A fluidized bed is a state of a two-phase mixture of particulate solid material and fluid, which is widely used in many modern technologies for efficient implementation of various physical and chemical processes. Fluidized beds have been used in technological processes such as: cracking and reforming of hydrocarbons (oil), carbonization and gasification of coal, ore roasting, Fischer-Tropsch synthesis, polyethylene manufacturing, limestone calcining, aluminum anhydride production, granulation, vinil-chloride production, combustion of waste, nuclear fuel preparation, combustion of solid, liquid and gaseous fuels, drying, adsorption, cooling, heating, freezing, conveying, storing and thermal treating of various particulate solid materials.
The term "fluidized bed" is unavoidably connected to the term "particulate solid material". Particulate materials are mechanical mixtures of multitude of solid particles. Natural particulate materials originate from many long-term natural processes: heating, cooling, thermal dilatation, coliding, crushing, chopping up, atmospheric changes, river erosion and erosion caused by sea waves. Many technological processes also produce particlate solid material: grinding, chopping up, milling, evaporation, crystalization, spraying and drying. Particulate materials can also be of organic (plant) origin: fruits and seeds.
Particulate materials most commonly consist of solid particles with a range of shape and size. The majority of inorganic particulate solid materials found in nature have an extremely wide range of particle sizes. Such materials are called polydisperse materials. By certain technological processes, it is possible to produce particles with practically the same shape and size. Organic particulate materials found in nature (fruits and seeds) consist of particles of similar shape and size. Such materials are called monodisperse materials.
The geometrical, physical and aerodynamical properties of particulate solid materials all affect the onset of fluidization, and the characteristics, behavior and the main parameters of fluidized beds. The most important solid properties are:
particle density (not taking porosity into account),
skeletal (true) density,
bulk density—mass per unit volume of fixed bed,
porosity (or void fraction) of the fixed bed—ratio of volume of space between the particles and the volume of the fixed bed,
mean equivalent particle diameter—particle characteristic dimension,
particle size distribution—probability distribution of particle distribution due to their size,
free fall (or terminal) velocity—velocity of falling particle at which gravitational, Archimedes and drag forces are in equilibrium.
For the exact definition of the term "fluidized bed," it is not sufficient to say that the fluidized bed is a state of the two-phase mixture of the particulate solid material and the fluid. Between two limiting states of the mixture—fluid percolation in the vertical direction through a fixed bed of particulate solids and the free fall of the particles through the stagnant fluid due to the gravitational force, a variety of different states of the solid-fluid two-phase mixture exist. The common characteristic of all these states in vertical, upward or downward, flow (of fluid, particles or both, in the same or opposite directions) is the existence of fluid-to-particle relative velocity and drag force. The various states of solid particle-fluid two-phase mixtures differ from each other by the following characteristics:
the solid particles can be stagnant, floating or moving chaotically,
the solid particles movement can be in a preferred direction or chaotic—one phase or both can be in movement,
the flow direction can be vertical or horizontal,
the fluid phase can be in cocurrent or countercurrent flow,
the movement of the solid material can be free or limited by some kind of mechanical device (a perforated plate, for example),
the density or concentration of the mixture may differ greatly from one state to another.
Possible solid particle fluid mixture states are: fixed bed, stationary fluidized bed, fluidized bed with particle feeding at the bottom and overflow at the free surface of the bed, or vice versa, vertical conveying in the dense bed, low density vertical and horizontal conveying, downward particle movement in the dense bed with cocurrent fluid flow, and low density conveying downwards. Special cases of the above states are the moving bed and spouted bed. Dense phase, nonfluidized solid flow, in which particles move en bloc, with little relative velocity, has been referred to as moving-bed flow, packed bed flow or slip-stick flow. The voidage is close to the minimum fluidization value. Vertical down flow (in stand-pipes) is often used with the fluid moving faster than solids. Upflow of nonfluidized particles is not common. The spouted bed is a combination of a jet-like upward-moving dilute fluidized phase surrounded by a slow downwards moving bed through which gas percolates upward. The use of such systems is limited to a few physical operations with large particles. Transition boundaries between these states of solid material-fluid mixture are defined by the well-known Zenz diagram.
