Augmenting CO2 Absorption Flux Through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers

membranes

Article Augmenting CO2 Absorption Flux through a Gas–Liquid Membrane Module by Inserting Carbon-Fiber Spacers

Luke Chen 1 , Chii-Dong Ho 2,*, Li-Yang Jen 2, Jun-Wei Lim 3,* and Yu-Han Chen 2

1 Department of Water Resources and Environmental Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] 2 Department of Chemical and Materials Engineering, Tamkang University, Tamsui, New Taipei 251, Taiwan; [email protected] (L.-Y.J.); [email protected] (Y.-H.C.) 3 Department of Fundamental and Applied Sciences, HICoE-Centre for Biofuel and Biochemical Research, Institute of Self-Sustainable Building, Universiti Teknologi PETRONAS, Seri Iskandar, Perak Darul Ridzuan 32610, Malaysia * Correspondence: [email protected] (C.-D.H.); [email protected] (J.-W.L.); Tel.: +886-2-26215656 (ext. 2724) (C.-D.H.) Received: 18 September 2020; Accepted: 19 October 2020; Published: 22 October 2020

Abstract: We investigated the insertion of eddy promoters into a parallel-plate gas–liquid polytetrafluoroethylene (PTFE) membrane contactor to effectively enhance carbon dioxide absorption through aqueous amine solutions (monoethanolamide—MEA). In this study, a theoretical model was established and experimental work was performed to predict and to compare carbon dioxide absorption efficiency under concurrent- and countercurrent-flow operations for various MEA feed flow rates, inlet CO2 concentrations, and channel design conditions. A Sherwood number’s correlated expression was formulated, incorporating experimental data to estimate the mass transfer coefficient of the CO2 absorption in MEA flowing through a PTFE membrane. Theoretical predictions were calculated and validated through experimental data for the augmented CO2 absorption efficiency by inserting carbon-fiber spacers as an eddy promoter to reduce the concentration polarization effect. The study determined that a higher MEA feed rate, a lower feed CO2 concentration, and wider carbon-fiber spacers resulted in a higher CO2 absorption rate for concurrent- and countercurrent-flow operations. A maximum of 80% CO2 absorption efficiency enhancement was found in the device by inserting carbon-fiber spacers, as compared to that in the empty channel device. The overall CO2 absorption rate was higher for countercurrent operation than that for concurrent operation. We evaluated the effectiveness of power utilization in augmenting the CO2 absorption rate by inserting carbon-fiber spacers in the MEA feed channel and concluded that the higher the flow rate, the lower the power utilization’s effectiveness. Therefore, to increase the CO2 absorption flux, widening carbon-fiber spacers was determined to be more effective than increasing the MEA feed flow rate.

Keywords: carbon dioxide absorption; MEA solvent; mass transfer; Sherwood number; membrane contactor; concentration polarization

1. Introduction Biogas contains more than just hydrocarbons (typically ranging between 35% and 75% vol). Through processing and conditioning, the purity of biogas is upgraded, which adds to its value. Upgrading is the process of the separation of methane from carbon dioxide and other gases from biogas. In the biogas upgrading process, impurities such as CO2 (30–45%) and H2S (0.5–1%) are removed

Membranes 2020, 10, 302; doi:10.3390/membranes10110302 www.mdpi.com/journal/membranes Membranes 2020, 10, 302 2 of 21 down to a level that satisfies specifications for biogas production or pipeline transport. Flue gases from fossil fuel combustion contain CO2 that needs to be removed in order to reduce greenhouse gas emissions. Of all these applications, absorption (physical or chemical) is the most common purification technology for gas separation. Many past CO2 absorption studies have focused on solvent development, aiming to optimize solvent formulation and achieve the lowest possible energy requirement in an efficient, stable, and environmentally friendly process [1,2]. Membrane separation technology has been widely applied to gas absorption and metal ion removal because of its simplicity, its low consumption of energy, the required pressure, and the possibility of using low-grade energy sources [3]. Ramakula et al. [4] investigated the membrane technique that is used to separate radioactive metal ions in many separation processes such as liquid/liquid and gas/liquid systems. The mass transfer behaviors of membrane consisting of Knudsen diffusion, molecular diffusion, surface diffusion, and viscous flow, referred to as the dusty gas model, have been studied by many researchers, and Knudsen molecular diffusion transition models [5,6] have been widely and successfully applied to express mass flux [7,8]. The membrane system’s simple configuration is easy for continuous operations, modulation arrangement, and scale-up extrapolation. The application of membrane contactors to the CO2 absorption process allows soluble gas mixture components to be selectively absorbed during a chemical reaction on the membrane’s surface in its liquid phase [9–11]. The durability and reusability of some materials such as PMSQ aerogel and Al2O3/SiO2-FAS for CO2 absorption were proven by Lin et al. [12]. The membranes of hybrid silica aerogels and highly porous PVDF/siloxane nanofibrous have been combined to enhance CO2 absorption flux considerably [13]. Microporous hydrophobic membrane devices act as a gas absorber when gas flows on one side and diffuses through the membrane pores while the amine solution flows on the other side in direct contact with the membrane surface [14]. The application of a gas-absorption membrane contactor aims to overcome operational limitations such as conventional packed columns, which suffer from liquid channeling, flooding, entrainment, and foaming [15]. Rongwong et al. [16] provided a better demonstration of the simultaneous removal of CO2 and H2S in the gas-absorption operations of membrane than conventional gas-absorption processes. The separation efficiency depends on the distribution coefficient of gas solute in both gas and liquid phases [17]. The membrane absorption method associated with the advantages of chemical absorption and the membrane separation technique allows us to selectively absorb the soluble gas mixture components in the solvent on the membrane surface [18]. Moreover, the advantage of a higher specific area can compensate for the disadvantages in the membrane contactor of an additional mass transfer resistance and control pressure due to the membrane’s presence in the contacting phases [19]. Concentration polarization builds up concentration gradients in the absorbent stream, leading to a decreased mass transfer rate [20] due to the diffusion and reaction occurring at the membrane–liquid interface, and thus decreasing the mass flux [21]. The concentration polarization effect plays a vital role in reducing transmembrane mass flux in the flat sheet membrane contactor system, as reported in the most studied configuration of the direct contact membrane absorption system. Kim et al. [22] conducted an experimental work in which they created a lab-scale module of enhanced CO2 absorption flux by conditioning membrane materials of both hydrophobic (bulk) and hydrophilic (surface) properties in order to simultaneously avoid wetting the solution and fouling the enzymes. Various approaches have been proposed to reduce the concentration polarization effect using eddy promoters in spacer-filled channels [23]. A prospective strategy proposing an alternative [24] included breaking down the laminar sublayer in a turbulent boundary layer region to destroy the viscous laminar sublayer adjacent to the absorber plate, and adding carbon-fiber spacers into the flowing channel. Moreover, Ho et al. [25] pointed out that if an eddy is only created close to the membrane surface where the mass transfer takes place, it should not be overly disturbed and should avoid exceptional power consumption. Santos et al. [26] explored how absorption efficiency in a parallel-plate gas–liquid polytetrafluoroethylene (PTFE) membrane contactor was enhanced by inserting eddy promoters, as compared to those of empty Membranes 2020, 10, 302 3 of 21 channel devices. The current design’s advantage by inserting eddy promoters is evident and provides a remarkable opportunity for the absorption efficiency of parallel-plate gas–liquid PTFE membrane contactor to be improved by a maximum of 80%, and the turbulence enhancement effectively raised to a higher convective mass-transfer coefficient [27]. Theoretical and computational studies have also been conducted to model the system of the CO2 absorption analogized to the membrane distillation system except for the occurring reactions [28]. Testing was carried out mathematically and experimentally to identify the influences of the mass-transfer rate of CO2 absorption efficiency based on physical absorption [29]. Research and development efforts can be made in the membrane contacting field employing spacer-filled channels [30] to minimize the concentration polarization effect to achieve higher mass transfer rates. The advantage of chemical absorption technology is that it has been commercialized for many decades with various and mixed amines [31], used widely to enhance CO2 capture efficiency and reduce the regeneration cost [32]. In the present work, we used a theoretical model and performed experimental work to investigate CO2 absorption into monoethanolamide (MEA) using a parallel-plate gas–liquid PTFE membrane contactor. The microporous hydrophobic membrane device acts as a gas absorber for which the gas flows on one side and diffuses through the membrane pores while the amine solution flows on the other side, directly in contact with the membrane surface. The mass-balance and chemical reaction equations were formulated to simulate the hydrophobic porous membrane contactor system [33]. The turbulent intensity induced by inserting carbon-fiber spacers in the MEA absorbent flow channel was examined. A one-dimensional steady-state theoretical model was developed to simulate a more efficient absorption module for CO2 by amine solutions as chemical absorbents under concurrent-flow and countercurrent-flow operations. The channel’s mass transfer enhancement factor with the insertion of carbon-fiber spacers was correlated with the experimental data. The trade-off between increasing CO2 permeates and the power utilization’s effectiveness was evaluated to find the trend of economic feasibility in channel designs and system operations.

