Modeling and Validation of an Electric Arc Furnace: Part 2, Thermo-chemistry

Transcription

1 ISIJ International Vol 5 0 No pp 4 4 odeling and Validation of an Electric Arc Furnace: art Thermo-chemistry Vito LOGAR Dejan DOVŽAN and Igor ŠKRJAN Laboratory of modeling simulation and control Faculty of Electrical Engineering University of Ljubljana Tržaška 5 SI-000 Ljubljana vitologar@feuni-ljsi dejandovzan@feuni-ljsi igorskrjanc@feuni-ljsi Received on September 0; accepted on October 0 The following paper presents an approach to the mathematical modeling of thermo-chemical reactions and relations in a phase 80 VA A electric arc furnace EAF and represents a continuation of our work on modeling the electric and hydraulic processes of an EAF This paper is part of the complete EAF model and addresses the issues relating to chemical reactions and the corresponng chemical energy in the EAF which are not included in part of the paper which is focused on mass temperature and energy-echange modeling art and part papers are related to each other accorngly and should be considered as a whole The developed and presented sub-models are obtained accorng to mathematical and thermo-chemical laws with the parameters fitting both eperimentally using the measured operational data of an EAF during fferent periods of the melting process and theoretically using the conclusions of fferent stues involved in EAF modeling art part and the already published electrical and hydraulic models of the EAF represent a complete EAF model which can further be used for the initial aims of our project ie optimization of the energy consumption and the development of an operator-training simulator Like with part the obtained results show high levels of similarity with both the operational measurements and theoretical data available in fferent stues from which we can conclude that the presented EAF model is developed in accordance with both the fundamental laws of thermodynamics and the practical aspects relating to EAF operation KEY WORDS: EAF; thermal model; chemical model; eperimental validation Introduction The paper presents an approach to the mathematical modeling of thermo-chemical processes in an 80 VA A electric arc furnace EAF The proposed models complement the previous work on the modeling of the electrical and hydraulic processes in an EAF and the work presented in part and represent the final stage of the complete EAF model The EAF sub-models derived in this paper address the most common chemical reactions which appear during the steel melting process and include the oidation and reduction of both chemical elements such as iron carbon silicon manganese chromium and phosphorus; and chemical compounds such as iron oide carbon monoide and oide silica manganese oide chromium oide and phosphorus oide Also the model takes into account the mechanisms of electrode oidation the oidation of combustible materials the oygen burners the relative pressure and the slag-foaming processes nce the chemical reactions can contribute up to 40% of the total EAF energy balance the model includes energy-echange uations for each chemical reaction For the needs of our study the model defines relatively accurate and reliable relations that describe the chemical reactions between the EAF regions ie the steel slag and gas zones Various approaches to the modeling of EAF chemistry and the appurtenant energy relations can be found in the literature such as general chemical models or more detailed sub-processes 4 6 Like with the heat temperature and mass models presented in part the thermo-chemical model proposed in this paper is inspired by the papers of Bekker and acrosty; however the proposed model in this study is more comple approached fferently and considers more chemical reactions and adtional energy transfers between the EAF zones Also the model includes relations describing O post-combustion 7 and slag-foaming processes based on the realities in the EAF and its impact on raative heat transfer Besides modeling the fundamental laws of mass and heat transfer special attention is devoted to the parameterization of the developed model using available initial endpoint and online measurements for the EAF s operation Like with the models developed in our previous work the model proposed here is based on the 80 VA A furnace installed in one of the ironworks in Slovenia Therefore for the needs of a successful model parameterization operational data of the EAF related to the chemical transfer processes were obtained inclung the initial and end-point steel and slag compositions the steel yields the temperatures etc nce some data the stage and rate of the chemical reactions temperatures masses etc cannot be obtained during the melting due to the nature of the process the uations and parameters of the sub-models relating to those values 4 0 ISIJ

