Simulation of Binary CO 2 / CH 4 Mixture Breakthrough Profiles in MIL-53 ( Al )

MIL-53 (Al) aluminum terephthalate, a commercialmetal-organic framework, has been studied as a potential candidate for pressure swing adsorption separation of CO 2 /CH 4 binary mixtures. Pure gas isotherms of CH 4 and CO 2 measured over 0–6MPa and at room temperature are fitted with the Dubinin-Astakhov (D-A) model. The D-A model parameters are used in the DoongYangMulticomponent adsorption model to predict the binary mixture isotherms. A one-dimensional multicomponent adsorption breakthroughmodel is then used to perform a parametric study of the effect of adsorbent particle diameter, inlet pressures, feed flow rates, and feed compositions on the breakthrough performance. CommercialMIL-53with a particle diameter of 20μmrenders high tortuous flow; therefore it is less effective for separation.More effective separation can be achieved ifMIL-53monoliths of diameters above 200 μm are used. Faster separation is possible by increasing the feed pressure or if the starting compositions are richer in CO 2 . More CH 4 is produced per cycle at higher feed pressures, but the shortened time at higher pressures can result in the reduction of the CH 4 purity.


Introduction
Pressure swing adsorption (PSA) is a well-established gas purification process which has already been employed in multiple applications, including hydrogen separation and purification [1][2][3], air purification [4], raw natural gas purification, and CO 2 capture [5,6].Due to its potential to purify CH 4 from CO 2 /CH 4 mixtures especially in small and medium industrial scales, PSA techniques are currently being extended to new areas like methane purification from biogas and landfill gas [7][8][9][10].For zeolites [11] or activated carbon [12], which are the most commonly used adsorbent materials for PSA purification of biogas/landfill gas, the adsorbent regeneration is still difficult and energy consuming, leading to lower productivity and higher expenses [9,13].
Breakthrough performance of adsorbent columns is an important characteristic required to evaluate the potential of adsorbents for PSA applications.There have been a few experimental measurements of breakthrough performance of MOF adsorbents for separating CO 2 /CH 4 mixtures [17,19].Heymans et al. used experiments and simulations to predict breakthrough performance of MIL-53 (Al) for acidic gas separation from CH 4 /CO 2 mixture [27].Even though they used both the experiments and simulations, their studies were restricted to a single gas mixture composition (50 : 50) at a single pressure of 1.06 bar and no parametric effects

Experimental
Particle size distribution, pure gas isotherms, and adsorption isosteric heat of commercial MIL-53 (Al) aluminum terephthalate C 8 H 5 AlO 5 were measured using standard methods.A JEOL Scanning Electron Microscope (JSM-5510) was used to measure the particle diameter and estimate the diameter distribution of the MOF particles.The pure gas adsorption isotherms of CO 2 and CH 4 were performed at room temperature in the range of pressures between 0 and 6 MPa using Sievert's volumetric gas adsorption system.The BET specific surface area, pore size distribution, and other pore characteristics were measured by adsorbing N 2 at 77 K in a Micromeritics ASAP 2020 analyzer.Gases used for the measurements are high purity gases (99.999%) supplied by Praxair Canada.Isosteric heat of adsorption and heat capacity of MIL-53 were measured using a coupled volumetriccalorimetric system.Powder X-ray diffractometer (Bruker D8 FOCUS, Cu K) was used to examine the crystalline structure of the MIL-53.The coefficients of diffusions for equimolar binary mixtures of CH 4 and CO 2 were measured using an isotope exchange system.

Theory
A one-dimensional multicomponent adsorption breakthrough model based on the approach proposed by Casas et al. is presented here [29].This model accounts for the mass and heat transfer inside a nonisothermal adsorbent column filled with MIL-53, the heat transfer in the fluid and in the gas-phase, and the conductive and convective heat transfer between the column wall and the surroundings.The following restrictions are assumed in the model: ambient temperature is considered to be constant, radial gradients in the column are negligible, mass transfer coefficients and isosteric heat of adsorption and heat capacities of the solid phase and of the wall are constants, and axial conductivity on the wall of the column is assumed to be zero.The adsorptive mass transfer rate is expressed in the form of a linear driving force (LDF) model.This breakthrough model was extensively validated by different authors for the PSA applications with good results [5,6,29,30].

