# Modeling and Simulation of the Off-gas in an Electric Arc Furnace

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## Abstract

The following paper describes an approach to process modeling and simulation of the gas phase in an electric arc furnace (EAF). The work presented represents the continuation of research by Logar, Dovžan, and Škrjanc on modeling the heat and mass transfer and the thermochemistry in an EAF. Due to the lack of off-gas measurements, Logar *et al*. modeled a simplified gas phase under consideration of five gas components and simplified chemical reactions. The off-gas is one of the main continuously measurable EAF process values and the off-gas flow represents a heat loss up to 30 pct of the entire EAF energy input. Therefore, gas phase modeling offers further development opportunities for future EAF optimization. This paper presents the enhancement of the previous EAF gas phase modeling by the consideration of additional gas components and a more detailed heat and mass transfer modeling. In order to avoid the increase of simulation time due to more complex modeling, the EAF model has been newly implemented to use an efficient numerical solver for ordinary differential equations. Compared to the original model, the chemical components H_{2}, H_{2}O, and CH_{4} are included in the gas phase and equilibrium reactions are implemented. The results show high levels of similarity between the measured operational data from an industrial scale EAF and the theoretical data from the simulation within a reasonable simulation time. In the future, the dynamic EAF model will be applicable for on- and offline optimizations, *e.g*., to analyze alternative input materials and mode of operations.

## List of symbols

## Greek letters

*λ*Latent heat of fusion

*ν*Stoichiometric coefficient

*ν*′Stoichiometric coefficient of the forward reaction

*ν*″Stoichiometric coefficient of the backward reaction

*ρ*Density

## Latin letters

- \( \Updelta H_{T}^{0} \)
Reaction enthalpy at temperature

*T*and standard pressure*p*^{0}- ΔH
_{298}^{0} Standard formation enthalpy at standard temperature (298 K) and standard pressure

*p*^{0}- \( \Updelta H_{{{\text{T}} - ()}}^{0} \)
Standard formation enthalpy at

*T*and standard pressure*p*^{0}for a specific reaction- \( \Updelta_{\text{R}} G^{0} \)
Free standard enthalpy

*A*Reacting element of the reaction \( |\nu_{\text{A}} |A + |\nu_{\text{B}} |B \to |\nu_{\text{C}} |C + |\nu_{\text{D}} | \)

*B*Reacting element of the reaction \( |\nu_{\text{A}} |A + |\nu_{\text{B}} |B \to |\nu_{\text{C}} |C + |\nu_{\text{D}} |D \)

*c*Concentration

*C*Reagent of the reaction \( |\nu_{\text{A}} |A + |\nu_{\text{B}} |B \to |\nu_{\text{C}} |C + |\nu_{\text{D}} |D \)

*C*_{p}Heat capacity

*D*Reagent of the reaction \( |\nu_{\text{A}} |A + |\nu_{\text{B}} |B \to |\nu_{\text{C}} |C + |\nu_{\text{D}} |D \)

*h*_{d}Characteristic dimension of duct are at the slip gap

*k*Reaction rate constant

*k*_{b}Backward reaction rate constant

*k*_{f}Forward reaction rate constant

*k*_{u}Dimensionless constant

- kd
Empirical velocity coefficient

- kd
_{C-1} Empirical velocity coefficient for oxidation of dissolved C with injected O

_{2}to CO- kd
_{C-2} Empirical velocity coefficient for oxidation of dissolved C with injected O

_{2}to CO_{2}- kd
_{C-3} Empirical velocity coefficient for dissolving of injected C

- kd
_{C-4} Empirical velocity coefficient for dissolving of C from charged coal

- kd
_{C-5} Empirical velocity coefficient for oxidation of injected C with O

_{2}from gas phase to CO- kd
_{C-6} Empirical velocity coefficient for oxidation of C from charged coal with O

_{2}from gas phase to CO- kd
_{C-D} Empirical velocity coefficient for dissolving C in melt

- kd
_{C-L} Empirical velocity coefficient for decarburization

- kd
_{CO-1} Empirical velocity coefficient for oxidation of CO with O

_{2}from the gas phase to CO_{2}- \( {\text{kd}}_{{{\text{CH}}_{4} {\text{ - post}}}} \)
Empirical velocity coefficient for oxidation of CH

_{4}with O_{2}from the gas phase- kd
_{comb} Empirical velocity coefficient for the oxidation of combustible material

- kd
_{gas-(ξ)} Empirical velocity coefficient of equilibrium reaction in gas phase (ξ = (q), (r), (s))

- \( {\text{kd}}_{{{\text{H}}_{2} {\text{ - post}}}} \)
Empirical velocity coefficient for oxidation of H

_{2}with O_{2}from the gas phase to H_{2}O- \( {\text{kd}}_{{{\text{H}}_{2} {\text{O}}}} \)
Empirical velocity coefficient for the dissociation of water

- kd
_{Mn-1} Empirical velocity coefficient for MnO decarburization

*K*Fractions of mass, which is available for a specific reaction

- K
_{burn-(n)} Fraction of the burner reaction volume for the reaction (n

_{1}), (n_{2}), or (n_{3})- \( K_{{{\text{leakair - O}}_{2} {\text{ - CO(1)}}}} \)
Fraction of O

_{2}, sucked in with leak air, available for the oxidation of injected C to CO- \( K_{{{\text{leakair - O}}_{2} {\text{ - CO(2)}}}} \)
Fraction of oxygen, sucked in with leak air, available for the oxidation of C from charged coal to CO

- \( K_{{{\text{O}}_{2} {\text{ - CH}}_{4} {\text{ - inj}}}} \)
Fraction of O

_{2}injected with CH_{4}from burners available for the direct combustion of CH_{4}- \( K_{{{\text{O}}_{2} {\text{ - CO}}}} \)
Fraction of injected O

_{2}available for the oxidation of dissolved C to CO- \( K_{{{\text{O}}_{2} {\text{ - CO}}_{2} }} \)
Fraction of injected O

_{2}available for the oxidation of dissolved C to CO_{2}- \( K_{{{\text{O}}_{2} {\text{ - post - CO}}}} \)
Fraction of injected O

_{2}available for the oxidation of CO to CO_{2}*K*_{c}*or K*_{c-(ξ)}Equilibrium constant (

*ξ*= (q), (r), (s))*K*_{p}Standard equilibrium constant

*K*_{PR}Constant defining the ration between mass flow and pressure

*K*_{sSc–lSc}Correction factor, which includes the influence of solid scrap on the size of the reaction surface of lSc

