**1. Introduction**

The Basic Oxygen Furance (BOF) is responsible for approximately 70% of the steel production worldwide [1]. A schematic diagram for the BOF in shown in Figure 1. Scrap metal and hot metal are charged to the BOF, and an oxygen jet at supersonic speed is injected from the top through the lance onto the surface of the metal bath. Some of the species in the metal bath are oxidized and form a less dense slag layer. Flux is added to prevent refractory wearing and to contribute to slag formation. Millions of metal droplets are generated at the impact zone due to the impingement of the supersonic oxygen jet on the liquid metal. Carbon in the metal droplets can react with iron oxide in the slag forming carbon monoxide [2]. Experiments using X-ray fluoroscopy have shown that gas bubbles can be formed within the metal droplet itself [2,3] and not only at the metal droplet-slag interface. Carbon monoxide and carbon dioxide are also formed due to decarburization taking place at the impact zone. The droplet-gas-slag mixture, commonly referred to as emulsion, can occupy most of the furnace volume during the main blow.

**Figure 1.** Schematic representation of the Basic Oxygen Furnace (BOF).

The process has limited automation and is highly dependent on operators' knowledge and past experience. Without a framework that can consistently aid the operators with the decision-making process, some of the more complex interactions between the process variables may be overlooked, leading ultimately to sub-optimal operation. Therefore, an optimization framework for the BOF operation that can consistently provide operators with the economically optimal operating conditions could greatly help steelshops reduce production costs. However, in order to have an optimization framework it is necessary to have an accurate enough dynamic model of the physical process.

Several dynamic models [4–9] for the BOF have been developed in recent years. Jalkanen [4] developed the CONSIM 5 simulator for the BOF. All reactions are assumed to take place in one zone and oxygen is partitioned according to its affinity to a certain element. The model accounts for slag formation, energy balance, scrap melting and decarburization.

Sarkar et al. [8] also developed a dynamic model for the BOF. They assumed that the refining reactions take place only in the emulsion zone, between elements dissolved in the droplets and FeO in slag. Oxygen is distributed between the elements in the upper part of the metal bath according to their concentration. The model does not include an energy balance and temperature is assumed to increase linearly during the blow.

Another dynamic model for the basic oxygen furnace was developed by Lytvynyuk et al. [7]. All the supplied oxygen is used to form iron oxide and all other refining reactions take place via reaction with FeO. The rate of the reactions taking place in the metal bath and slag is primarily dependent on the kinetics of mass transfer. For the energy balance, the slag and metal bath are assumed to have the same temperature. The model seems to give excellent prediction of the slag composition, metal bath composition and metal bath temperature at the end of the blow.

A few dynamic models based primarily on empirical relationships have also been developed. Kattenbelt and Roffel [5] used step responses to model the decarburization rate during the main blow. They studied the process response to step changes in lance height, oxygen flow rate and iron ore addition. The model makes extensive use of empirical relationships but provides limited physical insight.

A very comprehensive, first-priniciple dynamic model for the kinetics of decarburization in the BOF was developed by Dogan et al. [6]. Their model accounts for carbon oxidation in two zones: The emulsion and the impact zone (Figure 1). At the impact zone, carbon in the metal bath is assumed to react directly with oxygen and carbon dioxide, and in the emulsion zone carbon in the metal droplets is oxidized by FeO in the slag. The metal bath and slag temperature are assumed to increase linearly with blowing time and the slag composition is required as an input. Rout et al. [9] continued the work of Dogan et al. [6] by modeling the kinetics of manganese, phosphorus and silicon oxidation enabling the model to predict the slag composition.

The current study extends the work of Dogan et al. [6] by incoporating a model for slag formation as well as energy balances. The model for decarburization in the emulsion zone is modified to account for recent fidings [10] and the model for scrap melting is updated based on recent studies [11]. The mathematical model for the BOF is implemented as a system of Differential Algebraic Equations (DAEs) using CasADi [12] with a Python front-end. The resulting framework is used to simulate the Cicutti data [13] as well as 71 heats for the BOF of an industrial collaborator (Plant A).
