Energy Evaluation and Mathematical Modeling of Pellet Production from Metal-Bearing Waste with a Focus on Alternative Applications of Reducing Agents

Abstract

The authors of this study focused on the energy and material assessment of processes for processing pellets from metal-bearing waste, specifically Fe concentrate. A mathematical model was created for process evaluation, with which thermotechnical calculations of parameters in the processing of metallized pellets were carried out. Thermodynamic calculations were performed to determine the enthalpy of the charge in individual devices (drying chamber, rotary kiln, cooler). For the reduction of Fe oxides, carbon from coke (with Fe oxide reductions of 50%, 61%, and 92%) and lignite (with Fe oxide reductions of 69% and 92%) were considered as part of the pellets. The degree of reduction of iron oxides was a determining parameter, and the consumption of the reducing agent corresponded to the direct reduction of Fe oxides by carbon with a coefficient of 1.5. Another determining parameter was the input and output temperature in individual devices. For a more precise description of the processes in individual devices, calculations were carried out zonally. The results of the calculations are analyses and recommendations for feasible alternatives for the reducing agent and associated processes.

1. Introduction

Natural resources are a valuable commodity in every country, including those outside the European Union. In the past, heavy industry and raw material extraction prevailed in Slovakia. The mining industry, in particular, gained significant prominence in the national economy due to increasing productivity. However, since 2000, there have been signs of a decline resulting from national and local conditions in the mining industry [1]. More recently, these sectors have been phased out, but considerable environmental burdens remain, which have not been addressed for a long time.

The use of resources, production, consumption, and waste have become key topics in circular economy strategies and relevant policies in recent years. These initiatives aim to close the material cycle to maintain the value of products, materials, and resources in the economy for as long as possible. This effectively reduces waste production and the consumption of primary raw materials, leading to decreased environmental pressures [2].

The extraction, production, use, and disposal of resources, as well as waste production and processing, create significant environmental pressure. Environmental policy aims to reduce material consumption in the economy, use resources more efficiently, reduce waste production, and turn waste into a resource [2].

Waste in the European economy is increasingly valued as a valuable resource that can be further utilized. The increase in waste recycling gradually reduces the amount of waste deposited in landfills. Nevertheless, there are considerable differences in waste management among individual countries [2].

European environmental policy, within the framework of the Environmental Action Programme (EAP), has long set goals, including increasing resource efficiency. Priority targets have been set for 2030 and the necessary conditions for their achievement [3].

In line with environmental policy, it is in every state’s interest to reduce the amount of waste that can be further utilized. Large companies, such as metallurgical complexes, are currently analyzing individual production processes and seeking environmental solutions to minimize or eliminate the waste generated.

The production of pellets from metal-bearing materials is an energy-intensive and environmentally demanding process, and research in this area remains relevant. To optimize pellet production, parameters affecting individual processes were studied either through experimental measurements or by creating mathematical models. The properties of pellets processed in thermal aggregates, such as tubular rotary kilns, must meet certain conditions, including granulation, moisture, strength of raw pellets, resistance to rapid heating, and reducibility of oxides in the pellets [4,5].

In preparing raw pellets, it is important to know the properties of metal-bearing materials based on metallographic analyses of samples, which are the basis for the preparation of raw pellets. Laubertová et al. [6] emphasized that the quality of the material depends on the sampling method, which also influences the result of the chemical analysis. This is particularly important when using waste materials that exhibit a certain heterogeneity, thereby affecting the final parameters of the raw pellets. A significant parameter is the strength of the raw pellets, which can be influenced by adding reducing agents, additives, or colloidal particles that harden upon drying, forming mortar-like bridges that increase pellet strength. Otherwise, it is necessary to increase the addition of binding agents such as bentonite or cement and other [5].

Mathematical modeling of processes has focused mainly on the thermal processes that occur during processing. The authors [7] created a simulation model of temperature distribution in pellets and flue gases based on conduction, convection, and radiation in a tubular rotary kiln. Larsson [8] created a model of flow in a rotary kiln and the exit of the flame and flue gases from the burner, addressing the aerodynamics of flow and fuel combustion using CFD models. The heat transfer from the flame in the rotary kiln was also addressed by authors [9] who created a one-dimensional model capable of predicting axial temperature profiles of the flame and wall, and axial profiles of heat flux to the bed of solids and the refractory wall. Interesting models are also described in work [10] on the oxidation of magnetite during the hardening of iron ore pellets, and [11], which address the physicochemical processes occurring during the hardening of pellets. Despite the mathematical models, experimental research in the field of unconventional technologies is also important, as presented by the authors [12] in the preparation of Carbofer-type pellets. Among the interesting unconventional studies is the research published in [13], which focused on the use of plastics as a reducing agent. Using plastics, a degree of metallization greater than 90% was achieved with reduction in 30 min. The created mixture exhibited better reactivity, and syngas was simultaneously produced during thermal processing.

In the realm of environmental technologies, the application of hydrogen as a significant carbon-free reductant is being explored during the thermal processing of raw pellets and the reduction of oxides in the pellets. The goal is to reduce the production of CO₂ greenhouse gases in these technologies. Experimental research using hydrogen was presented in a research report [14], where hydrogen was used in combination with coke, resulting in a high degree of iron oxide reduction with 3.1 wt.% coke. In the study [15], the authors focused on using pure hydrogen to reduce pellets, and the research results indicate further possibilities for investigation in this area. Numerous other publications demonstrate that research in this field remains a highly discussed topic, with new opportunities emerging within environmental policy frameworks.

The authors aimed to investigate the energy assessment of pellet production from leach residue from Sereď, Slovakia. Leach residue is essentially an Fe concentrate suitable for the production of pellets for use in iron metallurgy. Research on the utilization of leach residue has been conducted previously, with results published in [16,17,18]. A subsequent study [14] evaluated the possibilities of pellet production and properties based on supplied samples. The results of the pre-reduction of pellets in a tubular rotary kiln were published in [19]. Despite positive outcomes, no project for utilizing the waste leach residue from the resulting waste heap was implemented.

However, renewed interest from investors led to revisiting the potential realization of this project at a decommissioned metallurgical plant, considering the revival of production. To support the implementation of this process, a mathematical model was developed for thermotechnical calculations involved in processing leach residue into raw pellets. The goal of the production process is to increase the metallic Fe content in the pellets through direct reduction of Fe oxides.

This paper presents a detailed approach to the material and energy evaluation of this process, focusing on the potential revival of production at the decommissioned plant. The authors conducted theoretical research to develop a mathematical model for processing leach residue. The Introduction provides background on the research and the mathematical methods used to model the physicochemical processes during pellet production.

In the Materials and Methods Section, the chemical composition of ore processed at NH Sereď is discussed, with laboratory tests showing that increasing coke content enhances Fe reduction efficiency. The leach residue sample, labeled Fe concentrate SE52, was analyzed and used as input data for the mathematical model. Tests indicated that the optimal amount of solid reducing agent is 1.5 times the theoretical carbon requirement.

This paper also describes the equipment required for processing raw pellets, including a technological scheme for pellet production in Nižná Slaná, Slovakia. Material and heat balances were calculated for various stages, such as drying, preheating, firing in the rotary kiln, and cooling, with thermodynamic calculations determining the enthalpy of the charge in each device. A detailed description of the processes and the main physical equations used in the model is provided.

The results, presented in tables, show the composition of raw and processed pellets and reveal that carbon was not completely consumed during reduction. Several physical parameters were calculated for different processing strategies, showing that producing pellets with a reduction degree of Fe oxides between 50–65% is feasible. The rotary kiln parameters were found suitable for processing raw pellets from the Fe concentrate in Sereď leach residue, supporting the potential realization of the project.

2. Materials and Methods

This study of raw pellet processing was based on the composition of waste after processing nickel ore at NH Sereď. NH Sereď processed ore from Albania, which contained 1.05% Ni, 0.06% Co, 49% Fe, and 2.6% Cr. The production was primarily focused on the extraction of Ni and Co, which were present in low concentrations. Despite the unprofitable production, there was a requirement to process the ore. Due to societal changes and the unprofitability of production, the facility was closed in 1992. Before its closure, NH Sereď produced 2500 tons of Ni and 60 tons of Co annually through hydrometallurgical processing. The process also resulted in a leach residue heap, following ammoniacal leaching, with high iron and chromium content, weighing approximately 6 million tons [20].

The resulting waste was stored in heaps, and due to its properties, it was very difficult to reclaim. The waste storage also posed a significant environmental burden, particularly due to its migration into the surrounding area caused by wind action. For this reason, a deeper analysis of this waste was undertaken, and the results indicate that it is suitable for further processing.

Studies on the properties of metal-bearing waste from the heap focused on its technological feasibility for processing. Technologies for thermal treatment were considered, including agglomeration on a sintering belt and its use in the form of pellets. The agglomeration process could be carried out directly at the metallurgical plant, where iron ore is primarily processed. Based on the results of the studies [16,17,18,20] and subsequent pilot-scale tests [19], the decision was made to utilize pelletization technology and the subsequent thermal treatment of raw pellets. Laboratory tests demonstrated that the input material had suitable parameters for producing raw pellets with sufficient strength and resistance to rapid heating without cracking during heating.

2.1. Leach Residue—Metal-Bearing Waste

The leach residue obtained as a byproduct of the hydrometallurgical processing of Ni ore is an inherently metal-bearing material with high Fe content, making it suitable for further processing in the form of pellets. Laboratory tests conducted on collected samples demonstrated the potential for its further processing.

Based on the thermodynamic analysis and laboratory tests of Fe concentrate reduction from Sereď, it is evident that the direct reduction of iron oxides using a solid internal reducing agent is the most advantageous method.

Based on the experimental tests with leach residue from Sereď mentioned in [14], it can be concluded that a 60% reduction of Fe is achieved in approximately 60 min. From Figure 1, it is evident that the direct reduction of Fe from Fe concentrate using a solid reducing agent—coke dust present in the pellets—achieved high efficiency of 81.02%, provided that the pellets contained a sufficient amount of reducing agent and the reduction process lasted for an adequate duration of 180 min [14].

Figure 1 illustrates the results of laboratory tests that monitored Fe reduction efficiency using coke in the pellets and in combination with hydrogen. The obtained results indicate that increasing the coke content leads to higher Fe reduction efficiency. The dependencies show a logarithmic relationship, which is also characteristic when combined with hydrogen reduction.

The calculation of average values for further computations was based on the composition of dry leach residue. The calculations account for 12.322% moisture content relative to 100% dry leach residue.

Based on the sieve analysis, the granulometry of the leach residue was determined as follows: greater than 9.53 mm/0%; greater than 6.35 mm/0%; greater than 0.149 mm/8.5%; less than 0.149 mm/91.5%.

For the preparation of this study, a sample was taken from the leach residue heap in Sereď, whose composition is shown in

Table 1. Composition of leach residue of Fe concentrate SE52.