2 ISIJ International Vol 5 0 No were obtained theoretically Other measurements such as the arc powers which are needed to complement the proposed models were obtained when modeling the electrical processes in the EAF nce the work presented in this paper complements the heat mass and temperature models presented in part a reference to part is added at each necessary point as ART odeling The following section presents the modeling approach to the thermo-chemical processes of the particular EAF nce this paper investigates the EAF sub-models and relations that are not addressed in part this paper follows the same modeling assumptions and simplifications as part ART Furthermore some adtional assumptions regarng the chemical model have been made such as: liquid steel is assumed to be a lute solution with mole fraction unit for molten steel activity coefficients are assumed constant and are close to unity with the respective reaction uilibrium constants computed accorngly 4 the reactions are started as soon as the corresponng reactants enter the liquid form with all other contions met presence of oygen carbon etc ideal solution is assumed for slag components In a similar way the EAF layout is vided into identical zones as with the previous work The values of all the parameters used in the developed model are listed in the Appen section milarly ual notation for EAF zones is used ie: solid scrap - ssc liquid metal - lsc solid slag - ssl liquid slag - lsl and gas - gas Thermo-chemical odel It is generally known that the chemical reactions in the steel bath the slag and the gas zone of the EAF represent an important part of the steel-melting processes The literature suggests that 0 40% 8 of the complete energy input is contributed by the chemical reactions meaning that the impact of the thermo-chemical relations in the EAF cannot be neglected Therefore the thermo-chemical model of the EAF is important for two reasons First it defines the relations between the fferent chemical elements and compounds and influences the final composition of the steel the slag and the off-gas Second the energy released from the reactions during the EAF melting process represents a significant amount of the total EAF energy balance Newer EAF designs tend to replace more and more electrical energy with chemical energy by adng increased quantities of oygen and carbon into the bath which can also be taken into the account when the thermo-chemical relations are modeled properly The chemical model assumes that all the chemical reactions ecept the O post-combustion and H 4 oidation oygen burners take place in the liquid metal and slag zones The notation used is as follows: m denotes the mass of an element or compound denotes the molar mass of an element or compound kd represents the reactionrate coefficient of an element is the molar fraction of the element or compound is the uilibrium molar fraction of the element or compound and k is the uilibrium constant of the element or compound unless specified otherwise hemical reactions The chemical reactions that are considered in the proposed model are chosen accorng to the influence of the particular reaction on the energy input/output to the complete EAF energy balance 4 the chemical composition of the steel or slag and the obtained initial and end-point data of the EAF The oidation and reduction reactions that are taken into account are given by Eq : a + O O b O+ + O c O + n + no d O + + O e O+ r + r O f 5O+ 5+ O 5 g + O O h O+ O O i + O O j no+ n+ O k no + n + O l + O O m r+ O ro n H + O O + H O 4 p H + 54O 9O + 90H O 9 0 The above reactions represent the basis for the development of the model ie computing the rates of change of the elements or compounds and the input or output energies of a particular reaction The details of the proposed reactions are presented below At this point the number of moles of liquid metal lsc and slag lsl zones shall be defined in Eq as they are fruently used later lsc lsl mlsc m m mr mn m mlsl mo mo mno mro mo lsl O O no ro O5 The molar fraction of an element or compound yy where denotes the particular element and yy the compound can be defined in a uniform way by Eqs and 4 The model assumes that all the elements are present ssolved in the liquid metal while the compounds yy are present in the liquid slag ecept the gases yy r m / lsc myy / lsl yy n 4 0 ISIJ 44

