Process algorithm, numerical model and techno-economic assessment of charge calculation and furnace bath optimization for target alloy for induction furnace-based steelmaking is presented in this study. The developed algorithm combines the make-to-order (MTO) and charge optimization planning (COP) of the steel melting shop in the production of target steel composition. Using a system-level approach, the unit operations involved in the melting process were analyzed with the purpose of initial charge calculation, prevailing alloy charge prediction and optimizing the sequence of melt chemistry modification. The model performance was established using real-time production data from a cast iron-based foundry with a 1- and 2-ton induction furnace capacity and a medium carbon-based foundry with a 10- and 15-ton induction furnace capacity. A simulation engine (CastMELT) was developed in Java IDE with a MySQL database for continuous interaction with changing process parameters to run the model for validation. The comparison between the model prediction and production results was analyzed for charge prediction, melt modification and ferroalloy optimization and possible cost savings. The model performance for elemental charge prediction and calculation purpose with respect to the charge input (at overall scrap meltdown) gave R-squared, Standard Error, Pearson correlation and Significance value of (0.934, 0.06, 0.97, 0.0003) for Carbon prediction, (0.962, 0.06, 0.98, 0.00009) for Silicon prediction, (0.999, 0.048, 0.999, 9E -11) for Manganese Prediction, and (0.997, 0.076, 0.999, 6E -7) for Chromium prediction respectively. Correlation analysis for melt modification (after charging of ferroalloy) using the model for after-alloying spark analysis compared with the target chemistry is at 99.82%. The results validate the suitability of the developed model as a functional system of induction furnace melting for combined charge calculation and melt optimization Techno-economic evaluation results showed that 0.98% - 0.25% ferroalloy saving per ton of melt is possible using the model. This brings about an annual production cost savings of 100,000 $/y in foundry A (medium carbon steel) and 20,000 $/y in foundry B (cast iron) on the use of different ferroalloy materials.
Melting as a major operation in the foundry is carried out by charging commercially pure metals, external and internal scrap, and additives to achieve a target alloy composition. The process includes melting the charge, refining the melt, adjusting the melt chemistry and tapping into the transport vessel [
It is noteworthy that charge calculation for foundry operation could be very cumbersome ranging from several hours to days [
Induction and crucible furnace using a system-level approach can be analyzed for stochastic modelling [
The numerical model is developed using the principle of materials balance and system-level analysis. The system-level approach involves the analysis of a large system as a unit without analytical consideration of the lower-level subsystems. This approach provides the requirements on systems and application program design in the form of explicit models of system behavior and defines the state-based architecture of the control system. The process algorithm, which was developed with the understanding of the operation sequence of induction furnace steel melting is presented in
The mode of production in the modern manufacturing enterprise is mainly referred to as MTO (Make-to-Order). However, to reasonably rearrange the production plan
to consumer target and standard is a very arduous and common problem for foundry managers amidst improving their inner production reformation in the competitive market environment. This will be handled by a charge analysis and fitness model. The material system model for the induction and crucible furnace is based on the principle of mass balance. The induction furnace operation for charging sequence and melt modification is assumed to be a closed system function in relation to the law of conservation of mass [
The general form for an open system is given by:
Mass input = Mass output + Net Accumulation within the system
TotalMassbalance = ∑ j = 1 m f i j F i − ∑ j = 1 k p i j P j = 0 (1)
where (Fi, Pi) are masses and (fij, pij) are analysis or content.
In the case of an industrial melting operation, where a large amount of assorted/ aggregate scraps are charged into the furnace, the simulation program algorithm recognizes such as online-real time unit operation path. Taking cognizance of the initial melting operation, the operational recovery lead to the retention of molten metal in the working region of the furnace.
The Heel Melting Factor (HMF) is observed in the empirical analysis (actual state analysis) as:
hmf = [ i-Melt ∗ 1.11 ] ∗ ( 100 − R ) / R (2)
hmf = [ i-Scrap ∗ ( 100 − R ) ] / R (3)
· Where hmf is the heel factor intended to predict the amount of molten metal retained in the working portion of the furnace.
· i-Melt is the amount of molten steel that was successfully tapped from the previous melt.
· i-Scrap is the amount of scrap charged in the previous melting operation.
· and R is the operational recovery of the steel melting shop.
