Research Article Computational Fluid Dynamics Simulation for Carbon Dioxide Gas Transport through Primitive-structured Polymeric Membranes

Computational Fluid Dynamics Simulation for Carbon Dioxide Gas Transport through Primitive-structured Polymeric Membranes

Low Wai How¹, Ling Gao Shi^1,2, Li Sze Lai^1*, Wee Horng Tay³

1Department of Chemical Engineering, Faculty of Engineering, UCSI University, Kuala Lumpur, Malaysia

2School of Medical Science, Guangxi University of Science and Technology, 545006 Guangxi, China

3Gensonic Technology, Persiaran SIBC 12, Seri Iskandar Business Centre, 32610 Seri Iskandar, Malaysia

* E-mail: LaiLS@ucsiuniversity.edu.my Abstract

Rapid prototyping can fabricate polymeric membranes with complicated microstructures. The complicated primitive structure of the membrane can enhance CO2 mass transfer with higher surface area. Therefore, it is essential to study the potential of the primitive-structured membrane in CO2 gas separation. Nonetheless, simulation for CO2 gas transported across the primitive-structured polymeric membranes is scarcely reported.

The simulation on evaluating the potential of different polymeric membranes in CO2 separation also has not yet been reported. In this paper, the gas separation potential of the primitive-structured polymeric membranes was investigated by using Computational Fluid Dynamics simulation.

The types of polymeric membranes studied include polysulfone, matrimid-5218, and PDMS membrane. The hydrodynamic profiles of the gas mixtures of CO2 and N2 flowing through the membranes were simulated at various operating conditions. It is found that the CO2 concentration decreased from 30 mol% to 9.04 mol%, 7.70 mol% and 11.52 mol% for polysulfone, matrimid-5218, and PDMS membrane, respectively, at a pressure difference of 1.5 bar and temperature of 300 K. Besides, CO2/N2 selectivity of the membranes increased slightly with the increasing operating temperature. The simulation results give a reliable statement over the separation efficiency of CO2 and flow pattern in the 3D printed polymeric membrane.

Keywords: Polymeric membrane; CO2 separation; CFD simulation.

Introduction

The emission of greenhouse gas such as methane (CH4), carbon dioxide (CO2), chlorofluorocarbon (CFCs), and nitrous oxide (N2O) have led to global warming and attracted extraordinary attention in recent years. CO2 contributes the most adverse impact with 55% of the determined global warming among these greenhouse gases. CO2

capture and storage (CCS) is the most suitable system to decrease atmospheric CO2 levels as it mainly includes pre-combustion and post- combustion capture. Chemical absorption is the most common CCS option in the past commercial applications in various industries, which include natural gas production, ammonia production and others.

However, problems such as high capital cost, large space, and corrosion may happen through chemical absorption. Hence, membrane, a promising alternative for CCS from the power plant is developed rapidly due to its economic and basic engineering advantages over contending separation technologies.

Membrane acted as a filter that permits certain molecules to permeate through while blocking other molecules from entering [1]. In recent years, the membrane has just been broadly utilized in liquid separations and is still developed for gas separation. Permeability and selectivity are the main parameters that govern the performance of the membrane. Membranes have an extraordinary opportunity in pre- combustion capture, which mainly focused on H2/CO2 separation.

Meanwhile, for post-combustion, the membrane is mainly focused on CO2/N2 separation using either organic polymeric membranes or

inorganic membranes such as metallic, zeolite, carbon, and ceramic.

The membrane also can be porous or non-porous [2]. This paper will mainly focus on the dense polymeric membranes. The polymeric membrane must have excellent chemical resistance towards moisture and several contaminants with high permeability and selectivity.

Moreover, membranes are appropriate for high CO2 concentration applications with more than 20 vol% of CO2 feed composition.

Therefore, flue gas streams from the power plant can be used as the feed gas in the membrane separation process. Several polymeric membranes have been applied in industries such as polysulfone, matrimid-5218, and polydimethylsiloxane (PDMS). Matrimid-5218, which is a glassy polymer, provides good thermal stability and chemical resistance [3]. Polysulfone can operate at higher plasticization pressure despite its lower CO2 permeability [4].

Polydimethylsiloxane (PDMS) presents the highest gas mixture permeabilities rate among rubbery polymers [5].

