Gaseous reduction of iron-bearing ores is of crucial importance for the production of iron via the dominant blast furnace (BF) route. In the shaft of the BF, the descending solid ores are gradually reduced by the ascending gas mixture that contains mainly carbon monoxide (CO) and hydrogen (H2) as reducing agents and a considerable fraction of nitrogen (N2) as a heat carrier for heating the solid burden. It has been identified that the presence of inert N2 can curb the reduction, and the prevailing mechanism is attributed to the dilution effect of interfacial chemical reaction, i.e., N2 lowers partial pressure of the reducing agent and consequently leads to a decrease in chemical driving force for the reduction reaction. According to the theory of multicomponent mass transfer , however, N2 is also likely to exert influence via mass transfer. This can be explained with the well-known concept of a topochemical reaction for an individual particle of iron ore: Before reaching the reaction site, the reducing agent must travel through an external boundary film and then an internal solid product shell, where both are occupied by a gas mixture containing N2. Thus, the amount of the reducing agent finally participating in the reaction is affected or even determined by the amount of N2. For a thorough understanding of the BF process, it is therefore necessary to shed more light on the complicated gas-solid system involving coupled phenomena of heterogeneous chemical reaction and multicomponent mass transfer.
There are various gas-solid systems in metals and materials processing industries, and gaseous reduction of iron ores has been paid extensive attention over the years, leading to numerous publications reporting experimental results and mathematical models [2,3,4,5,6,7]. In the field of ironmaking, the most frequently adopted mathematical models are the unreacted shrinking core model (USCM) and its refined variant, e.g., the grain model . In the original derivation of these two topochemical models, only a single-component reducing agent (e.g., pure CO or H2) was taken into account, and the mass transfer either in the external film or in the internal shell was regarded as equimolar counter diffusion of the gaseous reactant (referred to as A) and product (B). The corresponding molecular diffusion coefficient was thus given the binary diffusion coefficient with respect to A and B, i.e.,
Focussing on gaseous reduction of iron ores, Szekely and co-authors  were among the first who evaluated the applicability of
Starting with the Maxwell-Stefan relation for multicomponent mass transfer, Shao and co-authors developed a set of theoretical expressions for iron ore reduction characterised by equimolar counter diffusion of a gaseous reactant and a product in the presence of an inert component . The diffusion sub-steps of both the external film and internal shell were described in a more accurate manner, and the influence of N2 on the reduction was assessed in a quantitative way. The results showed that, for CO reduction of iron ores, the use of
The present paper is focussed on developing a more fundamental and accurate USCM for estimating the progress of iron ore reduction in H2-N2 atmosphere based on the theoretical expressions established previously. The underlying concepts and main expressions are first introduced, followed by an outline of the present model and the original USCM with
The current model takes into account the reversible gaseous reduction of wüstite, Fe
In the internal shell (cf. Figure 1), H2 diffuses inwards to the unreacted (shrinking) core surface through a mixture of H2, H2O and N2, while an identical amount of H2O diffuses outwards along the same path. As a result, the molar flow rates of H2 and of H2O are equal and opposite. For the inert N2, the molar flow rate is zero because it is neither consumed nor produced. However, this is not to say that the partial pressure/concentration difference of N2 along the diffusion path is zero since the local molar mean velocity of the three components is non-zero. Under pseudo steady state, the overall reduction rate can thus be equated with the molar flow rate of H2 through the internal shell. Starting with the Stefan-Maxwell relation for multicomponent mass transfer and after appreciable algebraic manipulation, the following two expressions for the overall reduction rate can be obtained:
Alternatively, when neglecting the influence of N2, i.e., using
In order to illustrate the two USCMs, experimental data reported by Murayama and co-authors  are used as a basis for the comparison. In the laboratory-scale experiments described in the work, wüstite pellets were first prepared by partial reduction of pure hematite pellets in a 50% CO-50% CO2 atmosphere at 1273 K. After that, the wüstite pellets were reduced at 1273 K in a H2-N2 atmosphere with different N2 fractions. A total gas flow rate of 2.0 NL/min was maintained throughout each experiment with the intent to eliminate the mass transfer resistance of the external film so the mole fraction of each component at the pellet surface can be considered equal to the corresponding one in the bulk stream. Furthermore, the authors demonstrated that the reduction process is in the mixed control regime of internal diffusion and interfacial chemical reaction. It is therefore implied that the two USCMs analysed in the present paper are applicable to the experimental data, of which the main parameters are listed in Table 1.
