Application of hollow fiber membrane contactor for the removal of carbon dioxide from water under liquid–liquid extraction mode

Journal of Membrane Science 375 (2011) 323–333

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Application of hollow fiber membrane contactor for the removal of carbon dioxide from water under liquid–liquid extraction mode Gunjan K. Agrahari, Nishith Verma, Prashant K. Bhattacharya ∗ Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

a r t i c l e

i n f o

Article history: Received 24 November 2010 Received in revised form 25 March 2011 Accepted 30 March 2011 Available online 7 April 2011 Keywords: Degasification Carbon dioxide Hollow fiber membrane contactor Permeation Mathematical model

a b s t r a c t In this study, we investigate the application of a hollow fiber membrane contactor operated in the LLE mode for the removal of dissolved CO2 from water. The membrane contactor consists of hydrophobic polypropylene microporous hollow fibers. Experiments are performed to determine the extent of CO2 removal from the feed water flowing through the lumens of the hollow fibers. The feed at different concentration levels of dissolved CO2 was extracted using aqueous diethanolamine solution flowing on the shell side of the contactor. A mathematical model was developed, incorporating radial and axial diffusion of solute CO2 in the lumen and its permeation through the pores of the membrane. The governing second order partial differential equation of species balance was numerically solved using the alternate direction implicit technique. The developed mathematical model was used to predict the concentration profiles of CO2 and study its transport through water and membrane pores. The numerical value of the permeation coefficient obtained for CO2 in the hollow fiber membrane was found to be in good agreement with the data in literature. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The presence of CO2 in natural water is attributed to the absorption of atmospheric CO2 , respiration activities of aquatic animals, photosynthesis of marine plants, decay and decomposition of organic substances in water bodies, and dissolution and subsequent decomposition of magnesium and carbonate salts as water percolates through the soil and rocks containing these salts. Studies show that some natural sources of water may contain high concentrations of dissolved carbon dioxide [1,2], which lowers its pH [3]. Water drawn from such sources cannot be directly used in chemical processing plants, especially in semiconductor industries where ultrapure water free from traces of CO2 is required. Large concentrations (>10 mg/L) of CO2 in water may also pose threat to marine life [4,5]. Although the presence of CO2 in water is mostly due to natural processes, the CO2 content is significantly increased by the effluence of industrial wastewater into water bodies. Industries manufacturing ammonia and urea generate wastewater that has high CO2 concentrations, which may ultimately find its way to natural reservoirs if left untreated. Industries typically employ measures such as aeration, forced draft degasification, and vacuum degasification for decarbonation, i.e., to remove CO2 . These conventional

∗ Corresponding author. Tel.: +91 512 2597093; fax: +91 512 2590104. E-mail address: [email protected] (P.K. Bhattacharya). 0376-7388/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2011.03.060

methods, however, involve high costs because heavy-duty equipment such as pumps and blowers are employed. The methods involving gas–liquid contactors also have operational drawbacks such as loading and flooding in the column. Further, such contactors require properly designed stripping columns and large volumes of air to reduce CO2 concentration levels (<10 mg/L) [6]. Aeration may also result in excess oxygenation of water, which may be undesirable. In recent years, the focus of research has shifted to the applications of a hollow fiber membrane contactor (HFMC), which has the potential to degasify liquid streams and to overcome many of the problems and limitations described above. The principle of separation through HFMC is based on inter-phase mass transfer. HFMC-based technology provides non-dispersive contact along with larger interfacial area per unit volume than conventional contactors [7]. The operation is free from loading and flooding, and it involves minimal pressure drop and independent flow control. Diffusion mass transfer occurs at high rates across the interface. Further, the membrane contactor system is advantageous owing to its compact operational setup. The hollow fibers of HFMC consist of a solid, microporous polymeric matrix that may be either hydrophobic or hydrophilic. Hydrophobic membranes are generally used for the removal of volatile species from water. Polypropylene (PP), polytetrafluoroethylene (PTFE), and polyvinylidene fluoride (PVDF) are reasonably good hydrophobic materials. These polymeric materials allow only gases to permeate through the solid membrane phase [8]. In the case of two aqueous phases flowing on either side of a

