*3.3. Simulation Results for Plant A Operations*

The developed framework model was also used to simulate 71 heats using the data provided by Plant A for its BOF operation. The model parameters, shown in Table 1, were manually adjusted based on data collected at the end of the blow for the end-point carbon content, slag composition and temperature. The extreme conditions in the BOF often prevent samples from being collected during the blow, therefore there is no data regarding the state of the system during the blow.

The goodness of the prediction was evaluated in terms of the average of the model predictions and process data for the 71 heats. Figure 12 shows the quality of the prediction for the end-point slag composition together with the standard deviation. The results indicate that the model is able to predict the slag composition at the end of the blow reasonably well.

**Figure 12.** Average process and predicted values for the end-point slag composition in weight percentage.

The carbon content of the metal bath can be measured using a carbon probe before tapping, or a sample is collected and the measurement is done in a laboratory setting, with the second giving the more accurate results. However, laboratory results are not available for all the heats for the current study. The average end-point carbon content and temperature measured using the probe and the model's prediction for the 71 batches are shown in Figure 13, based on which it is possible to conclude that the model performs fairly well. The model was able to predict the end-point carbon content of 80% of the heats with a precision of ±0.03%, and the end-point temperature of 61% of the heats with a precision of ±30 K.

**Figure 13.** Average and standard deviation of the model predictions and process data for the end-point (**a**) carbon content of the liquid metal and (**b**) temperature of the liquid metal.

The prediction error can be attributed to several factors. If the furnace is used back-to-back, there is always some slag left over from one heat to another, however its temperature and mass are not measured and the initial mass of slag present in the system is not accurately known. Moreover, the initial temperature of the hot metal charged to the furnace is also not precisely known since it is measured, on average, 40 minutes before the blow starts. Furthermore, due to the lack of data, it is assumed that all scrap types have similar properties, which can lead to inaccurate prediction of the heat needed for complete melting. Another potential reason could be the assumption that the off-gas and slag have the same temperature; however, the data available is not sufficient to estimate the actual off-gas temperature during the process. This, with the absence of sub-models to account for phosphorus oxidation, manganese oxidation and the formation of higher iron oxides, can explain the poorer performance of the model in predicting the end-point temperature.

For each heat, the mass of iron ore, flux, scrap and hot metal charged to the furnace is different, explaining the variation in the predicted and measured values. Since the inputs are always changing, it makes it challenging to identify the primary source for larger deviations between the simulated and actual data. Plant A has three different input profiles for the oxygen flow rate and lance height, however the overall quality of the predictions is not significantly affected by the different control profiles indicating that the model can potentially be used to simulate a wide range of operating conditions.

The trajectories for the temperature, carbon content and slag composition are shown in Figure 14 for one of the heats. We observe that the trajectories are similar to the Cicutti case. The content of SiO2 is lower for Plant A operation at the beginning of the blow because no gravel is added. Moreover, the rate of silicon oxidation is slower due to the lack of bottom stirring. As mentioned before, at low SiO2 contents, decarburization in the emulsion is enhanced due to the reduced slag viscosity. This is evident in Figure 14a by the larger difference between the carbon content of the droplets and the carbon content of the metal bath at high FeO contents at the beginning of the blow. As expected, due to the lack of bottom stirring, the FeO content of the slag increases much faster than that for Cicutti's case toward the end of the blow. The rapid increase can also be explained by the higher lance height towards the end of the blow compared to the mid-blow. The scaled control profiles for the oxygen flow rate and lance height for the given heat are shown in Figure 9b.

**Figure 14.** Evolution of: (**a**) Carbon content of liquid metal and final carbon content *CC*, *<sup>f</sup>* of the metal droplets, (**b**) silicon content of liquid metal, (**c**) slag and metal bath temperature and (**d**) slag composition. The values have been scaled for proprietary reasons.

Figure 14 indicates that the model is able to predict the end-point carbon content, silicon content and temperature of liquid metal reasonably well. It also provides insights about the trajectory followed by the variables and how the change in one or more of the inputs affects the system. The developed framework could potentially aid in finding more profitable operation modes as well as in understanding the more complex relationships between process variables.

#### **4. Conclusions**

The dynamic mathematical model presented in this study extends the work of Dogan et al. [6] by incorporating slag formation and energy balances. The models for the decarburization in the emulsion zone and scrap melting were updated with more recent findings, and an empirical relationship to calculate the calcium oxide saturation was obtained. Therefore, the main phenomena taking place in the BOF were accounted for, making the model suitable for further studies.

The mathematical model was translated as a DAE system to an open source environment (Python with CasADi [12]). The current implementation allowed for a significantly shorter simulation time compared with previous studies [6,8,9]. Moreover, as more complex and detailed models for the phenomena taking place in the BOF are developed, they can be incorporated relatively easily using the current framework.

It was shown that the updated model gives a better prediction of the carbon content trajectory for Cicutti et al. [13]'s data compared with the previous version, and more recently developed dynamic models for the BOF [8,9]. The dynamic model was also used to simulate 71 heats for a real industrial BOF operation. The model predictions for the end-point carbon content, slag composition and temperature agree reasonably well with the data for a wide range of operating conditions.

**Author Contributions:** Conceptualization, D.D., C.S and N.D.; Methodology, D.D., C.S and N.D.; Software, D.D.; Validation, D.D., C.S. and N.D.; Formal Analysis, D.D., C.S. and N.D.; Investigation, D.D., C.S. and N.D.; Resources, D.D., C.S. and N.D.; Data Curation, D.D.; Writing – Original Draft Preparation, D.D.; Writing – Review & Editing, D.D., C.S. and N.D.; Visualization, D.D.; Supervision, C.S. and N.D.; Project Administration, C.S. and N.D.; Funding Acquisition, C.S. and N.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by OCE (Ontario Centres of Excellence), Praxair, McMaster Steel Research Center (SRC) and McMaster Advanced Control Consortium (MACC).

**Acknowledgments:** We thank Ameya Kadrolkar for making the model for droplet decarburization available for this work. We are also grateful to Eugene Pretorious and John Thomson for helpful discussions and valuable suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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