In the case of a specialized melting, experimental melting plan and prescribed or on-request melt batch, the simulation program algorithm follows an offline patch with pseudo melting analysis with the artificial intelligence pathway of the furnace.
For a n-list of scrap charge with each scrap having an already known or recorded chemical analysis, the overall amount of scrap charge is defined in Equation (4):
j-Scrap = M a + M b + M c + M d + ⋯ + M n (4)
where M is the mass of the individual scrap a , b , c , d , ⋯ , n .
j-Scrap is the overall amount of all the scrap charge in Kg.
The overall percentage composition of an element (x) in the scrap a , b , c , d , ⋯ , n , is defined with Equation (5):
x n = 0.01 R ∗ j-Scrap ∑ a n x i ⋅ M (5)
where xn = the new % composition of an element (x) upon the overall addition of the scrap.
Individual melt analysis in kg of individual element in each scrap is defined by Equation (6)
x ( in kg ) = 0.01 ∗ [ x i ∗ j-Scrap ] (6)
Elemental difference between the bath analysis and the target standard composition is defined by the function in Equation (7)
0.01 ∗ j-Scrap [ x s t − x n ] (7)
· Where xst is % composition of element (x) in the target standard melt.
· xn is % composition of the element (x) in the bath analysis.
The estimation for the addition of flux is a function of the operational recovery of the melting shop which defines the amount of molten metal that did not report to tapping operation. The amount of flux (quicklime or dolomite) to be added to the melt is defined in Equation (8):
MassofFlux = [ 0.01 ( 100 − R ) ∗ j-Scrap ] ∗ % CaO / MgO . (8)
The use of scrap to correct the chemistry of the melt is a known practice in induction steel melting. This precludes the reason why efficient scrap sorting, classification, and selection is very inevitable in the foundry especially with the use of induction and crucible furnace melting.
When the bath analysis of the current melting is obtained from the spectrometric analysis, the data therein is used to determine the amount of scrap that will be required to change the bath analysis to the intended chemistry bearing in mind a particular element type. The mass of scrap to be injected into the current bath for chemistry adjustment is defined by the model in Equation (9):
M i n j = R i | [ j-Scrap ∗ ( x n − x s t ) ( x s t − x s c ) ] | (9)
· Where | | is an absolute value operator.
· Minj is Mass of the injected/incoming scrap.
· xsc is & composition of element (x) in the incoming scrap.
· Ri is Elemental Recovery of the injected scrap.
The new % composition of each element in the bath analysis after the injection of the new scrap is defined in Equation (10):
x b a t h = [ ( x n ∗ j-Scrap ) + ( x s c ∗ M i n j ) ( j-Scrap + M i n j ) ] (10)
· where xbath is the % composition of element (x) after the injection of scrap.
· xn = % composition of element (x) in the melt before the injection.
Ferroalloy addition (FeMn, SiMn) or other additives (graphite or mill scale) depending on the bath analysis after the initial scrap meltdown could be done before or after melt correction in the furnace. Depending on the type of major element that is a shortfall of the target composition, the ferroalloy is added. Most times scrap addition for chemistry adjustment is preferable for cost savings. This is because the cost of ferroalloys is expensive compared to the cost of scrap. This pathway, however, makes modelling a veritable tool for melt optimization and cost savings in the foundry.
Ferro alloy (additive) addition is defined by the function in Equation (11):
M f a = | j-Scrap ( x n − x s t ) / ( x s t − x f a ∗ R i ) | (11)
· where xfa is the % composition of the target element in the ferroalloy/additive to be added.
· Mfa is the mass of ferro alloy to be added to the bath.
· Ri is the elemental recovery of the element added from the ferro alloy/additives.
· Other symbols have their usual meaning.
Effect of the addition of ferroalloy/additives in the bath analysis is defined in Equation (12):
x b a t h = [ ( x n ∗ j-Scrap ) + ( x f a ∗ M f a ) ( j-Scrap + M f a ) ] (12)
· where xfa and Mfa is the % composition of the intended element in the ferroalloy/additive and mass in kg of the ferroalloy added respectively.
Upon the addition of more ferroalloys/additives or scrap, depending, the j-scrap becomes incremental with the addition of new weight of charges. For instance, the weight of the melt upon an initial scrap addition/ferro alloy/additives is defined by:
j-Scrapnew = ( j-Scrap + M f a M s c ) (13)
The new j-Scrap value is erstwhile used in the next calculation for bath analysis correction.