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hydrophobic HFMC, the pores are not wetted by the liquid and the phases form an interface at both sides of the pore openings, with the gas trapped inside the pores. However, wetting has been observed even employing hydrophobic polymeric microporous membranes for longer durations of operations, particularly under gas–liquid contact. Wang et al. [9] observed 20% reduction of the overall mass transfer coefficient when the membrane pores were 5% wetted. The problem of wetting may be addressed by the use of composite membrane with a dense top layer as demonstrated by Nymeijer et al. [10] in their study for separation of paraffins and olefins in a gas–liquid membrane contactor. The wastewater effluents, whether industrial or domestic, generally contain certain materials which may cause membrane fouling. Therefore, the membrane based wastewater treatment plants are operated such that the suspended or dissolved solid materials in water are removed a priori by employing properly chosen pretreatment steps, before subjecting the effluent to the membrane contactors [11]. Literature is replete with studies on the removal of ammonia and oxygen from aqueous solutions using HFMC operated in liquid–liquid extraction (LLE) mode [12–17]. Simons et al. [18] and various other researchers [19–22] have studied the separation of CO2 from a gas stream using HFMC modules operated under gas–liquid mode. HFMC systems operated in LLE mode have also been employed successfully on pilot scale in various water treatment plants [23,24]. To the best of our knowledge, however, studies on the removal of CO2 from water by employing HFMC in LLE mode have not been conducted extensively, and we could not find details of any related experimental data reported in open literature [25]. The present study has been undertaken to investigate the removal of dissolved CO2 from water using HFMC in LLE mode and to demonstrate its viability. Experiments to remove CO2 from an aqueous feed were carried out using PP HFMC operated in the LLE mode. Aqueous diethanolamine solution was used as the extractant liquid. The effects of feed flow-rate and concentration on the extent of removal were investigated. A mathematical model, incorporating transport of the solute (CO2 ) in the liquid (water) and thereafter in the solid (membrane) phase, was developed to predict the recovery of the solute and to obtain concentration profiles in the aqueous phase. While many of the theoretical models developed for degasification assumed plug flow behavior, the novel feature of this model lies in its consideration of axial and radial dispersion of CO2 in the liquid feed, along with that of the permeation of CO2 through the porous wall of lumen. The feed was made to flow through the lumen. The governing partial differential equation was solved by a numerical technique. The value of the permeation coefficient of CO2 through PP was estimated by fitting predicted values obtained from the developed model to the experimental data. In the present study, we examine the industrial viability of the application of HFMC-based degasifiers for the removal of CO2 from water.

2. Theoretical analysis and model development Fig. 1 illustrates the different transport steps that may be involved in the removal of dissolved CO2 from water using HFMC. As described in Fig. 2, CO2 laden water is fed at a constant flow-rate from a tank into the lumen side of the contactor. The extractant liquid (aqueous) diethanolamine (DEA) flows counter-currently at a constant rate on the shell side. The CO2 depleted exit water is continuously recycled and returned to the tank. The CO2 molecules are desorbed from water, diffuse into the air-filled pores of the fibers, and exit on the shell side. Maintaining DEA at levels of high concentration, it is assumed that permeated CO2 molecules instantaneously react with DEA causing no change in the resistance of the extract phase. Therefore, in such an arrangement the concentra-

tion of CO2 in the tank decreases from an initial concentration level before exponentially attaining a steady-state level of concentration. In the present study, the fibers were made of polypropylene, which is hydrophobic. Hence, neither of the aqueous phases present on either sides of the contactor may enter into the pores of the fibers. In other words, there may be an interface which may be created at the pore openings on both sides of the hollow fibers. Thus, the CO2 is transported from the aqueous phase on the lumen side to the pore opening and then reaches the extract phase after permeating through the pores of the membrane. Considering CO2 to be highly soluble in the aqueous DEA, no reaction zone is assumed to be formed and consequently, the concentration of CO2 is assumed to be zero at the interface on the shell side. The following assumptions are made in the development of the present model: 1. Isothermal conditions are assumed to prevail. 2. Flow on the lumen side is fully developed under laminar flow condition and velocity profiles are parabolic. 3. Liquid (feed) density is constant considering the feed to be dilute. 4. Pores are filled with air. 5. Volume of feed and that of extractant liquid are larger compared to that of HFMC module (i.e., no effects of hold-up volume). 6. Physical and transport properties remain constant with variation in the solute concentrations. 2.1. Species balance on the lumen side Consider the fully developed tubular flow of a liquid at low (<2100) Reynolds number. The velocity profile is parabolic. Allowing for diffusion in the axial and radial directions of the tube, the 2D unsteady-state species balance for CO2 in the liquid phase on the lumen side under such conditions may be written as follows: ∂Cl D ∂ ∂C ∂2 C + vz l = Dl 2l + l r ∂r ∂t ∂z ∂z



r

∂Cl ∂r



(1)

Here, Dl denotes diffusion coefficient of CO2 in water at the temperature and pressure of the system. Further, Cl denotes the concentration of solute (CO2 ) in water and may be measured as mg of CO2 per cm3 of water. The velocity profile of the liquid in the lumen is given [26] as:



vz (r) = 2V¯ 1 −

 r 2 

(2)

r1

where V¯ is the average velocity of feed-stream in the lumen, r is the radial distance, vz is the velocity of stream at r and r1 is the inner radius of the lumen. The average velocity of the fluid inside the lumen can be defined as: V=

Q

(3)

Nr12

where Q is the bulk flow rate of the feed and N is the number of fibers. The necessary conditions required to solve the above 2-D partial differential equation on Cl (t,z,r) are as follows. 2.1.1. Initial and boundary conditions t = 0, Cl = C0 for 0 < r < L



r = 0,

∂Cl ∂r



=0 r=0



r = r1 , z = 0,

− Dl

∂Cl  ∂r 

Cl = Ctank (t)

(4.2)



= −Dm r=r1

(4.1)

∂Cm  ∂r 

(4.3) r=r1

(4.4)

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

Fig. 1. Schematic of lumen depicting radial and axial diffusion of CO2 in the liquid and its permeation through membrane.

