Explicit Flue Gas Adsorption Isotherm Model for Zeolite 13X

Subscriber access provided by UNIVERSITY OF THE SUNSHINE COAST

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Explicit Flue Gas Adsorption Isotherm Model for Zeolite 13X Incorporating Enhancement of Nitrogen Loading by Adsorbed Carbon Dioxide and MultiSite Affinity Shielding of Co-Adsorbate Dependent Upon Water Vapor Content Mark John Purdue J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02071 • Publication Date (Web): 08 May 2018 Downloaded from http://pubs.acs.org on May 9, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Explicit Flue Gas Adsorption Isotherm Model for Zeolite 13X Incorporating Enhancement of Nitrogen Loading by Adsorbed Carbon Dioxide and Multi-Site Affinity Shielding of Co-adsorbate Dependent Upon Water Vapor Content Mark J. Purdue1,2,* 1

Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585 Cambridge Centre for Advanced Research in Energy Efficiency in Singapore (CARES), CARES at CREATE Tower. #05-05, 1 CREATE Way, Singapore, 138602

2

Abstract Carbon capture from flue gas by adsorption processes require a suitable isotherm model for use in process simulators. Comparative physical adsorption isotherm models are here tested on an adsorption equilibrium loading dataset for Zeolite 13X (Z13X) between 298K and 348K. Dry flue gas mixture adsorption was found to involve enhanced adsorption of N2 up to 85% relative to levels of N2 mixture adsorption predicted with pure species parameters. This relative N2 deviation was found strongly dependent upon the amount of adsorbed CO2 and suggested to be caused by optimization of molecular quadrupole interactions in the adsorbate layer. A supplemental isotherm expression dependent upon mixture fitting parameters characterized the phenomenon. Prediction of wet flue gas mixture adsorption on Z13X was tested with different numbers of adsorption sites in the α–cavity and logistic formulations to exclude CO2 and N2 from hydrophilic adsorption sites but without success. Shielding the affinity of Z13X towards co-adsorbates using the moisture content in the gas mixture improved regression residuals. This method of sticking parameter adjustment described the influence of adsorbed H2O hydrogen bonded clusters on CO2 and N2 and may provide a path to humid mixture adsorption prediction through studies of pure H2O in porous materials.

1. Introduction Dry and Wet Flue Gas Adsorption on Z13X was previously investigated using Grand Canonical Monte Carlo molecular simulations to generate an adsorption loading dataset over 1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the full gas composition range 1. In this study, with a simulated zeolite framework Si/Al ratio of 1.31, a parameterization of the Lennard-Jones forcefield describing the interaction of Z13X extra-framework Na+ cations with pure adsorbate species was performed to suitably match simulated and experimental adsorption isotherms. In-house dynamic column breakthrough (DCB) measurements on commercial samples of Z13X manufactured by Zeochem (Uetikon, Switzerland) served as reference experimental pure CO2 and N2 adsorption isotherms. For H2O adsorption isotherms, a literature review of pure H2O adsorption equilibrium isotherm data on Z13X was performed 2–6. Two studies were taken as bounding adsorption isotherms at 298K

5,6

. Following parameterization of the forcefield, the

resulting simulated isotherms at 298K were determined to lie reasonably within the bounding adsorption isotherms

1

and therefore considered representative of equilibrium data from the

literature review. The GCMC multicomponent adsorption loading dataset has not yet been described in mathematical form and the author is not aware of a previously published explicit humid gas adsorption isotherm model applicable to Z13X that simultaneously accounts for lateral molecular interactions and avoids the requirement of an iterative solution and power terms to help enable rapid convergence of a process simulator. Consistent with previous investigations of adsorption on molecular sieve Z13X 7, Ideal Adsorbed Solution Theory (IAST) 8 is expected to be insufficient to characterize the behaviour of wet flue gas on Z13X. Wet flue gas involves molecular constituents exhibiting both differences in polarity and size, leading to expected non-ideal solution behaviour over the composition range on an ionic adsorbent with localized variations in geometry and adsorption sites, such as extraframework cations acting as hydrophilic centres and anionic oxide pore walls in zeolites. For a departure from IAST, it may be necessary for the isotherm model to account for both heterogeneous vertical interaction energies of adsorption and lateral intermolecular interactions occurring between adsorbates within the adsorbed phase of an adsorbent exposed to wet flue gas. For dry flue gas adsorption on Z13X, an implicit real adsorbed solution theory (RAST) approach with a simplified 1-parameter Wilson activity coefficient 2 ACS Paragon Plus Environment

Page 2 of 48

Page 3 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


model has been employed to model non-ideal binary CO2/N2 equilibrium in Z13X 9. By comparison, a semi-empirical modified van der Waals (vdW) equation was employed for the prediction of binary CO2-N2 and CO-CO2 mixture equilibrium on Cu(I)–NaY zeolite using an additional parameter to modify the repulsive force term of the vdW equation 10. Explicit multicomponent isotherms for non-ideal dry and wet flue gas mixture adsorption are screened in this study. The adsorbate phase structural analysis in the study by Purdue et al.

1

indicated an association between the growth of hydrogen bonding in

adsorbed H2O in Z13X and a decay in CO2 loading. A shift in CO2 adsorption away from the framework structure towards α-cavity pore centres was observed with exclusion from Na+(II) sites that are known to be more shielded by surface oxygens in dry Z13X and strongly control the electric field gradients in the cavity that determine the extent of adsorption of quadrupolar CO2 and N2. Additionally, competitive adsorption of the residual CO2 at Na+(III) sites at up to a relative humidity (RH), RH=15% at 298K (0.5 mole % H2O) was identified with a significant degree of lateral adorbate-H2O interactions with increasing relative humidity. In this study, adsorbent energetic heterogeneity was considered through a multisite modelling approach for this highly non-ideal gas adsorption system. The species accessibility to these multiple adsorption sites and the form of lateral interactions between adsorbate species are detailed in the following section.

2. Models and Methods 2.1 Principles of Isotherm Models for Flue Gas Adsorption on Zeolite 13X. Adsorption site saturation capacities are assumed independent of temperature in the current study. Thermodynamic consistency for adsorption of CO2 and N2 at each site shall be adhered to. It is assumed that a perfect crystalline structure of molecular sieve zeolite applies with a constant void fraction and an isotropic distribution of adsorption sites across the pellet dimensions. Adsorption in the clay binder of zeolite pellets shall be neglected in the model. The multi-region (MR) isotherm approach

11

, which assumes more than one

3 ACS Paragon Plus Environment


Page 4 of 48

region or site exists on a surface with one region capable of excluding a species on the bases of size or energy, has physical relevance in the current study for the exclusion of CO2 and N2 from the β-cage of Z13X. Multiple sets of homotattic

12

adsorption sites in the Z13X

crystalline unit cell are considered: (i) Hydrophilic b-sites of high adsorption energy about the Na+(III) sites in the α-cavity (ii) Hydrophilic b*-sites of medium adsorption energy in the space between Na+(II) and Na+(III) in the α-cavity (iii) d-sites of low energy for the pore walls, centre and rings in the α-cavity (iv) e-sites located in the β-cage, with a constant limit of 4 H2O molecules for each of the 8 β-cages per unit cell and accessible only to H2O due to βcage blocking or steric exclusion of CO2 & N2. Distinguishing two types of hydrophilic adsorption sites is optionally compared to categorizing all hydrophilic adsorption sites into a single b-site. A three-site (TS) isotherm model for H2O at the (b,d,e) sites and a dual-site (DS) isotherm model for CO2 & N2 at the (b,d) sites shall therefore be compared to a foursite (FS) isotherm model for H2O at the (b,b*,d,e) sites and a TS isotherm model for CO2 & N2 at the (b,b*,d) sites. The FS isotherm model for H2O is considered justifiable to permit a corresponding bifurcation of the CO2 adsorption energy distribution (AED) associated with hydrophilic centres (b,b*), while remaining consistent with an effective bimodal H2O AED in the α-cavity for hydrophilic (b,b*) sites and d-sites

13

. As discussed, the b*-site is excluded

for CO2 and N2 adsorption under wet conditions. Furthermore, the b-site may be excluded for N2 under wet conditions and for CO2 adsorption under conditions with y H 2 O > 0.5% , corresponding to a threshold of RH=15% at 298K. A fixed saturation limit of H2O at the e-sites with a steeply rising isotherm can ensure that a constant equilibrium amount applies for all but the lowest moisture contents, at which point the possibility for adsorption at Na+(III’) in the α-cavity of NaX still occurs

13,14

. A fixed

saturation capacity of 4 H2O molecules per β-cage is employed in this study, corresponding to

qs,e,3 = 4×8×1000/13,352.7 = 2.396 mmol H2O / g Z13X , as discussed previously 1.

Application of this calculated capacity with a concentration dependent isotherm for the βcage is considered here while avoiding raising H2O concentration to a power to facilitate 4 ACS Paragon Plus Environment

Page 5 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


convergence with a process simulator. Although alternative isotherm models can account for H2O lateral interactions in the β-cage with apparent energetic heterogeneity there

15

, no

lateral interactions in the β-cage are considered in the current MR isotherm model. The Z13X saturation capacities of c.a. 18mmol/g H2O and c.a. 5mmol/g CO2 combined with the calculated saturation capacity of 2.396mmol/g H2O associated with β-cages indicates that c.a. 10.6mmol/g H2O deviates from thermodynamically consistency for competitive adsorption between all species in the α-cavity of NaX, without resorting to a multi-site occupancy model or introducing additional adsorption regions exclusive to H2O. The same conclusion is reached with 25% additional capacity (one extra molecule) of H2O in the βcage. The adsorbing components shall be indexed as 1 for CO2, 2 for N2 and 3 for H2O with a running index i = 1, 3 . Steric exclusion of both CO2 and N2 from β-cages requires

q1,* β = q2,* β = 0 . The temperature dependence of adsorbent affinity at site m ∈ {b, b*, d , e} towards species i is defined with the Van’t Hoff form, as follows:

 −∆U m.i  mi = m0,i exp    RT 

where m0,i is the m-site affinity pre-exponential factor,

∆Um.i

(1)

is the internal energy change

of adsorption for species i at site m. An adsorption model shall regress GCMC molecular simulation data 1 using the heat of adsorption for a component at a site as a fitting parameter and the returned value should reasonably correspond to the isosteric heats that have also been reported in the same molecular simulation study.