The simulation program algorithm defines a pathway in the overall model which creates the possibility for the user to perform a pseudo melting operation right from the computer without the real-time, physical operation of the furnace. This is intended to utilize the advantage of a neural network and mathematical iteration to create a pathway in which the simulation program mimics the melting environment of the furnace with the usability of a database of scrap inventory developed into this current algorithm as compared to that available in Seidu and Onigbajumo, 2015 [
The iteration continues in the form:
x i ( k + 1 ) = 1 a i ( b i − ∑ j ≠ i a i j x j ( k ) ) , i = 1 , 2 , ⋯ , n (14)
This implies that Equations ((4)-(6), (9) and (10)) is returned for n number of times in the general Gauss-Seidel iteration function in Equation (14) until the set value is approximately attained.
Resultant % composition of any element type (say x) when additional scrap is added and repeated until the target composition is attained using iteration is expressed in Equation (15):
% x 0 = x i ( k + 1 ) ( M s t × x i ) + ( M s c × x n × R o ) ( M s t + M s c ) × 100 % (15)
x 0 is the resultant composition of an element (x) upon new additions of scrap/ferro-alloy.
Ferro-alloy addition containing an element (x) is added according to Equation (16),
% x 0 = ( R i ⋅ M s t × x i ) + ( M f a × x m × R o ) ( M s t + M f a ) × 100 % (16)
When two additions were made i.e. (i and ii), the overall resultant composition will be an iteration of Equation (16)
% x 0 = x i ( k + 1 ) ( R i ⋅ M s t × x i ) + ( M s c × x n × R o ) + ( M f a × x m × R o ) ( M s t + M f a + M s c ) × 100 % (17)
We can deduce the mass of scrap to be added to achieve the expected target composition by re-arranging Equation (15), therefore,
M s c = M s t ( x i R i − x o ) ( x o − x n R o ) (18)
where Msc represents the mass of scrap that must be added.
Re-arranging Equation (17), we can calculate the mass of ferroalloy/additive to charge upon scrap upon an earlier correction.
M f a = M s t ( R i x i − x o ) + M s c ( x n + R o − x o ) ( x o − x m R o ) (19)
where Mfa represents the mass of scrap that must be added.
The implementation of the off-schedule Pseudo Melting algorithm brings in a lot of flexibility and allows user control and planning to offset material stock (for Charge Optimization Planning—COP). With the implementation of the iteration cycle, several charge continuums are possible with the furnace manager deciding the amount of material charge and new melt composition is implemented instantaneously based on the charge.
The charge optimization, melt modification, and ferroalloy addition models developed in this study to achieve target melt composition was established by testing against real-time operational data in two different commercial foundry plants. Plant A is a low-alloy medium carbon steelmaking foundry with 10- and 15-tons induction furnace and plant B produces high-alloy cast-iron products (high manganese, high chromium) with 1- and 2-ton induction furnace system. Four melts were obtained with foundry A and six melts achieved in foundry B in a total of 6 production days using aggregate scrap at plant A and known scrap composition at plant B. Real time simulation using the same operational data of both foundry shops were performed using the developed model through a computational simulation program engine (CastMELT), written in Java and MySQL database server to run the numerical models. The relationship between predicted data and real-time melting shop experiments were analysed using statistical tools in MS Excel.
In order to ascertain the compatibility of the developed model as well as its adaptation to industrial usage, real time operation data were obtained from an industrial plant with custom casting foundry operation. The analysis large scale commercial structural steel production analysis. The statistical validation analysis employed in the validation include—Regression Analysis, ANOVA, Pair-T Test, Pearson’s Correlation, and Scatter Plot Analysis Correlation using the Microsoft Excel Tool.
The following evaluations and validity were made to confirm the suitability of the model using the simulation engine:
i) Charge Analysis Prediction: this is for verification of the model in predicting values as obtainable during the melting operation of the plants visited.
ii) Melt Modification, Correction Function and Optimization Analysis: this is to subject the simulation engine (CastMELT) to melt correction function and analysis to verify its melt correction and material optimization functionality.
