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Fluidized Bed Reactor – An Overview

Submitted by :Antarim Dutta Reg

No : 2016CL04Discipline : Chemical Engg.

DepartmentCourse : Master of

TechnologyMNNIT, Allahabad

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Contents1. Introduction2. The Mechanics of Fluidized Beds

2.1. Pressure Versus Gas Velocity Curve 2.2. Description of the Phenomena2.3. The Minimum Fluidization Velocity2.4. Maximum Fluidization2.5. Descriptive Behavior of a Fluidized Bed - The Model of Kunii And

Levenspiel2.5. Bubble Velocity and Cloud Size2.6. Fraction of Bed in Bubble Phase

3. Mass Transfer in Fluidized Beds3.1. Gas – Solid Mass Transfer3.2. Mass Transfer Between the Fluidized-Bed Phases

4. Reaction Behaviour in a Fluidized Bed5. Mole Balance on the Bubble, the Cloud, and the Emulsion

5.1. Balance on Bubble Phase5.2. Balance on Cloud Phase5.3. Balance on the Emulsion5.4. Partitioning of the Catalyst5.5. Solution to the Balance Equations for a First-Order Reaction

6. Advantages & Disadvantages7. Current Applications of FBR8. References

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IntroductionO The catalytic reactor (which is in common use) is

analogous to the CSTR in that in content, though heterogeneous, are well mixed and this results in an even temperature distribution throughout the bed.

O It consists of a vertical cylindrical vessel containing fine solid catalyst particles. The fluid stream (usually a gas) is introduced through the bottom at a rate such that catalyst particle are suspended in the fluid stream without being carried out.

O With this reactor, it is possible to regenerate the catalyst continuously without shutting down the reactor. This reactor is particularly suitable when the heat effects are very large or when frequently catalyst regeneration is required.

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Continues…O Fluidization occurs when small

solid particles are suspended in an upward flowing stream of fluid.

O The fluid velocity is sufficient to suspend the particles, but it is not to large enough to carry them out of vessel.

O The solid particles swirl around the bed rapidly, creating excellent mixing among them.

O The material “fluidized” is almost always a solid and the “fluidizing medium” is either a liquid or gas.

O The characteristics and behavior of a fluidized bed are strongly dependent on both the solid and liquid or gas properties.

Figure : From Kunii and Levenspiel Fluidization Engineering, Melbourne, FL 32901: Robert E. Krieger Pub. Co. 1969.

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The Mechanics of Fluidized BedDescription of the Phenomena

Figure : Various kinds of contacting of a batch of solids by fluid.

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Continues…O At low velocity pressure drop resulting from

the drag follows Ergun equation given as,--------- (1)O The mass of solids in bed is given by,---------- (2)O After the drag exerted on the particles

equals the net gravitational force exerted on the particles, that is,

------------ (3)The pressure drop will not increase with an increase in velocity beyond this point.

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Pressure Versus Gas Velocity Curve

Figure : From Kunii and Levenspiel, Fluidization Engineering (Melbourne, FL: Robert E. Krieger, Publishing Co. 1977).

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The Minimum Fluidization Velocity

O The Ergun equation in (1) can be written as, = ----------- (4)O At the point of minimum fluidization, the weight of

the bed just equals the pressure drop across the bed

----------- (5)---------- (6)O The minimum fluidization is given by-------------- (7)Note : For Re < 10, (7) can be solved. Where, Re = ; Reynolds number less than 10 is usual in which fine particles are fluidized by gas.

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O Introduction of two parameters are there.O First one is , the “sphericity” which is the measure of a

particle’s non-ideality in both shape and roughness. And Calculated as,

---------- (8)O The second parameter is the void fraction at the time of

minimum fluidization .-------- (9)Another Correlation commonly used is that of Wen and Yu

------- (10) or, --------- (11)O If the distribution of sizes of the particles covers too large a

range, the equation will not apply because smaller particles can fill the interstices between larger particles. Then is calculated as,

------- (12) ; is the fraction of particles with diameter

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Maximum FluidizationO If the gas velocity is increased to a sufficiently high value,

however, the drag on an individual particle will surpass the gravitational force on the particle, and the particle will be entrained in a gas and carried out of the bed. The point at which the drag on an individual particle is about to exceed the gravitational force exerted on it is called the maximum fluidization velocity.

