1. Introduction
Biogas undergoes processing and conditioning to remove impurities such as CO
2 (30–45%) and H
2S (0.5–1%), enhancing its utility and meeting pipeline transport requirements. Addressing environmental concerns and global warming issues [
1], this process mitigates CO
2 emissions from fossil fuel combustion flue gases, which are significant greenhouse gases. Membrane contactors, recognized for their high separation efficiency [
2], play a crucial role in CO
2 capture [
3] from these emissions [
4], leveraging chemical potential differences across hydrophobic membranes. Purification technology is employed to selectively absorb soluble gas mixture components on the membrane surface within liquid/liquid and gas/liquid systems [
5,
6]. Gas/liquid membrane contactor technology facilitates efficient contact between liquid absorbents and flue gases, offering advantages such as an increased effective contact area, continuous operation, and reduced dimensions of absorption columns [
7]. The efficiency of membrane absorption depends heavily on the properties of selective membrane materials [
8], including hybrid silica aerogel, highly porous polyvinylidene fluoride (PVDF)/siloxane nanofibrous membranes [
9,
10], and composite membranes [
11], tailored for CO
2 absorption. Microporous hydrophobic membranes, with relatively low production costs, play a crucial role in selectively separating specific substances, utilizing non-wetted membrane pores at the gas/liquid interface [
12], which depends on the distribution coefficient and a composition gradient of gas solute in the gas/liquid system [
13]. The dusty gas model [
14] is widely employed to describe mass transfer characteristics across membranes, aiding in estimating process performance [
15] involving reactions and diffusion [
16]. Enhanced CO
2 capture efficiency is achieved through physical absorption based on CO
2 solubility in solvents, thereby reducing regeneration costs [
17], with alkanolamine solvents [
18] commonly utilized due to the associated chemical reactions [
19]. Previous research has extensively studied the mechanisms of CO
2 absorption in MEA solutions [
20], highlighting membrane contactors’ potential for alkanolamine-based CO
2 capture processes.
Previous studies have conducted comprehensive experiments on gas/liquid absorption using shell and tube membrane contactors, employing computational fluid dynamics (CFD) [
21]. These experiments have considered laminar liquid flow profiles [
22] and aimed to achieve highly efficient CO
2 removal under turbulent flow conditions. However, the membrane separation process is prone to concentration polarization near the membrane surface, which leads to decreased mass transfer rates. This effect is commonly observed in various membrane separation processes, resulting in reduced trans-membrane mass flux [
23,
24,
25]. To mitigate concentration polarization, turbulence promoters have been implemented to improve flow channels, such as roughened surfaces [
26], spacer-filled channels [
27], and carbon-fiber spacers [
28]. These enhancements effectively increase turbulent intensity within the gas/liquid membrane contactor system, thereby enhancing convective mass transfer coefficients [
29] under diverse operational conditions. Inserting a wire spiral into a concentric circular tube effectively modifies the convection flow dynamics, creating secondary flows or eddies that reduce mass transfer resistances across concentration boundary layers [
30]. Consequently, this design modification significantly boosts CO
2 absorption efficiency compared to modules lacking spiral rings. Studies on various spiral ring pitches [
31] have highlighted their hydrodynamic influence on mass transfer mechanisms, revealing their capability to overcome increased mass transfer resistance and reduce power consumption. This contrasts with the approach of using a constant spiral ring pitch, which has been previously applied in heavy water enrichment [
32] and demonstrated improved device performance with smaller spiral ring-filled channels in earlier work [
33]. A forward-looking strategy aims to reduce overall mass transfer resistance by disrupting mass transfer boundary layers and mitigating concentration polarization through dynamic flow adjustments and enhanced turbulent intensity achieved by embedding various spiral ring pitches [
34,
35]. A concentric circular membrane contactor was designed with a tightly fitted spiral ring in a narrow annular space to enhance CO
2 absorption flux by minimizing concentration polarization resistance. Previous research has shown that concentration polarization can be mitigated in ring–rod tubular membrane contactors, leading to increased turbulence intensity. However, the isothermal diffusion–reaction process and chemical reactions during MEA absorbent flow can increase mass transfer resistance towards the latter half of the module, exacerbating concentration polarization. In this study, device performance was further optimized by incorporating various spiral wire pitches along the flow channel. This approach aims to adjust the hydraulic diameter and spiral ring pitches to achieve a specified volumetric feed rate, effectively reducing undesired resistance while ensuring a manageable increase in power consumption for economic viability.
