Method for determining a degree of oxidation of a steel product, associated control and monitoring methods and systems

Abstract

A method for determining a degree of oxidation of a steel product, the method comprising: - acquiring one or more alloying elements contents for the steel product, among the following list: a Silicon content, an Aluminium content, a Chromium content, a Copper content, a Phosphorous content, a Carbon content, - computing a growth rate K p for a quantity X o 2 , where X o is representative of an amount of scale formed on the steel product, K p being computed according to the equation eqn-p2 below: formula (a) where K p0 is a rate coefficient computed depending on the one or more alloying elements contents.

Description

Method for determining a degree of oxidation of a steel product, associated control and monitoring methods and systems

[0001] The technical field is that of steelmaking, more particularly that of characterizing and controlling surface oxidation, that is scale growth and possibly decarburization.T e c h n i c a I b a c k g r o u n d

[0002] During a steel processing operation, when a steel product is hot and is in an oxidizing atmosphere, like in a reheating furnace for instance, an iron oxide layer called scale forms at the surface of the steel product.

[0003] Being able to predict the amount of scale that forms in the course of a steel processing operation is useful. Indeed, as a matter of example, there is an interplay between the scale growth and the evolution of the decarburized depth in the steel: if the scale growth is faster than the decarburization, the final decarburized depth at the steel surface is very small (most of the decarburized steel having been consumed - namely oxidized - to form the fast-growing scale), or even null, which has an impact on the mechanical properties of the final product.

[0004] Being able to predict the amount of scale that forms on a steel product is useful in particular for real-time control of the steel processing operation (eg: the product reheating), for allowing an operator to follow the impact of the in-course processing operation on the product properties, or for determining the properties obtained for a steel product that has been processed, depending on the processing conditions during the processing operation.

[0005] It is known to model the kinetic of the scale growth using two successive regimes: first a linear regime and then a parabolic regime. During the linear regime, the amount of scale grows linearly with time t and the growth speed is proportional to the oxygen partial pressure PO2 in the atmosphere surrounding the steel product. Once a layer of scale formed on the steel surface, the scale growth is limited by diffusion through the scale (in particular Fe2+diffusion via cation vacancies). During the second, parabolic regime, the amount of scale grows proportionally to jt - t *, instead of proportionally to t. In practice, the parabolic regime often takes over the linear regime quite quickly, for instance a few seconds after scale growth has begun, and plays an important role.

[0006] For the parabolic regime, when the temperature T of the steel is constant, it is known to compute the scale thickness eSCai according to escat= K. (t - 1 *) with K = Cst. PO^2. exp where Cst is a constant rate coefficient, R is the universal gas constantand Qp is an activation energy. More specifically, in “L'Oxydation des Metaux » by J. Benard, volume II, 1964 Gauthier-Villars & Cie., Paris, J. PaTdassi teaches to compute the scale thickness escai, in air, for pure iron, according to eScai (mm) = 24.6 exp [-^7^]

[0007] But in practice, in the steel making industry, it is not pure iron that is produced but steel with different alloying elements therein. So, the above formula is not necessarily adequate for accurately predicting scale growth, not to mention decarburization.Summary

[0008] In this context, a method according to claim 1 , is provided.

[0009] It has been observed that some alloying elements noticeably influence the diffusion through the scale, and thus the growth speed of the scale. More specifically, it has been observed that the alloying elements having the strongest influence are Silicon Si, Aluminium Al, Copper Cu, Phosphorous P and, to a smaller extent Chromium Cr and Carbon C. For each of these elements, the presence of the element slows down the scale growth. More precisely, the higher the element content, the smaller the growth rate. So, to improve prior art models, the growth rate of the scale is computed depending on one or more of the above-mentioned alloying elements, so as to be all the smaller than the alloying element content considered is high. The most accurate computation is obtained by taking into account all of the element contents above mentioned. But, even taking into account one of them allows for predicting the scale growth kinetics (in order to determine either the scale thickness, or the decarburized depth), for different kinds of steel, better than with prior art models in which the growth rate is independent of alloying elements contents, or is determined to suit specifically one given chemical composition only.

[0010] The method according to the instant technology may comprise one or several additional features, defined in claims 2 to 13, considered alone or in combination.

[0011] The instant technology also concerns an electronic device according to claim 14. It concerns also a computer program, whose execution on a computer makes the computer to execute the method according to anyone of claims 1 to 13 (the computer being possibly connected to sensors and / or actuators of steelmaking installation, or to a controller of the installation, or to one or more external storage devices, depending on the details of implementation of the method). It concerns also a non-volatile computer-readable storage medium comprising such a computer program.Detailed description

[0012] The instant technology will now be described in more detail and illustrated by examples without introducing limitations, with reference to the appended figures.

