Simulation and Techno-Economic Performance of a Novel Charge Calculation and Melt Optimization Planning Model for Steel Making

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) prediction, (0.999, 0.048, 0.999, 9E−11) for 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 calcula-How tion 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.


Introduction
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 [1] [2]. Refining is done to remove the deleterious gases and elements from the molten metal through material addition to bring the final tap chemistry within a specific range set by internal standard and/or industry [3]. Cast Iron and Steel scraps are the most important raw material in the foundry shop where cast products of the scrap melts are produced contributing about 60% to 80% of the total production costs [4] [5]. Cast products ranging from simple machine parts to special steel alloys are produced from an intelligent campaign in the foundry shop through programming intelligence [6]. In recent times, the extent to which the scrap mix for refining can be optimized, and the degree to which the melting operation can be controlled and automated to achieve the right chemistry of melt in the foundry is limited by the knowledge of the properties of the scrap and other raw materials in the charge mix [7] [8] [9].
It is noteworthy that charge calculation for foundry operation could be very cumbersome ranging from several hours to days [10] [11]. The quality of the steel produced from the EAF, crucible, or induction furnace largely depends on the charge mix, quality of scrap and additives [9] [12]. Static models are based on materials and heat balance by considering initial and final states of reactants.
In the material balance, mass of all input and output elements are considered alongside heat balance [6] [13] [14]. By coupling of mass balance, one can predict; the quantity of hot metal and scrap, amount of flux, the total quantity of oxygen required to be blown, amount of slag produced, the volume of exit gases, amount of ferro-additives [11] [15] [16]. It is however very much important that the prediction based upon the model is verified by the actual plant data. Tuning of the model is necessary because the predictions are based on equilibrium considerations and uncertainties due to simplified assumptions [17]. Reliability of predictions increases when the predictions of the model are compared with the plant data for several heats [18] [19]. Statistical correlations can then be eva-O. Adetunji, S. O. Seidu luated and used to assess the reliability of the model. For this purpose, it is of utmost necessity to collect reliable data from the high-precision instrument.
Induction and crucible furnace using a system-level approach can be analyzed for stochastic modelling [6]. A possible error in predictions makes a static model almost inadequate for intelligence control and automation of charge [12]. In a programmed model, these values are fed continuously, and corrections can be done during the melting operation. It becomes extremely difficult by foundry managers to combine the demand for a target quality through charge dynamics with energy and least cost operatives [20] [21]. The constraint with the induction furnace system with which the formation of oxides and decarburization through oxygen blowing is not permissible makes it very challenging for foundrymen to utilize it for alloy requiring close range compositions [22] [23] [24] [25] [26].
However, this area has received very little research attention. To the best of the author's knowledge, there is no research attempting a detailed numerical model for system-level material optimization and charge planning of induction furnace melting aimed at operational cost savings in steelmaking. Consequently, this work considers the parameters of the system-level and operations of the induction furnace to develop main and sub-models related to the stages involved in scrap charge and melting. Sub-equations relating to initial scrap analysis, bath chemistry of the initial melt, heel melting factor, mass density, scrap chemistry, ferroalloy composition, and final alloy target which cannot be obtained once melt modification begins due to the nature of the process are obtained on a theoretical basis. Through detailed modelling of the system-level parameters required for induction furnace melting of scrap, this study presents a parametric and validation study to understand the charge balancing, furnace bath melt optimization, and ferroalloys savings possible with induction furnace melting.

Materials and Method
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 Figure 1. The model framework assumes a steady-state metallurgical system in the melting of scrap using the induction furnace with equal electromagnetic induction energy incident upon all charged materials.

Modelling
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 O. Adetunji, S. O. Seidu 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 [6] [11].
The general form for an open system is given by: Mass input = Mass output + Net Accumulation within the system O. Adetunji, S. O. Seidu 1 1 Total Mass b ance 0 al where (F i , P i ) are masses and (f ij , p ij ) are analysis or content.

Composition Charge Analysis Model
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: • 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.

Scrap Charge Model
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) Elemental difference between the bath analysis and the target standard composition is defined by the function in Equation (7) [ ] 0.01 j-Scrap st n x x * − (7) • Where x st is % composition of element (x) in the target standard melt. • x n is % composition of the element (x) in the bath analysis.

Flux Addition Model
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):

Scrap-Bath Analysis Correction
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): • Where is an absolute value operator.
• M inj is Mass of the injected/incoming scrap. • x sc is & composition of element (x) in the incoming scrap.
• R i 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): • where x bath is the % composition of element (x) after the injection of scrap. • x n = % composition of element (x) in the melt before the injection. Ferro alloy (additive) addition is defined by the function in Equation (11):

Ferro Alloy and Additives Addition
• where x fa is the % composition of the target element in the ferroalloy/additive to be added.
• M fa is the mass of ferro alloy to be added to the bath.
• R i 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): • where x fa and M fa 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: The new j-Scrap value is erstwhile used in the next calculation for bath analysis correction.

Scrap Charge Optimization
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 [6].
The iteration continues in the form: 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 ex-  (15): x 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 When two additions were made i.e. (i and ii), the overall resultant composition will be an iteration of Equation (16) We can deduce the mass of scrap to be added to achieve the expected target composition by re-arranging Equation (15), therefore, where M sc 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.
where M fa 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.

Experimental Set-Up
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.

Cost Savings Methods
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.

Results and Discussion
The real-time operational data for both foundries include the information on the

Melt Modification and Ferroalloy Optimization
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 Figure 10 for foundry A for four (4) melts and Figure 11 for foundry B for six (6)

Techno-Economic Analysis
With respect to materials savings especially for ferro additives, the simulation of the developed model using the same operations data produced was able to pre- 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). Table   1 and Table 2

Conclusions
In this study, a numerical model for charge balancing and melt optimization has indicates a correlation coefficient of 81% for the low-alloy steel (foundry-A) and