Fig. 2. Line diagram of experimental setup to remove CO2 from water using hollow membrane contactor in LLE mode.

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z = L,

∂Cl =0 ∂z

(4.5)

where Dm is the diffusion coefficient of CO2 in the membrane phase. Cm denotes the concentration of CO2 in the porous membrane and may be measured in mg of CO2 per cm3 of the membrane bulk volume. L denotes the length of fiber lumen. The boundary condition given by Eq. (4.2) follows from the axial symmetry of the lumen. The boundary condition given by Eq. (4.3) is obtained by equating the flux of CO2 at the interface of the aqueous phase and the membrane. The condition given by Eq. (4.4) is obtained from the CO2 balance adopted for the feed in the tank, whereas the long tube approximation is assumed for the boundary condition given by Eq. (4.5). 2.2. CO2 balance over feed tank Under the assumption of uniform mixing in the tank, the species balance equation can be written as: V

dCtank = Q (Cexit − Ctank ) dt

(5)

Here, Cexit denotes the concentration of CO2 in water (recycled to the tank) at the exit of lumen and V is the volume of the liquid in the tank.

Table 1 Specifications of the experimental setup equipped with 2.5 × 8 LiquiCel® commercial HFMC module [29]. Module characteristics Average cartridge i.d. (m) Average cartridge o.d. (m) Average number of fibers Fiber length (m) Fiber packing fraction Total contact area (m2 ) Membrane characteristics Inside diameter (m) Outside diameter (m) Porosity Pore diameter (m) Material Set-up characteristics Feed and extractant tank dimensions (cm) Feed and extractant volumes (L) Tank material Tubing material

Dm ∂ ∂Cm = r ∂r ∂t



∂Cm r ∂r



(6)

Assuming quasi steady-state, Eq. (6) may be integrated from r = r1 (inner radius of the lumen) to r = r2 (outer radius of the fiber) to obtain: r2 Cm2 − Cm1 = A ln (7) r1 where Cm1 and Cm2 are the concentrations of CO2 in the membrane phase at r = r1 and r = r2 , respectively. ‘A’ is the integration constant. As CO2 is assumed to instantaneously react with DEA at the interface on the shell side, Cm2 may be assumed to be zero. Thus, ‘A’ is evaluated as: A=

Cm1 ln(r1 /r2 )

(8)

The flux of CO2 diffusing from the aqueous phase at the inner interface (r = r1 ) may be equated to that diffusing into the pores of the membrane as per Eq. (4.3). Therefore, from Eqs. (4.3) and (7), the diffusion flux at the inner surface (i.e., at r = r1 ) may be expressed in terms of the geometrical dimensions of the lumen, diffusion coefficients in the liquid and membrane phases, and Cm1 , the concentration of CO2 in the membrane phase as:

 ∂Cl  −Dl ∂r 

= −Dm r=r1

Cm1 1 × r1 ln(r1 /r2 )

(9)

The membrane phase Cm1 is related to the liquid phase concentration Cl according to the Henry’s law as [27]: Cm1 = S × Cl

(10)

where S is the dimensionless solubility coefficient (moles of gas per m3 of membrane-bulk volume divided by moles of the gas per m3

240 × 10−6 300 × 10−6 40% 0.03 × 10−6 Polypropylene Radius = 8, height = 27 5 PP autoclavable Polyolefin

of water) of CO2 in the polymeric membrane material. Substituting Cm1 in terms of the liquid phase concentration, Eq. (9) may be further modified to obtain the following equation:



−Dl

2.3. Permeation through the membrane On the lumen side of hollow fiber, CO2 desorbs from the liquid and diffuses through the air-filled pores of the fibers. The timedependent concentration of CO2 in the membrane phase may be obtained from the following equation:

0.022 0.055 10200 0.25 0.435 1.4

∂Cl  ∂r 

= −˘ r=r1

Cl 1 × r1 ln(r1 /r2 )

(11)

where ˘ is recognized as the permeation coefficient, the product of the solubility coefficient, S and diffusion coefficient, Dm . It is worth noting that under the present context of permeation of absorbed CO2 in water through the membrane phase; the permeation coefficient numerically assumes the same dimensions as that of diffusion coefficient. The common unit for the permeation coefficient reported in literature (converted to SI system) for the removal of CO2 from the gas phase is mol m/(s Pa m2 ) [28] whereas the same for the removal of CO2 from liquid is mol m/(s M m2 ) [27]. To this end, the boundary condition given by Eq. (4.3) at the lumen inner wall, r = r1 can be rewritten as



−Dl

∂Cl ∂r



= A × Cl

(12)

where A =

−˘ r1 ln(r1 /r2 )

(13)