[0013] Figure 1 schematically represents a linear than parabolic growth, over time t, of an amount of scale formed on a steel product.

[0014] Figure 2 is a schematic sectional side-view of the steel product.

[0015] Figure 3 is an Arrhenius-like plot of a parabolic growth rate for scale, as a function of the inverse of the temperature of the steel product, for different scale growth experimental tests carried out for numerous steel grades.

[0016] Figure 4 is a graph representing a mass increase due to scale growth, as determined according to the instant method, plotted against a corresponding measured value, for different test carried out on various steel samples.

[0017] Figure 5 represents a measured amount of scale formed on a steel product over time, together with an amount of scale predicted according to the instant method.

[0018] Figure 6 represents schematically an installation comprising a reheating furnace and a control and monitoring system for the reheating furnace.

[0019] Figure 7 represents schematically a system for determining a degree of oxidation of steel product based on a temperature path followed by the steel product.

[0020] As above mentioned, the instant technology concerns a method for determining a degree of oxidation for a steel product, more specifically a degree of surface oxidation resulting from a steel processing operation (such as a reheating, prior to a hot rolling) or from a part of a steel processing operation. The degree of oxidation of the steel product may be either:- a quantity noted Xo, which is representative of an amount of scale formed on a steel product, or- a decarburized depth Ddecat the steel surface.

[0021] In this regard, it is noted that both scale growth and decarburization result indeed from an oxidation (of Iron, and of Carbon respectively).

[0022] Alternatively, the degree of oxidation determined according to this method could be a steel denatured thickness Dden.

[0023] The quantity Xoin question may be either the thickness of the scale, a mass gain for the steel product (caused by iron oxidation at the surface of the steel product), or an amount (eg: a thickness) of consumed steel (namely an amount steel that has been oxidized) for the steel product.

[0024] Anyhow, the instant method for determining the degree of oxidation of the steel product comprises computing a growth rate for the quantitythis growth rate, noted Kp, being computed depending on one or more alloying elements contents in the steel of the steel product. The growth rate Kpmay then be employed to compute the quantity Xo, or directly to compute the decarburized depth Ddec(taking the growth rate of the scale into account), or to compute both Xoand Ddec. The steel product in question may be a steel semi-product such as a slab, a bloom, a billet, a wire or an ingot. It could also be a beam, a bar, a tube, a rail, or a steel sheet.Linear and parabolic regime for isothermal scale growth

[0025] The isothermal scale growth at the surface of a steel product can be modelized by, first, a linear growth regime (growth linear with time t) followed by a parabolic growth regime (growth proportional to the square root of time t), as represented in figure 1 .

[0026] During the initial linear regime, oxidation is mostly limited by surface reactions at the metal-oxide or the oxide-gas interface. For isothermal conditions, the increase of the quantity Xo, proportional to time t, is given by the following equation:Xo= KLt (eqn — Zl) wherewith PO2 the partial dioxygen pressure, Qi an activation energy and KiOa rate coefficient for the linear regime. The pre-exponential factor Kl0PO2may be expressed in g.cm-2.s-1for instance if the quantity Xois the mass gain, or in micron. s-1if the quantity Xois the scale thickness.

[0027] During the subsequent parabolic regime, oxidation is mostly limited by diffusion through the scale. For isothermal conditions, the increase of the quantity Xo, proportional to the square root of time t (with a time shift t*), is given by the following equation:Xo= (eqn — pl)wherewith Qpthe activation energy and KpOa rate coefficient for the parabolic regime.

[0028] It is assumed that the growth is limited by the slowest of these two regimes. In other words, it is the slowest of the two kinetics that is followed. So, the transition occurs when the linear and parabolic laws have the same slope. This is obtained for a critical thickness (or mass gain) Xo crit= for which the regime changes from linear to parabolic. When the scale’ 2 / thickness (or mass gain) is below the threshold value Xo crit, the linear law applies, while above it parabolic law is used. This transition criteria can be used at any temperature (that is, even for non-isothermal growth, as long as the values of Kpand Ki - which are temperaturedependent - are computed for the current temperature of the steel product).

[0029] For an isothermal growth, the time when the change of law occurs can be computed as tcrit= while the time offset t* for the parabolic law can be computed as t* =2Ki 4 iScale growth modelization

[0030] In practice, during a steel processing operation, for particular during re-heating in a reheating furnace, the temperature T of the steel product is usually not constant (i.e.: thetransformation is not isothermal). When the temperature T varies over time, instead using of equations eqn-11 and eqn-p1 , the quantity Xomay be computed time step by time step, based on the linear growth rate Ki, or on the parabolic growth rate Kp(whose value depends on the temperature T at the time step considered), depending on the growth regime at play.