2.2. Description of Adsorption Isotherm Models for Comparative Study Several different adsorption isotherm models are discussed in turn with pure fitting, mixture prediction and mixture fitting modes indicated by the addition of codes PF, MP and MF, 5 ACS Paragon Plus Environment


Page 6 of 48

respectively. Sections 2.2.1 - 2.2.4 apply to pure species and flue gas mixture adsorption, Section 2.2.5 applies to dry flue gas mixture adsorption and Sections 2.2.6 - 2.2.7 apply to wet flue gas mixture adsorption.

2.2.1 Multi-Site Extended Langmuir Isotherm The extended 3-site Langmuir (TSL) isotherm model, extended to multi-component adsorption in perfect positive (PP) form

16

, is applied to an energetically heterogeneous α-

cavity of Z13X using the three adsorption sites, m = b,b*,d  :

* i ,α

q

 q mC = ∑  s ,m,i i i m={b ,b*, d }  1 + ∑ ml Cl l 

    

(2)

An extended DSL isotherm model may alternatively be considered applicable in the α-cavity

(

of Z13X by setting bi* = 0, ∀i

)

in equation (2). Competition amongst all adsorbate species

for adsorption sites is considered in this equation. The assumption of equal adsorption capacities at the same adsorption site for thermodynamic equilibrium can be relaxed for the case of polar H2O but kept for quadrupolar CO2 and quadrupolar N2. Additionally, a separate single-site Langmuir (SSL) isotherm may be considered applicable to the β-cage for the adsorption of H2O at site e, without competition from CO2 and N2 due to steric restrictions by the β-cage windows:

q3,* β =

qs , e ,3e3C3 1 + e3C3

(3)

No lateral interactions are considered in the above explicit adsorption isotherm model and pure component equilibrium parameters are used for prediction of mixture equilibrium.


Page 7 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Depending on the number of types of hydrophilic site types, this MR isotherm model formulation for the α-cavity and β-cage may be referred to as the DSLα-SSLβ model or the TSLα-SSLβ model. These isotherm models are required to revert to the dry flue gas binary isotherm model and the pure gas isotherm models by using pure species adsorption isotherm parameters obtained from regression analysis of pure species adsorption loadings.

2.2.2 Multi-Site Extended Jovanovic Isotherm A MR approach is considered here with Jovanovic isotherm

17

kernels, which provide for an

adsorption energy distribution skewed to high energies. The adsorption loadings in the αcavity and β-cage of Z13X are given by the extended 3-site Jovanovic (TSJ) isotherm (extended in PP form

16

) and the single-site Jovanovic (SSJ) isotherm in equations (4) and

(5), respectively:

  qs,m i miCi      q = ∑  m C 1 − exp −  ∑ l l    m={b,b*,d}  ∑ ml Cl    l   l 

(4)

q3,* β = qs,e,3 (1− exp ( −e3C3 ) )

(5)

* i ,α

An extended DSJ isotherm model may alternatively be considered applicable in the α-cavity of Z13X by setting

(b

* i

= 0, ∀i ) in equation (4). As before, equation (1) applies for the

temperature dependence of adsorbent affinity for an adsorbate species. This MR isotherm model is referred to as either the DSJα-SSJβ model or the TSJα-SSJβ model. As with equations (2) and (3), pure species adsorption isotherm parameters obtained from regression analysis of pure species adsorption loadings are employed in equations (4) and (5) when applied to mixture equilibrium.

2.2.3 Hybrid DSLα and SSJβ Isotherm 7 ACS Paragon Plus Environment


Page 8 of 48

A hybrid MR adsorption isotherm may be formulated with competitive adsorption equilibrium in the α-cavity described by a DSLα or TSLα model from equation (2) and adsorption equilibrium of H2O in the β-cage described by a SSJβ isotherm model from equation (5). This hybrid isotherm formulation is referred to as either the DSLα-SSJβ model or the TSLαSSJβ model and may be compared to a type of segregated version of IAST (SIAST)

18

based upon the principle that any mixture isotherm model can be applied separately for each site constituting an independent adsorbate phase in separate equilibrium with the gas phase. Given the strength of H2O adsorption and the adsorption energy distribution of the Jovanovic isotherm skewed to high energies, it is conceivable that pure H2O adsorption is better predicted with this hybrid isotherm model than with a multi-site Langmuir isotherm model while simultaneously maintaining compatibility for extension with CO2 and N2 adsorption in the α-cavity of Z13X.

2.2.4 Multi-Site Extended Isotherm with enhanced water vapor concentrations An explicit extended isotherm was conceptualized to describe the adsorption of CO2 and N2 species in the presence of moisture by enhancing the vapor concentration of H2O at all sites to a level that may reduce the regression error with pure H2O adsorption and may further improve the correlation of species competitive adsorption with H2O. This multi-site isotherm may be formulated by substitution of gas phase concentration of a species, Cl , with

ClE in

earlier models, as follows:

, ( l = 1, 2 )  Cl  C =  P  Cl exp ( nyl ) =  RT  yl exp ( nyl ) , l = 3    E l

where

(6)

C3E corresponds to an artificially enhanced concentration of H2O vapor and n is an

empirical fitting parameter determined by regression analysis of pure H2O adsorption data 8 ACS Paragon Plus Environment

Page 9 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


corresponding to adsorption of a humidified inert gas. This formulation reduces to the expected isotherm under dry conditions. Rather than using the dimensionless product of affinity and concentration, the numerically smaller gas phase mole fraction of H2O was used to enhance the effective concentration of H2O vapor about adsorption sites in equation (6) by a factor in the range

[1,exp(n)] , n ≥ 0

(e.g. 2.72 when n = 1). An enhanced vapor

concentration or increased collision frequency of H2O molecules towards each adsorption site may not significantly alter the predicted macroscopic behavior since the affinity coefficients for H2O shall lower by way of compensation during regression analysis of pure H2O adsorption when compared to the base case values in the earlier described models. An alternative view of the approach in this section is that of enhanced affinity of a site towards H2O for a given concentration of H2O vapor. The enhancement of affinity for H2O may offer an advantage over affinity shielding of competing adsorbates discussed later, since the former is parameterized from pure species adsorption isotherms. The non-linear adjustment in equation (6) for a type I isotherm may be compared to that considered for multilayer adsorption using the same numerical range inside the exponential with np p

SAT

∈[ 0,n]

19

.

The latter term corresponds to a multiple of RH, which similarly features in the work of Ye and LeVan

20

to appropriately scale the vapor pressure of a competing organic species

during humid-gas mixture adsorption. In the current model, the scaling of a gas phase mole fraction relates directly to the amount of moisture and removes a reference to the compressed liquid state. With potentially one additional pure component fitting parameter, an isotherm model with a modified concentration of H2O is referred to by the addition of the code MCH2O.

2.2.5 Dry flue Gas: Enhanced adsorption of N2 by CO2 on Z13X by quadrupolar optimization In a recent experimental study, it was confirmed that non-ideality is evident for binary CO2/N2 adsorption on Z13X with the deviation most visible at high pressures up to 10bar 9. It was



Page 10 of 48

confirmed that IAST over-predicts CO2 adsorption and under-predicts the amount of N2 adsorption for Z13X and that this is most apparent at higher system pressures. By close inspection, the under-prediction of N2 adsorption by IAST compared to experimental data remains visible in the chart for binary adsorption equilibria of CO2 and N2 mixtures on Z13X at 25oC and 1.2 bar, which will be shown later to be consistent with dry flue gas data provided from a recent GCMC study 1. In comparison, the mentioned trend for overprediction of CO2 loading by IAST at these same conditions is of a relatively low magnitude compared to that for the under-prediction of N2 loading. A GCMC simulation study found IAST to be accurate for the adsorption of CO2, N2 and H2 mixtures in 4A Zeolite only at low CO2 pressures and over-predicted selectivity by as much as 70% in a CO2-rich gas phase 21. The RAST approach has also been used to model adsorption equilibrium of binary mixtures of CO2 with either CH4 or C2H6 on AC binary mixture adsorption on AC

23

22

, following earlier recommendations for CO2/CH4

. The former study on a homogeneous adsorbent

confirmed that adsorption of the heavier component enhanced the adsorption of the lighter component, attributing the non-ideality to lateral adsorbate interactions. RAST has also been considered to correlate GCMC simulation data for CO2, CH4 and N2 binary mixture adsorption equilibrium data on functionalized AC

24

. The authors correlated the activity

coefficients with a ternary Margules equation under the assumption that the adsorbent acts as an additional component. It was found that IAST predicted the adsorption of the heavier component very well but was not suitable for predicting the adsorbed amount of the lighter component. In more heterogeneous adsorbents such as with ZSM-5-280, deviations between IAST and experimental data are expected to be more pronounced for the weaker adsorbed species

25

. The authors of this study previously correlated the binary mixture

equilibrium for these adsorbates on ZSM-5 adsorbents with SiO2/Al2O3 ratios of 30 and 280 using a 5-parameter empirical isotherm (HT-CPM) model fit to experimental data obtained from the concentration pulse method (CPM)

26,27

. This HT-CPM binary isotherm model was

later applied successfully for the same adsorbates on Z13X

28

. In addition to adsorbent

heterogeneity considered through simulations of oxidized AC, deviations from IAST may be 10 ACS Paragon Plus Environment

Page 11 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


expected to increase in more microporous systems

24

. Binary mixture adsorption isotherms

of CH4, N2 and CO2 on dry AC over a wide range of pressures have been predicted using the two-dimensional Statistical Associating Fluid Theory for potentials of Variable Range (2D-SAFT-VR) approach

29

. This study outlined particular challenges for prediction with

quadrupolar species in their approach and previously that the relationship to pure compound values is not simple 30. An explanation for cooperative adsorption of N2 by CO2 may lie with considerations of the orientations of CO2 and N2 in the adsorbate phase and a tendency towards the minimization of the quadrupolar energy of the adsorbed structure, as has been studied for pure adsorption of CO2 and N2 on virtual graphitic slit pores with different degrees of surface oxidation at low temperatures 31. In this study by Gotzias et al.

