Puddling: a New Look at an Old Process

Home , Henry Cort, Puddling (metallurgy)

ISIJ International, Vol. 49 (2009), No. 12, pp. 1960–1966

Puddling: A New Look at an Old Process

Merton C. FLEMINGS1) and David V. RAGONE2)

1) Professor, Toyota Professor Emeritus, MIT, Room 4-415, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. E-mail: ﬂ[email protected] 2) Senior Lecturer Emeritus, MIT, President Emeritus, Case Western Reserve University, 8 Hillside Road, Wellesley, MA 02481, USA. E-mail: [email protected] (Received on May 7, 2009; accepted on September 9, 2009)

Throughout most of the 19th century, the process of choice in the west for producing wrought iron and steel was “puddling” of cast iron. A major development of the process, “wet puddling”, became wide- spread commercially beginning in 1830. That process is examined quantitatively using modern thermody- namic, solidification and rheologic understanding. The ‘clearing’ and ‘boiling’ steps are considered in detail. In the ‘clearing’ step, the silicon is oxidized (by iron oxide) resulting in bath heating. Subsequent carbon removal from the melt, prior to initiation of solid iron solidification results first in the ‘low boil’, with simultaneous melt cooling. Then, as decarburization continues, solidification of iron begins, and with it, the ‘high boil’, with vigorous gas evolution and significant temperature increase. The importance of the iron solidification in promoting the decarburization reaction has not, in our opinion been fully understood heretofore. The lower the carbon content at the start of the boil, the higher the final melt temperature, and the lower the carbon content in the fully solid iron. During the high boil the four phase slurry of slag, liquid iron, solid iron and gas is thixotropic in nature, readily agglomerates, and possesses a low viscosity up to fractions solid of 0.2–0.3, with that viscosity rising rapidly at higher fractions solid. Comparison of the model presented with observa- tions from the actual puddling process is made. The qualitative and quantitative model presented agrees in general outline with the historical record and serves to strengthen our respect for those master puddlers who could control such a complex process with little other than their senses to guide them. KEY WORDS: wrought iron; puddling; iron history.

ceed that of wrought iron in Great Britain, and wrought 1. The Puddling Process iron continued to be produced commercially until well into 1.1. Historical Aspects the 20th century. Henry Cort, in 1784, perfected the process of decarburiz- Hall’s development is often referred to as the ‘wet pud- ing cast iron in a reverberatory furnace fired with coke, the dling process’ to differentiate it from the earlier ‘dry pud- oxidizing agent being the furnace atmosphere.1,2) The dling process’ which involved much less slag. Both process required constant stirring and so came to be known processes have been described in a number of recent and as puddling. After about 1795, British iron masters quickly contemporaneous publications, as summarized by Gale,1) adopted Cort’s process, and by 1815 British annual wrought Turner,4) Gordon,5) Morton and Birt6) and Barraclough.7) iron output had risen to 140 000 tons, almost a five fold in- Our attention was first drawn to Hall’s process on realiz- crease from the production in 1788 of 29 000 tons.3) While ing its apparent uniqueness—that the driving force for the Cort’s process represented a significant advance over earlier chemical refining is directly impacted by crystallization of processes for producing wrought iron from cast iron, it was the iron. In this paper we examine quantitatively, using slow, wasteful of iron, and could be used only with a lim- modern thermodynamics and kinetics, this ‘wet puddling’ ited range of compositions of cast iron. process, aiming to highlight its originality and importance. The next, and last, major inventive contribution to the Hall’s process has often been viewed as a minor improve- puddling process was that of Joseph Hall, building on a ment on that developed originally by Cort, but from a met- suggestion of Rogers.1) His essential change was replace- allurgical point of view, it is a wholly new and innovative ment of the silica furnace bottom by iron oxide. The critical process, involving different chemistry and process path, contribution from a chemical reaction standpoint was oxi- with concomitant significant advantages in cost and quality. dation of the carbon, not by the oxygen from the furnace at- This remarkable process built on the work of others over mosphere, but by that from iron oxide. Hall had begun his the previous century, combined a number of non-obvious experiments in 1811, and by 1830 was able to apply the essential elements, and permitted large scale manufacture process commercially. His process was spectacularly suc- of high quality iron by artisans without recourse to modern cessful and was to become the predominant ironmaking means of sensing and control. process for all the years wrought iron remained a significant engineering material. Only in 1885 did steel production ex-

