data were attempted. Then, a one-step model incorporating the chemical reaction kinetics of the dolomite decomposition stage and the magnesium reduction stage and heat conduction was first developed. The simulations of the impact of different heating temperatures on the dolomite decomposition stage and magnesium reduction stage were carried out in the reduction retorts in the furnace utilizing this model. The distribution of dolomite decomposition rate in the retorts, the total rate of dolomite decomposition with time, the distribution of magnesium reduction rate in the retorts, and the total rate of magnesium reduction with time were studied in detail. The analysis showed that the one-step technology is effective not only in reducing the cycle time of dolomite decomposition stage and magnesium reduction stage but also in saving energy.

2. EXPERIMENTAL PROCEDURES 2.1. Materials. For the present study, the materials of qualified dolomite, 75% ferrosilicon alloy, and fluorite powder were provided by the Kaitai Magnesium Co., Ltd., in China. The chemical compositions of dolomite and 75% ferrosilicon alloy are listed in Tables S1 and S2, respectively. 2.2. Method. The mixture containing qualified dolomite, 75% ferrosilicon alloy, and calcium fluoride powder was 8884

DOI: 10.1021/acs.iecr.5b01830 Ind. Eng. Chem. Res. 2015, 54, 8883−8892

Article


When the new one-step technology is applied in industry to produce magnesium, the magnesium reduction process occurs after the dolomite decomposition process in the retorts. Thus, in our intrinsic chemical kinetics experiments, briquettes used in the magnesium reduction stage must be used in the dolomite decomposition stage. To study the influence of decomposition temperature on the chemical kinetics of the magnesium reduction process, briquettes completely calcined at a different temperature in the dolomite decomposition stage were used as experimental material in the magnesium reduction stage. The briquettes were also arranged parallel to each other on the preheated crucible and were promptly inserted into the retort, in which the required reduction temperature zone was maintained. Then, the retort was sealed and vacuumed by the vacuum pump with the shortest time to start the intrinsic chemical kinetics experiments. At the end of the experiments, the residual slag and the condenser were taken out and cooled in inert nitrogen atmosphere. Then both of them were weighed carefully to calculate the extent of reduction. For some experiments, the residual slag was analyzed chemically and physically by using XRD and SEM techniques. The extent of the dolomite decomposition process could be calculated according to the following equation:

pulverized to 200 mesh in a ball mill and briquetted in a plunger press at 150 MPa. For eliminating the effect of thickness of the briquettes on the results of intrinsic chemical dynamics experiments, the thickness of the briquettes must be controlled within 1 mm. In our experiments, the diameter of the briquettes was set to about 25 mm to make sure each of the experimental subjects has a certain weight. The geometry and size of the briquettes is shown in Figure 2.

Figure 2. Geometry and size of the briquettes.

The intrinsic chemical kinetics experiments were carried out at a laboratory-scale horizontal-tube vacuum furnace, in which a high-temperature zone was maintained. The experimental temperature is controlled by a dual platinum−rhodium (Pt− Rh) thermocouple with a precision on the order of 1 °C. The vacuum system, which is made up of a 2X-15 rotary pump, a vacuum gauge, and vacuum pipes, is used to maintain a highvacuum environment. When the hot gas is pumped out of the retort, the gas temperature could be cooled to ambient temperature by using a heat exchanger. The inert atmosphere is maintained if necessary by blowing argon gas that is provided by the argon gas cylinder. Figure 3 shows the layout of our experimental system.

Extent of decomposition (%) = (CO2i − CO2r )/CO2i × 100

(3)

where CO2i is the initial total quantity of carbon dioxide in the briquettes and CO2r is the quantity of residual carbon dioxide in the unreacted slag. The extent of the reduction process could be calculated according to the following equation: Extent of reduction (%) = (Mg i − Mg r)/Mg i × 100