The fluidized state occurs when a fixed bed of the particulate material is penetrated in the vertical direction with fluid at sufficient velocity to break up the bed. In a fixed bed, the particles are immobile, leaning on one another at numerous contact points and applying forces to one another. Gravity forces—particle weight and the weight of the whole bed—are spread in all directions through the particle contact points. When the critical velocity (minimum fluidization velocity) is reached, the solid particles start floating, moving chaotically and colliding. Mutual contacts between the particles are of short duration and the forces between them are weak; the particulate solid material is then in the fluidized state. In the fluidized state, particles are in constant, chaotic movement, and their mean particle distance grows with increasing fluid velocity causing the bed height to rise. The pressure drop in the fluid phase across the bed is constant and equal to the bed weight over unit surface of the bed cross section. This value is reached at the minimum (incipient) fluidization velocity.
When the bed is fluidized with liquids, we have the case of the "homogenous" fluidization. Gas fluidization leads to so-called "heterogenous" fluidization. At gas velocities just above the minimum fluidization velocity, bubbles form and the fluidized bed can be treated as if it consists of two phases: bubbles, in which there are virtually no particles and a particulate (emulsion) phase, which is in a condition similar to that of the bed at the minimum fluidization velocity. Bubbles which form near the distribution plate, rise up the bed, grow and coalesce, producing bigger bubbles which sometimes break up into smaller bubbles. On the bed surface, bubbles eruptively burst, ejecting the particles far from the bed surface. Such bubble behavior makes particle circulation in the bed very intensive. Behind the bubble, in its trail, particles move upwards. Around the bubbles and between them, and especially near the walls, particles move downwards. Bubble movement thus promotes intensive gas and particle axial mixing in the fluidized bed.
The chaotic movement of the particles in the fluidized bed is the main reason for the fact that the various fluidized bed characteristics are similar to those of liquids, which is why this state of two-phase fluid-solid mixture got its name. The free surface of the fluidized bed is horizontal, but of irregular shape due to the bubbles bursting; however it makes a clear, distinctive boundary between the bed of high concentration and the space above it (freeboard), in which particle concentration decreases exponentially. Bodies of greater density sink in the fluidized bed, and those of lower density float or chaotically move near the surface. In the fluidized state, particulate solid material flows out through the openings of the vessel. Just as in the liquids, mixing of two particulate materials is intensive and homogenous. Heat transfer is also intensive, maintaining a homogenous temperature field during the heating or cooling processes or when the heat is generated by fuel combustion in the bed. Fluidized beds obey the laws of hydrostatics.
The fluidized bed characteristics listed above enable its use in various devices for efficient implementation of physical and chemical processes.
The fluidized state, occuring between the filtration of the fixed bed and the pneumatic conveying regime, includes three different regimes: stationary bubbling fluidized bed, turbulent fluidized bed and the regime of fast fluidization. Recently, many technological processes are being carried out in the last two of the above mentioned regimes.
The bubbling fluidized bed best fits the already mentioned characteristics. The most outstanding difference between this and the other two regimes is the existence of large bubbles and a clearly outlined free surface. The bed is very nonhomogenous due to the presence of the bubbles and the pressure drop across the bed oscillates in time.
As the fluidization velocity increases, large bubbles break up into several smaller ones. When the break-up process overcomes the coalescence of the bubbles, oscillations of the pressure drop become smaller. This is the moment when turbulent regime occurs, with no big bubbles in the bed. In the particulate phase of the bed, which is becoming more homogenous, smaller voids exist in the form of the channels and jets, and particles form clusters. Neither the gaseous nor the emulsion phases can be said to be continuous. Mixing of particles becomes more intensive, and the interaction of phases is stronger. The free surface of the bed is very irregular and not clearly outlined. A lot of particles and clusters are being carried off the bed surface and then fall in to the bed again. The maximum velocity of the turbulent regime is the so-called "transport velocity," at which the fast fluidization regime occurs. At velocities above the transport velocity, particles are carried out of the system by the fluid and the bed can only be maintained by feeding new particulate material into it.
