Title of Invention

A METHOD FOR ON-LINE DETERMINATION OF A MOVING BILLET TEMPERATURE CORRESPONDING TO FURNACE TEMPERATURE IN RE-HEATING FURNACES

Abstract

A method for on-line determination of a moving billet temperature corresponding to furnace temperature in reheating furnaces, comprising determining heat- fluxes on each billet piece by averaging acquired readings from a plurality of thermocouples surroundingly disposed on the furnace wall and roof, the readings acquired constitute heat-fluxes at several locations of the billet, and heat transfer co-efficient; determining a heating profile of cross-sections of the moving billet using the boundary heat-fluxes and the radiative convective heat transfer coefficients; generating zonal set-points based on the temperature error between the user-defined heating profile of the billet and the calculated heating profile; generating a set-point of the billet using an error weightage factor between the zonal set points, wherein the number of thermocouples adapted is at least thirty.

Full Text

FIELD OF THE INVENTION This invention generally relates to a method of estimating the billet temperature and the thermal gradient over the built-depth at each location inside a reheating furnace. More particularly temperature with the user-defined heating profile and adjusts the firing rates accordingly. The system has lowered the furnace operating temperature for all possible grades operating conditions. More particularly, the invention relates to a method for on-line prediction and control of billet temperature including furnace temperature in retreating furnaces. BACKGROUND OF THE INVENTION Reheating furnace adapted in a wire and rod mill (WRM) generally constitutes a walking hearth furnace. It consists of three zones for example a) Pre-heating b) Heating ad c) Soaking zone. Pre-heating burners are switched on whenever preheating of billets is necessary otherwise they are remained shut. Flame in the preheating zone is a plug-flow type and propagates in a counter direction of the billet movement. In contrast, the flame in the heating and soaking zones are radiative type that more-or-less complete combustion inside the burners. Preheating burners are end-wall burners whereas the burners of the heat and soak zones are roof-top burners. Cross-sectional area of a typical billet of WRM is approx. 130x130 sq. mm while the length is of the range 4-6 m. Grades are grouped in high, medium and low carbon equivalences. The billets are charged inside the furnace through a side door which is located at a rear end of the furnace. The charged billets rest laterally inside the furnace and at the rear-end of a walking beam. The walking beam is a device which advances the billets in a regular frequency and thus makes the billets to move from a charge end of the furnace. The mechanical cycle of the walking beam is a) lifting the billets b) advancing the billets by a fixed distance, commonly known as a walking step c) lowering and resting the billets on a plurality of skids d) Returning to the home position. The walking beam ends to a narrow strip of the soaking hearth (~1.5 m) in the discharge end of the furnace, which can hold at the most three billets at a time. The billets are first dropped from the walking beam on the soaking hearth and then discharged out of the furnace using a pill-bar push-mechanism. The furnace is provided with a system which is equipped with a number of single-loop controllers to control air and fuel flows individually in said three zones. Air-fuel ratio is set in the controller. In the soaking zone a pair of said plurality controllers are used to control separately the front and rear burners. A separate controller is used to maintain furnace pressure. Initially the furnace is equipped with three pairs of thermocouples, each pair being installed at the roofs of each zones (Preheating, Heating and Soaking Zones). The operational method according to the prior art is to set the soak-zone temperature at the discharge temperature required for that particular grade of the billets that was rolled. For example the soak-zone temperature of the brand product TMT -42 is set at 1160 Deg C whereas that of WRM3 grade is set at 1180 Deg C. The heating zone is generally kept at the same temperature as that of the soak zone. The preheat zone is kept at constant temperature of 850 Deg C irrespective of the billet grades. The preheating burners are intermittently kept shut. Due to the complex nature of heat transfer mechanism in reheating furnace, the prior art numerical models are either plant specific or totally theoretical. No general consensus has been established so far about a particular model to determine the heating profiles inside a furnace. Hottel introduced a model to evaluate furnace heating phenomenon. In this method, the furnace chamber is divided into a number of isothermal gas and surface zones and the furnace gasses are modeled as a sum of gray gases. This approach enables the model to identify static geometric terms like total exchanges areas. For a given furnace geometry the geometric terms, total exchange areas easily computable. The model repeatedly uses the areas terms to evaluate the radiative exchange amongst the furnace wall, intervening gas media and the charge on the floor. Chapman at al used a zone method deploying a plurality of models to calculate radiative heat transfer in three dimensions. The models incorporated a four-gray gas model to simulate furnace atmosphere. Gas temperature were calculated from a energy balance that accounted for the sensible energy of the products of combustion as they traveled through the furnace. Temperature of the refractory and the charge were then calculated using the surface heat fluxes. The new surface temperatures were fed back into a chamber module to re-evaluate the gas temperature. The process was repeated until the gas temperature stabilized. Lee used a zone-method to develop a steady-state, three-dimensional, pusher type furnace model. This model differed from the previous in that it required the gas temperature profile to be specified. Stry and Felske also used the