31

, it was found that both pure

CO2 and pure N2 preferentially orient vertically to a heavily oxidized pore wall and horizontally in a pristine pore. A repulsion of the tail end oxygen of adsorbed CO2 away from the surface is physically consistent with the ion-dipole interaction schematic proposed by Little and Amberg SSZ-13

33

32

, discussed more recently with dry flue gas adsorption on high silica

, in which a partial positive charge forms at the tail end oxygen upon forming a

stable ion-CO2 interaction. This polarization of CO2 could result in a potential secondary attractive site on exposed CO2 for co-adsorbates, particularly to those species that lose competitive influence at the primary adsorption sites. A variation in the proportion of end-on CO2 coordinated in heterogeneous zeolites has been discussed for a range of cation types and window or cage adsorption site locations

34

. In this study, a tendency for the tail end of

polarized adsorbed CO2 to orient to framework oxygen atoms was described as dependent upon the cation-CO2 bond distance, which controls the contact angle of CO2 with the adsorbent surface. The strength of the cation-CO2 interaction, governed by the cation charge density, determines the bond length and the resulting double bond polarity change in the ion-dipole interaction scheme. Since a variation of cation charge density has been studied with respect to orientation of adsorbed CO2

34

, this selection may be made with a

consideration to reduce the extent of lateral CO2-N2 lateral interactions in favour of like11 ACS Paragon Plus Environment


Page 12 of 48

species lateral interactions and thus potentially improve selectivity for CO2, when appropriately balanced against possible larger CO2-framework interaction energies with associated higher adsorbent regeneration costs. Gotzias et al.

31

further reported that quadrupolar electrostatic interactions of a CO2

monolayer shifted the orientations of second layer particles towards a certain direction to maximize lateral CO2 interaction energy, which obtains the most stable configuration in a less pronounced but repeat pattern of the orientational distribution. Earlier GCMC simulations by Samios et al.

35

examined the role of 30% elongated CO2 molecules to

enhance quadrupole-quadrupole interactions and was found to be crucial to sustain highly structured configurations of alternating sublayers of almost normal and almost parallel-to36

the-wall molecules. Golebiowska et al.

identified a rotational-translational coupling in

multilayer adsorption of N2 in slit pores by MC simulations over varying low temperatures and surface coverage. This study identified facilitated diffusion of N2 between layers. Based upon in situ neutron diffraction measurements of CO2 adsorption on mesoporous silica, Steriotis et al. attributed orientational correlations of CO2 under confinement to vertical and lateral interactions enhanced by the large quadrupole moment of CO2

37

. Cracknell et al.

examined rotational restrictions of CO2 in narrow carbon pores that attract CO2 but repulse N2 by steric effects using GCMC to show increased selectivity of CO2

38

. Nasri et al.

identified large amplitude molecular motions in a computational chemistry study of the potential energy surface of the CO2-N2 vdW complex, with supporting evidence from earlier spectroscopic studies for N2 inversion

39

. In this study, the N2 molecule was considered to

preferentially point towards the carbon atom of CO2 in a T-shaped structure. In the aforementioned molecular simulation study on functionalized AC

24

, deviations

between IAST predictions and raw data decreased in the order: CH4-CO2, CO2-N2, CH4-N2. It may be noted that these adsorption systems with mixtures of at least one linear geometry molecular species adsorbing on heterogeneous surface sites may show a preference for a departure from IAST, in which the strongly adsorbed component can more easily act as a 12 ACS Paragon Plus Environment

Page 13 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


secondary surface for the weakly adsorbed species. Increasing non-ideality may therefore follow the order of an increasing ratio of the Pitzer-type acentric factor of the strongly adsorbed species to that for the weakly adsorbed species. Elevated levels of N2 adsorption compared to IAST for CH4-N2 binary mixture adsorption in carbon nanospaces was explained on geometrical arguments such that that spherical and polarizable CH4 molecules create fluid cages that serve as additional adsorption sites for linear N2 that are not present in pure N2 adsorption

40

. The proportion of CH4 cages presented to N2 were considerably

higher when the packing efficiency of CH4 was reduced by a random arrangement of graphitic planes. Conceivably, by similar means to the insights gained from these studies, the more quadrupolar CO2 may cooperatively enhance the adsorption of less quadrupolar N2 from flue gas mixtures above that expected from IAST on a strongly heterogeneous adsorbent surface that can adsorb large amounts of CO2. It is conceivable therefore that supplemental N2 adsorption on a secondary landscape measured by a deviation from that predicted by ideal adsorption has a strong CO2 composition dependency. The significance of a neglect of CO2-N2 lateral interactions for both CO2 and N2, both with and without thermodynamic consistency and N2 energetic homogeneity constraints, can be further tested using the DSLα isotherm model to fit the recently obtained GCMC data for dry flue gas mixture adsorption on Z13X. As a first approximation to account for enhanced N2 adsorption in the binary mixture, a BWA type expression (discussed later in equation (16) wet flue gas adsorption) to modify a generic affinity coefficient m for N2 using an attractive interaction energy between CO2 and N2 was tested by regression analysis without success. This approach was not recommended by an earlier study of CO2 adsorption on Ni2+ and Cr3+ exchanged X zeolites, which suggested it may not be appropriate for systems with adsorption at the extreme end of the linear molecule

41

. The possibility for a “flat adaption” of an adsorbate with respect to cations

to promote pure species lateral interactions was discussed for C3H6 on Cu-X but was not found for CO2 on a range of X zeolites

42

. More recently, Sillar et al.


43

have noted the


Page 14 of 48

improvement obtained with prediction of pure CO2 adsorption on a metal organic framework with Mg2+ sites using this mean field approximation and that the lateral interactions can increase surface coverage by 25% on average, suggesting the influence of cation charge density and the resultant contact angle is an important factor for applicability of a BWA. By contrast, lateral interactions with pure N2 adsorption were found to be very weak. It will be shown below that the relative increment in N2 adsorption by lateral cross-interactions for dry flue mixture adsorption can be significantly higher than 25%. To characterize enhanced N2 adsorption in dry flue gas adsorption, two alternative supplemental N2 non-ideal (NI) adsorption loading terms are described to determine the total loading on N2 in the binary mixture, q N 2 = q NMP2 + q NNI2 : (a) Equilibrium Constant for N2-CO2 complexation in adsorbate phase

N 2 + CO2

K N 2 , NI

N 2 − CO2

q NNI N 2 − CO2 ] [ = ≅ [ N 2 ][CO2 ] C N qCO 2

2

2

(7)

 −U N 2 ,NI  = K N 2 ,NI,0 exp    RT 

(8)

In equation (8), the gas phase concentration of N2 is provided as a driving force while the non-ideality is controlled by the adsorbed amount of CO2. The equilibrium constant is proposed to follow the Van’t Hoff form. (b) Power Law correlation of the relative N2 deviation from ideal mixture prediction The amount of N2 adsorbed in the wet flue gas mixture on Z13X may be determined using mixture prediction (MP) CO2 loadings, as follows:

qN 2 =

(

qNMP2

)

MP 1 − h qCO 100 2

(9)


Page 15 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(

NI

)

where h is a cubic polynomial to relate the relative deviation 100* qN 2 qN2 solely in terms of CO2 loading and whose coefficients are dry mixture temperature and pressure independent fitting parameters:

h ( Z ) = a3 Z 3 + a 2 Z 2 + a1 Z + a0

(10)

2.2.6 Wet Flue Gas: Exclusion of CO2 & N2 from hydrophilic sites The adsorption isotherm for H2O on Z13X rises steeply, approaching an irreversible rectangular form. Significant lateral interactions between H2O and competing quadrupolar species have been discussed with sharply reducing mixture adsorption isotherms at low RH for CO2 and N2 1. In order to energetically exclude CO2 and N2 from hydrophilic sites due to the dominance of H2O adsorption in the α-cavity, the following logistical relations can be applied to the dual-site α-cavity (DSα) and three-site α-cavity (TSα) model variants:

(i)

Full or partial α-cavity hydrophilic site exclusion of CO2 and N2 under wet conditions: (a) DSα: Exclusion of CO2 and N2 from α-cavity hydrophilic b-sites under wet conditions:

b1 = qs ,b ,1 = b2 = qs ,b,2 = 0 , y3 > 0

(11)

(b) TSα: i) Exclusion of CO2 from α-cavity b*-sites under wet conditions:

b1* = qs ,b* ,1 = 0 , y3 > 0


(12)


Page 16 of 48

ii) Exclusion of CO2 from α-cavity b-sites above a 0.5mol% threshold moisture content:

b1 = q s ,b ,1 = 0 ,

y3 > 0.005

(13)

iii) Exclusion of N2 from α-cavity hydrophilic (b,b*)-sites under wet conditions:

b2 = b2* = qs ,b,2 = qs ,b* ,2 = 0 , y3 > 0

(14)

An explicit extended isotherm model with energetic exclusion of CO2 and N2 from hydrophilic sites is referred to by the addition of the code –EXHS. The DSα and TSα α-cavity isotherm models may be considered with full exclusion from both hydrophilic sites (FEXHS), using a 0% threshold moisture content in equation (13) for the TSα α-cavity isotherm model. The TSα model may alternatively be considered with partial exclusion from hydrophilic b*-sites (PEXHS) using equations (12) and (14). Maintaining the PEXHS conditions, the TSα model may further consider RH dependent exclusion from hydrophilic b-sites (RHEXHS) using equation (13). Using pure species adsorption parameters, it will be shown later that these site exclusion models offer improve upon the regression analysis model residual, with the TSLα cavity isotherm model found as the best mixture predictive isotherm model. However, exclusion from hydrophilic sites is insufficient to fully characterize equilibrium under wet flue gas conditions. Additional considerations of the influence of moisture on CO2 and N2 adsorption are necessary, particularly due to effect of clustering of H2O at the low energy sites that is not considered by exclusion of CO2 and N2 from hydrophilic sites.

