Two-Dimensional CFD Study of Carburization and Carbon Partitioning in an ENERGIRON ZR Shaft Furnace

Abstract

This study develops a two-dimensional computational fluid dynamics model for the reactive zone of an industrial-scale shaft furnace operated under ENERGIRON ZR (zero-reforming) conditions, where carbon in direct reduced iron (DRI) is explicitly distinguished into combined carbon in Fe₃C and free carbon in graphitic form. The model is validated against available plant data and then applied to investigate the effects of reducing gas temperature, gas composition, and gas feed rate on reduction, carburization, and carbon partitioning. The results show that in situ reforming, iron oxide reduction, and carburization are strongly coupled near the gas inlet. Increasing the reducing gas temperature from 1273 K to 1373 K raises the metallization degree from 0.9426 to 1.000 and the total carbon mass fraction from 0.01722 to 0.04938, while decreasing the combined carbon fraction from 97.6% to 86.3% because of enhanced Fe₃C decomposition. The effect of CH₄ content is temperature-dependent: at 1273 K and 1323 K, increasing CH₄ from 15% to 25% decreases both metallization and total carbon because intensified endothermic reforming lowers the in-furnace thermal level, whereas at 1373 K the total carbon changes from 0.04849 to 0.04938 and then to 0.04179, reflecting a shift in the controlling factor from CH₄ availability to thermal limitation. Increasing gas feed rate from 1400 Nm³/t-pellet to 1600 Nm³/t-pellet improves both reduction and beneficial carburization, with the total carbon mass fraction increasing from 0.02360 to 0.04047, while the combined carbon fraction decreases slightly from 93.9% to 92.5%. The predicted carbon partitioning results also show qualitative agreement with the limited industrial data, particularly the decreasing combined carbon fraction with increasing total carbon content in DRI.

1. Introduction

The iron and steel industry is under increasing pressure to achieve deep decarbonization as it remains one of the largest industrial sources of greenhouse gases, contributing to approximately 7–9% of global anthropogenic carbon dioxide (CO₂) emissions [1,2]. Conventional steelmaking based on the blast furnace-basic oxygen furnace (BF-BOF) route, which accounts for roughly 70% of global steel production [3], relies heavily on carbonaceous reductants such as coke and pulverized coal and is therefore inherently limited in achieving substantial emission cuts. In this context, the direct reduction (DR) shaft furnace-electric arc furnace (EAF) route has attracted growing attention as one of the most promising options for low-carbon steelmaking. In this route, iron ore is first converted into direct reduced iron (DRI), which can be discharged either hot or cold, and is subsequently charged into an EAF for steelmaking. Compared with the coal-based BF-BOF route, the DR-EAF route, which uses natural gas as the primary energy source and reductant precursor for generating hydrogen (H₂) and carbon monoxide (CO), can reduce CO₂ emissions by about 40–60% [4,5].

To further lower the carbon footprint and ultimately approach carbon neutrality, industrial natural-gas-based DR processes, such as MIDREX and HYL/ENERGIRON, are currently transitioning towards H₂-rich and even pure H₂ variants [6,7]. This transition is generally realized by partially replacing natural gas with externally supplied hydrogen (e.g., green hydrogen). As a result, the H₂/CO ratio in the reducing gas increases, which inevitably alters the in-furnace thermochemical state. Thermodynamically, the reduction of iron oxides by H₂ is strongly endothermic, whereas reduction by CO is moderately exothermic. Therefore, increasing H₂ content tends to lower the thermal level in the shaft furnace, which may weaken reduction kinetics and deteriorate pellet metallization unless compensated by higher gas feed rates or additional thermal input. Another important consequence is the decline in carburization. In conventional DR operation, carburization is mainly associated with methane (CH₄)-involved reactions, especially methane decomposition, which is itself endothermic. The intensified heat shortage under H₂-rich conditions therefore suppresses carburization and makes it more difficult to maintain a desirable carbon level in DRI.

Although carbon-free DRI may eventually become the target product in a future pure-hydrogen ironmaking scenario, the carbon content of DRI remains a key quality indicator in current industrial practice because it is closely related to downstream melting behavior, energy efficiency, slag foaming, and product stability, particularly in terms of resistance to re-oxidation [8,9]. Therefore, from the perspective of near- to medium-term industrial operation, efficient carburization under low-carbon or hydrogen-rich shaft furnace conditions remains a highly relevant engineering concern. In response to practical production needs, both MIDREX and HYL/ENERGIRON have continued to develop technologies for increasing the carbon level of DRI [10,11]. Among these technologies, the ENERGIRON ZR (zero-reforming) process is of particular interest [12]. In this process, natural gas reforming takes place in situ in contact with metallic iron inside the shaft furnace, thereby eliminating the need for an external reformer. Owing to its relatively high operating temperature, elevated pressure, high H₂/CO ratio, and significant CH₄ content in the reducing gas, the ENERGIRON ZR process provides favorable conditions for producing high-carbon DRI. Industrial practice has shown that the DRI produced by this process can contain up to about 4.5 wt.% carbon, while the associated CO₂ emissions are reported to be lower than those of other DR processes [13,14].

However, carbon in DRI is not present in a single form. It mainly exists as combined carbon in iron carbide (Fe₃C) and as free carbon, usually graphitic carbon. These two forms of carbon have markedly different metallurgical implications. A high Fe₃C fraction is generally beneficial because it improves DRI stability, suppresses re-oxidation tendency, contributes chemical energy during melting, and supports more efficient downstream steelmaking [15]. By contrast, excessive graphitic carbon is usually undesirable because it is associated with lower DRI stability and less efficient carbon utilization. Moreover, carbon precipitation on or near pore surfaces may obstruct gas access and thereby affect subsequent carburization behavior. This distinction becomes particularly important under the high-carbon conditions characteristic of the ENERGIRON ZR process. Industrial evidence indicates that, although the total carbon content in DRI can be increased to relatively high levels, the fraction of free carbon also tends to rise with increasing total carbon content [14]. Accordingly, the practical objective is not simply to maximize total carbon, but rather to promote the formation of Fe₃C while suppressing excessive graphitic carbon.

Numerical modeling provides an effective means to describe and better understand the complex multiphase reactive flow in direct reduction shaft furnaces. In recent years, various mathematical models have been developed, including one-dimensional algebraic models and computational fluid dynamics (CFD) models. Many of these studies have focused primarily on the upper reduction zone, where the dominant concern is the reduction of iron oxides by H₂ and/or CO [16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Some more advanced models have extended the domain to the full shaft furnace, including the transition and cooling zones, and have incorporated carburization-related reactions, such as CH₄ decomposition and CO precipitation [30,31,32,33,34,35,36,37,38,39,40,41]. Nevertheless, most existing studies focus on the MIDREX process, while numerical investigations of the ENERGIRON process, particularly the ENERGIRON ZR variant characterized by high temperature (>1050 °C), elevated pressure (6–8 bar), and a high H₂/CO ratio (4–5), remain limited despite its strong capability to produce high-carbon DRI. Moreover, in most reported models, the carbon in DRI has been treated as a single quantity, i.e., total carbon, without explicitly distinguishing between Fe₃C and graphitic carbon. This simplification may be acceptable when the carbon level is relatively low (<2 wt.%), as is often the case in MIDREX-type operations, but becomes questionable under the high-carbon conditions of the ENERGIRON ZR process.

