Elsevier

Chemical Engineering Science

Volume 241, 21 September 2021, 116653
Chemical Engineering Science

A dynamic optimization framework for basic oxygen furnace operation

https://doi.org/10.1016/j.ces.2021.116653Get rights and content

Highlights

  • Dynamic optimization framework with fundamental modeling for a steelmaking process.

  • Determines economically optimal initial states and control profiles.

  • Collocation approximation applied to scrap melting PDE.

  • A hybrid approach proposed for solving ensuing dynamic optimization problem with steep fronts.

  • Increasing scrap usage shown to decrease steel production cost and carbon dioxide emissions.

Abstract

About 70% of the steel used worldwide is produced via the Basic Oxygen Furnace (BOF). This process has limited automation, and normal operation relies on invaluable operators’ knowledge and past experience. In this paper, we present a framework for dynamic optimization of BOF operation. The dynamic optimization problems utilize a first-principles based dynamic model, and are solved using a hybrid method in which the states are integrated using a differential–algebraic equation (DAE) solver over an initial time interval and full discretization over the remainder of the time horizon. Optimization case studies are presented in which the impact of constraints and different objective formulations are explored. The results suggest that the proposed framework can potentially aid steelmakers to significantly reduce process costs while meeting production and quality targets. The framework is implemented in Python using the open-source software tool, CasADi.

Introduction

The Basic Oxygen Furnace (BOF) is responsible for over 70% of the steel production worldwide (World Steel Association, 2016). A schematic representation of the basic oxygen furnace is given in Fig. 1. Hot metal from the blast furnace containing approximately 4.5% carbon, and scrap metal are charged to the BOF, and almost pure oxygen is blown at supersonic speed from the top through a water-cooled multi-nozzle lance. Fluxing agents such as lime and dolomite are typically added to help to control the final steel chemistry and protect the refractory walls of the furnace. The primary purpose of the BOF is to remove most of the carbon in the hot-metal via combustion with the injected oxygen, forming carbon monoxide and carbon dioxide; however, other refining reactions, such as dephosphorization, desiliconization and demanganization also take place (Deo and Boom, 1993). The heat released by the oxidation reactions is more than sufficient to raise the liquid metal temperature from approximately 1300C to 1600C (Deo and Boom, 1993, Dutta and Chokshi, 2020). In a typical BOF process, over 200 tons of hot metal can be converted to raw steel in around 20 min. The process of converting hot-metal into raw steel is commonly referred to as a “blow”.

The BOF operation is largely dependent on experience and invaluable operators’ knowledge. However, the lack of a framework that can consistently account for some of the more complex interactions between the process variables during the decision-making process can often lead to sub-optimal operation. Therefore, steelmakers could greatly benefit from a dynamic optimization routine that provides operators with the optimal control trajectories that minimize the production cost while meeting the final product specifications. Even though several dynamic models have been developed for the BOF operation (Jalkanen, 2006, Dogan et al., 2011, Lytvynyuk et al., 2014, Sarkar et al., 2015, Van Ende and Jung, 2018, Rout et al., 2018, Dering et al., 2020), there is scant literature regarding their use for dynamic optimization.

Zhang and Shi (2015) use historical data to obtain relationships between several process variables, including temperature and carbon content of the liquid metal, and use them within an optimal control strategy for the BOF. At every time step, the optimizer chooses the values of the control variables that minimize the difference between the current values of the states and reference values. Larsson and Dahl (2003) describe the use of an optimization model to minimize energy use in an integrated steel plant. The underlying mathematical model for the equipment is mostly based on empirical relationships. Through several case studies, they illustrate how the optimal operation mode is affected when the entire plant operation is optimized versus optimizing individual equipment. Chen et al. (2012) use a CFD model to obtain an optimum lance design that minimizes oxygen consumption and the time required for slag formation. None of these studies uses a first-principles based dynamic model for dynamic optimization of the BOF operation.

