Predicting CO2 Permeation through an Enhanced Ionic Liquid Mixed Matrix Membrane (IL3M)

Petroleum Engineering Department, Universiti Teknologi Petronas, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia Center of Enhanced Oil Recovery, Institute of Hydrocarbon Recovery, Universiti Teknologi Petronas, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia Chemical Engineering Department, Universiti Teknologi Petronas, 32610 Bandar Seri Iskandar, Perak Darul Ridzuan, Malaysia Adjunct Professors, Indian Institute of Technology, Kharagpur, India


Introduction
Membranes, both polymeric and inorganic, have several specific advantages over conventional separation processes and are finding increasing applications in both gas and liquid separation. is has accelerated research in this area, particularly in the identification and development of new membrane materials. In gas separation, the major challenge is to synthesize membranes that can touch, if not cross, the Robeson plot [1] in terms of flux and selectivity or separation factor. Mixed matrix membranes (MMMs) are promising novel materials, and their high potential in both gas and liquid separation has already been recognized.
Transport of small gas molecules through a polymeric dense membrane occurs when random molecular motions are projected by the polymer matrix. e driving force in this process of sorption, diffusion, and permeation is the concentration gradient or partial pressure difference across the membrane [2,3]. In sieving materials, gas transportation is driven by the difference in diffusion rates between permeating molecules of different shapes and sizes. More specifically, the rate of diffusion is determined by the gas penetrant and the sieving pore size [4]. Molecular sieving materials are known to offer high separation factors since their pore dimensions are similar to the dimensions of the gas molecules. Diffusion occurs when the molecules jump through a narrow opening between one sorption cavity and the next [5]. Adsorption and surface diffusion are further factors in gas permeation through small-pore-diameter membranes [6].
MMMs are heterogeneous membranes that generally constitute inorganic fillers dispersed within a polymer matrix, although the inclusion of organic or metal-organic framework materials has also shown excellent potential [7]. In the ideal MMM morphology, a defect-free boundary is assumed between the dispersed particles and polymer interface [8]. e strong adhesion between the polymer and filler reduces the free volume in the polymer [9]-a process known as polymer rigidification [10]. In most cases, this rigidification [11] improves selectivity while reducing permeability [12].
With proper selection of the filler, many MMMs are excellent separation media for use in gas separation. However, there remains a need to improve both the flux and selectivity of MMMs. is can be achieved by appropriate manipulation of the membrane. In the proposed approach, an ionic liquid is incorporated into the membrane matrix. Ionic liquids are a large family of green solvents that demonstrate excellent solvent properties in addition to being nonvolatile and stable even at high temperatures. For membrane gas separation, many studies have investigated the use of ionic liquids in the form of supported liquid membranes (SLMs) and have yielded encouraging results [13][14][15]. Ionic liquids have also been polymerized to produce ionic liquid polymeric membranes (ILPMs) [16][17][18]. However, the permeation separation performance of these membranes is still lower than that of SLM and is yet to exceed the 2008 Robeson upper bound. A study mentioned by Ilyas et al. [19] has successfully synthesized supported ionic liquid membranes with 41 CO 2 /CH 4 selectivity with no observation of ionic liquid leaching. It was a very good finding but it was limited to 10 bar, and the group has not focusing the effects of inorganic materials. Another work from Bhattacharya and Mandal [20], which was also not considering the effects of inorganic materials, has successfully tested their MMM at a maximum pressure of ∼7 bar and found the membranes work better for H 2 S/CH 4 separation. Based on these studies of using ionic liquid, it can be concluded that the ionic liquid can be the way forward of commercializing the membranes for gas separation purposes.
In this study, an ionic liquid was homogeneously distributed in the casting suspension and used to prepare an MMM comprising both fine adsorbent particles (SAPO-34) and an ionic liquid. e goal of this study was to achieve improvements in both flux and selectivity. e study also attempted to develop models suitable for predicting gas transportation in the membrane that considers the membrane's composition, characteristics, and morphology. A proper theoretical understanding of gas transportation in an MMM is required to support the design of research and development studies and to allow its implementation in industrial separation [21].
Gas transportation across MMMs has been a major focus of recent membrane research, mainly owing to their increasing use in gas-sweetening applications. Most existing theoretical models rely on old equations that were developed to address the quite different problem of estimating the electrical conductivity of a nonhomogeneous substance comprising a dispersed solid phase. By assuming that an analogy can be drawn with gas permeation, these conductivity models have been used to evaluate gas separation [22]. Similar electrical and thermal conductivity models have been applied to the analysis of MMMs [23].
Different models have used different approaches to predict the relative permeability of gases. Based on a review from Aroon et al. [8,24], there are few permeation models used to predict effective permeability of a gaseous penetrant for mixed matrix membranes comprising porous particles. Another study from Hashemifard et al. [23] was also considering the models reviewed in [24] for their prediction of the relative permeability. In this study, the Maxwell, Lewis-Nielson, and Maxwell-Wagner-Sillar (MWS) models were used. However, these models cannot predict the permeability of a gas species through an MMM comprising a third component. One objective of the study was therefore to evaluate the existing models and to establish the adjustments needed to make them applicable for predicting gas transport across an IL3M. e MMM used in this study was prepared using polyethersulfone (PES), SAPO-34, and an ionic liquid. e analysis focused on the effect of the ionic liquid on the dispersion geometry of the SAPO-34 particles. is reflected our reported finding that incorporation of an ionic liquid triggers agglomeration of an inorganic filler within the membrane matrix [25].