3 ISIJ International Vol 5 0 No Rate of change of carbon The rate of change of carbon in the bath L and D is determined by the following mechanisms: injection d injected decarburization d [Eq b] injected ssolving ssolved decarburization d [Eq b] ssolved oidation to O d [Eq g] ssolved increase due to ssolving of the injected reaction with no d4 [Eq j] and ssolved oidation to O d5 [Eq i] The rate of change of injected L is given by Eq 5: d d L inj mokd Lm L m + m + m + m + m + m lsl O O no ro O5 Tair m Lp lsc Tmelt λ + T T p melt air 5 where inj is the carbon injection rate kg/s kd -L is the decarburization rate and m -L is the mass of injected carbon present in the furnace The rate of change of the ssolved in the bath D is given by Eq 6: d kd D d kd Olance KO O kd d4 n no no no kd O K d5 D 5 lance O O 6 where kd -D is the O decarburization rate kd - is the oidation rate to O kd n- is the no decarburization rate kd - is the oidation rate to O O lance is the oygen lance rate K O-O and K O-O are the fractions of the lanced oygen used for oizing to O and O respectively The molar fractions of O no and O no and needed in Eq 6 are obtained with Eqs and 4; the uilibrium molar fraction of in the bath is defined similarly as proposed by Bekker; but in an etended form and is obtainable with Eq 7: k 7 O where k is the reaction uilibrium constant for the O + reaction [Eq b] defined as k and is obtainable with Eq 8: O k% O 00 5 lsl 8 k O k% As suggested by Ref 4 the uilibrium molar fraction of no used in Eq 6 can be described with Eq 9: O n no 9 kn where k n- is the reaction uilibrium constant for the no + reaction [Eq j] defined by Eq 0: 4 k k n no p 64 p n % O n no n k no where p O represents the partial pressure of O 0 Rate of change of silicon The rate of change of ssolved silicon in the bath is determined by the following mechanisms: desiliconization d [Eq d] oidation to O d [Eq l] and reaction with no [Eq k] The rate of change of ssolved can be obtained with Eq : where kd - is the O desiliconization rate kd - is the oidation rate to O kd - is the no desiliconization rate and K O-O is the fraction of the lanced oygen used for oizing to O The molar fractions of O no and are obtainable with Eqs and 4; the uilibrium molar fraction of in the bath is defined like in; but in an etended form and is obtainable with Eq : k O where k is the mensionless reaction uilibrium constant for the O + reaction [Eq d] defined as k and is obtainable with Eq : O k% O lsl lsl k k O % O00 As suggested by Ref 4 the uilibrium molar fraction of no can be for the particular reaction described by Eq 4: 4 k where k n- is the mensionless reaction-uilibrium constant for the no + reaction [Eq k] defined by Eq 5: n lsl n % no ao + go 8 6 no O 0 5 O d kd d kd Olance KO O kdn no no k n no n O no n n lsl O 45 0 ISIJ

4 ISIJ International Vol 5 0 No Rate of change of anganese n The rate of change of ssolved manganese in the bath n is determined by the following mechanisms: the n reaction with O 4 d [Eq c] the no reaction with 4 d [Eq j] and the no reaction with 4 [Eq k] The rate of change of ssolved n can be obtained with Eq 6: 4d kdn n n n 4 d d 4 n 4 d n 4 6 where kd n is the rate of the O + n reaction The molar fraction of n is obtainable with Eq while the uilibrium molar fraction of n in the bath is obtainable with Eq 7: no n 7 Okn where k n is the mensionless reaction uilibrium constant for the reaction [Eq c] defined as k n 89 and is obtained from the Eq 8: 4 k n% k n no O no O n n no 9 ± 0 On00 8 On00 kn% no Rate of change of chromium r The rate of change of ssolved chromium in the bath r is determined with the following mechanisms: the r reaction with O 5 d [Eq e] and r oidation 5 d [Eq m] The rate of change of ssolved r can be obtained with Eq 9: 5d kdr r r 5d 4kdr r r Olance KO ro 9 r 5 where kd r- kd r- are the reaction rates and K O-rO is the fraction of the lanced oygen used for oizing r to r O The molar fraction of r is obtainable with Eq while the uilibrium molar fraction of r in the bath is obtainable with Eq 0: ro r 0 Okr where k r is the mensionless reaction-uilibrium constant for the chromium defined as k r and is obtained from the Eq : 4 ro ro kr% 0 ± 0 r O r O00 ro r O00 kr kr% r O ro Rate of change of phosphorus The rate of change of ssolved phosphorus in the bath is determined with the following mechanism: oidation 6 d [Eq f] The rate of change of ssolved can be obtained with Eq : 6d kd 6 d where kd is the rate of reaction The molar fraction of is obtainable with Eq while the uilibrium molar fraction of in the bath is obtainable with Eq : O5 5 k O ao where k is the mensionless reaction-uilibrium constant for phosphorus defined as k 78 0 and is obtained from the Eq 4: 9 7 O5 O5 lsl k% 5 O 5 9 ao OaO O5 r O00 k k r% O ro O d5 d O d6 d r 4 Rate of change of iron oide O The rate of change of the iron oide in the slag O is determined by the following mechanism: injected decarburization 7 d [Eq b] desiliconization 7 d [Eq d] oidation 7 [Eq a] O added by DRI 7 d4 ssolved decarburization 7 d5 [Eq b] reaction with r 7 d6 [Eq e] reaction with n 7 d7 [Eq c] reaction with 7 d8 [Eq f] The rate of change of O in the slag can be obtained with Eq 5: O 7 d d O 7 d d O 7 O K lance O O O 7d 4 DRIadd KO DRI O d7 d n O d8 d O where K O-O is the fraction of the lanced oygen used for oizing to O DRI add is the DRI adtion rate and K O-DRI is the amount of O in the DRI stream 4 0 ISIJ 46

