Modeling Isothermal Reduction of Iron Ore Pellet Using Finite Element Analysis Method: Experiments & Validation

Abstract

Iron ore pellet reduction experiments were performed with pure hydrogen (H₂) and mixtures with carbon monoxide (CO) at different ratios. For direct reduction processes that switch dynamically between reformed natural gas and hydrogen as the reductant, it is important to understand the effects of the transition on the oxide reduction kinetics to optimize the residence time of iron ore pellets in a shaft reactor. Hence, the reduction rates were studied by varying experimental parameters such as the temperature (800, 850 & 900 °C), reactant gas flow rate (100, 150 & 200 cm³/min), pellet size and composition of the reactant gas mixture. The rate of reduction was observed to increase with an increase in temperature and reactant gas flow rate, but it decreased with an increase in pellet size. SEM greyscale analysis was performed to analyze the porosity and phase composition of partially reduced pellets. The porosity of the pellets was observed to increase from 0.3 for unreacted pellet to 0.42 for a completely reduced pellet. Energy-dispersive X-ray spectroscopy (EDAX) analysis was performed to identify the phases observed in the SEM images. The fraction of iron phase was observed to increase from the shell region of the pellet to the core region with an increase in the degree of reduction. A 2D-axisymmetric numerical model was developed on COMSOL Multiphysics, and it was validated using the conversion (X) vs. time curves obtained from each experiment. The model was able to accurately predict the total time needed for the complete conversion of a single iron ore pellet for multiple experiments. Effects of changes in the porosity and tortuosity of the pellet on the model were also studied and the rate of reduction was observed to be sensitive to changes in both porosity and tortuosity. The SEM analysis and the model results show that tortuosity is higher for pellets reduced with H₂ than for pellets reduced with H₂-CO gas mixtures.

1. Introduction

The modern iron and steel industry is the backbone of the global economy as it provides the basic building blocks for all major industries around the world including real estate, automotive, aviation, railways, shipbuilding, defense, etc. However, the basic manner in which the iron and steel industry operates will have to change due to its contribution towards global CO₂ emissions. Today, the iron and steel industry is responsible for approximately 7% of the total global CO₂ emissions and 16% of the total industrial CO₂ emissions globally. Hence, decarbonization is necessary and will play a significant role in mitigating the effects of climate change [1].

The ironmaking process involves the conversion of iron ores—hematite (Fe₂O₃) or magnetite (Fe₃O₄)—into metallic iron (Fe) using a suitable reducing agent. Among all the processes, the most common commercial ironmaking process currently employ carbon-based reducing agents such as coke in a blast furnace (BF) followed by carbon oxidation with oxygen steelmaking in a basic oxygen furnace (BOF) [2]. The use of carbon-based reducing agents is the primary source of CO₂ emissions in the conventional BF ironmaking process as the chemical reactions involved in this process produce CO₂ and CO [3]. However, the development of direct reduction iron (DRI) technologies such as the Midrex and Energiron processes has paved a path for a carbon-free ironmaking route. The DRI process involves a shaft furnace for ironmaking which uses reformed natural gas (NG) to form a CO/H₂ mixture for reducing iron ore. The Midrex process uses an external reformer, whereas the Energiron process reforms the natural gas in situ [4] to produce DRI or HBI. The conversion of Fe₂O₃ to Fe usually takes place in three steps, first Fe₂O₃ is converted into Fe₃O₄ which is then converted to FeO (>570 °C) and finally FeO is converted to Fe. The thermodynamics of the whole conversion process was reviewed extensively by Spreitzer and Schenk [5]. The solid-state reduction step is followed by a steelmaking step in an electric arc furnace (EAF). The use of DRI technology has resulted in a reduction of CO₂ emissions with the use of natural gas. Sarkar et al. reported a reduction in CO₂ emissions from 1.87 tons CO₂/tcs for conventional BF-BOF process to 1.269 tons CO₂/tcs for Midrex-Natural Gas-EAF process [6]. Nevertheless, the commercial state-of-the-art processes cannot be considered carbon-free as they do not eliminate CO₂ emissions completely from the ironmaking process.

In 2016, three companies from Sweden namely: LKAB (Luossavaara-Kiirunavaara Aktiebolag, mining company), SSAB (steel company), and Vattenfall AB (energy company) started a project aimed at developing a Hydrogen Breakthrough Ironmaking Technology (HYBRIT) to eliminate CO₂ emissions from ironmaking process using only fossil-free electricity as the primary source of energy [7]. In 2021, the United States Department of Energy also started the Grid-Interactive Steelmaking with Hydrogen (GISH) project. Within three years (2021–2024), the GISH project is aimed at demonstrating a pilot-scale reactor at 1 ton/week production of iron using H₂ and varying H₂-NG mixtures as reducing agent, using green hydrogen made available during off-peak demand periods on the grid. Models for EAF operation utilizing DRI feedstocks reduced with varying H₂-NG mixtures and carbon contents, and the development of a techno-economic model for optimizing the cost/performance tradeoffs for using excess electricity available on the grid to produce hydrogen and its use for reduction and melting process will also be developed. During the energy transition, which in the US is aimed to occur by 2035, the economically optimum ratio of NG/H₂ for achieving C emission free steel production will depend on the evolving cost of H₂ production [8], clean energy deployment [9] and evolution of CCUS [10]. It is therefore important to enable flexible operation of the reduction reactor which allows for a variable ratio of NG/H₂.

It is important to understand the reduction kinetics of iron ore pellets while transitioning from reformed natural gas to H₂ gas as a reducing agent to optimize the residence time of reactant gas mixture in a shaft reactor. In order to simulate the reduction kinetics and use these simulations to optimize reactor conditions, several analytic and numerical models have been developed over the last few decades. A detailed review of the fundamentals of the iron ore reduction process as well as the existing analytical and numerical models have been reported previously by several authors [5,11,12]. Briefly, the most common analytical model used to study the reduction kinetics is the unreacted shrinking core model which involves the diffusion of reactant gas through the reacted shell of the pellet to reach the unreacted core where the chemical reaction takes place [13]. Equations for the diffusion controlled regime were given by Ginstling model [14] and Jander model [15] to establish a relationship between conversion and the reaction rate constant. Similarly, the equations for the phase boundary controlled regime was reported previously by Ortega [16] and the equations for a mixed control regime were reported by Zuo et al. [17].

Several numerical models were also developed over the last two decades. The most common numerical model is the pellet-grain model which assumes the pellet to be made up of several small grains undergoing the shrinking core reaction [18]. Studies focused on non-isothermal reduction, comparison with the unreacted shrinking core model and numerical analysis of heat and mass transfer were also reported based on the pellet-grain model [19,20,21]. Other numerical models using finite element analysis were also reported, such as the 1D axisymmetric model by Beheshti et al. and the 2D axisymmetric model by Kazemi et al. [22,23]. Most of these numerical models do not report the changes in local concentrations of solid species and have a sharp boundary between the unreacted core and the reacted iron shell. These models also did not report the use of a variable porosity or tortuosity function.