2. Theoretical Model

The following assumptions regarding the CO2 absorbed by the MEA absorbent through a membrane system were made:

1. The system is operated under normal pressure conditions; 2. The membrane is a porous hydrophobic media and is not wetted by the liquid MEA; 3. The membrane material does not react with liquid MEA; 4. Henry’s law applies to the interface between the gas phase and the liquid phase.

Three mass transfer resistances were built up across the membrane between the two bulk flows in series, as illustrated in Figure1. The first resistance is the solute gas transfers into the membrane surface from the bulk gas flow. The second resistance is the transmembrane mass flux via Knudsen diffusion and molecular diffusion through the membrane pores. The third resistance is the gas solute that reaches the membrane–liquid interface and reacts with the MEA absorbent. The mass transfer across the concentration boundary layers to and from the membrane surfaces was determined through convective mass transfer coefficients and the dimensionless Henry’s law constant HC = C2/C1 = 0.73 [33]. Since the reaction is quick, resistance is controlled by a convective mass transfer that depends on the boundary layer’s flow regime of the MEA liquid stream. Membranes 2020, 10, 302 4 of 21 Membranes 2020, 10, x FOR PEER REVIEW 4 of 22

Membrane

Jg Jm Jl

C C Ca 1 Knudsen res. Molecular res. 2 Cb

FigureFigure 1. 1.Schematic Schematic diagram diagram ofof massmass transfer resistances in in a a gas gas–liquid–liquid membrane membrane contactor contactor..

TheThe mass mass transfer transfer in in the the gas gas phase phase ofof COCO22 is driven by by the the concentration concentration gradient gradient between between gas gas bulkbulk ﬂow flow and and membrane membrane surface surface on on the the gasgas sideside as depicted below: below:

J g = ka(Ca(g ) −C1(g) ) (1) Jg = ka C C (1) a(g) − 1(g) The mass transfer in the membrane is driven by the concentration gradient between both membraneThe mass surfaces. transfer inFor the mass membrane transfer is drivenin the bymembrane, the concentration both Knudsen gradient diffusion between and both molecular membrane surfaces.diffusion For we massre considered transfer in[34 the]. The membrane, mass flux of both CO Knudsen2 can be evaluated diffusion using and a molecular membrane di permeationffusion were considered [34]. The mass flux of CO can be evaluated using a membrane permeation coefficient (c ) coefficient ( cm ) and the trans-membrane2 saturation partial pressure differences ( P ) of CO2 [35]: m and the trans-membrane saturation partial pressure differences (∆P) of CO2 [35]: dP K ex C2() K ex C2() J m = cm (P1 − P2 ) = cm (C1 − C2(g) ) = cm RT(C1 − ) = K m (C1 − ) (2) K0exC ( ) K0exC ( ) dP dC C H C 2 ` H C 2 ` J = c (P P ) = c (mC ea n C ) = c RT(C ) = K (C ) (2) m m 1 2 m 1 2(g) m 1 m 1 − dC Cmean − − HC − HC - + −5 The equilibrium constant Kex = [MEACOO ][H ]/{[CO2 ][MEA]}=1.2510 with the reduced + 5 equilibriumThe equilibrium constant constant K ' =KKex =[MEA]/[H[MEACOO+ ] is− ][ specifiedH ]/ [ C O at2 ][TMEA= 298 ]K = [31.256] for10 CO− with2 absorbed the reduced in ex ex +i } × equilibriumaqueous MEA constant absorbent.Kex0 = BasedKex[MEA on ]the/[H meanis free specified path of at theT = CO2982 moleculeK [36] for and CO 2theabsorbed membra inne aqueous pore MEAsize, absorbent. Knudsen diffusion Based onand the molecular mean free diffusion path of[21 the,37] COwere2 moleculeconsidered and to determine the membrane the membrane pore size, Knudsenpermeation diff usioncoefficient: and molecular diffusion [21,37] were considered to determine the membrane permeation coefficient: −1 −1 −1  1/ 2 −1   1 1   r  M    1 D  M   c =  +  = 1.064  w   + m w  1 m  ! 1  " 1/2# 1 " #1  (3) c c −  r MRT  − Y D  MRT − −  1K 1M   ε m  wm    1m ln mmε wm   cm = + = 1.064  +  (3) cK cM  τδm RTm Ym δmτ RTm  | |ln where tortuosity (  ) can be estimated using the porosity of the membrane [38] as where tortuosity (τ) can be estimated using the porosity of the membrane [38] as  =1/ (4)

The CO2 mass transfer from the membraneτ = surface1/ε to the liquid phase is driven by the CO2(4) concentration gradient between the membrane surface and the liquid bulk flow and is depicted as The CO2 mass transfer from the membrane surface to the liquid phase is driven by the CO2 K C C concentration gradient between the membrane surfaceex 2() andb the()  liquid bulk ﬂow and is depicted as J = kb  −  (5)  H H   C C ! K0exC2(`) Cb(`) By continuity, the mass fluxes fromJ` = thekb gas feed side, transferring through the membrane and(5) HC − HC then being absorbed into the liquid feed side, are all equal in number as depicted below: By continuity, the mass ﬂuxes from the gas feed side, transferring through the membrane and J = J = J = J i = carbon, empty (6) then being absorbed into the liquidi g feed side,m are all equal in number as depicted below:

The CO2 concentration variation from the gas phase to the liquid phase through the membrane is illustrated in Figure 2. Ji = Jg = Jm = J` i = carbon, empty (6)

Membranes 2020, 10, 302 5 of 21

The CO2 concentration variation from the gas phase to the liquid phase through the membrane is illustratedMembranes 20 in20 Figure, 10, x FOR2. PEER REVIEW 5 of 22

ωg ωm ω

Membrane

C2(g)

C2()

Gas side Liquid side

Figure 2. Schematic representation of the CO2 concentration variation from the gas phase to the liquid Figure 2. Schematic representation of the CO2 concentration variation from the gas phase to the liquid phasephase through through the the membrane. membrane.

With the continuity of mass flux depicted in Equation (6), the CO2 concentrations in the buck With the continuity of mass ﬂux depicted in Equation (6), the CO2 concentrations in the buck ﬂow flow of both gas and liquid streams and the CO2 concentrations on the membrane surfaces of both of both gas and liquid streams and the CO2 concentrations on the membrane surfaces of both gas and liquidgas and sides liquid can besides related can be by related Equations by Eq (7)uations and (8). (7) and (8). K C km  ex 2() ! Ca(g) = C1(g) + kmC1(g) − K0exC2(`)  (7) Ca(g) = C1(g) +ka C1(g) H  (7) ka − H

C KK CC K CC ! bb((`)) ex0ex 22((`)) kkmm 0exex 22((`)) = − C1(gg) −  (8) (8) H HH −kkbb − HH 

SubtractingSubtracting Equation Equation (7) (7 from) from Equation Equation (8), (8 one), one can can obtain obtain Equation Equation (9) which(9) which can can be usedbe used to derive to a concentration polarization coefficient γm as defined in Equation (10). The concentration polarization derive a concentration polarization coefficient γm as defined in Equation (10). The concentration coefficient γ was used to measure the dominance of mass transfer resistances in the CO /MEA polarizationm coefficient was used to measure the dominance of mass transfer resistances in2 the absorption system. A higher γm value represents less mass transfer resistance. The concentration CO2/MEA absorption system. A higher γ value represents less mass transfer resistance. The polarization is controlled by the boundarym layers of both gas and liquid streams. To reduce the concentration polarization is controlled by the boundary layers of both gas and liquid streams. To undesirable influence on the permeate flux, one needs to disrupt the boundary layers to increase the reduce the undesirable influence on the permeate flux, one needs to disrupt the boundary layers to concentration polarization coefficient γ to reduce the mass transfer resistances. increase the concentration polarizationm coefficient to reduce the mass transfer resistances. ! ! Cb(`) K0exC2(`) km km Cb() = Kex C2()   + k +k  Ca(g) C1(g) 1 m m  (9) Ca(g) −− H = C1(g) − H  1+ ka + kb  (9) H  H   ka kb  K0exC2(`) C1(g) H − kakb γ = K ex C2()  = (10) m  C  C1(g ) − b(`) kakb + kmka + kmkb  C ( ) H   a g − H  ka kb  m = = (10) The CO /MEA membrane absorption C moduleb()  configurationka kb + kmka + includeskmkb two parallel-plate flow 2 C −   a(g )  channels separated by a membrane as a gas–liquidH  contactor. The system operates under both concurrent-flow and countercurrent-flow operations. The module has dimensions of length L and The CO2/MEA membrane absorption module configuration includes two parallel-plate flow channels separated by a membrane as a gas–liquid contactor. The system operates under both concurrent-flow and countercurrent-flow operations. The module has dimensions of length L and