Developments in polymer materials synthesis and fabrication, performance, and process design have contributed significantly to improve the potential applications for membranes [6]. Main objectives such as the thermal, mechanical, and chemical resistance of CO2

separation membrane materials have been considerably accomplished. However, CO2 separation from flue gas by utilizing membranes is operated under a low-pressure ratio between the feed stream and permeate stream of the membrane. Therefore, the advancement in CO2 permeability is crucial to decrease the membrane area and system cost. The need for well-defined and expeditious

separation of molecules is always growing, while the typical operation of well-defined membranes based on the solution-diffusion principle is not adequate for such need [7]. A perfect membrane for separation should be as thin as desirable to maximize its flux, have well-defined nanoscale pore sizes to ensure its selectivity, and be automatically robust to prevent it from membrane faulty. Current printing technology can print dense membranes in terms of porous size with resolutions of 100 nm [8]. The complicated membrane structure which is built using 3D printing technology can enhance mass transfer, selectivity, and lower concentration polarisation and fouling. Nonetheless, 3D printing in the polymeric membranes is scarcely developed and reported.

Further developments and advancements of 3D printers to print well- defined structures with industrial scale in a limited period are vital to contend with the current membrane fabrication techniques. A combination of computational, theoretical, and experimental ways can aid in the future development of 3D printed polymeric membranes.

Thus far, simulation in evaluating the effect of different polymeric membranes in CO2 separation has not yet been reported. In this paper, hydrodynamic profiles for CO2 transported across three types of polymeric membranes, including polysulfone, matrimid-5218, and PDMS membranes, were simulated via CFD simulations. Then, the effects of the operating conditions were described, including pressure drop, velocity magnitude and the pressure at the retentate side.

Research Methods

The simulation was performed using ANSYS Fluent 19.2 to investigate the potential performance of the 3D printed polymeric membrane for CO2 separation. One of the types of triply periodic minimal surfaces (TPMS) was selected as the geometry of the 3D printed membrane, which was a primitive lattice structure due to better mechanical properties when compared to gyroid or diamond lattice [9].

The geometry model was then meshed with structured tetrahedral elements to generate meshing structure from coarse to fine mesh size.

The structure was selected with the adaptive mesh refinement setting.

The geometry of polymeric membrane

Fig. 1 (a) shows the diagram of a polymeric membrane.

According to Fig. 1(a), feed enters the membrane by driving force in terms of pressure inlet.

Assumptions and model equations

The mass balances have been carried out at the feed side and permeate side of the membrane module. The binary gas separation process was required in this simulation work. The applied assumptions have been mentioned as follows:

1. Isothermal condition prevails in the membrane.

2. Process is steady state.

3. Ideal gas behavior is considered.

4. Gas is incompressible.

(a)

(b)

Fig. 1. (a) Polymeric membrane with inlet, outlet and permeate outlet. (b) Cross-section along Z-Y direction which cut through the

membrane.

Mass balance for the overall process and component i in the separation process is shown in (1).

𝑚̇_𝑓 = 𝑚̇_𝑟 + 𝑚̇_𝑝;

𝑚̇_𝑓 𝑥_𝑓,𝑖 = 𝑚̇_𝑟 𝑥_𝑟,𝑖 + 𝑚̇_𝑝 𝑥_𝑝,𝑖

(1)

Table 1 summarizes transport characteristics of polysulfone, matrimid-5218, and PDMS membranes. Meanwhile, Table 2 summarizes the characteristic of the porous zone, which was a primitive structure, in each polymeric membrane. In gas separation, membrane selectivity is used to compare the separation performance of a membrane for 2 or more species. Selectivity is an important parameter to define mass source term with the unit of kg m^-3 s^-1 in a porous zone of each polymeric membrane in this simulation work and it was calculated by (2).

α_{𝐶𝑂2/𝑁2} = ^{𝑃𝐶𝑂2}

𝑃_𝑁2 (2)

For gas flowing through porous media with sufficient high velocity, the pressure gradient dP/dx versus flow velocity was described using the Forchheimer equation [10] as in (3):

−^𝑑𝑃

𝑑𝑥 = ^𝜇𝑣

𝐾 + 𝛽^𝜌𝑣2

𝐾^{1 2⁄} ; 𝑣 = ^𝐺

𝜌𝐴𝑛

(3)

where 𝑣 is the velocity, 𝜇 is the fluid viscosity, 𝐾 is the absolute permeability, 𝛽 is the inertial coefficient, 𝐺 is the mass flow rate, 𝜌 is the fluid density, A is the surface area of the porous zone and n is the porosity. The viscosity of binary mixture can be calculated using (4):

𝜇 = ^{𝑥𝑖 𝜇𝑖}

𝑥_𝑗 ∅_𝑖𝑗;

∅_𝑖𝑗=¹

√8(1 + ^𝑀𝑖

𝑀_𝑗)^{−1 2⁄} [1 + (^𝜇𝑖

𝜇_𝑗)^{1 2⁄} (^𝑀𝑗

𝑀_𝑖)^{1 4⁄} ]²

(4)

The Forchheimer equation includes two terms denoting the viscous effect and the inertial effect, respectively. However, to simplify in finding the K value, the inertial effect can be ignored.