To the best of our knowledge, there have been no studies on the development of a numerical model for iron ore pellet reduction using finite element analysis which includes the effects of porosity and tortuosity as variables. This study focuses on filling this knowledge gap by developing a 2D-axysymmetric model using COMSOL Multiphysics and its validation using experimental data obtained from reduction experiments performed using H₂ gas mixture as well as CO-H₂ gas mixture at different temperatures, pellet size, gas flow rates and gas compositions. The output concentration profiles obtained from the model were also validated through characterizing partially reduced pellets by SEM-EDAX analysis. This analysis confirms the presence of a concentration gradient instead of a sharp boundary between the unreacted core region and the reacted shell region.

2. Materials and Methods

Iron ore pellets for reduction experiments were used as supplied by Voestalpine AG, Linz, Austria. As shown in

Table A3. Unreacted pellet composition.

Component	Fe (Total)	FeO	SiO2	CaO	Al2O3	Volatiles	Carbides
Mass (%)	67.8	0.35	1.34	0.76	0.49	0.13	0

, these pellets consisted of 67.8% Fe (total), 1.34% SiO₂, 0.76% CaO, 0.49% Al₂O₃ and 0.13% volatiles. An average of the minimum and maximum diameter of individual pellets was obtained for a random sampling of pellets using calipers. The average diameter of pellets was measured by a photographic analysis method for 251 samples. This average diameter of each pellet was then used to calculate the mean diameter of the random sample for 251 pellets. The mean diameter was measured to be 13.54 ± 2.2 mm as shown in Figure 1.

The furnace assembly for performing reduction experiments was supplied by Verder Scientific Inc. (Pittsburgh, PA, USA), which consisted of a Mettler Toledo ME4001 balance mounted on top of a resistance furnace with a nickel superalloy tube chamber (Height: 1050 mm, OD: 60 mm & wall thickness: 2.5 mm), a gas mixing unit, and an exhaust gas burner. The gas mixing unit consisted of mass flow controllers, an oxygen meter (measuring the percentage of O₂ inside the furnace tube), and a Eurotherm 6100xio system for data logging. Cylinders of industrial-grade H₂ (99.9% pure), CO (99.5% pure), and ultra-pure nitrogen gas (99.9% pure) were supplied by Linde Gas. A stainless-steel 304 wire (diameter: 0.5 mm) was used to suspend a single iron ore pellet from the balance inside the nickel superalloy tube through a 2 mm opening on top. Figure 2 shows a schematic of the experimental setup.

A two-part epoxy-set resin and hardener along with silicone cups and sand discs were supplied by John M. Cowley Center for High-Resolution Electron Microscopy at Arizona State University to perform scanning electron microscopy of iron ore pellets.

To perform the iron ore pellet reduction experiments, a single pellet was first suspended inside the nickel superalloy tube using a stainless-steel 304 wire, followed by heating of the furnace at a constant rate of 7 °C/min under a continuous flow of N₂ gas at 200 cm³/min. The upper end of the tube was cooled using a stainless-steel tube which was supplied with a constant flow of cold water. When the desired reduction temperature was reached and the O₂% inside the tube was below 0.05%, data logging was started to record the changes in the mass of the pellet vs. time during the reduction process. The flow of reducing gas (H₂, CO) was then initiated to supply a mixture of N₂ with reducing gas to the inlet at the bottom of the reactor tube.

The single pellet reduction experiments using H₂ were performed at three different temperatures at 100 cm³/min flow rate of H₂ gas: 800 °C (Experiment 1), 850 °C (Experiment 3), and 900 °C (Experiment 7), respectively. At a constant temperature of 850 °C, three experiments using H₂ were performed with flow rates: 100 cm³/min (Experiments 3), 150 cm³/min (Experiment 5), and 200 cm³/min (Experiment 6). Three experiments were performed with different pellet sizes of 15.90 mm (Experiment 2), 13.85 mm (Experiment 3), and 11.50 mm (Experiment 4) at 850 °C and 100 cm³/min H₂ flow rate.

Reduction experiments using a mixture of H₂ and CO at different ratios were also performed at 850 °C. The flow rates of H₂ and CO were varied between 90 and 10 cm³/min, respectively in experiments 8 through 56 and 36 cm³/min, respectively in experiment 12 (simulated Midrex process gas mixture). The variations in experimental conditions are tabulated in

Table 1. Parameters of iron ore pellet reduction experiments.

		$\mathbf{Pellet} \mathbf{Mass} ( {\mathit{m}}_{\mathit{p}})$	$\mathbf{Approximate} \mathbf{Pellet} \mathbf{Diameter} ( {\mathit{d}}_{\mathit{p}})$	Temperature	H2 Flow	CO Flow	N2 Flow
Variations	Units	Grams	mm	°C	cm3/min	cm3/min	cm3/min
Temperature	Experiment 1	6.57	15.25	800	100	0	200
Pellet size	Experiment 2	7.13	15.90	850	100	0	200
	Experiment 3 *	5.36	13.85	850	100	0	200
	Experiment 4	2.95	11.50	850	100	0	200
Gas flow rate	Experiment 5	4.33	13.00	850	150	0	200
	Experiment 6	4.41	13.00	850	200	0	200
Temperature	Experiment 7	4.81	13.25	900	100	0	200
Gas composition	Experiment 8	6.22	15.00	850	90	10	200
	Experiment 9	4.59	13.75	850	80	20	200
	Experiment 10	4.76	13.40	850	75	18	200
	Experiment 11	4.28	13.25	850	70	30	200
	Experiment 12	6.27	15.00	850	56	36	200

* Experiment 3 is also compared with variations in temperature, gas flow and gas composition.

.

Interrupted reduction experiments were also performed to obtain partially reduced pellets at 25%, 40%, and 80% conversion at a temperature of 850 °C for pure H₂ at a flow rate of 100 cm³/min and for the gas mixture and flow rates in experiment 10. To observe the changes in the diameter of reduced pellets, 10 pellets were reduced at 850 °C with 200 cm³/min flow for both H₂ and N₂, similar to experiment 6.

To obtain the SEM images, the partially reduced pellets were mounted in a two-part epoxy resin and hardener using silicone cups, which were then placed under a vacuum for a few minutes to eliminate the bubbles inside the epoxy. After 24 h, the interior surface of the pellet was exposed by cutting the epoxy mount in the middle. After polishing the side with the pellet section exposed, it was coated with gold via sputter-coating for 30 s. SEM images were obtained on Helios-5 using a circular back scatter detector (CBS) at a voltage of 15–20 kV and a current of 0.8 nA. EDAX analysis was also performed using a high-performance in-chamber electron and ion detector (ICE) at a voltage of 15–20 kV and current of 0.8 nA. EDAX analysis was performed to determine the elemental composition of iron-oxide, iron and gangue present at three different locations inside the partially reduced pellets. The images were obtained for shell region (r/R = ~1), middle region (r/R = ~0.5) and core region (r/R = ~0), where R is the approximate pellet radius and r is the approximate distance between the image spot and center of the pellet.

