The fluidized bed is a technology that involves multiple phases, allowing for efficient contact between them, therefore it is widely used in the chemical industry, metallurgy, oil and thermal power generation. In fluidized bed processes, the gas–solid interactions and chemical reactions generate a large number of variables to be handled, making the process very complex. Therefore, fluidized bed modeling and simulation is widely used to predict and analyze different processes, but it is possible to find in the literature many mathematical correlations that describe this type of flow. Based on this, the present work presents a review of the main mathematical models that describe the behavior of a fluidized bed reactor, and the state of the art regarding the use of modeling and simulation of the bed to predict and analyze different processes. As a result of this review, we can observe the importance of further development of the hydrodynamic modeling of fluidized beds, where understanding the interactions between the phases and the influence of this interaction is crucial for a better understanding and control of the processes. Generating experimental data of gas–solid and solid–solid interactions is also required for the validation of the numerical models.

The fluidized bed technology consists in the combustion of the particulate solid fuel in an inert material bed (usually sand), which is fluidized due to the flow of a gas. This type of flow allows efficient gas–solid contact, therefore it is widely used in covering particles, drying, granulation, blending, combustion and gasification processes. In this flow, there are many variables to be handled where the gas–solid interaction and chemical reaction characterizing a complex process. Because of this, there is a growing demand for mathematical models that allow the description and analysis for the development of a better understanding of processes and for creating new reactor projects.

The mathematical modeling of gas flow in fluidized beds began in the 60s with Davidson and Harrison [1] and Kunii and Levenspiel [2], where they analyzed mainly bubble motion, system instability and mass transfer. Based on these models, many authors studied this subject [3–8], among others who have contributed to the modeling of fluidized bed reactors with the aim of developing greater control of the system.

Computational Fluid Dynamics (CFD) is widely used to predict physical and chemical phenomena during the fluidized bed processes. CFD uses mathematical models based on mass transport phenomena, energy and momentum, along with theoretical and empirical correlations that require a long processing time, because it uses more complex and broader models, requiring more powerful computers.

In the literature, there are several mathematical correlations that describe a fluidized bed process, but these models depend on the application, since there is not a model with universal applicability [9]. For a very precise description of the process, there is a complex set of equations that must be analyzed before one can start the problem solving procedure. This analysis must be congruent with the goals to be achieved and with the available data [10–13].

In thermochemical conversion processes, efficiency is mainly connected to chemical reactions and heat transfer, where the mixture between gas and solids has great importance in mass and energy transfer [14]. Therefore, a hydrodynamic study of the fluidized bed is important to improve the process, because it is what determines the distribution of the phases and the species involved.

Improving the hydrodynamic description is one of the current challenges in order to improve understanding of the processes in fluidized beds [15]. A representation of the physical or hydrodynamic characteristics of the system, as realistically as possible, is required for modeling a chemical reactor [16,17]. Carvalho [10] and Deen et al. [18] also claim that improving the hydrodynamic description is necessary, especially for particles from group B, according to the further-presented Geldart Classification. For Van Lare [19], the fluid dynamics parameters influence the mass transfer between the bubble and emulsion phases in the bed, which should be the highest possible to maximize conversion in heterogeneous reactions in fluidized beds. This knowledge is important to establish correct parameters of the reaction and mass transport, and it is useful for making decisions about the reactor performance [12,20].

Based on this information, the present work presents a review of the main mathematical models that describe the hydrodynamic behavior of a fluidized bed reactor, and the state of the art regarding the use of modeling and simulation to predict and analyze different processes in fluidized beds, followed by the main considerations about the models used.

2Review: fluidized bed modeling2.1Hydrodynamic modelThe hydrodynamic models describe the motion and distribution of solids, gas–solid mixture, size, velocity and growth of bubbles, and the relation between bubble and emulsion phases and mass and heat transfer phenomena [9].

The hydrodynamics of a fluidized bed are given basically by the balance of forces between particles and gas velocity. By controlling the gas velocity, it is possible to set the required fluidization regime (Fig. 1). The fixed bed is characterized by a low gas velocity, keeping the bed static. The minimum fluidization regime is the starting point of the fluidization regime. The bubbling regime arises when gas velocity exceeds the minimum fluidization velocity, generating instability in the flow. Pneumatic transport occurs when gas velocity is greater than terminal velocity, and it is used in circulating fluidized beds [2,9,21].