	Composition of Fe Concentrate		Average Values for Calculations
	Min. wt.%	Max. wt.%	wt.%
Fe total from oxides	48.00	52.00
Fe2O3	42.00	43.00	45.539
FeO	27.00	28.00	29.466
Fe metal	0.25	0.35	0.3214
SiO2	8.00	10.00	9.643
Al2O3	4.00	6.00	5.357
CaO	3.00	4.50	4.018
MgO	2.00	3.00	2.679
Cr*	1.30	1.50	1.500
P2O5	0.06	0.18	0.129
SO3	0.08	0.10	0.096
MnO	0.30	0.40	0.375
K2O	0.08	0.10	0.096
Ni	0.27	0.29	0.300
CoO	0.062	0.062	0.066
Cu	0.01	0.02	0.016
Zn	0.03	0.03	0.032
V2O5	0.02	0.02	0.021
TiO2	0.10	0.12	0.118
Bi	0.001	0.01	0.006
Na2O	0.20	0.21	0.220
H2O	5.00	18.00	12.322
Σ	93.71	115.82	112.322

Cr*—in the form Cr₂O₃.

. The sample was labelled as Fe concentrate SE52, and average values from the minimum and maximum values were used for the calculations, serving as input data in the mathematical model. Laboratory tests revealed that the optimal amount of solid reducing agent is 1.5 times the theoretical amount of carbon needed to reduce the iron oxides present in the Fe concentrate.

The calculations considered solid reducing agents coke and lignite. These agents were selected based on their immediate availability, either produced or mined in Slovakia. The average compositions of the reducing agents are shown in

Table 2. Composition and calorific value of the proposed reducing agents.

Component	C	S	H	O	N	Ash	Water	LHV
	wt.%	wt.%	wt.%	wt.%	wt.%	wt.%	wt.%	MJ/kg
Coke	69.95	0.37	1.40	0.70	0.77	8.81	18.00	23.56
Lignite	41.36	1.84	3.16	15.93	0.67	13.45	23.60	15.44

.

From the composition of the reducing agents in Table 2, it is possible to compare the carbon content for direct reduction, which is 28.59 wt.% lower in lignite, thereby affecting the extent of direct reduction of oxides. The direct reduction of iron oxides from the Fe concentrate begins at a temperature of 956 °C, but according to laboratory tests, the optimal reduction temperature is considered to be between 1000 and 1100 °C.

Within this temperature range, it is expected that the gaseous product of the direct reduction of iron oxides will mainly be CO, which will need to be further oxidized to carbon dioxide outside the furnace’s working chamber. The generated CO will simultaneously create a reducing atmosphere in the rotary kiln, which will support the reduction of Fe oxides while preventing reoxidation.

Due to the high content of gangue components, such as CaO, SiO₂, and Al₂O₃, in the Fe concentrate from Sereď, the metal content of the reduced agglomerate or pellets can be increased above the theoretical limit concentration of 68% Fe only by adding iron-bearing waste, such as mill scale or converter dust or sludge, to the Fe concentrate. This method can increase the iron content in the reduced agglomerate or pellets to up to 86% Fe.

Due to the high temperatures, complex chemical and physical processes, as well as polymorphic transformations, occur in the calcined raw pellets. These processes determine the mechanical and metallurgical properties of the fired and cooled pellets. Since these processes reduce the particle surface area and the free surface energy of the system, sintering is an irreversible process [4].

During firing, changes occur in both the metal-bearing and gangue parts of the charge:

(a)

In the metal-bearing part of the charge, magnetite may oxidize to hematite, and recrystallization of magnetite and hematite may occur;

(b)

The oxides in the gangue part of the concentrate react with each other at lower temperatures in the solid state and during the transition from solid to liquid state, forming slag;

(c)

Additionally, reactions occur in both the solid and liquid states between the oxides in the metal-bearing and gangue parts of the concentrate.

2.2. Processes in Technological Equipment

The process of processing raw pellets requires the use of technology that includes various primary and support equipment. The most important equipment is the thermal aggregate—a rotary kiln with a burner system to provide thermal input for their processing. The rotary kiln is the basis of the mathematical model for further heat technical calculations in the other equipment.

For the proposed process of processing raw pellets from Fe concentrate, the thermal units in Nižná Slaná, Slovakia, are planned to be utilized. The technological operation in Nižná Slaná was shut down and is currently being considered for use in processing metal-bearing waste from metallurgical operations. Consideration is also given to their modification and the addition of auxiliary equipment for the processing of metal-bearing waste. This technology served as the basis for developing a mathematical model for the material and energy balance of processing raw pellets from metal-bearing waste, such as the described Fe concentrate from the waste heap after nickel ore processing.

Figure 2 shows the existing condition of the decommissioned technology, highlighting the placement of the burner system and the discharge of pellets from the rotary kiln into the cooler. As observed in Figure 2, the technology requires certain investments, but it can be brought back into operation after modifications. For this reason, an evaluation of the technology was undertaken in terms of material and energy aspects for processing waste leach residue from the heap in Sereď.

The burner system can be adapted for both gaseous and liquid fuels. Due to the short length of the rotary kiln, it is more advantageous to use gaseous fuel, also because of its availability from the distribution network. The calculations used the composition of natural gas as provided in [21], with the adjusted composition listed in

Table 3. Composition and calorific value of natural gas [21].

Component	vol. %	Component	vol. %
CH4	96.858	izo,n—C5H12	0.022
C2H6	1.421	C6H14 + higher	0.026
C3H8	0.444	CO2	0.212
izo,n—C4H10	0.139	N2	0.878
LHV *	36.329 MJ/m3

* The value is given under normal conditions of temperature 0 °C and pressure 101,325 Pa.

.

In the calculations of individual aggregates, from drying and preheating of the charge through firing in the rotary kiln to cooling, material and heat balances were used in these devices in combination with the kinetics of heat transfer within each device. Within the heat balance, thermodynamic calculations were carried out to determine the enthalpy of the charge in each device. In the process of reducing Fe oxides, carbon from coke and lignite, which are part of the charge, is considered. A mathematical model was developed in Excel to determine all the necessary thermotechnical parameters.

For more economical use of flue gas energy generated in the process of processing metal-bearing waste, a cogeneration unit was proposed and incorporated into the technological scheme of the process in some alternatives.

Using the created mathematical model, calculations of the following pellet production alternatives were carried out:

• Reducing agent—coke: reduction of Fe oxides in pellets to 50% (C_50R).
• Reducing agent—coke: reduction of Fe oxides in pellets to 61% (C_61R).
• Reducing agent—coke: reduction of Fe oxides in pellets to 92% (C_92R).
• Reducing agent—lignite: reduction of Fe oxides in pellets to 69% (BC_69R).
• Reducing agent—lignite: reduction of Fe oxides in pellets to 92% (BC_92R).
• Production of oxide pellets without reduction of Fe oxides (OX).

Figure 3 shows the basic technological process scheme for producing pellets from raw pellets. The processing of raw pellets begins in the drying chamber, where the raw pellets are heated and moisture is removed by controlling the temperature in the individual zones Z1, Z2, and Z3. Flue gases from the rotary kiln are introduced into these zones, and after separating the dust particles in the cyclone, they proceed to the afterburning chamber (DSK), where unburned gaseous components CO and H₂ are combusted along with gaseous fuel and combustion air. The flue gases from DSK continue to the mixer (M), where the temperature of the flue gases is adjusted to the required level before entering Z3. In the distributor after M, part of the mixed flue gases is directed into Z3, and another part continues to another mixer (M), where the temperature is further adjusted for Z2. The flue gases from Z3 and Z2, after passing through the raw pellets, are collectively led to the mixer (M), where their temperature is reduced by mixing with air to the required level before entering Z1 in the drying chamber. The flue gases from Z1, after passing through the raw pellets, are directed to the filter (F1) for cleaning before entering the chimney (K), where the dust particles from the pellets in the drying chamber are captured.

After the raw pellets are dried and heated in the drying chamber, they proceed to thermal processing in the rotary kiln, where their temperature is increased, and the actual induration process occurs, along with the reduction of iron oxides using reducing agents. The flue gases and the reduction process itself create a reducing atmosphere, which also influences the reduction or metallization process of the pellets. Gaseous fuel and a portion of preheated air from the cooler are used as heat sources.

In the cooler, the pellets from the rotary kiln, which are at a high temperature, are cooled to the desired temperature by introducing air from the surroundings. The hot air from the cooler is distributed to the rotary kiln and DSK for combustion.

Figure 4 presents a modified technological scheme, which is an enhanced version of the scheme in Figure 3, with the addition of a cogeneration unit (KG) after DSK and M. The modification of the scheme was proposed based on calculations of the required amounts of flue gases and air for mixing into the heating zones. The calculations revealed that in the case of a large volume of flue gases, it is not possible to reduce the temperature simply by mixing in air in M, but it is necessary to remove the heat by other means. To utilize the waste heat more efficiently, a KG unit without internal combustion was proposed. In this case, it is necessary to identify a type of heat exchanger that will not get clogged by dust particles, or at least one that is easy to maintain. A similar issue was discussed by the authors in [22], where they addressed the design of a heat exchanger for thermal air engines and their use in combined heat and power production. An ORC was also considered for the KG.

Brief Description of the Processes Occurring in Individual Equipment

• Drying chamber

Basic processes occurring during the preheating of raw pellets:

Z1—Preheating I

○

Heating raw pellets from ambient temperature to an estimated temperature of approximately 110–130 °C.

○

Evaporation of water from the raw pellets.

○

Decrease in the mass of raw pellets due to the evaporated water.

○

Increase in the volume of flue gases due to the evaporated water and solid particles from the charge passing through the preheating zone.

Z2—Preheating II

○

Heating and possibly further drying the raw pellets to approximately 230 °C.

○

The mass of the raw pellets does not change.

○

The volume of flue gases does not change.

Z3—Preheating III

○

Heating raw pellets from 230 °C to approximately 400–650 °C.

○

The mass of raw pellets decreases due to the combustion of sulfur in the raw pellets.

○

The volume of flue gases may change due to the combustion of sulfur and possibly some volatile substances.

• Rotary kiln

Basic processes occurring in the rotary kiln:

○

The charge is heated from 450–650 °C to 1100 °C.

○

As a result of the reduction of Fe oxides, CO is released into the flue gases, which partially burns to CO₂ in a slightly oxidizing atmosphere.

○

There is partial combustion of excess carbon from the raw pellets to CO₂ or CO.

○

The reduced charge exits to the cooler.

○

The primary source of thermal energy is supplied by burners (natural gas with excess combustion air, utilizing air from the charge cooler, preheated to approximately 400 °C).

○

The temperature of the flue gases at the kiln outlet varies depending on the specific alternative.