zone-method to develop a heating model for the walking beam surface of Bethlehem Steel plant. The formulation was for the two- dimensional solution domain along the centerline of the furnace. It relied on a specified gas temperature profile that was crudely estimated based on the firing rates. Barr at the University of British Columbia, developed a similar but much more detailed, pusher-type slab furnace model. This model included the radiative the radiative shielding effects on the bottom of the slabs that are caused by the skid support structure. Scholey used the zone method to develop a three-dimensional model for billet reheating furnace. The model incorporated scale formation and skid mark severity calculation. Roy Chaudhury used the zone method understand the process of a tunnel furnace. The zone-method technique has proven quite successful as most of the above work has been validated by plant data. However, the technique is confirmed to off-lime simulation and so far the methodology has not been tried for control purpose. The on-line system at Inland Steel incorporates a scheduling model to optimize slab charging. The scheduling model groups a plurality of slabs of similar heating profiles and are charged together. In this model both the furnace thermocouples and the predicted slab heating profiles are used to assess how the furnace should be fired. For example, when a furnace zone contains a mix-up of hot and cold charges a 'positional weight factor' is used to set the firing rates of the zone. The factor is a bias towards a slab leaving a zone, thus ensuring that the leaving slab is closer to the targeted temperature. Further details of the model is not available. Hoogoven Technical Services (HTS), Netherlands, in 1993 implemented an on- line-slab-temperature-control method in reheating furnace of Hot Strip Mill. The model is supported by two groups of thermo-couples of long wires, one being inserted vertically from the roof-top and along the center-line of the furnace, and the other being erected from the bottom-pit. The thermo-couples are sufficiently long such that the tips are close to the slab surfaces. The thermo-couples (Alias nodal TC) readings are considered as local temperature near the slab surfaces and are used in the model to determine heat flux to slab surfaces. The heat- transfer-coefficients at the slab surfaces are initially assigned with a certain value which are received continuously by tunning it with the slab temperature measured at the exit. Although the model has performed satisfactorily with a cold charge but not so with a hot and cold mixed charge. The model has been validated by data-logger device and instrumented test slab. Brickmont, US, has designed a heating control model adaptable to a furnace for RE-bar mill. The model details are not available in open literature. Reports and technical documents have specified that the Bricmont model, like the HTS, uses thermo-couple data, specially located for the model purpose, to determine heat- fluzes on the stock surface. Stock temperature is formulated from 2D heat conduction equations. The model tracks the least heated stock in a zone and adjusts the firing rates using the positional weightage as a bias for the least heated stock. In this control methodology it is likely that the furnace may deliver overheated stocks and allows scale formation. Bricmont could that it would be rather preferable to deliver over-heated stocks than an under-heated stock. The transient mathematical model used on-line in a furnace control system has been described by Yuen. In additional to slab heating profiles, the model also calculated skid-mark severity and scale thickness. Energy balances in each zone are calculated in real-time taking into account combustion energy, sensible energy in the products of combustion, and the thermal energy, contained in the preheated air. The model adjust zone firing rates based on the differences between the zone temperatures and the set-point values. The details of heating principle and heat transfer coefficient calculation are not available in the literature. The prior art reveals that numerous heating models that have been developed so far are either utilized off-line for process understanding or implemented on-line for furnace control. The design methodology of one model varies widely from the others. It has been observed that no unique methodology describing the furnace heating process is available in the open literature. OBJECTS OF THE INVENTION It is therefore an object of the present invention to propose a method for on-line prediction and control of billet temperature including furnace temperature in reheating furnaces. Another object of the present invention to propose a method for on-line prediction and control of billet temperature including furnace temperature in reheating furnaces which achieves an improved consistency in the furnace in respect of billet drop-out temperature. An yet another object of the present invention to propose a method for on-line prediction and control of billet temperature including furnace temperature in reheating furnaces which ensures easy handling of furnace operation and maintains lower furnace temperatures. A further object of the present invention to propose a method for on-line prediction and control of billet temperature including furnace temperature in reheating furnaces in which model validation is ensured with the results of the datalogger test. BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS Figure 1 - is a schematic diagram of a thermocouple configuration in a billet reheating furnace. Figure 2 - shows a billet cross-sectional grid Figures 3 and 4 - show the billet heating and tracking profile at control pulpits Figure 5 - shows a set-point graph of heating zone (1160 grade) on a specific day. Figure G - shows a set-point graph of heating zone (1160 grade) on next date to the specific date of Figure - 5. Figure 7 - shows a set-point graph of soaking zone south (1160 grade) on a specific date. Figure 8 - shows a set-point graph of heating zone (1180 grade) a weak after the specific date of Figure - 5. Figure 9 - shows