Fluidization & Mapping of Flow Regimes 건국대학교 화학공학과 최정후

Fluidization A type of fluid-solid contact Fluidization is the operation by which solids particles are transformed into a fluid-like state through suspension in a gas or liquid.

Various forms of contacting of a batch of solids by fluid (Kunii and Levenspiel, 1991)

Bubbling, turbulent, and fast fluidized bed; spouted bed (Kunii and Levenspiel, 1991) Turbulence Uniform temperature

Figure: Circulating fluidized bed combustor (Foster Wheeler type).

Liquid-like behavior of gas fluidized beds (Kunii and Levenspiel, 1991)

Solids circulation between two beds Contacting schemes with gas fluidized beds (Kunii and Levenspiel, 1991) Crosscurrent Solids circulation between two beds Countercurrent

Operating principle for solids circulation between two beds (Kunii and Levenspiel, 1991)

Types of contacting gas and solids (Kunii and Levenspiel, 1991) Gas flow Solids flow

Advantages and disadvantages of fluidized beds for industrial operation Broad residence time distribution of the gas due to dispersion and bypass in the form of bubbles. Broad residence time distribution of solids due to intense solids mixing. Erosion of internals. Attrition of catalyst particles. Difficult Scale-up due to complex hydrodynamics. It has the ability to process large volumes of fluid. Excellent gas-solid contacting. Heat and mass transfer rates between gas and particles are high when compared with other modes of contacting. No hot spot even with highly exothermal reaction. Ease of solids handling.

Process variables The ease with which particles fluidize and the range of operating conditions that sustain fluidization vary greatly among gas-solid systems. They are affected by numerous factors: size (size distribution), shape and density of solids; velocity, density and viscosity of gas; and column size(diameter, height).

Gas velocity: superficial gas velocity Gas Properties: Air density: Air viscosity: Gas velocity: superficial gas velocity

Screens; particle size analysis microne

Specific surface mean particle diameter dp: particle diameter x: weight fraction Shape factor

Particle Density True density - It uses true particle volume that excludes pore volume in particle. The concern is down to how small to determine the pore volume. Apparent density - It uses the apparent particle volume. - It is the apparent density that is used in calculation relating to fluidization. Bulk density - It uses the volume that includes the apparent particle volume and the void volume among particles. Bulk density is used in calculating the size of storage.

Pore classification (by Dubinin): 1) Macropore: 기공 폭>1000 Å, 모세관 응축이 없음 2) Mesopore: 15-1000 Å, 증기압 강하가 발생 3) Micropore: 5-14 Å (1 Å=10-10 m)

Hg porosimetry

Table: Repose angle for solid particles (adapted from Kunii and Levenspiel, 1991) Solids Mean bulk density [kg/m3] Repose Angle, θr [deg] Calcium oxide, powdered 433 43 Catalyst, fluid cracking, 60μm          TCC beads, 3mm 513 729 32 35 Coke, pulverized 400 34 Dolomite, pulverized 738 41 Glass bead, 290μm             5.4mm 1470 1360 26 Iron powder, 130μm-3.6mm 2200-2400 40-42 Lead shot, 1.3-6.4mm 6600-6800 23-33 Limestone, pulverized 47 Portland cement 1630 39 Sand, 480μm 1460 37 Steel balls, 8.9-13mm 4800-5000 33-37 Wheat 770 23

Gas fluidization: u: drag dp: (gravity-buoyance)

Pressure drop versus velocity For the relatively low flow rates in a fixed bed, the pressure drop is approximately proportional to gas velocity, and usually reaching a maximum Δpmax, slightly higher than the static pressure of bed . With a further increase in gas velocity, the fixed bed unlocks, in other words, the voidage increases from εm to εmf resulting in a decrease in pressure drop to the static pressure of the bed. With gas velocities beyond minimum fluidization, the bed expands and gas bubbles are seen to be present. Despite this rise in gas flow, the pressure drop remains practically unchanged.

Pressure drop in fixed bed (Ergun, 1952) uo : superficial gas velocity [m/s] dp : particle diameter [m] : gas density [kg/m3] Lm: static bed height [m] : gas viscosity [kg/m•s] : shape factor [-] : void fraction in bed -] : frictional pressure drop [Pa]

Fluidization without carryover of particles Minimum Fluidization velocity, umf When a bed of particles resting on the distributor, its onset of fluidization occurs when [drag force by upward moving gas]= [(Weight of particles)] [(pressure drop across bed)(cross sectional area of tube)] = [(volume of bed)(solid fraction)(specific weight of solids)] with Δp always positive,

By rearranging, we find for minimum fluidizing conditions that 1 By rearranging, we find for minimum fluidizing conditions that 2 Ergun equation (1952) 3 The superficial velocity at minimum fluidizing conditions, Umf, is found by combing equation 2 and 3.

In more simplified forms umf 4 where Rep,mf and Ar are defined as In more simplified forms 5 6 7

umf Superficial fluid velocity at which the packed bed becomes a fluidized bed is known as the minimum fluidization velocity, umf. Sometimes referred to as the velocity at incipient fluidization. umf increases with particle size and particle density and is affected by fluid properties.

Wen and Yu (1966) equation on Umf hence Umf ∝ Tb-n where Tb : bed temperature, n : 0.6~1.0 hence Umf ∝ Tb0.5

umf 가능한 한 측정하여 사용한다.

Particle classification diagram (Geldart, 1973)

Geldart's classification of powders Group A (Aeratable): (e.g., ammoxidation of propylene) small mean particle size and/or low particle density (<~1.4 g/cm3), gas bubbles appear at minimum bubbling velocity (umb). Group B (Sand-like): (e.g., starch) particle size 40 μm to 500 μm and density 1.4 to 4 g/cm3, gas bubbles appear at the minimum fluidization velocity (umb). Group C (Cohesive): very fine particle, particle size < 30 μm, difficult to fluidize because inter-particle forces are relatively large, compared to those resulting from the action of gas. Group D (Spoutable): (e.g., roasting coffee beans) large particle, stable spouted beds can be easily formed in this group of powders.

Particle terminal velocity Ut: particle terminal velocity [m/s] dp: particle diameter [m] p: particle density [kg/m3] g: particle density [kg/m3] g: acceleration of gravity, 9.8 [m/s2] Cd: drag coefficient [-] Cd=24/Rep for Rep  5.8, Cd=10/Rep0.5 for 5.8 < Rep  540, Cd=0.43 for 540 < Rep Rep: particle Reynolds number , dpUg/

Terminal velocity of single free-falling particles (Kunii and Levenspiel, 1991)

References D. Geldart, Powder Technology, 7, 285 (1973). D. Geldart and A.R. Abrahamsen, Powder Technology, 19, 133 (1978). D. Kunii and O. Levenspiel, “Fluidization Engineering,” Chapter 1 & 3, 2nd edition, Butterworth-Heinemann, Boston USA (1991). G.-S. Lee, “Pressure fluctuations and mixing characteristics in turbulent fluidized beds,” Ph.D. Thesis, KAIST, Daejeon, Korea (1990). H.-J. Ryu, “Slug characteristics and transition velocity to turbulent fluidization in gas fluidized beds,” Ph.D. Thesis, Konkuk University, Seoul, Korea (2000).