Abstract:
A process for optimizing steel fabrication. The process includes optimization of treatment in the ladle based on accurate determination of steel weight, slag carryover and furnace heel. The unification of the dip test process together with ladle profiling using information from the slag, side and bottom regions of the ladle results in the quantitative determination of key factors to optimize steel composition with minimum slag carryover in the absence of scales to determine required masses of metal charge and ladle weight as examples. Caprices of the process include significant improvements in ladle refractory and specification steel quality.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to an optimization procedure for fabricating steel and more particularly, the present invention relates to a process for optimizing the unit operations involved in steel fabrication. 
       BACKGROUND OF THE INVENTION 
       [0002]    Conventionally, in the steel making industry, the amount of steel tapped from steel making vessels into the ladle is generally measured with the aid of a weight scale or load cell. It is desirable to maximize the amount of steel tapped from the steel making vessel in order to increase productivity. Tapping, unfortunately, is encumbered since the amount of steel tapped into the ladle is limited by how much slag carry-over that occurs in the ladle during tapping. As is known, the greater the volume of slag carry-over, the greater the impact on the ladle refractory integrity resulting in not only reduced ladle refractory life, but also low alloy recovery with the increased chance of recontamination of the steel during casting. Certain grades of steel require minimum slag carry-over from the furnace to avoid subsequent contamination during refining and casting. 
         [0003]    Slag carryover into the ladle occurs due to vortex reaction or slag entrainment as the ferrostatic head decreases during tapping. Compared to liquid steel, liquid electric arc furnace slag has a distinctive grey colour, providing the ability to determine when a significant amount of slag is being tapped into the ladle. Most steel companies rely on the judgment of the operator to determine the end of tapping by visual assessment of the colour difference between the steel and the slag. In some steel companies the visual evaluation has been replaced with the slag detection system, examples of which include the Amepa TDS Technology, the Vesuvius Radar System and slag detection system developed by the Land Corporation. The purpose of the slag detection system is to determine the time to end tapping based on the different emissivity of the steel and slag or difference in vibration frequency between steel and slag. While this system presents an opportunity for a good management of slag carry-over, it does not provide a quantitative evaluation of the slag carry-over, furnace heel and tap steel. Estimation of the slag carry-over weight and ladle freeboard is often done during treatment of the steel in the ladle by visual assessment. If any measurement is required, it is usually done with the aid of the dip-test technique. This testing involves the use of a steel rod immersed into the metal bath for a short period of time, enough to burn off the rod at the steel/slag interface while the slag solidifies on the portion of the rod in the slag layer. By measuring the depth of the adhered slag, the volume and weight of the slag are estimated. The dip-test technique has been improved upon by other techniques developed and patented by Heraeus Electro-Nite and Nupro Corporation. 
         [0004]    Although the dip-test process and other subsequent techniques developed by Heraeus Electro-Nite and Nupro Corporation were useful techniques, they can only be used in the ladle once tapping has been completed and the slag fluidized in the ladle. Accordingly, these techniques do not offer the option of controlling or determining the amounts of slag carry-over and furnace heel. 
         [0005]    Tata Steel Limited developed a new procedure for detecting the percentage of slag in the steel ladle at BOF. The procedure is predicated on differentiation between different metals&#39; emissivity. An infrared camera is used for the thermal image of the object. The slag monitoring and detection system (SMDS) can identify the steel-slag transition under varying operating conditions. 
         [0006]    SMDS is operable in real time. The metal stream image is captured by the infrared digital camera and the thermal image of the tapping stream is displayed for the operator. Analysis of the stream image is continuous in order to ascertain the percentage of slag. Once detected, and using the permitted slag percentage value, logical algorithms are executed. The main principle of the detection system is the difference between the emissivity of the slag and steel. 
         [0007]    In other developments, in U.S. Pat. No. 6,166,681, issued Dec. 26, 2000, to Meszaros et al., there is disclosed a radar measuring process for determining the level of slag on molten steel as well as its thickness. The primary source of energy is microwave signals and the process essentially includes the transmission and reception of two microwave signals against the material to be measured. There is an analysis of the time of flight data from the individual signals and that a subsequent calculation of the difference between the distances to determine the thickness of the material. 
         [0008]    In the internet website, www.engineeringtalk.com, there is a discussion of a Land Instruments Company apparatus. The article is entitled “Slag Detection System Improved Steel Quality”. In the article there is discussion of the thermal imaging system devised by Land Instruments where a thermal imager is employed to measure infrared energy emitted from the tapping system. The system capitalizes on the fact that slag produces a significantly brighter thermal image than steel at the same temperature and accordingly, any difference between the two is safe to view from a distance. 
         [0009]    In an article from  Millennium Steel  2k4 there is a discussion article entitled: “The Ultra Slag Droplet Detector”. In the article there is a discussion of an electromagnetic slag detection process which takes advantage of the fact that slag droplets are often entrained in the steel stream at some time before the main slag flow begins. This gives rise to discreet slag droplets which vary in frequency and the time over a wide spectrum. This is generally attributable to the formation of the vortex characteristic electromagnetic fingerprint. 
         [0010]    In further attempts to minimize slag carryover, Stofanak et al, in U.S. Pat. No. 6,197,086, issued Mar. 6, 2001, described a system and process for minimizing slag carryover during the production of steel. In this patent, there is discussed a system which includes an infrared imaging or detecting apparatus primarily used to image the tap stream. As it is known, the stream transmits energy indicative of whether molten steel and/or slag is in the stream at any given time. A grey scale analysis is conducted on the pixels viewed from the tap stream to determine the number of steel pixels and the number of slag pixels in the stream at any one point. When the ratio or percentage of slag pixels exceeds a predetermined amount, an alarm is actuated to cause the operator to cease tapping. This system avoids the use of the visual detection system by the operator with a view to minimizing the slag carryover. 
         [0011]    In further attempts to avoid the use of operator judgment in reducing slag carryover, Koffron, in U.S. Pat. No. 6,280,499, issued Aug. 28, 2001, teaches a yield metal pouring system. Essentially, the patent is directed to the adjustment of the angle of the tilt of the furnace to an optimum angle in order to effect minimal slag entrainment in the liquid pouring through the tap. The optimum angle is calculated as a function of the furnace geometry and historical data of the furnace lining wear for the amount of metal residual within the metal furnace. 
         [0012]    In U.S. Pat. No. 6,562,285, issued May 13, 2003 to Demysh, there is disclosed a process and apparatus for detecting slag carryover. In the process and apparatus taught, digital images of the molten metal steam are obtained and stored with identification of areas of similarity on the basis of texture and intensity. A subset of these areas is defined with a further comparison of at least one selected property of the subset against a predetermined parameter. An output signal is generated on the basis of comparison and the output signal is generally indicative of the presence of or lack of presence of slag. An advantage to the system and the process is that the invention does not require the use of expensive optical equipment and can be effected with inexpensive means. 
         [0013]    It would be desirable to have an improved process of optimizing the unit operations involved in steel fabrication and in particular such a process that provides in-situ quantitative evaluation of the slag carry-over weight, tapped steel weight, heel in the steel in the steel making vessel, ladle freeboard together with a warning system for the operators to cue the end of tapping. 
         [0014]    The present invention is directed to providing elegant process control and optimization of the unit operations noted above. 
       SUMMARY OF THE INVENTION 
       [0015]    One object of the present invention is to provide an improved steel making process by optimizing the unit operations involved in the fabrication of the steel. 
         [0016]    A further object of one embodiment of the present invention is to provide a process of optimizing steel fabrication, comprising the steps of:
       providing a first carrier vessel for retaining liquid steel;   geometrically determining the volume of the carrier vessel;   determining, while tapping, a steel weight and slag weight for a given height of slag and steel in the carrier vessel;   profiling the carrier vessel using slag lining and barrel life information;   determining the height of steel in the carrier vessel;   determining slag carry-over weight and steel weight;   a refining stage including:
           deoxidizing the steel and slag and alloying the steel to bring chemical elements contained therein within predetermined limits; and   a casting stage including:
               discharging refined steel from the carrier vessel into an intermediate vessel for passage into a mould;   
               
           controlling discharge by timing the flow of steel; and   maintaining during discharge the level of steel in the mould, whereby liquid steel levels, flow control and casting are integrated for optimizing steel fabrication.       
 