a set-point graph of soaking zone south (1180 grade) on a couple of days later than the specific date of Figure - 7. Figure 10 - shows a set-point graph of soaking zone south (1180 grade) on a fortnight after the specific date of Figure - 7 SUMMARY OF THE INVENTION Level 2 system of the invention has introduced additional twenty-four thermocouples that are installed at various locations on the furnace wall and the roof. The thermocouples are provided to estimate heat flux on the billet surface for each position. A billet tracking means which constitutes a module, simulates the billet movement at a regular time-interval and tracks the billets accordingly. The residence time of the billet is estimated from the tracking means. The surface heat-flux and the residence time are used to calculate the billet core temperature and the thermal gradient. Temperature set-points of each zone are determined on the basis of the differences between the desired heating profile and the calculated billet temperature at each location. An adaptive control means to determine an error weight-age factor, and a proportional-integral methodology have been implemented for a bump-less control. DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OFTHE INVENTION Figure 1 shows a WRM having a thermo-couple configuration. The thermo- couples that are shown in this diagram are representative of either a pair of thermocouples or a group of four fixed in the same plane. The furnace is divided in four zones, the recuperative (RZ), preheating (PHZ), heating (HZ) and soaking zone (SZ). The preheating zone is subdivided into two virtual zones. Those are a) underneath slanting roof and b) underneath the plane roof. In the preheating and recuperative zones the gas flow of a plug type and flows in the direction towards the charge end. This ensures that gas temperature drops as it moves towards the charge end. The heating and soaking zones are more or less like closed chambers with the burners at the roof top. The gas inside those zones are considered as well stirred, homogeneous, and isothermal. With this knowledge following principles have been adopted. The furnace is embedded with atleast thirty thermocouples (TC). Atleast four thermocouples each are located and fixed vertically in the roof-top of the heating and soaking zones. The remaining thermocouples are fixed in the preheating and the recuperative zones and those are either in the roof or in the side walls of the zones. Atleast six strategic locations of the furnace are selected which are charged end (PO), exit of recuperative zone (PI), exit of slant roof in pre-heating zone (P2), exit of preheat zone (P3), exit of heat zone (P4) and exit of soak zone discharge end (P5). Temperature of these locations are estimated by averaging the thermocouples readings that are in the vicinity of the points. For example, at the charge end the temperature is the average of the thermocouple readings in the vicinity and the charge temperature; at the recuperative zone exit the temperature is the average of some of the thermocouples in recuperative zone and some of the thermocouples in the preheating zones; at the preheating zone exit the temperature of some of the heating zone thermocouples are considered. Selection of the thermocouples for the locations is based upon user's and model builder's experience. Any number of thermocouples can be inserted or delected from the averaging sets. These average thermo-couple temperatures are treated as localized furnace temperature for the billets that are residing as localized furnace temperature for the billets that are residing on those locations. Local temperatures of the intermittent billets sitting between two successive locations are interpolated within the range. A typical interpolation equation of local gas temperature of a billet sitting at a position P is: Temperature of the bottom part of the furnace where the skid structure holds the billetpieces remains almost at steady state during the furnace heating. This is due to the fact that in this region no burner is present. The local temperature at the strategic points are computed on the basis of thermocouple readings located in the vicinity of the strategic locations and the billet bottom surface temperature at that location. The heat fluxes that are received by a piece are as follows: • Heat fluxes received by the top and the bottom surfaces of the billet piece from the top and bottom chamber of the furnace. The heat equation is Where Troof = Local furnace gas temperature at the location (Either top or bottom chamber) T surf = Billet Surface Temperature £1-2 = Emmissivity o = Stephan's Boltzman Constant F1-2 = View Factor • Heat fluxes received by the side surfaces from the gap between the billet piece and the billet ahead and behind the piece. The heat equation is: Where, hconv = Heat transfer Coefficient (Convective) Tgap = Local temperature of the gap region (Either side of the billet piece) Tside - surf = Billet Side-Surface Temperature Normally the gap between two billets is the width of a billet itself. (One billet- width). In some cases the gaps are increased and the gap-size may vary from one to three billet widths. In abnormal condition the gap-size may be as large as ten billet-widths. As the gap size increase the heat influence of neighbour billet on the billet piece decrease proportionately. The Heat influence coefficients based on the gap size are determined as follows: 1. If Gap-size = 1 then CO = 0.5 and CI = 0.5 (i.e. one billet-width, normal condition) 2. If Gap-size = 2 then CO = 0.6 and CI = 0.4 3. If Gap-size = 3 then CO = 0.65 and CI = 0.35 4. if 3 The temperature of gap region is determined by the following equation: Where In WRM furnace the radiative heat transfer takes place between the surfaces of the billet and the furnace chamber. The side surfaces experience the convective heat exchange from the air gaps between the neighbour billets. Since the heat exchange in side surfaces is significant a 2D heat conduction equation is considered. The bottom surface receives heat flux from the underneath hearth. Since the furnace is neither bottom