[0031] Anyhow, the parabolic regime influences substantially the amount of scale formed on the steel product (and plays often a more important role than the linear regime, either because the linear regime ends quite quickly, or because the product surface was already oxidised). And it has been observed that the rate coefficient Kp0for the parabolic regime is noticeably influenced by some alloying elements, mostly Silicon Si, Aluminium Al, Copper Cu, Phosphorous P and, to a smaller extent Chromium Cr and Carbon C.

[0032] So, remarkably, the instant method for determining the quantity Xo, or more generally for determining the degree of oxidation of the steel product, comprises:- acquiring one or more alloying elements contents for the steel product, among the following list: a Silicon content xsi, an Aluminium content XAI, a Chromium content xcr, a Copper content xCu, a Phosphorous content xP, a Carbon content xc,- computing a growth rate for the quantitythis growth rate being equal to the above- mentioned quantity Kp, equal to where the rate coefficient Kp0iscomputed depending on the one or more alloying elements contents mentioned above, Kp0being equal to a base rate coefficient k0when each of the one or more alloying elements contents is null and wherein, for each of the one or more alloying elements contents, Kp0is all the smaller than the alloying element content considered is high.

[0033] The quantity Xois representative of the amount of scale formed on the steel product for instance between an initial time ti and a current time t, or between an initial time ti and a final time tf corresponding to an end of the steel processing operation. It is computed based, inter alia, on said growth rate Kp.

[0034] In this document, except otherwise specified, by “equal” it is meant equal within 10%, or even within 5% or within 2%.

[0035] From the point of view of an electronic device (such as a computer) executing this method, acquiring the one or more alloying elements means receiving data representative of the one or more alloying elements.

[0036] The one or more alloying elements contents in question are acquired by a computer or electronic device or system executing the instant method. In other words, data representing these contents are received by the computer or electronic device or system, and stored in a memory therein; these contents may be received from another device (such as a chemical analyzer), loaded from a production database, or input by an operator.

[0037] Determination of the rate coefficient KD0

[0038] For each of the above-mentioned alloying elements (Si, Al, Cr, Cu, P, C), it has been observed that the presence of the element considered slows down the scale growth. More precisely, the higher the element content, the smaller the growth rate.

[0039] The growth rate coefficient Kpomay be determined taking into account the Copper content xCuat least (and possibly also one or more of the others alloying elements). This is beneficial as steelmaking production is more and more based on steel scraps recycling using Electric Arc Furnaces, which results in steel products having a substantial copper content, for which it is thus desirable to take the copper content into account.

[0040] Besides, the growth rate coefficient Kpomay be determined taking into account at least two of the alloying element contents xSi, XAI, xCr, xCu, xP, xc, or even at least three of them. Indeed, the value of the growth rate coefficient Kpois more accurate when taking two or three of them (or even all of them) than when taking into account just one of these alloying elements.

[0041] For instance, the growth rate coefficient Kpomay be determined taking into account at least the Copper content xCu, the Silicon content xSiand the Aluminium content xAi. Indeed, it has been observed that these three elements (Cu, Si, Al) are the one that influence the more the scale growth kinetics.

[0042] The growth rate coefficient Kpomay, like here, be computed independently of the temperature T of the steel product, and independently of PO2.

[0043] More specifically, the growth rate coefficient Kpois computed here as being equal to k0 / (1 +S), with S being a sum of one or more of: asi.xsi , aAi.xAi, acr.xcr , acu-Xcu , ap.xP, ac.xc, where a&, aAi, acr, acu, ap and ac are positive coefficients.

[0044] For instance, if Kpois determined based on xSi, XAI, and xCu(alone), it is computed as k0 / (1 + asi.xsi + aAi.xAi+ acu-Xcu)-

[0045] When Kpois determined based on all of x&, xAi, xCr, xCu, xPand xc, like it is the case here, it is then computed as:

[0046] When the alloying elements contents are mass fractions each expressed as a weight%, the values of the coeficients a&, aAi, acr, acu, ap and ac are as follow:- aSi=150,- aAi=250,- aCr=40, acu=150,- ap=100- ac=20.

[0047] It is noted that Kpocould be determined, based on the one or more alloying elements contents, using a look-up-table instead of using eqn-p3, in alternative embodiments (or using another formulation than eqn-p3, that captures the main variations of Kpowith xSior xAi),

[0048] The values specified above for the coefficients as, aAi, acr, acu, ap and ac are derived, by regression, from experimental characterizations of steel oxidation carried out for numerous grades (23 different grades) with different chemical compositions covering at least the following content ranges (expressed in weight %): xSi<0.3 ; XAI<0.12 ; xCr<l ; xCu<0.3 ; xP<0.11 ; xc<0.5. The steel grades tested comprised, inter-alia, HSLA (High Strength Low Allow), IFS (Interstitial Free Steel), TRIP (T ansformation Induced Plasticity) and DP (Dual Phase) steels, Usibor® steel, and steel typically designed for food packaging, with Ultimate tensile Strength ranging from about 350 Mpa to more than 1500 MPa.