5 ISIJ International Vol 5 0 No Rate of change of silica O The rate of change of silicon oide in the slag O is determined by the following mechanism: desiliconization [Eq d] oidation to O [Eq l] and reaction with no [Eq k] As it is clear from Eq all three uations with either produce or consume O Therefore the rate of change of O in the slag is proportional to the rate of change of in the metal and can be obtained with Eq 6: O m O 6 m Rate of change of manganese oide no The rate of change of the manganese oide in the slag no is determined with the following mechanism: the n reaction with O [Eq c] the no reaction with [Eq j] and the no reaction with [Eq k] As is clear from Eq 6 all three uations with n either produce or consume no Therefore the rate of change of the no in the slag is proportional to the rate of change of n in the metal and can be obtained with Eq 7: m 7 Rate of change of chromium oide r O The rate of change of chromium oide in the slag ro is determined by the following mechanism: the r reaction with O [Eq e] and r oidation [Eq m] Like with the O and no reaction mechanisms Eq 9 shows that both reactions with r produce r O Therefore the rate of change of r O in the slag is proportional to the rate of change of r in the metal and can be obtained with Eq 8: r O mr O r 8 m Rate of change of phosphorus oide O 5 The rate of change of phosphorus oide in the slag O5 is determined using one mechanism ie oidation [Eq f] and is proportional to the rate of change of and can be obtained with Eq 9: O m O m Rate of change of iron All the reactions that include influence its overall mass in the bath Therefore the rate of change of iron in the bath is determined by the following mechanism: injected decarburization 8 d [Eq b] desiliconization 8 d [Eq d] oidation 8 [Eq a] added by the DRI stream 8 d4 ssolved decarburization 8 d5 [Eq b] O reaction with r 8 d6 [Eq e] O reaction with n 8 d7 [Eq c] and O reaction with 8 d8 [Eq f] The rate of change of in the bath can be obtained with Eq 0: no no n n r 8 d d 8 d 8d 7 O 8 DRI K 8 8 d d4 add DRI d5 d 5 d6 d r d7 d n d8 d where DRI add is the DRI adtion rate and K -DRI is the amount of in the DRI stream The overall mass of is obtained with Eq 44 in part ART Rate of change of carbon monoide O The rate of change of carbon monoide in the gas zone O is determined by the following mechanisms: O etraction through the off-gas vents 9 d O as a product of oidation 9 d [Eq g] O combustion with leak air 9 [Eq h] O etraction through the hatches 9 d4 and O post-combustion 9 d5 [Eq h] O rates 9 d 9 and 9 d4 are defined in a similar way as proposed by Bekker but in an etended form while other rates are added to satisfy the needs of the proposed model The rate of change of O in the gas can be obtained with Eq : hum d O 9d ku U + hd mo + mo + mn + mo O 9 d d + d + d + d4 9 OkAIRkRr krr mo 9d 4 mo + mo + mn + mo 9 d5 O post mo O K O if r > 0 then 9 9 O 5 if r < 0 then 9 9 O 5 where h d is the characteristic mension of the duct area at the slip gap u is an approimation of the off-gas mass flow k U is a mensionless constant used for improving the approimation set to the same value as proposed by Ref u is the slip-gap width k AIR is the molar amount of O in the leak air k R represents the mensionless constant which defines the ratio between the reaction rate and relative d ISIJ

