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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Metal-Organic Frameworks for Helium Recovery from Natural Gas via N/He Separation: A Computational Screening 2

Pezhman Zarabadi-Poor, and Radek Marek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07804 • Publication Date (Web): 18 Jan 2019 Downloaded from http://pubs.acs.org on January 21, 2019

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The Journal of Physical Chemistry

Metal-Organic Frameworks for Helium Recovery from Natural Gas via N2/He Separation: A Computational Screening

Pezhman Zarabadi-Poor*,† and Radek Marek*,†,‡

†

CEITEC – Central European Institute of Technology, Masaryk University, Kamenice 5,

CZ-62500 Brno, Czechia ‡

Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, CZ-62500

Brno, Czechia

Email: P.Z. : [email protected] R.M.: [email protected]

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Abstract In this account, almost 500 metal-organic frameworks (MOF) were subject of in silico screening for helium separation from natural gas. The equimolar mixture of helium and nitrogen was selected based on the available technical data for operating units. Geometry-based structural analysis followed by grand canonical Monte Carlo simulations were used to study several parameters including the effect of helium dilution in the gas mixture and electrostatic interactions in target gas uptake. We established structure-property relationships among various factors including adsorbent performance indicator (API) to rank MOFs based on their performance which also brought us valuable knowledge on the desired ranges of helium void fraction, accessible surface area, and pore diameter. We have identified top 10 performing MOFs for adsorption-based separation which have been consequently studied in more detail to obtain deeper insight on the possible adsorption sites and adsorptive behavior. We also assessed the diffusion-based separation to identify top performing MOFs based on the membrane selectivity.


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INTRODUCTION Although helium (He) is the second most abundant element in the universe, its escape to the space makes it relatively rare in the earth atmosphere and leaves the natural gas (NG) the only practically reliable source of helium. However, it has an irreplaceable role in various cryogenic applications such as cooling down the superconductor magnets that consumes around 35% of helium production.1,2 This clearly demonstrates its importance insomuch that nuclear magnetic resonance (NMR) spectrometers and magnetic resonance imaging (MRI) scanners cannot be operated to serve science and health care domains. The other significant roles of helium, such as carrier gas in gas chromatography, leak detector, and inert gas provider in welding, can be added to in-danger fields due to possible helium shortage and crisis happening.2 To emphasize the momentousness of this issue, European Union recently put helium in the list of critical raw materials.3 Therefore, searching for more feasible production and recovery procedures requires serious and urgent attention. The schematic representation of units dealing with helium production from NG is depicted in Figure 1.1,4 The process starts by the feedstock from nitrogen rejection unit (NRU) providing 1-3% He at ~1.2 bar to the helium recovery unit (HRU). In the second step, the helium upgrading unit (HUU) receives a crude feed containing 50-70% of He and delivers 90% He to the helium purification unit (HPU) where the outcoming gas is being ready to be sent for liquification. It is also noteworthy that not only all NG reservoirs do carry considerable helium content to be extracted but also not all NG refinery plants have helium production units. In the latter case, the helium is being purged to the atmosphere after NRU processing. It should be mentioned that like other large-scale gas separation processes, the cryogenic distillation is the main approach used in these units which is an energy intensive procedure. Consequently, it highlights again the critical situation with developing beyond state-of-the-art processes and materials to enhance performance of the aforesaid units. 3 ACS Paragon Plus Environment


Figure 1. Representation of units for helium extraction in a natural gas plant

Solid adsorbents are excellent candidates for cryogenic distillation to improve the operational efficiency. Metal-organic frameworks (MOF) with practically infinite number of structures are synthesized through concoction of limited number of organic linkers and metal nodes.5 Large surface area of MOFs combined with their tunable pore size and synthesis modularity delivers unique characteristics and subsequently make them auspicious for several applications6 such as gas adsorption and separation7–17, catalysis18,19, and electric devices.20–22 To the best of our knowledge, very few reports dealt with the helium separation utilizing MOFs and they all considered membrane-based upgrading approach.23–28 For instance, Keskin et al.23 recently studied helium upgrading by means of high throughput screening of MOFs for He/CH4 separation through molecular simulations and identified the adsorption and diffusion selectivities. However, our careful investigation of process according to the review by Rufford et. al.1 and Air Liquide Advanced Technologies paper by Fauve et. al.29 describing industrial working operation for helium recovery, illuminated us that the separation of helium and nitrogen in equimolar mixture at 1.2 bar seems more interesting and 4 ACS Paragon Plus Environment