(4)

where Mgi is the initial total quantity of magnesium in the briquettes and Mgr is the quantity of residual magnesium in the unreacted slag. 2.3. Experimental Results and Analysis. 2.3.1. Exploration of Chemical Kinetics Mechanism on the Dolomite Decomposition Stage. Knowledge of chemical kinetics decomposition of dolomite in the briquettes is very important for the whole one-step process in industrial production. Many researchers have studied the effects of gas pressures, particle size of the dolomite samples, presence of other impurities, heating rate, and other factors on the chemical kinetics of dolomite decomposition using different tools such as thermal analysis, thermogravimetric analyses, XRD technique, among others, and different values of the activation energies for this decomposition reaction’s order of reactions also have been obtained. However, the state of the dolomite used in our onestep technology is very different from theirs because we mixed the finely powdered dolomite with 75% ferrosilicon alloy and calcium fluoride powder that were pulverized to 200 mesh and briquetted in a plunger press at 150 MPa. In this case, the chemical kinetics mechanism of the thermal decomposition of the dolomite that will be used in the one-step technology should be investigated by using our experimental procedures mentioned above. In our experiments, all parts of the briquettes were under isothermal condition by controlling the thickness of the briquettes. For example, when the experimental temperature was 1473 K, the temperature of the center of the briquettes rose from 300 to 1470 K in 10s after they were inserted into the retort. The temperature rising time was also

Figure 3. Schematic diagram of the experiment system.

In the dolomite decomposition stage of the intrinsic chemical kinetics experiments, the retort and the crucible were heated in advance from room temperature to a required decomposition temperature, and the air in the system was completely replaced with argon gas. Then, several prepared briquettes were arranged parallel to each other on the preheated crucible and were promptly inserted into the retort, in which the required decomposition temperature zone was maintained. Then, the retort was sealed and vacuumed by the vacuum pump with the shortest time to start the intrinsic chemical kinetics experiments. At the end of the experiments, the residual slag was taken out and cooled in inert nitrogen atmosphere. Then, the slag was weighed carefully to calculate the extent of decomposition. 8885


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Industrial & Engineering Chemistry Research sufficiently long for the vacuum pump to vent gases. Thus, we think the temperature of the briquettes is uniform in the dolomite decomposition stage, and our experimental data could accurately reflect the intrinsic chemical kinetics mechanism of this process. Despite of many years of research, there are still lots of controversial results about the chemical kinetics mechanism of the dolomite decomposition process, but all of the models based on their experimental data could not accurately describe the intrinsic chemical kinetics mechanism of the dolomite decomposition stage of the new one-step technology. However, the chemical reaction of the dolomite decomposition process is still a solid−solid reaction, and the solid−solid reaction kinetics models listed in Table S3 could describe this decomposition process. In the present work, exploration of chemical kinetics mechanism was carried out according to the experimental data, and five different models (D1, D2, and R1−R3) that could best describe the dolomite decomposition stage were selected for the evaluation of the kinetic parameters and determination of the best model. The computation of the kinetic parameters was based on the use of the Arrhenius equation applied to each model. According to the Arrhenius expression, the relation between the apparent rate constant and the reaction temperature is given by k = A exp( −E /RT )

Figure 4. Descriptions of the intrinsic chemical kinetics of the dolomite decomposition process using the D1 model.

chemical kinetics mechanism has been thoroughly studied and the D1 model was identified as the best model for this stage, the exact decomposition temperature requirement for the mixture containing qualified dolomite, 75% ferrosilicon alloy, and calcium fluoride powder could not be determined by the chemical kinetics experiments. To our knowledge, this data had never been described in the indexed literature, so we did thermogravimetric analysis experiments to investigate the initial decomposition temperature of the briquettes. The results, shown in Figure 5, indicate that the exact initial decomposition temperature of the mixture is 744.2 °C and the end decomposition temperature of the mixture is 818.7 °C.

(5) −1

where k is the pre-exponential factor (min ), E is the apparent activation energy (J·mol−1), and R is the gas constant (J·mol−1· K−1). The values of the apparent activation energy E, the preexponential factor A, and correlation coefficient r2 calculated from application of each model are given in Table 1. Table 1. Kinetic Parameters for Each Kinetic Model model

E (KJ·mol−1)

A × 10−5 (min−1)

r2

D1 D2 R1 R2 R3

160.6 159.8 160.3 159.5 160.0

0.96 1.57 2.11 3.27 2.77

0.99705 0.94374 0.85266 0.96998 0.96385

It is noticeable that the D1 model has better correlation coefficients than other models, so the 1D diffusion model is identified as the best model for the dolomite decomposition stage of the one-step technology. The experimental dynamics data were fitted by use of this model and the fitting equations are listed as follows:

Figure 5. TG curves of the mixture.