Multiple SEM-backscatter images were also obtained starting from the outer edge of the pellet to its center in the radial direction. Greyscale analysis of these SEM images was performed using ImageJ software to obtain an approximate value of porosity and phase composition as shown in Figure A2 in Appendix A. Optical microscopy and EDAX mapping was also performed to observe the Fe₃C formation in the Midrex gas mixture reduced pellet. The sample preparation and the Fe₃C phase analysis process was reported previously by Kazemi and Sichen [24].

3. Experimental Results

3.1. Influence of Temperature, Pellet Size & Reactant Gas on Reduction Kinetics

The oxide pellet conversion (X) was calculated by assuming that the weight loss during the reduction experiments was caused by the removal of oxygen from hematite. 29.13% of the mass of the pellet was calculated to be oxygen in hematite. Hence, X was calculated using the following equation:

$$\mathrm{X}=\frac{w}{0.2913m_p}$$

(1)

where, m_p is the mass of pellet before reduction experiment and w is the weight loss. Figure 3 shows the comparison of X vs. time for different experiments.

The X vs. t curves for experiments 2, 3 and 4 can be compared to study the effects of pellet size and mass on the reduction kinetics (Figure 3a). Large sized pellet (d = 15.90 mm & mass = 7.13 g) was observed to take a longer time for complete reduction as compared to a medium sized pellet (d = 13.85 mm & mass = 5.36 g). Similarly, medium sized pellet was observed to take a longer time for complete reduction as compared to a smaller pellet (d = 11.50 mm & mass = 2.95 g). Hence, it can be concluded that pellets with larger diameters take a longer time for complete reduction when other experimental parameters are constant because the larger pellet contains more hematite for reduction and the reduction gas must diffuse through a thicker reaction product layer in order to reach the unreacted core.

The X vs. t curves for experiments 1, 3 and 7 can be compared to determine the influence of temperature on the reduction kinetics of the iron ore pellet reduction. As shown in Figure 3b, increasing the temperature of the reduction process from 800 °C to 900 °C resulted in an increase in the overall conversion rate of the iron ore pellet reduction process and a decrease in time for achieving a given value of X. This increase in the conversion rate was observed because of an increase in chemical reaction rate according to the Arrhenius equation as well as diffusion rate increase [12].

The influence of concentration of reducing gas on the iron ore pellet reduction kinetics can be determined by comparing the X vs. t curves of experiment 3, 5 and 6. Increasing the flow rate of H₂ gas from 100 cm³/min for experiment 3 to 150 cm³/min for experiment 5 and 200 cm³/min for experiment 6 resulted in an increase in the overall conversion rate of the iron ore pellet reduction process and a decrease in time for achieving a given value of X as shown in Figure 3c. The increase in reduction rate can be explained by a higher amount of reactant gas available for the reduction reactions.

The influence of gas mixture composition on the iron ore reduction process can be determined by comparing the X vs. t curves for experiments 3, 10 and 12 (Figure 3d). By increasing the CO/H₂, ratio starting from pure H₂ to H₂/CO = 75/18 to H₂/CO = 56/36, the overall reduction rate was observed to decrease. The X vs. t curve was approximately similar for experiment 3 and 10 because the pellet size was different. The pellet mass for experiment 3 was approximately 12% heavier than experiment 10. Conversion of wüstite to iron is reported to be the slowest reaction step (above 570 °C) and this decrease in the reduction rate can be explained by the lower rate of chemical reaction between wüstite and carbon monoxide when compared to chemical reaction between wüstite and H₂ along with a lower diffusion coefficient of CO as compared to H₂ [5,18,22,25]. The conversion of Fe₂O₃ to Fe (X > 0.95) using H₂ gas needed approximately 155.66 min while the same process needed approximately 229.66 min for CO/H₂ = 56/36 gas mixture.

The data for X vs. t for all the experiments can be found in Tables S1 and S2 of the Supplementary Materials for future use and research by other authors.

3.2. SEM-EDAX and Phase Composition Analysis of Partially Reduced Pellets

The SEM-EDAX analysis of partially reduced hematite pellets was performed to visualize the changes in structure and chemical composition of hematite pellet undergoing reduction reaction. Figure 4 and Figure 5 show the SEM images of partially reduced pellets for reduction with pure H₂ gas and H₂/CO = 75/18 gas mixture, respectively. ImageJ greyscale analysis was used to determine the phase composition of the SEM images and EDAX point analysis was performed to validate the elemental composition of different phases visible in the SEM images. Figure 6 gives a comparison between the phase and elemental composition for all the SEM images of partially reduced pellets for reduction with pure H₂ gas and H₂/CO = 75/18 gas mixture, respectively.

For partially reduced pellets obtained from both reducing gas mixtures, four different phase colors were observed in the SEM images: (1) Black for the pores, (2) Light grey for iron, (3) Grey for iron oxide and (4) Dark grey for gangue. For 25% reduced pellets (Figure 4A–C and Figure 5A–C), the iron phase was observed only in the shell region (2–10% of the area) while no iron phase was observed in the middle region and the core region. For 40% reduced pellets (Figure 4D–F and Figure 5D–F), the fraction of iron phase was observed to be higher in shell region for both reducing gas mixtures (19–24% of the area) as compared to 25% reduced pellet. In the middle region the iron phase was observed only for the H₂/CO = 75/18 gas mixture (22.16% of the area) while no iron phase was observed for both the gas mixtures in the core region. This indicates that CO presence in the reactant gas mixture enhances the pore channels and shifts the reaction from kinetic control to pore diffusion control (between 700 °C and 1200 °C) [26,27].

In case of 80% reduction and >95% reduction (Figure 4G–L and Figure 5G–L), the iron phase was observed in all regions of the pellet (26–61% of the area). To sum up, the iron phase was observed to increase continuously with an increase in the degree of reduction while the iron oxide phase was observed to reduce simultaneously. Further, the degree of reduction in shell region was observed to be higher than the degree of reduction in the core region of the pellet. High resolution images can be found in Figures S4–S11.

The phases with different shades observed in the SEM images were validated using EDAX-spot analysis which gives elemental composition. As shown in

Table A1. Phase analysis and EDAX point analysis for SEM images (H₂ gas reduction).