burns in small flames called ‘puddler’s candles’. This is the 1.2. Melting and Rabbling ‘high boil’. In the words of Davis: ‘This formation of gas in As is to be expected, details of wet puddling practice the molten puddle causes the whole charge to boil up like changed somewhat over time and differed from location to an ice cream soda. The slag overflows. Redder than straw- location. Differences, for example, were in furnace size, berry syrup and as hot as the fiery lake in Hades it flows to components of the furnace lining (the ‘fettling’), and when the rim of the hearth and out through the slag hole. My and if additions were made during the process. Comparison helper has pushed up a buggy there to receive it. More than of descriptions of puddling dating to the 1870’s with those an eighth and sometimes a quarter of the pig iron flows off of puddling in the early 20th century, indicates a significant in the slag and is carted away. Meanwhile I have got the job increase in heat size and decrease in cycle time. Nonethe- of my life on my hands. I must stir the boiling mess with all less, the furnace design and puddling process were essen- the strength of my body’. tially unchanged, including a furnace lining containing a The puddler increases the stirring of the bath while de- high percentage of iron oxide, a cooled metal base plate on creasing the heat until the metal ‘comes to nature’. Again, which the furnace lining rested, and a vigorous boil during in Davis’ words, ‘Little spikes of pure iron like frost spars the carbon reduction stage. glow white-hot and stick out of the churning slag. These Several eyewitness accounts of puddling in the early to must be stirred under at once; the long stream of the flame mid 20th century provide an excellent overview of the from the grate plays over the puddle, and the pure iron if process. Gale1) and Morton and Birt6) have given first hand lapped by these gases would be burned up. Pasty masses of detailed accounts of puddling in Great Britain and Davis8) iron form at the bottom of the puddle. These would stick has done the same for puddling in the United States. In ad- and become chilled if they were not constantly stirred. The dition, Gordon,5) Lankford9) and Bray10) have summarized whole charge must be mixed and mixed as it steadily thick- accounts of others. Following is a composite description of ens so that it will be uniform throughout’. As the reaction the puddling operation one would have seen in an iron nears completion it becomes pasty and hard to work. The works during these later years of puddling, based on ac- change occurs rapidly, over a period of 6–8 min. With the counts of Gordon, Bray and Davis. elimination of the carbon nearly complete, the boiling sub- The puddler first fires his furnace, which is a reverbera- sides and the apparent volume of the slag decreases, called tory furnace capable of handling a 250 kg cast iron charge. ‘the drop’ by puddlers. Grains of iron, each enveloped in