At velocities higher than transport velocity, depending on the flow rate of the solid particles returning to the bed, fast fluidization with higher or lower concentration occurs. In the fast fluidization regime, particles move upwards in clusters through the middle of the bed cross section. Near the walls, particles move downward. In this regime, particle mixing is even more intensive in both axial and radial directions. Particle concentration in the freeboard decreases exponentially in the upward direction.
All mentioned regimes of fluidization as well as the two boundary states—fixed bed and pneumatic conveying—have found their use in various devices and technological processes. Solid fuel (coal) combustion is the obvious example. Boilers with grates use fixed beds, fluidized bed combustion boilers use bubbling fluidized beds or turbulent regime (in this case with fly ash recirculation), circulating fluidized bed boilers use the fast fluidization regime and pulverized coal combustion boilers work in the pneumatic conveying regime.
Parameters that describe macroscopic, overall, behavior of the fluidized bed in the bubbling regime are: minimum fluidization velocity, pressure drop across the bed, bed height increase and particle elutriation.
The easiest way of detecting the transition from the fixed bed regime to the fluidized bed regime is to measure the pressure drop across the bed as a function of the fluid velocity. A curve of characteristic shape is obtained (shown in Figure 1).
When minimum fluidization velocity (–vmf) is reached, the Δpp vs vg curve bends and the pressure drop remains constant although the fluid velocity increases. Pressure drop across the fluidized bed becomes equal to the ratio of the overall particle weight and the bed cross section:
Pressure drop across a fixed bed is practically proportional to gas velocity and can be calculated from the well-known Ergun relation (see Fixed Beds):
When these two expressions are equalled, the Wen and Yu relation for minimum fluidization velocity is obtained:
Minimum fluidization velocity has the same physical meaning as the free fall velocity of the particle—that is the velocity at which all particles in the bed are floating. More accurate values for the minimum fluidization velocity for the particular particulate material can be obtained only by means of direct measurement.
The surface of the fluidized bed is not precisely horizontal. Rising through the bed, the bubbles grow and burst reaching the surface, eruptively ejecting particles into the space above the bed (the freeboard). Particles of greater size return (fall back) into the bed, but lots of smaller particles are carried away from the bed by the flowing gas. For that reason, the fluidized bed surface is very disturbed and there is no sudden change in particle concentration. In the region above the free surface, there is the area called the splash zone, in which the particle concentration is changed from very high value in the fluidized bed to the low value characteristic of the area far from the bed surface.
Although the surface of the bubbling fluidized bed cannot be easily defined, the fact is that the bed height increases with the fluidization velocity. Increase of the bed height, i.e., the increase in bed volume, is closely related to the fluidized bed porosity and the volume fraction occupied by bubbles. If we suppose, according to the Davidson two-phase model of the fluidized bed, that all particles are outside bubbles, and always in the state of the minimum fluidization, i.e., that the porosity of the particulate (emulsion) phase is equal to emf, then the increase in the bed height depends only on the volume fraction occupied by bubbles:
Calculation of the bed height, porosity of the bed or the bubble volume fraction, hasn't been solved satisfactorily yet. Empirical correlations of type:
don't yield good results, and the constants C and n need to be determined experimentally for each specific particulate material. A relation used more often is Todes' equation:
A recent approach to this problem uses the relations for the volume fraction occupied by the bubbles, and the corresponding relations for bubble diameter and velocity.
When the bubbles burst at the bed surface two processes take place; at the surface true local gas velocity can be much higher than the mean fluidization velocity, so the larger particles can also be thrown out far from the bed surface; only particles with low free fall velocity will be elutriated far from the bed surface. Due to these two processes, not only single particles are being thrown from the bed surface, but also particle clusters. Moving upwards, these clusters crumble and disintegrate. Some clusters continue their upward movement, and some start to fall back into bed. Particles separated from the clusters, or single particles thrown out of the bed, move upwards though some of them (the larger ones) begin to fall back into the bed. Only the smallest particles, whose free fall velocity is less than the gas velocity will be elutriated from the bed. The number of upward moving particles decreases as the height above the bed increases. Particle concentration and the density of the two-phase mixture decreases exponentially. For each particular fluidized bed and fluidization conditions, a maximum height exists, above which only particles whose free fall velocity is less than the gas velocity, can be found. In the case of a monodisperse material, above this height the particle concentration is zero. This height is called TDH—Transport Disengaging Height. In spite of thorough experimental research no reliable relation for TDH calculation has been developed yet. One of the relations currently in use is the Geldart equation:
obtained for particles with db = 75 μm-2000 μm.