Sample		ImageJ Phase Analysis		EDAX Point Analysis Composition (%)
Image Spot	Figure #	Phase	Composition (%)	Fe	O	Al	Si	Ca	Mg
r/R = ~1 (25% reduced)	4-A	Iron	9.92	100	-	-	-	-	-
		Iron Oxide	75.47	81.2	18.8	-	-	-	-
		Gangue	14.61	15.56	39.1	1.58	20.48	23.29	-
r/R = ~0.5 (25% reduced)	4-B	Iron	0	-	-	-	-	-	-
		Iron Oxide	84.72	80.9	19.1
		Gangue	15.28	13.74	35.89	1.67	21.32	27.37	-
r/R = ~0 (25% reduced)	4-C	Iron	0	-	-	-	-	-	-
		Iron Oxide	87.24	81.09	18.91	-	-	-	-
		Gangue	12.76	11.09	38.1	2.04	23.76	25.01	-
r/R = ~1 (40% reduced)	4-D	Iron	19.37	100	-	-	-	-	-
		Iron Oxide	63.56	80.23	19.77	-	-	-	-
		Gangue	17.07	28.29	31.08	1.79	17.6	20.32	-
r/R = ~0.5 (40% reduced)	4-E	Iron	0	-	-	-	-	-	-
		Iron Oxide	85.23	81.59	18.41	-	-	-	-
		Gangue	14.77	82.3	15.66	-	0.79	1.25	-
r/R = ~0 (40% reduced)	4-F	Iron	0	-	-	-	-	-	-
		Iron Oxide	82.05	79.69	20.31	-	-	-	-
		Gangue	17.95	52.07	23.35	1.04	12.17	11.38	-
r/R = ~1 (80% reduced)	4-G	Iron	58.7	100	-	-	-	-	-
		Iron Oxide	21.25	98	2	-	-	-	-
		Gangue	20.05	29.9	26.6	2.51	19.18	21.8	-
r/R = ~0.5 (80% reduced)	4-H	Iron	43.57	100	-	-	-	-	-
		Iron Oxide	41.89	94.34	5.66	-	-	-	-
		Gangue	14.54	32.85	22.53	2.4	20.78	20.16	1.29
r/R = ~0 (80% reduced)	4-I	Iron	29.82	100	-	-	-	-	-
		Iron Oxide	62.66	84.84	15.16	-	-	-	-
		Gangue	7.52	90.12	4.97	1.53	2.17	1.22	-
r/R = ~1 (>95% reduced)	4-J	Iron	56.67	100	-	-	-	-	-
		Iron Oxide	19.36	88.81	11.19	-	-	-	-
		Gangue	23.97	37.93	31.16	1.86	14.89	12.76	1.41
r/R = ~0.5 (>95% reduced)	4-K	Iron	47.93	100	-	-	-	-	-
		Iron Oxide	38.43	92.42	7.58	-	-	-	-
		Gangue	13.64	42.31	24.76	1.44	15.58	14.82	1.09
r/R = ~0 (>95% reduced)	4-L	Iron	41.56	100	-	-	-	-	-
		Iron Oxide	45.15	78.27	20.75	0.98	-	-	-
		Gangue	13.29	48.73	23.2	1.42	15.77	10.31	0.57

and

Table A2. Phase analysis and EDAX point analysis for SEM images (Enerigon III gas reduction).

Sample		ImageJ Phase Analysis		EDAX Point Analysis Composition (%)
Image Spot	Figure #	Phase	Composition (%)	Fe	O	Al	Si	Ca	Mg
r/R = ~1 (25% reduced)	5-A	Iron	2.18	100	-	-	-	-	-
		Iron Oxide	75.70	73.67	24.68	0.76	0.9	-	-
		Gangue	22.12	52.55	22.46	1.62	12.26	9.8	1.3
r/R = ~0.5 (25% reduced)	5-B	Iron	0.00	-	-	-	-	-	-
		Iron Oxide	87.49	81.21	18.51	0.17	0.12	-	-
		Gangue	12.51	59.11	26.28	1.06	6.71	6.83	-
r/R = ~0 (25% reduced)	5-C	Iron	0.00	-	-	-	-	-	-
		Iron Oxide	100.00	79.01	20.99	-	-	-	-
		Gangue	0.00	-	-	-	-	-	-
r/R = ~1 (40% reduced)	5-D	Iron	23.19	100	-	-	-	-	-
		Iron Oxide	64.65	85.63	14.37	-	-	-	-
		Gangue	12.16	37.84	24.87	1.93	16.52	18.83	-
r/R = ~0.5 (40% reduced)	5-E	Iron	22.16	100	-	-	-	-	-
		Iron Oxide	66.76	80.21	19.12	0.67	-	-	-
		Gangue	11.09	34.83	26.8	0.88	14.38	23.11	-
r/R = ~0 (40% reduced)	5-F	Iron	0.00	-	-	-	-	-	-
		Iron Oxide	79.78	83.7	16.3	-	-	-	-
		Gangue	20.22	23.28	34.21	2.44	22.87	17.2	-
r/R = ~1 (80% reduced)	5-G	Iron	44.47	99.68	-	0.32	-	-	-
		Iron Oxide	37.94	89.18	10.49	0.33	-	-	-
		Gangue	17.59	5.13	36.06	0.2	21.22	37.04	0.36
r/R = ~0.5 (80% reduced)	5-H	Iron	26.84	100	-	-	-	-	-
		Iron Oxide	60.79	91.24	8.76	-	-	-	-
		Gangue	12.37	30.79	27.55	0.66	16.54	24.45	-
r/R = ~0 (80% reduced)	5-I	Iron	32.39	100	-	-	-	-	-
		Iron Oxide	46.37	81.77	17.67	0.17	0.21	0.18	-
		Gangue	21.24	30.04	31.54	1.07	14.47	22.88	-
r/R = ~1 (>95% reduced)	5-J	Iron	56.35	100	-	-	-	-	-
		Iron Oxide	17.40	90.66	9.34	-	-	-	-
		Gangue	26.25	50.28	19.02	2.35	14.96	13.39	-
r/R = ~0.5 (>95% reduced)	5-K	Iron	60.34	100	-	-	-	-	-
		Iron Oxide	30.78	88.1	11.24	0.66	-	-	-
		Gangue	8.88	19.8	28.92	1.71	21.07	28.5	-
r/R = ~0 (>95% reduced)	5-L	Iron	41.47	100	-	-	-	-	-
		Iron Oxide	45.94	87.04	12.69	-	-	-	-
		Gangue	12.59	50.01	19.97	0.48	29.01	0.52	-

of Appendix B the light grey colored iron phase was observed to consist of 100% Fe. The grey colored iron oxide phase was observed to primarily consist of Fe (78–98%) and O (2–25%) and in some cases, they also consisted of traces (<1%) of Al and Si. The dark grey colored gangue phase was observed to consist of Si (0–30%), Ca (0–29%), Fe (13–91%) and O (4–40%), while small traces (0–3%) of Al and Mg were also observed.

3.3. SEM-Greyscale Porosity Analysis of Partially Reduced Pellets

The values of porosity were obtained using the SEM images captured in a radial direction from shell to the core. Four images were captured for each region starting from shell region towards the core region. The values of porosity obtained from ImageJ threshold analysis were compared for partially reduced pellets obtained using H₂ gas and H₂/CO = 75/18 gas mixture as shown in Figure 7A,B, respectively.

The porosity was observed to decrease from shell region to core region in most cases, this complements the observation that the degree of reduction in shell region was higher than the degree of reduction in the core region of the pellet. In some cases, a spike in the value of porosity was observed due to cracks in the pellet (example: Figure 7A: X = 0.25, image 7 & Figure 7B X = 0.95, image 7).