○

The flue gases at the kiln outlet, in addition to the components of complete fuel combustion, will contain the following:

• Unburned CO from the reduction of oxides,
• Solid particles from the raw pellets,
• Due to the reduction of Fe oxides, the combustion of part of the excess carbon from the raw pellets, and additional solid particles, the mass of the charge decreases.
• The resulting amount of flue gas is further cleaned, afterburned, and possibly mixed with air for the process of preheating and drying the charge.

• Cooler—pellet cooling

Basic processes occurring in the charge cooler:

○

The charge is cooled from approximately 1100 °C to 410 °C.

○

The primary cooling medium is air, which is heated from ambient temperature to approximately 380 °C.

○

Additional cooling can be achieved by using water to cool part of the shell.

• The mass of the pellets slightly decreases due to solid particles from the charge.
• The preheated air is used as combustion air in the rotary kiln or the combustion chamber.

• Combustion/Afterburner chamber DSK

Basic processes occurring in the DSK:

○

In the combustion chamber, the flammable components of the flue gases (CO, etc.) are fully combusted, raising the temperature of the flue gases. In the case of oxide pellets, natural gas is burned to provide the necessary amount of heat for the preheating and drying of raw pellets.

○

The source of thermal energy is supplied by burners (natural gas), with complete combustion of these fuels and the flammable components of the flue gases (CO, etc.) assumed, with the appropriate excess of combustion air. Air from the charge cooler or air from the surrounding atmosphere is used for combustion.

• The quantity and composition of the flue gases change;
• The flue gases at the outlet contain only components of complete combustion;
• The flue gases at the exit temperature proceed to Mixer I for cooling.

• Mixer I

Basic processes occurring in Mixer M after the DSK:

○

The flue gases from the DSK are cooled to approximately 800 °C;

○

The cooling medium is air at ambient temperature.

• The quantity and composition of the flue gases change.

• Cogeneration/Heat exchanger

Basic processes occurring during cogeneration:

○

If necessary, the flue gases from Mixer I are cooled to approximately 500 °C before entering Z3 preheating in the case of a reducing agent—lignite.

○

Part of the thermal energy from the flue gases is used to generate electricity in the cogeneration unit (KG).

• The quantity and composition of the flue gases change.

• Mixer II

Basic processes occurring in Mixer M:

○

A portion of the flue gases from Mixer I is cooled to approximately 400 °C before entering Z2.

○

The cooling medium is air at ambient temperature.

• The quantity and composition of the flue gases change.

• Mixer III

Basic processes occurring in Mixer M before entering Z1:

○

The flue gases, after passing through Z2 and Z3, are mixed and cooled to approximately 300 °C.

○

The cooling medium is air at ambient temperature.

• The quantity and composition of the flue gases change.

2.3. Calculation of the Energy Requirements of the Processes

The energy requirements of the processes involved in processing raw metallic pellets also determine the economic aspect of these processes. Describing the processes necessary or characterizing the needs related to the overall processing of metallic pellets can be approached as partial processes. The outputs of these partial processes are important control points for the subsequent energy processes.

In calculating the energy requirements, a mathematical model of the pellet production process in a rotary kiln was developed. This model covers the entire process of processing raw pellets from Sereď residue, including firing and cooling.

The mathematical model is based on the analysis of technology, material and energy balances, and heat flows of the processes occurring in the individual devices during the production of pellets from raw pellets made from Sereď residue.

The developed mathematical model incorporated equations and modules that have either been previously published or were formulated using the necessary literature sources. The fundamental relationship for determining the thermal content of gases is the temperature dependence of the calculation of the specific heat capacity of flue gases and air, which is given by Equation (1):

$${\mathrm{c}}_{\mathrm{p}}={\mathrm{a}}_0+{\mathrm{a}}_1\mathrm{T}+{\mathrm{a}}_2{\mathrm{T}}^2+{\displaystyle \frac{{\mathrm{a}}_3}{{\mathrm{T}}^2}}; ({\mathrm{k}\mathrm{J}/(\mathrm{m}}^3\mathrm{K}))$$

(1)

The coefficients ${\mathrm{a}}_0$, ${\mathrm{a}}_1$, ${\mathrm{a}}_2$, and ${\mathrm{a}}_3$ in Equation (1) were derived based on the regression of tabulated values of the mean specific heat capacity and are published in [23,24].

The primary calculation was the enthalpy calculation of the heat of pellets, which was based on the composition of raw pellets and the reactions that occurred according to Hess’s law [25]:

$$\Delta \mathrm{H}=\sum {\Delta \mathrm{H}}_{products}-\sum {\Delta \mathrm{H}}_{reactants}$$

(2)

${\Delta \mathrm{H}}_{reactants}$—enthalpy of reactants input to the process;

${\Delta \mathrm{H}}_{products}$—enthalpy of products output from the process.

A temperature dependence calculation model was used for the calculation:

$$\Delta {\mathrm{H}}_T^0=\Delta {\mathrm{H}}_{298}^0+\Delta \mathrm{a}\mathrm{T}+{\displaystyle \frac{\Delta \mathrm{b}}{2}}{\mathrm{T}}^2-{\displaystyle \frac{\Delta \mathrm{c}}{\mathrm{T}}}+\Delta \mathrm{d}; (\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$$

(3)

The coefficients a, b, c, and d are coefficients from [25].

The enthalpy balance of heat during the thermal processing of pellets was adjusted and supplemented by an additional term, and then the change in enthalpy was calculated according to the following relationship:

$$\Delta {\mathrm{H}}_T^0=\Delta {\mathrm{H}}_{298}^0+\Delta \mathrm{a}\mathrm{T}+{\displaystyle \frac{\Delta \mathrm{b}}{2}}{T}^2-{\displaystyle \frac{\Delta \mathrm{c}}{T}}+\Delta \mathrm{d}-\Delta {\mathrm{H}}_{phase}^0; (\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$$

(4)

For the combustion process and the composition of flue gases, a combustion statics model published in [24] was used. This model allows for the calculation of the composition of the resulting flue gases during the combustion of gaseous fuel, as well as the combustion temperature, which is necessary for calculations in other heat transfer modules.

The composition of flue gases and resulting gases in the individual devices was calculated based on combustion equations and reduction processes from the pellets. It is assumed that CO₂ is released from the reducing agent by the combustion of carbon, H₂O from the reaction with hydrogen, and SO₂ from the sulfur in the pellets. The composition of the flue gases also changed due to dilution with air when lowering the flue gas temperature to the required technological temperature.

Mathematical relationships for convection, conduction, and radiation, as published in [23,26,27,28], were used for the heat transfer calculations. Modules for individual heat transfer processes were developed. The module for heat transfer by radiation was published in [29], which also includes a convection calculation model for industrial furnaces. As part of the thermal calculations, the heat loss to the surroundings from the surface of equipment is calculated as thermal loss, based on the geometry and the overall heat transfer coefficient for radiation and convection.

Radiative heat transfer

Radiative heat transfer constitutes a significant portion of direct heat transfer in furnaces. As mentioned in [29] and supported by experimental data, convective heat transfer accounts for only a quarter of the heat transferred to the charge, with the remainder occurring through radiation. This transfer is particularly significant at higher temperatures.

In radiative heat transfer, it is important to distinguish between the radiation from solid bodies, such as furnace walls, and the radiation from gases.

(a) Gas Radiation

When developing a model for gas radiation, the internal dimensions of the equipment and the associated processes were considered. Experimental measurements revealed that gases with three or more atoms play the most significant role in gas radiation. In combustion, this primarily includes CO₂, H₂O, and SO₂. More information can be found in the cited literature [23,26,30,31].

Because gases emit and absorb heat energy throughout their entire volume, their ability to do so depends not only on temperature but also on the number of molecules that the heat ray encounters along its path. The number of molecules is determined by the thickness of the gas layer and the partial pressure of its components (CO₂, H₂O, SO₂, etc.). Thus, the emissivity or luminosity of the gas is a function of temperature and the product of the partial pressure and the thickness of the gas layer.

$${\epsilon }_g=f\left(T_g,p_p.l_{vp}\right)$$

(5)

T_g—absolute gas temperature, (K);

p_p—partial gas pressure, (Pa);

l_vp—thickness of the gas layer, (m).

The thickness of the radiating layer in different directions of the workspace is different. Therefore, for technical calculations, the term effective beam length was introduced, which is determined according to the relationship [23,26]:

$$l_{ef}=\eta .{\displaystyle \frac{4.V}{F_V}}$$

(6)

$\eta$—correction coefficient, (0.8 ≈ 0.9);

$V$—volume filled with glowing gas (flue gases), (m³);

$F_V$—the area of the walls delimiting this space, (m²).

Various mathematical models have been developed to determine the emissivity of individual radiative components of gases, which are described in numerous references, such as [26,30,31]. For the purpose of this model, it was decided to use the mathematical model created and thoroughly described by E. Kostowski in [32,33], which was successfully applied in [29], where its validity for the gas components CO₂ and H₂O was confirmed.

$${\epsilon }_i=1-e^{-k_i.{\left(p_{p_i}.l_{ef}\right)}^n}$$

(7)

$$k_i=a+b.{\displaystyle \frac{t_{fg}}{1000}}$$

(8)

ε_i—emissivity of the respective component, (—);

k_i—correction coefficient for the effect of temperature on emissivity, (—);

$p_{p_i}.l_{ef}$—the product indirectly defines the volume of the radiant component, (Pa.m);

n—exponent obtained from regression analysis, (—);

a, b—coefficients from regression analysis, (—);

t_fg—flue gas temperature, (°C).

The values of coefficients a, b and the exponent n for the respective components of CO₂ and H₂O flue gases are determined depending on the product $p_{p_i}.l_{ef}$ from tables in [32,33]. The radiation of gases is not directly proportional to the fourth power of temperature. For CO₂, the exponent is 3,5 ~ T^3,5, and for H₂O, the is exponent 3 ~ T³. For calculations, the power is chosen according to the Stefan–Boltzman law—T⁴ [23,26].

The necessary exponent correction is then included in the emissivity. The correction factor β is determined as follows [23,32,33]:

If $p_{p_{H_{2}O}}.l_{ef}>1 \mathrm{k}\mathrm{P}\mathrm{a}.\mathrm{m}$ (most cases), then:

$$\beta =1+\left[0.6225-0.1346.\log \left(p_{p_{H_{2}O}}.l_{ef}\right)\right].{\left({\displaystyle \frac{p_{p_{H_{2}O}}}{100}}\right)}^{0.86}$$

(9)

If $p_{p_{H_{2}O}}.l_{ef}\le 1 \mathrm{k}\mathrm{P}\mathrm{a}.\mathrm{m}$, then:

$$\beta =1+0.6225.{\left({\displaystyle \frac{p_{p_{H_{2}O}}}{100}}\right)}^{0.86}$$

(10)

Correction of the spectral radiation of CO₂ and H₂O (reduction) in the total radiation of the gas mixture due to the overlap of the spectral radiation of CO₂ and H₂O at the same wavelengths [23,26]:

$$\Delta \epsilon ={\epsilon }_{{CO}_2}.{\epsilon }_{H_{2}O}$$

(11)

For the determination of heat transfer by radiation, it is very important to determine the emissivity of flue gases, which is determined from the following relationship [23,26,30]:

$${\epsilon }_{fg}={\epsilon }_{{CO}_2}+\beta .{\epsilon }_{H_{2}O}+{\epsilon }_{{SO}_2}-\Delta \epsilon +{\epsilon }_{pm}$$

(12)

${\epsilon }_{{SO}_2}$—SO₂ emissivity, which was determined graphically from [26], (—);

${\epsilon }_{pm}$—emissivity of particulate matter (dust drifts), (—).

