(ii) 1D-distributed MP models for parallel permeate/retentate
flows using distributed driving forces and distributed balances (MPd-UOE).
3.1 Membrane-Permeation Unit Operation
Extensions: MPx-UOE and MPd-UOE
3.1.1 Premises
UOEs were developed with Visual Basic (VB) programming
language, generating DLLs to be installed in HYSYS. They
are loaded in HYSYS as customized operations, and after
installation, their icons appear on the HYSYS operations
palette. MPx-UOE and MPd-UOE have their own property
window to set specifications such as design parameters and
operational conditions. The property windows were
designed in View Editor, a software available in the
Aspentech HYSYS package.
MPx-UOE and MPd-UOE both simulate steady-state MP
units using a short-cut method to calculate the species
k transmembrane molar fluxes, N k (MMSm
3 /m
2 d), that
needs calibration of permeances. The model draws an
analogy between membrane units and shell and tube heat
exchangers, where the retentate would flow in the shell, and
permeate, in the tube. The permeation driving force is the
log mean difference of partial pressures of species k, DP
LN
k
(bar). The difference between the two units is that MPx-UOE
is a lumped model that considers the membrane unit as one
block with one feed and two products, and thus the short-cut
method is applied for this block and the fluids paths through
the membrane unit are not assessed.
Differently from MPx-UOE, MPd-UOE is a distributed
model; i.e., profiles of dependent variables are obtained
throughout the MP unit. MPd-UOE divides the membrane
unit into smaller membrane cells of same permeation area,
consecutively, applying the MP algorithm for each element.
The outlet condition of first MP cell is calculated based on
the specified inlet condition and will be the inlet condition of
the subsequent cell, and from then on until it completes the
entire membrane unit. Therefore, if the number of MP elements is high enough, the fluids paths can be attained. The
short-cut method error decreases for more distributed simulations, as the number of elements increases and the size of
permeation cells decreases, thus calculations are more
accurate.
Permeation area A MP (m
2 ), retentate and permeate pressures P
out
V ; P
out
L (bar), and membrane type—HFM or SWM,
as depicted in Fig. 1—must be selected by user in both
MPx-UOE and MPd-UOE property windows. The extensions automatically retrieve feed data—molar composition
Y
in , molar flow rate V
in (MMSm
3 /d), temperature T
in
V (K),
pressure (bar) P
in
V , and molar enthalpy H
in
V —from the
material stream connected to the unit operation. For
MPx-UOE, the user must also select the contact type—
counter-current contact (CC) or parallel contact (PC)—while
for MPd-UOE, only parallel contact type is admitted.
Transmembrane molar fluxes (N k ) are considered positive in
the direction retentate ! permeate. In MPd-UOE, the permeate head-loss is fixed as 0.1 bar and equally distributed
through the permeation elements.
Permeances P k of main species involved in CO 2 separation from NG are defined in the MP models for both
HFM and SWM, as shown in Table 4, yet can be set
otherwise in the UOE property window. Table 4 values
were calibrated in element with real MP separation data of
pre-salt offshore NG processing with CAM. Permeances of
H 2 S and H 2 O were estimated as equal to the CO 2 value,
since they are known to be high for skin-dense CAM,
showing good adherence when compared to the real data.
N 2 permeance was estimated as similar to the CH 4 value.
C3+ permeances are small, so they were estimated from the
C 2 H 6 value with reduction of 90% per additional C atom.
Permeation of C5+ species is negligible with CAM. Such
as in Arinelli et al. (2017), despite being calibrated with
real operation data, the permeances were adjusted as constant average values, independent of temperature, and CO 2
fugacity.
Retentate and permeate temperatures, T
out
V ; T
out
L (K), are
calculated via energy balance equations for both streams,
considering the partial molar enthalpies of species permeating from retentate to permeate (N k A MP H k
), and external
and internal heat exchanges. Considering the shell and tube
analogy of the short-cut method, the external heat transfer in
MP is between retentate and the vicinity, while the internal
heat transfer is between retentate and permeate streams. The
external temperature T E is defined as 25 °C in the MP
models but can be set otherwise in the UOE property window. Overall, the heat transfer coefficients for internal and
external heat exchanges are defined as 5 and 2 W/m
2 K,
respectively.
For determination of log mean of temperature differences
in membrane extremities for internal heat transfer calculation, temperature of permeate at the beginning of permeation
is needed. Since it is unknown, the parameter DT F was
created, where DT F ¼ T
out
V À T
in
L for counter-current contact
type, and DT F ¼ T
in
V À T
in
L for parallel contact type. DT F has
a default value of 3 °C in the extensions yet can be changed
by the user in the UOE property window. In MPd-UOE, DT F
specification is only valid for the first membrane element; it
can be calculated for the next elements as DT F ¼ T
in
V À T
in
L ,
where the inlet streams are the outlet streams of the previous
element. In Sect. 3.2.4, a sensitivity analysis is conducted to
assess the impact of DT F specification for both MPx-UOE
and MPd-UOE.
