Dominant Role of Temperature in Drying Kinetics of Magnetite Pellet: Experimental and Modeling Study

Abstract

Natural magnetite ore is commonly used to produce oxidized pellets as the raw material for blast furnace ironmaking. The drying of green pellets significantly affects the quality of oxidized pellets. However, the drying process in the traveling grate cannot be directly analyzed. To address this issue, in this study the influences of the drying medium temperature, medium velocity, and pellet diameter on the moisture removal, as well as the drying kinetics of the natural magnetite oxidized pellets were investigated. Orthogonal experimental results indicated that the drying medium temperature had the most significant effect on the drying rate, followed by the medium velocity, while the interaction between the pellet diameter and temperature had a minor influence. Drying kinetic model fitting revealed that the drying process followed a modified Page model (III). Model validation demonstrated that the experimental measurements closely aligned with the theoretical predictions, confirming that the Page model (III) accurately predicted the effects of the drying temperature and medium velocity on the pellet moisture content. Higher drying temperatures further improved the prediction accuracy. The findings provide valuable insights for analyzing and optimizing the drying process of the natural magnetite oxidized pellets in the industrial traveling grate systems.

1. Introduction

Oxidized pellets serve as one of the principal raw materials in modern blast furnace ironmaking processes [1]. The use of these pellets not only enhances the iron grade, pellet strength, and particle size distribution of the furnace charge, but also significantly improves the process permeability while optimizing the heat and mass transfer efficiency during smelting, thereby achieving energy conservation and carbon emission reduction [2,3,4,5,6]. The production of oxidized pellets typically employs the grate-kiln-cooler (GKC) process, where the drying stage of green pellets in the traveling grate plays a crucial role in determining the final product quality. Inadequate drying may result in residual moisture evaporation during the subsequent high-temperature oxidation, leading to pellet disintegration and consequent deterioration of bed permeability [7,8]. However, the drying section of the traveling grate systems operates as an essentially enclosed “black box”, making direct observation of the drying process impractical [9,10]. Consequently, industrial practice relies on investigating the correlation between the drying duration and moisture removal under various operational conditions to evaluate the drying performance and guide the production optimization [11].

Previous studies have investigated the drying kinetics of green pellets. Gabriel K.P. Barrios [12] et al. examined the heat transfer mechanisms during drying using a two-stage drying model and shrinking core model. Other researchers have developed drying models for spherical powder materials that effectively simulate the pellet drying characteristics under various conditions [13]. Guo [14] et al. established a mathematical model coupling the mass, momentum, and energy transfer during pellet drying based on the heat and mass transfer theory in porous media. In order to accurately describe and predict the heat and mass transfer behaviors during the drying process, researchers have proposed a variety of mathematical models and physical models. Lewis assumed that the drying rate is proportional to the difference in moisture content, which is simple in form but limited in accuracy. Whitaker obtained the control equation from the volume average of the microscopic conservation law. Lamnatou et al. developed a numerical program for convective drying of porous bodies and implemented Luikov’s model [15,16]. As a crucial raw material for oxidized pellets, natural magnetite offers advantages [17,18] including high density, large specific surface area, and excellent pelletization performance [19,20]. However, green pellets produced from natural magnetite typically exhibit higher moisture content, making the drying process particularly critical for the final product quality. Despite its importance, limited research has focused on the drying behavior of the natural magnetite-based oxidized pellets, resulting in insufficient theoretical guidance for the industrial traveling grate drying processes. The drying behavior of green pellets made from natural magnetite under industrially relevant conditions remains poorly understood. Existing models typically focus on generic powder systems or synthetic materials and fail to fully capture the complexity of drying of magnetite-based pellets. To address this gap, the present study systematically investigated the effects of the drying temperature, duration, and medium velocity on the moisture removal in the pellets produced from natural magnetite. Kinetic modeling of the drying process, combining systematic experimental analysis with kinetic modeling, uniquely addresses these deficiencies and lays a theoretical foundation for optimizing the industrial production of natural magnetite oxidized particles.

2. Experimental

2.1. Raw Materials Characterization

The iron concentrate used in this study was obtained from Chengchao Iron Ore Mine (WISCO Resources Group) after magnetic separation enrichment. The main chemical composition and pelletization-related physicochemical properties are presented in

Table 1. Chemical composition of the iron concentrate (wt.%).

Major Chemical Composition	TFe	FeO	Al2O3	SiO2	CaO	MgO	S	p	n	LOI (Loss on Ignition)
Content (wt.%)	65.52	25.39	1.37	3.69	1.85	1.93	0.25	0.00	0.00	—
Std. Dev. (%)	0.21	0.18	0.03	0.05	0.04	0.06	0.01	—	—	—

Note: “n” refers to trace components not listed individually. In this sample, their total content was below the detection limit.

and

Table 2. Physical properties of the iron concentrate.

