Effect of operating parameters on bed hydrodynamics

2.2 Bed hydrodynamics and heat transfer phenomena in CFB

2.2.2 Effect of operating parameters on bed hydrodynamics

The bed voidage (ε ) is the volume fraction of space occupied by the gas. The bed voidage can be determined experimentally by a number of methods, for instance, by measuring the bulk density and relating it to gas and particle densities.

( )

b g 1 s

ρ = ×ε ρ + −ε ×ρ

or, ^{s b b}

s g s B s

1 1

B

M A H

ρ ρ ρ

ε ρ ρ ρ ρ

= − ≈ − = −

−

(2.1)

The bed voidage can also be calculated by measuring pressure drops in U-tube manometer along the riser height. Other techniques for measuring voidage in fluidized beds involve the use of capacitance probes, optical fibres, X-ray or γ-ray attenuation and capacitance tomographic imaging [Yates (1997), Louge et al. (1999), Sidorenko and Rhodes (2004)]. The local voidage, and the gas and solid velocities change continuously from the axis to the wall as reported by many researchers [Hartge et al. (1988), Horio et al. (1988), Yates (1997), Li et al. (2010)]. The voidage is the highest along the axis of the riser column and the lowest in the wall as observed by Tang and Engstrom (1987), Horio (1988), and Li et al. (2010). The radial voidage distribution is much flatter in the upper section of the bed, as well as at the lower circulation rates. In case of fast fluidized beds, there is a gas-solid boundary layer, where the solid generally moves downward. This is investigated by Tang and Engstrom (1987), and Schaub (1989) in both large commercial boilers as well as laboratory units.

The axial variation of voidage is typically a flattened ‘S’ profile as shown in Fig.2.2. At the bottom of the riser solid fraction varies from 0.2 to 0.4, whereby it decreases and these remains almost constant throughout the height of the riser. The lower portions of the bed may be called as dense phase which is generally in bubbling or turbulent mode of fluidization. Above this, the upper entrained region where the solid fraction decreases progressively to about 0.02-0.05, is called as lean phase, and this is generally the fast fluidization mode. The area averaged voidage along the axis of the riser may also be found from the static pressure drop data and its dependence on the local heat transfer coefficient may be found out. Gupta and Nag (2002) investigated that with the increase in superficial velocity, the bed voidage increases in the bottom

portion and decreases in the top region as more solids are lifted up due to more drag force. The concentration of sand particles is more in the riser column for higher bed inventory, and hence, the bed voidage is lower.

Fig.2.2 Axial variation of voidage (“S” Profile) (Nag, 2001)

Knowlton (1977) studied the effect of pressure on bed expansion for widely sized solids with average sizes of approximately 250 µm. He found no clear correlation between pressure increase and bed expansion. Sobereiro and Monteiro (1982) investigated the hydrodynamic behavior of group B powders for pressure up to 35 bar. This work suggested that

ε

_mf is independent of pressure. King and Harrison (1982), who worked with group A and group B particles, report similar trends as observed by Jacob and Weimer for group A powders. Bouratona et al. (1993) suggested that for large particle (≥1.51 mm), the voidage can be determined by a single non- dimensional parameter Y, as given by,

3 gug

Y g

ρ

= µ (2.2)

The use of Y as a scaling parameter successfully regroups the expansion data from high pressure experiments, but fails to regroup the atmospheric one. Gupta and Nag (2002) observed that the axial bed voidage along the height of the bed is observed to be less in the bottom zone and is high in the top zone. Axial bed voidage increases at the bottom zone and decreases at the top zone with an increase in operating pressure. Shen et al. (1991) experimentally investigated the effects of bed voidage in a PCFB unit and found similar observation of Gupta and Nag (2002).

2.2.2.2 Suspension density

The amount of solids density at a particular section of the bed may be defined as suspension density. Mathematically, it can be expressed as

It is reported that, the particle size and the solid inventory have substantial practical influence on the suspension density profile in a CFB furnace

in particle size, the suspension density increases. Yue

the bed inventory, one can influence the suspension density. Suspension density alon of a CFB boiler varies exponentially as it does in the freeboard region of a bubbli bed [Li and Kwauk (1980), and

Stromberg (1986), and Andersson and Leckner

by a power-law equation. The solid holdup in a packed state is and decreases with increasing gas velocity as confirm

(2003) (Fig.2.3).

Fig.2.3 Typical axial profile of solids concentration in various fluidization regimes (Jiang

The amount of solids density at a particular section of the bed may be defined as suspension density. Mathematically, it can be expressed as,

( )

sus

1

s g

ρ = − ε ρ + ερ

It is reported that, the particle size and the solid inventory have substantial practical influence on in a CFB furnace (Basu, 2006). It is claimed that with the decrease suspension density increases. Yue et al. (2005) suggested that by changing the bed inventory, one can influence the suspension density. Suspension density alon

varies exponentially as it does in the freeboard region of a bubbli ), and Kunii and Levenspiel (1991)]. However,

Andersson and Leckner (1992) found the profile to be better represented The solid holdup in a packed state is typically in the range of 0.45 and decreases with increasing gas velocity as confirmed from the research findings of

Typical axial profile of solids concentration in various fluidization regimes (Jiang 2003)

The amount of solids density at a particular section of the bed may be defined as suspension

(2.3) It is reported that, the particle size and the solid inventory have substantial practical influence on . It is claimed that with the decrease suggested that by changing the bed inventory, one can influence the suspension density. Suspension density along the height varies exponentially as it does in the freeboard region of a bubbling fluidized However, Brereton and found the profile to be better represented typically in the range of 0.45-0.65 from the research findings of Jiang et al.