A furnace lining comprising usually mostly Fe3O4 forms slag, appear as clusters as the slag drains away from the sur- the melting basin. It is sintered to form a monolithic struc- face. The metal has ‘come to nature’, and is ready for ture, with the aid of some added iron or slag. The lining balling. rests on an air cooled iron base. To start a heat, the puddler shovels the 250 kg of pig iron 1.4. Final Steps into the furnace, and also adds some mill scale (iron oxide). With the temperature under the melting point of iron, the He and his helper then do their best to seal all openings to puddler next separates the pasty mass of metal and slag into minimize entrance of oxygen to the furnace interior and three ‘balls’, transports them with the aid of his helper to a open the damper to get maximum heating and minimum “squeezer”, where much of the slag is removed. Then, after oxidation of the melting iron. Charging the furnace takes shaping and passing the metal through a series of roughing about 2 min. The heating and melting another 30 min. The and finishing rolls, the resulting product is ‘muck bars’, puddler then lowers the damper to keep heat input low and iron bars of about 20 mm thick, by 60–200 mm wide, by make the atmosphere less oxidizing, while his helper begins 5–9 m long. Typically these muck bars were cut into lengths to stir the metal to better expose it to the oxide rich slag 0.6–1.2 m long for subsequent processing. which has formed. This step of the process, called “clearing,” takes 8 or 10 min and removes much of the silicon and 2. A Puddling Model phosphorus. When the puddler sees a subtle change in color of the metal from reddish to a bluish hue, he knows that as 2.1. Adiabatic much of the phosphorus as possible has been removed. This The puddling model we present uses enthalpy changes step has taken about 10 min. connected with the several reactions involved in the “clearing” and “boiling” steps of puddling to calculate the result- 1.3. The Boil ing temperature changes of the bath, assuming adiabatic As soon as the metal has ‘cleared’, the puddler brings on conditions. For illustrative purposes, and for comparison the boil by adding some mill scale. To keep the phosphorus with actual practice, the initial composition of the cast iron from reverting to the metal, he initially maintains a smoky, charge chosen is 3.0 wt% carbon and 1.4 wt% silicon. The reducing atmosphere by keeping the damper low. The bath small amounts of other impurities present in practice is hard to stir, but after about 10 min of strenuous stirring, (Mn, S, P) do not affect the heat balance significantly in the the bath becomes more fluid. Carbon begins to oxidize. The refining. We first consider the case where all reactions are slag is somewhat viscous; it begins to foam and rise in the adiabatic and then look at effects of non-adiabatic condi- furnace and is permitted to flow freely out of the furnace. tions. The ‘low boil’ has begun. The charge is melted and taken to 1 260°C, just above its After sufficient depletion of the carbon, iron begins to liquidus temperature (point O in Fig. 1). Gentle stirring is solidify, carbon elimination becomes more rapid, the tem- begun to initiate ‘clearing’, and silicon removal com- perature rises and the gas escapes in larger bubbles and mences, primarily by the reaction:

Fig. 2. Temperature at which iron solidiﬁcation is complete vs. temperature at start of the high boil.

Fig. 1. “Path” of temperature vs. composition during iron reﬁn- ing.

Si 2FeO(liq) SiO2(liq) 2Fe(liq)...... (1) where Si represents silicon in an iron solution, and FeO is from the molten slag, which at this point is assumed to be about 10% of the metal weight. This reaction is exothermic, taking place over approximately 10 min. In our adiabatic case, the temperature rises 132°C, from 1 260°C to 1 392°C, the point shown schematically as point “A” on a portion of the iron-carbon phase diagram, Fig. 1, and as Fig. 3. Carbon content at the end of the high boil vs. temperature calculated in Appendix A. at start of the high boil. A small amount of roll scale is next added to help initiate the carbon boil. Carbon removal begins by the endothermic the heat evolved in solidification of the iron. Appendix B reaction: derives this equation and its analytic solution. The result for our adiabatic example is shown schematically in Fig. 1. The FeO(liq)CCOFe(liq)...... (2) overall heat balance is now exothermic due to the heat of where C represents carbon in an iron solution and FeO in solidification, hence, the temperature rises while solidifica- the liquid slag is assumed to be the reactant. The silica tion of iron and carbon removal take place simultaneously. formed during silicon removal increases the amount of slag, The composition of the liquid moves along the liquidus and is now assumed to be 20% of the metal weight. Tem- line, following the line BC, and the solid follows along the perature declines while carbon is being removed, as shown solidus, BC. The average composition of the liquid and by the line AB in Fig. 1, and as calculated in Appendix A. solid moves along the line BC. The temperature declines until the liquidus is reached, at This period of simultaneous iron solidification, carbon approximately 1 338°C and 0.089 mol fraction carbon removal and temperature rise, we conclude, corresponds to (2.06 wt% C). We conclude that this portion of the boiling the period of the ‘high boil’ referred to in the early litera- corresponds to the “low boil”, and the line AB represents ture. The sudden change from the slow gas evolution and the “reaction path” of the low boil. temperature decrease during the “low boil” results from the Once the reaction path intersects the liquidus, further many gas nucleation sites provided by the solidifying iron, carbon removal requires solidification of iron, since at any and by the exothermic nature of the overall reaction when given temperature, the liquid composition would otherwise iron solidification take place. move leftward on the phase diagram of Fig. 1 into the two In the example given, when the temperature reaches phase region and be “undercooled”. The following differen- 1 475°C the iron present is fully solidified and no further tial equation describes the heat balance from this point on: heating occurs. At this point, the composition of the re- maining solid is 0.29 wt% carbon. aC dTDH dC¯DH df 0...... (3) p R s L The temperature and composition of the metal at the time where T temperature, DHR heat of the carbon oxidation of complete solidification depend sensitively on the compo- reaction, C¯average composition of the liquid plus solid sition of the liquid metal at the time solidification begins; iron during solidification, DHs heat of fusion of the iron, i.e., at the place where the ‘path’ of the composition-tem- fL fraction of the iron that is liquid, and a is a factor de- perature change intersects the liquidus line. Figure 2 plots, fined in Appendix B that accounts for the heat absorbed by for the model employed, the temperature at which the iron the slag during the solidification process. For the case of no is fully solidified versus the temperature at this intersection slag, a1. (i.e., the start of the ‘high boil’). Figure 3 plots the carbon The first term of Eq. (3) gives the heat involved in content of the solid iron at the end of the high boil versus change of temperature of the melt; the second the thermal the temperature at the start of the high boil. Of course, con- energy from the chemical reaction of Eq. (2), and the third tinued decarburization is anticipated after the end of the