The net mass flow rate of particles with mean diameter dpi at the distance h from the bed surface can be expressed by the relation:
where Fi∞ is the particle flow rate above the TDH:
and Ei∞ is elutriation constant for which one of the empirical relations obtained is the following:
Fi0 is the particle mass flow rate at the bed surface:
Elutriation constant at the bed surface is:
In order to acquire deeper knowledge and better understanding of the characteristic properties of the fluidized bed, it is necessary to research in more detail the local structure of the fluidized bed and the microprocesses taking place in it: bubble generation and growth, movement and mixing of particles and gas.
Bubbles in the heterogenous fluidized beds appear either immediatelly or just after the minimum fluidization velocity is reached. Bubble occurence is of statistically random nature. There is no place on the distribution plate predisposed for bubble occurence. Bubbles initially take a spherical shape, but as they grow they take the shape typical of gas bubbles in liquids—with a concave bottom. The irregularly and randomly spaced bubbles move mostly upward. The presence of other bubbles and particle circulation cause bubbles to move laterally, which leads to coalescence of bubbles. Moving upward, bubbles grow mainly by coalescence, causing the number of bubbles to decrease towards the bed surface. Large bubbles may be unstable so the bubbles can also break up before reaching the surface. Studying the bubbles assumes learning about: bubble generation, rise velocity, growth and coalescence, break up and bursting at the bed surface. All these processes are very complex and still inadequately explained. It has been noticed that, due to the particle size, bubbles can be "fast" and "slow", depending on their velocity, being higher or lower than the minimum fluidization velocity, i.e., velocity of the gas flowing through the bed emulsion phase. In fluidized beds with small particles (materials of the group B by the Geldart (1973) classification), bubbles are fast. In the beds with large particles (materials of the group D by Geldart classification), bubbles are slow. Fast bubbles pass through the fluidized bed with very low mass exchange between the gas in the bubble and the gas in the emulsion phase. At higher bubble velocities, a so-called "cloud" forms around the bubble, in which gas from the bubble circulates, while the gas from the emulsion phase travels around the bubble. Fluidized beds with "slow" bubbles are much more useful for chemical processes, since the bubbles are intensively washed out by the gas from the emulsion phase, so the whole of the gas flow can take part in the reaction. With the fast bubbles, gas passes through the bed not taking part in reactions with the particles.
Bubble rise velocity can be calculated from the following relation:
which is similar to the relation for the bubbles in liquids. One of the simple relations for calculating the size of the bubble at different distances of the distribution plate is Rowe's relation:
Upward gas flow through the bubble keeps the particles at the "roof" of the bubble, and the inflow of gas at the "bottom" turbulizes the particles behind the bubble and drags them up. This "wake" behind the bubble has a volume about 1/3 that of the bubble. Moving upwards, bubbles drag particles from the emulsion phase in their "wake". Because of the overall stationary state of the fluidized bed, upward movement of the particles causes downward movement in other areas of the bed. That is how quasi-stationary circulating particle flow in the emulsion phase of the fluidized bed is caused. The intensity, shape, character and number of these circulating flows depend on numerous parameters, but primarily on the size and the shape of the fluidized bed. That is the one of the basic reasons why it is not possible to obtain similarity between small beds in laboratories and the large industrial devices. Chaotic particle movement, and the organized circulation of particles caused by the bubbles are the main reason for particle mixing, uniformity of the temperature field in the fluidized bed, intensive heat transfer and favorable conditions for chemical reactions.
When gas mixing in the emulsion phase is taken into consideration, three processes must be considered: molecular gas diffusion, turbulent mixing and the directed gas movement as the result of the particle circulation. Bubbles, in their wake, along with particles also drag the gas upwards. In their downward movement, particles can significantly disturb the gas flow. Very intensive downward particle movement can even cause gas to move downward.
