Introduction

Magnesium is the lightest metal among commonly used structure metals. and its wide application in many fields, such as metallurgy, chemical industry, and automobile industry,1,2 implies huge global demands for this metal.

The Pidgeon process is widely used in thermal reduction of dolime, and is well established.3,4 Magnesium produced by the Pidgeon process in China accounts for approximately 87% of the global yields in 2014 (data from U.S. Geological Survey).5 However, in the Pidgeon process, an amount of dolomite with small particle size is produced during the crushing stage. This small particle size material is unusable, since the particle size of dolomite is limited by the size of the rotary kilns. For example, the required particle size is in the range of 15–35 mm for a rotary kiln of 1.6–1.9 m diameter and 36 m length.6 Particle sizes smaller than 15 mm are unusable.

To solve the problem, Zhang et al.7 proposed a novel process by which magnesium was extracted from pre-prepared dolomite pellets with ferrosilicon as reductant. In this method, powder materials including dolomite, ferrosilicon, fluorite and binder are mixed to produce pellets which are called pre-prepared dolomite pellets, and then calcined. The pellets are charged into the retorts immediately after calcination. The problem of dolomite particle size is solved since powdered dolomite is used. In addition, some other problems in the Pidgeon process can be solved by this process. In the Pidgeon process, (1) the temperature of the dolime discharged from the cooler is still 423–493 K and the energy carried by the dolime is lost to the environment in the following processes; and (2) the temperature of the dolime prepared for briquetting is decreased from the calcination temperature (1423–1523 K) to ambient temperature. However, dolime in pellets is heated to 1473 K again during the reduction stage. This will decrease the production efficiency of the Pidgeon process. According to Li et al.,8 in the Pidgeon process, a long heating time (6–8 h) is needed to heat the pellets in the center region (r < 50 mm) of the retort to the reaction temperature due to a lower thermal conductivity of the pellets. In the new process, the problem can be avoided since the hot pellets after calcination are heated to the reduction temperature immediately.

Pellet yield and quality are important factors for the process. Wen Ming et al. studied the effect of binder on pellet yield and strength,9 as well as the decomposition of the dolomite in the pre-prepared pellets.10 The results indicated that the high-quality pre-prepared dolomite pellets were obtained by using a composite binder and a compressive strength reaching 80 N. The decomposition rate of dolomite and the hydration of dolime in the pre-prepared dolomite pellets reached 45% (at 1 h) and 35%, respectively. The strength of the pre-prepared dolomite pellets after calcination was also studied.11,12 The results showed that the compressive strength reached 78 N after calcination.

The reduction ratio of the pre-prepared dolomite pellets is another important factor for the process, which has not yet been reported. In this paper, non-isothermal kinetics of silicothermic reduction of dolime in the pre-prepared dolomite pellets was studied.

Experimental

Materials

The raw materials include dolomite, ferrosilicon, calcium fluoride and organic binder. Chemical analysis of dolomite (Dashiqiao, Liaoning Province) with particle sizes less than 74 μm and the dolime produced from its calcination at 1323 K for 1 h are given in Table I. Chemical analysis of ferrosilicon (Boyu nonferrous metal material, Liaoning Province) with particle sizes less than 74 μm is shown in Table II. The content of silicon in ferrosilicon is 75.6% in mass fraction. Calcium fluoride and polyvinyl alcohol of analytical reagent grade were used as the catalyst and the organic binder, respectively. High purity argon gas (99.999%) was used in the experiments.