2.2.7 Wet Flue Gas: Semi-empirical CO2 & N2 affinity shielding by H2O lateral interactions For operation on a relatively narrow range of pressure and temperature, a semi-empirical explicit model of adsorption is considered as a first approximation to describe wet flue gas 16 ACS Paragon Plus Environment

Page 17 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


adsorption with lateral molecular interactions between adsorbates. An approach to account for the influence of lateral adsorbate-H2O interactions is sought based upon gas phase conditions. Shielding of the effective affinity coefficient pre-exponential factor of adsorbent eff

affinity m towards adsorbate k at a generic site m, m0,k , is proposed for competing adsorbates CO2 or N2 using a damping factor applied to the unshielded pure component preexponential parameter m0,k = m0,k U

Pure

to an extent dependent primarily upon gas phase

moisture content as follows:

(

)

m 0eff,k = m 0U,k ex p  − f 0 ,m , k + f 1,m , k   

,

(k

= 1, 2 )

  qs,m,3   ε k,3   m3U C3 f0,m,k (C1,C2 ,C3 ) = z0,m,k   U q    s,m,k   kBT   ∑ ml Cl  l

f1,m,k (y3 ) = z1,m,k y3 + z2,m,k

where

    

(15)

(16)

(17)

f0,m,k and f1,m,k represent zeroth and 1st order lateral interaction functions for species

k with H2O, respectively, to describe phenomenological shielding of adsorbates away from respective adsorption site m due to the close proximity of polar H2O. Physically, affinity shielding at an adsorption site m (ASM) corresponds to a reduction in the entropy of adsorption of component k at an adsorption site according to a probability dependent on the energetic state of that gas mixture. This approach is considered here to account for potential non-ideal adsorbate-adsorbate lateral interactions competing with adsorbate vertical interactions and the effect of hydrogen bonded networks of adsorbed H2O molecules acting to provide a modified adsorbate-adsorbent energy distribution to the competing species.

z0,m,k , z1,m,k and z2,m,k are optional empirical fitting parameters that require the availability of an adsorption dataset for correlation. For prediction of mixture equilibrium data, values of 0 and



Page 18 of 48

1 for these parameters may be used selectively to vary the form of affinity shielding.

mUk is an

unshielded species affinity coefficient corresponding to the pure component fitting parameter for CO2 and N2 at the same temperature. This formulation may be applicable to empirically shield CO2 and N2 from formerly accessible adsorption sites b or d in the α-cavity of Z13X. Equations (40) and (41) circumvented the use of local or overall adsorbed phase monolayer fractional patch coverage in the lateral interaction term to allow for an explicit solution suited to process simulations. The form of equation (16) can be discussed in more detail. The Fowler-Guggenheim (F-G) model mC =

θ 1−θ

44

, incorporates lateral interactions using a coefficient

α

applied generically as

exp ( −αθ ) , where θ is the overall fractional surface coverage on a

homogeneous surface. With a lateral interaction energy between adsorbed molecules, ε, the Bragg Williams approximation (BWA)

45,46

is given by α = −

zε , where z is the number of RT

nearest neighbour sites with respect to a given site and the negative sign is for attractive lateral interactions with ε < 0 . The BWA, originally developed for the effect of thermal agitation on atomic arrangement in alloys, attempts to estimate the equilibrium degree of long range order in a background mean field environment based on a required energy interchange at a particular temperature 47. This crude description neglects latent heat effects or short range ordering associated with higher order cluster variation methods. The consequences of assuming the BWA in mixed gas adsorption have been investigated for monolayer adsorption of a binary mixture in homogeneous, patch-wise and random adsorption site topographies

48

. For the case with random site topographies, it was

suggested to modify the constants of local Langmuir behaviour for a binary mixture as eff mkeff = mk exp (αkϑk + α12ϑl ) , k, l = 1,2 k ≠ l , where mk is the effective Langmuir affinity

constant, ϑk is the overall monolayer relative coverage for the kth component on a random heterogeneous surface and

αk , αkl are constants for the lateral interaction between like and 18 ACS Paragon Plus Environment

Page 19 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


unlike adsorbates, respectively. Lateral H2O-H2O interactions are not part of the multicomponent BWA expansion when the index k applies to CO2 or N2 and l for H2O for crossspecies interactions in quasi-binary mixtures. It is reasonable to neglect the

αk

like-

interaction term because the pure component parameters implicitly incorporate the net effect of such interactions based upon an isotherm model whose functional form is derived from an assumption that no lateral self-interactions occur and that has simultaneously fit pure component adsorption isotherm data. More generally ( l − i , i ≠ k ) interactions cancel out, as discussed previously

49

. The remaining

( k −i )

interactions refer to CO2 and N2 lateral

interactions that are discussed later in an independent supplemental term for N2 adsorption but here neglected. The affinity parameter for CO2 or N2 with H2O dominant lateral sorbate

(

interactions thus simplifies as mkeff ≅ mk exp α k ,3θ3

)

,

( k = 1, 2 ) .

An expression for the

argument of the exponential that is analogous to the BWA but designed to be explicit in gas phase properties is developed to produce equation(16). Sillar et al. 43 have also adopted this strategy for pure gas adsorption by substituting either a Langmuir or Henry’s law isotherm for the fractional adsorbate loading. The relationship for

f0,k in equation (16) empirically

describes mean-field background interactions between a number of H2O molecules and adsorbate i directly surrounding the adsorption site in a monolayer. Similar to the method of discount factors

50

, the ratio of adsorbate capacities are considered as a proxy for the

influence of relative adsorbate size or adsorbate density among species. The average number of H2O molecules surrounding an adsorbate is therefore estimated using a constant ratio of the adsorbate capacities in the first term in parenthesis in equation(16). Similarly, binary fitting parameters involving the ratio of adsorbate capacities as a proxy for the ratio of molecular cross-sectional areas was employed in two-dimensional fluid model

51

(

. ε k,3 kBT

represents an entropy per molecule to affect a system change. The W-H combining rules were applied to determine

)

52

εk3 for H2O interactions with adsorbates of significantly different 19 ACS Paragon Plus Environment


Page 20 of 48

polarity. The Berthelot mixing rule, ε kl = ε k ε l , yields similar values to the W-H rule for CO2 and N2 cross-interaction energies but significantly different values for cross-interactions with H2O. The third term in parenthesis in equation (16) approximates the mean fractional coverage of H2O at the local site using the bulk gas phase concentrations and unshielded site-dependent affinity coefficients. This dimensionless term represents an asymptotic limit in the extended Langmuir isotherm at high water vapor partial pressures and may underestimate the amount of H2O adsorbed due to implied competition from other species. It may be considered with modified concentrations of H2O through equation (6) or corrected by an empirical fitting parameter

z0,m,k .

At room temperature, the Bjerrum length in liquid water is about 7Å, which corresponds to the length scale when the Coulomb and thermal fluctuation energies balance. Given the pore size of the α-cavity of Z13X is about 12Å to 14Å, it is reasonable to consider a weighted average of Coulombic and mean-field factors to describe the influence of H2O on neighbouring sorbates i.e. a contribution from both short range associations and a long-range ionic screening cloud. An additional expression beyond the mean field approximation in equation (16) to account for a strong localized or non-random influence of H2O networks laterally interacting with CO2 and N2 to shield them from adsorption sites is sought by way of a practical alternative to an implicit quasi-chemical approximation (QCA) description. The recent molecular simulation study of adsorption of wet flue gas on Z13X

1

described an association between hydrogen bond growth and a decay of CO2 loading as a function of RH. The water loading has previously been associated with a decay of CO2 Henry’s law coefficient

53

. In the current study, the simplest expression for

f1,k was thus

determined as a term proportional to the H2O vapor mole fraction and may be linearly superimposed with a constant

z2,m,k . Compared to equation (16), it is expected that equation

(17) may more effectively account for the strong temperature dependence of gas phase moisture content and capture the resulting influence of the extent of H2O-H2O clustering on


Page 21 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


co-adsorption at higher H2O loadings. When considering the exponential decay in equation (15), this term may be viewed as a pseudo-first order affinity reduction for co-adsorption using the dimensionless mole fraction of H2O or alternatively as a simple expression for the shielding of adsorption sites by polar H2O molecules, akin to screened Coulombic interactions. The proportionality constant

z1,m,k and fitting parameter z2,m,k are expected to

depend upon the H2O cluster size associated with an adsorbent pore size and considered with a Van’t Hoff temperature dependency. The effect of empirically reducing an affinity parameter is to shift from a site-specific Dirac Delta AED to a gas-adsorbent system Hamiltonian dominated by humidity.

wet dry ∆U m,k = ∆U m,k + ( f 0,k + f1,k ) RT

,

( k = 1, 2 )

(18)

The sensitivity of the affinity coefficient pre-exponential factor for CO2 or N2 to humidity or moisture content may be examined by partial differentiation of equation (15) and employing the ideal gas assumption

eff ∂m0,k U = − m0,k exp ( − f 0,k − f1,k ) ∂ y3

Cl = yl P RT :

    U U U  qs ,m, 3   ε k,3  m3 m1 y1 + m2 y2   + z1,m,k  ,  2  z 0,m,k  q   k BT    s ,m,k   U    ∑ ml yl    l    

( )(

)

( k = 1, 2 )

(19)

An explicit extended isotherm model with affinity shielding for CO2 and N2 is referred to by the addition of the code AS followed by the particular site(s) under consideration. It is conceivable that affinity shielding could be considered at any of the b, b* or d sites:

m ∈( b, b*, d ) . This choice applies to both CO2 and N2 but should conform to the expected behaviour with respect to the greater quadrupole moment of CO2. Additionally, the shielded 21 ACS Paragon Plus Environment


Page 22 of 48

affinities should be consistently applied to the H2O loading, thereby reducing the competitive influence of adsorbates on the adsorption of H2O.

2.3

Methods: Isotherm Model Regression Analysis

The root sum of squared relative errors (RSSRE) was employed as an objective function for non-linear regression of the aforementioned isotherm models, whereby a constant least squares error is weighted by the equilibrium loading. This form was employed for the entire data-sets with significantly different loadings of both pure component and gas mixture adsorption:

RSSRE = M

1 df

* *  q n,T,k,m − q n,T,k,d ∑ ∑ ∑  q * k =1 T =1 n =1  n,T,k,d 3

3

N

  

2

(20)

where M is a coefficient, df denotes the degrees of freedom, subscript k is a species index,

T ∈(T1 = 298K ; T2 = 323K ; T3 = 348K ) , subscript n is a data-element index, subscript

m

denotes an isotherm model result from either pure species fitting, MP (without optimization) or MF modes and subscript d denotes raw data from either experimental or otherwise molecular simulations, respectively. With significantly higher H2O adsorbate loadings in Z13X, regression fitting using RSSRE reduces bias towards stronger adsorbing species when compared to a sum of squared errors (SSE) measure of deviation. When considering the entire composition range for CO2 and N2, a relative error measure such as equation(20) should involve only elements with non-zero loadings of a component. The total number of data elements in each set, N, shall consider summation across the range of RH for wet flue gas adsorption at a fixed temperature and total pressure. The total number of data-points

Nd

for the regression applies across species, temperature, pressure or composition in steps of fixed RH at a fixed total pressure. In the current study, M = df = 1 was used, similar to the


Page 23 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


residual considered for adsorption of water in zeolite 4A 15. Other authors have employed the average relative error (ARE) with as the objection function and

df = Nd − Npm ,

54

or the RSSRE with M = 100

to further account for a reduction in the degree of freedom by

Npm

parameters. The latter is referred to as Marquardt’s percentage standard deviation (MPSD) 55,56

. More detailed considerations of adsorption isotherm parameter errors

57

and regression

analysis of adsorption isotherms with limited sets of noisy experimental data

58

are not

considered in the current study when using molecular simulation data. The average percent deviations or ARE

59,60

and the degree of dispersion (DOD)

61

were also computed for post-

analysis of the regression fits to assess the goodness-of-fit:

ARE =

* * 100 3 3 N q n,T,k,m − q n,T,k,d ∑∑ * Nd ∑ q n,T,k,d k =1 T =1 n =1

* * 100 3 3 N q n,T,k,m − q n,T,k,d DOD = ∑∑ * Nd ∑ q n,T,k,d k =1 T =1 n =1

In addition, the degree of heterogeneity parameters.