Hydrodynamic behavior of a fluidized bed [21].

The fluidized bed is also characterized by the relation between pressure drop and gas velocity. When the gas passes through the porous bed, it loses pressure. In the fixed bed, the pressure drop increases linearly with increasing gas velocity until the pressure drop balances with the weight of the particles. This equilibrium is characterized by a minimum fluidization velocity (umf). In the bubbling regime, the pressure drop remains constant even with increasing gas velocity. The bed pressure drop decreases when gas velocity is above the terminal velocity of the particles (ut) and that is when pneumatic transport starts [2,9,21].

Fluidization is largely influenced by the characteristics of the particles. Geldart [5] classified particle behavior in fluidization into four groups, which are widely accepted and used in fluidized bed modeling.

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Group A: Small particles (30–150μm), and low density (<1.4g/cm3). The fluidization is easy, smooth and homogeneous. It makes possible operating with low gas flows and controlling the growth and speed of the bubbles.

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Group B: Particles with medium diameter (40–500μm) and density between 1.4 and 4g/cm3. The fluidization is good for high gas flow rates. The bubbles tend to grow a lot and appear at the beginning of fluidization (umf≈umb).

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Group C: Very small particles (d<30μm). Fluidization is difficult.

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Group D: Dense and large particles (d>500μm). Fluidization is difficult and non-uniform, ideal for spouted beds.

In fluidized bed modeling, the minimum fluidization condition is determined by the physical properties of the particles, where porosity, pressure drop, bed expansion and gas velocity are defined. These characteristics allow determination of bubble diameter and velocity, which influence mass and heat transfer between the bubble and emulsion phases. In Yang [9] it is possible to find many correlations about fluidization of particles.

2.1.1Gas–solid interface modelIn a gas–solid inter phase model in a fluidized bed it is generally used a two-phase model (bubble–emulsion) or a three-phase model (bubble–cloud/wake–emulsion).

The two-phase model consists of one dense phase, or emulsion, formed by a big number of particles, and a dilute phase, or bubble, without particles. Toomey and Johnstone [22] began the two-phase model development, which consists of perfect blending in emulsion phase, plug flow in bubble phase, heterogeneous reactions in emulsion phase, minimum fluidization condition in an emulsion phase. Solids motion occurs only while the bubbles pass through the emulsion and the thermal effects are reduced.

Based on this model, Davidson and Harrison [1] presented the first multiphase model, where they added that the bubble diameter is constant and mass transfer has a diffusion and convective contribution. The authors also developed an integrated model, which considers the emulsion and bubble phases as a plug flow. In Partridge and Rowe's [23] model, the authors consider just diffusive transport, where the cloud region belongs to emulsion phase or bubble phase. In Kato and Wen [4], the fluidized bed modeling considers compartments with height equal to bubble diameter, which is a bed height function.

According to Kunii and Levenspiel [2], depending on bubble velocity, a third region called cloud arises, where the gas recirculation occurs around the bubble, mostly observed in fast bubbles. This occurs mainly in reasonably high beds (>0.3m), in which the emulsion phase does not maintain the minimum fluidization conditions causing solids recirculation [24]. Based on this, the authors [2] developed the three-phase model (bubble cloud/wake and emulsion), where the wake phase belongs to the cloud phase, making it more complex than the two-phase model. This model assumes that the emulsion phase does not maintain the minimum fluidization conditions, there is solids recirculation in the bed, the mass transfer coefficient of bubble–emulsion has a contribution in mass transfer bubble–cloud and cloud–emulsion, there are heterogeneous chemical reactions occurring in the emulsion and cloud phase. Kunii and Levenspiel's model represents fluidized beds more efficiently, but it has disadvantages to computational implementation [24]. Following Kunii and Levenspiel's model, Grace [25] considers the existence of particles in bubble phase possibly reactive, and that all fluidizing gas passes through the bed in bubble form.

2.2Transfer phenomenaThe mass and heat transfer phenomena are associated with the contact between the phases involved. The higher the contact, the greater will be the coefficients of heat and mass transfer in the bed, which affects the reactor's performance.