Standard product quality vis-à-vis production cost management is key to the continuous operation of iron and steel plants. Large amount of production loss is incurred in the foundry through poor material sorting and selection, inaccurate material charging, excess energy consumption due to wrong materials charge, time loss due to melt correction. Foundry engineers, production manager and relevant stakeholders of a foundry plant are continuously seeking approaches to cost savings without bringing down the integrity of their cast products. Cost saving is achievable through:
1) Efficient material accounting and scrap sourcing.
2) Charge calculation and materials balancing.
3) Melt modification and optimization.
4) Energy management and heat recovery.
5) Production time management with the utilization of steel melting and casting software.
The real-time operational data for both foundries include the information on the scrap mix (steel, cast iron, and foundry returns), ferro additive type (mill scale, medium carbon FeMn, high carbon FeMn, FeCr, and FeSi), the weight of scrap and ferro-alloy charge, tapping temperature, cycle time (tap to tap time which includes all time losses). The operational or production data also includes the furnace used and the furnace power rating which determines the melting rate as presented in supplementary material 1 and 2. The developed simulation engine (CastMELT) was used to adapt this operational data and simulate the process outcome based on the models developed in the previous section. The numerical model was evaluated first for charge calculation predictions using the simulation engine with the results presented in supplementary material 3 and 4 for foundry A (medium carbon steel) and foundry B (cast iron) respectively. This is to verify the use of the numerical model in giving close output for charge balance using the same operation data for both foundries when loaded in the simulation engine database.
Figures 2-5 show the relationship between the melt composition for carbon, silicon, manganese, and chromium for foundry A for four (4) heats and Figures 6-9 show the same element relationship for foundry B for six (6) heats as a basis for statistical correlation analysis. Pearson’s correlation coefficient results show 81% to 95.7% and 0.12 - 0.47 respectively for foundry A and B, respectively. Standard error stands at 0.12 - 0.47 for foundry A and 0.005 - 0.089 for foundry
B. The high correlation in foundry B plant is largely due to the use of known scraps as compared to foundry A with the use of aggregate scrap. Foundry A also has a basic oxygen furnace where the steel melt is further treated especially when the amount of carbon which is very challenging to control in the induction furnace. This makes the overall melting activities to proceed in on-site with less
control compared to foundry A. Elemental compositions for charge calculation and material balance had the highest Pearson’s correlation for silicon and carbon at 96% and 90.7% respectively for foundry A melting practice. Carbon and manganese had the highest correlation at 99% each for charge calculation and material balance in foundry B based on the melting practice.
The numerical model using the simulation engine was also evaluated for melt treatment and modification using scrap and ferroalloy addition to achieve target melt composition. A comparison was made between the final melt composition, CastMELT simulation engine final melt prediction, and the target chemistry of the produced cast in both foundries. The simulation was done using the same real-time production data for the period of this evaluation. The results are presented in
From the results are shown in
98.85%. This did not only validate the correctness of the model and the simulation engine developed but also, show its suitability for an improved outcome for the steelmaking shop using induction furnace. Foundry B could achieve final alloy composition before casting with limits within the target composition since it has a better scrap and operation control in the use of lower production tonnage tested and known scrap when compared with foundry A.
Charge calculation assessment of the model for foundry-A melting test shows R-squared, Standard Error, Pearson correlation and Significance value of (0.921, 0.021, 0.908, 0.09) for Carbon prediction, (0.921, 0.021, 0.96, 0.04) for Silicon prediction, (0.814, 0.0662, 0.815, 0.186) for Manganese Prediction, and (0.792, 0.001, 0.89, 0.11) for Chromium Prediction respectively. The drawback in the correlation and confidence measurement was however due to the absence of a mill-scale record in the production record. The foundry practice of mill scale addition in foundry A is through trial-and-error. For comparison, the mill scale addition was computed using a reverse mass balance and stoichiometry calculations to give a rough estimate of what is to be charged into the melt during production.
With respect to materials savings especially for ferro additives, the simulation of the developed model using the same operations data produced was able to predict after alloy melt composition which falls within the range of the target composition but closer to the lower boundary value of the target chemistry for each element (supplementary material 3 and 4). The results using the model could be used to predict the optimized amount of ferroalloy addition which could bring large savings on material cost during melt treatment to achieve the target composition.
A comparison made between the ferroalloy addition in the real-time production at both foundries where the test is being carried out to validate this model and the ferroalloy predicted for using the simulation engine (CastMELT).