Particle mixing in the vertical direction is much more intensive than the mixing in the lateral direction. Using the analogy with the molecular diffusion and by defining the apparent particle diffusion coefficient, experimentally obtained values of this coefficient in the axial direction range from 100 to 1000 cm2/s, and in the lateral direction only 10 to 50 cm2/s. Gas and particle mixing is very important for processes in the fluidized beds. For example, in fluidized bed combustion of solid fuels, the following processes depend on the gas and particle mixing: mixing of the fuel and inert particulate material, even fuel distribution in the bed, the place and manner of feeding fuel, the number of feed points, ash behavior in the bed, heat transfer to the immersed surfaces, combustion of volatiles, erosion of the heating surfaces, etc.
For gas-gas and gas-particle chemical reactions, gas mixing processes in the fluidized bed are also important. If we suppose that the gas passes through the bed in bubbles, either very little or none at all, takes part in chemical reactions, then the gas mixing in the emulsion phase is the most important process concerning the chemical reactions. Apparent gas diffusion coefficient in the axial direction is 0.1 to 1 m2/s and in lateral direction several degrees of magnitude lower, namely, 10−3 to 10−4 m2/s.
Data on gas mixing in the fluidized beds are scarce and differ a lot from experiment to experiment. There is still no established opinion on the effects fluidization velocity, particle and bed size influence on the mixing processes. Yet, it is known that the mixing is more intensive in large fluidized beds and at the higher fluidization velocities.
Another process important for carrying on processes in the fluidized beds is gas exchange between bubbles and the emulsion phase. In this exchange, a very important role is played by "washing" out of the bubbles with gas, a process which is very different in the "slow" and the "fast" bubbles. Uniformity of the temperature and concentration fields is always pointed out as the basic property contributing to the extensive implementation of chemical reactions in fluidized beds. In reality, in large scale chemical reactors, it sometimes happens that these conditions are not fulfilled. If gas and particle mixing and the gas exchange between bubbles and the emulsion phase are not of the sufficient intensity, large temperature variations can occur in the bed. Hot spots and uneven distribution of the reacting gases, fuel particles and oxygen are present. The most frequent reason for these drawbacks is the nonuniform gas distribution due to the wrong choice of the distribution plate and its poor construction which causes nonuniform fluidization and bad particle and gas mixing.
Heat transfer in the fluidized bed is, apart from the particle and gas mixing, the most important process contributing to the intensity of the physical and chemical processes. In fact, several different processes can be distinguished: particle-gas heat transfer, heat transfer between different points in the bed, heat transfer between the fluidized bed particles and the larger particles floating in the bed and the heat transfer to the submerged surfaces in contact with the bed. All of these heat transfer processes are very intensive in fluidized beds.
In the case of uniform fluidization, the temperature difference between points in the bed does not exceed 2-5°C, with mean bed temperatures of several hundred, even 1000°C. Gas temperature, when leaving the bed, is practically the same as the particle temperature. These facts tell us of the great capability of the solid particles to exchange heat with the fluidizing gas. Intensive heat transfer is, first of all, a consequence of the large specific heat transfer surface (3000 to 45000 m2/m3), although heat transfer coefficients to the particles in the bed are relatively small, 6-25 W/m2°C. The large heat capacity of the solid particles also makes the temperature difference between gas and particles small. Gas temperature follows the particle temperature.
Gas to particle heat transfer coefficients can be calculated from the Gelperin and Einstein relation:
Despite the small values of the gas-to-particle heat transfer coefficient, even at a short distance from the distribution plate, the gas and particles temperature are practically equal. Five to ten particle diameters from the distribution plate, the temperature difference between gas and particles has decreased around 100 times. The temperature of gas in the bubbles also very quickly becomes equal to the particle temperature. Some ten millimeters from the plate is enough for this equalization to occur. If, in an inert fluidized bed, there are active particles (usually larger ones) which chemically react with the fluidizing gas, releasing heat (as in the solid fuel combustion), very complex processes of heat and mass transfer between these particles and the bed take place. At the begining, these larger particles heat up in the contact with the inert bed material. Simultaneously, evaporation and devolatilization take place. These processes depend on the intensity of heat transfer between the bed as a whole and these particles. When chemical reactions between gas and particles begin (combustion of the char), particle temperature is higher and the reverse process of heat exchange between active particles and fluidized bed takes place. The combustion process is limited by the mass transfer process, i.e., the diffusion of the reacting gas to the surface of the active particle. The mechanisms of mass transfer towards the active particles are molecular diffusion and the convective transport, while inert bed material disrupt these processes merely by being there. Because larger active particles mainly inhabit the emulsion phase, mass transfer intensity increases with the increase of the size of inert bed material (i.e., with vmf) and decreases with increase of the active particle diameter.