Evaluation of Existing MMM Transport Models
Predicting the permeability of an MMM has proved a challenge. Interestingly, the theoretical models developed to address electrical conductivity in a nonhomogeneous medium are applicable to this entirely different problem, including the models proposed by Maxwell, Bruggeman, Pal, and Lewis-Nielson [8,21,23,26,27]. ese models have received attention primarily because of their simplicity-the permeability of the MMM can be assumed to depend on those of the base polymer and the dispersed phase and the loading of the filler in terms of volume fraction [10]. e MWS model also incorporates the particle shape factor. Hashemifard et al. [15] and Nasir et al. [28] reviewed the applicability of the models at different particle loadings. Table 1 lists the available models and the parameters they require to estimate permeability. e Maxwell model (equation (1) in Table 1) was first developed in 1873 to predict the permittivity of dielectric conduction through a heterogeneous medium [34]. e model involves a constitutive equation in which the heterogeneous medium is assumed to be an analogue of the membrane flux. is allows the model to be applied for gas transportation in an MMM. However, the Maxwell model fails when a high loading of filler in the MMM produces the maximum packing of the volume fraction. Furthermore, this model is not suitable for predicting permeation when parameters such as the shape, size distribution, and aggregation of the particles must be considered.
An alternative model was originally proposed to derive the elastic modulus of particulate composites. is is known as the Lewis-Nielson model and is given by equation (4) in Table 1 [32]. For random close packing of uniform spheres, ϕ m is normally set at 0.64 [22]. When ϕ � ϕ m , the permeability ratio λ dm ⟶ ∞ as the relative permeability diverges.  Table 1) was developed for calculating the thermal conductivity of a composite particulate and has also been used to calculate permeability [35]. is model addresses the filler particle packing problem by applying a differential effective medium approach. e Pal model correctly predicts the behavior as ϕ ⟶ ϕ m by considering the effect of morphology on permeability through parameter ϕ m . However, it involves an implicit relationship that must be solved numerically for the relative permeability, P r .
Bouma et al. used the MWS model to predict the gas transportation characteristics of an MMM [33]. is model is given by equation (6) in Table 1, where n is the shape factor of the particle. Notably, the maximum and minimum values of the shape factor are used to derive the effective permeability of gas diffusion in an MMM, and these can be given by series or parallel models, respectively. However, no current model allows the effect of a third component (e.g., an ionic liquid) homogeneously distributed in the continuous membrane matrix to be considered when calculating the gas permeability of an IL3M. is study addressed the effect of adding an ionic liquid to an MMM and the optimization of the parameter affected by the ionic liquid in the theoretical calculation of CO 2 permeability.

Membrane Synthesis and Permeation Measurement
An MMM is a combination of polymer and molecular sieves. By combining the process characteristics of the polymer matrix and the superior transportation properties of the molecular sieve, MMMs combine the benefits of both materials [36]. In recent research, MMMs have been combined with ionic liquids to produce IL3Ms.

Synthesis of the Ionic Liquid Mixed Matrix Membranes.
In this study, PES was chosen to provide the polymer support required for fabricating the enhanced MMM. is was the commercial Ultrason E 6020 P used in industrial processing and was purchased from BASF, Germany, in flake form. e PES flakes were dried overnight prior to use to remove any trapped moisture. e ionic liquid was mixed with the N-methyl-2-pyrrolidone (NMP) solvent, and the SAPO-34 particles were dispersed in the mixture. e PES was then dried and weighed, before being dissolved in the mixture. e solution was stirred continuously to ensure homogeneity and degassed to remove bubbles prior to casting. e cast membranes were dried in an oven at 160°C for 24 h. e details of the materials used, method of membrane preparation, and membrane characterization are presented in more detail in our recent publication [25]. For use as a benchmark, a PES-based polymeric membrane was synthesized. e IL3Ms were synthesized using a fixed ionic-liquid concentration of 20 wt.% and SAPO-34 filler concentrations of 10, 20, and 30 wt.%.