Membranes 2020, 10, x FOR PEER REVIEW 6 of 22 Membranes 2020, 10, 302 6 of 21

2 width W. The spaces between the membrane and the left or right plate ( H a or H b ) are where the CO gaswidth feedW .or The MEA spaces liquid between absorbent the membraneflow through, and respectively, the left or right as shown plate (inHa Figureor Hb) 3. are where the CO2 gas feed or MEA liquid absorbent ﬂow through, respectively, as shown in Figure3.

Ha Hb Ha Hb

δ δ

z+dz z+dz

L CO2 L CO2

z z

Carbon Carbon Fiber Z Fiber Z PTFE PTFE

CO2,N2 MEA CO2,N2 MEA (a) concurrent-flow operations (b) countercurrent-flow operations

Figure 3. Schematic representationrepresentation of of CO CO2 absorption2 absorption by by monoethanolamide monoethanolamide (MEA) (MEA for) concurrent-for concurrent and- andcountercurrent-flow countercurrent-flow operations operations in parallel-plate in parallel-plate membrane membrane gas–liquid gas–liquid contactors. contactors (a). concurrent-flow (a) concurrent- flowoperations; operations (b) countercurrent-flow; (b) countercurrent- operations.flow operations.

The mass balances balances of gas gas feed feed and and liquid liquid absorbent absorbent streams streams made made within within a a finite finite system system element element respectively give: respectively give: " !# dCa W K0exC2(`) W = − Km C = − [Kmγm(Ca C )] (11) dC −W   1 Kex C2  −W b dza Qa  − HC()  Qa − = Km C1 −  = Km m (Ca − Cb ) (11) dz Q  H  Q a  WH ( k C C)  a K C dCb  CO2 b W 0ex 2(`) = − + Km C1 dz Qb Qb − HC WH( k C ) WH (−k − CCO2) b W  K C  (12a) dCb = CO2 b +W [Kmγm(Ca ex C2b()]) = Qb + QbK C −   m  1 −  dz Qb Qb  HC  for concurrent-flow  operations  WH (−kCO Cb ) W (12a) (WH2)k C K C dC= b CO2 +b WK m m (Ca −0Cex b 2)(`) = Q Q Km C1 dz b Qb − bQb − HC WH(k C ) CO2 b W (12b) for= concurrent-flow[ Koperationsmγm(Ca Cb)] Qb − Qb − for concurrent-flow operations ()WH k C Kex C2 dCb CO2 b W ( ) where z is the coordinate along= with the fluid flowing −KC direction,m 1 − and Equations (11), (12a) and (12b) are dzQQ H b b C the mass balances for the gas and liquid phases of CO2 in MEA absorbent under concurrent-flow and WH (kCO Cb ) W (12b) countercurrent-flow operations. = The CO2 concentrations− K  in(C the− C gas) feed stream, MEA liquid stream, Q Q m m a b and membrane surfaces along the module’sb lengthb were solved using the fourth-order Runge–Kutta method to determine the convective mass transfer coefficient. Hence, the CO2 absorption flux for countercurrent-flow operations was obtained. where z is the coordinate along with the fluid flowing direction, and Equations (11), (12a) and (12b) are the mass balances for the gas and liquid phases of CO2 in MEA absorbent under concurrent-flow and countercurrent-flow operations. The CO2 concentrations in the gas feed stream, MEA liquid

Membranes 2020, 10, x FOR PEER REVIEW 7 of 22 stream, and membrane surfaces along the module’s length were solved using the fourth-order RungeMembranes–Kutta2020, 10 method, 302 to determine the convective mass transfer coefficient. Hence, the 7 CO of 212 absorption flux was obtained. For the membrane contactor, using empty channels under laminar flow, the commonly used correlationFor the [39 membrane] is: contactor, using empty channels under laminar flow, the commonly used correlation [39] is: 0.8 0.330.33 Shlamlam =0.0230.023ReRe Sc (13(13)) TheThe extent extent of of mass mass-transfer-transfer rate rate enhancement enhancement is frequently is frequently expressed expressed by an byenhancement an enhancement factor, wfactor,hich is which the ratio is the of ratiothe improved of the improved channel’s channel’s mass transfer mass coefficient transfer coe toffi thatcient of to the that empty of the channel. empty Similarly,channel. Similarly, the enhancement the enhancement factor for factor the mass for the transfer mass transfer coefficient coeffi cancient be candefined be defined for membrane for membrane gas– liquidgas–liquid contactors contactors using using the inserti the insertionon of carbon of carbon-fiber-fiber spacers spacers instead instead of ofthe the empty empty channel channel as as follows follows:: k d ShEE = kbbdhh, ,carboncarbon =  EESh Sh = = α Shlamlam (14(14)) DDbb

TheThe Sherwood Sherwood number number of inserted of insert carbon-ﬁbered carbon spacers-fiber spacerscan be incorporated can be incorporated into four dimensionless into four dimensionlessgroups using Buckingham’s groups using Buckinghamπ theorem: ’s  theorem:

E dh,carbon Sh = f (dh,carbon ,Re,Sc) ShE = f ( , Re, Sc) (15(15)) dh,empty dh,empty where dh,c arbon is the equivalent diameter of inserted carbon-fiber spacers while d is the where dh,carbon is the equivalent diameter of inserted carbon-ﬁber spacers while dh,empty ish the,empty hydraulic hydraulicdiameter ofdiameter the empty of the channel, empty as channel, shown inas Figureshown4 in. Figure 4.

Membrane Carbon fiber plate + Spacer Nylon fiber +Spacer Acrylic plate Acrylic plate

Nylon fiber Carbon fiber plate

FigureFigure 4. ComponentsComponents of of a a gas gas–liquid–liquid membrane membrane contactor contactor for for the the empty empty channel channel and and the the channel withwith the insert inserteded carbon carbon-fiber-fiber spacers spacers.. The expenses linked to the increase in power consumption are inevitable because the The expenses linked to the increase in power consumption are inevitable because the device was device was inserted with carbon-fiber spacers into the MEA flowing channel as eddy promoters. inserted with carbon-fiber spacers into the MEA flowing channel as eddy promoters. Power Power consumption due to the friction losses of a gas–liquid membrane contactor, which includes consumption due to the friction losses of a gas–liquid membrane contactor, which includes the the contributions from the gas side and the MEA side, can be determined using the Fanning friction contributions from the gas side and the MEA side, can be determined using the Fanning friction factor factor fF [40]: f [40]: F = + = Hi Qa ρCO 2 `w f ,CO 2 Qb ρMEA`w f ,MEA i carbon, empty (16) H = Q  w + Q  w i a CO 2 f ,CO 2 b MEA2 f ,MEA i = carbon, empty (16) 2 fF,jvj L `w f ,j = , j = CO2, MEA (17) dh,i2 2 fF, jv j L The average velocity and equivalentw = hydraulic, diameterj = CO of,MEA each flow channel are estimated(17) as f , j d 2 follows: h,i q q = a = b The average velocity andν COequivalent2 hydraulic, νMEA diameter of each flow channel are estimated(18) as (HW) (HW D1W1N1) follows: − 4(HW) 4(HW D W N ) = = 1 1 1 dh,CO2 , dh,MEA − (19) 2(H + W) 2(H + W + D1N1) Membranes 2020, 10, 302 8 of 21

MembranesThe 20 Fanning20, 10, x FOR friction PEERfactor REVIEW can be estimated using a correlation based on the channel’s aspect9 of 22 ratio (β = H/W)[41]:

The precision index of experimental uncertainty of each individual measurement of S is 2 3 4 5 i fF = 24 1 1.3553β + 1.9467β 1.7012β + 0.9564β 0.2537β /Re (20) calculated as described by− Moffat [42] directly −from the experimental −runs as follows:

1/2 The relative extents IE and IP of massN ﬂuxexp enhancement2 and power consumption increment, ()exp − cal respectively, were illustrated by calculatingS = the percentage increase in the device with the inserted(24) i  carbon-ﬁber spacers, based on the device of thei=1 emptyNexp channel:−1

and the uncertainty of the reproducibility ofJcarbon molarJ fluxesempty is associated with the mean precision index IE = − 100% (21) Jempty × S S = i i (25) Hcarbon HemptyN IP = − exp 100% (22) Hempty × whereThe the mean subscripts precision “carbon” index andof the “empty” experimental represent measurements the channels of where absorption carbon-fiber efficiency spacers evaluated were −3 −2 insertedfor concurrent and the-flow empty and channel. countercurrent-flow operations is 8.8210  S 1.2010 . i The absorption flux’s experimental results prove the theoretical predictions’ validity by defining 3. Experimental Study the accuracy [42] between the numerical solutions and the experimental results as follows: A schematic diagram of the experimental setup of the parallel-plate gas–liquid membrane Nexp contactor for CO absorption by an MEA absorbent1  iscal assembled,− exp as illustrated in Figure5. A photo 2 E(%)100= (26) of the real experimental setup is shown inN Figureexpexpi=1 6. With acrylic plates used as the outside walls, the module contains two types of flow channels: the empty channel and the channel where carbon-fiber  exp  spacerswhere weree x p indicate inserteds the into theoretical the MEA feed prediction flow. The of emptycal , channelwhile N is constructed and e x p withare thea 0.2 number mm nylon of

fiber-routedexperimental supporting measurements sheet. Theand carbon-fiber the experimental spacer is data constructed of c a l with. The a 1 error mm-thick analysis carbon-fiber of the sheetexperimental with open measurements slots among a parallel determined carbon-fiber by Eq stripuation of 2 or(2 36) mm for width both placed analytical on the liquid model MEAs is side3.21 of E the5 membrane.81. acting as eddy promoters.

(A) Silicon spacer

(B) Supporting sheet

(D) Acrylic plate

(E) Flow meter

(F) Flow controller

(G) Gas mix adapter T T

Amine (H) Gas Cylinder

Amine T T (I) Chromatograph

(J) Thermostatic tank

N2 CO2 N CO 2 2 (a) concurrent-flow operations (b)countercurrent-flow operations

Figure 5. Experimental setup for parallel-plate membrane gas–liquid contactors. (a) concurrent-ﬂow Figure 5. Experimental setup for parallel-plate membrane gas–liquid contactors. (a) concurrent-flow operations; (b) countercurrent-ﬂow operations. operations; (b) countercurrent-flow operations.

Membranes 2020, 10, 302 9 of 21 Membranes 2020, 10, x FOR PEER REVIEW 10 of 22

FigureFigure 6. 6. AA photo photo of of a a real real experimental setup. setup.

4. NumericalA gas Study mixture containing CO2 and N2 was introduced from the gas mixing tank to feed into one side of the membrane contactor. Aqueous amine (MEA) solution was chosen as the liquid absorbentAn iterative ﬂowing procedure, through as the illustrated other side in of theFigure membrane 7, was fromuseda to reservoir. calculate Two the parallel-plate CO2 absorption ﬂow flux

c a l forsub-channels concurrent (L-flow= 0.21m, operationW = 0.29m,. The calculatedH = 0.02m) CO separated2 absorption with aflux gas–liquid was membrane, then compare contactord with made of hydrophobic polytetrafluoroethylene (PTFE) membrane (ADVANTEC, Tokyo, Japan) were experimental CO2 absorption flux e x p to check the convergence of the initial guess of the convective conducted as the experimental setup. The hydrophobic polytetrafluoroethylene (PTFE) membrane mass(ADVANTEC) transfer coefficients with a nominal Kb in the pore liquid size phase of 0.1,. porosityObtaining of 0.72,the convective and thickness mass of 130 transferµm was coefficients used. Kb, oneThe may experimental apply the runs Range were–Kutta carried scheme out for various to solve MEA Equations feed flow (11 rates), (12 withina), and the (12 rangeb) to of obtain 5~10 cm the3/s, CO2 3/ concentrationwhile the gasdistribution flow rate was not controlledonly in the at 5gas/liquid cm s with buck two inletflows CO but2 concentrations also on the membrane of 30% and 40%,surfaces of bothrespectively. the gas and The liquid CO2 concentration sides under in concurrent the gas outlet- and stream countercurrent was measured-flow using operations, gas chromatography respectively. In addition(Model HYto the 3000 initial Chromatograph, guess of the China convective Corporation, mass Newtransfer Taipei, coefficients Taiwan). Some Kb in experiments the liquid phase were for concurrentregulated-flow to control operation an appropriate calculation pressure, an additional gradient toguess avoid of bubbling CO2 concentration for both modules—that at the inlet of of the MEA feed emptyCb,j=n needs channel to andbe specified that of the as channel zero for with countercurrent the inserted carbon-fiber-flow operation spacers. calculation, as illustrated in The experimental measurements of absorption efficiency, ω were defined as Figure 8. Both experimental CO2 mass flux and CO2 concentration at the inlet of MEA feed Cb,j=n = ! 0 were used to check the convergence of the iterativeC Cout calculation via the shooting method for the ω(%) = in − 100 (23) calculation of countercurrent-flow operation. WhenCin the ×iterative calculation is converged, the CO2 concentrations on the membrane surfaces and mass transfer coefficients Kb were obtained, and the The precision index of experimental uncertainty of each individual measurement of Sωi is theoretical CO2 mass flux and CO2 absorption efficiency were then also obtained. Comparisons were calculated as described by Moffat [42] directly from the experimental runs as follows: made between the CO2 absorption efficiency of the channel where carbon-fiber spacers were inserted  1/2 and that of the empty channel under both concurrentNexp - and 2countercurrent-flow operations. X (ωexp ωcal)  =  −  Sωi   (24)  Nexp 1   i=1 − 

and the uncertainty of the reproducibility of molar ﬂuxes is associated with the mean precision index

S = ωi Sωi p (25) Nexp

The mean precision index of the experimental measurements of absorption efficiency evaluated for concurrent-flow and countercurrent-flow operations is 8.82 10 3 S 1.20 10 2. × − ≤ ωi ≤ × − The absorption flux’s experimental results prove the theoretical predictions’ validity by defining the accuracy [42] between the numerical solutions and the experimental results as follows:

Nexp 1 X ωcal ωexp E(%) = − 100 (26) Nexp ωexp × i=1

Membranes 2020, 10, 302 10 of 21

where ωexp indicates the theoretical prediction of ωcal, while Nexp and ωexp are the number of experimental measurements and the experimental data of ωcal. The error analysis of the experimental measurements determined by Equation (26) for both analytical models is 3.21 E 5.81. ≤ ≤ 4. Numerical Study

An iterative procedure, as illustrated in Figure7, was used to calculate the CO 2 absorption flux ωcal for concurrent-flow operation. The calculated CO2 absorption flux was ωcal, then compared with experimental CO2 absorption flux ωexp to check the convergence of the initial guess of the convective mass transfer coefficients Kb in the liquid phase. Obtaining the convective mass transfer coefficients Kb, one may apply the Range–Kutta scheme to solve Equations (11), (12a), and (12b) to obtain the CO2 concentration distribution not only in the gas/liquid buck flows but also on the membrane surfaces of both the gas and liquid sides under concurrent- and countercurrent-flow operations, respectively. In addition to the initial guess of the convective mass transfer coefficients Kb in the liquid phase for concurrent-flow operation calculation, an additional guess of CO2 concentration at the inlet of MEA feed Cb,j=n needs to be specified as zero for countercurrent-flow operation calculation, as illustrated in Figure8. Both experimental CO 2 mass flux ωexp and CO2 concentration at the inlet of MEA feed Cb,j=n = 0 were used to check the convergence of the iterative calculation via the shooting method for the calculation of countercurrent-flow operation. When the iterative calculation is converged, the CO2 concentrations on the membrane surfaces and mass transfer coefficients Kb were obtained, and the theoretical CO2 mass flux and CO2 absorption efficiency were then also obtained. Comparisons were made between the CO2 absorption efficiency of the channel where carbon-fiber spacers were inserted and that of the empty channel under both concurrent- and countercurrent-flow operations. The mass transfer coefficients expressed by the Sherwood number and determined by the theoretical model were used to compare and correlate with the experimental data, as shown in Figure9. The enhanced factor αE derived from the correlation of the Sherwood number for the channel with the inserted carbon-fiber spacers is determined via a regression analysis below:

!2.334 dh,carbon αE = 0.008 ln (27) dh,empty

The correlated Sherwood numbers for the empty channel are in linear relation with the experimental data, as shown in Figure9. The results validate that the correlation is also applicable to the channel where carbon-fiber spacers of 2 mm and 3 mm widths were inserted. The correlated Sherwood numbers, as shown in Figure9, indicate that the mass transfer of the channel with 3 mm width carbon-fiber spacers inserted has a higher mass transfer than that of the channel with 2 mm width, and the mass transfer in the channels with the inserted carbon-fiber spacers is higher than that of the empty channel. Inserting carbon-fiber spacers disrupts the boundary layer on the membrane surface that reduces mass transfer resistance; hence, the permeate flux was enhanced. The larger the width of the carbon-fiber spacers inserted, the higher the turbulence intensity produced that results in a higher mass transfer or CO2 absorption flux. Membranes 2020, 10, 302 11 of 21 Membranes 2020, 10, x FOR PEER REVIEW 11 of 22

Input ρ, μ, km , DA , ka ,Ca,in , Cb,in , Ca,j=0 ,Cb,j=0,ω expexp.

Assume

n=0 n=0 Calculate C 1 , C 2 ,

Calculate C n , n 1 C2 Obtained

Calculate ,

Yes No Fourth-Order Runge- Kutta method

Calculate ,

Let C a , j =Ca, j + 1

Cb, j =Cb, j +1

Until j=nstep

Calculate ω cal .

Yes

Confirm

End

Figure 7.Figure Calculation 7. Calculation flow ﬂowchart chart for for determining determining CO22concentrations concentrations in gas in andgas liquidand liquid phases underphases under concurrentconcurrent-ﬂow-flow operations operations..

Membranes 2020, 10, 302 12 of 21 Membranes 2020, 10, x FOR PEER REVIEW 12 of 22

Input ρ, μ, km , DA , ka ,Ca,in , Cb,in , Ca,j=0 ,Cb,j=nstep,ω exp.

Assume

n=0 n=0 Calculate C 1 , C 2 ,

Calculate C n , n 1 C2 Obtained

Calculate ,

No Yes Fourth-Order Runge- Kutta method

Calculate ,

Let C a , j =Ca, j + 1

Cb, j =Cb, j +1

Until No j=nstep Cb,j=nstep=0

Yes

Calculate ω cal .

Yes

Confirm

End

FigureFigure 8. Calculation 8. Calculation flow ﬂow chart chart for for determining determining CO 22 concentrationsconcentrations in in gas gas and and liquid liquid phases phases under under councountercurrent-ﬂowtercurrent-flow operations operations..

The mass transfer coefficients expressed by the Sherwood number and determined by the theoretical model were used to compare and correlate with the experimental data, as shown in Figure 9. The enhanced factor  E derived from the correlation of the Sherwood number for the channel with the inserted carbon-fiber spacers is determined via a regression analysis below:

2.334  d   E = 0.008ln h,carbon  (27)    dh,empty 

Membranes 2020, 10, x FOR PEER REVIEW 13 of 22 surface that reduces mass transfer resistance; hence, the permeate flux was enhanced. The larger the widthMembranes of 2020the ,carbon10, 302 -fiber spacers inserted, the higher the turbulence intensity produced that results13 of 21 in a higher mass transfer or CO2 absorption flux.

9.0

8.5

8.0

cor

7.5

carbon fiber 7.0 3mm 2mm Empty channel

7.0 7.5 8.0 8.5 9.0 Sh exp Figure 9. Comparison of calculated and experimental Sherwood num numbersbers for the empty channel and the channels with didifferentﬀerent widths of carbon-ﬁbercarbon-fiber spacers.spacers.

5. Results and Discussions 5. Results and Discussions 5.1. Concentration Polarization 5.1. Concentration Polarization The concentration polarization dominates the mass transfer resistances on the boundary layers for The concentration polarization dominates the mass transfer resistances on the boundary layers both the gas and liquid streams, especially on the liquid side. With the predicted CO2 concentration for both the gas and liquid streams, especially on the liquid side. With the predicted CO2 distributions, the concentration polarization coefficients (γm) along the channel direction for various concentration distributions, the concentration polarization coefficients ( γm ) along the channel MEA feed flow rates and feed CO2 concentrations can be determined, as indicated in Figure 10. direction for various MEA feed flow rates and feed CO2 concentrations can be determined, as The higher the γm value, the smaller the mass-transfer resistance. According to the concentration indicated in Figure 10. The higher the value, the smaller the mass-transfer resistance. According polarization coefficients (γm) shown in Figure 10, we found a higher γm value resulting from the higher tofeed the flow concentration rate. The γ mpolarizationvalue increases coefficients when MEA ( ) feedshown flow in rates Figure increase 10, we but found decreases a higher in the reverse value resultingflow direction from ofthe the higher MEA feed inlet flow feed rate. owing The to the value concentration increases gradient when MEA decreasing feed flow between rates increase gas and butliquid decreases sides, since in the a higherreverse feed flow flow direction rate can of createthe MEA a higher inlet feed turbulent owing intensity to the concentration on the boundary gradient layer decreasingof the membrane between surface gas and to disruptliquid sides the occurrence, since a higher of concentration feed flow rate polarization. can create a Inhigher evaluating turbulent the intensityeffect offeed on the CO boundary2 concentration layer of on the concentration membrane surface polarization, to disrupt we found the occurrence a higher γ ofm concentrationvalue for 30% polarizationfeed CO2 concentration. In evaluating when the comparing effect of feed with CO the2 γconcentrationm of 40% feed on CO concentration2 concentration. polarization, The higher thewe foundfeed CO a higher2 inlet concentration value for 30% was, feed the biggerCO2 concentration the CO2 concentration when compar accumulateding with the on the of membrane 40% feed surface was anticipated, and hence, lower concentration polarization coefficients ( ) or a larger mass CO2 concentration. The higher the feed CO2 inlet concentration was, the bigger theγ mCO2 concentration accumulatedtransfer resistance on the weremembrane found, surface as shown was inanticipated, Figure 10 .and A similarhence, lower effect concentration of the feed flow polarization rate and coefficientsfeed CO2 concentrations ( ) or a larger on concentrationmass transfer polarizationresistance were coeffi foundcients, γasm shownwere found in Figure in concurrent- 10. A similar and countercurrent-flow operations. effect of the feed flow rate and feed CO2 concentrations on concentration polarization coefficients The concentration polarization coefficient γm values of the channels with the inserted carbon-fiber were found in concurrent- and countercurrent-flow operations. spacers of 3 and 2 mm width for feed CO2 concentration of 30% and 40% were compared to those of the device with the empty channel for both concurrent- and countercurrent-flow operations, as shown in Figure 11 for the same MEA feed flow rate Q = 8.33 10 6 m3/s. The higher feed CO b × − 2 concentration causes a larger concentration polarization on the membrane surface, as explained before. When comparing the concentration polarization coefficient γm value for the devices with the inserted carbon-fiber spacers of 3 or 2 mm width and those of the empty channel, we found that the γm values are in descending order from 3 to 2 mm, and then the empty channel. The comparison concludes that the wider the carbon-fiber spacer the larger the turbulence intensity, hence resulting in a smaller mass transfer resistance. In other words, the turbulence induced by the wilder carbon-fiber spacers on the membrane surface results in a more convective mass transfer to disrupt concentration polarization that leads to a higher γm value or a higher mass transfer rate. Membranes 2020, 10, x FOR PEER REVIEW 14 of 22

0.30 0.30 2

2 CO2 = 30 %

N /

/ CO = 30 % 2

2 2

MEA

CO CO

0.25

m m

 

0.20

0.20 Qb Qb 6.67 6.67 CO2 = 40 % CO = 40 % 8.33 8.33 2 0.15 10.0 10.0 0.00 0.00 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 z z Membranes 20202020,, 10,, x 302 FOR PEER REVIEW 1414 of of 22 21 (a) concurrent-flow operations (b) countercurrent-flow operations