62

(21)

2

(22)

was determined from the resulting affinity

The tunable parameters, pm , for the pure component adsorption isotherm

model regression analysis may be listed as follows:

DSα-SSβ:  b kT1 , b kT 2 , b kT3 , d Tk1 , d Tk 2 , d Tk 3 , q s,b ,k , q s,d ,k , ( k = 1, 2, 3 ) e Tk1 , e Tk 2 , e Tk 3 , q s,e,k , n , ( k = 3 ) 

p PD S ∈ 

(23)

TSα-SSβ:

bkT1 , bkT2 , bkT3 , bk*T1 , bk*T2 , bk*T3 , d Tk1 , d Tk2 , d Tk3 , q s,b,k , q s,d,k , p TS ∈  P eTk1 , eTk2 , eTk3 , q s,e,k , n , ( k = 3 ) 


( k = 1, 2, 3 )

(24)


Page 24 of 48

Thermodynamic consistency among species for CO2 and N2 at each adsorption site in the αcavity constrains 2 of the listed tunable parameters (here the site saturation capacities for N2 equated to those for CO2) and requires the corresponding pure components isotherm model regression analysis to be performed simultaneously rather than independently. Energetic homogeneity for N2 (EHN2) in the α-cavity can optionally be considered by equating affinity parameters for N2 for each site in the α-cavity at each temperature to further constrain an additional 3 listed tunable parameters. Non-linear regression analysis was performed using the Solver tool in Microsoft Excel. Initially, an evolutionary optimization was performed using all of the pure component isotherms with the following computational options: convergence = 1.0 x 10-8, mutation rate = 0.99 (max. 1), population size = 150 (max. 200), an empty field for random seed for a different seed on each solve, wait time without improvement = 100s, bounds on all variables were required, constraint precision = 1.0 x 10-10, automatic scaling enabled and no maximum for the number of sub-problems or feasible solutions. As recommended for effective use of the evolutionary solver, an envelope of values was assigned using absolute parameter bound constraints to restrict each tunable parameter within an appropriate positive range. The following relative affinity constraints were employed to further guide the genetic optimization problem to be physically consistent with adsorption over the temperature range

(T1,T2 ,T3 ) : biT1 > biT2 > biT3 > 0 bi*T1 > bi*T2 > bi*T3 > 0 d iT1 > d Ti 2 > d Ti 3 > 0

(25)

e HT12 O > e HT22 O > e HT32 O > 0

For the case when heterogeneity of N2 adsorption is enforced, relative constraints of the type

bNTT2 > dNTT2 may be employed, as required to guide the solver. Furthermore, relative constraints


Page 25 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


on the heat of adsorption of any species where heterogeneity is considered can also be employed to help guide the solver towards a larger heat expected at a hydrophilic b-site. Additional relative constraints were required for non-linear regression of the H2O adsorption isotherms. A physically reasoned scheme was employed to ensure consistency with the known affinity of the ionic adsorbent towards the different components of wet flue gas due to differing polar and quadrupolar properties at a particular temperature:

T bHT 2O >> bCO >> bNT 2 2 *T >> bN*T2 bH*T2O >> bCO 2

(26)

T >> d NT 2 d HT 2O >> d CO 2

A set of relative constraints can be obtained from equation (26) to apply respective multipliers to H2O affinities, corresponding to the estimated ratio of the H2O affinity relative to the CO2 affinity e.g. an initial ratio may be considered in the hundreds but not far above 2000. The absolute and relative parameter bound constraints were obtained by trial and error using repeated solution attempts. Care was taken to ensure that no absolute or multiplier bounds were approached when accepting a reasonably low objective function. Otherwise, the evolutionary optimization was re-run with wider parameter bounds or lower multipliers. Once the evolutionary optimization reached an acceptable end-point, the minimization technique was switched to generalized reduced gradient (GRG) optimization to increase the likelihood of obtaining a global minimum with the model parameters for each species. Other options to tighten the convergence, increase the mutation rate or population size were already or nearly exhausted. The GRG optimization was performed using central derivatives, the same initial absolute constraints on all parameters with the multi-start option enabled using a population size of 50 and the same relative constraints (except for removing the multipliers associated with equation (26) by sufficiently lowering the limits). For the case of H2O isotherm regression using the GRG method, the relative constraints between H2O and CO2 were removed. A second stage check was made to ensure no absolute parameter 25 ACS Paragon Plus Environment


limits were exceeded. Depending upon the success of this check, the evolutionary solver can also be used again. In this second stage of minimization, some of the previous multiplier limits were passed to obtain a lower objective function for H2O, comparable in magnitude to that for CO2. In addition, the tight fitting required at very low H2O vapor pressures was achieved without cross-over of isotherms. The use of exponentials in the pure component isotherm regression analysis associated with the Van’t Hoff relation in equation (1) was avoided. This relation was subsequently used to determine the site-specific pre-exponential factors and internal energy of adsorption. Linear regression analysis of the natural logarithm of the optimal affinity coefficients against inverse temperature was confirmed to obtain high correlation coefficients above 0.99 for all values. By weighting the adsorption site internal energies of adsorption with site saturation capacities, a representative temperature independent internal energy change of adsorption is determined for the temperature range applicable to the regression analysis. This constant approximate value may be converted to temperature dependent heats of adsorption by the subtraction of RT, assuming an ideal gas phase. The negative of these exothermic heats may be compared against isosteric heats previously predicted by GCMC with the comparison expected to improve for higher correlation coefficients associated with improved representation of adsorbent energy landscape for a species 1. A constant heat of adsorption for the temperature range is clearly an approximation associated with the use of the Van't Hoff equation for each adsorption energy level and inconsistent with an expected decrease in the isosteric heat of adsorption with increasing temperature. Furthermore, the resulting pure component pre-exponential parameters served as unshielded affinity coefficient parameters for use in equation (16). The evolutionary and GRG optimization methods were also employed sequentially for the regression of gas mixture adsorption isotherms with the RSSRE objective function. The tunable parameters for gas mixture adsorption isotherm model regression analysis in MF mode may be listed as follows:


Page 26 of 48

Page 27 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


 K N 2 ,NI,0 , U N 2 ,NI  z 0, m , k , z1, m , k ,0 , U z ,1, m , k , z 2, m , k ,0 , U z ,2, m , k

pm ∈ 

,

( k = 1, 2 ) , ( m = b, b*, d )

(27)

3. Results and Discussion The following sections shall detail results of regression analysis. Results compare pure data (PD) from GCMC simulations with pure fitting (PF) results from regression analysis. Results further compare mixture data (MD) from GCMC simulations with mixture prediction (MP) data from proposed isotherm models and mixture fitting (MF) data from additional regression analysis.

3.1 Pure Species Adsorption on Zeolite 13X Tables S1 to S8 of the supplementary information detail the isotherm model parameters and the regression analysis results for pure species adsorption on Z13X for the components of wet flue gas. The optimal model for pure CO2 and pure N2 was obtained as either the DSLα or TSLα isotherm model. The final two columns of the tabulated regression analysis results in Tables S4 and S8 indicate the relative improvement in the isotherm model objective residual from the multi-site Langmuir model and the percentage allocation of H2O saturated capacity to the β-cage, respectively. No significant benefit was obtained with the MCH2O designated models to justify an extra fitting parameter. Although the optimal adsorption isotherm model for pure H2O was found to be with the DSJα-SSJβ or TSJα-SSJβ models, the chosen hybrid DSLα-SSJβ or TSLα-SSJβ models for H2O were selected using a multisite Langmuir model in the α-cavity for consistency with competing CO2 and N2. Figure 1 displays the pure species adsorption isotherm models fit to molecular simulation data using the DSLα isotherm model variant (which compares to the TSLα variant in Figure S1 of the supplementary information). For pure H2O adsorption in Figure 1(a), fitting was performed with reduced pressure, P P0 ( = RH 100) as the abscissa such that the isotherms appear more coincident than for CO2 and N2. The pure species heats of adsorption weighted by saturated 27 ACS Paragon Plus Environment


site capacities obtained with the selected isotherm models were in reasonable agreement with the GCMC reported values 1.

(a)

(b)

(c) Figure 1. Multi-Site Isotherm Model Fit to GCMC pure species adsorption simulation data: (a) DSLα-SSJβ H2O (b) DSLα CO2 (c) DSLα N2 [PD = Pure Data ; PF = Pure Fitting] 28 ACS Paragon Plus Environment

Page 28 of 48

Page 29 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.2 Dry Flue Gas Mixture Adsorption on Zeolite 13X Tables S9 and S10 of the supplementary information detail the regression analysis results for dry flue gas (DFG) adsorption using the optimal pure species parameters for DSLα and TSLα isotherm model variants, respectively. The MP result is superior for TSLα, while both MP models poorly predict the behaviour of N2 adsorption indicated by RSSREN2. A type of BWA with a cooperative interaction energy between N2 and CO2 was considered in the DSLα_EHN2_DFG_MF_A model to enhance the affinity of N2 towards Z13X but with limited success. The DSLα_EHN2_DFG_MF isotherm models with _B and _C identifiers employed equations (8) and (10), respectively, and were found to provide similar improved regression performance. The latter two modelling approaches were also applied to the corresponding TSLα models. Binary mixture fitting parameters are detailed in Table S11. Tables S9 and S10

indicate

the

total

residuals

for

the

DSLα_EHN2_DFG_MF_B

and

TSLα_EHN2_DFG_MF_B isotherm models are 0.365 and 0.328, respectively. The DSLα variant is nevertheless selected here on the basis of subsequent wet flue gas regression analysis results, while the _B identifier model is considered more physically meaningful with two fitting parameters based upon a Van’t Hoff temperature dependence. Figure 2(a) correlates binary mixture adsorption loadings using the DSLα_EHN2_DFG_MF_B isotherm model for both CO2 and N2 at a fixed total pressure of 1 atm. Figure 2(b) examines the adsorption of N2 from dry flue gas at a fixed gas phase composition of yCO2=0.15 as a further test of the quality of the binary fitting parameters. The corresponding TSLα results are shown in Figure S2. Figure 3 illustrates the percentage relative deviation of N2 adsorption from the mixture prediction using the DSLα_EHN2_DFG_MP isotherm model. In Figure 3(a), equation (10) is used to correlate the percentage relative deviation of N2 adsorption against the simulated amount of adsorbed CO2. A similar figure results using the output from equation (8).