*m*Mass

- \( \dot{m} \)
Mass flow

- \( \dot{m}_{\rm el} \)
Mass flow of C released from electrode consumption

- \( \dot{m}_{\text{water-in}} \)
Mass flow of water from electrode cooling

- \( \dot{m}_{\rm solidify} \)
Mass flow from liquid to solid scrap if solidification occurs

*M*Molar mass

*p*Pressure

*p*^{0}Pressure at standard conditions

*p*_{i}Partial pressure of element

*i**p*_{r}Relative pressure in EAF

*P*Power

*Q*_{lSc-chem}Heat from chemical reactions in melt

*Q*_{gas-chem}Heat from chemical reaction in gas phase

- \( \dot{Q} \)
Heat flow

*r*Molar reaction rate

*r*_{(ξ)}Molar reaction rate (

*ξ*= (q), (r), (s))*R*_{m}Molar gas constant

*t*Time

*t*_{tap}Tap time

*T*Temperature

*u*_{1}Off-gas mass flow

*u*_{2}Slip gap width

*V*Volume

*V*_{(ξ)}Reaction volume of equilibrium reaction (

*ξ*= (q), (r), (s))*w*Weight fraction

*x*_{(ξ)}Fraction of reaction volume of equilibrium reaction in the gas phase volume

*xi*Mass flow of element

*i**X*_{i}Molar fraction of element

*i*- \( X_{i}^{\text{eq}} \)
Equilibrium molar fraction of element

*i*in a specific reaction*Z*Actual mixing fraction of the supplied gas volume flows

*Z*_{St-(n)}Stoichiometric mixing fraction of the reaction (n

_{1}), (n_{2}), or (n_{3})

## Subscripts—Greek letters

*ξ*Equilibrium reaction (

*ξ*= (q), (r), (s))

## Subscripts—Latin letters

- air
Ambient air

- addition
Added to a phase

*xx*- b
Backward

- C-inj
With lances injected carbon

- C-D
Carbon dissolved in melt

- C-L
Carbon present in EAF

- C-S
Solid carbon

- CH
_{4}-inj Injected methane from burners

- CH
_{4}-in-natgas Methane in injected natural gas mass flow in burners

- coal
Charged coal

- f
Forward

- gas
Gas phase in the EAF

- H
_{2}O-gas Gaseous water

*i*Element (

*i*=1: C in EAF;*i*= 1coal: C from charged coal;*i*=2: dissolved C;*i*= 9: CO;*i*=10: CO_{2};*i*=11: N_{2};*i*=12: O_{2},*etc*.)*j*Number of individual mass flow (

*xi*_{dj})- i,meas
Measured value of property of element

*i*- i,sim
Simulated value of property of element

*i*- leakair
Leak air

- lSc
Liquid scrap phase in EAF

- lSl
Liquid slag phase in EAF

- melt,sSc
Melting point of solid scrap

- N
_{2}-air Nitrogen in ambient air

- N
_{2}-in-natgas Nitrogen in injected natural gas mass flow in burners

- N
_{2}-in-oxygen Nitrogen in injected O

_{2}mass flow- O
_{2}-air Oxygen in ambient air

- O
_{2}-CH_{4}-inj Oxygen injected with CH

_{4}in burners- O
_{2}-gas Oxygen in gas phase

- O
_{2},lance With lances injected oxygen

- O
_{2}-in-oxygen Oxygen in injected O

_{2}mass flow- O
_{2}-post Oxygen injected for post-combustion

- sSc
Solid scrap phase in EAF

- sSc,basket
Solid scrap charged with basket

*xx*Phase (sSc, lSc, sSl, lSl, gas, wall, el, arc)

## Abbreviations

- BDF
Backward differentiation formula

- Comb
Combustible material

- EAF
Electric arc furnace

- El
Electrode

- lSc
Liquid scrap

- lSl
Liquid slag

- meas
Measured

- NDF
Numerical differentiation formula

- ODE
Ordinary differential equations

- sim
Simulated

- sSc
Solid scrap

- sSl
Solid slag

- St
Stoichiometric

## Introduction

Electric steelmaking in an electric arc furnace (EAF) is the main process route for steel scrap recycling and the second most important steel production route in the world. As an energy-intensive process, the EAF is responsible for approximately 3 pct of the total industrial electricity consumption and a significant lever for energy efficiency optimization.[1] As the off-gas flow represents an energy output of 20 to 30 pct of the total EAF energy input, the off-gas is in the focus of current developments to increase the energy and resource efficiency of the EAF. As one of the main continuously measurable process values, the off-gas composition can be utilized to improve the process control and allows conclusions to be made concerning the process behavior. Here, process models have proven their applicability for process control and their capability to contribute toward a more detailed understanding of heat and mass transfer during the melting process. In times of continuously growing computational capacity, the complexity of the dynamic process simulation models has increased due to the consideration of more and more phenomena. Logar *et al*.[2, 3, 4] presented a comprehensive deterministic EAF model, which is based on fundamental physical and mathematical equations. The model includes all main thermal, chemical, and mass transfer phenomena in the EAF. These are implemented *via* first-order ordinary differential equations (ODEs). It was further developed and enhanced with a more detailed simulation of the arc heat distribution and a modified chemical module.[5,6] Due to the lack of off-gas data from the validation furnace, the gas phase was simplified. Five chemical components are taken into account and chemical reactions are only considered for post-combustion. As one of the best recently published EAF models, it was found to be suitable a starting point for further development of the gas phase modeling, which is described within this paper, which is therefore a continuation of the work done by Logar *et al*.

A detailed literature review shows that there are other papers addressing the modeling of the gas phase in an EAF, but with different approaches and simplifications. Opitz and Treffinger[7] use the model of Logar *et al*. to design a dynamic, physics-based model of a complete EAF plant which consists of four sub-systems (vessel, electric system, electrode regulation, and off-gas system). Matson and Ramirez[8,9] consider six chemical elements in the off-gas and determine the reaction rates with a chemical equilibrium algorithm by Gibbs free energy minimization. The simulation calculation time is not mentioned and is assumed slow compared to other approaches. Furthermore, the results of the gas phase simulation are not compared to measured data and the curves show a constant behavior over long periods. MacRosty and Swartz[10] consider all relevant species in the gas zone and assume chemical equilibrium in each zone. The model does not address gas radiation and requires a high computing capacity. Nyssen *et al*.[11] published another EAF model. The model seems to include all major processes, but no details are given in the publication.

