Use of a Mathematical Model GPRO to Describe Complex Gas ■ Metal Reactions Uporaba matematičnega modela GPRO pri opisovanju kompleksnih reakcij med plinsko in kovinsko fazo B. Koroušič*, Institute for Materials and Technologies, Ljubljana, Slovenia The knowledge of the thermodynamics in complexe systems consists of gases and metal shoud be valuable for the control of industrial processes. The Gibbs energy mmimization model has been implemented in the softvvare program GPRO and associated vvith a povverfull reliable database. This computer package can perform computation of the equilibrium composition in very complex chemical and metallurgieal systems. Some examples in this paper illustrate the simpliclty of the computation and use of the program in the field of typically metallurgieal applications vvhieh have been traditionally assigned to specialists. Key vvords: Equilibrium reactions, active gas-atmospheres, decarburisation of non-oriented electrical steels Poznavanje termodinamičnih odnosov v kompleksnih sistemih plin - kovina ima lahko izreden pomen za kontrolo industrijskih procesov. Gibbsov model o minimizaciji energije je implementiran v programsko opremo GPRO, ki mu služi kot osnova močna baza verificiranih termodinamičnih podatkov. Programska oprema omogoča izračunavanja ravnotežnih sestav v zelo kompleksnih kemijskih in metalurških sistemih. Navedeni primeri v tem članku ilustrirajo enostavnost izračunavanj in način uporabe programa na področju metalurških aplikacij, kijih večinoma izvajajo strokovnjaki na tem področju. Ključne besede: Ravnotežne reakcije, aktivne plinske atmosfere, razogljičenje neorientirane elektro pločevine. Introduction The application of thermodynamics to a system gas/solid en-ahles to calculate the composition at equilibtium and the direc-tion and extent of change vvhieh can take plače under specified conditions. In this paper an attempt is made to demonstrate the use of a personal computer software program as an elegant and sensitive method for numerous metallurgieal applications espe-ciallv for analysis of gas-metal svstems. It is expected, that user of this method vvill bc in good position to go more deeplv into learning thermodynamic correla-tions. Principles of the Gibbs method In the fields of heat treatment of metals as annealling, car-burizing, steel decarburizing, nitrocarburizing and many other operations. the metallurgist is concerned not with pure gases but with mixtures of various components (gases and solids) vvhieh form the atmosphere in the furnace. Description of used method for the complex equilibrium conditions Several excellent softvvare programs for general studing and calculating of equilibria reactions by high temperatures have ' Prof. dr. Blaženko KOROUŠIČ. IMT Ljubljana. Lepi poi 11. MIKU l Ljubl jana been developed in the last tvvo decades (e.g. SOLGASMIX, THERMOCALC, FACT, CHEMSAGE \ Hovvever. most of them are designed and vvritten in complex form requiring very strong computer units. few others are in-tented simply tis a tool to be applied for the purposes ot solving real problems. Therefore, it seemed vvorthvvhile to develop a program vvhieh vvill take some midway path betvveen these tvvo computer program designs. The nevv softvvare program, ealled GPRO is based on the method of free energy minimization and extended to systems containing numerous gaseous and con-densed phases mainly in accordance vvith SOLGASMIX-prin-ciples5 Thermodvnamical approaehes to the Gibbs-method The advantage of Gibbs method energy minimization is based on his simplicity for description of chemical reactions in complex systems and its ability to facilitate determination of the effect of a change in the external influences on the equilibrium state. In the GPRO softvvare program the user needs only to spec-ify the typc. the components present in the system and the conditions (for example: temperature and chemical composition of the system) for the calculation. The program vvill perform automatically the equilibrium thermodynamic computions typically associated with complex chemical cquilibria from a defined database. With Ihe