2.3.3. Effects of Decomposition Temperature on the Magnesium Reduction Stage. The magnesium reduction stage is the most important part of the one-step technology because the magnesium vapor is produced in this process and because the economy of the new technology is directly determined by the rate of magnesium production in this stage. In our recent study, we discovered that the decomposition temperature of the dolomite that was used in the magnesium reduction process can affect the magnesium reduction rate. Thus, the effects of decomposition temperature used in the dolomite decomposition stage on the magnesium reduction stage were first studied to investigate the optimal decomposition temperature, which could improve the magnesium production rate in the magnesium reduction stage and the one-step process economics. In the traditional decomposition process, dolomite is calcined at a high

α 2/2 = 95 869 exp( −16 637/RT )τ , T ∈ [1173 K, 1473 K]

(6)

where α is the extent of decomposition and τ is the decomposition time. The conclusion that the D1 model is the most appropriate laboratory model for describing the intrinsic chemical kinetics mechanism of the dolomite decomposition process could also be confirmed by the comparisons between model predictions and experimental results, which is shown in Figure 4. As seen in Figure 4, the model prediction results fit fairly well with the experimental data. 2.3.2. Exploration of the Initial Decomposition Temperature of the Briquettes. Although the dolomite decomposition 8886


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Industrial & Engineering Chemistry Research temperature over 1200 °C for about 4 h, and this leads to lower hydration activity of calcined dolomite, which could affect the magnesium production efficiency in the reduction process according to our previous studies. Thus, a dolomite decomposition temperature range of 900−1200 °C was selected in the dolomite decomposition stage of the one-step technology, and a same reduction temperature of 1200 °C was used in the magnesium reduction stage for best results. The effect of decomposition temperature on the magnesium reduction stage is shown in Figure 6. The notation “1173D1473R” means that the decomposition temperature is 1173 K and the reduction temperature is 1473 K.

where β is the extent of magnesium reduction, τ is the reduction time, and kS is the pre-exponential factor determined by the Arrhenius equation (eq 5). As we know, the apparent activation energy E will change over reduction time because the temperature and composition of the briquettes is constantly changing in the magnesium reduction stage. Thus, the apparent activation energy is directly correlated to both reaction time and reaction temperature. Previous research showed that the variation of the apparent activation energy with reaction time was more significant than that with reaction temperature. For the sake of convenience in calculations, the variation of the apparent activation energy with reaction temperature was neglected, and a quadratic polynomial is proposed to calculate the apparent activation energy in our study. Consequently, a regression calculation was carried out, and the experimental kinetics data of the magnesium reduction stage of the one-step technology were fitted by use of the surface reaction model and the fitting equations are listed as follows: 1 − (1 − β)1/3 = 3.5 exp( −(74 008 + 117.996τ − 0.30728τ 2)/RT )τ , T ∈ [1323 K, 1473 K]

(8)

Figure 7 compares the experimental data and calculation results. It can be found that the calculation results are in good

Figure 6. Curves of magnesium reduction extent with reduction time for different dolomite decomposition temperatures: 1173, 1273, 1373, and 1473 K.

We can see in Figure 6 that the extent of magnesium reduction decreases with the increase of dolomite decomposition temperature although they all show a similar trend. However, the extent of magnesium reduction decreases much more significantly at a decomposition temperature over 1273 K than that at a decomposition temperature below 1273 K. Such phenomenon might be attributed to many reasons, but the most important one is that the increase of dolomite decomposition temperature could lead to a much more violent reaction. The high-temperature carbon dioxide produced in the inside of the briquettes is sputtered from the surface, and the size of the cavity inside the briquettes increases with increasing decomposition temperature. Because the subsequent magnesium reduction process is also a solid−solid reaction, the chemistry reaction rate goes down with the increasing of the distance between reactants particles. High temperature can lead to reducing the dolomite decomposition cycle time, so we selected 1273 K as the best dolomite decomposition temperature. 2.3.4. Exploration of Chemical Kinetics Mechanism on the Magnesium Reduction Stage. In the magnesium reduction stage of the one-step technology, the reaction control conditions are similar to those used in the traditional reduction process; thus, the surface reaction model that was applied to the traditional reduction process by Li et al.47 could describe this similar reduction process. The expression of the surface reaction model is 1 − (1 − β)1/3 = k Sτ