© 2009 ISIJ 1962 ISIJ International, Vol. 49 (2009), No. 12 boil and well into the balling and initial shaping stages since the iron particles, which are anticipated to be quite small, are embedded in an oxidizing slag, and the diffusion coefﬁcient of carbon in iron at these temperatures is high.

2.2. Non-adiabatic Conditions Flow of heat into or out of the metal charge would, of course, either accentuate or ameliorate the temperature changes described above. In practice, rate of heat extraction is limited by the need to maintain a protective atmosphere in the furnace. Rate of heat input is limited by the fact that maximum furnace temperature attained, even in these later days of puddling, was 1 430–1 450°C.6.10) The maximum rate of heat input at any given temperature can be readily estimated from the fact that the melting point of the cast iron charge is known, and the time required to melt is also known, This is carried out in Appen- dix C. For the alloy used in this example, the maximum rate of heating of the metal from externally applied heat at about 1 260°C (just above the melting point of iron with 3 wt% carbon and 1.4 wt% silicon) is about 10°C per minute. However, at the beginning of the high boil in our example (1 338°C), the rate of heat input from, say a 1 430°C furnace, would be negligible, and in the later Fig. 4. Viscosity vs. fraction solid for different shear rates in two stages of the boil, the melt would be above the furnace tem- semi-solid steels.17) perature. Thus, our assumption of adiabatic conditions in developing a model for wet puddling appears reasonable. ing from overflow during the high boil ‘...always contain Although crude optical pyrometers were in use early in some shots or granules of metal, which are carried over by the 20th century, we have as yet found no evidence of their the turbulence of the boil, and in some cases examined by application to puddling. Their use in any case would have the author as much as 16% of metal was found in the form been limited due to the smoky environment of the furnace of small globules...’.4) Killick and Gordon13) in their mi- during operation. One thing seems clear, however, is that crostructural study of puddling slags, do not report en- when old puddling records speak of “cooling the metal”, or trained metal, but it is not clear from what stage of the pud- “increasing the temperature” of the metal, these phrases are dling process these slags came. It would be of considerable better read as “decreasing heat input to the metal”, or “in- interest to examine slag microstructures known to be from creasing heat input to the metal”, since no temperature the high boiling stage of puddling. measurements were made, and the reactions themselves The flow behavior of fine grained semi-solid alloys is were producing internal heating or cooling. thixotropic, with viscosity depending on shear rate, and building rapidly when the spheroids are at rest, as a result 2.3. Rheology during the High Boil of agglomeration of particles. At reasonable shear rates, The bath during the high boil comprises four phases: liq- however, viscosity remains low until quite high solid frac- uid metal, liquid slag, solid metal and gas. Flow is vigorous tions are obtained, and then viscosity builds rapidly. Figure due to the boiling and to the manual stirring. We know little 4 is an example of viscosity of semi-solid steel alloys at about the details of such complex flow, but can build a several shear rates, versus fraction solid. The globular mi- qualitative picture. We assume that the two liquids are inter- crostructure of a steel alloy solidified under conditions of mixed on as fine a scale as the boiling and the manual stir- high shear rate is compared in Fig. 5 to the dendritic struc- ring can achieve. Gas evolution is occurring at the metal– ture obtained in conventional castings and ingots. slag interface, and solidification is occurring within the We expect the behavior of the metal phase to be similar metal phase. to the foregoing, with fine solid particles forming from the We do know a good deal about morphology and flow liquid, and the liquid gradually disappearing, leaving the characteristics of the metal phase as a result of decades of solid suspended first within a three phase fluid, then a two study of ‘semi-solid metal processing’. From this work it is phase fluid as the liquid metal disappears and finally within known that vigorous stirring in the initial stages of solidifi- a single phase fluid as the boiling ceases. At this point the cation causes dendrites to “break up” into fine grains which puddler seeks to capitalize on the tendency of the material then grow more-or-less spherically, their size depending to agglomerate as he produces his ‘balls’. only on ripening kinetics and hence on time in the A slag composition suitable for our puddling operation 11,12) liquid–solid zone. Hence in our example of a 30 min would be in the range of 15–20 wt% SiO2, balance iron ox- boiling time with, say 20 min of that during the solidifica- ides,7.10) and slag weight 20% of metal charge weight. Vis- tion stage, the average size of these spheroids would be cosity of this slag would be under 0.04 Pa·s at temperatures about 60 microns. above 1 300°C15); i.e., viscosity would be about half that of Relating to the foregoing, Turner writes that slags result- olive oil, and the slag would flow readily, Appendix D.