In this context, a recent one-dimensional integrated two-scale shaft furnace model developed by Kumar et al. [41] represented an important step forward by simultaneously considering graphitic carbon and Fe₃C formation during carburization in MIDREX and HYL/ENERGIRON shaft furnaces. However, this approach remains fundamentally one-dimensional and therefore cannot capture radial variations in gas composition, temperature, reduction degree, and carbon form distribution, which are becoming increasingly significant as industrial shaft furnaces continue to grow in size and internal radial non-uniformity can no longer be neglected [42]. To address this gap, the present work develops a two-dimensional CFD model for the reactive zone of an industrial-scale shaft furnace operated under ENERGIRON ZR conditions, in which Fe₃C and graphitic carbon are explicitly distinguished in the solid phase. The model is first validated against available plant data, and is then applied to investigate the evolution and relative proportions of Fe₃C and graphitic carbon under different operating conditions, including reducing gas composition (CH₄ content), feed rate, and temperature. The findings of this study are expected to provide technical guidelines for promoting beneficial carburization in shaft furnaces during the green transition of ironmaking.

2. Modeling

2.1. Process Description

Figure 1 schematically illustrates ENERGIRON ZR shaft furnace and the reactive zone considered in the present study. Unlike conventional natural-gas-based DR processes equipped with an external reformer, the ENERGIRON ZR configuration eliminates the need for dedicated gas-reforming equipment by promoting reforming reactions directly inside the shaft furnace. In the gas recycling loop, the top gas leaving the furnace is first sent to a condenser for water removal, and the dried off-gas is then introduced into a CO₂ removal unit to reduce the CO₂ level before recycling. After mixing with fresh natural gas, steam, and, if needed, other gas sources such as hydrogen, the recycled gas is heated and re-injected into the shaft furnace as reducing gas. Owing to this flexible process arrangement, the reducing gas composition can be adjusted over a relatively wide range. A characteristic feature of the ZR process is that the reducing gas entering the furnace typically retains a relatively high CH₄ content because no external reformer is employed.

Figure 1. Schematic illustration of ENERGIRON ZR shaft furnace and the reactive zone considered in the present study.

In practical operation, iron oxide pellets are charged from the top of the furnace and descend by gravity through the burden bed, while the reducing gas is injected circumferentially through the bustle pipe located at the middle height of the furnace and flows upward in a countercurrent manner. Under the high-temperature, high-pressure conditions of the ENERGIRON ZR process, CH₄-containing gas undergoes in situ reforming in the presence of metallic iron, generating H₂ and CO as the main reducing species. These gases reduce iron oxides to metallic iron, while the gaseous products of reduction, mainly H₂O and CO₂, further participate in reforming-related reactions. As a result, reforming and reduction are strongly coupled inside the shaft furnace. At the same time, carburization is also expected to occur in the shaft furnace, particularly in the vicinity of the gas inlet, owing to the relatively high CH₄ content in the reducing gas and the favorable local thermochemical conditions in this region. Therefore, under ENERGIRON ZR conditions, in situ reforming, iron oxide reduction, and carburization occur simultaneously and interact with one another, forming a distinctive reactive zone in the upper part of the shaft furnace, as highlighted in Figure 1. This feature distinguishes this process from conventional DR shaft furnaces, in which the functional zones are more clearly separated. Depending on the process configuration, the produced DRI can be discharged either at a low temperature (e.g., about 50 °C) as cold DRI or at a relatively high temperature (e.g., above 600 °C) as hot DRI.

2.2. Model Basics and Numerical Treatment

The CFD model developed in the current work was derived from a simplified one developed by the present authors in an earlier publication [39], in which ten chemical reactions were considered, including the reduction of iron oxides by H₂ (R1–R3 in Table 1) and by CO (R4–R6 in Table 1), water–gas shift reaction (R7 in Table 1), and methane steam reforming (R8 in Table 1) and carburization reactions by methane decomposition and carbon monoxide precipitation. However, the carbon in DRI was not distinguished into different forms but was instead treated as a single quantity. In the present model, by contrast, iron carbide, namely cementite (Fe₃C) and graphite (C), are explicitly distinguished, as shown by R9–R11 in Table 1, corresponding to methane decomposition, carbon monoxide precipitation, and cementite decomposition, respectively. The enthalpy change in each reaction is also listed in Table 1.

Table 1. Reactions considered in the CFD model.

Reaction	Formula	Reaction Enthalpy, kJ/mol	Reaction Rate, kmol/m3/s
R1	3Fe2O3 + H2 → 2Fe3O4 + H2O	−9.6	R1
R2	Fe3O4 + H2 → 3FeO + H2O	87.2	R2
R3	FeO + H2 → Fe + H2O	23.9	R3
R4	3Fe2O3 + CO → 2Fe3O4 + CO2	−51.2	R4
R5	Fe3O4 + CO → 3FeO + CO2	45.6	R5
R6	FeO + CO → Fe + CO2	−17.7	R6
R7	CO + H2O ⇄ CO2 +H2	−41.6	R7
R8	CH4 + H2O ⇄ CO + 3H2	206.3	R8
R9	CH4 + 3Fe → Fe3C + 2H2	74.9	R9
R10	2CO + 3Fe → Fe3C + CO2	−173.0	R10
R11	Fe3C → 3Fe + C	−18.8	R11

The Eulerian two-fluid approach adopted in the previous model is retained in this work, treating both the gas and the solid as interpenetrating continua and solving their conservation equations separately. The shaft furnace is assumed to operate under steady-state conditions. Therefore, the generalized conservation equation for each phase can be written as

∇·(ε_pρ_pϕ_pu_p) = ∇·(ε_pΓ_ϕ∇ϕ_p) + S_ϕ,

(1)

where subscript p denotes gas (g) or solid (s) phase, ε_p, ρ_p, ϕ_p, and u_p are the volume fraction, density, field variable to be solved, and velocity vector of phase p, respectively, and Γ_ϕ and S_ϕ stand for the generalized diffusion coefficient and source term with respect to corresponding field variable ϕ. The specific forms of ϕ, together with the corresponding Γ_ϕ and S_ϕ in each conservation equation, are summarized in Table 2.

Table 2. Variables for the conservation equations of Equation (1).

Phase	Equation		ϕ	Γϕ	Sϕ
Gas	Continuity		1	0	MO·${\displaystyle {\sum }_{n=1}^6}{R}_n$ − MC·(R9 + R10)
	Momentum		ug	0	−εg·∇P + ∇·$\stackrel{̿}{{\tau }_{\mathrm{g}}}$ − Fgs
	Heat		hg	λg/Cp,g	−Egs
	Species	CO	wCO,g	ρg·DCO,g	−MCO·(${\displaystyle {\sum }_{n=4}^6}{R}_n$ + R7 − R8 + 2R10)
		CO2	wCO2,g	ρg·DCO2,g	MCO2·(${\displaystyle {\sum }_{n=4}^6}{R}_n$ + R7 + R10)
		H2O	wH2O,g	ρg·DH2O,g	MH2O·(${\displaystyle {\sum }_{n=1}^3}{R}_n$ − R7 − R8)
		CH4	wCH4,g	ρg·DCH4,g	−MCH4·(R8 + R9)
		N2	wN2,g	ρg·DN2,g	0
Solid	Continuity		1	0	−MO·${\displaystyle {\sum }_{n=1}^6}{R}_n$ + MC·(R9 + R10)
	Momentum		us	0	−εs·∇P + ∇·$\stackrel{̿}{{\tau }_{\mathrm{s}}}$ + Fgs
	Heat		hs	λs/Cp,s	Egs − ${\displaystyle {\sum }_{n=1}^{11}}{R}_n$·ΔHn
	Species	Fe3O4	wFe3O4,s	ρs·DFe3O4,s	MFe3O4·(2R1 − R2 + 2R4 − R5)
		FeO	wFeO,s	ρs·DFeO,s	MFeO·(3R2 − R3 + 3R5 − R6)
		Fe	wFe,s	ρs·DFe,s	MFe·(R3 + R6 − 3R9 − 3R10 + 3R11)
		Fe3C	wFe3C,s	ρs·DFe3C,s	MFe3C·(R9 + R10 − R11)
		C	wC,s	ρs·DC,s	MC·R11

In Table 2, P denotes the absolute pressure, h is the specific enthalpy, λ and Cp are the thermal conductivity and specific heat capacity, w and D stand for the intra-phase mass fraction and diffusion coefficient of species, M is the molecular mass of species, while ΔH is the reaction enthalpy, as listed in Table 1.