164
J. L. de Medeiros et al.
flows using distributed driving forces and distributed balances (MPd-UOE).
3.1 Membrane-Permeation Unit Operation
Extensions: MPx-UOE and MPd-UOE
3.1.1 Premises
UOEs were developed with Visual Basic (VB) programming
language, generating DLLs to be installed in HYSYS. They
are loaded in HYSYS as customized operations, and after
installation, their icons appear on the HYSYS operations
palette. MPx-UOE and MPd-UOE have their own property
window to set specifications such as design parameters and
operational conditions. The property windows were
designed in View Editor, a software available in the
Aspentech HYSYS package.
MPx-UOE and MPd-UOE both simulate steady-state MP
units using a short-cut method to calculate the species
k transmembrane molar fluxes, N k (MMSm
3 /m
2 d), that
needs calibration of permeances. The model draws an
analogy between membrane units and shell and tube heat
exchangers, where the retentate would flow in the shell, and
permeate, in the tube. The permeation driving force is the
log mean difference of partial pressures of species k, DP
LN
k
(bar). The difference between the two units is that MPx-UOE
is a lumped model that considers the membrane unit as one
block with one feed and two products, and thus the short-cut
method is applied for this block and the fluids paths through
the membrane unit are not assessed.
Differently from MPx-UOE, MPd-UOE is a distributed
model; i.e., profiles of dependent variables are obtained
throughout the MP unit. MPd-UOE divides the membrane
unit into smaller membrane cells of same permeation area,
consecutively, applying the MP algorithm for each element.
The outlet condition of first MP cell is calculated based on
the specified inlet condition and will be the inlet condition of
the subsequent cell, and from then on until it completes the
entire membrane unit. Therefore, if the number of MP elements is high enough, the fluids paths can be attained. The
short-cut method error decreases for more distributed simulations, as the number of elements increases and the size of
permeation cells decreases, thus calculations are more
accurate.
Permeation area A MP (m
2 ), retentate and permeate pressures P
out
V ; P
out
L (bar), and membrane type—HFM or SWM,
as depicted in Fig. 1—must be selected by user in both
MPx-UOE and MPd-UOE property windows. The extensions automatically retrieve feed data—molar composition
Y
in , molar flow rate V
in (MMSm
3 /d), temperature T
in
V (K),
pressure (bar) P
in
V , and molar enthalpy H
in
V —from the
material stream connected to the unit operation. For
MPx-UOE, the user must also select the contact type—
counter-current contact (CC) or parallel contact (PC)—while
for MPd-UOE, only parallel contact type is admitted.
Transmembrane molar fluxes (N k ) are considered positive in
the direction retentate ! permeate. In MPd-UOE, the permeate head-loss is fixed as 0.1 bar and equally distributed
through the permeation elements.
Permeances P k of main species involved in CO 2 separation from NG are defined in the MP models for both
HFM and SWM, as shown in Table 4, yet can be set
otherwise in the UOE property window. Table 4 values
were calibrated in element with real MP separation data of
pre-salt offshore NG processing with CAM. Permeances of
H 2 S and H 2 O were estimated as equal to the CO 2 value,
since they are known to be high for skin-dense CAM,
showing good adherence when compared to the real data.
N 2 permeance was estimated as similar to the CH 4 value.
C3+ permeances are small, so they were estimated from the
C 2 H 6 value with reduction of 90% per additional C atom.
Permeation of C5+ species is negligible with CAM. Such
as in Arinelli et al. (2017), despite being calibrated with
real operation data, the permeances were adjusted as constant average values, independent of temperature, and CO 2
fugacity.
Retentate and permeate temperatures, T
out
V ; T
out
L (K), are
calculated via energy balance equations for both streams,
considering the partial molar enthalpies of species permeating from retentate to permeate (N k A MP H k
), and external
and internal heat exchanges. Considering the shell and tube
analogy of the short-cut method, the external heat transfer in
MP is between retentate and the vicinity, while the internal
heat transfer is between retentate and permeate streams. The
external temperature T E is defined as 25 °C in the MP
models but can be set otherwise in the UOE property window. Overall, the heat transfer coefficients for internal and
external heat exchanges are defined as 5 and 2 W/m
2 K,
respectively.
For determination of log mean of temperature differences
in membrane extremities for internal heat transfer calculation, temperature of permeate at the beginning of permeation
is needed. Since it is unknown, the parameter DT F was
created, where DT F ¼ T
out
V À T
in
L for counter-current contact
type, and DT F ¼ T
in
V À T
in
L for parallel contact type. DT F has
a default value of 3 °C in the extensions yet can be changed
by the user in the UOE property window. In MPd-UOE, DT F
specification is only valid for the first membrane element; it
can be calculated for the next elements as DT F ¼ T
in
V À T
in
L ,
where the inlet streams are the outlet streams of the previous
element. In Sect. 3.2.4, a sensitivity analysis is conducted to
assess the impact of DT F specification for both MPx-UOE
and MPd-UOE.
164
J. L. de Medeiros et al.