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reasonable. In the present account, we benefit from advanced molecular simulation techniques to screen almost selected 500 structures for the helium upgrading application. We explore the structure-property nexus and discuss about the horizons and prospects for future applications. SIMULATION DETAILS Geometric Characteristics

The geometric and structural characteristics of MOFs were calculated by using Zeo++ code30 with high accuracy flag on. The code is shipped with implemented atomic radii from crystal structure database (CSD), however, we used the atomic values adopted from universal force field (UFF)31 to keep results consistent for all the atoms including those with insufficient data available from CSD. The largest included sphere (known as the largest cavity diameter; LCD) and the largest free sphere (known as the pore limiting diameter, PLD) were calculated by rolling nitrogen probe (3.64 Å; N2 kinetic diameter). The accessible surface area (ASA) was calculated using same probe by 100,000 Monte Carlo (MC) trial moves on each structure. Gas adsorption simulations

Grand canonical MC (GCMC)32,33 implementation in RASPA34 suite of codes was used to perform molecular simulations. Non-bonded interaction energies (Uij) were evaluated using Lennard-Jones (LJ) and Coulombic potentials32,33 expressed in Eq. 1.

𝑈𝑖𝑗 = 4𝜀𝑖𝑗

[( ) ( ) ] 𝜎𝑖𝑗 𝑟𝑖𝑗

12

―

𝜎𝑖𝑗 𝑟𝑖𝑗

6

+

𝑞𝑖𝑞𝑗

Eq. 1

4𝜋𝜀0𝑟𝑖𝑗

where, i and j are interacting atoms, σij and εij are the LJ diameter and well depth, respectively, and rij is the distance between atom i and j. The LJ parameters between different type of atoms are calculated using Lorentz-Berthelot mixing rules. The UFF31 parameters were adopted for all framework atoms while TraPPE35 force field parameters were used for the nitrogen molecule. N2 is considered as three-site linear rigid molecule (σN and εN/kB are 3.310 5 ACS Paragon Plus Environment


Å and 36.0 K, respectively) with a point charges located at nitrogen atoms (q = -0.482) and the center of mass (q = 0.964) to mimic the quadrupole moment of N2. The LJ parameters of helium are taken from Hirschfelder et. al. (σHe and εN/kB are 2.640 Å and 10.9 K, respectively). The adsorbate configurations within the MOFs was equilibrated by 20000 MC cycles which was followed by another 20000 cycles for producing ensemble averages. An MC cycle consists of n steps that is the greatest number between 20 and the number of molecules at the beginning of each given simulation point. Random translation, rotation, reinsertion, and swap moves with equal probability were performed in each simulation as well as particle identity change for the mixture simulations. Among published databases36–44 for high throughput screening, we chose Computational-Ready Experimental (CoRE) MOF structures which were optimized in solid state companying accurate density derived electrostatic and chemical (DDEC) charges.36 We modified the database based on a recent publication by Barthel et. al.45 where duplicate and problematic structures are identified. All MOFs are considered rigid and therefore all atoms are kept fixed at their positions taken from Crystallographic Information File. This assumption is widely used in the gas adsorption studies of MOFs and showed perfect agreement with experimental results.13,46,47 It has been also validated and implemented in this study (see method validation in SI). The cut-off value of 12.8 Å is chosen which implies constructing simulation box of n1 × n2 × n3 MOF unit cells in a manner to mimic periodic boundary condition and avoid minimum image convention. The Coulombic-potential computation is performed using DDEC charges and long-range electrostatic interactions were obtained by Ewald summation with the precision of 1×10-6. The adsorption isotherm data for single component (N2 at 0.05 and 0.6 bar) and equimolar binary mixture of He and N2 (at 0.1 and 1.2 bar) were calculated at 298 K. The Peng-Robinson equation of state (PR-EOS) was used to calculated Fugacities to run the GCMC simulations. Pre-tabulated energy grids with 0.1 Å spacing were used to accelerate the simulations.