[0049] The experimental characterizations of the scale growth were carried out by thermobalance measurements, that is by measuring the evolution over time t of the mass of a steel sample placed in an oxidizing atmosphere. The surface of the steel sample is initially deprived of scale (and polished and degreased before the test). The tests were each achieved at a given, fixed temperature (isothermal oxidation). The range of tested temperatures is from 700°C to 1200°C.

[0050] For each test, the scale growth is isothermal, and the linear regime and then parabolic regime are well observed and identified, enabling determining both the values of Ki and Kp(for the temperature and dioxygen pressure considered).

[0051] The tests were carried out for different atmosphere compositions, in particular for (proportions expressed as volume contents):- 3%C>2, 15%H2O, 10%CC>2, the rest being N2, with a total pressure of 1 atm; this atmosphere composition is typical of the one in a reheating furnace (heated by naturalgas combustion), and for- 20%C>2, 15%H2O, the rest being N2, with a total pressure of 1 atm; this atmosphere composition being typical of the atmosphere in the roll bite vicinity.

[0052] Tests with higher H2O contents were also carried out (1%O2, 27%H2O, the rest being N2, for instance) to test the influence, discussed further below, of moisture on scale growth.

[0053] To achieve such isothermal oxidation tests, the temperature of the sample is gradually increased with a neutral (non-oxidizing) atmosphere; then, once the test temperature is reached, one switches to the oxidizing atmosphere above mentioned.

[0054] The test results show that both Ki and Kpdepend indeed on the temperature T according to an Arrhenius Law (see eqn-12 and eqn-p2), with activation energies QI and Qp which are, to a good approximation, independent of the alloying element contents. The test results show also that a linear dependence of Ki with PO2, and a linear dependence of KpwithPO^2are indeed adequate modelizations of the influence of the dioxygen pressure on the scale growth.

[0055] The coefficients asi, 3AI, acr, acu, ap and ac mentioned above, as well as k0, can be determined by a multilinear regression of 1 / KP, as a function of the different alloying element contents x&, xAi, xCr, xCu, xPand xc, or using other numerical fitting technical (for instance, a linear regression in a log-log plane)

[0056] Figure 3 represents the quantity Kp.(1 +S) (in arbitrary units, and in log scale) as a function of the inverse of the temperature 1 / T (with T in kelvin) for the tests achieved (for the cases with an atmosphere composition with 20%O2, 15%H2O, the rest being N2). Figure 3 illustrates both that:- correcting k0by dividing it by the quantity (1 +S), S being computed depending on the chemical composition of the steel as above described, is an adequate way to take this chemical composition into account; indeed, the different points are reasonably well aligned and grouped, in figure 3, and that- the temperature dependence of Kpcan indeed be modelized by an Arrhenius law, with the corresponding activation energy Qp independent of the alloying elements contents.

[0057] Determination of the quantity Xo

[0058] As above mentioned, the quantity Xois representative of the amount of scale formed on the steel product during the steel processing operation. The steel processing operation starts at the initial time ti and ends at the final time tf, and time t is the current time considered, during this operation.

[0059] The steel processing operation is for instance: a reheating in a reheating furnace (prior to hot rolling), or a transfer from a reheating furnace to a hot roll mill entrance (hot roll bite vicinity), or a continuous casting, or temperature-maintaining storage (using heat containment enclosures), between the continuous casting output and the reheating furnace input. More generally, it is a steel process operation occurring at high temperature (typically above 600 °C, or even above 700°C) and in an oxidizing atmosphere.

[0060] As above mentioned, the quantity Xomay be representative of the amount of scale formed during the whole steel processing operation, that is from ti to tf, for instance to predict the total amount of scale expected at the end of the processing operation, in order for instance to adjust process parameters depending on a scale amount target, or depending on a decarburization target.

[0061] The quantity Xomay also is representative of the amount of scale formed during the steel processing operation from the initial time ti to the current time t, for instance for monitoringin real time (via the instant growth modelization) the amount of scale currently formed (or the decarburization that has currently occurred).

[0062] Anyhow, the quantity Xois determined using a time step by time step computation, starting from an initial value X0(ti). In practice, for a reheating operation in a reheating furnace, X0(ti) can often be taken as equal to zero.

[0063] If X0(ti) is below X0,Cnt, the increase of Xois first computed according to the linear growth regime, time step by time step, according to AX0=Ki.At (where AX0is the increase of Xoduring the time interval At), until Xoreaches X0,crit- Then, the growth is computed according to the parabolic growth regime. If X0(ti) is already above X0,cnt, the growth is computed from the beginning according to the parabolic growth regime.