nor side wall fired, the bottom heat flux is insignificant as compared to the top heat flux. The equation governing a 2d-Heat conduction is as follows: In this case, thermal conductivity is assumed to be invariant with the direction, so Kx= = Ky The Boundary Conditions at the four surfaces are as follows: At the top surface, the radiative heat flux is from the furnace chamber: At the bottom surface, the radiative heat flux is from the bottom chamber At the side surfaces, the convective heat fluxes are from neighbour billets The billet cross-section is square which is divided into numerous square cells. The division is such that each cell behaves isothermally. Figure 2. shows the billet cross-section node diagram Zonal set-points are determined on the basis of the temperature error between the user-defined heating profile of the billet and the model calculated heating profile. The objective of this calculation is to heat up the billet according to the user-defined heating profile. Following device relationship is adopted for the set- point generation: Where m= Control Zone (Preheating, Heating Soaking Zonel, soaking Zone2) Pstart,m = First Billet in Zone m Pend,m = Last Billet in Zone m (Error between user-defined heating profile and the model calculated temperature at location I) Wp = e (0,1) step=l N N= Number of billets in the control zone SET_POINT-TEMP=SET_POINT+TEMP+TEMP_DIFF The set-points are calculated every 30 seconds and downloaded every 3 minutes. Figures 3 & 4 show the billet tracking and heating profiles at control pulpits (CP1, CP2) of a PC of the WRM. Figure 3 shows the heating profile when the preheating burners are off and figure 4 shows the heating profiles when the preheating burners on. The colour change indicates that the furnace is running with two different grades. The blue dotted line shows the target temperature profile of the billets (Or user-defined heating profile of the billets). Figures 2 & 4 show that the heating profile of the billets closely match with the target profile with preheating burners on. The figures further show the set-point pattern in the heating and the soaking zones at different time periods. Yellow dotted lines indicate the set-points of the zones when furnace is operated in panel mode. The figures indicates that the furnace operates at lower set-points under the invented system than that under manual mode (Panel mode) which constitutes prior art. Figure 5 - shows a set-point graph of heating zone (1160 grade) on a specific day. Figure 6 - shows a set-point graph of heating zone (1160 grade) on next date to the specific date of Figure - 5. Figure 7 - shows a set-point graph of soaking zone south (1160 grade) on a specific date. Figure 8 - shows a set-point graph of heating zone (1180 grade) a weak after the specific date of Figure - 5. Figure 9 - shows a set-point graph of soaking zone south (1180 grade) on a couple of days later than the specific date of Figure - 7. Figure 10 - Shows a set-point graph of soaking zone south (1180 grade) on a fortnight after the specific date of Figure - 7 We claim: 1. A method for on-line determination of a moving billet temperature corresponding to furnace temperature in reheating furnaces, comprising - determining heat-fluxes on each billet piece by averaging acquired readings from a plurality of thermocouples surroundingly disposed on the furnace wall and roof, the readings acquired constitute heat-fluxes at several locations of the billet, and heat transfer co-efficient; determining a heating profile of cross-sections of the moving billet using the boundary heat-fluxes and the radiative convective heat transfer co- efficients; generating zonal set-points based on the temperature error between the user-defined heating profile of the billet and the calculated heating profile; generating a set-point of the billet using an error weightage factor between the zonal set points, wherein the number of thermocouples adapted is at least thirty. 2. The method as claimed in claim 1, wherein heat fluxes on the billet pieces are determined for top and bottom surfaces including side surfaces, and wherein, the respective heat equations for determining heat fluxes of top and bottom surfaces, and the side surfaces adapted:- where Troof = Local furnace gas temperature at the location (Either top or bottom chamber) Tsurf = Billet Surface Temperature £1-2 = Emmisivity a = Stephan's Boltzman Constant F1-2 = View Factor b) q = hconv (gap — TSjde-surf) where hconv = Heat transfer Coefficient (Convective) Tgap = Local temperature of the gap region (Either side of the billet piece) Tside-surf = Billet Side-Surface Temperature. 3. The method as claimed in claim 1, wherein boundary condition and radiative-convective heat transfer co-efficient for the top surface, bottom surface and the side surfaces respectively are evaluated by using the device features relationship of: 4. A method for on-line determination and control of a moving billet temperature corresponding to furnace temperature in reheating furnaces as substantially described herein and illustrated with reference to the accompanying drawings. ABSTRACT TITLE: A METHOD FOR ON-LINE DETERMINATION OF A MOVING BILLET TEMPERATURE CORRESPONDING TO FURNACE TEMPERATURE IN RE-HEATING FURNACES A method for on-line determination of a moving billet temperature corresponding to furnace temperature in reheating furnaces, comprising determining heat- fluxes on each billet piece by averaging acquired readings from a plurality of thermocouples surroundingly disposed on the furnace wall and roof, the readings acquired constitute heat-fluxes at several locations of the billet, and heat transfer co-efficient; determining a heating profile of cross-sections of the moving billet using the boundary heat-fluxes and the radiative convective heat transfer coefficients; generating zonal set-points based on the temperature error between the user-defined heating profile of the billet and the calculated heating profile; generating a set-point of the billet using an error weightage factor between the zonal set points, wherein the number of thermocouples adapted is at least thirty.