Figure 7. Comparison of the model results with the experimental data.

agreement with the experimental data and the surface reaction model could be used to describe the magnesium reduction stage of the one-step technology. It is clear that the new one-step technology we proposed is much improved compared to the traditional silicothermic magnesium reduction techniques. The intrinsic chemical kinetics mechanisms of the dolomite decomposition stage and magnesium reduction stage are controlled by the 1D diffusion model and the surface reaction model, respectively. From the present study, it is found that the 1D diffusion model could accurately describe the intrinsic chemical kinetics mechanism of the dolomite decomposition stage and the apparent activation energy can be calculated as 160.6 kJ·mol−1 by this model. To obtain best reduction results, we selected 1273 K as the best dolomite decomposition temperature. Thus, the surface reaction model was used to describe the following magnesium reduction stage and was testified to be reasonable and feasible.

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3. NUMERICAL DESCRIPTION 3.1. Physical Model. Though the intrinsic chemical kinetics mechanisms of the two stages of the new one-step technology were studied by kinetic experiments, the technical characteristic and commercial application of this technology could not be obtained by industrial experiments because of the high costs. To investigate the engineering application and effect evaluation of this new technology, a comprehensive numerical calculation model was developed in combination of the dolomite decomposition model, magnesium reduction model, and heat transfer model in present paper. In the traditional magnesium industrial production, the magnesium reduction process occurs in the retorts that are horizontally placed in the reduction furnace heated by high-temperature flue gas. To apply the new one-step technology to industrial production, the numerical calculation model was carried out in the retorts in the reduction furnace. The photo of the reduction furnace and a 2D geometrical model suitable for this simulation are illustrated in Figure 8.

where Md is the maximum carbon dioxide production per unit volume (mol·m−3), and Md = 26923 mol/m3 according the ratio of reactants. ϕd is the thermal energy required per mole of carbon dioxide in the decomposition reaction (J·mol−1), and the expression of ϕd could be given as follows: ϕd = 15 8477 − 14.52T

(11)

((dα)/(dτ)) is the change in rate of decomposition extent with time derived from the intrinsic chemical kinetics (eq 6), and it can be expressed as dα = dτ

47934.5 exp(− 160 637/RT ) , τ

T ∈ [1173 K, 1473 K]

(12)

In the magnesium reduction stage, the chemical reaction heat source Sb can be calculated by S b = M rϕr

dβ dτ

(13)

where Mr is the maximum magnesium production per unit volume (mol·m−3), and Mr = 13461.5 mol·m−3 according the ratio of reactants. ϕr is the thermal energy required per mole of magnesium in the reduction reaction (J·mol−1), and the expression of ϕr could be given as follows: ϕr = 249 020 − 21.16T

(14)

((dβ)/(dτ)) is the change in rate of reduction extent with time derived from the intrinsic chemical kinetics eq 8, and it can be expressed as dβ = 10.5(1 − 3.5 exp(− (74 008 + 117.996τ − 0.30728τ 2)/RT )τ ) dτ (1 + (0.61456τ 2 − 117.996τ )/RT ) exp(− (74 008 + 117.996τ − 0.30728τ 2)/RT ), T ∈ [1323 K, 1473 K]

(15)

3.4. Thermophysical Properties. In the new one-step technology process, the density, thermal conductivity, and specific heat of the briquettes change over the extent of the decomposition in the dolomite decomposition stage and over the extent of the reduction in the magnesium reduction stage. Therefore, the extent-dependent properties were used in our numerical calculation process in order to obtain more accurate results. Table 2 lists the extent-dependence thermophysical properties of the briquettes in the numerical computations. 3.5. Simulation Procedures. In the new one-step technology process, the briquettes charged in the retorts will first go through the dolomite decomposition stage at a constant fuel gas temperature about 1000 °C. When the dolomite decomposition stage is complete and the high-temperature

Figure 8. Reduction furnace and the geometrical model.