The transfer phenomenon can happen in two ways. The first occurs between gas and particles, like many others processes that involve gas and solids. The second way happens between the bed phases (bubble, cloud and emulsion), and occurs only in fluidized bed processes. Because of this, understanding bubble hydrodynamics is important in bubbling fluidized bed (BFB) modeling, since they are responsible for the turbulence that favors the transfer phenomena, maintaining the supply of reactant gas for the emulsion, and they move the solids. They also favor particles elutriation and bed expansion [24].

Bubbles in fluidized beds behave just like liquid bubbles with low viscosity. Generally, they are assumed to have spherical shape, be dependent on bubble velocity and diameter, be dependent on the increase in diameter, near the surface due to decreased hydrostatic pressure and be dependent on the coalescence phenomenon of adjacent bubbles.

2.3Numerical simulationThe numerical simulation of the fluidized bed is based on the classical equations of mass conservation, energy and momentum, coupled with equations that describe the interactions between the phases. This is based on chemical kinetics, in experimental correlations and models derived from the Kinetic Theory of Granular Flows (KTGF) [15,26,27]. To describe gas–solid flow in fluidized beds, some numerical models were developed in the last years, such as Lattice–Boltzmann (LBM), Discrete Particle Model (DPM) and the Two Fluid Model (TFM). Van der Hoef et al. [28] describe these models.

The hydrodynamic numerical model can be described in two ways, with Euler–Euler's approach or Euler–Lagrange's approach [27]. The computational cost, in the latter approach, is higher than in the Eulerian one, therefore, the first approach is more used in numerical simulation of fluidized beds. Boemer et al. [29] stated that the Euler–Euler approach with the Kinetic Theory (KTGF) describes the processes in fluidized beds in agreement with experimental data.

Nowadays there is an availability of commercial codes like CFX, FLUENT, ASPEN and MFIX, which use the finite volumes method to model phenomena that involve fluid mechanics, heat transfer, combustion and gasification [30].

3State of the art: modeling and simulation of BFBFluidized bed modeling and simulation studies can be divided into two types, one that uses the CFD tool applied to the analysis of a process, and another applied to the analysis of the model, based on the approach and the numerical method, aiming at the improvement of the CFD tool.

Chavarie and Grace [31] conducted a study about catalytic decomposition of ozone in a fluidized bed, where they evaluated the results of some mathematical models comparing with experimental data. The models analyzed were Davidson and Harrison's [1], Partridge and Rowe's [23], Kunii and Levenspiel's [2] and Kato and Wen's [4], and the last two presented the best results. Kunii and Levenspiel's [2] model is useful to describe the chemical reactions, while Kato and Wen's [4] model is useful to represent the hydrodynamics of the fluidized bed.

Van Lare [19] studied the influence of particle size on mass transfer in a fluidized bed. The author used the two-phase model along with Van Deemter's model [32] and experimental data, to obtain a simple model that produces reasonable predictions. The author indicated that to maximize heterogeneous reaction conversions, bubble–emulsion mass transfer should be the highest possible. The results showed that group B particles [5] are more efficient than the smaller particles.

Carvalho [10] studied methanol production in BFB. The author modeled, scaled and simulated a reactor using the operational conditions of the fixed bed. The author also used the two-phase model and the perfect blend model, and concluded that the latter one is more advantageous for preliminary calculations of reactor performance. It generates a less complex system of equations as well as required information.

Matos [33] studied coke combustion in a fluidized bed, based on Davidson and Harrison's [1] two-phase model, which presented many numerical problems in fast reactions, requiring better development of the numerical method. The CSTR-PFR model, where bubbles have a sub model given by Toomey and Jonhstone [22], proved suitable to describe the flow in a fluidized bed with injector holes distributor, since the velocity is 2–3 times higher than the minimum fluidization velocity. The influence of many variables in fluidized bed models for rate constants of the first order proved relatively limited. The numerical model proved very applicable in tested cases.

Mota [34] developed a mass transfer mechanisms based on coke combustion in a fluidized bed. The author analyzed coke combustion with high ash content and uniform size, particle combustion rate with varied initial sizes, and the O2 transfer from bubbles to the dense phase. A theoretical model for each subject was developed and then experimentally proved. The results show that O2 transfer resistance depends on their diffusion that increases with the fraction of fixed carbon. The tortuosity (diffusion path in the particle porous matrix) varies between 3 and 8 and has no relation with fraction fixed carbon. Another important conclusion shows that O2 transfer during bubble formation has an important role in overall mass transfer (bubble–emulsion). The author says that it is important to consider the interaction between consecutive bubbles and the coalescence phenomenon.