In this study, device performance was enhanced by integrating descending and ascending spiral ring pitches along the flow channel. The theoretical development included mass balance considerations and chemical reaction analyses, complemented by experimental validation using a spiral-ring concentric circular module made of PTFE/PP (polytetrafluoroethylene/polypropylene). The effectiveness of the absorption process was evaluated through a mass transfer enhancement factor, assessing the impacts of spiral wire pitch, CO
2 feed concentration, and MEA feed flow rate on CO
2 absorption flux under varying spiral ring pitch configurations. The mass transfer behaviors across the membrane exhibited distinct characteristics, and mathematical formulations were developed building upon prior studies [
33], successfully improving membrane absorption rates. Additionally, the incorporation of turbulence promoters in membrane contactor systems was found to increase pressure drop in the feed channel [
36]. Thus, the study also evaluated the trade-off between achieving high CO
2 absorption flux and managing energy consumption, aiming to provide an economic assessment for membrane module applications [
37]. Gas absorption mechanisms within the spiral ring-filled module were investigated through modeling mass balance equations and chemical reactions using PTFE membranes. This approach facilitated a balanced consideration between enhancing CO
2 absorption flux and managing energy consumption, ensuring technical and economic feasibility in designing gas membrane absorption modules. The mathematical formulation developed for spiral-ring concentric circular tubes in this study represents a valuable contribution, potentially applicable to various hydrophobic membrane systems.
2. Theory and Analysis
This study presents mathematical modeling of CO
2 absorption in an MEA solution flowing through the shell side of a spiral-ring concentric membrane module, while a gas mixture of CO
2/N
2 flows through the tube side, as depicted in
Figure 1. The schematic representations illustrate both ascending and descending spiral ring pitch operations. Two different spiral ring pitches were utilized: ascending pitches of 1 cm to 3 cm and 2 cm to 3 cm in
Figure 1a,b, and descending pitches ranging from 3 cm to 1 cm and 3 cm to 2 cm in
Figure 1c,d. Device performances were evaluated and compared with those in previous work [
33] using constant spiral ring pitches.
2.1. Mass Transfer
A representation of the mass transfer in the membrane contactor is depicted in
Figure 2.
and
are the bulk concentrations of the gas feed and MEA liquid solution, respectively, and the membrane surface concentration drops to the concentration
at the membrane–liquid interface lower than the bulk concentration
while the membrane surface concentration raises to a higher concentration
than the bulk concentration
. Henry’s law defined by the dimensionless Henry’s law constant
[
20] is expressed in terms of the solubility of a gas in a liquid according to the equilibrium with the concentration of the gas in the liquid, or
or
The mathematical modeling equations considered the isothermal diffusion–reaction process occurring within the lumen tube and chemical reactions at the membrane surface on the shell side. These equations were derived to analyze CO2 absorption rates in the concentric circular membrane contactor module. The trans-membrane mass flux of CO2 is primarily governed by the concentration difference across the membrane, influenced by concentration boundary layers in both bulk streams, membrane properties, and operating conditions. The diffusion–reaction mechanism in the gas/liquid membrane contactor involves three key regions for CO2 transfer from the gas feed to the liquid feed: (a) from the bulk gas phase to the membrane surface, (b) through the membrane via its pores, and (c) absorption by the MEA absorbent along with chemical reactions.
The absorption flux
according to the dusty gas model [
14] depends [
38] on the trans-membrane saturation partial pressure differences (
) [
39] at the membrane surface in the MEA absorbent solution and CO
2/N
2 gas side as well as the membrane permeation coefficient (
) [
40] as represented in Equation (3)
in which
is the overall mass transfer coefficient of the membrane,
is the reduced equilibrium constant with the equilibrium constant
at
[
41], and the tortuosity
was determined [
42].
The mass diffusion of CO
2 is transported by the concentration driving force gradient between both gas and liquid bulk streams and membrane surfaces, respectively, as represented below:
The individual mass transfer coefficient, based on a resistance-in-series model, in the gas feed (
), membrane (
), liquid feed (
), and CO
2 concentration variations are illustrated in
Figure 3. Equating the mass fluxes by the conservation law of mass in each region for three intervals, (
and (
as shown in Equation (8), leads to the overall heat transfer coefficient of the gas feed stream and MEA feed stream, respectively.