The objective of this work was to consider all major measurable gas components in an EAF process model. Therefore, in addition to CO, CO_{2}, N_{2}, O_{2}, and CH_{4}, the components H_{2}, H_{2}O, and CH_{4} are also included in the gas phase of this study. The components are considered in chemical reactions for post-combustion, major equilibrium reactions, and dissociation. To prevent the increase of simulation time, the EAF model was newly implemented in MATLAB to use the internal ODE-solver instead of the fixed step Euler method, which was chosen by Logar *et al*.

The further development is based on an industrial scale 140 t EAF. The operational data of the EAF are used for the model parametrization and final validation of the simulation results. The input powers and mass flows of the periphery are used as input data for the simulation. The simulation results are evaluated concerning off-gas composition, temperature, and energy.

## Modeling

*et al*.[2,3] Therefore, the paper follows the basic assumptions and simplifications as addressed in part 1[2] and part 2[3] of the EAF model publication from Logar

*et al*., which are also valid for this enhanced model and will not be repeated in this paper. The EAF is divided into eight different zones:

- (1)
Solid scrap (sSc),

- (2)
Liquid scrap (lSc),

- (3)
Solid slag (sSl),

- (4)
Liquid slag (lSl),

- (5)
Gas phase (gas),

- (6)
Walls (wall),

- (7)
Electrode/s (el),

- (8)
Electric arc/s (arc).

Each zone and chemical component has assigned physical properties, *i.e*., specific heat capacity *C* _{p}, density *ρ*, molar mass *M*, *etc*. The values used for the parameters are listed in Appendix in Table V.

### New Model Implementation

To overcome the contradiction between simulation accuracy, simulation calculation time, and numerical integration time steps, the EAF model has been newly implemented to use efficient ODE-solving methods within the software MATLAB. While Logar *et al*.[2] used a fixed step Euler method with a chosen time step of 10^{−4} seconds, numerical integration methods with a variable calculation of the integration time step have proven their efficiency to solve complex ODE-systems.[12]

The usage of the MATLAB ODE-solving methods required several model modifications. Sudden changes caused by if-else conditions were replaced by continuous algorithms to realize on/off behavior. In detail, the variable that has to be switched is multiplied with a modified hyperbolic tangent function, which results in values of zero and one with a continuous transition. Furthermore, the calculation of the melting geometry is performed by modeling the scrap heap as a body of revolution around the middle axis of the EAF. A variable angle of the borehole in the scrap is used to determine the geometrical data for the view factor calculation.[13]

*xx*(with mass

*m*

_{ xx }, temperature

*T*

_{ xx }, and heat capacity

*C*

_{p,xx}) changes its temperature due to adding a mass (with mass flow \( \dot{m}_{\rm addition}, \) temperature

*T*

_{addition}, and heat capacity

*C*

_{p,addition}) by the temperature rate \( \frac{{{\text{d}}T_{xx} }}{{{\text{d}}t}}. \) The resulting net heat flow is \( \dot{Q}_{\text{xx}} , \) which is positive or negative, depending on the temperature difference (

*T*

_{ xx }−

*T*

_{addition}). One example is the temperature change of the liquid steel melt (lSc), which is calculated according to Eq. [2]:

*λ*

_{sSc}is the latent heat of fusion, \( \dot{m}_{\rm sSc} \) is the negative mass change rate of scrap, \( \dot{m}_{{{\text{O}}_{2} {\text{ - lance}}}} \) and \( \dot{m}_{\text{C-inj}} \) are the injection of oxygen and carbon into the melt, and

*T*

_{i}are the corresponding temperatures with the ambient temperature

*T*

_{air}.

After the re-implementation, it was found that the ODE-system of the model is stiff. As the multi-step backward differentiation formula/numerical differentiation formula (BDF/NDF) solver ode15s is most suitable for stiff ODE-systems and delivered best results in terms of accuracy and speed, it was chosen for future developments. Further investigation on numerical solution methods for EAF modeling was done by Meier *et al*.[12]

### Relevant Chemical Off-gas Elements

The gas phase (gas) in Logar’s model consists of the five elements CO, CO_{2}, N_{2}, O_{2}, and CH_{4}, where total combustion of CH_{4} is assumed.[2,3] Due to the fact that the H_{2}O and H_{2} mass fractions reach significant values during off-gas composition measurements, whereby CH_{4} is detected in the off-gas as well, those elements are considered in the gas phase of the new enhanced EAF model using the following modifications. The mass flows of H_{2}, H_{2}O, and CH_{4} into the EAF and their outflow due to the off-gas removal and blow out are described in the following section as well as the chemical reactions and the reaction enthalpies.

### Chemical Reactions

*e.g*., due to electrode consumption and contaminants adhering to the scrap, such as paint or plastics. They are assumed to be nonane (C

_{9}H

_{20}). Logar

*et al*.[3] defined 15 reactions (a) to (p) [(o) is missing] which are occurring in the liquid melt, the lSl, and the gas phase. The reaction equations (a) to (m) were adopted unchanged. The reactions concerning methane (n) and nonane (p) were slightly adapted and further reactions [from (q) to (u)] were implemented for the gas phase. The altered and added reactions are listed in Eq. [3]:

These reactions present the enhancement of the current models gas phase. They mainly effect the rates of change of elements and the calculation of reaction enthalpies. This is addressed in the following section.

#### Equilibrium reactions

*r*can be determined by Eq. [4], while the equilibrium constant

*K*

_{ c }is determined by the forward and backward reaction rate constant according to Eq. [5]. The mole concentrations

*c*

_{ i }are obtained using Eq. [6].[15]

Here, \( v_{i}^{\prime} \) and \( v_{i}^{\prime\prime} \) represent the stoichiometric coefficients of the forward (′) and backward (″) reaction.

*k*

_{f}and

*k*

_{b}from

*K*

_{c}or other data available to the model. Therefore, to be able to solve the equation, the backward reaction rate constant is assumed to be

*k*

_{b}= 1, leading to the simplified Eq. [7]. In addition, in Eq. [10] an empirical velocity coefficient is added.