For partially reduced pellets obtained from both the H₂ gas and H₂/CO = 75/18 gas mixture experiments, the porosity was observed to increase from 25% reduction to >95% reduction. The average value of porosity for whole pellet was calculated to be 0.3 for H₂ gas experiment and 0.33 for H₂/CO = 75/18 gas experiment at 25% reduction. At >95% reduction this value was observed to increase to 0.43 for both H₂ gas experiment and H₂/CO = 75/18 gas experiment. This can be explained by the fact that oxygen molecules are being removed from the pellet and the dense iron phase is being formed because of the reduction process.

Overall, the average porosity for pellets obtained from H₂/CO = 75/18 gas mixture experiment was observed to be higher than the H₂ gas experiment. The values of average porosity observed for H₂ gas experiment and H₂/CO = 75/18 gas mixture experiment at 25% reduction was 0.30 and 0.33, at 40% reduction it was 0.32 and 0.38 and at 80% reduction it was 0.42 and 0.39, respectively. Figure A1 in Appendix A shows the different phases in detail and Figure A2 shows the process of phase identification.

3.4. Changes in Diameter of Reduced Pellets

Experiments were performed at 850 °C using H₂ gas with 10 pellets to observe the changes in the pellet diameter after the reduction process. As shown in Figure 8, the pellets were observed to swell as well as contract and in some cases no changes were observed in pellet size. We were unable to establish a clear trend, unlike Yi et al., who reported an increase in swelling with increase in reduction temperature and CO content in the reducing gas mixture [28].

3.5. Fe₃C Phase Detection for Pellets Reduced Using CO-H₂ Gas Mixture

Images obtained from optical microscopy for pellets reduced using Midrex gas mixture confirm the presence of Fe₃C in the pellet. Previously white colored phase of Fe₃C in optical microscope images was reported by Kazemi and Sichen after etching the pellet sample [24]. In this study, the presence of Fe₃C phase was confirmed using the same method along with the SEM-EDAX mapping as shown in Figure 9A,B. The phase containing Fe, C and O was approximately 8% of the total area of the SEM image. It was also observed that the concentration of Fe₃C (white phase) was higher in the shell region of the pellet as compared to the core region where white phase was found only sporadically, as shown in Figure 9C,D. Based on the EDAX mapping results (Figure 9B) together with point analysis of carbide phase (Table S5), the amount of carbon in the shell region of the pellet could be estimated as 0.25 wt.% approximately. This implies a very low amount of carbon in the pellet, probably below 0.1 wt.%. This indicates a very weak carburization of the DRI pellets obtained from the lab reactor.

4. Numerical Modelling

4.1. Model Description and Assumptions

The reduction process of a single hematite pellet using reactant gas mixture can be simulated by modelling a section of the reactor tube containing the pellet. Figure 10 shows a schematic which gives a description of the model containing a small section of the reactor tube. The reactant gases from the bulk diffuse inside the pellet followed by the reduction of hematite to iron and the product gases diffuse through the porous pellet back to the bulk. The model for this study was developed using COMSOL Multiphysics 5.6, where a 2D-axisymmetric geometry was used to describe a porous pellet and the bulk containing reactant and product gas. The following interfaces were used to build the model:

• Transport of Diluted Species: To calculate the concentration fields of solid reactants and products as well as the gases in the bulk.
• Transport of Diluted Species in Porous Media: To calculate concentration fields of gases and to define the chemical reactions involved.
• Laminar Flow: To obtain the velocity profile of flow of gases in the bulk.
• Brinkman Equations: To obtain the velocity profile of gases inside the porous pellet.
• Multiphysics-Reacting flow: To couple the chemical reactions with the flow profile of the gases inside the porous pellet.

The following assumptions were made while building the 2D axisymmetric model:

• The pellet is assumed to be a sphere with reduction process taking place isothermally without any changes in pellet diameter and effects of heat of reaction are ignored because of the small scale of the single pellet reduction and external heat source.
• Reactant and product gases follow ideal gas laws, and they diffuse as a single stream.
• Hematite to wüstite conversion is assumed to be a single step reaction and all chemical reactions are assumed to follow first order reaction kinetics [29].
• Density and kinematic viscosity of gas mixture was assumed to be constant and calculated using the data available online on NIST Chemistry Webbook [30].
• The diffusion coefficients of gas mixture was assumed to remain constant with changes in gas concentrations and calculated using the theory of diffusion in gases at low density [31]. N₂ (carrier gas) did not undergo any chemical reactions, but it affected the diffusion coefficients of gas mixture.

4.2. Geometry, Domain and Mesh

The model was defined using a 2D-axyssimetric geometry with a semicircular domain representing the porous pellet and a rectangular domain representing the bulk inside the reactor tube. The approximate pellet diameter (dp) measured for each pellet was used to simulate the model for each experiment. As shown in Figure 11A, the height of the rectangular domain was assumed to be dp + 1 mm, while the width was assumed to be 37.5 mm, which is equivalent to the inner diameter of the nickel-superalloy tube. The reactant gas is flowing from bottom of tube and escaping at the top. The gas on top of the pellet is carried towards the exit by the fluid flow as well as convection. Hence, the complete height of reactor was not considered in the model. The bulk gas below the pellet is assumed to be same as that at the inlet of the tube as there is no chemical reaction happening until the gas reached the pellet. As shown in Figure 11B, the mesh for the model was obtained automatically using the physics-controlled mesh sequence type with extremely fine element size from the COMSOL Multiphysics interface. The boundary layer selected to obtain the mesh was the reactor wall as well as the edge of spherical pellet.

4.3. Diffusion and Transport of Gases

The flow of gaseous species in bulk was defined by the ‘transport of dilute species’ physics which requires diffusion coefficients of each gaseous species. The velocity profile of the bulk was defined by the ‘laminar flow’ physics. The diffusion coefficients for the gas mixtures were calculated using the theory of diffusion in gases at low density using the following equation [31]:

$$D_{AB}=0.0018583\sqrt{T^3\left(\frac{1}{M_A}+\frac{1}{M_B}\right)}\frac{1}{p{\sigma }_{AB}^2{\Omega }_{D,AB}}; {\sigma }_{AB}=\frac{1}{2}\left({\sigma }_A+{\sigma }_B\right)$$

(2)

where, D_AB: Diffusion coefficient of gas A in gas B [cm²/s], T: temperature [K], M_A: molecular mass of gas A [g/mol], M_B: molecular mass of gas B [g/mol] and p: pressure [atm]. ${\Omega }_{D,AB}$ is evaluated by extrapolating the data for $\left(T/\left(\frac{{\epsilon }_{AB}}{K}\right)\right)vs {\Omega }_{D,AB}$, provided by Bird et al. [32]. Where, σ and ε/K are the Lennard-Jones parameters for gas A and gas B.