Mass and Energy
Balance.The total mass balance in the breakthrough column is given by Mass balance for each species is given by where  is the total concentration of the fluid phase,   the fluid phase concentration for each component,   the adsorbed phase concentration for each species,  the superficial gas velocity,   the total porosity,   the bed porosity,   the column bulk density,   the axial dispersion coefficient (for all components),  the time,  the longitudinal coordinate on the column,   the gas-phase mole fraction of the th component, and  the number of components in the gas mixture.The pressure drop is calculated from Darcy's law, where pressure gradient, velocity, and porosity are correlated as Here,  is the permeability of the material,  the dynamic viscosity, and   the particle diameter.The time-dependent variation of the absolute adsorption is described using the LDF adsorption kinetics model: where   is the mass transfer coefficient,  * the solid phase concentration at equilibrium pressure, and  the solid phase concentration at time .To describe the adsorption isotherms, we use the D-A isotherm model.The absolute adsorption in the D-A model is given by Here,   is the absolute adsorption of th component of the mixture,  max the maximum absolute adsorption corresponding to saturation pressure   ,  the characteristic energy of adsorption,  the measure of the pore heterogeneity of the microporous material [31][32][33],  the ideal gas constant,  the temperature, and  the gas pressure.The measured excess adsorptions of pure gases are converted into absolute adsorption using [34]  abs =  exc 1 −  gas / sat , where  abs ,  exc ,  gas , and  sat are the absolute adsorption, the excess of adsorption, and the density of the gas phase and of the adsorbed phase, respectively.

State Equation (EOS).
In the range of temperature and pressures considered in this study, we note that the compressibility factors of CO 2 /CH 4 gas mixtures (reported in the NIST REFPROP Standard Reference Database [35]) are between 0.9 and 1. Hence to describe the state of the gases, we use the equation of state of an ideal gas: 3.3.Porosity.The porosities are determined using where   is the bulk density,  sk the skeletal density,   the bed porosity,  mi the microporosity,   the total porosity, and   the micropore volume.The skeleton density  sk is determined using the helium expansion method in standard Sievert's apparatus,   is the bulk density measured using ASTM standard procedure (ASTM D 2854-96), and the micropore volume   is obtained from the measurements of the pore size distribution with nitrogen at 77 K in an ASAP instrument.
For describing the multicomponent adsorption isotherms, we use the Doong-Yang Model.The DYM is based on the pure gas isotherms D-A model parameters reported in Table 3.The DYM adsorption model for a multicomponent mixture is given by For binary gas adsorption, the respective amount of each adsorbed component is given by Equations ( 10) can be written as by substituting In ( 10)-( 11)  0 is the limiting micropore volume of component  and   the volumetric amount of adsorbate for each component.For converting the experimental isotherms between molar and volume units, the following expressions are used: Further details of DYM are available in Doong and Yang, Rege et al. [4,36], and the authors' previous work [34].
The energy balance equation for the column (fluid and the solid phase) is given by the following equation: where   is the heat capacity of the gas,   the heat capacity of the solid,  ads the heat capacity of the adsorbed phase, Δ  the isosteric heat of adsorption for each component, ℎ  the heat transfer coefficient (inside the column + wall),   the axial thermal conductivity in the fluid phase,  the temperature inside the column,   the temperature of the column's external wall, and   the inner diameter of the tube.The energy balance is also defined for the heat exchange between the wall and the surroundings, where the effects of conduction between the column and the ambient are considered.This is given by where   is the heat transfer coefficient between the wall and the surroundings,   the heat capacity of the column wall,   the area of the cross section of the column, and   the column's external diameter.