         [0029]    As a particularly convenient advantage, the processes set forth herein provide management and optimization of the treatment of the steel and ladle and metallic charge design in the electric arc furnace. 
         [0030]    By incorporating the methodology of this development, a number of significant advantages are realized. As an example, precise determination of steel weight is achievable which, in turn, will result in optimization of alloy and steel mechanical properties. 
         [0031]    Further, the ability to control tap weight, slag carryover and furnace heel translates into cost savings resulting from increased alloy recovery (Al, Ti, Mn, Si . . . ). Perhaps one of the most advantageous features relates to the fact that the use of scales at tap is unnecessary. This eliminates the cost of buying and maintaining scales which are inherent in the prior art techniques. 
         [0032]    A further object of one embodiment of the present invention is to provide a process for controlling and determining the amount of slag carryover in steel fabrication during tapping, comprising:
       providing an algorithm for the quantitative relationship between slag carryover and furnace heel;   determining required mass of tapped steel and level within a ladle for a mass of metallic charge and furnace heel from the algorithm;   providing level detection means for detecting the level of liquid steel within the ladle;   comparing determined level of steel within the level with a detected value; and   ceasing tapping when the detected value and determined value for the steel level in the ladle are equivalent, whereby slag carryover is minimized.       
 
         [0038]    The practice of the protocol described herein facilitates vastly improved control of EAF charge weights, furnace heels, refining in the ladle and cleanliness of steel and the casting process. 
         [0039]    Ancillary benefits also include the reduction of off specs and downgraded/scrapped heats and improved ladle life. 
         [0040]    A further object of one embodiment of the present invention is to provide a process of quantitatively determining at least one of slag carryover, furnace heel, ladle freeboard and tapped steel for optimizing steel fabrication, comprising:
       measuring slag depth and ladle freeboard;   generating a ladle profile equation from measurements of the slag depth, ladle freeboard and historical data on refractory brick dimension changes with increasing lives of the slag line, barrel and bottom regions of the ladle;   determining volumes of steel and slag, slag depth and freeboard height for a given ladle;   determining the amount of slag carryover during tapping;   correlating slag carryover to furnace heel;   determining volume and mass of steel at various levels for a given ladle;   calculating required tapped mass of steel and freeboard height for a given ladle; and   comparing the freeboard height with a calculated value during tapping to determine when to end tapping.       
 
         [0049]    A further object of one embodiment of the present invention is to provide a process for optimizing the fabrication of steel, comprising: 
         [0050]    providing a computational model for estimating the weight of steel in a furnace used in the process; 
         [0051]    providing the model with required furnace heel or tap weight, slag line life, ladle number and ladle life; 
         [0052]    determining with the model required freeboard for the ladle; 
         [0053]    communicating freeboard value to a freeboard detecting means; 
         [0054]    tapping the steel; 
         [0055]    measuring the freeboard during tapping with the freeboard detecting means; 
         [0056]    comparing measured freeboard with the model required freeboard; 
         [0057]    terminating tapping when compared values are equivalent; and 
         [0058]    computing the weight of tapped steel, carryover and furnace heel, whereby the process quantitatively determines requisite values for the process for optimization. 
         [0059]    A further object of one embodiment of the present invention is to provide a process for optimizing the fabrication of steel, comprising: 
         [0060]    i) geometrically profiling a ladle used in the fabrication to determine weight of tapped steel, slag carryover and furnace heel; 
         [0061]    ii) quantitatively determining the requisite alloy addition for predetermined steel product specifications; and 
         [0062]    iii) controlling casting liquid steel with properties inherent from i) and ii), and steps i) through iii) being conducted in sequence and based on quantitative information derived from each precursory step, whereby the process quantitatively determines requisite values for the process for optimization. 
         [0063]    A platform for the technology discussed herein is the dip-test process known to those skilled in the metallurgical field. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0064]      FIG. 1  is a cross section illustrating the components of a dip-test process; 
           [0065]      FIG. 2  is a graphical representation of slag carry-over versus furnace heel; 
           [0066]      FIG. 3  is a cross section of a ladle illustrating the slag line, barrel and bottom regions of the ladle; 
           [0067]      FIG. 4  is a schematic illustration of an apparatus suitable for use in determining ladle freeboard with the aid of a radar system; 
           [0068]      FIG. 5  is a schematic illustration of a continuous casting machine for steel slab casting; 
           [0069]      FIG. 6  is a schematic illustration of a slide gate system for controlling the flow of steel during continuous casting; 
           [0070]      FIG. 7  is a schematic illustration of a radar system for monitoring the level of steel in the tundish and mould; 
           [0071]      FIG. 8  is a cross section of the mould; 
           [0072]      FIG. 9  is a cross section of tundish and the unit volumes; and 
           [0073]      FIGS. 10 through 12  are flow diagrams illustrating the steps involved in the model. 
       
    
    