The momentum transfer rate between the gas and solid phases is given by Ergun’s equation in vector form:

$${\mathbf{F}}_{\mathrm{gs}}=\left[150{\displaystyle \frac{{\epsilon }_{\mathrm{s}}\left(1-{\epsilon }_{\mathrm{g}}\right){\mu }_{\mathrm{g}}}{{\epsilon }_{\mathrm{g}}{d}_{\mathrm{s}}^2}}+1.75{\displaystyle \frac{{\rho }_{\mathrm{g}}{\epsilon }_{\mathrm{s}}\left|{\mathbf{u}}_{\mathrm{g}}-{\mathbf{u}}_{\mathrm{s}}\right|}{d_{\mathrm{s}}}}\right]\left({\mathbf{u}}_{\mathrm{g}}-{\mathbf{u}}_{\mathrm{s}}\right),$$

(2)

where μ_g refers to the dynamic viscosity of the gas phase, while d_s stands for the effective diameter of the solid phase.

The heat transfer rate between the gas and solid phases, E_gs, is expressed using the modified Ranz equation by Akiyama [43]:

$$E_{\mathrm{gs}}={\displaystyle \frac{6{\lambda }_{\mathrm{g}}{\epsilon }_{\mathrm{s}}}{d_{\mathrm{s}}^2}}\left(2.0+0.39R{e}^{1/2}P{r}^{1/3}\right)\left(T_{\mathrm{g}}-T_{\mathrm{s}}\right),$$

(3)

where T_g and T_s denote gas and solid temperature, and Re and Pr are the relative Reynolds number on the basis of ds and the Prandtl number of the gas phase, respectively.

The gas phase is assumed as ideal gas and its density is expressed as

$${\rho }_{\mathrm{g}}=\frac{P}{R^{*}{T}_{\mathrm{g}}{\sum }_i\frac{w_i}{M_i}},$$

(4)

where R* represents the universal gas constant while subscript i denotes the gaseous species.

The reaction rates of R1–R6 obey the mechanism of the unreacted shrinking core model (USCM), which is well-established and widely used in shaft furnace modeling. For simplicity, the detailed rate expressions are not presented here; the reader is referred to Ref. [44] for the original formulation. Meanwhile, the corresponding correlations for kinetic parameters, including the equilibrium constant, rate constant, and effective diffusion coefficient, can be found in the earlier publications of the present authors [39].

The rates of R7 and R8, both of which are reversible homogeneous gas-phase reactions, are expressed as

$$R_7={\epsilon }_{\mathrm{s}}{k}_7\left(P_{\mathrm{CO}}{P}_{{\mathrm{H}}_2\mathrm{O}}-{\displaystyle \frac{P_{{\mathrm{CO}}_2}{P}_{{\mathrm{H}}_2}}{K_7}}\right),$$

(5)

$$R_8={\epsilon }_{\mathrm{s}}{k}_8\left(P_{{\mathrm{CH}}_4}{P}_{{\mathrm{H}}_2\mathrm{O}}-{\displaystyle \frac{P_{\mathrm{CO}}{P}_{{\mathrm{H}}_2}^3}{K_8}}\right),$$

(6)

where the correlations of reaction rate constants (k₇ and k₈) and equilibrium constants (K₇ and K₈) are listed in Table 3. It is seen that the rate constants are associated with the reduction degree (X) of pellets. The reason lies in the fact that the water–gas shift reaction is catalyzed by metallic iron and its oxides to different extents, while the methane reforming reaction is catalyzed solely by metallic iron. Here, X = 0.5 represents the appearance of metallic iron.

As a central aspect of the present model, carburization modeling is of particular importance in this work. Kumar et al. [41] considered the methane decomposition into iron carbide or graphite as two parallel processes in their one-dimensional models. However, experimental evidence reported in the literature suggests that the occurrence of graphite is more likely to result from the cementite decomposition, as the iron carbide is a metastable phase and can easily decompose to metallic iron and graphite, even under strongly carburizing atmospheres [45,46,47]. Therefore, the present model represents carbon form evolution as a progressive Fe₃C-formation-decomposition pathway, as represented by R9–R11 in Table 1. It should be noted that the graphite can be generated directly through methane decomposition and carbon monoxide precipitation in reality; however, these pathways are not explicitly considered in the current work.

The reaction rates of CH₄ decomposition (R9) and CO precipitation (R10) are given by

$$R_9={\displaystyle \frac{{\epsilon }_{\mathrm{s}}}{d_{\mathrm{s}}}}{\displaystyle \frac{k_9}{P_{{\mathrm{H}}_2}^{0.5}}}\left(P_{{\mathrm{CH}}_4}-{\displaystyle \frac{P_{{\mathrm{H}}_2}^2{a}_{\mathrm{C}}}{K_9}}\right);$$

(7)

$$R_{10}={\displaystyle \frac{{\epsilon }_{\mathrm{s}}}{d_{\mathrm{s}}}}\left({\displaystyle \frac{k_{10}{K}_{10}{P}_{\mathrm{CO}}^2}{a_{\mathrm{C}}}}-k_{10}^{\prime }{P}_{{\mathrm{CO}}_2}\right).$$

(8)

Corresponding kinetic constants are also outlined in Table 3.

The carbon activity in DRI, a_C, which is assumed to govern carburization rate and subsequent cementite decomposition rate, is calculated from Chipman’s correlation:

$${\mathrm{l}\mathrm{o}\mathrm{g}}_{10}{a}_{\mathrm{C}}={\displaystyle \frac{2300}{T_{\mathrm{s}}}}-0.92+\left({\displaystyle \frac{3860}{T_{\mathrm{s}}}}\right)C+{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\displaystyle \frac{C}{1-C}}\right),$$

(9)

where C denotes the atomic ratio of carbon to metallic iron.

Following the correlation proposed by Longbottom et al. [46] based on experimental results, the reaction rate of cementite decomposition is expressed as

$$R_{11}=b\cdot a_{\mathrm{C}}\cdot D_{\mathrm{C},\mathrm{iron}},$$

(10)

where b is a temperature-independent coefficient, and D_C,iron is a carbon diffusion coefficient, representing the carbon diffusion in iron phase, with a correlation of

$$D_{\mathrm{C},\mathrm{iron}}=0.47\mathrm{e}\mathrm{x}\mathrm{p}\left(-1.6c^{\prime }-{\displaystyle \frac{37000-6600c^{\prime }}{R^{*}{T}_{\mathrm{s}}}}\right),$$

(11)

where c′ denotes graphite in weight percent. The general principle is that D_C,iron increases significantly with increasing temperature, leading to a growth trend of R₁₁ with temperature, although a_C decreases moderately with temperature.

Table 3. Correlations of kinetic parameters for homogeneous gas-phase and carburization reactions [35,48,49].

