Dynamic Modeling and Optimization of Basic Oxygen Furnace (BOF) Operation

There are two main routes to produce steel, the Electric Arc Furnace route, and the integrated Blast Furnace (BF) and Basic Oxygen Furnace (BOF) route, with the latter one being responsible for approximately 70% of the steel produced worldwide in 2017 [1]. In the integrated route, iron ore is melted and reduced in the BF, producing hot metal saturated in carbon, which is then charged to the BOF to produce raw steel. The primary function of the BOF is to remove most of the carbon via combustion with an oxygen jet, injected at supersonic speed, forming carbon monoxide and carbon dioxide. Other elements in the hot metal, such as manganese and silicon are also oxidized and help to form a slag layer. The impinging oxygen jet causes metal droplets to be splashed into the slag, which also traps gas bubbles due to its relatively high viscosity. Scrap metal is usually charged to the BOF to consume some of the heat generated by the oxidation reactions, increase the throughput, and lower production cost. Finer temperature control is achieved by iron ore additions during the blow. Limestone and dolomite are added to stabilize the acidic components of the slag and prevent wearing of the furnace’s refractory. While the BOF process is over 60 years old, it involves little automation and relies heavily on the operator’s knowledge and experience. This can lead to sub-optimal operation since more complex interactions between the process variables are often overlooked. In this work, a dynamic optimization framework for the BOF process that can aid operators with the decision-making process is developed.

Several dynamic models for the BOF process, empirical and first-principles based, can be found in the literature [2]–[9]. While empirical models may be able to track the data reasonably well, they often fail to give meaningful insight into the process. On the other hand, entirely first-principles based models are challenging to develop and may not provide reasonable predictions. For this work, a comprehensive, first-principle based dynamic model [4] was further developed and fine-tuned using industrial data. To increase computational speed, some parts of the model were replaced by approximate algebraic models, and discontinuities were treated using hyperbolic tangent functions. The final mathematical model was then implemented as a system of Differential Algebraic Equations (DAEs) using CasADi [10] with a Python front-end. The DAE system was integrated using the DAE solver IDAS [11]. The model was used to simulate over 71 heats for an industrial BOF operation giving reasonable prediction accuracy. In addition to improved accuracy, the computational time for one simulation is shown to be more than 100 times faster, compared with previous works [6], [7], [12].

Following validation, the mathematical model was built into a sequential optimization framework. For better performance, all the variables were scaled to range between 0-300, and further tuning of the hyperbolic tangent coefficients was performed to ensure smoothness and differentiability. By performing only mathematical treatment, the optimization time using the NLP solver IPOPT [13] was reduced from 40 to 20 minutes, without significant loss in model accuracy. Further reductions in computation time were recently achieved with a hybrid sequential-simultaneous solution approach using a variable step size DAE integrator for an initial time interval followed by the discretized DAE system for the remainder of the time horizon.

The dynamic framework was used to obtain the optimal input profiles that minimize the production cost for a fixed process time and also including the processing time as an optimization variable. The results showed that potential savings of $8,000,000.00 per year might be achieved by using the optimized control profiles.

References

[1] World Steel Association, “Fact Sheet: Steel and Raw materials,” 2019.

[2] H. Jalkanen, “Experiences in physicochemical modelling of oxygen converter process (BOF),” 2006.

[3] C. Kattenbelt and B. Roffel, “Dynamic modeling of the main blow in basic oxygen steelmaking using measured step responses,” Metall. Mater. Trans. B Process Metall. Mater. Process. Sci., vol. 39, no. 5, pp. 764–769, 2008.

[4] N. Dogan, G. A. Brooks, and M. A. Rhamdhani, “Comprehensive Model of Oxygen Steelmaking Part 1: Model Development and Validation,” ISIJ Int., vol. 51, no. 7, pp. 1086–1092, 2011.

[5] Y. Lytvynyuk, J. Schenk, M. Hiebler, and A. Sormann, “Thermodynamic and Kinetic Model of the Converter Steelmaking Process. Part 1: The Description of the BOF Model,” steel Res. Int., vol. 85, no. 4, pp. 537–543, Apr. 2014.

[6] R. Sarkar, P. Gupta, S. Basu, and N. B. Ballal, “Dynamic Modeling of LD Converter Steelmaking: Reaction Modeling Using Gibbs’ Free Energy Minimization,” Metall. Mater. Trans. B, vol. 46, no. 2, pp. 961–976, 2015.

[7] B. K. Rout, G. Brooks, M. A. Rhamdhani, Z. Li, F. N. H. Schrama, and J. Sun, “Dynamic Model of Basic Oxygen Steelmaking Process Based on Multi-zone Reaction Kinetics: Model Derivation and Validation,” Metall. Mater. Trans. B, vol. 49, no. 2, pp. 537–557, Apr. 2018.

[8] M. Han and Y. Zhao, “Dynamic control model of BOF steelmaking process based on ANFIS and robust relevance vector machine,” Expert Syst. Appl., vol. 38, no. 12, pp. 14786–14798, Nov. 2011.

[9] G.-H. Li et al., “A process model for BOF process based on bath mixing degree,” Int. J. Miner. Metall. Mater., vol. 17, no. 6, 2010.

[10] J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, “CasADi: a software framework for nonlinear optimization and optimal control,” Math. Program. Comput., 2018.

[11] R. Serban, C. Petra, and A. C. Hindmarsh, “User Documentation for IDAS v1.2.2 (Sundials v2.6.2),” vol. 1, 2012.

[12] N. Dogan, G. A. Brooks, and M. A. Rhamdhani, “Comprehensive model of oxygen steelmaking part 2: Application of bloated droplet theory for decarburization in emulsion zone,” ISIJ Int., vol. 51, no. 7, pp. 1093–1101, 2011.

[13] A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., vol. 106, no. 1, pp. 25–57, 2006.