z ¼ 0 : L k ¼ 0 ðk ¼ 1. . .ncÞ
P L ¼ P
ð0Þ
L ; T L ¼ T
ð0Þ
L
ð2:23Þ
z ¼ Z M : P L ¼ P
out
L
ð2:24Þ
The initial permeate temperature at z = 0, T L
(0) , is irrelevant and can be assumed with any value since the initial
condition of all permeate species flow rate is zero (L k
(z = 0)
= 0), which turns the initial permeate into a fluid with zero
isobaric heat capacity and, consequently, with a promptly
adjustable temperature even if T L
(0) is badly chosen. On the
other hand, the initial permeate pressure P L
(z = 0) has a relevant physical role because the permeate must flow through
the inner HFM space toward the permeate outlet at P L
OUT
which is an important MP process specification. In other
words, P L
(z = 0) must be greater than P L
OUT and must be
adjusted so that Eq. (2.24) is satisfied. In SPM2010, a
shooting strategy is used to adjust P L
(z = 0) in order to
achieve the specified P L
OUT at the permeate outlet. Normally, an initial P L
(z = 0) guess is generated by assuming
isothermal laminar gas flow through the inner HFM space
with an estimated flow rate taking into account the expected
average behavior of MP modules for CO 2 -rich NG processing and the mol% of CO 2 in the feed gas.
2.2 CO 2 -Rich Natural Gas Feed for Simulation
of Membrane-Permeation Units
A dehydrated CO 2 -rich NG is chosen as gas feed for MP
simulation with the HFM model. It is a NG with 60 mol%
CO 2 labeled as G60 with data in Table 3. Figures 5, 6, 7, 8,
and 9 depict vapor–liquid equilibrium (VLE) loci of G60
rendered by SPM2010 using PR-EOS. Figure 5 shows the
VLE locus of G60 on plane T Â P, while Fig. 6 shows the
T Â P G60 VLE locus superposing the single-phase molar
isobaric heat capacity C P map under constant composition.
Figures 7, 8, and 9 are similar plots onto the T Â P G60
VLE locus, respectively, superposing the single-phase density q map, the single-phase sound speed map, and the
single-phase isobaric expansivity C T ¼
@q
@T
P;Z
map. All
maps were created under constant G60 composition. The
property maps let clear that G60 is modeled in SPM2010
with appropriate PR-EOS thermodynamic framework,
including second-order properties (e.g., C T ) for the HFM
model Eqs. (2.2) to (2.7). All forthcoming process and MP
simulations adopted PR-EOS for thermodynamic modeling.
2.3 Process FGc40p20: Production of Fuel-Gas
with 40 mol% CO 2 from G60
This example #1 aims at producing the maximum possible
flow rate of fuel-gas (FG) with 40 mol% CO 2 from
1.5 MMNm
3 /d of G60 at T = 55 °C and P = 53 bar.
This FG is appropriated for burning in some gas-fired turbines and this is the primary target. A secondary target is to
produce the CO 2 -rich permeate at highest possible mol%
CO 2 and at highest possible pressure in order to reduce
hydrocarbon losses and compression power necessary to
dispatch this fluid for enhanced oil recovery (EOR). Thus, a
first attempt is to generate the CO 2 -rich permeate at
P = 20 bar. Process specifications (Sect. 2.1.4) comprise:
N M = 38 (per battery); P L
out = 20 bar; (iii) G60 feed (F
Feed ,
Y
Feed , P
Feed , T
Feed ) in Table 3; (iv) DP
HEX = 0.5 bar, T
Heater = 45 °C, TCooler = 30 °C; (v) compressor adiabatic efficiency η% = 75%; (vi) the temperature of the two-phase
mixer-cooler M2F is T
M2F = 5 °C.