Parameter	+0.15 mm/%	−0.075 mm/%	−0.045 mm/%	Bulk Density (g/cm3)	True Density (g/cm3)	Pelletization Index (K)
Specification	1.96	82.97	63.93	2.17	4.82	0.41
Std. Dev. (%)	0.07	0.50	0.48	0.03	0.06	0.08

Note: Porosity (ε) = (1 − ρ_bulk/ρ_true) × 100%.

, respectively. As shown in Table 1, determined by XRF analysis, the concentrate contained 65.52 wt.% TFe and 25.39 wt.% FeO, with an [FeO/TFe] ratio of 38.75%, indicating magnetite as the predominant iron-bearing phase. Notably, the concentrate contained relatively high levels of impurities, including 0.25 wt.% S and 1.37 wt.% Al₂O₃, which may adversely affect the flue gas desulfurization during pellet production and contribute to the ring formation in the rotary kiln.

As shown in Table 2, the iron concentrate exhibited a fine particle size distribution, with 82.97% of particles below 75 μm and 63.93% below 45 μm. The material demonstrated a specific surface area of 1616 cm²/g and a porosity of 54.98%. The pelletization index (K) of 0.41 indicated a moderate pelletization capability, classifying this iron concentrate as a medium-grade pellet feed material.

The bentonite ore used in pelletization was supplied by WISCO Honghua Co., Ltd. (Wuhan, China). The physicochemical properties of the bentonite ore are presented in

Table 3. Chemical composition of bentonite (wt.%).

Component	SiO2	Al2O3	Fe2O3	CaO	MgO	K2O	Na2O	TiO2	SO3	P2O5
Content (wt.%)	57.32	15.10	7.29	3.41	2.72	1.23	1.21	1.39	0.020	0.38
Std. Dev. (%)	0.11	0.08	0.15	0.07	0.06	0.03	0.04	0.02	0.003	0.01
Component	MnO	ZnO	SrO	ZrO2	BaO	Cl	LOI (Loss on Ignition)
Content (wt.%)	0.10	0.011	0.033	0.027	0.053	0.022	9.51
Std. Dev. (%)	0.001	0.001	0.002	0.001	0.003	0.002	0.10

and

Table 4. Physical properties of the bentonite.

Parameter	Methylene Blue Absorption	2 h Water Absorption	Swelling Volume	Swelling Index
Value	27.59	145	19.1	5.5
Std. Dev. (%)	0.45	3.6	0.4	0.15
Unit	g/100 g	%	mL/3 g	mL/2 g

. Chemical composition analysis (Table 3) revealed that the bentonite ore primarily consisted of SiO₂ (57.32 wt.%), Al₂O₃ (15.10 wt.%), and Fe₂O₃ (7.29 wt.%). Notably, the SiO₂ and Al₂O₃ contents were lower than the theoretical values for standard bentonite. Standard bentonite usually contains more than 60% silicon dioxide and more than 18% aluminum oxide. The relatively high Si and Al contents may increase the levels of these elements in the final pellets while reducing the overall iron grade. As shown in Table 4, the bentonite ore exhibited a methylene blue absorption capacity of 27.59 g/100 g, corresponding to a montmorillonite content of 62.42%. The material demonstrated favorable binding properties for pelletization, as evidenced by a water absorption capacity of 145% (2 h test), a colloidal index of 99.8 mL/15 g, and a swelling volume of 8.5 mL/g.

2.2. Experimental Methods

The optimal pelletizing conditions were determined as follows: bentonite dosage of 2.0%, raw material moisture content of 9.5%, disc pelletizer rotation speed of 27 r/min, and pelletizing time of 18 min. Under these conditions, the green pellets exhibited a compressive strength of 16.2 N/pellet and a drop strength of 5.5 times/0.5 m. The cracking temperature reached 560 °C, and the overall pellet quality met the required standards.

The moisture content of the green pellets was measured using the experimental setup illustrated in Figure 1. A 200 g sample of the pellets obtained under optimal pelletizing conditions was placed in a sample tray and gently transferred into the drying apparatus. Drying was initiated using air as the drying medium. The surface temperature of the pellets was recorded by thermocouple 3 in the setup, while the weight of the sample after moisture evaporation was directly measured using a thermobalance to obtain the drying kinetics data. Throughout the experiment, the drying temperature was maintained below the cracking temperature of the pellets, and a uniform pellet diameter was ensured. Since the bed thickness influenced the drying efficiency, a thin-layer configuration was adopted in this study to eliminate its effects.