[0064] For the parabolic growth regime, the increase of Xois computed by calculating, time step by time step, the increase of X , that is AX„ = Kp. At. The value of Xois then deduced form the value of X . Computing elementary increases of X , rather than computing AX0= - - .At,2X0is beneficial from a numerical point of view. Indeed, it avoids having evaluations errors on Xoimpacting the evaluation of the increment of scale amount. And it avoids also possible numerical errors arising from the computation of 1 / X0for small values of Xo.

[0065] At each time step, either the value of Ki, or the value of Kpis determined based on the value of the temperature T at that time step.

[0066] In Figure 4, predicted values for the mass gain (Xo), after 30 seconds of oxidation (in arbitrary units), are plotted against corresponding measured values X0,m, for various test conditions (same test conditions as for figure 3). The predicted values are determined based on the value of Kpodetermined according to eqn-p2, with the values of the coefficients asi, HAI, aCr, acu, ap, ac specified above. Figure 4 illustrates that the values of Xo, predicted according to the instant method, are in good agreement with the one directly measured.

[0067] Figure 5 represents Xo, more precisely the mass gain (arbitrary unit), as a function of time t (in seconds), as measured during a thermobalance test carried on at 900°C. The sample was an Usibor® 1500 sample. The atmosphere contained (volume fraction) 20% O2, 15% H2O the rest being N2, at 1 atm. The measured values are represented by the plain line while the values determined by computation, according to the above-described method, are represented by the dashed line and are in good agreement with the measured values.

[0068] Figure 6 represents tests results for a non-isothermal oxidation, with a thermal path representative of a typical reheating in a reheating furnace of a steel making line. Figure 6 represents Xo, more precisely the scale thickness (in microns) against time t (in hours), determined as above explained. The steel is a leaf spring grade whose composition is given below. Figure 3 also represents the temperature T of the steel product, against time t. For this test, the temperature T is measured thanks to a temperature sensor fitted on the steel sample.Figure 6 also represents a decarburized depth Ddec, determined as explained further below, against time t. The final value of scale thickness, determined as above described, is 0.437 mm, in good agreement with the measured value, which is 0.428 mm. It illustrates that the instant method can indeed be used for processing operations during which the temperature varies with time. The chemical composition of the steel is the following, for this test (in weight%): Xsi=0.263 ; XAI=0.011 ; Xcr=0.99 ; Xcu=0.04 ; Xc=0.51 (and XMn=0.94, xv=0.1 and XPnegligible).

[0069] It is noted that, for this test, the temperature of the steel product was measured directly all along the steel processing operation (so as to test the scale growth computation itself). Yet, in several applications of the method for determining Xo, such as the applications presented later below, the temperature T(t) could be determined non-directly, using thermal models.

[0070] Second parabolic regime

[0071] Optionally, if the temperature becomes higher than a given temperature threshold TH during the steel processing operation, a second parabolic growth rate Kp2higher than Kpmay be used instead of Kpfor the computations of AX done above TH. The temperature threshold TH is typically from 1 100 to 1200°C. It corresponds to a temperature above which oxides of some alloying elements melt, in the scale, which accelerates scale growth.

[0072] Influence of moisture

[0073] Optionally also, the parabolic growth rate Kpmay be corrected to take the influence of moisture into account. More specifically, it has been observed that, at low temperature (below a temperature TH.HSO, which is typically of 1100°C), the presence or not of H2O, in the atmosphere where the steel product is, does not modify substantially the scale growth kinetics. On the contrary, at high temperature (above TH.HSO), the presence of H2O may slightly accelerate this kinetics. So, optionally, when the temperature is above T ,H2O, instead of using Kpdirectly to compute AXQ , KPis corrected first, for instance by adding a correction term to Kp, this correction term depending on the partial pressure of H20 in the atmosphere surrounding the steel product.

[0074] The method for determining the quantity Xomay be implemented differently than in the detailed example presented above. For instance, the transition from the linear growth regime to the parabolic regime may be achieved based on another threshold than X0,Crit, or so as to be more gradual. Possibly, the computation of Xocould be based directly on the parabolic growth regime, the linear growth regime being neglected (when the steel product is maintained at high temperature for a long time, typically several minutes, the influence of the linear regime is often negligible).Decarburization

[0075] Figure 2 schematically represents some aspects of the scale growth and steel decarburization mechanisms. Figure 2 is a schematic cross-section sideview of the steelproduct 2. The scale 21 forms at the surface of the steel 20, due to the presence of dioxygen O2 in the atmosphere 3 where the steel product 2 is. Some of the chemical reactions occurring at the steel-scale interface, and at the scale-atmosphere interface are represented in figure 2. Some chemical species fluxes are schematically represented by arrows. Not only iron is oxidized, but carbon too. More precisely, the carbon initially contained in the steel is oxidized in the form of gaseous species (CO and CO2) and the carbon content at the steel surface (steel-scale interface) thus decreases, compared to the carbon content Cbuik in the bulk of the steel. The carbon profile 22 schematically represents the evolution of the carbon content (carbon concentration) as a function of depth, in an exemplary case for which the steel is assumed to be entirely in the form of austenite. As represented, the carbon content decreases from the in-depth content Cbuik to a lower content Csat the steel-scale interface. The thickness of the carbon-lean region is the decarburized depth Ddec. It may be defined as the depth for which the carbon concentration is equal to Pdec-Cbuik, with Pdec a constant, for instance from 0.7 to 0.95.