tances over which carbon needs to diffuse out of the liquid and solid iron phases. Details of the flow behavior of the four phase mixture existing during the solidification stage are certainly complex. Nonetheless, results of research on ‘semi-solid forming’ provide an excellent qualitative understanding of that behavior as it is reported in the historical literature. The mathematical model and its general agreement with the historic record serve to strengthen the view of the wet puddling process as a remarkable technological development, employing materials, furnaces and techniques at their then state of the art, and of their practitioners as remarkable in their strength, fortitude and skill. The technological ele- gance of the wet puddling process leads one to wonder if there may not yet be some practical application of the prin- Fig. 5. Grain structure of a conventionally cast stainless steel ciples of its operation. (left), and one solidified under conditions of high shear rate, (right).17) REFERENCES 1) W. K. V. Gale: Trans. Newcomen Soc., 36 (1963), 1. 3 Taking slag density as 4 000 kg/m and metal density as 2) R. A. Mott: Henry Cort: The Great Finer, ed. by P. Singer, The Met- 7 000 kg/m3, the slag at 20% of metal weight comprises a als Society, London, (1983). volume fraction of the slag plus metal of about 0.26. This 3) C. K. Hyde: The Coal and Iron Industries, ed. by R. A. Church and liquid volume fraction plus the metal liquid volume fraction E. A. Wrigley, Oxford, (1994), 244. 4) T. Turner: The Metallurgy of Iron, 6th ed., Griffin, London, (1920), provides an ample fluid vehicle for the particles forming in 339. the solid. Then, when boiling begins, the foaming slag itself 5) R. B. Gordon: American Iron, 1607–1900, Johns Hopkins, Balti- comprises an adequate volume to maintain a readily flow- more, (1996), 125. able slurry of the increasingly solid metal. Finally, when the 6) G. R. Morton and R. G. Birt: Hist. Metall., 8 (1974), 96. boiling ceases, and the slag settles back to its original vol- 7) K. Barraclough: J. Iron Steel Inst., 209 (1971), 785. 8) J. J. Davis: The Iron Puddler, My Life in the Rolling Mills and What ume fraction, it begins to drain away from the surface Came of It, Kissinger Reprint, (1922). grains, the phenomenon known as “the drop”. The remain- 9) W. T. Lankford, N. L. Samways, R. F. Craven, H. E. McGannon, eds.: ing solid metal/slag mixture no longer behaves as a fluid. The Making, Shaping and Treating of Steel, 10th ed., United State The metal has “come to nature”. Steel, Pittsburgh, (1985), 1. 10) J. L. Bray: Ferrous Production Metallurgy, Wiley, New York, (1942), 200. 3. The Model and the Historical Record 11) R. A. Martinez and M. C. Flemings: Metall. Mater. Trans. A, 36 (2005), 2205. The qualitative and quantitative model described above 12) M. C. Flemings: Metall. Mater. Trans. A, 22, (1991), 957. agree in general with the historical record and serves to 13) D. Killick and R. B. Gordon: His. Metall., 21 (1987). strengthen our respect for those master puddlers who could 14) B. Stoughton: The Metallurgy of Iron and Steel, McGraw-Hill,New York, (1911), 67. control such a complex process with little other than their 15) J. F. Elliott, M. Gleiser and V. Ramakrishna: Thermochemistry for senses to guide them. The process involves a complex inter- Steelmaking, Vol. II, Addison-Wesley, London, (1964), 664. play of heat flow, fluid flow, chemical reaction and solidifi- 16) E. T. Turkdogan: Fundamentals of Steelmaking, Institute of Materi- cation. Temperature, furnace atmosphere, slag chemistry als, London, (1996), 173. and amount, stirring and its timing, all needed to be con- 17) K. P. Young, R. G. Riek and M. C. Flemings: Solidification Process- ing 1977, Institute of Metals, London, (1977), 510. trolled independently with none of the measuring and control tools we have today. We conclude that the ‘low boil’ comprises that period of Appendix A. Thermodynamics of Silicon and Carbon carbon removal before solidification of iron begins; i.e., be- Removal fore the reaction “path” intersects the liquidus. Then, as so- Oxidation of Silicon lidification begins, the temperature begins to rise as a result After the pig iron has melted, iron oxide in the slag oxi- of heat of solidification evolved, and the solid iron grains dizes the impurities. Silicon is the first to be oxidized. The provide nuclei for rapid evolution of carbon monoxide, both chemical equation representing this process is given by Eq. factors leading to the ‘high boil’. These critical roles of the 1. The enthalpy change for this reaction, DHr is a negative solidification in changing an endothermic process to an 369.7 kilojoules, that is, the reaction is strongly exothermic. exothermic one, and providing heterogeneous nucleation The pig iron charged originally contained 1.4 wt% sili- sites, do not appear to be recognized in the literature. con, but a fraction of that (0.40 wt%) is assumed to be The vigorous action of both puddling and gas evolution burned off by the furnace atmosphere before oxidation by results in a degree of homogeneity of the iron not attainable the slag. When 1 wt% silicon (0.0178 mol fraction) is oxi- in earlier processes for producing wrought from cast iron. dized, the temperature change may be calculated as follows: Of equal importance, the fine structure produced permits m DH C DT ...... (A1) the process to proceed with great rapidity, both due to the Si r p high liquid–solid surface area, and to the very small dis- where Cp is the heat capacity of the iron/slag mixture. A