aid of Ihe GPRO-program, a user is able to perform most of the following operations: I he energv for pre-heating the initial mixture from the initial temperature T„ to the reaction temperature T. The heat of reaction, - The eomputation of the complex chemical equilibria in gaseous mixtures and activitv of solid compounds, - Displaying and printing data of compounds and solutions at any temperatures and eompositions. Associated databases for the thermodynamic equilibrium coinputations From manv excellent standard treatises on thermodynamics it is knovvn. that vvithout reliable thermodynamic data most of the equations are ineffective and numerical ansvvcrs vvill be vvrong.GPRO softvvare program is based 011 use of both formula for calculations of the standard Gibbs energies of the formation of the phase: 1. in the form: A G= — + B + CT+DT2 +ET-+FTI11T 1 T (a) 2. over the enthalpy AW( entropv AS.r and heat capacity C,,(T): agv= +-T^iMur (b) Cp(T) = A + BT + CTJ + DT: Both methods used from the database involve a search for a minimum value of the free energv G of a svstem and give equiv-alent results. Hovvever the second method considering the enthalpv H. entropv S and heat capacitv Cp has more advantages by combining heat and equilibrium calculation. Typical example is the determination of the adiabatic flame temperature, vv here enthalpv of reaction serves as the eriterion of the heat balance. Exploiting the (iPRO-program for heat and standard free enthalpv calculations Traditionallv the concept of heat enthalpv and standard free enthalpv as a stale funetion are introduced bv considering the behaviour and properties of many chemical and metallurgical reaetions. Since the equilibrium stale has been obtained. the heat gen-eration or the total heat of process can be computed, using the therniodvnamical funetions .H.g. the energy necessarv for preheating the initial mixture from the initial temperature T to the reaction temperature T. H - H,„ (taking into the account the transition values vvithin the aetual temperature interval T - T„ added to the heat of reaction - H,,i. gives the H„ - total total heat of the system. Exainplc No. I StatcmaU ofthe problem A mixture of Fe. (O,). SiO, present in the molar ration 2 : I : 1 is adiabatically heated from 298 K lo 1 173 K. Calculate H„ - H:,w and G„ for the reaction: 2< Fe) + (o2) + {SiO,) = (Fe: SiO,) (1) vvhere: o = solid, () = gas Compare the obtained results vv ith results from literature for the Gibbs free energv ofthe favalite formation4: AG? = -555504 + 135.23r(j. mo/"1 )(900... 1478tf) (2 i AGy. = -505263 + 101,32r(/. moF>) (147,S... 15(IS K) (3) Since the end temperature is higher then 1773 K ali transition and latent heats of the reactants and products must be considered: 1. Fe|a —>/j) = 1033K, A//^^ = 5024j/.mol 1), 2. /v(jS-> y)= 1 lX3K.A///( y =92l(././ti<»/ 1). 3. Fe(y -> <5) = 1674 K.AH ^. = 879(j.mor1). 4. Fe(r,„) = 1809X.AHrm = 13S6()( J. mor'). 5. Fc2Si04[Tm = 1493 K). AH n = 92lo( J .mol '). Solution : Fig. 1 shovvs a plot of G„ versus T for the reaction ( 1). There is a change of the entalpv due to melting Fe,Si04 at T = 1492 K and calculated values for G,, over Cp - expression and from a formels (2) and (3). Fe + C + 3 % Si Figure 1: Plot ol thermodv namical data for Fe Si(); as a funetion of temperature calculated u ith GPRO-program. 1 Model I and I Lit.) using data from Richardson and Jeffes4 Slika 1: Diagram termodinamičnih podatkov /a Fe.SiO, kot funkcija temperature izračunano s programom GPRO. Exploiting the GPRO-program for complex equilibria calculations In this chapter, some examples of work performed in our lab-oratorv on the application ofthe computer-based model GPRO vvill be revievved. The accuracv of the gaseous atmosphere con-trol in steel decarburizing furnaces has been remarkably improved ovving to the application of computer control systems and the development of nevv measuring techniques (for example: oxygen and/or carbon sensors). Gaseous active atmospheres There is relativelv little emphasis in the literature about use of the thermodvnamical models on the field of active atmospheres. Such mixtures containing both gaseous and condensed components (for example: Fe + C + O + H + N are extremly complicated for the numerical calculations). Detailed experi-mental studies are difficult and also thermodynamical results are mostlv presented in the graphical form, vvhich are very useful in research vvork but of little effectivness in searching solutions for a current practical operation. To obtain equilibrium compositions in the real gaseous mix-tures bv high temperatures, taking into account both energy and material balances. development of nevv approaches are strongly required. E.