2.2. Concentration Polarization Coefficient
The concentration differences between two membrane surfaces associated with two gas and MEA bulk streams, respectively, result in the concentration polarization effect. Various factors govern the mass transfer resistance in membrane absorption modules. The concentration polarization coefficient
can be considered as a measure of the relative impact of the magnitude of the membrane mass transfer resistance, as indicated in
Figure 4. However, the concentration polarization effect could be diminished when turbulence promoters are introduced. The concentration polarization coefficient
is defined as follows:
Accordingly, both membrane surface concentrations (
and
) and the convective mass transfer coefficients (
and
) were obtained by equating Equations (3) and (6) (say
) as well as Equations (3) and (7) (say
), respectively. The concentration polarization effect was reduced and demonstrated by using the microscopic description in
Figure 4 with the implementation of a spiral-ring channel resulting in the amplified driving force concentration gradient (say
). Implementing spiral-ring channels was confirmed to achieve a higher permeate flux owing to disrupting the mass transfer boundary layer of flow characteristics near the membrane surface, where the intensive turbulence was strengthened to overwhelm the concentration polarization effect.
2.3. Design of Spiral-Ring Module
The experimental setup involved detailed fabrication of the spiral ring embedded within the annulus of a concentric circular tube, as illustrated in
Figure 5. Turbulence intensity enhancement was achieved by integrating spiral rings as eddy promoters with various spiral ring pitches into the flow channel, effectively disrupting mass transfer boundary layers near the membrane surface within the MEA absorbent feed stream. This approach reduced concentration polarization and led to improvements in convective heat transfer coefficients and overall device performance.
Figure 5 provides a graphical representation of key components of the spiral-ring concentric membrane contactor. The experimental setup included an empty channel (without an embedded spiral wire) consisting of a 0.2 m long concentric tubular spiral-ring tube. Spiral ring pitches were fabricated using a photopolymer (light-activated resin), demonstrating stability without degradation during operational experimental runs. The spiral ring-filled annulus channel featured spiral rings with a cross-sectional area of 2 mm × 2 mm, serving as eddy promoters with varying spiral wire pitches. Both ascending (ranging from 1 cm to 3 cm and 2 cm to 3 cm baffled ring distances) and descending (ranging from 3 cm to 1 cm and 3 cm to 2 cm baffled ring distances) spiral ring pitches were tested with MEA flowing through channels of lengths 0.63 m and 0.39 m, respectively. The inner lumen tube, made of light-activated photopolymer resin (He-Yi Precision Co., Taoyuan, Taiwan), had an inside diameter of 1.3 cm and outside diameter of 1.5 cm. It was fabricated using 3D printing technology, which enabled up to 70% perforating holes, a significant advancement compared to traditional manufacturing methods [
43], utilizing a layer-by-layer machining process as depicted in
Figure 5a. This highlights the capability of 3D printing to produce complex geometric shapes for tubular conduits [
44], tailored precisely to the manufacturing process requirements. The inner lumen tube was wrapped with a hydrophobic PTFE/PP composite membrane (J020A330R, ADVANTEC, Toyo Roshi Kaisha, Ltd., Tokyo, Japan) featuring a nominal pore size of 0.2 µm to facilitate gas diffusion through the membrane. It possesses a porosity of 0.72 and a thickness of 130 µm (PTFE 98 µm and PP 32 µm), as depicted in
Figure 5b. The spiral ring-filled channel was created by embedding concentric spiral-ring rods around the circumference of the membrane surface on the outer side of the inner lumen tube. These rods were arranged with ascending or descending baffled ring distances, as illustrated in
Figure 5c. For the MEA feed stream, the annulus channel dimensions were constructed using an effective 0.2 m long concentric tubular acrylic tube with an inside diameter of 1.9 cm and an outside diameter of 3.0 cm (with a channel thickness of 2 mm), as indicated in
Figure 5d. In
Figure 5e, the spiral-ring annulus channel, utilizing descending spiral ring pitches such as 3 cm to 1 cm, is displayed. This configuration demonstrates various inner and outer tube radii used in modeling CO
2 absorption in concentric membrane contactors, illustrated in
Figure 5f. Photographic images in
Figure 5g,h showcase the membrane tube with spiral wire pitches of 1 cm to 3 cm and 3 cm to 2 cm, respectively. These visuals provide a clear representation of the experimental setup and configuration used in the study.
2.4. Model Building by Using Macroscopic Description
The one-dimensional mathematical modeling equations were derived by presenting the mass flux diagram in a finite control element according to the conservation law under steady-state operations, as illustrated by following the schematic diagram of plug flow description in
Figure 6 for both CO
2/N
2 and MEA feed streams, respectively.
Equations (10) and (11) were derived by using the mass balances with the plug flow description for CO2 absorption in the MEA absorbent stream while the coordinate along z is the flowing direction. The plug flow description deals with only the largest concentration gradient in the mass transfer balance equation while neglecting all diffusion terms. The numerical scheme was solved using the 4th order Runge–Kutta method along the module’s length, while the marching solutions of the CO2 concentrations in both CO2/N2 and MEA feed streams were obtained to determine the CO2 absorption flux and absorption flux improvement as well.