       [0074]    Similar numerals used in the drawings denote similar elements. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Ladle Profiling Technique 
       [0075]      FIG. 1  is cross section illustrating the components of a dip test process. 
         [0076]    The apparatus includes a ladle  10 , steel rod  12  which rod  12  includes a tip portion  14 . The rod also includes a support plate or other means  16  for resting on the ladle  12 . Disposed within the ladle  10  is the steel (liquid) represented by numeral  18 . The slag or contaminant layer resting thereon is denoted by numeral  20  and freeboard area denoted by numeral  22 . 
         [0077]      FIG. 3  illustrates the ladle  10  in cross-section. The ladle includes three regions, namely, the slag line region  24 , barrel region  26  and bottom region  28 . The slag line and barrel regions  24  and  26 , respectively, of the ladle  10  have the overall shape of a frustum of a cone while the bottom region  28  has the shape of a frustum of a sphere. As is known, the ladle is lined with refractory bricks  30 . Using historical data on brick life and thickness in the slag line  24 , barrel  26  and bottom region  28 , ladle refractory wear rates can be established. Each course of bricks  30  has a distinctive wear rate. In modeling the process, the slag line region  24  and barrel region  26  were divided into minute frusta of a cone of known and variable diameters. Once the level of steel and thickness of the slag are known for the frusta, a volume determination is obtainable. The slag line and barrel regions of the ladle have a shape of a frustum of a cone, while the bottom region has a shape of a frustum of a sphere. Hence, the volume of the ladle can be calculated from known formulae for frusta of cones and frusta of spheres. 
         [0078]    In greater detail, the volume of ladle increases with ladle life and slag line life. The slag line region  24  consists of 12 courses of 7″ bricks  30  and the barrel region  26  consists of 17 courses of 7″ thick brick. The bottom region  28  consists of one course of 9″ thick bricks  30 . To account for increase in volume due to refractory brick wear with ladle life, the wear rate for each course of bricks in each region is established based on historical records. Each course of refractory is considered a cone. By factoring in the wear rate the volume of each frustum of cone can be calculated with increasing lives of the slag line and barrel regions. As a result an algorithm was created for modeling ladle profile. 
         [0079]    The established ladle profile provided the basis for calculating ladle volume, steel weight and slag weight for given heights of steel and slag. Using a modified dip-test technique, the apparatus for which is shown in  FIG. 1 , measurements of steel and slag heights were performed in the ladle for several heats of steel. The heights of the steel and slag determined by the dip-test process were used in determining the weight of steel and slag in the ladle. The amount of slag carryover for each heat of steel was determined by subtracting the weight of the flux added into the ladle from the determined ladle slag. The furnace heel was determined by subtracting the calculated steel weight in the ladle from the liquid steel in the EAF. The liquid steel in the EAF was determined by multiplying the metallic scrap weight by the liquid yield from the scrap. The slag carryover was correlated to the furnace heel as shown in  FIG. 2 . The dependence of the slag carryover on the furnace heel showed a high correlation coefficient, R 2  of 0.83. 
         [0080]    The dependence of the slag carryover on the furnace heel presents an opportunity to minimize slag carryover at tap if the level of the steel can be established while tapping into the ladle. If the level of steel can be determined in-situ, then with the given information on ladle slag line and barrel life the model for ladle profiling will calculate the weight of steel in the ladle and amount of slag carryover with rising steel level in the ladle. It was determined that the level of steel in the ladle can be determined with the aid of a radar system as depicted in  FIG. 4 . 
         [0081]    Referring to  FIG. 4 , numeral  34  denotes the overall system. Liquid steel  18  is transferred into ladle  10  as illustrated from the furnace generally denoted by numeral  36 . A radar system is provided, denoted by numeral  38 , which includes an extension arm  40  for transmitting the radar to the rising surface  40  of the steel  18 . It will be appreciated that the surface of the steel  40  and the top 42 of the ladle  10 , i.e., the area between these two is the freeboard and that the freeboard constantly changes as additional steel is tapped into ladle  10 . 
         [0082]    For a given tap weight and ladle, the protocol as discussed herein results in the calculation of the required freeboard and this value is sent to the radar system  38 . As steel  18  is being tapped into ladle  10 , the radar system  38  will detect the relative position of the liquid steel, the top 40 thereof in the ladle  10  to the ladle rim  42  and determine the distance from the ladle rim  42  to the top 40 of the steel in the ladle  10 . The radar system  38  compares the distance to the freeboard height determined by the protocol discussed herein. When the distance determined by the radar system  38  is equivalent to the freeboard height, the radar system  38  sounds an alarm (not shown) to the furnace operator (not shown) to end tapping. The radar system  38  continues to monitor the level of steel  18  in the ladle  10  until no further change is registered. The system communicates the final freeboard height back to the protocol which then recalculates the weights of steel slag and furnace heel. 
         [0083]    Ultimately, with this technique, the weights of slag carryover, steel and furnace heel can be determined and used in steel making optimization, specifically charge scrap weight, and ladle alloying and refining optimization as depicted in  FIG. 5  and discussed herein after. 
       Ladle Alloying and Refining Optimization 
       [0084]    Once tapping is complete and the tapped weights of steel and slag have been calculated, the ladle optimization model immediately calculates the bulk amounts of various alloying agents to be added into the steel. Given the high Oxygen potential of the slag and steel, it is necessary to avoid early additions of certain alloying agents that have high Oxygen potential until the steel is reasonably de-oxidized to ensure good recovery. Therefore, the first alloying agents to be added are Aluminum, Manganese alloys and Silicon alloys. In general, the model recommendation for alloy addition follows a certain order. 
       a) Sequence of Alloy Additions 
       [0000]    
       
         
           
             1) Aluminum—Aluminum is mainly used for de-oxidation of the slag and steel but some limited amount of the added Aluminum ends up dissolving in the steel. Therefore, in calculating how much Aluminum to be added to the steel, it is necessary to account for the dissolved Aluminum. Sometimes Silicon is used for de-oxidation. In this case, the total amount of Silicon to be added will include the amount required to de-oxidize the steel and the slag and the amount required to get the Silicon content of the steel to the level required in the specification. 
             2) Manganese and Silicon Alloys—Manganese and Silicon alloys are recommended at the same time with Aluminum. The amounts first recommended for Manganese and Silicon should be just sufficient to get the Manganese and Silicon to the lowest limits in the specification. Further trim amounts as required are recommended based on ladle test results. If any addition is required at tap the alloys are placed in the alloy chute such that the Aluminum goes into the steel first followed by the Manganese and Silicon alloys. If no alloy additions are required at tap (open tap practice), then the steel is de-oxidized to a certain degree prior to adding Manganese and Silicon alloys. 
             3) Once the first ladle test is obtained, the model recommends the required addition amounts for all other elements (Cr, Ni, Nb, Mo, V etc.) except Ti, B and Ca to reach the minimum specified levels for the product being manufactured. 
             4) Once the steel is totally de-oxidized and all elements except Titanium, Boron and Calcium are within the specification limits the model will recommend the required trim amounts of Titanium and Boron alloys to get the concentrations of Titanium and Boron within the specified ranges. However, the model will recommend that Titanium should be added first and stirred in for 3 minutes prior to trimming for Boron. This is necessary to ensure that Boron is not tied down by the dissolved Nitrogen reducing its efficiency to provide the required hardenability. 
             5) After Titanium or Boron addition and once the Sulfur content has reached a suitable level for inclusion modification CaSi powder or FeCa wire or other Calcium-bearing alloy is added. 
           
         
       
     
         [0090]    In general, the ladle optimization process can be divided into five major sub-processes: 1) de-oxidation; 2) alloying; 3) inclusion modification; 4) Phosphorous content prediction; and 5) ladle slag composition prediction. 
       b) De-oxidation 
       [0091]    As stated above the amount of Aluminum or Silicon required for de-oxidation is dependent on the weights of tapped steel and slag, the Oxygen potential of the slag, the Oxygen potential of the steel and the required contents of the elements in the steel. From the slag analysis at tap, chemistry analysis of the steel and the tap weights of steel and slag, the total amount of Oxygen available for reaction is determined. The available Oxygen from the slag carryover for reaction with the Aluminum or Silicon is calculated from the FeO, SO 2 , MnO, P 2 O 5  and TiO 2  components of the slag. Of the oxide components of the slag only FeO, SO 2 , MnO, P 2 O 5  and TiO 2  are considered to contribute significantly to the total Oxygen available for reaction with the de-oxidants. If for example the concentrations of FeO, SO 2 , MnO, P 2 O 5  and TiO 2  are a %, b %, c %, d % and e % with molecular weights designated as M FeO , M SiO     2   , M MnO , M P     2     O     5    and M TiO     2    respectively, the slag carryover weight in kg designated as W slag  and the atomic weight of Oxygen designated as A Oxygen , the total Oxygen available in kg is a sum of the weight of oxygen in all the above components of the slag: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           A 
                           Oxygen 
                         
                          
                         