Typical axial profile of solids concentration in various fluidization regimes (Jiang et al.,

2.2.2.3 Minimum fluidization velocity

Minimum fluidization velocity is the basic information required for the design and development of a fluidized bed. Many researchers have studied how an increased pressure affects the minimum fluidization velocity. They have experimentally found that the effect of pressure on the minimum fluidization velocity depends on the particle size. The results of their experiments show a clear decrease in the minimum fluidization velocity with increasing pressure for particles larger than 100 µm (Geldart B and D materials) [Wen and Yu (1966a), Knowlton (1977), Saxena and Vogel (1977), King and Harrison (1982), Chitester et al. (1984), Nakamura et al. (1985), Chiba et al. (1986), Bouratona et al. (1993), Marzocchella and Salatino (2000), Vogt (2001)].

Other experiments showed that for fine Geldart A particles (less than 100 µm), the minimum fluidization velocity remains unaffected by pressure [Knowlton (1977), King and Harrison (1982), Sobreiro and Monteiro (1982), Chitester (1984)]. To estimate the effect of pressure on minimum fluidization velocity, Ergun (1952) has developed an expression of the form,

( )

^{2 3}

( )

3 2 3 2

1.75 1 1

mf p mf g 150 mf p mf g p g p g

mf s mf

d u d u gd

ε ρ ε ρ ρ ρ ρ

φε µ φ ε µ µ

−   −   −

+ =

   

   

Or,

( )

²

( )

³

( )

3 2 3 2

1.75 1

Re_mf 150 ^mf Re_mf ^{p g p g}

mf s mf

gd ρ ρ ρ

ε

φε φ ε µ

− −

+ =

(2.4)

As observed in the Eq. (2.4), for the laminar flow region (for Re_mf <2) and small/light particles with d_p <100

µ

m the viscous loss is dominant compared to the kinetic loss; and the minimum fluidization velocity (u_mf ) is inversely proportional to the gas viscosity (Second left term of Eq.

(2.4)). The minimum fluidization velocity (u_mf ) is therefore expected to decrease with temperature, since µ increases with temperature and because there is no dependence on density, pressure should have no significant effect.

( )

2 2

p p g

mf

u d ρ ρ

µ

∝ − (2.5)

For larger/denser particles and turbulent flow (Re_mf >1000), where the kinetic loss predominates, the minimum fluidization velocity is inversely proportional to the square root of the gas density or pressure, and therefore, it decreases with pressure.

( )

p p g

mf

g

d

u ρ ρ

ρ

∝ −

(2.6) Equation (2.4) may be rewritten as,

( )

( ) ( )

( ) ( )

3

2

2 3 2 3

2

3 2 3

1.75 1

Re 150 Re

1.75 1

, Re 150 Re

p g p g mf

mf mf

mf s mf

mf

mf mf

mf s mf

gd

or Ar

ρ ρ ρ ε

µ φε φ ε

ε

φε φ ε

− −

= +

= + − (2.7)

Various correlations has been developed to calculate particle Reynolds number (Re_mf) at onset of fluidization based on shape, size and pressure. The generic expression of the particle Reynolds number (Re_mf) at onset of fluidization, is given by,

2

1 2 1

Re_mf = C +C Ar−C (2.8)

where

( )

3 2

p g p g

Ar d gρ ρ ρ

µ

= −

(2.9)

As reported, Ergun Eq. (2.4) gave a closer fit for spherical particles and Wen and Yu (1966a) correlation was in better agreement for irregular solids. Table-2.1 provides the comparison of correlation constants

C

₁ and

C

₂ developed by various researchers for prediction of the minimum fluidization velocity at elevated pressures.

Table-2.1 Comparison of correlation constants

Correlation Pressure

range Bed Material

Constant

C

1

Constant

C

2 ^{2 3}

1 _mf

s mf

ε φ ε

−

3

1

s mf

φ ε

Wen and Yu (1966a)

Atmospheric pressure

Fine powders 33.70 0.0408 11 14

Saxena and Vogel (1977)

179-834 kPa Core dolomite particles

25.28 0.0571 --- ---

Borodulya et al.

(1982)

8000 kPa Quartz and glass ballotini

16.00 0.0370 --- ---

Chitester et al.

(1984)

2169, 4238 and 6306 kPa

Ballotini particles 28.70 0.0494 7.94 11.57

Nakamura et al.

(1985)

4900 kPa Geldart B and D Glass beads

33.95 0.0465 --- ---

Basu (2006) High pressure --- 25.25 0.0651 5.19 8.81

Effect of pressure and temperature on gas solid fluidization in both bubbling and circulating fluidized bed was studied by Yates (1996) for Geldart A and Geldart B particles. As observed, the minimum fluidization velocity, the bubbling velocity and the terminal velocity were found to decrease with an increase of operating pressure. Due to increase in gas density with pressure, high pressure may cause the appearance of homogenous fluidization conditions in systems that fluidize heterogeneously at atmospheric pressure. Sidorenko and Rhodes (2003) also reviewed the effect of pressure on gas-solid fluidized bed behavior and observed similar findings reported by Yates (1996).