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Although the reported data are based on absolute amount of adsorbed gas in MOFs, they are converted to the excess adsorption data applying Eq. 2 where comparison to the experiment is done: Eq. 2

𝑁𝑡𝑜𝑡𝑎𝑙 = 𝑁𝑒𝑥𝑐𝑒𝑠𝑠 + 𝜌𝑔𝑎𝑠 × 𝑉𝑝

, where Ntotal and Nexcess are the absolute and excess adsorbed amount of the gas, ρgas is the bulk density of the gas at simulation condition computed by PR-EOS, and Vp is the pore volume. RASPA internally calculates the Vp using the provided helium void fraction which is pre-calculated by Widom particle insertion..48 Equilibrium Molecular Dynamics (EMD) simulations for calculation of N2 and He selfdiffusivities were also performed using RASPA. EMD simulations were done in the canonical (NVT) ensemble using Nosé-Hoover thermostat49 to maintain the temperature at 298 K. The velocity Verlet algorithm32 was used to integrate the equations of motion in a 1.0 fs time step. All systems were initialized and equilibrated for 20 ps and 1 ns, respectively. It followed by a production run of 10 ns where the order-n algorithm50 was used for convenient and efficient measurement of mean squared displacements (MSD). To increase the statistical accuracy, three independent simulations were performed for each case. The self-diffusion coefficient (Dself) is related to the movement of individual tagged particles and is extracted from diffusive region of MSD via applying Einstein equation (Eq. 4).32,34

𝐷𝑠𝑒𝑙𝑓 𝑖

𝑁𝑖

〈∑

1 𝑑 = lim 2𝑑𝑁𝑖𝑛→∞ 𝑑𝑡

𝑛=1

〉

2

(𝑟𝑖𝑛(𝑡) ― 𝑟𝑖𝑛(0))

Eq. 4

where, Ni is the number of molecules of component i, d is the spatial dimension, t is the time, and 𝑟𝑖𝑛 is the center of mass of molecule n of component i. The other parameters in our simulation setup were the same as those for the gas adsorption simulations. Dself values are averaged among diffusive paths.



RESULTS AND DISCUSSION Geometry-Based Screening

We constructed a database of MOFs along with the corresponding calculated geometrical properties. Afterward, we considered two criteria for initial selection of potential structures: PLD larger than 3.64 Å and ASA greater than zero. Our initial screening criteria implies that we select MOFs which can accommodate both components (based on their kinetic diameter) and exclude those without available surface area. This resulted in 213 MOFs with 15 structures which exhibit non-accessible surface area. We treated them separately with an extra step of blocking non-accessible pockets before performing gas adsorption simulations. We added corresponding results later to the whole set of studied structures. Dilution and Charge Effects

It is known that helium is not adsorbed at room temperature. Therefore, it should not have effect on the adsorption of nitrogen and, consequently, single component adsorption data can be used to study the separation of nitrogen from helium. To evaluate the validity of this hypothesis, we performed the adsorption isotherm simulations for the equimolar mixture of nitrogen and helium at 1.2 bar and also for unary nitrogen at 0.6 bar (Figure 2). We observe that these two sets of data nicely correlate (R2 = 0.9999) with each other meaning that we can benefit from it to accelerate the screening process.


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Figure 2. Unary N2 adsorbed amount at 0.6 bar versus N2 adsorbed amount in equimolar mixture with helium at 1.2 bar.

Because nitrogen carries a small quadrupole moment, we consider electrostatic interaction in simulations including nitrogen by assigning point charges on nitrogen atoms and center of mass of N2. This, in turn, increases the computational costs through both adsorption simulations and indispensable partial charge assignment step. We evaluated that how much electrostatic contribution affects the uptake results by correlating data calculated using DDEC charges and those obtained solely by using VdW interactions (Figure 3). It reveals that for the most of MOFs in this study, the electrostatic contribution is negligible and, therefore, there is a nice correlation (R2 = 0.9867) between the aforementioned calculated uptake values. Thus, we can propose that in similar high-throughput screening studies, one may omit electrostatic interactions at least for initial steps of the screening process.



Figure 3. Unary N2 adsorbed amount at 0.6 bar with and without considering electrostatic interaction.

N2/He Separation:

We benefited from several parameters established and explained elsewhere51,52 to assess the aptness of MOFs in adsorption-based separation of N2 from He. The first level parameters are represented by uptake at adsorption pressure (Nads), working capacity (∆N), and adsorption selectivity (𝛼𝑎𝑑𝑠 𝑁2/𝐻𝑒) and regenerability factors (R). Since we are dealing with a cyclic process implying that in each cycle a certain amount of target gas is adsorbed at adsorption pressure (1.2 bar) and then recovered at desorption pressure (0.1 bar). Note that not all of the adsorption sites are regenerated thus reducing the uptake capacity of solid adsorbent for the next cycle. We elucidated such information by calculating ∆N and R, respectively. However, each of these parameters reflect a specific part of the separation process and ranking MOFs by considering separate parameters may not result in a conclusive order. Therefore, it is 10 ACS Paragon Plus Environment