\ample No. 2 Statement ofthe problem The use of gaseous atmosphere vvith a vvell-defined oxygen potential for decarburisation of lovv carbon iron-silicon steels in the continuous furnace can be simulated by use of thermody-namical model. h20/hj_ 10 10° / > '— ovca s.,«, £ -160 -180 -200 -220 c0,/c0 10 10° 10 -7-7—7 7 7 -SiOl : ?fe Vf .01*' ,-.2f eO —^ ^ C 01 i 200 400 600 800 1000 1200 u00 1600 1800 2000 2200 Temperature (°C) s .;■■ Po2(Bafl 1 coj/co 10" * 10"1' 10 10 \ i \ J \- P0,(Bar) 10"°10"M Att^ ^^—^ v,v\v —v- H20/H2 10 "10" 10™ Figure 2: Equilibrium behavior of different oxide phases during the decarburization of Fe-C-Si alloys in active gas atmosphere (CO + CO, + H, + H;0 + N2) Slika 2: Ravnotežni odnosi različnih oksidnih faz. ki nastajajo med razogljičenjem jekel Fe-C-Si v aktivni plinski mešanici iCO + CO,+ H,+ H,0 + N,) Equilibrium calculations and practical measurements shovv that solubilitv and carbon activity in Fe-C-Si steels depend on the gaseous atmosphere, temperature and steel composition. The thermodynamic analysis permit on the base of thermodvnamical data to prediet the equilibrium carbon contents in electrical steels (Fig. 2). Concluding Remarks One of the widely knovvn methods for chemical and metallurgical equilibrium calculations bv the high temperatures is Gibbs energy minimization method. Based upon these principles and implementing some algorithms from computer program SOLGASMIX, the nevv user-friendly computer program called GPRO vvas developed. GPRO-softvvare program is designed as a system vvhich can perform equilibria thermodynamic computations in systems containing gaseous and stoichiometric and/or non-stoichiometric condensed phases. The computer program lists options as menu and the user is slowly direeted through the program, choosing one option at a time. Before using the level ofthe main menu, user must create the relevant thermodynamic data lile vvhich contains the reliable thermodvnamic data as heat capacity, enthalpy, entropy vvith re-spect to a chosen references state. In this paper some typical examples are presented to illus-trate the simplicity of the computation in the complex chemical and metallurgical systems at high temperatures for typical in-dustrial applications. Reference Gaskel, D. R.: Introduction to Metallurgical Thermodvnamic McGravv - Hill Book Company, (Washington, D.C), (1973) : Christopher, W. B., G. Erriksson: Metallurgical Thermochemical Databases - a revievv. Canadian Metallurg. Quat. Pergamon Press. (Oxford) 29, 1990, 2, 105-132. Eriksson, G., K. Hack: ChemSage - A Computer Program for the Calculation of Complex Chemical Equilibria. Metallurgical Transactions H. (Materials Park, OH) 21B. 1990, 1013-1023 4 Richardson, F. D.. J. H. E. Jeffes:,/. Iron Steel Inst., (London) 160, 1948, 261-270 Koroušič, B.: Computerized thermodynamical expression of gas-metal reactions in industrial application of carburizing vvith in situ produced atmosphere process. Journal of Heat Treating, JHTRDR. (Franklin, WI) to appear 6 Koroušič, B.: Študij ravnotežnih reakcij v plinskih mešanicah l.del: Varovalne atmosfere. Rudarsko-metalurški zbornik. 40. 1993, 1-2,5-17 Koroušič, B., J. Langervveger., E. Kolb: Fortschritte in den Optimierungsrechnungen des Entkohlungsprozesses von Silizium-legierten Stahlen, HTM (1994) (to appear) s Koroušič, B.. A. Rosina: Contributions to the computer pre-dietions of the homogeneous and heterogeneous equilibrium compositions for the gas atmospheres. Veitscli - Radex Rundschau (1994), 1-2, 523-530.