Figure 10. Effects of the MEA flow rate and feed CO2 concentration on γm . (a) concurrent-flow 0.30 0.30

operations; (b) countercurrent-flow operations. 2

2 CO2 = 30 %

N /

/ CO = 30 % 2

2 2

MEA

CO CO The concentration polarization coefficient values of the channels with the inserted carbon- 0.25 fiber spacers0.25 of 3 and 2 mm width for feed CO2 concentration of 30% and 40% were compared to

those ofm the device with the empty channel for both concurrentm - and countercurrent-flow operations,   −6 b 8.33 10 3 2 as shown in Figure 11 for the same MEA feed flow rate0.20 Q = m /s. The higher feed CO concentration0.20 causes a larger concentration polarization on the membrane surface, as explained Qb Qb before. When comparing the concentration polarization coefficient value for the devices6.67 with the 6.67 CO2 = 40 % CO = 40 % 8.33 8.33 2 inserted carbon-fiber spacers of 3 or 2 mm width and those0.15 of the empty channel, we10.0 found that the 10.0 0.00 0.00 values 0.00are in0.03 descending0.06 0.09 order0.12 from0.15 0.183 to 0.212 mm, and0.00 then0.03 the emp0.06 ty0.09 channel.0.12 0.15 The 0.18comparison0.21 concludes that the wider the z carbon -fiber spacer the larger the turbulence intensity,z hence resulting in a smaller mass(a) concurrent transfer- flowresistance. operations In other words, the (turbulenceb) countercurrent induced-flow by operations the wilder carbon- fiber spacers on the membrane surface results in a more convective mass transfer to disrupt Figure 10. EffectsEffects of of the the MEA MEA flow flow rate rate and and feed feed CO22 concentrationconcentration on on γm .(. (a)) concurrentconcurrent-flow-flow concentration polarization that leads to a higher value or a higher mass transfer rate. operationsoperations;; ( b)) countercurrent countercurrent-flow-flow operations.operations.

The concentration0.55 polarization coefficient value0.55s of the channels with the inserted carbon- Carbon fiber channel Carbon fiber channel 2 fiber spacers0.50 of 3 and 2 mm width for feed2 CO concentration0.50 of 30% and 40% were compared to

3mm N 3mm

/ /

2 2

2 MEA

2mm N / those of the device with the empty channel forCO both concurrent2mm- and countercurrent-flow operations, 0.45 0.45 2 empty channel MEA empty channel CO −6 3 CO = 30 % CO2 = 30 % b 8.33 10 2 2 as shown in0.40 Figure 11 for the same MEA feed flow rate0.40 Q = m /s. The higher feed CO

concentration causes a larger concentration polarization on the membrane surface, as explained m m 0.35 0.35

 

before. When comparing the concentration polarization coefficient value for the devices with the 0.30 0.30 inserted carbon-fiber spacers of 3 or 2 mm width and those of the empty channel, we found that the 0.25 0.25 values are in descending order from 3 to 2 mm, and then the empty channel. The comparison 0.20 0.20 concludes that the wider theCO 2carbon = 40 % -fiber spacer the larger the turbulenceCO intensity,2 = 40 % hence resulting 0.00 0.00 in a smaller mass0.00 0.03transfer0.06 resistance.0.09 0.12 0.15 In other0.18 words,0.21 the 0.00turbulence0.03 0.06 induced0.09 0.12 by 0.15the wilder0.18 0.21 carbon- fiber spacers on the membranez surface results in a more convective z mass transfer to disrupt concentration polarization(a) concurrent that-flow leads operations to a higher value(b or) countercurrent a higher mass-flow transfer operations rate.

FigureFigure 11. EffectsEffects of thethe widthwidth of of carbon-fiber carbon-fiber spacers spacers and and CO CO2 concentration2 concentration on onγm .(a). concurrent-flow(a) concurrent- operations; (b) countercurrent-flow operations. flow operations0.55 ; (b) countercurrent-flow operations. 0.55 Carbon fiber channel Carbon fiber channel

0.50 2 0.50

5.2. CO2 Absorption3mm Flux Enhancement N 3mm

/ / 2 2

2 2 MEA

5.2. CO Absorption2mm Flux Enhancement N /

CO 2mm 0.45 0.45 2 empty channel MEA empty channel CO In addition to investigating the effects of the feed flow rate and the width ofCO carbon-fiber = 30 % spacers CO2 = 30 % 2 In addition0.40 to investigating the effects of the feed flow0.40 rate and the width of carbon-fiber spacers on concentration polarization, this study also measured, predicted, and compared the effects on CO2

on concentration polarization, this study also measured, predicted, and compared the effects on CO2 m m 0.35 0.35

 

absorption flux for both concurrent- and countercurrent-flow operations, as depicted in Figure 12. absorption flux for both concurrent- and countercurrent-flow operations, as depicted in Figure 12. As As expected,0.30 both the increase of the MEA feed flow rate0.30 and that of the width of the carbon-fiber expected, both the increase of the MEA feed flow rate and that of the width of the carbon-fiber spacers spacers results0.25 in more permeate flux. The measured CO0.252 absorption rate, concentration polarization

coefficient 0.20γm for various MEA feed flow rates, and feed0.20 CO2 concentration under concurrent- and countercurrent-flow operationsCO2 = 40 are % summarized in Tables1 and2, respectively.CO2 = 40A % relative increase of 0.00 0.00 permeate flux0.00IE was0.03 used0.06 to0.09 compare0.12 0.15 the0.18 permeate0.21 flux of0.00 the0.03 channel0.06 0.09 with0.12 carbon-fiber0.15 0.18 spacers0.21 to z z that of the empty channel. The comparison showed that the increased IE ranged from 19.6% to 34.7% and from 49.7%(a) to concurrent 80.0% for-flow the channeloperations with carbon-fiber(b spacers) countercurrent of 2 and-flow 3 mm operations widths, respectively. In general,Figure the11. Effects CO2 absorption of the width rate of enhancedcarbon-fiber by spacers the insertion and CO of2 concentration carbon-fiber on spacers . ( isa) moreconcurrent significant- in countercurrent-flowflow operations; (b) countercurrent operations than-flow in operations concurrent-flow. operations.

5.2. CO2 Absorption Flux Enhancement In addition to investigating the effects of the feed flow rate and the width of carbon-fiber spacers on concentration polarization, this study also measured, predicted, and compared the effects on CO2 absorption flux for both concurrent- and countercurrent-flow operations, as depicted in Figure 12. As expected, both the increase of the MEA feed flow rate and that of the width of the carbon-fiber spacers

MembranesMembranes 20202020,, 1010,, x 302 FOR PEER REVIEW 1615 of of 22 21

15 15

14 2 14

MEA

CO MEA 13 13 CO

12 12

11 11

10 5

x 10 10

9 9

8 8

7 CO2 = 30% 7 CO2 = 30% Carbon fiber Theo. Exp. Carbon fiber Theo. Exp. 6 3mm 6 2mm 3mm 5 empty channel 5 2mm empty channel 0.00 0.00 0.00 5 6 7 8 9 10 0.00 5 6 7 8 9 10 6 6 Q x10 Q x10 b b (a) concurrent-flow operations (b) countercurrent-flow operations