For a total of 41 tons of low-alloy medium carbon steel produced in foundry A and 9 tons of high-alloy cast iron melt produced during the performance assessment of the model, an average of 0.98% - 2.5% savings is achieved using the developed model to achieve target melt composition when compared with the material utilization in both foundries that were used for the validation. For techno-economic evaluation based on 1 USD to NGN 360, a possible savings of 350 - 380 $/ton and 75 - 81.4 $/ton of melt produced is achieved on ferroalloy addition for foundry A and B, respectively. This results in an annual savings of 100,000 $/y in foundry-A and 20,000 $/y foundry-B for ferroalloy materials charge.
In this study, a numerical model for charge balancing and melt optimization has been developed and validated using real-time experimental investigations at a high-alloy cast iron and low-alloy medium steel carbon foundries. Process algorithm which combines a charge optimization and make-to-order approach for induction furnace melting of scrap was developed and used as the basis for developing a numerical model to establish the algorithm. The numerical model was developed using the system-level methodology for plant systems, Gauss-Seidel method of successive displacement, boundary value problem and partial differential equations to analyse the overall architecture of materials charge and melt optimization in the induction furnace. A simulation engine was also developed in Java IDE with a MySQL database server script to run the model.
The performance of this model was assessed in two separate foundries for high-alloy cast iron and low-allow medium carbon steel production with a real-time production data analysis. The validation investigates the utilization of the model for charge calculation and material balancing, melt adjustment, and optimization of ferro additives. The results using the simulation engine (CastMELT) indicates a correlation coefficient of 81% for the low-alloy steel (foundry-A) and
| CastMELT Material Optimization Savings—Foundry A* | ||||||||
|---|---|---|---|---|---|---|---|---|
| FeSi | HCFeMn | Mill Scale | SiMn | Total Charge | Total Savings (N) | |||
| 1 | 1,170,346—NFL | 9860 | * | * | 190 | 149 | 10,199 | |
| CastMELT | 9860 | 46 | 77 | 101.36 | * | 10,136 | 20,430 | |
| Material Savings/Loss | −46 | −77 | 37 | 149 | ||||
| Savings on Production Cost (N) | −18,216 | −27,720 | 1998 | 64,368 | ||||
| 2 | 2,170,340 | 9170 | * | * | 200 | 100 | 9470 | |
| CastMELT | 9170 | 19 | 32.5 | 32 | * | 9253.5 | 33,048 | |
| Material Savings/Loss | −19 | −32.5 | 168 | 100 | ||||
| Savings on Production Cost (N) | −7524 | −11,700 | 9072 | 43200 | ||||
| 3 | 2,170,342 | 11400 | * | * | 220 | 205 | 11825 | |
| CastMELT | 11400 | 36 | 31 | 79 | * | 11546 | 70,758 | |
| Material Savings/Loss | −36 | −31 | 141 | 205 | 4.8 | |||
| Savings on Production Cost (N) | 14,256 | 11,160 | 7614 | 88,560 | ||||
| 4 | 2,170,343 | 9600 | * | * | 160 | 120 | 9880 | |
| CastMELT | 9600 | 42 | 70 | 112 | * | 9824 | 12,600 | |
| Material Savings/Loss | −42 | −70 | 48 | 120 | ||||
| Savings on Production Cost (N) | 16,632 | −25,200 | 2592 | 51,840 | ||||
*Cost per ton—FeSi: $1100, SiMn: $1200, MCFeMn: $1000, Mill Scale: $150, Graphite: $600.