Membrane Morphology Characterization.
Membrane morphology is critical for understanding transport mechanisms. is was characterized in the present study to clarify the effect of the added ionic liquid on the SAPO-34 orientation in the membrane matrix. Field emission scanning electron microscopy (FESEM, ZEIS SUPRA TM 55VP) was used for this characterization. Before scanning, the membranes were cut using liquid nitrogen to provide a smooth surface. Figure 1 shows the FESEM membrane sample of PES-SAPO-34 mixed matrix membrane with 10 wt.% ionic liquids. e average membrane thickness of all synthesized membranes is ∼10 µm.
(1) P: permeability of penetrants [29] Bruggeman Pal Lewis-Nielson (4) P m : polymer matrix permeability [31,32] ϕ m : maximum volume fraction of filler [33] n: shape factor 3.3. Gas Separation Performance Analysis. Gas permeance analyses were conducted following the procedure reported in our previous study [25]. Gas permeation was then calculated from the time taken by the gas mixture to pass across the membrane at constant volume. is was recorded using a bubble ow meter, after a steady-state condition had been reached. e separation performance study was conducted at a pressure range of 10-30 bar. To ensure the reliability of the results, three membranes were fabricated using each composition, and all the fabricated membranes were tested using the same gas permeation method.

Present Model
ree of the models listed in Table 1 were selected for validation purposes: the Maxwell, Lewis-Nielson, and MWS models. Statistical analysis was performed to assess the level of agreement between the experimental data and the predictions made by the models. When deriving the gas permeance using the theoretical models, a defect-free PES membrane was assumed. e experimental data on CO 2 permeance are given in Table 2.
e CO 2 permeance of SAPO-34 was taken from the literature [37]. Since the only data available on CO 2 permeance through an inorganic SAPO-34 membrane were obtained at a test pressure of 20 bar, the experimental data were also recorded at 20 bar. Two types of imidazolium-based ionic liquids were used to synthesize the IL3Ms. e gas permeation data for the IL3Memim[Tf 2 N] were used for model development.
e MWS model required the shape factor of the SAPO-34 particles to be speci ed. Based on [38], a value of n 0.33 was used because SAPO-34 has a cubic form, as shown in the FESEM image in Figure 2. Figure 3 compares the relative permeance of CO 2 against SAPO-34 loading predicted by the above-mentioned three models with the experimentally determined values. e absolute average error (AARE) was calculated using equation (1), and Table 3 summarizes the deviations between the models and the experimental data: From Table 3, the relative permeability predicted by the existing models showed a major deviation from the experimental data; the AARE values were high (>50%), suggesting the need for model improvement and modication. Figure 4 shows FESEM images of the SAPO-34 orientation in the PES polymer matrix at di erent      loadings. e FESEM analysis allowed the e ective shape of the llers to be determined as the loading was increased. e addition of ionic liquid caused the SAPO-34 to agglomerate, thereby changing the overall orientation of the inorganic ller. e analyses conducted using the theoretical models highlighted the importance of considering the morphology of the particles. As noted above, MWS is the only model that allows this. is model was therefore selected for modication, to bring it into line with the experimental data. A corrected parameter is needed to enable use of the model for accurate prediction of gas separation in an IL3M. e FESEM cross sections revealed that the orientation of the SAPO-34 depended on the ller and the ionic liquid loading. e addition of ionic liquid changed the overall orientation of the SAPO-34 such that the resulting shape was no longer cubic, as shown in Figure 2. is resulted from the SAPO-34 particles agglomerating and combining with each other.
is agglomeration became more pronounced as the SAPO-34 loading was increased. e FESEM results established that the shape factor is an important parameter in determining the P r theoretical value since it may also favor enhancement of permeation via the hopping mechanism. As shown in Figure 4, the orientation of the ller within the membranes changed as the SAPO-34 loading in the membrane was increased. e SAPO-34 agglomerated locally.
is became more pronounced as the loadings reached 20 and 30 w/w%, suggesting that the overall shape of the combined ller was also changing. To consider the shape factor, the MWS model required the optimization and improvement discussed in the following section.

