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 in 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 well as 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]. Therefore, it is crucial to understand the process of inter-particle cohesion by solid bridge force in the DRI method, which causes defluidization of fluidized bed combustion plants.
Thus, different approaches to numerical simulations, such as the two-fluid method and the discrete element method (DEM), provide tools to investigate the fluidization phenomena that take place in fluidized bed combustion. The numerical model simulation strategy developed by Tazleem et al. uses two fluid approaches based on the Eularian–Eulatian technique to predict agglomeration. The established modeling technique is verified using experimental data from the literature for a simplified two-dimensional geometry of a pilot-scale fluidized bed combustor [
18]. Another numerical model based on the DEM approach was developed by Kuwagi et al. [
12] to investigate metallic solid bridge forces in agglomeration. This model encompasses a surface diffusion mechanism that considers the surface roughness. Further, particle sintering in agglomeration is analyzed by Mansourpour et al. [
19,
20] with a CFD-DEM simulation. Their study incorporates the effect on the agglomerate sizes by temperature and gas velocity.
There are several studies that have utilized CFD-DEM simulations to investigate the sintering behavior of iron/iron oxide fines in fluidized beds. However, the high computing cost makes it challenging to simulate large-scale experiments using the CFD-DEM approach. The computer simulation cost of the DEM is significantly affected by the enormous number of particles in the micron-sized cohesive iron/iron oxide powder. To overcome this challenge and to expand the modeling capability to a large/industrial scale, the two-fluid modeling approaches can be applied. However, there is very little research work conducted using the two-fluid approach to simulate agglomeration in fluidized beds for the production of iron/iron oxide powder. Even the available literature does not provide proper agglomeration behavior with significant parameters, like solid pressure. They do not provide solid fraction variations with defluidization in the fluidized bed, which is crucial for understanding the agglomeration patterns in the fluidized bed. In this model, solid fraction variation aligned with the solid pressure variation is analyzed in detail and validated with the CFD-DEM study. Moreover, this study provides a cost-effective multiphase CFD model that can be scaled up for industrial-level reactors to predict agglomeration.
Therefore, in this study, a simplified yet comprehensive CFD 3D numerical model using the Eularian–Eularian method was developed using AVL Fire advanced simulation software (2024 R1) and user-defined FORTRAN subroutines. The gas phase of the model was modeled using the inbuilt AVL Fire algorithms, while the solid phase was developed explicitly using user-defined subroutines and coupled with the software AVL Fire.
In this work, defluidization behavior of iron particles were analyzed at various temperatures in a controlled adiabatic and reduced atmosphere. It is crucial to understand the process of sintering iron particles in DRI method. When in the DRI process, sintering can also occur at lower temperatures due to chemical reactions of converting iron oxide to metallic iron [
6]. This model includes a variety of temperature settings, from low to high, to analyze the micron-sized iron particle sintering in the fluidized bed.
Further, the paper provides a detailed explanation modeling procedure and the application of solid bridge force into the model in
Section 2.
Section 3 of this paper includes a detailed description of the geometry of the reactor and other parameters.
Section 4 covers the numerical results achieved with this model and validation of the results with CFD-DEM model results produced for the same experiment.
Section 5 outlines the conclusions drawn from the previous section of results and discussion and the intended future work of this model.
4. Results and Discussion
This section examines the findings of simulated cases that were carried out with varying degrees of sintering force and temperatures during the process. The primary focus of this investigation was on the downward trend in the pressure drop of the solid bed surface with the presence of a sintering force. Further, visual representations of the solid fraction and solid velocity are also presented. The features of (de)fluidization of combusted iron powder at increased gas velocities are presented and evaluated in this section.
4.1. Minimum Fluidized Velocity and Bed Conditions
To validate the CFD model for solid hydrodynamics of combustion iron powder, the minimum fluidization velocity (umf) must be estimated. Minimum fluidization velocity is the minimum velocity required to make the bed fluidized by keeping the upward drag force of the gas equal to the total solid bed weight. This is one of the most crucial elements in fluidized bed combustion. Numerical simulations were run to estimate the umf with an N2 environment by varying the flow rate at a constant temperature of 20 °C.
Minimum fluidized velocity (u
mf) for this simulation setup was found to be 0.01 m/s, while 0.15 m/s was found to be excessive based on the range of simulations carried out from 0.001 m/s to 0.15 m/s. Solids climbed to the top of the gasifier at a velocity of 0.15 m/s, suggesting that the velocity was too high. On the other hand, the velocity of 0.001 m/s resulted in non-fluidized behavior because the velocity was not enough to fluidize the bed. This result for minimum fluidization velocity estimation aligns with DEM simulations conducted by Liu et al., indicating that 0.01 m/s is the minimal fluidization velocity for this arrangement, though there are some discrepancies with theoretical calculations derived using Beestra’s correlation [
26]. The variation of the particle size distribution can be attributed to the slight variation in theoretical and numerical results [
17,
30].