© 2009 ISIJ 1964 ISIJ International, Vol. 49 (2009), No. 12 value of 49.7 joules per mol °C is used to account for slag ement, simultaneously causing a change in the carbon con- weight, assumed to be 10% of the metal weight, Appendix tent of the element, its temperature and its fraction solid. D. The calculated value of DT is 132°C for the silicon oxi- We will assume equilibrium at the liquid–solid iron inter- dation. face and uniform temperature and uniform compositions of Assuming that the initial melt temperature was 1 260°C the liquid and solid within the element. Thus, as will be (point O in Fig. 1), just above the liquidus temperature for seen, the carbon content in the liquid portion of the element the pig iron, the temperature of the melt at the end of the will move along the liquidus from B to C during the reac- silicon oxidation (Point “A” in Fig. 1) would be about tion, and the solid composition will move along the solidus 1 392°C, assuming adiabatic conditions. In this and subse- from B to C, while the fraction liquid decreases. The only quent thermal calculations, heat required to raise the tem- iron considered is that produced by crystallization from the perature of additions and incorporate them in the slag is melt; the iron resulting directly from reduction of the slag is neglected. neglected. From a solute mass balance, assuming uniform solid and Oxidation of Carbon liquid compositions, Cs and CL and fractions solid and liq- Oxidation of carbon from the melt is represented by the uid fS and fL respectively: following reaction: ¯ fSCs fLCL C ...... (B1) FeO(liq)CCOFe(liq)...... (A2) The liquidus and solidus of the iron carbon diagram for Where C signiﬁes carbon in an iron solution. The enthalpy austenite–liquid equilibrium are shown schematically in change for this reaction, DHr is a positive 83.1 kilojoules, Fig. 1. We are concerned in this calculation with the tem- that is, the reaction is endothermic. Assuming adiabatic perature region where the solid is austenite. Taking the liq- conditions, the temperature of the melt drops as the carbon uidus, TL, and solidus, TS, as straight lines intersecting the is oxidized. The line representing the temperature of the ordinate at C0, melt as a function of carbon content will intersect the liq- C kC ...... (B2) uidus curve in the iron–carbon phase diagram. The compo- s L sition of the liquidus at the intersection of the two lines can Substituting Eq. (B2) in Eq. (B1), letting fS 1 fL, and dif- be calculated using the following relationship: ferentiating relates the change in average composition of the element to changes in liquid composition and fraction C WT(* T ) C 0 ...... (A3) liquid: L 11WmLLWm ¯ dC [fL(1 k) k]dCL CL(1 k)dfL...... (B3) where: C0 is the initial carbon composition The liquid composition is given by: T* is the melting temperature of pure iron C (T T*)/m ...... (B4) T is the temperature of the melt at the beginning of L L L carbon oxidation where T* is the temperature of intersection of the liquidus