To include the effects of water vapor (H₂O) and carbon dioxide (CO₂) in the diffusion coefficients, calculations were done by assuming that H₂ and N₂, CO and N₂ diffuse as a single specie, respectively. As shown in

Table 2. Diffusion coefficients of gas mixtures.

Temperature [°C]	${\mathit{D}}_{{\mathbf{H}}_2\mathbf{O}+{\mathbf{H}}_2+{\mathbf{N}}_2} [{\mathbf{m}}^2/\mathbf{s}]$	${\mathit{D}}_{\mathsf{C}{\mathsf{O}}_2+\mathsf{C}\mathsf{O}+{\mathsf{N}}_2} [{\mathbf{m}}^2/\mathbf{s}]$
800	0.000274562	0.000137686
850	0.000296142	0.000148508
900	0.000318367	0.000159653

, the diffusion coefficient used for the flow of H_2, and H₂O is given as $D_{{\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2+{\mathrm{N}}_2}$ and for CO and CO₂ the diffusion coefficient is given by $D_{{\mathrm{CO}}_2+\mathrm{CO}+{\mathrm{N}}_2}$.

The transport of gases inside the porous pellet was defined using the ‘transport of dilute species in porous media’ physics. Apart from the diffusion coefficients, this physics module needs porosity and tortuosity as an input to define the effective diffusion coefficient. The equation of effective diffusion coefficient (De) with porosity (ε), tortuosity (τ), and diffusion coefficient (D) in bulk is as follows [18]:

$$D_e=\frac{\epsilon }{\tau }D$$

(3)

In this study we used five different types of porosity to define the pellet: (1) Smoothed step function of conversion starting from 0.3 to 0.5, (2) Continuously increasing porosity function as reported by Murayama et al., (3) Porosity as a function of X obtained from partially reduced pellets from H₂ experiment, (4) Porosity as a function of X obtained from partially reduced pellets from H₂-CO experiment and (5) constant porosity of 0.05, 0.1 and 0.5. As shown in the equations below, the porosity of wüstite (ε_w) and iron (ε_Fe) was defined as a function of porosity of hematite (ε_h) by Murayama et al. [33].

$${\epsilon }_w=0.122+0.878{\epsilon }_h \& {\epsilon }_{\mathrm{Fe}}=0.435+0.565{\epsilon }_h$$

(4)

The porosity vs. conversion function obtained from the ImageJ porosity analysis of partially reduced pellets is given below. The details of derivation of the same is given in the Supplementary Materials in Figures S1 and S2.

P(H₂) = −1.4653 X⁴ + 2.3913 X³ − 0.9614 X² + 0.1454 X + 0.3000

(5)

P(CO) = 0.1786 X³ − 0.3225 X² + 0.2761 X + 0.2962

(6)

Valipour et al., reported that the tortuosity of porous iron pellets vary within the range of 1–4 while developing their pellet-grain model [18]. Seven different cases of tortuosity were used to study its effect on the outcomes of the model. These involved the predefined Millington and Quirk model (τ = ε^−1/3), Bruggeman model (τ = ε^−1/2) available on the interface of COMSOL Multiphysics software and constant tortuosity varying between 2–10 [34].

The tortuosity was assumed to follow the Millington and Quirk model when the simulations were performed to study the effects of porosity while the porosity was assumed to follow the function defined by Murayama et al. when the simulations were done to study the effects of tortuosity. Figure 12 shows the curves for (A) Porosity vs. X and (B) Tortuosity vs. X for the different models and constants used to define the same.

The transport of the gas mixture in bulk was described by adding the convection mechanism to the mass balance equation. The time dependent equation for concentration of bulk gas species was as follows:

$$\left(\partial {\mathrm{c}}_i/\partial \mathrm{t}\right)+\nabla ·{\mathrm{J}}_i+\mathrm{u}·\nabla c_i=R_i \mathrm{and} {\mathrm{J}}_i=-D_i\nabla c_i$$

(7)

The transport of the gas mixture in pellet was described by adding the mass transport in porous media mechanism to the mass balance equation. The time dependent equation for concentration of gas species inside porous pellet was as follows:

$$\left(\partial \left({\in }_p{\mathrm{c}}_i\right)/\partial \mathrm{t}\right)+\left(\partial \left({\mathsf{\rho }\mathrm{c}}_{\mathrm{P},i}\right)/\partial \mathrm{t}\right)+\nabla ·{\mathrm{J}}_i=R_i \mathrm{and} {\mathrm{J}}_i=-(D_{D,i}+D_{e,i})\nabla c_i$$

(8)

Here, c is the concentration of the species [mol/m³], D is the diffusion coefficient [m²/s], R is a reaction rate expression for the species [mol/(m³·s)], u is the mass averaged velocity vector [m/s], J is the mass flux diffusive flux vector [m²/s]. c_p,i is the concentration adsorbed to solid particles [moles/dry weight of solid] and ε_p is the porosity of the pellet.

4.4. Reaction Kinetics

COMSOL Multiphysics software requires volumetric reaction rates for a 2D-axisymmetric geometry, to be defined in the “Transport of diluted species” and “Transport of diluted species in porous media”. Hence, the surface reaction rates were converted to volumetric reaction rates for the two-step conversion of hematite to iron were calculated using the following equations:

$$R_1=\left(3/r_o\right)\times (k_1{C}_{r\left(P\right)})y_{{\mathrm{Fe}}_2{\mathrm{O}}_3} \& R_2=\left(3/r_o\right)\times (k_2{C}_{r\left(P\right)})y_{\mathrm{FeO}}$$

(9)

where, R_i: Rate of reaction i and k_i: chemical rate constant derived from Arrhenius equation as shown below for reaction i, with i = 1, 2; C_r(P): local concentration of reactant gas inside the pellet, y_Fe2O3: mole fraction of hematite, y_FeO: mole fraction of wüstite and r_o: radius of the pellet.

$$k_i=k_{oi}{e}^{\frac{-E_{ai}}{RT}}$$

(10)

where, k_oi: pre-exponential factor, E_ai: activation energy of reaction i, T: reaction temperature and R: Universal gas constant. The parameters used for conversion of hematite to wüstite using CO was assumed to be equivalent to the parameters for conversion of magnetite to wüstite using CO as it was slower as compared to conversion of hematite to magnetite using CO.

Table 3. Parameters of chemical reaction rates used for the model (between 800 °C & 1100 °C).

i	Reaction	${\mathit{k}}_{\mathit{o}\mathit{i}} [\mathbf{m}/\mathbf{s}]$	${\mathit{E}}_{\mathit{a}\mathit{i}} [\mathbf{J}/\mathbf{mol}]$	References
1	Fe2O3 + H2 → 2FeO + H2	80	66,516	[29]
2	FeO + H2 → Fe + H2O	2858.34	117,230	[22]
3	Fe2O3 + CO → 2FeO + CO2	25	73,674
4	FeO + CO → Fe + CO2	17	69,488
5	CO + H2O → CO2 + H2	1400	44,895
6	CO + H2O ↔ CO2 + H2	93.32 × 106 (Catalyst: Fe)	−128,200	[35]
		18.27 (Catalyst: FeO)	137.3

gives the parameters of reactions rates used to define the chemical reactions in the model.