| CastMELT Material Optimization Savings** | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| FeSi | Graphite | HC FeMn | Mc FeMn | HC FeCr | Mins | Total Savings | ||||||||
| 1 | 105171212 (NFL) | 1605 | 3 | * | 3 | 25 | * | 1636 | 1508 | 350 | 175 | |||
| CastMELT | 1605 | 0.88 | 14.206 | 1620 | 1508 | 350 | 152 | 6415.4 | ||||||
| Material Savings | 2.12 | 3 | 10.794 | 16 | ||||||||||
| Savings on Production Cost (N) | 1007 | 1134 | 4274 | |||||||||||
| 2 | 105171211 (NFL) | 1980 | * | * | 10 | 80 | * | 2070 | 1508 | 300 - 350 | 260 | |||
| CastMELT | 1980 | * | * | * | 77 | * | 2057 | 1508 | 300 - 350 | 227 | 4806 | |||
| Material Savings | 10 | 3 | 13 | |||||||||||
| Savings on Production Cost (N) | 3780 | 1026 | ||||||||||||
| 3 | 10517611 (NFL) | 802 | 7.5 | * | 10.5 | * | * | 820 | 1580 | 150 | 200 | |||
| CastMELT | 802 | 6 | * | * | 7.2 | * | 815.2 | 1580 | 150 | 185 | 1611 | |||
| Material Savings | 1.5 | 10.5 | −7.2 | 4.8 | ||||||||||
| Savings on Production Cost (N) | 594 | 1017 | ||||||||||||
| 4 | 8517611 (NFL) | 1000 | 5 | * | * | * | 10 | 1015 | 1520 | 300 | 120 | |||
| CastMELT | 1000 | 5.34 | * | * | * | * | 1005.34 | 1520 | 300 | 111.69 | 3286 | |||
| Material Savings | −0.34 | 10 | ||||||||||||
| Savings on Production Cost (N) | −134.4 | 3420 | ||||||||||||
| 5 | 185171221 (NFL) | 2875 | 15 | * | * | 50 | * | 2940 | 1575 | 450 | 230 | |||
| CastMELT | 2875 | 17.8 | * | * | 18 | * | 2911 | 1575 | 450 | 220 | ||||
| Material Savings | −2.8 | 32 | 9886 | |||||||||||
| Savings on Production Cost (N) | 1108 | 10944 | ||||||||||||
| 6 | 95171221 (NFL) | 2050 | 14 | * | 30 | * | * | 2094 | 1580 | 300 - 350 | 237 | |||
| CastMELT | 2050 | 15.4 | 7 | 19 | * | * | 2091 | 1580 | 300 - 350 | 237 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Material Savings | −1.4 | −7 | 11 | |||||||||
| Savings on Production Cost (N) | 554.4 | 1512 | 4158 | 3301 | ||||||||
**Cost per ton—FeSi: $1100, HCFeMn: $1050, MCFeMn: $1000, HCFeCr: $950, Graphite: $600.
95.7% for the high-alloy cast iron (foundry-B). Based on the elemental prediction, Pearson’s correlation for silicon and carbon results in 96% and 90.7% respectively for foundry-A melting practice. Carbon and manganese had the highest correlation at 99% each for charge calculation and material balance in foundry-B based on the melting practice and approach. A convergence of 91.05% and 97.87% for final bath alloy prediction was obtained in foundries A and B, respectively, when compared with the final target composition which is being worked towards in both foundries.
Using the make-to-order the model achieves optimum addition of ferroalloy by bringing the element that is deficient in the melt within the range that is aimed for the final melt. This is done by a selective target of specific elements and solving for the lower boundary value problem of the standard melt composition. The model achieves convergence of 97.87 for final alloy melt simulation for foundry A compared with 91.05% convergence of the melting shop and 97.87% convergence for final melt alloy simulation compared with 97.82% in foundry B for overall melting correlation. Techno-economic evaluation of the use of the model in place of the current practice at the test foundries showed that 0.98% - 0.25% ferroalloy saving per ton of melt is possible using the model. This brings about an annual production cost savings of 100,000 $/y in foundry A and 20,000 $/y in foundry B on the use of different ferroalloy materials.
The authors declare no conflicts of interest regarding the publication of this paper.
Adetunji, O. and Seidu, S.O. (2020) Simulation and Techno-Economic Performance of a Novel Charge Calculation and Melt Optimization Planning Model for Steel Making. Journal of Minerals and Materials Characterization and Engineering, 8, 277-300. https://doi.org/10.4236/jmmce.2020.84017
NL: New Lining/F1: First furnace sample/BA: Before Alloy/AA: After Alloy.
Supplementary Material 2. Operational Data for Cast Iron Production in Factory BSupplementary Material 3. Comparison between Real Time Spectrometric Result in Foundry A and the Final Chemical Composition Output from CastMELT Simulation EngineSupplementary Material 4. Comparison between Real Time Spectrometric Result in Foundry B and the Final Chemical Composition Output from CastMELT Simulation Engine