Reaction	Rate Constant	Equilibrium Constant
R7	$k_7=93.3\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{7320}{R^{*}{T}_{\mathrm{g}}}}\right),$ X > 0.5	$K_7=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{3863.7}{T_{\mathrm{g}}}}-3.5414\right)$
	$k_7=1.83\times {10}^{-5}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{7.84}{R^{*}{T}_{\mathrm{g}}}}\right),$ X ≤ 0.5
R8	$k_8=392\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{6770}{R^{*}{T}_{\mathrm{g}}}}\right),$ X > 0.5	$K_8=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{23700}{T_{\mathrm{g}}}}-8.424{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}{T}_{\mathrm{g}}-1.571\right)$
	$k_8=0,$ X ≤ 0.5
R9	$k_9=1.365\times {10}^6\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{230120}{R^{*}{T}_{\mathrm{s}}}}\right)$	$K_9={\displaystyle \frac{k_9}{k_9^{\prime }}}$
	$k_9^{\prime }=2.6\times {10}^{-2}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{105855}{R^{*}{T}_{\mathrm{s}}}}\right)$
R10	$k_{10}=1.8\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{27200}{R^{*}{T}_{\mathrm{s}}}}\right)$	$K_{10}={\displaystyle \frac{k_{10}}{k_{10}^{\prime }}}$
	$k_{10}^{\prime }=2.2\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{8800}{R^{*}{T}_{\mathrm{s}}}}\right)$

X: reduction degree of pellets.

Table 3. Correlations of kinetic parameters for homogeneous gas-phase and carburization reactions [35,48,49].

Reaction	Rate Constant	Equilibrium Constant
R7	$k_7=93.3\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{7320}{R^{*}{T}_{\mathrm{g}}}}\right),$ X > 0.5	$K_7=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{3863.7}{T_{\mathrm{g}}}}-3.5414\right)$
	$k_7=1.83\times {10}^{-5}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{7.84}{R^{*}{T}_{\mathrm{g}}}}\right),$ X ≤ 0.5
R8	$k_8=392\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{6770}{R^{*}{T}_{\mathrm{g}}}}\right),$ X > 0.5	$K_8=\mathrm{e}\mathrm{x}\mathrm{p}\left({\displaystyle \frac{23700}{T_{\mathrm{g}}}}-8.424{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}{T}_{\mathrm{g}}-1.571\right)$
	$k_8=0,$ X ≤ 0.5
R9	$k_9=1.365\times {10}^6\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{230120}{R^{*}{T}_{\mathrm{s}}}}\right)$	$K_9={\displaystyle \frac{k_9}{k_9^{\prime }}}$
	$k_9^{\prime }=2.6\times {10}^{-2}\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{105855}{R^{*}{T}_{\mathrm{s}}}}\right)$
R10	$k_{10}=1.8\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{27200}{R^{*}{T}_{\mathrm{s}}}}\right)$	$K_{10}={\displaystyle \frac{k_{10}}{k_{10}^{\prime }}}$
	$k_{10}^{\prime }=2.2\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\displaystyle \frac{8800}{R^{*}{T}_{\mathrm{s}}}}\right)$

X: reduction degree of pellets.

In this work, the governing conservation equations (Equation (1)) are solved using the finite volume method, in which the convective terms are discretized with a second-order upwind scheme and the diffusive terms are discretized using the central difference scheme to ensure an accurate and robust calculation. The coupling between velocity and pressure is achieved using the coupled SIMPLE algorithm. The calculation is considered converged when the residuals of all discretized equations become less than 1 × 10⁻⁷, with the under-relaxation factors carefully adjusted during the solution process.

2.3. Model Validation and Boundary Conditions

Since publicly available industrial data for the ENERGIRON ZR process remain very limited, the accuracy of the present CFD model was assessed by reproducing published industrial measurements from a MIDREX shaft furnace with a productivity of 26.4 t-DRI/h. This industrial furnace has been widely used in previous modeling studies: detailed information regarding its geometry, operating conditions, and material properties can be found in Refs. [34,35,50].

Table 4 compares the predicted values with the reported plant data for several key performance indicators, including gas composition, DRI metallization degree, and carbon content. Reasonable agreement is obtained for all these variables, indicating that the model is capable of reproducing the essential transport and reaction behavior in an industrial shaft furnace. For the carbon content, the model predicts that Fe₃C is the dominant carbon-bearing phase, accounting for approximately 99% of the total carbon. Since one of the key features of the present model is the explicit distinction between Fe₃C and graphitic carbon, the validity of the predicted proportion between these two carbon forms will be further discussed in the subsequent simulation results. It should also be noted that the present comparison with MIDREX plant data should be regarded as validation of the general transport, heat-transfer, reduction, and reaction framework rather than as direct validation of the model under ENERGIRON ZR conditions. Further quantitative validation against detailed ENERGIRON ZR plant data, particularly measurements distinguishing the two carbon forms, is required when such data become available.

Table 4. Comparisons between the MIDREX plant data and model predictions.

Indicators		Plant Data	Predictions
Top gas composition, (Vol%)	H2	37.0	37.20
	CO	18.9	19.00
	H2O	21.2	21.49
	CO2	14.3	13.77
	CH4 + N2	8.6	8.54
DRI	Metallization degree, -	0.93	0.9312
	Carbon (wt), -	0.02	Fe3C (0.02) C (0.00019)

In the following simulations, the computational domain is restricted to the upper reactive zone of the shaft furnace, whose geometric parameters, boundary conditions, and corresponding spatial discretization are illustrated in Figure 2. This section is taken directly from the reduction-zone geometry of the reference MIDREX furnace. The mesh resolution was confirmed to be sufficient based on a grid independence test [25]. The solid flow pattern, including pellet velocity, pellet size, and bed voidage, is also kept consistent with that of the reference MIDREX furnace. On this basis, the gas operating conditions are modified to represent ENERGIRON ZR-like conditions, characterized by a high top-gas pressure of 6 bar, a high H₂/CO ratio of 4.0, elevated gas temperatures above 1273 K, and relatively high CH₄ contents in the reducing gas, exceeding 15%. The present study focuses on this upper reactive zone because, under ENERGIRON ZR conditions, in situ reforming, iron oxide reduction, and carburization are expected to occur predominantly in this region.

Figure 2. Geometry and corresponding spatial discretization of computational domain.

3. Results and Discussion

Table 5 summarizes the operating conditions and corresponding performance indicators of DRI for all simulation cases considered in the present study. The base case corresponds to a representative ENERGIRON ZR operating condition, with a reducing gas temperature of 1323 K, a gas feed rate of 1500 Nm³/t-pellet, and a gas composition of 60% H₂, 15% CO, 20% CH₄, 1% H₂O, 1% CO₂, and 3% N₂. Based on this reference condition, parametric studies were carried out to investigate the effects of reducing gas temperature, gas composition, and gas feed rate, as summarized in Table 5. It should be noted that, in the composition variation cases, the H₂O, CO₂, and N₂ contents as well as the H₂/CO ratio were kept constant. The relatively low H₂O and CO₂ levels were selected to reflect the process characteristics of the ENERGIRON ZR process, as shown in Figure 1, in which the humidifier and CO₂ removal unit allow these gas species to be adjusted to low levels before the recycled gas is re-injected into the shaft furnace. In addition, all performance indicators listed in Table 5 are mass-weighted average values at the furnace bottom. For convenience in cross-referencing the cases discussed in the following subsections, some cases appear in more than one parametric group, as noted at the bottom of the table.

Table 5. Summary of operating conditions and outlet-averaged metallization and carbon partitioning results for all simulation cases.