Figure 12. Effects of the MEA flow rate and carbon-fiber spacers’ width on CO2 absorption flux. Figure 12. Effects of the MEA flow rate and carbon-fiber spacers’ width on CO2 absorption flux. (a) (a) concurrent-flow operations; (b) countercurrent-flow operations. concurrent-flow operations; (b) countercurrent-flow operations. Table 1. Effects of operating condition and spacers’ width on γm for concurrent-flow operations. 5.3. Energy Consumption Inserted Carbon-Fiber Spacers 6 Empty Channel CinConcerningQb 10 the flow resistance caused by the2 mm insertion of carbon-fiber in 3 the mm MEA channel, 3× 1 (%) (m s− ) 5 5 5 which consumes moreJtheo 10 power, this studyJtheo 10 further evaluated the channelJtheo 10 design’s effectiveness by ×2 1 γm ×2 1 E (%) γm IE ×2 1 E (%) γm IE (mol m− s− ) (mol m− s− ) (mol m− s− ) comparing the ratio of increment of CO2 absorption flux to the increment of power consumption, 6.67 7.42 0.2450 9.27 3.52 0.3500 24.9 12.4 0.29 0.3709 67.1 I E / I P . The effect of the feed flow rate, the width of carbon-fiber spacers, feed CO2 concentration, and 30 8.33 8.39 0.2578 10.7 2.55 0.3527 27.5 13.7 1.14 0.3725 63.3 concurrent10.0-/countercurrent 8.84-flow 0.2630 operations 11.0 on 3.55 are 0.3566 summarized 24.4 in 14.0 Figure 1 1.603. The 0.3749 turbulence 58.4 promotor6.67 through the 8.75 insertion 0.1946 of carbon 10.5-fiber spacers 4.02 in 0.3122 both 20.0concurrent 13.1- and countercurrent 4.04 0.3482 49.7-flow operations40 8.33 aimed to 9.45 achieve 0.2062 the augmented 11.4 turbulence 0.34 0.3153 intensity 20.6 in 14.3 shrinking 0.17 concentration 0.3501 51.3 polarization10.0 layers and 9.79 enlarge 0.2109 the mass 12.2 transfer 0.80coefficient 0.3189 as 24.6 well, and 15.0 thus, the 2.26 absorption 0.3522 53.2 flux was enhanced.γ mThedata reason are the averagebehind value the ofdifference the parallel-plate is that gas–liquid the countercurrent membrane contactor-flow module.operations run with a larger concentration gradient between gas and liquid than the concurrent-flow operations do. A higher feed CO2 concentration gives a higher ratio. The increase of the MEA feed flow rate gives Table 2. Effects of operating condition and spacers’ width on γm for countercurrent-flow operations. a lower value of , which implies that increasing the CO2 absorption flux with the expense of power by increasing the MEA feed rate is a less effectiveInserted approach Carbon-Fiber than changing Spacers carbon-fiber spacer 6 Empty Channel Cin Qb 10 2 mm 3 mm widths. Comparing3× 1 the effectiveness of the concurrent- and countercurrent-flow operation, we found (%) (m s− ) 5 5 5 Jtheo 10 Jtheo 10 Jtheo 10 that the values×2 of1 theγ m countercurrent×2 1 -flowE (%) operationγm I E are all higher×2 1 thaE (%)n thoseγm ofI Ethe (mol m− s− ) (mol m− s− ) (mol m− s− ) concurrent6.67-flow operation. 7.11 Th 0.2426e comparison 9.58 reveals 4.34 that the 0.3407 countercurrent 34.7 12.8-flow operation 5.32 0.3653 can utilize 80.0 power30 to 8.33increase the 8.45 CO2 absorption 0.2578 flux 10.9 more effectively 6.09 0.3451 than 29.0 the concurrent 14.0-flow 6.67 operation 0.3679 65.5 can. The increase10.0 of CO2 8.80concentration 0.2614 gives 11.2a higher value 2.46 of 0.3493 27.3, which 14.4reflects that 4.43 this 0.3704 expense 63.6 of energy consumption6.67 8.65 is more 0.1882 effective 10.9 in increasing 12.3 0.2999 the absorption 26.0 13.8 flux. In 4.83other 0.3408words, 59.5 the percentage40 8.33 of enhancement 9.88 of 0.2124 the absorption 11.9 flux 0.97 is higher 0.3051 than 20.4 that 15.1 of the increment 5.16 0.3439 of energy 52.8 consumption.10.0 In fact 10.2, consideration 0.2162 of the 12.2 use of carbon 1.84- 0.3091fiber spacers 19.6 as turbulence 15.5 3.51 promotors 0.3463 when 52.0 making economicγm data analyses are the average creates value of two the parallel-plate conflicting gas–liquideffects: membrane the desirable contactor improvement module. of the absorption flux and the undesirable increment of power consumption. The power consumption increment is relatively higher at a higher MEA feed flow rate with an essentially large turbulence resulting in a higher mass transfer coefficient for the device where carbon-fiber spacers are inserted.

Membranes 2020, 10, 302 16 of 21

In fact, the higher deviation occurred at the lower feed flow rate due to the insensitivity of the flowmeter regulation, especially for Q = 6.67 10 6 m3s 1. However, the theoretical predictions’ b × − − validity for both operations is in the good agreement with the experimental results confirmed by the precision index of experimental uncertainty of each individual measurement.

5.3. Energy Consumption Concerning the flow resistance caused by the insertion of carbon-fiber in the MEA channel, which consumes more power, this study further evaluated the channel design’s effectiveness by comparing the ratio of increment of CO2 absorption flux to the increment of power consumption, IE/IP. The effect of the feed flow rate, the width of carbon-fiber spacers, feed CO2 concentration, and concurrent-/countercurrent-flow operations on IE/IP are summarized in Figure 13. The turbulence promotor through the insertion of carbon-fiber spacers in both concurrent- and countercurrent-flow operations aimed to achieve the augmented turbulence intensity in shrinking concentration polarization layers and enlarge the mass transfer coefficient as well, and thus, the absorption flux was enhanced. The reason behind the difference is that the countercurrent-flow operations run with a larger concentration gradient between gas and liquid than the concurrent-flow operations do. A higher feed CO2 concentration gives a higher IE/IP ratio. The increase of the MEA feed flow rate gives a lower value of IE/IP, which implies that increasing the CO2 absorption flux with the expense of power by increasing the MEA feed rate is a less effective approach than changing carbon-fiber spacer widths. Comparing the effectiveness of the concurrent- and countercurrent-flow operation, we found that the IE/IP values of the countercurrent-flow operation are all higher than those of the concurrent-flow operation. The comparison reveals that the countercurrent-flow operation can utilize power to increase the CO2 absorption flux more effectively than the concurrent-flow operation can. The increase of CO2 concentration gives a higher value of IE/IP, which reflects that this expense of energy consumption is more effective in increasing the absorption flux. In other words, the percentage of enhancement of the absorption flux is higher than that of the increment of energy consumption. In fact, consideration of the use of carbon-fiber spacers as turbulence promotors when making economic analyses creates two conflicting effects: the desirable improvement of the absorption flux and the undesirable increment of power consumption. The power consumption increment is relatively higher at a higher MEA feed flow rate with an essentially large turbulence resulting in a higher mass transfer coefficient for the device where carbon-fiber spacers are inserted. However, the higher absorption flux, in terms of IE/IP, indicates that a larger power consumption increment cannot create more absorption flux due to the relative rate of CO2 consumed by the limited equilibrium constant of the chemical reaction in the liquid side. Therefore, the improvement of absorption flux using the device with the inserted carbon-fiber spacers can compensate for the increment of power consumption more effectively than increasing the MEA feed flow rate would. As the IE/IP values decrease when the MEA feed flow rate increases, one may notice that a 6 3 comparatively smaller change of IE/IP values was observed, as the feed flow rate is over 8.33 10 m /s × − for both the carbon-fiber spacer with a width of 3 mm and that with a width of 2 mm. The same observation was also found for both concurrent- and countercurrent-flow operations. Note that the IE/IP ratio of the channel with carbon-fiber spacers of a 3 mm width is higher than that of the channel with a 2 mm width. The comparison also confirms that to increase the CO2 absorption flux, widening carbon-fiber spacers is more effective than increasing the MEA feed flow rate. Therefore, comparisons between the 2 mm and 3 mm carbon-fiber spacers were made, considering the effective utilization of power consumption relative to the increase of the CO2 absorption flux to indicate the trend of economic feasibility when inserting a wider carbon-fiber spacer for the specific MEA feed rates used in this study. Membranes 2020, 10, x FOR PEER REVIEW 17 of 22

However, the higher absorption flux, in terms of I E / I P , indicates that a larger power consumption increment cannot create more absorption flux due to the relative rate of CO2 consumed by the limited equilibrium constant of the chemical reaction in the liquid side. Therefore, the improvement of absorption flux using the device with the inserted carbon-fiber spacers can compensate for the increment of power consumption more effectively than increasing the MEA feed flow rate would. As the values decrease when the MEA feed flow rate increases, one may notice that a comparatively smaller change of values was observed, as the feed flow rate is over 8.3310−6 m3/s for both the carbon-fiber spacer with a width of 3 mm and that with a width of 2 mm. The same observation was also found for both concurrent- and countercurrent-flow operations. Note that the ratio of the channel with carbon-fiber spacers of a 3 mm width is higher than that of the channel

with a 2 mm width. The comparison also confirms that to increase the CO2 absorption flux, widening carbon-fiber spacers is more effective than increasing the MEA feed flow rate. Therefore, comparisons between the 2 mm and 3 mm carbon-fiber spacers were made, considering the effective utilization of power consumption relative to the increase of the CO2 absorption flux to indicate the trend of economic feasibility when inserting a wider carbon-fiber spacer for the specific MEA feed rates used

Membranesin this study.2020, 10 , 302 17 of 21

0.20 0.50

30% CO2 countercurrent flow 0.45 40% CO2 0.18 Carbon fiber Carbon fiber 2mm countercurrent flow 0.40 2mm 0.16 3mm 3mm 0.35 0.14 concurrent flow

0.30

P / I / 0.12 I /

E concurrent flow

E I I 0.25

0.10 0.20

0.08 0.15

0.10 0.00 0.0 5 6 7 6 8 9 10 0.00 Q x10 b 0.0 5 6 7 6 8 9 10 Q x10 b (a) ratio for 30% CO2 (b) ratio for 40% CO2

FigureFigure 13. 13.E Effectsﬀects ofof feedfeed ﬂowflow rate rate,, spacers spacers’’ width width,, and and feed feed CO CO2 concentration2 concentration on on IE/I.P (.(a) a) IE/IP ratioratio for for 30% 30% CO CO2;(2; b(b) )I E/IP ratio ratio for 40%for 40% CO 2.CO2.