4.5. Boundary Conditions and Solvers

In the bulk domain, the inflow of gas mixture was assigned to the lower edge of the rectangular geometry shown in Figure 11A with H₂, CO and N₂ as the gases flowing in, no flux condition was assigned to the edge on the right which represents the walls of the furnace tube and the outflow of all the gases was assigned to the edge on the top.

In the pellet domain, the bulk concentration was applied to the circumference of the semicircle which represents the boundary between the bulk and the pellet. The circumference was also assigned as the outflow for the product gases. For the velocity profile of bulk, a no slip condition was assigned to the right edge of the rectangular geometry and the circumference of the circle.

The PARDISO solver was used to solve the differential equations in a fully coupled configuration to solve the ‘reacting flow’ multi-physics. The end time of the simulation was chosen by observing the total reduction time of each experiment.

5. Modelling Results and Validation

5.1. Mole Fraction of Solid Species and Concentration Profiles of Solid and Gaseous Species

The 2D axisymmetric model developed in this study is able to provide changes in moles vs. time for solid species. As shown in Figure 13, the model was used to simulate experiment 3 (H₂ mixture), experiment 10 (H₂/CO = 75/18 mixture) & 12 (Midrex gas mixture) and a comparison between changes in mole fraction of solid species was obtained. For H₂ gas experiment, a sharp peak was observed for the mole fraction of wüstite (X(FeO) > 0.7), while a sharp decrease was observed for mole fraction of hematite. This can be explained by the fact that the reaction kinetics used to build the model for H₂ gas experiments considers the rate of conversion of wüstite to iron to be slower than rate of conversion of hematite to wüstite [22,29]. The mole fraction of iron was observed to increase exponentially throughout the simulation.

For the H₂/CO = 75/18 and H₂/CO = 56/36 gas mixture experiments, the peak of wüstite mole fraction was less than the peak observed for the H₂ gas experiment (X(FeO) < 0.6), the decrease in hematite mole fraction was also not as sharp as compared to the H₂ gas experiment. This can be explained by a decrease in the overall rate of reaction due to an increase in the fraction of CO in the reactant gas as per the reaction rate parameters used in the model.

The 2D-axisymmetric model is also able to provide 3D concentrations profiles of the solid species. Figure 14 shows the 3D concentration profiles of hematite, wüstite and iron at 1%, 50% and 95% conversion for H₂ gas mixture (Experiment 3). It was observed that the concentration of hematite continuously decreases in the form of a shrinking core (Figure 14A,D,G). The concentration of wüstite was observed to grow from shell to core in the beginning before it reached its peak and then it was observed to decrease in the form of a shrinking core (Figure 14B,E,H). The concentration of iron was observed to increase continuously from shell to core of the pellet (Figure 14C,F,I). These results complement the observations from the ImageJ phase analysis of SEM images as shown in Figure 6, where the iron phase was observed to grow from shell region to core region with an increase in the degree of reduction. The model also predicts the presence of wüstite in the pellet at 95% conversion which complements the observation of iron oxide phase in different regions of pellet in the ImageJ phase analysis of SEM images. Previously, the reduction fraction in 2D plane was reported for the pellet grain model [20,21], however it was not validated using EDAX analysis and a sharp phase boundary was reported in contrast to our observations where iron phase was observed in core region in SEM images. A 2D axisymmetric model was also developed by Kazemi et al. but the concentration profiles for solid species were not reported as they assumed a single step chemical reaction along with a sharp phase boundary between unreacted core and reacted shell [23].

The local concentration profiles of gaseous species are shown in Figure 15 for H₂ gas mixture (Figure 15A,D) and Midrex gas mixture (Figure 15B,C,E,F) at 50% conversion. For both the experiments a concentration gradient was observed inside the pellet for reactant gases (H₂ & CO) with the concentration decreasing from shell region to core region. The concentration of H₂O in the shell region for H₂ gas mixture and Midrex gas mixture was 3.59 and 2.06 mol/m³, respectively, in the core region this concentration decreased to 2.7 and 1.54 mol/m³, respectively. Similarly for CO₂, the concentration decreased from 1.32 to 0.93 mol/m³. This gradient was a result of consumption of reactant gases in the chemical reactions inside the pellet. In the bulk region the local concentration of reactant gases on top of pellet was observed to be lower due to an increase in the fraction of product gases escaping from the top of the pellet.

The concentration gradient inside the pellet was also observed for product gases. In the case of H₂ gas mixture, the concentration of H₂O decreased from 2.27 mol/m³ in core region to 0.05 mol/m³ in shell region. In the case of Midrex gas mixture, the concentration of CO₂ decreased from 0.4 mol/m³ in core region to 0.02 mol/m³ in shell region. On the other hand, the concentration of H₂O decreased from 2.06 mol/m³ in the shell region to 1.54 mol/m³ in the core region due to its consumption in the water gas shift reaction.

The 2D-axisymmetric model built using COMSOL Multiphysics reported in this study, uses the “Laminar Flow” interface to obtain the velocity profile of reactant gas in bulk and the “Brinkman Equations” interface to obtain the velocity of reactant gas inside the porous pellet [36,37]. As shown in Figure 16, the velocity streamlines for flow of reactant gases were obtained from the simulations for both the bulk region and the porous media. The bulk velocity streamlines starting from the inlet just below the pellet were observed to curl around the pellet as the velocity at pellet surface approaches zero (Figure 15 shows the same in 2D). Inside the porous pellet, the velocity streamlines converge towards the center of the pellet from where the majority of the streamlines move towards the upper region of the pellet and some of the streamlines move towards the lower region of the pellet. The concentration slices of H₂ were also obtained along with the streamlines to study the effects of velocity profile on gas concentration profile. It can be clearly observed that the concentration of H₂ is lower in the direction of flow of most of the velocity streamlines inside the pellet. This complements the fact that the reactant gas molecules should diffuse from a region of high concentration towards a region of lower concentration. Figure 15 also shows a concentration gradient with a lower concentration of reactant gases in the upper region of the pellet as compared to the lower region of the pellet. Velocity streamlines for reactant gases along with concentration slices inside a pellet were not reported in previously developed numerical models for iron ore reduction [18,19,20,21,22,23].

5.2. Conversion (X) vs. Time Curves of Model and Validation with Experimental Data

The porosity is usually assumed to be constant in most of the numerical models that exist in the literature [18,19,20,21,22,23]. To evaluate the sensitivity of the 2D-axisymmertic model developed in this study, porosity was defined in five ways: (1) Ps: Smoothed step function of conversion starting from 0.3 to 0.5, (2) Pm: Continuously increasing porosity function as reported by Murayama et al., (3) PH₂: Porosity as a function of X obtained from SEM ImageJ analysis of partially reduced pellets obtained from the H₂ gas experiment, (4) PCO: Porosity as a function of X obtained from SEM ImageJ analysis of partially reduced pellets obtained from the H₂-CO experiment and (5) constant porosity of 5%, 10% and 50%. Figure 17 shows the X vs. t curves obtained from simulations of all the experiments. All these simulations assumed that the tortuosity was defined by Millington and Quirk model [34]. The experimental X vs. t data was also plotted on these curves to validate the model.