Boundary and Initial Conditions.
The boundary conditions used in the model are described below.
Inlet boundary conditions of the system (i.e., at  = 0) are Outlet boundary conditions (i.e., at  = ) are Initial conditions at  = 0 for 0 ≤  ≤  are The heat capacities of the fluid and the adsorbed phase in (15) are defined using where the specific heat capacities  mol , are calculated as an average over a range of temperatures from ambient temperature to the highest temperature reached in the adsorption column for each pressure under study.This assumption will add also more simplicity to the model, without affecting the accuracy of the results [29].Note that the concentration and heat capacity of the fluid and of the adsorbed phase are temperature-dependent quantities.
The heat transfer coefficient ℎ  is obtained from the Nusselt number,   : where In ( 21) and ( 22),   is the internal radius of the column,   the axial thermal conductivity in the fluid phase, and Re the Reynolds number.The values for  1 and  2 are calculated from the correlation of heat transfer coefficients for gases through packed tubes [37].
The thermal conductivity is estimated using where   is the axial dispersion coefficient which is calculated with the Edwards-Richardson correlation [38]: where  is the velocity,   is the molecular diffusion coefficient calculated according to the Fuller method [39], and   is the particle diameter.The heat transfer coefficient between the wall and surrounding is calculated using where the heat transfer parameters  and  are reported in the literature for free convection cases [40]. max is the maximum temperature during the adsorption process and  min is assumed to be room temperature.
The system of mass and energy balance partial differential equations is solved using the commercial software platform COMSOL Multiphysics using modules for heat transfer of porous media, heat transfer of fluids, transport of diluted species, and Darcy's law.The default equations of COMSOL modules are redefined according to the aforementioned system of equations.Table 1 lists the model parameters used in our study.Column properties used are typical values of stainless steel.

Material Characterization. The XRD pattern of MIL-53
shown in Figure 1(a) is similar to that of MIL-53 samples reported previously [41].Results for the particle size and particle size distribution are shown in Figures 1(b) and 1(c).The particle size distribution histogram obtained using a bin width of 1 m shows that most particles have diameters between 17 and 25 m with a peak distribution at ∼20 m.Pore and surface characterization, densities, and porosities of MIL-53 are given in Table 2.
Since no reported diffusion coefficients of CO 2 and CH 4 in MIL-53 are available yet, we used those available for MOF-5.These coefficients of diffusion   were measured for an equimolar mixture of CO 2 and CH 4 on MOF-5 using the isotope exchange technique [34].Diffusion coefficients of CO 2 /CH 4 on different MOFs (MIL-53, MIL-101, and Cu-BTC) are found to have similar order of magnitudes, so this approximation is not expected to cause significant errors [42,43].The mass transfer coefficients are listed in Table 1.
The isosteric heat of CO 2 and CH 4 adsorption on MIL-53 is measured using a coupled volumetric-calorimetric system.The absolute adsorption required for the isosteric heat is obtained using Tóth's adsorption model fit for the measured excess adsorption isotherms [44].The specific heat capacity of MIL-53 was measured using a SETARAM calorimeter and is given in Table 1.