6 ISIJ International Vol 5 0 No pressure r is the relative pressure in the EAF Eq 5 O post is the oygen rate for O post-combustion and K mo is the coefficient of O mass [0 ] which denotes whether there is enough O in the gas zone for post-combustion Rate of change of carbon oide O The rate of change of carbon oide in the gas zone O is determined with the following mechanisms: O etraction through the off-gas vents 0 d O as a product of O combustion with leak air 0 d [Eq h] O post-combustion 0 [Eq h] O as a product of oygen burners 0 d4 [Eq n] electrode oidation 0 d5 [Eq i] oidation of the combustible materials 0 d6 [Eq p] O etraction through the hatches 0 d7 and rect oidation to O 0 d8 [Eq i] The rate of change of O in the gas can be obtained with Eq : hum d O 0d ku U + hd mo + mo + mn + mo 0d OkAIRkRr O 0 O K post mo O O 0 H d 4 4inj H 4 O 0d5 el m O 0d6 9 comb 9H0 krr mo 0d7 mo + mo +mn + mo O 0 d8 d5 if r > 0 then m O 0 0 d O 8 if r < 0 then Rate of change of nitrogen N The rate of change of nitrogen in the gas zone N is determined by the following mechanisms: N etraction through the off-gas vents d N sucked in leak air d and N etraction through the hatches The rate of change of N in the gas can be obtained with Eq : d7 hum d N d ku U + hd mo + mo + mn + mo k k r d N AIR R krr mn m + m + m + m O O N O if r > 0 then N if r < 0 then N d where k AIR is the molar amount of N in leak air Rate of change of oygen O The rate of change of oygen in the gas zone O is determined by the following mechanisms: O etraction through the off-gas vents d O sucked in leak air d O leak-air combustion [Eq h] O postcombustion d4 [Eq h] electrode oidation d5 [Eq i] oidation of the combustible materials d6 [Eq p] O etraction through the hatches d7 and rect oidation to O d8 [Eq a] The rate of change of O in the gas can be obtained with Eq 4: hum d O d ku U + hd mo + mo + mn + mo d OkAIRk Rr O d d 0 O O K d4 post mo O d5 el O d6 4 comb 4 d7 9H 0 krr mo m + m + m + m O d8 7 O O N O O if r > 0 then O if r < 0 then O 8 8 When the amount of O in the gas phase is insufficient to carry out all the oidation processes the model decreases the amount of available O for those reactions accorngly Relative ressure The relative pressure in the EAF gas zone changes as a consuence of the gases produced in the chemical reactions off-gas vents carbon and oygen adtion etc and as a consuence of the temperature change The pressure in the furnace can be obtained by following the ideal gas uation which yields Eq 5: 5 where R gas represents the gas constant and V gas represents the volume of the gas zone The first part of Eq 5 accounts for the pressure change due to the change of the gas masses and the second part for the change in the temperature of the gas zone Electrode Oidation and ombustible aterials As is generally known while operating an EAF the d d7 RgasTgas O O N O r Vgas O O N O RgasT gas mo mo mn m O Vgas O O N O 0 ISIJ 48

7 ISIJ International Vol 5 0 No Besides the above chemical reactions the model also con- graphite electrodes are oized which also represents a minor source of energy which has to be added to the total EAF energy balance Accorng to Bowman 5 the consumption of the electrodes el can be described by the following Eq 6: Iarc Aside el Rtip + Rside where R tip and R side are the average oidation rates for the electrode tip [kg/ka per h] and side [kg/m per h] I arc represents the arc current and A side represents the electrode side surface area A minor source of energy can also be found in the combustible materials present in the solid scrap such as oil grease coatings colors etc These materials burn very quickly at the beginning of the melting process when the temperature of the scrap is sufficiently high The rate of change of the combustible materials comb can be defined with Eq 7: TsSc comb kdcombmcomb 7 Tmelt TsSc where kd comb is the combustion rate and represents the Tmelt increasing rate of combustion with the increasing temperature of the solid steel 4 Energy of hemical Reactions With the chemical reactions and mass transfers of the elements defined the energies of the chemical reactions can be computed In general the enthalpy of a reaction can be obtained with Eq 8: 4 Δ HT ΔH98 products ΔH98 reactants T 8 + p products reactants dt 98 p meaning that the change of the enthalpy accompanying the given reaction is given by the fference between the enthalpies of the products and those of the reactants and by the temperature integral from the initial 98 K to the actual temperature of the fference between the specific heat capacities of the products and the reactants Using the actual variables and reactions presented here the change of the enthalpies can be obtained from Eqs 9 to 5 where the suffies -a to -n in ΔH T denote the associated reaction from Eq in Section : 8 Δ HT a ΔHO ΔH S 9 + po p p O dt d + Δ HT b lsc + + ΔH ΔH ΔH T 98 p p O p p O d O S O dt 40 4d Δ H T c ΔHnO ΔHO ΔHn S n 4 + p + 98 pno po pn dt d Δ HT d Δ HO +ΔHO S ΔHO ΔH S T lsc + 98 p + p O p O p dt 4 5d Δ HT e ΔHrO ΔHO ΔHr S r 4 + p + 98 p ro p O p r dt 6d Δ HT f ΔHO5 5ΔHO ΔH S p + 98 p O5 5p O p dt d Δ HT g ΔHO ΔH S 45 + po p 05 po d 98 T 9+ 9d4 if r < 0 then Δ HT h ΔHO ΔHO O Tgas + 98 p O p O 05 p O dt 9d4 if r > 0 then Δ HT h ΔHO ΔHO O Tgas + po po po dt d Δ H 5 T i ΔHO ΔH S 47 + po p po dt 98 4d Δ H T j Δ HO +ΔHn S ΔHnO ΔH S n + pn + dt 98 p O p no p 48 Δ HT k Δ HO +ΔHO S ΔHnO ΔH S 49 T lsc + 98 p n + p O p no p dt d Δ H T l Δ HO +ΔHO S ΔH S 50 + po 98 p po dt 5d Δ HT m ΔHrO ΔHr S r 5 + pr O 98 pr 05 po dt H4 inj Δ HT n Δ HO + ΔHH O ΔHH 4 H 4 5 Tgas + po + 98 ph O ph 4 po dt 49 0 ISIJ