3.2. Control Equation. The control equation for this 2D numerical model in the Cartesian coordinate can be expressed as follows: ∂(ρb cbT ) ∂τ

=

∂ ⎛ ∂T ⎞ ⎜λ b ⎟ + S b ∂xi ⎝ ∂xi ⎠

(9)

where ρb, cb, and λb are the density, specific heat capacity, and thermal conductivity of briquette, respectively. Sb is the heat source caused by the decomposition reaction occurred in the dolomite decomposition stage and the reduction reaction occurred in the magnesium reduction stage, which will subsequently be calculated and added to the control equation as a source term via the user defined function. 3.3. Chemical Reaction Heat Source. As we know, both the dolomite decomposition process and magnesium reduction process are endothermic reactions, and the value of the heat source depends on the rate of chemical reaction in different stage. In the dolomite decomposition stage, the chemical reaction heat source Sb can be calculated by

S b = Mdϕd

dα dτ

Table 2. Thermophysical Properties of the Briquettes expressions

properties density ρb (kg·m−3) thermal conductivity λb (W·m−1·K−1) specific heat Cb (J·mol−1·K−1)

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dolomite decomposition stage

magnesium reduction stage

2800 − 1185α 0.9 − 0.2α 0.0994T + 138.24 − (0.075T + 55.58)α

1615 − 323β 0.7 − 0.15β 0.0194T + 82.66 + (0.0081T − 19.85)β


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Industrial & Engineering Chemistry Research carbon dioxide is recycled, the fuel gas temperature is raised to 1200 °C, and the magnesium reduction stage starts. In numerical modeling of this new one-step technology process, the simulation procedures were divided into two steps. First, the retorts were heated up to 1000 °C by the constanttemperature fuel gas. The briquettes were then charged into the retorts, and the dolomite decomposition stage began. In this process, the source Sb of decomposition reaction heat was added as source term via a user-defined function, and the initial temperature of the briquettes was set as room temperature (300 K). In this stage, the D1 model was used in the dolomite decomposition numerical calculation through the user-defined function compiled by Language C. Through this user-defined function, the distributions of temperature and decomposition extent under simultaneous action of heat conduction and dolomite decomposition reaction could be monitored during the numerical calculation process. This unsteady process was solved by the time-marching method. The time step was set to 60 s, and interphase coupling iterations were performed to get a convergent solution at each time step. The extent of the decomposition was monitored, and once the dolomite decomposition process was completed, the temperature of the fuel gas is raised to 1200 °C, starting the magnesium reduction stage. In this process, the source Sb of reduction reaction heat was added as source term via a user-defined function and this process was also solved by the time-marching method. In this stage, the surface reaction model was used in the magnesium reduction numerical calculation through the user-defined function compiled by Language C. Through this user-defined function, the distributions of temperature and reduction extent under simultaneous action of heat conduction and magnesium reduction reaction could be monitored during the numerical calculation process. 3.6. Simulation Methodology. In the dolomite decomposition stage of the new one-step technology process, the control equation can be expressed as follows: ∂(ρb cbT ) ∂τ

⎛ ∂2 ∂2 ∂2 ⎞ = ⎜ 2 + 2 + 2 ⎟ × (λ bT ) ∂y ∂z ⎠ ⎝ ∂x ⎡ d α (τ , T ) ⎤ + ⎢ −Mdϕd ⎥ ⎣ ⎦ dτ

This equation was spatially and temporally discretized using the finite-volume method with a fully implicit first-order upwind scheme: (ρb cbT )in,+j 1 − (ρb cbT )in, j Δτ ⎛ 1 1 1 ⎞ ⎟[(λbT )in−+2,1j − 2(λbT )in−+1,1j + (λbT )in,+j 1] =⎜ 2 + + 2 Δy Δz 2 ⎠ ⎝ Δx ⎡ β(τ + Δτ , Tin, j+ 1) − β(τ , Tin, j+ 1) ⎤ ⎥ + ⎢ −M rϕr ⎢⎣ ⎥⎦ Δτ (19)

3.7. Numerical Results and Discussion. 3.7.1. Dolomite Decomposition and Magnesium Reduction Characteristics in Industrial Production. In the dolomite decomposition stage of the new one-step technology because the temperature of the fuel gas is set to 1000 °C the total decomposition extent and decomposition rate were investigated in the case of heating temperature of 1000 °C. In the later magnesium reduction stage, the temperature of the fuel gas is raised to 1200 °C. Because the reduction temperature is so high, the range of temperature in the reduction furnace is from 1150 to 1200 °C, which was measured in the magnesium reduction furnaces used in several magnesium enterprises. Therefore, the magnesium reduction characteristics were investigated in the cases of three typical heating temperatures: 1150, 1175, and 1200 °C. Figure 9 shows the curves of the total decomposition extent and reduction extent with time in constant decomposition

(16)

Then, it was spatially and temporally discretized using the finite-volume method with a fully implicit first-order upwind scheme:52 (ρb cbT )in,+j 1 − (ρb cbT )in, j

Figure 9. Curves of decomposition extent and reduction extent with time in constant decomposition temperature of 1273 K and different reduction temperatures of 1423, 1448, and 1473 K.