Main parameters of experiments regarding hydrogen reduction of wüstite pellets .
|4.88 × 104|
|12.48 (at 1273 K)|
|11.43 (at 1273 K)|
|4.45 (at 1273 K)|
|0.673 (at 1273 K)|
The two USCMs are first applied to the data of Exp. 1 as a reference, and the macro-kinetic parameters were estimated based on regression analysis. As can be seen in Figure 2 and its insert, the macro-kinetic parameters obtained by the USCM with
In the USCM with
Using the corresponding
As for the deviation shown in Figure 3, the emphasis can be put on inspecting the mathematical model where
In order to substantiate the argument above, the relationships between reduction degree and reaction time under the conditions of Exp. 2 and Exp. 3 were estimated by the USCM with
The noticeable difference in the performance of the two USCMs is explained in the following text, where calculations are made mainly under the conditions of Exp. 2 for the sake of brevity.
In the USCM with
The concentration difference of N2 along its diffusion path was calculated using the USCM with
As can be seen in Figure 5, the N2 concentration difference is positive and increases with an increase in the reduction degree. This implies that the mole fraction of N2 at reaction interface is smaller than that in the bulk stream. In other words, the sum of mole fractions of H2 and H2O at reaction interface is bigger than the sum in bulk stream, i.e.,
To further demonstrate the differences between the two models, the chemical driving forces were calculated and depicted in Figure 8, where the driving force representing the USCM with
Using the two models with the macro-kinetic parameters estimated based on the data of Exp. 1, the influence of N2 on hydrogen reduction of iron ores is finally illustrated in Figure 9. Here, the relative modelling error is a positive value and increases with an increase in either the reduction degree or in N2 mole fraction of the bulk stream. As can be found in the figure, the relative modelling error is generally bigger than 5%, and it is thus suggested to adopt the USCM with
An USCM with multicomponent gas diffusion (i.e., USCM with
In summary, the main findings and conclusions are drawn as follows:
Using In addition to the dilution effect, the chemical driving force is also influenced by the multicomponent gas diffusion process. Under the conditions considered in the present study, the relative modelling error is generally bigger than 5%, and it is thus suggested to adopt the USCM with multicomponent gas diffusion for modelling gaseous reduction of iron ores in H2-N2 atmosphere.
In addition to the dilution effect, the chemical driving force is also influenced by the multicomponent gas diffusion process.
Under the conditions considered in the present study, the relative modelling error is generally bigger than 5%, and it is thus suggested to adopt the USCM with multicomponent gas diffusion for modelling gaseous reduction of iron ores in H2-N2 atmosphere.
The present model can be adopted to shed more light on the process of gaseous reduction in H2-N2 atmosphere. After appreciable algebraic manipulation, it can be used to further characterise a more complicated scenario regarding the gaseous reduction in CO-H2-N2 atmosphere, where the effect of water gas shift reaction plays an importance role. For this, the model will be extended in the near future. In addition, attempts will be made to integrate the present USCM into a simulation framework for mimicking the complicated gas-solid countercurrent flow involving coupled heat and mass transfers and chemical reactions in the BF.
Main parameters of experiments regarding hydrogen reduction of wüstite pellets .
|4.88 × 104|
|12.48 (at 1273 K)|
|11.43 (at 1273 K)|
|4.45 (at 1273 K)|
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