4.2.
Pure and Mixed Gas Isotherms.Pure gas adsorption isotherms of methane and carbon dioxide on MIL-53 are given as symbols in Figure 2.These measurements are made at 294.15 K for a pressure range between 0 and 6 MPa using a conventional Sieverts volumetric apparatus.The detailed description of the method is available from earlier works [34,45].and pressure ranges [4,36].One of the very important factors we need to consider when using the models is the ease of applicability of the models in computational fluid dynamics simulations.The parameters from the DYM/D-A models can be directly used to express the adsorptive mass source terms in the mass balance equation (, (1)).Additionally, they provide an analytical expression for loading dependentadsorption isosteric heat which can be easily implemented in the energy balance equation (Δ, , (15)).This is unlike certain other models, such as multipotential theory of adsorption, which requires either the parameterization of the predicted isotherms or the use of iterative techniques within the CFD models [46,47].Both D-A model and DYM are based on the theory of micropore volume filling which postulates that adsorption in microporous adsorbent occurs by filling of the micropore volume.
The pure gas isotherms are fitted with the D-A model and are given as lines in Figure 2   isotherm model [36] using the pure gas isotherm regressions parameters.In Figure 2(b), the predicted binary adsorption isotherms are compared with the experimental equimolar binary adsorption isotherms on MIL-53 (Cr) measured by Hamon et al.Even though the isotherms cannot be quantitatively compared, they exhibit similar behavior for CH 4 and CO 2 .We can conclude that our predictions are in agreement with the experimental data.The DYM isotherm equations are summarized in ( 9) to (14a), (14b), and (14c).
The efficiency of MOF MIL-53 (Al) for the separation of a binary CH 4 /CO 2 mixture can be analyzed and compared in terms of the sorption selectivity.The selectivity of th component in a mixture of components  and  is defined on a molar basis as  , = ( sat, /  )/( sat, /  ).Here, we compare the selectivity of our sample to selectively remove CO 2 from an equimolar CO 2 /CH 4 mixture with the selectivities of other MOFs reported in the literature.In the pressure range below 0.5 MPa, the selectivity of our sample shown in Figure 3 decreases initially rapidly with pressure of about 0.1 MPa, after which it remains almost constant.The selectivity of MIL-53 reported by Hamon et al. on the other hand shows a step-like decrease, by a factor of ∼3 at 0.6 MPa, after which it shows only a slight decrease [19].The sample used by Hamon et al. showed two characteristic adsorption steps which were attributed to the breathing phenomenon.As the CO 2 pressure increases, a step is observed at around 0.6 MPa [13] leading to larger uptake.This uptake is attributed to the change of MIL-53 from "narrow pore" to "large-pore" structure.On the other hand, the sample used in our work is a commercial material that shows no breathing phenomena.No drastic change in the selectivity is observed at around 0.6 MPa.Among all MOFs compared here, Cu-BTC [18] has We used the validated model to study the effects of particle size, inlet pressure, feed composition, and gas flow rate on the breakthrough of CO 2 /CH 4 gas mixtures through the MIL-53 adsorbent column.The inlet and wall temperatures are set to 294.15 K.A 25 cm column length is considered for all simulations.For monitoring the evolution of temperature in the bed, four axial positions at 5, 10, 15, and 20 cm from the inlet of the column are chosen.

Effect of Particle Diameter.
In order to study the effect of MIL-53 (Al) particle size on breakthrough performance, we considered particle diameters 20, 200, 300, 500, and 1000 m.
Inlet pressure is fixed at 0.2 MPa and an equimolar CO 2 /CH 4 mixture is fed at a rate of 30 mL/min.In general, for the simulations with particle diameters lower than 20 m, we found that the numerical model presents some limitations.An examination of the mass balance shows that the numerical results start to deviate from the mass predicted by the local pressure.This perhaps arises due to the large pressure drop caused by smaller particles, which is consistent with the general recommendation to use particle sizes of the order of 1 mm to avoid large pressure drops in gas-phase separations [6,7,17].Therefore, we present the results only for 200, 500, and 1000 m.Based on the literature, we set the particle size to 500 m to investigate the effects of inlet pressure, flow rates, and feed concentration in further sections.
In left panels of Figure 5, breakthrough times for   / 0 = 10%, where   is the molar fraction of the component and  0 is the feed concentration, are found to be around 7.9 minutes when particle sizes are 200 and 500 m, while they are 7.7 minutes when the particle size is 1000 m.In the right panels of Figure 5, the evolution of temperature at the positions 5, 10, 15, and 20 cm from the inlet of the column is shown.As adsorption is an exothermic process, the resulting adsorption heat is released into the bed.This increases the column temperature as the gas fronts move from the inlet to the outlet.We simulate the temperature evolution at four axial positions in the column.The temperature rises to around 333 K when 200 and 500 m particles are used, while for the 1000 m particles the temperature rises up to 336 K.At each position two different temperature peaks are observed; the low temperature peak corresponds to the CH 4 front and the higher temperature peak to the CO 2 front.From the simulation results, we find that the CH 4 front moves faster than CO 2 front.The peaks shape is influenced by the mass and heat transfer parameters: the initial fast abrupt front indicates fast mass transfer, whereas the shape of the tail is controlled mainly by the heat transfer from the column to the environment.The latter one is responsible for the time required to reach the feed composition at the outlet of the column, once the CO 2 breakthrough is noticed.Since the temperature of the column continues to decrease until it reaches the initial temperature, more CO 2 is adsorbed which finally results in a CO 2 flat front.
Larger particles can be prepared either by mechanically compacting pristine MOFs to monoliths or by applying a binder, such as polyvinyl alcohol (PVA) or expanded natural graphite (ENG).Depending on the activation temperature, the preparation of monoliths by the addition of binder will cause partial pore blocking.The blocked pores reduce the adsorption capacity by as much as 19% of pristine powder MOF material.But this has minimum impact on the overall pore size distribution [17].Binderless mechanical compaction of MOFs on the other hand causes partial collapse of frameworks, which reduces the sorption capacity by ∼15% [49].Our results are in agreement with Grande who recommends using the pellets instead of powder materials for efficient PSA separation [50].