In gaseous fuels like natural gas, sulfur is present only in trace amounts, so the hot component SO₂ can be disregarded. However, during the combustion of sulfur from the reducing agent, its content may increase. Nevertheless, its content remained below 1 vol.%, and for this reason, its value in the calculations was determined graphically using a nomogram from [26].

The emissivity of particulate matter increases the overall emissivity in flue gases, and in thermal equipment, particulate matter contributes to the increase in radiant energy from the volume of flue gases. The calculations considered dust drifts during the movement of pellets through the equipment, and even after flue gas cleaning, dust particles were still present in the flue gases. The following calculation was used to determine the emissivity of particulate matter [26,30]:

$${\epsilon }_{pm}=1-e^{-x}$$

(13)

$$x=0.75{\displaystyle \frac{273.15}{T_{pm}}}{\displaystyle \frac{m_i}{{\rho }_{o,pm}{r}_{pm}}}{\mathrm{d}}_h$$

(14)

$$m_i={\displaystyle \frac{{\dot{m}}_{pm}}{{\dot{V}}_{fg}}}$$

(15)

$T_{pm}$—thermodynamic temperature of particulate matter, (K);

${\rho }_{o,pm}$—density of particulate matter, (kg/m³);

$r_{pm}$—radius of particulate matter, (m);

${\mathrm{d}}_h$—hydraulic diameter of the free cross-section of the device, (m);

$m_i$—particulate matter content in 1 m³ of flue gas, (kg/m³);

${\dot{m}}_{pm}$—mass flow of particulate matter (dust drift), (kg/h);

${\dot{V}}_{fg}$—flue gas volume flow, (m³/h).

The area density of the heat flux by radiation from the flue gas can be calculated using the following relation [23,31]:

$$q_r={\epsilon }_{fg}.c_o.{\left({\displaystyle \frac{T_{fg}}{100}}\right)}^4=c.{\left({\displaystyle \frac{T_{fg}}{100}}\right)}^4$$

(16)

${\epsilon }_{fg}$—total emissivity of the flue gases (Equation (12)), (—);

$c_o$—absolute black body radiation coefficient, 5.67 W/(m²K⁴);

$T_{fg}$—thermodynamic temperature of flue gases, (K).

In the case of radiation from the flue gas to the charge, the previous relation (16) needs to be extended to the following form [23,31]:

$$q_r=c.\left[{\left({\displaystyle \frac{T_{fg}}{100}}\right)}^4-{\left({\displaystyle \frac{T_m}{100}}\right)}^4\right]={\alpha }_r.\Delta t$$

(17)

$T_m$—thermodynamic temperature of the charge, (K);

$c$—grey body radiation coefficient, (W/(m²K⁴));

${\alpha }_r$—radiation heat transfer coefficient, (W/(m²K));

$\Delta t$—the temperature difference between the flue gases and the body, (°C).

(b) Radiative heat transfer between two grey bodies

Solid bodies are defined as gray bodies, meaning they cannot completely absorb or emit energy, but instead reflect part of it. Equation (17) can also be used to calculate heat transfer by radiation within a thermal unit from the walls of the unit to the charge, with the coefficient c being calculated based on Equation (19) [23,31].

$$q_r=c.\left[{\left({\displaystyle \frac{T_2}{100}}\right)}^4-{\left({\displaystyle \frac{T_1}{100}}\right)}^4\right]={\alpha }_r.\Delta t$$

(18)

$$c={\displaystyle \frac{c_0}{1+\left(\frac{1}{{\epsilon }_2}-1\right){\phi }_{21}+\left(\frac{1}{{\epsilon }_1}-1\right){\phi }_{12}}}$$

(19)

$T_1$—thermodynamic temperature of the first body, (K);

$T_2$—thermodynamic temperature of the second body, (K);

${\epsilon }_1$—first body emissivity, (—);

${\epsilon }_2$—second body emissivity, (—);

${\phi }_{12}$—the directionality of radiation from the first body to the second body, (—);

${\phi }_{21}$—the directionality of radiation from the second body to the first body, (—).

The directionality of radiation is determined based on the geometry of the interior of the furnace, utilizing the rules of enclosure and reciprocity for the individual radiating surfaces. Due to the complexity of some cases, more information can be found in [23,26,30,31].

The amount of heat involved in the radiation heat exchange between two gray (real) bodies is given by the following equation [23]:

$${\dot{Q}}_r=c.\left[{\left({\displaystyle \frac{T_2}{100}}\right)}^4-{\left({\displaystyle \frac{T_1}{100}}\right)}^4\right]{\phi }_{12}{S}_1={\alpha }_r\Delta t{\phi }_{12}{S}_1$$

(20)

Convection heat transfer

Heat transfer by convection is a part of the heat exchange not only inside the equipment but also on its surface. The convective heat exchange component depends on the nature of the flow, which also determines the choice of the appropriate mathematical relationships.

In high-temperature furnaces, the heat transferred to the material by convection typically accounts for 10–30% of the total heat transfer. This is sometimes adjusted by applying a correction factor of 1.1–1.3 to the radiant component. A more precise calculation can be achieved using Newton’s relation for surface heat flux density [23,34]:

$$q_c={\alpha }_c.\Delta t$$

(21)

${\alpha }_c$—convection heat transfer coefficient, (W/(m²K));

$\Delta t$—the temperature difference of the flue gases and the body, (°C).

To determine ${\alpha }_c$, it is possible to use the approximate formula recommended by M.A. Micheev for convection heat transfer in furnaces using the dimensionless Nusselt number [23,26]:

$$Nu={\displaystyle \frac{{\alpha }_c.L}{{\lambda }_t}}$$

(22)

$L$—characteristic dimension, (m),

${\lambda }_t$—coefficient of thermal conductivity of the fluid, (W/(mK)).

For flow in furnaces, simplified empirical relationships can be used:

- For laminar mode:

$$Nu=0.57.{Re}^{0.5}$$

(23)

- For turbulent mode:

$$Nu=0.032.{Re}^{0.8}$$

(24)

For heat exchange by convection within the charge layer, mathematical models of the volumetric heat transfer coefficient ${\alpha }_V$ were considered. The relationship between Newton’s coefficient ${\alpha }_c$ and ${\alpha }_V$ can be determined as follows:

$${\alpha }_c={\displaystyle \frac{{\alpha }_V}{{\mathrm{a}}_{\mathrm{s}}}}; ({\mathrm{W}/(\mathrm{m}}^2\mathrm{K}))$$

(25)

${\mathrm{a}}_{\mathrm{s}}$—specific surface area of the particle layer, (m²/m³).

$${\mathrm{a}}_{\mathrm{s}}=6{\displaystyle \frac{1-f}{\mathrm{d}}}; ({\mathrm{m}}^2/{\mathrm{m}}^3)$$

(26)

$f$—layer porosity in the range <0;1>;

$\mathrm{d}$—diameter of particles/lump, (m).

Volume coefficient of heat transfer according to Kitajev [35]:

$${\propto }_{\mathrm{V}}=\mathrm{A}{\displaystyle \frac{T^{0.3}{w}_o^{0.7}}{d^{0.9}}}M; ({\mathrm{W}/(\mathrm{m}}^3\mathrm{K}))$$

(27)

A—coefficient, characteristic of the material, —);

$T$—average gas temperature, (K);

$w_0$—gas velocity, referred to 0 °C and the shaft cross-sectional area, (m/s).

$d$—lump diameter, (m);

$M$—coefficient, dependent only on bed porosity, (—).

$$\mathrm{M}={10}^{1.68f-3.56f^2}; (-)$$

(28)

Alternatively, Newton’s coefficient ${\alpha }_c$ can be determined direct using a model for the dimensionless criterion Nu, as proposed by Viktorin [36]:

$$\mathrm{N}\mathrm{u}=0.33{Re}^{0.77}+0.42; (-)$$

(29)

In the created model, Equations (27)–(29) were used in the calculation of heat transfer by convection in the drying chamber.

An important component of the heat balance is the amount of heat dissipated from the surfaces of individual devices. This heat loss is defined as free convection, but since the surface of the equipment is at a higher temperature, the radiative component from the surface to the surroundings must also be considered. For the model, overall heat transfer coefficients from the surfaces of the equipment were chosen according to Heiligenstaedt, as mentioned in [37]:

- For masonry walls:

$${\propto }_{c+r}=7.1+0.057t_a; ({\mathrm{W}/(\mathrm{m}}^2\mathrm{K}))$$

(30)

$t_a$—external wall surface temperature, (°C).

- For metal walls:

$${\propto }_{c+r}=6.3+0.039t_a; ({\mathrm{W}/(\mathrm{m}}^2\mathrm{K}))$$

(31)

Many sources in the literature present a range of additional models for calculating heat transfer coefficients, but most are more focused on the convective component, such as those by Nusselt [37], Brunklaus [37], and others.

• Calculation algorithm
  • Determination of the composition of leach residue;
  • Determination of the material and thermal balance of processes in the rotary kiln;
  • Determination of the energy requirements of processes in the rotary kiln: calculation of natural gas consumption and the corresponding reducing agent, as well as the residence time of material in the kiln—Rotary Kiln;
  • Determination of the material and thermal balance of processes in the cooler: calculation of the amount and temperature of cooling air and the outlet temperature of pellets—Pellet Cooler;
  • Resolution of the post-combustion process (combustion for oxide pellets) of flue gases exiting the rotary kiln—Afterburner/Combustion chamber;
  • Cooling of produced flue gases before entering the 3rd zone (preheating of raw pellets) on the Lepol grate—Flue gas Cooler I + Cogeneration (if necessary);
  • Cooling of flue gases before entering the 2nd zone (pre-drying and preheating of raw pellets) on the Lepol grate—Flue gas Cooler II;
  • Cooling of flue gases before entering the 1st zone (drying of raw pellets) on the Lepol grate—Flue gas Cooler I;
  • Calculation of flue gas temperatures before entering the filter and in the chimney.

