MEA and MDEA. This GLMC model adopts rigorous
modeling of one-dimensional (1D) single and multi-phase
compressible flows of retentate and permeate, where we take
the liberty to denominate the two GLMC products as
retentate and permeate in an analogy with the MP case
(though, literally, there is no permeation here). In a GLMC,
the permeate can become a two-phase multi-reactive system
due to the reactive absorption of CO 2 into the alkaline solvent phase and some trans-membrane transport of CH 4 and
other light hydrocarbons that create a (initially, non-existent)
vapor phase flowing jointly with the alkaline solvent. In this
case, the GLMC has both retentate and permeate flows as
compressible steady-state flows; where the latter is a
two-phase multi-reactive equilibrium compressible flow.
Such GLMC model is evidently far beyond MP modeling
in terms of complexity. But its modeling kernel can be
adapted to model MP operations with similar compressible
flow geometry and similar HFM configuration. By removing
the GLMC formalism related to the two-phase reactive
permeate of CO 2 absorption into alkaline solvents, the
GLMC model of de Medeiros et al. (2013b) can be reduced
to a rigorous 1D model for HFM MP units.
1.2 Outline of This Chapter
This chapter has two subjects committed to steady-state
modeling of MP units for decarbonation of CO 2 -rich NG. The
last paragraph of Sect. 1.1 introduced one of these two subjects (Sect. 2): By suppressing the reactive two-phase nature
of the permeate in the GLMC model of de Medeiros et al.
(2013b), a phenomenological steady-state 1D-distributed MP
simulation model—SPM2010—is developed for rigorous
simulation of CO 2 removal and NG purification flowsheets
using MP batteries operating with hollow-fiber membranes
(HFM) and parallel (co-current) retentate and permeate flows.
SPM2010 solves mass/momentum/energy balances of permeate and retentate and is numerically processed in
MATLAB 2008 environment (The Mathworks) rendering
several graphical results.
The second subject of this chapter (Sect. 3) comprehends
simulation models of MP units appropriate for insertion in
gas processing flowsheets solved by professional process
simulators, such as HYSYS 8.8 and HYSYS 10.0
(ASPENTECH). These models are grouped into two types,
both solving mass/energy balances of permeate and retentate
for hollow-fiber membrane (HFM) and spiral-wound membranes (SWM): (i) Lumped MP models for parallel and
counter-current permeate/retentate flows using average
driving forces and lumped balances (Arinelli et al. 2017,
2019; Araújo et al. 2017); (ii) 1D-distributed MP models for
parallel permeate/retentate flows using distributed driving
forces and distributed balances.
2 Modeling of Steady-State 1D-Distributed
MP Units with Hollow-Fiber Membranes
and Parallel Flows: SPM2010 for MATLAB
SPM2010 models MP units assuming a fixed steady-state
HFM configuration with co-current (parallel) permeate and
retentate flows. Rigorous mass, energy, and momentum
steady-state balances are written for compressible
single-phase gas flow of both permeate (low-pressure side)
and retentate (high-pressure side), where the flow geometry
is 1D along the axis of permeate and retentate flows. Rigorous 1D compressible fluid flow—including thermalcompressibility effects, friction effects, and acceleration
from depressurization—is supported via rigorous thermodynamic calculations with Peng–Robinson equation of state
(PR-EOS) or Soave–Redlich–Kwong equation of state
(SRK-EOS) (Reid et al. 1987). All thermodynamic properties—e.g., enthalpies, densities, fugacities, heat capacities,
sound velocity, and differential coefficients of the density
with temperature and pressure—are calculated along the
flow paths with PR-EOS or SRK-EOS. Transport properties
—e.g., dynamic viscosities and friction factors—are estimated with correlations for high-pressure multicomponent
gas flow. The thermodynamic completeness of this MP 1D
model enables it to make reasonable predictions of cooling
effects which is common in MP units and characteristic of
gas permeation phenomena. SPM2010 also has a built-in
tool for generation of dew-point locus and bubble-point
locus to evaluate condensation risks within the high-pressure
retentate in consequence of the rising of retentate dew-point
(thanks to the dominant permeation of lighter species) and
MP cooling effects.
The MP model of SPM2010 was calibrated with operational data of offshore platforms in Brazil. The calibration
parameters are basically trans-membrane permeances (e.g.,
for CO 2 and CH 4 ), but heat transfer coefficients, HFM
module geometry, and HFM area per module also participated in model calibration. This work was conducted at
CE-GN—Center of Excellence in Natural Gas of the Federal
University of Rio de Janeiro (UFRJ), a joint venture between
UFRJ and PETROBRAS, the Brazil’s state oil company.