The moisture content of the pellets is typically calculated using Equation (1).

$$\mathrm{M}={\displaystyle \frac{\mathsf{\omega }}{{\mathrm{W}}_{\mathrm{\infty }}}}\times 100\mathrm{\%}$$

(1)

where M represents the moisture content of the pellet (g/g), ω denotes the weight of water in the pellet (g), and W_∞ is the weight of the fully dried pellet (g).

The moisture content of pellets at any given time (t) during drying can be calculated using Equation (2):

$${\mathrm{M}}_{\mathrm{t}}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{t}}-{\mathrm{W}}_{\mathrm{\infty }}}{{\mathrm{W}}_{\mathrm{\infty }}}}\times 100\mathrm{\%}$$

(2)

where M_t represents the moisture content (g/g) at drying time t, W_t represents the instantaneous pellet weight (g) at arbitrary time ‘t’ during the drying process. The variable ‘t’ denotes the elapsed drying time (s).

Therefore, the moisture ratio (MR) [21] at drying time t can be determined using Equation (3).

$$\mathrm{M}\mathrm{R}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{t}}-{\mathrm{M}}_{\mathrm{e}}}{{\mathrm{M}}_0-{\mathrm{M}}_{\mathrm{e}}}}$$

(3)

where MR represents the moisture ratio (%) at time t during the drying process. M₀ denotes the initial moisture content (g/g) of the pellets, and M_e corresponds to the equilibrium moisture content (g/g) achieved upon complete drying.

At equilibrium drying state, the value of Me becomes significantly smaller compared to both M₀ and M_t. Consequently, Equation (3) can be simplified to Equation (4) [22].

$$\mathrm{M}\mathrm{R}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{M}}_0}}$$

(4)

The drying rate during specific time intervals of green pellet drying was calculated using Equation (5).

$$\mathrm{D}\mathrm{R}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{t}1}-{\mathrm{M}}_{\mathrm{t}2}}{{\mathrm{t}}_1-{\mathrm{t}}_2}}$$

(5)

where [23] M_t1 and M_t2 represent the moisture content (%) of pellets at drying times t₁ and t₂, respectively.

During the drying of the green pellets, the moisture content, moisture ratio (MR), and drying rate at time t were determined through thermogravimetric analysis by measuring the weight variations under different drying conditions. The drying kinetics were subsequently characterized by plotting MR-t and DR-t curves.

In order to systematically evaluate the influence of various process parameters on the drying effect of pellets, this paper adopts the orthogonal experimental design method (L₁₈(3⁶)) to carry out experiments, and uses SPSS 26.0 software to perform statistical analysis on the experimental data. First, the mean and standard deviation of each factor level are obtained through descriptive statistical analysis to determine the data distribution trend; then, one-way ANOVA and multi-factor ANOVA (General Linear Model—Univariate) are used to test the significant influence of various influencing factors (such as temperature, wind speed, pellet diameter) and their interactions on the moisture content of pellets; in addition, in order to clarify the quantitative relationship between factors, a multivariate linear regression model is constructed to predict the drying effect. The above methods are used to ensure the scientificity and reliability of the experimental results.

3. Results

3.1. Drying Experiments

In the green pellet drying process, the drying rate was significantly influenced by the temperature and velocity of the drying medium, as well as the pellet diameter. As the temperature of the drying medium increases, the heat energy in the system increases, the water molecules gain more kinetic energy, and the movement between molecules becomes more intense. This increase in kinetic energy helps the water molecules overcome the adsorption force between them and the surface of the pellet material, especially the bound water adsorbed in the pores or on the surface of the particles, and the required desorption energy is more easily satisfied under high temperature conditions. Therefore, it is easier for water molecules to migrate from the inside or surface of the particles to the interface and further diffuse into the drying medium. In addition, higher temperatures also increase the water diffusion coefficient inside the material, speeding up the transfer rate of internal water to the surface, thereby speeding up the overall drying rate. The coupling of heat transfer and mass transfer is strengthened during the drying process, making the drying efficiency under high temperature conditions significantly better than those under low temperature environments [24,25].

This section focuses on investigating these three key factors affecting the drying of the iron ore concentrate pellets [26,27,28]. Based on the parameter ranges used in actual industrial drying processes, the following experimental levels were selected: drying medium temperature (350 °C, 400 °C, and 450 °C, all below the bursting temperature limit of 560 °C), medium velocity (0.7356 m/s, 1.1884 m/s, and 1.6411 m/s), and pellet diameter (9.5 mm, 12.5 mm, and 15.5 mm). An L₁₈(3⁶) orthogonal array was employed for the experimental design, with the specific test arrangements detailed in

Table 5. Orthogonal experimental design matrix for green pellet drying tests (L₁₈(3⁶)).