Case	Gas Composition, Vol. %			Gas Temperature, K	Gas Feed Rate, Nm3/t-Pellet	Metallization Degree of DRI, -	Total Carbon Mass Fraction in DRI, -	Combined Carbon/Total Carbon, %	Free Carbon/Total Carbon, %
	H2	CO	CH4
Baseline case
Base	60	15	20	1323	1500	0.9797	0.03128	93.4	6.6
Temperature variation cases
T1	60	15	20	1273	1500	0.9426	0.01722	97.6	2.4
T2	60	15	20	1323	1500	0.9797	0.03128	93.4	6.6
T3	60	15	20	1373	1500	1	0.04938	86.3	13.7
Composition variation cases
C1	64	16	15	1273	1500	0.9877	0.02048	97.8	2.2
C2	60	15	20	1273	1500	0.9426	0.01722	97.6	2.4
C3	56	14	25	1273	1500	0.9001	0.01615	97.2	2.8
C4	64	16	15	1323	1500	1	0.03536	93.9	6.1
C5	60	15	20	1323	1500	0.9797	0.03128	93.4	6.6
C6	56	14	25	1323	1500	0.9430	0.02805	92.6	7.4
C7	64	16	15	1373	1500	1	0.04849	84.3	15.7
C8	60	15	20	1373	1500	1	0.04938	86.3	13.7
C9	56	14	25	1373	1500	0.9794	0.04179	87.5	12.5
Feed rate variation cases
F1	60	15	20	1323	1400	0.9339	0.02360	93.9	6.1
F2	60	15	20	1323	1500	0.9797	0.03128	93.4	6.6
F3	60	15	20	1323	1600	1	0.04047	92.5	7.5
Additional cases
A1	60	15	20	1373	1600	1	0.05364	83.4	16.6
A2	60	15	20	1373	1800	1	0.05617	80.2	19.8
A3	60	15	20	1373	2000	1	0.05784	78.1	21.9

Base = T2 = C5 = F2, T1 = C2, T3 = C8.

3.1. In-Furnace Thermochemical State

In this subsection, the in-furnace thermochemical state under the operating conditions of the base case is presented in detail.

Figure 3 shows the distributions of gas temperature and gas-phase composition in the furnace. A pronounced high-temperature region is observed in the vicinity of the gas inlet, where the hot reducing gas is injected. As the gas flows upward, its temperature gradually decreases, indicating continuous heat consumption by endothermic reactions, including H₂ reduction, CH₄ reforming, and CH₄ decomposition, together with heat transfer to the descending burden bed. The CH₄ mole fraction is highest near the gas inlet and decreases rapidly as the gas penetrates into the bed, confirming its active participation in the in situ reforming and carburization processes. In contrast, H₂ and CO are initially enriched in the lower part of the reactive zone and then gradually decrease towards the furnace top due to their continuous consumption in the reduction of iron oxides. Correspondingly, H₂O and CO₂, as gaseous reduction products, exhibit the opposite trend, with relatively low levels near the gas inlet and progressively higher concentrations towards the upper part of the furnace. These gas-phase distributions clearly indicate that the lower shaft region near the gas inlet is the main zone where reforming and reduction are most strongly coupled.

Figure 3. Distributions of (a) gas temperature and gas-phase mole fraction of (b) CH₄, (c) H₂, (d) CO, (e) H₂O, and (f) CO₂ under the conditions of the base case.

The corresponding solid-phase evolution is presented in Figure 4. The reduction of iron oxide proceeds sequentially along the descending path of the burden. Hematite is mainly preserved in the uppermost part of the furnace, while magnetite and wüstite appear as intermediate phases during the descent of the burden bed. Metallic iron is predominantly formed in the lower part of the reactive zone, where the gas temperature is higher and the reducing potential is stronger. This distribution is consistent with the gas-phase fields shown in Figure 3. Carbon deposition takes place only after sufficient metallic iron has been generated. As a result, combined carbon, i.e., carbon present as Fe₃C, is mainly distributed in the lower part of the furnace, especially near the gas inlet where both metallic iron availability and carburizing potential are high. Free carbon shows a more localized distribution and is confined to the most strongly carburized region. The calculation results listed in Table 5 show that most of the deposited carbon remains in the form of Fe₃C (93.4%), while only a relatively small fraction is converted into graphitic carbon (6.6%).

Figure 4. Distributions of solid-phase mass fractions of (a) Fe₂O₃, (b) Fe₃O₄, (c) FeO, (d) Fe, (e) combined carbon, and (f) free carbon under the conditions of the base case.

Figure 5 further clarifies the underlying reaction mechanism through the distributions of representative reaction rates. The final reduction of wüstite to metallic iron by H₂ and CO, represented by R3 and R6, is concentrated in the lower part of the reactive zone, in agreement with the distribution of metallic iron in Figure 4. By comparison, the H₂-based reduction is much stronger than the CO-based route, reflecting the H₂-rich nature of the ENERGIRON ZR process. Methane reforming, R8, is strongly localized near the gas inlet, where CH₄, H₂O, high temperature, and catalytic metallic iron coexist. This reforming reaction continuously generates H₂ and CO, which in turn sustain the reduction of iron oxides. The carburization reactions, R9 and R10, are also concentrated in the same region, indicating that carbon uptake occurs mainly after the local reduction degree has become sufficiently high. Compared with the CO-based carburization route (R10), CH₄-based carburization (R9) plays a more dominant role under the baseline condition, accounting for approximately 87.6% of the total carbon uptake, as estimated from the integrated reaction rates (mol/s) of the two carburization routes within the furnace. In addition, the decomposition of Fe₃C to free carbon, represented by R11, is restricted to the hottest and most strongly carburized zone, which explains why free carbon appears only locally in Figure 4.

Figure 5. Distributions of reaction rates of (a) R3, (b) R6, (c) R8, (d) R9, (e) R10, and (f) R11 (cf. Table 1) under the conditions of the base case.

Overall, the baseline results reveal a clear spatial sequence of thermochemical behavior in the ENERGIRON ZR shaft furnace: CH₄-containing reducing gas first undergoes strong in situ reforming near the gas inlet, generating additional reducing species; these gases then promote rapid reduction of iron oxides to metallic iron in the lower shaft region; finally, carburization takes place predominantly in the same region, with Fe₃C as the dominant carbon-bearing phase and graphitic carbon forming only in a limited local zone.

3.2. Effect of Reducing Gas Temperature

In this subsection, the effect of reducing gas feed temperature is clarified by comparing the results of Case T1, Case T2, and Case T3 in Table 5, whose gas temperatures are 1273 K, 1323 K, and 1373 K, respectively. The temperature of 1373 K may be regarded as the upper limit of the reducing gas feed temperature, since a high temperature of 1366 K has been reported for industrial shaft furnaces [41], whereas a further increase would pose a high risk of pellet sticking, which is extremely detrimental to shaft furnace operation.

Figure 6 illustrates the gas temperature distributions under three different reducing gas feed temperatures. As the gas temperature increases from 1273 K to 1373 K, the temperature level in the shaft furnace progressively increases, particularly in the lower part of the reactive zone. In general, the improved thermal condition is beneficial for the endothermic reactions involving CH₄ reforming, H₂ reduction, and CH₄ decomposition from both thermodynamic and kinetic points of view, suggesting improved performance in both metallization and carburization under higher gas feed temperatures.

Figure 6. Gas temperature distributions under different reducing gas feed temperatures.

Figure 7 shows the distributions of the solid metallization degree in the furnace. As the reducing gas temperature increases from 1273 K to 1373 K, the high-metallization region expands progressively. This behavior is consistent with the thermal state shown in Figure 6. As a result, the outlet-averaged metallization degree increases from 0.9426 at 1273 K to 0.9797 at 1323 K, and finally reaches complete metallization at 1373 K, as listed in Table 5.

Figure 7. Distributions of solid metallization degree under different reducing gas feed temperatures.