The potential of a dynamic optimization framework applied to the BOF operation was illustrated in a preliminary study by the present authors (Dering et al., 2019). Three case studies were used to demonstrate how the dynamic optimization problem could potentially be formulated in order to account for distinct quality targets and process constraints. The study presented the optimal control trajectories that minimized oxygen usage. Because an earlier version of the dynamic model was used, some important interactions between the process variables were not accounted for, effectively limiting the number of optimization variables.

In this paper, a dynamic optimization framework for the BOF operation that minimizes an economic objective function is presented, and potential applications to the steel industry illustrated through a series of case studies. A recently developed first-principles based dynamic model, that accounts for the main phenomena taking place in the BOF is used. The manuscript is organized as follows: Section 2 presents a literature review of dynamic models for the BOF and dynamic optimization methods. In Section 3, we give an overview of the mathematical model used within the dynamic optimization framework. Some simulation results are also presented to show the quality of the model predictions. An orthogonal collocation method is used to solve the partial differential equation (PDE) for the temperature profile within a melting metal plate. Section 4 presents the formulation of the dynamic optimization problem for the basic oxygen furnace. Process and quality constraints are listed and explained. We also present a hybrid approach, that combines the use of a DAE solver and full discretization, to solve the optimization problem. Several case studies are presented in Section 5, through which we illustrate how the developed dynamic optimization framework can potentially be used to reduce costs and maximize profits associated with the BOF operation. Section 6 summarizes the main findings and contributions of the paper.

Section snippets

Dynamic models for the BOF

In the BOF a supersonic oxygen jet is injected through the lance on the surface of the liquid metal (Fig. 1). The oxygen reacts with elements in the metal bath forming CO, FeO, SiO2, P2O5, MnO among others (Deo and Boom, 1993). Except for the gases, the other oxides (FeO, SiO2, P2O5, MnO) together with the fluxing agents form a less dense layer that floats on top of the liquid metal, known as slag. The mixture of metal droplets, formed by the splashing of liquid metal, gas bubbles, generated

Mathematical model for the BOF

The first-principles based mathematical model used in this study has been published elsewhere (Dering et al., 2020). Therefore, here we provide an overview and focus on a novel strategy for handling the scrap melting.

Problem formulation

The dynamic optimization problem for the BOF operation takes the form given in Eqs. (1), (2), (3), (4), (5), (6), (7), (8). The optimization variables are the control trajectories u(t) for the lance height, oxygen and bottom stirring gas flow rates, and the initial state values x0 of the mass of hot metal, scrap, lime, dolomite and iron ore charged to the furnace. The composition of the hot metal and the two scrap types used, and the initial scrap thickness, are given in Table 2.

The optimal

Case studies

The nominal values for the optimization variables are the same as those reported by Cicutti et al. (2000) for a 200-ton BOF operation. To simplify the problem, all the lime and dolomite are charged to the furnace at once, at the beginning of the blow, and only two scrap types are considered. The simulation results obtained using the nominal values define the base case against which the optimal solution for the case studies is compared. For the analysis of the case studies, it is important to

Conclusion

In this paper, we presented a dynamic optimization framework for the basic oxygen furnace. Through a series of case studies, it was shown how the framework can potentially aid steelmakers to reduce the cost per ton of raw steel produced, or increase the profit per blow time. We also briefly presented the concept of multitiered optimization, which allows the trade-off between competing objectives to be explicitly defined. This is especially helpful if there are different combinations of the

CRediT authorship contribution statement

Daniela Dering: Conceptualization, Methodology, Software, Investigation, Writing - original draft, Visualization. Christopher Swartz: Supervision, Conceptualization, Methodology, Writing - review & editing, Funding acquisition. Neslihan Dogan: Supervision, Conceptualization, Methodology, Writing - review & editing, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors gratefully acknowledge support from the Ontario Centres of Excellence (OCE), Praxair, the McMaster Steel Research Centre (SRC), and the McMaster Advanced Control Consortium (MACC).

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