Table I Chemical composition of dolomite
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Table II Chemical composition of ferrosilicon alloy
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Experimental Procedures and Apparatus

Dolomite, ferrosilicon and 3 wt.% CaF2 were mixed for 8 h at a stoichiometric ratio according to reaction (1) and reaction (2). The mixture containing an additional 3% binder was pressed into cylindrical pellets of 15 mm diameter and 15 mm height. The pellets were placed in dry air for 3 days to remove water before the experiments.

$$ {\text{CaCO}}_{3} \cdot{\text{MgCO}}_{{3({\text{s}})}} = {\text{CaO}}\cdot{\text{MgO}}_{{({\text{s}})}} + 2{\text{CO}}_{{2({\text{g}})}} $$
(1)
$$ 2\left( {{\text{CaO}}\cdot{\text{MgO}}} \right)_{{({\text{s}})}} + {\text{Si}}_{{({\text{s}})}} = 2{\text{CaO}}\cdot{\text{SiO}}_{{2({\text{s}})}} + 2{\text{Mg}}_{{({\text{g}})}} $$
(2)

A pellet was placed into an alumina crucible for each experiment, which was carried out in flowing argon. After purging the furnace with Ar for 10 min, the sample was heated from room temperature to 1323 K at a heating rate of 10 K/min and maintained at this temperature for 60 min. From 1323 K to 1673 K, the sample was heated at a constant heating rate which varied, by experiment, between 1 K/min and 9 K/min. The weight change was measured at 30-s intervals and recorded by a computer. The thermobalance apparatus is shown in Fig. 1. The balance has a detection precision of 0.001 g.

Fig. 1
figure 1

Schematic diagram of thermobalance device

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The reduction ratio of magnesium oxide (η) is defined as the ratio of magnesium mass loss during the reduction (ΔW) to the initial magnesium mass in the pellets (W 0 ). Since release of the produced magnesium vapor is the only reason for the change in the pellet mass from 1323 K to 1673 K, the change in the pellet mass is taken as the magnesium mass loss (ΔW). The balance reading was reduced by about 0.01–0.03 g due to the upward flowing argon. This error can be eliminated during the calculation of ΔW. The reduction residues were qualitatively investigated by x-ray diffraction (XRD) (PW3040/60 PANALYTICAL, using the Cu(Kα) target).

$$ \eta = \, \left( {\Delta W/W_{0} } \right) \, \times 100\%. $$
(3)

Results

Thermogravimetric Analysis of Dolomite and the Pre-prepared Dolomite Pellet

Figure 2 shows the thermogravimetric (TG) curves of the dolomite and the pre-prepared dolomite pellets. The observed weight loss of dolomite was 45.98% between 860 K and 1223 K. The observed weight loss of the pre-prepared dolomite pellet was 2.4% below 860 K and 40.14% between 860 K and 1223 K. Above 1323 K, a weight loss of 8.66% was observed. The weight loss below 860 K was attributed to the decomposition of organic binder. The decomposition of carbonates occurred between 860 K and 1223 K. The weight loss detected above 1323 K was attributed to the reduction of dolime in the pre-prepared dolomite pellets. After calcination, porous pellets were obtained and the density reached 1.1 g/cm3.

Fig. 2
figure 2

TG analysis of dolomite and pre-prepared dolomite pellet

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Dolomite in the pre-prepared dolomite pellets was completely decomposed after soaking at 1323 K for 60 min. The XRD pattern of the sample is shown in Fig. 3. Calcium silicide (CaSi2) and calcium silicate (Ca2SiO4) phases were found. It is deduced that the reaction (4) occurs based on the thermodynamic analysis.13

Fig. 3
figure 3

XRD pattern of the sample after soaking at 1323 K for 60 min

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$$ 5{\text{Si}}_{{({\text{s}})}} + \, 4{\text{CaO}}_{{({\text{s}})}} = \, 2{\text{CaSi}}_{{2({\text{s}})}} + {\text{Ca}}_{2} {\text{SiO}}_{{4({\text{s}})}} $$
$$ \Delta {\text{G}}^{\theta } = - 63880 + 19.69{\text{T}}\left( {\text{J/mol}} \right) $$
(4)

Effect of Heating Rate on Reduction Ratio

Figure 4 shows the changes in reduction ratio with temperature at different heating rates. The initial reaction temperature was increased with the increasing heating rate. For example, at the heating rate of 9 K/min, the initial reaction temperature was about 1400 K, which was decreased to 1340 K at a heating rate of 1 K/min. The final reduction ratio increased with the decrease in the heating rate, and reached 61.6%, 72.5%, 81.7%, 86.3% and 89.3%, respectively.