It was observed that the model was sensitive to changes in porosity with the X vs. t curve shifting towards a pore diffusion-controlled regime upon decrease in the value of porosity. This can be explained by the fact that the effective diffusion coefficient decreases upon decrease in the value of porosity. Similar sensitivity was observed for the pellet-grain model developed by M. S. Valipour et al. [18]. It was also observed that the X vs. t curves obtained from porosity functions Ps, Pm and PH₂/PCO as well as constant porosity of 50% were coinciding with each other approximately. When comparing the X vs. t curve obtained from the models with the X vs. t data obtained from the experiments as shown in Figure 17, it can be observed that the model fits very well with the data of H₂-CO mixed gas experiments as compared to data of H₂ gas experiments. The experimental data for H₂ gas experiments was observed to fit well for simulations with 10% porosity. However, this value of porosity cannot exist in reality as the initial porosity of the unreacted pellet was about 30%.

Table A4. Conversion (X) vs. t comparison of model (Pm) and experiment.

Experiment #	Experiment Data		Model Data (Pm)
	Conversion (X)	Time (min)	Conversion (X)	Time (min)
1	0.88	200.16	0.88	170.5
2	0.99	247.7	0.99	188
3	0.96	155.66	0.96	141.5
4	0.99	138.23	0.99	138
5	0.95	100.8	0.95	99.5
6	0.93	59.96	0.93	73
7	0.99	149.26	0.99	117.5
8	0.99	206.83	0.99	207
9	0.97	145.33	0.97	165.5
10	0.93	154.66	0.93	154.5
11	0.99	152	0.99	178
12	0.98	229.66	0.98	224.5

in Appendix C also gives a comparison of conversion (X) vs. time for experimental and model data for validating the model for each experiment.

To further investigate the deviation of the model from the X vs. t data of H₂ gas experiments, tortuosity values were varied to check the sensitivity of the model towards the same. Figure 18 shows the variation in X vs. t curves obtained by varying the tortuosity of the pellet. It was observed that by increasing the value of tortuosity from 2 to 10, the curves shift, as expected, towards a pore diffusion control regime and also starts to fit the data for H₂ gas experiments. Increasing the tortuosity results in a decrease in the effective diffusion coefficient of gaseous species which slows down the overall reduction rate. This is possible due to the formation of micropores and close ended pores during the reduction experiments using H₂ gas. As shown in Figure 4J–L), micropores, single ended and close ended pores can be observed for partially reduced pellets with H₂ gas. On the other hand, wider and well-connected pores as well as macropores can be observed for H₂-CO gas mixture, as shown in Figure 5J–L). The decrease in reduction rate due to the formation of closed ended as well as single ended pores was previously reported by Rouquerol et al. as well as Shin, S.G. and Min, D.J. [38,39]. The improvement in reduction rate due to the presence of wider macropores has also been reported previously in the literature [5,40]. Hence, it can be concluded from the observations in SEM images in Figure 4 and Figure 5, as well as the X vs. t curves in Figure 17 and Figure 18, that the tortuosity of the pellet is higher in case of pellets reduced with H₂ gas mixture as compared to the pellets reduced with H₂-CO gas mixture.

It was also observed in Figure 18 that the experimental data starts to deviate from the model with an increase in temperature. Increasing the tortuosity helps to fit the model at higher temperatures. However, an increase in tortuosity value means an increase in resistance for diffusion of gas through the porous product layer. In other words, reaction in real pellet goes slower than in the model. The porosity of the model is in the range of real pellet porosity values, and it is not very sensitive to small changes in that range (0.3–0.42). The gas flow rate and temperature of feed gas is the same at the inlet of the tube, but convection rate is considerably different at 900 °C as compared to 800 °C after the gas is heated. Since the tube is exposed to atmosphere via a small opening at the top, gas at 900 °C should escape the tube at a higher rate [41]. This factor is not accounted for in the current model. It is also important to note that the change in pellet diameter during the reduction process was not considered for the 2D-axisymmetric model, which may also contribute to the deviation of experimental data from the model data as shown in Figure S3 in the Supplementary Materials.

6. Conclusions

This study reports the results from iron ore pellet reduction experiments performed at different temperatures, flow rates, pellet size and gas composition. It can be concluded from the observations that the rate of reduction increases with an increase in temperature of experiments from 800 °C to 900 °C, flow rate of gas from 100 cm³/min to 200 cm³/min and increasing the hydrogen content in a CO-H₂ feed gas mixture. The reduction rate was also found to increase with a decrease in pellet size from 7.13 g in mass, 15.9 mm approximate pellet diameter to 2.95 g in mass, 11.5 mm approximate pellet diameter.

SEM-EDAX and phase composition analysis of partially reduced pellets revealed that the iron oxide content in a pellet decreases with an increase in the degree of reduction. Further, the amount of iron oxide in the core region was found to be higher than the amount of iron oxide in shell region. The SEM-EDAX and phase composition analysis also revealed that the iron content in the pellet increases with an increase in the degree of reduction from shell region to core region. The SEM-greyscale porosity analysis revealed that the porosity of pellet increases with an increase in degree of reduction. Further, the porosity at >95% reduction was observed to be higher for pellets reduced using H₂/CO = 75/18 gas mixture as compared the pellets reduced with H₂ gas mixture. Some traces of Fe₃C were also observed in the pellet reduced using the Midrex gas mixture. The concentration of Fe₃C phase was higher in the shell region of the pellet as compared to the core region.

The 2D-axisymmetrical model developed in this study was able to provide 3D concentrations profiles of solid species inside the pellet. The results obtained from the model complement the results obtained from SEM-EDAX phase analysis as shown in Figure 6 and Figure 14. The mole fraction vs. time curves of solid species reveal a peak of wüstite mole fraction which decreases and a continuously increasing mole fraction of iron which plateaus towards complete reduction.

The conversion (X) vs. time curves obtained from the model for variable porosity functions as well as a constant porosity of 50% were observed to overlap each other approximately. The curves for CO-H₂ gas mixtures were observed to fit the experimental data very well for lower tortuosity values (between 1–2) defined by the Millington and Quirk model. The curves for H₂ gas mixtures were observed to fit the experimental data very well for higher tortuosity values (~10). The high tortuosity values in case of H₂ experiments was justified by the presence of close ended as well as single ended micropores observed in the SEM images of partially reduced pellets. The lower value of tortuosity in case of H₂-CO mixed gas experiments was justified by the well-connected and wider pores as well as macropores. Similar observations were also made previously by some authors. In conclusion, tortuosity affects the outcomes of the 2D axisymmetric model and it also changes with the reducing gas mixture.

Further improvements in the model are required to account for the changes in pellet size during the reduction process.