Meanwhile, the mass diffusivity of each species can be calculated by using Fick’s law based on (5):

J = 𝐷_𝑖 × ^∆𝐶𝑖

𝑡 × 𝑥_𝑖; ∆𝐶_𝑖 = 𝜌_𝑚 =

𝑚_𝑡

∑𝑚_𝑖 𝜌_𝑖

⁄

(5)

where J is mass flux and ∆𝐶_𝑖 is the total concentration of the mixture, as in fluid density. Table 3 summarizes the average surface roughness of each polymeric membrane.

Table 1. Transport Characteristics of polysulfone membranes, matrimid-5218 membrane, and PDMS membrane.

Material Polysulfone Matrimid-5218 PDMS

Operating condition 4 bar, 25℃ 6 bar, 35℃ 1 bar, 35℃

Membrane thickness (µm) 20 40 250

CO2 permeability (barrer) 25.75 7.68 3800

CO2 molar flux (kg m^-2 s^-1)

7.568 × 10^-6 1.693 × 10^-6 2.234 × 10^-5 N2 permeability

(barrer)

0.93 0.29 400

N2 molar flux (kg m^-2 s^-1)

1.739 × 10^-7 4.068 × 10^-8 1.496 × 10^-6

Selectivity (CO2/N2) 27.5 26.5 9.5

Reference [11] [12] [13]

Table 2. Characteristics of the porous zone in each polymeric membrane.

Properties Values

Effective area 6.6376 × 10^-3 m² Volume 1.8814 × 10^-6 m³

Thickness 9 × 10^-4 m

Length 0.036 m

Width 0.036 m

Porosity 0.6

Table 3. Surface roughness of each polymeric membrane.

Polymeric material used Average Surface roughness, Ra (nm) Reference

Polysulfone 2.90 [8]

Matrimid-5218 0.20 [14]

PDMS 0.88 [15]

Results and Discussion Pressure drop

Pressure drop across porous zone is one of the important aspects that affect the performance of a membrane. Fig. 2 shows the pressure profile in a cross-section view of different polymeric membranes. Matrimid showed the highest pressure drop within the membrane, followed by polysulfone and PDMS.

Velocity magnitude

Fig. 3 shows the velocity profile in a cross-sectional view of different polymeric membranes. The velocity magnitude of permeate outlet in the matrimid-5218 membrane was the highest among other polymeric membranes, which was 121 m/s, while the velocity magnitude of permeate outlet in polysulfone membrane was the lowest one, which was 115 m/s.

The main cause which leads to different velocity magnitude of permeate outlet in different polymeric membranes is the membrane’s surface roughness. 𝑘_𝑠⁺ is introduced, as shown in (6):

𝑘_𝑠⁺ = ^{𝑘𝑠 𝑢𝑇}

𝑣 (6)

where 𝑘_𝑠 is the sand grain roughness, 𝑢_𝑇 is the velocity tangent to the wall and 𝑣 is the dynamic viscosity of the fluid. Sand grain roughness, one of the input parameters of wall boundary in ANSYS fluent is equivalent to 5.863Ra where Ra is measured as the average- roughness parameter of different polymeric materials based on literature [16].

(a)

(b)

(c)

Fig. 2. Contour plot of absolute pressure on cross-section view along Z-Y direction of (a) Polysulfone membrane, (b) Matrimid-5218

membrane, (c) PDMS membrane.

(a)

(b)

(c)

Fig. 3. Contour plot of velocity magnitude on cross-section view along Z-Y direction of (a) Polysulfone membrane, (b) Matrimid-5218

membrane, (c) PDMS membrane.

Grid Independence Analysis

Element with a smaller size of 0.005 m was used to run the simulation and the cross-section view of the meshed membrane module is shown in Fig. 4. Meanwhile, Fig. 5 shows the insignificant change in the velocity magnitude of the gas flowing within the membrane module by using the meshing with a refined element.

Relative error of 16.17 was shown for the different sizes of elements.

This has indicated that the meshing with the element size of 0.01 m is sufficient to simulate the hydrodynamic profiles results for the membrane module in the study.