Documents:

00701-kol-2006 assignment.pdf

00701-kol-2006 claims.pdf

00701-kol-2006 correspondence others.pdf

00701-kol-2006 description (complete).pdf

00701-kol-2006 drawings.pdf

00701-kol-2006 form-1.pdf

00701-kol-2006 form-2.pdf

00701-kol-2006 form-3.pdf

00701-kol-2006 priority document.pdf

701-KOL-2006-(05-04-2013)-ABSTRACT.pdf

701-KOL-2006-(05-04-2013)-CLAIMS.pdf

701-KOL-2006-(05-04-2013)-CORRESPONDENCE.pdf

701-KOL-2006-(05-04-2013)-FORM 13.pdf

701-KOL-2006-(05-04-2013)-PA.pdf

701-KOL-2006-(16-12-2011)-ABSTRACT.pdf

701-KOL-2006-(16-12-2011)-AMANDED CLAIMS.pdf

701-KOL-2006-(16-12-2011)-CORRESPONDENCE.pdf

701-KOL-2006-(16-12-2011)-EXAMINATION REPORT REPLY RECEIVED.pdf

701-KOL-2006-(16-12-2011)-OTHER PATENT DOCUMENT.pdf

701-KOL-2006-(16-12-2011)-OTHERS.pdf

701-KOL-2006-(16-12-2011)-PA-CERTIFIED COPIES.pdf

701-KOL-2006-(23-04-2012)-CORRESPONDENCE.pdf

701-KOL-2006-CANCELLED PAGES.pdf

701-KOL-2006-CORRESPONDENCE-1.1.pdf

701-KOL-2006-CORRESPONDENCE.pdf

701-KOL-2006-EXAMINATION REPORT.pdf

701-KOL-2006-FORM 18.pdf

701-KOL-2006-GPA.pdf

701-KOL-2006-GRANTED-ABSTRACT.pdf

701-KOL-2006-GRANTED-CLAIMS.pdf

701-KOL-2006-GRANTED-DESCRIPTION (COMPLETE).pdf

701-KOL-2006-GRANTED-DRAWINGS.pdf

701-KOL-2006-GRANTED-FORM 1.pdf

701-KOL-2006-GRANTED-FORM 2.pdf

701-KOL-2006-GRANTED-FORM 3.pdf

701-KOL-2006-GRANTED-SPECIFICATION-COMPLETE.pdf

701-KOL-2006-PETITION UNDER RULE 137.pdf

701-KOL-2006-REPLY TO EXAMINATION REPORT.pdf

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