Is it true that Increasing gas velocity alone is sufficient to fluidize fine, cohesive powders.?

Cohesive powders have large inter-particle interactions that prevent fluidization with increased gas velocity alone; methods like adding energy (vibration, acoustic) or changing the powder composition are needed.

Is it true that Bubbling fluidization is common in both gas and liquid systems.?

Bubbling fluidization is common in gas systems, while non-bubbling fluidization is more typical in liquid systems.

Particle-Fluid Systems: Flow Through Particle Beds

Understanding fluid flow through particle beds is crucial for optimizing industrial processes, involving calculations for pressure drop, minimum fluidization velocity, and fluidization behavior across Newtonian and non-Newtonian fluids.

Core Principles

Fluidization is a phenomenon where solid material behaves like a fluid due to upward flow of gas or liquid, finding applications in petrochemicals, food processing, and environmental technologies.
Pressure drop in packed beds is governed by the Hagen-Poiseuille equation for laminar flow and the Carman-Kozeny equation, which can be extended by the Ergun equation for turbulent flow.
Minimum fluidization velocity (Umf) is the superficial fluid velocity at which a packed bed becomes fluidized, equating the upward thrust force to the apparent weight of particles.
Bubbling fluidization, common in gas systems, occurs when bubbles appear in the fluidized bed due to cohesive powders and small pressure/momentum by the fluid.
Non-bubbling fluidization, common in liquid systems, involves bed expansion with increasing voidage as fluid velocity increases, while pressure drop remains constant.
Entrainment, or loss of particles, is uncontrollable in bubbling beds and can affect process safety and efficiency, leading to the identification of splash, disengagement, and dilute-phase transport zones above the bed.
Filtration, used to separate particles from suspension, can be analyzed using packed bed equations like Carman-Kozeny, considering both cake and medium resistance.

Action Steps

Calculate the pressure drop across fixed and fluidized particle beds using appropriate equations (Hagen-Poiseuille, Carman-Kozeny, Ergun).
Determine the minimum fluidization velocity (Umf) and minimum bubbling velocity (Umb) for Newtonian and non-Newtonian fluids.
Analyze fluidized bed behaviors by considering particle and fluid characteristics, especially for cohesive powders.
Calculate necessary fluid flow rates for non-bubbling bed expansion, determining expanded bed height and voidage.
Estimate filtration pressure drop or duration using Carman-Kozeny equation and considering cake and medium resistance.

Formulas

Mass of particles in a packed bed: $m = (1 – ε)ρ_pAH$
Voidage of a packed bed: $ε = 1 - \frac{m}{ρ_pAH}$
Hagen-Poiseuille equation for laminar flow in a pipe: $-\frac{Δp}{L} = \frac{32μU}{D^2}$
Carman-Kozeny equation for laminar flow in a packed bed: $-\frac{Δp}{H} = 180 \frac{μU(1 – ε)^2}{d^2 ε^3}$
Ergun equation for flow in packed beds (laminar, transitional, turbulent): $-\frac{Δp}{H} = \frac{150μU(1 – ε)^2}{d^2 ε^3} + \frac{1.75ρ_fU^2(1 – ε)}{dε^3}$
Minimum fluidization velocity (Newtonian fluid): $Ar = \frac{150(1 - ε_{mf})Re_{mf}}{ε_{mf}^3} + \frac{1.75Re_{mf}^2}{ε_{mf}}$ where $Ar = \frac{ρ_f(ρ_p - ρ_f)gd^3}{μ^2}$ and $Re_{mf} = \frac{U_{mf}dρ_f}{μ}$
Minimum bubbling velocity correlation: $U_{mb} = 2.07e^{0.76} \frac{d_p^{0.06}ρ_f^{0.06}}{μ^{0.347}}$
Bed expansion in non-bubbling fluidization: $U = U_{Tε^z}$ where $z = 4.65$ for creeping flow, and $z = 2.4$ when $Re_p ≥ 500$
Total height of freeboard: $H = H_{bed} + 18.2 \cdot d_b$
Carman-Kozeny equation for filtration: $-\frac{Δp}{H} = 180 \frac{μU(1 – ε)^2}{d^2 ε^3}$
Filtration duration for constant pressure drop: $t = \frac{r_cμΦ}{2A^2(-Δp)} V^2 + \frac{μr_mH_m}{A(-Δp)} V$

Key Terms

Fluidization: A phenomenon where a solid material behaves like a fluid when exposed to an upward flow of gas or liquid.
Packed Bed: A bed of particles through which a fluid flows, creating frictional resistance and pressure loss.
Minimum Fluidization Velocity (Umf): The superficial fluid velocity at which the upward thrust force equals the apparent weight of particles, causing the bed to become fluidized.
Minimum Bubbling Velocity (Umb): The fluid velocity at which bubbles first appear in a fluidized bed, typically observed in gas systems.
Voidage (ε): The fraction of the bed volume occupied by the fluid, or the empty space between particles.
Entrainment: The loss of fluidized particles from the bed, often occurring uncontrollably in bubbling beds.
Cake Filtration: A filtration process where a cake of particles builds up on a porous filter medium, increasing its resistance over time.

Pro Tips

For non-Newtonian fluids, flow conditions rarely extend beyond the laminar regime due to high apparent viscosity.
In cohesive powders, interactions between particles are large, requiring methods beyond simply increasing gas velocity to achieve fluidization.
Nanoparticles (like nano-silica) can be mixed with cohesive powders (less than 1 vol%) to reduce cohesion by acting as spacers and introducing electrostatic/van der Waals forces.
Particle size distribution matters; powders with more very fine particles can fluidize very differently even with the same median particle size.

Pitfalls to Avoid

Premature bubbling in gas fluidization systems can cause poor particle distribution and loss of particles (entrainment).
Ignoring medium resistance (rm) in filtration can lead to inaccurate pressure drop calculations.
Assuming constant cake voidage for compressible cakes in filtration will lead to significant errors.

Myth vs Reality

Increasing gas velocity alone is sufficient to fluidize fine, cohesive powders.: Cohesive powders have large inter-particle interactions that prevent fluidization with increased gas velocity alone; methods like adding energy (vibration, acoustic) or changing the powder composition are needed.
Bubbling fluidization is common in both gas and liquid systems.: Bubbling fluidization is common in gas systems, while non-bubbling fluidization is more typical in liquid systems.

Real World Examples

Natural gas purification for methanol production.: A reactor uses a packed bed of zinc oxide particles to remove hydrogen sulfide, demonstrating calculations for packed bed voidage, minimum fluidization velocity, and pressure drop.
Fluidizing cohesive silica powder (8 µm) in industry.: X-ray images show that unassisted beds form elongated channels, while vibrated and pulsed beds improve gas distribution, illustrating methods for fluidizing cohesive powders.

Statistics

Reynolds number range for laminar flow in packed beds (Re*): ε (0, 10]
Reynolds number range for transitional flow in packed beds (Re*): (10, 100]
Reynolds number range for turbulent flow in packed beds (Re*): (100,+∞)
Exponent for creeping flow in non-bubbling bed expansion (z): 4.65
Exponent for Rep ≥ 500 in non-bubbling bed expansion (z): 2.4
Factor for transport disengagement height (TDH): 18.2

People

Bryan Li: Instructor for CHEMMAT 302