Eq. (1) with the initial and boundary conditions (Eqs. (4.1), (4.2), (4.4) and (12)) are numerically solved, along with Eq. (5), using alternate direction implicit (ADI) technique. The permeation coefficient, ˘ was used as the adjusting parameter in the model. The governing equations were solved in the non-dimensionalized forms. The non-dimensionalized equations and the associated boundary conditions are presented in Appendix A. 3. Experimental 3.1. Materials HFMC (Liqui-Cel® Extra Flow) comprising hollow fibers (lumens) made of PP was procured from Membrana-Charlotte, Celgard, NC, USA. The characteristics of module and membrane are given in Table 1 [29]. Qualigens Fine Chemicals, India supplied sodium bicarbonate, trisodium citrate, diethanolamine, hydrochloric acid. Deionized water (DI) was prepared using the water purification system supplied by Millipore® Inc., USA.

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

3.2. Preparation of aqueous solution of CO2

3.3. Analysis A CO2 gas-sensing electrode (ISTEK, Korea) was used to detect dissolved CO2 in water. The electrode was connected to a dual channel ion and pH meter procured from Eutech Instruments Ltd., Mumbai (India) to measure CO2 concentrations. The pH of the feed was monitored using pH glass electrode (Eutech Instruments, Ltd., India). The ionmeter was calibrated for three different concentrations (100, 300, 500 ppm) of the prepared aqueous CO2 solutions before each test run. The minimum detection limit of the gas sensor was 40 ppm, with a measurement error of ±10%.

3.4. Experimental setup The scheme and line diagram of the experimental setup used in the study are presented in Fig. 2. The setup may be assumed to consist of HFMC module, feed and extractant liquid delivery systems, including recycle loop. Degasification was carried out in liquid–liquid extraction (LLE) mode. As shown in Fig. 2, the feed was delivered from an overhead tank at constant flow rate (0.2, 0.5, and 0.8 LPM) to the lumen side using a gear pump with the speed controller. The treated water was returned to the feed tank via a flowmeter. The flowmeter was equipped with a back pressure control valve to regulate the line pressure. Similarly, the extractant solution was delivered from an overhead tank at constant flow rate of 1.5 LPM to the shell side of HFMC using a gear pump with the speed controller. The spent solution was also returned to the tank via a flowmeter equipped with a back pressure control valve. Stainless steel pressure gauges were installed on both the inlet and outlet lines to and from the shell and lumen side, as shown in the figure. A three-way stainless steel valve was fitted to the feed tank to withdraw sample. All tubing and fittings were made of chemically resistant polyolefin. The entire experimental setup was mounted on a steel panel.

3.5. Experimental variables The experimental variables in the study included feed flow rates (0.2, 0.5 and 0.8 LPM) and CO2 concentrations (300, 600, 900, 1200 ppm) in water. The extractant flow rate was maintained at 1.5 LPM for all the runs. The feed and shell side operating pressures were kept constant at 8 psi(g) and 3 psi(g) in order to maintain the appropriate pressure differential between the two phases for interface control, as per the guidelines specified by the manufacturer of HFMC module.

1.0

0.8

C/Cinitial

The synthetic CO2 laden water of different concentrations (300–1200 ppm) was prepared by dissolving the appropriate amounts of sodium bicarbonate in 5 L of DI water. Considering the solubility limit of CO2 in water at 30 ◦ C [30], the maximum CO2 concentration in water set in this study was 1200 ppm. The correlation developed by Munjal and Stewart [30] was used for CO2 solubility in water (refer Appendix B). The pH level of the prepared aqueous solution of sodium bicarbonate was controlled during the test runs (pH ≤ 5), using a trisodium citrate buffer solution in 10:1 volume ratio, for converting dissolved inorganic carbon in water to free molecular CO2 . The buffer solution was prepared by dissolving 1 mol of trisodium citrate in 1 L of DI water. The pH level of the buffer solution was maintained below 5 by the addition of 1 M HCl. A stock solution of 1 M aqueous solution of diethanolamine was prepared as extractant.

327

0.6

0.4

300 9 2 600 Π x 10 , mol m/(s M m ) 20 900 1200

0.2

0.0 0

1200

2400

3600

Time, s Fig. 3. Comparison of non-dimensionalized experimental data to model prediction (Q = 0.5 LPM) for the removal of CO2 with time at the lumen exit. Inset figure: dimensional form of actual data.