                           W 
                           Slag 
                         
                       
                       100 
                     
                     ) 
                   
                    
                   
                     ( 
                     
                       
                         a 
                         
                           M 
                           FeO 
                         
                       
                       + 
                       
                         
                           2 
                            
                           b 
                         
                         
                           M 
                           
                             Si 
                              
                             
                                 
                             
                              
                             
                               O 
                               2 
                             
                           
                         
                       
                       + 
                       
                         c 
                         
                           M 
                           
                             Mn 
                              
                             
                                 
                             
                              
                             O 
                           
                         
                       
                       + 
                       
                         
                           5 
                            
                           d 
                         
                         
                           M 
                           
                             
                               P 
                               2 
                             
                              
                             
                               O 
                               5 
                             
                           
                         
                       
                       + 
                       
                         
                           2 
                            
                           e 
                         
                         
                           M 
                           
                             Ti 
                              
                             
                                 
                             
                              
                             
                               O 
                               2 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    From the weight of steel and dissolved Oxygen in steel at tap, the Oxygen available for reaction with Aluminum and Silicon is calculated. Let Z % designate the percentage of Oxygen in steel and let W steel  be the weight of tapped steel in kg, then the available Oxygen in kg is 
         [0000]    
       
         
           
             
               
                 
                   
                     Z 
                      
                     
                         
                     
                      
                     
                       W 
                       steel 
                     
                   
                   100 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0092]    Aluminum and silicon react with Oxygen as per the following thermodynamic equilibrium reactions: 
         [0000]      2[Al]+3[O]═(Al 2 O 3 )  (3)
 
         [0000]      [Si]+2[O]═(SiO 2 )  (4)
 
         [0093]    From expression (3), 2 atoms of Aluminum combine with 3 atoms of Oxygen. Based on mass balance, Aluminum content in Aluminum addition agent and recovery coefficient of Aluminum (R Aluminum %), from (1) and (2), we can determine the amount of Aluminum addition agent required to fully de-oxidize the steel and slag as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       200 
                        
                       
                         A 
                         Aluminum 
                       
                     
                     
                       3 
                        
                       
                         R 
                         Aluminum 
                       
                        
                       
                         C 
                         Aluminum 
                       
                     
                   
                    
                   
                     ( 
                     
                       
                         
                           W 
                           slag 
                         
                          
                         
                           ( 
                           
                             
                               a 
                               
                                 M 
                                 
                                   Fe 
                                    
                                   
                                       
                                   
                                    
                                   O 
                                 
                               
                             
                             + 
                             
                               
                                 2 
                                  
                                 b 
                               
                               
                                 M 
                                 
                                   Si 
                                    
                                   
                                       
                                   
                                    
                                   
                                     O 
                                     2 
                                   
                                 
                               
                             
                             + 
                             
                               c 
                               
                                 M 
                                 
                                   Mn 
                                    
                                   
                                       
                                   
                                    
                                   O 
                                 
                               
                             
                             + 
                             
                               
                                 5 
                                  
                                 d 
                               
                               
                                 M 
                                 
                                   
                                     P 
                                     2 
                                   
                                    
                                   
                                     O 
                                     5 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 2 
                                  
                                 e 
                               
                               
                                 M 
                                 
                                   Ti 
                                    
                                   
                                       
                                   
                                    
                                   
                                     O 
                                     2 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         
                           Z 
                            
                           
                               
                           
                            
                           
                             W 
                             steel 
                           
                         
                         
                           A 
                           Oxygen 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where A Aluminum  is the atomic weight of Aluminum and C Aluminum % is the concentration of Aluminum in Aluminum addition agent. 
         [0094]    Similar expression is derived for Silicon-deoxidized steel. The dissolved Oxygen in steel at equilibrium is considered negligible. 
         [0095]    Taking into account the required dissolved Aluminum in steel, designated as X %, the total amount of Aluminum addition agent required for addition can be calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         200 
                          
                         
                           A 
                           Aluminum 
                         
                       
                       
                         3 
                          
                         
                           R 
                           Aluminum 
                         
                          
                         
                           C 
                           Aluminum 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           
                             W 
                             slag 
                           
                            
                           
                             ( 
                             
                               
                                 a 
                                 
                                   M 
                                   
                                     Fe 
                                      
                                     
                                         
                                     
                                      
                                     O 
                                   
                                 
                               
                               + 
                               
                                 
                                   2 
                                    
                                   b 
                                 
                                 
                                   M 
                                   
                                     Si 
                                      
                                     
                                         
                                     
                                      
                                     
                                       O 
                                       2 
                                     
                                   
                                 
                               
                               + 
                               
                                 c 
                                 
                                   M 
                                   
                                     Mn 
                                      
                                     
                                         
                                     
                                      
                                     O 
                                   
                                 
                               
                               + 
                               
                                 
                                   5 
                                    
                                   d 
                                 
                                 
                                   M 
                                   
                                     
                                       P 
                                       2 
                                     
                                      
                                     
                                       O 
                                       5 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   2 
                                    
                                   e 
                                 
                                 
                                   M 
                                   
                                     Ti 
                                      
                                     
                                         
                                     
                                      
                                     
                                       O 
                                       2 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             Z 
                              
                             
                                 
                             
                              
                             
                               W 
                               steel 
                             
                           
                           
                             A 
                             Oxygen 
                           
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       100 
                        
                       X 
                        
                       
                           
                       
                        
                       
                         W 
                         steel 
                       
                     
                     
                       
                         R 
                         Aluminum 
                       
                        
                       
                         C 
                         Aluminum 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0096]    If Silicon is used for de-oxidation similar expression as in equation (6) is established. 
         [0097]    Generally, some Aluminum is added at tap except for some specialized products where additions of Aluminum and other alloying agents at tap are not required. Where Aluminum addition is required at tap the model will recommend adding ⅓ of the total amount of Aluminum determined for complete de-oxidation of steel at tap with the remainder being added gradually during refining in the ladle. 
       c) Alloying 
       [0098]    Coefficient of recovery for each element from its primary alloying agent was established (see Tables 1 and 2). The concentration of each element in steel is affected by the residual level of that element in other alloying agents and this is taken into consideration in calculating the resulting concentration of each element in steel. 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Coefficients of Alloy Recovery 
               
             
          
           
               
                   
                 Element 
                 Pickup from Alloying Agent 
                 Residual Pickup 
               
               
                   
                   
               
               
                   
                 Cu 
                 1.00 
                 1.00 
               
               
                   
                 Cr 
                 0.95 
                 0.95 
               
               
                   
                 Ni 
                 0.95 
                 0.95 
               
               
                   
                 N 
                   
                 1.00 
               
               
                   
                 Si 
                 0.85 
                 0.85 
               
               
                   
                 Sn 
                   
                 1.00 
               
               
                   
                 Sb 
                   
                 1.00 
               
               
                   
                 Pb 
                   
                 1.00 
               
               
                   
                 Al 
                 0.70 
                 0.70 
               
               
                   
                 C 
                   
                 0.75 
               
               
                   
                 Zr 
                   
                 1.00 
               
               
                   
                 B 
                 0.90 
                 0.90 
               
               
                   
                 S 
                   
                 1.00 
               
               
                   
                 P 
                   
                 1.00 
               
               
                   
                 W 
                   
                 1.00 
               
               
                   
                 V 
                 0.95 
                 0.95 
               
               
                   
                 As 
                   
                 1.00 
               
               
                   