O Maximum Velocity through the bed is given for fine particles, the Reynolds number will be small, and the two relationships presented by Kunii and Levenspiel are,

for Re < 0.4 ---------- (13)for 0.4 < Re < 500 ------- (14)

O The entering superficial velocity, must be above the the minimum fluidization velocity but below the slugging and terminal, velocities.

Therefore, both and these conditions must be satisfied for proper bed operation.

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Descriptive Behavior of a Fluidized Bed – The Model of Kunii and Levenspiel

O Early investigators saw that the fluidized bed had to be treated as a two-phase system – an emulsion phase and a bubble phase (often called the dense and lean phases). The bubbles contain very small amounts of solids. They are not spherical; rather they have an approximately hemispherical top and a pushed-in bottom. Each bubble of gas has a wake that contains a significant amount of solids.

O These characteristics are illustrated in Figure, which were obtained from x-rays of the wake and emulsion, the darkened portion being the bubble phase.

Figure : Schematic of bubble, cloud, wake and emulsion.

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Assumptions in The Kunii- Levenspiel Model

O The bubbles are all of one size.O The solids in the emulsion phase flow smoothly downward, essentially

in plug flow.O The emulsion phase exists at minimum fluidizing conditions. The gas

occupies the same void fraction in this phase as it had in the entire bed at the minimum fluidization point. In addition, because the solids are flowing downward, the minimum fluidizing velocity refers to the gas velocity relative to the moving solids, that is,

------ (15)The velocity of the moving solids, , is positive in the downward direction here, as in most of the fluidization literature. The velocity of the gas in the emulsion, , is taken as a positive in the upward direction, but note that it can be negative under some conditions.O In the wakes, the concentration of solids is equal to the concentration

of solids in the emulsion phase, and therefore the gaseous void fraction in the wake is also the same as in the emulsion phase. Because the emulsion phase is at the minimum fluidizing condition, the void fraction in the wake is equal to .

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Bubble Velocity and Cloud SizeO For single bubble, -------- (16)O Velocities of bubble rise are given by,

+ ( --------- (17) + ---------- (18)

O The best relationship between bubble diameter and height in the column at this writing seems to be that of Mori and Wen, who correlated the data of studies covering bed diameters of 7 to 130 cm, minimum fluidization velocities of 0.5 to 20 cm/s, and solid particle sizes of 0.006 to 0.045 cm. Their principal equation was

-------- (19)O The maximum bubble diameter, has been observed to follow

the relationship --------- (20) for all beds.

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O While the initial bubble diameter depends upon the type of distributor plate. For porous plates, the relationship

-------- (21) is observed, and for the perforated plates, the relationship

-------- (22) is observed.O Werther developed the following correlation based on a

statistical coalescence model:-------- (23)

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Fraction of Bed in the Bubble Phase

O fraction of total bed occupied by the part of the bubbles that does not include the wake.

O volume of wake per volume of bubble.

O bed fraction in the wakes.O (1 - - ) = bed fraction in

the emulsion phase (which includes the clouds).

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O Letting and represent the cross-sectional area of the bed and the density of the solid particles, respectively, a material balance on the solids gives

O A material balance on the gas flows gives

O The velocity of gas rise in the emulsion phase is

Solids flowingdownward in

emulsion

= Solids flowingupward in wakes

(1 - - ) =or, = -------- (24)

= + +Total gasflow rate

= Gas flowin

bubbles

+ Gas flowin

wakes

+ Gas flow inemulsion

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O By combining the equations mentioned in the earlier slide, we obtain an expression for the fraction of the bed occupied by the bubbles

--------- (25)O The wake parameter, α, is a function of the particle size.

The value of has been observed experimentally to vary between 0.25 and 1.0, with typical values close to 0.4. Kunii and Levenspiel assume that the last equation can be simplified to

--------- (26) which is valid for >> e.g.

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Mass Transfer In Fluidized BedO There are two types of mass transport important in fluidized-

bed operations.O Transport between gas and solid.O Transfer of materials between the bubbles and the clouds, and

between the clouds and the emulsion.