Test Group	Factor
	Drying Medium Temperature, T (°C)	Medium Velocity, V (m/s)	T × V	Pellet Diameter, L (mm)	T × L	Blank
1	350 (1)	0.7356 (1)	1	9.5 (1)	1	1
2	350 (1)	1.1884 (2)	2	12.5 (2)	2	2
3	350 (1)	1.6411 (3)	3	15.5 (3)	3	3
4	400 (2)	0.7356 (1)	1	12.5 (2)	2	3
5	400 (2)	1.1884 (2)	2	15.5 (3)	3	1
6	400 (2)	1.6411 (3)	3	9.5 (1)	1	2
7	450 (3)	0.7356 (1)	2	9.5 (1)	3	3
8	450 (3)	1.1884 (2)	3	12.5 (2)	1	1
9	450 (3)	1.6411 (3)	1	15.5 (3)	2	2
10	350 (1)	0.7356 (1)	3	15.5 (3)	2	1
11	350 (1)	1.1884 (2)	1	9.5 (1)	3	2
12	350 (1)	1.6411 (3)	2	12.5 (2)	1	3
13	400 (2)	0.7356 (1)	2	15.5 (3)	1	2
14	400 (2)	1.1884 (2)	3	9.5 (1)	2	3
15	400 (2)	1.6411 (3)	1	12.5 (2)	3	1
16	450 (3)	0.7356 (1)	3	12.5 (2)	3	2
17	450 (3)	1.1884 (2)	1	15.5 (3)	1	3
18	450 (3)	1.6411 (3)	2	9.5 (1)	2	1

. In this study, an L₁₈(3⁶) orthogonal array was employed to systematically investigate the effects of multiple factors on the drying behavior of magnetite pellets. This design, based on the Taguchi method, enables efficient experimentation by allowing one factor at two levels and seven factors at three levels to be tested using only 18 experimental runs. The orthogonality of the array ensures statistical independence among factors, facilitating clear identification of main effects while minimizing the number of required experiments. This approach is widely recognized for its effectiveness in optimizing industrial processes and enhancing experimental efficiency. The drying results under different temperature conditions are presented in

Table 6. Temperature drying test result of 350 °C.

Time, t (min)	Moisture Ratio, MR (Dimensionless)
	0.7356 m/s		1.1884 m/s		1.6411 m/s
	9.5	15.5	9.5	12.5	12.5	15.5
0	1	1	1	1	1	1
0.25	0.94	0.94	0.93	0.93	0.91	0.91
0.5	0.84	0.85	0.81	0.81	0.78	0.78
0.75	0.74	0.74	0.69	0.69	0.64	0.64
1	0.63	0.63	0.57	0.57	0.51	0.51
1.25	0.53	0.53	0.46	0.46	0.39	0.39
1.5	0.43	0.43	0.37	0.37	0.3	0.3
1.75	0.35	0.35	0.29	0.29	0.22	0.22
2	0.28	0.28	0.22	0.22	0.16	0.16
2.5	0.17	0.17	0.12	0.12	0.08	0.08
3	0.1	0.1	0.06	0.07	0.04	0.04
3.5	0.06	0.06	0.03	0.03	0.02	0.02
4	0.03	0.03	0.02	0.02	0.01	0.01
4.5	0.02	0.02	0.01	0.01	0	0
5	0.01	0.01	0	0
5.5	0	0

,

Table 7. Temperature drying test result of 400 °C.

Time, t (min)	Moisture Ratio, MR (Dimensionless)
	0.7356 m/s		1.1884 m/s		1.6411 m/s
	12.5	15.5	9.5	15.5	9.5	12.5
0	1	1	1	1	1	1
0.25	0.91	0.91	0.89	0.89	0.87	0.87
0.5	0.78	0.78	0.74	0.74	0.7	0.7
0.75	0.64	0.64	0.59	0.6	0.53	0.53
1	0.52	0.52	0.46	0.46	0.39	0.39
1.25	0.41	0.41	0.35	0.35	0.28	0.28
1.5	0.31	0.31	0.26	0.26	0.19	0.19
1.75	0.24	0.23	0.19	0.18	0.13	0.13
2	0.18	0.17	0.13	0.13	0.09	0.09
2.5	0.09	0.09	0.06	0.06	0.04	0.04
3	0.05	0.05	0.03	0.03	0.01	0.01
3.5	0.02	0.02	0.01	0.01	0.01	0.01
4	0.01	0.01	0.01	0	0	0
4.5	0	0	0

and

Table 8. Temperature drying test result of 450 °C.