Tarelho [17] studied the control of gaseous emissions during coal combustion in a fluidized bed, and stated that for chemical reactor modeling, before introducing the chemical parameters, first it is necessary to represent the physical and hydrodynamic characteristics of the system as realistically as possible. The numerical modeling used was based on Rajan and Wen's model [35], where mathematical simulations that describe particular aspects of combustion processes have been used, by considering that these models simulations should be simple enough not to require extensive calculations. The results showed that the model makes possible a reasonable description of the qualitative behavior of gaseous species along the reactor. The kinetic mechanism of some gaseous species cannot be described by simple kinetics and must include the radicals (O, H and OH). Thus, the influence of the solid particles present in the environment in the concentration of these radicals must be added. Although the model reasonably simulates the NO along the reactor, the model predicts a high decrease in concentration with increasing temperature, which is not observed experimentally. In relation to the mathematical model used, Tarelho [17] suggested a sensitivity analysis on the model to some hydrodynamic parameters, such as diameter of the bubble fluidization velocity, and gas exchange between bubble phase and emulsion phase.

Gambetta [36] developed a simplified generic dynamic model for polymerization reactors in a fluidized bed to predict operating conditions and product properties. The author used Kunii and Levenspiel's [21] and Choi and Ray's models [37]. The reduced model used other measures for the reactor without changing its kinetics. The need for simultaneous estimation of the kinetic parameters and for adjustment parameters of the control mesh was removed, besides reducing iteration time by at least ten times. The results showed that the method of estimation of kinetic parameters using the reduced model is valid.

Farias Júnior [38] modeled and simulated the dynamics of a natural gas combustor in a fluidized bed, where he adopted three different approaches, two one-dimensional (plug flow modified and the two-phase theory) and one two-dimensional with the MFIX code (CFD). The one-dimensional models are simpler and require less computational resources, offering answers timely for advanced control systems. The two-dimensional model is able to provide more detailed profiles on several variables along the bed, which is useful for assessing its behavior. The simulation of one-dimensional models developed (Fluidization Simulator) showed a much better performance in the FORTRAN version enabling a real-time simulation. The two-dimensional model (CFD), as expected, showed high computational cost.

Neves [24] studied the heterogeneous reactions in coal gasification in a BFB, in such study he analyzed the kinetic NO reduction with experimental data from Matos [33]. The author used Davidson and Harrison's model [1], which allows an evaluation of the kinetic and diffusive limitations of the boundary layer of particles and of the hydrodynamics of the bed. The methodology used is intended to correct the rate of chemical reactions observed in association with effects of the reactor hydrodynamics and mass transfer phenomena in the boundary layer and within the particle. This is an alternative model for global constant of heterogeneous chemical reaction, based on the concentration of NO in the entrance of the reactor, originally developed by Matos [39], and it also allows us to determine the intrinsic constant based on the contribution of diffusive and hydrodynamic limitations modeling for the global constant. The characterization of heterogeneous kinetics in fluidized beds lacks a quantitative assessment of the role of the various phenomena of mass transfer to the apparent rate of chemical reaction. The proposed model allows us to conclude that the study of kinetics of heterogeneous reactions in a fluidized bed should involve a review of the effects of mass transfer and hydrodynamics of the reactor at the rate of chemical reaction observed. This is especially relevant when carrying out trials with large particles and high temperatures for it is likely to cause a significant conversion of the gaseous reactant in the fluidized bed.

Silva [40] used Tarelho's [17] model to understand how the release location of volatile matter influences during biomass combustion in a fluidized bed through mass balance. One of the parameters analyzed in the simulations was the excess of air, which proved to be very important in relation to the behavior of gaseous species and carbonized matter along the reactor. Species such as CO2, CO, H2 and H2O have, according to simulations, maximum concentration between the bed surface and the secondary air feeding point and biomass. Due to high turbulence in the surface of the bed, it becomes difficult to model this region. Compared with experimental data, the simulation results showed that the kinetics used for CO is not the best one. One of the limitations of the model lies in the fact that it considers complete mixing in each compartment, which in reality does not happen. However, overall, the model used is valid because it showed concordance in the concentration profiles.