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recommended to screen them based on indices which reflect combinatorial effect of various factors. For instance, Wiersum et al.52 studied several factors and devised a powerful descriptor called “adsorbent performance indicator, API” which is calculated using Eq. 3. 𝐴

𝐴𝑃𝐼 =

𝐵 (𝛼𝑎𝑑𝑠 𝑁2/𝐻𝑒 ― 1) (∆𝑁𝑁2)

Eq. 3

|∆𝐻𝑎𝑑𝑠,𝑁2|𝐶

, where they introduced enthalpy of adsorption (∆Hads) in the equation. API has a capability that allows one to tune the formula based on the type of separation process and mixture composition to obtain more solid outcomes. On the grounds that we are also dealing with bulk separation in the current account, we adopted the proposed values52 of 0.5, 2.0, and 1.0 for A, B, and C exponents, respectively. Selection of this set of parameters implies that we are looking for the higher working capacity with waiving the selectivity share which is sensible choice because of the presence of an additional purification unit (HPU, Figure 1).

Figure 4. Structure–Property (API vs. PLD) nexus plots for 263 MOFs calculated at 298 K. 11 ACS Paragon Plus Environment


We plotted calculated parameters versus PLD along with coloring the individual points by a corresponding value of the third descriptors – helium void fraction, enthalpy of adsorption, LCD/PLD, or accessible surface area (Figure 4 and Figure S3-S6; see Supporting Information). The dotted line separates top 10 performing MOFs in the N2/He separation with APIs differing 20 times between the first (~700) and tenth (~35) structure. These MOFs along with their selected geometric and adsorption properties are summarized in Table 1. We observe that they are all exhibiting helium void fraction in the range 0.25-0.5 without certain correlation. As it can be estimated, top 10 MOFs show high enthalpy of adsorption (varying from 20 to 26 kJ/mol) due to the stronger interaction with nitrogen. MIMVEJ with lower enthalpy of adsorption comparing to KAXQIL and FUDQIF occupies the second position in ranking which illustrates the adequacy of API descriptor in considering all influencing factors in highthroughput screening procedure. Note in passing that these structures having LCD/PLD ratios of around 1.2 show that LCD slightly larger than PLD is desirable for the better performing candidates. In the case of ASA, we observe that very high accessible surface area is not essential for a good performance as the ASA range for the top 10 MOFs identified here is 180770 m2/g. The top 10 MOFs selected based on various descriptors are summarized in Table S1 (see Supporting Information) for the comparison purposes. This emphasizes the importance of considering a multi-factor descriptor like API to have a conclusive ranking in future screening studies.


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Table 1. Characteristics of top 10 performing MOFs for adsorption-based separation d g ∆Ne ∆Hads f 𝑁𝑎𝑑𝑠 𝛼𝑎𝑑𝑠 rank CSD ID APIa PLDb VFc 𝑁2 𝑁2/𝐻𝑒 1 UVEXAV 680 4.304 0.50 40.2 34.5 26.08 222.7 2 MIMVEJ 190 4.297 0.44 22.9 20.5 23.74 114.9 3 KAXQIL 98 4.083 0.27 15.8 13.9 24.21 150.4 4 FIPWOS 94 4.170 0.36 16.4 14.8 23.18 99.1 5 COYTEQ 81 4.623 0.48 15.9 14.3 21.03 69.3 6 FUDQIF 71 3.787 0.34 14.9 13.5 25.09 96.6 7 ZERQOE 64 4.303 0.25 13.2 11.7 23.95 126.8 8 PORVUO 49 3.899 0.46 13.0 11.8 21.32 57.5 9 CUMDIY 40 3.977 0.26 10.8 9.7 22.74 91.1 10 QOJVAM 35 3.700 0.54 11.9 10.8 20.53 37.8 a Adsorbent performance indicator, b pore limiting diameter, c helium void fraction, d N uptake 2 at 0.6 bar (cm3(STP)/ cm3), e N2 working capacity (cm3(STP)/ cm3), f N2 isosteric heat of adsorption (kJ/mol), and g adsorption selectivity of N2 toward helium.

Although the screening delivered us a short list of top-performing MOFs in each desired application, we continued our investigation by simulating N2 adsorption isotherms up to 1.0 bar (Figure 5a). We observe from adsorption isotherms that UVEXAV significantly outperforms the other MOFs being followed by MIMVEJ and KAXQIL. It is also interesting that the amount of adsorbed nitrogen increases with a high slope that can be an indication of a high saturation capacity. To investigate more, we recorded 20,000 snapshots during the gas adsorption simulations at 0.6 bar and then plotted spatial probability density (SPD) of nitrogen for each structure (Figure 5b-d and Figures S7-S15). SPD plots show that N2 molecules are present in the middle of pores (channels) and there is still plenty of space that can be filled by gas molecules – this agrees with isotherm observations. It is promising fact that the performance of separation unit can be enhanced dramatically by pressurizing the feedstock before adsorption step.