Model Improvement and Optimization
To improve the MWS model, an additional parameter was incorporated. is modeled the e ect that addition of the ionic liquid had on the orientation of the particle shapes. It was assumed that the addition of ionic liquid wetted the inorganic llers, producing an unde ned geometrical orientation of the llers in the polymer matrix. Figure 5 shows these parameters. e ionic liquid was assumed to wet the inorganic particles, making ϕ d and n sensitive to their distribution, size, and orientation. e presence of ionic liquid also caused the SAPO-34 to become wetted, thereby increasing the volume fraction of the llers. In practice, these parameters are di cult to determine directly via FESEM analysis. e model prediction can be made accurate if these parameters are tted for each ller loading, as the morphology is a function of the ller loading. e MWS model developed in this study for use with an IL3M was modi ed to incorporate a corrected shape factor, n i , and the volume fraction of the wetted dispersed phase, ϕ w : where n i is the ideal shape factor (corrected shape factor) and ϕ w is the wetted volume fraction of the dispersed phase through the IL3M. e volume fraction of the wetted dispersed phase, ϕ w , was then rede ned as follows: where ϕ IL is the ratio of the ionic liquid distance that has surrounded the particles as shown in Figure 5, determined as follows: where r IL is the radius of the ionic liquid surrounding the dispersed phase, r d is the radius of the dispersed phase itself, and ϕ IL is determined from the correlation between ϕ w and ϕ d obtained from the tting analysis. If there is no wetting e ect from the ionic liquid, ϕ w will reduce to ϕ d . International Journal of Chemical Engineering 5 Physically, the ideal shape factor, n i , is the shape factor of the SAPO-34 particles after incorporation of ionic liquid since the ionic liquid a ects the SAPO-34 orientation in the polymer matrix.
is is de ned as follows: where n o is the optimized shape factor from the tting exercise and ϕ m is the maximum packing volume fraction of the inorganic ller (ϕ m 0.64). If ϕ w ϕ m , n i is reduced to n o . Sikander (2015) obtained an expression similar to equation (5) when optimizing the shape factor [39]. Any intermediate point value should therefore be directly obtainable from equation (5).

Determination of Volume Fraction of Wetted Dispersed
Phase ϕ w . e objective of this approach is to optimize the volume fraction of the wetted dispersed phase and to nd the correlation between ϕ w and ϕ d , as given by equation (3). e optimization procedures conducted against the experimental data were used to generate the ϕ w values shown in Table 4. ese values demonstrate that the incorporation of ionic liquid was su cient to wet the SAPO-34, eventually increasing the volume fraction of the wetted dispersed phase, ϕ w .

Determination of Ideal Shape Factor, n i .
e ideal shape factor, n i , used in equation (5) was determined via optimization analysis. Figure 6 shows the optimization curve obtained by applying the optimization procedure to the original MWS model against the experimental data. e evaluation of relative CO 2 permeability was repeated using the optimized shape factor n o 0.020, and a lower AARE (<25%) was returned. is analysis con rmed that the n parameter can be used to improve the predictions made by the model if the optimized values are known. Even the use of a single optimized value of n o improved the MWS model predictions, and the accuracy could be further improved if the shape factor could be tted at a speci c SAPO-34 loading.
is re ects the fact that the membrane morphology is a function of the distribution and aggregation of the particles.
If the shape factor at a speci c SAPO-34 loading is known, the gas relative permeability at any operating pressure can be predicted since the shape factor is independent of pressure. e n i factor was introduced to re ect the orientation and distribution of the particles. Optimization of the n i value produced the results shown in Table 5.
As equation (5) shows, the ideal shape factor depends on the value of ϕ w . e n i value is therefore expected to increase in line with the SAPO-34 loadings.

Determination of the Corrected Dispersed Phase Permeability, P d .
e actual dispersed phase permeability, P d , of CO 2 across SAPO-34 is critical to determine P r(e ) in equation (6) in Table 1. Since the P d value given in [37] was for SAPO-34 loading at 20-bar pressure, P d (CO 2 ) 1731.4 GPU was used in the present study to evaluate the theoretical performance only at this pressure. In addition, the e ect of pressure on relative permeability was investigated, and the P d values for CO 2 at the other testing pressures needed to be optimized accordingly. e tting and optimization for P d was performed using an indirect method. e least squares method was applied to the variable parameter values to reduce the predicted errors from the model. e corrected P d was obtained when the least error resulted. Since the tting method worked for 10 wt.% of SAPO-34, it was also used to determine the corrected P d at 20 wt.% and 30 wt.%. Table 6 summarizes the tted CO 2 P d values for all SAPO-34 loadings at pressures of 10, 15, 25, and 30 bar. e P d value at 20 bar was as stated and maintained accordingly.
As can be seen from Table 6, the optimized CO 2 P d values decreased with increasing pressure. is might be due to the concentration polarization of the intrinsic SAPO-34 inorganic membrane. Van de Graaf et al. reported that CH 4 became enriched at the support pores, eventually depleting the driving force of the quickly permeating gas. e depletion of CO 2 at increased pressures was also attributed to Shape factor, n Figure 6: Optimization curve of shape factor, n, through a shape factor data tting.