Wanderley [41] modeled and simulated the BFB reactor to obtain 1,2-dichloroethane from an oxychlorination reaction. The author used a phenomenological model based on the two-phase theory, in which he considered a system of one-dimensional flow in axial direction and steady state. The effects of fluid dynamics variables, the bubble–emulsion mass transfer and the importance of the freeboard region in the overall conversion were also considered. The study showed that the model adequately represents an industrial reactor. The simplifying assumptions adopted were also adequate, because they did not influence the results. The results showed that the process is very sensitive to operating pressure, temperature of the cooling water, minimum fluidization height, and variation of the particle diameter as well as the bubble and the reactor diameter. With the exception of the bubble diameter, the increase in other parameters causes a rise in the conversion reactor. The diffusion phenomenon exercises a more important role than the residence time in the reactor conversion. Increasing the diameter of the reactor causes a significant reduction in the height of the expanded bed and a significant increase in conversion, given the wider diffusion of species in the bubble–emulsion interface caused by the reduction of the bubbles’ diameter. The air distributor is an important step in the design of reactors, because it has a direct influence on bubble size. This should be designed to produce bubbles initially of small diameter and low velocities of the gases, favoring mass transfer in bubble–emulsion interface. The catalyst particle diameter affects more significantly the conversion. The increase of particle diameter causes a reduction not only in the bubble size, but also in the expanded bed height and in minimum fluidization height. Wanderley [41] stated that the diffusive effect exerts considerable influence on the process, where the contribution bubble–emulsion is more important than the emulsion–bubble one. The freeboard region is very important in the overall performance of the reactor, and should not be neglected in modeling work of fluidized bed reactors, especially when it comes to real industrial plants that operate at high flow rates. In this region, the particle size is important to conversion, where the small particles are more easily drawn into this region, resulting in higher conversion rates. For particles with higher diameter, the contribution of the freeboard region becomes less significant.

Moraes [42] developed a modeling and simulation of atmospheric BFB combustion of coal with high ash and sulfur with desulfurization by limestone. The author used a phenomenological approach that showed the need for improvement. In comparison with experimental data generated in a pilot plant, some differences and concordances in gas concentration and particle size distribution profiles were reported, as well as quantitative results of sulfur absorption efficiency compared with the experimental data.

Table 1 summarizes the aforementioned studies that used the modeling and simulation of a BFB applied to specific cases.

Summary of studies which used modeling and simulation to analyze processes in a fluidized bed.

Author | Institution/Country | Process/analysis |
---|---|---|

[10] | Universidade Estadual de Campinas, Brazil | Methanol production |

[17] | Universidade de Aveiro, Portugal | Coal combustion |

[19] | Technische Universiteit Eindhoven, The Netherlands | Particle size influence in mass transfer |

[24] | Universidade de Aveiro, Portugal | Coal gasification |

[31] | McGill University, Canada | Catalytic decomposition of ozone |

[33] | Universidade de Aveiro, Portugal | Coke combustion |

[34] | Universidade do Porto, Portugal | Mass transfer mechanisms in coke combustion |

[36] | Universidade Federal do Rio Grande do Sul, Brazil | Polymerization process |

[38] | Universidade Federal de Pernambuco, Brazil | Natural gas combustion |

[40] | Universidade de Aveiro, Portugal | Biomass combustion |

[41] | Universidade Federal de Alagoas, Brazil | Oxychlorination reaction |

[42] | Universidade de São Paulo, Brazil | Coal combustion with high ash and sulfur contents |

The CFD tool is widely used to analyze fluidized bed reactor behavior, but the modeling still presents numerical instability in the equations, and the gas–solid interphase is transient and known only in some regions [43]. Because of this, nowadays it is possible to find many studies in the literature on numerical modeling of a fluidized bed that seeks to improve the CFD tool. The following are some of these relevant studies.

Kuipers et al. [44] analyzed numerically the hydrodynamics of the fluidized bed and the model used was Euler–Euler's, two-fluid 2-D, applying the finite differences method. The authors observed that the bubbles’ shape is sensitive to the rheology of the bed, but the size (growth) is not greatly influenced by this physical property. The model needs better development of rheology and numerical method.