The development of the mathematical model was based on information obtained from studies [14,16,17,18,19] that dealt with the processing of slag from Sereď, or the production of pellets from metalliferous waste:

• The consumption of reducing agents corresponding to the direct reduction of iron oxides with carbon (C) with a coefficient of 1.5.
• The degree of reduction of iron oxides for Sereď slag (see Figure 1). Other conditions for the mathematical model:
• The flue gas temperature in the rotary kiln at the side where natural gas and air—necessary for burning excess carbon from the reducing agent and a portion of the released CO from the reduction, as well as volatiles from the reducing agent—are introduced should not drop below 800 °C.
• Based on the distribution of material temperatures along the length of the kiln, the reduction of iron oxides, the burning of CO and volatiles, and the burning of excess carbon from the reducing agent were determined.

Since the determining process for thermal calculations is the heating and reduction of iron oxides in the rotary kiln, parts of the mathematical model that addressed processes in the rotary kiln and subsequently in the pellet cooler were treated zonally to obtain temperature profiles of the flue gases and the charge along the length of these units.

3. Results

The modelling results are based on a calculation algorithm that utilizes modules for material and energy balance calculations in the individual units. The obtained results are presented in tables and graphs.

3.1. Material Balance of Pellet Composition

Based on the composition of the raw pellets and the amount of reducing agent, the mathematical model calculations included a recalculation of the pellet composition after thermal processing and cooling. The output pellet composition is the final composition and is provided for each calculation variant in

Table 4. Composition of raw pellets at the inlet and pellets at the outlet of the process.

Reducing Agents	Coke						Lignite				Oxidized Pellets
Degree of Reduction	50%		61%		92%		69%		92%		0%
	Input	Output	Input	Output	Input	Output	Input	Output	Input	Output	Input	Output
	wt.%		wt.%		wt.%		wt.%		wt.%		wt.%
Fe total		60.339		61.670		65.525		60.444		62.177		55.244
Fe	0.244	21.346	0.238	31.014	0.224	59.010	0.213	36.407	0.200	55.995	0.273	0.320
FeO	22.497	50.134	21.977	39.416	20.702	8.376	19.679	30.906	18.475	7.948	25.239	29.530
Fe2O3	34.779	0.000	33.975	0.000	32.003	0.000	30.423	0.000	28.561	0.000	39.019	45.652
CaO	3.040	4.286	2.970	4.380	2.798	4.654	2.660	4.293	2.497	4.416	3.411	3.924
SiO2	7.329	10.508	7.160	10.740	6.744	11.411	6.411	10.526	6.019	10.828	8.223	9.621
MgO	2.027	2.906	1.980	2.970	1.865	3.156	1.773	2.911	1.665	2.995	2.274	2.661
C *	8.620	0.206	10.392	0.260	14.739	0.416	10.482	0.287	13.153	0.789	0.000	0.000
Al2O3	4.054	5.812	3.960	5.940	3.730	6.312	3.546	5.822	3.329	5.989	4.548	5.321
P2O5	0.096	0.137	0.094	0.140	0.088	0.149	0.084	0.138	0.079	0.142	0.108	0.126
CaOSO3	0.073	0.179	0.072	0.183	0.067	0.194	0.064	0.179	0.060	0.184	0.082	0.164
K2O	0.073	0.105	0.072	0.107	0.067	0.114	0.064	0.105	0.060	0.108	0.082	0.096
ZnO (s)	0.025	0.035	0.024	0.036	0.023	0.038	0.021	0.035	0.020	0.036	0.028	0.032
Ni(NiO)	0.229	0.328	0.224	0.335	0.211	0.356	0.200	0.329	0.188	0.338	0.257	0.300
CoO	0.012	0.017	0.012	0.018	0.011	0.019	0.011	0.017	0.010	0.018	0.014	0.016
V2O5(V2O3)	0.016	0.023	0.016	0.024	0.015	0.025	0.014	0.024	0.013	0.024	0.018	0.021
TiO2	0.090	0.129	0.088	0.131	0.083	0.140	0.078	0.129	0.074	0.132	0.101	0.118
MnO	0.285	0.408	0.278	0.417	0.262	0.443	0.249	0.409	0.234	0.420	0.319	0.374
Cr2O5(Cr2O3)	1.142	1.638	1.116	1.674	1.051	1.778	0.999	1.641	0.938	1.688	1.282	1.499
Bi(Bi2O3)	0.004	0.006	0.004	0.006	0.004	0.007	0.004	0.006	0.004	0.006	0.005	0.006
Na2O	0.168	0.240	0.164	0.246	0.154	0.261	0.147	0.241	0.138	0.248	0.188	0.220
Ash	1.086	1.556	1.309	1.963	1.856	3.141	3.409	5.596	4.278	7.695	0.000	0.000
N2 + O2 + H2 + S	0.399	0.000	0.481	0.000	0.683	0.000	5.474	0.000	6.869	0.000	0.000	0.000
H2O	13.713	0.000	13.396	0.000	12.619	0.000	13.995	0.000	13.138	0.000	14.530	0.000

* C recalculated from the reducing agents.

.

The amount of reducing agent in the raw pellets corresponds to the amount of carbon in Table 4. The results after reduction show that in no case was the carbon completely consumed for reduction when using the reducing agent. The ballast substances from the reducing agent are reflected in the ash content, and as can be observed, the value is higher when using lignite compared to coke. The input ratio of ash in lignite to coke is, on average, 2.71, and at the output, it is 2.99. The average moisture content in the raw pellets was approximately 13.372 wt.%, with the oxide pellets having an increased moisture content of 8 wt.%.

3.2. Outputs of Calculations for Individual Equipment

The results from the calculations using the developed mathematical model, which formed the basis for the overall material and energy balance, are presented in

Table 5. Outputs from the mathematical model for the different variants of reduction and reducing agent in the individual process equipment.