Moreover, in the CFD-DEM study, 0.15 m/s is used to analyze the effect of fluidization velocity on particle agglomeration. However, 0.15 m/s was found to be excessive for this simulation setup. This distinction can be ascribed to the fact that these simulations were carried out using the Eularian–Eularian two-fluid approach, in which the solid is considered as a fluid, but the CFD-DEM method is based on the Lagrangian approach, which considers solid as discrete particles. However, in general, the simulation outcomes reasonably agree with the outcomes of the other referenced literature mentioned above, providing evidence for the applications of accurate hydrodynamic theories.
4.2. Solid Bed Hydrodynamics
In a proper bubbling fluidized bed, bubbles originate at the bottom of the solid bed and rise to the top, increasing in bubble size until their buoyancy force exceeds the solid drag force. The buoyancy force rises as the bubble diameter increases, causing the bubbles to climb to the surface of the solid substrate and burst. This situation recurs in the fluidized bed reactor to enhance fuel mixing capabilities for improved combustion. As the bubble ascends, solid particles move, resulting in the formation of zones with lower solid fraction. However, when agglomeration occurs, it affects the bubble growth in the fluidized bed, driving the bed toward defludization. This numerical model has the capability to analyze the strength of the solid bridge force for various temperatures and four different agglomeration force models.
Figure 3 illustrates the normalized bed pressure drop profiles over time for each sintering force model temperature varying from 500 °C to 1000 °C. The standard deviation (STD) of the pressure drop curves was calculated from 0.5 s to 15 s. At low temperatures (e.g., 500 °C), the cohesive force impact was observed to be negligible in any sintering force model. This can be identified in the snapshots of
Figure 4, as both cohesive and non-cohesive cases have healthy bubbling behavior at 500 °C. Comparatively, the standard deviation was increased in the three-micro contact-point model (C = 0.417) at 650 °C compared with the 500 °C model cases despite there being no agglomeration visible in
Figure 4b. This is because even with reduced sintering force, the bed may have difficulty maintaining bubbling at temperatures exceeding 650 °C. Additionally, when C = 0.417 (three-micro contact-point model) at 1000 °C, a consistent reduction in pressure drop is observed after 8 s. It is further demonstrated by the snapshots in
Figure 4d. Images captured at 1000 °C with a C value of 0.417 display blue areas indicating minimal solid presence and channeling caused by particle sintering. The void fraction snapshots from the CFD-DEM model performed by Liu et al. provide similar evidence to this discussion. However, there are some distinctions in the three-micro contact-point model (C = 0.417) at 1000 °C in the CFD-DEM study, as it shows good bubbling hydrodynamics in the CFD-DEM study even with a higher STD value. In this study, agglomeration occurred after 8 s, which shows significant pressure reduction. To illustrate that behavior, 15 s of run time was maintained in this study [
26].
In sintering force models at higher temperatures (i.e., 800 °C and 1000 °C), the fluctuations of the pressure drop increased gradually, showing higher standard deviation (STD) values. This notable variation proposes an increase in bubble sizes, resulting in more extreme bed dynamics. The sintering force models of a smooth surface (C = 1) and the nine-microcontact-point model (C = 1.251) had significant differences in terms of the magnitude (approximately 2.4 to 3 times) compared with the three-micro contact-point model (C = 0.417). Hence, the rate of particle clumping was high when in higher sintering force models (C ≥ 1), leading to inhomogeneity in the bed. This scenario can be well captured in a three-micro contact-point model sintering model at 1000 °C. Then, when the sintering force was further increased by applying the smooth surface model (C = 1) and the nine-microcontact-point model (C = 1.251) at the maximum temperature used in this study (i.e., 1000 °C), the pressure drop and the standard deviation (STD) decreases rapidly, clearly indicating particle agglomeration in
Figure 3d and
Figure 4d. Despite the similar trend observed in the CFD-DEM study, the sintering bonds remain permeable in the CFD-DEM cases, whereas in this model, some solid movements were still visible. This model demonstrates the occurrence of cohesive bonding, where both the formation and dissolution of bonds take place. However, it is important to note that healthy bubbling is entirely halted at 1000 °C in both the smooth surface and nine-micro contact-point model. These arguments are supported by
Figure 5, as solid velocities decrease with the increase of sintering force impact and with the rise of temperature.