Time, t (min)	Moisture Ratio, MR (Dimensionless)
	0.7356 m/s		1.1884 m/s		1.6411 m/s
	9.5	12.5	12.5	15.5	9.5	15.5
0	1	1	1	1	1	1
0.25	0.85	0.85	0.83	0.83	0.79	0.79
0.5	0.67	0.67	0.64	0.64	0.57	0.57
0.75	0.51	0.52	0.47	0.47	0.39	0.39
1	0.38	0.38	0.34	0.33	0.26	0.26
1.25	0.28	0.28	0.23	0.23	0.17	0.17
1.5	0.2	0.2	0.16	0.16	0.1	0.1
1.75	0.14	0.14	0.11	0.11	0.06	0.06
2	0.1	0.1	0.07	0.07	0.04	0.04
2.5	0.04	0.04	0.03	0.03	0.01	0.01
3	0.02	0.02	0.01	0.01	0	0
3.5	0.01	0.01	0	0
4	0	0

.

Based on the results presented in Table 6, Table 7 and Table 8, the complete drying time (F_t) and average drying rate under different experimental conditions were calculated, as summarized in

Table 9. Orthogonal test array and results for oxidized pellet drying interactions (L₁₈(3⁶)).

Test Group		Factor						Experimental Results
		Drying Medium Temperature, T (°C)	Gas Velocity, V (m/s)	T × V	Pellet Diameter, L (mm)	T × L	Blank	Complete Drying Time, Ft (min)	Average Drying Rate (g·g−1·min−1)
1		1	1	1	1	1	1	5.5	0.2231
2		1	2	2	2	2	2	5	0.2473
3		1	3	3	3	3	3	4.5	0.2764
4		2	1	1	2	2	3	4.5	0.2736
5		2	2	2	3	3	1	4	0.3054
6		2	3	3	1	1	2	4	0.3146
7		3	1	2	1	3	3	4	0.3161
8		3	2	3	2	1	1	3.5	0.3508
9		3	3	1	3	2	2	3	0.3955
10		1	1	3	3	2	1	5.5	0.2231
11		1	2	1	1	3	2	5	0.2473
12		1	3	2	2	1	3	4.5	0.2764
13		2	1	2	3	1	2	4.5	0.275
14		2	2	3	1	2	3	4.5	0.2836
15		2	3	1	2	3	1	4	0.3146
16		3	1	3	2	3	2	4	0.3162
17		3	2	1	3	1	3	3.5	0.3508
18		3	3	2	1	2	1	3	0.3955
Complete Drying Time, Ft	EI	30	28	25.5	26	25.5	25.5	ET = 76.5
	EII	25.5	25.5	25	25.5	25.5	26
	EIII	21	23	26	25	25.5	25
	${\overline{\mathrm{E}}}_{\mathrm{I}}$	5	4.6667	4.25	4.3333	4.25	4.25	${\overline{\mathrm{E}}}_0$ = 4.25
	${\overline{\mathrm{E}}}_{\mathrm{II}}$	4.25	4.25	4.1667	4.25	4.25	4.3333
	${\overline{\mathrm{E}}}_{\mathrm{III}}$	3.5	3.8333	4.3333	4.1667	4.25	4.1667
	r	1.5	0.8333	0.1667	0.1667	0	0.1667
Average Drying Rate	EI	1.4938	1.6271	1.8049	1.7803	1.7908	1.8001	ET = 5.3854
	EII	1.7666	1.7853	1.8158	1.7789	1.8185	1.7667
	EIII	2.1249	1.9730	1.7647	1.8262	1.7761	1.8186
	${\overline{\mathrm{E}}}_{\mathrm{I}}$	0.2490	0.2712	0.3008	0.2967	0.2985	0.3000	${\overline{\mathrm{E}}}_0$ = 0.2992
	${\overline{\mathrm{E}}}_{\mathrm{II}}$	0.2945	0.2975	0.3026	0.2965	0.3031	0.2944
	${\overline{\mathrm{E}}}_{\mathrm{III}}$	0.3541	0.3288	0.2941	0.3044	0.2960	0.3031
	r	0.1052	0.0576	0.0085	0.0079	0.0071	0.0087

. The corresponding analysis of variance (ANOVA) is provided in

Table 10. ANOVA results for orthogonal test of parameter effects on drying characteristics.