Effect of the Inlet Pressure.
In order to study the effect of the inlet pressure on the breakthrough curves, we set the inlet pressure to 0.5, 1, and 2.5 MPa. Figure 6 displays the breakthrough and temperature profiles for different inlet pressures.The particle size is fixed at 500 m for all simulations.As seen in the left panels of Figure 6, the breakthrough time decreases with increasing feed pressure.The breakthrough times of 5, 3.3, and 1.9 minutes are obtained with the feed pressures 0.5, 1, and 2.5 MPa, respectively.Furthermore, the higher the feed pressure, the higher the temperature along the column, ∼358, 388, and 444 K, respectively, for 0.5, 1, and 2.5 MPa.As gas with higher inlet pressure flows through the bed, larger amounts of gases are adsorbed, leading to higher amounts of adsorption heat released into the bed.

Effect of the Mass Flow Rate.
In order to study the impact of the mass flow rates on the breakthrough curves, we set the mass flow rate to 10, 25, and 50 mL/min.Figure 7  displays the breakthrough and the temperature profiles for different mass flow rates.As in the case of previous simulations, the particle size is fixed at 500 m for all simulations.
As seen in the left panels of Figure 7, the breakthrough time decreases with increasing of the mass flow rate.For mass flow rates of 10, 25, and 50 mL/min, the breakthrough times are 10.65, 4, and 1.9 minutes.Also, the higher the mass flow rate, the higher the temperature along the column, ∼375, 385, and 392 K for 10, 25, and 50 mL/min.Gas with the higher mass flow rate leads to larger amount of adsorption.This leads to higher amounts of adsorption heat released into the bed.CO 2 concentration in the feed gas mixture accelerates the breakthrough time [29,51].Similar behavior is also observed for the 0.5 and 2.5 MPa feed pressures.Larger concentration difference between the compositions results in faster saturation of the adsorbent with one component which eventually leads to shorter breakthrough times.The lowest breakthrough time of as short as 1.55 minutes is observed for the highest feed pressure (2.5 MPa) and highest CO 2 molar concentrations (75%).The behavior of the temperature evolution on the other hand shows an increase at increasing the feed concentration and the feed pressure which is attributed to the larger amount of gases adsorbed.
The different breakthrough times for CH 4 and CO 2 obtained with different feed pressures and molar compositions directly affect the amount of pure CH 4 produced in each PSA cycle.The amount of pure CH 4 produced in a cycle can be calculated from the outlet flow rate and time between the onset of the flow and breakthrough.Note that the reduction of adsorption capacity due to pelletization should also be accounted for while calculating the amount of pure CH 4 produced in each cycle.Based on the reported adsorption capacities of monoliths, we used 15% reduction factor to calculate the amount of pure CH 4 produced.As seen in Figure 9, at higher feed pressure, more CH 4 is produced per cycle, even though each cycle lasts less than that for lower feed pressures (from left to right of Figure 8).On the other hand, the amount of CH 4 produced at the specified purity with respect to the feed composition decreases with the increasing pressure.This means more CH 4 remains in the column by the time CO 2 breaks through, as it is confirmed in a similar case for a CO 2 /H 2 gas mixture [6,29].In a continuous process this is circumvented by adjusting the cycle time in such a way that the CH 4 loss is minimized [29].
The separation capacity of MIL-53 (Al) for CO 2 and CH 4 is between 7.8 at 0.1 MPa and 7.1 at 1.5 MPa at 294.15 K based on the selectivity correlation  , = ( sat, /  )/( sat, /  ) [34].These values are consistent with the values reported by Finsy et al. on the separation of an equimolar CH 4 /CO 2 mixture at 303 K in a packed column with MIL-53 (Al, PVA) pellets containing 13 wt% PVA binder [17].Selectivities calculated from pure component isotherms on the 13X zeolite [11] and the activated carbon material Norit R1 Extra [12] are 2 and 2.7 at 1 MPa compared with 5.5 for MIL-53 (Al).