(a)

(b) Figure 2. DSLα_EHN2_DFG_MF_B Isotherm Model Fit to binary GCMC simulation data: (a) CO2 and N2 adsorption on Z13X at 1atm (b) N2 adsorption from dry flue gas with yCO2=0.15 [MD = Mixture Data ; MP=Mixture Prediction ; MF = Mixture Fitting]


Page 30 of 48

Page 31 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

Increasing Total Pressure at fixed yCO2=0.15

(b)

Increasing yCO2 at 1atm

(

MP Figure 3. 100*  qN 2 − qN2 

)

(c)

qN2  for binary N2 adsorption from dry flue gas on Z13X

using the DSLα_EHN2_DFG_MP isotherm model: (a) qCO2 dependence fit with

(

)

(

)

equation (10) (b) Ln qCO2 qN 2 dependence at yCO2=0.15 (c) Ln qCO2 qN 2 dependence at 1atm 31 ACS Paragon Plus Environment


In Figures 3(b) and 3(c), the percentage relative deviation of N2 adsorption is compared on a semi-logarithmic plot against the adsorbate loading ratio of CO2 to N2 at a fixed gas phase composition of yCO2=0.15 and a total pressure of 1atm, respectively. The value of

(

100*  qN2 − qNMP2 

)

qN2  depends on the isotherm model employed for the mixture prediction 

of qNMP . Figure S3 illustrates lower deviations for the TSLα_EHN2_DFG_MP isotherm model, 2 with a corresponding smaller RSSREN2 for the MP result when comparing Tables S9 and S10. The planes of figures 3(b) and 3(c) are not perpendicular. In Figure 3(b), at fixed yCO2=0.15, N2 is the major component of the gas phase resulting in decreased levels of adsorbed CO2 relative to adsorbed N2 with increased total pressure and corresponding higher deviations on account of a stronger driving force for N2 non-ideal behaviour. With an increasing proportion of CO2 in the gas phase at a fixed pressure of 1atm, increased levels of adsorbed CO2 relative to adsorbed N2 create larger deviations in N2 adsorption.

3.3 Wet Flue Gas Mixture Adsorption on Zeolite 13X Tables S12 and S13 of the supplementary information detail the regression analysis results for wet flue gas adsorption using an objective function residual across all species, RH values and temperatures with two and three adsorption sites in the α-cavity, respectively. Pure species adsorption isotherm parameters were employed and combined with mixture fitting parameters where indicated by MF. The last columns of Tables S12 and S13 quantify the improvement obtained relative to the simple DSLα-SSLβ and TSLα-SSJβ MP isotherm models, respectively. The best wet flue gas MP models for both DSLα and TSLα variants employed full exclusion of CO2 and N2 from hydrophilic sites. As for dry flue gas adsorption, the MP result is superior for TSLα. The TSLα_EHN2_WFG_FEXHS_MP model provided a 77% lower RSSRETOT than the DSLα_EHN2_WFG_FEXHS_MP model. However, MF models far outperformed the MP model results with the best wet flue gas MF model 32 ACS Paragon Plus Environment

Page 32 of 48

Page 33 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


determined with affinity shielding of CO2 and N2 at all adsorption sites. The TSLα_EHN2_WFG_ASBBSTD_MF isotherm model provided a RSSRETOT of 3.46, representing an 88% improvement on the TSLα_EHN2_WFG_FEXHS_MP isotherm model (RSSRETOT of 28.93). The DSLα_EHN2_WFG_ASBD_MF isotherm model provided an even lower

RSSRETOT

of

2.82,

representing

a

97.8%

improvement

on

the

DSLα_EHN2_WFG_FEXHS_MP model and was marginally better than the DSLα case combining full exclusion and affinity shielding only at the lower energy site with a RSSRETOT of 2.88. Therefore, combining near exclusion of CO2 from high energy sites and shielding of CO2 from pore walls by hydrogen bonded networks of H2O provides for the majority of regression of CO2 adsorption from wet flue gas on Z13X. High correlation coefficients were found for the temperature dependence of affinity shielding parameters following the Van’t Hoff form. In these wet flue gas adsorption isotherm models, supplemental N2 adsorption on CO2 was accounted for using equation (8). Although this relationship was not determined under wet gas conditions, it is nevertheless maintained since the wet flue gas isotherm model is required to revert to dry flue gas adsorption.

The full set of wet flue gas adsorption isotherms at

[ 298,323,348] K

and 1atm fit to

simulated GCMC data are detailed in the supplementary information for the range of

RH ∈[ 0.25,0.5,1,2,5,10,15,20,25,50,75,100] % in Figures S5 to S12 using both DSLα_EHN2_WFG_ ASBD_MF and TSLα_EHN2_WFG_ASBBSTD_MF isotherm models. By selecting the lowest RSSRETOT corresponding to the DSLα variant with empirical affinity shielding at all sites, a sample of wet flue gas adsorption isotherms for CO2 and N2 parameterized

at

three

levels

of

RH

are

shown

in

Figure

4

using

the

DSLα_EHN2_WFG_ASBD_MF isotherm model. Figure 5 illustrates the corresponding adsorption isotherms for H2O.



Page 34 of 48

3.4 Residuals of Isotherm Model Fits to Flue Gas Adsorption Equilibrium Data on Z13X Table 1 details a summary of key results from regression analysis using the optimal isotherm models determined with two and three adsorption sites in the α-cavity of Z13X. For wet flue gas adsorption, the residual for CO2 is lowest using the dual-site model with RSSRECO2=2.07. Using this model in process studies is expected to both lead to more accurate performance measures for carbon capture, in additional to being simpler to use. Table 1. Root Sum of Squared Relative Errors (RSSRE) for Optimal Isotherm Models of Pure Species, Dry and Wet Flue Gas Adsorption on Zeolite 13X at [25, 50, 75]oC

Multi-Site (M)

Pure

Pure

Pure

Dry Flue Gas c

Wet Flue Gas d

in α-cavity

CO2 a

N2 a

H2O b

(IV)

(V)

(M = D or T)

(I)

(II)

(III)

Mixture

Mixture

Mixture

Mixture

Mixture

CO2

N2

CO2

N2

H2O

0.365 DSLα

0.090

0.029

0.047 *

0.230

2.82 0.284

2.07

0.328 TSLα

0.054

0.035

0.051 *

0.185

1.86

0.43

3.46 0.270

2.84

1.86

a

MSLα_CO2EHN2_PF: 0.01 ≤ P (bar) ≤ 1.013

b

MSLα_SSJβ_H2O_PF: 0.026 ≤ P P0 ≤ 1

c

MSLα_EHN2_DFG_MF_B: 0 ≤ yCO2 ≤ 1 ; P = 1atm ; (IV) = Equation (2) for MP with (I) &

0.66

(II) + Equation (8) MSLα_EHN2_WFG_ASB(BST)D_MF: 0.25 ≤ RH (%) ≤ 100 ; P = 1atm ; (V) = Equation (15) for AS of CO2 and N2 at all α-cavity sites + (IV) + Equations (2) & (3) for MP with (III) * RSSREH2O = 0.033 occurs with MSJα-SSJβ_H2O_PF (section 2.2.2) but not compatible with (V) d

Note: PF = Pure Fitting ; MP = Mixture Prediction ; MF = Mixture Fitting ; EHN2 = Energetic Homogeneity for N2 ; AS = Affinity Shielding (section 2.2.7) ; DFG = Dry Flue Gas ; WFG = Wet Flue Gas ; P0 = Temperature Dependent Saturation Vapor Pressure of Water


Page 35 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

(c)

Figure 4. CO2 and N2 wet flue gas adsorption Isotherms parameterized by RH using the DSLα_EHN2_WFG_ASBD_MF isotherm model: (a) 5% (b) 50% (c) 100%



(a)

(b)

(c) Figure 5. H2O wet flue gas adsorption Isotherms parameterized by RH using the DSLα_EHN2_WFG_ASBD_MF isotherm model: (a) 5% (b) 50% (c) 100%


Page 36 of 48

Page 37 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4.

Conclusions

The isotherm models considered were explicit in gas phase composition to avoid iterative solutions during process simulations and further did not include power terms that can lead to poor convergence during the onset of numerical oscillations encountered in adsorption column dynamics and process simulations. Pure species adsorption isotherm models were able to capture the underlying data well over the studied pressure and temperature ranges. A cooperative enhancement of weakly adsorbed linear N2 due to strongly adsorbed linear CO2 at relatively low pressures on Z13X was identified and attributed to quadrupolar optimization of these species in the adsorbate phase. Dry flue gas mixture adsorption isotherms were obtained using a dual mode formalism accounting for vertical and lateral interactions in superimposed expressions, with the latter based upon binary mixture fitting parameters. Higher differences in species Pitzer-type acentric factors, accounting for both molecular shape and polarity, were hypothesized to lead to larger deviations from IAST by lateral adsorbate interactions, when the strongly adsorbed species orients in a manner to present a secondary adsorption landscape for the adsorption of the weaker species e.g. linear molecules on a high energy surface or spherical molecules on a highly random surface. Similar to the molecular simulation study by Gotzias et al.

31

, future studies on

molecular mechanisms of dry flue gas mixture adsorption could benefit from considerations of equilibrium adsorbate molecular orientations relative to different homotattic sites and among co-adsorbates through angular and radial distributions for CO2 and N2. Understanding these effects may lead to a predictive model of binary dry flue gas mixture parameters. Furthermore, a controlled adsorbent surface capable of disrupting an enhancement of adsorption of N2 by CO2 could improve adsorbent selectivity and reduce the requirement for a supplement N2 adsorption expression such as equation(8).