3.6. Experimental procedure The tanks and interconnecting tubes were flushed with DI water to remove any undesirable substances from the system before starting the test runs. The tanks were filled with the prepared feed and extractant solutions. The feed solution was pumped into the contactor and the interconnecting tubes. After the steady-state flow and pressures were attained, typically within 10 min, the extractant solution was delivered into the shell side of the contactor and the respective interconnecting tubing. The system was run for further 10 min to stabilize the flow and pressure conditions. The buffer solution was added into the feed and samples were collected every 5 min by opening the sampling valve in the tank and were immediately analyzed in the ionmeter. The test runs were continued until the concentration in the tank asymptotically attained a steady state value. All the experiments were conducted at room temperature (∼30 ◦ C). The maximum line pressure was maintained at 8 psi(g). After the completion of each run, the entire system was cleansed by passing DI water through the lumen and shell sides of HFMC to remove the remaining solutions. 4. Results and discussion 4.1. Separation experiment Fig. 3 describes the decrease of CO2 concentrations in the feed tank for four different initial concentrations. The other operating variables, feed and extractant flow rates were kept constant. As shown, it took approximately 1 h for the concentration in the tank to attain steady-state levels. Under the experimental conditions, the steady-state (final) concentration values obtained were between 20 and 50 ppm, corresponding to the initial feed concentration range of 300–1200 ppm. The data for each case are, however, presented in the non-dimensionalized form for comparison purpose. As observed from the figure, the concentration in that tank initially decreases at a relatively faster rate, before gradually attaining the steady-state level. For example, the concentration decreases by approximately 50% in the first 5 min of the test, before leveling off to the final level typically within 1 h, suggesting relatively larger mass transfer rates of CO2 during the initial period of the experiment. The large mass transfer rate is due to a combination of the following effects: desorption of CO2 from water, permeation through the membrane, and subsequent reaction with the amine. As the concentration of CO2 decreases in the feed, the rate decreases causing the separation to slow down.

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

1.0

Concentrations x 10

-3 , ppm

1.4

0.8

C/Cinitial

The predictions for the unsteady-state concentrations of CO2 in the system were made using the mathematical model developed in this study. The simulation conditions were chosen to be identical as those in the experiment. As previously discussed, the permeation coefficient of CO2 in PP was used as the adjustable parameter in the predictive model. In the present case, the numerical value of the permeation coefficient was adjusted and set at 20 × 10−9 mol m/(s M m2 ) to rationalize the data. As observed, the agreement between the experimental data and the model predictions for the concentration of CO2 in the feed tank is reasonably good. Two points are worth noting. Firstly, as observed from the figure, there is variation in the concentrations of CO2 at different initial concentration levels, although the times taken to attain steady-state concentration levels are almost the same in each case. Referring to the theoretical analysis of the model development presented in Section 2, the governing Eqs. (1) and (6) are linear on Cl and Cm , CO2 concentration in water and membrane, respectively. Considering that the aqueous solution of CO2 is dilute, the physical properties such as Dl , Dm , and S may be assumed to be constant over the dissolved gas concentrations range between 40 and 1200 ppm. Therefore, the boundary conditions given by Eqs. (4.3) and (10) may be considered to be linear on CO2 concentrations. It follows that rate of decrease in CO2 concentration is independent of the feed concentration. Therefore, the observed difference between the predicted values obtained from the model and experimental data for the CO2 concentrations at different feed concentrations may be attributed to errors in the numerical and experimental measurements. The inset of Fig. 3 also shows the dimensional form of the variables and the plot aptly describes the rate of decrease of CO2 concentration in relation to the initial CO2 concentration in the feed, especially during the initial stage of permeation. Secondly, the model adjusted value of the permeation coefficient for CO2 in PP in this study may be compared to the literature data. Teramae and Kumazawa [28] have carried out permeability measurements of CO2 gas in plasma treated PP and obtained the permeation coefficient as approximately 6.24 × 10−9 mol m/(s M m2 ) (after converting to present system of units), over a pressure-range between 0.2 and 1.2 MPa. Cole et al. [27] also determined the permeation coefficient (∼6.0 × 10−9 mol m/(s M m2 )) of CO2 in PP membrane over a concentration range corresponding to 500–700 ppm of CaCO3 alkalinity during decarbonation and deaeration of water using hollow fibers. In both studies, the measurements were made at 30 ◦ C. Hence, the model adjusted value of 20 × 10−9 mol m/(s M m2 ) may be considered comparable to the value of permeation coefficient available in literature [27,28]. In general, the permeation coefficient of a solute in the polymeric material is dependent on temperature [31], pressure, and the type of solid-surface and structure [32,33]. Swelling of the polymeric material by water is also known to affect the permeation coefficient of the material for a gas [27,34]. Fig. 4 describes the experimental data corresponding to the feed flow rate of 0.8 LPM. The inset of Fig. 4 also shows the dimensional form of the variables. The initial feed concentrations were the same as those for the data shown in Fig. 3. As shown in the Fig. 4, the trend in decrease of CO2 concentration is similar to that recorded in the previous case. The rate of decrease is observed to be slightly larger than that in the previous case, with a relatively shorter time taken for the tank concentration to attain a steady-state value. The model simulation was carried out, with the permeation coefficient set at the same value (20 × 10−9 mol m/(s M m2 )) as obtained in the previous case. As observed, the model prediction may be considered to be in reasonable agreement with the data within the numerical and experimental errors. It may be noted that the fluid hydrodynamic conditions affect the boundary layers near the membrane surfaces, and thus the permeability. In the present case, however,

0.6

Inlet feed, ppm

1.2

300 600 900 1200

1.0 0.8 0.6

Π x 10 9, mol m/(s M m 2)