Figure : Transfer between bubble, cloud, and emulsion.

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Gas – Solid Mass TransferO In the bubble phase of a fluidized bed, the solid particles are

sufficiently separated so that in effect there is mass transfer between a gas and single particles. The most widely used correlation for this purpose is the 1938 equation of Fröessling (1938) for mass transfer to single spheres given by

----------- (27)O In the emulsion phase, the equation would be one that applied

to fixed-bed operation with a porosity in the bed equal to and a velocity of . The equation recommended by Kunii and Levenspiel :

----------- (28)For 5 < Re < 120, and < 0.84

O Mass transfer coefficients obtained from these relationships may then be combined with mass transfer among the various phases in the fluidized bed to yield the overall behavior with regard to the transport of mass.

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Mass Transfer between the Fluidized-Bed PhasesO For the gas interchange

between the bubble and the cloud, Kunii and Levenspiel defined the mass transfer coefficient in the following manner :

------ (29)O For the products, the rate of

transfer into the bubble from the cloud is given by a similar equation :

------ (30)represents the number of moles of A transferred from the bubble to the cloud & represents the number of moles of B transferred from the cloud to the bubble per unit time per unit volume of bubble.

Figure : Sketch of flow pattern in a fluidized bed for down flow of emulsion gas, or

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O The mass transfer coefficient can also be thought of as an exchange volume q between the bubble and the cloud.

------ (31)Where, = Volume of gas flowing from the bubble to the cloud per unit time per unit volume of bubble. = Volume of gas flowing from the cloud to the bubble per unit time per unit volume of bubble. = Exchange volume between the bubble and cloud per unit time per unit volume of bubble (i.e., )O Using Davidson’s expression for gas transfer between the bubble and the

cloud, and then basing it on the volume of the bubble, Kunii and Levenspiel obtained this equation for evaluating :

----------- (32)O Note, = O Similarly,

------ (34)O Using Higbie’s penetration theory and his analogy for mass transfer from a

bubble to a liquid, Kunii and Levenspiel developed an equation for evaluating :

---------- (35)

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Reaction Behaviour in a Fluidized BedO To use the Kunii-Levenspiel model to predict reaction rates in a

fluidized-bed reactor, the reaction rate law for the heterogeneous reaction per gram (or other fixed unit) of solid must be known. Then the reaction rate in the bubble phase, the cloud, and the emulsion phase, all per unit of bubble volume, can be calculated. Assuming that these reaction rates are known, the overall reaction rate can be evaluated using the mass transfer relationships presented in the preceding section. All this is accomplished in the following fashion.

O We consider an nth order, constant-volume catalytic reaction.O In the bubble phase, ; in which the reaction rate is defined per

unit volume of bubble.O In the cloud, O In the emulsion, Where , and are the specific reaction rates in the bubble, cloud and emulsion respectively.

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Mole Balance on the bubble, the Cloud, and the Emulsion

O Material balance will be written over an incremental height for substance A in each of the three phases (bubble, cloud, and emulsion)

Figure : Section of a bubbling fluidized bed

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Balance on Bubble Phase

The amount of A entering at z in the bubble phase by flow,

A similar expression can be written for the amount of A leaving in the bubble phase n flow at z + Δz.

Dividing by and taking limit as 0.A balance in bubble phase for steady state operation in section ,

----------- (36)

= Molar flow rate of A assuming the

entire bed is filled with bubbles

Fraction of thebed occupiedby bubbles

In by flow

_ Out by flow

_ Out by mass

transport

+ Generation =

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Balance on Cloud PhaseO Similarly for Cloud phase, --------------- (37)

Balance on the EmulsionO Similarly for the emulsion phase,

----------- (38)O The three material balances thus result in three coupled

ordinary differential equations, with one independent variable (z) and three dependent variables ( ). These equations can be solved numerically.