One of the most recent relations for calculating mass transfer coefficient β is that of La Nauze and Jang:
who proposed two mass transfer mechanisms: "packets" (clusters) of particles carry fresh gas from the bulk bed towards the active particle, the movement of these packets is controlled by the bubble flow; the other mechanism is classical convective mass transfer by gas which percolates through the emulsion phase with a velocity equal to vmf.
Heat transfer between the active particle and the fluidized bed is controlled by three mechanisms: gas convection, particle convection and radiation. Depending on the active particle size and temperature, the mechanisms mentioned above do not have the same contribution to the overall heat transfer. These processes are also involved in the heat transfer between the bed and the immersed surfaces. Heat transfer by radiation becomes significant only when temperature differences exceed 400-500°C. For active particle size less or equal to the inert material particle size, the main transfer process is convective heat transfer; for larger particles, heat transfer due to the collision and contact with the fluidized bed particles may be important. Heat transfer coefficients αp for active particles or immersed surfaces have a maximum for optimal fluidization velocity.
For active particle size close to the inert material particle size, relations (15) and (16) can be used. For larger active particles, Agarwall's relation:
When the fluidization velocity increases from vmf to the optimal value, heat transfer coefficients for the surfaces in contact with the fluidized bed also increase, due to the increase of heat transfer by particle contacts. For velocities greater than the optimal, the main contribution to the heat transfer is the gas convection because of the decrease of particle concentration, i.e., the increase of the bed porosity. Optimum velocity can be calculated from the Todes relation:
The factor with the greatest influence on the heat transfer, apart from the fluidization velocity, is the particle size. Particle size influences the change of the relative contribution of various mechanisms in the overall heat transfer. In the fluidized bed with small (< 0.1 mm) particles, convection by particles account for 90% of the overall heat transfer, while in the beds of large particles (> 1 mm) only 20% of the heat transfer is done by particle convection. Particle heat capacity is also important for the amount of heat transfered by particle convection. The maximum heat transfer coefficient is often calculated from the Zabrodski relation:
In the literature, numerous relationships can be found for calculating the heat transfer to immersed surfaces of different shape: vessel walls, single horizontal or vertical pipe, tube bundles with smooth and finned tubes in in-line or staggered arrangement. Parameters that influence the heat transfer to these surfaces are: height and dimensions of the bed, bubble size, tube diameter, arrangement and position of tubes, tube distance, quality and shape of the surface. Existing relationships for calculating the heat transfer coefficient do not include all these parameters and for that reason, experimental data is greatly scattered and the accuracy of the formulas proposed is in the range up to ±50%.
Davidson, J. P. and Harrison, D. (1963) Fluidized Particles. Cambridge University Press, Cambridge, England.
Grace, J. R. (1982) Fluidization. Chapter 8 of Handbook of Multiphase Systems, McGraw-Hill, New York.
Geldart, D. (1973) Types of gas fluidization. Powder Technology, 7, 285-292. DOI: 10.1016/0032-5910(73)80037-3
- Davidson, J. P. and Harrison, D. (1963) Fluidized Particles. Cambridge University Press, Cambridge, England.
- Grace, J. R. (1982) Fluidization. Chapter 8 of Handbook of Multiphase Systems, McGraw-Hill, New York.
- Geldart, D. (1973) Types of gas fluidization. Powder Technology, 7, 285-292. DOI: 10.1016/0032-5910(73)80037-3
Heat & Mass Transfer, and Fluids Engineering