Results of Model Modi cation.
After applying the above modi cations, the theoretical predictions of CO 2 relative permeability (P r(e ) ) for the PES-SAPO-34 IL3Ms were calculated using equation (2). Table 7 shows the relationship between P r -experimental and P r -calculated for CO 2 . e AARE between the experimental and calculated P r values was less than 2%.
For clarity, the relationship between P r -experimental and P r -calculated is plotted in Figure 7. e results con rm that the modi ed model successfully predicted the CO 2 relative permeability of the IL3M.

Model Validation
6.1. Validation Using Di erent Data. As noted above, IL3Memim[CF 3 SO 3 ] was used for validation. e value of the dispersed phase permeability, P d , was that used in the previous section. However, the volume fraction of the wetted dispersed phase, ϕ w , and the ideal shape factor, n i , needed correction since a di erent ionic liquid was used. To determine these values, the correlations obtained from equations (3) and (5) were applied to ϕ w and n i , respectively. Table 8 shows the ϕ w and n i values for the IL3M-emim [CF 3 SO 3 ]. e CO 2 relative permeability (P r(e ) ) of the PES-SAPO-34-emim[CF 3 SO 3 ] IL3M was predicted theoretically using equation (12). Table 9 shows the relationship between the P rexperimental and P r -calculated values. e AARE between the experimental and calculated P r values was less than 3%. e approach was shown to achieve better agreement between the experimental and calculated values of P r(e ) . e experimental and calculated values of P r are shown in Figure 8, with R 2 0.95.

Validation
Using Data from the Literature. In this section, we review data from the literature on membrane fabrication incorporating ionic liquids. Hudiono et al. investigated CO 2 /CH 4 separation using MMMs comprising a styrene-based polymer, SAPO-34 as the zeolite ller, and emim[Tf 2 N] as the ionic liquid [17]. e CO 2 permeability reported in that study is shown in Table 10. e study con rmed that the incorporation of a su cient volume of ionic liquid into the styrene-based-SAPO-34 MMM increased CO 2 permeability and selectivity. ey concluded that the addition of ionic liquid had wetted the surface of the SAPO-34, making it compatible with the styrene-based poly(RTIL). e high CO 2 di usivity of the emim[Tf 2 N] produced an overall enhancement of gas permeability.     is study suggested that the presence of ionic liquid changed the orientation of the SAPO-34. e ideal shape factor, n i , was therefore introduced by incorporating the ionic liquid concentration into the model. e SAPO-34 llers were also believed to have been wetted by the RTIL, and ϕ w was also calculated using equation (3). e ideal shape factor, n i , was calculated using equation (5). e CO 2 relative permeability was recalculated using equation (12), which incorporated both ϕ w and n i . e calculated data are shown in Table 11, and the relationship between the experimental and theoretical data is presented in Figure 9.
As can be seen from Table 11, the AARE fell below 5% when the MWS model was modi ed by incorporating ϕ w and n i .

Conclusions
ree of the most widely used models for estimating the permeability of a gas through an MMM were applied to     International Journal of Chemical Engineering membranes modi ed by adding an ionic liquid. All three models showed high rates of error. e e ective shape factor was found to be a critical parameter in the MWS model. e addition of ionic liquid had produced local agglomeration of SAPO-34 within the membrane matrix, thereby changing the overall orientation of the ller. erefore, the shape factor was modi ed to include both the ionic liquid and ller loading e ects. e ideal shape factor, n i , and volume fraction of wetted dispersed phase, ϕ w , were determined. Calculating relative permeance using a modi ed MWS model incorporating ϕ w and n i showed better agreement between the experimental and predicted values. e modi ed model was validated against a di erent set of experimental data and against values reported in the literature. Both showed good agreement between the predicted and experimental values, with an AARE of less than 5%. Our results con rm that the modi ed MWS model can be used to predict the performance of IL3Ms.

Data Availability
Previously reported CO 2 and CH 4 permeability data were used to support this study and are available at https://doi. org/10.1016/j.seppur.2014.08.019. ese prior studies (and datasets) are cited at relevant places within the text as reference [22].

Conflicts of Interest
e authors declare that they have no con icts of interest. International Journal of Chemical Engineering 9