*K*

_{c}can be determined by the idea of the free Gibbs energy minimization through Eqs. [8] and [9]:

*K*

_{p}is the standard equilibrium constant,

*Δ*

_{ R }

*G*

^{0}represents the free standard enthalpy,

*p*

^{0}is the pressure at standard conditions,

*p*

_{ i }is the partial pressure, and

*R*

_{m}is the molar gas constant.

*K*

_{c}is pre-calculated for each of the three equilibrium reactions with the help of the chemical equilibrium toolbox

*MediumModel*[16] within MATLAB, based on the “NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species” and stored in a temperature-dependent database. The database is evaluated at each time step with a corresponding temperature to obtain the equilibrium constant

*K*

_{c-(ξ)}for the equilibrium reaction [

*ξ*= (q), (r), and (s)]. The mass change for each element is then calculated using Eq. [10]:

*V*

_{(ξ)}is the available volume for the reaction and kd

_{gas-(ξ)}is an empirical velocity coefficient. These velocity coefficients either were taken from Logar

*et al*.[3] or were developed during the parameterization of the modified model using the available operating data. They are listed in Table II in Appendix.

In contrast to the described equilibrium reactions above, the dissociation of H_{2}O, which is the reverse reaction of Eq. [3t], is modeled using a simplified empirical approach which is described later.

#### Rate of change of carbon (C)

Since carbon is involved in reactions within the gas phase, the equations of the carbon mass transfer were modified in comparison to those of Logar *et al*.[3] In accordance with Logar and for a better overview, the mass flows of the respective elements *i* are divided based on their physical–chemical cause. These individual mass flows are denoted by the variable *xi* _{dj} (*j* = number for the individual mass flow). With their summation, the net mass flow of the element *i* (\( \dot{m}_{i} \)) is determined.

The rate of change of carbon is calculated for three different masses of C in the EAF: first, the mass of C present in the EAF (*m* _{C-L}), second, the dissolved C in the liquid melt (*m* _{C-D}), and third, the C from charge coal (*m* _{coal}).

*m*

_{C-L}): C is injected in the furnace (

*x*1

_{d1}). This injected C and the C present in the EAF are used in the decarburization of the melt (

*x*1

_{d2}). Furthermore, C is dissolved in the melt (

*x*1

_{d3}). C is formed during the dissociation of combustible material. This amount and the C from charged coal are available for further reactions (

*x*1

_{d4}). During the oxidation of C to CO with the oxygen of the gas phase (

*x*1

_{d5}) and with leak air (

*x*1

_{d6}), C is used. Finally, C is taking part in the heterogeneous water–gas reaction Eq. [3s] (

*x*1

_{d7}). The rate of change of C present in the EAF (\( \dot{m}_{\text{C-L}} \)) is given by Eq. [11]:

The equation for the variable *x*1_{d2} is an empirical equation, which was developed during the parameterization of the adapted model using the available operating data. kd_{C-L} is the constant decarburization velocity and *m* _{lSl} is the total slag mass. The second summand (0.6*x*1_{d1}) represents a direct reaction of injected C with FeO. *V* _{sSc} is the actual bulk volume of the sSc and *V* _{sSc,basket} is the initial charged volume of sSc. The factor causes the chemical reaction in the simulation to start with increasing molten mass. If the furnace is full of scrap, the injected C does not reach the melt surface.

The equation for *x*1_{d3} is also an empirical equation, which resulted from the adaptation of Logar’s equation during parameterization. The equation is dependent on the constant dissolving velocity kd_{C-3}, the temperatures of the melt *T* _{lSc}, of the ambient air *T* _{air} and the scrap’s liquidus temperature *T* _{melt,sSc}, the heat capacities of C *C* _{p,C} and the melt *C* _{p,lSc}, and the latent heat of fusion of C *λ* _{C}.

The combustible material consists of nonane and is denoted by \( \dot{m}_{\rm comb} .\)

kd_{C-5} is the constant C oxidation velocity. *K* _{sSc–lSc} is the exposure coefficient of the liquid bath, because the reactionary surface of the melt decreases with increasing sSc volume. \( c_{{{\text{O}}_{2} {\text{ - gas}}}} \) is the concentration of oxygen in the gas phase.

\( w_{{{\text{O}}_{2} {\text{ - air}}}} \) is the mass fraction of O_{2} in the ambient air, which is sucked in as leak air \( \dot{m}_{\rm leakair} \) through the slag door and other gaps. \( K_{{{\text{leakair - O}}_{2} {\text{ - CO}}(1)}} \) is the fraction of leak air available for direct C combustion to CO. The equation is divided into two cases, because otherwise the simulation would lead to negative masses as calculation results.

*x*1

_{d5}and

*x*1

_{d6}are based on the empirical reaction kinetic approach according to Eq. [12] for the reaction given by Eq. [13]:

*A*and

*B*are reactants with the concentration

*c*

_{A}or

*c*

_{B}. The stoichiometric coefficients are signified with

*ν*, while

*k*is the corresponding reaction rate.

*r*

_{(s)}in

*x*1

_{d7}follows Eqs. [14] and [15]. The database for

*K*

_{c}is evaluated for the assumed average temperature between the gas phase and the lSc. The reaction volume

*V*

_{(s)}is determined for each equilibrium reaction

*ξ*by Eq. [16] as a fraction of the total gas volume

*V*

_{gas}.

*p*

_{r}, the total mass flow of leak air enters the furnace. This is determined by Eq. [17] with

*K*

_{PR}representing a constant defining the ratio between mass flow and pressure:

*x*1coal

_{d1}) is transferred from

*m*

_{coal}to

*m*

_{C-L}for decarburization, dissolving, and combustion. Analogous to

*x*1

_{d5}and

*x*1

_{d6}, the amount of C from coal decreases due to the combustion of C to CO with the oxygen from the gas phase (

*x*1coal

_{d2}) and from the leak air (

*x*1coal

_{d3}). C is taking part in the Boudouard reaction Eq. [3r] (

*x*1coal

_{d4}). The mass change \( \dot{m}_{\rm coal} \) is given by Eq. [18]:

_{C-4}and kd

_{C-6}represent the coal reactivity coefficients. The equations for

*x*1coal

_{d1}and

*x*1coal

_{d2}are developed empirical equations, which were validated by means of parametrization. The calculation of

*r*

_{(r)}follows Eqs. [19] and [20], whereby the database for

*K*

_{c}is evaluated for the assumed average temperature.