Fig. 4
figure 4

Effect of heating rate on reduction ratio

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A self-pulverizing phenomenon was observed for the pellets after the experiments due to the transformation from β-Ca2SiO4 to γ-Ca2SiO4. Figure 5 shows the XRD pattern of the residue after reduction at a heating rate of 1 K/min. It can be seen that the main phase is γ-Ca2SiO4. The weak peaks of MgO indicate that a high reduction ratio has been obtained.

Fig. 5
figure 5

XRD pattern of the residue after reduction at a heating rate of 1 K/min

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Discussion

By employing the Doyle method,14 the following equation is used for calculating the apparent activation energy.

$$ \lg \beta F(\alpha ) = \lg \frac{AE}{R} - 2.315 - 0.4567\frac{E}{RT} $$
(5)

where α is the reduction ratio, β the heating rate, T the temperature, A the pre-exponential factor, E the apparent activation energy of the reduction process, and R a constant, 8.314 J mol−1 K−1. The functions f(α) and F(α) in Eq. 5 reported in the Ref. 15 are used in this paper, which are shown in supplementary Table I.

Some α values were obtained from Fig. 4 between 1423 K and 1673 K in intervals of 10 K. The values of lgβF(α) for all mechanism functions were calculated by using these α values and corresponding to heating rate β. The linear fitting was carried out between lgβF(α) and 1/T. Some Adj. R-squared values were obtained, indicating the linearity (see supplementary Figure 3). The linear relationships calculated from the function C2 (second-order chemical reaction) were the best for all heating rates, for which all Adj.R-squared values were larger than 0.99. The relationships between lgβF(α) and 1/T calculated by the mechanism function C2 are plotted in Fig. 6. The apparent activation energy E values were calculated from the slopes of the straight lines to be 280.9 kJ/mol, 289.3 kJ/mol, 280 kJ/mol, 283.4 kJ/mol and 266.5 kJ/mol for the heating rates of 1 K/min, 3 K/min, 5 K/min, 7 K/min and 9 K/min, respectively. The average value of 280 kJ/mol was determined as the apparent activation energy of the reduction process.

Fig. 6
figure 6

Relationships between lgβF(α) and 1/T calculated by the mechanism function C2

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The mass transfer coefficient was calculated by using a method reported in the literature,16,17 which can also be found in the supplementary material (see Eqs. S1–S6). The mass transfer coefficient of magnesium vapor in argon at a temperature range of 1425–1650 K and gas flow rate of 5.56 × 10−5 m3/s, was between 0.11 m/s and 0.14 m/s. In comparison, the mass transfer coefficient of magnesium in argon at a temperature of 1573 K and a relatively low flow rate (1.3 × 10−6– 1.7 × 10−5 m3/s) was between 0.09 m/s and 0.11 m/s.16 From the mass transfer coefficient calculations, the pressure of magnesium vapor on the surface of the briquettes and in the bulk gas phase can be estimated, as shown in Fig. 7.

Fig. 7
figure 7

Calculated partial pressure of magnesium vapor on the surface of briquette and bulk phase at various temperatures

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A large difference between the actual pressure and the equilibrium pressure indicated a low generated rate of magnesium, which may result from out-diffusion of magnesium, diffusion of reactants or an intrinsic low chemical reaction rate.

The partial pressure of magnesium vapors on the briquette surface and in the bulk gas shows little change with increasing temperature. The calculated pressure in the bulk gas was estimated to be between 1 kPa and 1.7 kPa and that on the briquette surface was between 1.4 kPa and 2.4 kPa. The pressure drop between the bulk phase and the surface of the briquette was between 0.4 kPa and 0.7 kPa, which accounted for approximately 40% of the bulk phase. In addition, the reduction ratio was increased with increasing carrier gas flow rate (supplementary Fig. 1). These results indicate that the gas–film mass transfer (mass transfer of magnesium vapor from the surface of the briquette to the bulk vapor phase) may have some effect on the magnesium recovery. It is well known that decreasing the pellet size can improve the out-diffusion of magnesium vapor. However, the effect of pellet size on the reduction rate was not obvious (see supplementary Fig. 2). In addition, porous pellets (ρ = 1.1 g/cm3) in the present study benefit the out-diffusion of magnesium vapor. Therefore, it is deduced that the reduction process of the pre-prepared dolomite pellets may not be controlled by the diffusion of magnesium vapor in the pores.