Δτ ⎛ 1 1 1 ⎞ ⎟[(λbT )in−+2,1j − 2(λbT )in−+1,1j + (λbT )in,+j 1] =⎜ 2 + + 2 Δy Δz 2 ⎠ ⎝ Δx ⎡ α(τ + Δτ , Tin, j+ 1) − α(τ , Tin, j+ 1) ⎤ ⎥ + ⎢ −Mdϕd ⎢⎣ ⎥⎦ Δτ (17)

temperature of 1273 K and three reduction temperatures of 1423, 1448, and 1473 K. A wealth of information is to be found in the numerical computing results, indicating that the application of the new one-step technology reduced the dolomite decomposition cycle time and magnesium reduction cycle time compared to that of the old technology and gained distinct effects. In traditional industrial production, a 4−5 h dolomite decomposition cycle is often operated by using a high heating temperature over 1473 K. However, a decomposition temperature of 1273 K was used in the dolomite decomposition stage of the new one-step technology, and the decomposition cycle is calculated as about 5 h. In this case, the new technology could save a lot of fuel, and the carbon dioxide released in this

In the magnesium reduction stage of the new one-step technology process, the control equation can be expressed as follows: ∂(ρb cbT ) ∂τ

⎛ ∂2 ∂2 ∂2 ⎞ = ⎜ 2 + 2 + 2 ⎟ ( λ bT ) ∂y ∂z ⎠ ⎝ ∂x ⎡ d β (τ , T ) ⎤ + ⎢ −M rϕr ⎥ ⎣ ⎦ dτ

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1035 K under a constant flue gas temperature of 1273 K in the decomposition stage. Because the flue gas temperature increased to 1473 K at the beginning of the magnesium reduction stage, the minimum temperature in the retorts increased from 1035 to 1317 K in the first reduction hour. However, in the following several hours, the increase in the minimum temperature was almost negligible. This is mainly because there was a large temperature gradient and because the temperature of most briquettes had barely reached starting reaction temperature, which did not cause a lot of heat absorption in the early phases. As time progressed, the temperature gradient decreased and the heat absorption caused by the reactions also increased greatly. This means that changes in total decomposition extent and reduction extent are more closely associated with intrinsic chemical kinetics than heat transfer in each later stage of the new one-step technology process.

process also could be recycled into use. The results indicate that the magnesium reduction cycle is about 6, 7.5, and >10 h for obtaining 80% total extent of reduction for different reduction temperatures of 1473, 1448, and 1423 K, respectively. Compared with that of traditional technology, the productivity of this new one-step technology is higher, and the consumption of energy is reduced greatly. In addition, the reduction temperature should be controlled at no less than 1448 K in order to achieve the best production effect in industrial production. 3.7.2. Dolomite Decomposition and Magnesium Reduction Characteristics. Figure 10 shows the dolomite decom-

4. CONCLUSIONS In this study, a new efficient one-step technical method was first developed for the production of magnesium in the industry. The one-step method could combine the two processes of dolomite decomposition and magnesium reduction in the magnesium reduction retort. Thus, the high-temperature carbon dioxide produced by the dolomite decomposition process could be collected in a timely manner instead of being emitted into the atmosphere, and excessive heat loss caused by the two separate processes could also be almost completely avoided. This paper presents an experimental study on the intrinsic chemical kinetics mechanisms of this new efficient one-step technology. By applying each of the most likely solid-state kinetic models, the kinetic parameters of the two reactions that reacted during the dolomite decomposition stage and magnesium reduction stage were evaluated, and the kinetic models that best verify the experimental data were attempted. The exact decomposition temperature of the briquettes was first estimated by TGA experiments, and a trend that the magnesium reduction extent decreased with the increase of dolomite decomposition temperature was found by the chemical kinetics experiments. Then, a one-step model incorporating the chemical reaction kinetics of the dolomite decomposition stage and the magnesium reduction stage as well as heat conduction was first developed. The simulations of the impact of heating temperature on the dolomite decomposition stage and magnesium reduction stage were carried out on the reduction retorts in the furnace utilizing this model. The distribution of dolomite decomposition extent in the retorts, the total extent of dolomite decomposition with time, the distribution of magnesium reduction extent in the retorts, the total extent of magnesium reduction with time were studied in detail. The analysis showed that the one-step technology is effective not only in reducing the cycle time of dolomite decomposition stage and magnesium reduction stage but also in saving energy. It is also concluded from the numerical results that the intrinsic chemical kinetics is the main factor limiting carbon dioxide and magnesium production in each later stage, so improving the chemistry reaction rate could increase the magnesium production capacity and shorten the productive cycle.