                   
               
             
          
         
       
     
         [0099]    Complete chemical analyses were performed on various alloying agents and consumables from different suppliers. The chemical compositions of the alloying agents and consumables were compiled into a data base for the model. By referencing the compositions of the alloying agents and specified chemistry limits of the steel being manufactured, the model will first compute the respective amounts of alloying agents required to achieve the minimum content for each element in the specification. The model recommends a combination of alloying agents such that residual element pickups are maximized or minimized whatever the required case may be. The selection of a combination of alloying agents is also based on minimizing cost. For example, for products where the Carbon content required is 0.04% maximum, to ensure that Carbon pickup is kept to a minimum, the model will not recommend trim amounts for alloys which will result in a significant Carbon pickup (i.e. where Carbon pickup is not required, the model will recommend the use of LcMn instead of McMn). Another example is where there is a need to trim for Silicon and Manganese, the model will recommend the optimum amount of SiMn required to minimize the amount of LcMn or McMn for cost savings. The model will forecast the pickups from different alloying agents and will provide the expected total percentage of each element. Further, based on actual chemical analysis the model will compute how much additional trim is required for its concentration to reach the mid-point between the minimum and maximum specified values in the metallurgical practice. The model will recommend the combination of trim amount of different alloys required to ensure that the sum of certain elements are within specification (i.e. Carbon equivalent number, Titanium to Nitrogen Ratio, Ideal Diameter (DI) value etc.). For example, the model will recommend how much and which element (s) should be trimmed further to ensure that the value specified for carbon equivalent is met while individual contents of respective elements still remain within specified ranges. 
       d) Inclusion Modification 
       [0100]    Once the concentrations of all elements except Calcium and Sulfur are within specified ranges the model will then recommend that CaSi or FeCa treatment be performed. The Sulfur level of the bath will have to reach a certain percentage prior to the model recommending the amount of CaSi or FeCa required for treatment. Example, for Sulfur practice of 0.001 or 0.002%, the model will recommend that CaSi (FeCa) treatment be performed once the Sulfur level of the bath is less than or equal to 0.003% etc. 
         [0101]    For each Sulfur practice and depending on the Sulfur level of the bath the model computes how much CaSi (we will consider only CaSi henceforth) is required for complete treatment. In calculating the amount of CaSi required the model accounts for the dissolved Calcium in steel, Calcium fade (due to re-oxidation), reaction with the oxygen in slag and steel, reaction with Sulfur and recovery coefficient of Calcium, R Calcium  (its value is less than or equal to 1 but it varies depending on the Calcium-bearing alloy).The effect of Oxygen from slag and steel were accounted for by establishing a relationship between the Aluminum content in steel and total Oxygen based on de-oxidation equilibrium by Aluminum (see Table 2). The actual Oxygen levels are several times greater than the equilibrium oxygen levels as equilibrium is never truly achieved in metallurgical systems. In this work the actual oxygen was considered to be about 15 times the equilibrium values. 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Relationship between Aluminum and Oxygen Contents of Steel 
               
             
          
           
               
                   
                 % Al 
                 % O 
               
               
                   
                   
               
               
                   
                 0.01 
                 0.01110 
               
               
                   
                 0.02 
                 0.00749 
               
               
                   
                 0.03 
                 0.00609 
               
               
                   
                 0.04 
                 0.00536 
               
               
                   
                 0.05 
                 0.00492 
               
               
                   
                 0.06 
                 0.00470 
               
               
                   
                 0.07 
                 0.00450 
               
               
                   
                 0.08 
                 0.00435 
               
               
                   
                   
               
             
          
         
       
     
         [0102]    Any Oxygen present in the steel is considered to be present in the form of oxides and for Aluminum-de-oxidized steel the Oxygen is tied down in the form of alumina. A completely modified alumina inclusion will have a chemical formula of 12CaO.7Al 2 O 3 . Therefore, if the concentration of Oxygen is designated as N %, based on mass balance the amount of CaSi required to modify the alumina completely is calculated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     4 
                      
                     N 
                      
                     
                         
                     
                      
                     
                       W 
                       steel 
                     
                      
                     
                       A 
                       Calcium 
                     
                   
                   
                     7 
                      
                     
                       A 
                       Oxygen 
                     
                      
                     
                       R 
                       Calcium 
                     
                      
                     
                       C 
                       Calcium 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where R Calcium , a value less than or equal to 1, is the recovery coefficient of Calcium from and C Calcium  is the % of Calcium in the Calcium-bearing alloy.
 
The amount of CaSi required to modify the sulphide is calculated based on the following thermodynamic equilibrium reaction:
 
         [0000]      [Ca]+[S]=(CaS)  (8)
 
         [0000]    The amount of CaSi required for modification of dissolved Sulfur depends on whether a complete or partial modification is desired. In general, the amount is determined as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     100 
                      
                     Y 
                      
                     
                         
                     
                      
                     
                       W 
                       steel 
                     
                      
                     
                       A 
                       Calcium 
                     
                   
                   
                     
                       A 
                       sulfur 
                     
                      
                     
                       C 
                       Calcium 
                     
                      
                     
                       R 
                       Calcium 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where Y is the concentration of Sulfur in steel in %.
 
The amount of CaSi required for maximum solubility (S Calcium ) of Calcium in steel (about 0.0035%) is calculated as follows:
 
         [0000]    
       
         
           
             
               
                 
                   
                     100 
                      
                     
                       S 
                       Calcium 
                     
                      
                     
                       W 
                       steel 
                     
                   
                   
                     
                       C 
                       Calcium 
                     
                      
                     
                       R 
                       Calcium 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0103]    The sum of the amounts of the CaSi for all the three cases above will be the total amount required to be added for complete inclusion modifications. 
       e) Prediction of Phosphorous Content of the Steel 
       [0104]    There are three major sources that contribute to the total Phosphorous content of the steel: a) carryover slag from the EAF, b) Phosphorous content in steel at tap and 3) Phosphorous contents in alloying agents. In a completely de-oxidized steel the P 2 O 5  (Phosphorous is assumed to exist in slag as P 2 O 5 ) component of the slag is completely de-oxidized reverting all the Phosphorous to the steel. The amount of Phosphorous in % resulting from carryover slag with P 2 O 5  content of P O  % is calculated as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       A 
                       Phosphorus 
                     
                      
                     
                       P 
                       o 
                     
                      
                     
                       W 
                       slag 
                     
                   
                   
                     
                       M 
                       
                         
                           P 
                           2 
                         
                          
                         
                           O 
                           5 
                         
                       
                     
                      
                     