Alternative		C_50R	C_61R	C_92R	BC_69R	BC_92R	OX
Fuel for the rotary kiln
Natural gas (NG) (m3/kgfuels)		1.351	1.351	1.351	1.351	1.351	1.351
LHV (kJ/kgfuels)		49,096	49,096	49,096	49,096	49,096	49,096
Excess air coefficient for combustion NG (-)		1.1	1.1	1.1	1.1	1.1	1.1
Mass flow of wet charge (kg/h)		69,694	72,916	82,246.6	79,811	87,452	56,875
Cooler
Mass flow of charge (kg/h)	input	47,639	47,639	47,639	47,639	47,639	47,639
	output	47,639	47,639	47,639	47,639	47,639	47,639
Temperature of charge (°C)	input	1100	1100	1100	1100	1100	1100
	output	410	410	410	410	410	410
Volumetric air flow (m3/h)		35,000	35,000	35,000	35,000	35,000	35,000
Air temperature (°C)	input	20	20	20	20	20	20
	output	380	380	380	380	380	380
Heat supplied by the charge (kJ/h)		28,837	28,364	26,991	28,285	27,504	31,004
Heat fluxes per charge (kJ/h)		27,559	27,559	27,559	33,848	33,848	33,848
Useful heat—air (kJ/h)		16,778	16,778	16,778	16,778	16,778	16,778
Rotary kiln
Mass flow of charge (kg/h)	input	60,137	63,148	71,868	68,642	75,962	48,611
	output	47,639	47,639	47,639	47,639	47,639	47,639
Temperature of charge (°C)	input	650	650	650	400	400	500
	output	1100	1100	1100	1100	1100	1100
Flue gas temperature (°C)	input	850	844	837	837	883	2057
	output	973	1006	1051	904	955	643
Volumetric air flow—total (m3/h)		34,167	43,481	73,227	36,494	49,650	14,831
Preheated air temperature (°C)		380	380	380	380	380	380
Mass flow of fuel (kg/h)		518	740	1480	555	962	1036
Fuel volume flow (m3/h)		700	1000	2000	750	1300	1400
Flue gas volume flow (fuel) (m3/h)		8125	11,607	23,214	8705	15,089	16,250
Flue gas volume flow—total (m3/h)		42,132	53,824	90,285	54,369	74,803	16,250
Flue gas composition (vol.%)	CO	10.729	10.605	10.976	8.999	9.760	0.000
	CO2	17.147	17.139	15.938	20.651	19.762	8.791
	H2O	3.975	3.730	5.049	2.769	3.489	17.297
	SO2	0.053	0.052	0.050	0.000	0.000	0.000
	N2	64.205	63.959	64.211	53.239	52.651	72.170
	O2	1.335	1.360	1.368	1.193	1.198	1.742
Degree of reduction		50	61	92	69	92.3	0
Degree of free C combustion		0.95	0.95	0.95	0.95	0.9	0
Degree of C combustion to CO2		1	1	1	1	1	0
Degree of CO Combustion from reduction		0.40	0.40	0.35	0.53	0.49	0
Mass flow of dust drifts (kg/h)		972	972	972	972	972	972
Mass flow of dust drifts—total (kg/h)		972	972	972	972	972	972
Flue gas velocity in the rotary kiln (m/s)		6.494	8.275	13.922	5.278	7.415	1.906
Residence time of flue gases in the rotary kiln (s)		3.080	2.417	1.437	0.758	0.539	10.493
Heat supplied by the charge (kJ/h)		147,291	182,418	292,217	204,316	270,678	51,245
Heat fluxes per charge (kJ/h)		22,515	20,532	20,236	39,453	43,894	27,542
Useful heat of charge (kJ/h)		78,143	92,380	133,519	116,831	147,667	28,159
Heat fluxes required per charge (kJ/h)		22,855	20,736	22,855	37,878	42,803	28,159
Specific fuel consumption (m3/t)		14.7	21.0	42.0	15.7	27.3	29.4
Cyclone
Fuel volume flow (m3/h)	input	42,132	53,824	90,285	54,369	74,803	16,250
Flue gas temperature (°C)	input	973	1006	1051	904	955	643
Flue gas composition (vol.%)	H2	2.56	3.16	2.41	9.00	9.760	0.000
	CO	10.729	10.605	10.976	8.999	9.760	0.000
	CO2	17.147	17.139	15.938	20.651	19.762	8.791
	H2O	3.975	3.730	5.049	2.769	3.489	17.297
	SO2	0.053	0.052	0.050	0.000	0.000	0.000
	N2	64.205	63.959	64.211	53.239	52.651	72.170
	O2	1.335	1.360	1.368	1.193	1.198	1.742
Mass flow of dust drifts (kg/h)	output	972	972	972	972	972	972
Mass flow of dust drifts—total (kg/h)	output	194	194	194	194	194	194
Fuel composition—combustion chamber
Natural gas(NG) (kg/kgfuels)		1	1	1	1	1	1
Natural gas(NG) (m3/kgfuels)		1.351	1.351	1.351	1.351	1.351	1.351
LHV (kJ/kgfuels)		49,096	49,096	49,096	49,096	49,096	49,096
Afterburner chamber (DSK)
Mass flow of fuel (kg/h)		148	0	0	37	337	1110
Fuel volume flow (m3/h)		200	0	0	50	50	1500
Volumetric flow rate of CO + H2 afterburning (m3/h)		5597	1698	2174	12,041	17,130	0
Volumetric combustion air flow (m3/h)		16,996	19,398	31,648	33,431	42,270	16,684
Flue gas volume flow—total (m3/h)		56,314	69,518	115,891	81,568	113,199	51,976
Flue gas temperature (°C)	input	1410	1418	1474	1227	1292	1085
Flue gas composition (vol.%)	input
	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	21.217	21.480	20.968	19.826	19.553	5.693
	H2O	5.600	5.331	5.809	10.733	11.078	11.202
	SO2	0.039	0.040	0.039	0.000	0.000	0.000
	N2	71.576	71.563	71.597	67.864	67.780	74.577
	O2	1.567	1.586	1.587	1.578	1.589	8.528
Mass flow of dust drifts (kg/h)	output	194	194	194	194	194	194
Mass flow of dust drifts—total (kg/h)	output	194	194	194	194	194	194
Specific fuel consumption (m3/t)		4.20	0.00	0.00	1.05	1.05	31.5
Flue gas cooling
Flue gas volume flow (m3/h)		56,314	69,518	115,891	81,568	113,199	51,976
Flue gas temperature (°C)		1410	1418	1474	1227	1292	1085
Flue gas composition		DSK	DSK	DSK	DSK	DSK	DSK
Volumetric cooling air flow (m3/h)		48,000	50,000	60,000	75,000	62,000	35,000
Flue gas volume flow (m3/h)	input	56,314	69,518	115,891	81,568	113,199	51,976
	output	104,314	119,518	175,891	156,568	175,199	86,976
Flue gas temperature (°C)	input	1410	1418	1474	1227	1292	1085
	output	813	871	1015	686	877	667
Flue gas composition (vol.%)	input	DSK	DSK	DSK	DSK	DSK	DSK
	output
	CO	0	0	0	0	0	0
	CO2	11.4542	12.494	13.82	10.3287	12.63	3.40
	H2O	3.0231	3.101	3.83	5.5915	7.16	6.69
	SO2	0.0213	0.0235	0.03	0.0000	0.00	0.00
	N2	74.9922	74.674	74.12	73.1982	71.75	76.36
	O2	10.5093	9.708	8.21	10.8815	8.46	13.55
Cogeneration I
Flue gas volume flow (m3/h)			11,9518	175,891	156,568	175,199
Flue gas temperature (°C)	input		871	1015	686	877
	output		800	775	575	570
Theoretical heat output (MW)			3.8	19.21	7.46	24.02
Flue gas redistribution after cooling (%)	Zone 3	62	62	67	30	35	36
	Zone 2	38	38	33	70	65	64
Flue gas cooling for Zone 2
Flue gas volume flow (m3/h)		39,639	45,417	58,044	109,598	113,879	55,665
Flue gas temperature (°C)		813	800	775	575	570	667
Flue gas composition		DSK	DSK	DSK	DSK	DSK	DSK
Volumetric cooling air flow (m3/h)		48,000	55,000	60,000	55,000	75,000	45,000
Flue gas volume flow (m3/h)	input	39,639	45,417	58,044	109,598	113,879	55,665
	output	87,639	100,417	118,044	164,598	188,879	100,665
Flue gas temperature (°C)	input	813	800	775	575	570	667
	output	391	385	409	388	360	381
Flue gas composition (vol.%)	input	DSK	DSK	DSK	DSK	DSK	DSK
	output
	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	5.181	5.651	6.793	6.877	7.617	1.881
	H2O	1.367	1.402	1.882	3.723	4.315	3.702
	SO2	0.010	0.011	0.013	0.000	0.000	0.000
	N2	77.187	77.043	76.602	75.137	74.629	77.538
	O2	16.255	15.893	14.711	14.263	13.438	16.879
Preheating Zone 3
Mass flow of charge (kg/h)	input	60,137	63,148	71,868	68,642	75,962	48,611
	output	60,137	63,148	71,868	68,642	75,962	48,611
Temperature of charge (°C)	input	225	225	225	200	200	230
	output	650	650	650	400	400	500
Flue gas volume flow (m3/h)	input	64,675	74,101	117,847	46,970	61,320	31,311
	output	64,675	74,101	117,847	46,970	61,320	31,311
Flue gas temperature (°C)	input	813	800	775	575	570	667
	output	527	538	589	378	403	374
Flue gas composition (vol.%)	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	11.454	12.494	13.815	10.329	12.634	3.402
	H2O	3.023	3.101	3.828	5.592	7.157	6.694
	SO2	0.021	0.023	0.026	0.000	0.000	0.000
	N2	74.992	74.674	74.122	73.198	71.751	76.357
	O2	10.509	9.708	8.209	10.881	8.458	13.547
Heat fluxes per charge (kJ/h)		25,516	26,057	31,209	11,998	13,613	11,796
Useful heat of charge (kJ/h)		25,013	26,601	31,198	11,922	13,077	11,930
Cogeneration II
Flue gas volume flow (m3/h)		-	-	-	-	117,847	-
Flue gas temperature (°C)	input	-	-	-	-	589	-
	output	-	-	-	-	409	-
Theoretical heat output (MW)		-	-	-	-	15.47	-
Preheating Zone 2
Mass flow of charge (kg/h)	input	60,137	63,148	71,868	68,642	75,962	48,611
	output	60,137	63,148	71,868	68,642	75,962	48,611
Temperature of charge (°C)	input	130	130	130	110	110	140
	output	225	225	225	200	200	230
Flue gas volume flow (m3/h)	input	87,639	100,417	118,044	164,598	188,879	100,665
	output	87,639	100,417	118,044	164,598	188,879	100,665
Flue gas temperature (°C)	input	391	385	409	388	360	381
	output	325	322	345	349	321	335
Flue gas composition (vol.%)	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	5.181	5.651	6.793	6.877	7.617	1.881
	H2O	1.367	1.402	1.882	3.723	4.315	3.702
	SO2	0.010	0.011	0.013	0.000	0.000	0.000
	N2	77.187	77.043	76.602	75.137	74.629	77.538
	O2	16.255	15.893	14.711	14.263	13.438	16.879
Heat fluxes per charge (kJ/h)		4997	51,125	5834	8051	6932	6429
Useful heat of charge (kJ/h)		4847	5143	6000	4672	5113	3539
Flue gas cooling for Zone 1
Volumetric cooling air flow (m3/h)		40,000	40,000	40,000	40,000	35,000	23,000
Flue gas volume flow (m3/h)	input	152,314	174,518	235,891	211,568	250,199	131,976
	output	192,314	214,518	275,891	251,568	285,199	154,976
Flue gas temperature (°C)	output	305	316	299	283	289	278
Flue gas composition (vol.%)	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	6.213	6.961	8.808	6.428	7.761	1.909
	H2O	1.640	1.728	2.440	3.480	4.397	3.757
	SO2	0.012	0.013	0.016	0.000	0.000	0.000
	N2	76.826	76.490	75.890	75.389	74.547	77.517
	O2	15.310	14.708	12.845	14.703	13.296	16.817
Preheating Zone 1 drying
Mass flow of charge (kg/h)	input	69,694	72,916	82,247	79,811	87,452	56,875
	output	601,37	63,148	71,868	68,642	75,962	48,611
Temperature of charge (°C)	input	25	25	25	25	25	25
	output	130	130	130	110	110	140
Flue gas volume flow (m3/h)	input	192,314	214,518	275,891	251,568	285,199	154,976
	output	204,207	226,674	288,807	265,468	299,497	165,260
Flue gas temperature (°C)	input	305	316	299	283	289	278
	output	165	183	188	167	182	132
Flue gas composition (vol.%)	input
	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	6.213	6.961	8.808	6.428	7.76	1.909
	H2O	1.640	1.728	2.440	3.480	4.40	3.757
	SO2	0.012	0.013	0.016	0.000	0.00	0.000
	N2	76.826	76.590	75,890	75.389	74.55	77.517
	O2	15.310	14.708	12.845	14.703	13.30	18.817
	output
	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	5.851	6.588	8.414	6.092	7.390	1.791
	H2O	7.368	6.998	6.803	8.534	8.961	9.746
	SO2	0.011	0.012	0.016	0.000	0.000	0.000
	N2	72.352	72.483	72.496	71.442	70.988	72.693
	O2	14.418	13.920	12.271	13.933	12.661	15.771
Mass flow of dust drifts (kJ/h)		194	194	194	194	194	194
Heat fluxes per charge (kJ/h)		28,222	31,897	32,169	29,445	31,283	22,953
Useful heat of charge (kJ/h)		29,317	30,129	32,480	32,611	33,770	25,339
Filter before the chimney
Flue gas volume flow (m3/h)	input	204,207	226,674	288,807	265,468	299,497	165,260
	output	204,207	226,674	288,807	265,468	299,497	165,260
Flue gas temperature (°C)	input	163	181	186	165	180	130
	output	161	179	184	163	178	128
Flue gas composition (vol.%)	CO	0.000	0.000	0.000	0.000	0.000	0.000
	CO2	5.851	6.588	8.414	6.092	7.390	1.791
	H2O	7.368	6.998	6.803	8.534	8.961	9.746
	SO2	0.011	0.012	0.016	0.000	0.000	0.000
	N2	72.352	72.483	72.496	71.442	70.988	72.693
	O2	14.418	13.920	12.271	13.933	12.661	15.771
Filter efficiency (%)		99.95	99.95	99.95	99.95	99.95	99.95
Mass flow of dust drifts (kg/h)	input	194	194	194	194	194	194
	output	0.097	0.097	0.097	0.097	0.097	0.097
Chimney
Flue gas volume flow (m3/h)		204,207	226,674	288,807	265,468	299,497	165,260
Flue gas temperature in the chimney (°C)	input	161	179	184	163	178	128
	output	155	173	179	158	174	123
Fuel consumption
Natural gas (kg/h)		666	740	1480	592	999	2146
(m3/h)		900	1000	2000	800	1350	2900
Consumption of reducing agent
Coke (kg/h)		8588	10,832	17,330	-	-	-
Lignite (kg/h)		-	-	-	20,228	27,814	-
Total heat (MJ/h)		235,036	291,534	480,951	341,408	478,511	105,353
Specific fuel consumption (m3/t)		18.51	20.57	41.14	16.46	27.77	60.87
Specific heat consumption (GJ/t)		4.835	5.997	9.894	7.023	9.844	2.167

. The individual units, which are sequentially linked in the raw pellet processing process, are listed progressively.

The results of the calculations for various alternatives indicate the overall energy consumption of the entire processing operation. The data show that achieving a 92% reduction of oxides in pellets using coke requires 3.87 GJ/t of pellets more energy compared to a 61% reduction. For lignite, achieving a 69% reduction of oxides requires 2.821 GJ/t of pellets more energy, which on average represents a 40% increase in energy consumption compared to the energy required for a 92% reduction of oxides using both coke and lignite. Therefore, it is essential to assess the practical feasibility of these alternatives.

