Mathematical modelling of chemical kinetics and rate phenomena in the AOD Process

Abstract Argon-oxygen decarburisation (AOD) is the most common unit process for refining stainless steel. The AOD process consists of multiple stages, in which the rate of processing is determined by complex reaction mechanisms. The main objective of this work was to study the chemical rate phenomena in selected process stages. For this purpose, an extensive literature review was conducted to clarify the main assumptions of the existing reaction models. Based on the literature review, a new categorisation of the models was proposed. In addition, a literature review was conducted to identify the main phenomena that affect the reaction kinetics in the AOD process. In this work, based on the law of mass action, a novel kinetic approach and its application for modelling of parallel mass transfer controlled reactions were studied. The developed approach enables the simultaneous solution of the chemical equilibrium and mass transfer rate which controls it. A simplified reaction model was employed for studying the effect of mass transfer rates and residual affinity on the constrained equilibrium at the reaction interface. An earlier-proposed AOD model was extended with two phenomenon-based sub-models. The top-blowing model is based on the assumption that reactions take place simultaneously at the surface of the cavity formed by the momentum of the gas jet and on the surface of the metal droplets caused by the shear force of the gas jet. The reduction model describes the reactions during the reduction stage of the AOD process by assuming that all reactions take place between the metal bath and emulsified slag droplets. The results obtained with the models were in good agreement with the measurement data collected from a steel plant. Owing to their phenomenon-based structure, the developed models are well-suited for the analysis of both existing and new production practices.Tiivistelmä Argon-happimellotus (AOD) on yleisin ruostumattoman teräksen valmistamiseen käytettävä yksikköprosessi. AOD-prosessi koostuu useista vaiheista, joissa prosessointinopeutta määrittävät monimutkaiset reaktiomekanismit. Tutkimuksen päätavoitteena oli tutkia kemiallisia nopeusilmiöitä valituissa prosessivaiheissa. Tähän liittyen tehtiin kattava kirjallisuuskatsaus, jonka tavoitteena oli tunnistaa olemassa olevien reaktiomallien pääoletukset. Kirjallisuuskatsauksen pohjalta esitettiin uusi mallien kategorisointi. Lisäksi tehtiin kirjallisuuskatsaus, jonka tavoitteena oli tunnistaa tärkeimmät reaktiokinetiikkaan vaikuttavat ilmiöt AOD-prosessissa. Tässä työssä tutkittiin uudenlaista massavaikutuksen lakiin perustuvaa lähestymistapaa sekä sen soveltamista rinnakkaisten aineensiirron rajoittamien reaktioiden mallinnukseen. Kehitetty lähestymistapa mahdollistaa kemiallisen tasapainotilan sekä sitä rajoittavan aineensiirron samanaikaisen ratkaisun. Aineensiirtonopeuksien ja jäännösaffiniteetin vaikutusta reaktiopinnalla vallitsevaan rajoitettuun tasapainotilaan tutkittiin käyttämällä yksinkertaistettua reaktiomallia. Aiemmin kehitettyä AOD-mallia laajennettiin kahdella ilmiöpohjaisella alimallilla. Lanssipuhallusmalli perustuu oletukseen, että reaktiot tapahtuvat samanaikaisesti kaasusuihkun liikemäärän muodostaman tunkeuman ja kaasusuihkun leikkausvoiman aiheuttamien metallipisaroiden pinnalla. Pelkistysmalli kuvaa AOD-prosessin pelkistysvaiheen aikana tapahtuvia reaktioita olettaen, että kaikki reaktiot tapahtuvat terässulan ja emulgoituneiden kuonapisaroiden välillä. Malleilla saadut tulokset vastasivat hyvin terästehtaalta kerättyä mittausaineistoa. Ilmiöpohjaisen rakenteensa ansiosta kehitetyt mallit soveltuvat hyvin sekä olemassa olevien että uusien tuotantopraktiikoiden analysoimiseen

A Gibbs energy minimization approach for modeling of chemical reactions in a basic oxygen furnace