6. Conclusions 6. Conclusions A parallel-plate gas–liquid PTFE membrane contactor where carbon-fiber spacers were inserted to A parallel-plate gas–liquid PTFE membrane contactor where carbon-fiber spacers were inserted be used as eddy promoters to enhance the CO2 absorption by MEA was investigated. The theoretical to be used as eddy promoters to enhance the CO2 absorption by MEA was investigated. The predictions of the enhancement of CO2 absorption by inserting carbon-fiber spacers were calculated theoretical predictions of the enhancement of CO2 absorption by inserting carbon-fiber spacers were and validated using experimental data, and the correlated expression of the Sherwood number was calculated and validated using experimental data, and the correlated expression of the Sherwood obtained. Thorough comparisons of the CO2 absorption efficiency for various MEA feed flow rates, number was obtained. Thorough comparisons of the CO2 absorption efficiency for various MEA feed CO2 feed concentrations, and carbon-fiber spacer widths under concurrent- and countercurrent-flow flow rates, CO2 feed concentrations, and carbon-fiber spacer widths under concurrent- and operationscountercurrent were- completed.flow operations The comparisonswere completed helped. The us comparisons to draw the helped following us to conclusions: draw the following conclusions: 1. The higher the MEA feed rate, the lower the feed CO2 concentration, and wider carbon-fiber

1. spacersThe higher result the in aMEA larger feed CO 2rate,absorption the lower rate the for feed concurrent- CO2 concentration, and countercurrent-flow and wider carbon operations.-fiber Aspacers maximum result of 80% in a enhancement larger CO2 inabsorption CO2 absorption rate for effi concurrentciency was- foundand countercurrent in the device where-flow carbon-fiberoperations. spacersA maximum were insertedof 80% enhancement compared to thatin CO in2 theabsorption empty channel efficiency device. was found in the 2. Thedevice CO2 whereabsorption carbon rate-fiber is higher spacers for were countercurrent inserted compared operation to thanthat in that the for empty concurrent channel operation. device. 2. TheThe CO CO2 absorption2 absorption flux rate is mainly is higher driven for bycountercurrent the overall CO operation2 concentration than that gradient for concurrent along the channeloperation. direction. The CO The2 absorption overall CO flux2 concentration is mainly driven gradient by the for overall countercurrent CO2 concentration operation isgradient higher than that for concurrent operation of the system.

3. The ratio of increment of the CO2 absorption flux to the increment of power consumption was used to evaluate the power utilization’s effectiveness in augmenting the CO2 absorption rate in this system. The evaluation concluded that the power utilization is more effective for the channel where carbon-fiber spacers of 3mm were inserted than that of 2mm, and the higher the feed MEA flow rate, the lower the effectiveness of the power utilization. To increase the CO2 absorption flux, widening the carbon-fiber spacers is more effective than increasing the MEA feed flow rate.

A new device in this study includes the desirable effect of raising turbulence intensity as an alternative strategy [28] to the CO2 absorption in MEA through the membrane contactor. Though the mass transfer mechanism in this gas–liquid membrane contactor could be analogized from that of the previous work [28], the manners of transport through the membrane module are somewhat different, including the chemical reaction. In this paper, only the CO2 absorption efficiency and power utilization effectiveness were evaluated by inserting carbon-fiber spacers as an eddy promoter in the MEA feed channel. The alternative absorbent, membrane material, and module design require further investigation. Membranes 2020, 10, 302 18 of 21

Author Contributions: Conceptualization, C.-D.H.; data curation, L.-Y.J.; validation, Y.-H.C.; writing—original draft, L.C.; Writing—review and editing, J.-W.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology of the Republic of China (Taiwan) for the financial support. Acknowledgments: The authors wish to thank the Ministry of Science and Technology of the Republic of China (Taiwan) for the financial support. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

3 C Concentration (mol m− ) 3 Cmean Mean value of C (mol m− ) 2 1 1 ck Membrane coefficient based on the Knudsen diffusion model (mol m− Pa− s− ) 2 1 1 cM Membrane coefficient based on the molecular diffusion model (mol m− Pa− s− ) 2 1 1 cm Membrane permeation coefficient (mol m− Pa− s− ) D1 Width of the inserting carbon-fiber spacers (m) 2 1 Db Diffusion coefficient of CO2 in MEA (m s− ) 2 1 Dm Diffusion coefficient of N2 and CO2 in the membrane (m s− ) dh,i Equivalent hydraulic diameter of channel (m), i = carbon, empty E Deviation of experimental results from the theoretical predictions fF Fanning friction factor H Channel height (m) HC Dimensionless Henry’s constant 1 Hi Hydraulic dissipate energy (J kg− ), i = carbon, empty IE Mass flux enhancement, defined by Equation (21) IP Power consumption relative index, defined by Equation (22) 2 1 Ji Molar flux (mol m− s− ) 1 ka Mass transfer coefficient in the gas feed flow side (m s− ) 1 kb Mass transfer coefficient in the liquid absorbent flow side (m s− ) Kex Equilibrium constant K0ex Reduced equilibrium constant 1 Km Overall mass transfer coefficient of membrane (m s− ) 2 1 kCO2 Mass transfer of carbon dioxide (mol m− s− ) 1 `w f ,j Friction loss of CO2 (J kg− ), j = CO2, MEA L Channel length (m) 1 MW Molecular weight of water (kg mol− ) Nexp Number of experimental measurements N1 Number of inserting carbon-fiber fins P1 Saturation vapor pressure in the gas feed flow side (Pa) P2 Saturation vapor pressure in the liquid absorbent flow side (Pa) 3 1 Qa Volumetric flow rate of the gas feed flow side (m s− ) 3 1 Qb Volumetric flow rate of the liquid absorbent flow side (m s− ) 1 1 R Gas constant (8.314 J mol− K− ) Re Reynolds number r Membrane pore radius (m) 2 1 Sω The precision index of an experimental measurements of molar flux (mol m− s− ) 2 1 Sωi The mean value of Sωi (mol m− s− ) Sc Dimensionless Schmidt number ShE Enhanced dimensionless Schmidt number Shlam Dimensionless Schmidt number for laminar flow T Temperature (◦C) Tm Mean temperature in membrane (◦C) W Channel width (m) Membranes 2020, 10, 302 19 of 21

W1 Channel width of the inserting carbon-fiber spacers (m) ω Absorption efficiency, defined by Equation (23) 2 1 Jg Mass flux in the gas feed flow side (mol m− s− ) 2 1 Ji Mass flux, i = carbon, empty (mol m− s− ) 2 1 J` Mass flux in the liquid absorbent flow side (mol m− s− ) 2 1 Jm Mass flux in the membrane (mol m− s− ) 2 1 ωexp Experimental result of CO2 absorption flux (mol m− s− ) 2 1 ωcal Theoretical predicted CO2 absorption flux (mol m− s− ) Ym Natural log mean CO mole fraction in the membrane | |`n 2 z Axial coordinate along the flow direction (m) Greek letters αE Mass transfer enhancement factor β Aspect ratio of the channel δm Thickness of membrane (µm) ε Membrane porosity 1 ν Average velocity ( m s− ) 3 ρi Density ( kg m− ), i = CO2, MEA γm Concentration polarization coefficients Subscripts 1 Membrane surface on gas side 2(l) Liquid phase on membrane surface on MEA side 2 ( g) Gas phase on membrane surface on MEA side a In the gas feed flow channel b In the liquid absorbent flow channel cal Calculated results carbon Inserting carbon-fiber as supporters empty Inserting nylon fiber as supporters exp Experimental results in Inlet out Outlet theo Theoretical predictions

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