3.3. Pellet Cooling

For all alternatives, a constant amount of air is considered, which has been determined to prevent or limit the reoxidation of the produced pellets. Figure 5 shows the temperatures of the pellets and the cooling air. The cooler is designed as a counterflow heat exchanger, where the pellet temperature decreases from approximately 1100 °C to 410 °C, and the air is heated to about 380 °C.

This type is the most efficient for maximizing the cooling of the pellets using a constant amount of air while simultaneously achieving a high temperature for the preheated air.

3.4. Basic Calculation Parameters of Processes in a Rotary Kiln

The necessary input calculations for each alternative were conducted using a developed mathematical model, which was used to establish the overall material and energy balances in the rotary kiln. The results of these calculations are presented through graphs and summarized in tables that illustrate the performance of each alternative. This chapter provides a detailed description of these alternatives, their calculations, and the analysis of results for the rotary kiln.

3.4.1. Reducing Agent: Coke—50% Reduction

To achieve the minimum amount of total iron in the pellet, a reduction with coke at the 50% reduction boundary of oxides was proposed. Figure 6a shows the temperature profiles of the exhaust gases and pellets along the length of the rotary kiln. The calculations revealed that the residence time of the pellets in the rotary kiln is 103 min.

The raw pellets, after entering the rotary kiln, are heated to the required reduction temperature of at least 950 °C approximately 17 m into the kiln, corresponding to a residence time of 43 min. During the movement of the raw pellets, reduction and the combustion of carbon within them occurs. This affects the temperature of the raw pellets and the exhaust gases along the rotary kiln.

The expected course of excess carbon combustion, CO combustion from reduction, and volatile matter combustion can be observed in Figure 6b.

Analyses conducted for the reduction of iron ore pellets indicate that, in addition to temperature, the residence time of the pellets within these temperature zones is crucial. Reduction begins at temperatures of approximately 950 °C. Figure 6a,b show that at 50% reduction, the material remains in the kiln at temperatures above 950 °C for approximately 60 min. Experiments suggest that the time required for approximately 50% reduction of iron oxides is around 50 min.

From the production requirements, it follows that for the alternative of 50% reduction of iron oxides with coke, a feedstock with the following mass flow or ratio of individual raw materials per ton of produced pellets is necessary, as presented in

Table 6. Material and energy balance for reduction with coke.

Degree of Reduction	50%		61%		92%
	kg/h	kg/t	kg/h	kg/t	kg/h	kg/t
Dry leach residue	53,094	1092.22707	54,266	1116.322829	57,658	1186.101
Water in the leach residue	6381	131.271976	6522	134.1679836	6930	142.5544
Dry matter in coke	7042	144.8723758	8882	182.7225414	14,211	292.3313
Water in the coke	1546	31.80125323	1950	40.10982615	3119	64.17028
Added water	1630	33.52764336	1296	26.66029946	329	6.773442
Raw pellets total	69,694	1433.700318	72,916	1499.983479	82,247	1691.93
Water leach residue +coke	7927	163.0732292	8472	174.2778097	10,049	206.7247
Dry matter in raw pellets	60,137	1237.099445	63,148	1299.04537	71,868	1478.432
Added water	1630	33.52764336	1296	26.66029946	329	6.773442
Total water	9557	196.6008725	9768	200.9381092	10,378	213.4981
Raw pellets total	69,694	1433.700318	72,916	1499.983479	82,247	1691.93
Wet leach residue	59,476	1223.499046	60,788	1250.490812	64,587	1328.655
Wet coke	8588	176.673629	10,832	222.8323675	17,330	356.5016
Added water	1630	33.52764336	1296	26.66029946	329	6.773442
Raw pellets total	69,694	1433.700318	72,916	1499.983479	82,247	1691.93
Pellets	48,611		48,611		48,611
	m3/h	m3/tpellets	m3/h	m3/tpellets	m3/h	m3/tpellets
Gas consumption (NG)	900	18.51428571	1000	20.57142857	2000	41.14286
Air consumption	187,163	3850.209098	207,879	4276.358675	264,875	5448.863
Produced flue gases	204,207	4200.836778	226,674	4663.000971	288,807	5941.166
	MJ/h	GJ/tpellets	MJ/h	GJ/tpellets	MJ/h	GJ/tpellets
Energy consumption	235,036	4.835031312	291,534	5.997264592	480,951	9.893845

.

3.4.2. Reducing Agent: Coke—61% Reduction

The minimum threshold of 50% reduction of oxides in raw pellets was determined based on experimental measurements and calculations related to the reactivity of coke, considering the degree of reduction and residence time in the kiln. Based on these calculations from sources [18,19], a second threshold was also established for the variant with a 61% reduction level using coke.

The results of the temperature profile calculations along the length of the kiln are shown in Figure 7a. Similar to the previous variant, in this case, the combustion of carbon in the pellets begins once the pellets reach a sufficient temperature, and complete combustion is calculated to occur at the end of the rotary kiln (Figure 7b).

Figure 7a indicates that in the final meters of the rotary kiln, the raw pellets are not heated by the flue gases but by the reactions occurring within them and the combustion of coke. However, the flue gases are crucial for achieving the required temperature of the raw pellets to initiate and sustain the reduction of Fe oxides.

Compared to the 50% reduction with coke, there is no significant difference in the residence time of the raw pellets in the rotary kiln or their temperature. The residence time is approximately 60 min, and experiments indicate that the time required for about a 60% reduction of iron oxides is around 55–60 min.

3.4.3. Reducing Agent: Coke—92% Reduction

To determine the degree of Fe oxide reduction using coke as a reducing agent, calculations were conducted similarly to the previous variant. This alternative was chosen to maximize the reduction of iron oxides from the original material. The results of the temperature profiles of the flue gases and pellet temperatures are shown in Figure 8a.

From Figure 8a, it can be observed that the residence time of the raw pellets at temperatures above 950 °C is approximately 60 min. Experiments indicate that the time required to achieve an Fe oxide reduction of over 90% is 180 min. This parameter can be achieved by adjusting the feed rate in the rotary kiln.

Table 6 presents the input parameters of the raw pellets for each variant using coke as a reducing agent. The calculations were performed for the material and energy balance, considering mass and volumetric flows and converted per ton of material according to the relevant sections.

The energy consumption increases in a slightly parabolic manner as the degree of Fe oxide reduction increases. Compared to the maximum reduction level of 92%, the energy consumption increases by 51.1% over the chosen minimum reduction level and by 39.4% over a 61% reduction level. These results demonstrate the significant rise in required energy in the raw pellet processing. Energy consumption was selected as one of the criteria for evaluating the practical feasibility of each alternative.

3.4.4. Reducing Agent: Lignite—69% Reduction

As an alternative reducing agent, lignite was defined, which differs significantly from coke in terms of volatile combustible content, ash content, and moisture. The degree of Fe oxide reduction was determined based on experimental measurements [18,19] and calculations that were derived from the reactivity of lignite, the degree of Fe oxide reduction, and the residence time in the kiln. In this case, the minimum degree of Fe oxide reduction was set at 69%.

As the analysis shows, the rotary kiln can reach the temperatures required for reduction; however, the raw pellets only achieve these temperatures in the middle of the kiln, significantly shortening the time the raw pellets spend at temperatures above the minimum reduction temperature of approximately 950 °C.

From Figure 9a, it is evident that the residence time of the raw pellets at temperatures above 950 °C is around 40 min. Experiments indicate that the time required to achieve approximately 70% reduction of Fe oxides is about 70–80 min. This implies that to achieve a higher degree of reduction, either a longer kiln or a slower feed rate would be necessary.

3.4.5. Reducing Agent: Lignite—92% Reduction

The chosen reduction level of 92% Fe oxides represents the maximum possible reduction of iron oxides using lignite. The results of the temperature profile calculations for the flue gases and pellets along the length of the kiln are shown in Figure 10a.

Again, Figure 10a shows the short residence time of the raw pellets at temperatures above 950 °C, which is approximately 40 min. Experiments referenced in [18,19] indicate that the time required for over 90% reduction of iron oxides is 180 min.

Table 7. Material and energy balance for reduction with lignite.

Degree of Reduction	69%		92%
	kg/h	kg/t	kg/h	kg/t
Dry leach residue	53,190	1094.193	53,699	1104.669
Water in the leach residue	6393	131.5082	6454	132.7673
Dry matter in lignite	15,455	317.9388	20,857	429.0683
Water in the lignite	4773	98.18759	6441	132.5072
Added water	0	0	−1618	−33.2941
Raw pellets total	79,811	1641.827	85,833	1765.717
Water leach residue + lignite	11,165	229.684	13,138	270.2765
Dry matter in raw pellets	68,642	1412.059	75,962	1562.657
Added water	4	0.084647	−1649	−33.9219
Total water	11,169	229.7686	11,489	236.3546
Raw pellets total	79,811	1641.827	87,452	1799.011
Wet leach residue	59,583	1225.701	61,287	1260.769
Wet lignite	20,228	416.1264	27,814	572.1646
Added water	0	0	−1649	−33.9219
Raw pellets total	79,811	1641.827	87,452	1799.011
Pellets	48,611		48,611
	m3/h	m3/tpellets	m3/h	m3/tpellets
Gas consumption (NG)	800	16.45714	1350	27.77143
Air consumption	239,925	4935.596	268,920	5532.058
Produced flue gases	265,468	5461.054	299,497	6161.078
	MJ/h	GJ/tpellets	MJ/h	GJ/tpellets
Energy consumption	341,408	7.02325	478,511	9.843661

presents the calculated energy consumption values for the variant using lignite as the reducing agent. The results show an increase of 2.82 GJ/t of pellets, corresponding to a 28.65% increase in energy consumption.

3.4.6. Oxide Pellets: Without Reduction of Fe Oxides

Another option for utilizing the leach residue is the production of pellets without reducing agents. In this case, the reduction of iron oxides does not occur; rather, the process focuses on creating conditions or improving the properties of the pellets (abrasion resistance, absorbency, strength, etc.) for their further use.

The temperature profile of the raw pellet heating process, shown in Figure 11, illustrates a steady increase in pellet temperature depending on the heating regime in the rotary kiln. Heat transfer occurs through convection, radiation, and, most significantly, conduction between the pellets and the inner wall of the rotary kiln. The temperature of the pellets may be influenced by internal phase transformations within the pellet composition, though this change is negligible.

Natural gas is used for each stage of the process. For the production of oxide pellets, the residence time of the raw pellets in the rotary kiln (due to the absence of reduction) is less important; the primary concern is reaching the required pelletizing temperature.