The flowsheet FGc40p20 proposes to produce 40 mol%
CO 2 FG using two serial MP batteries (Fig. 2) with N M = 38
HFM 10 m  0.2 m elements each (Table 2) both with
permeate at P L
out = 20 bar, but the second MP battery
(MP#2) is used only if the first MP battery (MP#1) does not
accomplish the targets. Figure 10 shows the flowsheet
FGc40p20 using the rules of stream names as shown in
Fig. 4. Since the load of CO 2 removal is not too high (from
60 to 40 mol%), it seems reasonable to produce permeate at
high-pressure of P L
out = 20 bar. Moreover, since MP operations generate temperature falls, FGc40p20 firstly apply a
hydrocarbon dew-point adjustment (HCDPA) of G60 by
cooling it to T = 5 °C in a two-phase mixer-cooler (M2F)
followed by a two-phase separator (S2F) for liquid separation. M2F + S2F produce a small condensation of natural
gas liquids (NGL) reducing the split vapor flow rate to
1.4581 MMNm
3 /d. As a result, the split vapor V@m2fG60
has a hydrocarbon dew-point (HCDP) of 5 °C at P = 53 bar
and its dew-point locus retrocedes toward lower
Table 3 Data of G60 gas feed
for simulation of HFM MP unit
Flow rate F
Feed
T
Feed , P
Feed
Species molar fractions Y
Feed
774.64 mol/s
96,067 kg/h
1.5 MMNm
3
/d
T
Feed = 55 °C
P
Feed = 53 bar
CO 2 = 60.006% mol; CH 4 = 33.983% mol; C 2 H 6 = 2.39% mol
C 3 H 8 = 1.41% mol; N 2 = 0.85% mol; iC 4 H 10 = 0.25% mol
C 4 H 10 = 0.45% mol; iC 5 H 12 = 0.13% mol; C 5 H 12 = 0.16% mol
C 6 H 14 = 0.14% mol; C 7 H 16 = 0.07% mol; C 8 H 18 = 0.08% mol
C 9 H 20 = 0.04% mol; C 10 H 22 = 0.02% mol; C 11 H 24 = 0.02% mol
152
J. L. de Medeiros et al.
P L ¼ P
ð0Þ
L ; T L ¼ T
ð0Þ
L
ð2:23Þ
z ¼ Z M : P L ¼ P
out
L
ð2:24Þ
The initial permeate temperature at z = 0, T L
(0) , is irrelevant and can be assumed with any value since the initial
condition of all permeate species flow rate is zero (L k
(z = 0)
= 0), which turns the initial permeate into a fluid with zero
isobaric heat capacity and, consequently, with a promptly
adjustable temperature even if T L
(0) is badly chosen. On the
other hand, the initial permeate pressure P L
(z = 0) has a relevant physical role because the permeate must flow through
the inner HFM space toward the permeate outlet at P L
OUT
which is an important MP process specification. In other
words, P L
(z = 0) must be greater than P L
OUT and must be
adjusted so that Eq. (2.24) is satisfied. In SPM2010, a
shooting strategy is used to adjust P L
(z = 0) in order to
achieve the specified P L
OUT at the permeate outlet. Normally, an initial P L
(z = 0) guess is generated by assuming
isothermal laminar gas flow through the inner HFM space
with an estimated flow rate taking into account the expected
average behavior of MP modules for CO 2 -rich NG processing and the mol% of CO 2 in the feed gas.
2.2 CO 2 -Rich Natural Gas Feed for Simulation
of Membrane-Permeation Units
A dehydrated CO 2 -rich NG is chosen as gas feed for MP
simulation with the HFM model. It is a NG with 60 mol%
CO 2 labeled as G60 with data in Table 3. Figures 5, 6, 7, 8,
and 9 depict vapor–liquid equilibrium (VLE) loci of G60
rendered by SPM2010 using PR-EOS. Figure 5 shows the
VLE locus of G60 on plane T Â P, while Fig. 6 shows the
T Â P G60 VLE locus superposing the single-phase molar
isobaric heat capacity C P map under constant composition.