*X*

_{ i }and \( X_{i}^{\text{eq}} \) are the molar fractions and equilibrium molar fractions, respectively, kd

_{C-D}is the FeO decarburization rate, kd

_{C-1}and kd

_{C-2}are the oxidation rates of C to CO and CO

_{2}, respectively, kd

_{Mn-1}is the MnO decarburization rate, and \( K_{{{\text{O}}_{2} {\text{ - CO}}}} \) and \( K_{{{\text{O}}_{2} {\text{ - CO}}_{2} }} \) are representing the fractions of the lanced oxygen used for direct oxidization. The two change rates \( \dot{m}_{\text{C-L}} \) and \( \dot{m}_{\text{C-D}} \) can be further improved by the solution presented by Fathi

*et al*.[5] All other rates of change for the components of the steel and slag zone are not changed and are implemented according to Logar

*et al*.[3]

#### Rate of change of carbon monoxide (CO)

*x*9

_{d1}) and through openings (

*x*9

_{d4}). CO is produced during the incomplete oxidation of C from coal, injected carbon (

*x*9

_{d2}), and CH

_{4}(

*x*9

_{d8}). Furthermore, sources are electrode oxidation and the oxidation of coal (

*x*9

_{d6}). CO is consumed by the CO post-combustion (

*x*9

_{d3}) and changed due to the equilibrium reactions of the homogeneous water–gas shift reaction (

*x*9

_{d5}), the Boudouard reaction (

*x*9

_{d7}), and the heterogeneous water–gas reaction (

*x*9

_{d9}). The rate of change of CO is obtained by Eq. [22]:

The equation for *x*9_{d1} is equal to Logar *et al*.’s[3] implementation with *h* _{d} being the characteristic dimension of the duct area at the slip gap, *u* _{1} is the off-gas mass flow, *k* _{u} is a dimensionless constant and set to the same value as proposed by Bekker *et al*.,[17] and *u* _{2} is the slip gap width.

kd_{CO-1} is the reaction velocity of the CO post-combustion. In order to promote this reaction in the EAF, an oxygen mass flow \( \dot{m}_{{{\text{O}}_{2} {\text{ - post}}}} \) is injected *via* lance. Furthermore, \( K_{{{\text{O}}_{2} {\text{ - post - CO}}}} \) is the fraction of this post-combustion O_{2} mass flow used for CO post-combustion.

The outflow of gas through openings is modeled analogously to the inflow of leak air in Eq. [16]. If an overpressure prevails in the vessel, furnace gas is discharged.

*r*

_{(q)}of

*x*9

_{d5}is determined with the equilibrium constant

*K*

_{c-(q)}by Eqs. [23] and [24]:

_{gas-(q)}is the reaction velocity of the homogeneous water–gas shift reaction and is—like all other reaction velocities kd—given in Table II in Appendix.

The graphite electrode oxidizes during the EAF operation. A minor mass of C (\( \dot{m}_{\rm el} \)) releases, which can react with the gas phase. The corresponding calculation is described in Logar *et al*.[3]

#### Rate of change of carbon dioxide (CO_{2})

_{2}is extracted with the off-gas (

*x*10

_{d1}) and flows out through openings (

*x*10

_{d7}). CO

_{2}arises from CO post-combustion (

*x*10

_{d2}), CH

_{4}combustion (

*x*10

_{d4}and

*x*10

_{d6}), and from dissolved C oxidation (

*x*10

_{d8}). CO

_{2}takes part in the equilibrium reactions of the homogeneous water–gas shift reaction (

*x*10

_{d3}) and the Boudouard reaction (

*x*10

_{d5}). The rate of change of CO

_{2}is obtained by Eq. [25]:

#### Rate of change of nitrogen (N_{2})

*x*11

_{d1}) and the outflow through openings (

*x*11

_{d2}for

*p*

_{r}> 0). For a negative relative pressure, N

_{2}is sucked in with the leak air (

*x*11

_{d2}for

*p*

_{r}< 0). Furthermore, N

_{2}is injected together with the injected O

_{2}, CH

_{4}, and C mass flows (

*x*11

_{d3}). Compared to Logar

*et al*.,[3] the rate of change of N

_{2}is supplemented by

*x*11

_{d3}and determined by Eq. [26]:

*w*

_{ i }are the mass fractions of the following mass flows. \( w_{{{\text{N}}_{2} {\text{ - air}}}} \) is the mass fraction of N

_{2}in the leak air, \( w_{{{\text{N}}_{2} {\text{ - in - natgas}}}} \) and \( w_{{{\text{CH}}_{4} {\text{ - in - natgas}}}} \) are the mass fractions of N

_{2}and CH

_{4}in the injected natural gas, respectively, \( w_{{{\text{N}}_{2} {\text{ - in - oxygen}}}} \) and \( w_{{{\text{O}}_{2} {\text{ - in - oxygen}}}} \) are the mass fractions of N

_{2}and O

_{2}in the injected oxygen mass flows. Therefore, the considered O

_{2}is injected

*via*lance for the reduction of Fe (\( \dot{m}_{{{\text{O}}_{2} {\text{ - lance}}}} \)),

*via*tuyere for post-combustion (\( \dot{m}_{{{\text{O}}_{2} {\text{ - post}}}} \)), and

*via*the burner system (\( \dot{m}_{{{\text{O}}_{2} {\text{ - CH}}_{4} {\text{ - inj}}}} \)).

#### Rate of change of oxygen (O_{2})

_{2}is extracted with the off-gas (

*x*12

_{d1}) and flows out through openings in the EAF vessel (

*x*12

_{d7}for

*p*

_{r}> 0). For a negative relative pressure, O

_{2}is sucked in with leak air (

*x*12

_{d7}for

*p*

_{r}< 0). Further, a residual O

_{2}mass flow remains of all O

_{2}lanced into the gas phase (

*x*12

_{d2}) due to incomplete oxidation reactions,

*e.g*., during the oxidation of dissolved C in the liquid melt (

*x*2

_{d2}and

*x*2

_{d5}), Si (

*x*3

_{d2}), Cr (

*x*5

_{d2}), P (

*x*6

_{d2}), and Fe (

*x*7

_{d3}). O

_{2}is injected with the natural gas though the burner system into the EAF (\( \dot{m}_{{{\text{O}}_{2} {\text{ - CH}}_{4} {\text{ - inj}}}} \)), which reacts with CH

_{4}in different burner zones (

*x15*

_{ di }) and leaves a residual O

_{2}mass flow (

*x*12

_{d3}). O

_{2}is injected (\( \dot{m}_{{{\text{O}}_{2} {\text{ - post}}}} \)) for CO post-combustion (