Conclusions
To conclude, we presented a parametric study of MIL-53 aluminum terephthalate particle size, inlet pressure, mass flow rate, and feed composition on the breakthrough of CO 2 /CH 4 binary gas mixtures.Pure gas CO 2 and CH 4 adsorption isotherms on commercial MIL-53 were measured using Sieverts method and were fitted with the D-A analytical model.Using the D-A model fit parameters, binary adsorption isotherms were predicted.These isotherms agree well with the reported experimental binary isotherms measured on isotypic MIL-53 chromium terephthalate.A one-dimensional multicomponent adsorption model was used to simulate the breakthrough behavior of CO 2 /CH 4 mixtures in a column packed with MIL-53 (Al).The model was initially validated by applying it to simulate the breakthrough of H 2 /CO 2 mixtures reported in the literature.Experimentally measured particle size, porosity, kinetic diffusion parameters, isosteric heat, and specific heat were used in the model to increase the reliability of its predictions.In the parametric study, we considered the effect of adsorbent particle diameters (5,20,200, 300, 500, and 1000 m), feed pressures (0.2, 1, and 2.5 MPa), feed flow rates (10, 25, and 50 mL/min), and inlet compositions (25%, 50%, and 75% CO 2 ) on the breakthrough performance.As-purchased MIL-53, with a peak particle diameter of 20 m, was found to be less effective for separation because of the higher pressure drops.Effective separation within two minutes of the onset of flow was achieved for MIL-53 monoliths of diameters above 200 m.We found that faster separation can be made possible by increasing the feed pressure from 0.2 MPa to 2.5 MPa and also if the starting compositions are rich in CO 2 .As higher pressure CO 2 richer stream passed through the column, more heat was generated in the column when compared with the low-feed pressure CH 4 rich stream.More CH 4 was produced per cycle at higher feed pressures, even though each cycle lasted less than that for lower feed pressures.On the other hand, increasing pressure decreases the CH 4 recovery.
(a).The data are compared with CO 2 and CH 4 pure gas isotherms on isotypic MIL-53 (Cr) reported by Hamon et al.The structures of both Al and Cr variants of MIL-53 MOFs series are built up from similar infinite chains of corner-sharing MO 4 (OH) 2 (M = Al 3+ , Cr 3+ )

Figure 6 :
Figure 6: Effect of feed pressure on the breakthrough profile and temperature on MIL-53 for an equimolar CO 2 /CH 4 mixture.

Figure 7 :
Figure 7: Effect of the mass flow rate on the breakthrough profile and temperature on MIL-53 for an equimolar CO 2 /CH 4 mixture.
‡Properties are determined from NIST REFPROP as functions of the pressure and temperature at the inlet.

Table 2 :
Pore and surface characterization, densities, and porosities of MIL-53., CH 4 , and N 2 on microporous adsorbents.We have used this model in the past to predict the isotherms of binary mixtures of CH 4 and CO 2 on MOF: Cu-BTC.DYM model is an extension of Dubinin-Astakhov analytical model, which accurately predicts the pure gas adsorption isotherms on microporous adsorbents over wide temperature

Table 3 :
[13,48]el parameters for the adsorption of pure methane and carbon dioxide on MIL-53 (Al).Isotherms of CO 2 and CH 4 on MIL-53 (Al) compare well with those on MIL-53 (Cr).This agrees well with earlier results on isotypic MIL-53 reported by Bourrelly et al. and Alhamami et al.[13,48].Both pure gas isotherms are fitted with the D-A model with a standard error of estimate (SEE) of 1.05 for CO 2 and of 0.626 for CH 4 .The corresponding fit parameters are presented in Table3.The mixed gas isotherms on MIL-53 (Al) are constructed using the Doong-Yang Multicomponent MPa inlet pressure appears at 9.8 minutes, while shorter breakthrough times of 7.8 and 6.7 minutes are observed when the CO 2 feed composition is increased to 50 and 75%.In other words, we see that the larger