2.1 MP Unit Modeling
A MP unit is modeled as a battery of N M parallel individual
MP modules (elements or cartridges). Only hollow-fiber
membrane (HFM) modules with parallel (co-current) 1D
flows of retentate and permeate are considered here. All
modules in the MP battery are supposed to have same spatial
orientation relative to the horizontal direction. Let h represents such angle between the module axis and the horizontal
Membrane-Permeation Modeling for Carbon Capture …
147
modeling of one-dimensional (1D) single and multi-phase
compressible flows of retentate and permeate, where we take
the liberty to denominate the two GLMC products as
retentate and permeate in an analogy with the MP case
(though, literally, there is no permeation here). In a GLMC,
the permeate can become a two-phase multi-reactive system
due to the reactive absorption of CO 2 into the alkaline solvent phase and some trans-membrane transport of CH 4 and
other light hydrocarbons that create a (initially, non-existent)
vapor phase flowing jointly with the alkaline solvent. In this
case, the GLMC has both retentate and permeate flows as
compressible steady-state flows; where the latter is a
two-phase multi-reactive equilibrium compressible flow.
Such GLMC model is evidently far beyond MP modeling
in terms of complexity. But its modeling kernel can be
adapted to model MP operations with similar compressible
flow geometry and similar HFM configuration. By removing
the GLMC formalism related to the two-phase reactive
permeate of CO 2 absorption into alkaline solvents, the
GLMC model of de Medeiros et al. (2013b) can be reduced
to a rigorous 1D model for HFM MP units.
1.2 Outline of This Chapter
This chapter has two subjects committed to steady-state
modeling of MP units for decarbonation of CO 2 -rich NG. The
last paragraph of Sect. 1.1 introduced one of these two subjects (Sect. 2): By suppressing the reactive two-phase nature
of the permeate in the GLMC model of de Medeiros et al.
(2013b), a phenomenological steady-state 1D-distributed MP
simulation model—SPM2010—is developed for rigorous
simulation of CO 2 removal and NG purification flowsheets
using MP batteries operating with hollow-fiber membranes
(HFM) and parallel (co-current) retentate and permeate flows.
SPM2010 solves mass/momentum/energy balances of permeate and retentate and is numerically processed in
MATLAB 2008 environment (The Mathworks) rendering
several graphical results.
The second subject of this chapter (Sect. 3) comprehends
simulation models of MP units appropriate for insertion in
gas processing flowsheets solved by professional process
simulators, such as HYSYS 8.8 and HYSYS 10.0
(ASPENTECH). These models are grouped into two types,
both solving mass/energy balances of permeate and retentate
for hollow-fiber membrane (HFM) and spiral-wound membranes (SWM): (i) Lumped MP models for parallel and
counter-current permeate/retentate flows using average
driving forces and lumped balances (Arinelli et al. 2017,
2019; Araújo et al. 2017); (ii) 1D-distributed MP models for
parallel permeate/retentate flows using distributed driving
forces and distributed balances.
2 Modeling of Steady-State 1D-Distributed
MP Units with Hollow-Fiber Membranes
and Parallel Flows: SPM2010 for MATLAB
SPM2010 models MP units assuming a fixed steady-state
HFM configuration with co-current (parallel) permeate and
retentate flows. Rigorous mass, energy, and momentum
steady-state balances are written for compressible
single-phase gas flow of both permeate (low-pressure side)
and retentate (high-pressure side), where the flow geometry
is 1D along the axis of permeate and retentate flows. Rigorous 1D compressible fluid flow—including thermalcompressibility effects, friction effects, and acceleration
from depressurization—is supported via rigorous thermodynamic calculations with Peng–Robinson equation of state
(PR-EOS) or Soave–Redlich–Kwong equation of state
(SRK-EOS) (Reid et al. 1987). All thermodynamic properties—e.g., enthalpies, densities, fugacities, heat capacities,
sound velocity, and differential coefficients of the density
with temperature and pressure—are calculated along the
flow paths with PR-EOS or SRK-EOS. Transport properties
—e.g., dynamic viscosities and friction factors—are estimated with correlations for high-pressure multicomponent
gas flow. The thermodynamic completeness of this MP 1D
model enables it to make reasonable predictions of cooling
effects which is common in MP units and characteristic of
gas permeation phenomena. SPM2010 also has a built-in
tool for generation of dew-point locus and bubble-point
locus to evaluate condensation risks within the high-pressure
retentate in consequence of the rising of retentate dew-point
(thanks to the dominant permeation of lighter species) and
MP cooling effects.
The MP model of SPM2010 was calibrated with operational data of offshore platforms in Brazil. The calibration
parameters are basically trans-membrane permeances (e.g.,
for CO 2 and CH 4 ), but heat transfer coefficients, HFM
module geometry, and HFM area per module also participated in model calibration. This work was conducted at
CE-GN—Center of Excellence in Natural Gas of the Federal
University of Rio de Janeiro (UFRJ), a joint venture between
UFRJ and PETROBRAS, the Brazil’s state oil company.
2.1 MP Unit Modeling
A MP unit is modeled as a battery of N M parallel individual
MP modules (elements or cartridges). Only hollow-fiber
membrane (HFM) modules with parallel (co-current) 1D
flows of retentate and permeate are considered here. All
modules in the MP battery are supposed to have same spatial
orientation relative to the horizontal direction. Let h represents such angle between the module axis and the horizontal
Membrane-Permeation Modeling for Carbon Capture …
147