Item	Source of Variation	Sum of Squares (SS)	Degrees of Freedom (df)	Mean Square (MS)	F-Value	p-Value	Significance
Complete Drying Time, Ft	T	3.375	2	1.6875	152.2121	0.0065	Significant
	V	1.0417	2	0.5208	46.9760	0.0211	Significant
	TV	0.0417	2	0.0208	1.8761	0.3039	Insignificant
	L	0.0417	2	0.0208	1.8761	0.3039	Insignificant
	TL	0	2	0	/	1.0000	Insignificant
	Error	0	2	0	/	/	/
	Total	4.5	12	/	/	/	/
Average Drying Rate	T	0.0167	2	0.008348	316.63	0.0031	Significant
	V	0.0050	2	0.002498	94.75	0.0105	Significant
	TV	1.20 × 10−4	2	6.02 × 10−5	2.2848	0.304	Insignificant
	L	1.21 × 10−4	2	6.04 × 10−5	2.2923	0.303	Insignificant
	TL	7.74 × 10−5	2	3.87 × 10−5	1.4672	0.404	Insignificant
	Error	5.27 × 10−5	2	2.64 × 10−5	/	/	/
	Total	0.02206	12	/	/	/	/

. In the ANOVA table, F denotes the F-test statistic, with a confidence level (α) of 0.05 for the significance testing. For the F-test, the first and second degrees of freedom were set to 1 and 2, respectively.

As shown in Table 9, the order of influence on the complete drying time of the green pellets was ${\mathrm{r}}_{\mathrm{T}}>{\mathrm{r}}_{\mathrm{V}}>{\mathrm{r}}_{\mathrm{T}\mathrm{V}}>{\mathrm{r}}_{\mathrm{T}\mathrm{L}}>{\mathrm{r}}_{\mathrm{L}}$, indicating that the drying medium temperature had the most significant effect, followed by the medium velocity, while the pellet diameter exhibited a relatively minor impact. The interaction effects between the temperature and pellet diameter and between the temperature and velocity were less pronounced. Similarly, the analysis of the average drying rate revealed the following influence hierarchy: ${\mathrm{r}}_{\mathrm{T}}>{\mathrm{r}}_{\mathrm{V}}>{\mathrm{r}}_{\mathrm{T}\mathrm{V}}>{\mathrm{r}}_{\mathrm{L}}>{\mathrm{r}}_{\mathrm{T}\mathrm{L}}$, further confirming that the drying temperature and medium velocity were the dominant factors, whereas the interaction effects among these three factors were found to be relatively minor.

Based on the F-distribution tables with the first and second degrees of freedom of 1 and 2, respectively, at α = 0.05 confidence level, the critical F-value (F_0.05) was 18.51. This indicated that when the calculated F-value exceeded 18.51, the corresponding factor had a statistically [29] significant effect on the experimental results. The analysis of the complete drying time in Table 10 revealed that both F_T (152.21) and F_V values significantly exceeded 18.51, demonstrating that the drying medium temperature and gas velocity had substantial effects on the drying duration. Notably, the extremely high F_T value (152.21 >> 18.51) confirmed the exceptionally significant influence of the temperature. Conversely, F_TV and F_L values remained below the threshold, indicating negligible effects from the temperature–velocity interaction and pellet diameter. Similarly, the average drying rate analysis showed that both temperature and velocity significantly affected the drying kinetics, with the temperature again exhibiting particularly strong influence. The interaction term (T × V) and pellet diameter showed no statistically significant impact on the drying rate.

3.2. Drying Kinetics of Pellets

3.2.1. Drying Kinetic Models

The drying of powdered materials represents a fundamental industrial operation, the kinetics of which have been extensively investigated [30]. The earliest theoretical framework was established by Lewis [31] in 1921 through combined experimental and analytical approaches, as represented by Equation (6). The Lewis model, while simple and widely used, assumes a first-order linear relationship between drying rate and moisture content. It neglects internal diffusion, resistance control, and the multi-stage nature of real drying processes, making it less accurate in the later stages of drying and limiting its applicability to more complex systems. Subsequently, Page [32] developed a modified kinetic model (Equation (7)) specifically for the thin-layer drying of granular materials like cereal grains. Given the significant influences of the material properties and process parameters on the drying behavior, Overhults [33] and Wang [34] further refined the Page model, resulting in Page model (II) and Page model (III), respectively.

$$\mathrm{Lewis} \mathrm{Drying} \mathrm{Model}: \mathrm{MR}= {\displaystyle \frac{{\mathrm{M}}_{\mathrm{t}}-{\mathrm{M}}_{\mathrm{e}}}{{\mathrm{M}}_0-{\mathrm{M}}_{\mathrm{e}}}} = \exp (-\mathrm{kt})$$

(6)

Page Drying Model:  MR = exp(−ktⁿ)

(7)

Modified Page Model (II):  MR = exp(−(kt)ⁿ)

(8)

Modified Page Model (III):  MR = aexp(−ktⁿ)

(9)

In the equations, ‘a’, ‘k’, and ‘n’ represent empirical constants related to the drying conditions, while ‘t’ denotes the drying time.

The experimental data were preliminarily fitted using the four aforementioned drying kinetic models, with the results summarized in

Table 11. Statistical analysis of four drying kinetic models fitting.