*x*9

_{d3}) and leaves a residual mass flow (

*x*12

_{d4}). The oxidation of the electrodes consumes O

_{2}(

*x*12

_{d5}) as well as the combustion of coal and C in the EAF (

*x*12

_{d6}). In addition, the post-combustion of CH

_{4}(

*x*12

_{d8}) also uses up O

_{2}. The post-combustion of H

_{2}(

*x*13

_{d4}) is combined with the dissociation of H

_{2}O (

*x*14

_{d5}) in the change of O

_{2}(

*x*12

_{d9}). The total rate of change of O

_{2}is determined with Eq. [27]:

#### Rate of change of hydrogen (H_{2})

_{2}is extracted with the off-gas (

*x*13

_{d1}) and flows out through openings (

*x*13

_{d2}). There is an assumed H

_{2}residual mass flow caused by an incomplete CH

_{4}combustion from burners (

*x*13

_{d3}). H

_{2}is produced during the dissociation of combustible materials (

*x*13

_{d7}) and H

_{2}is consumed during post-combustion (

*x*13

_{d4}). Furthermore, H

_{2}takes part in the equilibrium reactions of the heterogeneous (

*x*13

_{d5}) and homogeneous water–gas reactions (

*x*13

_{d6}). The rate of change is obtained by Eq. [28]:

_{2}post-combustion.

#### Rate of change of water vapor (H_{2}O)

_{2}O is extracted with the off-gas (

*x*14

_{d1}) and flows out through openings (

*x*14

_{d2}) and enters the EAF

*via*the electrode cooling (

*x*14

_{d3}). To decrease the electrode consumption, the graphite electrode is equipped with a water spray cooling system at its top. The water (\( \dot{m}_{\text{water-in}} \)) flows down the electrode and evaporates, whereby a part of the steam is assumed to enter the EAF vessel. Furthermore, H

_{2}O is a product of the CH

_{4}(

*x*14

_{d4}and

*x*14

_{d6}) and H

_{2}combustion (

*x*14

_{d7}). H

_{2}O takes part in the equilibrium reactions of the heterogeneous (

*x*14

_{d8}) and homogeneous water–gas reactions (

*x*14

_{d9}).

*x*14

_{d5}describes a simplified exponential approach for the dissociation of water, as the dissociation is encouraged by attendance of metal oxides.[18] The rate of change is obtained by Eq. [29]:

#### Rate of change of methane (CH_{4})

_{4}is extracted with the off-gas (

*x*15

_{d1}) and flows out through openings (

*x*15

_{d2}). Natural gas, which consists mainly of CH

_{4}, is injected through the burner system (

*x*15

_{d3}). The CH

_{4}is assumed to react in three different ways (

*x*15

_{d4},

*x*15

_{d5}, and

*x*15

_{d6}) and, finally, CH

_{4}is post-combusted (

*x*15

_{d7}). The rate of change is obtained by Eq. [30]:

_{4}post-combustion. It is assumed that there are three different reaction zones of the burner flame due to the non-premixed supply of CH

_{4}and O

_{2}. Within the reaction volumes, the respective reactions of Eqs. [6n

_{1}], [6n

_{2}], and [6n

_{3}] take place. Therefore,

*K*

_{burn-(n1)},

*K*

_{burn-(n2)}, and

*K*

_{burn-(n3)}are the corresponding percentages of the reaction volumes.

_{2}to CH

_{4}. The stoichiometric mixture fraction

*Z*

_{St-(ni)}according to Peters[19] is compared with the actual mixture fraction

*Z*of the supplied gas mass flows, which is defined according to Eq. [31]:

*Z*

_{St-(ni)}is obtained in general by Eq. [32] and for the three reactions according to Eqs. [33] through [35]:

*Z*≤

*Z*

_{St}, the natural gas mass flow

*x*15

_{d3}is completely consumed and for

*Z*>

*Z*

_{St}the reaction rate is limited by the available fraction of the burner oxygen. \( K_{{{\text{O}}_{2} {\text{ - CH}}_{4} {\text{ - inj}}}} \) is the fraction of the injected O

_{2}mass flow available for direct CH

_{4}combustion. This empirical factor is calculated according to the coverage of the burner nozzle openings by scrap (

*e.g*., after scrap charging). In this case, only an insufficient mixing of the two gases CH

_{4}and O

_{2}is assumed, which leads to an incomplete reaction of CH

_{4}. \( K_{{{\text{O}}_{2} {\text{ - CH}}_{4} {\text{ - inj}}}} \) is calculated with Eq. [36], which has been empirically derived based on the scrap meltdown progress in front of the burner nozzle:

*m*

_{sSc,basket}represents the mass of scrap charged into the EAF.

_{9}H

_{20}) and it is assumed that C

_{9}H

_{20}dissociates before further reactions take place. The dissociation follows the empirical approach in Eq. [37], which has been adopted from Logar

*et al*.[3] and adjusted to improve the agreement of simulation and measurement results.

### Reaction Enthalpies

*et al*.[3] by Eq. [39]:

*et al*.,[3] the change of enthalpy is obtained for the implemented reactions according to Eqs. [39] through [47] in Table I.

Enthalpy Reactions

Implemented Formula for the Enthalpy of the According Reaction | Equations | |
---|---|---|

(g) | \( \Updelta H_{\text{T - (g)}}^{0} = \frac{{x1_{{{\text{d}}5}} + x1_{{{\text{d}}6}} + x1{\text{coal}}_{{{\text{d}}2}} + x1{\text{coal}}_{{{\text{d}}3}} + x2_{{{\text{d}}2}} }}{{M_{\text{C}} }} \left[ {(\Updelta H_{\text{CO}}^{0} - \Updelta H_{\text{C - S}}^{0} ) + \int\limits_{{298\;{\text{K}}}}^{T} {\left( {C_{{{\text{p}},{\text{CO}}}} - C_{{{\text{p}},{\text{C}}}} - \frac{1}{2}C_{{{\text{p}},{\text{O}}_{2} }} } \right)} {\text{d}}T} \right] \) | (39) |