As for carburization, Figure 8 depicts the total carbon distributions under the three temperatures of 1273 K, 1323 K, and 1373 K. It is seen that the total carbon distribution is highly sensitive to the reducing gas feed temperature. With increasing temperature, the carbon-rich region near the lower shaft becomes progressively larger and extends further into the burden bed. This behavior is consistent with the temperature and metallization fields shown in Figure 6 and Figure 7, as carbon uptake is favored by both elevated temperature and the availability of metallic iron. Consequently, the outlet-averaged total carbon mass fraction rises significantly from 0.01722 at 1273 K to 0.03128 at 1323 K, and then to 0.04938 at 1373 K. These results confirm that increasing the reducing gas temperature is highly effective in strengthening the reduction and carburization performance of the ENERGIRON ZR shaft furnace.

Figure 8. Distributions of total carbon mass fraction under different reducing gas feed temperatures.

The corresponding distributions of the Fe₃C decomposition rate (R11) are presented in Figure 9, where a clear temperature dependence can be observed. At 1273 K, R11 is very weak and only appears in a narrow local region near the gas inlet, indicating a highly limited formation of free carbon. As the reducing gas temperature increases, however, both the intensity and spatial extent of R11 increase progressively, suggesting that Fe₃C decomposition becomes much stronger under higher temperature conditions. This behavior is consistent with the model formulation, in which the Fe₃C decomposition rate is strongly promoted by increasing carbon diffusivity in the iron phase (cf. Equation (11)) at elevated temperatures. Overall, although higher temperatures promote total carbon uptake, they also favor the subsequent decomposition of Fe₃C into free carbon. As a result, the rise in total carbon at higher temperatures is accompanied by a shift in carbon partitioning, with the fraction of combined carbon decreasing and that of free carbon increasing, as summarized in Table 5.

Figure 9. Distributions of reaction rate of Fe₃C decomposition (R11 of Table 1) under different reducing gas feed temperatures.

To shed more light on carbon partitioning in the final DRI product, Figure 10 shows the radial distributions of combined carbon and free carbon at the furnace bottom. In all three cases, pronounced radial non-uniformity is observed. To quantify the radial variation in the overall carburization level, a total carbon non-uniformity coefficient, U_TC, is defined as

$$U_{\mathrm{T}\mathrm{C}}={\displaystyle \frac{w_{\mathrm{T}\mathrm{C},\mathrm{m}\mathrm{a}\mathrm{x}}-w_{\mathrm{T}\mathrm{C},\mathrm{m}\mathrm{i}\mathrm{n}}}{{\overline{w}}_{\mathrm{T}\mathrm{C}}}},$$

(12)

where $w_{\mathrm{T}\mathrm{C},\mathrm{m}\mathrm{a}\mathrm{x}}$, $w_{\mathrm{T}\mathrm{C},\mathrm{m}\mathrm{i}\mathrm{n}}$, and ${\overline{w}}_{\mathrm{T}\mathrm{C}}$ denote the maximum, minimum, and mass-weighted average total carbon mass fractions at the furnace outlet, respectively. According to this definition, a larger value of U_TC indicates stronger non-uniformity in total carbon distribution. In addition, the radial non-uniformity of carbon partitioning is evaluated based on the variation in the combined carbon fraction from the furnace center to the near-wall region.

Figure 10. Radial carbon distributions in DRI at the furnace bottom under different reducing gas feed temperatures: (a) 1273 K, (b) 1323 K, and (c) 1373 K.

The carbon content is generally lower in the central region and increases towards the wall side, which is consistent with the total carbon distribution results shown in Figure 8. At 1273 K (Figure 10a), the overall carbon level remains relatively low, and the deposited carbon is dominated by combined carbon, while the amount of free carbon is very limited across the whole radius. In this case, U_TC is calculated to be 1.898, indicating a pronounced center-to-wall variation in the overall carburization level, while the combined carbon fraction decreases slightly from 99.9% at the center to 96.5% near the wall. This suggests that, under the lower gas feed temperature, carburization remains relatively weak and the decomposition of Fe₃C is largely suppressed.

At 1323 K (Figure 10b), both the combined carbon and the total carbon level increase significantly over the entire radius, with the near-wall region exhibiting the highest carbon concentration. Meanwhile, free carbon becomes more pronounced than that at 1273 K, especially close to the wall, indicating that the enhancement of carburization is accompanied by stronger Fe₃C decomposition. As a result, U_TC decreases to 1.508, indicating improved radial uniformity of the total carbon distribution, while the combined carbon fraction declines more markedly, from 99.9% at the center to 89.8% near the wall.

At 1373 K (Figure 10c), the radial non-uniformity of carbon partitioning becomes even more evident. Although U_TC further decreases to 1.046, indicating a more uniform radial distribution of the overall carbon content, the combined carbon fraction decreases markedly from 99.5% at the center to 78.8% near the wall, demonstrating substantial near-wall enrichment of free carbon. These results show that increasing the gas feed temperature not only enhances overall carburization and improves the radial uniformity of total carbon, but also promotes Fe₃C decomposition, thereby shifting carbon partitioning towards free carbon in the most strongly carburized near-wall region. Therefore, a more uniform radial distribution of total carbon does not necessarily correspond to a more uniform distribution of carbon forms.

3.3. Effect of Reducing Gas Composition

In this subsection, the effect of reducing gas composition is clarified by comparing the results of Cases C1–C9 in Table 5, in which the CH₄ content in the reducing gas is varied from 15% to 25% under three different gas feed temperatures, namely 1273 K, 1323 K, and 1373 K.

Figure 11 summarizes the effects of CH₄ content in the reducing gas on the final metallization degree and the total carbon level of DRI under the above three gas feed temperatures. Although the corresponding values are already listed in Table 5, they are replotted here to more clearly illustrate the overall trends. It can be seen that the effect of CH₄ content on metallization is generally consistent at different gas feed temperatures: increasing CH₄ tends to deteriorate the final reduction performance. At both 1273 K and 1323 K, the outlet-averaged metallization degree decreases monotonically as the CH₄ content increases from 15% to 25%. At 1373 K, although complete metallization is maintained at 15% and 20% CH4, a further increase to 25% CH₄ still lowers the metallization degree.

Figure 11. Effect of CH₄ content in the reducing gas on (a) final metallization degree and (b) total carbon under different gas feed temperatures.

By contrast, the response of total carbon is temperature dependent. At 1273 K and 1323 K, the total carbon mass fraction decreases monotonically with increasing CH₄ content, from 0.02048 to 0.01615 at 1273 K, and from 0.03536 to 0.02805 at 1323 K. However, at 1373 K, a different trend is observed: the total carbon first increases slightly from 0.04849 at 15% CH₄ to 0.04938 at 20% CH₄, and then decreases to 0.04179 at 25% CH₄. To clarify the underlying mechanism, the following discussion first focuses on the representative cases at 1323 K and then returns to the 1373 K condition to explain the non-monotonic variation in total carbon.

Figure 12 presents the gas temperature distributions at CH₄ contents of 15%, 20%, and 25% under a gas feed temperature of 1323 K. A clear decline in the furnace thermal level can be observed as the CH₄ content increases, since the high-temperature region at the lower part of the reactive zone shrinks continuously. This behavior can be attributed to the results shown in Figure 13, where the distributions of the CH₄ reforming rate (R8) are illustrated. It can be seen that increasing the CH₄ content clearly intensifies the reforming reaction in the lower region near the gas inlet, where high CH₄ concentration, high temperature, and abundant metallic iron coexist. Since CH₄ reforming is a strongly endothermic reaction, this intensification leads to greater local heat consumption and therefore lowers the thermal level within the furnace. As a result, the outlet-averaged metallization degree decreases from 1.0 at 15% CH₄ to 0.9797 at 20% CH₄ and further to 0.9430 at 25% CH₄, since the lowered temperature level limits the reduction process, particularly the H₂-based reduction.