Model	Drying Medium Temperature, T (°C)	Medium Velocity, V (m/s)	Pellet Diameter, L (mm)	R2	F-Value	Prob > F
Lewis model	350	1.1884	15.5	0.9691	1070	1
	400	1.6411	12.5	0.9793	1126	1
	450	0.7356	9.5	0.9876	1911	1
Page model	350	1.1884	15.5	0.9952	5357	3.54 × 10−11
	400	1.6411	12.5	0.9943	1612	0
	450	0.7356	9.5	0.9971	29,680	0
Modified Page model (II)	350	1.1884	15.5	0.9945	1352	0
	400	1.6411	12.5	0.9982	32,221	0
	450	0.7356	9.5	0.9895	752	1.43 × 10−12
Modified Page model (III)	350	1.1884	15.5	0.9976	13,245	0
	400	1.6411	12.5	0.9993	43,222	0
	450	0.7356	9.5	0.9986	1234	0

. The Lewis model exhibited poor fitting performance (p = 1 > 0.05), as indicated by its failure to meet the statistical significance threshold. In contrast, both the Page model and its modified versions demonstrated statistically significant fits (Prob < 0.05). Notably, under identical conditions, the modified Page model (III) achieved the highest determination coefficient (R²), confirming its superior capability to describe the drying behavior of green pellets.

3.2.2. Drying Kinetics Analysis

The orthogonal experimental data for the green pellet drying were analyzed by fitting with the modified Page model (III), with detailed results presented in

Table 12. Fitted parameters of modified Page model (III) for pellet drying tests.

Test Group	Drying Medium Temperature, T (°C)	Medium Velocity, V (m/s)	Pellet Diameter, L (mm)	R2	a	k	n
1	350	0.7356	9.5	0.9976	0.99944	0.46321	1.45651
2	350	0.7356	15.5	0.9984	1.00093	0.46207	1.46248
3	350	1.1884	9.5	0.9971	1.00004	0.56	1.44077
4	350	1.1884	12.5	0.9992	1.00104	0.56168	1.43049
5	350	1.6411	12.5	0.9986	0.99988	0.67628	1.43463
6	350	1.6411	15.5	0.9986	0.99988	0.67628	1.43463
7	400	0.7356	12.5	0.9972	0.99992	0.65731	1.39734
8	400	0.7356	15.5	0.9981	0.99933	0.65936	1.41191
9	400	1.1884	9.5	0.9983	0.99912	0.77629	1.3752
10	400	1.1884	15.5	0.9989	0.99748	0.77146	1.39752
11	400	1.6411	9.5	0.9982	1.00044	0.93989	1.37834
12	400	1.6411	12.5	0.9982	1.00044	0.93989	1.37834
13	450	0.7356	9.5	0.9964	1.00063	0.96538	1.27144
14	450	0.7356	12.5	0.9971	0.99957	0.95884	1.28082
15	450	1.1884	12.5	0.9953	0.99939	1.08877	1.28318
16	450	1.1884	15.5	0.9983	1.00016	1.0957	1.28166
17	450	1.6411	9.5	0.9991	0.99909	1.35378	1.27041
18	450	1.6411	15.5	0.9991	0.99909	1.35378	1.27041

.

As demonstrated in Table 12, the modified Page model (III) achieved excellent fitting performance with R² values consistently exceeding 0.99, confirming its capability to accurately describe the drying behavior of the natural magnetite oxidized pellets. To further quantify the parameter dependencies, polynomial regression analyses were conducted on the model coefficients (‘a’, ‘k’, and ‘n’) using the dataset from Table 12, with the resulting empirical relationships presented in Equations (10)–(12).

a = 1.0021 + 6.1023 × 10⁻¹¹T³ + 1.0100 × 10⁻²⁷T⁹   R² = 0.982

(10)

k = 0.45292 + 1.4738 × 10⁻⁸T³ + 1.9833 × 10⁻²⁵T⁹ − 0.00317TV + 4.24825 × 10⁻¹²T⁴V⁴ − 3.15761 × 10⁻²¹T⁷V⁷ +
0.43966V³ + 3.9451 × 10⁻⁵V⁹ − 6.20379 × 10⁻⁶L³ + 4.02891 × 10⁻¹³L⁹   R² = 0.999

(11)

n = 1.63179 − 3.20584 × 10⁻⁹T³ + 8.5724 × 10⁻²⁶T⁹ − 2.16 × 10⁻⁴TV + 2.6513 × 10⁻¹³T⁴V⁴ − 1.73346 × 10⁻²²T⁷V⁷ −
0.016822V³ + 8.7612 × 10⁻⁵V⁹ + 4.3775 × 10⁻⁶L³ + 1.0491 × 10⁻¹³L⁹   R² = 0.987

