Nomenclature#

Symbols#

Symbol	Description	Unit
A	area	m²
a	interfacial area of bubbles/granules	m^-1
Ar	Archimedes number	-
c	concentration	kg m^-3
C_D	drag coefficient	-
D	diffusion or dispersion coefficient	m² s^-1
d	diameter	m
EF	emission factor	-
F	fouling factor	-
f	fraction	-
G	number of granules in a cluster	-
g	gravitational acceleration	m s^-2
H	height of the reactor	m
K	monod constant	kg m^-3
M	molar mass	g mol^-1
m	mass	kg
N	number of clusters in a set	-
n	expansion index	-
P	breaking chance of granule clusters	-
p	pressure	Pa
q	biomass specific substrate uptake rate	kg kg^-1 s^-1
R	volumetric reaction rate	kg m^-3 s^-1
r	radial position	m
Re	Reynolds number	-
T	temperature	K
t	time	s
V	volume	m³
v	velocity	m s^-1
x	position from the bottom of the reactor	m
Y	yield coefficient	kg kg^-1

Greek symbol	Description	Unit
α	MTR correction factor	-
ε	voidage fraction	-
μ	dynamic viscosity of water	kg m^-1 s^-1
ν	kinematic viscosity of bulk-liquid	m² s^-1
ρ	density	kg m^-3
θ	volumetric concentration	-

Subscript	Description
0	start or reference value
AN	anaerobic
ax	axial direction
B	biofilm phase
d	deficit
e	effluent
G	gas phase
GFS	granule forming substrate
i	index of set of biomass clusters
in	influent
j	index of biomass cluster or class
L	bulk-liquid phase
N	nitrogen
O	oxygen
PHA	polyhydroxyalkanoates
R	reactor
s	solubility
f	fluidizing (velocity)
t	terminal (velocity)
TN	total nitrogen

Constant	Description	Unit
k	correction factor for wall effects	-
kHC	Henry correction factor	K
kH	Henry coefficient	mol m^-3 Pa^-1
kLB	mass transfer coefficient for bulk-liquid/biofilm interface	m s^-1