In
Figure 3c, a decrease in bed height and flow inhomogeneity can be observed in sintering force models, especially when increasing the impact of sintering force at 800 °C. This is attributed to the impact of agglomeration, which is noticeable even without complete defluidization.
A reduction in the bed expansion can be seen
Figure 4d from three-micro contact point model after 8 s. Further, a significant reduction in bed expansion is observed in
Figure 4d for the smooth and nine-micro contact-point models. This was also clearly observed in the CFD-DEM study.
The creation of significantly larger agglomerates and the strong adhesion of particles to the bed wall within a few seconds is observed, as shown in
Figure 4c,d, which depicts smooth and nine-micro contact-point model situations, respectively. In
Figure 4c, in the smooth and nine-micro contact-point models, making and breaking agglomerates can be seen closer to the wall after 10 s. In
Figure 4d, for sintering force cases, the formation of agglomerates can be observed. This behavior is indicated in the smooth and nine-micro contact-point models due to the high intensities of the sintering force. Agglomeration can be observed clearly in those images of smooth and nine-micro contact-point model situations at 1000 °C, which suggests that the solid bridge force that was forecasted with this model at this temperature is very high. This observation, similar to the CFD-DEM study results, suggests that this two-fluid model reasonably accurately predicts the particle agglomeration leading to defluidization in fluidized bed combustion.
In the CFD-DEM work, it is demonstrated that there is no movement in any of the particles in the smooth and nine-micro contact-point model situations when the temperature is 1000 °C, which indicates that the defluidization pressure drop remains constant. Nevertheless, this study demonstrates that even in smooth and nine-micro contact-point model cases at a temperature of 1000 °C, there is little motion in solid particles, which indicates that there are slight differences in pressure drops, and certain solid particles have low-velocity values. There is evidence of this in the pressure drop graphs shown in
Figure 3d and the solid velocity snapshots shown in
Figure 5b. A potential reason for this variance is that the different methods of calculating contact time that were discussed in the previous section can cause it.
The results of this model reasonably reflect the observation of the experiment and CFD-DEM findings. It is noticed that, in general, low-temperature runs (500 °C and 650 °C) could operate continuously for more than two hours without any defluidization appearance. Nonetheless, the experiments conducted at 950 °C were soon found to be non-fluidized behavior within several minutes [
17].
Moreover,
Figure 5b depicts that the solid toward the bottom of the bed has lower velocities than the top in agglomerated models, whereas when C = 0, the bottom of the bed has higher velocities than the top. According to the experimental findings, non-fluidized zones initially started from the bottom of the bed. Thus, it is fair to say that the smooth-surface model and the nine-micro contact-point model provide better predictions of solid sintering force, which is closely related to the experimental observations. The neck size of the solid bridge grows with the particle temperature and the contact time according to Equation (14). Particle cohesion begins from the lower part of the bed, particularly at the beds’ corners, because of the high density, as depicted in
Figure 4c,d. Then, with the contact period of the particles rising, more particles tend to accumulate into the existing agglomerates, increasing the size of the agglomerates [
17].
4.3. Effects of the Gas Superficial Velocity
Defluidization occurs due to the interaction between the sintering force (solid bridge force) and the breakage force in the reactor. Combining forces of drag force and the particle collision force establishes the breakage force needed to break down the agglomerated particles. Increasing the gas’s superficial velocities can provide the breakage force to separate particles, reducing the contact time. Thus, high fluidization velocities have the ability to break the particles that stick together. Another set of simulations was performed to study the effect of gas superficial velocity on particle agglomeration by increasing the velocity to 0.12 m/s. The simulations were carried out for a smooth surface (C = 1) and a nine-micro contact-point model (C = 1.251) at 1000 °C.
When the gas superficial velocity is increased to 0.12 m/s, the bed seems more dynamic for both the smooth and nine-micro contact-point cases model compared with the previously stated scenarios. After 13 s, the smooth surface model bed begins to lose its fluid-like properties, whereas the nine-micro contact-point model starts to do so after 9 s.
After 9 s of the nine-micro contact point model, the sintering region has expanded from the bottom of the bed over the whole bed, indicating almost defluidization. The results indicate that higher gas surface velocities can lead to an increased gas flow through the bed, resulting in the formation of big bubbles and higher collision frequencies between particles. Consequently, the decreased contact time between colliding particles weakens the solid bridge, potentially delaying defluidization. However, defluidization could still be observed in those simulations, as indicated in
Figure 6, the pressure drop curve, and the snapshots of solid fraction in
Figure 7. This phenomenon is further proved by the solid velocity snapshots depicted in
Figure 8.