Fluidized Bed: Two-Phase Bubble Population

Reactor Controls

Superficial gas velocity U 18 cm/s

Catalyst particle size d_p 70 μm

Bed temperature T 520 °C

Fluidization State

U_mf (Wen–Yu)

— cm/s

U / U_mf

—

Regime

Fixed bed

Bed expansion H/H₀ (TPT)

1.00×

Bubble fraction δ

0.00

Catalytic Cracking

Conversion X

— %

Catalyst activity a

100 %

Coke on catalyst

0.00 wt%

How it works

Same reactor chemistry as the 3D fluidized bed, drawn a different way: instead of instanced 3D particles following canned motion paths, this cross-section runs an actual Kunii–Levenspiel two-phase-theory (TPT) bubble population — every bubble you see is nucleated, grown and risen from its own real equations, and the bed-expansion number comes directly out of that population instead of a cosmetic scale factor.

Ar = dp³ρg(ρs−ρg)g / μ²          (Archimedes number, Wen–Yu)
Re_mf = √(33.7² + 0.0408·Ar) − 33.7
U_mf = Re_mf·μ / (dp·ρg)

Bubble growth with height h (Mori–Wen):
 db(h) = dbm − (dbm−db0)·exp(−0.3h/D)
 dbm = 0.652·[A_bed·(U−U_mf)]^0.4
Bubble rise (Davidson–Harrison): u_br = 0.711·√(g·db)
Absolute rise: u_b = (U−U_mf) + u_br
Bubble fraction (continuity): δ = (U−U_mf) / u_b
Bed expansion: H/H_mf = 1 / (1−δ)

Bubbles nucleate at the distributor at a rate set by the excess gas flow (U−U_mf), grow as they climb (bigger bubbles higher up, exactly as Mori–Wen predicts), rise faster than the surrounding emulsion, and merge when they touch — each merge conserves cross-sectional bubble area (r² adds, not r). The bed-expansion stat is the actual δ produced by that live population, not a preset animation curve.

Catalytic cracking & deactivation — unchanged from the 3D model: first-order Arrhenius kinetics acting on catalyst whose activity falls as Voorhies coke accumulates on its acid sites.

k(T) = k0·exp(−Ea / R·T)
X = 1 − exp(−k·a·τ)
C_coke = A·t^n            (Voorhies)
a = exp(−α·C_coke)

Coke builds on an accelerated clock so the decay is visible in seconds; Regenerate burns it off and restores fresh-catalyst activity, mirroring the real FCC regenerator loop.

Zeolite catalyst (emulsion) Gas bubbles (TPT population) Uncracked feed Cracked product