Goldschmitt et al. [45] analyzed the effect of the coefficient of restitution in hydrodynamic modeling of dense gas fluidized beds using the kinetic theory of granular flow (KTGF) and the two-fluid Euler–Euler's model. The authors concluded that the hydrodynamics of the dense fluidized bed depends strongly on the amount of energy dissipated due to solid–solid interactions. Goldschmitt et al. [45] used the discrete particle model as a useful tool for the analysis of solid–solid interaction. However, it lacked experiments on interactions between the particles for correct validation of the numerical models. They also argue that it is necessary a further development of KTGF multi-fluid models.

Pain et al. [46] studied the application of chaos theory in the transient fluidized bed simulation, using the finite elements method. The authors claimed that the scheme is stable, allowing large time steps, and has good flexibility for complex geometries, but the chaotic behavior requires further mesh refinement. The results of the average bed height and average velocity vectors turned out to be qualitatively consistent with the experimental findings.

Huilin et al. [47] simulated the fluidized bed to analyze the motion of the particles, assuming a binary mixture as well as the KTGF and Euler–Euler's approach. The authors concluded from this study that, in order to obtain the correct dynamics of the bed, it is important to consider the distribution of particle size and the energy dissipation due to solid–solid interactions. The effect of these interactions is as critical as the rheology and particle collision parameters, but it lacks experimental studies for validation.

Mineto et al. [48] studied the influence of particle diameter on the hydrodynamic simulation of the fluidized bed using the two-phase models by Euler–Euler and KTGF. The authors observed that in dense regions, the granular temperature is minimal, and in the bubble region is maximum. For particles with an average diameter of 500μm, the cohesive forces can be neglected, where the central bubbles are well defined and with lower speeds. In simulations of particles with an average diameter of 125μm, the cohesive forces are considered the main factor in the stability of the flow, where they show a homogeneous flow and are well mixed with higher speeds.

Papadikis et al. [49] simulated the fast pyrolysis process of biomass in a fluidized bed using the Euler–Euler approach and the KTGF. The authors concluded that the drag force is an important parameter that defines particle motion. In the dense region, the drag is more important than the virtual mass effect, and in the diluted region, the drag is induced by gas. An increased gas velocity gradient increases the importance of the effect of virtual mass. Particle behavior is similar in both cases, 2-D and 3-D. The authors stated that for studies concerning hydrodynamics of the bed, the 2-D simulation provides good results, but for heat, mass and momentum transfer, the 3-D simulation is more suitable. The model was considered valid by Papadikis et al. [49] for the design of reactors, since it permits to analyze the motion of the particles. In Papadikis et al. [13,50], there was a continuation of this study about modeling and simulation of fast pyrolysis of biomass in BFB. In another work, Papadikis et al. [51] analyzed the effect of particle size on the drag of the carbonized in coal combustion in BFB.

Souza [52] investigated the diffusion effects in the numerical discretization of the convection terms and the dependence on computational mesh size of the fluidized bed in the simulation using the two-phase Euler–Euler model and KTGF. The author noted that the first order method FOUP (First Order UPwind) is highly diffusive requiring refined meshes. The high order method called “Superbee”, presented results of better quality compared to the experimental results of Kuipers et al. [44], and it allows the use of coarser mesh. The effects of numerical diffusion decrease with increasing number of iterations the Superbee. The author further stated that high-order methods tend to produce numerical oscillations near high gradients, requiring the application of a flow restrictor.

Philippsen [53] analyzed four gas–solid drag models [26,54–56] in hydrodynamic simulation of a fluidized bed, which used the Euler–Euler approach and KTGF. The results showed that the Syamlal and O’Brien correlation [26] presents good results about volume fraction of the phases involved and gas velocity profile. Additionally, it has the best mesh convergence and uses the lowest computational time; about half of the time used by other models. For a bubble study, the models by Gidaspow [54] and Hill-Koch-Ladd [56] are the most appropriate because their presented results were more congruent with experimental data.

