S2F
Two-phase separator
SWM
Spiral-wound membrane
TEG
Triethylene glycol
UOE
Unit operation extension
VB
Visual basic
VLE
Vapor-liquid equilibrium
WDP
Water dew-point
WDPA
Water dew-point adjustment
Nomenclature
A MP
MP area (m²)
A I ; A E
Internal and external MP heat exchange
areas (m²)
C P
@H
@T
P;Z
Molar heat capacity at const. P,
Z (J/K mol, kJ/K mol)
D
MP shell internal diameter (m)
d i , d o
Internal and external HFM diameters (m)
E
Total molar energy of fluid (J/mol, kJ/mol)
E
V
k ; E
L
k
Retentate and permeate partial molar
energy of kth species (J/mol, kJ/mol)
^ f
V
k ; ^ f
L
k
Retentate and permeate fugacities of
species k (bar)
f V , f L
Retentate and permeate Darcy friction
factors (dimensionless)
F
Molar flow rate of fluid (mol/s, MMNm
3 /
d, MMSm
3 /d)
H
Molar enthalpy of multiphase or
single-phase fluid (J/mol, kJ/mol)
H k
Partial molar enthalpy of kth species
(J/mol, kJ/mol)
K
Molar kinetic energy of multiphase or
single-phase fluid (J/mol, kJ/mol)
L
Permeate molar flow rate (mol/s,
MMNm
3 /d, MMSm
3 /d)
L
Length (m)
M M
Molar mass of multiphase or single-phase
fluid (kg/mol)
nc
Number of components (species)
N k
Species k permeation rate (mol/s,
MMNm
3 /d, MMSm
3 /d)
N M
Number of MP modules in MP battery
N HF
Number of HFM’s within a HFM module
P, P V , P L
Pressure, retentate pressure and permeate
pressure (Pa, bar)
P
out
V , P
out
L
MP retentate/permeate outlet pressures
(bar)
P
in
V ; P
in
L
MP retentate/permeate inlet pressures
(bar)
DP
LN
k
MP log mean difference of partial
pressures of species k (bar)
q
Mass flow rate of multiphase or
single-phase fluid (kg/s)
REC%CO 2
Percent recovery of CO 2
T
Temperature (K, °C)
T L , T V
Temperatures of permeate/retentate
(K, °C)
T
out
V , T
out
L
MP retentate/permeate outlet temperatures
(K, °C)
T
in
V ; T
in
L
MP retentate/permeate inlet temperatures
(K, °C)
DT F
MP Temperature difference at the initial
condition of permeate flow (°C)
DT
LN
I ; DT
LN
E
MP log-mean temperature difference for
internal/external heat transfers (°C)
U I ; U E
MP internal and external heat transfer
coefficients (W/m² K)
v
Axial velocity of fluid (m/s)
V
Molar flow rate of retentate (mol/s,
MMNm
3 /d, MMSm
3 /d)
X
Vector (nc  1) of permeate (or liquid
phase) mol fractions
Y
in
k , Y
out
k , X
out
k
Species k mol fraction in
retentate/permeate inlet/outlet MP streams
Y
Vector (nc  1) of retentate (or vapor
phase) mol fractions
z
MP axial position (m)
Z M
Length (m) of HFM’s in the HFM module
Z
Vector (nc  1) of total mol fractions of
multiphase or single-phase fluid
Greek Symbols
P k
Permeance of species k (mol/s m² bar,
MMNm
3 /d m² bar, MMSm
3 /d m² bar)
e V , e L
Retentate and permeate flow roughnesses
(m)
η%
Expander/compressor adiabatic efficiencies
(%)
^
/ k ; / k
Fugacity coefficients of species
k (dimensionless)
q
Multiphase or single-phase fluid density
(kg/m³)
N P
@q
@P
T;Z
Derivative of q with P at const. T,
Z (kg/Pa m
3 , kg/bar m
3 )
N T
@q
@T
P;Z
Derivative of q with T at const. P,
Z (kg/K m
3 )