[0076] In Figure 2, the initial position of the steel surface, before oxidation starts (before scale growth starts), is represented by the dashed-line 23. As already mentioned, the quantity Xo, representative of the amount of scale formed on the steel product 2, can be indifferently the scale thickness, the mass gain, or the thickness of consumed (oxidised) metal which is more specifically noted Xoc(see Figure 2). The total thickness of denatured steel (denatured by iron oxidation and by decarburization) is noted Ddenand is the sum of Xocand Ddec.

[0077] The instant method may comprise a determination of the decarburized depth Ddecor a determination of the denatured thickness Dden, instead of, or in addition to the determination of the quantity Xo. The determination of Ddecor Ddenis based on the quantity Xodetermined as above described, or on the growth rate Kp. Indeed, the scale growth influences directly the evolution of the decarburized depth Ddecand of the denatured thickness Dden, because the scale grows by consuming steel at the scale-steel interface (steel whose iron is oxidized). For example, if the scale grows quickly compared to the decarburization process (i.e.: compared to carbon diffusion in steel), the decarburized steel near the steel-scale interface is consumed faster than its forms and the decarburized depth Ddecdecreases with time, or remain negligible.

[0078] The computation of the evolution of Ddecover time t can be achieved by computing at each time step an updated carbon content profile, said profile being computed by numerically solving a 1 -dimensionnal Fick equation for carbon diffusion, with a frontier condition being that, at Xoc(t), the carbon content is Cs.

[0079] The evolution of Ddeccould also be computed based on the following equation:where Xdecis a distance between the initial position of the steel surface 23, prior to oxidation, and an end 24 of a zone that is decarburized, in the steel product, at time t,(Xdecbeing determined based on carbon-diffusion computation). Regarding A gC, it is computed as above explained; in particular, for the parabolic growth regime, it equals Kp. t.

[0080] Alternatively, the evolution of the decarburized depth Ddeccould be determined using other computation methods based on carbon diffusion, from the bulk to the steel-scale interface.

[0081] Regarding the carbon content Csat the steel-scale interface, it can be determined based on chemical equilibriums at said interface, in particular the chemical equilibriums between C, O2, CO and CO2. Alternatively, Cscould be approximated to be null (which can be an acceptable approximation when scale growth is slow compared to carbon diffusion in steel). Process monitoring and control

[0082] Figure 6 schematically represents an installation 1 for reheating steel products, such as slabs or billets. The installation 1 comprises a reheating furnace 30 and a monitoring and control system 10 for monitoring and controlling the steel products reheating.

[0083] The reheating furnace 30, for instance a walking beam furnace, has an input port 31 , to input the steel products, and an output port 32 for outputting the heated steel products. The reheating furnace 30 comprises actuators for controlling the reheating process, such as electrovalves for controlling fuel gas fluxes, electric power supplies for adjusting electric power supplied to electric heaters, or electric motors or servomotors for controlling the displacement of the steel products, from the input port to the output port.

[0084] One or more of these actuators is controlled by control data 18 output by the monitoring and control system 10. The control data 18 may take the form of control signals suitable to directly control the actuators, or may take the form of setpoints for controlling the actuators through the intermediary of low-level automation modules (such as PID control loops, for instance).

[0085] The installation 1 comprises one or more temperature sensors, arranged to measure the temperature T of the steel product 2 considered, before or during its reheating. It may be a temperature sensor placed upstream of the input port 31 and measuring an ambient temperature upstream of the reheating furnace. It may also be a temperature sensor such as a pyrometer arranged in the reheating furnace and measuring a (surface) temperature of the steel product at a given moment during its reheating. The reheating furnace 30 may comprise multiple such temperatures sensors.

[0086] Temperature-related signals 17 are acquired by the monitoring and control system 10. They comprise at least the temperature(s) measured by the one or more temperature sensors. Here, they comprise also data representative of heating powers, for instance data representative of fuel gas fluxes, or representative of an electric power supplied. Thetemperature-related signals 17 mays also comprise data representative of a position over time of the steel product 2 considered.