20

0.4 0.2 0.0

0

1200

2400

3600

Time, s

0.4

Inlet feed, ppm 300 Π x 10 9, mol m/(s M m2) 600 20 900 1200

0.2

0.0 0

1200

2400

3600

Time, s Fig. 4. Comparison of non-dimensionalized experimental data to model prediction (Q = 0.8 LPM) for the removal of CO2 with time at the lumen exit. Inset figure: dimensional form of actual data.

the permeability is considered invariant to liquid flow rate as well as feed CO2 concentrations. The above consideration is according to its weak dependence on the aqueous phase concentration of CO2 over the entire concentration range chosen in the study and low Reynolds number (from 2 to 10) applied at the feed side. The results for the other feed flow rates are not presented here for the sake of brevity. Fig. 5 describes the results for the percentage removal of CO2 calculated with respect to the different initial concentrations in the feed tank. The data are presented for three different feed flow rates (0.2, 0.5 and 0.8 LPM) at each initial feed concentration level (300, 500, 900, and 1200 ppm) selected in the experiment. The percentage removal of CO2 decreases with increasing feed flow rate at the initial feed concentration of 300 ppm, with the maximum removal (approximately 95%) obtained at the lowest flow rate (0.2 LPM). The removal decreases to approximately 90% at 0.8 LPM. Similar trends are observed at large feed concentrations. However, in these cases the removal efficiency varies slightly with increasing feed flow rates. The decrease in the percentage removal with increasing feed flow rates may be attributed to the fact that at low flow rate, the residence time of the fluid elements is relatively larger. As a consequence, increased contact time between the fluid and the permeating surface of the membrane enhances the mass transfer rate of CO2 molecules diffusing through the liquid phase and reaching the inner walls of the lumen. Considering that the range of the Reynolds number was 2–10 corresponding to flow rates between 0.2 and 0.8 LPM, the liquid flow on the lumen side was in the laminar

Feed flow rate, LPM 0.2 0.5 0.8

1.0

Percent Recovery

328

0.8 0.6 0.4 0.2 0.0

300

600

900

1200

Feed Concentration, ppm Fig. 5. Percent removal of CO2 with feed concentration at varying feed flow-rates.

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

1.00

329

Plot Title 0.348 Cexit / Cinitial

Cexit/Cinitial

0.80

0.345 0.342

0.60

0.339 0.336

0.40

0.0

0.2

0.4

0.6

0.8

1.0

r/R

0.20

0.00 0

500

1000

1500

2000

2500

3000

1.00 0.80 0.60 0.40 r/R 0.20 0.00

Time, s Fig. 6. Model prediction for the unsteady-state CO2 concentrations at the exit of lumen at different radial locations (Q = 0.5 LPM). Inset shows negligible variation of the radial concentration at t = 500 s.

region, with the parabolic velocity profiles, the effect of increasing flow rate results in short residence time in the tube and therefore, shorter time for CO2 molecules to diffuse from the bulk volume to the inner walls of the lumen or the permeating surface of the membrane. Therefore, the separation decreases. 4.2. Unsteady state model simulations and predictions For a system of single component, CO2 , transferred across the membrane, the concentration of CO2 in the liquid flowing through the lumen is a function of time, radial distance from the lumen axis, and the axial distance from the entrance to the lumen. The model simulations were carried out to obtain the unsteady-state concentrations profiles of CO2 at various locations inside the lumen. As discussed in the theoretical section (Section 2), there are two dependent variables, Cl and Cm , and as many model governing differential equations to solve.

Fig. 6 describes the model simulated results for the unsteadystate concentration profiles of CO2 at the lumen’s exit for different radial locations. The simulation was carried out for Reynolds number = 5.3. The value of diffusion coefficient of CO2 in water at temperature of 293 K was taken to be 1.76 × 10−5 cm2 s−1 [35]. The permeation coefficient was assumed to have the same value as that obtained to fit the experimental data. There are two salient observations to make. (1) Concentration decreases exponentially for all five radial locations. The rate is relatively faster within the first few minutes and asymptotically becomes zero in approximately 1 h. (2) Decrease in the concentration near the wall is larger, although marginal, than that at the center of the lumen. In other words, difference in concentrations at two locations (wall and center) may be considered insignificant during separation. The data plotted in the inset of the figure corroborates the effects. As observed, the CO2 concentration at the center, measured relative to the inlet concentration, is 0.349 in comparison to 0.337 near the wall. These

t = 500 s 0.5

t = 1000 s

0.3

1.00 0.80 0.60

0.2

0.40 0.1 0.00

0.20

r/R

C / Cinitial

0.4

0.20 0.40

0.60

z/L

0.80

1.00

0.00

Fig. 7. Model prediction for the unsteady-state axial variation of CO2 concentrations at different radial locations in the lumen (Q = 0.5 LPM).