Figure 12. Gas temperature distributions under different CH₄ contents in feed gas with a temperature of 1323 K.

Figure 13. Distributions of reaction rate of CH₄ reforming (R8 of Table 1) under different CH₄ contents in feed gas with a temperature of 1323 K.

As for the effect of CH₄ content on carburization, Figure 14 shows the corresponding distributions of total carbon mass fraction in the furnace. At 15% CH₄, the carbon-enriched zone extends over a relatively wide area in the lower part of the reactive zone, indicating that carburization can proceed over a larger portion of the burden bed. As the CH₄ content increases, it is observed that the spatial region with appreciable carbon content becomes progressively smaller, while the local carbon level near the wall becomes somewhat higher. However, this local increase is not sufficient to compensate for the simultaneous shrinkage of the overall carburized region. As a result, the outlet-averaged total carbon mass fraction decreases from 0.03536 at 15% CH₄ to 0.03128 at 20% CH₄, and further to 0.02805 at 25% CH₄, as already summarized in Table 5 and Figure 11. To better understand this behavior, the radial carbon distributions at the furnace bottom are further examined in Figure 15. Under all three CH₄ contents, the carbon distribution is clearly non-uniform in the radial direction, with a lower carbon level in the central region and a higher carbon level towards the furnace wall. At 15% CH₄, the radial variation is relatively weak, and the combined carbon is distributed more uniformly across the furnace bottom, while the free carbon level remains relatively low throughout the radius. The corresponding value of U_TC is 0.694, and the combined carbon fraction decreases from 98.3% at the center to 90.6% near the wall.

Figure 14. Distributions of total carbon mass fraction under different CH₄ contents in feed gas with a temperature of 1323 K.

Figure 15. Radial carbon distributions in DRI at the furnace bottom under different CH₄ contents in feed gas with a temperature of 1323 K: (a) 15%, (b) 20%, and (c) 25%.

As the CH₄ content increases to 20% and further to 25%, the radial non-uniformity becomes more pronounced. In particular, the carbon level near the wall increases, whereas the carbon content in the central region decreases noticeably. As a result, U_TC increases markedly to 1.508 at 20% CH₄ and further to 1.793 at 25% CH₄. Meanwhile, the increase in free carbon is also mainly concentrated in the near-wall region, where the combined carbon fraction decreases to 89.8% and to 89.0%, respectively. These results suggest that increasing the CH₄ content does not enhance carburization uniformly across the entire outlet section; instead, it makes the carburization behavior more localized and radially non-uniform. Therefore, increasing the CH₄ content intensifies not only the radial non-uniformity of the overall carbon level but also the near-wall enrichment of free carbon. Although the near-wall carbon enrichment becomes stronger at higher CH₄ contents, the simultaneous decrease in carbon uptake in the central region leads to a lower outlet-averaged total carbon level overall.

The origin of the increasing radial non-uniformity with CH₄ content can be further understood from the carburization rate distributions shown in Figure 16. It is seen that the CH₄-based carburization route, R9, becomes progressively stronger as the CH₄ content increases from 15% to 25%, as shown in panel a, but this enhancement is increasingly concentrated in a narrow region near the gas inlet and close to the wall. By contrast, at 15% CH₄, the CO-based carburization route, R10, is not only more intense than in the higher-CH₄ cases, but also extends over a much broader region, as illustrated in panel b. This is related to the more favorable thermal condition (cf. Figure 12) and the higher metallization level at lower CH₄ content. Integrated results show that at 15%, 20%, and 25% CH₄, the CO-based route contributes to approximately 14.9%, 12.4%, and 11.4% of the total carbon uptake, respectively. Therefore, although increasing CH₄ enhances the local intensity of R9, the simultaneous contraction of the R9-active region together with the weakening of the CO-based carburization reduces the overall carbon content in DRI.

Figure 16. Rate distributions of carburization by (a) CH₄ decomposition (R9 of Table 1) and (b) CO precipitation (R10 of Table 1) under different CH₄ contents in feed gas with a temperature of 1323 K.

Thus, under the present 1323 K condition, a seemingly contradictory result is obtained: increasing the CH₄ content is expected to enhance carburization by raising the nominal carbon potential of the reducing gas, yet the overall carbon uptake actually decreases due to the heat shortage in the furnace caused by the intensified, strongly endothermic reforming reaction. This mechanism is also expected to hold for the 1273 K cases, where the sensible heat supply is even more limited, thereby explaining the similar variation trends of metallization degree and total carbon with CH₄ content at these two temperatures.

However, when the gas feed temperature is further increased to 1373 K, the situation becomes different, as shown in Figure 17. Compared with the 20% CH₄ case, the CH₄-based carburization route, R9, is clearly weakened at 15% CH₄, although the CO-based route, R10, remains noticeably stronger and more broadly distributed under the latter condition. This indicates that, under the higher-temperature condition of 1373 K, the furnace thermal level is already sufficiently high, and the limiting factor for carburization is no longer dominated by sensible heat alone. Instead, when the CH₄ content is reduced to 15%, the CH₄ supply itself becomes insufficient to sustain a higher overall carburization level. As a result, although the more favorable thermal condition and the stronger CO-based carburization at 15% CH₄ are beneficial, they cannot fully compensate for the weaker CH₄-based carburization, and the total carbon remains slightly lower than that at 20% CH₄.

Figure 17. Rate distributions of carburization by (a) CH₄ decomposition (R9 of Table 1) and (b) CO precipitation (R10 of Table 1) under different CH₄ contents in feed gas with a temperature of 1373 K.

When the CH₄ content is further increased from 20% to 25%, the dominant limitation shifts again. In this case, the additional CH₄ intensifies the strongly endothermic reforming reaction and causes a deterioration in the furnace thermal level, as already discussed for the 1323 K cases. Consequently, the total carbon decreases from 0.04938 at 20% CH₄ to 0.04179 at 25% CH₄. Therefore, the results at 1373 K suggest that the controlling factor for carburization changes with CH₄ content: at 15% CH₄, CH₄ availability becomes insufficient, whereas at 25% CH₄, the thermal shortage associated with excessive reforming becomes dominant. The 20% CH₄ case thus represents a balance between these two competing effects and yields the highest total carbon under the present high-temperature condition.

3.4. Effect of Reducing Gas Feed Rate

In this subsection, the effect of reducing gas feed rate is clarified by comparing Cases F1–F3 in Table 5, in which the gas feed rate is varied from 1400 to 1600 Nm³/t-pellet while the gas composition and feed temperature are kept the same as those of the base case.

Figure 18 shows the gas temperature distributions under three different reducing gas feed rates. As the feed rate increases, the thermal level in the shaft furnace is clearly enhanced, particularly in the lower part of the reactive zone as the high-temperature region (red zone) becomes progressively larger and extends further inward into the burden bed. The increased amounts of reducing gas and sensible heat indicate an improved thermochemical condition for both reduction and carburization.

Figure 18. Gas temperature distributions under different gas feed rates.