(h) | \( \Updelta H_{\text{T - (h)}}^{0} = \frac{{x9_{{{\text{d}}3}} }}{{M_{\text{CO}} }}\left[ {(\Updelta H_{{{\text{CO}}_{2} }}^{0} - \Updelta H_{\text{CO}}^{0} )} { + \int\limits_{{298\;{\text{K}}}}^{T} {\left( {C_{{{\text{p}},{\text{CO}}_{2} }} - C_{{{\text{p}},{\text{CO}}}} - \frac{1}{2}C_{{{\text{p}},{\text{O}}_{2} }} } \right)} {\text{d}}T} \right] \) | (40) |

(n) | \( \Updelta H_{\text{T}} - ({\text{n}})^{0} = \frac{{x15_{{{\text{d}}4}} }}{{M_{{{\text{CH}}_{4} }} }}\left[ {(\Updelta H_{{{\text{CO}}_{2} }}^{0} + \Updelta H_{{{\text{H}}_{2} {\text{O}}}}^{0} - \Updelta H_{{{\text{CH}}_{4} }}^{0} )} + \int\limits_{{298\;{\text{K}}}}^{T} {(C_{{{\text{p}},{\text{CO}}_{2} }} + 2C_{{{\text{p}},{\text{H}}_{2} {\text{O - g}}}} - C_{{{\text{p}},{\text{CH}}_{4} }} - 2C_{{{\text{p}},{\text{O}}_{2} }} )} {\text{d}}T \right] + \frac{{x15_{{{\text{d}}5}} + x15_{{{\text{d}}8}} }}{{M_{{{\text{CH}}_{4} }} }}\left[ {(\Updelta H_{\text{CO}}^{0} + 2\Updelta H_{{{\text{H}}_{2} {\text{O}}}}^{0} - \Updelta H_{{{\text{CH}}_{4} }}^{0} )} + \int\limits_{{298\;{\text{K}}}}^{T} {\left( {C_{{{\text{p}},{\text{CO}}}} + 2C_{{{\text{p}},{\text{H}}_{2} {\text{O - g}}}} - C_{{{\text{p}},{\text{CH}}_{4} }} - \frac{3}{2}C_{{{\text{p}},{\text{O}}_{2} }} } \right)} {\text{d}}T \right] + \frac{{x15_{{{\text{d}}6}} }}{{M_{{{\text{CH}}_{4} }} }}\left[ {(\Updelta H_{{{\text{CO}}_{2} }}^{0} - \Updelta H_{{{\text{CH}}_{4} }}^{0} )} + \int\limits_{{298\;{\text{K}}}}^{T} {(C_{{{\text{p}},{\text{CO}}_{2} }} + 2C_{{{\text{p}},{\text{H}}_{2} }} - C_{{{\text{p}},{\text{CH}}_{4} }} - C_{{{\text{p}},{\text{O}}_{2} }} )} {\text{d}}T \right]\) | (41) |

(p) | \( \Updelta H_{\text{T - (p)}}^{0} = \frac{{\dot{m}_{\text{comb}} }}{{M_{{{\text{C}}_{9} {\text{H}}_{20} }} }}\left[ {(9\Updelta H_{\text{C - S}}^{0} - \Updelta H_{{{\text{C}}_{9} {\text{H}}_{20} }}^{0} ) + \int\limits_{{298\;{\text{K}}}}^{T} {C_{{{\text{p}},{\text{H}}_{2} }} } {\text{d}}T} \right] \) | (42) |

(q) | \(\Updelta H_{\text{T}} {\text{-}} ({\text{q}})^{0} = \frac{{x9_{{{\text{d}}5}} }}{{M_{\text{CO}} }}\left[ {(\Updelta H_{{{\text{CO}}_{2} }}^{0} - \Updelta H_{\text{CO}}^{0} - \Updelta H_{{{\text{H}}_{2} {\text{O}}}}^{0} )} + \int\limits_{{298\;{\text{K}}}}^{T} {(C_{{{\text{p}},{\text{CO}}_{2} }} + C_{{{\text{p}},{\text{H}}_{2} }} - C_{{{\text{p}},{\text{CO}}}} - C_{{{\text{p}},{\text{H}}_{2} {\text{O}}}} )} {\text{d}}T \right] \) | (43) |

(r) | \( \Updelta H_{\text{T - (r)}}^{0} = \frac{{x10_{{{\text{d}}5}} }}{{M_{{{\text{CO}}_{2} }} }}\left[ {(2\Updelta H_{\text{CO}}^{0} - \Updelta H_{\text{C - S}}^{0} - \Updelta H_{{{\text{CO}}_{2} }}^{0} )} { + \int\limits_{{298\;{\text{K}}}}^{T} {(2C_{{{\text{p}},{\text{CO}}}} - C_{{{\text{p}},{\text{C}}}} - C_{{{\text{p}},{\text{CO}}_{2} }} )} {\text{d}}T} \right] \) | (44) |

(s) | \( \Updelta H_{\text{T - (s)}}^{0} = \frac{{x14_{{{\text{d}}8}} }}{{M_{{{\text{H}}_{2} {\text{O}}}} }}\left[ {(\Updelta H_{\text{CO}}^{0} - \Updelta H_{\text{C - S}}^{0} - \Updelta H_{{{\text{H}}_{2} {\text{O}}}}^{0} )} { + \int\limits_{{298\;{\text{K}}}}^{T} {(C_{{{\text{p}},{\text{CO}}}} + C_{{{\text{p}},{\text{H}}_{2} }} - C_{{{\text{p}},{\text{C}}}} - C_{{{\text{p}},{\text{H}}_{2} {\text{O}}}} )} {\text{d}}T} \right] \) | (45) |

(t) | \( \Updelta H_{\text{T - (t)}}^{0} = \left( {\frac{{x13_{{{\text{d}}4}} }}{{M_{{{\text{H}}_{2} }} }} - \frac{{x14_{{{\text{d}}5}} }}{{M_{{{\text{H}}_{2} {\text{O}}}} }}} \right)\left[ {\Updelta H_{{{\text{H}}_{2} {\text{O}}}}^{0} } { + \int\limits_{{298\;{\text{K}}}}^{T} {\left( {C_{{{\text{p}},{\text{H}}_{2} {\text{O - g}}}} - C_{{{\text{p}},{\text{O}}_{2} }} - \frac{1}{2}C_{{{\text{p}},{\text{H}}_{2} }} } \right)} {\text{d}}T} \right] \) | (46) |