                       W 
                       steel 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0105]    The Phosphorous contents in the alloying agents are also completed dissolved in the steel. By adding up all the Phosphorous contributions from the three sources above the model is able to determine the total Phosphorous content of the steel. The Phosphorous contents of the steel determined as described above are very close to measured values. 
       f) Prediction of Ladle Slag Compositions 
       [0106]    By considering composition of slag carryover from the EAF, composition and amount of desulphurizing powder added into the ladle and composition and wear rate of the ladle refractory, the model computes the composition of ladle slag based on mass balance. 
         [0107]    For example, the % of alumina was determined by considering 1) how much alumina is produced from de-oxidation of the slag and steel, 2) % alumina in the de-sulphurizing mix and amount of alumina dissolving in steel from the ladle refractory. 
         [0108]    % CaO was determined base on three sources: 1) CaO in EAF slag carryover, Ca % in desulphurizing mix and 3) CaO resulting from CaSi (FeCa) treatment. 
         [0109]    % MgO was determined based on three sources: 1) MgO from EAF slag carryover, MgO from desulphuring mix and 3) MgO from the ladle refractory. 
         [0110]    % SiO 2  was determined based on three sources: 1) Partial or full de-oxidation by Silicon from alloys, 2) SiO 2  from the refractory and 3) SiO 2  from the desulphurizing mix. 
         [0111]    % S was determined based on two sources: 1) Sulfur from EAF slag carryover and 2) Sulfur from the steel. It is well known that some Sulfur is lost to the atmosphere via reaction with Oxygen but this loss was not accounted for in this calculation. 
         [0112]    % TiO 2  was determined was based on two sources: 1) Formation of TiO 2  by reaction of some of the Ti in the FeTi with oxygen in the slag or air and 2) TiO 2  from the ladle refractory. 
         [0113]    % FeO in the slag was considered to be from the ladle refractory only. The FeO dissolving from the refractory is considered impossible to reduce as the FeO is considered to be present in spinel form. 
         [0114]    The compositions of the ladle slag determined as described above are very close to measured values. An example of comparison is shown in Table 6. 
         [0115]    Tables 3 to 6 are typical examples of values computed by the model. As shown in  FIG. 1 , one of the dip test measurements had the sum of X and Y to be equal to 29.73 inches. The first slag line brick course from the top is at 10 inches below the ladle rim. This indicates that for this example the top level of steel in the ladle is at 3.73 inches from the top of the fifth brick course (each brick course is 4 inches in height). The changes in diameters at the start of and end of each brick course in the slag line, barrel and bottom regions of the ladle as a function of wear rates and ladle life were established. It should be noted that the height of the barrel portion of the ladle increases with ladle life due to refractory wear of the bottom region. The change in barrel height due to the wear of refractory in the bottom region of the ladle is factored into the calculation of the volume of steel in the ladle. Using the calculated diameters and the heights of each course of brick the model calculates the volume of each course of bricks using the formula for frustum of cones for slag line and barrel regions and formula for frustum of sphere for the bottom region of the ladle. The sum of all the unit volumes gives the total volume of the steel in the ladle. In this example the total volume was calculated to be equal to 17.63 m 3 . By multiplying this number by the steel density, we got 134011 kg of steel in the ladle. The weight of slag was determined in a similar fashion with the only difference being the density of slag (density of slag used was 2700 kg/m 3 ). 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Calculation of Slag and Steel Weights 
               
             
          
           
               
                   
                 Ladle 
                   
                 Measured and 
               
               
                   
                 Information 
                 Dip Test 
                 Calculated Weight 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                 Cal- 
                   
               
               
                 Metallic 
                   
                   
                   
                   
                   
                 Slag 
                 culated 
                 Scale 
               
               
                 Charge 
                 La- 
                 Slag 
                 Bar- 
                   
                   
                 Carry- 
                 Steel 
                 Read- 
               
               
                 Weight 
                 dle 
                 Line 
                 rel 
                 Y 
                 X 
                 over 
                 Weight 
                 ing 
               
               
                 (kg) 
                 # 
                 Life 
                 Life 
                 (inches)  
                 (inches) 
                 (kg) 
                 (kg) 
                 (kg) 
               
               
                   
               
               
                 149443 
                 3 
                 6 
                 6 
                 7 
                 22.73 
                 1532 
                 134011 
                 129820 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Alloy Additions 
               
             
          
           
               
                   
                   
                 LcMn 
                 LcSiMn 
                 FeNb 
                 FeTi 
                 FeMo 
               
               
                   
                   
               
               
                   
                 Model (kg) 
                 1795 
                 1061 
                 129 
                 33 
                 103 
               
               
                   
                 Actual (kg) 
                 1880 
                 1100 
                 128 
                 35 
                 108 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Steel Chemistry 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                   
                   
                 Nb  
                   
               
               
                   
                 C  
                 Mn  
                 Si  
                 Cu  
                 Ni 
                 Cr 
                 V 
                 (Cb)  
                 Mo 
               
               
                   
               
               
                 Model  
                 0.026  
                 1.664  
                 0.237  
                 0.182 
                 0.08 
                 0.052 
                 0.001 
                 0.0597 
                 0.176 
               
               
                 (%) 
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Actual  
                 0.025  
                 1.620  
                 0.240  
                 0.190  
                 0.08 
                 0.060 
                 0.001  
                 0.057  
                 0.174 
               
               
                 (%) 
               
               
                   
               
             
          
         
       
     
         [0000]                                                          TABLE 6                   Ladle Slag Composition                Al 2 O 3     CaO   MgO   SiO 2     S   TiO 2     FeO   Balance               Model (%)   19.59   55.01   12.55   4.71   1.79    0.67   0.10   5.58       Actual (%)   21.00   49.40   14.00   5.50   1.40   0.30   0.00   8.40                    
Control of Steel Flow from One Vessel to Another Vessel During Continuous Casting
 
         [0116]    Once the required chemical composition and reasonable degree of refining have been attained in the ladle at the ladle metallurgy station, the ladle is delivered to the caster for casting.  FIGS. 5 and 6  show the continuous casting machine where the steel flows from the ladle  42  into an intermediary vessel, the tundish,  50  from where it flows into the mould  54  for conversion into solid slabs. In a continuous casting process, several ladles of steel, usually of the same grade, are continuously cast. As one ladle is emptied, the next ladle  42  is opened immediately to ensure a continuous casting process. The flow of steel from the ladle to the tundish and from the tundish to the mould is controlled by a slide gate system as shown in  FIG. 6 . The amount of flow is determined by the degree of alignment of the bores in the upper and lower plates  44  and  46  respectively. With the aid of a hydraulic cylinder  60 , which displaces the lower plate to change the degree of alignment of the bores in the plates, the amount of steel entering each vessel is controlled. The bores in the upper  44  and lower  46  plates are usually of the same diameter and maximum flow rate is achieved when the bores are completely aligned. 
         [0117]    At the start of casting when the first ladle is opened, the tundish  50  is filled to a certain level prior to establishing steel flow into the mould  54 . Once flow to the mould  54  is initiated, the mould  54  is filled with steel to a certain level before the strand is gradually withdrawn to give a sufficient time for solidification of the steel on the dummy bar claw (not shown). Once a steady state casting has been attained and the levels of the steel in the tundish  50  and mould  54  have reached their maximum set points, the flow rate of steel from the ladle  42  to the tundish  50  and from tundish  50  to the mould  54  have to be equal to each other as well as the amount of steel being cast per unit time to prevent overflow of steel from the vessels and maintain continuity of casting. At ladle interchange time (the time between switching an empty ladle and opening a new ladle with steel) the level of the steel in the tundish  50  drops, but both from operational and quality stand points the level of steel in the mould  54  must not be allowed to drop. The time elapsed between closing one ladle and opening the other is usually short, typically only a couple of minutes, such that the tundish  50  is not completely drained by the time a flow of steel from the new ladle to the tundish  50  is established. However, where this time is extended due to operational issues, the cast speed and flow rate of steel from the tundish  50  to the mould  54  are adjusted as required. As an example, levels of the steel in the tundish  50  and mould  54  and the flow of steel from one vessel to the other are controlled as follows: 
       a) Mould Level Control 
       [0118]    The mould level control system uses an integrated control system that meters the flow of liquid metal from the tundish  50  to the mould  54 . The system combines a three-plate tundish gate system, Berthold mould level measuring system, PLC and a hydraulic system (all not shown). 
         [0119]    The Berthold mould level gauge, as is known to those skilled, is essentially a highly sensitive radiation unit which, in conjunction with a radioactive rod source, monitors the level of molten metal in the mould and provides a proportional output signal to the Interstop PLC, the latter device being known to those skilled. This integrated control system is used to control the interaction of the middle plate cylinder, operator station and the algorithm that solves the variance between the actual mould level and the mold level set-point. 
       b) Tundish Level Control 
       [0120]    The tundish level control system meters the flow of liquid metal from the ladle to the tundish. The system uses a Vesuvius LV 80 slide gate with a two plate system to accomplish the control of this steel flow.
 