Figure 19 presents the corresponding metallization distributions. As expected, the high-metallization region expands progressively upward and inward with increasing gas feed rate. As a result, the outlet-averaged metallization degree rises from 0.9339 at 1400 Nm³/t-pellet to 0.9797 at 1500 Nm³/t-pellet, and finally reaches complete metallization at 1600 Nm³/t-pellet. The corresponding effect on carburization is reflected in Figure 20, which shows the distributions of total carbon mass fraction under different reducing gas feed rates. It is observed that a higher gas feed rate not only intensifies local carburization, but also enlarges the spatial region in which carbon uptake can proceed effectively. Consequently, the outlet-averaged total carbon mass fraction increases from 0.02360 at 1400 Nm³/t-pellet to 0.03128 at 1500 Nm³/t-pellet, and further to 0.04047 at 1600 Nm³/t-pellet. These results confirm that increasing the reducing gas feed rate is highly beneficial for both reduction and carburization performance.

Figure 19. Distributions of solid metallization degree under different gas feed rates.

Figure 20. Distributions of total carbon mass fraction under different gas feed rates.

Further insight into the outlet carbon state can be obtained from the radial carbon distributions at the furnace bottom, as shown in Figure 21. Under all three feed rates, the carbon distribution remains radially non-uniform, showing a consistently increasing carbon level from the central region towards the furnace wall. As the reducing gas feed rate increases from 1400 to 1600 Nm³/t-pellet, the carbon level is elevated over almost the entire outlet section. Quantitatively, U_TC decreases from 1.886 at 1400 Nm³/t-pellet to 1.508 at 1500 Nm³/t-pellet and further to 1.110 at 1600 Nm³/t-pellet. This decrease demonstrates that increasing the gas feed rate improves the radial uniformity of the overall carburization level by promoting carbon uptake in the central region.

Figure 21. Radial carbon distributions in DRI at the furnace bottom under different gas feed rates: (a) 1400 Nm³/t-pellet, (b) 1500 Nm³/t-pellet, and (c) 1600 Nm³/t-pellet.

At the same time, the near-wall region still exhibits the strongest carbon enrichment. The combined carbon fraction near the wall decreases from 91.1% at 1400 Nm³/t-pellet to 89.8% at 1500 Nm³/t-pellet and further to 88.0% at 1600 Nm³/t-pellet, indicating a gradual increase in the local free carbon fraction at higher feed rates. However, the outlet-averaged combined carbon fraction decreases only slightly, from 93.9% to 92.5%. Therefore, increasing the reducing gas feed rate enhances carbon uptake over a broad portion of the outlet section and improves the radial uniformity of total carbon, while Fe₃C remains the dominant carbon-bearing phase in the final DRI.

3.5. Comparison with Industrial Carbon Partitioning Trend

To further evaluate the industrial relevance of the present model, the predicted carbon partitioning in DRI is compared with the reported industrial data in Figure 22. The industrial data were digitized from the published graph in Ref. [14] and replotted by the present authors. The simulation results are represented by the outlet-section-averaged values of the cases listed in Table 5, including three additional high-carbon cases introduced to extend the predicted carbon range. It can be seen that the simulation results essentially show qualitative agreement with the industrial data: as the total carbon level in DRI increases, the fraction of combined carbon decreases progressively, indicating a corresponding increase in the proportion of free carbon. This agreement confirms that the present model captures the essential relationship between the overall carburization level and carbon partitioning in industrial shaft furnace operation. Combined with the preceding analyses, these results suggest that beneficial carburization in the ENERGIRON ZR shaft furnace requires a balance among CH₄ availability, furnace thermal level, and gas throughput: insufficient thermal support suppresses overall carburization, whereas excessively strong carburization conditions promote the decomposition of Fe₃C and the formation of free carbon.

Figure 22. Comparison of carbon partitioning in DRI between industrial data [14] and simulation results.

4. Conclusions and Future Prospects

In this work, a two-dimensional computational fluid dynamics (CFD) model was developed for the reactive zone of an industrial-scale shaft furnace operated under ENERGIRON ZR (zero-reforming) conditions, in which carbon in direct reduced iron (DRI) was explicitly distinguished into combined carbon in Fe₃C and free carbon in graphitic form. Based on the model validation against available plant data, the effects of reducing gas temperature, gas composition, and gas feed rate on reduction, carburization, and carbon partitioning were systematically investigated. The main conclusions are summarized as follows.

• Under the baseline ENERGIRON ZR condition, in situ reforming, iron oxide reduction, and carburization are strongly coupled in the lower part of the reactive zone near the gas inlet. CH₄ reforming generates additional H₂ and CO to sustain reduction, while carburization mainly occurs after sufficient metallic iron has been formed. The predicted carbon in DRI is dominated by Fe₃C, whereas graphitic carbon appears only in a relatively limited local region.
• Increasing the reducing gas feed temperature from 1273 K to 1373 K increases the outlet-averaged metallization degree from 0.9426 to 1.000 and the total carbon mass fraction from 0.01722 to 0.04938. However, a higher temperature also promotes Fe₃C decomposition, reducing the combined carbon fraction from 97.6% to 86.3%. Meanwhile, the total carbon non-uniformity coefficient, U_TC, decreases from 1.898 to 1.046, indicating that the radial distribution of total carbon becomes more uniform, although the center-to-wall variation in carbon partitioning becomes more pronounced.
• The effect of CH₄ content on carburization is temperature dependent. At 1273 K and 1323 K, increasing the CH₄ content from 15% to 25% leads to decreases in both metallization degree and total carbon content, due to the deteriorated in-furnace thermal level caused mainly by the intensified endothermic reforming reaction. By contrast, at 1373 K, the total carbon first increases slightly from 15% CH₄ to 20% CH₄, and then decreases at 25% CH₄. The results suggest that at 15% CH₄, methane availability becomes insufficient to sustain a higher overall carburization level, whereas at 25% CH₄, the thermal shortage caused by excessive reforming becomes dominant. In addition, under a temperature of 1323 K, U_TC increases from 0.694 at 15% CH₄ to 1.793 at 25% CH₄, demonstrating that a higher CH₄ content intensifies the radial non-uniformity of carburization.
• Increasing the reducing gas feed rate from 1400 Nm³/t-pellet to 1600 Nm³/t-pellet enhances the thermal level, and thus increases the overall metallization degree from 0.9339 to 1.000 and total carbon mass fraction from 0.02360 to 0.04047. Meanwhile, U_TC decreases from 1.886 to 1.110, showing that the radial distribution of total carbon becomes more uniform. In addition, the outlet-averaged combined carbon fraction decreases slightly from 93.9% to 92.5%, confirming that Fe₃C remains the predominant carbon-bearing phase in the final DRI. Therefore, increasing the gas feed rate is an effective way to strengthen both reduction and overall carburization while maintaining a high combined carbon fraction.
• Comparison with the limited industrial carbon partitioning data shows that the model predictions capture the qualitative trend of a decreasing combined carbon fraction with increasing total carbon content in DRI. However, because direct industrial measurements distinguishing Fe₃C and graphitic carbon under known operating conditions are unavailable, this comparison should be interpreted as trend-level support rather than quantitative validation of the predicted carbon partitioning.

As for future work, several aspects deserve further investigation. First, the present model is restricted to the upper reactive zone of the shaft furnace; extension to the full furnace domain would allow the influence of the lower zones to be assessed more comprehensively. Second, the direct formation of graphitic carbon through methane decomposition and carbon monoxide precipitation was not explicitly modeled in the current work, and its incorporation may further improve the description of carbon form evolution under highly carburizing conditions. Moreover, a systematic thermodynamic assessment of the competition between methane availability and the thermal demand of reforming under different temperatures, pressures, and gas compositions will also be considered in future work. Finally, further validation against plant data for ENERGIRON ZR furnaces, especially data on carbon partitioning between Fe₃C and graphitic carbon, together with sensitivity or uncertainty analysis regarding model inputs and kinetic parameters, would be highly valuable for strengthening the industrial applicability of the model.