330

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1.0

1.0

Feed Flow rate, L/min 0.8

0.35 0.5 0.65 0.8

0.6

Cexit / Cinitial

C / Cinitial

0.8

0.4

9

2

Π x 10 , mol m/(s M m )

1 20 60 90 120

0.4

0.2

0.2

0.0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0

z/L

results are significant. Although the velocity profile in the lumen is parabolic, radial concentration gradients in the tube are negligible. Considering instantaneous reaction at the outer walls of the membrane on the shell side, the permeation rate through the membrane is fast under the conditions chosen for the simulation. Fig. 7 describes the 3D concentration profiles of CO2 in the lumen at t = 500 and 1000 s. The figure may be considered as a snap shot of the profiles in the lumen at two different times. As observed, concentration gradients exist along the length of the tube in both cases. The concentration gradients along radial direction, however, are insignificant (3–4% drop; refer inset of Fig. 6). After t = 1000 s, the concentration levels at the exit of the tube have reached approximately 12% of the initial concentration value, while the same have decreased to only 35% at t = 500 s. Fig. 8 describes the radially averaged axial concentration profiles of CO2 for different flow rates at t = 500 s. The bulk average concentration at any axial location inside the tube is calculated by calculating the net flux due to convection and diffusion, using the following equation:

R 0

500

1000

1500

2000

2500

3000

3500

4000

Time, s

Fig. 8. Variation in radially averaged axial concentration at different feed flow rates (t = 500 s, Permeation coefficient = 20 × 10−9 mol m/(s M m2 )).

Cl(average) =

0.6

(v(r)Cl (r) − Dl (∂Cl /∂z))2rdr

(14)

Q

Fig. 9. Model predictions for time variation in lumen exit concentration for different values of permeation coefficient.

The graphs show that the concentration of CO2 decreases, as expected, along the length of the lumen, as CO2 is extracted from the bulk flow by permeation through the membrane wall of the lumen. The graphs also indicate that CO2 concentration as well as the concentration gradient at a small flow rates are larger than at large flow rates. The model simulation was carried out by numerically varying permeation coefficients. It was shown in the theoretical section (Section 2) that the permeation coefficient is not a fundamental property of the material; rather it is a combined effect of both the solubility and diffusion coefficients. Consequently, the permeation coefficient appears as the product of solubility and diffusion coefficients of CO2 in polymeric material. Considering that both solubility and diffusion coefficients have Arrhenius-type of temperature dependence, the permeation coefficient is also temperature dependent. Therefore, in the present context of separation of CO2 from water by using PP hollow fibers, the model simulation for different permeation coefficients may be considered as simulating separation from water at different temperatures. Fig. 9 describes the time variation of CO2 concentrations at the lumen exit for

45

Pe x 10

35

-7

25 15 5

1.00

0.80

α

0.60

0.40 0.20

50

60

70

80

90

0.00 100

Percent Removal Fig. 10. Model predictions for percent removal of CO2 in 1 h for different values of dimensionless constant ˛ and axial Peclet number Pe where ˛ = (LD)/(vR2 ) and Pe = vL/D.

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

five different values of permeation coefficient, varying over the range between 1 × 10−9 to 120 × 10−9 mol m/(s M m2 ). As pointed out earlier in the text, the permeation coefficient obtained in this study by fitting the experimental data with the model prediction was 20 × 10−9 mol m/(s M m2 ). As observed from the figure, the rate of exit concentration expectedly increases with increasing permeation coefficient, while the remaining variables are kept constant. The maximum variation in the CO2 concentration is observed to occur at around 750 s, between 15% and 40% of the inlet concentration. The concentration levels, however, asymptotically attain the final concentration at approximately the same time. Fig. 10 describes percent removal of CO2 in an hour against different values of dimensionless constant ˛ and axial Peclet number, Pe. The two dimensionless numbers incorporate the effect of lumen dimensions and flow conditions along with the diffusion coefficient on removal efficiency. It is observed, that removal efficiency of HFMC gets improved with increasing values of ˛, however it gets reduced at high Peclet numbers. Since high Pe values signify high flow velocities, the enhanced performance of HFMC can thus be achieved at lower Pe values; i.e., at lower flow velocities. From the experimental data, the average permeating flux of CO2 was calculated as 3.7 × 10−5 mol/(s m2 ). Hasanoglu et al. [36] have performed an experimental and theoretical analysis on the removal of ammonia from water using (PP) HFMC in LLE mode, and reported the average flux of 3 × 10−5 mol/(s m2 ). Ashrafizadeh and Khorasani [37] have also studied ammonia removal using the similar HFMC system and obtained the average value of around 40 × 10−5 mol/(s m2 ). Based on the present experimental results and the literature data, it may be concluded that the present study on the removal of CO2 from water using HFMC in the LLE mode has the potential for scale-up. The proposed system may be applied for the treatment of industrial streams by using a cascade of large size HFMC modules operated in series and/or parallel configurations. However, a separate comprehensive study is required to specifically address the scale-up aspects.