The multi-

site Jovanovic isotherm was found to best correlate pure H2O adsorption on Z13X, in which strong adsorption of H2O occurs. However, this isotherm model was also found unsuitable for characterizing the adsorption of other wet flue gas mixture components. Challenges remain to accurately fit wet flue gas adsorption isotherms. Significant exclusion of CO2 and 37 ACS Paragon Plus Environment


N2 from adsorption sites by hydrogen bonded clustering of H2O molecules was accomplished using either logistical relations at hydrophilic adsorption sites or affinity shielding of CO2 and N2 dependent upon the H2O moisture content using equation (17) at any adsorption site. Similar to the analysis of dry flue gas adsorption, a combination of pure species and ternary mixture fitting adsorption isotherm parameters were employed. All mixture fitting parameters were associated with lateral molecular interactions, which cannot currently be obtained from pure species adsorption experiments. The described empirical modification of affinity coefficients by an exponential damping factor to account for lateral molecular interactions in the adsorbate phase can be viewed as a humidity dependent sticking coefficient adjustment. A simple clustering function using the H2O moisture content was found effective to significantly reduce the isotherm model residual. Equation (17) was found applicable using a Van’t Hoff temperature dependency for both z1,m,k and z2,m,k to describe clustering. It is not clear if z2,m,k bears physical significance to the clustering model or whether this is a correction term that was most often determined as a constant. Referring to the directional nature of hydrogen bonding and resultant bridging complexes discussed in the molecular simulation study [1], it is likely that a more complex isotherm model than a BWA analogue for affinity shielding at accessible high energy sites is required to further lower the isotherm model residual. A higher value of z1,m,k at lower temperatures may be interpreted as stronger hydrogen bonded clustering, despite the lower saturation moisture content in the vapor phase driving the extent of adsorption of H2O. To enable a prediction of the magnitude of adsorbate loading decay by adsorption site affinity shielding at a given moisture content in wet flue gas, future research may explore the relationship between H2O pore diffusivity, the strength of hydrogen bond clustering over a range of temperature and RH and the extent of adsorption site affinity shielding. Stronger hydrogen bond networks likely lead to both greater site affinity shielding of co-adsorbates and lower H2O diffusivity. This association may provide an experimental means towards predicting wet flue gas adsorption behaviour, 38 ACS Paragon Plus Environment

Page 38 of 48

Page 39 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


particularly by considering ratios of H2O pore diffusivities at different inert gas moisture contents as a probe of hydrogen bonded clustering in an adsorbent. The isotherm models reported here for wet flue gas adsorption on Z13X may assist to validate process simulations against pilot plant measurements using this industrially established and commercially available hydrophilic adsorbent with high moisture sensitivity and moderate selectivity towards CO2 over N2. The presence of typically up to about 10% mole fraction of moisture in power plant flue gas has a highly negative impact on the working capacity of Z13X for carbon capture. High regeneration costs for dehydration of Z13X prevents a traditional single column adsorption process design to achieve a sufficiently low process parasitic energy. A dualcolumn VSA process with wet flue gas was previously proposed incorporating dehydration of wet flue gas using a silica gel guard bed and subsequent carbon capture by Z13X, using preliminary equilibrium isotherm data for the treatment of wet flue gas equilibrium on Zeolite 13X

63

. Realistically, trace levels of moisture at the exit of a dehydration process are always

present and thus sensitivity of Z13X to moisture is essential to predict by accurate adsorbent characterization and experimental validation. In order to reduce the levelized cost of electricity generation for power plants with adsorption-based carbon capture technology, accurate process optimization studies should be performed with a validated wet flue gas adsorbent equilibrium isotherm model and subsequently validated by pilot plant demonstration.

Supporting Information Isotherm model parameters, associated isotherm model regression analysis performance results and graphical presentation of model fits to underlying molecular simulation data are provided in the supporting information file for pure species, dry flue gas and wet flue gas adsorption on Z13X.

Acknowledgement 39 ACS Paragon Plus Environment


The author is grateful for helpful discussions with Prof. Shamsuzzaman Farooq, National University of Singapore. Funding sources: This research is supported by the National Research Foundation, Prime Minister’s Office, Singapore under its CREATE programme.

Conflicts of Interest None.

*Corresponding author’s contact: Department of Chemical and Biomolecular Engineering, National University of Singapore, 117585, Singapore. E-mail: [email protected], [email protected] (M.J. Purdue).

References (1)

Purdue, M. J.; Qiao, Z. Molecular Simulation Study of Wet Flue Gas Adsorption on Zeolite 13X. Microporous Mesoporous Mater. 2018, 261, 181–197.

(2)

Mohamadinejad, H. The Adsorption of CO2/H2O/N2 on 5A Zeolite and Silica Gel in a Packed Column in One and Two-Dimensional Flows, The University of Alabama in Huntsville, 1999.

(3)

Li, G.; Xiao, P.; Webley, P.; Zhang, J.; Singh, R.; Marshall, M. Capture of CO2 from High Humidity Flue Gas by Vacuum Swing Adsorption with Zeolite 13X. Adsorption 2008, 14 (2–3), 415–422.

(4)

Mette, B.; Kerskes, H.; Drück, H.; Müller-Steinhagen, H. Experimental and Numerical Investigations on the Water Vapor Adsorption Isotherms and Kinetics of Binderless Zeolite 13X. Int. J. Heat Mass Transf. 2014, 71, 555–561.

(5)

Flanigen, E. M.; Bennett, J. M.; Grose, R. W.; Cohen, J. P.; Patton, R. L.; Kirchner, R. M.; Smith, J. V. Silicalite, a New Hydrophobic Crystalline Silica Molecular Sieve. Nature 1978, 271 (5645), 512–516.

(6)

Wang, Y.; LeVan, M. D. Adsorption Equilibrium of Carbon Dioxide and Water Vapor 40 ACS Paragon Plus Environment

Page 40 of 48

Page 41 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


on Zeolites 5A and 13X and Silica Gel: Pure Components. J. Chem. Eng. Data 2009, 54 (10), 2839–2844. (7)

Wang, Y.; LeVan, M. D. Adsorption Equilibrium of Binary Mixtures of Carbon Dioxide and Water Vapor on Zeolites 5A and 13X. J. Chem. Eng. Data 2010, 55 (9), 3189– 3195.

(8)

Myers, A. L.; Prausnitz, J. M. Thermodynamics of Mixed-Gas Adsorption. AIChE J. 1965, 11 (1), 121–127.

(9)

Hefti, M.; Marx, D.; Joss, L.; Mazzotti, M. Adsorption Equilibrium of Binary Mixtures of Carbon Dioxide and Nitrogen on Zeolites ZSM-5 and 13X. Microporous Mesoporous Mater. 2015, 215, 215–226.

(10)

Zheng, Y.; Gu, T. Modified van Der Waals Equation for the Prediction of Multicomponent Isotherms. J Colloid Interface Sci 1998, 206 (2), 457–463.

(11)

Bai, R.; Yang, R. T. A Thermodynamically Consistent Langmuir Model for Mixed Gas Adsorption. J. Colloid Interface Sci. 2001, 239 (2), 296–302.

(12)

Sanford, C.; Ross, S. Homotattic Surface—A Suggested New Word. J. Phys. Chem. 1954, 58 (3), 288–288.

(13)

Shirono, K.; Endo, A.; Daiguji, H. Molecular Dynamics Study of Hydrated FaujasiteType Zeolites. J. Phys. Chem. B 2005, 109 (8), 3446–3453.

(14)

Di Lella, A.; Desbiens, N.; Boutin, A.; Demachy, I.; Ungerer, P.; Bellat, J.-P.; Fuchs, A. H. Molecular Simulation Studies of Water Physisorption in Zeolites. Phys. Chem. Chem. Phys. 2006, 8 (46), 5396.

(15)

Loughlin, K. F. Water Isotherm Models for 4A (NaA) Zeolite. Adsorption 2009, 15 (4), 337–353.

(16)

Ritter, J. A.; Bhadra, S. J.; Ebner, A. D. On the Use of the Dual-Process Langmuir Model for Correlating Unary Equilibria and Predicting Mixed-Gas Adsorption Equilibria. Langmuir 2011, 27 (8), 4700–4712.

(17)

Jaroniec, M. Adsorption of Gas Mixtures on Homogeneous Surfaces Extension of Jovanovic Equation on Adsorption from Gaseous Mixtures. Chem. zvesti 1975, 29 (4), 41 ACS Paragon Plus Environment


512–516. (18)

Swisher, J. A.; Lin, L.-C.; Kim, J.; Smit, B. Evaluating Mixture Adsorption Models Using Molecular Simulation. AIChE J. 2013, 59 (8), 3054–3064.

(19)

Zhang, P.; Wang, L. Extended Langmuir Equation for Correlating Multilayer Adsorption Equilibrium Data. Sep. Purif. Technol. 2010, 70 (3), 367–371.

(20)

Ye, X.; Qi, N.; Levan, M. D. Equation : Organic – Water Vapor Mixtures on BPL Carbon. Carbon N. Y. 2003, 41, 2519–2525.

(21)

Akten, E. D.; Siriwardane, R.; Sholl, D. S. Monte Carlo Simulation of Single- and Binary-Component Adsorption of CO2, N2, and H2 in Zeolite Na-4A. Energy and Fuels 2003, 17 (4), 977–983.

(22)

Li, M.; Xu, E.; Wang, T.; Liu, J. Adsorption Equilibria of Binary Gas Mixtures on Graphitized Carbon Black. Langmuir 2012, 28 (5), 2582–2588.

(23)

Van Der Vaart, R.; Huiskes, C.; Bosch, H.; Reith, T. Single and Mixed Gas Adsorption Equilibria of Carbon Dioxide/methane on Activated Carbon. Adsorption 2000, 6 (4), 311–323.

(24)

Furmaniak, S.; Koter, S.; Terzyk, A. P.; Gauden, P. A.; Kowalczyk, P.; Rychlicki, G. New Insights into the Ideal Adsorbed Solution Theory. Phys. Chem. Chem. Phys. 2015, 17 (11), 7232–7247.

(25)

Harlick, P. J. .; Tezel, F. . Adsorption of Carbon Dioxide, Methane and Nitrogen: Pure and Binary Mixture Adsorption for ZSM-5 with SiO2/Al2O3 Ratio of 280. Sep. Purif. Technol. 2003, 33 (2), 199–210.

(26)

Harlick, P. J. E.; Tezel, F. H. CO2-N2 and CO2-CH4 Binary Adsorption Isotherms with H-ZSM5: The Importance of Experimental Data Regression with the Concentration Pulse Method. Can. J. Chem. Eng. 2001, 79 (April), 236–245.

(27)

Harlick, P. J. E.; Tezel, F. H. Use of Concentration Pulse Chromatography for Determining Binary Isotherms: Comparison with Statically Determined Binary Isotherms. Adsorption 2003, 9 (3), 275–286.