Figure 10. Decomposition extent and reduction extent distributions with time.

position extent and magnesium reduction extent distributions with time at a constant decomposition temperature of 1273 K and reduction temperature of 1473 K in the retorts. As seen in Figure 10, both the dolomite decomposition stage and magnesium reduction stage are a reaction process occurring layer by layer. In the decomposition stage, the decomposition extent increases with reaction time, but the growth rate drops quickly. It is clear that most of the briquettes in the retorts have completed this process, and an average decomposition extent 0.8 is obtained at the end of 3 h. The duration of the dolomite decomposition process is about 5 h. In the reduction stage, the reduction extent also increases rapidly at first and then slowly with time. The magnesium reduction extent reaches a higher value than 0.8 at the end of 11 h, and the reduction period is about 6 h. 3.7.3. Temperature Characteristics. Figure 11 shows the temperature distribution and its variation with reduction time in the retorts. The results show that the temperature of the briquettes went up quickly at the decomposition stage, but the trend became quite slow at the later reduction stage. The minimum temperature in the retorts increased from 300 to

Figure 11. Temperature distributions at certain times in the retorts. 8890


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b01830. Chemical analysis of qualified dolomite (Table S1), chemical analysis of 75% ferrosilicon alloy (Table S2), solid−solid chemical kinetics models and corresponding equations (Table S3), basis of selection of thermophysical properties data. (PDF)

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((dα)/(dτ)) = Change in rate of decomposition extent with time β = Extent of magnesium reduction ((dβ)/(dτ)) = The change in rate of reduction extent with time λb = Thermal conductivity of briquette (W·m−1·K−1)

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AUTHOR INFORMATION

Corresponding Author

*Phone: (+86) 029-82669033. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for the financial support from the National Natural Science Foundation of China (grant no. 51236007). NOMENCLATURE A = Pre-exponential factor (min−1) CO2i = Initial quantity of carbon dioxide in the experimental briquettes (kg) CO2r = Quantity of residual magnesium in the unreacted slag (kg) Cb = Specific heat of briquette (J·kg−1) E = Apparent activation energy (J·mol−1) k = Kinetics reaction constant (min−1) kF1 = Kinetics reaction constant in F1 model (min−1) kF2 = Kinetics reaction constant in F2 model (min−1) kF3 = Kinetics reaction constant in F3 model (min−1) kD1 = Kinetics reaction constant in D1 model (min−1) kD2 = Kinetics reaction constant in D2 model (min−1) kD3 = Kinetics reaction constant in D3 model (min−1) kR1 = Kinetics reaction constant in R1 model (min−1) kR2 = Kinetics reaction constant in R2 model (min−1) kR3 = Kinetics reaction constant in R3 model (min−1) kS = Kinetics reaction constant in surface reaction model (min−1) Md = Maximum carbon dioxide production per unit volume (mol·m−3) Mr = Maximum magnesium production per unit volume (mol·m−3) Mgi = Initial quantity of magnesium in the experimental briquettes (kg) Mgr = Quantity of residual magnesium in the unreacted slag (kg) r2 = Correlation coefficient R = Gas constant (J·mol−1·K−1) Sb = Reaction heat source (W·m−3) τ = Reaction time in experiment and numerical model (min) T = Local temperature (K) xi = Coordinate (m) ϕd = Thermal energy required per mole of carbon dioxide (J· mol−1) ϕr = Thermal energy required per mole of magnesium (J· mol−1) ρb = Density of the briquette (kg·m−3) α = Extent of dolomite decomposition 8891


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