W is the heat capacity of the melt and slag divided with the vertical axis and mL is its slope. Now, with equilib- by the enthalpy of the reaction rium at the liquid–solid interface and uniform temperature

mL is the slope of the liquidus line on the Fe–C and compositions of the liquid and solid within the element, phase diagram the temperature, T, of the volume element is: Using C 0.125 mol fraction (3 wt% C) , T1 392°C 0 TT T ...... (B5) (from the calculation on silicon oxidation above), W56.3/ L S 83 100, and mL 2 234, and Cp 55.3 J/mol °C (a value Where TS is the solidus temperature at solid composition which accounts for slag weight, assumed to be 20% of the CS. Let the reaction now take place, oxidizing the carbon metal weight in both the low and high boils, Appendix D). from the molar element. Taking DHR as the heat of reaction The liquid composition at the intersection is 0.089 mol frac- per mol of carbon oxidized and DHs as heat of fusion per tion carbon (2.06 wt% C) at a temperature of 1 338°C. mol of iron, and assuming adiabatic conditions, a heat balance yields: Appendix B. A Thermal Model for the High Boil aC dTDH dC¯DH df 0 ...... (B6) In the key step of the wet puddling process, molten cast p R s L iron at its liquidus is vigorously stirred in intimate contact where, from Eq. (B4): with an oxidizing slag consisting primarily of a solution of dTm dC ...... (B7) iron oxides with lesser amounts of silica and other oxides. L L The carbon in the liquid cast iron is oxidized in this key Substituting Eqs. (B3) and (B7) in Eq. (B6) yields: step, resulting in the crystallization of low carbon iron. Consider an element of liquid plus solid iron containing dC df L L 0 ...... (B8) an overall average composition of carbon, C, in two phases, CkqL ()11fkknL () liquid iron and solid. The element is small enough to be treated as a differential element. Associated with the ele- where: ment is an amount of slag sufﬁcient to increase the effective ac m H pL Δ s speciﬁc heat of the element from Cp to aCp where a 1 for n , q no slag. An oxidation reaction removes carbon from the el- ΔH R ΔH R

