# Eulerian-Eularian Model for Agglomeration Behavior of Combusted Iron Particles
## 1 Introduction  
The current state of the global energy supply requires cleaner, renewable, and CO\({}_{2}\)-neutral energy sources to replace fossil fuels and address the threats of climate change globally. In recent times, the DRI method has been identified as one of the core technologies for the decarbonizing iron process in favor of the road map of climate change mitigation targets [1]. Further, industry metal fuels were identified as a very encouraging and environmentally beneficial energy source due to their higher energy density and zero CO\({}_{2}\) emissions when the DRI process [1, 2]. Iron powders, particularly those in micron size, are initially prioritized because of their high volumetric energy density and widespread availability [2, 3, 4, 5]. Iron powders undergo combustion to produce thermal energy. The essential step in achieving a carbon dioxide-free iron fuel cycle is the DRI, utilizing sustainable energy sources such as hydrogen (H\({}_{2}\)) after the combustion process [6, 7]. It is beneficial to use fluidized bed combustion plants for the DRI process due to their flexibility in using fine iron particles and their cost-effectiveness. It is estimated that a fluidized bed reduces the material cost by half compared with the MIDREX method using a shaft furnace of DRI technology [8]. Nevertheless, a significant issue arises in agglomeration caused by particle sintering; this often occurs when iron oxides are chemically reduced at high temperatures. Agglomeration/sintering has been detected in reactors that promote efficient mass/heat transmission and adequate solid mixing, such as fluidized beds [9]. As a result, when agglomeration is not avoided, fluidization is significantly reduced or even stopped completely, negatively impacting the operation's efficiency. A detailed understanding of the agglomeration, as wellas defluidization characteristics of iron/iron oxide fines at high temperatures, is necessary to create an operational design of fluidized bed DRI. Agglomeration occurs in the fluidized bed combustion due to several types of cohesive forces [10; 11; 12; 13]. Those inter-particle cohesive forces fall under several categories according to their natures. They include electrostatic forces, van der Walls forces, solid bridge, or liquid bridge forces. Any of these forces can become dominant according to the specific case. Out of these force categories, it was identified that the liquid bridge force is most influential at high temperatures of the DRI method [14]. Liquid bridges are more versatile than van der Waals forces in practical applications. They can be adjusted. Liquid bridges are more complex as they involve both dynamic and static forces, and they use up energy. The static liquid bridge force arises from the combination of surface tension and pressure deficit within the liquid bridge. This emphasizes how these factors work together to influence liquid bridges in industrial processes. When a particle's surface is coated with a mobile liquid film, liquid bridges will develop at points of contact with other particles and surfaces. Moreover, if the partial pressure of a suitable vapor in the surrounding gas is high enough, condensation will take place at these contact points, leading to the formation of additional liquid bridges [14]. The geometrical/physical parameters of the iron/iron oxide particles and operating conditions play a major role in particle agglomeration behavior [15; 16]. The physical parameters include the composition of the particle, size, shape and microstructure, while operational conditions encompass operating temperature, reduction of gas composition, and flow rate of the gas. Hence, it has become very difficult to model the solid bridge force accurately in agglomeration. Although experimental studies can be conducted to understand the agglomeration behavior, the operational costs of these experiments are very high. Therefore, agglomeration formation in the DRI method has become a challenge to be addressed because it mitigates the efficiencies of the process [17].