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O The Kunii-Levenspiel model simplifies these still further, by assuming that the derivative terms on the left-hand side of the material balances on the cloud and emulsion are negligible in comparison with the terms on the right-hand side. Using this assumption, and letting (i.e., the time the bubble has spent in the bed), the three equations take the form :

----------- (39)

-------------- (40)

--------------- (41)

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Partitioning of the CatalystO To solve these equations, it is necessary to have values of , ,

and . Three new parameters are defined:

O First of all the specific reaction rate of solid catalyst, must be known. It is normally determined from laboratory experiments. The term is the g-moles reacted per volume of solid catalyst. Then

; ------------- (42)O The volume fraction of catalyst in the clouds and wakes is . The

volume of cloud and wakes per volume of bubble is

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O So the expression for ------ (43)O It turns out that the value of is normally far from insignificant in

this expression for and represents a weakness in the model because there does not yet exist a reliable method for determining .

O The volume fraction of the solids in the emulsion phase is again . The volume of emulsion per volume of bubble is

And the expression for is : - ---------- (44)O Using all the above equation, the three balance equations

become ----------- (45)

-------------- (46) --------------- (47)

NOTE : For reactors other than first order and zero order, these equations must be solved numerically.

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Solution to the Equations for a First-Order ReactionO If the reaction is first order, then the and can be eliminated using

the two algebraic equations, and the differential equation can be solved analytically for as a function of t. An analogous situation would exist if the reaction were zero. Except for these two situations, solution to these two equations must be obtained numerically.

O To arrive at our fluidized-bed design equation for a first order reaction, we simply express both the concentration of A in the emulsion, , and the cloud, in terms if the bubble concentration, . First, we use the emulsion balance

---------- (48)to solve for in terms of .Rearranging equation (48), for a first-order reaction (n = 1), we obtain

----------- (49)We now use this equation to substitute for in the cloud balance

=

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O Solving for in terms of

----------- (50)We now substitute for in the bubble balance

------- (51)Rearranging,

After some further arrangements, ----------- (52)

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O The overall transport coefficient for a first-order reaction. ---------- (53) ------- (54)

Expressing as a function of X, that is We can substitute to obtain And integrating

-------------- (55)

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Advantages & DisadvantagesADVANTAGESO Uniform Particle

MixingO Uniform

Temperature Gradients

O Ability to Operate Reactor in Continuous State

DISADVANTAGESO Increased Reactor

Vessel SizeO Pumping

Requirements and Pressure Drop

O Particle EntrainmentO Erosion of Internal

ComponentsO Pressure Loss

ScenariosO Lack of Current

Understanding

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Current Application of FBRPETROLEUM SECTOR

O GasolinesO Aviation FuelO Diesel FeedstocksO Jet Fuel FeedstocksO PropaneO ButaneO Propylene ; For

Liquified Petroleum Gas (LPG) and Butanes

O Butylene ; For Liquified Petroleum Gas (LPG) and Butanes

O IsobutaneO Cracked NapthaO Gasoline from

MethanolFuel O Oils from Polyethylene

PETROCHEMICAL SECTOR

O Acetone RecoveryO AnilineO Aniline from

NitrobenzeneO Ethanol from ButadieneO PolyethyleneO Hydrogen from SteamO Coal GasificationO Styrenes from

HydrocarbonsO Cracking of

MethylcyclohexaneO Maleic AnhydrideO Maleic Anhydride from

Benzene and ButylenesO Vinyl ChlorideO Vulcanization of Rubber

OTHERS Fertilizers from

Coal Oil

Decontamination of Sand

Industrial and Municipal Waste Treatment

Radioactive Waste Solidification

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References1. nptel.ac.in/courses/103103026/module2/lec18/1.html2. D. Kunii and O. Levenspiel, Fluidization Engineering (New

York: Wiley, 1968).3. H. S. Fogler and L. F. Brown [Reactors, ACS Symposium

Series, vol.168, p. 31 1981, H. S. Fogler ed.]4. T.E. Broadhurst and H.A. Becker, AIChE J., 21, 238 (1975).5. J. F. Davidson and D. Harrison, Fluidized Particles (New

York: Cambridge University Press, 1963).6. S. Mori and C. Y. Wen, AIChE J., 21, 109 (1975).7. J. Werther, ACS Symposium Series., 72, D. Luss & V. W.

Weekman, eds. (1978).8. https://en.wikipedia.org/wiki/Fluidized_bed_reactor9. http://faculty.washington.edu/finlayso/Fluidized_Bed/

FBR_Intro/uses_scroll.htm

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