As shown in

Table 8. Material and energy balance for oxide pellets without reduction.

	kg/h	kg/t
Dry leach residue	48,611	1000
Water in the leach residue	5842	120.1874
Added water	2421	49.81256
Raw pellets total	56,875	1170
Water in the leach residue	5842	120.1874
Dry matter in raw pellets	48,611	1000
Added water	2421	49.81256
Total water	8264	170
Raw pellets total	56,875	1170
Wet leach residue	54,454	1120.187
Added water	2421	49.81256
Raw pellets total	56,875	1170
Pellets	48,611
	m3/h	m3/tpellets
Gas consumption (NG)	2900	59.65714
Air consumption	134,515	2767.168
Produced flue gases	165,260	3399.639
	MJ/h	GJ/tpellets
Energy consumption	105,353	2.167269

, energy consumption is the lowest when compared to the energy consumption of other alternatives that use reducing agents. This alternative appears to be the most suitable from an energy efficiency standpoint. However, attention must be paid to the quality (% Fe in the pellet) and the cost of energy commodities. Currently, prices are changing dynamically depending on demand but especially due to the global social situation and extraordinary events around the world.

4. Discussion

Thermodynamic calculations indicate that it is possible to produce pellets with a reduction degree of iron oxides from the Sereď leach residue in the metallurgical facilities of Nižná Slaná, achieving 50–65% reduction. This corresponds to a residence time of the feedstock in the temperature zone of 950–1100° C for approximately 50–65 min (Figure 6a). A higher reduction degree is not feasible or would be inefficient due to technological constraints.

The calculations for the material’s residence time in the rotary kiln were based on a kiln length of 40 m, a kiln inclination of 3%, and a rotation speed of 0.5 revolutions per minute. The residence time in the kiln is approximately 103 min. At higher rotation speeds, the residence time in the kiln would decrease.

In the production of reduced pellets using coke as a reducing agent, it is possible to achieve a total Fe content of 60% in the produced pellets at a 50% reduction of iron oxides (Figure 1 and Figure 6b). In the Nižná Slaná technology, it is also possible to achieve a reduction of iron oxides to 62%, which would increase the total Fe content in the pellets to approximately 62% (Figure 1 and Figure 7a). Theoretically, the maximum increase in total Fe content in the pellets would be around 65% at a 92% reduction of iron oxides in the feedstock (Figure 1 and Figure 7b), but this alternative is unrealistic under the conditions of the facilities in Nižná Slaná and is likely economically inefficient.

In the production of reduced pellets using lignite as a reducing agent, it is possible to achieve a total Fe content of 60% in the produced pellets with a 69% reduction of iron oxides (Figure 1 and Figure 9a). However, this is beyond the operational limits of the Nižná Slaná technology in terms of the required residence time of the material in the kiln at the necessary temperatures for the reduction of iron oxides. When using lignite as a reducing agent, raw pellets can be preheated on the Lepol grate to a maximum temperature of 400 °C. At higher temperatures, volatile substances start to release, which cannot be economically burned before entering the chimney (due to the large volume of exhaust gases, 200,000–300,000 m³/h, at a relatively low temperature of around 200 °C).

A disadvantage of lignite as a reducing agent is its composition; in addition to high moisture content, it also has a high ash content, which remains in the pellets after reduction and reduces the total Fe content. Therefore, even with a 92% reduction of iron oxides, the total Fe content in the pellet only increases to about 62% (Table 4). The moisture content of the lignite also plays a crucial role; lignite with a moisture content higher than 23.6% should not be added to the feedstock. Higher moisture content degrades the quality of the feedstock and increases energy consumption for drying.

In the case of oxide pellet production, the process from a thermal–technical perspective involves only the drying and heating of the feedstock, with structural changes occurring at higher temperatures from a technological standpoint. The energy demand for this process is determined by the consumption of natural gas (Table 8).

Key data from the energy evaluation for various production scenarios of the feedstock from the Sereď leach residue (Fe concentrate SE552) are presented in

Table 9. Overall evaluation of calculation alternatives.

		Coke			Lignite		Oxidized Pellets
Alternative		C_50R	C_61R	C_92R	BC_69R	BC_92R	OX
Degree of reduction	%	50	61	92	69	92	0
Total Fe in pellet	%	60.3	61.7	65.5	60.4	62.2	55.2
Mass flow of raw pellets	t/h	69,694	72,916	82,247	79,811	87,452	56,875
Mass flow of pellets	t/h	48,611	48,611	48,611	48,611	48,611	48,611
Consumption of raw pellets per 1t of pellets	kg/t	1433.70	1499.98	1691.93	1641.83	1799.01	1170.00
Gas consumption	m3/t	18.51	20.57	41.14	16.46	27.77	59.66
Reducing agent consumption	kg/t	176.67	222.83	356.50	416.13	572.16	0.00
Energy consumption	GJ/t	4.835	5.997	9.894	7.023	9.844	2.167
Residence time in RK in reduction zone	Min	60	60	60	45	45	-
Required residence time in RK in reduction zone	Min	50	60	180	70	180	-
Combustion of preheated air in RK		Yes	Yes	Yes	Yes	Yes	No
Need for an afterburner/combustion chamber		Yes	Yes	Yes	Yes	Yes	Yes
Need for mixing chamber I.		Yes	Yes	Yes	Yes	Yes	Yes
Need for flue gas cogeneration I.		No	Yes	Yes	Yes	Yes	No
Need for flue gas cogeneration II.		No	No	Yes	No	No	No
Need for mixing chamber II.		Yes	Yes	Yes	Yes	Yes	Yes
Need for mixing chamber III.		Yes	Yes	Yes	Yes	Yes	Yes
Utilization of energy in cogeneration or heat exchanger	MW	0	3.799	34.685	7.460	24.02	0.000
Air consumption for the process	m3/t	3850	4276	5449	4936	5532	2767
Outgoing flue gas flow	m3/t	4201	4663	5941	5461	6161	3400
Flue gas temperature before entering the chimney	°C	165	183	187.5	167	182	132
Feasibility of the alternative		YES	YES	No	YES *	No	YES

* The alternative is feasible only under certain conditions.

.

Cooling the produced pellets with air in a cooler should be carefully considered, as it may lead to partial reoxidation of the reduced pellets. An alternative cooling method, such as indirect water cooling, should be explored. However, this would increase the consumption of natural gas in the rotary kiln by approximately 650 m³/h or increase the energy demand of the process for 50% reduction with coke to 5.32 GJ/t (an increase of 0.49 GJ/t) and would also require the establishment of a water management system.

A potential drawback of the rotary kiln process could be the introduction of combustion air for burning residual carbon during direct reduction and the combustion of a portion of CO from the reduction, as well as H₂ and hydrocarbons from the volatiles in the reducing agent. The most advantageous approach is to ensure the supply of air into the kiln’s working chamber from two to three locations (kiln entry—gas supply side; at one-quarter of the kiln; at half of the kiln). This would help to even out the combustion of carbon, CO, and volatiles in the kiln and ensure higher flue gas temperatures at the flue gas entry side, which could also lead to a partial reduction in natural gas consumption.

In the case of utilizing waste heat, it is possible to use cogeneration units without combustion, only with heat exchangers, due to the potential contamination of the exhaust gases from the afterburner. Two solutions were proposed for this scenario:

The first solution involves placing the cogeneration unit behind the mixing chamber located after the afterburner. For this case, an ORC-type cogeneration unit would be suitable. These units operate at lower input temperatures due to the properties of the heat transfer medium.

The second solution considers placing a cogeneration unit with indirect heating directly behind the afterburner. Such a cogeneration unit operates as an open Brayton cycle, using air as the working medium, which, after expansion, can be further utilized in the technological process, for example, as preheated air for the afterburner or the mixing chamber.

If we were to compare energy consumption in similar operations, for example, the study [38] reports the minimum energy consumption for selected processes in steel production. The authors indicate the necessary minimum energy, and for the reduction of iron oxides, they calculated an energy consumption of 8.6 GJ/t. In another work [39], the authors describe the energy consumption during the pelletizing process. The overall energy consumption for pellet production, compared to study [38], is particularly interesting, as it is only 793.4 MJ/t of pellets produced. In another study [40], the authors compared energy consumption in the production of pellets from hematite and magnetite, where the energy consumption ranged between 1.2 and 1.7 GJ/t of pellets produced.

These studies indicate that it is possible to reduce energy consumption and thereby operational costs by introducing more modern technologies or by modernizing existing ones. However, it is very difficult to compare each technology fully due to the specificity of the equipment and input materials, which makes it necessary to analyze the possibilities for modifications or the introduction of more environmentally friendly and energy-efficient technologies. The answer to these challenges lies in the energy and material balance of the entire process, which was also the authors’ aim in this article.

For comparing energy consumption in similar operations, it is essential to consider the processing method and the equipment used. Comparing alternatives with a reduction degree of 50–69%, energy consumption ranges from 4.835 to 7.023 GJ/t of pellets produced. In the production of oxide pellets, where no reducing agent was used, the total energy consumption is only 2.167 GJ/t of pellets produced. This suggests that the described technology in Nižná Slaná has the potential for producing pellets from metal-bearing waste.

5. Conclusions

The authors conducted a material and energy evaluation of the process for processing raw pellets made from waste material that has not yet been utilized. In line with environmental policy goals for the years 2030 and 2050, European countries are interested in addressing such environmental issues.

One advantage of the waste from the Sereď leach residue dump is its high Fe content, which can be utilized in the metallurgical industry either as sinter or pellets. The study of the energy assessment for processing raw pellets from the Fe concentrate SE52 leach residue demonstrated the feasibility of processing these materials in the decommissioned Nižná Slaná metallurgical plant. The calculations were based on the actual parameters of the existing equipment, which could be repurposed for waste disposal and utilization. The advantage lies in the existence of equipment that could be brought back into operation with additional investments in renovation and environmental upgrades.

The calculation results showed that from an energy and process perspective, it is feasible to produce pellets with a reduction degree of Fe oxides between 50 and 65%. The rotary kiln parameters proved to be suitable for processing raw pellets from the Fe concentrate SE52 leach residue. Coke and lignite were used as reducing agents for direct reduction in the raw pellets, and their suitability was confirmed by calculations. The high carbon content in these reducing agents—69.95% in coke and 41.36% in lignite—contributed to this suitability. However, the high moisture content in lignite was identified as a challenge, as it adversely affects the processing of raw pellets and increases the energy demands of the entire process. A higher degree of Fe oxide reduction can be achieved at the cost of increased energy consumption, with a 92% reduction requiring 40% more energy compared to a 61% reduction with coke and a 69% reduction with lignite.

Experiments with leach residue samples showed that the degree of Fe oxide reduction could be further increased by changing the reducing agent to hydrogen (Figure 1). The research on using different reducing agents is ongoing, with oil showing promise due to its high carbon content of 76.95%. However, a drawback of using oil as a reducing agent is its rapid evaporation in the drying chamber, which would require redesigning the exhaust system for afterburning volatiles from the oil.

This study fulfilled its purpose, and the recommendations based on the material and energy balance indicate the feasibility in reviving the decommissioned technology. The processed pellets are intended for use as part of the charge in the production of pig iron at a nearby metallurgical plant.