(28)

Mulgundmath, V. P.; Tezel, F. H.; Saatcioglu, T.; Golden, T. C. Adsorption and 42 ACS Paragon Plus Environment

Page 42 of 48

Page 43 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Separation of CO2/N2 and CO2/CH4 by 13X Zeolite. Can. J. Chem. Eng. 2012, 90 (3), 730–738. (29)

Castro, M.; Martínez, A. 2D-SAFT-VR Approach to Study of the Adsorption Isotherms for Binary Mixtures. Adsorption 2013, 19 (1), 63–70.

(30)

Castro, M.; Martínez, A.; Gil-Villegas, A. Modelling Adsorption Isotherms of Binary Mixtures of Carbon Dioxide, Methane and Nitrogen. Adsorpt. Sci. Technol. 2011, 29 (1), 59–70.

(31)

Gotzias, A.; Charalambopoulou, G.; Steriotis, T. On the Orientation of N 2 and CO 2 Molecules Adsorbed in Slit Pore Models with Oxidised Graphitic Surface. Mol. Simul. 2016, 42 (3), 186–195.

(32)

Little, L. H.; Amberg, C. H. Infrared Spectra of Carbon Monoxide and Carbon Dioxide Adsorbed on Chromia–Alumina and on Alumina. Can. J. Chem. 1962, 40 (10), 1997– 2006.

(33)

Pham, T. D.; Liu, Q.; Lobo, R. F. Carbon Dioxide and Nitrogen Adsorption on CationExchanged SSZ-13 Zeolites. Langmuir 2013, 29 (2), 832–839.

(34)

Pham, T. D.; Hudson, M. R.; Brown, C. M.; Lobo, R. F. Molecular Basis for the High CO 2 Adsorption Capacity of Chabazite Zeolites. ChemSusChem 2014, 7 (11), 3031– 3038.

(35)

Samios, S.; Stubos, A. K.; Papadopoulos, G. K.; Kanellopoulos, N. K.; Rigas, F. The Structure of Adsorbed CO2 in Slitlike Micropores at Low and High Temperature and the Resulting Micropore Size Distribution Based on GCMC Simulations. J. Colloid Interface Sci. 2000, 224 (2), 272–290.

(36)

Golebiowska, M.; Firlej, L.; Kuchta, B.; Fabianski, R. Structural Transformations of Nitrogen Adsorbed on Graphite: Monte Carlo Studies of Spatial Heterogeneity in Multilayer System. J. Chem. Phys. 2009, 130 (20).

(37)

Steriotis, T. A.; Stefanopoulos, K. L.; Katsaros, F. K.; Gläser, R.; Hannon, A. C.; Ramsay, J. D. F. In Situ Neutron Diffraction Study of Adsorbed Carbon Dioxide in a Nanoporous Material: Monitoring the Adsorption Mechanism and the Structural 43 ACS Paragon Plus Environment


Characteristics of the Confined Phase. Phys. Rev. B - Condens. Matter Mater. Phys. 2008, 78 (11), 1–10. (38)

Cracknell, R. F.; Nicholson, D.; Tennison, S. R.; Bromhead, J. Adsorption and Selectivity of Carbon Dioxide with Methane and Nitrogen in Slit-Shaped Carbonaceous Micropores: Simulation and Experiment. Adsorption 1996, 2 (3), 193– 203.

(39)

Nasri, S.; Ajili, Y.; Jaidane, N.-E.; Kalugina, Y. N.; Halvick, P.; Stoecklin, T.; Hochlaf, M. Potential Energy Surface of the CO 2 –N 2 van Der Waals Complex. J. Chem. Phys. 2015, 142 (17), 174301.

(40)

Vasanth Kumar, K.; Rodríguez-Reinoso, F. Co-Adsorption of N2 in the Presence of CH4 within Carbon Nanospaces: Evidence from Molecular Simulations. Nanotechnology 2013, 24 (3).

(41)

Khelifa, A.; Benchehida, L.; Derriche, Z. Adsorption of Carbon Dioxide by X Zeolites Exchanged with Ni2+ and Cr3+: Isotherms and Isosteric Heat. J. Colloid Interface Sci. 2004, 278 (1), 9–17.

(42)

Khelifa, A.; Derriche, Z.; Bengueddach, A. Sorption of Carbon Dioxide by Zeolite X Exchanged with Zn2+ and Cu2+. Microporous Mesoporous Mater. 1999, 32 (1–2), 199–209.

(43)

Sillar, K.; Kundu, A.; Sauer, J. Ab Initio Adsorption Isotherms for Molecules with Lateral Interactions: CO 2 in Metal–Organic Frameworks. J. Phys. Chem. C 2017, 121 (23), 12789–12799.

(44)

Fowler, R. H.; Guggenheim, E. A. Statistical Thermodynamics: A Version of Statistical Mechanics for Students of Physics and Chemistry. Cambridge University Press: Cambridge [Eng.] 1956.

(45)

Rudziński, W.; Jagiełło, J. Low-Temperature Adsorption of Gases on Heterogeneous Solid Surfaces: Surfaces with Random Topography. J. Low Temp. Phys. 1981, 45 (1– 2), 1–19.

(46)

Rudziński, W.; Jagiełło, J.; Grillet, Y. Physical Adsorption of Gases on Heterogeneous 44 ACS Paragon Plus Environment

Page 44 of 48

Page 45 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Solid Surfaces: Evaluation of the Adsorption Energy Distribution from Adsorption Isotherms and Heats of Adsorption. J. Colloid Interface Sci. 1982, 87 (2), 478–491. (47)

Bragg, W. , Williams, E. The Effect of Thermal Agitation on Atomic Arrangement in Alloys. Proc. Roy. Soc. 1934, A145, 699–730.

(48)

Jaroniec, M.; Borówko, M.; Patrykiejew, A. Consequences of Assuming the BraggWilliams Approximation in Mixed-Gas Adsorption. Surf. Sci. 1978, 78 (2), L501–L503.

(49)

Al-Muhtaseb, S. A.; Ritter, J. A. New Model That Describes Adsorption of Laterally Interacting Gas Mixtures on Random Heterogeneous Surfaces. 2. Correlation of Complex Binary and Prediction of Multicomponent Adsorption Equilibria. Langmuir 1999, 15 (22), 7732–7744.

(50)

Gu, T.; Tsai, G.-J.; Tsao, G. T. Multicomponent Adsorption and Chromatography with Uneven Saturation Capacities. AIChE J. 1991, 37 (9), 1333–1340.

(51)

Nitta, T.; Yamaguchi, A.; Tokunaga, N.; Katayama, T. A Practical Isotherm Equation for Adsorption on a Heterogeneous Surface and Its Applications to Single and Mixed Gas Adsorption on an Activated Carbon Fiber. Journal of Chemical Engineering of Japan. 1991, pp 312–319.

(52)

Waldman, M.; Hagler, A. T. New Combining Rules for Rare Gas van Der Waals Parameters. J. Comput. Chem. 1993, 14 (9), 1077–1084.

(53)

Brandani, F.; Ruthven, D. M. The Effect of Water on the Adsorption of CO 2 and C 3 H 8 on Type X Zeolites. Ind. Eng. Chem. Res. 2004, 43 (26), 8339–8344.

(54)

Ritter, J. A.; Bhadra, S. J.; Ebner, A. D. On the Use of the Dual-Process Langmuir Model for Correlating Unary Equilibria and Predicting Mixed-Gas Adsorption Equilibria. Langmuir 2011, 27 (8), 4700–4712.

(55)

Seidel, A.; Gelbin, D. On Applying the Ideal Adsorbed Solution Theory to Multicomponent Adsorption Equilibria of Dissolved Organic Components on Activated Carbon. Chem. Eng. Sci. 1988, 43 (1), 79–88.

(56)

Foo, K. Y.; Hameed, B. H. Insights into the Modeling of Adsorption Isotherm Systems. Chem. Eng. J. 2010, 156 (1), 2–10. 45 ACS Paragon Plus Environment


(57)

Yan, F.; Chu, Y.; Zhang, K.; Zhang, F.; Bhandari, N.; Ruan, G.; Dai, Z.; Liu, Y.; Zhang, Z.; Kan, A. T.; et al. Determination of Adsorption Isotherm Parameters with Correlated Errors by Measurement Error Models. Chem. Eng. J. 2015, 281, 921–930.

(58)

Markovit, D. D.; Lekit, B. M.; Rajakovit-Ognjanovit, V. N.; Onjia, A. E.; Rajakovit, L. V; Markovi, D. D. A New Approach in Regression Analysis for Modeling Adsorption Isotherms. 2014, 2014.

(59)

Li, G.; Xiao, P.; Webley, P. Binary Adsorption Equilibrium of Carbon Dioxide and Water Vapor on Activated Alumina. Langmuir 2009, 25 (18), 10666–10675.

(60)

Ritter, J. A.; Al-Muhtaseb, S. A. New Model That Describes Adsorption of Laterally Interacting Gas Mixtures on Random Heterogeneous Surfaces. 1. Parametric Study and Correlation with Binary Data. Langmuir 1998, 14 (22), 6528–6538.

(61)

Kim, J. H.; Lee, C. H.; Kim, W. S.; Lee, J. S.; Kim, J. T.; Suh, J. K.; Lee, J. M. Adsorption Equilibria of Water Vapor on Alumina, Zeolite 13X, and a Zeolite X/activated Carbon Composite. J. Chem. Eng. Data 2003, 48 (1), 137–141.

(62)

Mathias, P. M.; Kumar, R.; Moyer, J. D.; Schork, J. M.; Srinivasan, S. R.; Auvil, S. R.; Talu, O. Correlation of Multicomponent Gas Adsorption by the Dual-Site Langmuir Model. Application to Nitrogen/Oxygen Adsorption on 5A-Zeolite. Ind. Eng. Chem. Res. 1996, 5885 (95), 2477–2483.

(63)

Krishnamurthy, S.; Haghpanah, R.; Rajendran, A.; Farooq, S. Simulation and Optimization of a Dual-Adsorbent, Two-Bed Vacuum Swing Adsorption Process for CO 2 Capture from Wet Flue Gas. Ind. Eng. Chem. Res. 2014, 53 (37), 14462– 14473.


Page 46 of 48

Page 47 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




TOC Graphic

WET: RH=0.25% ; P=1atm


Page 48 of 48

Explicit Flue Gas Adsorption Isotherm Model for Zeolite 13X

Recommend Documents