(u) | \( \Updelta H_{\text{T - (u)}}^{0} = \frac{{x1_{{{\text{d}}5}} }}{{M_{\text{C}} }}\left[ {(\Updelta H_{\text{CO}}^{0} - \Updelta H_{\text{C - S}}^{0} )} { + \int\limits_{{298\;{\text{K}}}}^{T} {\left( {C_{{{\text{p}},{\text{CO}}}} - C_{{{\text{p}},{\text{C}}}} - \frac{1}{2}C_{{{\text{p}},{\text{O}}_{2} }} } \right)} {\text{d}}T} \right] \) | (47) |

Compared to Logar *et al*.,[3] the enthalpy of the reaction of the combustibles C_{9}H_{20} is calculated according to the dissociation reaction in Eq. [3p], where C_{9}H_{20} and C are assumed with standard temperature. All other reaction enthalpies \( \Updelta H_{{{\text{T - }}({\text{a}})}}^{0} \) to \( \Updelta H_{{{\text{T - }}({\text{m}})}}^{0} \) are implemented according to Logar *et al*.[3] with adaptions in the equations for \( \Updelta H_{{{\text{T - }}({\text{g}})}}^{0} \) and \( \Updelta H_{{{\text{T - }}({\text{h}})}}^{0} . \)

*via*the heats

*Q*

_{lSc-chem}and

*Q*

_{gas-chem}according to Eqs. [48] and [49]:

*Q*

_{gas-chem}is a further summand in the balance of

*Q*

_{gas}, which is implemented according to Logar

*et al*.[2]

## Results and Discussion

This section present the simulation results, which are relevant for the modeling and simulation of the EAF off-gas. The results are compared to measured data from an industrial scale EAF with a tapping weight of approximately 140 t. The process simulation was performed with MATLAB R2015b on a PC with 3.4 GHz, 16 GB RAM, and Windows 7 64 bit. The relative integration tolerance was set to 10^{−9}. For the simulation, the input data for scrap and operational data for power and mass flows into the EAF were used, while the hot heel was assumed constant with a mass of 30 t. The operational data used have a resolution of 5 seconds and were evaluated with an interpolation approach for each integration time step to determine the input mass flows and powers. In total, 126 heats were simulated and evaluated in terms of energy and mass balance. Furthermore, the steel, slag, and gas compositions and temperatures were compared.

In the following, the results from single heats are compared as well as averaged results from all 126 heats. Thereby, transient behavior that cannot be reproduced by the simulation is smoothed over and leads to a better comparability of the results.

_{2}in gray as parts of the gas phase for a single heat. The charging of the second scrap basket is obvious at 20 pct relative time. The curves for CO are in the same range of magnitude with the biggest differences of 20 pct occurring at approximately 38 and 50 pct relative process time. For CO

_{2}, the mass fractions are in the same range of magnitude during the melting of the first scrap basket. During the melting of the second scrap basket and the refining phase, the simulated mass fraction is about 8 pct higher than the measured fraction. In this case, the post-combustion, carbon reactions in the EAF, and the equilibrium reactions need further adjustment but the results are already satisfactory. Further conclusions can be drawn by analyzing the mass fractions of H

_{2}and H

_{2}O.

_{2}, so that the scale of the

*y*-axis has to be adjusted accordingly. The course of the measured and simulated mass fractions are in the same range of magnitude with a bigger difference in H

_{2}at 40 pct process time, which can be associated with non-stationary behavior of the melting.

_{2}for 126 heats are presented in Figure 4. It is obvious that the simulated fraction of CO is approximately 10 pct higher than the measured fraction after charging the second scrap basket. In contrast, the simulated CO fraction is below the measured fraction during the refining phase. The conversion of CO in the EAF through combustion and decarburization needs to be shifted further to the refining. In case of CO

_{2}, the simulated fractions are close to the measured values.

_{2}and H

_{2}O are presented in Figure 5. For H

_{2}O, the simulation results are higher than the measured values at 10 and 30 pct process time. Here, the natural gas injection is at a maximum and more water vapor is created through CH

_{4}combustion in the simulation than in the real process. Further adjustment of the CH

_{4}reactions is necessary, but the results are already satisfactory.

^{−1}, which is the chemical energy of CO, H

_{2}, and CH

_{4}, the sensible enthalpy with medians at around 50 kWh t

^{−1}is lower. The difference of the simulated off-gas temperature has less influence on the off-gas energy output than a difference in the simulated off-gas composition compared to the real process.

^{−1}demonstrate the relevance of considering these reactions in the gas phase modeling.

It can be seen that the consideration of further gas components and equilibrium reactions in the gas phase lead to a better gas phase simulation in a dynamic process simulation model of an EAF. This is important, as the off-gas temperature and composition are continuously measurable process values and represent one of the biggest energy outputs of the EAF.

Finally, the duration of the simulation is important for the applicability of the dynamic process model. The further enhancement of the model leads to a higher complexity, while the ODE-solver accelerates the simulation. For a single heat, the simulation time is between 65 and 85 seconds. Due to the ability of parallel computing, the 126 heats are simulated on four processor cores in less than 1 hour. That means that the model is applicable for online process optimization.

## Conclusion

In this paper, the enhancement of the gas phase of the dynamic EAF process model by Logar *et al*.[2,3] is presented. The gas components H_{2}, H_{2}O, and CH_{4} were included in the gas phase modeling. These components were integrated into the calculation of chemical reactions under consideration of the equilibrium reactions of Boudouard and the water–gas reaction. To prevent the increase of simulation time due to the higher complexity, the model was re-implemented in MATLAB to use the more efficient ODE-solver ode15s for stiff ODE-systems.

The presented results of the enhanced EAF model were compared to measured data from an industrial scale EAF. The off-gas mass fractions for single heats as well as averaged data show a satisfactory similarity. The simulation of the gas phase temperature shows bigger differences, which have a negligible influence on the simulated off-gas energy output. The implemented equilibrium reactions show their significance on the CO production in the EAF. Further optimization is still necessary. Especially the conversion of C through combustion and decarburization has to be improved. Therefore, further measurements and data are necessary, especially concerning the slag mass and mass of the hot heel. In the future, the model has to prove its applicability for different EAFs and thereby the extrapolation capability for offline investigations.

The simulation results were obtained in about 1 minute for each heat, so that the model is applicable for online optimization. In addition, the parallel computing allows the simulation of hundreds of different settings, input materials, or operation strategies within a reasonable time. With that, the model is appropriate for operator training and offline investigations on input materials and modes of operation to reduce costs and energy consumption and increase the energy and resource efficiency.

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