The tundish level control system consists of:
       i. A slide gate mounted to the bottom of the ladle which contains a movable lower plate driven by a hydraulic cylinder;   ii. Hydraulic power pack and valve manifold to provide the power and control of the cylinder; and   iii. An integrated control system used to control the interaction of the tundish level weight and tundish level weight set point to act as the basis of an algorithm that solves the variance and sends a compensating pulse to the ladle gate hydraulic manifold to correct the variance.       
 
         [0124]    There are other patented techniques, like electromagnetic processes, using thermal signal from thermocouples etc, for mould level control and tundish level control. Each of these techniques has its advantages and disadvantages. The disadvantage of all of these techniques is that they are not well integrated to form a unified system to monitor and control steel flow during casting. The other disadvantage of using radiation rod source is the danger associated with mishandling and over exposure of employees to radiation. 
         [0125]    The basis for the current invention is to create an integrated, unified and comprehensive system for the control of liquid steel levels, flow of steel from one vessel to the other and optimization of casting process. Such system will be easily incorporated into the existing PLC control logic for interaction with the hydraulic system for adjusting slide gate and casting speed. 
         [0126]      FIG. 7  shows an example of an apparatus for monitoring and controlling the flow of steel from the ladle to the tundish and from the tundish to the mould. With this technology the control of flow from ladle to the tundish and from the tundish constitutes one comprehensive control loop for level regulator in the tundish and the mould. The system will function as outlined below: 
         [0127]    A radar system  38  will be used to monitor the level of steel in the tundish  50  and in the mould  54 . The radar system will determine any deviation of steel level in the mould from the required set point level. An on-line model which computes the volume/weight of steel in the tundish and mould at different steel levels based on the geometries of tundish and mould operates in conjunction with the radar system. The radar system which monitors the steel level in the mould communicates any deviation from the set point level range to the model. Using the geometry of the mould the model in turn computes the required increase or decrease in the weight of steel due to the deviation from the set point level. This calculated value is communicated through the gate control circuit to the hydraulic cylinder which adjust the gate accordingly. 
         [0128]      FIG. 8  is a schematic of the mould which generally has the shape of a trapezoid. The volume of the mould is calculated as follows: a) the volume of an inner rectangular box represented by “begd” is computed as a function of mould height; b) the volume of the outer rectangular box represented by “afhc” is computed as a function of height; c) the volume of steel in the mould at different levels is computed by adding the difference in the volumes of the outer and inner boxes to the volume of the inner box. Usually, the required steel level in the mould should be maintained within a certain established operational range. It is not desirable to allow the steel level to rise above or fall below the upper or lower limits respectively. To prevent steel level going outside the operational limits a tighter range is established within the operational range to ensure that steel level is compensated for sooner enough thereby maintaining the level within the operational limits at all times during casting. Whenever the mould level exceeds or drops below the system limits the radar system deter mines the increment or decrease in the levels, which it communicates to the model. The model computes the additional increase or decrease in the flow rate of steel required and communicates to the PLC system, which execute the required hydraulic cylinder movement to adjust the degree of opening of the slide gate. By continuous communication between the model and the radar system any small deviation in mould level is instantaneously adjusted preventing significant change in mould level fluctuation which could result in operational and quality issues. Once the required correction has been made in the mould and the level of steel has stabilized, the radar system monitoring the level of steel in the tundish determines the resulting change in the level of steel in the tundish. This change in tundish level is communicated to the model which computes the difference in volume and uses it to adjust flow rate of steel from ladle to tundish in a similar manner to mould level adjustment. The tundish has an irregular shape of a trapezoid tapered on all of its four sides. The tundish is divided into different volumes of regular shapes as shown in  FIG. 9 . Hence, the tundish, comprises five different unit volumes a, b, c, d and e. Volumes b and c are computed as function of height starting from c, d, g, h, j, k and l plane. The volume of the steel in the tundish at a specific height is determined by adding the difference in volume between the volumes of the outer box “afel” and inner box “bekd” to the volumes d, c, e and the inner box. 
         [0129]    It is possible that the flow rate from the tundish to the mould is not adjusted even though the slide gate opening adjustment was performed as required. This can occur due to plugged ports in the submerged entry nozzle or some other reasons. Whatever the case may be, the cast speed needs to be adjusted accordingly. To correct this situation, the model monitors the level in the mould and if it detects a continuous drop or increase in the level for the next five seconds it will communicate to the cast speed regulation system to slow down or increase the speed of casting to a value sufficient to bring mould level back to the required level. The ability of the system reacting quickly to correct cast speed gives the operator time to make a decision with respect to aborting the cast if the problem persists. Once the required mould level is attained the cast speed is adjusted to match the current flow rate from the tundish. 
         [0130]    The control of casting is monitored from the beginning of cast to the end and must follow the following sequence of events. 
         [0131]    At the start of casting a sequence of heats, once the mould radar monitoring system detects that a flow of steel has been initiated to the mould, it starts determining the change in steel height. At the start of the sequence, the tundish slide gates always have the bores in the upper and lower plates aligned to some extent (assume 82% alignment). At the maximum bore alignment of 82% the model will determine the maximum flow rate and store the flow rate as the maximum allowable flow rate for the sequence of heats. Based on the diameter of the bore the model computes the distance the plate has to move in the opposite direction for the bores in the plates to be completely misaligned in order to end the flow of steel through the gate. With this analysis, the model will understand the relation of the position of the lower plate to the flow rate of steel from the tundish to the mould and use this logic to determine how the plate should be displaced to increase or decrease steel flow rate. 
         [0132]    Once the flow of steel into the mould has been detected, the model begins recording level change in the steel in the tundish communicated by the radar system. At the start of a sequence and whenever a new ladle is opened the bores in the lower and upper plates are aligned 100% to ensure that the tundish is filled up within the shortest time possible. The model will compute the volume change per unit time in the tundish and it will record the sum of the flow rates to the tundish and mould as equal to the total amount flow rate through the ladle slide gate at 100% open. This value is stored by the model in its memory as the maximum flow rate possible which will be used in determining the direction of displacement of the hydraulic cylinder to compensate for level change in the tundish during steady state casting. 
         [0133]    Once the level of the steel in the mould reaches 95% of the specified height in the mould the mathematical model will start decreasing the alignment of the lower and upper plates while ensuring that once the steel level reaches 100% of the specified level the flow rate from the tundish to the mould is equal to the casting through put. 
         [0134]    Once the steel level in the tundish reaches 95% of the specified height in the tundish the mathematical model will start decreasing the alignment of the bores in the lower and upper plates while ensuring that once the steel level reaches 100% of the specified level the flow rate from the ladle to the tundish is equal to the flow rate from the tundish to the mould. 
         [0135]    Steady state is considered achieved once both the tundish level and mould level have attained 100% of their specified levels. 
         [0136]    a) As soon as steel is detected in the mould the model will start computing the volume of the steel left in the ladle as follows:
       1. Let the initial starting height of steel in the mould be h 0   m  and the initial height of steel in the tundish be h 0   t .   2. Let the volume change at any time in the mould at non-steady and steady states be ΔV i   m,nonsteady  and ΔV i   m,steady  respectively.   3. Let the volume change for the tundish at non steady and steady states be ΔV i   t,nonsteady  and ΔV i   t,steady  respectively.   4. Let the cast speed be C i      5. Let the cast width be W   6. Let the cast thickness be X   7. Let ρ be the density of liquid steel   8. Then the weight of steel left in the ladle equals;       
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     Ladle 
                   