2.5. Assessment of Mass Transfer Rate Enhancement
The assessment of mass transfer enhancement using spiral-ring concentric circular membrane contactors was carried out and evaluated using ascending or descending spiral ring pitches and compared to the no-spiral-ring condition. A mass transfer enhancement factor
[
29] was defined as the ratio of the mass transfer rate improvement of the module with the embedded spiral ring to that of the module without a spiral-ring channel, which depends on inserting various spiral ring pitches and operating different flow configurations. The mass transfer coefficient was analyzed based on the extent of the mass transfer enhancement factor, which was lumped into the augmented mass transfer coefficients and expressed in terms of the effective Sherwood number as follows:
in which the effective Sherwood number
is defined as the module of inserting varying-spiral-ring-pitch channels while incorporating four dimensionless groups into Buckingham’s
theorem while the Sherwood number
is the membrane contactor with the no-spiral-ring channel under laminar flow operations, with the regressed correlation equation [
45] as:
in which
where
is the equivalent hydraulic diameter of the inserted spiral rings while
is the hydraulic diameter for laminar flow (no-spiral-ring channel).
2.6. Power Consumption Increment
This present study offers a possible investigation to utilize spiral-ring channel designs as turbulence promoters for membrane contactor applications. The individual in-depth impact contributes towards device performance improvement by using the spiral ring-filled channels along with the extra unavoidable power consumption. Further focused research based on economic consideration is needed to report the influence of spiral-ring channels. There is a need for specific understanding to evaluate the increased frictional loss by employing a spiral ring-filled channel in the concentric-tube membrane contactor module. The power consumption includes the contributions from both the gas side and MEA side for the innovative spiral ring-filled channel design, which can be developed by using the Fanning friction factor
for both laminar and turbulent flows [
46]:
This quantity comprises the pressure drop due to the friction losses in both feed streams, as given by Equation (15), in a concentric circular membrane contactor of known length. The average velocity and equivalent hydraulic diameter of each flow channel are calculated as follows:
The percentage increment in power consumption for the module with the spiral ring-filled channel as compared to the module with an empty channel is illustrated as the relative extents
where the subscripts of
spiral and
empty represent the modules using the spiral ring-filled channel and empty channel, respectively.
3. Membrane Absorption Experiments
The gas/liquid membrane contactor for CO
2 absorption by the MEA absorbent (Uni-Onward Corp., New Taipei, Taiwan) was conducted in an acrylic concentric tube scale setup, as illustrated in
Figure 7. A photo of the operating experimental apparatus is shown in
Figure 8.
The experimental setup involved injecting a gas mixture of CO2/N2 at 293 K into the inner lumen tube of a membrane absorption contactor, while the MEA absorbent solution flowed through the annulus channel. The aqueous MEA absorbent solution was heated to 303 K using a thermostat (G-50, DENG YNG, New Taipei, Taiwan) and controlled by a flow meter (MB15GH-4-1, Fong-Jei, New Taipei, Taiwan) and liquid pump (5IK40RA-A, ASTK Motor Co. Ltd., New Taipei, Taiwan) to regulate flow rates ranging from 5 to 10 cm3/s (5.0, 6.67, 8.33, 10.0 cm3/s). The MEA absorbent was prepared by diluting it with distilled water to a 30% mass concentration and it was then introduced into the shell side of the contactor at various feed rates. After contacting with the CO2/N2 gas mixture, the MEA absorbent containing CO2 was collected separately. Industrial-grade gas mixtures containing 30%, 35%, and 40% CO2 (balance N2) were mixed in a gas mixing tank (EW-06065-02, Cole Parmer Company, Vernon Hills, IL, USA) and adjusted using a mass flow controller (N12031501PC-540, Protec, Brooks Instrument, Hatfield, PA, USA) to maintain a steady flow rate of 5 cm3/s into the inner lumen side of the membrane module. The CO2 diffused through the microporous hydrophobic membrane pores into the MEA absorbent on the shell side of the contactor. All experiments were conducted with concurrent flows and single-throughput operations. The CO2 exiting the membrane lumen-side outlet was sampled and injected into column heating systems for rapid sample heating within a collection capillary tube. Gas chromatography (Model HY 3000, China Chromatograph Co., Ltd., Xinzhuang, New Taipei, Taiwan) with helium as a carrier gas and conventional thermal conductivity detectors (TCD) were used to analyze CO2 concentrations at steady state. The reproducibility of concentration measurements was monitored, ensuring accuracy within 5% to determine CO2 absorption efficiency.