[0087] The monitoring and control system 10 comprises: one or more memories, including a non-transitory memory; one or more processors; a communication interface, such as a network of bus interface card, for acquiring the temperature-related signals 17 and for outputting the control data 18. Here, the electronic device comprises also a Human-Machine Interface 12 (including for instance one or more screens or indicators and input devices like a keyboard, buttons or selectors). The monitoring and control system 10 may be a programmable electronic unit, based for instance on an FPGA (Field Programmable Gate Array) or other programmable circuit. It may also be a computer (for instance a server), or a computer system. All or part of the monitoring and control system 10 may be implemented in a distributed manner (somehow “virtually”), using so-called “cloud” resources (computing and storing resources distributed among distinct physical systems in a network).

[0088] The monitoring and control system 10 is configured to determine, here by numerical simulation, a thermal path TP followed by the steel product 2 considered during its reheating. This determination is carried out based on the temperature-related signals 17. The thermal path TP may be represented by the temperature T(t) over time t, for the steel product 2, during its reheating, at least from the initial time ti (entry into the furnace) to the instant time t. Here, the thermal path comprises also predictions of the temperature to come for the steel product 2, that is T(t) from ti to the final time tf (time expected for the output of the steel product, out of the furnace). Here, the thermal path TP is determined by a thermal path module 13 of the monitoring and control system 10.

[0089] The monitoring and control system 10 is configured also to determine the control data 18 for controlling the heating route followed by the steel products, based on the thermal path TP and based on one or more heating targets, such as a final temperature target to be reached, or such as a minimum time to be spent over an austenitization threshold temperature. The control data 18 may be determined according to an optimization procedure, so as to minimize an energy consumption, or to comply with the heating targets for the highest number of steel products currently being reheated. Here, the control data 18 are determined by a control module 14 of the monitoring and control system 10.

[0090] The monitoring and control system 10 is configured also to determine the degree of oxidation of the steel product 2, at the current time t and / or at the final time tf, based on the thermal path TP. The degree of oxidation is transmitted to the Human-Machine Interface 12, which outputs it (displays it). The Human-Machine Interface 12 outputs for instance, X0(t), X0(tf), Ddec(t) and Ddec(tf), or just one or some of these quantities. Here, the degree of oxidation is determined by a surface oxidation module 1 1 of the monitoring and control system 10.

[0091] The degree of oxidation is also transmitted to the control module 14, which is configured to determine the control data 18 taking into account the degree of oxidation expected for the steel product, and taking into account surface oxidation specifications. For example, the control data 18 is determined taking into account Ddec(tf) and a maximum decarburized depth Ddec,max, to avoid that Ddec(tf) overcomes Ddec,max. To this end, if Ddec(tf) turns out to be higher than Ddec.max, the heating may be controlled so as to have a late heating (to limit the decarburization) rather than an early heating, for instance. The control data 18 may be determined by adding a penalty in the optimization procedure, so as to penalize cases for which Ddec(tf) overcomes Ddec, max-10092] The different modules presented above (11 , 13 and 14) may each take the form of a dedicated electronic unit (distinct one from each other), or of a dedicated group of instructions (a distinct program or sub-program). Besides, the different functionalities of the control and monitoring system 10 could be arranged, distributed in different modules or on the contrary gathered differently than in figure 6.

[0093] Monitoring a steel processing operation, and even controlling it, based on the degree of oxidation expected for the steel product, has been presented above for a reheating operation but it can be applied similarly to other steel processing operations. Besides, in alternative embodiments, the control features above described could be omitted, the installation comprising an electronic monitoring system, rather than the control and monitoring system above described.Steel product non-direct characterization

[0094] The instant technology concerns also a non-direct characterization of a steel product, possibly achieved after the steel processing operation, based on a thermal path TP followed by the steel product during this operation. A degree of oxidation for the steel product (for instance X0(tf), or Ddec(tf)), resulting from the steel processing operation, is computed by a computer 1 T (figure 7) or electronic device (based on the above-described method for determining the degree of oxidation), and transmitted to an industrial production database where it is recorded, associated to an individual identifier (such as a serial or production number) for the steel product.

[0095] The thermal path TP may be a thermal path directly measured during the steel processing operation. It may also be a thermal path derived, by numerical simulation, from temperature-related signals (like above explained in terms of process monitoring).

[0096] By industrial production database, it is meant a database where product features (dimensions, steel grade, measured or modelized ultimate tensile strength, etc...) are stored, associated to an individual identifier of the product considered, for different steel semiproducts.Computer Assisted Design of a steel processing operation

[0097] The instant method for determining a degree of oxidation of a steel product, resulting from a steel processing operation, can also be used for determining, in a Computer Aided Design way, processing conditions, in particular a thermal path for the steel processing operation such that the degree of oxidation is in accordance with surface oxidation specifications (such as a range or a maximum value for the decarburized depth, or for the amount of scale formed during the steel processing operation).