Figures 7, 8, and 9 are similar plots onto the T Â P G60
VLE locus, respectively, superposing the single-phase density q map, the single-phase sound speed map, and the
single-phase isobaric expansivity C T ¼
@q
@T
P;Z
map. All
maps were created under constant G60 composition. The
property maps let clear that G60 is modeled in SPM2010
with appropriate PR-EOS thermodynamic framework,
including second-order properties (e.g., C T ) for the HFM
model Eqs. (2.2) to (2.7). All forthcoming process and MP
simulations adopted PR-EOS for thermodynamic modeling.
2.3 Process FGc40p20: Production of Fuel-Gas
with 40 mol% CO 2 from G60
This example #1 aims at producing the maximum possible
flow rate of fuel-gas (FG) with 40 mol% CO 2 from
1.5 MMNm
3 /d of G60 at T = 55 °C and P = 53 bar.
This FG is appropriated for burning in some gas-fired turbines and this is the primary target. A secondary target is to
produce the CO 2 -rich permeate at highest possible mol%
CO 2 and at highest possible pressure in order to reduce
hydrocarbon losses and compression power necessary to
dispatch this fluid for enhanced oil recovery (EOR). Thus, a
first attempt is to generate the CO 2 -rich permeate at
P = 20 bar. Process specifications (Sect. 2.1.4) comprise:
N M = 38 (per battery); P L
out = 20 bar; (iii) G60 feed (F
Feed ,
Y
Feed , P
Feed , T
Feed ) in Table 3; (iv) DP
HEX = 0.5 bar, T
Heater = 45 °C, TCooler = 30 °C; (v) compressor adiabatic efficiency η% = 75%; (vi) the temperature of the two-phase
mixer-cooler M2F is T
M2F = 5 °C.
The flowsheet FGc40p20 proposes to produce 40 mol%
CO 2 FG using two serial MP batteries (Fig. 2) with N M = 38
HFM 10 m  0.2 m elements each (Table 2) both with
permeate at P L
out = 20 bar, but the second MP battery
(MP#2) is used only if the first MP battery (MP#1) does not
accomplish the targets. Figure 10 shows the flowsheet
FGc40p20 using the rules of stream names as shown in
Fig. 4. Since the load of CO 2 removal is not too high (from
60 to 40 mol%), it seems reasonable to produce permeate at
high-pressure of P L
out = 20 bar. Moreover, since MP operations generate temperature falls, FGc40p20 firstly apply a
hydrocarbon dew-point adjustment (HCDPA) of G60 by
cooling it to T = 5 °C in a two-phase mixer-cooler (M2F)
followed by a two-phase separator (S2F) for liquid separation. M2F + S2F produce a small condensation of natural
gas liquids (NGL) reducing the split vapor flow rate to
1.4581 MMNm
3 /d. As a result, the split vapor V@m2fG60
has a hydrocarbon dew-point (HCDP) of 5 °C at P = 53 bar
and its dew-point locus retrocedes toward lower
Table 3 Data of G60 gas feed
for simulation of HFM MP unit
Flow rate F
Feed
T
Feed , P
Feed
Species molar fractions Y
Feed
774.64 mol/s
96,067 kg/h
1.5 MMNm
3
/d
T
Feed = 55 °C
P
Feed = 53 bar
CO 2 = 60.006% mol; CH 4 = 33.983% mol; C 2 H 6 = 2.39% mol
C 3 H 8 = 1.41% mol; N 2 = 0.85% mol; iC 4 H 10 = 0.25% mol
C 4 H 10 = 0.45% mol; iC 5 H 12 = 0.13% mol; C 5 H 12 = 0.16% mol
C 6 H 14 = 0.14% mol; C 7 H 16 = 0.07% mol; C 8 H 18 = 0.08% mol
C 9 H 20 = 0.04% mol; C 10 H 22 = 0.02% mol; C 11 H 24 = 0.02% mol
152
J. L. de Medeiros et al.