Subscripts
i, o Inside, outside
k
Species index
144
J. L. de Medeiros et al.
Two-phase separator
SWM
Spiral-wound membrane
TEG
Triethylene glycol
UOE
Unit operation extension
VB
Visual basic
VLE
Vapor-liquid equilibrium
WDP
Water dew-point
WDPA
Water dew-point adjustment
Nomenclature
A MP
MP area (m²)
A I ; A E
Internal and external MP heat exchange
areas (m²)
C P
@H
@T
P;Z
Molar heat capacity at const. P,
Z (J/K mol, kJ/K mol)
D
MP shell internal diameter (m)
d i , d o
Internal and external HFM diameters (m)
E
Total molar energy of fluid (J/mol, kJ/mol)
E
V
k ; E
L
k
Retentate and permeate partial molar
energy of kth species (J/mol, kJ/mol)
^ f
V
k ; ^ f
L
k
Retentate and permeate fugacities of
species k (bar)
f V , f L
Retentate and permeate Darcy friction
factors (dimensionless)
F
Molar flow rate of fluid (mol/s, MMNm
3 /
d, MMSm
3 /d)
H
Molar enthalpy of multiphase or
single-phase fluid (J/mol, kJ/mol)
H k
Partial molar enthalpy of kth species
(J/mol, kJ/mol)
K
Molar kinetic energy of multiphase or
single-phase fluid (J/mol, kJ/mol)
L
Permeate molar flow rate (mol/s,
MMNm
3 /d, MMSm
3 /d)
L
Length (m)
M M
Molar mass of multiphase or single-phase
fluid (kg/mol)
nc
Number of components (species)
N k
Species k permeation rate (mol/s,
MMNm
3 /d, MMSm
3 /d)
N M
Number of MP modules in MP battery
N HF
Number of HFM’s within a HFM module
P, P V , P L
Pressure, retentate pressure and permeate
pressure (Pa, bar)
P
out
V , P
out
L
MP retentate/permeate outlet pressures
(bar)
P
in
V ; P
in
L
MP retentate/permeate inlet pressures
(bar)
DP
LN
k
MP log mean difference of partial
pressures of species k (bar)
q
Mass flow rate of multiphase or
single-phase fluid (kg/s)
REC%CO 2
Percent recovery of CO 2
T
Temperature (K, °C)
T L , T V
Temperatures of permeate/retentate
(K, °C)
T
out
V , T
out
L
MP retentate/permeate outlet temperatures
(K, °C)
T
in
V ; T
in
L
MP retentate/permeate inlet temperatures
(K, °C)
DT F
MP Temperature difference at the initial
condition of permeate flow (°C)
DT
LN
I ; DT
LN
E
MP log-mean temperature difference for
internal/external heat transfers (°C)
U I ; U E
MP internal and external heat transfer
coefficients (W/m² K)
v
Axial velocity of fluid (m/s)
V
Molar flow rate of retentate (mol/s,
MMNm
3 /d, MMSm
3 /d)
X
Vector (nc  1) of permeate (or liquid
phase) mol fractions
Y
in
k , Y
out
k , X
out
k
Species k mol fraction in
retentate/permeate inlet/outlet MP streams
Y
Vector (nc  1) of retentate (or vapor
phase) mol fractions
z
MP axial position (m)
Z M
Length (m) of HFM’s in the HFM module
Z
Vector (nc  1) of total mol fractions of
multiphase or single-phase fluid
Greek Symbols
P k
Permeance of species k (mol/s m² bar,
MMNm
3 /d m² bar, MMSm
3 /d m² bar)
e V , e L
Retentate and permeate flow roughnesses
(m)
η%
Expander/compressor adiabatic efficiencies
(%)
^
/ k ; / k
Fugacity coefficients of species
k (dimensionless)
q
Multiphase or single-phase fluid density
(kg/m³)
N P
@q
@P
T;Z
Derivative of q with P at const. T,
Z (kg/Pa m
3 , kg/bar m
3 )
N T
@q
@T
P;Z
Derivative of q with T at const. P,
Z (kg/K m
3 )
Subscripts
i, o Inside, outside
k
Species index
144
J. L. de Medeiros et al.