Abstract In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations

Modeling the residence time of metal droplets in slag during BOF steelmaking

Abstract The ejection of metal droplets into slag due to top-blowing is characteristic of the BOF process. The residence time of the metal droplets in the slag plays a significant role in the kinetics of the metal–slag reactions. In this study, the residence time of ejected metal in slag during BOF steelmaking is investigated and various approaches, based on the blowing number theory and mass balances are compared. Previously published blowing number theories are evaluated in comparison with physically based upper and lower boundaries. The results illustrate that only some of the laboratory-scale blowing number correlations apply to industrial blowing conditions. A mathematical model is developed to predict mass fraction return rates and thus the residence time of droplets in the slag emulsion. Combined with a previously published model for ejected droplet size distribution, it is possible to predict dynamic changes in the interfacial area and mass transfer conditions for metal–slag reactions

A mathematical model for the thermal state of a steel ladle

Abstract A dynamic one-dimensional mathematical model was developed for predicting the thermal state of a steelmaking ladle. The model is intended to be used in process control applications, in which fast computational times are desirable alongside model accuracy. The calculation domain was discretized using the finite difference method, and time integration was performed using both the implicit Euler and Crank–Nicolson methods, the performances of which were compared. The model was implemented in Python programming language and validated using data from our own measurements and other studies available in the literature. The results indicate that the model can reproduce the measured temperature evolution of the ladles within 5°C at best. The worst performance was observed during cooling, where the model underestimates the temperature at the innermost measurement point by up to 200°C. With computation times of around 16–23 s for one hour of simulation, the model is computationally sufficiently fast for online applications

Thermodynamic description of ternary Fe–B–X systems. Part 8:Fe–B–Mo, with extension to quaternary Fe–B–Cr–Mo system

Abstract Thermodynamic optimizations of the ternary Fe-B-Mo system and its binary sub-system B-Mo are presented. The Fe-B-Mo description is then extended to the quaternary Fe-B-Cr-Mo system by assessing the ternary B-Cr-Mo system. The thermodynamic descriptions of the other binaries (Fe-B, Fe-Cr, Fe-Mo, B-Cr, and Cr-Mo) and the other ternaries (Fe-B-Cr and Fe-Cr-Mo) are taken from earlier studies. In this study, the adjustable parameters of the B-Mo, Fe-B-Mo, and B-Cr-Mo systems were optimized using the experimental thermodynamic and the phase equilibrium data from the literature. The solution phases of the system (liquid, bcc and fcc) are described with the substitutional solution model, and most borides are treated as stoichiometric phases or semistoichiometric phases, using a simple two-sublattice model for the latter. The system’s intermetallic phases, Chi, Mu, R, and Sigma (not dissolving boron) as well as boride M₃B₂, based on a formulation of (Cr,Fe)(Cr,Fe,Mo)₂(B)₂, are described with a three-sublattice model. Reasonable agreement is obtained between the calculated and measured phase equilibria in all four systems: B-Mo; Fe-B-Mo; B-Cr-Mo; and Fe-B-Cr-Mo

Mathematical Modeling of the Ejected Droplet Size Distribution in the Vicinity of a Gas–Liquid Impingement Zone

Abstract The controlled splashing of metal droplets plays a decisive role in the kinetics of the basic oxygen furnace (BOF) process. In this work, a mathematical model was developed for predicting the size distribution of spherical droplets ejected at an impingement zone. Harmonic oscillators are used to describe the ejection sites, and the upper limit for the droplet population is calculated through a force balance. The model was validated against literature data from high-temperature crucible experiments involving different supply pressures and lance heights as well as both single-hole and multihole lances. The predicted size distribution of the metal droplets was found to be in good agreement with the droplet size distributions measured from outside the crucible. The model was also applied for predicting the size distribution parameters of the Rosin–Rammler–Sperling (RRS) size distribution function. The model developed is computationally light and is suitable to be used as a part of offline and online simulation tools for the BOF process

Thermodynamic description of ternary Fe–B–X systems. Part 9:Fe-B-Cu

Abstract Thermodynamic descriptions of the ternary Fe-B-Cu system and its binary sub-system B-Cu aredeveloped in the context of a new Fe-B-X (X = Cr, Cu, Mn, Mo, Ni, Si, Ti, V, C) database. The thermodynamic parameters of the other binary sub-systems (Fe-B and Fe-Cu) are taken from earlier assessments. Experimental thermodynamic and phase equilibrium data available in the literature have been used for the optimization of the Fe-B-Cu and B-Cu systems’ thermodynamic parameters. The solution phases are described using a substitutional solution model and the compounds (two borides of the Fe-B system) are treated as stoichiometric phases. A good agreement was obtained between the calculated and the experimental thermodynamic and phase equilibrium data