In the initial stage of the reaction (i.e. below 1475 K), in which the reduction rate was below 20%, the product layer was not completely formed and the diffusion between the reactants was relatively easy due to the direct contact. If the reaction rate was limited by the diffusion of the reactants, the actual magnesium pressure should approach the equilibrium pressure in the initial stage of the reaction. However, a large difference between the actual pressure and the equilibrium pressure was found in Fig. 7. For example, the equilibrium pressure (4.9 kPa) was 2.7 times larger than the pressure on the pellet surface (1.8 kPa) at 1475 K. In addition, the density (1.1 g/cm3) of the pre-prepared dolomite pellets after calcination was smaller than that of pellets prepared according to Pidgeon process (between 1.8 g/cm3 and 2.1 g/cm3). However, the apparent activation energy obtained from the pre-prepared dolomite pellets is slightly smaller than that obtained by Morsi et al. (306 kJ/mol),18 and Wulandari et al. (between 299 kJ/mol and 322 kJ/mol),16 who suggested that the reaction in the Pidgeon process was controlled by solid-state diffusion of the reactants. These results indicate that diffusion of the reactants in the pre-prepared dolomite pellets is not the rate-controlling step. In the present study, the possible reason was the formation of CaSi2 during calcinations of the pre-prepared dolomite pellets. CaSi2 transformed into liquid alloy when the temperature was larger than 1300 K. According to the Si–Ca phase diagram, a larger amount of silicon was dissolved into the liquid alloy with increasing temperature. Therefore, the silicothermic process in the pre-prepared dolomite pellets is likely a solid–liquid reaction. The liquid alloy reduced the diffusion resistance of the silicon resulting in the lower activation energy. Some researchers19,20 have found calcium silicide, which was recognized as an effective reductant, during the silicothermic process. Morsi et al.,18 found that magnesium and iron were dissolved in the calcium silicide. The metallic phase formed during the reduction process was a mixture of metallic phases of magnesium, iron, silicon and calcium.

From these results, indirect evidence was obtained that an intrinsically low chemical reaction rate may be the main reason for the large difference between the actual pressure and the equilibrium pressure. This is consistent with the result obtained from the non-isothermal kinetics. The definite chemical reaction which is the rate-limiting step and the role of CaSi2 in the reduction process will be studied further.

Conclusion

The kinetics of the reduction of dolime in porous pellets (ρ = 1.1 g/cm3) by ferrosilicon was investigated using a non-isothermal gravimetric technique in the temperature range from 1323 K to 1673 K. The experiments were carried out in flowing argon. The following results are summarized from the present study.

  1. 1.

    A novel process was proposed in which powder materials including dolomite, ferrosilicon, fluorite and binder are mixed to produce pellets (pre-prepared dolomite pellets). A high reduction ratio was obtained from the pellets, indicating that the process is viable.

  2. 2.

    The second-order chemical reaction model can represent the kinetics of the process. The apparent activation energy of the process is 280 kJ/mol.

  3. 3.

    Calcium silicide (CaSi2) was found in the pellets after calcination. It transformed into liquid alloy, which reduced the diffusion resistance of the silicon during the reduction process. The silicothermic process in the pre-prepared dolomite pellets is possibly a solid–liquid reaction due to the formation of CaSi2.

  4. 4.

    The mass transfer coefficient for the transfer of Mg to bulk argon gas at an argon flow rate of 5.56 × 10−5 m3/s and a temperature range of 1425–1650 K is between 0.11 m/s and 0.14 m/s. The gas–film mass transfer may have some effect on the reduction kinetics. The chemical reaction is the major rate-limiting step according to the results of the non-isothermal kinetics and mass transfer kinetics.