0 Integrating Eq. (B8) from CL at fL 1 to CL, fL gives the re- ing and cooling, the rate of heating at any temperature, T, in lationship between liquid composition and hence tempera- a furnace of temperature TF can then be written: ture through Eq. (B4): dT hA ⎛ TT ⎞ F ...... (C1) ⎡ 1 n ⎤⎛ q ⎞ q dt m ⎜ C ⎟ C C 0 ...(B9) ⎝ p ⎠ L ⎢ ⎥⎜ L ⎟ ⎢ fkknL ()111⎥⎝ k ⎠ k ⎣ ⎦ Where h is the heat transfer coefficient, A the effective sur- and the temperature change of the volume element is, from face area and m the moles of metal slag mixture. Making the slope of the liquidus: the simplifying assumption that the iron melts at a single, average temperature, T , within the melting range, the rate DTm (C0C )...... (B10) M L L L at which heat is added to the melt, Q, is: where: mH 0 Δ f DT T T ...... (B11) QhATT()FM ...... (C2) tM And T 0 is the temperature on the liquidus line at the start of the reaction. Combining Eqs. (B9) to (B11) yields: where tM is time of melting. Combining (C1) and (C2) yields: ⎛ q ⎞ ⎛ 1 n ⎞ ΔTmC0 1 ....(B12) LL⎜ ⎟ ⎜ ⎟ dT ⎡ H ⎤ ⎡ TT ⎤ ⎝ 1 k ⎠ ⎝ fkknL ()1 ⎠ Δ f F ⎢ ⎥ ⎢ ⎥ ...... (C3) dt Ct TT ⎣⎢ pM⎦⎥ ⎣⎢ FM⎦⎥ Input data: DHR 83.1 kJ/mol Approximating the melting point as 1 200°C (intermediate DHs 13.8 kJ/mol within the melting range of the iron), the furnace tempera- Cp 44.1 J/mol C ture as 1 430°C and the melting time as 20 min (of the a1.25 30 min reported for heating and melting the charge), gives a 0 CL 3 wt% 0.125 mol fraction maximum rate at which heat can be introduced from the CE 0.175 (eutectic composition) furnace to the melt. It is less than 10°C/min at the melting T*1 538°C point of 1 260°C, much less than an average of 1°C per TE 1 147°C (eutectic temperature) minute during the high boil, and negative at furnace tem- ⎛ C ⎞ 008. peratures above 1 430°C. S k ⎜ ⎟ 046. ⎝ CE ⎠ 0. 175 Appendix D. The Slag TT * 1147 1538 We assume for the model a slag at the high boil in the E mL range of 15 wt% silica, with the balance primarily iron ox- CE 0. 175 ides, in general agreement with analyses reported by 2 234 (liquidus slope) Stoughton (p. 67) and by Bray10) and Stoughton.14) Slags in 13. 8 this range of composition would have a viscosity under q 0. 166 83. 1 0.04 Pa·s at temperatures above 1 300°C, and so would 15) (.125 )( 441 .)( 2234 ) flow readily. Slag density would be approximately n 148. 4 000 kg/m3.16) 83100 Slag weight during the high boil, according to Bray, is in Another form of Eq. (B9) is: the range of one quarter to one third of the metal weight for irons containing in the range of 1% silicon (Bray, p. 67). A ⎡ CZ0 ⎤ ⎡1 n ⎤ ⎡ nk ⎤ simple calculation yields a slag weight after silicon oxida- f L ⋅ ...... (B13) L ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ tion comparable to, but less than, that mentioned by Bray. ⎢ CZL ⎥ ⎣⎢11k ⎦⎥ ⎣⎢ k ⎦⎥ ⎣ ⎦ The calculation assumes all the silicon in the metal is con- where: Z q/(1 k) verted to silica in a slag containing 15 wt% SiO2, with the Notes: Two approximations have been made to facilitate balance FeO. This calculation gives a slag weight of ap- simple analytic solution. These are: a) the austenite liquidus proximately 20% of the metal weight. In calculations and solidus are taken as straight lines which intersect at herein, slag weight is assumed to be an average of 10% of their extrapolaton to zero carbon, and b) in Eq.(B12), the the metal weight during silicon removal, and 20% of metal only iron solidifying is that iron in the original charge. The weight during the low and high boils. Taking the slag spe- added iron from the chemical reaction (less than about 15% cific heat as 1.00 kJ/kg·°C, that of the iron as 0.79 kJ/kg°C, of the total) is neglected. the effective specific heat of the slag/metal mixture is there- fore 0.89 kJ/kg·°C (49.7 joules per mole °C) during the sil- Appendix C. Estimate of External Heat Input to the icon removal and 0.99 kJ/kg·°C (55.3 J/mol °C) during the Iron Charge low and high boils. The value of “a” used in calculations Assume convective heat transfer from the furnace atmos- for the high boil is then 0.99/0.791.25. phere to the metal/slag surface. From Newton’s law of heat-