Thermodynamic description of the Fe–Al–Mn–Si–C system for modelling solidification of steels

Abstract Advanced high-strength (AHS) steels containing aluminium, manganese, silicon and carbon have widely been studied for automotive applications. It is particularly important to know their solidification behaviour and final structure after the austenite decomposition process. A thermodynamic database named the Iron Alloy Database (IAD) has been developed to provide consistent thermodynamic data for the purpose of simulating the solidification of steels. This work presents a thermodynamic assessment of the Fe–Al–Mn–Si–C system and 19 subsystems. The results suggest a good agreement between thermodynamic descriptions and the measured data.Tiivistelmä Alumiinia, mangaania, piitä ja hiiltä sisältäviä kehittyneitä suurlujuusteräksiä on tutkittu runsaasti autoteollisuuden sovelluskohteiden näkökulmasta. Erityisen mielenkiinnon kohteena on niiden jähmettyminen ja lopullinen rakenne austeniitin hajoamisprosessin jälkeen. Termodynaaminen Iron Alloys Database (IAD) –tietokanta on kehitetty tuottamaan konsistenttia termodynaamista dataa terästen jähmettymisen simulointiin. Tämä työ esittelee Fe–Al–Mn–Si–C –systeemin ja 19 alisysteemin termodynaamisen arvioinnin. Tulokset osoittavat, että termodynaamiset kuvaukset vastaavat mitattua aineistoa

Carbon-containing thermodynamic descriptions of the Fe–Cr–Cu–Mo–Ni–C system for modeling the solidification of steels

Abstract The thermodynamic Iron Alloy Database (IAD) has been developed since 2000 to provide consistent thermodynamic data for modeling the solidification of steels. This work presents the carbon containing thermodynamic descriptions of the Fe–Cr–Cu–Mo–Ni–C system, extending the two earlier publications on that database. The results suggest a good agreement of the thermodynamic descriptions with measured data.Tiivistelmä Vuodesta 2000 lähtien on kehitetty rautapohjaisten seosten termodynaamista datakantaa (Iron Alloy Database, IAD), jonka tarkoituksena on tuottaa yksinkertaista ja konsistenttia termodynaamista dataa terästen jähmettymisen mallintamiseen. Tämä työ esittelee systeemin Fe–Cr–Cu–Mo–Ni–C alikuvaukset hiilen osalta. Kuvaukset laajentavat aiemmissa tutkimuksissa esitetyistä Fe–Al–Mn–Si–C ja Fe–Al–Cr–Cu–Mn–Mo–Ni–Si kuvauksista luotua IAD-datakantaa. Tulokset osoittavat termodynaamisten kuvausten vastaavan hyvin mitattua aineistoa

Chromium-, copper-, molybdenum-, and nickel-containing thermodynamic descriptions of the Fe–Al– Cr–Cu–Mn–Mo–Ni–Si system for modeling the solidification of steels

Abstract The Thermodynamic Iron Alloy Database (IAD) has been developed since 2000 to provide consistent thermodynamic data for modeling solidification of steels. This work presents the chromium, copper, molybdenum and nickel containing thermodynamic descriptions of the Fe–Al–Cr–Cu–Mn–Mo–Ni–Si system, extending the earlier published Fe–Al–Mn–Si–C description of that database. The results suggest a good agreement of the thermodynamic descriptions with the measured data.Tiivistelmä Vuodesta 2000 lähtien on kehitetty rautapohjaisten seosten termodynaamista datakantaa, IAD, jonka tarkoituksena on tuottaa yksinkertaista ja konsistenttia termodynaamista dataa terästen jähmettymisen mallintamiseen. Tämä työ esittelee systeemin Fe–Al–Cr– Cu–Mn–Mo–Ni–Si alikuvaukset kromin, kuparin, molybdeenin ja nikkelin osalta. Kuvaukset laajentavat aiemmassa tutkimuksessa esitetystä Fe–Al–Mn–Si–C –systeemin kuvauksesta luotua IAD-datakantaa. Tulokset osoittavat termodynaamisten kuvausten vastaavan hyvin mitattua aineistoa