                   = 
                   
                     
                       W 
                       Ladle 
                       tap 
                     
                     - 
                     
                       ρ 
                        
                       
                         ( 
                         
                           
                             
                               
                                 
                                   V 
                                   
                                     h 
                                     0 
                                     t 
                                   
                                 
                                 + 
                                 
                                   V 
                                   
                                     h 
                                     0 
                                     m 
                                   
                                 
                                 + 
                                 
                                   ∑ 
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       V 
                                       i 
                                       
                                         t 
                                         , 
                                         nonsteady 
                                       
                                     
                                   
                                 
                                 + 
                                 
                                   ∑ 
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       V 
                                       i 
                                       
                                         m 
                                         , 
                                         nonsteady 
                                       
                                     
                                   
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 
                                   ∑ 
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       V 
                                       i 
                                       
                                         t 
                                         , 
                                         steady 
                                       
                                     
                                   
                                 
                                 + 
                                 
                                   ∑ 
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       V 
                                       i 
                                       
                                         m 
                                         , 
                                         steady 
                                       
                                     
                                   
                                 
                                 + 
                                 
                                   ( 
                                   
                                     W 
                                      
                                     
                                         
                                     
                                      
                                     X 
                                      
                                     
                                       
                                         ∑ 
                                         
                                           i 
                                           = 
                                           1 
                                         
                                         n 
                                       
                                        
                                       
                                         
                                           C 
                                           i 
                                         
                                          
                                         Δ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           t 
                                           i 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0145]    b) Along with estimating the remaining weight of steel in the ladle, the model estimates how long it will take to empty each ladle as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                       
                   
                    
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         t 
                         Casting 
                         remaining 
                       
                     
                     = 
                     
                       
                         W 
                         Ladle 
                         Steady 
                       
                       
                         ρ 
                          
                         
                             
                         
                          
                         
                           C 
                           i 
                         
                          
                         W 
                          
                         
                             
                         
                          
                         X 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   Where 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     W 
                     Ladle 
                     Steady 
                   
                   = 
                   
                     
                       W 
                       Ladle 
                       tap 
                     
                     - 
                     
                       ρ 
                        
                       
                         ( 
                         
                           
                             V 
                             
                               h 
                               0 
                               t 
                             
                           
                           + 
                           
                             V 
                             
                               h 
                               0 
                               m 
                             
                           
                           + 
                           
                             ∑ 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 i 
                                 
                                   t 
                                   , 
                                   nonsteady 
                                 
                               
                             
                           
                           + 
                           
                             ∑ 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               
                                 V 
                                 i 
                                 
                                   m 
                                   , 
                                   nonsteady 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0146]    c) The total cast time for each heat can be calculated as follows; 
         [0000]    
       
         
           
             
               
                 
                   
                     t 
                     Casttime 
                     total 
                   
                   = 
                   
                     
                       
                         ρ 
                          
                         
                           ( 
                           
                             
                               V 
                               
                                 h 
                                 0 
                                 l 
                               
                             
                             + 
                             
                               V 
                               
                                 h 
                                 0 
                                 m 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   V 
                                   i 
                                   
                                     t 
                                     , 
                                     nonsteady 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 n 
                               
                                
                               
                                 Δ 
                                  
                                 
                                     
                                 
                                  
                                 
                                   V 
                                   i 
                                   
                                     m 
                                     , 
                                     nonsteady 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       
                         R 
                         ladle 
                         nonsteady 
                       
                     
                     + 
                     
                       
                         
                           W 
                           Ladle 
                           steady 
                         
                          
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                            
                           
                             Δ 
                              
                             
                                 
                             
                              
                             
                               t 
                               i 
                             
                           
                         
                       
                       
                         ρ 
                          
                         
                             
                         
                          
                         W 
                          
                         
                             
                         
                          
                         X 
                          
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             n 
                           
                            
                           
                             
                               C 
                               i 
                             
                              
                             Δ 
                              
                             
                                 
                             
                              
                             
                               t 
                               i 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
       
         
           
             Where W Ladle   Steady  is the weight of steel left in the ladle when steady state casting is attained and R Ladle   nonsteady  is the flow rate of steel from the ladle to the tundish at 100% gate open during the filling up of the tundish. For second and other heats in the sequence V h     0       1    and V h     0       m    values equal zero. 
           
         
       
     
         [0148]    d) The calculated weight of steel in the ladle as in the equation (10) is used to determine when to arm the slag detection system, which determines when to shut the ladle off due to entrainment of slag into the tundish during casting. An audible alarm can be used to alert the operators to arm the system or aiming of the system can be done automatically. 
         [0149]    e) The model determines that the ladle slide gate is closed if the backward displacement of the hydraulic cylinder is equal to or greater than the diameter of the lower plate. 
         [0150]    f) Once the model determines that the ladle has been closed based on the backward displacement of the hydraulic cylinder, communication between the tundish radar system and the model is discontinued until a new ladle is opened. However, communication between the model and mould radar system continues until the tundish slide gate is closed. 
         [0151]    It should be noted that using the radar system in conjunction with geometrical profiling of any vessel or reservoir similar analysis outlined in this invention can be employed for calculating volumes or weight of any liquid and controlling the flow from one vessel to the other for any system. It is equally important to note that controlling steel flow from vessel to vessel during continuous casting and profiling of the vessels as described in this invention can be integrated with other level monitoring systems beside a radar system. The overall advantage of this system is that its response to deviations from steel level in the tundish and mould will be instantaneous and highly accurate. 
       Charge Scrap Management 
       [0152]    With accurate determination of the EAF heel the amount of metallic scrap required to be charged into the furnace as specified by the production schedule can be managed better to prevent over or under charging of the furnace. Generally, the furnace operators eyeball the level of heel in the furnace and estimate how much steel is left in the furnace. A gross misjudgement can result in under or over charging of the furnace. The consequences of misjudgement includes yield loss due to loss of steel through the slag door, increased power consumption due to exposure of arc to atmosphere, excessive nitrogen pickup from the atmosphere, increase refractory wear rate, and low productivity. Accurate determination of furnace heel will ensure consistent bath level, high productivity and good process control. 
         [0153]      FIGS. 10 through 12  represent flow charts depicting the overall steps of the model as described herein. 
         [0154]    Although the invention has been described with reference to certain specific embodiments, various modifications thereof will be apparent to those skilled in the art without departing from the spirit and scope of the invention as outlined in the claims appended hereto. The entire disclosures of all references recited above are incorporated herein by reference.