[0098] This thermal path can be determined, for instance, by executing the method for determining a degree of oxidation for different candidate thermal paths, and then selecting the candidate thermal path that leads to the degree of oxidation, at the end of the steel processing operation, that is the closest to surface oxidation specifications aimed at. Alternatively, a candidate thermal path can be adjusted iteratively, by gradually modifying the thermal path until leading to a degree of oxidation close enough (i.e.: within a given precision range) to the surface oxidation specifications. Other schemes for determining (or, in other words optimizing) such a thermal path can also be employed.

[0099] Once the thermal path, or more generally the operation conditions leading to surface oxidation specifications are identified, the steel processing operation may be executed according to these operating conditions.

[0100] The determination of such operating conditions, and then control of a steel processing installation accordingly, can be executed by an electronic device or system configured to this end.

Claims

CLAIMS1 . A method for determining a degree of oxidation of a steel product (2), the method comprising:- acquiring one or more alloying elements contents for the steel product, among the following list: a Silicon content (xsi), an Aluminium content (XAI), a Chromium content (xCr), a Copper content (xCu), a Phosphorous content (xP), a Carbon content (xc),- computing a growth rate Kpfor a quantitywhere Xois a quantity representative of an amount of scale formed on the steel product, the growth rate Kpbeing computed according to the equation eqn-p2 below:where Qp is an activation energy, R is the universal gas constant, T is the temperature of the steel product, PO2 is the oxygen partial pressure in an atmosphere surrounding the steel product and Kp0is a rate coefficient computed depending on the one or more alloying elements contents, Kp0being equal to a base rate coefficient k0when each of the one or more alloying elements contents is null and wherein, for each of the one or more alloying elements contents, Kp0is all the smaller than the alloying element content considered is high,- determining the degree of oxidation of the steel product based on the growth rate Kp, the degree of oxidation being said quantity Xo, or being a decarburization thickness Ddec at a surface of the steel product.

2. A method according to claim 1 , wherein the one or more alloying elements contents comprise at least the Copper content (xCu).

3. A method according to anyone of the preceding claims, wherein the one or more alloying elements contents comprise at least two alloying elements contents among said list.

4. A method according to anyone of the preceding claims, wherein the one or more alloying elements contents comprise at least three alloying elements contents among said list.

5. A method according to the preceding claim, wherein the one or more alloying elements contents comprise at least the Copper content (xCu), the Silicon content (xSi) and the Aluminum content (XAI).

6. A method according to the preceding claim, wherein the one or more alloying elements contents comprise also the Phosphorus content (xP).

7. A method according to anyone of the preceding claims, wherein the rate coefficient Kp0is equal to k0 / (1 +S),S being a sum of one or more of: asi.xsi , 3AI.XAI , acr.xcr acu-Xcu , ap.xP, ac.xc- where xSi, XAI, xCr, xCu, xPand xcare respectively the Silicon, Aluminum, Chromium, Copper, Phosphorous, and Carbon contents,- and where as, HAI, acr, acu, ap and ac are positive coefficients.

8. A method according to the preceding claim wherein, the alloying elements contents being mass fractions each expressed as a weight%:- aSi=150,- aAi=250,- aCr=40, acu=150,- ap=100,- ac=20.

9. A method according to anyone of the preceding claims wherein the temperature T of the steel product is measured directly, or is derived from at least one temperature measurement and using a thermal model for a thermal evolution of the steel product.

10. A method according to claim 9, comprising:- acquiring thermal path data, representative of a thermal path (TP) followed by the steel product (2) during a steel processing operation,- determining the degree of oxidation of the steel product, and recording the degree of oxidation in an industrial production database.1 1 . A method according to claim 9 or 10, the method being executed while the steel product (2) is undergoing a steel processing operation, the method comprising displaying the degree of oxidation using a human-machine interface (12).

12. A method according to anyone of claims 9 to 1 1 , the method being executed while the steel product is undergoing a steel processing operation, the method comprisingadjusting one or more process setpoints (18) employed for controlling said processing operation, depending on the degree of oxidation of the steel product.

13. A method for processing a steel product (2), the method comprising: - acquiring a surface oxidation specification for a steel processing operation achieved using a steel processing installation,- determining one or more processing conditions for said steel processing operation such that the degree of oxidation, determined according to the method according to anyone of claims 1 to 8, is in accordance with the surface oxidation specification, - controlling the steel processing installation to execute the steel processing operation according to the one or more process conditions.

14. An electronic device (10; 11 ; 11’) comprising at least a processor and a memory, configured for executing the method according to anyone of claims 1 to 13.

15. A computer program, comprising instructions whose execution on a computer make the computer to execute the method according to anyone of claims 1 to 13.