Fig. 4. Meshing results with element size of 0.005 m.

(a)

(b)

(c)

Fig. 5. Contour plot of velocity magnitude on cross-section view along Z-Y direction of (a) Polysulfone membrane, (b) Matrimid-5218

membrane, (c) PDMS membrane after grid independent analysis.

Effect of retentate pressure

The CO2 mole fraction in the inlet gas stream was set at a constant value of 0.3 and the retentate pressure was set at 1.1, 1.2, 1.3, 1.4, 1.5 bar, respectively, at a constant temperature of 300 K to carry out the effects of retentate pressure on membrane performance.

The variations in the CO2 and N2 mole fraction at retentate and permeate sides were summarized in Figs. 6 – 8. CO2/N2 selectivity for three polymeric membranes was calculated and summarized in Fig. 9.

Fig. 6. CO2 and N2 mole fraction at retentate and permeate sides of polysulfone membrane with varying retentate pressure at 300 K.

Fig. 7. CO2 and N2 mole fraction at retentate and permeate sides of the matrimid-5218 membrane with varying retentate pressure at 300

K.

Based on Fig. 9, high-pressure differences between retentate and permeate sides reduce the CO2/N2 selectivity. This is mainly because higher concentration gradient will create larger force to push the gas molecules passing through the membrane voids.

Fig. 8. CO2 and N2 mole fraction at retentate and permeate sides of the matrimid-5218 membrane with varying retentate pressure at 300

K.

Fig. 9. The trend of CO2/N2 separation ratio with varying retentate pressure at 300 K.

Effect of operating temperature

The CO2 mole fraction in the inlet gas stream was set at a constant value of 0.3, and the feed, retentate, permeate pressures were set at 1.55, 1.5, 1.0 bar, respectively, with varying temperatures, which was set at 300, 310, 320, 330K to carry out the effects of operating temperature on membrane performance. The variations in the CO2 and N2 mole fraction in the retentate and permeate were summarized in Figs. 10 – 12.

Fig. 10. CO2 and N2 mole fraction at retentate and permeate sides of polysulfone membrane with the varying operating temperature at

constant retentate pressure of 1.1 bar.

Fig. 11. CO2 and N2 mole fraction at retentate and permeate sides of the matrimid-5218 membrane with the varying operating temperature

at constant retentate pressure of 1.1 bar.

Fig. 12. CO2 and N2 mole fraction at retentate and permeate sides of PDMS membrane with the varying operating temperature at constant

retentate pressure of 1.1 bar.

By increasing the temperature, CO2/N2 selectivity was slightly increased for three polymeric membranes. This leads to the increase in permeation flux of CO2 and N2.

As the temperature increases, diffusion rate through the membrane also increases, and hence, diffusion activation energy of the membrane decreases. This will lead to the increase in permeation flux of CO2 and N2.

Conclusion

The CO2 gas separation performance of the 3D printed membrane using various polymeric materials was studied via Computational Fluid Dynamics simulation using ANSYS Fluent 19.2.

The primitive structure which was one of the complex geometries was selected and designed as the porous zone of the membrane. A complete structure of the polymeric membrane with a porous zone was built and meshed to the appropriate number of cell elements. The absolute pressure, velocity profile, and CO2 concentration within the different polymeric membranes have been simulated based on the experimental data of CO2 and N2 permeability. Based on the simulation results, CO2/N2 selectivities of 1.698, 2.367, and 1.366 were obtained for polysulfone, matrimid-5218, and PDMS membrane, respectively, at initial operating conditions. However, CO2/N2 selectivity was decreased for three polymeric membranes with increasing retentate pressure. Moreover, other operating conditions such as inlet pressure, CO2 mole fraction, and other characteristics of the membrane such as membrane thickness and effective surface area, also can affect the CO2/N2 separation performance of the polymeric membrane.

Nevertheless, the feasibility of the polymeric membranes with complex structures which were built based on 3D printing technology still requires further improvement due to the immaturity of 3D printing technology. Furthermore, experimental work is needed to validate the simulation results. Overall, the compatibility of 3D printing polymeric membrane offers a potential outlook for CO2/N2 separation at proper operating conditions.

The significance of the research is to investigate the potential of the 3D printed membrane with complicated microstructure in CO2

separation. This is essential in membrane field of study by developing alternative approach to fabricate high performance membranes at large scale.

Acknowledgment

The financial and technical supports provided by UCSI University, KL Campus under REIG grant (grant no. REIG-FETBE- 2020/014) are duly acknowledged.

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