8 ISIJ International Vol 5 0 No siders graphite electrode oidation and the burning of the combustible materials present in the solid scrap The energies of the reactions can be represented by the Eqs 5 and 54 The model assumes the electrode graphite oizes to O The burning of the combustible materials is approimated by oizing 9H 0 to O and H O: el Δ HT o ΔHO 5 Tgas + dt ; 98 po p po comb Δ HT p Δ HO +ΔHH O ΔH9H 0 9H0 54 Tgas + + dt ; 98 po ph O p 9H0 po The total energy of the chemical reactions for the liquid metal Q lsc-chem and the O post-combustion Q O-post zones which are used in part paper ART can be obtained with Eq 55: Q ΔH H var a p Q lsc chem T vari T h i i ΔH O post T h 55 5 Foaming Slag Height Slag foaming represents an important part of the EAF steel-making processes since it has several positive characteristics The most important characteristic of the foaming slag is its ability to revert a great portion of the raative energy ssipated from the electric arcs to the bath instead to the furnace roof and walls In this way greater input powers to the EAF can be achieved since the raative impact to the furnace lining is reduced The other advantage of the foaming slag is that among others it captures the O bubbles which increases the O post-combustion efficiency Another advantage of the slag is also its influence on stabilizing the burning of the arcs and consuently reducing their chaotic behavior and lowering the arc impedance load The slag-foaming inde Ξ can be defined by Eq 56: 4 η Ξ σ ρd B where η σ and ρ represent the slag s viscosity surface tension and density respectively while D B represents the foambubble ameter and these are obtainable from the uations proposed by Zhang and Frueham in Ref 4 The change of slag height can be obtained from Eq 57: H f ΞVg 57 where Ξ is the slag inde obtained from Eq 56 and V g is the superficial gas velocity obtained from Eq 58: V g 9 R T O r + a πr d gas gas 58 where 9 d is the O produced from oidation R gas is the universal gas constant T gas is the temperature of the gas obtainable from Eq 7 in part ART r is the relative pressure in the furnace obtainable from Eq 5 a is the atmospheric pressure while πr accounts for the crosssectional area of the EAF 0 The factor that determines the relation between the slag height and the corresponng view-factor change was modeled in a similar way to that proposed by acrosty with the following Eq 59: mssc Kslag 07 tanh 5Hf 5 + tanh + m 9 init 59 where H f is the slag height m ssc is the mass of solid steel ART and m init is the initial mass of the steel scrap loaded during each charge The factor -K slag is used to multiply the calculated view factors from arcs to roof VF 5- and walls VF 5- ART which models the decrease of the latter with the increasing slag height nce the view factors from arc to solid VF 5- and liquid VF 5-4 metal are obtained from the reciprocity rule from VF 5- and VF 5- they increase with the increasing slag height accorngly Results and Discussion The following section presents the simulation results that are relevant to the proposed thermo-chemical model and were obtained by combining the developed mathematical models for the mass and heat transfer and the chemical reactions Some of the obtained results are compared with the available endpoint measurements such as the composition of the steel and the slag Other non-measured values are compared to the results of the stues which address similar EAF topics mulation Timeline The following results were obtained using the same simulation timeline as presented in part ART paper Initial Steel and Slag omposition As is generally known the initial composition of the steel scrap and the added slag-forming materials are crucial for obtaining the end-point compositions; therefore the compositions used for the simulation are defined as in a real operation as follows: Steel composition: 04% 06% 0% r 005% 06% n and % combustibles Slag composition: 567% ao 4% go 07% O and 045% Al O Also an assumption is made that all the slag-forming material added during the melting process has the same chemical composition Thermo-chemical odel Figure shows the powers left panel and energies right panel of the chemical reactions occurring in the furnace H4 and Q H4 represent the oygen burners Eqs n and 5 electrodes and Q electrodes represent the electrode oidation Eqs 6 and 5 combustible and Q combustible represent the oidation of combustible materials Eqs 7 and 54 while chemical and Q chemical represent the sum of all the chemical reactions described in section It can be seen that the largest increase in the chemical power occurs after the O stream is started t 000 s which incates the importance of O lancing for an adtional energy input and 0 ISIJ 40