Figure 5. a) N2 adsorption isotherms of selected top 10 performing MOFs (based on API) and spatial probability densities (calculated from 20,000 snapshots) of N2 within b) UVEXAV (ydirection view), c) MIMVEJ (x-direction view), and d) KAXQIL (z-direction view). In addition, we calculated the self-diffusion constant of nitrogen and helium to assess the diffusion-based separation of our set of MOFs. We followed the procedure reported by Qiao et. al.13 and considered the infinite dilution condition as it would provide rankings with a reasonable computational cost. In this regard, we have added 30 gas molecules into the simulation box but turned off the adsorbate-adsorbate interactions to mimic desired condition while having statistically accurate results. We provided top 10 performing MOFs based on obtained membrane selectivity in Table 2.


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Table 2. Characteristics of top 10 performing MOFs for membrane-based separation rank

CSD ID

a 𝑆𝑑𝑖𝑓𝑓 𝑁2/𝐻𝑒

b 𝑆𝑚𝑒𝑚 𝑁2/𝐻𝑒

1 2 3 4 5 6 7 8 9 10

LIFWOO ZERQOE UVEXAV MIMVEJ FIPWOS QOKCID XADGAM KAXQIL DOGZIJ DEYLUQ

0.84 0.30 0.13 0.22 0.25 0.43 0.33 0.12 0.60 0.89

44.91 37.48 29.07 25.08 25.05 24.74 18.61 17.95 17.65 17.62

a b

𝑠𝑒𝑙𝑓 Diffusion Selectivity: 𝐷𝑠𝑒𝑙𝑓 𝑁2 /𝐷𝐻𝑒 𝑑𝑖𝑓𝑓 Membrane Selectivity: 𝑆𝑁2/𝐻𝑒 × 𝑆𝑎𝑑𝑠 𝑁2/𝐻𝑒

Clearly, the membrane separation of nitrogen from helium is driven by the adsorption because the diffusion selectivities are in favor of the helium separation, Table 2. The bestperforming MOF in this regard is LIFWOO (which is absent in Table 1), the second candidate is ZERQOE (ranked seventh in Table 1), and UVEXAV is ranked third in our set for the membrane separation. The comparison of our results presented in Table 2 with ones from Cao et. al.28 exhibits very promising improvements which needs further analysis for more solid discussion on the applicability of identified MOFs for membrane application.

CONCLUSION AND PROSPECTS We screened almost 500 of duplicate-free DFT-optimized CoRE MOFs–with accurate partial charges assigned by DDEC approach–in several steps including geometric parameters, first-level adsorption factors, and second-level adsorbent performance indices. We identified top 10 performing MOFs for the N2/He adsorption- and diffusion-based separation in helium upgrading units of natural gas refinery plants with outstanding API of ~700 for the best MOF in our ranking. We found out that the best performing structures exhibit helium void fractions



in the range of 0.25-0.50 while the enthalpy of adsorption is ranging between 20 and 26 kJ/mol. We also found out that very high specific surface, which is a characteristic of MOFs, is not the essential parameter for investigating the adsorption-based nitrogen–helium separation. We also identified top 10 performing MOFs based on their membrane selectivity which show tendency toward nitrogen separation ranging from 18 to 45. It also discussed that the membrane-based separation is also driven by high adsorption selectivity toward N2. We believe that this work provides a solid ground for future studies of the N2/He separation. This applies not only to the adsorption-based processes but also to diffusion-based separation through membranes.

NOTE: Authors declare no competing financial interest. ASSOCIATED CONTENT: Supporting Information (SI) Available: Validation of simulation setup, database diversity graphs, structure-property relationship plots, and spatial probability density plots. ACKNOWLEDGMENTS The authors would like to thank the funding received from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions and cofinancing by the South Moravian Region under agreement No. 665860. This article reflects only the authors' view and the EU is not responsible for any use that may be made of the information it contains. This work was carried out in part under the project CEITEC 2020 (LQ1601) with financial support from the Ministry of Education, Youth, and Sports of the Czech Republic under the National Sustainability Program II. Computational resources were provided by CESNET LM2015042, CERIT Scientific Cloud LM2015085, and the


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