5. Conclusions Degasification using HFMC made of PP was successfully employed to remove CO2 dissolved in water, over a concentration range of 300–1200 ppm. The aqueous CO2 solution to be treated was delivered on the lumen side of the HFMC. An aqueous diethanolamine solution flowing in the shell side was used as the extractant. The performance (percentage recovery) of HFMC increased with decreasing feed flow rate; however, the steadystate levels of concentration were attained after a relatively long period of time. A mathematical model was developed to explain the unsteady state mass transfer data of CO2 in the HFMC module. The theoretical analysis incorporates radial and axial concentration distribution of the species on the lumen side, along with the permeation of the gas molecule through the PP membrane. The predictive model explains the data reasonably well at the adjusted value of 20 × 10−9 mol m/(s M m2 ) for the permeation coefficient of CO2 through PP at 30 ◦ C. From the experimental data, the average permeating flux of CO2 was calculated as 3.7 × 10−5 mol/s m2 .

Acknowledgement For the partial fulfillment of the present work, one of the authors (PKB) gratefully acknowledges the financial support received from CSIR; vide sponsored project sanction letter number 22(0496)/10/EMR-II.

331

Appendix A. A.1. Governing equations Transport of CO2 in the tubes (lumen) of contactor can be expressed by a convection diffusion equation as follows:



∂Cl ∂C ∂2 C D ∂ + vz l = Dl 2l + l r ∂r ∂t ∂z ∂z

r

∂Cl ∂r



(A.1)

The velocity distribution in the lumen side under laminar flow conditions is given by



vz (r) = 2V¯ 1 −

 r 2 

(A.2)

R

The following dimensionless variables are considered: =

z ; L

=

r ; R

t∗ =

t tv = ;  L

Cl∗ =

Cl ; Co

∗ Cm =

Cm Co

(A.2.1)

Introducing these dimensionless variables in the above equation, ∂Cl∗ ∂t ∗

2

+ 2(1 −  )

∂Cl∗ ∂



=˛

∂2 Cl∗ ∂ 2

∗

1 ∂Cl +  ∂



+

1

∂2 Cl∗

Peaxial ∂ 2

(A.3)

where ˛ = DL/vR2 and Peaxial = vL/Dl is the axial Peclet number. Further ˛=

L L = R(vR/D) R(Peradial )

(A.4)

where Peradial = vR/D is the radial Peclet number. A.2. Non-dimensional Initial and Boundary conditions At t ∗ < 0,



Cl∗ = 1

(A.5)

At  = 0; all  and t* ∂Cl∗ ∂



=0

(A.6)

=0

At  = 0, all  and t* ∗ Cl∗ = Ctank,

exit

=

Cl (t) =1 Ctank, exit (t)

(A.7)

At  = 1; all  and t* ∂Cl∗ ∂

=0

(A.8)

At  = 1; all  and t* −Dl

  ∗  ∂Cm   = −D m ∂  ∂  = =

∂Cl∗ 

1

(A.9)

1

A.3. Permeation through the membrane The continuity equation for the component CO2 diffusing through the membrane can be written as ∂Cm Dm ∂ = r ∂r ∂t



∂Cm r ∂r



(A.10)

Eq. (A.10) can be non-dimensionalized as follows



∗ ∗ ∗ ∂Cm ∂2 Cm 1 ∂Cm =˛ + ∂t ∗  ∂ ∂ 2



(A.11)

332

G.K. Agrahari et al. / Journal of Membrane Science 375 (2011) 323–333

A.4. Material balance over feed tank V

dCtank = Q (Cexit − Ctank ) dt

(A.12)

which can be written as tank

dCtank = Cexit − Ctank dt

(A.13)

where  tank = V/Q. Integrating for a time period t, assuming Cexit to be constant during t, the final equation is obtained as: Ctank,

t

= Cexit − (Cexit − Ctank,t0 )e−t/tank

(A.14)

Appendix B. B.1. Solubility of CO2 in water The correlation developed by Munjal and Stewart [30] was used for CO2 solubility in water:



ln x = ln p −

16.43 −

 p 2  119.76

+

R

T

2698 T +



−

p R



9.756 × 104 203.14 − − 0.00662R T T2

552.22 3.964 × 107 9.517 × 108 − + 2 3 T T T4





(B.1)

Nomenclature C D d L M N p Q R R r S t

v V V¯ x z

concentration (mol m−3 ) diffusion coefficient (m2 s−1 ) internal diameter of fiber (m) fiber length (m) molarity (mol L−1 ) number of hollow fibers pressure (atm (Eq. (B.1))) bulk feed flow rate (m3 s−1 ) universal gas constant (= 82.0053 cm3 atm/(g mol K) (Eq. (B.1)) fiber radius (m) radial length (m) solubility coefficient time (s) velocity (m s−1 ) volume of feed tank (m3 ) average velocity of feed (m s−1 ) mole fraction of CO2 in water axial length (m)

Greek symbols   ˛  

permeation coefficient (mol m/(s M m2 )) residence time of solute (s) dimensionless constant (Eq. (A.3)) non-dimensionalized axial length in the fiber non-dimensionalized radial distance in the fiber

Subscript l pertaining to water m pertaining to membrane o initial value 1, 2 location at the beginning and end of membrane wall

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