9 ISIJ International Vol 5 0 No Fig Left panel: ower of chemical reactions; Right panel: energy of chemical reactions Fig Left panel: Slag composition - m slag marked with + represents the sum of compounds ao go and Al O m denotes the endpoint percentage of a given compound in slag; Right panel: steel composition m denotes the endpoint percentage of a given element in steel bath Fig Left panel: Gas composition with O post-combustion; Right panel: Gas composition without O post-combustion the endpoint composition of the slag and the steel Figure shows the slag left panel and steel right panel compositions With regard to the initial slag and steel compositions and the suggestions of other stues 58 both compositions obtained with the proposed model are satisfactory Like with the energy of the chemical reactions the rate of change of an invidual element or compound in the slag or steel is subject to O t 000 s and injection which further incates the importance of the oygen-lancing technology for the energy balance and the final composition of the steel Figure shows the gas composition profiles when simulating the EAF model with left panel and without right panel O post-combustion It can be seen that in the case of O post-combustion all the O and O are consumed When an adtional O stream used for the O postcombustion is turned off the amount of O in the gas zone reaches up to 40% Also observable when charging baskets and is a rapid release of O which is a consuence of burning the combustible materials shortly after the steel is loaded and other oidation reactions which produce O 4 odel Validation To further validate the developed EAF model and to 4 0 ISIJ

10 ISIJ International Vol 5 0 No Fig 4 omparison between measured m and simulated s initial and endpoint steel composition values incating minimum in average Ave and maimum a values Fig 5 Table omparison between measured m and simulated s endpoint slag composition values incating minimum in average Ave and maimum a values omparison between the initial and endpoint measured and simulated mean steel composition values inclung standard deviations [%] [%] n [%] r [%] [%] easured initial 05±00 057± ± ± ±0009 mulated initial 04± ± ±005 07± ±0008 easured endpoint 006± ± ±004 05± ±000 mulated endpoint 006± ± ± ± ±000 Table omparison between the endpoint measured and simulated mean slag composition values inclung standard deviations O [%] O [%] no [%] r O [%] O 5 [%] ao [%] go [%] Al O [%] easured 46±8 7±7 5±09 5±04 5±0 80±59 00± 4± mulated 8±49 8±9 9±05 5±05 ±05 9±50 0±9 9±5 ensure its appropriateness for the initial aims of this study the simulated initial and endpoint steel and slag compositions were compared to the measured operational data and are presented in Figs 4 and 5 and Tables and The measured average values were obtained from the data for 40 fferent heats while the simulated values were obtained from the model using fferent initial contions As can be seen in Figs 4 and 5 and Tables and the measured and simulated endpoint data are similar which Fig 6 Energy balance of the EAF obtained from the proposed models incates the accuracy of the proposed chemical model and its usability for further analysis ie the energy optimization and the operator-training simulator Other values important for the validation such as: energy consumption steel yield temperatures and power-on-times are given in part paper ART or were already presented Figure 6 shows the energy balance of the particular EAF obtained from the proposed models The total electric energy input and electric losses were obtained using an electrical model of the EAF while other energies were obtained with the presented models It can be seen that total input and output energies of the EAF coincide with other similar EAF assemblies 5 which further proves the appropriateness of the developed EAF model Energy from the chemical reactions accounts up to 5% of the total energy which incates that more and O could be added into the bath to reduce electrical energy and achieve better energy balance 4 onclusion In this paper an approach to the mathematical modeling and validation of thermo-chemical reactions for the EAF processes is presented The proposed model covers the most common chemical processes and reactions and includes 0 ISIJ 4

