A = cross sectional area of bed; m2
a = surface area of particles per unit bed volume; m2
Ar = Archimedes number; 
C0 = concentration of reactant at distributor; mol/m3
Cp = concentration of reactant in the particulate
phase; mol/m3
CB = concentration of the reactant in the bubble phase
at height h; mol/m3
CBH = concentration of reactant leaving the bubble
phase; mol/m3
CH = concentration of reactant leaving the reactor;
mol/m3
Cg = specific heat capacity of gas; J/kg.K
dBv = equivalent volume diameter of a bubble; m
dBvs = equivalent volume diameter of a bubble at the surface; m
dBvmax = equivalent volume diameter of a bubble
(maximum); m
D = bed diameter; m
g = acceleration due to gravity; m/s2
hgp = gas-to-particle heat transfer coefficient;
W/(m2 K)
hpc = particle convective heat transfer coefficient;
W/(m2 K)
hgc = gas convective heat transfer coefficient;
W/(m2 K)
hr = radiative heat transfer coefficient;
W/(m2 K)
hmax = maximum bed-to-surface heat transfer
coefficient; W/(m2 K)
H = height of bed; m
Hmf = height of bed at incipient fluidization; m
j = reaction order; -
K*ih = elutriation constant for size range xi
at height h above distributor; kg/(m2 s)
= elutriation constant for size range xi
above TDH; kg/(m2 s)
KC = interphase mass transfer coefficient
per unit bubble volume; 1/s
k = reaction rate constant per unit volume of solids
kg = gas conductivity; W/mK
L = height above the distributor; m
M = mass of solids in the bed; kg
MB = mass of solids in the bed; kg
mBi = mass fraction of size range xi in the bed; -
n = exponent in Richardson-Zaki equation; -
Nu = Nusselt number (h kg / x); -
Numax = Nusselt number corresponding to hmax; -
N = number of holes per unit area in the distributor; 1/m2
p = pressure drop across packed bed
or fluidized bed; N/m2
Pr = Prandtl number (Cg m / kg); -
Q = volume flow rate of gas into bed (=UA); m3/s
Qmf = volume flow rate of gas into bed
at Umf (=Umf A); m3/s
Ri = rate of entrainment of solids
in size range xi; kg/s
Rep = single particle Reynolds number
(Urel x 
f / 
); -
Remf = Reynolds number at incipient fluidization
(Umf xsv f
/ ); -
t = time; s
Ts = solids temperature; K
Tp = gas temperature; K
TDH = transport disengagement height; m
U = superficial gas velocity; m/s
Uf = actual fluid velocity; m/s
Ufs = superficial fluid velocity; m/s
UB = mean bubble rise velocity; m/s
Um = superficial velocity at which hmax occurs; m/s
Umf = superficial gas velocity at minimum fluidization; m/s
Umb = superficial gas velocity at minimum bubbling; m/s
Ums = minimum velocity for slugging; m/s
Up = actual particle velocity; m/s
Usp = superficial particle velocity; m/s
Urel = relative velocity between particle and fluid; m/s
UT = single particle terminal velocity; m/s
UT2.7 = single particle terminal velocity for a particle 2.7
times the mean size; m/s
UTi = single particle terminal velocity for particle size
xi; m/s
xp = mean sieve size of a powder; m
xsv = mean surface-volume diameter of a powder (diameter of
a sphere having the same surface/volume ratio as the particle; m
xv = mean volume diameter of a powder (diameter of a sphere
having the same volume as the particle); m
Y = factor in Equation 5.30; -
= (U - Umf) / U; -
= bed voidage (volume of voids/total volume); -
B = volume fraction of bed
occupied by bubbles; -
mf = voidage at Umf; -
B = factor in Equation 5.32; -
= fluid viscosity; Pa.s
f = fluid density; kg/m3
g = gas density; kg/m3
i = solids loading of particle
size xi; kg/m3
p = particle density; kg/m3
T = total solids loading of
all solids; kg/m3
= number of interphase transfer units
(KC H / UB); -