Review of the Pressure Swing Adsorption Process for the Production of Biofuels and Medical Oxygen: Separation and Purification Technology

Table 1

Nomenclature.

Parameter	Description	Units
a	Specific particle surface	m^2m^-3
aHi	Specific heat exchanger surface	m^2m^-3
ap	Specific particle surface per unit volume bed	m^2m^-3
A	Area
AA	Placeholder variable used for Dubinin-Astakhov isotherm evaluation
b	Kinetic Langmuir factor	bar^-1
cbi	Bulk gas phase concentration	kmolm^-3
ci	Molar concentration of component i	kmolm^-3
cmsi	Macropore gas phase concentration	kmolm^-3
csol	Concentration of solid phase reactant	kmolkg^-1
cpai	Specific heat capacity of adsorbed phase	MJkmol^-1K^-1
cpcat	Specific heat capacity of catalyst	MJkg^-1K^-1
cpg	Specific gas phase heat capacity at constant pressure	MJkmol^-1K^-1
cps	Specific heat capacity of adsorbent	MJkg^-1K^-1
cpW	Specific heat capacity of column wall	MJkg^-1K^-1
cvg	Specific gas phase heat capacity at constant volume	MJkmol^-1K^-1
DB	Bed diameter	m
Defc	Effective micropore diffusion coefficient	m^2s^-1
Defp	Effective macropore diffusion coefficient	m^2s^-1
Dek	Effective adsorbed phase diffusivity of component	m^2s^-1
Dki	Knudsen diffusion coefficient of component	m^2s^-1
Dmi	Mean molecular diffusion coefficient of component	MJkmol^-1
Eact	Activation energy for Arrhenius relationship	MJkmol^-1
Eii	Radial dispersion coefficient of component	m^2s^-1
Ezi	Axial dispersion coefficient of component	m^2s^-1
Hamb	Wall-ambient heat transfer coefficient	MWm^2K^-1
HB	Height of adsorbent layer	m
Hi	Rate of change of heat of adsorbed phase	MJm^-3s^-1
HR	Combined heats of homogenous and heterogeneous reactions	MJm^-3s^-1
HRcat	Heat of catalytic reaction	MJkmol^-1
HRgas	Gas phase heat of reaction	MJkmol^-1
HTi	Heat of adsorption contribution to solid phase energy balance	MJm^-3s^-1
HW	Gas-wall heat transfer coefficient	MJm^-3s^-1
ΔHi	Heat of adsorption of component	MJkmol^-1
HTC	Gas-solid heat transfer coefficient	MJm^-3s^-1
IP	Isotherm parameter, units depend on isotherm
j	Colburn j-factor for heat or mass transfer
Jads,i	Mass transfer rate of component owing to adsorption	kmolm^-3s^-1
Jcat,reac,i	Mass transfer rate of component owing to heterogeneous catalytic reactions	kmolm^-3s^-1
Jgas, reac ,i	Mass transfer rate of component owing to homogenous, gas phase reactions	kmolm^-3s^-1
Ji	Mass transfer rate of component to/from adsorbent	kmolm^-3s^-1
k0,i	Pre-exponential factor for Arrhenius relationship	ms^-1
k0P,i	Pre-exponential factor for pressure dependent Arrhenius relationship	ms^-1
kfi	Film mass transfer coefficient of component	ms^-1
kfi	Gas phase thermal conductivity	MWm^-1K^-1
kgr	Effective radial gas phase thermal conductivity	MWm^-1K^-1
ki	Effective, lumped mass transfer coefficient of component	s^-1
ks	Solid thermal conductivity	MWm^-1K^-1
kgs	Effective axial gas phase thermal conductivity	MWm^-1K^-1
ksr	Effective radial solid phase thermal conductivity	MWm^-1K^-1
ksg	Effective axial solid phase thermal conductivity	MWm^-1K^-1
kW	Thermal conductivity of column wall	MWm^-1K^-1
Kmac	Macropore mass transfer coefficient	s^-1
Kmic	Micropore mass transfer coefficient	s^-1
Kp	Darcy’s constant	barsm^-2
Kpi	Macropore diffusion coefficient	m^2s^-1
L	Length of horizontal bed	m
M	Molecular weight	kgkmol^-1
MTCg	Gas film mass transfer coefficient	s^-1
MTCs	Solid film mass transfer coefficient	s^-1
P	Pressure	bar
Psat	Saturation pressure	bar
QHi	Heat transfer rate to internal heat exchanger	MJm^-2s^-1
r	Radial coordinate (in packed bed or particle)	m
rc	Microparticle (crystal) radius	m
rp	Particle radius	m
R	Universal gas constant	barm^-3kmol^-1K^-1
Rcat	Catalytic reaction rate	kmolkg^-1s^-1
Rgas	Gas phase reaction rate	kmolm^-3s^-1
Rsol	Solid phase reaction rate	kmolkg^-1s^-1
t	Time	s
tcycle	Adsorption cycle time	s
T	Temperature	K
T0	Initial temperature	K
Tamb	Ambient temperature	K
Tc	Critical temperature	K
Ts	Solid phase temperature	K
Tg	Gas phase temperature	K
THi	Heat exchange medium temperature	K
TW	Wall temperature	K
Tort	Adsorbent tortuosity
vg	Gas phase superficial velocity	ms^-1
Wi	Loading	kmolkg^-1
Wi^0	Pure component loading of component	kmolkg^-1
yi	Mole fraction of component in the gas phase	kmolkg^-1
z	Axial coordinate	m
Greek symbols
ϵi	Bed (interparticle) voidage	m^3 m^-3
ϵp	Intraparticle voidage	m^3 m^-3
μ	Dynamic viscosity	N s m^-2
Ω	Parameter in Glueckauf expression
ψ	Particle shape factor
ρb	Bed packing density	kg m^-3
ρg	Gas phase molar density	kmol km^-3
ρp	Particle density	kmol km^-3
ρs	Adsorbent bulk density	kg m^-3
Subscripts
b	Bulk or packed bed
F	Feed stream
g, s	Gas and solid phase
i	Component water () or ethanol ()
p	Particle