11 ISIJ International Vol 5 0 No some other important aspects such as O post-combustion oygen burners electrode oidation and other processes that are often neglected in the EAF modeling practice The developed model could be etended with other reactions for the steel-melting process of lower importance; however due to the lack of endpoint composition measurements which would include the percentages of the particular elements or compounds and a relative simplicity of the proposed model the uations describing those reactions were omitted at this point The obtained model is developed in accordance with the fundamental laws of thermo-chemistry arameterization of the model is carried out using available initial and endpoint operational measurements theoretical data and conclusions of fferent stues eamining such processes in the EAF as some of the parameters could not be obtained from the available operational data Whether some adtional measurements could be performed better estimation of some parameters could be achieved Even though comparing the presented results to the available measurements the proposed model can be considered as appropriate for the aims of the study as high levels of similarity were achieved between the simulated results and both the theoretical and practical data available By incorporating the thermo-chemical model into the already developed framework of electrical hydraulic heat mass and temperature models ART a complete EAF model is obtained which shall further be used for operator training simulator and enhancement of the EAF process in terms of energy and cost reduction/optimization Acknowledgement The work presented in this paper was funded by Slovenian Research Agency ARRS project J-0 onitoring and ontrol of Steel elt Quality in Electric Arc Furnace REFERENES V Logar D Dovžan and I Škrjanc: ISIJ Int 5 0 No 8 J G Bekker I K raig and istorius: ISIJ Int No 4 R D acrosty and L E Swartz: Ind Eng hem Res No E T Turkdogan and R J Frueham: The aking Shaping and Treating of Steel 0th ed hapter : Fundamentals of Iron and Steelmaking The AISE Steel Foundation ittsburgh A USA J A T Jones B Bowman and A Lefrank: The aking Shaping and Treating of Steel; 0th ed hapter 0: Electric Furnace Steelmaking The AISE Steel Foundation ittsburgh A USA Kirschen V Velikorodov and H feifer: Energy 006 No G Grant: 58th Electric Furnace onference ISS Warrendale A USA E T Turkdogan: Fundamentals of Steelmaking Institute of aterials London UK S Basu: hd thesis Royal Institute of Technology Stockholm Sweden D J Oosthuizen J H Viljoen I K raig and istorius: ISIJ Int 4 00 No 4 99 H Sun: ISIJ Int No 0 48 H S Kim J G Kim and Y Sasaki: ISIJ Int No H Sun Y Lone S Ganguly and O Ostrovski: ISIJ Int No Y E Lee L Kolbeinsen: ISIJ Int No S Kitamura K iyamoto H Shibata N aruoka and atsuo: ISIJ Int No 9 6 W Kurz and D J Fisher: Fundamentals of Solification Trans Tech ublications Ltd Switzerland 005 Appen Table gives the values of the reaction rates kg/s for the presented chemical reactions The splayed rates are relatively approimate and rounded to a nearest integer since minor deviations from the estimated rates do not significantly change the simulation results Rate estimations can be obtained from fferent sources studying thermochemical processes In this manner kd -L can be obtained from kd -D and kd - can be obtained from 4 kd - and kd - can be obtained from 4 kd n- can be obtained from kd n- kd - kd r- and kd r- can be obtained from 4 kd n can be obtained from 4 and kd can be obtained from 5 Table 4 gives the values of enthalpies of formation used in Eqs 9 to 54 All rates are in kj/mol and can be obtained from 4 Table 5 gives the values of all other parameters used in the model inclung the units Some parameters such as: V gas R tip R side A side and r are EAF specific k AIR k AIR k R h d k U and u can be obtained from λ can be obtained from 6 K O-O K O-O K O-rO K O-O K O-O K O-DRI K -DRI and kd comb can be with minor approimations obtained from 458 while R gas T melt and a represent universal gas constant steel melting point and atmospheric pressure Table Table 4 Reaction rates used in the model All rates are in kg/s kd -L kd -D kd - kd - kd n- kd n kd n kd - kd - kd r- kd r- kd Enthalpies of formation used in the model All units are in kj/mol ΔH O ΔH S ΔH O ΔH O ΔH S ΔH n S ΔH no ΔH S ΔH O ΔH O S ΔH r S ΔH ro ΔH S ΔH O5 ΔH HO ΔH H Table 5 Values of other parameters used in the model λ K O-O K O-O K O-rO K O-O K O-O K O-DRI K -DRI kj 7 mol k AIR k AIR k R h d k U u R gas V gas mol mol J m 84 kg kg molk 45 m R tip R side A side T melt a r kd comb u kg kg 00 0 ka hr m hr 05 m 809 K 0 ka m 0 s 5 kg/s 4 0 ISIJ