(12)

The high fitting R² values confirmed the robust performance of the drying kinetic model MR = aexp(−ktⁿ) in describing the experimental data. Parameter analysis revealed distinct operational dependencies: the pellet diameter significantly influenced the drying time at lower temperatures but became negligible under high-temperature conditions [35]. Similarly, the drying medium velocity exhibited greater impact on the drying kinetics at lower temperatures compared to elevated temperatures under identical flow conditions. The parameter ‘a’ was related to the initial moisture content of the green pellets, which was considered a constant value in this experiment. Therefore, the drying temperature had a significant impact on the drying process of the natural magnetite oxidized pellets.

3.2.3. Validation of Drying Kinetics

To verify the adaptability and accuracy of the modified Page model (III) in the drying process of the natural magnetite oxidized pellets, three experimental groups (D, E, and F) were designed with distinct operational parameters. Group D was conducted under a drying temperature of 250 °C, a medium flow rate of 1.1884 m/s, and a green pellet size of 9.5 mm. With Group E 350 °C, 1.6411 m/s and 9.5 mm were employed, while with Group F 500 °C, 1.1884 m/s and 12.5 mm were utilized. The experimental results are presented in Figure 2 and

Table 13. Correlation coefficients for fitted drying models in Group D tests.

Item	Parameter	Theoretical Value	Fitted Value
Theoretical Calculation	Pearson Correlation	1	0.999 **
	Sig. (2-tailed)	/	0.000
	Sum of Squares and CP	2.132	2.075
	Covariance	0.133	0.130
	N	17	17
Experimental Measurement	Pearson Correlation	0.999 **	1
	Sig. (2-tailed)	0.000	/
	Sum of Squares and CP	2.075	2.022
	Covariance	0.130	0.126
	N	17	17

Note: ** indicates a significant correlation at the 0.01 level (two-tailed).

,

Table 14. Correlation coefficients for fitted drying models in Group E tests.

Item	Parameter	Theoretical Value	Fitted Value
Theoretical Calculation	Pearson Correlation	1	1.000 **
	Sig. (2-tailed)	/	0.000
	Sum of Squares and CP	1.471	1.463
	Covariance	0.123	0.122
	N	13	13
Experimental Measurement	Pearson Correlation	1.000 **	1
	Sig. (2-tailed)	0.000	/
	Sum of Squares and CP	1.463	1.456
	Covariance	0.122	0.121
	N	13	13

Note: “**” indicates a significant correlation at the 0.01 level (two-tailed).

and

Table 15. Correlation coefficients for fitted drying models in Group F tests.

Item	Parameter	Theoretical Value	Fitted Value
Theoretical Calculation	Pearson Correlation	1	1.000 **
	Sig. (2-tailed)	/	0.000
	Sum of Squares and CP	1.264	1.265
	Covariance	0.115	0.115
	N	12	12
Experimental Measurement	Pearson Correlation	1.000 **	1
	Sig. (2-tailed)	0.000	/
	Sum of Squares and CP	1.265	1.267
	Covariance	0.115	0.115
	N	12	12

Note: “**” indicates a significant correlation at the 0.01 level (two-tailed).

.

As shown in Figure 2 and Table 13, Table 14 and Table 15, the Pearson correlation coefficients (r) for the three datasets were all close to 1, demonstrating that the Page model (Model III) was highly applicable to the drying process of the natural magnetite oxidized pellets. This model accurately predicted the influence of the drying temperature and medium velocity on the moisture content of the pellets during drying. Notably, the Pearson coefficient increased with elevated drying temperatures, and the experimental values aligned more closely with the theoretical predictions under higher temperatures. This suggested that the predictive accuracy of the model improved at higher temperatures [36,37].

4. Conclusions

• Drying tests of the natural magnetite oxidized pellets revealed that the drying medium temperature significantly influenced the drying rate, while the interaction between the pellet diameter and temperature exhibited minimal effects. The drying process was best described by the modified Page model (III).
• The modified Page model (III) achieved excellent fitting performance, and the polynomial regression analysis of the model coefficients (‘a’, ‘k’ and ‘n’) using the dataset showed R² values always exceeding 0.99. The high fitting R² values confirmed the robust performance of the drying kinetics model MR = aexp(−ktⁿ) in describing the experimental data.
• Validation of the pellet drying kinetic model demonstrated close agreement between the experimental measurements and theoretical predictions, with Pearson correlation coefficients approaching 1. The modified Page model (III) accurately predicted the effects of the drying temperature and medium velocity on the moisture content evolution, while exhibiting enhanced predictive precision at elevated temperatures.