Studies about BFB simulation using the CFD tool may be found in [11,43,57,58] among others. In Brazil, fluidized bed simulation has been studied by some research groups like the Graduate Program in Mechanical Engineering from UNISINOS – RS, the CTCL group (Centro Tecnológico de Carvão Limpo) from SATC – SC, the Faculty of Engineering from São Paulo State University “Júlio de Mesquita Filho” – SP, and São Carlos School of Engineering of from USP, SP. These groups have some publications on the use of the CFD tool [12,48,52,59–61].

4Final commentsModeling and simulation of a fluidized bed is largely used nowadays, not only to predict but also to analyze and improve different processes, and it has presented good results even though it still needs improvement. In the present work, the hydrodynamic modeling state of the art works regarding the use of simulation applied to the analysis of processes were reviewed.

Based on the studies reviewed, it was concluded that the hydrodynamic modeling of a fluidized bed lacks important details for a more precise analysis of the process. There is also a need of experimental data, particularly relating to gas–solid and solid–solid interactions for the validation of existing mathematical models. Understanding the interactions between the phases and the influence of these interactions in the process is crucial, since they affect the dynamic behavior of the reactor and the chemical species conversion.

In the numerical simulation of a fluidized bed, due to the complexity of the equations that describe the flow, there is a need for the improvement of numerical technique and more powerful computers, because using the CFD tool for simulating processes in fluidized beds still has a high computational cost.

Conflicts of interestThe authors declare no conflicts of interest.

The authors wish to acknowledge CNPq and Rede Carvão for supporting and sponsoring this research.

Caterina Gonçalves Philippsen graduated in physics from University of Vale do Rio dos Sinos (UNISINOS) in 2008, and master in Mechanical Engineering from UNISINOS in 2012. Now she is currently pursuing her PhD in Mining Engineering, Metallurgical and Materials from Federal University of Rio Grande do Sul (UFRGS). Her research, under Dr. Antônio Cezar Faria Vilela and Dr. Leandro Dalla Zen, studies the fluid dynamics behavior and their influences in combustion processes in bubbling fluidized beds. Since beginning his doctorate in 2012, Philippsen conducts this study in the combustion laboratory of the Foundation for Science and Technology, CIENTEC. Philippsen looks to complete her studies by 2016.

Antônio Cezar Faria Vilela graduated in Metallurgical Engineering from UFRGS in 1977, master in Metallurgical Engineering from UFRGS in 1980 and doctorate (Dr.-Ing) in the Steel Institute – Rheinisch – Technische Hochschule Westfälischer/Aachen/Germany (1986). He is currently associate professor, level 04, at the UFRGS. Operates at graduation in the Department of Metallurgy in the graduate program, in Graduate in Mining Engineering, Metallurgical and Materials (PPGE3M), and coordinates the Laboratory Steel since its foundation in the School of Engineering. Has experience in guiding students and Technology Center, in conducting projects in Metallurgical and Materials Engineering. Has served on the editorial board of scientific and technical magazines, in organizing annual events in the areas of reduction and steelmaking and in supporting the activities of several promoters research bodies such as the CNPq, CAPES, and FINEP FAPERGS. Was elected Director of ABM – Brazilian Association of Metallurgy, Mining and Materials – for the term 2007/2009. Currently a Director of ABM. In 2007, his work was recognized by the Foundation for Research Support of the State of Rio Grande do Sul – FAPERGS, statewide, with FAPERGS AWARD – RESEARCHER FEATURED IN ENGINEERING. In 2012, his work has also been recognized nationally by the Brazilian Association of Metallurgy, Mining and Materials with MEDAL VICENTE Chiaverini – MERIT IN PROCESS.

Leandro Dalla Zen graduated in Mechanical Engineering from UFRGS in 1977, master in Mechanical Engineering from UFRGS in 1981 and doctorate in Mining Engineering, Metallurgical and Materials from UFRGS in 2000. Currently is an adjunct professor at the UNISINOS, and consultant of the City of Santa Vitória do Palmar, a consultant for the Center of Investigaciones Energéticas Medioambientales Y Tecnologicas from Spain and technical adviser of the Federation of Industries of Rio Grande do Sul. Has experience in Mechanical Engineering with emphasis on Harnessing of Energy, acting on the following topics: rice husk, combustion of biomass and waste into fluidized bed, energy conservation and alternative energy sources. Also provides advice and design of passive energy systems in architecture: natural ventilation, thermal inertia, solar energy.